YES 30.685000000000002 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
  ((plusFM :: Ord b => FiniteMap [b] a  ->  FiniteMap [b] a  ->  FiniteMap [b] a) :: Ord b => FiniteMap [b] a  ->  FiniteMap [b] a  ->  FiniteMap [b] a)

module FiniteMap where
  import qualified Maybe
import qualified Prelude

  data FiniteMap b a = EmptyFM  | Branch b a Int (FiniteMap b a) (FiniteMap b a


  instance (Eq a, Eq b) => Eq (FiniteMap b a) where 
   
(==) fm_1 fm_2 sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2

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

  addToFM_C :: Ord 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_rnew_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

  emptyFM :: FiniteMap b a
emptyFM EmptyFM

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

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

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

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

  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_rrmkBranch 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_rrmkBranch 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_lrfm_r mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r)
size_l sizeFM fm_L
size_r sizeFM fm_R

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

  mkVBalBranch :: Ord b => b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a
mkVBalBranch key elt EmptyFM fm_r addToFM fm_r key elt
mkVBalBranch key elt fm_l EmptyFM addToFM fm_l key elt
mkVBalBranch key elt fm_l@(Branch key_l elt_l _ fm_ll fm_lrfm_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

  plusFM :: Ord b => FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a
plusFM EmptyFM fm2 fm2
plusFM fm1 EmptyFM fm1
plusFM fm1 (Branch split_key elt1 _ left right
mkVBalBranch split_key elt1 (plusFM lts left) (plusFM gts right) where 
gts splitGT fm1 split_key
lts splitLT fm1 split_key

  sIZE_RATIO :: Int
sIZE_RATIO 5

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

  splitGT :: Ord b => FiniteMap b a  ->  b  ->  FiniteMap b a
splitGT EmptyFM split_key emptyFM
splitGT (Branch key elt _ fm_l fm_rsplit_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_rsplit_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
\keyeltrest→(key,elt: rest

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

The following Lambda expression
\oldnewnew

is transformed to
addToFM0 old new = new



↳ HASKELL
  ↳ LR
HASKELL
      ↳ CR

mainModule FiniteMap
  ((plusFM :: Ord b => FiniteMap [b] a  ->  FiniteMap [b] a  ->  FiniteMap [b] a) :: Ord b => FiniteMap [b] a  ->  FiniteMap [b] a  ->  FiniteMap [b] a)

module FiniteMap where
  import qualified Maybe
import qualified Prelude

  data FiniteMap b a = EmptyFM  | Branch b a Int (FiniteMap b a) (FiniteMap b a


  instance (Eq a, Eq b) => Eq (FiniteMap a b) where 
   
(==) fm_1 fm_2 sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2

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

  
addToFM0 old new new

  addToFM_C :: Ord 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_rnew_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

  emptyFM :: FiniteMap b a
emptyFM EmptyFM

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

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

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

  
fmToList0 key elt rest (key,elt: rest

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

  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_rrmkBranch 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_rrmkBranch 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_lrfm_r mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r)
size_l sizeFM fm_L
size_r sizeFM fm_R

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

  mkVBalBranch :: Ord a => a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b
mkVBalBranch key elt EmptyFM fm_r addToFM fm_r key elt
mkVBalBranch key elt fm_l EmptyFM addToFM fm_l key elt
mkVBalBranch key elt fm_l@(Branch key_l elt_l _ fm_ll fm_lrfm_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

  plusFM :: Ord b => FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a
plusFM EmptyFM fm2 fm2
plusFM fm1 EmptyFM fm1
plusFM fm1 (Branch split_key elt1 _ left right
mkVBalBranch split_key elt1 (plusFM lts left) (plusFM gts right) where 
gts splitGT fm1 split_key
lts splitLT fm1 split_key

  sIZE_RATIO :: Int
sIZE_RATIO 5

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

  splitGT :: Ord b => FiniteMap b a  ->  b  ->  FiniteMap b a
splitGT EmptyFM split_key emptyFM
splitGT (Branch key elt _ fm_l fm_rsplit_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_rsplit_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



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

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

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

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

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

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

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

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

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

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



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
HASKELL
          ↳ IFR

mainModule FiniteMap
  ((plusFM :: Ord a => FiniteMap [a] b  ->  FiniteMap [a] b  ->  FiniteMap [a] b) :: Ord a => FiniteMap [a] b  ->  FiniteMap [a] b  ->  FiniteMap [a] 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 
   
(==) fm_1 fm_2 sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2

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

  
addToFM0 old new new

  addToFM_C :: Ord a => (b  ->  b  ->  b ->  FiniteMap a b  ->  a  ->  b  ->  FiniteMap a b
addToFM_C combiner EmptyFM key elt unitFM key elt
addToFM_C combiner (Branch key elt size fm_l fm_rnew_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

  emptyFM :: FiniteMap a b
emptyFM EmptyFM

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

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

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

  
fmToList0 key elt rest (key,elt: rest

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

  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_rrmkBranch 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_rrmkBranch 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_lrfm_r mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r)
size_l sizeFM fm_L
size_r sizeFM fm_R

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

  mkVBalBranch :: Ord a => a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b
mkVBalBranch key elt EmptyFM fm_r addToFM fm_r key elt
mkVBalBranch key elt fm_l EmptyFM addToFM fm_l key elt
mkVBalBranch key elt fm_l@(Branch key_l elt_l _ fm_ll fm_lrfm_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

  plusFM :: Ord b => FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a
plusFM EmptyFM fm2 fm2
plusFM fm1 EmptyFM fm1
plusFM fm1 (Branch split_key elt1 _ left right
mkVBalBranch split_key elt1 (plusFM lts left) (plusFM gts right) where 
gts splitGT fm1 split_key
lts splitLT fm1 split_key

  sIZE_RATIO :: Int
sIZE_RATIO 5

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

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

  splitLT :: Ord b => FiniteMap b a  ->  b  ->  FiniteMap b a
splitLT EmptyFM split_key emptyFM
splitLT (Branch key elt _ fm_l fm_rsplit_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



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

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

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

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



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

mainModule FiniteMap
  ((plusFM :: Ord a => FiniteMap [a] b  ->  FiniteMap [a] b  ->  FiniteMap [a] b) :: Ord a => FiniteMap [a] b  ->  FiniteMap [a] b  ->  FiniteMap [a] 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 
   
(==) fm_1 fm_2 sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2

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

  
addToFM0 old new new

  addToFM_C :: Ord b => (a  ->  a  ->  a ->  FiniteMap b a  ->  b  ->  a  ->  FiniteMap b a
addToFM_C combiner EmptyFM key elt unitFM key elt
addToFM_C combiner (Branch key elt size fm_l fm_rnew_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

  emptyFM :: FiniteMap a b
emptyFM EmptyFM

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

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

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

  
fmToList0 key elt rest (key,elt: rest

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

  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_rrmkBranch 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_rrmkBranch 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_lrfm_r mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r)
size_l sizeFM fm_L
size_r sizeFM fm_R

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

  mkVBalBranch :: Ord a => a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b
mkVBalBranch key elt EmptyFM fm_r addToFM fm_r key elt
mkVBalBranch key elt fm_l EmptyFM addToFM fm_l key elt
mkVBalBranch key elt fm_l@(Branch key_l elt_l _ fm_ll fm_lrfm_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

  plusFM :: Ord a => FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b
plusFM EmptyFM fm2 fm2
plusFM fm1 EmptyFM fm1
plusFM fm1 (Branch split_key elt1 _ left right
mkVBalBranch split_key elt1 (plusFM lts left) (plusFM gts right) where 
gts splitGT fm1 split_key
lts splitLT fm1 split_key

  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_rsplit_key 
 | split_key > key = 
splitGT fm_r split_key
 | split_key < key = 
mkVBalBranch key elt (splitGT fm_l split_key) fm_r
 | otherwise = 
fm_r

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude



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

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

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

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



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

mainModule FiniteMap
  ((plusFM :: Ord a => FiniteMap [a] b  ->  FiniteMap [a] b  ->  FiniteMap [a] b) :: Ord a => FiniteMap [a] b  ->  FiniteMap [a] b  ->  FiniteMap [a] 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 
   
(==) fm_1 fm_2 sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2

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

  
addToFM0 old new new

  addToFM_C :: Ord b => (a  ->  a  ->  a ->  FiniteMap b a  ->  b  ->  a  ->  FiniteMap b a
addToFM_C combiner EmptyFM key elt unitFM key elt
addToFM_C combiner (Branch key elt size fm_l fm_rnew_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

  emptyFM :: FiniteMap b a
emptyFM EmptyFM

  findMax :: FiniteMap b a  ->  (b,a)
findMax (Branch key elt vwy vwz EmptyFM(key,elt)
findMax (Branch key elt vxu vxv fm_rfindMax fm_r

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

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

  
fmToList0 key elt rest (key,elt: rest

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

  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 vvy (Branch key_rl elt_rl vvz fm_rll fm_rlr) fm_rrmkBranch 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 vuz fm_ll (Branch key_lr elt_lr vvu 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 vwu vwv vww 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 vvv vvw vvx 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 vwx fm_rl fm_rrmkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr
single_R (Branch key_l elt_l vuy fm_ll fm_lrfm_r mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r)
size_l sizeFM fm_L
size_r sizeFM fm_R

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

  mkVBalBranch :: Ord b => b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a
mkVBalBranch key elt EmptyFM fm_r addToFM fm_r key elt
mkVBalBranch key elt fm_l EmptyFM addToFM fm_l key elt
mkVBalBranch key elt (Branch yz zu zv zw zx) (Branch zz vuu vuv vuw vux
 | sIZE_RATIO * size_l < size_r = 
mkBalBranch zz vuu (mkVBalBranch key elt (Branch yz zu zv zw zx) vuw) vux
 | sIZE_RATIO * size_r < size_l = 
mkBalBranch yz zu zw (mkVBalBranch key elt zx (Branch zz vuu vuv vuw vux))
 | otherwise = 
mkBranch 13 key elt (Branch yz zu zv zw zx) (Branch zz vuu vuv vuw vux) where 
size_l sizeFM (Branch yz zu zv zw zx)
size_r sizeFM (Branch zz vuu vuv vuw vux)

  plusFM :: Ord a => FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b
plusFM EmptyFM fm2 fm2
plusFM fm1 EmptyFM fm1
plusFM fm1 (Branch split_key elt1 yx left right
mkVBalBranch split_key elt1 (plusFM lts left) (plusFM gts right) where 
gts splitGT fm1 split_key
lts splitLT fm1 split_key

  sIZE_RATIO :: Int
sIZE_RATIO 5

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

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

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude



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

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

splitLT0 key elt xx fm_l fm_r split_key True = fm_l

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

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

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

splitLT4 EmptyFM split_key = emptyFM
splitLT4 wwv www = splitLT3 wwv www

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

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

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

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

splitGT0 key elt xy fm_l fm_r split_key True = fm_r

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

splitGT4 EmptyFM split_key = emptyFM
splitGT4 wwz wxu = splitGT3 wwz wxu

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 yz zu zv zw zx) (Branch zz vuu vuv vuw vux)
 | sIZE_RATIO * size_l < size_r
 = mkBalBranch zz vuu (mkVBalBranch key elt (Branch yz zu zv zw zxvuwvux
 | sIZE_RATIO * size_r < size_l
 = mkBalBranch yz zu zw (mkVBalBranch key elt zx (Branch zz vuu vuv vuw vux))
 | otherwise
 = mkBranch 13 key elt (Branch yz zu zv zw zx) (Branch zz vuu vuv vuw vux)
where 
size_l  = sizeFM (Branch yz zu zv zw zx)
size_r  = sizeFM (Branch zz vuu vuv vuw vux)

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 yz zu zv zw zx) (Branch zz vuu vuv vuw vux) = mkVBalBranch3 key elt (Branch yz zu zv zw zx) (Branch zz vuu vuv vuw vux)

mkVBalBranch3 key elt (Branch yz zu zv zw zx) (Branch zz vuu vuv vuw vux) = 
mkVBalBranch2 key elt yz zu zv zw zx zz vuu vuv vuw vux (sIZE_RATIO * size_l < size_r)
where 
mkVBalBranch0 key elt yz zu zv zw zx zz vuu vuv vuw vux True = mkBranch 13 key elt (Branch yz zu zv zw zx) (Branch zz vuu vuv vuw vux)
mkVBalBranch1 key elt yz zu zv zw zx zz vuu vuv vuw vux True = mkBalBranch yz zu zw (mkVBalBranch key elt zx (Branch zz vuu vuv vuw vux))
mkVBalBranch1 key elt yz zu zv zw zx zz vuu vuv vuw vux False = mkVBalBranch0 key elt yz zu zv zw zx zz vuu vuv vuw vux otherwise
mkVBalBranch2 key elt yz zu zv zw zx zz vuu vuv vuw vux True = mkBalBranch zz vuu (mkVBalBranch key elt (Branch yz zu zv zw zxvuwvux
mkVBalBranch2 key elt yz zu zv zw zx zz vuu vuv vuw vux False = mkVBalBranch1 key elt yz zu zv zw zx zz vuu vuv vuw vux (sIZE_RATIO * size_r < size_l)
size_l  = sizeFM (Branch yz zu zv zw zx)
size_r  = sizeFM (Branch zz vuu vuv vuw vux)

mkVBalBranch4 key elt fm_l EmptyFM = addToFM fm_l key elt
mkVBalBranch4 wxy wxz wyu wyv = mkVBalBranch3 wxy wxz wyu wyv

mkVBalBranch5 key elt EmptyFM fm_r = addToFM fm_r key elt
mkVBalBranch5 wyx wyy wyz wzu = mkVBalBranch4 wyx wyy wyz wzu

The following Function with conditions
mkBalBranch1 fm_L fm_R (Branch vvv vvw vvx 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 vvv vvw vvx fm_ll fm_lr) = mkBalBranch12 fm_L fm_R (Branch vvv vvw vvx fm_ll fm_lr)

mkBalBranch11 fm_L fm_R vvv vvw vvx fm_ll fm_lr True = single_R fm_L fm_R
mkBalBranch11 fm_L fm_R vvv vvw vvx fm_ll fm_lr False = mkBalBranch10 fm_L fm_R vvv vvw vvx fm_ll fm_lr otherwise

mkBalBranch10 fm_L fm_R vvv vvw vvx fm_ll fm_lr True = double_R fm_L fm_R

mkBalBranch12 fm_L fm_R (Branch vvv vvw vvx fm_ll fm_lr) = mkBalBranch11 fm_L fm_R vvv vvw vvx fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll)

The following Function with conditions
mkBalBranch0 fm_L fm_R (Branch vwu vwv vww 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 vwu vwv vww fm_rl fm_rr) = mkBalBranch02 fm_L fm_R (Branch vwu vwv vww fm_rl fm_rr)

mkBalBranch00 fm_L fm_R vwu vwv vww fm_rl fm_rr True = double_L fm_L fm_R

mkBalBranch01 fm_L fm_R vwu vwv vww fm_rl fm_rr True = single_L fm_L fm_R
mkBalBranch01 fm_L fm_R vwu vwv vww fm_rl fm_rr False = mkBalBranch00 fm_L fm_R vwu vwv vww fm_rl fm_rr otherwise

mkBalBranch02 fm_L fm_R (Branch vwu vwv vww fm_rl fm_rr) = mkBalBranch01 fm_L fm_R vwu vwv vww 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 vvy (Branch key_rl elt_rl vvz fm_rll fm_rlrfm_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 vuz fm_ll (Branch key_lr elt_lr vvu 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 vwu vwv vww 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 vvv vvw vvx 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 vwx fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rlfm_rr
single_R (Branch key_l elt_l vuy fm_ll fm_lrfm_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 vvy (Branch key_rl elt_rl vvz fm_rll fm_rlrfm_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 vuz fm_ll (Branch key_lr elt_lr vvu 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 vwu vwv vww fm_rl fm_rr) = mkBalBranch02 fm_L fm_R (Branch vwu vwv vww fm_rl fm_rr)
mkBalBranch00 fm_L fm_R vwu vwv vww fm_rl fm_rr True = double_L fm_L fm_R
mkBalBranch01 fm_L fm_R vwu vwv vww fm_rl fm_rr True = single_L fm_L fm_R
mkBalBranch01 fm_L fm_R vwu vwv vww fm_rl fm_rr False = mkBalBranch00 fm_L fm_R vwu vwv vww fm_rl fm_rr otherwise
mkBalBranch02 fm_L fm_R (Branch vwu vwv vww fm_rl fm_rr) = mkBalBranch01 fm_L fm_R vwu vwv vww fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr)
mkBalBranch1 fm_L fm_R (Branch vvv vvw vvx fm_ll fm_lr) = mkBalBranch12 fm_L fm_R (Branch vvv vvw vvx fm_ll fm_lr)
mkBalBranch10 fm_L fm_R vvv vvw vvx fm_ll fm_lr True = double_R fm_L fm_R
mkBalBranch11 fm_L fm_R vvv vvw vvx fm_ll fm_lr True = single_R fm_L fm_R
mkBalBranch11 fm_L fm_R vvv vvw vvx fm_ll fm_lr False = mkBalBranch10 fm_L fm_R vvv vvw vvx fm_ll fm_lr otherwise
mkBalBranch12 fm_L fm_R (Branch vvv vvw vvx fm_ll fm_lr) = mkBalBranch11 fm_L fm_R vvv vvw vvx 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 vwx fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rlfm_rr
single_R (Branch key_l elt_l vuy fm_ll fm_lrfm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r)
size_l  = sizeFM fm_L
size_r  = sizeFM fm_R

The following Function with conditions
addToFM_C combiner EmptyFM key elt = unitFM key elt
addToFM_C combiner (Branch key elt size fm_l fm_rnew_key new_elt
 | new_key < key
 = mkBalBranch key elt (addToFM_C combiner fm_l new_key new_eltfm_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_eltsize 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_rnew_key new_elt = addToFM_C3 combiner (Branch key elt size fm_l fm_rnew_key new_elt

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

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

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

addToFM_C3 combiner (Branch key elt size fm_l fm_rnew_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 wzz xuu xuv xuw = addToFM_C3 wzz xuu xuv xuw

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

is transformed to
compare x y = compare3 x y

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

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

compare0 x y True = GT

compare3 x y = compare2 x y (x == y)

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

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

gcd'0 x y = gcd' y (x `rem` y)

gcd'1 True x xux = x
gcd'1 xuy xuz xvu = gcd'0 xuz xvu

gcd'2 x xux = gcd'1 (xux == 0) x xux
gcd'2 xvv xvw = gcd'0 xvv xvw

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

is transformed to
gcd xvx xvy = gcd3 xvx xvy
gcd x y = gcd0 x y

gcd0 x y = 
gcd' (abs x) (abs y)
where 
gcd' x xux = gcd'2 x xux
gcd' x y = gcd'0 x y
gcd'0 x y = gcd' y (x `rem` y)
gcd'1 True x xux = x
gcd'1 xuy xuz xvu = gcd'0 xuz xvu
gcd'2 x xux = gcd'1 (xux == 0) x xux
gcd'2 xvv xvw = gcd'0 xvv xvw

gcd1 True xvx xvy = error []
gcd1 xvz xwu xwv = gcd0 xwu xwv

gcd2 True xvx xvy = gcd1 (xvy == 0) xvx xvy
gcd2 xww xwx xwy = gcd0 xwx xwy

gcd3 xvx xvy = gcd2 (xvx == 0) xvx xvy
gcd3 xwz xxu = gcd0 xwz xxu

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

is transformed to
absReal x = absReal2 x

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

absReal0 x True = `negate` x

absReal2 x = absReal1 x (x >= 0)

The following Function with conditions
undefined 
 | False
 = undefined

is transformed to
undefined  = undefined1

undefined0 True = undefined

undefined1  = undefined0 False

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

is transformed to
reduce x y = reduce2 x y

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



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

mainModule FiniteMap
  ((plusFM :: Ord a => FiniteMap [a] b  ->  FiniteMap [a] b  ->  FiniteMap [a] b) :: Ord a => FiniteMap [a] b  ->  FiniteMap [a] b  ->  FiniteMap [a] b)

module FiniteMap where
  import qualified Maybe
import qualified Prelude

  data FiniteMap b a = EmptyFM  | Branch b a Int (FiniteMap b a) (FiniteMap b a


  instance (Eq a, Eq b) => Eq (FiniteMap b a) where 
   
(==) fm_1 fm_2 sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2

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

  
addToFM0 old new new

  addToFM_C :: Ord b => (a  ->  a  ->  a ->  FiniteMap b a  ->  b  ->  a  ->  FiniteMap b a
addToFM_C combiner EmptyFM key elt addToFM_C4 combiner EmptyFM key elt
addToFM_C combiner (Branch key elt size fm_l fm_rnew_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_rnew_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 wzz xuu xuv xuw addToFM_C3 wzz xuu xuv xuw

  emptyFM :: FiniteMap b a
emptyFM EmptyFM

  findMax :: FiniteMap a b  ->  (a,b)
findMax (Branch key elt vwy vwz EmptyFM(key,elt)
findMax (Branch key elt vxu vxv fm_rfindMax fm_r

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

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

  
fmToList0 key elt rest (key,elt: rest

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

  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 vvy (Branch key_rl elt_rl vvz fm_rll fm_rlr) fm_rrmkBranch 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 vuz fm_ll (Branch key_lr elt_lr vvu 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 vwu vwv vww fm_rl fm_rrmkBalBranch02 fm_L fm_R (Branch vwu vwv vww fm_rl fm_rr)
mkBalBranch00 fm_L fm_R vwu vwv vww fm_rl fm_rr True double_L fm_L fm_R
mkBalBranch01 fm_L fm_R vwu vwv vww fm_rl fm_rr True single_L fm_L fm_R
mkBalBranch01 fm_L fm_R vwu vwv vww fm_rl fm_rr False mkBalBranch00 fm_L fm_R vwu vwv vww fm_rl fm_rr otherwise
mkBalBranch02 fm_L fm_R (Branch vwu vwv vww fm_rl fm_rrmkBalBranch01 fm_L fm_R vwu vwv vww fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr)
mkBalBranch1 fm_L fm_R (Branch vvv vvw vvx fm_ll fm_lrmkBalBranch12 fm_L fm_R (Branch vvv vvw vvx fm_ll fm_lr)
mkBalBranch10 fm_L fm_R vvv vvw vvx fm_ll fm_lr True double_R fm_L fm_R
mkBalBranch11 fm_L fm_R vvv vvw vvx fm_ll fm_lr True single_R fm_L fm_R
mkBalBranch11 fm_L fm_R vvv vvw vvx fm_ll fm_lr False mkBalBranch10 fm_L fm_R vvv vvw vvx fm_ll fm_lr otherwise
mkBalBranch12 fm_L fm_R (Branch vvv vvw vvx fm_ll fm_lrmkBalBranch11 fm_L fm_R vvv vvw vvx 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 vwx fm_rl fm_rrmkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr
single_R (Branch key_l elt_l vuy fm_ll fm_lrfm_r mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r)
size_l sizeFM fm_L
size_r sizeFM fm_R

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

  mkVBalBranch :: Ord a => a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b
mkVBalBranch key elt EmptyFM fm_r mkVBalBranch5 key elt EmptyFM fm_r
mkVBalBranch key elt fm_l EmptyFM mkVBalBranch4 key elt fm_l EmptyFM
mkVBalBranch key elt (Branch yz zu zv zw zx) (Branch zz vuu vuv vuw vuxmkVBalBranch3 key elt (Branch yz zu zv zw zx) (Branch zz vuu vuv vuw vux)

  
mkVBalBranch3 key elt (Branch yz zu zv zw zx) (Branch zz vuu vuv vuw vux
mkVBalBranch2 key elt yz zu zv zw zx zz vuu vuv vuw vux (sIZE_RATIO * size_l < size_r) where 
mkVBalBranch0 key elt yz zu zv zw zx zz vuu vuv vuw vux True mkBranch 13 key elt (Branch yz zu zv zw zx) (Branch zz vuu vuv vuw vux)
mkVBalBranch1 key elt yz zu zv zw zx zz vuu vuv vuw vux True mkBalBranch yz zu zw (mkVBalBranch key elt zx (Branch zz vuu vuv vuw vux))
mkVBalBranch1 key elt yz zu zv zw zx zz vuu vuv vuw vux False mkVBalBranch0 key elt yz zu zv zw zx zz vuu vuv vuw vux otherwise
mkVBalBranch2 key elt yz zu zv zw zx zz vuu vuv vuw vux True mkBalBranch zz vuu (mkVBalBranch key elt (Branch yz zu zv zw zx) vuw) vux
mkVBalBranch2 key elt yz zu zv zw zx zz vuu vuv vuw vux False mkVBalBranch1 key elt yz zu zv zw zx zz vuu vuv vuw vux (sIZE_RATIO * size_r < size_l)
size_l sizeFM (Branch yz zu zv zw zx)
size_r sizeFM (Branch zz vuu vuv vuw vux)

  
mkVBalBranch4 key elt fm_l EmptyFM addToFM fm_l key elt
mkVBalBranch4 wxy wxz wyu wyv mkVBalBranch3 wxy wxz wyu wyv

  
mkVBalBranch5 key elt EmptyFM fm_r addToFM fm_r key elt
mkVBalBranch5 wyx wyy wyz wzu mkVBalBranch4 wyx wyy wyz wzu

  plusFM :: Ord b => FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a
plusFM EmptyFM fm2 fm2
plusFM fm1 EmptyFM fm1
plusFM fm1 (Branch split_key elt1 yx left right
mkVBalBranch split_key elt1 (plusFM lts left) (plusFM gts right) where 
gts splitGT fm1 split_key
lts splitLT fm1 split_key

  sIZE_RATIO :: Int
sIZE_RATIO 5

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

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

  
splitGT0 key elt xy fm_l fm_r split_key True fm_r

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

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

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

  
splitGT4 EmptyFM split_key emptyFM
splitGT4 wwz wxu splitGT3 wwz wxu

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

  
splitLT0 key elt xx fm_l fm_r split_key True fm_l

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

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

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

  
splitLT4 EmptyFM split_key emptyFM
splitLT4 wwv www splitLT3 wwv www

  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 vvy (Branch key_rl elt_rl vvz fm_rll fm_rlrfm_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 vuz fm_ll (Branch key_lr elt_lr vvu 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 vwu vwv vww fm_rl fm_rr) = mkBalBranch02 fm_L fm_R (Branch vwu vwv vww fm_rl fm_rr)
mkBalBranch00 fm_L fm_R vwu vwv vww fm_rl fm_rr True = double_L fm_L fm_R
mkBalBranch01 fm_L fm_R vwu vwv vww fm_rl fm_rr True = single_L fm_L fm_R
mkBalBranch01 fm_L fm_R vwu vwv vww fm_rl fm_rr False = mkBalBranch00 fm_L fm_R vwu vwv vww fm_rl fm_rr otherwise
mkBalBranch02 fm_L fm_R (Branch vwu vwv vww fm_rl fm_rr) = mkBalBranch01 fm_L fm_R vwu vwv vww fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr)
mkBalBranch1 fm_L fm_R (Branch vvv vvw vvx fm_ll fm_lr) = mkBalBranch12 fm_L fm_R (Branch vvv vvw vvx fm_ll fm_lr)
mkBalBranch10 fm_L fm_R vvv vvw vvx fm_ll fm_lr True = double_R fm_L fm_R
mkBalBranch11 fm_L fm_R vvv vvw vvx fm_ll fm_lr True = single_R fm_L fm_R
mkBalBranch11 fm_L fm_R vvv vvw vvx fm_ll fm_lr False = mkBalBranch10 fm_L fm_R vvv vvw vvx fm_ll fm_lr otherwise
mkBalBranch12 fm_L fm_R (Branch vvv vvw vvx fm_ll fm_lr) = mkBalBranch11 fm_L fm_R vvv vvw vvx 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 vwx fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rlfm_rr
single_R (Branch key_l elt_l vuy fm_ll fm_lrfm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r)
size_l  = sizeFM fm_L
size_r  = sizeFM fm_R

are unpacked to the following functions on top level
mkBalBranch6Double_L xxv xxw xxx xxy fm_l (Branch key_r elt_r vvy (Branch key_rl elt_rl vvz fm_rll fm_rlrfm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 xxv xxw fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr)

mkBalBranch6MkBalBranch01 xxv xxw xxx xxy fm_L fm_R vwu vwv vww fm_rl fm_rr True = mkBalBranch6Single_L xxv xxw xxx xxy fm_L fm_R
mkBalBranch6MkBalBranch01 xxv xxw xxx xxy fm_L fm_R vwu vwv vww fm_rl fm_rr False = mkBalBranch6MkBalBranch00 xxv xxw xxx xxy fm_L fm_R vwu vwv vww fm_rl fm_rr otherwise

mkBalBranch6MkBalBranch3 xxv xxw xxx xxy key elt fm_L fm_R True = mkBalBranch6MkBalBranch1 xxv xxw xxx xxy fm_L fm_R fm_L
mkBalBranch6MkBalBranch3 xxv xxw xxx xxy key elt fm_L fm_R False = mkBalBranch6MkBalBranch2 xxv xxw xxx xxy key elt fm_L fm_R otherwise

mkBalBranch6MkBalBranch11 xxv xxw xxx xxy fm_L fm_R vvv vvw vvx fm_ll fm_lr True = mkBalBranch6Single_R xxv xxw xxx xxy fm_L fm_R
mkBalBranch6MkBalBranch11 xxv xxw xxx xxy fm_L fm_R vvv vvw vvx fm_ll fm_lr False = mkBalBranch6MkBalBranch10 xxv xxw xxx xxy fm_L fm_R vvv vvw vvx fm_ll fm_lr otherwise

mkBalBranch6Size_r xxv xxw xxx xxy = sizeFM xxx

mkBalBranch6Double_R xxv xxw xxx xxy (Branch key_l elt_l vuz fm_ll (Branch key_lr elt_lr vvu fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 xxv xxw fm_lrr fm_r)

mkBalBranch6Single_L xxv xxw xxx xxy fm_l (Branch key_r elt_r vwx fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 xxv xxw fm_l fm_rlfm_rr

mkBalBranch6MkBalBranch2 xxv xxw xxx xxy key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R

mkBalBranch6Size_l xxv xxw xxx xxy = sizeFM xxy

mkBalBranch6MkBalBranch0 xxv xxw xxx xxy fm_L fm_R (Branch vwu vwv vww fm_rl fm_rr) = mkBalBranch6MkBalBranch02 xxv xxw xxx xxy fm_L fm_R (Branch vwu vwv vww fm_rl fm_rr)

mkBalBranch6MkBalBranch4 xxv xxw xxx xxy key elt fm_L fm_R True = mkBalBranch6MkBalBranch0 xxv xxw xxx xxy fm_L fm_R fm_R
mkBalBranch6MkBalBranch4 xxv xxw xxx xxy key elt fm_L fm_R False = mkBalBranch6MkBalBranch3 xxv xxw xxx xxy key elt fm_L fm_R (mkBalBranch6Size_l xxv xxw xxx xxy > sIZE_RATIO * mkBalBranch6Size_r xxv xxw xxx xxy)

mkBalBranch6MkBalBranch10 xxv xxw xxx xxy fm_L fm_R vvv vvw vvx fm_ll fm_lr True = mkBalBranch6Double_R xxv xxw xxx xxy fm_L fm_R

mkBalBranch6MkBalBranch12 xxv xxw xxx xxy fm_L fm_R (Branch vvv vvw vvx fm_ll fm_lr) = mkBalBranch6MkBalBranch11 xxv xxw xxx xxy fm_L fm_R vvv vvw vvx fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll)

mkBalBranch6Single_R xxv xxw xxx xxy (Branch key_l elt_l vuy fm_ll fm_lrfm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 xxv xxw fm_lr fm_r)

mkBalBranch6MkBalBranch1 xxv xxw xxx xxy fm_L fm_R (Branch vvv vvw vvx fm_ll fm_lr) = mkBalBranch6MkBalBranch12 xxv xxw xxx xxy fm_L fm_R (Branch vvv vvw vvx fm_ll fm_lr)

mkBalBranch6MkBalBranch5 xxv xxw xxx xxy key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R
mkBalBranch6MkBalBranch5 xxv xxw xxx xxy key elt fm_L fm_R False = mkBalBranch6MkBalBranch4 xxv xxw xxx xxy key elt fm_L fm_R (mkBalBranch6Size_r xxv xxw xxx xxy > sIZE_RATIO * mkBalBranch6Size_l xxv xxw xxx xxy)

mkBalBranch6MkBalBranch02 xxv xxw xxx xxy fm_L fm_R (Branch vwu vwv vww fm_rl fm_rr) = mkBalBranch6MkBalBranch01 xxv xxw xxx xxy fm_L fm_R vwu vwv vww fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr)

mkBalBranch6MkBalBranch00 xxv xxw xxx xxy fm_L fm_R vwu vwv vww fm_rl fm_rr True = mkBalBranch6Double_L xxv xxw xxx xxy fm_L fm_R

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

are unpacked to the following functions on top level
mkBranchLeft_size xxz xyu xyv = sizeFM xxz

mkBranchBalance_ok xxz xyu xyv = True

mkBranchRight_size xxz xyu xyv = sizeFM xyu

mkBranchLeft_ok0 xxz xyu xyv fm_l key EmptyFM = True
mkBranchLeft_ok0 xxz xyu xyv fm_l key (Branch left_key vw vx vy vz) = mkBranchLeft_ok0Biggest_left_key fm_l < key

mkBranchRight_ok xxz xyu xyv = mkBranchRight_ok0 xxz xyu xyv xyu xyv xyu

mkBranchUnbox xxz xyu xyv x = x

mkBranchLeft_ok xxz xyu xyv = mkBranchLeft_ok0 xxz xyu xyv xxz xyv xxz

mkBranchRight_ok0 xxz xyu xyv fm_r key EmptyFM = True
mkBranchRight_ok0 xxz xyu xyv fm_r key (Branch right_key wu wv ww wx) = key < mkBranchRight_ok0Smallest_right_key fm_r

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

are unpacked to the following functions on top level
mkBranchResult xyw xyx xyy xyz = Branch xyw xyx (mkBranchUnbox xyy xyz xyw (1 + mkBranchLeft_size xyy xyz xyw + mkBranchRight_size xyy xyz xyw)) xyy xyz

The bindings of the following Let/Where expression
mkVBalBranch2 key elt yz zu zv zw zx zz vuu vuv vuw vux (sIZE_RATIO * size_l < size_r)
where 
mkVBalBranch0 key elt yz zu zv zw zx zz vuu vuv vuw vux True = mkBranch 13 key elt (Branch yz zu zv zw zx) (Branch zz vuu vuv vuw vux)
mkVBalBranch1 key elt yz zu zv zw zx zz vuu vuv vuw vux True = mkBalBranch yz zu zw (mkVBalBranch key elt zx (Branch zz vuu vuv vuw vux))
mkVBalBranch1 key elt yz zu zv zw zx zz vuu vuv vuw vux False = mkVBalBranch0 key elt yz zu zv zw zx zz vuu vuv vuw vux otherwise
mkVBalBranch2 key elt yz zu zv zw zx zz vuu vuv vuw vux True = mkBalBranch zz vuu (mkVBalBranch key elt (Branch yz zu zv zw zxvuwvux
mkVBalBranch2 key elt yz zu zv zw zx zz vuu vuv vuw vux False = mkVBalBranch1 key elt yz zu zv zw zx zz vuu vuv vuw vux (sIZE_RATIO * size_r < size_l)
size_l  = sizeFM (Branch yz zu zv zw zx)
size_r  = sizeFM (Branch zz vuu vuv vuw vux)

are unpacked to the following functions on top level
mkVBalBranch3MkVBalBranch0 xzu xzv xzw xzx xzy xzz yuu yuv yuw yux key elt yz zu zv zw zx zz vuu vuv vuw vux True = mkBranch 13 key elt (Branch yz zu zv zw zx) (Branch zz vuu vuv vuw vux)

mkVBalBranch3Size_r xzu xzv xzw xzx xzy xzz yuu yuv yuw yux = sizeFM (Branch xzu xzv xzw xzx xzy)

mkVBalBranch3Size_l xzu xzv xzw xzx xzy xzz yuu yuv yuw yux = sizeFM (Branch xzz yuu yuv yuw yux)

mkVBalBranch3MkVBalBranch2 xzu xzv xzw xzx xzy xzz yuu yuv yuw yux key elt yz zu zv zw zx zz vuu vuv vuw vux True = mkBalBranch zz vuu (mkVBalBranch key elt (Branch yz zu zv zw zxvuwvux
mkVBalBranch3MkVBalBranch2 xzu xzv xzw xzx xzy xzz yuu yuv yuw yux key elt yz zu zv zw zx zz vuu vuv vuw vux False = mkVBalBranch3MkVBalBranch1 xzu xzv xzw xzx xzy xzz yuu yuv yuw yux key elt yz zu zv zw zx zz vuu vuv vuw vux (sIZE_RATIO * mkVBalBranch3Size_r xzu xzv xzw xzx xzy xzz yuu yuv yuw yux < mkVBalBranch3Size_l xzu xzv xzw xzx xzy xzz yuu yuv yuw yux)

mkVBalBranch3MkVBalBranch1 xzu xzv xzw xzx xzy xzz yuu yuv yuw yux key elt yz zu zv zw zx zz vuu vuv vuw vux True = mkBalBranch yz zu zw (mkVBalBranch key elt zx (Branch zz vuu vuv vuw vux))
mkVBalBranch3MkVBalBranch1 xzu xzv xzw xzx xzy xzz yuu yuv yuw yux key elt yz zu zv zw zx zz vuu vuv vuw vux False = mkVBalBranch3MkVBalBranch0 xzu xzv xzw xzx xzy xzz yuu yuv yuw yux key elt yz zu zv zw zx zz vuu vuv vuw vux otherwise

The bindings of the following Let/Where expression
mkVBalBranch split_key elt1 (plusFM lts left) (plusFM gts right)
where 
gts  = splitGT fm1 split_key
lts  = splitLT fm1 split_key

are unpacked to the following functions on top level
plusFMLts yuy yuz = splitLT yuy yuz

plusFMGts yuy yuz = splitGT yuy yuz

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 yvu = fst (findMax yvu)

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 yvv = fst (findMin yvv)

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

are unpacked to the following functions on top level
reduce2Reduce0 yvw yvx x y True = x `quot` reduce2D yvw yvx :% (y `quot` reduce2D yvw yvx)

reduce2D yvw yvx = gcd yvw yvx

reduce2Reduce1 yvw yvx x y True = error []
reduce2Reduce1 yvw yvx x y False = reduce2Reduce0 yvw yvx x y otherwise

The bindings of the following Let/Where expression
gcd' (abs x) (abs y)
where 
gcd' x xux = gcd'2 x xux
gcd' x y = gcd'0 x y
gcd'0 x y = gcd' y (x `rem` y)
gcd'1 True x xux = x
gcd'1 xuy xuz xvu = gcd'0 xuz xvu
gcd'2 x xux = gcd'1 (xux == 0) x xux
gcd'2 xvv xvw = gcd'0 xvv xvw

are unpacked to the following functions on top level
gcd0Gcd'2 x xux = gcd0Gcd'1 (xux == 0) x xux
gcd0Gcd'2 xvv xvw = gcd0Gcd'0 xvv xvw

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

gcd0Gcd'1 True x xux = x
gcd0Gcd'1 xuy xuz xvu = gcd0Gcd'0 xuz xvu

gcd0Gcd' x xux = gcd0Gcd'2 x xux
gcd0Gcd' x y = gcd0Gcd'0 x y



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

mainModule FiniteMap
  ((plusFM :: Ord b => FiniteMap [b] a  ->  FiniteMap [b] a  ->  FiniteMap [b] a) :: Ord b => FiniteMap [b] a  ->  FiniteMap [b] a  ->  FiniteMap [b] a)

module FiniteMap where
  import qualified Maybe
import qualified Prelude

  data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b


  instance (Eq a, Eq b) => Eq (FiniteMap a b) where 
   
(==) fm_1 fm_2 sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2

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

  
addToFM0 old new new

  addToFM_C :: Ord b => (a  ->  a  ->  a ->  FiniteMap b a  ->  b  ->  a  ->  FiniteMap b a
addToFM_C combiner EmptyFM key elt addToFM_C4 combiner EmptyFM key elt
addToFM_C combiner (Branch key elt size fm_l fm_rnew_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_rnew_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 wzz xuu xuv xuw addToFM_C3 wzz xuu xuv xuw

  emptyFM :: FiniteMap b a
emptyFM EmptyFM

  findMax :: FiniteMap b a  ->  (b,a)
findMax (Branch key elt vwy vwz EmptyFM(key,elt)
findMax (Branch key elt vxu vxv fm_rfindMax fm_r

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

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

  
fmToList0 key elt rest (key,elt: rest

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

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

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

  
mkBalBranch6Double_L xxv xxw xxx xxy fm_l (Branch key_r elt_r vvy (Branch key_rl elt_rl vvz fm_rll fm_rlr) fm_rrmkBranch 5 key_rl elt_rl (mkBranch 6 xxv xxw fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr)

  
mkBalBranch6Double_R xxv xxw xxx xxy (Branch key_l elt_l vuz fm_ll (Branch key_lr elt_lr vvu fm_lrl fm_lrr)) fm_r mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 xxv xxw fm_lrr fm_r)

  
mkBalBranch6MkBalBranch0 xxv xxw xxx xxy fm_L fm_R (Branch vwu vwv vww fm_rl fm_rrmkBalBranch6MkBalBranch02 xxv xxw xxx xxy fm_L fm_R (Branch vwu vwv vww fm_rl fm_rr)

  
mkBalBranch6MkBalBranch00 xxv xxw xxx xxy fm_L fm_R vwu vwv vww fm_rl fm_rr True mkBalBranch6Double_L xxv xxw xxx xxy fm_L fm_R

  
mkBalBranch6MkBalBranch01 xxv xxw xxx xxy fm_L fm_R vwu vwv vww fm_rl fm_rr True mkBalBranch6Single_L xxv xxw xxx xxy fm_L fm_R
mkBalBranch6MkBalBranch01 xxv xxw xxx xxy fm_L fm_R vwu vwv vww fm_rl fm_rr False mkBalBranch6MkBalBranch00 xxv xxw xxx xxy fm_L fm_R vwu vwv vww fm_rl fm_rr otherwise

  
mkBalBranch6MkBalBranch02 xxv xxw xxx xxy fm_L fm_R (Branch vwu vwv vww fm_rl fm_rrmkBalBranch6MkBalBranch01 xxv xxw xxx xxy fm_L fm_R vwu vwv vww fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr)

  
mkBalBranch6MkBalBranch1 xxv xxw xxx xxy fm_L fm_R (Branch vvv vvw vvx fm_ll fm_lrmkBalBranch6MkBalBranch12 xxv xxw xxx xxy fm_L fm_R (Branch vvv vvw vvx fm_ll fm_lr)

  
mkBalBranch6MkBalBranch10 xxv xxw xxx xxy fm_L fm_R vvv vvw vvx fm_ll fm_lr True mkBalBranch6Double_R xxv xxw xxx xxy fm_L fm_R

  
mkBalBranch6MkBalBranch11 xxv xxw xxx xxy fm_L fm_R vvv vvw vvx fm_ll fm_lr True mkBalBranch6Single_R xxv xxw xxx xxy fm_L fm_R
mkBalBranch6MkBalBranch11 xxv xxw xxx xxy fm_L fm_R vvv vvw vvx fm_ll fm_lr False mkBalBranch6MkBalBranch10 xxv xxw xxx xxy fm_L fm_R vvv vvw vvx fm_ll fm_lr otherwise

  
mkBalBranch6MkBalBranch12 xxv xxw xxx xxy fm_L fm_R (Branch vvv vvw vvx fm_ll fm_lrmkBalBranch6MkBalBranch11 xxv xxw xxx xxy fm_L fm_R vvv vvw vvx fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll)

  
mkBalBranch6MkBalBranch2 xxv xxw xxx xxy key elt fm_L fm_R True mkBranch 2 key elt fm_L fm_R

  
mkBalBranch6MkBalBranch3 xxv xxw xxx xxy key elt fm_L fm_R True mkBalBranch6MkBalBranch1 xxv xxw xxx xxy fm_L fm_R fm_L
mkBalBranch6MkBalBranch3 xxv xxw xxx xxy key elt fm_L fm_R False mkBalBranch6MkBalBranch2 xxv xxw xxx xxy key elt fm_L fm_R otherwise

  
mkBalBranch6MkBalBranch4 xxv xxw xxx xxy key elt fm_L fm_R True mkBalBranch6MkBalBranch0 xxv xxw xxx xxy fm_L fm_R fm_R
mkBalBranch6MkBalBranch4 xxv xxw xxx xxy key elt fm_L fm_R False mkBalBranch6MkBalBranch3 xxv xxw xxx xxy key elt fm_L fm_R (mkBalBranch6Size_l xxv xxw xxx xxy > sIZE_RATIO * mkBalBranch6Size_r xxv xxw xxx xxy)

  
mkBalBranch6MkBalBranch5 xxv xxw xxx xxy key elt fm_L fm_R True mkBranch 1 key elt fm_L fm_R
mkBalBranch6MkBalBranch5 xxv xxw xxx xxy key elt fm_L fm_R False mkBalBranch6MkBalBranch4 xxv xxw xxx xxy key elt fm_L fm_R (mkBalBranch6Size_r xxv xxw xxx xxy > sIZE_RATIO * mkBalBranch6Size_l xxv xxw xxx xxy)

  
mkBalBranch6Single_L xxv xxw xxx xxy fm_l (Branch key_r elt_r vwx fm_rl fm_rrmkBranch 3 key_r elt_r (mkBranch 4 xxv xxw fm_l fm_rl) fm_rr

  
mkBalBranch6Single_R xxv xxw xxx xxy (Branch key_l elt_l vuy fm_ll fm_lrfm_r mkBranch 8 key_l elt_l fm_ll (mkBranch 9 xxv xxw fm_lr fm_r)

  
mkBalBranch6Size_l xxv xxw xxx xxy sizeFM xxy

  
mkBalBranch6Size_r xxv xxw xxx xxy sizeFM xxx

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

  
mkBranchBalance_ok xxz xyu xyv True

  
mkBranchLeft_ok xxz xyu xyv mkBranchLeft_ok0 xxz xyu xyv xxz xyv xxz

  
mkBranchLeft_ok0 xxz xyu xyv fm_l key EmptyFM True
mkBranchLeft_ok0 xxz xyu xyv fm_l key (Branch left_key vw vx vy vzmkBranchLeft_ok0Biggest_left_key fm_l < key

  
mkBranchLeft_ok0Biggest_left_key yvu fst (findMax yvu)

  
mkBranchLeft_size xxz xyu xyv sizeFM xxz

  
mkBranchResult xyw xyx xyy xyz Branch xyw xyx (mkBranchUnbox xyy xyz xyw (1 + mkBranchLeft_size xyy xyz xyw + mkBranchRight_size xyy xyz xyw)) xyy xyz

  
mkBranchRight_ok xxz xyu xyv mkBranchRight_ok0 xxz xyu xyv xyu xyv xyu

  
mkBranchRight_ok0 xxz xyu xyv fm_r key EmptyFM True
mkBranchRight_ok0 xxz xyu xyv fm_r key (Branch right_key wu wv ww wxkey < mkBranchRight_ok0Smallest_right_key fm_r

  
mkBranchRight_ok0Smallest_right_key yvv fst (findMin yvv)

  
mkBranchRight_size xxz xyu xyv sizeFM xyu

  mkBranchUnbox :: Ord a =>  ->  (FiniteMap a b) ( ->  (FiniteMap a b) ( ->  a (Int  ->  Int)))
mkBranchUnbox xxz xyu xyv x x

  mkVBalBranch :: Ord a => a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b
mkVBalBranch key elt EmptyFM fm_r mkVBalBranch5 key elt EmptyFM fm_r
mkVBalBranch key elt fm_l EmptyFM mkVBalBranch4 key elt fm_l EmptyFM
mkVBalBranch key elt (Branch yz zu zv zw zx) (Branch zz vuu vuv vuw vuxmkVBalBranch3 key elt (Branch yz zu zv zw zx) (Branch zz vuu vuv vuw vux)

  
mkVBalBranch3 key elt (Branch yz zu zv zw zx) (Branch zz vuu vuv vuw vuxmkVBalBranch3MkVBalBranch2 zz vuu vuv vuw vux yz zu zv zw zx key elt yz zu zv zw zx zz vuu vuv vuw vux (sIZE_RATIO * mkVBalBranch3Size_l zz vuu vuv vuw vux yz zu zv zw zx < mkVBalBranch3Size_r zz vuu vuv vuw vux yz zu zv zw zx)

  
mkVBalBranch3MkVBalBranch0 xzu xzv xzw xzx xzy xzz yuu yuv yuw yux key elt yz zu zv zw zx zz vuu vuv vuw vux True mkBranch 13 key elt (Branch yz zu zv zw zx) (Branch zz vuu vuv vuw vux)

  
mkVBalBranch3MkVBalBranch1 xzu xzv xzw xzx xzy xzz yuu yuv yuw yux key elt yz zu zv zw zx zz vuu vuv vuw vux True mkBalBranch yz zu zw (mkVBalBranch key elt zx (Branch zz vuu vuv vuw vux))
mkVBalBranch3MkVBalBranch1 xzu xzv xzw xzx xzy xzz yuu yuv yuw yux key elt yz zu zv zw zx zz vuu vuv vuw vux False mkVBalBranch3MkVBalBranch0 xzu xzv xzw xzx xzy xzz yuu yuv yuw yux key elt yz zu zv zw zx zz vuu vuv vuw vux otherwise

  
mkVBalBranch3MkVBalBranch2 xzu xzv xzw xzx xzy xzz yuu yuv yuw yux key elt yz zu zv zw zx zz vuu vuv vuw vux True mkBalBranch zz vuu (mkVBalBranch key elt (Branch yz zu zv zw zx) vuw) vux
mkVBalBranch3MkVBalBranch2 xzu xzv xzw xzx xzy xzz yuu yuv yuw yux key elt yz zu zv zw zx zz vuu vuv vuw vux False mkVBalBranch3MkVBalBranch1 xzu xzv xzw xzx xzy xzz yuu yuv yuw yux key elt yz zu zv zw zx zz vuu vuv vuw vux (sIZE_RATIO * mkVBalBranch3Size_r xzu xzv xzw xzx xzy xzz yuu yuv yuw yux < mkVBalBranch3Size_l xzu xzv xzw xzx xzy xzz yuu yuv yuw yux)

  
mkVBalBranch3Size_l xzu xzv xzw xzx xzy xzz yuu yuv yuw yux sizeFM (Branch xzz yuu yuv yuw yux)

  
mkVBalBranch3Size_r xzu xzv xzw xzx xzy xzz yuu yuv yuw yux sizeFM (Branch xzu xzv xzw xzx xzy)

  
mkVBalBranch4 key elt fm_l EmptyFM addToFM fm_l key elt
mkVBalBranch4 wxy wxz wyu wyv mkVBalBranch3 wxy wxz wyu wyv

  
mkVBalBranch5 key elt EmptyFM fm_r addToFM fm_r key elt
mkVBalBranch5 wyx wyy wyz wzu mkVBalBranch4 wyx wyy wyz wzu

  plusFM :: Ord a => FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b
plusFM EmptyFM fm2 fm2
plusFM fm1 EmptyFM fm1
plusFM fm1 (Branch split_key elt1 yx left rightmkVBalBranch split_key elt1 (plusFM (plusFMLts fm1 split_key) left) (plusFM (plusFMGts fm1 split_key) right)

  
plusFMGts yuy yuz splitGT yuy yuz

  
plusFMLts yuy yuz splitLT yuy yuz

  sIZE_RATIO :: Int
sIZE_RATIO 5

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

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

  
splitGT0 key elt xy fm_l fm_r split_key True fm_r

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

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

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

  
splitGT4 EmptyFM split_key emptyFM
splitGT4 wwz wxu splitGT3 wwz wxu

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

  
splitLT0 key elt xx fm_l fm_r split_key True fm_l

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

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

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

  
splitLT4 EmptyFM split_key emptyFM
splitLT4 wwv www splitLT3 wwv www

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude



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

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

mainModule FiniteMap
  (plusFM :: Ord a => FiniteMap [a] b  ->  FiniteMap [a] b  ->  FiniteMap [a] b)

module FiniteMap where
  import qualified Maybe
import qualified Prelude

  data FiniteMap b a = EmptyFM  | Branch b a Int (FiniteMap b a) (FiniteMap b a


  instance (Eq a, Eq b) => Eq (FiniteMap b a) where 
   
(==) fm_1 fm_2 sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2

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

  
addToFM0 old new new

  addToFM_C :: Ord 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_rnew_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_rnew_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 wzz xuu xuv xuw addToFM_C3 wzz xuu xuv xuw

  emptyFM :: FiniteMap a b
emptyFM EmptyFM

  findMax :: FiniteMap b a  ->  (b,a)
findMax (Branch key elt vwy vwz EmptyFM(key,elt)
findMax (Branch key elt vxu vxv fm_rfindMax fm_r

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

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

  
fmToList0 key elt rest (key,elt: rest

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

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

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

  
mkBalBranch6Double_L xxv xxw xxx xxy fm_l (Branch key_r elt_r vvy (Branch key_rl elt_rl vvz fm_rll fm_rlr) fm_rrmkBranch (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) key_rl elt_rl (mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))) xxv xxw fm_l fm_rll) (mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) key_r elt_r fm_rlr fm_rr)

  
mkBalBranch6Double_R xxv xxw xxx xxy (Branch key_l elt_l vuz fm_ll (Branch key_lr elt_lr vvu 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))))))))))))) xxv xxw fm_lrr fm_r)

  
mkBalBranch6MkBalBranch0 xxv xxw xxx xxy fm_L fm_R (Branch vwu vwv vww fm_rl fm_rrmkBalBranch6MkBalBranch02 xxv xxw xxx xxy fm_L fm_R (Branch vwu vwv vww fm_rl fm_rr)

  
mkBalBranch6MkBalBranch00 xxv xxw xxx xxy fm_L fm_R vwu vwv vww fm_rl fm_rr True mkBalBranch6Double_L xxv xxw xxx xxy fm_L fm_R

  
mkBalBranch6MkBalBranch01 xxv xxw xxx xxy fm_L fm_R vwu vwv vww fm_rl fm_rr True mkBalBranch6Single_L xxv xxw xxx xxy fm_L fm_R
mkBalBranch6MkBalBranch01 xxv xxw xxx xxy fm_L fm_R vwu vwv vww fm_rl fm_rr False mkBalBranch6MkBalBranch00 xxv xxw xxx xxy fm_L fm_R vwu vwv vww fm_rl fm_rr otherwise

  
mkBalBranch6MkBalBranch02 xxv xxw xxx xxy fm_L fm_R (Branch vwu vwv vww fm_rl fm_rrmkBalBranch6MkBalBranch01 xxv xxw xxx xxy fm_L fm_R vwu vwv vww fm_rl fm_rr (sizeFM fm_rl < Pos (Succ (Succ Zero)) * sizeFM fm_rr)

  
mkBalBranch6MkBalBranch1 xxv xxw xxx xxy fm_L fm_R (Branch vvv vvw vvx fm_ll fm_lrmkBalBranch6MkBalBranch12 xxv xxw xxx xxy fm_L fm_R (Branch vvv vvw vvx fm_ll fm_lr)

  
mkBalBranch6MkBalBranch10 xxv xxw xxx xxy fm_L fm_R vvv vvw vvx fm_ll fm_lr True mkBalBranch6Double_R xxv xxw xxx xxy fm_L fm_R

  
mkBalBranch6MkBalBranch11 xxv xxw xxx xxy fm_L fm_R vvv vvw vvx fm_ll fm_lr True mkBalBranch6Single_R xxv xxw xxx xxy fm_L fm_R
mkBalBranch6MkBalBranch11 xxv xxw xxx xxy fm_L fm_R vvv vvw vvx fm_ll fm_lr False mkBalBranch6MkBalBranch10 xxv xxw xxx xxy fm_L fm_R vvv vvw vvx fm_ll fm_lr otherwise

  
mkBalBranch6MkBalBranch12 xxv xxw xxx xxy fm_L fm_R (Branch vvv vvw vvx fm_ll fm_lrmkBalBranch6MkBalBranch11 xxv xxw xxx xxy fm_L fm_R vvv vvw vvx fm_ll fm_lr (sizeFM fm_lr < Pos (Succ (Succ Zero)) * sizeFM fm_ll)

  
mkBalBranch6MkBalBranch2 xxv xxw xxx xxy key elt fm_L fm_R True mkBranch (Pos (Succ (Succ Zero))) key elt fm_L fm_R

  
mkBalBranch6MkBalBranch3 xxv xxw xxx xxy key elt fm_L fm_R True mkBalBranch6MkBalBranch1 xxv xxw xxx xxy fm_L fm_R fm_L
mkBalBranch6MkBalBranch3 xxv xxw xxx xxy key elt fm_L fm_R False mkBalBranch6MkBalBranch2 xxv xxw xxx xxy key elt fm_L fm_R otherwise

  
mkBalBranch6MkBalBranch4 xxv xxw xxx xxy key elt fm_L fm_R True mkBalBranch6MkBalBranch0 xxv xxw xxx xxy fm_L fm_R fm_R
mkBalBranch6MkBalBranch4 xxv xxw xxx xxy key elt fm_L fm_R False mkBalBranch6MkBalBranch3 xxv xxw xxx xxy key elt fm_L fm_R (mkBalBranch6Size_l xxv xxw xxx xxy > sIZE_RATIO * mkBalBranch6Size_r xxv xxw xxx xxy)

  
mkBalBranch6MkBalBranch5 xxv xxw xxx xxy key elt fm_L fm_R True mkBranch (Pos (Succ Zero)) key elt fm_L fm_R
mkBalBranch6MkBalBranch5 xxv xxw xxx xxy key elt fm_L fm_R False mkBalBranch6MkBalBranch4 xxv xxw xxx xxy key elt fm_L fm_R (mkBalBranch6Size_r xxv xxw xxx xxy > sIZE_RATIO * mkBalBranch6Size_l xxv xxw xxx xxy)

  
mkBalBranch6Single_L xxv xxw xxx xxy fm_l (Branch key_r elt_r vwx fm_rl fm_rrmkBranch (Pos (Succ (Succ (Succ Zero)))) key_r elt_r (mkBranch (Pos (Succ (Succ (Succ (Succ Zero))))) xxv xxw fm_l fm_rl) fm_rr

  
mkBalBranch6Single_R xxv xxw xxx xxy (Branch key_l elt_l vuy fm_ll fm_lrfm_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)))))))))) xxv xxw fm_lr fm_r)

  
mkBalBranch6Size_l xxv xxw xxx xxy sizeFM xxy

  
mkBalBranch6Size_r xxv xxw xxx xxy sizeFM xxx

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

  
mkBranchBalance_ok xxz xyu xyv True

  
mkBranchLeft_ok xxz xyu xyv mkBranchLeft_ok0 xxz xyu xyv xxz xyv xxz

  
mkBranchLeft_ok0 xxz xyu xyv fm_l key EmptyFM True
mkBranchLeft_ok0 xxz xyu xyv fm_l key (Branch left_key vw vx vy vzmkBranchLeft_ok0Biggest_left_key fm_l < key

  
mkBranchLeft_ok0Biggest_left_key yvu fst (findMax yvu)

  
mkBranchLeft_size xxz xyu xyv sizeFM xxz

  
mkBranchResult xyw xyx xyy xyz Branch xyw xyx (mkBranchUnbox xyy xyz xyw (Pos (Succ Zero+ mkBranchLeft_size xyy xyz xyw + mkBranchRight_size xyy xyz xyw)) xyy xyz

  
mkBranchRight_ok xxz xyu xyv mkBranchRight_ok0 xxz xyu xyv xyu xyv xyu

  
mkBranchRight_ok0 xxz xyu xyv fm_r key EmptyFM True
mkBranchRight_ok0 xxz xyu xyv fm_r key (Branch right_key wu wv ww wxkey < mkBranchRight_ok0Smallest_right_key fm_r

  
mkBranchRight_ok0Smallest_right_key yvv fst (findMin yvv)

  
mkBranchRight_size xxz xyu xyv sizeFM xyu

  mkBranchUnbox :: Ord a =>  ->  (FiniteMap a b) ( ->  (FiniteMap a b) ( ->  a (Int  ->  Int)))
mkBranchUnbox xxz xyu xyv x x

  mkVBalBranch :: Ord a => a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b
mkVBalBranch key elt EmptyFM fm_r mkVBalBranch5 key elt EmptyFM fm_r
mkVBalBranch key elt fm_l EmptyFM mkVBalBranch4 key elt fm_l EmptyFM
mkVBalBranch key elt (Branch yz zu zv zw zx) (Branch zz vuu vuv vuw vuxmkVBalBranch3 key elt (Branch yz zu zv zw zx) (Branch zz vuu vuv vuw vux)

  
mkVBalBranch3 key elt (Branch yz zu zv zw zx) (Branch zz vuu vuv vuw vuxmkVBalBranch3MkVBalBranch2 zz vuu vuv vuw vux yz zu zv zw zx key elt yz zu zv zw zx zz vuu vuv vuw vux (sIZE_RATIO * mkVBalBranch3Size_l zz vuu vuv vuw vux yz zu zv zw zx < mkVBalBranch3Size_r zz vuu vuv vuw vux yz zu zv zw zx)

  
mkVBalBranch3MkVBalBranch0 xzu xzv xzw xzx xzy xzz yuu yuv yuw yux key elt yz zu zv zw zx zz vuu vuv vuw vux True mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))) key elt (Branch yz zu zv zw zx) (Branch zz vuu vuv vuw vux)

  
mkVBalBranch3MkVBalBranch1 xzu xzv xzw xzx xzy xzz yuu yuv yuw yux key elt yz zu zv zw zx zz vuu vuv vuw vux True mkBalBranch yz zu zw (mkVBalBranch key elt zx (Branch zz vuu vuv vuw vux))
mkVBalBranch3MkVBalBranch1 xzu xzv xzw xzx xzy xzz yuu yuv yuw yux key elt yz zu zv zw zx zz vuu vuv vuw vux False mkVBalBranch3MkVBalBranch0 xzu xzv xzw xzx xzy xzz yuu yuv yuw yux key elt yz zu zv zw zx zz vuu vuv vuw vux otherwise

  
mkVBalBranch3MkVBalBranch2 xzu xzv xzw xzx xzy xzz yuu yuv yuw yux key elt yz zu zv zw zx zz vuu vuv vuw vux True mkBalBranch zz vuu (mkVBalBranch key elt (Branch yz zu zv zw zx) vuw) vux
mkVBalBranch3MkVBalBranch2 xzu xzv xzw xzx xzy xzz yuu yuv yuw yux key elt yz zu zv zw zx zz vuu vuv vuw vux False mkVBalBranch3MkVBalBranch1 xzu xzv xzw xzx xzy xzz yuu yuv yuw yux key elt yz zu zv zw zx zz vuu vuv vuw vux (sIZE_RATIO * mkVBalBranch3Size_r xzu xzv xzw xzx xzy xzz yuu yuv yuw yux < mkVBalBranch3Size_l xzu xzv xzw xzx xzy xzz yuu yuv yuw yux)

  
mkVBalBranch3Size_l xzu xzv xzw xzx xzy xzz yuu yuv yuw yux sizeFM (Branch xzz yuu yuv yuw yux)

  
mkVBalBranch3Size_r xzu xzv xzw xzx xzy xzz yuu yuv yuw yux sizeFM (Branch xzu xzv xzw xzx xzy)

  
mkVBalBranch4 key elt fm_l EmptyFM addToFM fm_l key elt
mkVBalBranch4 wxy wxz wyu wyv mkVBalBranch3 wxy wxz wyu wyv

  
mkVBalBranch5 key elt EmptyFM fm_r addToFM fm_r key elt
mkVBalBranch5 wyx wyy wyz wzu mkVBalBranch4 wyx wyy wyz wzu

  plusFM :: Ord b => FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a
plusFM EmptyFM fm2 fm2
plusFM fm1 EmptyFM fm1
plusFM fm1 (Branch split_key elt1 yx left rightmkVBalBranch split_key elt1 (plusFM (plusFMLts fm1 split_key) left) (plusFM (plusFMGts fm1 split_key) right)

  
plusFMGts yuy yuz splitGT yuy yuz

  
plusFMLts yuy yuz splitLT yuy yuz

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

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

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

  
splitGT0 key elt xy fm_l fm_r split_key True fm_r

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

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

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

  
splitGT4 EmptyFM split_key emptyFM
splitGT4 wwz wxu splitGT3 wwz wxu

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

  
splitLT0 key elt xx fm_l fm_r split_key True fm_l

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

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

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

  
splitLT4 EmptyFM split_key emptyFM
splitLT4 wwv www splitLT3 wwv www

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

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

new_primEqNat(Succ(yvy400000), Succ(yvy300000)) → new_primEqNat(yvy400000, yvy300000)

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

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



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

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

new_primCmpNat(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat(yvy40000, yvy30000)

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

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



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

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

new_primMinusNat(Succ(yvy118200), Succ(yvy54200)) → new_primMinusNat(yvy118200, yvy54200)

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

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



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

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

new_primPlusNat(Succ(yvy30700), Succ(yvy4001000)) → new_primPlusNat(yvy30700, yvy4001000)

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

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



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

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

new_primMulNat(Succ(yvy300000), Succ(yvy400100)) → new_primMulNat(yvy300000, Succ(yvy400100))

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

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



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

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

new_esEs2(Just(yvy40000), Just(yvy30000), app(app(app(ty_@3, bba), bbb), bbc)) → new_esEs1(yvy40000, yvy30000, bba, bbb, bbc)
new_esEs3(Right(yvy40000), Right(yvy30000), bda, app(ty_[], bdb)) → new_esEs(yvy40000, yvy30000, bdb)
new_esEs(:(yvy40000, yvy40001), :(yvy30000, yvy30001), app(app(ty_@2, ba), bb)) → new_esEs0(yvy40000, yvy30000, ba, bb)
new_esEs2(Just(yvy40000), Just(yvy30000), app(ty_[], baf)) → new_esEs(yvy40000, yvy30000, baf)
new_esEs1(@3(yvy40000, yvy40001, yvy40002), @3(yvy30000, yvy30001, yvy30002), gc, app(app(app(ty_@3, gg), gh), ha), fa) → new_esEs1(yvy40001, yvy30001, gg, gh, ha)
new_esEs0(@2(yvy40000, yvy40001), @2(yvy30000, yvy30001), app(app(ty_Either, dc), dd), cc) → new_esEs3(yvy40000, yvy30000, dc, dd)
new_esEs1(@3(yvy40000, yvy40001, yvy40002), @3(yvy30000, yvy30001, yvy30002), gc, app(app(ty_Either, hc), hd), fa) → new_esEs3(yvy40001, yvy30001, hc, hd)
new_esEs1(@3(yvy40000, yvy40001, yvy40002), @3(yvy30000, yvy30001, yvy30002), gc, eh, app(app(ty_Either, bad), bae)) → new_esEs3(yvy40002, yvy30002, bad, bae)
new_esEs3(Right(yvy40000), Right(yvy30000), bda, app(app(ty_Either, bea), beb)) → new_esEs3(yvy40000, yvy30000, bea, beb)
new_esEs0(@2(yvy40000, yvy40001), @2(yvy30000, yvy30001), de, app(app(app(ty_@3, ea), eb), ec)) → new_esEs1(yvy40001, yvy30001, ea, eb, ec)
new_esEs1(@3(yvy40000, yvy40001, yvy40002), @3(yvy30000, yvy30001, yvy30002), gc, eh, app(app(app(ty_@3, hh), baa), bab)) → new_esEs1(yvy40002, yvy30002, hh, baa, bab)
new_esEs3(Right(yvy40000), Right(yvy30000), bda, app(app(app(ty_@3, bde), bdf), bdg)) → new_esEs1(yvy40000, yvy30000, bde, bdf, bdg)
new_esEs3(Left(yvy40000), Left(yvy30000), app(app(app(ty_@3, bcc), bcd), bce), bbh) → new_esEs1(yvy40000, yvy30000, bcc, bcd, bce)
new_esEs3(Left(yvy40000), Left(yvy30000), app(ty_[], bbg), bbh) → new_esEs(yvy40000, yvy30000, bbg)
new_esEs1(@3(yvy40000, yvy40001, yvy40002), @3(yvy30000, yvy30001, yvy30002), gc, eh, app(app(ty_@2, hf), hg)) → new_esEs0(yvy40002, yvy30002, hf, hg)
new_esEs0(@2(yvy40000, yvy40001), @2(yvy30000, yvy30001), de, app(app(ty_Either, ee), ef)) → new_esEs3(yvy40001, yvy30001, ee, ef)
new_esEs2(Just(yvy40000), Just(yvy30000), app(ty_Maybe, bbd)) → new_esEs2(yvy40000, yvy30000, bbd)
new_esEs3(Left(yvy40000), Left(yvy30000), app(app(ty_Either, bcg), bch), bbh) → new_esEs3(yvy40000, yvy30000, bcg, bch)
new_esEs1(@3(yvy40000, yvy40001, yvy40002), @3(yvy30000, yvy30001, yvy30002), app(app(ty_@2, fb), fc), eh, fa) → new_esEs0(yvy40000, yvy30000, fb, fc)
new_esEs0(@2(yvy40000, yvy40001), @2(yvy30000, yvy30001), de, app(ty_[], df)) → new_esEs(yvy40001, yvy30001, df)
new_esEs(:(yvy40000, yvy40001), :(yvy30000, yvy30001), app(ty_Maybe, bf)) → new_esEs2(yvy40000, yvy30000, bf)
new_esEs1(@3(yvy40000, yvy40001, yvy40002), @3(yvy30000, yvy30001, yvy30002), app(app(app(ty_@3, fd), ff), fg), eh, fa) → new_esEs1(yvy40000, yvy30000, fd, ff, fg)
new_esEs3(Left(yvy40000), Left(yvy30000), app(ty_Maybe, bcf), bbh) → new_esEs2(yvy40000, yvy30000, bcf)
new_esEs0(@2(yvy40000, yvy40001), @2(yvy30000, yvy30001), de, app(ty_Maybe, ed)) → new_esEs2(yvy40001, yvy30001, ed)
new_esEs(:(yvy40000, yvy40001), :(yvy30000, yvy30001), ca) → new_esEs(yvy40001, yvy30001, ca)
new_esEs1(@3(yvy40000, yvy40001, yvy40002), @3(yvy30000, yvy30001, yvy30002), gc, app(ty_Maybe, hb), fa) → new_esEs2(yvy40001, yvy30001, hb)
new_esEs(:(yvy40000, yvy40001), :(yvy30000, yvy30001), app(app(app(ty_@3, bc), bd), be)) → new_esEs1(yvy40000, yvy30000, bc, bd, be)
new_esEs(:(yvy40000, yvy40001), :(yvy30000, yvy30001), app(app(ty_Either, bg), bh)) → new_esEs3(yvy40000, yvy30000, bg, bh)
new_esEs3(Left(yvy40000), Left(yvy30000), app(app(ty_@2, bca), bcb), bbh) → new_esEs0(yvy40000, yvy30000, bca, bcb)
new_esEs3(Right(yvy40000), Right(yvy30000), bda, app(app(ty_@2, bdc), bdd)) → new_esEs0(yvy40000, yvy30000, bdc, bdd)
new_esEs0(@2(yvy40000, yvy40001), @2(yvy30000, yvy30001), app(ty_Maybe, db), cc) → new_esEs2(yvy40000, yvy30000, db)
new_esEs1(@3(yvy40000, yvy40001, yvy40002), @3(yvy30000, yvy30001, yvy30002), app(ty_[], eg), eh, fa) → new_esEs(yvy40000, yvy30000, eg)
new_esEs1(@3(yvy40000, yvy40001, yvy40002), @3(yvy30000, yvy30001, yvy30002), gc, eh, app(ty_Maybe, bac)) → new_esEs2(yvy40002, yvy30002, bac)
new_esEs0(@2(yvy40000, yvy40001), @2(yvy30000, yvy30001), app(app(ty_@2, cd), ce), cc) → new_esEs0(yvy40000, yvy30000, cd, ce)
new_esEs1(@3(yvy40000, yvy40001, yvy40002), @3(yvy30000, yvy30001, yvy30002), app(ty_Maybe, fh), eh, fa) → new_esEs2(yvy40000, yvy30000, fh)
new_esEs0(@2(yvy40000, yvy40001), @2(yvy30000, yvy30001), app(ty_[], cb), cc) → new_esEs(yvy40000, yvy30000, cb)
new_esEs1(@3(yvy40000, yvy40001, yvy40002), @3(yvy30000, yvy30001, yvy30002), app(app(ty_Either, ga), gb), eh, fa) → new_esEs3(yvy40000, yvy30000, ga, gb)
new_esEs3(Right(yvy40000), Right(yvy30000), bda, app(ty_Maybe, bdh)) → new_esEs2(yvy40000, yvy30000, bdh)
new_esEs0(@2(yvy40000, yvy40001), @2(yvy30000, yvy30001), app(app(app(ty_@3, cf), cg), da), cc) → new_esEs1(yvy40000, yvy30000, cf, cg, da)
new_esEs1(@3(yvy40000, yvy40001, yvy40002), @3(yvy30000, yvy30001, yvy30002), gc, app(app(ty_@2, ge), gf), fa) → new_esEs0(yvy40001, yvy30001, ge, gf)
new_esEs1(@3(yvy40000, yvy40001, yvy40002), @3(yvy30000, yvy30001, yvy30002), gc, eh, app(ty_[], he)) → new_esEs(yvy40002, yvy30002, he)
new_esEs2(Just(yvy40000), Just(yvy30000), app(app(ty_Either, bbe), bbf)) → new_esEs3(yvy40000, yvy30000, bbe, bbf)
new_esEs0(@2(yvy40000, yvy40001), @2(yvy30000, yvy30001), de, app(app(ty_@2, dg), dh)) → new_esEs0(yvy40001, yvy30001, dg, dh)
new_esEs1(@3(yvy40000, yvy40001, yvy40002), @3(yvy30000, yvy30001, yvy30002), gc, app(ty_[], gd), fa) → new_esEs(yvy40001, yvy30001, gd)
new_esEs(:(yvy40000, yvy40001), :(yvy30000, yvy30001), app(ty_[], h)) → new_esEs(yvy40000, yvy30000, h)
new_esEs2(Just(yvy40000), Just(yvy30000), app(app(ty_@2, bag), bah)) → new_esEs0(yvy40000, yvy30000, bag, bah)

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

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



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

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

new_ltEs0(@3(yvy1000, yvy1001, yvy1002), @3(yvy1010, yvy1011, yvy1012), app(ty_[], bdc), bag, bcb) → new_lt(yvy1000, yvy1010, bdc)
new_ltEs1(@2(yvy1000, yvy1001), @2(yvy1010, yvy1011), bed, app(app(ty_@2, bfa), bfb)) → new_ltEs1(yvy1001, yvy1011, bfa, bfb)
new_ltEs1(@2(yvy1000, yvy1001), @2(yvy1010, yvy1011), app(ty_[], bff), bfg) → new_lt(yvy1000, yvy1010, bff)
new_ltEs3(Left(yvy1000), Left(yvy1010), app(app(ty_Either, cba), cbb), cab) → new_ltEs3(yvy1000, yvy1010, cba, cbb)
new_compare22(yvy107, yvy108, False, app(ty_[], cce), ccf) → new_ltEs(yvy107, yvy108, cce)
new_compare21(@3(yvy1000, yvy1001, yvy1002), @3(yvy1010, yvy1011, yvy1012), False, app(app(app(ty_@3, app(ty_[], bdc)), bag), bcb)) → new_lt(yvy1000, yvy1010, bdc)
new_compare21(Left(yvy1000), Left(yvy1010), False, app(app(ty_Either, app(ty_[], caa)), cab)) → new_ltEs(yvy1000, yvy1010, caa)
new_compare20(yvy165, yvy166, yvy167, yvy168, False, hc, app(ty_Maybe, bab)) → new_ltEs2(yvy166, yvy168, bab)
new_compare4(Just(yvy4000), Just(yvy3000), bf) → new_compare21(yvy4000, yvy3000, new_esEs9(yvy4000, yvy3000, bf), bf)
new_ltEs1(@2(yvy1000, yvy1001), @2(yvy1010, yvy1011), bed, app(ty_Maybe, bfc)) → new_ltEs2(yvy1001, yvy1011, bfc)
new_ltEs0(@3(yvy1000, yvy1001, yvy1002), @3(yvy1010, yvy1011, yvy1012), app(ty_Maybe, bea), bag, bcb) → new_lt2(yvy1000, yvy1010, bea)
new_compare23(yvy114, yvy115, False, cdg, app(app(ty_@2, ced), cee)) → new_ltEs1(yvy114, yvy115, ced, cee)
new_compare20(yvy165, yvy166, yvy167, yvy168, False, app(ty_Maybe, gh), gb) → new_lt2(yvy165, yvy167, gh)
new_primCompAux(@3(yvy4000, yvy4001, yvy4002), @3(yvy3000, yvy3001, yvy3002), yvy51, app(app(app(ty_@3, ba), bb), bc)) → new_compare2(yvy4000, yvy4001, yvy4002, yvy3000, yvy3001, yvy3002, new_asAs(new_esEs4(yvy4000, yvy3000, ba), new_asAs(new_esEs5(yvy4001, yvy3001, bb), new_esEs6(yvy4002, yvy3002, bc))), ba, bb, bc)
new_compare2(yvy152, yvy153, yvy154, yvy155, yvy156, yvy157, False, app(ty_[], ca), cb, cc) → new_compare(yvy152, yvy155, ca)
new_ltEs3(Right(yvy1000), Right(yvy1010), cbc, app(app(app(ty_@3, cbe), cbf), cbg)) → new_ltEs0(yvy1000, yvy1010, cbe, cbf, cbg)
new_ltEs0(@3(yvy1000, yvy1001, yvy1002), @3(yvy1010, yvy1011, yvy1012), app(app(ty_@2, bdg), bdh), bag, bcb) → new_lt1(yvy1000, yvy1010, bdg, bdh)
new_compare20(yvy165, yvy166, yvy167, yvy168, False, hc, app(app(ty_Either, bac), bad)) → new_ltEs3(yvy166, yvy168, bac, bad)
new_primCompAux(yvy400, yvy300, yvy51, app(ty_[], h)) → new_compare(yvy400, yvy300, h)
new_compare21(Left(yvy1000), Left(yvy1010), False, app(app(ty_Either, app(app(app(ty_@3, cac), cad), cae)), cab)) → new_ltEs0(yvy1000, yvy1010, cac, cad, cae)
new_compare21(@3(yvy1000, yvy1001, yvy1002), @3(yvy1010, yvy1011, yvy1012), False, app(app(app(ty_@3, app(ty_Maybe, bea)), bag), bcb)) → new_lt2(yvy1000, yvy1010, bea)
new_ltEs2(Just(yvy1000), Just(yvy1010), app(app(app(ty_@3, bha), bhb), bhc)) → new_ltEs0(yvy1000, yvy1010, bha, bhb, bhc)
new_compare22(yvy107, yvy108, False, app(ty_Maybe, cdd), ccf) → new_ltEs2(yvy107, yvy108, cdd)
new_compare20(yvy165, yvy166, yvy167, yvy168, False, app(ty_[], ga), gb) → new_lt(yvy165, yvy167, ga)
new_compare20(yvy165, yvy166, yvy167, yvy168, False, app(app(ty_Either, ha), hb), gb) → new_lt3(yvy165, yvy167, ha, hb)
new_compare23(yvy114, yvy115, False, cdg, app(ty_Maybe, cef)) → new_ltEs2(yvy114, yvy115, cef)
new_compare21(Just(yvy1000), Just(yvy1010), False, app(ty_Maybe, app(app(ty_Either, bhg), bhh))) → new_ltEs3(yvy1000, yvy1010, bhg, bhh)
new_ltEs3(Right(yvy1000), Right(yvy1010), cbc, app(app(ty_Either, ccc), ccd)) → new_ltEs3(yvy1000, yvy1010, ccc, ccd)
new_ltEs3(Right(yvy1000), Right(yvy1010), cbc, app(ty_[], cbd)) → new_ltEs(yvy1000, yvy1010, cbd)
new_compare23(yvy114, yvy115, False, cdg, app(app(app(ty_@3, cea), ceb), cec)) → new_ltEs0(yvy114, yvy115, cea, ceb, cec)
new_compare21(Right(yvy1000), Right(yvy1010), False, app(app(ty_Either, cbc), app(app(app(ty_@3, cbe), cbf), cbg))) → new_ltEs0(yvy1000, yvy1010, cbe, cbf, cbg)
new_compare21(Just(yvy1000), Just(yvy1010), False, app(ty_Maybe, app(app(app(ty_@3, bha), bhb), bhc))) → new_ltEs0(yvy1000, yvy1010, bha, bhb, bhc)
new_compare21(Right(yvy1000), Right(yvy1010), False, app(app(ty_Either, cbc), app(app(ty_Either, ccc), ccd))) → new_ltEs3(yvy1000, yvy1010, ccc, ccd)
new_ltEs0(@3(yvy1000, yvy1001, yvy1002), @3(yvy1010, yvy1011, yvy1012), baf, bag, app(app(app(ty_@3, bba), bbb), bbc)) → new_ltEs0(yvy1002, yvy1012, bba, bbb, bbc)
new_compare21(@3(yvy1000, yvy1001, yvy1002), @3(yvy1010, yvy1011, yvy1012), False, app(app(app(ty_@3, baf), app(ty_[], bca)), bcb)) → new_lt(yvy1001, yvy1011, bca)
new_ltEs0(@3(yvy1000, yvy1001, yvy1002), @3(yvy1010, yvy1011, yvy1012), baf, app(app(ty_@2, bcf), bcg), bcb) → new_lt1(yvy1001, yvy1011, bcf, bcg)
new_compare21(@3(yvy1000, yvy1001, yvy1002), @3(yvy1010, yvy1011, yvy1012), False, app(app(app(ty_@3, baf), bag), app(app(ty_Either, bbg), bbh))) → new_ltEs3(yvy1002, yvy1012, bbg, bbh)
new_compare21(@2(yvy1000, yvy1001), @2(yvy1010, yvy1011), False, app(app(ty_@2, app(app(app(ty_@3, bfh), bga), bgb)), bfg)) → new_lt0(yvy1000, yvy1010, bfh, bga, bgb)
new_compare5(Left(yvy4000), Left(yvy3000), bg, bh) → new_compare22(yvy4000, yvy3000, new_esEs10(yvy4000, yvy3000, bg), bg, bh)
new_compare2(yvy152, yvy153, yvy154, yvy155, yvy156, yvy157, False, app(app(ty_Either, dc), dd), cb, cc) → new_compare5(yvy152, yvy155, dc, dd)
new_ltEs1(@2(yvy1000, yvy1001), @2(yvy1010, yvy1011), bed, app(ty_[], bee)) → new_ltEs(yvy1001, yvy1011, bee)
new_ltEs3(Left(yvy1000), Left(yvy1010), app(ty_[], caa), cab) → new_ltEs(yvy1000, yvy1010, caa)
new_compare2(yvy152, yvy153, yvy154, yvy155, yvy156, yvy157, False, de, app(ty_[], eg), cc) → new_lt(yvy153, yvy156, eg)
new_ltEs0(@3(yvy1000, yvy1001, yvy1002), @3(yvy1010, yvy1011, yvy1012), baf, bag, app(app(ty_@2, bbd), bbe)) → new_ltEs1(yvy1002, yvy1012, bbd, bbe)
new_compare23(yvy114, yvy115, False, cdg, app(app(ty_Either, ceg), ceh)) → new_ltEs3(yvy114, yvy115, ceg, ceh)
new_lt3(yvy152, yvy155, dc, dd) → new_compare5(yvy152, yvy155, dc, dd)
new_compare21(Just(yvy1000), Just(yvy1010), False, app(ty_Maybe, app(ty_Maybe, bhf))) → new_ltEs2(yvy1000, yvy1010, bhf)
new_compare2(yvy152, yvy153, yvy154, yvy155, yvy156, yvy157, False, de, app(app(ty_@2, fc), fd), cc) → new_lt1(yvy153, yvy156, fc, fd)
new_compare3(@2(yvy4000, yvy4001), @2(yvy3000, yvy3001), bd, be) → new_compare20(yvy4000, yvy4001, yvy3000, yvy3001, new_asAs(new_esEs7(yvy4000, yvy3000, bd), new_esEs8(yvy4001, yvy3001, be)), bd, be)
new_ltEs(yvy100, yvy101, bae) → new_compare(yvy100, yvy101, bae)
new_compare21(Just(yvy1000), Just(yvy1010), False, app(ty_Maybe, app(ty_[], bgh))) → new_ltEs(yvy1000, yvy1010, bgh)
new_compare2(yvy152, yvy153, yvy154, yvy155, yvy156, yvy157, False, de, app(app(ty_Either, fg), fh), cc) → new_lt3(yvy153, yvy156, fg, fh)
new_ltEs0(@3(yvy1000, yvy1001, yvy1002), @3(yvy1010, yvy1011, yvy1012), app(app(ty_Either, beb), bec), bag, bcb) → new_lt3(yvy1000, yvy1010, beb, bec)
new_compare2(yvy152, yvy153, yvy154, yvy155, yvy156, yvy157, False, app(app(app(ty_@3, cd), ce), cf), cb, cc) → new_compare1(yvy152, yvy155, cd, ce, cf)
new_ltEs0(@3(yvy1000, yvy1001, yvy1002), @3(yvy1010, yvy1011, yvy1012), baf, app(ty_Maybe, bch), bcb) → new_lt2(yvy1001, yvy1011, bch)
new_lt1(yvy152, yvy155, cg, da) → new_compare3(yvy152, yvy155, cg, da)
new_ltEs3(Left(yvy1000), Left(yvy1010), app(app(ty_@2, caf), cag), cab) → new_ltEs1(yvy1000, yvy1010, caf, cag)
new_compare21(@3(yvy1000, yvy1001, yvy1002), @3(yvy1010, yvy1011, yvy1012), False, app(app(app(ty_@3, app(app(ty_@2, bdg), bdh)), bag), bcb)) → new_lt1(yvy1000, yvy1010, bdg, bdh)
new_compare21(@3(yvy1000, yvy1001, yvy1002), @3(yvy1010, yvy1011, yvy1012), False, app(app(app(ty_@3, baf), bag), app(ty_Maybe, bbf))) → new_ltEs2(yvy1002, yvy1012, bbf)
new_primCompAux(Just(yvy4000), Just(yvy3000), yvy51, app(ty_Maybe, bf)) → new_compare21(yvy4000, yvy3000, new_esEs9(yvy4000, yvy3000, bf), bf)
new_ltEs0(@3(yvy1000, yvy1001, yvy1002), @3(yvy1010, yvy1011, yvy1012), baf, bag, app(app(ty_Either, bbg), bbh)) → new_ltEs3(yvy1002, yvy1012, bbg, bbh)
new_ltEs2(Just(yvy1000), Just(yvy1010), app(app(ty_@2, bhd), bhe)) → new_ltEs1(yvy1000, yvy1010, bhd, bhe)
new_compare21(@3(yvy1000, yvy1001, yvy1002), @3(yvy1010, yvy1011, yvy1012), False, app(app(app(ty_@3, baf), app(ty_Maybe, bch)), bcb)) → new_lt2(yvy1001, yvy1011, bch)
new_compare21(@2(yvy1000, yvy1001), @2(yvy1010, yvy1011), False, app(app(ty_@2, app(ty_[], bff)), bfg)) → new_lt(yvy1000, yvy1010, bff)
new_compare2(yvy152, yvy153, yvy154, yvy155, yvy156, yvy157, False, de, cb, app(app(ty_@2, eb), ec)) → new_ltEs1(yvy154, yvy157, eb, ec)
new_compare21(Right(yvy1000), Right(yvy1010), False, app(app(ty_Either, cbc), app(app(ty_@2, cbh), cca))) → new_ltEs1(yvy1000, yvy1010, cbh, cca)
new_compare20(yvy165, yvy166, yvy167, yvy168, False, hc, app(app(ty_@2, hh), baa)) → new_ltEs1(yvy166, yvy168, hh, baa)
new_compare2(yvy152, yvy153, yvy154, yvy155, yvy156, yvy157, False, app(app(ty_@2, cg), da), cb, cc) → new_compare3(yvy152, yvy155, cg, da)
new_compare23(yvy114, yvy115, False, cdg, app(ty_[], cdh)) → new_ltEs(yvy114, yvy115, cdh)
new_compare1(@3(yvy4000, yvy4001, yvy4002), @3(yvy3000, yvy3001, yvy3002), ba, bb, bc) → new_compare2(yvy4000, yvy4001, yvy4002, yvy3000, yvy3001, yvy3002, new_asAs(new_esEs4(yvy4000, yvy3000, ba), new_asAs(new_esEs5(yvy4001, yvy3001, bb), new_esEs6(yvy4002, yvy3002, bc))), ba, bb, bc)
new_primCompAux(Right(yvy4000), Right(yvy3000), yvy51, app(app(ty_Either, bg), bh)) → new_compare23(yvy4000, yvy3000, new_esEs11(yvy4000, yvy3000, bh), bg, bh)
new_ltEs0(@3(yvy1000, yvy1001, yvy1002), @3(yvy1010, yvy1011, yvy1012), app(app(app(ty_@3, bdd), bde), bdf), bag, bcb) → new_lt0(yvy1000, yvy1010, bdd, bde, bdf)
new_ltEs1(@2(yvy1000, yvy1001), @2(yvy1010, yvy1011), bed, app(app(app(ty_@3, bef), beg), beh)) → new_ltEs0(yvy1001, yvy1011, bef, beg, beh)
new_compare21(@3(yvy1000, yvy1001, yvy1002), @3(yvy1010, yvy1011, yvy1012), False, app(app(app(ty_@3, app(app(app(ty_@3, bdd), bde), bdf)), bag), bcb)) → new_lt0(yvy1000, yvy1010, bdd, bde, bdf)
new_compare22(yvy107, yvy108, False, app(app(ty_Either, cde), cdf), ccf) → new_ltEs3(yvy107, yvy108, cde, cdf)
new_compare21(@3(yvy1000, yvy1001, yvy1002), @3(yvy1010, yvy1011, yvy1012), False, app(app(app(ty_@3, baf), bag), app(app(ty_@2, bbd), bbe))) → new_ltEs1(yvy1002, yvy1012, bbd, bbe)
new_compare20(yvy165, yvy166, yvy167, yvy168, False, app(app(app(ty_@3, gc), gd), ge), gb) → new_lt0(yvy165, yvy167, gc, gd, ge)
new_compare2(yvy152, yvy153, yvy154, yvy155, yvy156, yvy157, False, de, app(app(app(ty_@3, eh), fa), fb), cc) → new_lt0(yvy153, yvy156, eh, fa, fb)
new_compare21(@2(yvy1000, yvy1001), @2(yvy1010, yvy1011), False, app(app(ty_@2, app(app(ty_@2, bgc), bgd)), bfg)) → new_lt1(yvy1000, yvy1010, bgc, bgd)
new_compare21(Just(yvy1000), Just(yvy1010), False, app(ty_Maybe, app(app(ty_@2, bhd), bhe))) → new_ltEs1(yvy1000, yvy1010, bhd, bhe)
new_ltEs2(Just(yvy1000), Just(yvy1010), app(ty_[], bgh)) → new_ltEs(yvy1000, yvy1010, bgh)
new_ltEs2(Just(yvy1000), Just(yvy1010), app(app(ty_Either, bhg), bhh)) → new_ltEs3(yvy1000, yvy1010, bhg, bhh)
new_compare20(yvy165, yvy166, yvy167, yvy168, False, hc, app(app(app(ty_@3, he), hf), hg)) → new_ltEs0(yvy166, yvy168, he, hf, hg)
new_primCompAux(Left(yvy4000), Left(yvy3000), yvy51, app(app(ty_Either, bg), bh)) → new_compare22(yvy4000, yvy3000, new_esEs10(yvy4000, yvy3000, bg), bg, bh)
new_lt0(yvy152, yvy155, cd, ce, cf) → new_compare1(yvy152, yvy155, cd, ce, cf)
new_ltEs0(@3(yvy1000, yvy1001, yvy1002), @3(yvy1010, yvy1011, yvy1012), baf, app(ty_[], bca), bcb) → new_lt(yvy1001, yvy1011, bca)
new_compare21(Right(yvy1000), Right(yvy1010), False, app(app(ty_Either, cbc), app(ty_[], cbd))) → new_ltEs(yvy1000, yvy1010, cbd)
new_compare21(@2(yvy1000, yvy1001), @2(yvy1010, yvy1011), False, app(app(ty_@2, bed), app(ty_Maybe, bfc))) → new_ltEs2(yvy1001, yvy1011, bfc)
new_compare2(yvy152, yvy153, yvy154, yvy155, yvy156, yvy157, False, de, cb, app(ty_[], df)) → new_ltEs(yvy154, yvy157, df)
new_lt(yvy152, yvy155, ca) → new_compare(yvy152, yvy155, ca)
new_compare2(yvy152, yvy153, yvy154, yvy155, yvy156, yvy157, False, de, cb, app(app(ty_Either, ee), ef)) → new_ltEs3(yvy154, yvy157, ee, ef)
new_compare21(Left(yvy1000), Left(yvy1010), False, app(app(ty_Either, app(app(ty_@2, caf), cag)), cab)) → new_ltEs1(yvy1000, yvy1010, caf, cag)
new_ltEs0(@3(yvy1000, yvy1001, yvy1002), @3(yvy1010, yvy1011, yvy1012), baf, app(app(app(ty_@3, bcc), bcd), bce), bcb) → new_lt0(yvy1001, yvy1011, bcc, bcd, bce)
new_compare21(@3(yvy1000, yvy1001, yvy1002), @3(yvy1010, yvy1011, yvy1012), False, app(app(app(ty_@3, baf), bag), app(ty_[], bah))) → new_ltEs(yvy1002, yvy1012, bah)
new_compare21(@2(yvy1000, yvy1001), @2(yvy1010, yvy1011), False, app(app(ty_@2, bed), app(ty_[], bee))) → new_ltEs(yvy1001, yvy1011, bee)
new_compare20(yvy165, yvy166, yvy167, yvy168, False, app(app(ty_@2, gf), gg), gb) → new_lt1(yvy165, yvy167, gf, gg)
new_ltEs0(@3(yvy1000, yvy1001, yvy1002), @3(yvy1010, yvy1011, yvy1012), baf, bag, app(ty_[], bah)) → new_ltEs(yvy1002, yvy1012, bah)
new_compare2(yvy152, yvy153, yvy154, yvy155, yvy156, yvy157, False, de, cb, app(app(app(ty_@3, dg), dh), ea)) → new_ltEs0(yvy154, yvy157, dg, dh, ea)
new_compare22(yvy107, yvy108, False, app(app(app(ty_@3, ccg), cch), cda), ccf) → new_ltEs0(yvy107, yvy108, ccg, cch, cda)
new_compare21(Left(yvy1000), Left(yvy1010), False, app(app(ty_Either, app(ty_Maybe, cah)), cab)) → new_ltEs2(yvy1000, yvy1010, cah)
new_compare21(Right(yvy1000), Right(yvy1010), False, app(app(ty_Either, cbc), app(ty_Maybe, ccb))) → new_ltEs2(yvy1000, yvy1010, ccb)
new_compare21(@3(yvy1000, yvy1001, yvy1002), @3(yvy1010, yvy1011, yvy1012), False, app(app(app(ty_@3, baf), bag), app(app(app(ty_@3, bba), bbb), bbc))) → new_ltEs0(yvy1002, yvy1012, bba, bbb, bbc)
new_compare21(@3(yvy1000, yvy1001, yvy1002), @3(yvy1010, yvy1011, yvy1012), False, app(app(app(ty_@3, app(app(ty_Either, beb), bec)), bag), bcb)) → new_lt3(yvy1000, yvy1010, beb, bec)
new_ltEs1(@2(yvy1000, yvy1001), @2(yvy1010, yvy1011), app(app(ty_Either, bgf), bgg), bfg) → new_lt3(yvy1000, yvy1010, bgf, bgg)
new_ltEs3(Right(yvy1000), Right(yvy1010), cbc, app(ty_Maybe, ccb)) → new_ltEs2(yvy1000, yvy1010, ccb)
new_ltEs1(@2(yvy1000, yvy1001), @2(yvy1010, yvy1011), app(app(ty_@2, bgc), bgd), bfg) → new_lt1(yvy1000, yvy1010, bgc, bgd)
new_compare20(yvy165, yvy166, yvy167, yvy168, False, hc, app(ty_[], hd)) → new_ltEs(yvy166, yvy168, hd)
new_compare2(yvy152, yvy153, yvy154, yvy155, yvy156, yvy157, False, app(ty_Maybe, db), cb, cc) → new_compare4(yvy152, yvy155, db)
new_ltEs0(@3(yvy1000, yvy1001, yvy1002), @3(yvy1010, yvy1011, yvy1012), baf, bag, app(ty_Maybe, bbf)) → new_ltEs2(yvy1002, yvy1012, bbf)
new_compare21(@2(yvy1000, yvy1001), @2(yvy1010, yvy1011), False, app(app(ty_@2, bed), app(app(app(ty_@3, bef), beg), beh))) → new_ltEs0(yvy1001, yvy1011, bef, beg, beh)
new_compare2(yvy152, yvy153, yvy154, yvy155, yvy156, yvy157, False, de, app(ty_Maybe, ff), cc) → new_lt2(yvy153, yvy156, ff)
new_compare2(yvy152, yvy153, yvy154, yvy155, yvy156, yvy157, False, de, cb, app(ty_Maybe, ed)) → new_ltEs2(yvy154, yvy157, ed)
new_ltEs2(Just(yvy1000), Just(yvy1010), app(ty_Maybe, bhf)) → new_ltEs2(yvy1000, yvy1010, bhf)
new_compare(:(yvy4000, yvy4001), :(yvy3000, yvy3001), h) → new_compare(yvy4001, yvy3001, h)
new_compare21(@3(yvy1000, yvy1001, yvy1002), @3(yvy1010, yvy1011, yvy1012), False, app(app(app(ty_@3, baf), app(app(app(ty_@3, bcc), bcd), bce)), bcb)) → new_lt0(yvy1001, yvy1011, bcc, bcd, bce)
new_ltEs1(@2(yvy1000, yvy1001), @2(yvy1010, yvy1011), app(app(app(ty_@3, bfh), bga), bgb), bfg) → new_lt0(yvy1000, yvy1010, bfh, bga, bgb)
new_compare(:(yvy4000, yvy4001), :(yvy3000, yvy3001), h) → new_primCompAux(yvy4000, yvy3000, new_compare0(yvy4001, yvy3001, h), h)
new_lt2(yvy152, yvy155, db) → new_compare4(yvy152, yvy155, db)
new_compare21(@2(yvy1000, yvy1001), @2(yvy1010, yvy1011), False, app(app(ty_@2, app(app(ty_Either, bgf), bgg)), bfg)) → new_lt3(yvy1000, yvy1010, bgf, bgg)
new_ltEs1(@2(yvy1000, yvy1001), @2(yvy1010, yvy1011), bed, app(app(ty_Either, bfd), bfe)) → new_ltEs3(yvy1001, yvy1011, bfd, bfe)
new_ltEs3(Right(yvy1000), Right(yvy1010), cbc, app(app(ty_@2, cbh), cca)) → new_ltEs1(yvy1000, yvy1010, cbh, cca)
new_compare21(@3(yvy1000, yvy1001, yvy1002), @3(yvy1010, yvy1011, yvy1012), False, app(app(app(ty_@3, baf), app(app(ty_@2, bcf), bcg)), bcb)) → new_lt1(yvy1001, yvy1011, bcf, bcg)
new_compare21(@2(yvy1000, yvy1001), @2(yvy1010, yvy1011), False, app(app(ty_@2, app(ty_Maybe, bge)), bfg)) → new_lt2(yvy1000, yvy1010, bge)
new_compare21(yvy100, yvy101, False, app(ty_[], bae)) → new_compare(yvy100, yvy101, bae)
new_compare21(@2(yvy1000, yvy1001), @2(yvy1010, yvy1011), False, app(app(ty_@2, bed), app(app(ty_@2, bfa), bfb))) → new_ltEs1(yvy1001, yvy1011, bfa, bfb)
new_compare21(@3(yvy1000, yvy1001, yvy1002), @3(yvy1010, yvy1011, yvy1012), False, app(app(app(ty_@3, baf), app(app(ty_Either, bda), bdb)), bcb)) → new_lt3(yvy1001, yvy1011, bda, bdb)
new_ltEs0(@3(yvy1000, yvy1001, yvy1002), @3(yvy1010, yvy1011, yvy1012), baf, app(app(ty_Either, bda), bdb), bcb) → new_lt3(yvy1001, yvy1011, bda, bdb)
new_compare22(yvy107, yvy108, False, app(app(ty_@2, cdb), cdc), ccf) → new_ltEs1(yvy107, yvy108, cdb, cdc)
new_ltEs1(@2(yvy1000, yvy1001), @2(yvy1010, yvy1011), app(ty_Maybe, bge), bfg) → new_lt2(yvy1000, yvy1010, bge)
new_ltEs3(Left(yvy1000), Left(yvy1010), app(app(app(ty_@3, cac), cad), cae), cab) → new_ltEs0(yvy1000, yvy1010, cac, cad, cae)
new_ltEs3(Left(yvy1000), Left(yvy1010), app(ty_Maybe, cah), cab) → new_ltEs2(yvy1000, yvy1010, cah)
new_compare21(Left(yvy1000), Left(yvy1010), False, app(app(ty_Either, app(app(ty_Either, cba), cbb)), cab)) → new_ltEs3(yvy1000, yvy1010, cba, cbb)
new_compare5(Right(yvy4000), Right(yvy3000), bg, bh) → new_compare23(yvy4000, yvy3000, new_esEs11(yvy4000, yvy3000, bh), bg, bh)
new_compare21(@2(yvy1000, yvy1001), @2(yvy1010, yvy1011), False, app(app(ty_@2, bed), app(app(ty_Either, bfd), bfe))) → new_ltEs3(yvy1001, yvy1011, bfd, bfe)
new_primCompAux(@2(yvy4000, yvy4001), @2(yvy3000, yvy3001), yvy51, app(app(ty_@2, bd), be)) → new_compare20(yvy4000, yvy4001, yvy3000, yvy3001, new_asAs(new_esEs7(yvy4000, yvy3000, bd), new_esEs8(yvy4001, yvy3001, be)), bd, be)

The TRS R consists of the following rules:

new_compare210(yvy100, yvy101, False, ffg) → new_compare112(yvy100, yvy101, new_ltEs24(yvy100, yvy101, ffg), ffg)
new_compare7(@2(yvy4000, yvy4001), @2(yvy3000, yvy3001), bd, be) → new_compare24(yvy4000, yvy4001, yvy3000, yvy3001, new_asAs(new_esEs7(yvy4000, yvy3000, bd), new_esEs8(yvy4001, yvy3001, be)), bd, be)
new_esEs24(Left(yvy40000), Left(yvy30000), app(ty_Ratio, fcb), deh) → new_esEs21(yvy40000, yvy30000, fcb)
new_ltEs19(yvy1002, yvy1012, app(ty_[], bah)) → new_ltEs8(yvy1002, yvy1012, bah)
new_compare112(yvy189, yvy190, True, fgb) → LT
new_lt22(yvy1000, yvy1010, ty_Int) → new_lt17(yvy1000, yvy1010)
new_ltEs22(yvy114, yvy115, app(app(ty_@2, ced), cee)) → new_ltEs12(yvy114, yvy115, ced, cee)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Int, deh) → new_esEs25(yvy40000, yvy30000)
new_esEs6(yvy4002, yvy3002, app(app(app(ty_@3, dbg), dbh), dca)) → new_esEs22(yvy4002, yvy3002, dbg, dbh, dca)
new_esEs27(yvy1000, yvy1010, app(ty_[], bdc)) → new_esEs16(yvy1000, yvy1010, bdc)
new_esEs20(True, True) → True
new_esEs35(yvy153, yvy156, app(ty_[], eg)) → new_esEs16(yvy153, yvy156, eg)
new_compare8(Integer(yvy4000), Integer(yvy3000)) → new_primCmpInt(yvy4000, yvy3000)
new_esEs8(yvy4001, yvy3001, ty_Bool) → new_esEs20(yvy4001, yvy3001)
new_esEs11(yvy4000, yvy3000, ty_Integer) → new_esEs18(yvy4000, yvy3000)
new_esEs27(yvy1000, yvy1010, app(app(ty_@2, bdg), bdh)) → new_esEs17(yvy1000, yvy1010, bdg, bdh)
new_ltEs20(yvy154, yvy157, app(ty_Ratio, fef)) → new_ltEs9(yvy154, yvy157, fef)
new_esEs36(yvy1000, yvy1010, ty_Double) → new_esEs13(yvy1000, yvy1010)
new_esEs28(yvy1001, yvy1011, ty_Float) → new_esEs14(yvy1001, yvy1011)
new_lt6(yvy1000, yvy1010, ty_@0) → new_lt19(yvy1000, yvy1010)
new_esEs9(yvy4000, yvy3000, ty_Int) → new_esEs25(yvy4000, yvy3000)
new_compare10(yvy199, yvy200, True, che, chf) → LT
new_esEs24(Right(yvy40000), Right(yvy30000), deg, ty_Double) → new_esEs13(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, app(app(ty_@2, efh), ega)) → new_esEs17(yvy40002, yvy30002, efh, ega)
new_ltEs24(yvy100, yvy101, app(ty_Ratio, ecf)) → new_ltEs9(yvy100, yvy101, ecf)
new_esEs24(Right(yvy40000), Right(yvy30000), deg, ty_@0) → new_esEs19(yvy40000, yvy30000)
new_ltEs19(yvy1002, yvy1012, ty_Float) → new_ltEs11(yvy1002, yvy1012)
new_esEs11(yvy4000, yvy3000, app(ty_[], daa)) → new_esEs16(yvy4000, yvy3000, daa)
new_lt23(yvy165, yvy167, app(app(app(ty_@3, gc), gd), ge)) → new_lt4(yvy165, yvy167, gc, gd, ge)
new_esEs9(yvy4000, yvy3000, ty_Char) → new_esEs15(yvy4000, yvy3000)
new_esEs7(yvy4000, yvy3000, ty_Double) → new_esEs13(yvy4000, yvy3000)
new_ltEs23(yvy166, yvy168, ty_Ordering) → new_ltEs6(yvy166, yvy168)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Bool, cab) → new_ltEs16(yvy1000, yvy1010)
new_esEs39(yvy165, yvy167, app(ty_Ratio, ffe)) → new_esEs21(yvy165, yvy167, ffe)
new_esEs10(yvy4000, yvy3000, ty_@0) → new_esEs19(yvy4000, yvy3000)
new_esEs21(:%(yvy40000, yvy40001), :%(yvy30000, yvy30001), deb) → new_asAs(new_esEs37(yvy40000, yvy30000, deb), new_esEs38(yvy40001, yvy30001, deb))
new_lt5(yvy1001, yvy1011, app(ty_Ratio, dhh)) → new_lt10(yvy1001, yvy1011, dhh)
new_compare13(:%(yvy4000, yvy4001), :%(yvy3000, yvy3001), ty_Integer) → new_compare8(new_sr(yvy4000, yvy3001), new_sr(yvy3000, yvy4001))
new_ltEs22(yvy114, yvy115, app(ty_Ratio, ffd)) → new_ltEs9(yvy114, yvy115, ffd)
new_ltEs23(yvy166, yvy168, ty_Int) → new_ltEs15(yvy166, yvy168)
new_primMulNat0(Zero, Zero) → Zero
new_ltEs24(yvy100, yvy101, ty_Ordering) → new_ltEs6(yvy100, yvy101)
new_ltEs14(Right(yvy1000), Right(yvy1010), cbc, ty_Float) → new_ltEs11(yvy1000, yvy1010)
new_esEs39(yvy165, yvy167, app(ty_Maybe, gh)) → new_esEs23(yvy165, yvy167, gh)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Bool, deh) → new_esEs20(yvy40000, yvy30000)
new_compare15(LT, LT) → EQ
new_esEs6(yvy4002, yvy3002, app(app(ty_@2, dbd), dbe)) → new_esEs17(yvy4002, yvy3002, dbd, dbe)
new_esEs4(yvy4000, yvy3000, ty_Integer) → new_esEs18(yvy4000, yvy3000)
new_esEs26(yvy40000, yvy30000, app(ty_[], dgc)) → new_esEs16(yvy40000, yvy30000, dgc)
new_esEs36(yvy1000, yvy1010, ty_Char) → new_esEs15(yvy1000, yvy1010)
new_esEs28(yvy1001, yvy1011, app(app(ty_Either, bda), bdb)) → new_esEs24(yvy1001, yvy1011, bda, bdb)
new_esEs34(yvy152, yvy155, ty_@0) → new_esEs19(yvy152, yvy155)
new_sr(Integer(yvy30000), Integer(yvy40010)) → Integer(new_primMulInt(yvy30000, yvy40010))
new_esEs7(yvy4000, yvy3000, ty_Float) → new_esEs14(yvy4000, yvy3000)
new_compare12(True, False) → GT
new_lt7(yvy152, yvy155) → new_esEs12(new_compare15(yvy152, yvy155), LT)
new_lt22(yvy1000, yvy1010, app(ty_Maybe, bge)) → new_lt14(yvy1000, yvy1010, bge)
new_ltEs24(yvy100, yvy101, app(ty_Maybe, chg)) → new_ltEs5(yvy100, yvy101, chg)
new_esEs35(yvy153, yvy156, app(app(ty_Either, fg), fh)) → new_esEs24(yvy153, yvy156, fg, fh)
new_esEs35(yvy153, yvy156, ty_@0) → new_esEs19(yvy153, yvy156)
new_ltEs15(yvy100, yvy101) → new_fsEs(new_compare16(yvy100, yvy101))
new_esEs6(yvy4002, yvy3002, app(ty_[], dbc)) → new_esEs16(yvy4002, yvy3002, dbc)
new_esEs26(yvy40000, yvy30000, ty_@0) → new_esEs19(yvy40000, yvy30000)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_@0, deh) → new_esEs19(yvy40000, yvy30000)
new_ltEs16(False, True) → True
new_esEs10(yvy4000, yvy3000, app(ty_Maybe, ddd)) → new_esEs23(yvy4000, yvy3000, ddd)
new_esEs26(yvy40000, yvy30000, app(app(app(ty_@3, dgg), dgh), dha)) → new_esEs22(yvy40000, yvy30000, dgg, dgh, dha)
new_ltEs24(yvy100, yvy101, ty_Bool) → new_ltEs16(yvy100, yvy101)
new_compare30(yvy400, yvy300, app(app(ty_@2, bd), be)) → new_compare7(yvy400, yvy300, bd, be)
new_esEs17(@2(yvy40000, yvy40001), @2(yvy30000, yvy30001), ddh, dea) → new_asAs(new_esEs29(yvy40000, yvy30000, ddh), new_esEs30(yvy40001, yvy30001, dea))
new_esEs11(yvy4000, yvy3000, ty_Char) → new_esEs15(yvy4000, yvy3000)
new_lt20(yvy152, yvy155, app(app(app(ty_@3, cd), ce), cf)) → new_lt4(yvy152, yvy155, cd, ce, cf)
new_esEs27(yvy1000, yvy1010, ty_Bool) → new_esEs20(yvy1000, yvy1010)
new_ltEs23(yvy166, yvy168, app(ty_Ratio, fff)) → new_ltEs9(yvy166, yvy168, fff)
new_esEs34(yvy152, yvy155, ty_Double) → new_esEs13(yvy152, yvy155)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Double) → new_esEs13(yvy40000, yvy30000)
new_esEs10(yvy4000, yvy3000, ty_Int) → new_esEs25(yvy4000, yvy3000)
new_esEs26(yvy40000, yvy30000, ty_Char) → new_esEs15(yvy40000, yvy30000)
new_compare30(yvy400, yvy300, ty_Int) → new_compare16(yvy400, yvy300)
new_fsEs(yvy306) → new_not(new_esEs12(yvy306, GT))
new_ltEs16(True, False) → False
new_ltEs14(Right(yvy1000), Right(yvy1010), cbc, ty_Char) → new_ltEs7(yvy1000, yvy1010)
new_esEs7(yvy4000, yvy3000, ty_Int) → new_esEs25(yvy4000, yvy3000)
new_ltEs19(yvy1002, yvy1012, ty_Bool) → new_ltEs16(yvy1002, yvy1012)
new_esEs34(yvy152, yvy155, ty_Ordering) → new_esEs12(yvy152, yvy155)
new_esEs12(LT, GT) → False
new_lt5(yvy1001, yvy1011, ty_Integer) → new_lt15(yvy1001, yvy1011)
new_esEs27(yvy1000, yvy1010, ty_Char) → new_esEs15(yvy1000, yvy1010)
new_esEs12(GT, LT) → False
new_ltEs22(yvy114, yvy115, ty_Ordering) → new_ltEs6(yvy114, yvy115)
new_compare18(Float(yvy4000, yvy4001), Float(yvy3000, yvy3001)) → new_compare16(new_sr0(yvy4000, yvy3000), new_sr0(yvy4001, yvy3001))
new_ltEs18(yvy107, yvy108, app(ty_Ratio, dhf)) → new_ltEs9(yvy107, yvy108, dhf)
new_ltEs23(yvy166, yvy168, ty_Float) → new_ltEs11(yvy166, yvy168)
new_ltEs18(yvy107, yvy108, app(ty_[], cce)) → new_ltEs8(yvy107, yvy108, cce)
new_ltEs20(yvy154, yvy157, app(app(ty_@2, eb), ec)) → new_ltEs12(yvy154, yvy157, eb, ec)
new_esEs31(yvy40000, yvy30000, app(ty_Maybe, eeb)) → new_esEs23(yvy40000, yvy30000, eeb)
new_lt6(yvy1000, yvy1010, app(ty_Ratio, dhg)) → new_lt10(yvy1000, yvy1010, dhg)
new_esEs37(yvy40000, yvy30000, ty_Integer) → new_esEs18(yvy40000, yvy30000)
new_ltEs14(Left(yvy1000), Left(yvy1010), app(app(ty_@2, caf), cag), cab) → new_ltEs12(yvy1000, yvy1010, caf, cag)
new_esEs35(yvy153, yvy156, app(app(ty_@2, fc), fd)) → new_esEs17(yvy153, yvy156, fc, fd)
new_esEs5(yvy4001, yvy3001, app(app(app(ty_@3, dfe), dff), dfg)) → new_esEs22(yvy4001, yvy3001, dfe, dff, dfg)
new_lt22(yvy1000, yvy1010, ty_Char) → new_lt8(yvy1000, yvy1010)
new_compare110(yvy233, yvy234, yvy235, yvy236, True, yvy238, feg, feh) → new_compare111(yvy233, yvy234, yvy235, yvy236, True, feg, feh)
new_ltEs24(yvy100, yvy101, app(app(ty_@2, bed), bfg)) → new_ltEs12(yvy100, yvy101, bed, bfg)
new_ltEs13(yvy100, yvy101) → new_fsEs(new_compare29(yvy100, yvy101))
new_esEs5(yvy4001, yvy3001, app(app(ty_Either, dga), dgb)) → new_esEs24(yvy4001, yvy3001, dga, dgb)
new_esEs24(Right(yvy40000), Right(yvy30000), deg, ty_Bool) → new_esEs20(yvy40000, yvy30000)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Float) → new_ltEs11(yvy1000, yvy1010)
new_esEs8(yvy4001, yvy3001, ty_Double) → new_esEs13(yvy4001, yvy3001)
new_esEs31(yvy40000, yvy30000, app(ty_Ratio, edf)) → new_esEs21(yvy40000, yvy30000, edf)
new_esEs29(yvy40000, yvy30000, app(ty_Maybe, eba)) → new_esEs23(yvy40000, yvy30000, eba)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Int) → new_ltEs15(yvy1000, yvy1010)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Double) → new_ltEs13(yvy1000, yvy1010)
new_esEs30(yvy40001, yvy30001, ty_Double) → new_esEs13(yvy40001, yvy30001)
new_ltEs21(yvy1001, yvy1011, app(app(ty_@2, bfa), bfb)) → new_ltEs12(yvy1001, yvy1011, bfa, bfb)
new_esEs10(yvy4000, yvy3000, ty_Bool) → new_esEs20(yvy4000, yvy3000)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Char, cab) → new_ltEs7(yvy1000, yvy1010)
new_ltEs16(True, True) → True
new_lt21(yvy153, yvy156, app(app(ty_@2, fc), fd)) → new_lt12(yvy153, yvy156, fc, fd)
new_lt6(yvy1000, yvy1010, ty_Bool) → new_lt18(yvy1000, yvy1010)
new_pePe(False, yvy305) → yvy305
new_compare15(GT, EQ) → GT
new_esEs7(yvy4000, yvy3000, ty_Char) → new_esEs15(yvy4000, yvy3000)
new_esEs31(yvy40000, yvy30000, app(ty_[], edc)) → new_esEs16(yvy40000, yvy30000, edc)
new_esEs39(yvy165, yvy167, ty_@0) → new_esEs19(yvy165, yvy167)
new_esEs23(Just(yvy40000), Just(yvy30000), app(ty_Maybe, fbd)) → new_esEs23(yvy40000, yvy30000, fbd)
new_lt21(yvy153, yvy156, ty_Char) → new_lt8(yvy153, yvy156)
new_esEs9(yvy4000, yvy3000, app(app(ty_@2, ehb), ehc)) → new_esEs17(yvy4000, yvy3000, ehb, ehc)
new_esEs26(yvy40000, yvy30000, ty_Bool) → new_esEs20(yvy40000, yvy30000)
new_compare14(yvy218, yvy219, yvy220, yvy221, yvy222, yvy223, False, ech, eda, edb) → GT
new_lt9(yvy152, yvy155, ca) → new_esEs12(new_compare0(yvy152, yvy155, ca), LT)
new_esEs28(yvy1001, yvy1011, ty_Integer) → new_esEs18(yvy1001, yvy1011)
new_esEs5(yvy4001, yvy3001, ty_Ordering) → new_esEs12(yvy4001, yvy3001)
new_esEs4(yvy4000, yvy3000, ty_Float) → new_esEs14(yvy4000, yvy3000)
new_esEs5(yvy4001, yvy3001, ty_Int) → new_esEs25(yvy4001, yvy3001)
new_compare15(GT, LT) → GT
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Char, deh) → new_esEs15(yvy40000, yvy30000)
new_esEs29(yvy40000, yvy30000, ty_Int) → new_esEs25(yvy40000, yvy30000)
new_compare30(yvy400, yvy300, app(app(ty_Either, bg), bh)) → new_compare27(yvy400, yvy300, bg, bh)
new_lt22(yvy1000, yvy1010, ty_Double) → new_lt13(yvy1000, yvy1010)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Char) → new_esEs15(yvy40000, yvy30000)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Ordering) → new_esEs12(yvy40000, yvy30000)
new_esEs29(yvy40000, yvy30000, app(app(ty_@2, eac), ead)) → new_esEs17(yvy40000, yvy30000, eac, ead)
new_esEs24(Right(yvy40000), Right(yvy30000), deg, app(app(ty_@2, fdb), fdc)) → new_esEs17(yvy40000, yvy30000, fdb, fdc)
new_ltEs23(yvy166, yvy168, app(app(ty_Either, bac), bad)) → new_ltEs14(yvy166, yvy168, bac, bad)
new_esEs31(yvy40000, yvy30000, ty_Integer) → new_esEs18(yvy40000, yvy30000)
new_compare12(True, True) → EQ
new_esEs36(yvy1000, yvy1010, app(ty_[], bff)) → new_esEs16(yvy1000, yvy1010, bff)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Ordering, deh) → new_esEs12(yvy40000, yvy30000)
new_ltEs6(GT, EQ) → False
new_ltEs18(yvy107, yvy108, app(app(ty_Either, cde), cdf)) → new_ltEs14(yvy107, yvy108, cde, cdf)
new_esEs32(yvy40001, yvy30001, app(ty_Maybe, efd)) → new_esEs23(yvy40001, yvy30001, efd)
new_esEs35(yvy153, yvy156, ty_Integer) → new_esEs18(yvy153, yvy156)
new_esEs33(yvy40002, yvy30002, ty_Integer) → new_esEs18(yvy40002, yvy30002)
new_esEs31(yvy40000, yvy30000, ty_Double) → new_esEs13(yvy40000, yvy30000)
new_esEs10(yvy4000, yvy3000, ty_Ordering) → new_esEs12(yvy4000, yvy3000)
new_primCompAux1(yvy400, yvy300, yvy51, ffh) → new_primCompAux0(yvy51, new_compare30(yvy400, yvy300, ffh))
new_esEs33(yvy40002, yvy30002, ty_Float) → new_esEs14(yvy40002, yvy30002)
new_ltEs14(Right(yvy1000), Right(yvy1010), cbc, app(app(app(ty_@3, cbe), cbf), cbg)) → new_ltEs10(yvy1000, yvy1010, cbe, cbf, cbg)
new_ltEs23(yvy166, yvy168, app(ty_[], hd)) → new_ltEs8(yvy166, yvy168, hd)
new_lt23(yvy165, yvy167, app(app(ty_@2, gf), gg)) → new_lt12(yvy165, yvy167, gf, gg)
new_esEs34(yvy152, yvy155, ty_Integer) → new_esEs18(yvy152, yvy155)
new_esEs23(Just(yvy40000), Just(yvy30000), app(app(ty_Either, fbe), fbf)) → new_esEs24(yvy40000, yvy30000, fbe, fbf)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Ordering, cab) → new_ltEs6(yvy1000, yvy1010)
new_lt22(yvy1000, yvy1010, ty_Bool) → new_lt18(yvy1000, yvy1010)
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_esEs39(yvy165, yvy167, ty_Float) → new_esEs14(yvy165, yvy167)
new_ltEs22(yvy114, yvy115, ty_Bool) → new_ltEs16(yvy114, yvy115)
new_ltEs4(yvy100, yvy101) → new_fsEs(new_compare8(yvy100, yvy101))
new_esEs33(yvy40002, yvy30002, app(ty_[], efg)) → new_esEs16(yvy40002, yvy30002, efg)
new_ltEs8(yvy100, yvy101, bae) → new_fsEs(new_compare0(yvy100, yvy101, bae))
new_compare30(yvy400, yvy300, ty_Char) → new_compare11(yvy400, yvy300)
new_esEs36(yvy1000, yvy1010, ty_Integer) → new_esEs18(yvy1000, yvy1010)
new_esEs39(yvy165, yvy167, ty_Bool) → new_esEs20(yvy165, yvy167)
new_esEs36(yvy1000, yvy1010, ty_Bool) → new_esEs20(yvy1000, yvy1010)
new_esEs32(yvy40001, yvy30001, app(ty_Ratio, eeh)) → new_esEs21(yvy40001, yvy30001, eeh)
new_compare12(False, True) → LT
new_esEs5(yvy4001, yvy3001, ty_Char) → new_esEs15(yvy4001, yvy3001)
new_esEs34(yvy152, yvy155, ty_Char) → new_esEs15(yvy152, yvy155)
new_esEs31(yvy40000, yvy30000, app(app(ty_@2, edd), ede)) → new_esEs17(yvy40000, yvy30000, edd, ede)
new_ltEs18(yvy107, yvy108, ty_Integer) → new_ltEs4(yvy107, yvy108)
new_lt21(yvy153, yvy156, ty_@0) → new_lt19(yvy153, yvy156)
new_esEs30(yvy40001, yvy30001, ty_@0) → new_esEs19(yvy40001, yvy30001)
new_ltEs18(yvy107, yvy108, app(ty_Maybe, cdd)) → new_ltEs5(yvy107, yvy108, cdd)
new_esEs12(LT, LT) → True
new_ltEs24(yvy100, yvy101, ty_Char) → new_ltEs7(yvy100, yvy101)
new_esEs31(yvy40000, yvy30000, app(app(ty_Either, eec), eed)) → new_esEs24(yvy40000, yvy30000, eec, eed)
new_ltEs18(yvy107, yvy108, ty_Double) → new_ltEs13(yvy107, yvy108)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Int, cab) → new_ltEs15(yvy1000, yvy1010)
new_esEs28(yvy1001, yvy1011, app(ty_Maybe, bch)) → new_esEs23(yvy1001, yvy1011, bch)
new_lt5(yvy1001, yvy1011, ty_@0) → new_lt19(yvy1001, yvy1011)
new_compare15(EQ, LT) → GT
new_pePe(True, yvy305) → True
new_compare0([], [], h) → EQ
new_primEqNat0(Zero, Zero) → True
new_ltEs21(yvy1001, yvy1011, ty_Double) → new_ltEs13(yvy1001, yvy1011)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Float) → new_esEs14(yvy40000, yvy30000)
new_esEs6(yvy4002, yvy3002, ty_Double) → new_esEs13(yvy4002, yvy3002)
new_lt5(yvy1001, yvy1011, ty_Bool) → new_lt18(yvy1001, yvy1011)
new_esEs4(yvy4000, yvy3000, app(ty_Maybe, def)) → new_esEs23(yvy4000, yvy3000, def)
new_lt23(yvy165, yvy167, ty_Integer) → new_lt15(yvy165, yvy167)
new_esEs5(yvy4001, yvy3001, ty_Float) → new_esEs14(yvy4001, yvy3001)
new_lt21(yvy153, yvy156, app(app(ty_Either, fg), fh)) → new_lt16(yvy153, yvy156, fg, fh)
new_esEs8(yvy4001, yvy3001, app(app(app(ty_@3, cgg), cgh), cha)) → new_esEs22(yvy4001, yvy3001, cgg, cgh, cha)
new_lt11(yvy152, yvy155) → new_esEs12(new_compare18(yvy152, yvy155), LT)
new_lt20(yvy152, yvy155, app(ty_[], ca)) → new_lt9(yvy152, yvy155, ca)
new_esEs13(Double(yvy40000, yvy40001), Double(yvy30000, yvy30001)) → new_esEs25(new_sr0(yvy40000, yvy30000), new_sr0(yvy40001, yvy30001))
new_esEs7(yvy4000, yvy3000, ty_Bool) → new_esEs20(yvy4000, yvy3000)
new_compare30(yvy400, yvy300, ty_@0) → new_compare9(yvy400, yvy300)
new_esEs29(yvy40000, yvy30000, ty_@0) → new_esEs19(yvy40000, yvy30000)
new_esEs6(yvy4002, yvy3002, ty_Ordering) → new_esEs12(yvy4002, yvy3002)
new_ltEs18(yvy107, yvy108, app(app(app(ty_@3, ccg), cch), cda)) → new_ltEs10(yvy107, yvy108, ccg, cch, cda)
new_ltEs22(yvy114, yvy115, ty_@0) → new_ltEs17(yvy114, yvy115)
new_lt5(yvy1001, yvy1011, app(app(ty_Either, bda), bdb)) → new_lt16(yvy1001, yvy1011, bda, bdb)
new_lt5(yvy1001, yvy1011, ty_Char) → new_lt8(yvy1001, yvy1011)
new_ltEs19(yvy1002, yvy1012, ty_Ordering) → new_ltEs6(yvy1002, yvy1012)
new_esEs15(Char(yvy40000), Char(yvy30000)) → new_primEqNat0(yvy40000, yvy30000)
new_esEs24(Left(yvy40000), Left(yvy30000), app(app(app(ty_@3, fcc), fcd), fce), deh) → new_esEs22(yvy40000, yvy30000, fcc, fcd, fce)
new_esEs26(yvy40000, yvy30000, ty_Int) → new_esEs25(yvy40000, yvy30000)
new_esEs32(yvy40001, yvy30001, ty_Integer) → new_esEs18(yvy40001, yvy30001)
new_ltEs23(yvy166, yvy168, ty_Double) → new_ltEs13(yvy166, yvy168)
new_esEs9(yvy4000, yvy3000, app(ty_[], eha)) → new_esEs16(yvy4000, yvy3000, eha)
new_lt22(yvy1000, yvy1010, app(ty_[], bff)) → new_lt9(yvy1000, yvy1010, bff)
new_ltEs23(yvy166, yvy168, ty_Integer) → new_ltEs4(yvy166, yvy168)
new_esEs33(yvy40002, yvy30002, ty_Bool) → new_esEs20(yvy40002, yvy30002)
new_esEs11(yvy4000, yvy3000, ty_Double) → new_esEs13(yvy4000, yvy3000)
new_esEs29(yvy40000, yvy30000, ty_Bool) → new_esEs20(yvy40000, yvy30000)
new_lt5(yvy1001, yvy1011, app(ty_[], bca)) → new_lt9(yvy1001, yvy1011, bca)
new_ltEs21(yvy1001, yvy1011, ty_Bool) → new_ltEs16(yvy1001, yvy1011)
new_esEs9(yvy4000, yvy3000, ty_Integer) → new_esEs18(yvy4000, yvy3000)
new_ltEs6(EQ, GT) → True
new_esEs11(yvy4000, yvy3000, ty_Ordering) → new_esEs12(yvy4000, yvy3000)
new_esEs23(Nothing, Just(yvy30000), def) → False
new_esEs23(Just(yvy40000), Nothing, def) → False
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_ltEs18(yvy107, yvy108, ty_Ordering) → new_ltEs6(yvy107, yvy108)
new_esEs23(Just(yvy40000), Just(yvy30000), app(app(app(ty_@3, fba), fbb), fbc)) → new_esEs22(yvy40000, yvy30000, fba, fbb, fbc)
new_ltEs24(yvy100, yvy101, ty_Double) → new_ltEs13(yvy100, yvy101)
new_esEs10(yvy4000, yvy3000, ty_Double) → new_esEs13(yvy4000, yvy3000)
new_esEs24(Right(yvy40000), Right(yvy30000), deg, ty_Float) → new_esEs14(yvy40000, yvy30000)
new_compare110(yvy233, yvy234, yvy235, yvy236, False, yvy238, feg, feh) → new_compare111(yvy233, yvy234, yvy235, yvy236, yvy238, feg, feh)
new_ltEs20(yvy154, yvy157, ty_Bool) → new_ltEs16(yvy154, yvy157)
new_ltEs24(yvy100, yvy101, ty_@0) → new_ltEs17(yvy100, yvy101)
new_ltEs5(Just(yvy1000), Just(yvy1010), app(app(ty_@2, bhd), bhe)) → new_ltEs12(yvy1000, yvy1010, bhd, bhe)
new_ltEs20(yvy154, yvy157, ty_Int) → new_ltEs15(yvy154, yvy157)
new_esEs8(yvy4001, yvy3001, ty_@0) → new_esEs19(yvy4001, yvy3001)
new_lt22(yvy1000, yvy1010, app(app(ty_Either, bgf), bgg)) → new_lt16(yvy1000, yvy1010, bgf, bgg)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Float, cab) → new_ltEs11(yvy1000, yvy1010)
new_compare26(yvy107, yvy108, False, dhe, ccf) → new_compare10(yvy107, yvy108, new_ltEs18(yvy107, yvy108, dhe), dhe, ccf)
new_lt21(yvy153, yvy156, app(ty_Ratio, fee)) → new_lt10(yvy153, yvy156, fee)
new_compare30(yvy400, yvy300, ty_Float) → new_compare18(yvy400, yvy300)
new_primEqInt(Neg(Succ(yvy400000)), Neg(Succ(yvy300000))) → new_primEqNat0(yvy400000, yvy300000)
new_esEs10(yvy4000, yvy3000, app(app(app(ty_@3, dda), ddb), ddc)) → new_esEs22(yvy4000, yvy3000, dda, ddb, ddc)
new_esEs23(Nothing, Nothing, def) → True
new_esEs39(yvy165, yvy167, app(app(ty_@2, gf), gg)) → new_esEs17(yvy165, yvy167, gf, gg)
new_ltEs14(Right(yvy1000), Right(yvy1010), cbc, app(app(ty_@2, cbh), cca)) → new_ltEs12(yvy1000, yvy1010, cbh, cca)
new_ltEs5(Just(yvy1000), Nothing, chg) → False
new_esEs11(yvy4000, yvy3000, app(ty_Maybe, dah)) → new_esEs23(yvy4000, yvy3000, dah)
new_esEs28(yvy1001, yvy1011, ty_Char) → new_esEs15(yvy1001, yvy1011)
new_lt14(yvy152, yvy155, db) → new_esEs12(new_compare31(yvy152, yvy155, db), LT)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_ltEs14(Right(yvy1000), Right(yvy1010), cbc, ty_@0) → new_ltEs17(yvy1000, yvy1010)
new_ltEs14(Right(yvy1000), Left(yvy1010), cbc, cab) → False
new_esEs12(EQ, LT) → False
new_esEs12(LT, EQ) → False
new_ltEs19(yvy1002, yvy1012, app(ty_Ratio, eaa)) → new_ltEs9(yvy1002, yvy1012, eaa)
new_lt22(yvy1000, yvy1010, app(app(ty_@2, bgc), bgd)) → new_lt12(yvy1000, yvy1010, bgc, bgd)
new_ltEs23(yvy166, yvy168, ty_Bool) → new_ltEs16(yvy166, yvy168)
new_compare111(yvy233, yvy234, yvy235, yvy236, True, feg, feh) → LT
new_esEs7(yvy4000, yvy3000, app(ty_[], cfa)) → new_esEs16(yvy4000, yvy3000, cfa)
new_esEs5(yvy4001, yvy3001, ty_Bool) → new_esEs20(yvy4001, yvy3001)
new_lt23(yvy165, yvy167, ty_Int) → new_lt17(yvy165, yvy167)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs30(yvy40001, yvy30001, app(app(app(ty_@3, ebh), eca), ecb)) → new_esEs22(yvy40001, yvy30001, ebh, eca, ecb)
new_esEs11(yvy4000, yvy3000, app(app(ty_Either, dba), dbb)) → new_esEs24(yvy4000, yvy3000, dba, dbb)
new_esEs35(yvy153, yvy156, app(app(app(ty_@3, eh), fa), fb)) → new_esEs22(yvy153, yvy156, eh, fa, fb)
new_ltEs14(Right(yvy1000), Right(yvy1010), cbc, ty_Int) → new_ltEs15(yvy1000, yvy1010)
new_esEs10(yvy4000, yvy3000, app(app(ty_Either, dde), ddf)) → new_esEs24(yvy4000, yvy3000, dde, ddf)
new_esEs28(yvy1001, yvy1011, ty_Double) → new_esEs13(yvy1001, yvy1011)
new_lt20(yvy152, yvy155, ty_Ordering) → new_lt7(yvy152, yvy155)
new_ltEs6(EQ, EQ) → True
new_compare31(Just(yvy4000), Nothing, bf) → GT
new_esEs11(yvy4000, yvy3000, app(app(app(ty_@3, dae), daf), dag)) → new_esEs22(yvy4000, yvy3000, dae, daf, dag)
new_ltEs22(yvy114, yvy115, app(app(ty_Either, ceg), ceh)) → new_ltEs14(yvy114, yvy115, ceg, ceh)
new_esEs28(yvy1001, yvy1011, app(app(app(ty_@3, bcc), bcd), bce)) → new_esEs22(yvy1001, yvy1011, bcc, bcd, bce)
new_esEs32(yvy40001, yvy30001, ty_Float) → new_esEs14(yvy40001, yvy30001)
new_ltEs19(yvy1002, yvy1012, ty_Integer) → new_ltEs4(yvy1002, yvy1012)
new_esEs27(yvy1000, yvy1010, app(ty_Ratio, dhg)) → new_esEs21(yvy1000, yvy1010, dhg)
new_primEqInt(Neg(Succ(yvy400000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(yvy300000))) → False
new_primCompAux0(yvy56, GT) → GT
new_compare30(yvy400, yvy300, app(app(app(ty_@3, ba), bb), bc)) → new_compare6(yvy400, yvy300, ba, bb, bc)
new_esEs39(yvy165, yvy167, ty_Integer) → new_esEs18(yvy165, yvy167)
new_compare26(yvy107, yvy108, True, dhe, ccf) → EQ
new_esEs23(Just(yvy40000), Just(yvy30000), app(app(ty_@2, faf), fag)) → new_esEs17(yvy40000, yvy30000, faf, fag)
new_esEs24(Right(yvy40000), Right(yvy30000), deg, app(app(ty_Either, fea), feb)) → new_esEs24(yvy40000, yvy30000, fea, feb)
new_ltEs6(GT, GT) → True
new_ltEs21(yvy1001, yvy1011, app(app(ty_Either, bfd), bfe)) → new_ltEs14(yvy1001, yvy1011, bfd, bfe)
new_esEs38(yvy40001, yvy30001, ty_Integer) → new_esEs18(yvy40001, yvy30001)
new_esEs32(yvy40001, yvy30001, app(ty_[], eee)) → new_esEs16(yvy40001, yvy30001, eee)
new_esEs34(yvy152, yvy155, ty_Int) → new_esEs25(yvy152, yvy155)
new_compare31(Nothing, Nothing, bf) → EQ
new_esEs29(yvy40000, yvy30000, app(ty_[], eab)) → new_esEs16(yvy40000, yvy30000, eab)
new_esEs26(yvy40000, yvy30000, app(ty_Ratio, dgf)) → new_esEs21(yvy40000, yvy30000, dgf)
new_esEs7(yvy4000, yvy3000, app(ty_Maybe, cfh)) → new_esEs23(yvy4000, yvy3000, cfh)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_@0) → new_ltEs17(yvy1000, yvy1010)
new_lt21(yvy153, yvy156, app(ty_[], eg)) → new_lt9(yvy153, yvy156, eg)
new_ltEs20(yvy154, yvy157, app(ty_[], df)) → new_ltEs8(yvy154, yvy157, df)
new_esEs36(yvy1000, yvy1010, ty_Int) → new_esEs25(yvy1000, yvy1010)
new_esEs19(@0, @0) → True
new_compare6(@3(yvy4000, yvy4001, yvy4002), @3(yvy3000, yvy3001, yvy3002), ba, bb, bc) → new_compare25(yvy4000, yvy4001, yvy4002, yvy3000, yvy3001, yvy3002, new_asAs(new_esEs4(yvy4000, yvy3000, ba), new_asAs(new_esEs5(yvy4001, yvy3001, bb), new_esEs6(yvy4002, yvy3002, bc))), ba, bb, bc)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_esEs7(yvy4000, yvy3000, ty_Integer) → new_esEs18(yvy4000, yvy3000)
new_esEs4(yvy4000, yvy3000, ty_Bool) → new_esEs20(yvy4000, yvy3000)
new_esEs39(yvy165, yvy167, ty_Ordering) → new_esEs12(yvy165, yvy167)
new_lt20(yvy152, yvy155, ty_Char) → new_lt8(yvy152, yvy155)
new_esEs31(yvy40000, yvy30000, ty_Bool) → new_esEs20(yvy40000, yvy30000)
new_lt4(yvy152, yvy155, cd, ce, cf) → new_esEs12(new_compare6(yvy152, yvy155, cd, ce, cf), LT)
new_esEs6(yvy4002, yvy3002, ty_Int) → new_esEs25(yvy4002, yvy3002)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Double, cab) → new_ltEs13(yvy1000, yvy1010)
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_lt6(yvy1000, yvy1010, app(ty_Maybe, bea)) → new_lt14(yvy1000, yvy1010, bea)
new_ltEs14(Left(yvy1000), Left(yvy1010), app(ty_Maybe, cah), cab) → new_ltEs5(yvy1000, yvy1010, cah)
new_esEs4(yvy4000, yvy3000, app(ty_Ratio, deb)) → new_esEs21(yvy4000, yvy3000, deb)
new_lt5(yvy1001, yvy1011, app(ty_Maybe, bch)) → new_lt14(yvy1001, yvy1011, bch)
new_primEqInt(Pos(Succ(yvy400000)), Pos(Succ(yvy300000))) → new_primEqNat0(yvy400000, yvy300000)
new_compare10(yvy199, yvy200, False, che, chf) → GT
new_esEs34(yvy152, yvy155, app(ty_Maybe, db)) → new_esEs23(yvy152, yvy155, db)
new_esEs5(yvy4001, yvy3001, app(ty_[], dfa)) → new_esEs16(yvy4001, yvy3001, dfa)
new_ltEs14(Right(yvy1000), Right(yvy1010), cbc, ty_Double) → new_ltEs13(yvy1000, yvy1010)
new_ltEs14(Right(yvy1000), Right(yvy1010), cbc, ty_Integer) → new_ltEs4(yvy1000, yvy1010)
new_ltEs21(yvy1001, yvy1011, ty_Float) → new_ltEs11(yvy1001, yvy1011)
new_ltEs14(Right(yvy1000), Right(yvy1010), cbc, app(ty_Maybe, ccb)) → new_ltEs5(yvy1000, yvy1010, ccb)
new_compare13(:%(yvy4000, yvy4001), :%(yvy3000, yvy3001), ty_Int) → new_compare16(new_sr0(yvy4000, yvy3001), new_sr0(yvy3000, yvy4001))
new_esEs26(yvy40000, yvy30000, app(ty_Maybe, dhb)) → new_esEs23(yvy40000, yvy30000, dhb)
new_ltEs24(yvy100, yvy101, ty_Float) → new_ltEs11(yvy100, yvy101)
new_esEs34(yvy152, yvy155, app(app(ty_@2, cg), da)) → new_esEs17(yvy152, yvy155, cg, da)
new_esEs8(yvy4001, yvy3001, ty_Integer) → new_esEs18(yvy4001, yvy3001)
new_ltEs22(yvy114, yvy115, app(app(app(ty_@3, cea), ceb), cec)) → new_ltEs10(yvy114, yvy115, cea, ceb, cec)
new_primEqNat0(Succ(yvy400000), Succ(yvy300000)) → new_primEqNat0(yvy400000, yvy300000)
new_esEs6(yvy4002, yvy3002, ty_Bool) → new_esEs20(yvy4002, yvy3002)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Ordering) → new_ltEs6(yvy1000, yvy1010)
new_ltEs24(yvy100, yvy101, ty_Int) → new_ltEs15(yvy100, yvy101)
new_esEs26(yvy40000, yvy30000, ty_Ordering) → new_esEs12(yvy40000, yvy30000)
new_esEs24(Right(yvy40000), Right(yvy30000), deg, app(ty_Ratio, fdd)) → new_esEs21(yvy40000, yvy30000, fdd)
new_esEs11(yvy4000, yvy3000, app(ty_Ratio, dad)) → new_esEs21(yvy4000, yvy3000, dad)
new_esEs30(yvy40001, yvy30001, ty_Integer) → new_esEs18(yvy40001, yvy30001)
new_esEs39(yvy165, yvy167, ty_Char) → new_esEs15(yvy165, yvy167)
new_ltEs14(Left(yvy1000), Left(yvy1010), app(ty_Ratio, fac), cab) → new_ltEs9(yvy1000, yvy1010, fac)
new_esEs26(yvy40000, yvy30000, app(app(ty_@2, dgd), dge)) → new_esEs17(yvy40000, yvy30000, dgd, dge)
new_lt5(yvy1001, yvy1011, ty_Float) → new_lt11(yvy1001, yvy1011)
new_esEs32(yvy40001, yvy30001, ty_@0) → new_esEs19(yvy40001, yvy30001)
new_esEs33(yvy40002, yvy30002, app(ty_Maybe, egf)) → new_esEs23(yvy40002, yvy30002, egf)
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_lt6(yvy1000, yvy1010, ty_Int) → new_lt17(yvy1000, yvy1010)
new_esEs24(Right(yvy40000), Right(yvy30000), deg, app(app(app(ty_@3, fde), fdf), fdg)) → new_esEs22(yvy40000, yvy30000, fde, fdf, fdg)
new_lt23(yvy165, yvy167, app(app(ty_Either, ha), hb)) → new_lt16(yvy165, yvy167, ha, hb)
new_esEs12(EQ, EQ) → True
new_lt23(yvy165, yvy167, ty_Char) → new_lt8(yvy165, yvy167)
new_ltEs18(yvy107, yvy108, app(app(ty_@2, cdb), cdc)) → new_ltEs12(yvy107, yvy108, cdb, cdc)
new_lt21(yvy153, yvy156, ty_Double) → new_lt13(yvy153, yvy156)
new_esEs35(yvy153, yvy156, ty_Ordering) → new_esEs12(yvy153, yvy156)
new_lt5(yvy1001, yvy1011, ty_Int) → new_lt17(yvy1001, yvy1011)
new_esEs10(yvy4000, yvy3000, ty_Char) → new_esEs15(yvy4000, yvy3000)
new_primEqInt(Pos(Succ(yvy400000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(yvy300000))) → False
new_ltEs5(Nothing, Just(yvy1010), chg) → True
new_lt20(yvy152, yvy155, ty_Int) → new_lt17(yvy152, yvy155)
new_esEs35(yvy153, yvy156, app(ty_Maybe, ff)) → new_esEs23(yvy153, yvy156, ff)
new_esEs27(yvy1000, yvy1010, ty_@0) → new_esEs19(yvy1000, yvy1010)
new_ltEs18(yvy107, yvy108, ty_Float) → new_ltEs11(yvy107, yvy108)
new_compare25(yvy152, yvy153, yvy154, yvy155, yvy156, yvy157, True, de, cb, cc) → EQ
new_esEs37(yvy40000, yvy30000, ty_Int) → new_esEs25(yvy40000, yvy30000)
new_primCmpNat0(Zero, Zero) → EQ
new_esEs27(yvy1000, yvy1010, app(app(ty_Either, beb), bec)) → new_esEs24(yvy1000, yvy1010, beb, bec)
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_compare27(Left(yvy4000), Right(yvy3000), bg, bh) → LT
new_lt22(yvy1000, yvy1010, ty_@0) → new_lt19(yvy1000, yvy1010)
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_compare9(@0, @0) → EQ
new_esEs28(yvy1001, yvy1011, ty_Int) → new_esEs25(yvy1001, yvy1011)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Float, deh) → new_esEs14(yvy40000, yvy30000)
new_esEs6(yvy4002, yvy3002, ty_Float) → new_esEs14(yvy4002, yvy3002)
new_ltEs9(yvy100, yvy101, ecf) → new_fsEs(new_compare13(yvy100, yvy101, ecf))
new_compare17(yvy218, yvy219, yvy220, yvy221, yvy222, yvy223, True, yvy225, ech, eda, edb) → new_compare14(yvy218, yvy219, yvy220, yvy221, yvy222, yvy223, True, ech, eda, edb)
new_esEs32(yvy40001, yvy30001, ty_Char) → new_esEs15(yvy40001, yvy30001)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_ltEs14(Left(yvy1000), Left(yvy1010), app(ty_[], caa), cab) → new_ltEs8(yvy1000, yvy1010, caa)
new_ltEs19(yvy1002, yvy1012, app(app(ty_@2, bbd), bbe)) → new_ltEs12(yvy1002, yvy1012, bbd, bbe)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Double, deh) → new_esEs13(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, app(app(ty_Either, egg), egh)) → new_esEs24(yvy40002, yvy30002, egg, egh)
new_esEs4(yvy4000, yvy3000, ty_Int) → new_esEs25(yvy4000, yvy3000)
new_compare28(yvy114, yvy115, True, cdg, ffc) → EQ
new_primEqInt(Pos(Succ(yvy400000)), Neg(yvy30000)) → False
new_primEqInt(Neg(Succ(yvy400000)), Pos(yvy30000)) → False
new_esEs24(Right(yvy40000), Right(yvy30000), deg, ty_Int) → new_esEs25(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, ty_Ordering) → new_esEs12(yvy40002, yvy30002)
new_esEs29(yvy40000, yvy30000, app(app(app(ty_@3, eaf), eag), eah)) → new_esEs22(yvy40000, yvy30000, eaf, eag, eah)
new_esEs26(yvy40000, yvy30000, ty_Double) → new_esEs13(yvy40000, yvy30000)
new_ltEs20(yvy154, yvy157, ty_Integer) → new_ltEs4(yvy154, yvy157)
new_compare210(yvy100, yvy101, True, ffg) → EQ
new_lt6(yvy1000, yvy1010, ty_Ordering) → new_lt7(yvy1000, yvy1010)
new_esEs29(yvy40000, yvy30000, app(ty_Ratio, eae)) → new_esEs21(yvy40000, yvy30000, eae)
new_esEs20(False, False) → True
new_esEs24(Left(yvy40000), Left(yvy30000), app(ty_[], fbg), deh) → new_esEs16(yvy40000, yvy30000, fbg)
new_lt23(yvy165, yvy167, app(ty_[], ga)) → new_lt9(yvy165, yvy167, ga)
new_ltEs22(yvy114, yvy115, ty_Integer) → new_ltEs4(yvy114, yvy115)
new_ltEs5(Just(yvy1000), Just(yvy1010), app(app(ty_Either, bhg), bhh)) → new_ltEs14(yvy1000, yvy1010, bhg, bhh)
new_lt23(yvy165, yvy167, ty_Bool) → new_lt18(yvy165, yvy167)
new_esEs30(yvy40001, yvy30001, ty_Ordering) → new_esEs12(yvy40001, yvy30001)
new_lt6(yvy1000, yvy1010, ty_Integer) → new_lt15(yvy1000, yvy1010)
new_primEqInt(Pos(Zero), Neg(Succ(yvy300000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(yvy300000))) → False
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_compare30(yvy400, yvy300, app(ty_Maybe, bf)) → new_compare31(yvy400, yvy300, bf)
new_esEs9(yvy4000, yvy3000, ty_Ordering) → new_esEs12(yvy4000, yvy3000)
new_esEs7(yvy4000, yvy3000, ty_@0) → new_esEs19(yvy4000, yvy3000)
new_esEs11(yvy4000, yvy3000, ty_Float) → new_esEs14(yvy4000, yvy3000)
new_lt6(yvy1000, yvy1010, app(ty_[], bdc)) → new_lt9(yvy1000, yvy1010, bdc)
new_esEs36(yvy1000, yvy1010, ty_@0) → new_esEs19(yvy1000, yvy1010)
new_esEs5(yvy4001, yvy3001, ty_@0) → new_esEs19(yvy4001, yvy3001)
new_esEs36(yvy1000, yvy1010, app(app(app(ty_@3, bfh), bga), bgb)) → new_esEs22(yvy1000, yvy1010, bfh, bga, bgb)
new_esEs28(yvy1001, yvy1011, ty_Ordering) → new_esEs12(yvy1001, yvy1011)
new_esEs10(yvy4000, yvy3000, app(ty_[], dce)) → new_esEs16(yvy4000, yvy3000, dce)
new_primCompAux0(yvy56, LT) → LT
new_esEs6(yvy4002, yvy3002, app(app(ty_Either, dcc), dcd)) → new_esEs24(yvy4002, yvy3002, dcc, dcd)
new_esEs6(yvy4002, yvy3002, ty_Integer) → new_esEs18(yvy4002, yvy3002)
new_esEs36(yvy1000, yvy1010, app(app(ty_@2, bgc), bgd)) → new_esEs17(yvy1000, yvy1010, bgc, bgd)
new_esEs9(yvy4000, yvy3000, ty_Float) → new_esEs14(yvy4000, yvy3000)
new_esEs7(yvy4000, yvy3000, app(app(ty_@2, cfb), cfc)) → new_esEs17(yvy4000, yvy3000, cfb, cfc)
new_lt5(yvy1001, yvy1011, ty_Double) → new_lt13(yvy1001, yvy1011)
new_ltEs22(yvy114, yvy115, app(ty_Maybe, cef)) → new_ltEs5(yvy114, yvy115, cef)
new_not(False) → True
new_esEs27(yvy1000, yvy1010, ty_Int) → new_esEs25(yvy1000, yvy1010)
new_esEs34(yvy152, yvy155, app(ty_Ratio, ecg)) → new_esEs21(yvy152, yvy155, ecg)
new_compare30(yvy400, yvy300, ty_Bool) → new_compare12(yvy400, yvy300)
new_esEs25(yvy4000, yvy3000) → new_primEqInt(yvy4000, yvy3000)
new_esEs28(yvy1001, yvy1011, app(ty_[], bca)) → new_esEs16(yvy1001, yvy1011, bca)
new_esEs31(yvy40000, yvy30000, ty_Char) → new_esEs15(yvy40000, yvy30000)
new_esEs11(yvy4000, yvy3000, ty_@0) → new_esEs19(yvy4000, yvy3000)
new_esEs14(Float(yvy40000, yvy40001), Float(yvy30000, yvy30001)) → new_esEs25(new_sr0(yvy40000, yvy30000), new_sr0(yvy40001, yvy30001))
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_esEs12(EQ, GT) → False
new_esEs12(GT, EQ) → False
new_esEs36(yvy1000, yvy1010, ty_Float) → new_esEs14(yvy1000, yvy1010)
new_esEs9(yvy4000, yvy3000, app(app(ty_Either, faa), fab)) → new_esEs24(yvy4000, yvy3000, faa, fab)
new_esEs4(yvy4000, yvy3000, ty_Ordering) → new_esEs12(yvy4000, yvy3000)
new_lt6(yvy1000, yvy1010, app(app(app(ty_@3, bdd), bde), bdf)) → new_lt4(yvy1000, yvy1010, bdd, bde, bdf)
new_esEs4(yvy4000, yvy3000, app(app(ty_@2, ddh), dea)) → new_esEs17(yvy4000, yvy3000, ddh, dea)
new_esEs24(Right(yvy40000), Right(yvy30000), deg, ty_Integer) → new_esEs18(yvy40000, yvy30000)
new_ltEs18(yvy107, yvy108, ty_@0) → new_ltEs17(yvy107, yvy108)
new_esEs39(yvy165, yvy167, ty_Int) → new_esEs25(yvy165, yvy167)
new_compare15(LT, EQ) → LT
new_esEs34(yvy152, yvy155, ty_Float) → new_esEs14(yvy152, yvy155)
new_ltEs14(Right(yvy1000), Right(yvy1010), cbc, app(ty_[], cbd)) → new_ltEs8(yvy1000, yvy1010, cbd)
new_esEs36(yvy1000, yvy1010, app(ty_Ratio, ffa)) → new_esEs21(yvy1000, yvy1010, ffa)
new_esEs30(yvy40001, yvy30001, app(ty_Ratio, ebg)) → new_esEs21(yvy40001, yvy30001, ebg)
new_compare30(yvy400, yvy300, app(ty_Ratio, fga)) → new_compare13(yvy400, yvy300, fga)
new_esEs24(Left(yvy40000), Right(yvy30000), deg, deh) → False
new_esEs24(Right(yvy40000), Left(yvy30000), deg, deh) → False
new_lt20(yvy152, yvy155, app(app(ty_Either, dc), dd)) → new_lt16(yvy152, yvy155, dc, dd)
new_esEs30(yvy40001, yvy30001, app(app(ty_@2, ebe), ebf)) → new_esEs17(yvy40001, yvy30001, ebe, ebf)
new_esEs32(yvy40001, yvy30001, app(app(ty_Either, efe), eff)) → new_esEs24(yvy40001, yvy30001, efe, eff)
new_esEs34(yvy152, yvy155, app(ty_[], ca)) → new_esEs16(yvy152, yvy155, ca)
new_lt20(yvy152, yvy155, ty_Double) → new_lt13(yvy152, yvy155)
new_esEs35(yvy153, yvy156, ty_Double) → new_esEs13(yvy153, yvy156)
new_compare0(:(yvy4000, yvy4001), [], h) → GT
new_lt6(yvy1000, yvy1010, ty_Char) → new_lt8(yvy1000, yvy1010)
new_esEs8(yvy4001, yvy3001, ty_Int) → new_esEs25(yvy4001, yvy3001)
new_esEs38(yvy40001, yvy30001, ty_Int) → new_esEs25(yvy40001, yvy30001)
new_ltEs24(yvy100, yvy101, ty_Integer) → new_ltEs4(yvy100, yvy101)
new_ltEs20(yvy154, yvy157, app(ty_Maybe, ed)) → new_ltEs5(yvy154, yvy157, ed)
new_ltEs20(yvy154, yvy157, ty_@0) → new_ltEs17(yvy154, yvy157)
new_ltEs24(yvy100, yvy101, app(app(ty_Either, cbc), cab)) → new_ltEs14(yvy100, yvy101, cbc, cab)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Int) → new_esEs25(yvy40000, yvy30000)
new_esEs34(yvy152, yvy155, app(app(ty_Either, dc), dd)) → new_esEs24(yvy152, yvy155, dc, dd)
new_lt13(yvy152, yvy155) → new_esEs12(new_compare29(yvy152, yvy155), LT)
new_esEs30(yvy40001, yvy30001, app(app(ty_Either, ecd), ece)) → new_esEs24(yvy40001, yvy30001, ecd, ece)
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_lt19(yvy152, yvy155) → new_esEs12(new_compare9(yvy152, yvy155), LT)
new_ltEs18(yvy107, yvy108, ty_Char) → new_ltEs7(yvy107, yvy108)
new_esEs4(yvy4000, yvy3000, app(app(ty_Either, deg), deh)) → new_esEs24(yvy4000, yvy3000, deg, deh)
new_esEs8(yvy4001, yvy3001, app(ty_Ratio, cgf)) → new_esEs21(yvy4001, yvy3001, cgf)
new_esEs33(yvy40002, yvy30002, app(ty_Ratio, egb)) → new_esEs21(yvy40002, yvy30002, egb)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Integer) → new_esEs18(yvy40000, yvy30000)
new_lt17(yvy152, yvy155) → new_esEs12(new_compare16(yvy152, yvy155), LT)
new_esEs10(yvy4000, yvy3000, app(app(ty_@2, dcf), dcg)) → new_esEs17(yvy4000, yvy3000, dcf, dcg)
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_ltEs7(yvy100, yvy101) → new_fsEs(new_compare11(yvy100, yvy101))
new_esEs31(yvy40000, yvy30000, ty_Float) → new_esEs14(yvy40000, yvy30000)
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_compare15(EQ, GT) → LT
new_esEs32(yvy40001, yvy30001, ty_Int) → new_esEs25(yvy40001, yvy30001)
new_esEs29(yvy40000, yvy30000, ty_Char) → new_esEs15(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, app(app(app(ty_@3, egc), egd), ege)) → new_esEs22(yvy40002, yvy30002, egc, egd, ege)
new_primEqNat0(Zero, Succ(yvy300000)) → False
new_primEqNat0(Succ(yvy400000), Zero) → False
new_compare15(LT, GT) → LT
new_lt15(yvy152, yvy155) → new_esEs12(new_compare8(yvy152, yvy155), LT)
new_ltEs5(Nothing, Nothing, chg) → True
new_ltEs23(yvy166, yvy168, app(app(app(ty_@3, he), hf), hg)) → new_ltEs10(yvy166, yvy168, he, hf, hg)
new_lt20(yvy152, yvy155, app(app(ty_@2, cg), da)) → new_lt12(yvy152, yvy155, cg, da)
new_ltEs6(LT, LT) → True
new_ltEs6(EQ, LT) → False
new_esEs6(yvy4002, yvy3002, app(ty_Ratio, dbf)) → new_esEs21(yvy4002, yvy3002, dbf)
new_ltEs19(yvy1002, yvy1012, ty_Char) → new_ltEs7(yvy1002, yvy1012)
new_ltEs5(Just(yvy1000), Just(yvy1010), app(ty_[], bgh)) → new_ltEs8(yvy1000, yvy1010, bgh)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs9(yvy4000, yvy3000, app(ty_Maybe, ehh)) → new_esEs23(yvy4000, yvy3000, ehh)
new_ltEs21(yvy1001, yvy1011, app(ty_Ratio, ffb)) → new_ltEs9(yvy1001, yvy1011, ffb)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Bool) → new_ltEs16(yvy1000, yvy1010)
new_lt21(yvy153, yvy156, app(ty_Maybe, ff)) → new_lt14(yvy153, yvy156, ff)
new_compare15(GT, GT) → EQ
new_esEs11(yvy4000, yvy3000, app(app(ty_@2, dab), dac)) → new_esEs17(yvy4000, yvy3000, dab, dac)
new_esEs8(yvy4001, yvy3001, app(app(ty_Either, chc), chd)) → new_esEs24(yvy4001, yvy3001, chc, chd)
new_compare24(yvy165, yvy166, yvy167, yvy168, True, hc, gb) → EQ
new_esEs32(yvy40001, yvy30001, ty_Bool) → new_esEs20(yvy40001, yvy30001)
new_lt21(yvy153, yvy156, ty_Float) → new_lt11(yvy153, yvy156)
new_esEs16(:(yvy40000, yvy40001), [], ddg) → False
new_esEs16([], :(yvy30000, yvy30001), ddg) → False
new_compare31(Just(yvy4000), Just(yvy3000), bf) → new_compare210(yvy4000, yvy3000, new_esEs9(yvy4000, yvy3000, bf), bf)
new_lt21(yvy153, yvy156, ty_Ordering) → new_lt7(yvy153, yvy156)
new_lt20(yvy152, yvy155, ty_Bool) → new_lt18(yvy152, yvy155)
new_ltEs14(Right(yvy1000), Right(yvy1010), cbc, app(ty_Ratio, fad)) → new_ltEs9(yvy1000, yvy1010, fad)
new_ltEs19(yvy1002, yvy1012, ty_@0) → new_ltEs17(yvy1002, yvy1012)
new_esEs7(yvy4000, yvy3000, app(app(app(ty_@3, cfe), cff), cfg)) → new_esEs22(yvy4000, yvy3000, cfe, cff, cfg)
new_esEs5(yvy4001, yvy3001, ty_Integer) → new_esEs18(yvy4001, yvy3001)
new_esEs31(yvy40000, yvy30000, ty_Int) → new_esEs25(yvy40000, yvy30000)
new_ltEs19(yvy1002, yvy1012, app(ty_Maybe, bbf)) → new_ltEs5(yvy1002, yvy1012, bbf)
new_esEs27(yvy1000, yvy1010, app(app(app(ty_@3, bdd), bde), bdf)) → new_esEs22(yvy1000, yvy1010, bdd, bde, bdf)
new_lt21(yvy153, yvy156, ty_Integer) → new_lt15(yvy153, yvy156)
new_esEs29(yvy40000, yvy30000, app(app(ty_Either, ebb), ebc)) → new_esEs24(yvy40000, yvy30000, ebb, ebc)
new_esEs10(yvy4000, yvy3000, app(ty_Ratio, dch)) → new_esEs21(yvy4000, yvy3000, dch)
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_ltEs12(@2(yvy1000, yvy1001), @2(yvy1010, yvy1011), bed, bfg) → new_pePe(new_lt22(yvy1000, yvy1010, bed), new_asAs(new_esEs36(yvy1000, yvy1010, bed), new_ltEs21(yvy1001, yvy1011, bfg)))
new_ltEs23(yvy166, yvy168, ty_@0) → new_ltEs17(yvy166, yvy168)
new_esEs5(yvy4001, yvy3001, app(ty_Maybe, dfh)) → new_esEs23(yvy4001, yvy3001, dfh)
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Char) → new_ltEs7(yvy1000, yvy1010)
new_compare0(:(yvy4000, yvy4001), :(yvy3000, yvy3001), h) → new_primCompAux1(yvy4000, yvy3000, new_compare0(yvy4001, yvy3001, h), h)
new_esEs20(False, True) → False
new_esEs20(True, False) → False
new_compare19(yvy206, yvy207, True, fec, fed) → LT
new_sr0(yvy3000, yvy4001) → new_primMulInt(yvy3000, yvy4001)
new_esEs28(yvy1001, yvy1011, app(app(ty_@2, bcf), bcg)) → new_esEs17(yvy1001, yvy1011, bcf, bcg)
new_lt6(yvy1000, yvy1010, app(app(ty_Either, beb), bec)) → new_lt16(yvy1000, yvy1010, beb, bec)
new_esEs34(yvy152, yvy155, ty_Bool) → new_esEs20(yvy152, yvy155)
new_lt22(yvy1000, yvy1010, ty_Integer) → new_lt15(yvy1000, yvy1010)
new_esEs26(yvy40000, yvy30000, app(app(ty_Either, dhc), dhd)) → new_esEs24(yvy40000, yvy30000, dhc, dhd)
new_compare30(yvy400, yvy300, ty_Ordering) → new_compare15(yvy400, yvy300)
new_esEs30(yvy40001, yvy30001, app(ty_[], ebd)) → new_esEs16(yvy40001, yvy30001, ebd)
new_esEs24(Left(yvy40000), Left(yvy30000), app(app(ty_@2, fbh), fca), deh) → new_esEs17(yvy40000, yvy30000, fbh, fca)
new_lt23(yvy165, yvy167, ty_@0) → new_lt19(yvy165, yvy167)
new_esEs10(yvy4000, yvy3000, ty_Float) → new_esEs14(yvy4000, yvy3000)
new_compare29(Double(yvy4000, yvy4001), Double(yvy3000, yvy3001)) → new_compare16(new_sr0(yvy4000, yvy3000), new_sr0(yvy4001, yvy3001))
new_ltEs14(Right(yvy1000), Right(yvy1010), cbc, ty_Bool) → new_ltEs16(yvy1000, yvy1010)
new_ltEs22(yvy114, yvy115, app(ty_[], cdh)) → new_ltEs8(yvy114, yvy115, cdh)
new_esEs39(yvy165, yvy167, app(app(ty_Either, ha), hb)) → new_esEs24(yvy165, yvy167, ha, hb)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs32(yvy40001, yvy30001, ty_Double) → new_esEs13(yvy40001, yvy30001)
new_esEs28(yvy1001, yvy1011, ty_Bool) → new_esEs20(yvy1001, yvy1011)
new_esEs5(yvy4001, yvy3001, app(ty_Ratio, dfd)) → new_esEs21(yvy4001, yvy3001, dfd)
new_esEs23(Just(yvy40000), Just(yvy30000), app(ty_Ratio, fah)) → new_esEs21(yvy40000, yvy30000, fah)
new_ltEs14(Left(yvy1000), Right(yvy1010), cbc, cab) → True
new_compare24(yvy165, yvy166, yvy167, yvy168, False, hc, gb) → new_compare110(yvy165, yvy166, yvy167, yvy168, new_lt23(yvy165, yvy167, hc), new_asAs(new_esEs39(yvy165, yvy167, hc), new_ltEs23(yvy166, yvy168, gb)), hc, gb)
new_compare30(yvy400, yvy300, app(ty_[], h)) → new_compare0(yvy400, yvy300, h)
new_esEs9(yvy4000, yvy3000, app(ty_Ratio, ehd)) → new_esEs21(yvy4000, yvy3000, ehd)
new_ltEs20(yvy154, yvy157, app(app(ty_Either, ee), ef)) → new_ltEs14(yvy154, yvy157, ee, ef)
new_asAs(False, yvy184) → False
new_compare27(Right(yvy4000), Left(yvy3000), bg, bh) → GT
new_esEs9(yvy4000, yvy3000, ty_Double) → new_esEs13(yvy4000, yvy3000)
new_esEs36(yvy1000, yvy1010, app(ty_Maybe, bge)) → new_esEs23(yvy1000, yvy1010, bge)
new_ltEs19(yvy1002, yvy1012, app(app(ty_Either, bbg), bbh)) → new_ltEs14(yvy1002, yvy1012, bbg, bbh)
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_lt20(yvy152, yvy155, ty_@0) → new_lt19(yvy152, yvy155)
new_esEs4(yvy4000, yvy3000, ty_@0) → new_esEs19(yvy4000, yvy3000)
new_esEs27(yvy1000, yvy1010, ty_Double) → new_esEs13(yvy1000, yvy1010)
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_esEs36(yvy1000, yvy1010, ty_Ordering) → new_esEs12(yvy1000, yvy1010)
new_compare16(yvy400, yvy300) → new_primCmpInt(yvy400, yvy300)
new_esEs35(yvy153, yvy156, ty_Bool) → new_esEs20(yvy153, yvy156)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Bool) → new_esEs20(yvy40000, yvy30000)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Integer, cab) → new_ltEs4(yvy1000, yvy1010)
new_esEs9(yvy4000, yvy3000, ty_Bool) → new_esEs20(yvy4000, yvy3000)
new_compare14(yvy218, yvy219, yvy220, yvy221, yvy222, yvy223, True, ech, eda, edb) → LT
new_esEs30(yvy40001, yvy30001, app(ty_Maybe, ecc)) → new_esEs23(yvy40001, yvy30001, ecc)
new_esEs8(yvy4001, yvy3001, ty_Char) → new_esEs15(yvy4001, yvy3001)
new_lt5(yvy1001, yvy1011, ty_Ordering) → new_lt7(yvy1001, yvy1011)
new_ltEs14(Right(yvy1000), Right(yvy1010), cbc, ty_Ordering) → new_ltEs6(yvy1000, yvy1010)
new_esEs24(Left(yvy40000), Left(yvy30000), app(app(ty_Either, fcg), fch), deh) → new_esEs24(yvy40000, yvy30000, fcg, fch)
new_esEs8(yvy4001, yvy3001, app(ty_[], cgc)) → new_esEs16(yvy4001, yvy3001, cgc)
new_compare27(Left(yvy4000), Left(yvy3000), bg, bh) → new_compare26(yvy4000, yvy3000, new_esEs10(yvy4000, yvy3000, bg), bg, bh)
new_esEs29(yvy40000, yvy30000, ty_Double) → new_esEs13(yvy40000, yvy30000)
new_esEs27(yvy1000, yvy1010, ty_Integer) → new_esEs18(yvy1000, yvy1010)
new_esEs18(Integer(yvy40000), Integer(yvy30000)) → new_primEqInt(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, ty_Char) → new_esEs15(yvy40002, yvy30002)
new_ltEs5(Just(yvy1000), Just(yvy1010), app(ty_Maybe, bhf)) → new_ltEs5(yvy1000, yvy1010, bhf)
new_ltEs11(yvy100, yvy101) → new_fsEs(new_compare18(yvy100, yvy101))
new_ltEs14(Right(yvy1000), Right(yvy1010), cbc, app(app(ty_Either, ccc), ccd)) → new_ltEs14(yvy1000, yvy1010, ccc, ccd)
new_esEs30(yvy40001, yvy30001, ty_Float) → new_esEs14(yvy40001, yvy30001)
new_lt23(yvy165, yvy167, ty_Float) → new_lt11(yvy165, yvy167)
new_esEs28(yvy1001, yvy1011, ty_@0) → new_esEs19(yvy1001, yvy1011)
new_compare12(False, False) → EQ
new_ltEs23(yvy166, yvy168, ty_Char) → new_ltEs7(yvy166, yvy168)
new_esEs24(Right(yvy40000), Right(yvy30000), deg, app(ty_Maybe, fdh)) → new_esEs23(yvy40000, yvy30000, fdh)
new_esEs29(yvy40000, yvy30000, ty_Float) → new_esEs14(yvy40000, yvy30000)
new_esEs7(yvy4000, yvy3000, ty_Ordering) → new_esEs12(yvy4000, yvy3000)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Integer, deh) → new_esEs18(yvy40000, yvy30000)
new_lt20(yvy152, yvy155, app(ty_Maybe, db)) → new_lt14(yvy152, yvy155, db)
new_esEs39(yvy165, yvy167, app(app(app(ty_@3, gc), gd), ge)) → new_esEs22(yvy165, yvy167, gc, gd, ge)
new_esEs31(yvy40000, yvy30000, ty_@0) → new_esEs19(yvy40000, yvy30000)
new_esEs24(Right(yvy40000), Right(yvy30000), deg, app(ty_[], fda)) → new_esEs16(yvy40000, yvy30000, fda)
new_compare111(yvy233, yvy234, yvy235, yvy236, False, feg, feh) → GT
new_lt21(yvy153, yvy156, ty_Bool) → new_lt18(yvy153, yvy156)
new_ltEs6(LT, GT) → True
new_esEs33(yvy40002, yvy30002, ty_Int) → new_esEs25(yvy40002, yvy30002)
new_compare30(yvy400, yvy300, ty_Integer) → new_compare8(yvy400, yvy300)
new_ltEs23(yvy166, yvy168, app(ty_Maybe, bab)) → new_ltEs5(yvy166, yvy168, bab)
new_lt23(yvy165, yvy167, app(ty_Maybe, gh)) → new_lt14(yvy165, yvy167, gh)
new_ltEs21(yvy1001, yvy1011, ty_Char) → new_ltEs7(yvy1001, yvy1011)
new_ltEs14(Left(yvy1000), Left(yvy1010), app(app(ty_Either, cba), cbb), cab) → new_ltEs14(yvy1000, yvy1010, cba, cbb)
new_ltEs23(yvy166, yvy168, app(app(ty_@2, hh), baa)) → new_ltEs12(yvy166, yvy168, hh, baa)
new_ltEs21(yvy1001, yvy1011, ty_Ordering) → new_ltEs6(yvy1001, yvy1011)
new_esEs32(yvy40001, yvy30001, app(app(ty_@2, eef), eeg)) → new_esEs17(yvy40001, yvy30001, eef, eeg)
new_esEs24(Left(yvy40000), Left(yvy30000), app(ty_Maybe, fcf), deh) → new_esEs23(yvy40000, yvy30000, fcf)
new_lt22(yvy1000, yvy1010, app(ty_Ratio, ffa)) → new_lt10(yvy1000, yvy1010, ffa)
new_lt12(yvy152, yvy155, cg, da) → new_esEs12(new_compare7(yvy152, yvy155, cg, da), LT)
new_esEs35(yvy153, yvy156, ty_Int) → new_esEs25(yvy153, yvy156)
new_lt10(yvy152, yvy155, ecg) → new_esEs12(new_compare13(yvy152, yvy155, ecg), LT)
new_esEs4(yvy4000, yvy3000, ty_Double) → new_esEs13(yvy4000, yvy3000)
new_esEs8(yvy4001, yvy3001, app(app(ty_@2, cgd), cge)) → new_esEs17(yvy4001, yvy3001, cgd, cge)
new_esEs5(yvy4001, yvy3001, app(app(ty_@2, dfb), dfc)) → new_esEs17(yvy4001, yvy3001, dfb, dfc)
new_esEs16([], [], ddg) → True
new_lt22(yvy1000, yvy1010, ty_Float) → new_lt11(yvy1000, yvy1010)
new_esEs32(yvy40001, yvy30001, ty_Ordering) → new_esEs12(yvy40001, yvy30001)
new_ltEs19(yvy1002, yvy1012, ty_Int) → new_ltEs15(yvy1002, yvy1012)
new_ltEs21(yvy1001, yvy1011, ty_Integer) → new_ltEs4(yvy1001, yvy1011)
new_ltEs20(yvy154, yvy157, ty_Float) → new_ltEs11(yvy154, yvy157)
new_lt5(yvy1001, yvy1011, app(app(ty_@2, bcf), bcg)) → new_lt12(yvy1001, yvy1011, bcf, bcg)
new_esEs11(yvy4000, yvy3000, ty_Int) → new_esEs25(yvy4000, yvy3000)
new_esEs32(yvy40001, yvy30001, app(app(app(ty_@3, efa), efb), efc)) → new_esEs22(yvy40001, yvy30001, efa, efb, efc)
new_lt6(yvy1000, yvy1010, ty_Double) → new_lt13(yvy1000, yvy1010)
new_lt20(yvy152, yvy155, ty_Float) → new_lt11(yvy152, yvy155)
new_ltEs14(Left(yvy1000), Left(yvy1010), app(app(app(ty_@3, cac), cad), cae), cab) → new_ltEs10(yvy1000, yvy1010, cac, cad, cae)
new_esEs26(yvy40000, yvy30000, ty_Integer) → new_esEs18(yvy40000, yvy30000)
new_lt22(yvy1000, yvy1010, app(app(app(ty_@3, bfh), bga), bgb)) → new_lt4(yvy1000, yvy1010, bfh, bga, bgb)
new_esEs36(yvy1000, yvy1010, app(app(ty_Either, bgf), bgg)) → new_esEs24(yvy1000, yvy1010, bgf, bgg)
new_ltEs19(yvy1002, yvy1012, ty_Double) → new_ltEs13(yvy1002, yvy1012)
new_esEs27(yvy1000, yvy1010, ty_Ordering) → new_esEs12(yvy1000, yvy1010)
new_lt21(yvy153, yvy156, ty_Int) → new_lt17(yvy153, yvy156)
new_lt20(yvy152, yvy155, ty_Integer) → new_lt15(yvy152, yvy155)
new_esEs24(Right(yvy40000), Right(yvy30000), deg, ty_Ordering) → new_esEs12(yvy40000, yvy30000)
new_lt8(yvy152, yvy155) → new_esEs12(new_compare11(yvy152, yvy155), LT)
new_esEs9(yvy4000, yvy3000, ty_@0) → new_esEs19(yvy4000, yvy3000)
new_ltEs24(yvy100, yvy101, app(ty_[], bae)) → new_ltEs8(yvy100, yvy101, bae)
new_esEs22(@3(yvy40000, yvy40001, yvy40002), @3(yvy30000, yvy30001, yvy30002), dec, ded, dee) → new_asAs(new_esEs31(yvy40000, yvy30000, dec), new_asAs(new_esEs32(yvy40001, yvy30001, ded), new_esEs33(yvy40002, yvy30002, dee)))
new_esEs8(yvy4001, yvy3001, ty_Float) → new_esEs14(yvy4001, yvy3001)
new_esEs7(yvy4000, yvy3000, app(ty_Ratio, cfd)) → new_esEs21(yvy4000, yvy3000, cfd)
new_ltEs20(yvy154, yvy157, ty_Double) → new_ltEs13(yvy154, yvy157)
new_ltEs18(yvy107, yvy108, ty_Bool) → new_ltEs16(yvy107, yvy108)
new_compare28(yvy114, yvy115, False, cdg, ffc) → new_compare19(yvy114, yvy115, new_ltEs22(yvy114, yvy115, ffc), cdg, ffc)
new_esEs6(yvy4002, yvy3002, app(ty_Maybe, dcb)) → new_esEs23(yvy4002, yvy3002, dcb)
new_lt5(yvy1001, yvy1011, app(app(app(ty_@3, bcc), bcd), bce)) → new_lt4(yvy1001, yvy1011, bcc, bcd, bce)
new_esEs31(yvy40000, yvy30000, app(app(app(ty_@3, edg), edh), eea)) → new_esEs22(yvy40000, yvy30000, edg, edh, eea)
new_esEs31(yvy40000, yvy30000, ty_Ordering) → new_esEs12(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, ty_Double) → new_esEs13(yvy40002, yvy30002)
new_lt6(yvy1000, yvy1010, ty_Float) → new_lt11(yvy1000, yvy1010)
new_esEs7(yvy4000, yvy3000, app(app(ty_Either, cga), cgb)) → new_esEs24(yvy4000, yvy3000, cga, cgb)
new_esEs4(yvy4000, yvy3000, ty_Char) → new_esEs15(yvy4000, yvy3000)
new_compare112(yvy189, yvy190, False, fgb) → GT
new_esEs12(GT, GT) → True
new_ltEs21(yvy1001, yvy1011, app(app(app(ty_@3, bef), beg), beh)) → new_ltEs10(yvy1001, yvy1011, bef, beg, beh)
new_esEs5(yvy4001, yvy3001, ty_Double) → new_esEs13(yvy4001, yvy3001)
new_compare17(yvy218, yvy219, yvy220, yvy221, yvy222, yvy223, False, yvy225, ech, eda, edb) → new_compare14(yvy218, yvy219, yvy220, yvy221, yvy222, yvy223, yvy225, ech, eda, edb)
new_esEs8(yvy4001, yvy3001, app(ty_Maybe, chb)) → new_esEs23(yvy4001, yvy3001, chb)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_@0) → new_esEs19(yvy40000, yvy30000)
new_compare25(yvy152, yvy153, yvy154, yvy155, yvy156, yvy157, False, de, cb, cc) → new_compare17(yvy152, yvy153, yvy154, yvy155, yvy156, yvy157, new_lt20(yvy152, yvy155, de), new_asAs(new_esEs34(yvy152, yvy155, de), new_pePe(new_lt21(yvy153, yvy156, cb), new_asAs(new_esEs35(yvy153, yvy156, cb), new_ltEs20(yvy154, yvy157, cc)))), de, cb, cc)
new_compare31(Nothing, Just(yvy3000), bf) → LT
new_esEs29(yvy40000, yvy30000, ty_Ordering) → new_esEs12(yvy40000, yvy30000)
new_esEs4(yvy4000, yvy3000, app(ty_[], ddg)) → new_esEs16(yvy4000, yvy3000, ddg)
new_primPlusNat1(Zero, Zero) → Zero
new_compare0([], :(yvy3000, yvy3001), h) → LT
new_ltEs6(LT, EQ) → True
new_lt23(yvy165, yvy167, ty_Ordering) → new_lt7(yvy165, yvy167)
new_ltEs21(yvy1001, yvy1011, app(ty_Maybe, bfc)) → new_ltEs5(yvy1001, yvy1011, bfc)
new_ltEs6(GT, LT) → False
new_lt18(yvy152, yvy155) → new_esEs12(new_compare12(yvy152, yvy155), LT)
new_esEs24(Right(yvy40000), Right(yvy30000), deg, ty_Char) → new_esEs15(yvy40000, yvy30000)
new_asAs(True, yvy184) → yvy184
new_esEs26(yvy40000, yvy30000, ty_Float) → new_esEs14(yvy40000, yvy30000)
new_esEs35(yvy153, yvy156, ty_Float) → new_esEs14(yvy153, yvy156)
new_ltEs21(yvy1001, yvy1011, app(ty_[], bee)) → new_ltEs8(yvy1001, yvy1011, bee)
new_compare11(Char(yvy4000), Char(yvy3000)) → new_primCmpNat0(yvy4000, yvy3000)
new_ltEs22(yvy114, yvy115, ty_Float) → new_ltEs11(yvy114, yvy115)
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_esEs28(yvy1001, yvy1011, app(ty_Ratio, dhh)) → new_esEs21(yvy1001, yvy1011, dhh)
new_esEs39(yvy165, yvy167, ty_Double) → new_esEs13(yvy165, yvy167)
new_esEs11(yvy4000, yvy3000, ty_Bool) → new_esEs20(yvy4000, yvy3000)
new_ltEs22(yvy114, yvy115, ty_Double) → new_ltEs13(yvy114, yvy115)
new_lt22(yvy1000, yvy1010, ty_Ordering) → new_lt7(yvy1000, yvy1010)
new_esEs4(yvy4000, yvy3000, app(app(app(ty_@3, dec), ded), dee)) → new_esEs22(yvy4000, yvy3000, dec, ded, dee)
new_lt20(yvy152, yvy155, app(ty_Ratio, ecg)) → new_lt10(yvy152, yvy155, ecg)
new_ltEs16(False, False) → True
new_lt23(yvy165, yvy167, ty_Double) → new_lt13(yvy165, yvy167)
new_ltEs17(yvy100, yvy101) → new_fsEs(new_compare9(yvy100, yvy101))
new_esEs29(yvy40000, yvy30000, ty_Integer) → new_esEs18(yvy40000, yvy30000)
new_esEs8(yvy4001, yvy3001, ty_Ordering) → new_esEs12(yvy4001, yvy3001)
new_esEs30(yvy40001, yvy30001, ty_Bool) → new_esEs20(yvy40001, yvy30001)
new_lt23(yvy165, yvy167, app(ty_Ratio, ffe)) → new_lt10(yvy165, yvy167, ffe)
new_esEs30(yvy40001, yvy30001, ty_Int) → new_esEs25(yvy40001, yvy30001)
new_esEs27(yvy1000, yvy1010, ty_Float) → new_esEs14(yvy1000, yvy1010)
new_ltEs21(yvy1001, yvy1011, ty_Int) → new_ltEs15(yvy1001, yvy1011)
new_ltEs20(yvy154, yvy157, app(app(app(ty_@3, dg), dh), ea)) → new_ltEs10(yvy154, yvy157, dg, dh, ea)
new_esEs23(Just(yvy40000), Just(yvy30000), app(ty_[], fae)) → new_esEs16(yvy40000, yvy30000, fae)
new_esEs34(yvy152, yvy155, app(app(app(ty_@3, cd), ce), cf)) → new_esEs22(yvy152, yvy155, cd, ce, cf)
new_esEs9(yvy4000, yvy3000, app(app(app(ty_@3, ehe), ehf), ehg)) → new_esEs22(yvy4000, yvy3000, ehe, ehf, ehg)
new_esEs16(:(yvy40000, yvy40001), :(yvy30000, yvy30001), ddg) → new_asAs(new_esEs26(yvy40000, yvy30000, ddg), new_esEs16(yvy40001, yvy30001, ddg))
new_ltEs19(yvy1002, yvy1012, app(app(app(ty_@3, bba), bbb), bbc)) → new_ltEs10(yvy1002, yvy1012, bba, bbb, bbc)
new_ltEs20(yvy154, yvy157, ty_Ordering) → new_ltEs6(yvy154, yvy157)
new_compare19(yvy206, yvy207, False, fec, fed) → GT
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Integer) → new_ltEs4(yvy1000, yvy1010)
new_esEs6(yvy4002, yvy3002, ty_@0) → new_esEs19(yvy4002, yvy3002)
new_ltEs10(@3(yvy1000, yvy1001, yvy1002), @3(yvy1010, yvy1011, yvy1012), baf, bag, bcb) → new_pePe(new_lt6(yvy1000, yvy1010, baf), new_asAs(new_esEs27(yvy1000, yvy1010, baf), new_pePe(new_lt5(yvy1001, yvy1011, bag), new_asAs(new_esEs28(yvy1001, yvy1011, bag), new_ltEs19(yvy1002, yvy1012, bcb)))))
new_esEs33(yvy40002, yvy30002, ty_@0) → new_esEs19(yvy40002, yvy30002)
new_esEs35(yvy153, yvy156, app(ty_Ratio, fee)) → new_esEs21(yvy153, yvy156, fee)
new_ltEs22(yvy114, yvy115, ty_Int) → new_ltEs15(yvy114, yvy115)
new_ltEs24(yvy100, yvy101, app(app(app(ty_@3, baf), bag), bcb)) → new_ltEs10(yvy100, yvy101, baf, bag, bcb)
new_compare27(Right(yvy4000), Right(yvy3000), bg, bh) → new_compare28(yvy4000, yvy3000, new_esEs11(yvy4000, yvy3000, bh), bg, bh)
new_ltEs21(yvy1001, yvy1011, ty_@0) → new_ltEs17(yvy1001, yvy1011)
new_lt16(yvy152, yvy155, dc, dd) → new_esEs12(new_compare27(yvy152, yvy155, dc, dd), LT)
new_compare15(EQ, EQ) → EQ
new_ltEs22(yvy114, yvy115, ty_Char) → new_ltEs7(yvy114, yvy115)
new_compare30(yvy400, yvy300, ty_Double) → new_compare29(yvy400, yvy300)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCompAux0(yvy56, EQ) → yvy56
new_lt6(yvy1000, yvy1010, app(app(ty_@2, bdg), bdh)) → new_lt12(yvy1000, yvy1010, bdg, bdh)
new_esEs27(yvy1000, yvy1010, app(ty_Maybe, bea)) → new_esEs23(yvy1000, yvy1010, bea)
new_ltEs20(yvy154, yvy157, ty_Char) → new_ltEs7(yvy154, yvy157)
new_esEs10(yvy4000, yvy3000, ty_Integer) → new_esEs18(yvy4000, yvy3000)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_@0, cab) → new_ltEs17(yvy1000, yvy1010)
new_ltEs18(yvy107, yvy108, ty_Int) → new_ltEs15(yvy107, yvy108)
new_lt21(yvy153, yvy156, app(app(app(ty_@3, eh), fa), fb)) → new_lt4(yvy153, yvy156, eh, fa, fb)
new_esEs6(yvy4002, yvy3002, ty_Char) → new_esEs15(yvy4002, yvy3002)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_esEs30(yvy40001, yvy30001, ty_Char) → new_esEs15(yvy40001, yvy30001)
new_ltEs5(Just(yvy1000), Just(yvy1010), app(app(app(ty_@3, bha), bhb), bhc)) → new_ltEs10(yvy1000, yvy1010, bha, bhb, bhc)
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_esEs39(yvy165, yvy167, app(ty_[], ga)) → new_esEs16(yvy165, yvy167, ga)
new_esEs35(yvy153, yvy156, ty_Char) → new_esEs15(yvy153, yvy156)
new_not(True) → False
new_ltEs5(Just(yvy1000), Just(yvy1010), app(ty_Ratio, chh)) → new_ltEs9(yvy1000, yvy1010, chh)

The set Q consists of the following terms:

new_esEs36(x0, x1, ty_Char)
new_esEs29(x0, x1, ty_Float)
new_esEs7(x0, x1, ty_Int)
new_esEs24(Left(x0), Left(x1), ty_@0, x2)
new_esEs39(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs21(x0, x1, ty_Int)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs10(x0, x1, ty_Float)
new_ltEs16(True, True)
new_esEs6(x0, x1, ty_Int)
new_lt11(x0, x1)
new_lt6(x0, x1, app(ty_Maybe, x2))
new_compare110(x0, x1, x2, x3, True, x4, x5, x6)
new_lt6(x0, x1, app(ty_Ratio, x2))
new_ltEs20(x0, x1, ty_Int)
new_lt5(x0, x1, ty_Char)
new_ltEs23(x0, x1, app(ty_[], x2))
new_esEs31(x0, x1, app(ty_[], x2))
new_esEs9(x0, x1, app(ty_Maybe, x2))
new_esEs36(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs21(x0, x1, ty_@0)
new_esEs29(x0, x1, ty_Char)
new_ltEs22(x0, x1, ty_Integer)
new_esEs23(Just(x0), Just(x1), app(ty_Maybe, x2))
new_lt21(x0, x1, app(ty_Ratio, x2))
new_esEs32(x0, x1, ty_Int)
new_lt6(x0, x1, app(ty_[], x2))
new_esEs23(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs11(x0, x1, ty_Int)
new_lt5(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs23(x0, x1, app(ty_Ratio, x2))
new_esEs24(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs14(Left(x0), Left(x1), ty_Int, x2)
new_esEs4(x0, x1, ty_Float)
new_ltEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare17(x0, x1, x2, x3, x4, x5, False, x6, x7, x8, x9)
new_ltEs19(x0, x1, ty_Integer)
new_esEs16(:(x0, x1), [], x2)
new_compare30(x0, x1, ty_Int)
new_esEs34(x0, x1, app(app(ty_Either, x2), x3))
new_pePe(True, x0)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs11(x0, x1, ty_@0)
new_esEs35(x0, x1, ty_Integer)
new_esEs11(x0, x1, ty_Char)
new_esEs6(x0, x1, ty_Float)
new_compare28(x0, x1, False, x2, x3)
new_ltEs5(Nothing, Nothing, x0)
new_compare0([], [], x0)
new_esEs4(x0, x1, ty_Int)
new_lt14(x0, x1, x2)
new_lt22(x0, x1, ty_@0)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_[], x3))
new_compare30(x0, x1, ty_Bool)
new_lt20(x0, x1, ty_@0)
new_esEs29(x0, x1, ty_Ordering)
new_lt22(x0, x1, ty_Float)
new_esEs34(x0, x1, app(ty_Maybe, x2))
new_lt23(x0, x1, ty_Integer)
new_esEs5(x0, x1, app(ty_[], x2))
new_lt7(x0, x1)
new_esEs24(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs8(x0, x1, ty_Integer)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_esEs23(Just(x0), Just(x1), ty_Float)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(x0, x1, ty_Integer)
new_lt5(x0, x1, ty_@0)
new_esEs8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare10(x0, x1, False, x2, x3)
new_esEs32(x0, x1, app(ty_Ratio, x2))
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_lt23(x0, x1, app(ty_Ratio, x2))
new_esEs11(x0, x1, ty_Bool)
new_compare12(False, True)
new_compare10(x0, x1, True, x2, x3)
new_compare12(True, False)
new_esEs24(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs5(x0, x1, app(ty_Ratio, x2))
new_ltEs7(x0, x1)
new_esEs34(x0, x1, app(ty_[], x2))
new_ltEs18(x0, x1, app(ty_[], x2))
new_primCompAux0(x0, EQ)
new_esEs8(x0, x1, app(ty_Ratio, x2))
new_ltEs14(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs10(x0, x1, ty_Integer)
new_esEs32(x0, x1, ty_Ordering)
new_ltEs21(x0, x1, ty_Float)
new_ltEs24(x0, x1, ty_Integer)
new_esEs33(x0, x1, app(ty_Ratio, x2))
new_esEs34(x0, x1, ty_Float)
new_esEs35(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare112(x0, x1, False, x2)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs6(x0, x1, ty_@0)
new_lt6(x0, x1, ty_Float)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_lt21(x0, x1, app(ty_Maybe, x2))
new_esEs9(x0, x1, ty_Int)
new_compare30(x0, x1, ty_Integer)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_esEs36(x0, x1, ty_Int)
new_esEs24(Left(x0), Right(x1), x2, x3)
new_esEs24(Right(x0), Left(x1), x2, x3)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_esEs35(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, ty_Bool)
new_ltEs12(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs23(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs11(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_compare14(x0, x1, x2, x3, x4, x5, False, x6, x7, x8)
new_esEs24(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs9(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt5(x0, x1, ty_Double)
new_compare15(LT, LT)
new_esEs10(x0, x1, ty_Char)
new_esEs33(x0, x1, app(ty_Maybe, x2))
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_lt6(x0, x1, app(app(ty_@2, x2), x3))
new_esEs34(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_lt22(x0, x1, app(ty_[], x2))
new_esEs12(GT, GT)
new_compare14(x0, x1, x2, x3, x4, x5, True, x6, x7, x8)
new_esEs30(x0, x1, ty_Double)
new_ltEs21(x0, x1, ty_Ordering)
new_esEs24(Right(x0), Right(x1), x2, ty_Int)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_lt21(x0, x1, ty_Float)
new_esEs11(x0, x1, ty_Integer)
new_esEs5(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_lt5(x0, x1, app(ty_Maybe, x2))
new_esEs16([], :(x0, x1), x2)
new_compare31(Nothing, Nothing, x0)
new_esEs23(Just(x0), Just(x1), ty_Double)
new_esEs10(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, ty_Char)
new_esEs38(x0, x1, ty_Integer)
new_esEs10(x0, x1, app(app(ty_Either, x2), x3))
new_esEs39(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Bool)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs6(EQ, EQ)
new_esEs32(x0, x1, ty_@0)
new_esEs7(x0, x1, ty_Float)
new_esEs24(Left(x0), Left(x1), ty_Float, x2)
new_ltEs22(x0, x1, ty_Char)
new_esEs24(Right(x0), Right(x1), x2, ty_@0)
new_lt16(x0, x1, x2, x3)
new_esEs6(x0, x1, ty_Double)
new_ltEs14(Left(x0), Left(x1), ty_Float, x2)
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_esEs5(x0, x1, ty_Bool)
new_esEs31(x0, x1, ty_Int)
new_esEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt22(x0, x1, app(ty_Maybe, x2))
new_esEs33(x0, x1, ty_Double)
new_esEs8(x0, x1, ty_Float)
new_ltEs14(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs18(x0, x1, ty_@0)
new_compare30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs22(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs5(Just(x0), Just(x1), ty_@0)
new_lt5(x0, x1, ty_Int)
new_ltEs6(LT, EQ)
new_ltEs6(EQ, LT)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_primCompAux0(x0, LT)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs38(x0, x1, ty_Int)
new_compare210(x0, x1, True, x2)
new_esEs7(x0, x1, app(ty_Ratio, x2))
new_esEs24(Right(x0), Right(x1), x2, ty_Bool)
new_esEs23(Just(x0), Just(x1), ty_Int)
new_ltEs20(x0, x1, ty_@0)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Int)
new_lt17(x0, x1)
new_esEs24(Right(x0), Right(x1), x2, ty_Double)
new_ltEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs36(x0, x1, ty_Bool)
new_primEqNat0(Zero, Zero)
new_compare13(:%(x0, x1), :%(x2, x3), ty_Int)
new_compare30(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Left(x0), Left(x1), ty_Char, x2)
new_esEs26(x0, x1, ty_@0)
new_esEs6(x0, x1, app(ty_Maybe, x2))
new_esEs7(x0, x1, ty_Bool)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs5(x0, x1, ty_Float)
new_esEs11(x0, x1, app(ty_Ratio, x2))
new_ltEs22(x0, x1, ty_Float)
new_esEs7(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_compare15(GT, GT)
new_esEs31(x0, x1, ty_Double)
new_ltEs20(x0, x1, ty_Integer)
new_lt22(x0, x1, ty_Bool)
new_esEs36(x0, x1, app(app(ty_@2, x2), x3))
new_esEs34(x0, x1, ty_Bool)
new_esEs31(x0, x1, ty_Integer)
new_ltEs14(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare24(x0, x1, x2, x3, True, x4, x5)
new_compare7(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, ty_Char)
new_lt20(x0, x1, ty_Double)
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs15(x0, x1)
new_esEs4(x0, x1, ty_Integer)
new_esEs39(x0, x1, ty_Bool)
new_compare31(Nothing, Just(x0), x1)
new_ltEs24(x0, x1, ty_Float)
new_compare27(Right(x0), Left(x1), x2, x3)
new_esEs6(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, ty_Float)
new_esEs4(x0, x1, app(ty_Ratio, x2))
new_compare27(Left(x0), Right(x1), x2, x3)
new_primMulNat0(Zero, Zero)
new_asAs(True, x0)
new_compare110(x0, x1, x2, x3, False, x4, x5, x6)
new_esEs10(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Double)
new_esEs5(x0, x1, ty_Double)
new_fsEs(x0)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs24(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs5(Just(x0), Just(x1), ty_Integer)
new_compare27(Left(x0), Left(x1), x2, x3)
new_lt6(x0, x1, ty_Double)
new_lt22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs9(x0, x1, app(app(ty_Either, x2), x3))
new_esEs35(x0, x1, ty_Double)
new_lt23(x0, x1, app(ty_Maybe, x2))
new_ltEs18(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_Float)
new_esEs36(x0, x1, app(ty_[], x2))
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(Just(x0), Just(x1), ty_Double)
new_lt22(x0, x1, ty_Ordering)
new_ltEs21(x0, x1, app(ty_Ratio, x2))
new_ltEs14(Left(x0), Left(x1), ty_Bool, x2)
new_esEs9(x0, x1, ty_@0)
new_esEs35(x0, x1, ty_Bool)
new_esEs35(x0, x1, ty_Char)
new_ltEs23(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, ty_Bool)
new_esEs31(x0, x1, ty_@0)
new_ltEs14(Right(x0), Right(x1), x2, ty_Double)
new_ltEs19(x0, x1, ty_Double)
new_ltEs24(x0, x1, ty_Double)
new_esEs13(Double(x0, x1), Double(x2, x3))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_ltEs24(x0, x1, app(ty_Maybe, x2))
new_esEs23(Nothing, Nothing, x0)
new_esEs26(x0, x1, ty_Ordering)
new_compare112(x0, x1, True, x2)
new_ltEs14(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_compare31(Just(x0), Nothing, x1)
new_esEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs20(True, True)
new_lt22(x0, x1, ty_Int)
new_ltEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(x0, x1, ty_Integer)
new_esEs30(x0, x1, ty_Bool)
new_lt21(x0, x1, ty_@0)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs33(x0, x1, ty_Float)
new_ltEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, ty_Integer)
new_ltEs21(x0, x1, ty_Integer)
new_lt21(x0, x1, app(ty_[], x2))
new_primPlusNat0(Zero, x0)
new_compare25(x0, x1, x2, x3, x4, x5, False, x6, x7, x8)
new_compare19(x0, x1, True, x2, x3)
new_esEs4(x0, x1, ty_Ordering)
new_esEs8(x0, x1, ty_Bool)
new_esEs24(Right(x0), Right(x1), x2, ty_Float)
new_compare111(x0, x1, x2, x3, False, x4, x5)
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_esEs5(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Left(x0), Left(x1), app(ty_[], x2), x3)
new_primPlusNat0(Succ(x0), x1)
new_ltEs4(x0, x1)
new_esEs9(x0, x1, app(ty_Ratio, x2))
new_compare31(Just(x0), Just(x1), x2)
new_esEs34(x0, x1, ty_Integer)
new_esEs31(x0, x1, ty_Ordering)
new_esEs7(x0, x1, app(ty_[], x2))
new_ltEs6(GT, LT)
new_ltEs6(LT, GT)
new_esEs11(x0, x1, app(ty_Maybe, x2))
new_esEs11(x0, x1, ty_Double)
new_lt19(x0, x1)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs22(x0, x1, app(ty_[], x2))
new_esEs4(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs4(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Double)
new_esEs39(x0, x1, ty_Char)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_compare15(EQ, EQ)
new_esEs16([], [], x0)
new_lt6(x0, x1, ty_Int)
new_ltEs10(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_lt21(x0, x1, ty_Ordering)
new_esEs28(x0, x1, ty_Ordering)
new_ltEs14(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs22(x0, x1, ty_Ordering)
new_esEs11(x0, x1, app(ty_[], x2))
new_ltEs11(x0, x1)
new_lt20(x0, x1, ty_Float)
new_lt21(x0, x1, ty_Integer)
new_esEs32(x0, x1, ty_Bool)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs39(x0, x1, ty_Float)
new_ltEs5(Nothing, Just(x0), x1)
new_lt5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs8(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(x0, x1, app(ty_[], x2))
new_lt6(x0, x1, ty_Integer)
new_esEs10(x0, x1, ty_Double)
new_sr0(x0, x1)
new_esEs23(Just(x0), Just(x1), ty_Integer)
new_esEs20(False, True)
new_esEs20(True, False)
new_esEs29(x0, x1, ty_Bool)
new_ltEs23(x0, x1, ty_Integer)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs34(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs20(False, False)
new_esEs36(x0, x1, app(ty_Ratio, x2))
new_compare12(False, False)
new_esEs12(LT, EQ)
new_esEs12(EQ, LT)
new_lt21(x0, x1, ty_Int)
new_lt22(x0, x1, ty_Char)
new_lt10(x0, x1, x2)
new_esEs31(x0, x1, ty_Float)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_primPlusNat1(Zero, Zero)
new_ltEs21(x0, x1, ty_Bool)
new_ltEs20(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_Float)
new_esEs12(EQ, EQ)
new_esEs23(Just(x0), Just(x1), ty_Bool)
new_esEs27(x0, x1, ty_Char)
new_esEs9(x0, x1, ty_Integer)
new_esEs30(x0, x1, ty_Float)
new_ltEs20(x0, x1, ty_Float)
new_ltEs14(Right(x0), Right(x1), x2, ty_Bool)
new_compare0([], :(x0, x1), x2)
new_ltEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs28(x0, x1, ty_Double)
new_esEs30(x0, x1, ty_Char)
new_compare30(x0, x1, ty_@0)
new_esEs6(x0, x1, ty_Bool)
new_lt6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(Left(x0), Left(x1), ty_Char, x2)
new_ltEs23(x0, x1, ty_Float)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_ltEs9(x0, x1, x2)
new_esEs17(@2(x0, x1), @2(x2, x3), x4, x5)
new_compare15(EQ, GT)
new_compare15(GT, EQ)
new_ltEs24(x0, x1, ty_Ordering)
new_esEs8(x0, x1, app(ty_[], x2))
new_compare30(x0, x1, ty_Char)
new_primEqNat0(Succ(x0), Zero)
new_compare15(LT, GT)
new_compare15(GT, LT)
new_esEs32(x0, x1, app(ty_Maybe, x2))
new_esEs36(x0, x1, ty_Double)
new_esEs39(x0, x1, ty_Ordering)
new_ltEs14(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs4(x0, x1, app(app(ty_@2, x2), x3))
new_compare6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs37(x0, x1, ty_Int)
new_esEs9(x0, x1, ty_Double)
new_primMulInt(Neg(x0), Neg(x1))
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, app(ty_[], x2))
new_ltEs17(x0, x1)
new_esEs9(x0, x1, ty_Ordering)
new_esEs26(x0, x1, ty_Char)
new_esEs12(GT, LT)
new_esEs12(LT, GT)
new_ltEs23(x0, x1, ty_Int)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs21(:%(x0, x1), :%(x2, x3), x4)
new_esEs32(x0, x1, app(ty_[], x2))
new_esEs24(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare28(x0, x1, True, x2, x3)
new_esEs8(x0, x1, ty_Int)
new_esEs23(Just(x0), Just(x1), app(ty_[], x2))
new_compare30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare30(x0, x1, app(ty_[], x2))
new_ltEs5(Just(x0), Just(x1), ty_Int)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs33(x0, x1, ty_Int)
new_esEs36(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs23(x0, x1, ty_@0)
new_ltEs14(Right(x0), Right(x1), x2, ty_Float)
new_esEs33(x0, x1, ty_Bool)
new_esEs10(x0, x1, ty_Ordering)
new_esEs35(x0, x1, ty_@0)
new_esEs4(x0, x1, ty_Char)
new_lt23(x0, x1, ty_Int)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs30(x0, x1, app(ty_[], x2))
new_ltEs18(x0, x1, ty_Double)
new_lt23(x0, x1, ty_Bool)
new_esEs8(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_lt21(x0, x1, ty_Bool)
new_compare111(x0, x1, x2, x3, True, x4, x5)
new_esEs9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(Left(x0), Left(x1), ty_Integer, x2)
new_compare18(Float(x0, x1), Float(x2, x3))
new_ltEs5(Just(x0), Just(x1), ty_Float)
new_ltEs14(Right(x0), Right(x1), x2, ty_@0)
new_lt21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, ty_Bool)
new_lt6(x0, x1, ty_Bool)
new_esEs30(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Integer)
new_ltEs21(x0, x1, app(ty_Maybe, x2))
new_esEs8(x0, x1, ty_Double)
new_lt21(x0, x1, ty_Char)
new_lt5(x0, x1, ty_Float)
new_compare11(Char(x0), Char(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs7(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs30(x0, x1, ty_Integer)
new_esEs25(x0, x1)
new_esEs24(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs29(x0, x1, ty_@0)
new_sr(Integer(x0), Integer(x1))
new_ltEs8(x0, x1, x2)
new_lt5(x0, x1, app(ty_[], x2))
new_primEqInt(Neg(Zero), Neg(Zero))
new_compare24(x0, x1, x2, x3, False, x4, x5)
new_esEs7(x0, x1, ty_@0)
new_esEs8(x0, x1, app(app(ty_@2, x2), x3))
new_primMulNat0(Succ(x0), Succ(x1))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs34(x0, x1, ty_Char)
new_esEs10(x0, x1, ty_Bool)
new_compare210(x0, x1, False, x2)
new_esEs6(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(x0, x1, ty_@0)
new_esEs24(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs39(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_@0)
new_esEs24(Left(x0), Left(x1), ty_Int, x2)
new_esEs7(x0, x1, app(app(ty_@2, x2), x3))
new_esEs31(x0, x1, ty_Bool)
new_ltEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_lt22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqNat0(Zero, Succ(x0))
new_esEs39(x0, x1, app(ty_Maybe, x2))
new_primPlusNat1(Succ(x0), Zero)
new_lt23(x0, x1, ty_Char)
new_lt20(x0, x1, ty_Char)
new_esEs11(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs24(x0, x1, app(ty_Ratio, x2))
new_esEs6(x0, x1, ty_Ordering)
new_esEs33(x0, x1, ty_Char)
new_esEs24(Left(x0), Left(x1), ty_Double, x2)
new_lt22(x0, x1, app(ty_Ratio, x2))
new_esEs32(x0, x1, ty_Integer)
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_esEs34(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs5(Just(x0), Just(x1), app(ty_[], x2))
new_pePe(False, x0)
new_ltEs24(x0, x1, ty_Int)
new_compare0(:(x0, x1), [], x2)
new_lt8(x0, x1)
new_ltEs14(Left(x0), Right(x1), x2, x3)
new_ltEs14(Right(x0), Left(x1), x2, x3)
new_lt23(x0, x1, ty_Double)
new_ltEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs32(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Bool)
new_esEs35(x0, x1, app(ty_Maybe, x2))
new_esEs29(x0, x1, ty_Int)
new_esEs31(x0, x1, app(ty_Maybe, x2))
new_esEs30(x0, x1, ty_Ordering)
new_lt23(x0, x1, ty_Float)
new_lt6(x0, x1, ty_@0)
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs33(x0, x1, app(app(ty_Either, x2), x3))
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs31(x0, x1, ty_Char)
new_lt22(x0, x1, ty_Double)
new_lt21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs22(x0, x1, ty_@0)
new_esEs39(x0, x1, ty_Int)
new_esEs30(x0, x1, ty_@0)
new_esEs31(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs16(False, True)
new_ltEs16(True, False)
new_ltEs6(GT, GT)
new_esEs24(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs24(Left(x0), Left(x1), ty_Bool, x2)
new_lt23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs10(x0, x1, ty_Int)
new_compare26(x0, x1, True, x2, x3)
new_esEs32(x0, x1, ty_Char)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_ltEs18(x0, x1, ty_Int)
new_esEs6(x0, x1, app(ty_Ratio, x2))
new_esEs4(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(Just(x0), Just(x1), ty_Ordering)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_ltEs19(x0, x1, ty_Char)
new_ltEs22(x0, x1, app(ty_Maybe, x2))
new_ltEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs5(Just(x0), Just(x1), ty_Char)
new_esEs27(x0, x1, ty_Int)
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs24(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_lt21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs5(Just(x0), Just(x1), ty_Bool)
new_lt22(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_@0)
new_ltEs22(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_Integer)
new_esEs33(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Int)
new_primCmpNat0(Zero, Zero)
new_esEs35(x0, x1, ty_Float)
new_asAs(False, x0)
new_lt5(x0, x1, ty_Integer)
new_ltEs24(x0, x1, ty_@0)
new_ltEs19(x0, x1, ty_Int)
new_lt23(x0, x1, ty_@0)
new_esEs39(x0, x1, app(ty_Ratio, x2))
new_esEs34(x0, x1, ty_Int)
new_ltEs6(LT, LT)
new_esEs9(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_ltEs23(x0, x1, app(ty_Maybe, x2))
new_esEs31(x0, x1, app(app(ty_Either, x2), x3))
new_esEs11(x0, x1, ty_Ordering)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs22(x0, x1, ty_Double)
new_compare30(x0, x1, app(ty_Ratio, x2))
new_ltEs24(x0, x1, ty_Char)
new_esEs34(x0, x1, app(ty_Ratio, x2))
new_esEs18(Integer(x0), Integer(x1))
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Int)
new_esEs23(Just(x0), Just(x1), ty_@0)
new_compare17(x0, x1, x2, x3, x4, x5, True, x6, x7, x8, x9)
new_ltEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, ty_Float)
new_esEs6(x0, x1, ty_Char)
new_lt21(x0, x1, ty_Double)
new_esEs35(x0, x1, app(ty_[], x2))
new_ltEs14(Right(x0), Right(x1), x2, ty_Char)
new_lt4(x0, x1, x2, x3, x4)
new_esEs16(:(x0, x1), :(x2, x3), x4)
new_compare26(x0, x1, False, x2, x3)
new_ltEs14(Left(x0), Left(x1), ty_@0, x2)
new_compare19(x0, x1, False, x2, x3)
new_esEs5(x0, x1, app(app(ty_@2, x2), x3))
new_esEs10(x0, x1, app(ty_Maybe, x2))
new_ltEs21(x0, x1, app(ty_[], x2))
new_lt5(x0, x1, ty_Bool)
new_esEs23(Just(x0), Just(x1), ty_Char)
new_ltEs13(x0, x1)
new_esEs35(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs24(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs23(x0, x1, ty_Bool)
new_compare15(LT, EQ)
new_compare15(EQ, LT)
new_compare9(@0, @0)
new_lt23(x0, x1, app(app(ty_@2, x2), x3))
new_lt13(x0, x1)
new_esEs36(x0, x1, ty_Integer)
new_esEs29(x0, x1, ty_Double)
new_compare27(Right(x0), Right(x1), x2, x3)
new_esEs31(x0, x1, app(ty_Ratio, x2))
new_ltEs14(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs18(x0, x1, ty_Float)
new_lt18(x0, x1)
new_ltEs5(Just(x0), Nothing, x1)
new_lt5(x0, x1, ty_Ordering)
new_lt15(x0, x1)
new_compare8(Integer(x0), Integer(x1))
new_esEs28(x0, x1, app(ty_[], x2))
new_lt6(x0, x1, app(app(ty_Either, x2), x3))
new_primCompAux1(x0, x1, x2, x3)
new_esEs8(x0, x1, ty_@0)
new_esEs33(x0, x1, app(ty_[], x2))
new_esEs5(x0, x1, ty_Int)
new_not(True)
new_compare30(x0, x1, ty_Float)
new_esEs27(x0, x1, ty_Ordering)
new_primMulInt(Pos(x0), Pos(x1))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_lt22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(x0, x1, ty_Bool)
new_esEs32(x0, x1, ty_Float)
new_esEs36(x0, x1, ty_Ordering)
new_esEs9(x0, x1, ty_Bool)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_not(False)
new_compare29(Double(x0, x1), Double(x2, x3))
new_lt5(x0, x1, app(ty_Ratio, x2))
new_compare13(:%(x0, x1), :%(x2, x3), ty_Integer)
new_primCmpNat0(Succ(x0), Succ(x1))
new_esEs7(x0, x1, ty_Ordering)
new_ltEs23(x0, x1, ty_Char)
new_esEs8(x0, x1, ty_Ordering)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_esEs39(x0, x1, ty_@0)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs21(x0, x1, ty_Char)
new_esEs24(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs15(Char(x0), Char(x1))
new_esEs4(x0, x1, app(ty_[], x2))
new_esEs24(Right(x0), Right(x1), x2, ty_Char)
new_ltEs6(GT, EQ)
new_ltEs6(EQ, GT)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_esEs33(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpNat0(Zero, Succ(x0))
new_lt5(x0, x1, app(app(ty_Either, x2), x3))
new_esEs39(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs35(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs21(x0, x1, ty_Double)
new_compare30(x0, x1, app(app(ty_@2, x2), x3))
new_compare30(x0, x1, ty_Double)
new_primCmpNat0(Succ(x0), Zero)
new_esEs34(x0, x1, ty_Double)
new_esEs39(x0, x1, app(ty_[], x2))
new_ltEs14(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs24(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs7(x0, x1, app(ty_Maybe, x2))
new_ltEs22(x0, x1, ty_Int)
new_esEs27(x0, x1, app(ty_[], x2))
new_compare16(x0, x1)
new_ltEs20(x0, x1, ty_Double)
new_ltEs24(x0, x1, ty_Bool)
new_esEs35(x0, x1, ty_Ordering)
new_ltEs18(x0, x1, ty_Integer)
new_compare25(x0, x1, x2, x3, x4, x5, True, x6, x7, x8)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs34(x0, x1, ty_@0)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs37(x0, x1, ty_Integer)
new_ltEs18(x0, x1, ty_Char)
new_esEs7(x0, x1, ty_Double)
new_lt23(x0, x1, ty_Ordering)
new_esEs33(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs9(x0, x1, ty_Float)
new_esEs23(Just(x0), Just(x1), ty_Ordering)
new_lt6(x0, x1, ty_Char)
new_ltEs23(x0, x1, app(app(ty_Either, x2), x3))
new_lt23(x0, x1, app(ty_[], x2))
new_esEs9(x0, x1, ty_Char)
new_esEs8(x0, x1, ty_Char)
new_esEs10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs35(x0, x1, ty_Int)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs33(x0, x1, ty_@0)
new_lt12(x0, x1, x2, x3)
new_esEs5(x0, x1, ty_Ordering)
new_esEs32(x0, x1, ty_Double)
new_esEs23(Just(x0), Nothing, x1)
new_ltEs14(Right(x0), Right(x1), x2, ty_Int)
new_esEs14(Float(x0, x1), Float(x2, x3))
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, ty_Integer)
new_esEs5(x0, x1, ty_@0)
new_esEs5(x0, x1, ty_Char)
new_esEs7(x0, x1, ty_Char)
new_lt23(x0, x1, app(app(ty_Either, x2), x3))
new_compare12(True, True)
new_esEs36(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs23(Nothing, Just(x0), x1)
new_esEs5(x0, x1, ty_Integer)
new_esEs32(x0, x1, app(app(ty_Either, x2), x3))
new_compare30(x0, x1, ty_Ordering)
new_lt20(x0, x1, app(ty_[], x2))
new_primMulNat0(Zero, Succ(x0))
new_ltEs23(x0, x1, ty_Double)
new_ltEs24(x0, x1, app(ty_[], x2))
new_ltEs14(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs14(Left(x0), Left(x1), ty_Double, x2)
new_esEs6(x0, x1, app(ty_[], x2))
new_primCompAux0(x0, GT)
new_lt6(x0, x1, ty_Ordering)
new_primPlusNat1(Zero, Succ(x0))
new_esEs36(x0, x1, ty_Float)
new_esEs19(@0, @0)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs24(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs36(x0, x1, ty_@0)
new_esEs12(LT, LT)
new_esEs28(x0, x1, ty_Integer)
new_esEs4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt9(x0, x1, x2)
new_ltEs18(x0, x1, ty_Ordering)
new_ltEs16(False, False)
new_ltEs22(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs33(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, ty_Ordering)
new_esEs28(x0, x1, ty_@0)
new_esEs11(x0, x1, ty_Float)
new_ltEs22(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs39(x0, x1, ty_Integer)

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

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



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

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

new_addToFM_C(Branch(:(yvy500, yvy501), yvy51, yvy52, yvy53, yvy54), [], yvy41, h, ba) → new_addToFM_C(yvy53, [], yvy41, h, ba)
new_addToFM_C(Branch(:(yvy500, yvy501), yvy51, yvy52, yvy53, yvy54), :(yvy400, yvy401), yvy41, h, ba) → new_addToFM_C2(yvy500, yvy501, yvy51, yvy52, yvy53, yvy54, yvy400, yvy401, yvy41, new_primCompAux1(yvy400, yvy500, new_compare0(yvy401, yvy501, h), h), h, ba)
new_addToFM_C20(yvy500, yvy501, yvy51, yvy52, yvy53, yvy54, yvy400, yvy401, yvy41, h, ba) → new_addToFM_C1(yvy500, yvy501, yvy51, yvy52, yvy53, yvy54, yvy400, yvy401, yvy41, new_compare0(:(yvy400, yvy401), :(yvy500, yvy501), h), h, ba)
new_addToFM_C10(yvy51, yvy52, yvy53, yvy54, yvy400, yvy401, yvy41, GT, h, ba) → new_addToFM_C(yvy54, :(yvy400, yvy401), yvy41, h, ba)
new_addToFM_C11(yvy51, yvy52, yvy53, yvy54, yvy41, GT, h, ba) → new_addToFM_C(yvy54, [], yvy41, h, ba)
new_addToFM_C2(yvy500, yvy501, yvy51, yvy52, yvy53, yvy54, yvy400, yvy401, yvy41, EQ, h, ba) → new_addToFM_C1(yvy500, yvy501, yvy51, yvy52, yvy53, yvy54, yvy400, yvy401, yvy41, new_compare0(:(yvy400, yvy401), :(yvy500, yvy501), h), h, ba)
new_addToFM_C2(yvy500, yvy501, yvy51, yvy52, yvy53, yvy54, yvy400, yvy401, yvy41, LT, h, ba) → new_addToFM_C(yvy53, :(yvy400, yvy401), yvy41, h, ba)
new_addToFM_C(Branch([], yvy51, yvy52, yvy53, yvy54), [], yvy41, h, ba) → new_addToFM_C11(yvy51, yvy52, yvy53, yvy54, yvy41, new_compare0([], [], h), h, ba)
new_addToFM_C1(yvy500, yvy501, yvy51, yvy52, yvy53, yvy54, yvy400, yvy401, yvy41, GT, h, ba) → new_addToFM_C(yvy54, :(yvy400, yvy401), yvy41, h, ba)
new_addToFM_C(Branch([], yvy51, yvy52, yvy53, yvy54), :(yvy400, yvy401), yvy41, h, ba) → new_addToFM_C10(yvy51, yvy52, yvy53, yvy54, yvy400, yvy401, yvy41, new_compare0(:(yvy400, yvy401), [], h), h, ba)
new_addToFM_C2(yvy500, yvy501, yvy51, yvy52, yvy53, yvy54, yvy400, yvy401, yvy41, GT, h, ba) → new_addToFM_C20(yvy500, yvy501, yvy51, yvy52, yvy53, yvy54, yvy400, yvy401, yvy41, h, ba)

The TRS R consists of the following rules:

new_compare210(yvy100, yvy101, False, fee) → new_compare112(yvy100, yvy101, new_ltEs24(yvy100, yvy101, fee), fee)
new_compare7(@2(yvy4000, yvy4001), @2(yvy3000, yvy3001), be, bf) → new_compare24(yvy4000, yvy4001, yvy3000, yvy3001, new_asAs(new_esEs7(yvy4000, yvy3000, be), new_esEs8(yvy4001, yvy3001, bf)), be, bf)
new_esEs24(Left(yvy40000), Left(yvy30000), app(ty_Ratio, def), hf) → new_esEs21(yvy40000, yvy30000, def)
new_ltEs19(yvy1002, yvy1012, app(ty_[], bhh)) → new_ltEs8(yvy1002, yvy1012, bhh)
new_compare112(yvy189, yvy190, True, fgc) → LT
new_lt22(yvy1000, yvy1010, ty_Int) → new_lt17(yvy1000, yvy1010)
new_ltEs22(yvy114, yvy115, app(app(ty_@2, fba), fbb)) → new_ltEs12(yvy114, yvy115, fba, fbb)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Int, hf) → new_esEs25(yvy40000, yvy30000)
new_esEs6(yvy4002, yvy3002, app(app(app(ty_@3, bbe), bbf), bbg)) → new_esEs22(yvy4002, yvy3002, bbe, bbf, bbg)
new_esEs27(yvy1000, yvy1010, app(ty_[], bfd)) → new_esEs16(yvy1000, yvy1010, bfd)
new_esEs20(True, True) → True
new_esEs35(yvy153, yvy156, app(ty_[], dhh)) → new_esEs16(yvy153, yvy156, dhh)
new_compare8(Integer(yvy4000), Integer(yvy3000)) → new_primCmpInt(yvy4000, yvy3000)
new_esEs8(yvy4001, yvy3001, ty_Bool) → new_esEs20(yvy4001, yvy3001)
new_esEs11(yvy4000, yvy3000, ty_Integer) → new_esEs18(yvy4000, yvy3000)
new_esEs27(yvy1000, yvy1010, app(app(ty_@2, bga), bgb)) → new_esEs17(yvy1000, yvy1010, bga, bgb)
new_ltEs20(yvy154, yvy157, app(ty_Ratio, ebc)) → new_ltEs9(yvy154, yvy157, ebc)
new_esEs36(yvy1000, yvy1010, ty_Double) → new_esEs13(yvy1000, yvy1010)
new_esEs28(yvy1001, yvy1011, ty_Float) → new_esEs14(yvy1001, yvy1011)
new_lt6(yvy1000, yvy1010, ty_@0) → new_lt19(yvy1000, yvy1010)
new_compare10(yvy199, yvy200, True, ed, ee) → LT
new_esEs9(yvy4000, yvy3000, ty_Int) → new_esEs25(yvy4000, yvy3000)
new_esEs24(Right(yvy40000), Right(yvy30000), he, ty_Double) → new_esEs13(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, app(app(ty_@2, cgh), cha)) → new_esEs17(yvy40002, yvy30002, cgh, cha)
new_ltEs24(yvy100, yvy101, app(ty_Ratio, cdf)) → new_ltEs9(yvy100, yvy101, cdf)
new_esEs24(Right(yvy40000), Right(yvy30000), he, ty_@0) → new_esEs19(yvy40000, yvy30000)
new_ltEs19(yvy1002, yvy1012, ty_Float) → new_ltEs11(yvy1002, yvy1012)
new_esEs11(yvy4000, yvy3000, app(ty_[], egh)) → new_esEs16(yvy4000, yvy3000, egh)
new_lt23(yvy165, yvy167, app(app(app(ty_@3, fcb), fcc), fcd)) → new_lt4(yvy165, yvy167, fcb, fcc, fcd)
new_esEs7(yvy4000, yvy3000, ty_Double) → new_esEs13(yvy4000, yvy3000)
new_esEs9(yvy4000, yvy3000, ty_Char) → new_esEs15(yvy4000, yvy3000)
new_ltEs23(yvy166, yvy168, ty_Ordering) → new_ltEs6(yvy166, yvy168)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Bool, daa) → new_ltEs16(yvy1000, yvy1010)
new_esEs39(yvy165, yvy167, app(ty_Ratio, fca)) → new_esEs21(yvy165, yvy167, fca)
new_esEs10(yvy4000, yvy3000, ty_@0) → new_esEs19(yvy4000, yvy3000)
new_esEs21(:%(yvy40000, yvy40001), :%(yvy30000, yvy30001), gh) → new_asAs(new_esEs37(yvy40000, yvy30000, gh), new_esEs38(yvy40001, yvy30001, gh))
new_lt5(yvy1001, yvy1011, app(ty_Ratio, bgg)) → new_lt10(yvy1001, yvy1011, bgg)
new_compare13(:%(yvy4000, yvy4001), :%(yvy3000, yvy3001), ty_Integer) → new_compare8(new_sr(yvy4000, yvy3001), new_sr(yvy3000, yvy4001))
new_ltEs22(yvy114, yvy115, app(ty_Ratio, fae)) → new_ltEs9(yvy114, yvy115, fae)
new_ltEs23(yvy166, yvy168, ty_Int) → new_ltEs15(yvy166, yvy168)
new_primMulNat0(Zero, Zero) → Zero
new_ltEs24(yvy100, yvy101, ty_Ordering) → new_ltEs6(yvy100, yvy101)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbd, ty_Float) → new_ltEs11(yvy1000, yvy1010)
new_esEs39(yvy165, yvy167, app(ty_Maybe, fcg)) → new_esEs23(yvy165, yvy167, fcg)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Bool, hf) → new_esEs20(yvy40000, yvy30000)
new_compare15(LT, LT) → EQ
new_esEs6(yvy4002, yvy3002, app(app(ty_@2, bbb), bbc)) → new_esEs17(yvy4002, yvy3002, bbb, bbc)
new_esEs4(yvy4000, yvy3000, ty_Integer) → new_esEs18(yvy4000, yvy3000)
new_esEs26(yvy40000, yvy30000, app(ty_[], bcc)) → new_esEs16(yvy40000, yvy30000, bcc)
new_esEs36(yvy1000, yvy1010, ty_Char) → new_esEs15(yvy1000, yvy1010)
new_esEs28(yvy1001, yvy1011, app(app(ty_Either, bhf), bhg)) → new_esEs24(yvy1001, yvy1011, bhf, bhg)
new_esEs34(yvy152, yvy155, ty_@0) → new_esEs19(yvy152, yvy155)
new_sr(Integer(yvy30000), Integer(yvy40010)) → Integer(new_primMulInt(yvy30000, yvy40010))
new_esEs7(yvy4000, yvy3000, ty_Float) → new_esEs14(yvy4000, yvy3000)
new_compare12(True, False) → GT
new_lt7(yvy152, yvy155) → new_esEs12(new_compare15(yvy152, yvy155), LT)
new_lt22(yvy1000, yvy1010, app(ty_Maybe, edg)) → new_lt14(yvy1000, yvy1010, edg)
new_ltEs24(yvy100, yvy101, app(ty_Maybe, ef)) → new_ltEs5(yvy100, yvy101, ef)
new_esEs35(yvy153, yvy156, app(app(ty_Either, eah), eba)) → new_esEs24(yvy153, yvy156, eah, eba)
new_esEs35(yvy153, yvy156, ty_@0) → new_esEs19(yvy153, yvy156)
new_ltEs15(yvy100, yvy101) → new_fsEs(new_compare16(yvy100, yvy101))
new_esEs6(yvy4002, yvy3002, app(ty_[], bba)) → new_esEs16(yvy4002, yvy3002, bba)
new_esEs26(yvy40000, yvy30000, ty_@0) → new_esEs19(yvy40000, yvy30000)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_@0, hf) → new_esEs19(yvy40000, yvy30000)
new_ltEs16(False, True) → True
new_esEs26(yvy40000, yvy30000, app(app(app(ty_@3, bcg), bch), bda)) → new_esEs22(yvy40000, yvy30000, bcg, bch, bda)
new_esEs10(yvy4000, yvy3000, app(ty_Maybe, ege)) → new_esEs23(yvy4000, yvy3000, ege)
new_ltEs24(yvy100, yvy101, ty_Bool) → new_ltEs16(yvy100, yvy101)
new_compare30(yvy400, yvy300, app(app(ty_@2, be), bf)) → new_compare7(yvy400, yvy300, be, bf)
new_esEs17(@2(yvy40000, yvy40001), @2(yvy30000, yvy30001), gf, gg) → new_asAs(new_esEs29(yvy40000, yvy30000, gf), new_esEs30(yvy40001, yvy30001, gg))
new_esEs11(yvy4000, yvy3000, ty_Char) → new_esEs15(yvy4000, yvy3000)
new_lt20(yvy152, yvy155, app(app(app(ty_@3, bb), bc), bd)) → new_lt4(yvy152, yvy155, bb, bc, bd)
new_esEs27(yvy1000, yvy1010, ty_Bool) → new_esEs20(yvy1000, yvy1010)
new_ltEs23(yvy166, yvy168, app(ty_Ratio, fdc)) → new_ltEs9(yvy166, yvy168, fdc)
new_esEs34(yvy152, yvy155, ty_Double) → new_esEs13(yvy152, yvy155)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Double) → new_esEs13(yvy40000, yvy30000)
new_esEs10(yvy4000, yvy3000, ty_Int) → new_esEs25(yvy4000, yvy3000)
new_esEs26(yvy40000, yvy30000, ty_Char) → new_esEs15(yvy40000, yvy30000)
new_compare30(yvy400, yvy300, ty_Int) → new_compare16(yvy400, yvy300)
new_fsEs(yvy306) → new_not(new_esEs12(yvy306, GT))
new_ltEs16(True, False) → False
new_ltEs14(Right(yvy1000), Right(yvy1010), dbd, ty_Char) → new_ltEs7(yvy1000, yvy1010)
new_esEs7(yvy4000, yvy3000, ty_Int) → new_esEs25(yvy4000, yvy3000)
new_ltEs19(yvy1002, yvy1012, ty_Bool) → new_ltEs16(yvy1002, yvy1012)
new_esEs34(yvy152, yvy155, ty_Ordering) → new_esEs12(yvy152, yvy155)
new_esEs12(GT, LT) → False
new_esEs12(LT, GT) → False
new_esEs27(yvy1000, yvy1010, ty_Char) → new_esEs15(yvy1000, yvy1010)
new_lt5(yvy1001, yvy1011, ty_Integer) → new_lt15(yvy1001, yvy1011)
new_ltEs22(yvy114, yvy115, ty_Ordering) → new_ltEs6(yvy114, yvy115)
new_compare18(Float(yvy4000, yvy4001), Float(yvy3000, yvy3001)) → new_compare16(new_sr0(yvy4000, yvy3000), new_sr0(yvy4001, yvy3001))
new_ltEs18(yvy107, yvy108, app(ty_Ratio, bdh)) → new_ltEs9(yvy107, yvy108, bdh)
new_ltEs23(yvy166, yvy168, ty_Float) → new_ltEs11(yvy166, yvy168)
new_ltEs18(yvy107, yvy108, app(ty_[], bdg)) → new_ltEs8(yvy107, yvy108, bdg)
new_ltEs20(yvy154, yvy157, app(app(ty_@2, ebg), ebh)) → new_ltEs12(yvy154, yvy157, ebg, ebh)
new_esEs31(yvy40000, yvy30000, app(ty_Maybe, cfb)) → new_esEs23(yvy40000, yvy30000, cfb)
new_lt6(yvy1000, yvy1010, app(ty_Ratio, bfe)) → new_lt10(yvy1000, yvy1010, bfe)
new_esEs37(yvy40000, yvy30000, ty_Integer) → new_esEs18(yvy40000, yvy30000)
new_ltEs14(Left(yvy1000), Left(yvy1010), app(app(ty_@2, dag), dah), daa) → new_ltEs12(yvy1000, yvy1010, dag, dah)
new_esEs35(yvy153, yvy156, app(app(ty_@2, eae), eaf)) → new_esEs17(yvy153, yvy156, eae, eaf)
new_esEs5(yvy4001, yvy3001, app(app(app(ty_@3, bac), bad), bae)) → new_esEs22(yvy4001, yvy3001, bac, bad, bae)
new_lt22(yvy1000, yvy1010, ty_Char) → new_lt8(yvy1000, yvy1010)
new_compare110(yvy233, yvy234, yvy235, yvy236, True, yvy238, ecd, ece) → new_compare111(yvy233, yvy234, yvy235, yvy236, True, ecd, ece)
new_ltEs24(yvy100, yvy101, app(app(ty_@2, ecf), ecg)) → new_ltEs12(yvy100, yvy101, ecf, ecg)
new_ltEs13(yvy100, yvy101) → new_fsEs(new_compare29(yvy100, yvy101))
new_esEs5(yvy4001, yvy3001, app(app(ty_Either, bag), bah)) → new_esEs24(yvy4001, yvy3001, bag, bah)
new_esEs24(Right(yvy40000), Right(yvy30000), he, ty_Bool) → new_esEs20(yvy40000, yvy30000)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Float) → new_ltEs11(yvy1000, yvy1010)
new_esEs8(yvy4001, yvy3001, ty_Double) → new_esEs13(yvy4001, yvy3001)
new_esEs31(yvy40000, yvy30000, app(ty_Ratio, cef)) → new_esEs21(yvy40000, yvy30000, cef)
new_esEs29(yvy40000, yvy30000, app(ty_Maybe, cca)) → new_esEs23(yvy40000, yvy30000, cca)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Int) → new_ltEs15(yvy1000, yvy1010)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Double) → new_ltEs13(yvy1000, yvy1010)
new_esEs30(yvy40001, yvy30001, ty_Double) → new_esEs13(yvy40001, yvy30001)
new_ltEs21(yvy1001, yvy1011, app(app(ty_@2, eeg), eeh)) → new_ltEs12(yvy1001, yvy1011, eeg, eeh)
new_esEs10(yvy4000, yvy3000, ty_Bool) → new_esEs20(yvy4000, yvy3000)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Char, daa) → new_ltEs7(yvy1000, yvy1010)
new_ltEs16(True, True) → True
new_lt21(yvy153, yvy156, app(app(ty_@2, eae), eaf)) → new_lt12(yvy153, yvy156, eae, eaf)
new_lt6(yvy1000, yvy1010, ty_Bool) → new_lt18(yvy1000, yvy1010)
new_pePe(False, yvy305) → yvy305
new_compare15(GT, EQ) → GT
new_esEs7(yvy4000, yvy3000, ty_Char) → new_esEs15(yvy4000, yvy3000)
new_esEs31(yvy40000, yvy30000, app(ty_[], cec)) → new_esEs16(yvy40000, yvy30000, cec)
new_esEs39(yvy165, yvy167, ty_@0) → new_esEs19(yvy165, yvy167)
new_esEs23(Just(yvy40000), Just(yvy30000), app(ty_Maybe, ddf)) → new_esEs23(yvy40000, yvy30000, ddf)
new_lt21(yvy153, yvy156, ty_Char) → new_lt8(yvy153, yvy156)
new_esEs26(yvy40000, yvy30000, ty_Bool) → new_esEs20(yvy40000, yvy30000)
new_esEs9(yvy4000, yvy3000, app(app(ty_@2, ffb), ffc)) → new_esEs17(yvy4000, yvy3000, ffb, ffc)
new_compare14(yvy218, yvy219, yvy220, yvy221, yvy222, yvy223, False, cdh, cea, ceb) → GT
new_lt9(yvy152, yvy155, dhd) → new_esEs12(new_compare0(yvy152, yvy155, dhd), LT)
new_esEs28(yvy1001, yvy1011, ty_Integer) → new_esEs18(yvy1001, yvy1011)
new_esEs5(yvy4001, yvy3001, ty_Ordering) → new_esEs12(yvy4001, yvy3001)
new_esEs5(yvy4001, yvy3001, ty_Int) → new_esEs25(yvy4001, yvy3001)
new_esEs4(yvy4000, yvy3000, ty_Float) → new_esEs14(yvy4000, yvy3000)
new_compare15(GT, LT) → GT
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Char, hf) → new_esEs15(yvy40000, yvy30000)
new_esEs29(yvy40000, yvy30000, ty_Int) → new_esEs25(yvy40000, yvy30000)
new_compare30(yvy400, yvy300, app(app(ty_Either, efd), efe)) → new_compare27(yvy400, yvy300, efd, efe)
new_lt22(yvy1000, yvy1010, ty_Double) → new_lt13(yvy1000, yvy1010)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Ordering) → new_esEs12(yvy40000, yvy30000)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Char) → new_esEs15(yvy40000, yvy30000)
new_esEs29(yvy40000, yvy30000, app(app(ty_@2, cbc), cbd)) → new_esEs17(yvy40000, yvy30000, cbc, cbd)
new_esEs24(Right(yvy40000), Right(yvy30000), he, app(app(ty_@2, dff), dfg)) → new_esEs17(yvy40000, yvy30000, dff, dfg)
new_ltEs23(yvy166, yvy168, app(app(ty_Either, feb), fec)) → new_ltEs14(yvy166, yvy168, feb, fec)
new_esEs31(yvy40000, yvy30000, ty_Integer) → new_esEs18(yvy40000, yvy30000)
new_compare12(True, True) → EQ
new_esEs36(yvy1000, yvy1010, app(ty_[], ech)) → new_esEs16(yvy1000, yvy1010, ech)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Ordering, hf) → new_esEs12(yvy40000, yvy30000)
new_ltEs6(GT, EQ) → False
new_ltEs18(yvy107, yvy108, app(app(ty_Either, beg), beh)) → new_ltEs14(yvy107, yvy108, beg, beh)
new_esEs32(yvy40001, yvy30001, app(ty_Maybe, cgd)) → new_esEs23(yvy40001, yvy30001, cgd)
new_esEs35(yvy153, yvy156, ty_Integer) → new_esEs18(yvy153, yvy156)
new_esEs33(yvy40002, yvy30002, ty_Integer) → new_esEs18(yvy40002, yvy30002)
new_esEs31(yvy40000, yvy30000, ty_Double) → new_esEs13(yvy40000, yvy30000)
new_esEs10(yvy4000, yvy3000, ty_Ordering) → new_esEs12(yvy4000, yvy3000)
new_primCompAux1(yvy400, yvy300, yvy51, h) → new_primCompAux0(yvy51, new_compare30(yvy400, yvy300, h))
new_esEs33(yvy40002, yvy30002, ty_Float) → new_esEs14(yvy40002, yvy30002)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbd, app(app(app(ty_@3, dbg), dbh), dca)) → new_ltEs10(yvy1000, yvy1010, dbg, dbh, dca)
new_ltEs23(yvy166, yvy168, app(ty_[], fdb)) → new_ltEs8(yvy166, yvy168, fdb)
new_lt23(yvy165, yvy167, app(app(ty_@2, fce), fcf)) → new_lt12(yvy165, yvy167, fce, fcf)
new_esEs34(yvy152, yvy155, ty_Integer) → new_esEs18(yvy152, yvy155)
new_esEs23(Just(yvy40000), Just(yvy30000), app(app(ty_Either, ddg), ddh)) → new_esEs24(yvy40000, yvy30000, ddg, ddh)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Ordering, daa) → new_ltEs6(yvy1000, yvy1010)
new_lt22(yvy1000, yvy1010, ty_Bool) → new_lt18(yvy1000, yvy1010)
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_esEs39(yvy165, yvy167, ty_Float) → new_esEs14(yvy165, yvy167)
new_ltEs22(yvy114, yvy115, ty_Bool) → new_ltEs16(yvy114, yvy115)
new_ltEs4(yvy100, yvy101) → new_fsEs(new_compare8(yvy100, yvy101))
new_esEs33(yvy40002, yvy30002, app(ty_[], cgg)) → new_esEs16(yvy40002, yvy30002, cgg)
new_ltEs8(yvy100, yvy101, fed) → new_fsEs(new_compare0(yvy100, yvy101, fed))
new_compare30(yvy400, yvy300, ty_Char) → new_compare11(yvy400, yvy300)
new_esEs36(yvy1000, yvy1010, ty_Integer) → new_esEs18(yvy1000, yvy1010)
new_esEs39(yvy165, yvy167, ty_Bool) → new_esEs20(yvy165, yvy167)
new_esEs36(yvy1000, yvy1010, ty_Bool) → new_esEs20(yvy1000, yvy1010)
new_esEs32(yvy40001, yvy30001, app(ty_Ratio, cfh)) → new_esEs21(yvy40001, yvy30001, cfh)
new_compare12(False, True) → LT
new_esEs5(yvy4001, yvy3001, ty_Char) → new_esEs15(yvy4001, yvy3001)
new_esEs34(yvy152, yvy155, ty_Char) → new_esEs15(yvy152, yvy155)
new_esEs31(yvy40000, yvy30000, app(app(ty_@2, ced), cee)) → new_esEs17(yvy40000, yvy30000, ced, cee)
new_ltEs18(yvy107, yvy108, ty_Integer) → new_ltEs4(yvy107, yvy108)
new_lt21(yvy153, yvy156, ty_@0) → new_lt19(yvy153, yvy156)
new_esEs30(yvy40001, yvy30001, ty_@0) → new_esEs19(yvy40001, yvy30001)
new_ltEs18(yvy107, yvy108, app(ty_Maybe, bef)) → new_ltEs5(yvy107, yvy108, bef)
new_esEs12(LT, LT) → True
new_ltEs24(yvy100, yvy101, ty_Char) → new_ltEs7(yvy100, yvy101)
new_esEs31(yvy40000, yvy30000, app(app(ty_Either, cfc), cfd)) → new_esEs24(yvy40000, yvy30000, cfc, cfd)
new_ltEs18(yvy107, yvy108, ty_Double) → new_ltEs13(yvy107, yvy108)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Int, daa) → new_ltEs15(yvy1000, yvy1010)
new_esEs28(yvy1001, yvy1011, app(ty_Maybe, bhe)) → new_esEs23(yvy1001, yvy1011, bhe)
new_lt5(yvy1001, yvy1011, ty_@0) → new_lt19(yvy1001, yvy1011)
new_compare15(EQ, LT) → GT
new_pePe(True, yvy305) → True
new_compare0([], [], fef) → EQ
new_primEqNat0(Zero, Zero) → True
new_ltEs21(yvy1001, yvy1011, ty_Double) → new_ltEs13(yvy1001, yvy1011)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Float) → new_esEs14(yvy40000, yvy30000)
new_esEs6(yvy4002, yvy3002, ty_Double) → new_esEs13(yvy4002, yvy3002)
new_esEs4(yvy4000, yvy3000, app(ty_Maybe, hd)) → new_esEs23(yvy4000, yvy3000, hd)
new_lt5(yvy1001, yvy1011, ty_Bool) → new_lt18(yvy1001, yvy1011)
new_lt23(yvy165, yvy167, ty_Integer) → new_lt15(yvy165, yvy167)
new_esEs5(yvy4001, yvy3001, ty_Float) → new_esEs14(yvy4001, yvy3001)
new_lt21(yvy153, yvy156, app(app(ty_Either, eah), eba)) → new_lt16(yvy153, yvy156, eah, eba)
new_esEs8(yvy4001, yvy3001, app(app(app(ty_@3, df), dg), dh)) → new_esEs22(yvy4001, yvy3001, df, dg, dh)
new_lt11(yvy152, yvy155) → new_esEs12(new_compare18(yvy152, yvy155), LT)
new_lt20(yvy152, yvy155, app(ty_[], dhd)) → new_lt9(yvy152, yvy155, dhd)
new_esEs13(Double(yvy40000, yvy40001), Double(yvy30000, yvy30001)) → new_esEs25(new_sr0(yvy40000, yvy30000), new_sr0(yvy40001, yvy30001))
new_esEs7(yvy4000, yvy3000, ty_Bool) → new_esEs20(yvy4000, yvy3000)
new_compare30(yvy400, yvy300, ty_@0) → new_compare9(yvy400, yvy300)
new_esEs29(yvy40000, yvy30000, ty_@0) → new_esEs19(yvy40000, yvy30000)
new_esEs6(yvy4002, yvy3002, ty_Ordering) → new_esEs12(yvy4002, yvy3002)
new_ltEs18(yvy107, yvy108, app(app(app(ty_@3, bea), beb), bec)) → new_ltEs10(yvy107, yvy108, bea, beb, bec)
new_ltEs22(yvy114, yvy115, ty_@0) → new_ltEs17(yvy114, yvy115)
new_lt5(yvy1001, yvy1011, ty_Char) → new_lt8(yvy1001, yvy1011)
new_lt5(yvy1001, yvy1011, app(app(ty_Either, bhf), bhg)) → new_lt16(yvy1001, yvy1011, bhf, bhg)
new_ltEs19(yvy1002, yvy1012, ty_Ordering) → new_ltEs6(yvy1002, yvy1012)
new_esEs15(Char(yvy40000), Char(yvy30000)) → new_primEqNat0(yvy40000, yvy30000)
new_esEs24(Left(yvy40000), Left(yvy30000), app(app(app(ty_@3, deg), deh), dfa), hf) → new_esEs22(yvy40000, yvy30000, deg, deh, dfa)
new_esEs26(yvy40000, yvy30000, ty_Int) → new_esEs25(yvy40000, yvy30000)
new_esEs32(yvy40001, yvy30001, ty_Integer) → new_esEs18(yvy40001, yvy30001)
new_ltEs23(yvy166, yvy168, ty_Double) → new_ltEs13(yvy166, yvy168)
new_lt22(yvy1000, yvy1010, app(ty_[], ech)) → new_lt9(yvy1000, yvy1010, ech)
new_ltEs23(yvy166, yvy168, ty_Integer) → new_ltEs4(yvy166, yvy168)
new_esEs9(yvy4000, yvy3000, app(ty_[], ffa)) → new_esEs16(yvy4000, yvy3000, ffa)
new_esEs33(yvy40002, yvy30002, ty_Bool) → new_esEs20(yvy40002, yvy30002)
new_esEs11(yvy4000, yvy3000, ty_Double) → new_esEs13(yvy4000, yvy3000)
new_esEs29(yvy40000, yvy30000, ty_Bool) → new_esEs20(yvy40000, yvy30000)
new_lt5(yvy1001, yvy1011, app(ty_[], bgf)) → new_lt9(yvy1001, yvy1011, bgf)
new_ltEs21(yvy1001, yvy1011, ty_Bool) → new_ltEs16(yvy1001, yvy1011)
new_ltEs6(EQ, GT) → True
new_esEs9(yvy4000, yvy3000, ty_Integer) → new_esEs18(yvy4000, yvy3000)
new_esEs11(yvy4000, yvy3000, ty_Ordering) → new_esEs12(yvy4000, yvy3000)
new_esEs23(Just(yvy40000), Nothing, hd) → False
new_esEs23(Nothing, Just(yvy30000), hd) → False
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_ltEs18(yvy107, yvy108, ty_Ordering) → new_ltEs6(yvy107, yvy108)
new_esEs23(Just(yvy40000), Just(yvy30000), app(app(app(ty_@3, ddc), ddd), dde)) → new_esEs22(yvy40000, yvy30000, ddc, ddd, dde)
new_ltEs24(yvy100, yvy101, ty_Double) → new_ltEs13(yvy100, yvy101)
new_esEs10(yvy4000, yvy3000, ty_Double) → new_esEs13(yvy4000, yvy3000)
new_esEs24(Right(yvy40000), Right(yvy30000), he, ty_Float) → new_esEs14(yvy40000, yvy30000)
new_compare110(yvy233, yvy234, yvy235, yvy236, False, yvy238, ecd, ece) → new_compare111(yvy233, yvy234, yvy235, yvy236, yvy238, ecd, ece)
new_ltEs20(yvy154, yvy157, ty_Bool) → new_ltEs16(yvy154, yvy157)
new_ltEs24(yvy100, yvy101, ty_@0) → new_ltEs17(yvy100, yvy101)
new_ltEs5(Just(yvy1000), Just(yvy1010), app(app(ty_@2, fd), ff)) → new_ltEs12(yvy1000, yvy1010, fd, ff)
new_ltEs20(yvy154, yvy157, ty_Int) → new_ltEs15(yvy154, yvy157)
new_esEs8(yvy4001, yvy3001, ty_@0) → new_esEs19(yvy4001, yvy3001)
new_lt22(yvy1000, yvy1010, app(app(ty_Either, edh), eea)) → new_lt16(yvy1000, yvy1010, edh, eea)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Float, daa) → new_ltEs11(yvy1000, yvy1010)
new_compare26(yvy107, yvy108, False, bde, bdf) → new_compare10(yvy107, yvy108, new_ltEs18(yvy107, yvy108, bde), bde, bdf)
new_lt21(yvy153, yvy156, app(ty_Ratio, eaa)) → new_lt10(yvy153, yvy156, eaa)
new_compare30(yvy400, yvy300, ty_Float) → new_compare18(yvy400, yvy300)
new_primEqInt(Neg(Succ(yvy400000)), Neg(Succ(yvy300000))) → new_primEqNat0(yvy400000, yvy300000)
new_esEs23(Nothing, Nothing, hd) → True
new_esEs10(yvy4000, yvy3000, app(app(app(ty_@3, egb), egc), egd)) → new_esEs22(yvy4000, yvy3000, egb, egc, egd)
new_esEs39(yvy165, yvy167, app(app(ty_@2, fce), fcf)) → new_esEs17(yvy165, yvy167, fce, fcf)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbd, app(app(ty_@2, dcb), dcc)) → new_ltEs12(yvy1000, yvy1010, dcb, dcc)
new_ltEs5(Just(yvy1000), Nothing, ef) → False
new_esEs28(yvy1001, yvy1011, ty_Char) → new_esEs15(yvy1001, yvy1011)
new_esEs11(yvy4000, yvy3000, app(ty_Maybe, ehg)) → new_esEs23(yvy4000, yvy3000, ehg)
new_lt14(yvy152, yvy155, dhe) → new_esEs12(new_compare31(yvy152, yvy155, dhe), LT)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbd, ty_@0) → new_ltEs17(yvy1000, yvy1010)
new_ltEs14(Right(yvy1000), Left(yvy1010), dbd, daa) → False
new_esEs12(EQ, LT) → False
new_esEs12(LT, EQ) → False
new_ltEs19(yvy1002, yvy1012, app(ty_Ratio, caa)) → new_ltEs9(yvy1002, yvy1012, caa)
new_lt22(yvy1000, yvy1010, app(app(ty_@2, ede), edf)) → new_lt12(yvy1000, yvy1010, ede, edf)
new_ltEs23(yvy166, yvy168, ty_Bool) → new_ltEs16(yvy166, yvy168)
new_compare111(yvy233, yvy234, yvy235, yvy236, True, ecd, ece) → LT
new_esEs7(yvy4000, yvy3000, app(ty_[], bg)) → new_esEs16(yvy4000, yvy3000, bg)
new_esEs5(yvy4001, yvy3001, ty_Bool) → new_esEs20(yvy4001, yvy3001)
new_lt23(yvy165, yvy167, ty_Int) → new_lt17(yvy165, yvy167)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs30(yvy40001, yvy30001, app(app(app(ty_@3, cch), cda), cdb)) → new_esEs22(yvy40001, yvy30001, cch, cda, cdb)
new_esEs11(yvy4000, yvy3000, app(app(ty_Either, ehh), faa)) → new_esEs24(yvy4000, yvy3000, ehh, faa)
new_esEs35(yvy153, yvy156, app(app(app(ty_@3, eab), eac), ead)) → new_esEs22(yvy153, yvy156, eab, eac, ead)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbd, ty_Int) → new_ltEs15(yvy1000, yvy1010)
new_esEs10(yvy4000, yvy3000, app(app(ty_Either, egf), egg)) → new_esEs24(yvy4000, yvy3000, egf, egg)
new_esEs28(yvy1001, yvy1011, ty_Double) → new_esEs13(yvy1001, yvy1011)
new_lt20(yvy152, yvy155, ty_Ordering) → new_lt7(yvy152, yvy155)
new_ltEs6(EQ, EQ) → True
new_compare31(Just(yvy4000), Nothing, feh) → GT
new_esEs11(yvy4000, yvy3000, app(app(app(ty_@3, ehd), ehe), ehf)) → new_esEs22(yvy4000, yvy3000, ehd, ehe, ehf)
new_ltEs22(yvy114, yvy115, app(app(ty_Either, fbd), fbe)) → new_ltEs14(yvy114, yvy115, fbd, fbe)
new_esEs28(yvy1001, yvy1011, app(app(app(ty_@3, bgh), bha), bhb)) → new_esEs22(yvy1001, yvy1011, bgh, bha, bhb)
new_esEs32(yvy40001, yvy30001, ty_Float) → new_esEs14(yvy40001, yvy30001)
new_esEs27(yvy1000, yvy1010, app(ty_Ratio, bfe)) → new_esEs21(yvy1000, yvy1010, bfe)
new_ltEs19(yvy1002, yvy1012, ty_Integer) → new_ltEs4(yvy1002, yvy1012)
new_primEqInt(Neg(Succ(yvy400000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(yvy300000))) → False
new_primCompAux0(yvy56, GT) → GT
new_compare30(yvy400, yvy300, app(app(app(ty_@3, gb), gc), gd)) → new_compare6(yvy400, yvy300, gb, gc, gd)
new_esEs39(yvy165, yvy167, ty_Integer) → new_esEs18(yvy165, yvy167)
new_compare26(yvy107, yvy108, True, bde, bdf) → EQ
new_esEs23(Just(yvy40000), Just(yvy30000), app(app(ty_@2, dch), dda)) → new_esEs17(yvy40000, yvy30000, dch, dda)
new_esEs24(Right(yvy40000), Right(yvy30000), he, app(app(ty_Either, dge), dgf)) → new_esEs24(yvy40000, yvy30000, dge, dgf)
new_ltEs6(GT, GT) → True
new_ltEs21(yvy1001, yvy1011, app(app(ty_Either, efb), efc)) → new_ltEs14(yvy1001, yvy1011, efb, efc)
new_esEs38(yvy40001, yvy30001, ty_Integer) → new_esEs18(yvy40001, yvy30001)
new_esEs32(yvy40001, yvy30001, app(ty_[], cfe)) → new_esEs16(yvy40001, yvy30001, cfe)
new_esEs34(yvy152, yvy155, ty_Int) → new_esEs25(yvy152, yvy155)
new_compare31(Nothing, Nothing, feh) → EQ
new_esEs29(yvy40000, yvy30000, app(ty_[], cbb)) → new_esEs16(yvy40000, yvy30000, cbb)
new_esEs26(yvy40000, yvy30000, app(ty_Ratio, bcf)) → new_esEs21(yvy40000, yvy30000, bcf)
new_esEs7(yvy4000, yvy3000, app(ty_Maybe, cf)) → new_esEs23(yvy4000, yvy3000, cf)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_@0) → new_ltEs17(yvy1000, yvy1010)
new_lt21(yvy153, yvy156, app(ty_[], dhh)) → new_lt9(yvy153, yvy156, dhh)
new_ltEs20(yvy154, yvy157, app(ty_[], ebb)) → new_ltEs8(yvy154, yvy157, ebb)
new_esEs36(yvy1000, yvy1010, ty_Int) → new_esEs25(yvy1000, yvy1010)
new_esEs19(@0, @0) → True
new_compare6(@3(yvy4000, yvy4001, yvy4002), @3(yvy3000, yvy3001, yvy3002), gb, gc, gd) → new_compare25(yvy4000, yvy4001, yvy4002, yvy3000, yvy3001, yvy3002, new_asAs(new_esEs4(yvy4000, yvy3000, gb), new_asAs(new_esEs5(yvy4001, yvy3001, gc), new_esEs6(yvy4002, yvy3002, gd))), gb, gc, gd)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_esEs7(yvy4000, yvy3000, ty_Integer) → new_esEs18(yvy4000, yvy3000)
new_esEs4(yvy4000, yvy3000, ty_Bool) → new_esEs20(yvy4000, yvy3000)
new_esEs39(yvy165, yvy167, ty_Ordering) → new_esEs12(yvy165, yvy167)
new_lt20(yvy152, yvy155, ty_Char) → new_lt8(yvy152, yvy155)
new_esEs31(yvy40000, yvy30000, ty_Bool) → new_esEs20(yvy40000, yvy30000)
new_lt4(yvy152, yvy155, bb, bc, bd) → new_esEs12(new_compare6(yvy152, yvy155, bb, bc, bd), LT)
new_esEs6(yvy4002, yvy3002, ty_Int) → new_esEs25(yvy4002, yvy3002)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Double, daa) → new_ltEs13(yvy1000, yvy1010)
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_lt6(yvy1000, yvy1010, app(ty_Maybe, bgc)) → new_lt14(yvy1000, yvy1010, bgc)
new_ltEs14(Left(yvy1000), Left(yvy1010), app(ty_Maybe, dba), daa) → new_ltEs5(yvy1000, yvy1010, dba)
new_esEs4(yvy4000, yvy3000, app(ty_Ratio, gh)) → new_esEs21(yvy4000, yvy3000, gh)
new_lt5(yvy1001, yvy1011, app(ty_Maybe, bhe)) → new_lt14(yvy1001, yvy1011, bhe)
new_primEqInt(Pos(Succ(yvy400000)), Pos(Succ(yvy300000))) → new_primEqNat0(yvy400000, yvy300000)
new_compare10(yvy199, yvy200, False, ed, ee) → GT
new_esEs34(yvy152, yvy155, app(ty_Maybe, dhe)) → new_esEs23(yvy152, yvy155, dhe)
new_esEs5(yvy4001, yvy3001, app(ty_[], hg)) → new_esEs16(yvy4001, yvy3001, hg)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbd, ty_Double) → new_ltEs13(yvy1000, yvy1010)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbd, ty_Integer) → new_ltEs4(yvy1000, yvy1010)
new_ltEs21(yvy1001, yvy1011, ty_Float) → new_ltEs11(yvy1001, yvy1011)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbd, app(ty_Maybe, dcd)) → new_ltEs5(yvy1000, yvy1010, dcd)
new_compare13(:%(yvy4000, yvy4001), :%(yvy3000, yvy3001), ty_Int) → new_compare16(new_sr0(yvy4000, yvy3001), new_sr0(yvy3000, yvy4001))
new_esEs26(yvy40000, yvy30000, app(ty_Maybe, bdb)) → new_esEs23(yvy40000, yvy30000, bdb)
new_ltEs24(yvy100, yvy101, ty_Float) → new_ltEs11(yvy100, yvy101)
new_esEs34(yvy152, yvy155, app(app(ty_@2, dea), deb)) → new_esEs17(yvy152, yvy155, dea, deb)
new_esEs8(yvy4001, yvy3001, ty_Integer) → new_esEs18(yvy4001, yvy3001)
new_ltEs22(yvy114, yvy115, app(app(app(ty_@3, faf), fag), fah)) → new_ltEs10(yvy114, yvy115, faf, fag, fah)
new_primEqNat0(Succ(yvy400000), Succ(yvy300000)) → new_primEqNat0(yvy400000, yvy300000)
new_esEs6(yvy4002, yvy3002, ty_Bool) → new_esEs20(yvy4002, yvy3002)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Ordering) → new_ltEs6(yvy1000, yvy1010)
new_ltEs24(yvy100, yvy101, ty_Int) → new_ltEs15(yvy100, yvy101)
new_esEs26(yvy40000, yvy30000, ty_Ordering) → new_esEs12(yvy40000, yvy30000)
new_esEs24(Right(yvy40000), Right(yvy30000), he, app(ty_Ratio, dfh)) → new_esEs21(yvy40000, yvy30000, dfh)
new_esEs11(yvy4000, yvy3000, app(ty_Ratio, ehc)) → new_esEs21(yvy4000, yvy3000, ehc)
new_esEs30(yvy40001, yvy30001, ty_Integer) → new_esEs18(yvy40001, yvy30001)
new_esEs39(yvy165, yvy167, ty_Char) → new_esEs15(yvy165, yvy167)
new_ltEs14(Left(yvy1000), Left(yvy1010), app(ty_Ratio, dac), daa) → new_ltEs9(yvy1000, yvy1010, dac)
new_esEs26(yvy40000, yvy30000, app(app(ty_@2, bcd), bce)) → new_esEs17(yvy40000, yvy30000, bcd, bce)
new_lt5(yvy1001, yvy1011, ty_Float) → new_lt11(yvy1001, yvy1011)
new_esEs32(yvy40001, yvy30001, ty_@0) → new_esEs19(yvy40001, yvy30001)
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_esEs33(yvy40002, yvy30002, app(ty_Maybe, chf)) → new_esEs23(yvy40002, yvy30002, chf)
new_lt6(yvy1000, yvy1010, ty_Int) → new_lt17(yvy1000, yvy1010)
new_esEs24(Right(yvy40000), Right(yvy30000), he, app(app(app(ty_@3, dga), dgb), dgc)) → new_esEs22(yvy40000, yvy30000, dga, dgb, dgc)
new_lt23(yvy165, yvy167, app(app(ty_Either, fch), fda)) → new_lt16(yvy165, yvy167, fch, fda)
new_esEs12(EQ, EQ) → True
new_lt23(yvy165, yvy167, ty_Char) → new_lt8(yvy165, yvy167)
new_ltEs18(yvy107, yvy108, app(app(ty_@2, bed), bee)) → new_ltEs12(yvy107, yvy108, bed, bee)
new_lt21(yvy153, yvy156, ty_Double) → new_lt13(yvy153, yvy156)
new_esEs35(yvy153, yvy156, ty_Ordering) → new_esEs12(yvy153, yvy156)
new_lt5(yvy1001, yvy1011, ty_Int) → new_lt17(yvy1001, yvy1011)
new_esEs10(yvy4000, yvy3000, ty_Char) → new_esEs15(yvy4000, yvy3000)
new_primEqInt(Pos(Succ(yvy400000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(yvy300000))) → False
new_ltEs5(Nothing, Just(yvy1010), ef) → True
new_lt20(yvy152, yvy155, ty_Int) → new_lt17(yvy152, yvy155)
new_esEs35(yvy153, yvy156, app(ty_Maybe, eag)) → new_esEs23(yvy153, yvy156, eag)
new_esEs27(yvy1000, yvy1010, ty_@0) → new_esEs19(yvy1000, yvy1010)
new_ltEs18(yvy107, yvy108, ty_Float) → new_ltEs11(yvy107, yvy108)
new_compare25(yvy152, yvy153, yvy154, yvy155, yvy156, yvy157, True, dha, dhb, dhc) → EQ
new_esEs37(yvy40000, yvy30000, ty_Int) → new_esEs25(yvy40000, yvy30000)
new_primCmpNat0(Zero, Zero) → EQ
new_esEs27(yvy1000, yvy1010, app(app(ty_Either, bgd), bge)) → new_esEs24(yvy1000, yvy1010, bgd, bge)
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_compare27(Left(yvy4000), Right(yvy3000), efd, efe) → LT
new_lt22(yvy1000, yvy1010, ty_@0) → new_lt19(yvy1000, yvy1010)
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_compare9(@0, @0) → EQ
new_esEs28(yvy1001, yvy1011, ty_Int) → new_esEs25(yvy1001, yvy1011)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Float, hf) → new_esEs14(yvy40000, yvy30000)
new_esEs6(yvy4002, yvy3002, ty_Float) → new_esEs14(yvy4002, yvy3002)
new_ltEs9(yvy100, yvy101, cdf) → new_fsEs(new_compare13(yvy100, yvy101, cdf))
new_compare17(yvy218, yvy219, yvy220, yvy221, yvy222, yvy223, True, yvy225, cdh, cea, ceb) → new_compare14(yvy218, yvy219, yvy220, yvy221, yvy222, yvy223, True, cdh, cea, ceb)
new_esEs32(yvy40001, yvy30001, ty_Char) → new_esEs15(yvy40001, yvy30001)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_ltEs14(Left(yvy1000), Left(yvy1010), app(ty_[], dab), daa) → new_ltEs8(yvy1000, yvy1010, dab)
new_ltEs19(yvy1002, yvy1012, app(app(ty_@2, cae), caf)) → new_ltEs12(yvy1002, yvy1012, cae, caf)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Double, hf) → new_esEs13(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, app(app(ty_Either, chg), chh)) → new_esEs24(yvy40002, yvy30002, chg, chh)
new_esEs4(yvy4000, yvy3000, ty_Int) → new_esEs25(yvy4000, yvy3000)
new_compare28(yvy114, yvy115, True, fab, fac) → EQ
new_primEqInt(Pos(Succ(yvy400000)), Neg(yvy30000)) → False
new_primEqInt(Neg(Succ(yvy400000)), Pos(yvy30000)) → False
new_esEs24(Right(yvy40000), Right(yvy30000), he, ty_Int) → new_esEs25(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, ty_Ordering) → new_esEs12(yvy40002, yvy30002)
new_esEs29(yvy40000, yvy30000, app(app(app(ty_@3, cbf), cbg), cbh)) → new_esEs22(yvy40000, yvy30000, cbf, cbg, cbh)
new_esEs26(yvy40000, yvy30000, ty_Double) → new_esEs13(yvy40000, yvy30000)
new_ltEs20(yvy154, yvy157, ty_Integer) → new_ltEs4(yvy154, yvy157)
new_compare210(yvy100, yvy101, True, fee) → EQ
new_lt6(yvy1000, yvy1010, ty_Ordering) → new_lt7(yvy1000, yvy1010)
new_esEs29(yvy40000, yvy30000, app(ty_Ratio, cbe)) → new_esEs21(yvy40000, yvy30000, cbe)
new_esEs20(False, False) → True
new_esEs24(Left(yvy40000), Left(yvy30000), app(ty_[], dec), hf) → new_esEs16(yvy40000, yvy30000, dec)
new_lt23(yvy165, yvy167, app(ty_[], fbh)) → new_lt9(yvy165, yvy167, fbh)
new_ltEs22(yvy114, yvy115, ty_Integer) → new_ltEs4(yvy114, yvy115)
new_ltEs5(Just(yvy1000), Just(yvy1010), app(app(ty_Either, fh), ga)) → new_ltEs14(yvy1000, yvy1010, fh, ga)
new_lt23(yvy165, yvy167, ty_Bool) → new_lt18(yvy165, yvy167)
new_esEs30(yvy40001, yvy30001, ty_Ordering) → new_esEs12(yvy40001, yvy30001)
new_lt6(yvy1000, yvy1010, ty_Integer) → new_lt15(yvy1000, yvy1010)
new_primEqInt(Pos(Zero), Neg(Succ(yvy300000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(yvy300000))) → False
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_compare30(yvy400, yvy300, app(ty_Maybe, feh)) → new_compare31(yvy400, yvy300, feh)
new_esEs9(yvy4000, yvy3000, ty_Ordering) → new_esEs12(yvy4000, yvy3000)
new_esEs7(yvy4000, yvy3000, ty_@0) → new_esEs19(yvy4000, yvy3000)
new_esEs11(yvy4000, yvy3000, ty_Float) → new_esEs14(yvy4000, yvy3000)
new_lt6(yvy1000, yvy1010, app(ty_[], bfd)) → new_lt9(yvy1000, yvy1010, bfd)
new_esEs36(yvy1000, yvy1010, ty_@0) → new_esEs19(yvy1000, yvy1010)
new_esEs5(yvy4001, yvy3001, ty_@0) → new_esEs19(yvy4001, yvy3001)
new_esEs36(yvy1000, yvy1010, app(app(app(ty_@3, edb), edc), edd)) → new_esEs22(yvy1000, yvy1010, edb, edc, edd)
new_esEs28(yvy1001, yvy1011, ty_Ordering) → new_esEs12(yvy1001, yvy1011)
new_esEs10(yvy4000, yvy3000, app(ty_[], eff)) → new_esEs16(yvy4000, yvy3000, eff)
new_primCompAux0(yvy56, LT) → LT
new_esEs6(yvy4002, yvy3002, app(app(ty_Either, bca), bcb)) → new_esEs24(yvy4002, yvy3002, bca, bcb)
new_esEs6(yvy4002, yvy3002, ty_Integer) → new_esEs18(yvy4002, yvy3002)
new_esEs36(yvy1000, yvy1010, app(app(ty_@2, ede), edf)) → new_esEs17(yvy1000, yvy1010, ede, edf)
new_esEs7(yvy4000, yvy3000, app(app(ty_@2, bh), ca)) → new_esEs17(yvy4000, yvy3000, bh, ca)
new_esEs9(yvy4000, yvy3000, ty_Float) → new_esEs14(yvy4000, yvy3000)
new_lt5(yvy1001, yvy1011, ty_Double) → new_lt13(yvy1001, yvy1011)
new_ltEs22(yvy114, yvy115, app(ty_Maybe, fbc)) → new_ltEs5(yvy114, yvy115, fbc)
new_not(False) → True
new_esEs27(yvy1000, yvy1010, ty_Int) → new_esEs25(yvy1000, yvy1010)
new_esEs34(yvy152, yvy155, app(ty_Ratio, cdg)) → new_esEs21(yvy152, yvy155, cdg)
new_compare30(yvy400, yvy300, ty_Bool) → new_compare12(yvy400, yvy300)
new_esEs25(yvy4000, yvy3000) → new_primEqInt(yvy4000, yvy3000)
new_esEs28(yvy1001, yvy1011, app(ty_[], bgf)) → new_esEs16(yvy1001, yvy1011, bgf)
new_esEs31(yvy40000, yvy30000, ty_Char) → new_esEs15(yvy40000, yvy30000)
new_esEs14(Float(yvy40000, yvy40001), Float(yvy30000, yvy30001)) → new_esEs25(new_sr0(yvy40000, yvy30000), new_sr0(yvy40001, yvy30001))
new_esEs11(yvy4000, yvy3000, ty_@0) → new_esEs19(yvy4000, yvy3000)
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_esEs12(GT, EQ) → False
new_esEs12(EQ, GT) → False
new_esEs36(yvy1000, yvy1010, ty_Float) → new_esEs14(yvy1000, yvy1010)
new_esEs4(yvy4000, yvy3000, ty_Ordering) → new_esEs12(yvy4000, yvy3000)
new_esEs9(yvy4000, yvy3000, app(app(ty_Either, fga), fgb)) → new_esEs24(yvy4000, yvy3000, fga, fgb)
new_lt6(yvy1000, yvy1010, app(app(app(ty_@3, bff), bfg), bfh)) → new_lt4(yvy1000, yvy1010, bff, bfg, bfh)
new_esEs4(yvy4000, yvy3000, app(app(ty_@2, gf), gg)) → new_esEs17(yvy4000, yvy3000, gf, gg)
new_esEs24(Right(yvy40000), Right(yvy30000), he, ty_Integer) → new_esEs18(yvy40000, yvy30000)
new_ltEs18(yvy107, yvy108, ty_@0) → new_ltEs17(yvy107, yvy108)
new_esEs39(yvy165, yvy167, ty_Int) → new_esEs25(yvy165, yvy167)
new_compare15(LT, EQ) → LT
new_esEs34(yvy152, yvy155, ty_Float) → new_esEs14(yvy152, yvy155)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbd, app(ty_[], dbe)) → new_ltEs8(yvy1000, yvy1010, dbe)
new_esEs36(yvy1000, yvy1010, app(ty_Ratio, eda)) → new_esEs21(yvy1000, yvy1010, eda)
new_esEs30(yvy40001, yvy30001, app(ty_Ratio, ccg)) → new_esEs21(yvy40001, yvy30001, ccg)
new_compare30(yvy400, yvy300, app(ty_Ratio, feg)) → new_compare13(yvy400, yvy300, feg)
new_esEs24(Left(yvy40000), Right(yvy30000), he, hf) → False
new_esEs24(Right(yvy40000), Left(yvy30000), he, hf) → False
new_lt20(yvy152, yvy155, app(app(ty_Either, dhf), dhg)) → new_lt16(yvy152, yvy155, dhf, dhg)
new_esEs30(yvy40001, yvy30001, app(app(ty_@2, cce), ccf)) → new_esEs17(yvy40001, yvy30001, cce, ccf)
new_esEs32(yvy40001, yvy30001, app(app(ty_Either, cge), cgf)) → new_esEs24(yvy40001, yvy30001, cge, cgf)
new_esEs34(yvy152, yvy155, app(ty_[], dhd)) → new_esEs16(yvy152, yvy155, dhd)
new_lt20(yvy152, yvy155, ty_Double) → new_lt13(yvy152, yvy155)
new_esEs35(yvy153, yvy156, ty_Double) → new_esEs13(yvy153, yvy156)
new_compare0(:(yvy4000, yvy4001), [], fef) → GT
new_lt6(yvy1000, yvy1010, ty_Char) → new_lt8(yvy1000, yvy1010)
new_esEs8(yvy4001, yvy3001, ty_Int) → new_esEs25(yvy4001, yvy3001)
new_esEs38(yvy40001, yvy30001, ty_Int) → new_esEs25(yvy40001, yvy30001)
new_ltEs24(yvy100, yvy101, ty_Integer) → new_ltEs4(yvy100, yvy101)
new_ltEs20(yvy154, yvy157, app(ty_Maybe, eca)) → new_ltEs5(yvy154, yvy157, eca)
new_ltEs20(yvy154, yvy157, ty_@0) → new_ltEs17(yvy154, yvy157)
new_ltEs24(yvy100, yvy101, app(app(ty_Either, dbd), daa)) → new_ltEs14(yvy100, yvy101, dbd, daa)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Int) → new_esEs25(yvy40000, yvy30000)
new_esEs34(yvy152, yvy155, app(app(ty_Either, dhf), dhg)) → new_esEs24(yvy152, yvy155, dhf, dhg)
new_lt13(yvy152, yvy155) → new_esEs12(new_compare29(yvy152, yvy155), LT)
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_esEs30(yvy40001, yvy30001, app(app(ty_Either, cdd), cde)) → new_esEs24(yvy40001, yvy30001, cdd, cde)
new_lt19(yvy152, yvy155) → new_esEs12(new_compare9(yvy152, yvy155), LT)
new_ltEs18(yvy107, yvy108, ty_Char) → new_ltEs7(yvy107, yvy108)
new_esEs4(yvy4000, yvy3000, app(app(ty_Either, he), hf)) → new_esEs24(yvy4000, yvy3000, he, hf)
new_esEs8(yvy4001, yvy3001, app(ty_Ratio, de)) → new_esEs21(yvy4001, yvy3001, de)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Integer) → new_esEs18(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, app(ty_Ratio, chb)) → new_esEs21(yvy40002, yvy30002, chb)
new_lt17(yvy152, yvy155) → new_esEs12(new_compare16(yvy152, yvy155), LT)
new_esEs10(yvy4000, yvy3000, app(app(ty_@2, efg), efh)) → new_esEs17(yvy4000, yvy3000, efg, efh)
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_ltEs7(yvy100, yvy101) → new_fsEs(new_compare11(yvy100, yvy101))
new_esEs31(yvy40000, yvy30000, ty_Float) → new_esEs14(yvy40000, yvy30000)
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_compare15(EQ, GT) → LT
new_esEs32(yvy40001, yvy30001, ty_Int) → new_esEs25(yvy40001, yvy30001)
new_esEs29(yvy40000, yvy30000, ty_Char) → new_esEs15(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, app(app(app(ty_@3, chc), chd), che)) → new_esEs22(yvy40002, yvy30002, chc, chd, che)
new_primEqNat0(Zero, Succ(yvy300000)) → False
new_primEqNat0(Succ(yvy400000), Zero) → False
new_compare15(LT, GT) → LT
new_lt15(yvy152, yvy155) → new_esEs12(new_compare8(yvy152, yvy155), LT)
new_ltEs5(Nothing, Nothing, ef) → True
new_ltEs23(yvy166, yvy168, app(app(app(ty_@3, fdd), fde), fdf)) → new_ltEs10(yvy166, yvy168, fdd, fde, fdf)
new_lt20(yvy152, yvy155, app(app(ty_@2, dea), deb)) → new_lt12(yvy152, yvy155, dea, deb)
new_ltEs6(LT, LT) → True
new_ltEs6(EQ, LT) → False
new_esEs6(yvy4002, yvy3002, app(ty_Ratio, bbd)) → new_esEs21(yvy4002, yvy3002, bbd)
new_ltEs5(Just(yvy1000), Just(yvy1010), app(ty_[], eg)) → new_ltEs8(yvy1000, yvy1010, eg)
new_ltEs19(yvy1002, yvy1012, ty_Char) → new_ltEs7(yvy1002, yvy1012)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_ltEs21(yvy1001, yvy1011, app(ty_Ratio, eec)) → new_ltEs9(yvy1001, yvy1011, eec)
new_esEs9(yvy4000, yvy3000, app(ty_Maybe, ffh)) → new_esEs23(yvy4000, yvy3000, ffh)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Bool) → new_ltEs16(yvy1000, yvy1010)
new_lt21(yvy153, yvy156, app(ty_Maybe, eag)) → new_lt14(yvy153, yvy156, eag)
new_compare15(GT, GT) → EQ
new_esEs11(yvy4000, yvy3000, app(app(ty_@2, eha), ehb)) → new_esEs17(yvy4000, yvy3000, eha, ehb)
new_esEs8(yvy4001, yvy3001, app(app(ty_Either, eb), ec)) → new_esEs24(yvy4001, yvy3001, eb, ec)
new_compare24(yvy165, yvy166, yvy167, yvy168, True, fbf, fbg) → EQ
new_esEs32(yvy40001, yvy30001, ty_Bool) → new_esEs20(yvy40001, yvy30001)
new_lt21(yvy153, yvy156, ty_Float) → new_lt11(yvy153, yvy156)
new_esEs16(:(yvy40000, yvy40001), [], ge) → False
new_esEs16([], :(yvy30000, yvy30001), ge) → False
new_compare31(Just(yvy4000), Just(yvy3000), feh) → new_compare210(yvy4000, yvy3000, new_esEs9(yvy4000, yvy3000, feh), feh)
new_lt21(yvy153, yvy156, ty_Ordering) → new_lt7(yvy153, yvy156)
new_lt20(yvy152, yvy155, ty_Bool) → new_lt18(yvy152, yvy155)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbd, app(ty_Ratio, dbf)) → new_ltEs9(yvy1000, yvy1010, dbf)
new_ltEs19(yvy1002, yvy1012, ty_@0) → new_ltEs17(yvy1002, yvy1012)
new_esEs7(yvy4000, yvy3000, app(app(app(ty_@3, cc), cd), ce)) → new_esEs22(yvy4000, yvy3000, cc, cd, ce)
new_esEs5(yvy4001, yvy3001, ty_Integer) → new_esEs18(yvy4001, yvy3001)
new_esEs31(yvy40000, yvy30000, ty_Int) → new_esEs25(yvy40000, yvy30000)
new_esEs27(yvy1000, yvy1010, app(app(app(ty_@3, bff), bfg), bfh)) → new_esEs22(yvy1000, yvy1010, bff, bfg, bfh)
new_ltEs19(yvy1002, yvy1012, app(ty_Maybe, cag)) → new_ltEs5(yvy1002, yvy1012, cag)
new_lt21(yvy153, yvy156, ty_Integer) → new_lt15(yvy153, yvy156)
new_esEs29(yvy40000, yvy30000, app(app(ty_Either, ccb), ccc)) → new_esEs24(yvy40000, yvy30000, ccb, ccc)
new_esEs10(yvy4000, yvy3000, app(ty_Ratio, ega)) → new_esEs21(yvy4000, yvy3000, ega)
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_ltEs12(@2(yvy1000, yvy1001), @2(yvy1010, yvy1011), ecf, ecg) → new_pePe(new_lt22(yvy1000, yvy1010, ecf), new_asAs(new_esEs36(yvy1000, yvy1010, ecf), new_ltEs21(yvy1001, yvy1011, ecg)))
new_ltEs23(yvy166, yvy168, ty_@0) → new_ltEs17(yvy166, yvy168)
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_esEs5(yvy4001, yvy3001, app(ty_Maybe, baf)) → new_esEs23(yvy4001, yvy3001, baf)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Char) → new_ltEs7(yvy1000, yvy1010)
new_compare0(:(yvy4000, yvy4001), :(yvy3000, yvy3001), fef) → new_primCompAux1(yvy4000, yvy3000, new_compare0(yvy4001, yvy3001, fef), fef)
new_esEs20(False, True) → False
new_esEs20(True, False) → False
new_compare19(yvy206, yvy207, True, dgg, dgh) → LT
new_sr0(yvy3000, yvy4001) → new_primMulInt(yvy3000, yvy4001)
new_esEs28(yvy1001, yvy1011, app(app(ty_@2, bhc), bhd)) → new_esEs17(yvy1001, yvy1011, bhc, bhd)
new_lt6(yvy1000, yvy1010, app(app(ty_Either, bgd), bge)) → new_lt16(yvy1000, yvy1010, bgd, bge)
new_esEs34(yvy152, yvy155, ty_Bool) → new_esEs20(yvy152, yvy155)
new_lt22(yvy1000, yvy1010, ty_Integer) → new_lt15(yvy1000, yvy1010)
new_esEs26(yvy40000, yvy30000, app(app(ty_Either, bdc), bdd)) → new_esEs24(yvy40000, yvy30000, bdc, bdd)
new_compare30(yvy400, yvy300, ty_Ordering) → new_compare15(yvy400, yvy300)
new_esEs30(yvy40001, yvy30001, app(ty_[], ccd)) → new_esEs16(yvy40001, yvy30001, ccd)
new_esEs24(Left(yvy40000), Left(yvy30000), app(app(ty_@2, ded), dee), hf) → new_esEs17(yvy40000, yvy30000, ded, dee)
new_lt23(yvy165, yvy167, ty_@0) → new_lt19(yvy165, yvy167)
new_esEs10(yvy4000, yvy3000, ty_Float) → new_esEs14(yvy4000, yvy3000)
new_compare29(Double(yvy4000, yvy4001), Double(yvy3000, yvy3001)) → new_compare16(new_sr0(yvy4000, yvy3000), new_sr0(yvy4001, yvy3001))
new_ltEs14(Right(yvy1000), Right(yvy1010), dbd, ty_Bool) → new_ltEs16(yvy1000, yvy1010)
new_ltEs22(yvy114, yvy115, app(ty_[], fad)) → new_ltEs8(yvy114, yvy115, fad)
new_esEs39(yvy165, yvy167, app(app(ty_Either, fch), fda)) → new_esEs24(yvy165, yvy167, fch, fda)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs32(yvy40001, yvy30001, ty_Double) → new_esEs13(yvy40001, yvy30001)
new_esEs28(yvy1001, yvy1011, ty_Bool) → new_esEs20(yvy1001, yvy1011)
new_esEs23(Just(yvy40000), Just(yvy30000), app(ty_Ratio, ddb)) → new_esEs21(yvy40000, yvy30000, ddb)
new_esEs5(yvy4001, yvy3001, app(ty_Ratio, bab)) → new_esEs21(yvy4001, yvy3001, bab)
new_ltEs14(Left(yvy1000), Right(yvy1010), dbd, daa) → True
new_compare24(yvy165, yvy166, yvy167, yvy168, False, fbf, fbg) → new_compare110(yvy165, yvy166, yvy167, yvy168, new_lt23(yvy165, yvy167, fbf), new_asAs(new_esEs39(yvy165, yvy167, fbf), new_ltEs23(yvy166, yvy168, fbg)), fbf, fbg)
new_compare30(yvy400, yvy300, app(ty_[], fef)) → new_compare0(yvy400, yvy300, fef)
new_esEs9(yvy4000, yvy3000, app(ty_Ratio, ffd)) → new_esEs21(yvy4000, yvy3000, ffd)
new_ltEs20(yvy154, yvy157, app(app(ty_Either, ecb), ecc)) → new_ltEs14(yvy154, yvy157, ecb, ecc)
new_asAs(False, yvy184) → False
new_compare27(Right(yvy4000), Left(yvy3000), efd, efe) → GT
new_esEs36(yvy1000, yvy1010, app(ty_Maybe, edg)) → new_esEs23(yvy1000, yvy1010, edg)
new_esEs9(yvy4000, yvy3000, ty_Double) → new_esEs13(yvy4000, yvy3000)
new_ltEs19(yvy1002, yvy1012, app(app(ty_Either, cah), cba)) → new_ltEs14(yvy1002, yvy1012, cah, cba)
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_lt20(yvy152, yvy155, ty_@0) → new_lt19(yvy152, yvy155)
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_esEs4(yvy4000, yvy3000, ty_@0) → new_esEs19(yvy4000, yvy3000)
new_esEs27(yvy1000, yvy1010, ty_Double) → new_esEs13(yvy1000, yvy1010)
new_esEs36(yvy1000, yvy1010, ty_Ordering) → new_esEs12(yvy1000, yvy1010)
new_compare16(yvy400, yvy300) → new_primCmpInt(yvy400, yvy300)
new_esEs35(yvy153, yvy156, ty_Bool) → new_esEs20(yvy153, yvy156)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Bool) → new_esEs20(yvy40000, yvy30000)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Integer, daa) → new_ltEs4(yvy1000, yvy1010)
new_compare14(yvy218, yvy219, yvy220, yvy221, yvy222, yvy223, True, cdh, cea, ceb) → LT
new_esEs30(yvy40001, yvy30001, app(ty_Maybe, cdc)) → new_esEs23(yvy40001, yvy30001, cdc)
new_esEs8(yvy4001, yvy3001, ty_Char) → new_esEs15(yvy4001, yvy3001)
new_esEs9(yvy4000, yvy3000, ty_Bool) → new_esEs20(yvy4000, yvy3000)
new_lt5(yvy1001, yvy1011, ty_Ordering) → new_lt7(yvy1001, yvy1011)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbd, ty_Ordering) → new_ltEs6(yvy1000, yvy1010)
new_esEs24(Left(yvy40000), Left(yvy30000), app(app(ty_Either, dfc), dfd), hf) → new_esEs24(yvy40000, yvy30000, dfc, dfd)
new_esEs8(yvy4001, yvy3001, app(ty_[], db)) → new_esEs16(yvy4001, yvy3001, db)
new_compare27(Left(yvy4000), Left(yvy3000), efd, efe) → new_compare26(yvy4000, yvy3000, new_esEs10(yvy4000, yvy3000, efd), efd, efe)
new_esEs29(yvy40000, yvy30000, ty_Double) → new_esEs13(yvy40000, yvy30000)
new_esEs27(yvy1000, yvy1010, ty_Integer) → new_esEs18(yvy1000, yvy1010)
new_esEs18(Integer(yvy40000), Integer(yvy30000)) → new_primEqInt(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, ty_Char) → new_esEs15(yvy40002, yvy30002)
new_ltEs5(Just(yvy1000), Just(yvy1010), app(ty_Maybe, fg)) → new_ltEs5(yvy1000, yvy1010, fg)
new_ltEs11(yvy100, yvy101) → new_fsEs(new_compare18(yvy100, yvy101))
new_ltEs14(Right(yvy1000), Right(yvy1010), dbd, app(app(ty_Either, dce), dcf)) → new_ltEs14(yvy1000, yvy1010, dce, dcf)
new_esEs30(yvy40001, yvy30001, ty_Float) → new_esEs14(yvy40001, yvy30001)
new_lt23(yvy165, yvy167, ty_Float) → new_lt11(yvy165, yvy167)
new_compare12(False, False) → EQ
new_esEs28(yvy1001, yvy1011, ty_@0) → new_esEs19(yvy1001, yvy1011)
new_ltEs23(yvy166, yvy168, ty_Char) → new_ltEs7(yvy166, yvy168)
new_esEs24(Right(yvy40000), Right(yvy30000), he, app(ty_Maybe, dgd)) → new_esEs23(yvy40000, yvy30000, dgd)
new_esEs29(yvy40000, yvy30000, ty_Float) → new_esEs14(yvy40000, yvy30000)
new_esEs7(yvy4000, yvy3000, ty_Ordering) → new_esEs12(yvy4000, yvy3000)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Integer, hf) → new_esEs18(yvy40000, yvy30000)
new_lt20(yvy152, yvy155, app(ty_Maybe, dhe)) → new_lt14(yvy152, yvy155, dhe)
new_esEs39(yvy165, yvy167, app(app(app(ty_@3, fcb), fcc), fcd)) → new_esEs22(yvy165, yvy167, fcb, fcc, fcd)
new_esEs31(yvy40000, yvy30000, ty_@0) → new_esEs19(yvy40000, yvy30000)
new_esEs24(Right(yvy40000), Right(yvy30000), he, app(ty_[], dfe)) → new_esEs16(yvy40000, yvy30000, dfe)
new_compare111(yvy233, yvy234, yvy235, yvy236, False, ecd, ece) → GT
new_lt21(yvy153, yvy156, ty_Bool) → new_lt18(yvy153, yvy156)
new_ltEs6(LT, GT) → True
new_esEs33(yvy40002, yvy30002, ty_Int) → new_esEs25(yvy40002, yvy30002)
new_compare30(yvy400, yvy300, ty_Integer) → new_compare8(yvy400, yvy300)
new_ltEs23(yvy166, yvy168, app(ty_Maybe, fea)) → new_ltEs5(yvy166, yvy168, fea)
new_lt23(yvy165, yvy167, app(ty_Maybe, fcg)) → new_lt14(yvy165, yvy167, fcg)
new_ltEs21(yvy1001, yvy1011, ty_Char) → new_ltEs7(yvy1001, yvy1011)
new_ltEs14(Left(yvy1000), Left(yvy1010), app(app(ty_Either, dbb), dbc), daa) → new_ltEs14(yvy1000, yvy1010, dbb, dbc)
new_ltEs23(yvy166, yvy168, app(app(ty_@2, fdg), fdh)) → new_ltEs12(yvy166, yvy168, fdg, fdh)
new_ltEs21(yvy1001, yvy1011, ty_Ordering) → new_ltEs6(yvy1001, yvy1011)
new_esEs32(yvy40001, yvy30001, app(app(ty_@2, cff), cfg)) → new_esEs17(yvy40001, yvy30001, cff, cfg)
new_esEs24(Left(yvy40000), Left(yvy30000), app(ty_Maybe, dfb), hf) → new_esEs23(yvy40000, yvy30000, dfb)
new_lt22(yvy1000, yvy1010, app(ty_Ratio, eda)) → new_lt10(yvy1000, yvy1010, eda)
new_lt12(yvy152, yvy155, dea, deb) → new_esEs12(new_compare7(yvy152, yvy155, dea, deb), LT)
new_esEs35(yvy153, yvy156, ty_Int) → new_esEs25(yvy153, yvy156)
new_lt10(yvy152, yvy155, cdg) → new_esEs12(new_compare13(yvy152, yvy155, cdg), LT)
new_esEs4(yvy4000, yvy3000, ty_Double) → new_esEs13(yvy4000, yvy3000)
new_esEs8(yvy4001, yvy3001, app(app(ty_@2, dc), dd)) → new_esEs17(yvy4001, yvy3001, dc, dd)
new_esEs5(yvy4001, yvy3001, app(app(ty_@2, hh), baa)) → new_esEs17(yvy4001, yvy3001, hh, baa)
new_esEs16([], [], ge) → True
new_lt22(yvy1000, yvy1010, ty_Float) → new_lt11(yvy1000, yvy1010)
new_esEs32(yvy40001, yvy30001, ty_Ordering) → new_esEs12(yvy40001, yvy30001)
new_ltEs19(yvy1002, yvy1012, ty_Int) → new_ltEs15(yvy1002, yvy1012)
new_ltEs21(yvy1001, yvy1011, ty_Integer) → new_ltEs4(yvy1001, yvy1011)
new_ltEs20(yvy154, yvy157, ty_Float) → new_ltEs11(yvy154, yvy157)
new_lt5(yvy1001, yvy1011, app(app(ty_@2, bhc), bhd)) → new_lt12(yvy1001, yvy1011, bhc, bhd)
new_esEs11(yvy4000, yvy3000, ty_Int) → new_esEs25(yvy4000, yvy3000)
new_esEs32(yvy40001, yvy30001, app(app(app(ty_@3, cga), cgb), cgc)) → new_esEs22(yvy40001, yvy30001, cga, cgb, cgc)
new_lt6(yvy1000, yvy1010, ty_Double) → new_lt13(yvy1000, yvy1010)
new_lt20(yvy152, yvy155, ty_Float) → new_lt11(yvy152, yvy155)
new_ltEs14(Left(yvy1000), Left(yvy1010), app(app(app(ty_@3, dad), dae), daf), daa) → new_ltEs10(yvy1000, yvy1010, dad, dae, daf)
new_esEs26(yvy40000, yvy30000, ty_Integer) → new_esEs18(yvy40000, yvy30000)
new_lt22(yvy1000, yvy1010, app(app(app(ty_@3, edb), edc), edd)) → new_lt4(yvy1000, yvy1010, edb, edc, edd)
new_esEs36(yvy1000, yvy1010, app(app(ty_Either, edh), eea)) → new_esEs24(yvy1000, yvy1010, edh, eea)
new_esEs27(yvy1000, yvy1010, ty_Ordering) → new_esEs12(yvy1000, yvy1010)
new_ltEs19(yvy1002, yvy1012, ty_Double) → new_ltEs13(yvy1002, yvy1012)
new_lt21(yvy153, yvy156, ty_Int) → new_lt17(yvy153, yvy156)
new_lt20(yvy152, yvy155, ty_Integer) → new_lt15(yvy152, yvy155)
new_esEs24(Right(yvy40000), Right(yvy30000), he, ty_Ordering) → new_esEs12(yvy40000, yvy30000)
new_lt8(yvy152, yvy155) → new_esEs12(new_compare11(yvy152, yvy155), LT)
new_ltEs24(yvy100, yvy101, app(ty_[], fed)) → new_ltEs8(yvy100, yvy101, fed)
new_esEs9(yvy4000, yvy3000, ty_@0) → new_esEs19(yvy4000, yvy3000)
new_esEs22(@3(yvy40000, yvy40001, yvy40002), @3(yvy30000, yvy30001, yvy30002), ha, hb, hc) → new_asAs(new_esEs31(yvy40000, yvy30000, ha), new_asAs(new_esEs32(yvy40001, yvy30001, hb), new_esEs33(yvy40002, yvy30002, hc)))
new_esEs8(yvy4001, yvy3001, ty_Float) → new_esEs14(yvy4001, yvy3001)
new_esEs7(yvy4000, yvy3000, app(ty_Ratio, cb)) → new_esEs21(yvy4000, yvy3000, cb)
new_ltEs20(yvy154, yvy157, ty_Double) → new_ltEs13(yvy154, yvy157)
new_ltEs18(yvy107, yvy108, ty_Bool) → new_ltEs16(yvy107, yvy108)
new_compare28(yvy114, yvy115, False, fab, fac) → new_compare19(yvy114, yvy115, new_ltEs22(yvy114, yvy115, fac), fab, fac)
new_esEs6(yvy4002, yvy3002, app(ty_Maybe, bbh)) → new_esEs23(yvy4002, yvy3002, bbh)
new_lt5(yvy1001, yvy1011, app(app(app(ty_@3, bgh), bha), bhb)) → new_lt4(yvy1001, yvy1011, bgh, bha, bhb)
new_esEs31(yvy40000, yvy30000, app(app(app(ty_@3, ceg), ceh), cfa)) → new_esEs22(yvy40000, yvy30000, ceg, ceh, cfa)
new_esEs31(yvy40000, yvy30000, ty_Ordering) → new_esEs12(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, ty_Double) → new_esEs13(yvy40002, yvy30002)
new_lt6(yvy1000, yvy1010, ty_Float) → new_lt11(yvy1000, yvy1010)
new_esEs4(yvy4000, yvy3000, ty_Char) → new_esEs15(yvy4000, yvy3000)
new_esEs7(yvy4000, yvy3000, app(app(ty_Either, cg), da)) → new_esEs24(yvy4000, yvy3000, cg, da)
new_compare112(yvy189, yvy190, False, fgc) → GT
new_esEs12(GT, GT) → True
new_ltEs21(yvy1001, yvy1011, app(app(app(ty_@3, eed), eee), eef)) → new_ltEs10(yvy1001, yvy1011, eed, eee, eef)
new_esEs5(yvy4001, yvy3001, ty_Double) → new_esEs13(yvy4001, yvy3001)
new_compare17(yvy218, yvy219, yvy220, yvy221, yvy222, yvy223, False, yvy225, cdh, cea, ceb) → new_compare14(yvy218, yvy219, yvy220, yvy221, yvy222, yvy223, yvy225, cdh, cea, ceb)
new_esEs8(yvy4001, yvy3001, app(ty_Maybe, ea)) → new_esEs23(yvy4001, yvy3001, ea)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_@0) → new_esEs19(yvy40000, yvy30000)
new_compare25(yvy152, yvy153, yvy154, yvy155, yvy156, yvy157, False, dha, dhb, dhc) → new_compare17(yvy152, yvy153, yvy154, yvy155, yvy156, yvy157, new_lt20(yvy152, yvy155, dha), new_asAs(new_esEs34(yvy152, yvy155, dha), new_pePe(new_lt21(yvy153, yvy156, dhb), new_asAs(new_esEs35(yvy153, yvy156, dhb), new_ltEs20(yvy154, yvy157, dhc)))), dha, dhb, dhc)
new_compare31(Nothing, Just(yvy3000), feh) → LT
new_esEs29(yvy40000, yvy30000, ty_Ordering) → new_esEs12(yvy40000, yvy30000)
new_esEs4(yvy4000, yvy3000, app(ty_[], ge)) → new_esEs16(yvy4000, yvy3000, ge)
new_primPlusNat1(Zero, Zero) → Zero
new_compare0([], :(yvy3000, yvy3001), fef) → LT
new_ltEs6(LT, EQ) → True
new_lt23(yvy165, yvy167, ty_Ordering) → new_lt7(yvy165, yvy167)
new_ltEs21(yvy1001, yvy1011, app(ty_Maybe, efa)) → new_ltEs5(yvy1001, yvy1011, efa)
new_ltEs6(GT, LT) → False
new_lt18(yvy152, yvy155) → new_esEs12(new_compare12(yvy152, yvy155), LT)
new_esEs24(Right(yvy40000), Right(yvy30000), he, ty_Char) → new_esEs15(yvy40000, yvy30000)
new_asAs(True, yvy184) → yvy184
new_esEs26(yvy40000, yvy30000, ty_Float) → new_esEs14(yvy40000, yvy30000)
new_esEs35(yvy153, yvy156, ty_Float) → new_esEs14(yvy153, yvy156)
new_ltEs21(yvy1001, yvy1011, app(ty_[], eeb)) → new_ltEs8(yvy1001, yvy1011, eeb)
new_compare11(Char(yvy4000), Char(yvy3000)) → new_primCmpNat0(yvy4000, yvy3000)
new_ltEs22(yvy114, yvy115, ty_Float) → new_ltEs11(yvy114, yvy115)
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_esEs28(yvy1001, yvy1011, app(ty_Ratio, bgg)) → new_esEs21(yvy1001, yvy1011, bgg)
new_esEs39(yvy165, yvy167, ty_Double) → new_esEs13(yvy165, yvy167)
new_esEs11(yvy4000, yvy3000, ty_Bool) → new_esEs20(yvy4000, yvy3000)
new_ltEs22(yvy114, yvy115, ty_Double) → new_ltEs13(yvy114, yvy115)
new_lt22(yvy1000, yvy1010, ty_Ordering) → new_lt7(yvy1000, yvy1010)
new_esEs4(yvy4000, yvy3000, app(app(app(ty_@3, ha), hb), hc)) → new_esEs22(yvy4000, yvy3000, ha, hb, hc)
new_lt20(yvy152, yvy155, app(ty_Ratio, cdg)) → new_lt10(yvy152, yvy155, cdg)
new_ltEs16(False, False) → True
new_lt23(yvy165, yvy167, ty_Double) → new_lt13(yvy165, yvy167)
new_ltEs17(yvy100, yvy101) → new_fsEs(new_compare9(yvy100, yvy101))
new_esEs29(yvy40000, yvy30000, ty_Integer) → new_esEs18(yvy40000, yvy30000)
new_esEs8(yvy4001, yvy3001, ty_Ordering) → new_esEs12(yvy4001, yvy3001)
new_esEs30(yvy40001, yvy30001, ty_Bool) → new_esEs20(yvy40001, yvy30001)
new_lt23(yvy165, yvy167, app(ty_Ratio, fca)) → new_lt10(yvy165, yvy167, fca)
new_esEs30(yvy40001, yvy30001, ty_Int) → new_esEs25(yvy40001, yvy30001)
new_esEs27(yvy1000, yvy1010, ty_Float) → new_esEs14(yvy1000, yvy1010)
new_ltEs21(yvy1001, yvy1011, ty_Int) → new_ltEs15(yvy1001, yvy1011)
new_ltEs20(yvy154, yvy157, app(app(app(ty_@3, ebd), ebe), ebf)) → new_ltEs10(yvy154, yvy157, ebd, ebe, ebf)
new_esEs23(Just(yvy40000), Just(yvy30000), app(ty_[], dcg)) → new_esEs16(yvy40000, yvy30000, dcg)
new_esEs34(yvy152, yvy155, app(app(app(ty_@3, bb), bc), bd)) → new_esEs22(yvy152, yvy155, bb, bc, bd)
new_esEs16(:(yvy40000, yvy40001), :(yvy30000, yvy30001), ge) → new_asAs(new_esEs26(yvy40000, yvy30000, ge), new_esEs16(yvy40001, yvy30001, ge))
new_esEs9(yvy4000, yvy3000, app(app(app(ty_@3, ffe), fff), ffg)) → new_esEs22(yvy4000, yvy3000, ffe, fff, ffg)
new_ltEs19(yvy1002, yvy1012, app(app(app(ty_@3, cab), cac), cad)) → new_ltEs10(yvy1002, yvy1012, cab, cac, cad)
new_ltEs20(yvy154, yvy157, ty_Ordering) → new_ltEs6(yvy154, yvy157)
new_compare19(yvy206, yvy207, False, dgg, dgh) → GT
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Integer) → new_ltEs4(yvy1000, yvy1010)
new_esEs6(yvy4002, yvy3002, ty_@0) → new_esEs19(yvy4002, yvy3002)
new_ltEs10(@3(yvy1000, yvy1001, yvy1002), @3(yvy1010, yvy1011, yvy1012), bfa, bfb, bfc) → new_pePe(new_lt6(yvy1000, yvy1010, bfa), new_asAs(new_esEs27(yvy1000, yvy1010, bfa), new_pePe(new_lt5(yvy1001, yvy1011, bfb), new_asAs(new_esEs28(yvy1001, yvy1011, bfb), new_ltEs19(yvy1002, yvy1012, bfc)))))
new_esEs33(yvy40002, yvy30002, ty_@0) → new_esEs19(yvy40002, yvy30002)
new_esEs35(yvy153, yvy156, app(ty_Ratio, eaa)) → new_esEs21(yvy153, yvy156, eaa)
new_ltEs22(yvy114, yvy115, ty_Int) → new_ltEs15(yvy114, yvy115)
new_ltEs24(yvy100, yvy101, app(app(app(ty_@3, bfa), bfb), bfc)) → new_ltEs10(yvy100, yvy101, bfa, bfb, bfc)
new_compare27(Right(yvy4000), Right(yvy3000), efd, efe) → new_compare28(yvy4000, yvy3000, new_esEs11(yvy4000, yvy3000, efe), efd, efe)
new_ltEs21(yvy1001, yvy1011, ty_@0) → new_ltEs17(yvy1001, yvy1011)
new_lt16(yvy152, yvy155, dhf, dhg) → new_esEs12(new_compare27(yvy152, yvy155, dhf, dhg), LT)
new_compare15(EQ, EQ) → EQ
new_ltEs22(yvy114, yvy115, ty_Char) → new_ltEs7(yvy114, yvy115)
new_compare30(yvy400, yvy300, ty_Double) → new_compare29(yvy400, yvy300)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCompAux0(yvy56, EQ) → yvy56
new_lt6(yvy1000, yvy1010, app(app(ty_@2, bga), bgb)) → new_lt12(yvy1000, yvy1010, bga, bgb)
new_esEs27(yvy1000, yvy1010, app(ty_Maybe, bgc)) → new_esEs23(yvy1000, yvy1010, bgc)
new_ltEs20(yvy154, yvy157, ty_Char) → new_ltEs7(yvy154, yvy157)
new_esEs10(yvy4000, yvy3000, ty_Integer) → new_esEs18(yvy4000, yvy3000)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_@0, daa) → new_ltEs17(yvy1000, yvy1010)
new_ltEs18(yvy107, yvy108, ty_Int) → new_ltEs15(yvy107, yvy108)
new_lt21(yvy153, yvy156, app(app(app(ty_@3, eab), eac), ead)) → new_lt4(yvy153, yvy156, eab, eac, ead)
new_esEs6(yvy4002, yvy3002, ty_Char) → new_esEs15(yvy4002, yvy3002)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_esEs30(yvy40001, yvy30001, ty_Char) → new_esEs15(yvy40001, yvy30001)
new_ltEs5(Just(yvy1000), Just(yvy1010), app(app(app(ty_@3, fa), fb), fc)) → new_ltEs10(yvy1000, yvy1010, fa, fb, fc)
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_esEs39(yvy165, yvy167, app(ty_[], fbh)) → new_esEs16(yvy165, yvy167, fbh)
new_esEs35(yvy153, yvy156, ty_Char) → new_esEs15(yvy153, yvy156)
new_not(True) → False
new_ltEs5(Just(yvy1000), Just(yvy1010), app(ty_Ratio, eh)) → new_ltEs9(yvy1000, yvy1010, eh)

The set Q consists of the following terms:

new_esEs36(x0, x1, ty_Char)
new_esEs35(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, ty_Float)
new_esEs7(x0, x1, ty_Int)
new_esEs32(x0, x1, app(ty_[], x2))
new_ltEs21(x0, x1, ty_Int)
new_esEs10(x0, x1, ty_Float)
new_ltEs16(True, True)
new_esEs6(x0, x1, ty_Int)
new_lt11(x0, x1)
new_ltEs20(x0, x1, ty_Int)
new_lt5(x0, x1, ty_Char)
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs23(x0, x1, app(ty_Maybe, x2))
new_esEs32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs21(x0, x1, ty_@0)
new_esEs29(x0, x1, ty_Char)
new_ltEs22(x0, x1, ty_Integer)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_compare10(x0, x1, False, x2, x3)
new_esEs32(x0, x1, ty_Int)
new_esEs11(x0, x1, ty_Int)
new_esEs24(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs4(x0, x1, ty_Float)
new_lt23(x0, x1, app(ty_[], x2))
new_esEs33(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Integer)
new_compare30(x0, x1, ty_Int)
new_pePe(True, x0)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs11(x0, x1, ty_@0)
new_esEs35(x0, x1, ty_Integer)
new_esEs11(x0, x1, ty_Char)
new_esEs6(x0, x1, ty_Float)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(x0, x1, ty_Int)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_lt22(x0, x1, ty_@0)
new_compare30(x0, x1, ty_Bool)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_@0)
new_esEs29(x0, x1, ty_Ordering)
new_lt22(x0, x1, ty_Float)
new_lt23(x0, x1, ty_Integer)
new_esEs11(x0, x1, app(ty_Ratio, x2))
new_lt7(x0, x1)
new_esEs8(x0, x1, ty_Integer)
new_esEs23(Just(x0), Just(x1), ty_Float)
new_compare30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs5(Nothing, Nothing, x0)
new_esEs6(x0, x1, ty_Integer)
new_lt5(x0, x1, ty_@0)
new_esEs23(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs11(x0, x1, ty_Bool)
new_lt6(x0, x1, app(app(ty_@2, x2), x3))
new_esEs36(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare12(False, True)
new_compare12(True, False)
new_compare26(x0, x1, True, x2, x3)
new_lt21(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(Left(x0), Left(x1), ty_@0, x2)
new_ltEs7(x0, x1)
new_ltEs18(x0, x1, app(ty_[], x2))
new_primCompAux0(x0, EQ)
new_ltEs14(Right(x0), Right(x1), x2, ty_Char)
new_esEs36(x0, x1, app(app(ty_Either, x2), x3))
new_esEs39(x0, x1, app(ty_Ratio, x2))
new_ltEs14(Right(x0), Right(x1), x2, ty_Float)
new_esEs10(x0, x1, ty_Integer)
new_esEs32(x0, x1, ty_Ordering)
new_ltEs21(x0, x1, ty_Float)
new_ltEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs24(x0, x1, ty_Integer)
new_compare19(x0, x1, False, x2, x3)
new_lt5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs34(x0, x1, ty_Float)
new_ltEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs24(Left(x0), Left(x1), ty_@0, x2)
new_esEs6(x0, x1, ty_@0)
new_lt6(x0, x1, ty_Float)
new_ltEs14(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs9(x0, x1, app(app(ty_Either, x2), x3))
new_esEs9(x0, x1, ty_Int)
new_compare30(x0, x1, ty_Integer)
new_esEs12(GT, EQ)
new_esEs12(EQ, GT)
new_esEs36(x0, x1, ty_Int)
new_ltEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, ty_Bool)
new_esEs11(x0, x1, app(app(ty_@2, x2), x3))
new_esEs10(x0, x1, app(app(ty_Either, x2), x3))
new_lt6(x0, x1, app(ty_Ratio, x2))
new_compare28(x0, x1, False, x2, x3)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt5(x0, x1, ty_Double)
new_lt5(x0, x1, app(ty_[], x2))
new_esEs24(Right(x0), Right(x1), x2, ty_Float)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare15(LT, LT)
new_esEs34(x0, x1, app(ty_Maybe, x2))
new_lt5(x0, x1, app(ty_Ratio, x2))
new_esEs10(x0, x1, ty_Char)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs39(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(Right(x0), Right(x1), x2, ty_Double)
new_esEs34(x0, x1, ty_Ordering)
new_esEs39(x0, x1, app(ty_[], x2))
new_esEs12(GT, GT)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs30(x0, x1, ty_Double)
new_esEs24(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs21(x0, x1, ty_Ordering)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_lt21(x0, x1, ty_Float)
new_esEs11(x0, x1, ty_Integer)
new_compare0(:(x0, x1), [], x2)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(Just(x0), Nothing, x1)
new_esEs23(Just(x0), Just(x1), ty_Double)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs5(Just(x0), Nothing, x1)
new_esEs11(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, ty_Char)
new_esEs38(x0, x1, ty_Integer)
new_esEs27(x0, x1, ty_Bool)
new_esEs10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs6(EQ, EQ)
new_esEs32(x0, x1, ty_@0)
new_esEs7(x0, x1, ty_Float)
new_esEs23(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs22(x0, x1, ty_Char)
new_esEs9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(x0, x1, ty_Double)
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_esEs5(x0, x1, ty_Bool)
new_esEs31(x0, x1, ty_Int)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs32(x0, x1, app(ty_Ratio, x2))
new_esEs33(x0, x1, ty_Double)
new_ltEs14(Right(x0), Right(x1), x2, ty_Int)
new_esEs8(x0, x1, ty_Float)
new_ltEs18(x0, x1, ty_@0)
new_esEs36(x0, x1, app(app(ty_@2, x2), x3))
new_esEs16(:(x0, x1), :(x2, x3), x4)
new_lt9(x0, x1, x2)
new_ltEs5(Just(x0), Just(x1), ty_@0)
new_lt5(x0, x1, ty_Int)
new_ltEs6(LT, EQ)
new_ltEs6(EQ, LT)
new_primCompAux0(x0, LT)
new_esEs38(x0, x1, ty_Int)
new_esEs23(Just(x0), Just(x1), ty_Int)
new_ltEs20(x0, x1, ty_@0)
new_esEs5(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Int)
new_lt17(x0, x1)
new_esEs36(x0, x1, ty_Bool)
new_primEqNat0(Zero, Zero)
new_compare13(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs23(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_@0)
new_compare30(x0, x1, app(ty_[], x2))
new_esEs7(x0, x1, ty_Bool)
new_esEs9(x0, x1, app(ty_[], x2))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs10(x0, x1, app(ty_Maybe, x2))
new_esEs5(x0, x1, ty_Float)
new_ltEs22(x0, x1, ty_Float)
new_compare15(GT, GT)
new_esEs31(x0, x1, ty_Double)
new_compare27(Right(x0), Right(x1), x2, x3)
new_ltEs20(x0, x1, ty_Integer)
new_lt22(x0, x1, ty_Bool)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs34(x0, x1, ty_Bool)
new_esEs31(x0, x1, ty_Integer)
new_esEs6(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, ty_Char)
new_lt20(x0, x1, ty_Double)
new_ltEs22(x0, x1, app(app(ty_Either, x2), x3))
new_compare17(x0, x1, x2, x3, x4, x5, True, x6, x7, x8, x9)
new_ltEs15(x0, x1)
new_esEs4(x0, x1, ty_Integer)
new_esEs31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs39(x0, x1, ty_Bool)
new_ltEs24(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Float)
new_primMulNat0(Zero, Zero)
new_asAs(True, x0)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Double)
new_esEs5(x0, x1, ty_Double)
new_esEs34(x0, x1, app(ty_[], x2))
new_fsEs(x0)
new_esEs6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs8(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(:%(x0, x1), :%(x2, x3), x4)
new_ltEs5(Just(x0), Just(x1), ty_Integer)
new_lt6(x0, x1, ty_Double)
new_compare28(x0, x1, True, x2, x3)
new_esEs35(x0, x1, ty_Double)
new_ltEs18(x0, x1, ty_Bool)
new_lt6(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, ty_Float)
new_ltEs5(Just(x0), Just(x1), ty_Double)
new_lt22(x0, x1, ty_Ordering)
new_esEs9(x0, x1, ty_@0)
new_esEs35(x0, x1, ty_Bool)
new_ltEs14(Left(x0), Right(x1), x2, x3)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(Right(x0), Left(x1), x2, x3)
new_ltEs14(Right(x0), Right(x1), x2, ty_Integer)
new_esEs35(x0, x1, ty_Char)
new_ltEs23(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, ty_Bool)
new_esEs31(x0, x1, ty_@0)
new_esEs24(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs19(x0, x1, ty_Double)
new_ltEs24(x0, x1, ty_Double)
new_esEs13(Double(x0, x1), Double(x2, x3))
new_esEs32(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, ty_Ordering)
new_lt23(x0, x1, app(ty_Ratio, x2))
new_esEs20(True, True)
new_lt20(x0, x1, app(ty_[], x2))
new_lt22(x0, x1, ty_Int)
new_ltEs12(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs7(x0, x1, ty_Integer)
new_esEs30(x0, x1, ty_Bool)
new_lt21(x0, x1, ty_@0)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs33(x0, x1, ty_Float)
new_esEs29(x0, x1, ty_Integer)
new_compare31(Nothing, Nothing, x0)
new_ltEs21(x0, x1, ty_Integer)
new_primPlusNat0(Zero, x0)
new_lt21(x0, x1, app(ty_Ratio, x2))
new_lt22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(x0, x1, app(ty_[], x2))
new_esEs4(x0, x1, ty_Ordering)
new_ltEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs8(x0, x1, ty_Bool)
new_esEs7(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs31(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_primPlusNat0(Succ(x0), x1)
new_ltEs14(Right(x0), Right(x1), x2, ty_Double)
new_ltEs4(x0, x1)
new_compare10(x0, x1, True, x2, x3)
new_compare24(x0, x1, x2, x3, False, x4, x5)
new_esEs34(x0, x1, ty_Integer)
new_esEs31(x0, x1, ty_Ordering)
new_ltEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs6(GT, LT)
new_ltEs6(LT, GT)
new_ltEs14(Left(x0), Left(x1), ty_Char, x2)
new_compare210(x0, x1, True, x2)
new_lt23(x0, x1, app(app(ty_@2, x2), x3))
new_compare0([], [], x0)
new_esEs11(x0, x1, ty_Double)
new_esEs16(:(x0, x1), [], x2)
new_lt19(x0, x1)
new_ltEs23(x0, x1, app(ty_Ratio, x2))
new_compare111(x0, x1, x2, x3, True, x4, x5)
new_esEs4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(x0, x1, ty_Double)
new_compare30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Double)
new_esEs39(x0, x1, ty_Char)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_compare15(EQ, EQ)
new_esEs24(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_lt6(x0, x1, ty_Int)
new_lt5(x0, x1, app(app(ty_@2, x2), x3))
new_lt21(x0, x1, ty_Ordering)
new_esEs24(Left(x0), Left(x1), ty_Bool, x2)
new_esEs28(x0, x1, ty_Ordering)
new_ltEs22(x0, x1, ty_Ordering)
new_ltEs11(x0, x1)
new_esEs16([], :(x0, x1), x2)
new_esEs24(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_lt20(x0, x1, ty_Float)
new_lt21(x0, x1, ty_Integer)
new_esEs32(x0, x1, ty_Bool)
new_esEs39(x0, x1, ty_Float)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt6(x0, x1, ty_Integer)
new_ltEs14(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs10(x0, x1, ty_Double)
new_sr0(x0, x1)
new_esEs23(Just(x0), Just(x1), ty_Integer)
new_esEs24(Left(x0), Left(x1), ty_Integer, x2)
new_esEs20(False, True)
new_esEs20(True, False)
new_lt22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, ty_Bool)
new_ltEs23(x0, x1, ty_Integer)
new_lt22(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs20(False, False)
new_compare12(False, False)
new_ltEs22(x0, x1, app(ty_Ratio, x2))
new_esEs23(Nothing, Nothing, x0)
new_esEs12(LT, EQ)
new_esEs12(EQ, LT)
new_lt21(x0, x1, ty_Int)
new_lt22(x0, x1, ty_Char)
new_esEs31(x0, x1, app(ty_Maybe, x2))
new_compare14(x0, x1, x2, x3, x4, x5, True, x6, x7, x8)
new_esEs31(x0, x1, ty_Float)
new_esEs24(Right(x0), Right(x1), x2, ty_Int)
new_primPlusNat1(Zero, Zero)
new_ltEs21(x0, x1, ty_Bool)
new_esEs34(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs20(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_Float)
new_esEs12(EQ, EQ)
new_compare25(x0, x1, x2, x3, x4, x5, False, x6, x7, x8)
new_esEs23(Just(x0), Just(x1), ty_Bool)
new_esEs27(x0, x1, ty_Char)
new_esEs4(x0, x1, app(app(ty_Either, x2), x3))
new_esEs9(x0, x1, ty_Integer)
new_esEs30(x0, x1, ty_Float)
new_ltEs20(x0, x1, ty_Float)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs28(x0, x1, ty_Double)
new_esEs30(x0, x1, ty_Char)
new_ltEs14(Right(x0), Right(x1), x2, ty_@0)
new_compare30(x0, x1, ty_@0)
new_esEs6(x0, x1, ty_Bool)
new_ltEs5(Nothing, Just(x0), x1)
new_esEs24(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs23(x0, x1, ty_Float)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_lt23(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs7(x0, x1, app(ty_Ratio, x2))
new_compare15(EQ, GT)
new_compare15(GT, EQ)
new_ltEs24(x0, x1, ty_Ordering)
new_compare30(x0, x1, ty_Char)
new_primEqNat0(Succ(x0), Zero)
new_compare15(LT, GT)
new_compare15(GT, LT)
new_esEs24(Right(x0), Right(x1), x2, ty_@0)
new_lt14(x0, x1, x2)
new_esEs36(x0, x1, ty_Double)
new_esEs39(x0, x1, ty_Ordering)
new_esEs4(x0, x1, app(ty_[], x2))
new_ltEs21(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_esEs37(x0, x1, ty_Int)
new_esEs4(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs9(x0, x1, ty_Double)
new_primMulInt(Neg(x0), Neg(x1))
new_compare14(x0, x1, x2, x3, x4, x5, False, x6, x7, x8)
new_ltEs17(x0, x1)
new_compare30(x0, x1, app(ty_Ratio, x2))
new_esEs9(x0, x1, ty_Ordering)
new_esEs8(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, ty_Char)
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_ltEs23(x0, x1, ty_Int)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_esEs8(x0, x1, ty_Int)
new_ltEs5(Just(x0), Just(x1), ty_Int)
new_esEs33(x0, x1, ty_Int)
new_ltEs23(x0, x1, ty_@0)
new_esEs24(Left(x0), Left(x1), ty_Double, x2)
new_lt5(x0, x1, app(app(ty_Either, x2), x3))
new_esEs33(x0, x1, ty_Bool)
new_esEs10(x0, x1, ty_Ordering)
new_ltEs14(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs35(x0, x1, ty_@0)
new_esEs4(x0, x1, ty_Char)
new_ltEs14(Left(x0), Left(x1), ty_Integer, x2)
new_lt23(x0, x1, ty_Int)
new_esEs6(x0, x1, app(ty_[], x2))
new_esEs24(Left(x0), Left(x1), ty_Float, x2)
new_ltEs23(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs34(x0, x1, app(ty_Ratio, x2))
new_ltEs18(x0, x1, ty_Double)
new_lt23(x0, x1, ty_Bool)
new_ltEs14(Left(x0), Left(x1), ty_Float, x2)
new_esEs7(x0, x1, app(ty_Maybe, x2))
new_ltEs24(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_ltEs21(x0, x1, app(ty_Maybe, x2))
new_lt21(x0, x1, ty_Bool)
new_compare18(Float(x0, x1), Float(x2, x3))
new_ltEs5(Just(x0), Just(x1), ty_Float)
new_ltEs22(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_lt22(x0, x1, app(app(ty_Either, x2), x3))
new_compare110(x0, x1, x2, x3, True, x4, x5, x6)
new_esEs26(x0, x1, ty_Bool)
new_lt6(x0, x1, ty_Bool)
new_esEs30(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Integer)
new_ltEs14(Left(x0), Left(x1), ty_Bool, x2)
new_esEs8(x0, x1, ty_Double)
new_lt21(x0, x1, ty_Char)
new_lt5(x0, x1, ty_Float)
new_compare11(Char(x0), Char(x1))
new_compare31(Nothing, Just(x0), x1)
new_compare30(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs30(x0, x1, ty_Integer)
new_esEs7(x0, x1, app(app(ty_@2, x2), x3))
new_esEs33(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, ty_@0)
new_sr(Integer(x0), Integer(x1))
new_esEs16([], [], x0)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs7(x0, x1, ty_@0)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs23(Nothing, Just(x0), x1)
new_esEs11(x0, x1, app(ty_[], x2))
new_esEs34(x0, x1, ty_Char)
new_esEs10(x0, x1, ty_Bool)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs10(x0, x1, ty_@0)
new_compare7(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs39(x0, x1, ty_Double)
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_@0)
new_lt6(x0, x1, app(app(ty_Either, x2), x3))
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_esEs31(x0, x1, ty_Bool)
new_primEqNat0(Zero, Succ(x0))
new_primPlusNat1(Succ(x0), Zero)
new_lt23(x0, x1, ty_Char)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_lt22(x0, x1, app(ty_[], x2))
new_lt12(x0, x1, x2, x3)
new_lt20(x0, x1, ty_Char)
new_lt4(x0, x1, x2, x3, x4)
new_esEs39(x0, x1, app(ty_Maybe, x2))
new_ltEs22(x0, x1, app(ty_[], x2))
new_esEs6(x0, x1, ty_Ordering)
new_esEs33(x0, x1, ty_Char)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt22(x0, x1, app(ty_Maybe, x2))
new_esEs10(x0, x1, app(ty_Ratio, x2))
new_esEs32(x0, x1, ty_Integer)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_esEs33(x0, x1, app(ty_Ratio, x2))
new_pePe(False, x0)
new_ltEs24(x0, x1, ty_Int)
new_ltEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_lt8(x0, x1)
new_ltEs14(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs10(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_lt23(x0, x1, ty_Double)
new_ltEs22(x0, x1, app(ty_Maybe, x2))
new_esEs31(x0, x1, app(app(ty_Either, x2), x3))
new_lt5(x0, x1, app(ty_Maybe, x2))
new_compare110(x0, x1, x2, x3, False, x4, x5, x6)
new_lt20(x0, x1, ty_Bool)
new_esEs29(x0, x1, ty_Int)
new_ltEs14(Left(x0), Left(x1), ty_Double, x2)
new_esEs30(x0, x1, ty_Ordering)
new_lt23(x0, x1, ty_Float)
new_esEs6(x0, x1, app(ty_Ratio, x2))
new_lt6(x0, x1, ty_@0)
new_esEs35(x0, x1, app(app(ty_@2, x2), x3))
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs31(x0, x1, ty_Char)
new_esEs23(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_lt22(x0, x1, ty_Double)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs22(x0, x1, ty_@0)
new_esEs39(x0, x1, ty_Int)
new_esEs30(x0, x1, ty_@0)
new_ltEs16(False, True)
new_ltEs16(True, False)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_ltEs6(GT, GT)
new_compare112(x0, x1, True, x2)
new_esEs10(x0, x1, ty_Int)
new_lt21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs32(x0, x1, ty_Char)
new_lt21(x0, x1, app(ty_Maybe, x2))
new_ltEs18(x0, x1, ty_Int)
new_ltEs5(Just(x0), Just(x1), ty_Ordering)
new_esEs33(x0, x1, app(ty_[], x2))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_ltEs19(x0, x1, ty_Char)
new_ltEs5(Just(x0), Just(x1), ty_Char)
new_esEs27(x0, x1, ty_Int)
new_compare26(x0, x1, False, x2, x3)
new_esEs23(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs21(x0, x1, app(ty_[], x2))
new_ltEs5(Just(x0), Just(x1), ty_Bool)
new_ltEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_lt22(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_@0)
new_ltEs22(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_Integer)
new_esEs33(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Int)
new_primCmpNat0(Zero, Zero)
new_esEs35(x0, x1, ty_Float)
new_asAs(False, x0)
new_ltEs19(x0, x1, app(ty_[], x2))
new_lt5(x0, x1, ty_Integer)
new_ltEs24(x0, x1, ty_@0)
new_esEs6(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs19(x0, x1, ty_Int)
new_lt23(x0, x1, ty_@0)
new_esEs34(x0, x1, ty_Int)
new_ltEs6(LT, LT)
new_compare30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs35(x0, x1, app(app(ty_Either, x2), x3))
new_esEs11(x0, x1, ty_Ordering)
new_esEs28(x0, x1, app(ty_[], x2))
new_ltEs14(Left(x0), Left(x1), ty_Int, x2)
new_ltEs22(x0, x1, ty_Double)
new_esEs9(x0, x1, app(ty_Ratio, x2))
new_ltEs24(x0, x1, ty_Char)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare27(Right(x0), Left(x1), x2, x3)
new_compare27(Left(x0), Right(x1), x2, x3)
new_esEs36(x0, x1, app(ty_[], x2))
new_esEs18(Integer(x0), Integer(x1))
new_esEs32(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Int)
new_esEs34(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(Just(x0), Just(x1), ty_@0)
new_esEs4(x0, x1, app(ty_Maybe, x2))
new_compare24(x0, x1, x2, x3, True, x4, x5)
new_ltEs19(x0, x1, ty_Float)
new_esEs6(x0, x1, ty_Char)
new_lt21(x0, x1, ty_Double)
new_ltEs14(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_compare210(x0, x1, False, x2)
new_esEs30(x0, x1, app(ty_[], x2))
new_esEs24(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_lt5(x0, x1, ty_Bool)
new_esEs23(Just(x0), Just(x1), ty_Char)
new_ltEs13(x0, x1)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs23(x0, x1, ty_Bool)
new_esEs24(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs5(x0, x1, app(ty_[], x2))
new_compare15(LT, EQ)
new_compare15(EQ, LT)
new_compare9(@0, @0)
new_lt13(x0, x1)
new_esEs36(x0, x1, ty_Integer)
new_esEs29(x0, x1, ty_Double)
new_esEs8(x0, x1, app(ty_Maybe, x2))
new_esEs5(x0, x1, app(ty_Ratio, x2))
new_ltEs18(x0, x1, ty_Float)
new_compare25(x0, x1, x2, x3, x4, x5, True, x6, x7, x8)
new_lt18(x0, x1)
new_esEs24(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs8(x0, x1, app(ty_Ratio, x2))
new_lt5(x0, x1, ty_Ordering)
new_esEs5(x0, x1, app(ty_Maybe, x2))
new_lt15(x0, x1)
new_compare8(Integer(x0), Integer(x1))
new_esEs34(x0, x1, app(app(ty_Either, x2), x3))
new_esEs31(x0, x1, app(ty_Ratio, x2))
new_esEs23(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs11(x0, x1, app(ty_Maybe, x2))
new_esEs8(x0, x1, ty_@0)
new_esEs5(x0, x1, ty_Int)
new_not(True)
new_compare30(x0, x1, ty_Float)
new_esEs33(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Ordering)
new_primMulInt(Pos(x0), Pos(x1))
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs4(x0, x1, ty_Bool)
new_esEs32(x0, x1, ty_Float)
new_esEs24(Right(x0), Right(x1), x2, ty_Char)
new_esEs36(x0, x1, ty_Ordering)
new_ltEs5(Just(x0), Just(x1), app(ty_[], x2))
new_esEs9(x0, x1, ty_Bool)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_not(False)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_compare29(Double(x0, x1), Double(x2, x3))
new_esEs6(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(Right(x0), Right(x1), x2, ty_Ordering)
new_compare13(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs24(Left(x0), Left(x1), ty_Int, x2)
new_primCmpNat0(Succ(x0), Succ(x1))
new_esEs7(x0, x1, ty_Ordering)
new_esEs10(x0, x1, app(app(ty_@2, x2), x3))
new_lt23(x0, x1, app(ty_Maybe, x2))
new_ltEs23(x0, x1, ty_Char)
new_esEs8(x0, x1, ty_Ordering)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_lt6(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs39(x0, x1, ty_@0)
new_ltEs21(x0, x1, ty_Char)
new_esEs15(Char(x0), Char(x1))
new_ltEs6(GT, EQ)
new_ltEs6(EQ, GT)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpNat0(Zero, Succ(x0))
new_ltEs24(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Ordering)
new_ltEs24(x0, x1, app(ty_Ratio, x2))
new_ltEs21(x0, x1, app(ty_Ratio, x2))
new_ltEs21(x0, x1, ty_Double)
new_compare6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_compare30(x0, x1, ty_Double)
new_compare27(Left(x0), Left(x1), x2, x3)
new_compare19(x0, x1, True, x2, x3)
new_lt21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt21(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, app(ty_[], x2))
new_ltEs14(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_primCmpNat0(Succ(x0), Zero)
new_lt16(x0, x1, x2, x3)
new_esEs34(x0, x1, ty_Double)
new_compare0([], :(x0, x1), x2)
new_ltEs14(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs22(x0, x1, ty_Int)
new_esEs4(x0, x1, app(ty_Ratio, x2))
new_esEs35(x0, x1, app(ty_Maybe, x2))
new_compare16(x0, x1)
new_ltEs20(x0, x1, ty_Double)
new_esEs22(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs24(x0, x1, ty_Bool)
new_esEs35(x0, x1, ty_Ordering)
new_ltEs18(x0, x1, ty_Integer)
new_esEs35(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs34(x0, x1, ty_@0)
new_esEs5(x0, x1, app(app(ty_@2, x2), x3))
new_esEs37(x0, x1, ty_Integer)
new_ltEs18(x0, x1, ty_Char)
new_esEs7(x0, x1, ty_Double)
new_lt23(x0, x1, ty_Ordering)
new_ltEs24(x0, x1, app(ty_Maybe, x2))
new_esEs24(Left(x0), Right(x1), x2, x3)
new_esEs24(Right(x0), Left(x1), x2, x3)
new_esEs9(x0, x1, ty_Float)
new_esEs32(x0, x1, app(ty_Maybe, x2))
new_esEs23(Just(x0), Just(x1), ty_Ordering)
new_lt6(x0, x1, ty_Char)
new_esEs9(x0, x1, app(app(ty_@2, x2), x3))
new_esEs9(x0, x1, ty_Char)
new_compare31(Just(x0), Nothing, x1)
new_esEs8(x0, x1, ty_Char)
new_esEs35(x0, x1, ty_Int)
new_esEs33(x0, x1, ty_@0)
new_esEs5(x0, x1, ty_Ordering)
new_esEs35(x0, x1, app(ty_Ratio, x2))
new_esEs32(x0, x1, ty_Double)
new_compare111(x0, x1, x2, x3, False, x4, x5)
new_esEs39(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(x0, x1, app(ty_[], x2))
new_esEs14(Float(x0, x1), Float(x2, x3))
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs24(Left(x0), Left(x1), ty_Char, x2)
new_esEs26(x0, x1, ty_Integer)
new_esEs5(x0, x1, ty_@0)
new_esEs5(x0, x1, ty_Char)
new_esEs7(x0, x1, ty_Char)
new_ltEs21(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs9(x0, x1, x2)
new_compare12(True, True)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs36(x0, x1, app(ty_Maybe, x2))
new_esEs5(x0, x1, ty_Integer)
new_esEs33(x0, x1, app(app(ty_@2, x2), x3))
new_primCompAux1(x0, x1, x2, x3)
new_compare30(x0, x1, ty_Ordering)
new_primMulNat0(Zero, Succ(x0))
new_esEs17(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs23(x0, x1, ty_Double)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_compare17(x0, x1, x2, x3, x4, x5, False, x6, x7, x8, x9)
new_esEs9(x0, x1, app(ty_Maybe, x2))
new_esEs24(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs24(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs8(x0, x1, app(app(ty_@2, x2), x3))
new_primCompAux0(x0, GT)
new_esEs39(x0, x1, app(app(ty_@2, x2), x3))
new_lt6(x0, x1, ty_Ordering)
new_primPlusNat1(Zero, Succ(x0))
new_compare0(:(x0, x1), :(x2, x3), x4)
new_esEs36(x0, x1, ty_Float)
new_esEs19(@0, @0)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs36(x0, x1, app(ty_Ratio, x2))
new_esEs24(Right(x0), Right(x1), x2, ty_Integer)
new_esEs31(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs8(x0, x1, x2)
new_esEs36(x0, x1, ty_@0)
new_esEs12(LT, LT)
new_esEs28(x0, x1, ty_Integer)
new_esEs24(Right(x0), Right(x1), x2, ty_Bool)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_ltEs18(x0, x1, ty_Ordering)
new_ltEs16(False, False)
new_compare31(Just(x0), Just(x1), x2)
new_esEs7(x0, x1, app(app(ty_Either, x2), x3))
new_esEs33(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, ty_Ordering)
new_esEs28(x0, x1, ty_@0)
new_esEs11(x0, x1, ty_Float)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_lt10(x0, x1, x2)
new_esEs39(x0, x1, ty_Integer)
new_compare112(x0, x1, False, x2)
new_esEs24(Left(x0), Left(x1), app(ty_Maybe, x2), x3)

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

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

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

new_addToFM_C20(yvy500, yvy501, yvy51, yvy52, yvy53, yvy54, yvy400, yvy401, yvy41, h, ba) → new_addToFM_C1(yvy500, yvy501, yvy51, yvy52, yvy53, yvy54, yvy400, yvy401, yvy41, new_compare0(:(yvy400, yvy401), :(yvy500, yvy501), h), h, ba)
new_addToFM_C(Branch(:(yvy500, yvy501), yvy51, yvy52, yvy53, yvy54), :(yvy400, yvy401), yvy41, h, ba) → new_addToFM_C2(yvy500, yvy501, yvy51, yvy52, yvy53, yvy54, yvy400, yvy401, yvy41, new_primCompAux1(yvy400, yvy500, new_compare0(yvy401, yvy501, h), h), h, ba)
new_addToFM_C10(yvy51, yvy52, yvy53, yvy54, yvy400, yvy401, yvy41, GT, h, ba) → new_addToFM_C(yvy54, :(yvy400, yvy401), yvy41, h, ba)
new_addToFM_C2(yvy500, yvy501, yvy51, yvy52, yvy53, yvy54, yvy400, yvy401, yvy41, EQ, h, ba) → new_addToFM_C1(yvy500, yvy501, yvy51, yvy52, yvy53, yvy54, yvy400, yvy401, yvy41, new_compare0(:(yvy400, yvy401), :(yvy500, yvy501), h), h, ba)
new_addToFM_C2(yvy500, yvy501, yvy51, yvy52, yvy53, yvy54, yvy400, yvy401, yvy41, LT, h, ba) → new_addToFM_C(yvy53, :(yvy400, yvy401), yvy41, h, ba)
new_addToFM_C1(yvy500, yvy501, yvy51, yvy52, yvy53, yvy54, yvy400, yvy401, yvy41, GT, h, ba) → new_addToFM_C(yvy54, :(yvy400, yvy401), yvy41, h, ba)
new_addToFM_C(Branch([], yvy51, yvy52, yvy53, yvy54), :(yvy400, yvy401), yvy41, h, ba) → new_addToFM_C10(yvy51, yvy52, yvy53, yvy54, yvy400, yvy401, yvy41, new_compare0(:(yvy400, yvy401), [], h), h, ba)
new_addToFM_C2(yvy500, yvy501, yvy51, yvy52, yvy53, yvy54, yvy400, yvy401, yvy41, GT, h, ba) → new_addToFM_C20(yvy500, yvy501, yvy51, yvy52, yvy53, yvy54, yvy400, yvy401, yvy41, h, ba)

The TRS R consists of the following rules:

new_compare210(yvy100, yvy101, False, fee) → new_compare112(yvy100, yvy101, new_ltEs24(yvy100, yvy101, fee), fee)
new_compare7(@2(yvy4000, yvy4001), @2(yvy3000, yvy3001), be, bf) → new_compare24(yvy4000, yvy4001, yvy3000, yvy3001, new_asAs(new_esEs7(yvy4000, yvy3000, be), new_esEs8(yvy4001, yvy3001, bf)), be, bf)
new_esEs24(Left(yvy40000), Left(yvy30000), app(ty_Ratio, def), hf) → new_esEs21(yvy40000, yvy30000, def)
new_ltEs19(yvy1002, yvy1012, app(ty_[], bhh)) → new_ltEs8(yvy1002, yvy1012, bhh)
new_compare112(yvy189, yvy190, True, fgc) → LT
new_lt22(yvy1000, yvy1010, ty_Int) → new_lt17(yvy1000, yvy1010)
new_ltEs22(yvy114, yvy115, app(app(ty_@2, fba), fbb)) → new_ltEs12(yvy114, yvy115, fba, fbb)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Int, hf) → new_esEs25(yvy40000, yvy30000)
new_esEs6(yvy4002, yvy3002, app(app(app(ty_@3, bbe), bbf), bbg)) → new_esEs22(yvy4002, yvy3002, bbe, bbf, bbg)
new_esEs27(yvy1000, yvy1010, app(ty_[], bfd)) → new_esEs16(yvy1000, yvy1010, bfd)
new_esEs20(True, True) → True
new_esEs35(yvy153, yvy156, app(ty_[], dhh)) → new_esEs16(yvy153, yvy156, dhh)
new_compare8(Integer(yvy4000), Integer(yvy3000)) → new_primCmpInt(yvy4000, yvy3000)
new_esEs8(yvy4001, yvy3001, ty_Bool) → new_esEs20(yvy4001, yvy3001)
new_esEs11(yvy4000, yvy3000, ty_Integer) → new_esEs18(yvy4000, yvy3000)
new_esEs27(yvy1000, yvy1010, app(app(ty_@2, bga), bgb)) → new_esEs17(yvy1000, yvy1010, bga, bgb)
new_ltEs20(yvy154, yvy157, app(ty_Ratio, ebc)) → new_ltEs9(yvy154, yvy157, ebc)
new_esEs36(yvy1000, yvy1010, ty_Double) → new_esEs13(yvy1000, yvy1010)
new_esEs28(yvy1001, yvy1011, ty_Float) → new_esEs14(yvy1001, yvy1011)
new_lt6(yvy1000, yvy1010, ty_@0) → new_lt19(yvy1000, yvy1010)
new_compare10(yvy199, yvy200, True, ed, ee) → LT
new_esEs9(yvy4000, yvy3000, ty_Int) → new_esEs25(yvy4000, yvy3000)
new_esEs24(Right(yvy40000), Right(yvy30000), he, ty_Double) → new_esEs13(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, app(app(ty_@2, cgh), cha)) → new_esEs17(yvy40002, yvy30002, cgh, cha)
new_ltEs24(yvy100, yvy101, app(ty_Ratio, cdf)) → new_ltEs9(yvy100, yvy101, cdf)
new_esEs24(Right(yvy40000), Right(yvy30000), he, ty_@0) → new_esEs19(yvy40000, yvy30000)
new_ltEs19(yvy1002, yvy1012, ty_Float) → new_ltEs11(yvy1002, yvy1012)
new_esEs11(yvy4000, yvy3000, app(ty_[], egh)) → new_esEs16(yvy4000, yvy3000, egh)
new_lt23(yvy165, yvy167, app(app(app(ty_@3, fcb), fcc), fcd)) → new_lt4(yvy165, yvy167, fcb, fcc, fcd)
new_esEs7(yvy4000, yvy3000, ty_Double) → new_esEs13(yvy4000, yvy3000)
new_esEs9(yvy4000, yvy3000, ty_Char) → new_esEs15(yvy4000, yvy3000)
new_ltEs23(yvy166, yvy168, ty_Ordering) → new_ltEs6(yvy166, yvy168)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Bool, daa) → new_ltEs16(yvy1000, yvy1010)
new_esEs39(yvy165, yvy167, app(ty_Ratio, fca)) → new_esEs21(yvy165, yvy167, fca)
new_esEs10(yvy4000, yvy3000, ty_@0) → new_esEs19(yvy4000, yvy3000)
new_esEs21(:%(yvy40000, yvy40001), :%(yvy30000, yvy30001), gh) → new_asAs(new_esEs37(yvy40000, yvy30000, gh), new_esEs38(yvy40001, yvy30001, gh))
new_lt5(yvy1001, yvy1011, app(ty_Ratio, bgg)) → new_lt10(yvy1001, yvy1011, bgg)
new_compare13(:%(yvy4000, yvy4001), :%(yvy3000, yvy3001), ty_Integer) → new_compare8(new_sr(yvy4000, yvy3001), new_sr(yvy3000, yvy4001))
new_ltEs22(yvy114, yvy115, app(ty_Ratio, fae)) → new_ltEs9(yvy114, yvy115, fae)
new_ltEs23(yvy166, yvy168, ty_Int) → new_ltEs15(yvy166, yvy168)
new_primMulNat0(Zero, Zero) → Zero
new_ltEs24(yvy100, yvy101, ty_Ordering) → new_ltEs6(yvy100, yvy101)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbd, ty_Float) → new_ltEs11(yvy1000, yvy1010)
new_esEs39(yvy165, yvy167, app(ty_Maybe, fcg)) → new_esEs23(yvy165, yvy167, fcg)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Bool, hf) → new_esEs20(yvy40000, yvy30000)
new_compare15(LT, LT) → EQ
new_esEs6(yvy4002, yvy3002, app(app(ty_@2, bbb), bbc)) → new_esEs17(yvy4002, yvy3002, bbb, bbc)
new_esEs4(yvy4000, yvy3000, ty_Integer) → new_esEs18(yvy4000, yvy3000)
new_esEs26(yvy40000, yvy30000, app(ty_[], bcc)) → new_esEs16(yvy40000, yvy30000, bcc)
new_esEs36(yvy1000, yvy1010, ty_Char) → new_esEs15(yvy1000, yvy1010)
new_esEs28(yvy1001, yvy1011, app(app(ty_Either, bhf), bhg)) → new_esEs24(yvy1001, yvy1011, bhf, bhg)
new_esEs34(yvy152, yvy155, ty_@0) → new_esEs19(yvy152, yvy155)
new_sr(Integer(yvy30000), Integer(yvy40010)) → Integer(new_primMulInt(yvy30000, yvy40010))
new_esEs7(yvy4000, yvy3000, ty_Float) → new_esEs14(yvy4000, yvy3000)
new_compare12(True, False) → GT
new_lt7(yvy152, yvy155) → new_esEs12(new_compare15(yvy152, yvy155), LT)
new_lt22(yvy1000, yvy1010, app(ty_Maybe, edg)) → new_lt14(yvy1000, yvy1010, edg)
new_ltEs24(yvy100, yvy101, app(ty_Maybe, ef)) → new_ltEs5(yvy100, yvy101, ef)
new_esEs35(yvy153, yvy156, app(app(ty_Either, eah), eba)) → new_esEs24(yvy153, yvy156, eah, eba)
new_esEs35(yvy153, yvy156, ty_@0) → new_esEs19(yvy153, yvy156)
new_ltEs15(yvy100, yvy101) → new_fsEs(new_compare16(yvy100, yvy101))
new_esEs6(yvy4002, yvy3002, app(ty_[], bba)) → new_esEs16(yvy4002, yvy3002, bba)
new_esEs26(yvy40000, yvy30000, ty_@0) → new_esEs19(yvy40000, yvy30000)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_@0, hf) → new_esEs19(yvy40000, yvy30000)
new_ltEs16(False, True) → True
new_esEs26(yvy40000, yvy30000, app(app(app(ty_@3, bcg), bch), bda)) → new_esEs22(yvy40000, yvy30000, bcg, bch, bda)
new_esEs10(yvy4000, yvy3000, app(ty_Maybe, ege)) → new_esEs23(yvy4000, yvy3000, ege)
new_ltEs24(yvy100, yvy101, ty_Bool) → new_ltEs16(yvy100, yvy101)
new_compare30(yvy400, yvy300, app(app(ty_@2, be), bf)) → new_compare7(yvy400, yvy300, be, bf)
new_esEs17(@2(yvy40000, yvy40001), @2(yvy30000, yvy30001), gf, gg) → new_asAs(new_esEs29(yvy40000, yvy30000, gf), new_esEs30(yvy40001, yvy30001, gg))
new_esEs11(yvy4000, yvy3000, ty_Char) → new_esEs15(yvy4000, yvy3000)
new_lt20(yvy152, yvy155, app(app(app(ty_@3, bb), bc), bd)) → new_lt4(yvy152, yvy155, bb, bc, bd)
new_esEs27(yvy1000, yvy1010, ty_Bool) → new_esEs20(yvy1000, yvy1010)
new_ltEs23(yvy166, yvy168, app(ty_Ratio, fdc)) → new_ltEs9(yvy166, yvy168, fdc)
new_esEs34(yvy152, yvy155, ty_Double) → new_esEs13(yvy152, yvy155)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Double) → new_esEs13(yvy40000, yvy30000)
new_esEs10(yvy4000, yvy3000, ty_Int) → new_esEs25(yvy4000, yvy3000)
new_esEs26(yvy40000, yvy30000, ty_Char) → new_esEs15(yvy40000, yvy30000)
new_compare30(yvy400, yvy300, ty_Int) → new_compare16(yvy400, yvy300)
new_fsEs(yvy306) → new_not(new_esEs12(yvy306, GT))
new_ltEs16(True, False) → False
new_ltEs14(Right(yvy1000), Right(yvy1010), dbd, ty_Char) → new_ltEs7(yvy1000, yvy1010)
new_esEs7(yvy4000, yvy3000, ty_Int) → new_esEs25(yvy4000, yvy3000)
new_ltEs19(yvy1002, yvy1012, ty_Bool) → new_ltEs16(yvy1002, yvy1012)
new_esEs34(yvy152, yvy155, ty_Ordering) → new_esEs12(yvy152, yvy155)
new_esEs12(GT, LT) → False
new_esEs12(LT, GT) → False
new_esEs27(yvy1000, yvy1010, ty_Char) → new_esEs15(yvy1000, yvy1010)
new_lt5(yvy1001, yvy1011, ty_Integer) → new_lt15(yvy1001, yvy1011)
new_ltEs22(yvy114, yvy115, ty_Ordering) → new_ltEs6(yvy114, yvy115)
new_compare18(Float(yvy4000, yvy4001), Float(yvy3000, yvy3001)) → new_compare16(new_sr0(yvy4000, yvy3000), new_sr0(yvy4001, yvy3001))
new_ltEs18(yvy107, yvy108, app(ty_Ratio, bdh)) → new_ltEs9(yvy107, yvy108, bdh)
new_ltEs23(yvy166, yvy168, ty_Float) → new_ltEs11(yvy166, yvy168)
new_ltEs18(yvy107, yvy108, app(ty_[], bdg)) → new_ltEs8(yvy107, yvy108, bdg)
new_ltEs20(yvy154, yvy157, app(app(ty_@2, ebg), ebh)) → new_ltEs12(yvy154, yvy157, ebg, ebh)
new_esEs31(yvy40000, yvy30000, app(ty_Maybe, cfb)) → new_esEs23(yvy40000, yvy30000, cfb)
new_lt6(yvy1000, yvy1010, app(ty_Ratio, bfe)) → new_lt10(yvy1000, yvy1010, bfe)
new_esEs37(yvy40000, yvy30000, ty_Integer) → new_esEs18(yvy40000, yvy30000)
new_ltEs14(Left(yvy1000), Left(yvy1010), app(app(ty_@2, dag), dah), daa) → new_ltEs12(yvy1000, yvy1010, dag, dah)
new_esEs35(yvy153, yvy156, app(app(ty_@2, eae), eaf)) → new_esEs17(yvy153, yvy156, eae, eaf)
new_esEs5(yvy4001, yvy3001, app(app(app(ty_@3, bac), bad), bae)) → new_esEs22(yvy4001, yvy3001, bac, bad, bae)
new_lt22(yvy1000, yvy1010, ty_Char) → new_lt8(yvy1000, yvy1010)
new_compare110(yvy233, yvy234, yvy235, yvy236, True, yvy238, ecd, ece) → new_compare111(yvy233, yvy234, yvy235, yvy236, True, ecd, ece)
new_ltEs24(yvy100, yvy101, app(app(ty_@2, ecf), ecg)) → new_ltEs12(yvy100, yvy101, ecf, ecg)
new_ltEs13(yvy100, yvy101) → new_fsEs(new_compare29(yvy100, yvy101))
new_esEs5(yvy4001, yvy3001, app(app(ty_Either, bag), bah)) → new_esEs24(yvy4001, yvy3001, bag, bah)
new_esEs24(Right(yvy40000), Right(yvy30000), he, ty_Bool) → new_esEs20(yvy40000, yvy30000)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Float) → new_ltEs11(yvy1000, yvy1010)
new_esEs8(yvy4001, yvy3001, ty_Double) → new_esEs13(yvy4001, yvy3001)
new_esEs31(yvy40000, yvy30000, app(ty_Ratio, cef)) → new_esEs21(yvy40000, yvy30000, cef)
new_esEs29(yvy40000, yvy30000, app(ty_Maybe, cca)) → new_esEs23(yvy40000, yvy30000, cca)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Int) → new_ltEs15(yvy1000, yvy1010)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Double) → new_ltEs13(yvy1000, yvy1010)
new_esEs30(yvy40001, yvy30001, ty_Double) → new_esEs13(yvy40001, yvy30001)
new_ltEs21(yvy1001, yvy1011, app(app(ty_@2, eeg), eeh)) → new_ltEs12(yvy1001, yvy1011, eeg, eeh)
new_esEs10(yvy4000, yvy3000, ty_Bool) → new_esEs20(yvy4000, yvy3000)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Char, daa) → new_ltEs7(yvy1000, yvy1010)
new_ltEs16(True, True) → True
new_lt21(yvy153, yvy156, app(app(ty_@2, eae), eaf)) → new_lt12(yvy153, yvy156, eae, eaf)
new_lt6(yvy1000, yvy1010, ty_Bool) → new_lt18(yvy1000, yvy1010)
new_pePe(False, yvy305) → yvy305
new_compare15(GT, EQ) → GT
new_esEs7(yvy4000, yvy3000, ty_Char) → new_esEs15(yvy4000, yvy3000)
new_esEs31(yvy40000, yvy30000, app(ty_[], cec)) → new_esEs16(yvy40000, yvy30000, cec)
new_esEs39(yvy165, yvy167, ty_@0) → new_esEs19(yvy165, yvy167)
new_esEs23(Just(yvy40000), Just(yvy30000), app(ty_Maybe, ddf)) → new_esEs23(yvy40000, yvy30000, ddf)
new_lt21(yvy153, yvy156, ty_Char) → new_lt8(yvy153, yvy156)
new_esEs26(yvy40000, yvy30000, ty_Bool) → new_esEs20(yvy40000, yvy30000)
new_esEs9(yvy4000, yvy3000, app(app(ty_@2, ffb), ffc)) → new_esEs17(yvy4000, yvy3000, ffb, ffc)
new_compare14(yvy218, yvy219, yvy220, yvy221, yvy222, yvy223, False, cdh, cea, ceb) → GT
new_lt9(yvy152, yvy155, dhd) → new_esEs12(new_compare0(yvy152, yvy155, dhd), LT)
new_esEs28(yvy1001, yvy1011, ty_Integer) → new_esEs18(yvy1001, yvy1011)
new_esEs5(yvy4001, yvy3001, ty_Ordering) → new_esEs12(yvy4001, yvy3001)
new_esEs5(yvy4001, yvy3001, ty_Int) → new_esEs25(yvy4001, yvy3001)
new_esEs4(yvy4000, yvy3000, ty_Float) → new_esEs14(yvy4000, yvy3000)
new_compare15(GT, LT) → GT
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Char, hf) → new_esEs15(yvy40000, yvy30000)
new_esEs29(yvy40000, yvy30000, ty_Int) → new_esEs25(yvy40000, yvy30000)
new_compare30(yvy400, yvy300, app(app(ty_Either, efd), efe)) → new_compare27(yvy400, yvy300, efd, efe)
new_lt22(yvy1000, yvy1010, ty_Double) → new_lt13(yvy1000, yvy1010)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Ordering) → new_esEs12(yvy40000, yvy30000)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Char) → new_esEs15(yvy40000, yvy30000)
new_esEs29(yvy40000, yvy30000, app(app(ty_@2, cbc), cbd)) → new_esEs17(yvy40000, yvy30000, cbc, cbd)
new_esEs24(Right(yvy40000), Right(yvy30000), he, app(app(ty_@2, dff), dfg)) → new_esEs17(yvy40000, yvy30000, dff, dfg)
new_ltEs23(yvy166, yvy168, app(app(ty_Either, feb), fec)) → new_ltEs14(yvy166, yvy168, feb, fec)
new_esEs31(yvy40000, yvy30000, ty_Integer) → new_esEs18(yvy40000, yvy30000)
new_compare12(True, True) → EQ
new_esEs36(yvy1000, yvy1010, app(ty_[], ech)) → new_esEs16(yvy1000, yvy1010, ech)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Ordering, hf) → new_esEs12(yvy40000, yvy30000)
new_ltEs6(GT, EQ) → False
new_ltEs18(yvy107, yvy108, app(app(ty_Either, beg), beh)) → new_ltEs14(yvy107, yvy108, beg, beh)
new_esEs32(yvy40001, yvy30001, app(ty_Maybe, cgd)) → new_esEs23(yvy40001, yvy30001, cgd)
new_esEs35(yvy153, yvy156, ty_Integer) → new_esEs18(yvy153, yvy156)
new_esEs33(yvy40002, yvy30002, ty_Integer) → new_esEs18(yvy40002, yvy30002)
new_esEs31(yvy40000, yvy30000, ty_Double) → new_esEs13(yvy40000, yvy30000)
new_esEs10(yvy4000, yvy3000, ty_Ordering) → new_esEs12(yvy4000, yvy3000)
new_primCompAux1(yvy400, yvy300, yvy51, h) → new_primCompAux0(yvy51, new_compare30(yvy400, yvy300, h))
new_esEs33(yvy40002, yvy30002, ty_Float) → new_esEs14(yvy40002, yvy30002)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbd, app(app(app(ty_@3, dbg), dbh), dca)) → new_ltEs10(yvy1000, yvy1010, dbg, dbh, dca)
new_ltEs23(yvy166, yvy168, app(ty_[], fdb)) → new_ltEs8(yvy166, yvy168, fdb)
new_lt23(yvy165, yvy167, app(app(ty_@2, fce), fcf)) → new_lt12(yvy165, yvy167, fce, fcf)
new_esEs34(yvy152, yvy155, ty_Integer) → new_esEs18(yvy152, yvy155)
new_esEs23(Just(yvy40000), Just(yvy30000), app(app(ty_Either, ddg), ddh)) → new_esEs24(yvy40000, yvy30000, ddg, ddh)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Ordering, daa) → new_ltEs6(yvy1000, yvy1010)
new_lt22(yvy1000, yvy1010, ty_Bool) → new_lt18(yvy1000, yvy1010)
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_esEs39(yvy165, yvy167, ty_Float) → new_esEs14(yvy165, yvy167)
new_ltEs22(yvy114, yvy115, ty_Bool) → new_ltEs16(yvy114, yvy115)
new_ltEs4(yvy100, yvy101) → new_fsEs(new_compare8(yvy100, yvy101))
new_esEs33(yvy40002, yvy30002, app(ty_[], cgg)) → new_esEs16(yvy40002, yvy30002, cgg)
new_ltEs8(yvy100, yvy101, fed) → new_fsEs(new_compare0(yvy100, yvy101, fed))
new_compare30(yvy400, yvy300, ty_Char) → new_compare11(yvy400, yvy300)
new_esEs36(yvy1000, yvy1010, ty_Integer) → new_esEs18(yvy1000, yvy1010)
new_esEs39(yvy165, yvy167, ty_Bool) → new_esEs20(yvy165, yvy167)
new_esEs36(yvy1000, yvy1010, ty_Bool) → new_esEs20(yvy1000, yvy1010)
new_esEs32(yvy40001, yvy30001, app(ty_Ratio, cfh)) → new_esEs21(yvy40001, yvy30001, cfh)
new_compare12(False, True) → LT
new_esEs5(yvy4001, yvy3001, ty_Char) → new_esEs15(yvy4001, yvy3001)
new_esEs34(yvy152, yvy155, ty_Char) → new_esEs15(yvy152, yvy155)
new_esEs31(yvy40000, yvy30000, app(app(ty_@2, ced), cee)) → new_esEs17(yvy40000, yvy30000, ced, cee)
new_ltEs18(yvy107, yvy108, ty_Integer) → new_ltEs4(yvy107, yvy108)
new_lt21(yvy153, yvy156, ty_@0) → new_lt19(yvy153, yvy156)
new_esEs30(yvy40001, yvy30001, ty_@0) → new_esEs19(yvy40001, yvy30001)
new_ltEs18(yvy107, yvy108, app(ty_Maybe, bef)) → new_ltEs5(yvy107, yvy108, bef)
new_esEs12(LT, LT) → True
new_ltEs24(yvy100, yvy101, ty_Char) → new_ltEs7(yvy100, yvy101)
new_esEs31(yvy40000, yvy30000, app(app(ty_Either, cfc), cfd)) → new_esEs24(yvy40000, yvy30000, cfc, cfd)
new_ltEs18(yvy107, yvy108, ty_Double) → new_ltEs13(yvy107, yvy108)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Int, daa) → new_ltEs15(yvy1000, yvy1010)
new_esEs28(yvy1001, yvy1011, app(ty_Maybe, bhe)) → new_esEs23(yvy1001, yvy1011, bhe)
new_lt5(yvy1001, yvy1011, ty_@0) → new_lt19(yvy1001, yvy1011)
new_compare15(EQ, LT) → GT
new_pePe(True, yvy305) → True
new_compare0([], [], fef) → EQ
new_primEqNat0(Zero, Zero) → True
new_ltEs21(yvy1001, yvy1011, ty_Double) → new_ltEs13(yvy1001, yvy1011)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Float) → new_esEs14(yvy40000, yvy30000)
new_esEs6(yvy4002, yvy3002, ty_Double) → new_esEs13(yvy4002, yvy3002)
new_esEs4(yvy4000, yvy3000, app(ty_Maybe, hd)) → new_esEs23(yvy4000, yvy3000, hd)
new_lt5(yvy1001, yvy1011, ty_Bool) → new_lt18(yvy1001, yvy1011)
new_lt23(yvy165, yvy167, ty_Integer) → new_lt15(yvy165, yvy167)
new_esEs5(yvy4001, yvy3001, ty_Float) → new_esEs14(yvy4001, yvy3001)
new_lt21(yvy153, yvy156, app(app(ty_Either, eah), eba)) → new_lt16(yvy153, yvy156, eah, eba)
new_esEs8(yvy4001, yvy3001, app(app(app(ty_@3, df), dg), dh)) → new_esEs22(yvy4001, yvy3001, df, dg, dh)
new_lt11(yvy152, yvy155) → new_esEs12(new_compare18(yvy152, yvy155), LT)
new_lt20(yvy152, yvy155, app(ty_[], dhd)) → new_lt9(yvy152, yvy155, dhd)
new_esEs13(Double(yvy40000, yvy40001), Double(yvy30000, yvy30001)) → new_esEs25(new_sr0(yvy40000, yvy30000), new_sr0(yvy40001, yvy30001))
new_esEs7(yvy4000, yvy3000, ty_Bool) → new_esEs20(yvy4000, yvy3000)
new_compare30(yvy400, yvy300, ty_@0) → new_compare9(yvy400, yvy300)
new_esEs29(yvy40000, yvy30000, ty_@0) → new_esEs19(yvy40000, yvy30000)
new_esEs6(yvy4002, yvy3002, ty_Ordering) → new_esEs12(yvy4002, yvy3002)
new_ltEs18(yvy107, yvy108, app(app(app(ty_@3, bea), beb), bec)) → new_ltEs10(yvy107, yvy108, bea, beb, bec)
new_ltEs22(yvy114, yvy115, ty_@0) → new_ltEs17(yvy114, yvy115)
new_lt5(yvy1001, yvy1011, ty_Char) → new_lt8(yvy1001, yvy1011)
new_lt5(yvy1001, yvy1011, app(app(ty_Either, bhf), bhg)) → new_lt16(yvy1001, yvy1011, bhf, bhg)
new_ltEs19(yvy1002, yvy1012, ty_Ordering) → new_ltEs6(yvy1002, yvy1012)
new_esEs15(Char(yvy40000), Char(yvy30000)) → new_primEqNat0(yvy40000, yvy30000)
new_esEs24(Left(yvy40000), Left(yvy30000), app(app(app(ty_@3, deg), deh), dfa), hf) → new_esEs22(yvy40000, yvy30000, deg, deh, dfa)
new_esEs26(yvy40000, yvy30000, ty_Int) → new_esEs25(yvy40000, yvy30000)
new_esEs32(yvy40001, yvy30001, ty_Integer) → new_esEs18(yvy40001, yvy30001)
new_ltEs23(yvy166, yvy168, ty_Double) → new_ltEs13(yvy166, yvy168)
new_lt22(yvy1000, yvy1010, app(ty_[], ech)) → new_lt9(yvy1000, yvy1010, ech)
new_ltEs23(yvy166, yvy168, ty_Integer) → new_ltEs4(yvy166, yvy168)
new_esEs9(yvy4000, yvy3000, app(ty_[], ffa)) → new_esEs16(yvy4000, yvy3000, ffa)
new_esEs33(yvy40002, yvy30002, ty_Bool) → new_esEs20(yvy40002, yvy30002)
new_esEs11(yvy4000, yvy3000, ty_Double) → new_esEs13(yvy4000, yvy3000)
new_esEs29(yvy40000, yvy30000, ty_Bool) → new_esEs20(yvy40000, yvy30000)
new_lt5(yvy1001, yvy1011, app(ty_[], bgf)) → new_lt9(yvy1001, yvy1011, bgf)
new_ltEs21(yvy1001, yvy1011, ty_Bool) → new_ltEs16(yvy1001, yvy1011)
new_ltEs6(EQ, GT) → True
new_esEs9(yvy4000, yvy3000, ty_Integer) → new_esEs18(yvy4000, yvy3000)
new_esEs11(yvy4000, yvy3000, ty_Ordering) → new_esEs12(yvy4000, yvy3000)
new_esEs23(Just(yvy40000), Nothing, hd) → False
new_esEs23(Nothing, Just(yvy30000), hd) → False
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_ltEs18(yvy107, yvy108, ty_Ordering) → new_ltEs6(yvy107, yvy108)
new_esEs23(Just(yvy40000), Just(yvy30000), app(app(app(ty_@3, ddc), ddd), dde)) → new_esEs22(yvy40000, yvy30000, ddc, ddd, dde)
new_ltEs24(yvy100, yvy101, ty_Double) → new_ltEs13(yvy100, yvy101)
new_esEs10(yvy4000, yvy3000, ty_Double) → new_esEs13(yvy4000, yvy3000)
new_esEs24(Right(yvy40000), Right(yvy30000), he, ty_Float) → new_esEs14(yvy40000, yvy30000)
new_compare110(yvy233, yvy234, yvy235, yvy236, False, yvy238, ecd, ece) → new_compare111(yvy233, yvy234, yvy235, yvy236, yvy238, ecd, ece)
new_ltEs20(yvy154, yvy157, ty_Bool) → new_ltEs16(yvy154, yvy157)
new_ltEs24(yvy100, yvy101, ty_@0) → new_ltEs17(yvy100, yvy101)
new_ltEs5(Just(yvy1000), Just(yvy1010), app(app(ty_@2, fd), ff)) → new_ltEs12(yvy1000, yvy1010, fd, ff)
new_ltEs20(yvy154, yvy157, ty_Int) → new_ltEs15(yvy154, yvy157)
new_esEs8(yvy4001, yvy3001, ty_@0) → new_esEs19(yvy4001, yvy3001)
new_lt22(yvy1000, yvy1010, app(app(ty_Either, edh), eea)) → new_lt16(yvy1000, yvy1010, edh, eea)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Float, daa) → new_ltEs11(yvy1000, yvy1010)
new_compare26(yvy107, yvy108, False, bde, bdf) → new_compare10(yvy107, yvy108, new_ltEs18(yvy107, yvy108, bde), bde, bdf)
new_lt21(yvy153, yvy156, app(ty_Ratio, eaa)) → new_lt10(yvy153, yvy156, eaa)
new_compare30(yvy400, yvy300, ty_Float) → new_compare18(yvy400, yvy300)
new_primEqInt(Neg(Succ(yvy400000)), Neg(Succ(yvy300000))) → new_primEqNat0(yvy400000, yvy300000)
new_esEs23(Nothing, Nothing, hd) → True
new_esEs10(yvy4000, yvy3000, app(app(app(ty_@3, egb), egc), egd)) → new_esEs22(yvy4000, yvy3000, egb, egc, egd)
new_esEs39(yvy165, yvy167, app(app(ty_@2, fce), fcf)) → new_esEs17(yvy165, yvy167, fce, fcf)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbd, app(app(ty_@2, dcb), dcc)) → new_ltEs12(yvy1000, yvy1010, dcb, dcc)
new_ltEs5(Just(yvy1000), Nothing, ef) → False
new_esEs28(yvy1001, yvy1011, ty_Char) → new_esEs15(yvy1001, yvy1011)
new_esEs11(yvy4000, yvy3000, app(ty_Maybe, ehg)) → new_esEs23(yvy4000, yvy3000, ehg)
new_lt14(yvy152, yvy155, dhe) → new_esEs12(new_compare31(yvy152, yvy155, dhe), LT)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbd, ty_@0) → new_ltEs17(yvy1000, yvy1010)
new_ltEs14(Right(yvy1000), Left(yvy1010), dbd, daa) → False
new_esEs12(EQ, LT) → False
new_esEs12(LT, EQ) → False
new_ltEs19(yvy1002, yvy1012, app(ty_Ratio, caa)) → new_ltEs9(yvy1002, yvy1012, caa)
new_lt22(yvy1000, yvy1010, app(app(ty_@2, ede), edf)) → new_lt12(yvy1000, yvy1010, ede, edf)
new_ltEs23(yvy166, yvy168, ty_Bool) → new_ltEs16(yvy166, yvy168)
new_compare111(yvy233, yvy234, yvy235, yvy236, True, ecd, ece) → LT
new_esEs7(yvy4000, yvy3000, app(ty_[], bg)) → new_esEs16(yvy4000, yvy3000, bg)
new_esEs5(yvy4001, yvy3001, ty_Bool) → new_esEs20(yvy4001, yvy3001)
new_lt23(yvy165, yvy167, ty_Int) → new_lt17(yvy165, yvy167)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs30(yvy40001, yvy30001, app(app(app(ty_@3, cch), cda), cdb)) → new_esEs22(yvy40001, yvy30001, cch, cda, cdb)
new_esEs11(yvy4000, yvy3000, app(app(ty_Either, ehh), faa)) → new_esEs24(yvy4000, yvy3000, ehh, faa)
new_esEs35(yvy153, yvy156, app(app(app(ty_@3, eab), eac), ead)) → new_esEs22(yvy153, yvy156, eab, eac, ead)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbd, ty_Int) → new_ltEs15(yvy1000, yvy1010)
new_esEs10(yvy4000, yvy3000, app(app(ty_Either, egf), egg)) → new_esEs24(yvy4000, yvy3000, egf, egg)
new_esEs28(yvy1001, yvy1011, ty_Double) → new_esEs13(yvy1001, yvy1011)
new_lt20(yvy152, yvy155, ty_Ordering) → new_lt7(yvy152, yvy155)
new_ltEs6(EQ, EQ) → True
new_compare31(Just(yvy4000), Nothing, feh) → GT
new_esEs11(yvy4000, yvy3000, app(app(app(ty_@3, ehd), ehe), ehf)) → new_esEs22(yvy4000, yvy3000, ehd, ehe, ehf)
new_ltEs22(yvy114, yvy115, app(app(ty_Either, fbd), fbe)) → new_ltEs14(yvy114, yvy115, fbd, fbe)
new_esEs28(yvy1001, yvy1011, app(app(app(ty_@3, bgh), bha), bhb)) → new_esEs22(yvy1001, yvy1011, bgh, bha, bhb)
new_esEs32(yvy40001, yvy30001, ty_Float) → new_esEs14(yvy40001, yvy30001)
new_esEs27(yvy1000, yvy1010, app(ty_Ratio, bfe)) → new_esEs21(yvy1000, yvy1010, bfe)
new_ltEs19(yvy1002, yvy1012, ty_Integer) → new_ltEs4(yvy1002, yvy1012)
new_primEqInt(Neg(Succ(yvy400000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(yvy300000))) → False
new_primCompAux0(yvy56, GT) → GT
new_compare30(yvy400, yvy300, app(app(app(ty_@3, gb), gc), gd)) → new_compare6(yvy400, yvy300, gb, gc, gd)
new_esEs39(yvy165, yvy167, ty_Integer) → new_esEs18(yvy165, yvy167)
new_compare26(yvy107, yvy108, True, bde, bdf) → EQ
new_esEs23(Just(yvy40000), Just(yvy30000), app(app(ty_@2, dch), dda)) → new_esEs17(yvy40000, yvy30000, dch, dda)
new_esEs24(Right(yvy40000), Right(yvy30000), he, app(app(ty_Either, dge), dgf)) → new_esEs24(yvy40000, yvy30000, dge, dgf)
new_ltEs6(GT, GT) → True
new_ltEs21(yvy1001, yvy1011, app(app(ty_Either, efb), efc)) → new_ltEs14(yvy1001, yvy1011, efb, efc)
new_esEs38(yvy40001, yvy30001, ty_Integer) → new_esEs18(yvy40001, yvy30001)
new_esEs32(yvy40001, yvy30001, app(ty_[], cfe)) → new_esEs16(yvy40001, yvy30001, cfe)
new_esEs34(yvy152, yvy155, ty_Int) → new_esEs25(yvy152, yvy155)
new_compare31(Nothing, Nothing, feh) → EQ
new_esEs29(yvy40000, yvy30000, app(ty_[], cbb)) → new_esEs16(yvy40000, yvy30000, cbb)
new_esEs26(yvy40000, yvy30000, app(ty_Ratio, bcf)) → new_esEs21(yvy40000, yvy30000, bcf)
new_esEs7(yvy4000, yvy3000, app(ty_Maybe, cf)) → new_esEs23(yvy4000, yvy3000, cf)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_@0) → new_ltEs17(yvy1000, yvy1010)
new_lt21(yvy153, yvy156, app(ty_[], dhh)) → new_lt9(yvy153, yvy156, dhh)
new_ltEs20(yvy154, yvy157, app(ty_[], ebb)) → new_ltEs8(yvy154, yvy157, ebb)
new_esEs36(yvy1000, yvy1010, ty_Int) → new_esEs25(yvy1000, yvy1010)
new_esEs19(@0, @0) → True
new_compare6(@3(yvy4000, yvy4001, yvy4002), @3(yvy3000, yvy3001, yvy3002), gb, gc, gd) → new_compare25(yvy4000, yvy4001, yvy4002, yvy3000, yvy3001, yvy3002, new_asAs(new_esEs4(yvy4000, yvy3000, gb), new_asAs(new_esEs5(yvy4001, yvy3001, gc), new_esEs6(yvy4002, yvy3002, gd))), gb, gc, gd)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_esEs7(yvy4000, yvy3000, ty_Integer) → new_esEs18(yvy4000, yvy3000)
new_esEs4(yvy4000, yvy3000, ty_Bool) → new_esEs20(yvy4000, yvy3000)
new_esEs39(yvy165, yvy167, ty_Ordering) → new_esEs12(yvy165, yvy167)
new_lt20(yvy152, yvy155, ty_Char) → new_lt8(yvy152, yvy155)
new_esEs31(yvy40000, yvy30000, ty_Bool) → new_esEs20(yvy40000, yvy30000)
new_lt4(yvy152, yvy155, bb, bc, bd) → new_esEs12(new_compare6(yvy152, yvy155, bb, bc, bd), LT)
new_esEs6(yvy4002, yvy3002, ty_Int) → new_esEs25(yvy4002, yvy3002)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Double, daa) → new_ltEs13(yvy1000, yvy1010)
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_lt6(yvy1000, yvy1010, app(ty_Maybe, bgc)) → new_lt14(yvy1000, yvy1010, bgc)
new_ltEs14(Left(yvy1000), Left(yvy1010), app(ty_Maybe, dba), daa) → new_ltEs5(yvy1000, yvy1010, dba)
new_esEs4(yvy4000, yvy3000, app(ty_Ratio, gh)) → new_esEs21(yvy4000, yvy3000, gh)
new_lt5(yvy1001, yvy1011, app(ty_Maybe, bhe)) → new_lt14(yvy1001, yvy1011, bhe)
new_primEqInt(Pos(Succ(yvy400000)), Pos(Succ(yvy300000))) → new_primEqNat0(yvy400000, yvy300000)
new_compare10(yvy199, yvy200, False, ed, ee) → GT
new_esEs34(yvy152, yvy155, app(ty_Maybe, dhe)) → new_esEs23(yvy152, yvy155, dhe)
new_esEs5(yvy4001, yvy3001, app(ty_[], hg)) → new_esEs16(yvy4001, yvy3001, hg)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbd, ty_Double) → new_ltEs13(yvy1000, yvy1010)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbd, ty_Integer) → new_ltEs4(yvy1000, yvy1010)
new_ltEs21(yvy1001, yvy1011, ty_Float) → new_ltEs11(yvy1001, yvy1011)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbd, app(ty_Maybe, dcd)) → new_ltEs5(yvy1000, yvy1010, dcd)
new_compare13(:%(yvy4000, yvy4001), :%(yvy3000, yvy3001), ty_Int) → new_compare16(new_sr0(yvy4000, yvy3001), new_sr0(yvy3000, yvy4001))
new_esEs26(yvy40000, yvy30000, app(ty_Maybe, bdb)) → new_esEs23(yvy40000, yvy30000, bdb)
new_ltEs24(yvy100, yvy101, ty_Float) → new_ltEs11(yvy100, yvy101)
new_esEs34(yvy152, yvy155, app(app(ty_@2, dea), deb)) → new_esEs17(yvy152, yvy155, dea, deb)
new_esEs8(yvy4001, yvy3001, ty_Integer) → new_esEs18(yvy4001, yvy3001)
new_ltEs22(yvy114, yvy115, app(app(app(ty_@3, faf), fag), fah)) → new_ltEs10(yvy114, yvy115, faf, fag, fah)
new_primEqNat0(Succ(yvy400000), Succ(yvy300000)) → new_primEqNat0(yvy400000, yvy300000)
new_esEs6(yvy4002, yvy3002, ty_Bool) → new_esEs20(yvy4002, yvy3002)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Ordering) → new_ltEs6(yvy1000, yvy1010)
new_ltEs24(yvy100, yvy101, ty_Int) → new_ltEs15(yvy100, yvy101)
new_esEs26(yvy40000, yvy30000, ty_Ordering) → new_esEs12(yvy40000, yvy30000)
new_esEs24(Right(yvy40000), Right(yvy30000), he, app(ty_Ratio, dfh)) → new_esEs21(yvy40000, yvy30000, dfh)
new_esEs11(yvy4000, yvy3000, app(ty_Ratio, ehc)) → new_esEs21(yvy4000, yvy3000, ehc)
new_esEs30(yvy40001, yvy30001, ty_Integer) → new_esEs18(yvy40001, yvy30001)
new_esEs39(yvy165, yvy167, ty_Char) → new_esEs15(yvy165, yvy167)
new_ltEs14(Left(yvy1000), Left(yvy1010), app(ty_Ratio, dac), daa) → new_ltEs9(yvy1000, yvy1010, dac)
new_esEs26(yvy40000, yvy30000, app(app(ty_@2, bcd), bce)) → new_esEs17(yvy40000, yvy30000, bcd, bce)
new_lt5(yvy1001, yvy1011, ty_Float) → new_lt11(yvy1001, yvy1011)
new_esEs32(yvy40001, yvy30001, ty_@0) → new_esEs19(yvy40001, yvy30001)
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_esEs33(yvy40002, yvy30002, app(ty_Maybe, chf)) → new_esEs23(yvy40002, yvy30002, chf)
new_lt6(yvy1000, yvy1010, ty_Int) → new_lt17(yvy1000, yvy1010)
new_esEs24(Right(yvy40000), Right(yvy30000), he, app(app(app(ty_@3, dga), dgb), dgc)) → new_esEs22(yvy40000, yvy30000, dga, dgb, dgc)
new_lt23(yvy165, yvy167, app(app(ty_Either, fch), fda)) → new_lt16(yvy165, yvy167, fch, fda)
new_esEs12(EQ, EQ) → True
new_lt23(yvy165, yvy167, ty_Char) → new_lt8(yvy165, yvy167)
new_ltEs18(yvy107, yvy108, app(app(ty_@2, bed), bee)) → new_ltEs12(yvy107, yvy108, bed, bee)
new_lt21(yvy153, yvy156, ty_Double) → new_lt13(yvy153, yvy156)
new_esEs35(yvy153, yvy156, ty_Ordering) → new_esEs12(yvy153, yvy156)
new_lt5(yvy1001, yvy1011, ty_Int) → new_lt17(yvy1001, yvy1011)
new_esEs10(yvy4000, yvy3000, ty_Char) → new_esEs15(yvy4000, yvy3000)
new_primEqInt(Pos(Succ(yvy400000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(yvy300000))) → False
new_ltEs5(Nothing, Just(yvy1010), ef) → True
new_lt20(yvy152, yvy155, ty_Int) → new_lt17(yvy152, yvy155)
new_esEs35(yvy153, yvy156, app(ty_Maybe, eag)) → new_esEs23(yvy153, yvy156, eag)
new_esEs27(yvy1000, yvy1010, ty_@0) → new_esEs19(yvy1000, yvy1010)
new_ltEs18(yvy107, yvy108, ty_Float) → new_ltEs11(yvy107, yvy108)
new_compare25(yvy152, yvy153, yvy154, yvy155, yvy156, yvy157, True, dha, dhb, dhc) → EQ
new_esEs37(yvy40000, yvy30000, ty_Int) → new_esEs25(yvy40000, yvy30000)
new_primCmpNat0(Zero, Zero) → EQ
new_esEs27(yvy1000, yvy1010, app(app(ty_Either, bgd), bge)) → new_esEs24(yvy1000, yvy1010, bgd, bge)
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_compare27(Left(yvy4000), Right(yvy3000), efd, efe) → LT
new_lt22(yvy1000, yvy1010, ty_@0) → new_lt19(yvy1000, yvy1010)
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_compare9(@0, @0) → EQ
new_esEs28(yvy1001, yvy1011, ty_Int) → new_esEs25(yvy1001, yvy1011)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Float, hf) → new_esEs14(yvy40000, yvy30000)
new_esEs6(yvy4002, yvy3002, ty_Float) → new_esEs14(yvy4002, yvy3002)
new_ltEs9(yvy100, yvy101, cdf) → new_fsEs(new_compare13(yvy100, yvy101, cdf))
new_compare17(yvy218, yvy219, yvy220, yvy221, yvy222, yvy223, True, yvy225, cdh, cea, ceb) → new_compare14(yvy218, yvy219, yvy220, yvy221, yvy222, yvy223, True, cdh, cea, ceb)
new_esEs32(yvy40001, yvy30001, ty_Char) → new_esEs15(yvy40001, yvy30001)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_ltEs14(Left(yvy1000), Left(yvy1010), app(ty_[], dab), daa) → new_ltEs8(yvy1000, yvy1010, dab)
new_ltEs19(yvy1002, yvy1012, app(app(ty_@2, cae), caf)) → new_ltEs12(yvy1002, yvy1012, cae, caf)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Double, hf) → new_esEs13(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, app(app(ty_Either, chg), chh)) → new_esEs24(yvy40002, yvy30002, chg, chh)
new_esEs4(yvy4000, yvy3000, ty_Int) → new_esEs25(yvy4000, yvy3000)
new_compare28(yvy114, yvy115, True, fab, fac) → EQ
new_primEqInt(Pos(Succ(yvy400000)), Neg(yvy30000)) → False
new_primEqInt(Neg(Succ(yvy400000)), Pos(yvy30000)) → False
new_esEs24(Right(yvy40000), Right(yvy30000), he, ty_Int) → new_esEs25(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, ty_Ordering) → new_esEs12(yvy40002, yvy30002)
new_esEs29(yvy40000, yvy30000, app(app(app(ty_@3, cbf), cbg), cbh)) → new_esEs22(yvy40000, yvy30000, cbf, cbg, cbh)
new_esEs26(yvy40000, yvy30000, ty_Double) → new_esEs13(yvy40000, yvy30000)
new_ltEs20(yvy154, yvy157, ty_Integer) → new_ltEs4(yvy154, yvy157)
new_compare210(yvy100, yvy101, True, fee) → EQ
new_lt6(yvy1000, yvy1010, ty_Ordering) → new_lt7(yvy1000, yvy1010)
new_esEs29(yvy40000, yvy30000, app(ty_Ratio, cbe)) → new_esEs21(yvy40000, yvy30000, cbe)
new_esEs20(False, False) → True
new_esEs24(Left(yvy40000), Left(yvy30000), app(ty_[], dec), hf) → new_esEs16(yvy40000, yvy30000, dec)
new_lt23(yvy165, yvy167, app(ty_[], fbh)) → new_lt9(yvy165, yvy167, fbh)
new_ltEs22(yvy114, yvy115, ty_Integer) → new_ltEs4(yvy114, yvy115)
new_ltEs5(Just(yvy1000), Just(yvy1010), app(app(ty_Either, fh), ga)) → new_ltEs14(yvy1000, yvy1010, fh, ga)
new_lt23(yvy165, yvy167, ty_Bool) → new_lt18(yvy165, yvy167)
new_esEs30(yvy40001, yvy30001, ty_Ordering) → new_esEs12(yvy40001, yvy30001)
new_lt6(yvy1000, yvy1010, ty_Integer) → new_lt15(yvy1000, yvy1010)
new_primEqInt(Pos(Zero), Neg(Succ(yvy300000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(yvy300000))) → False
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_compare30(yvy400, yvy300, app(ty_Maybe, feh)) → new_compare31(yvy400, yvy300, feh)
new_esEs9(yvy4000, yvy3000, ty_Ordering) → new_esEs12(yvy4000, yvy3000)
new_esEs7(yvy4000, yvy3000, ty_@0) → new_esEs19(yvy4000, yvy3000)
new_esEs11(yvy4000, yvy3000, ty_Float) → new_esEs14(yvy4000, yvy3000)
new_lt6(yvy1000, yvy1010, app(ty_[], bfd)) → new_lt9(yvy1000, yvy1010, bfd)
new_esEs36(yvy1000, yvy1010, ty_@0) → new_esEs19(yvy1000, yvy1010)
new_esEs5(yvy4001, yvy3001, ty_@0) → new_esEs19(yvy4001, yvy3001)
new_esEs36(yvy1000, yvy1010, app(app(app(ty_@3, edb), edc), edd)) → new_esEs22(yvy1000, yvy1010, edb, edc, edd)
new_esEs28(yvy1001, yvy1011, ty_Ordering) → new_esEs12(yvy1001, yvy1011)
new_esEs10(yvy4000, yvy3000, app(ty_[], eff)) → new_esEs16(yvy4000, yvy3000, eff)
new_primCompAux0(yvy56, LT) → LT
new_esEs6(yvy4002, yvy3002, app(app(ty_Either, bca), bcb)) → new_esEs24(yvy4002, yvy3002, bca, bcb)
new_esEs6(yvy4002, yvy3002, ty_Integer) → new_esEs18(yvy4002, yvy3002)
new_esEs36(yvy1000, yvy1010, app(app(ty_@2, ede), edf)) → new_esEs17(yvy1000, yvy1010, ede, edf)
new_esEs7(yvy4000, yvy3000, app(app(ty_@2, bh), ca)) → new_esEs17(yvy4000, yvy3000, bh, ca)
new_esEs9(yvy4000, yvy3000, ty_Float) → new_esEs14(yvy4000, yvy3000)
new_lt5(yvy1001, yvy1011, ty_Double) → new_lt13(yvy1001, yvy1011)
new_ltEs22(yvy114, yvy115, app(ty_Maybe, fbc)) → new_ltEs5(yvy114, yvy115, fbc)
new_not(False) → True
new_esEs27(yvy1000, yvy1010, ty_Int) → new_esEs25(yvy1000, yvy1010)
new_esEs34(yvy152, yvy155, app(ty_Ratio, cdg)) → new_esEs21(yvy152, yvy155, cdg)
new_compare30(yvy400, yvy300, ty_Bool) → new_compare12(yvy400, yvy300)
new_esEs25(yvy4000, yvy3000) → new_primEqInt(yvy4000, yvy3000)
new_esEs28(yvy1001, yvy1011, app(ty_[], bgf)) → new_esEs16(yvy1001, yvy1011, bgf)
new_esEs31(yvy40000, yvy30000, ty_Char) → new_esEs15(yvy40000, yvy30000)
new_esEs14(Float(yvy40000, yvy40001), Float(yvy30000, yvy30001)) → new_esEs25(new_sr0(yvy40000, yvy30000), new_sr0(yvy40001, yvy30001))
new_esEs11(yvy4000, yvy3000, ty_@0) → new_esEs19(yvy4000, yvy3000)
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_esEs12(GT, EQ) → False
new_esEs12(EQ, GT) → False
new_esEs36(yvy1000, yvy1010, ty_Float) → new_esEs14(yvy1000, yvy1010)
new_esEs4(yvy4000, yvy3000, ty_Ordering) → new_esEs12(yvy4000, yvy3000)
new_esEs9(yvy4000, yvy3000, app(app(ty_Either, fga), fgb)) → new_esEs24(yvy4000, yvy3000, fga, fgb)
new_lt6(yvy1000, yvy1010, app(app(app(ty_@3, bff), bfg), bfh)) → new_lt4(yvy1000, yvy1010, bff, bfg, bfh)
new_esEs4(yvy4000, yvy3000, app(app(ty_@2, gf), gg)) → new_esEs17(yvy4000, yvy3000, gf, gg)
new_esEs24(Right(yvy40000), Right(yvy30000), he, ty_Integer) → new_esEs18(yvy40000, yvy30000)
new_ltEs18(yvy107, yvy108, ty_@0) → new_ltEs17(yvy107, yvy108)
new_esEs39(yvy165, yvy167, ty_Int) → new_esEs25(yvy165, yvy167)
new_compare15(LT, EQ) → LT
new_esEs34(yvy152, yvy155, ty_Float) → new_esEs14(yvy152, yvy155)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbd, app(ty_[], dbe)) → new_ltEs8(yvy1000, yvy1010, dbe)
new_esEs36(yvy1000, yvy1010, app(ty_Ratio, eda)) → new_esEs21(yvy1000, yvy1010, eda)
new_esEs30(yvy40001, yvy30001, app(ty_Ratio, ccg)) → new_esEs21(yvy40001, yvy30001, ccg)
new_compare30(yvy400, yvy300, app(ty_Ratio, feg)) → new_compare13(yvy400, yvy300, feg)
new_esEs24(Left(yvy40000), Right(yvy30000), he, hf) → False
new_esEs24(Right(yvy40000), Left(yvy30000), he, hf) → False
new_lt20(yvy152, yvy155, app(app(ty_Either, dhf), dhg)) → new_lt16(yvy152, yvy155, dhf, dhg)
new_esEs30(yvy40001, yvy30001, app(app(ty_@2, cce), ccf)) → new_esEs17(yvy40001, yvy30001, cce, ccf)
new_esEs32(yvy40001, yvy30001, app(app(ty_Either, cge), cgf)) → new_esEs24(yvy40001, yvy30001, cge, cgf)
new_esEs34(yvy152, yvy155, app(ty_[], dhd)) → new_esEs16(yvy152, yvy155, dhd)
new_lt20(yvy152, yvy155, ty_Double) → new_lt13(yvy152, yvy155)
new_esEs35(yvy153, yvy156, ty_Double) → new_esEs13(yvy153, yvy156)
new_compare0(:(yvy4000, yvy4001), [], fef) → GT
new_lt6(yvy1000, yvy1010, ty_Char) → new_lt8(yvy1000, yvy1010)
new_esEs8(yvy4001, yvy3001, ty_Int) → new_esEs25(yvy4001, yvy3001)
new_esEs38(yvy40001, yvy30001, ty_Int) → new_esEs25(yvy40001, yvy30001)
new_ltEs24(yvy100, yvy101, ty_Integer) → new_ltEs4(yvy100, yvy101)
new_ltEs20(yvy154, yvy157, app(ty_Maybe, eca)) → new_ltEs5(yvy154, yvy157, eca)
new_ltEs20(yvy154, yvy157, ty_@0) → new_ltEs17(yvy154, yvy157)
new_ltEs24(yvy100, yvy101, app(app(ty_Either, dbd), daa)) → new_ltEs14(yvy100, yvy101, dbd, daa)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Int) → new_esEs25(yvy40000, yvy30000)
new_esEs34(yvy152, yvy155, app(app(ty_Either, dhf), dhg)) → new_esEs24(yvy152, yvy155, dhf, dhg)
new_lt13(yvy152, yvy155) → new_esEs12(new_compare29(yvy152, yvy155), LT)
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_esEs30(yvy40001, yvy30001, app(app(ty_Either, cdd), cde)) → new_esEs24(yvy40001, yvy30001, cdd, cde)
new_lt19(yvy152, yvy155) → new_esEs12(new_compare9(yvy152, yvy155), LT)
new_ltEs18(yvy107, yvy108, ty_Char) → new_ltEs7(yvy107, yvy108)
new_esEs4(yvy4000, yvy3000, app(app(ty_Either, he), hf)) → new_esEs24(yvy4000, yvy3000, he, hf)
new_esEs8(yvy4001, yvy3001, app(ty_Ratio, de)) → new_esEs21(yvy4001, yvy3001, de)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Integer) → new_esEs18(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, app(ty_Ratio, chb)) → new_esEs21(yvy40002, yvy30002, chb)
new_lt17(yvy152, yvy155) → new_esEs12(new_compare16(yvy152, yvy155), LT)
new_esEs10(yvy4000, yvy3000, app(app(ty_@2, efg), efh)) → new_esEs17(yvy4000, yvy3000, efg, efh)
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_ltEs7(yvy100, yvy101) → new_fsEs(new_compare11(yvy100, yvy101))
new_esEs31(yvy40000, yvy30000, ty_Float) → new_esEs14(yvy40000, yvy30000)
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_compare15(EQ, GT) → LT
new_esEs32(yvy40001, yvy30001, ty_Int) → new_esEs25(yvy40001, yvy30001)
new_esEs29(yvy40000, yvy30000, ty_Char) → new_esEs15(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, app(app(app(ty_@3, chc), chd), che)) → new_esEs22(yvy40002, yvy30002, chc, chd, che)
new_primEqNat0(Zero, Succ(yvy300000)) → False
new_primEqNat0(Succ(yvy400000), Zero) → False
new_compare15(LT, GT) → LT
new_lt15(yvy152, yvy155) → new_esEs12(new_compare8(yvy152, yvy155), LT)
new_ltEs5(Nothing, Nothing, ef) → True
new_ltEs23(yvy166, yvy168, app(app(app(ty_@3, fdd), fde), fdf)) → new_ltEs10(yvy166, yvy168, fdd, fde, fdf)
new_lt20(yvy152, yvy155, app(app(ty_@2, dea), deb)) → new_lt12(yvy152, yvy155, dea, deb)
new_ltEs6(LT, LT) → True
new_ltEs6(EQ, LT) → False
new_esEs6(yvy4002, yvy3002, app(ty_Ratio, bbd)) → new_esEs21(yvy4002, yvy3002, bbd)
new_ltEs5(Just(yvy1000), Just(yvy1010), app(ty_[], eg)) → new_ltEs8(yvy1000, yvy1010, eg)
new_ltEs19(yvy1002, yvy1012, ty_Char) → new_ltEs7(yvy1002, yvy1012)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_ltEs21(yvy1001, yvy1011, app(ty_Ratio, eec)) → new_ltEs9(yvy1001, yvy1011, eec)
new_esEs9(yvy4000, yvy3000, app(ty_Maybe, ffh)) → new_esEs23(yvy4000, yvy3000, ffh)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Bool) → new_ltEs16(yvy1000, yvy1010)
new_lt21(yvy153, yvy156, app(ty_Maybe, eag)) → new_lt14(yvy153, yvy156, eag)
new_compare15(GT, GT) → EQ
new_esEs11(yvy4000, yvy3000, app(app(ty_@2, eha), ehb)) → new_esEs17(yvy4000, yvy3000, eha, ehb)
new_esEs8(yvy4001, yvy3001, app(app(ty_Either, eb), ec)) → new_esEs24(yvy4001, yvy3001, eb, ec)
new_compare24(yvy165, yvy166, yvy167, yvy168, True, fbf, fbg) → EQ
new_esEs32(yvy40001, yvy30001, ty_Bool) → new_esEs20(yvy40001, yvy30001)
new_lt21(yvy153, yvy156, ty_Float) → new_lt11(yvy153, yvy156)
new_esEs16(:(yvy40000, yvy40001), [], ge) → False
new_esEs16([], :(yvy30000, yvy30001), ge) → False
new_compare31(Just(yvy4000), Just(yvy3000), feh) → new_compare210(yvy4000, yvy3000, new_esEs9(yvy4000, yvy3000, feh), feh)
new_lt21(yvy153, yvy156, ty_Ordering) → new_lt7(yvy153, yvy156)
new_lt20(yvy152, yvy155, ty_Bool) → new_lt18(yvy152, yvy155)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbd, app(ty_Ratio, dbf)) → new_ltEs9(yvy1000, yvy1010, dbf)
new_ltEs19(yvy1002, yvy1012, ty_@0) → new_ltEs17(yvy1002, yvy1012)
new_esEs7(yvy4000, yvy3000, app(app(app(ty_@3, cc), cd), ce)) → new_esEs22(yvy4000, yvy3000, cc, cd, ce)
new_esEs5(yvy4001, yvy3001, ty_Integer) → new_esEs18(yvy4001, yvy3001)
new_esEs31(yvy40000, yvy30000, ty_Int) → new_esEs25(yvy40000, yvy30000)
new_esEs27(yvy1000, yvy1010, app(app(app(ty_@3, bff), bfg), bfh)) → new_esEs22(yvy1000, yvy1010, bff, bfg, bfh)
new_ltEs19(yvy1002, yvy1012, app(ty_Maybe, cag)) → new_ltEs5(yvy1002, yvy1012, cag)
new_lt21(yvy153, yvy156, ty_Integer) → new_lt15(yvy153, yvy156)
new_esEs29(yvy40000, yvy30000, app(app(ty_Either, ccb), ccc)) → new_esEs24(yvy40000, yvy30000, ccb, ccc)
new_esEs10(yvy4000, yvy3000, app(ty_Ratio, ega)) → new_esEs21(yvy4000, yvy3000, ega)
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_ltEs12(@2(yvy1000, yvy1001), @2(yvy1010, yvy1011), ecf, ecg) → new_pePe(new_lt22(yvy1000, yvy1010, ecf), new_asAs(new_esEs36(yvy1000, yvy1010, ecf), new_ltEs21(yvy1001, yvy1011, ecg)))
new_ltEs23(yvy166, yvy168, ty_@0) → new_ltEs17(yvy166, yvy168)
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_esEs5(yvy4001, yvy3001, app(ty_Maybe, baf)) → new_esEs23(yvy4001, yvy3001, baf)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Char) → new_ltEs7(yvy1000, yvy1010)
new_compare0(:(yvy4000, yvy4001), :(yvy3000, yvy3001), fef) → new_primCompAux1(yvy4000, yvy3000, new_compare0(yvy4001, yvy3001, fef), fef)
new_esEs20(False, True) → False
new_esEs20(True, False) → False
new_compare19(yvy206, yvy207, True, dgg, dgh) → LT
new_sr0(yvy3000, yvy4001) → new_primMulInt(yvy3000, yvy4001)
new_esEs28(yvy1001, yvy1011, app(app(ty_@2, bhc), bhd)) → new_esEs17(yvy1001, yvy1011, bhc, bhd)
new_lt6(yvy1000, yvy1010, app(app(ty_Either, bgd), bge)) → new_lt16(yvy1000, yvy1010, bgd, bge)
new_esEs34(yvy152, yvy155, ty_Bool) → new_esEs20(yvy152, yvy155)
new_lt22(yvy1000, yvy1010, ty_Integer) → new_lt15(yvy1000, yvy1010)
new_esEs26(yvy40000, yvy30000, app(app(ty_Either, bdc), bdd)) → new_esEs24(yvy40000, yvy30000, bdc, bdd)
new_compare30(yvy400, yvy300, ty_Ordering) → new_compare15(yvy400, yvy300)
new_esEs30(yvy40001, yvy30001, app(ty_[], ccd)) → new_esEs16(yvy40001, yvy30001, ccd)
new_esEs24(Left(yvy40000), Left(yvy30000), app(app(ty_@2, ded), dee), hf) → new_esEs17(yvy40000, yvy30000, ded, dee)
new_lt23(yvy165, yvy167, ty_@0) → new_lt19(yvy165, yvy167)
new_esEs10(yvy4000, yvy3000, ty_Float) → new_esEs14(yvy4000, yvy3000)
new_compare29(Double(yvy4000, yvy4001), Double(yvy3000, yvy3001)) → new_compare16(new_sr0(yvy4000, yvy3000), new_sr0(yvy4001, yvy3001))
new_ltEs14(Right(yvy1000), Right(yvy1010), dbd, ty_Bool) → new_ltEs16(yvy1000, yvy1010)
new_ltEs22(yvy114, yvy115, app(ty_[], fad)) → new_ltEs8(yvy114, yvy115, fad)
new_esEs39(yvy165, yvy167, app(app(ty_Either, fch), fda)) → new_esEs24(yvy165, yvy167, fch, fda)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs32(yvy40001, yvy30001, ty_Double) → new_esEs13(yvy40001, yvy30001)
new_esEs28(yvy1001, yvy1011, ty_Bool) → new_esEs20(yvy1001, yvy1011)
new_esEs23(Just(yvy40000), Just(yvy30000), app(ty_Ratio, ddb)) → new_esEs21(yvy40000, yvy30000, ddb)
new_esEs5(yvy4001, yvy3001, app(ty_Ratio, bab)) → new_esEs21(yvy4001, yvy3001, bab)
new_ltEs14(Left(yvy1000), Right(yvy1010), dbd, daa) → True
new_compare24(yvy165, yvy166, yvy167, yvy168, False, fbf, fbg) → new_compare110(yvy165, yvy166, yvy167, yvy168, new_lt23(yvy165, yvy167, fbf), new_asAs(new_esEs39(yvy165, yvy167, fbf), new_ltEs23(yvy166, yvy168, fbg)), fbf, fbg)
new_compare30(yvy400, yvy300, app(ty_[], fef)) → new_compare0(yvy400, yvy300, fef)
new_esEs9(yvy4000, yvy3000, app(ty_Ratio, ffd)) → new_esEs21(yvy4000, yvy3000, ffd)
new_ltEs20(yvy154, yvy157, app(app(ty_Either, ecb), ecc)) → new_ltEs14(yvy154, yvy157, ecb, ecc)
new_asAs(False, yvy184) → False
new_compare27(Right(yvy4000), Left(yvy3000), efd, efe) → GT
new_esEs36(yvy1000, yvy1010, app(ty_Maybe, edg)) → new_esEs23(yvy1000, yvy1010, edg)
new_esEs9(yvy4000, yvy3000, ty_Double) → new_esEs13(yvy4000, yvy3000)
new_ltEs19(yvy1002, yvy1012, app(app(ty_Either, cah), cba)) → new_ltEs14(yvy1002, yvy1012, cah, cba)
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_lt20(yvy152, yvy155, ty_@0) → new_lt19(yvy152, yvy155)
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_esEs4(yvy4000, yvy3000, ty_@0) → new_esEs19(yvy4000, yvy3000)
new_esEs27(yvy1000, yvy1010, ty_Double) → new_esEs13(yvy1000, yvy1010)
new_esEs36(yvy1000, yvy1010, ty_Ordering) → new_esEs12(yvy1000, yvy1010)
new_compare16(yvy400, yvy300) → new_primCmpInt(yvy400, yvy300)
new_esEs35(yvy153, yvy156, ty_Bool) → new_esEs20(yvy153, yvy156)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Bool) → new_esEs20(yvy40000, yvy30000)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Integer, daa) → new_ltEs4(yvy1000, yvy1010)
new_compare14(yvy218, yvy219, yvy220, yvy221, yvy222, yvy223, True, cdh, cea, ceb) → LT
new_esEs30(yvy40001, yvy30001, app(ty_Maybe, cdc)) → new_esEs23(yvy40001, yvy30001, cdc)
new_esEs8(yvy4001, yvy3001, ty_Char) → new_esEs15(yvy4001, yvy3001)
new_esEs9(yvy4000, yvy3000, ty_Bool) → new_esEs20(yvy4000, yvy3000)
new_lt5(yvy1001, yvy1011, ty_Ordering) → new_lt7(yvy1001, yvy1011)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbd, ty_Ordering) → new_ltEs6(yvy1000, yvy1010)
new_esEs24(Left(yvy40000), Left(yvy30000), app(app(ty_Either, dfc), dfd), hf) → new_esEs24(yvy40000, yvy30000, dfc, dfd)
new_esEs8(yvy4001, yvy3001, app(ty_[], db)) → new_esEs16(yvy4001, yvy3001, db)
new_compare27(Left(yvy4000), Left(yvy3000), efd, efe) → new_compare26(yvy4000, yvy3000, new_esEs10(yvy4000, yvy3000, efd), efd, efe)
new_esEs29(yvy40000, yvy30000, ty_Double) → new_esEs13(yvy40000, yvy30000)
new_esEs27(yvy1000, yvy1010, ty_Integer) → new_esEs18(yvy1000, yvy1010)
new_esEs18(Integer(yvy40000), Integer(yvy30000)) → new_primEqInt(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, ty_Char) → new_esEs15(yvy40002, yvy30002)
new_ltEs5(Just(yvy1000), Just(yvy1010), app(ty_Maybe, fg)) → new_ltEs5(yvy1000, yvy1010, fg)
new_ltEs11(yvy100, yvy101) → new_fsEs(new_compare18(yvy100, yvy101))
new_ltEs14(Right(yvy1000), Right(yvy1010), dbd, app(app(ty_Either, dce), dcf)) → new_ltEs14(yvy1000, yvy1010, dce, dcf)
new_esEs30(yvy40001, yvy30001, ty_Float) → new_esEs14(yvy40001, yvy30001)
new_lt23(yvy165, yvy167, ty_Float) → new_lt11(yvy165, yvy167)
new_compare12(False, False) → EQ
new_esEs28(yvy1001, yvy1011, ty_@0) → new_esEs19(yvy1001, yvy1011)
new_ltEs23(yvy166, yvy168, ty_Char) → new_ltEs7(yvy166, yvy168)
new_esEs24(Right(yvy40000), Right(yvy30000), he, app(ty_Maybe, dgd)) → new_esEs23(yvy40000, yvy30000, dgd)
new_esEs29(yvy40000, yvy30000, ty_Float) → new_esEs14(yvy40000, yvy30000)
new_esEs7(yvy4000, yvy3000, ty_Ordering) → new_esEs12(yvy4000, yvy3000)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Integer, hf) → new_esEs18(yvy40000, yvy30000)
new_lt20(yvy152, yvy155, app(ty_Maybe, dhe)) → new_lt14(yvy152, yvy155, dhe)
new_esEs39(yvy165, yvy167, app(app(app(ty_@3, fcb), fcc), fcd)) → new_esEs22(yvy165, yvy167, fcb, fcc, fcd)
new_esEs31(yvy40000, yvy30000, ty_@0) → new_esEs19(yvy40000, yvy30000)
new_esEs24(Right(yvy40000), Right(yvy30000), he, app(ty_[], dfe)) → new_esEs16(yvy40000, yvy30000, dfe)
new_compare111(yvy233, yvy234, yvy235, yvy236, False, ecd, ece) → GT
new_lt21(yvy153, yvy156, ty_Bool) → new_lt18(yvy153, yvy156)
new_ltEs6(LT, GT) → True
new_esEs33(yvy40002, yvy30002, ty_Int) → new_esEs25(yvy40002, yvy30002)
new_compare30(yvy400, yvy300, ty_Integer) → new_compare8(yvy400, yvy300)
new_ltEs23(yvy166, yvy168, app(ty_Maybe, fea)) → new_ltEs5(yvy166, yvy168, fea)
new_lt23(yvy165, yvy167, app(ty_Maybe, fcg)) → new_lt14(yvy165, yvy167, fcg)
new_ltEs21(yvy1001, yvy1011, ty_Char) → new_ltEs7(yvy1001, yvy1011)
new_ltEs14(Left(yvy1000), Left(yvy1010), app(app(ty_Either, dbb), dbc), daa) → new_ltEs14(yvy1000, yvy1010, dbb, dbc)
new_ltEs23(yvy166, yvy168, app(app(ty_@2, fdg), fdh)) → new_ltEs12(yvy166, yvy168, fdg, fdh)
new_ltEs21(yvy1001, yvy1011, ty_Ordering) → new_ltEs6(yvy1001, yvy1011)
new_esEs32(yvy40001, yvy30001, app(app(ty_@2, cff), cfg)) → new_esEs17(yvy40001, yvy30001, cff, cfg)
new_esEs24(Left(yvy40000), Left(yvy30000), app(ty_Maybe, dfb), hf) → new_esEs23(yvy40000, yvy30000, dfb)
new_lt22(yvy1000, yvy1010, app(ty_Ratio, eda)) → new_lt10(yvy1000, yvy1010, eda)
new_lt12(yvy152, yvy155, dea, deb) → new_esEs12(new_compare7(yvy152, yvy155, dea, deb), LT)
new_esEs35(yvy153, yvy156, ty_Int) → new_esEs25(yvy153, yvy156)
new_lt10(yvy152, yvy155, cdg) → new_esEs12(new_compare13(yvy152, yvy155, cdg), LT)
new_esEs4(yvy4000, yvy3000, ty_Double) → new_esEs13(yvy4000, yvy3000)
new_esEs8(yvy4001, yvy3001, app(app(ty_@2, dc), dd)) → new_esEs17(yvy4001, yvy3001, dc, dd)
new_esEs5(yvy4001, yvy3001, app(app(ty_@2, hh), baa)) → new_esEs17(yvy4001, yvy3001, hh, baa)
new_esEs16([], [], ge) → True
new_lt22(yvy1000, yvy1010, ty_Float) → new_lt11(yvy1000, yvy1010)
new_esEs32(yvy40001, yvy30001, ty_Ordering) → new_esEs12(yvy40001, yvy30001)
new_ltEs19(yvy1002, yvy1012, ty_Int) → new_ltEs15(yvy1002, yvy1012)
new_ltEs21(yvy1001, yvy1011, ty_Integer) → new_ltEs4(yvy1001, yvy1011)
new_ltEs20(yvy154, yvy157, ty_Float) → new_ltEs11(yvy154, yvy157)
new_lt5(yvy1001, yvy1011, app(app(ty_@2, bhc), bhd)) → new_lt12(yvy1001, yvy1011, bhc, bhd)
new_esEs11(yvy4000, yvy3000, ty_Int) → new_esEs25(yvy4000, yvy3000)
new_esEs32(yvy40001, yvy30001, app(app(app(ty_@3, cga), cgb), cgc)) → new_esEs22(yvy40001, yvy30001, cga, cgb, cgc)
new_lt6(yvy1000, yvy1010, ty_Double) → new_lt13(yvy1000, yvy1010)
new_lt20(yvy152, yvy155, ty_Float) → new_lt11(yvy152, yvy155)
new_ltEs14(Left(yvy1000), Left(yvy1010), app(app(app(ty_@3, dad), dae), daf), daa) → new_ltEs10(yvy1000, yvy1010, dad, dae, daf)
new_esEs26(yvy40000, yvy30000, ty_Integer) → new_esEs18(yvy40000, yvy30000)
new_lt22(yvy1000, yvy1010, app(app(app(ty_@3, edb), edc), edd)) → new_lt4(yvy1000, yvy1010, edb, edc, edd)
new_esEs36(yvy1000, yvy1010, app(app(ty_Either, edh), eea)) → new_esEs24(yvy1000, yvy1010, edh, eea)
new_esEs27(yvy1000, yvy1010, ty_Ordering) → new_esEs12(yvy1000, yvy1010)
new_ltEs19(yvy1002, yvy1012, ty_Double) → new_ltEs13(yvy1002, yvy1012)
new_lt21(yvy153, yvy156, ty_Int) → new_lt17(yvy153, yvy156)
new_lt20(yvy152, yvy155, ty_Integer) → new_lt15(yvy152, yvy155)
new_esEs24(Right(yvy40000), Right(yvy30000), he, ty_Ordering) → new_esEs12(yvy40000, yvy30000)
new_lt8(yvy152, yvy155) → new_esEs12(new_compare11(yvy152, yvy155), LT)
new_ltEs24(yvy100, yvy101, app(ty_[], fed)) → new_ltEs8(yvy100, yvy101, fed)
new_esEs9(yvy4000, yvy3000, ty_@0) → new_esEs19(yvy4000, yvy3000)
new_esEs22(@3(yvy40000, yvy40001, yvy40002), @3(yvy30000, yvy30001, yvy30002), ha, hb, hc) → new_asAs(new_esEs31(yvy40000, yvy30000, ha), new_asAs(new_esEs32(yvy40001, yvy30001, hb), new_esEs33(yvy40002, yvy30002, hc)))
new_esEs8(yvy4001, yvy3001, ty_Float) → new_esEs14(yvy4001, yvy3001)
new_esEs7(yvy4000, yvy3000, app(ty_Ratio, cb)) → new_esEs21(yvy4000, yvy3000, cb)
new_ltEs20(yvy154, yvy157, ty_Double) → new_ltEs13(yvy154, yvy157)
new_ltEs18(yvy107, yvy108, ty_Bool) → new_ltEs16(yvy107, yvy108)
new_compare28(yvy114, yvy115, False, fab, fac) → new_compare19(yvy114, yvy115, new_ltEs22(yvy114, yvy115, fac), fab, fac)
new_esEs6(yvy4002, yvy3002, app(ty_Maybe, bbh)) → new_esEs23(yvy4002, yvy3002, bbh)
new_lt5(yvy1001, yvy1011, app(app(app(ty_@3, bgh), bha), bhb)) → new_lt4(yvy1001, yvy1011, bgh, bha, bhb)
new_esEs31(yvy40000, yvy30000, app(app(app(ty_@3, ceg), ceh), cfa)) → new_esEs22(yvy40000, yvy30000, ceg, ceh, cfa)
new_esEs31(yvy40000, yvy30000, ty_Ordering) → new_esEs12(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, ty_Double) → new_esEs13(yvy40002, yvy30002)
new_lt6(yvy1000, yvy1010, ty_Float) → new_lt11(yvy1000, yvy1010)
new_esEs4(yvy4000, yvy3000, ty_Char) → new_esEs15(yvy4000, yvy3000)
new_esEs7(yvy4000, yvy3000, app(app(ty_Either, cg), da)) → new_esEs24(yvy4000, yvy3000, cg, da)
new_compare112(yvy189, yvy190, False, fgc) → GT
new_esEs12(GT, GT) → True
new_ltEs21(yvy1001, yvy1011, app(app(app(ty_@3, eed), eee), eef)) → new_ltEs10(yvy1001, yvy1011, eed, eee, eef)
new_esEs5(yvy4001, yvy3001, ty_Double) → new_esEs13(yvy4001, yvy3001)
new_compare17(yvy218, yvy219, yvy220, yvy221, yvy222, yvy223, False, yvy225, cdh, cea, ceb) → new_compare14(yvy218, yvy219, yvy220, yvy221, yvy222, yvy223, yvy225, cdh, cea, ceb)
new_esEs8(yvy4001, yvy3001, app(ty_Maybe, ea)) → new_esEs23(yvy4001, yvy3001, ea)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_@0) → new_esEs19(yvy40000, yvy30000)
new_compare25(yvy152, yvy153, yvy154, yvy155, yvy156, yvy157, False, dha, dhb, dhc) → new_compare17(yvy152, yvy153, yvy154, yvy155, yvy156, yvy157, new_lt20(yvy152, yvy155, dha), new_asAs(new_esEs34(yvy152, yvy155, dha), new_pePe(new_lt21(yvy153, yvy156, dhb), new_asAs(new_esEs35(yvy153, yvy156, dhb), new_ltEs20(yvy154, yvy157, dhc)))), dha, dhb, dhc)
new_compare31(Nothing, Just(yvy3000), feh) → LT
new_esEs29(yvy40000, yvy30000, ty_Ordering) → new_esEs12(yvy40000, yvy30000)
new_esEs4(yvy4000, yvy3000, app(ty_[], ge)) → new_esEs16(yvy4000, yvy3000, ge)
new_primPlusNat1(Zero, Zero) → Zero
new_compare0([], :(yvy3000, yvy3001), fef) → LT
new_ltEs6(LT, EQ) → True
new_lt23(yvy165, yvy167, ty_Ordering) → new_lt7(yvy165, yvy167)
new_ltEs21(yvy1001, yvy1011, app(ty_Maybe, efa)) → new_ltEs5(yvy1001, yvy1011, efa)
new_ltEs6(GT, LT) → False
new_lt18(yvy152, yvy155) → new_esEs12(new_compare12(yvy152, yvy155), LT)
new_esEs24(Right(yvy40000), Right(yvy30000), he, ty_Char) → new_esEs15(yvy40000, yvy30000)
new_asAs(True, yvy184) → yvy184
new_esEs26(yvy40000, yvy30000, ty_Float) → new_esEs14(yvy40000, yvy30000)
new_esEs35(yvy153, yvy156, ty_Float) → new_esEs14(yvy153, yvy156)
new_ltEs21(yvy1001, yvy1011, app(ty_[], eeb)) → new_ltEs8(yvy1001, yvy1011, eeb)
new_compare11(Char(yvy4000), Char(yvy3000)) → new_primCmpNat0(yvy4000, yvy3000)
new_ltEs22(yvy114, yvy115, ty_Float) → new_ltEs11(yvy114, yvy115)
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_esEs28(yvy1001, yvy1011, app(ty_Ratio, bgg)) → new_esEs21(yvy1001, yvy1011, bgg)
new_esEs39(yvy165, yvy167, ty_Double) → new_esEs13(yvy165, yvy167)
new_esEs11(yvy4000, yvy3000, ty_Bool) → new_esEs20(yvy4000, yvy3000)
new_ltEs22(yvy114, yvy115, ty_Double) → new_ltEs13(yvy114, yvy115)
new_lt22(yvy1000, yvy1010, ty_Ordering) → new_lt7(yvy1000, yvy1010)
new_esEs4(yvy4000, yvy3000, app(app(app(ty_@3, ha), hb), hc)) → new_esEs22(yvy4000, yvy3000, ha, hb, hc)
new_lt20(yvy152, yvy155, app(ty_Ratio, cdg)) → new_lt10(yvy152, yvy155, cdg)
new_ltEs16(False, False) → True
new_lt23(yvy165, yvy167, ty_Double) → new_lt13(yvy165, yvy167)
new_ltEs17(yvy100, yvy101) → new_fsEs(new_compare9(yvy100, yvy101))
new_esEs29(yvy40000, yvy30000, ty_Integer) → new_esEs18(yvy40000, yvy30000)
new_esEs8(yvy4001, yvy3001, ty_Ordering) → new_esEs12(yvy4001, yvy3001)
new_esEs30(yvy40001, yvy30001, ty_Bool) → new_esEs20(yvy40001, yvy30001)
new_lt23(yvy165, yvy167, app(ty_Ratio, fca)) → new_lt10(yvy165, yvy167, fca)
new_esEs30(yvy40001, yvy30001, ty_Int) → new_esEs25(yvy40001, yvy30001)
new_esEs27(yvy1000, yvy1010, ty_Float) → new_esEs14(yvy1000, yvy1010)
new_ltEs21(yvy1001, yvy1011, ty_Int) → new_ltEs15(yvy1001, yvy1011)
new_ltEs20(yvy154, yvy157, app(app(app(ty_@3, ebd), ebe), ebf)) → new_ltEs10(yvy154, yvy157, ebd, ebe, ebf)
new_esEs23(Just(yvy40000), Just(yvy30000), app(ty_[], dcg)) → new_esEs16(yvy40000, yvy30000, dcg)
new_esEs34(yvy152, yvy155, app(app(app(ty_@3, bb), bc), bd)) → new_esEs22(yvy152, yvy155, bb, bc, bd)
new_esEs16(:(yvy40000, yvy40001), :(yvy30000, yvy30001), ge) → new_asAs(new_esEs26(yvy40000, yvy30000, ge), new_esEs16(yvy40001, yvy30001, ge))
new_esEs9(yvy4000, yvy3000, app(app(app(ty_@3, ffe), fff), ffg)) → new_esEs22(yvy4000, yvy3000, ffe, fff, ffg)
new_ltEs19(yvy1002, yvy1012, app(app(app(ty_@3, cab), cac), cad)) → new_ltEs10(yvy1002, yvy1012, cab, cac, cad)
new_ltEs20(yvy154, yvy157, ty_Ordering) → new_ltEs6(yvy154, yvy157)
new_compare19(yvy206, yvy207, False, dgg, dgh) → GT
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Integer) → new_ltEs4(yvy1000, yvy1010)
new_esEs6(yvy4002, yvy3002, ty_@0) → new_esEs19(yvy4002, yvy3002)
new_ltEs10(@3(yvy1000, yvy1001, yvy1002), @3(yvy1010, yvy1011, yvy1012), bfa, bfb, bfc) → new_pePe(new_lt6(yvy1000, yvy1010, bfa), new_asAs(new_esEs27(yvy1000, yvy1010, bfa), new_pePe(new_lt5(yvy1001, yvy1011, bfb), new_asAs(new_esEs28(yvy1001, yvy1011, bfb), new_ltEs19(yvy1002, yvy1012, bfc)))))
new_esEs33(yvy40002, yvy30002, ty_@0) → new_esEs19(yvy40002, yvy30002)
new_esEs35(yvy153, yvy156, app(ty_Ratio, eaa)) → new_esEs21(yvy153, yvy156, eaa)
new_ltEs22(yvy114, yvy115, ty_Int) → new_ltEs15(yvy114, yvy115)
new_ltEs24(yvy100, yvy101, app(app(app(ty_@3, bfa), bfb), bfc)) → new_ltEs10(yvy100, yvy101, bfa, bfb, bfc)
new_compare27(Right(yvy4000), Right(yvy3000), efd, efe) → new_compare28(yvy4000, yvy3000, new_esEs11(yvy4000, yvy3000, efe), efd, efe)
new_ltEs21(yvy1001, yvy1011, ty_@0) → new_ltEs17(yvy1001, yvy1011)
new_lt16(yvy152, yvy155, dhf, dhg) → new_esEs12(new_compare27(yvy152, yvy155, dhf, dhg), LT)
new_compare15(EQ, EQ) → EQ
new_ltEs22(yvy114, yvy115, ty_Char) → new_ltEs7(yvy114, yvy115)
new_compare30(yvy400, yvy300, ty_Double) → new_compare29(yvy400, yvy300)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCompAux0(yvy56, EQ) → yvy56
new_lt6(yvy1000, yvy1010, app(app(ty_@2, bga), bgb)) → new_lt12(yvy1000, yvy1010, bga, bgb)
new_esEs27(yvy1000, yvy1010, app(ty_Maybe, bgc)) → new_esEs23(yvy1000, yvy1010, bgc)
new_ltEs20(yvy154, yvy157, ty_Char) → new_ltEs7(yvy154, yvy157)
new_esEs10(yvy4000, yvy3000, ty_Integer) → new_esEs18(yvy4000, yvy3000)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_@0, daa) → new_ltEs17(yvy1000, yvy1010)
new_ltEs18(yvy107, yvy108, ty_Int) → new_ltEs15(yvy107, yvy108)
new_lt21(yvy153, yvy156, app(app(app(ty_@3, eab), eac), ead)) → new_lt4(yvy153, yvy156, eab, eac, ead)
new_esEs6(yvy4002, yvy3002, ty_Char) → new_esEs15(yvy4002, yvy3002)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_esEs30(yvy40001, yvy30001, ty_Char) → new_esEs15(yvy40001, yvy30001)
new_ltEs5(Just(yvy1000), Just(yvy1010), app(app(app(ty_@3, fa), fb), fc)) → new_ltEs10(yvy1000, yvy1010, fa, fb, fc)
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_esEs39(yvy165, yvy167, app(ty_[], fbh)) → new_esEs16(yvy165, yvy167, fbh)
new_esEs35(yvy153, yvy156, ty_Char) → new_esEs15(yvy153, yvy156)
new_not(True) → False
new_ltEs5(Just(yvy1000), Just(yvy1010), app(ty_Ratio, eh)) → new_ltEs9(yvy1000, yvy1010, eh)

The set Q consists of the following terms:

new_esEs36(x0, x1, ty_Char)
new_esEs35(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, ty_Float)
new_esEs7(x0, x1, ty_Int)
new_esEs32(x0, x1, app(ty_[], x2))
new_ltEs21(x0, x1, ty_Int)
new_esEs10(x0, x1, ty_Float)
new_ltEs16(True, True)
new_esEs6(x0, x1, ty_Int)
new_lt11(x0, x1)
new_ltEs20(x0, x1, ty_Int)
new_lt5(x0, x1, ty_Char)
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs23(x0, x1, app(ty_Maybe, x2))
new_esEs32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs21(x0, x1, ty_@0)
new_esEs29(x0, x1, ty_Char)
new_ltEs22(x0, x1, ty_Integer)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_compare10(x0, x1, False, x2, x3)
new_esEs32(x0, x1, ty_Int)
new_esEs11(x0, x1, ty_Int)
new_esEs24(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs4(x0, x1, ty_Float)
new_lt23(x0, x1, app(ty_[], x2))
new_esEs33(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Integer)
new_compare30(x0, x1, ty_Int)
new_pePe(True, x0)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs11(x0, x1, ty_@0)
new_esEs35(x0, x1, ty_Integer)
new_esEs11(x0, x1, ty_Char)
new_esEs6(x0, x1, ty_Float)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(x0, x1, ty_Int)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_lt22(x0, x1, ty_@0)
new_compare30(x0, x1, ty_Bool)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_@0)
new_esEs29(x0, x1, ty_Ordering)
new_lt22(x0, x1, ty_Float)
new_lt23(x0, x1, ty_Integer)
new_esEs11(x0, x1, app(ty_Ratio, x2))
new_lt7(x0, x1)
new_esEs8(x0, x1, ty_Integer)
new_esEs23(Just(x0), Just(x1), ty_Float)
new_compare30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs5(Nothing, Nothing, x0)
new_esEs6(x0, x1, ty_Integer)
new_lt5(x0, x1, ty_@0)
new_esEs23(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs11(x0, x1, ty_Bool)
new_lt6(x0, x1, app(app(ty_@2, x2), x3))
new_esEs36(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare12(False, True)
new_compare12(True, False)
new_compare26(x0, x1, True, x2, x3)
new_lt21(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(Left(x0), Left(x1), ty_@0, x2)
new_ltEs7(x0, x1)
new_ltEs18(x0, x1, app(ty_[], x2))
new_primCompAux0(x0, EQ)
new_ltEs14(Right(x0), Right(x1), x2, ty_Char)
new_esEs36(x0, x1, app(app(ty_Either, x2), x3))
new_esEs39(x0, x1, app(ty_Ratio, x2))
new_ltEs14(Right(x0), Right(x1), x2, ty_Float)
new_esEs10(x0, x1, ty_Integer)
new_esEs32(x0, x1, ty_Ordering)
new_ltEs21(x0, x1, ty_Float)
new_ltEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs24(x0, x1, ty_Integer)
new_compare19(x0, x1, False, x2, x3)
new_lt5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs34(x0, x1, ty_Float)
new_ltEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs24(Left(x0), Left(x1), ty_@0, x2)
new_esEs6(x0, x1, ty_@0)
new_lt6(x0, x1, ty_Float)
new_ltEs14(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs9(x0, x1, app(app(ty_Either, x2), x3))
new_esEs9(x0, x1, ty_Int)
new_compare30(x0, x1, ty_Integer)
new_esEs12(GT, EQ)
new_esEs12(EQ, GT)
new_esEs36(x0, x1, ty_Int)
new_ltEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, ty_Bool)
new_esEs11(x0, x1, app(app(ty_@2, x2), x3))
new_esEs10(x0, x1, app(app(ty_Either, x2), x3))
new_lt6(x0, x1, app(ty_Ratio, x2))
new_compare28(x0, x1, False, x2, x3)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt5(x0, x1, ty_Double)
new_lt5(x0, x1, app(ty_[], x2))
new_esEs24(Right(x0), Right(x1), x2, ty_Float)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare15(LT, LT)
new_esEs34(x0, x1, app(ty_Maybe, x2))
new_lt5(x0, x1, app(ty_Ratio, x2))
new_esEs10(x0, x1, ty_Char)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs39(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(Right(x0), Right(x1), x2, ty_Double)
new_esEs34(x0, x1, ty_Ordering)
new_esEs39(x0, x1, app(ty_[], x2))
new_esEs12(GT, GT)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs30(x0, x1, ty_Double)
new_esEs24(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs21(x0, x1, ty_Ordering)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_lt21(x0, x1, ty_Float)
new_esEs11(x0, x1, ty_Integer)
new_compare0(:(x0, x1), [], x2)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(Just(x0), Nothing, x1)
new_esEs23(Just(x0), Just(x1), ty_Double)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs5(Just(x0), Nothing, x1)
new_esEs11(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, ty_Char)
new_esEs38(x0, x1, ty_Integer)
new_esEs27(x0, x1, ty_Bool)
new_esEs10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs6(EQ, EQ)
new_esEs32(x0, x1, ty_@0)
new_esEs7(x0, x1, ty_Float)
new_esEs23(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs22(x0, x1, ty_Char)
new_esEs9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(x0, x1, ty_Double)
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_esEs5(x0, x1, ty_Bool)
new_esEs31(x0, x1, ty_Int)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs32(x0, x1, app(ty_Ratio, x2))
new_esEs33(x0, x1, ty_Double)
new_ltEs14(Right(x0), Right(x1), x2, ty_Int)
new_esEs8(x0, x1, ty_Float)
new_ltEs18(x0, x1, ty_@0)
new_esEs36(x0, x1, app(app(ty_@2, x2), x3))
new_esEs16(:(x0, x1), :(x2, x3), x4)
new_lt9(x0, x1, x2)
new_ltEs5(Just(x0), Just(x1), ty_@0)
new_lt5(x0, x1, ty_Int)
new_ltEs6(LT, EQ)
new_ltEs6(EQ, LT)
new_primCompAux0(x0, LT)
new_esEs38(x0, x1, ty_Int)
new_esEs23(Just(x0), Just(x1), ty_Int)
new_ltEs20(x0, x1, ty_@0)
new_esEs5(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Int)
new_lt17(x0, x1)
new_esEs36(x0, x1, ty_Bool)
new_primEqNat0(Zero, Zero)
new_compare13(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs23(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_@0)
new_compare30(x0, x1, app(ty_[], x2))
new_esEs7(x0, x1, ty_Bool)
new_esEs9(x0, x1, app(ty_[], x2))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs10(x0, x1, app(ty_Maybe, x2))
new_esEs5(x0, x1, ty_Float)
new_ltEs22(x0, x1, ty_Float)
new_compare15(GT, GT)
new_esEs31(x0, x1, ty_Double)
new_compare27(Right(x0), Right(x1), x2, x3)
new_ltEs20(x0, x1, ty_Integer)
new_lt22(x0, x1, ty_Bool)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs34(x0, x1, ty_Bool)
new_esEs31(x0, x1, ty_Integer)
new_esEs6(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, ty_Char)
new_lt20(x0, x1, ty_Double)
new_ltEs22(x0, x1, app(app(ty_Either, x2), x3))
new_compare17(x0, x1, x2, x3, x4, x5, True, x6, x7, x8, x9)
new_ltEs15(x0, x1)
new_esEs4(x0, x1, ty_Integer)
new_esEs31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs39(x0, x1, ty_Bool)
new_ltEs24(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Float)
new_primMulNat0(Zero, Zero)
new_asAs(True, x0)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Double)
new_esEs5(x0, x1, ty_Double)
new_esEs34(x0, x1, app(ty_[], x2))
new_fsEs(x0)
new_esEs6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs8(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(:%(x0, x1), :%(x2, x3), x4)
new_ltEs5(Just(x0), Just(x1), ty_Integer)
new_lt6(x0, x1, ty_Double)
new_compare28(x0, x1, True, x2, x3)
new_esEs35(x0, x1, ty_Double)
new_ltEs18(x0, x1, ty_Bool)
new_lt6(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, ty_Float)
new_ltEs5(Just(x0), Just(x1), ty_Double)
new_lt22(x0, x1, ty_Ordering)
new_esEs9(x0, x1, ty_@0)
new_esEs35(x0, x1, ty_Bool)
new_ltEs14(Left(x0), Right(x1), x2, x3)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(Right(x0), Left(x1), x2, x3)
new_ltEs14(Right(x0), Right(x1), x2, ty_Integer)
new_esEs35(x0, x1, ty_Char)
new_ltEs23(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, ty_Bool)
new_esEs31(x0, x1, ty_@0)
new_esEs24(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs19(x0, x1, ty_Double)
new_ltEs24(x0, x1, ty_Double)
new_esEs13(Double(x0, x1), Double(x2, x3))
new_esEs32(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, ty_Ordering)
new_lt23(x0, x1, app(ty_Ratio, x2))
new_esEs20(True, True)
new_lt20(x0, x1, app(ty_[], x2))
new_lt22(x0, x1, ty_Int)
new_ltEs12(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs7(x0, x1, ty_Integer)
new_esEs30(x0, x1, ty_Bool)
new_lt21(x0, x1, ty_@0)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs33(x0, x1, ty_Float)
new_esEs29(x0, x1, ty_Integer)
new_compare31(Nothing, Nothing, x0)
new_ltEs21(x0, x1, ty_Integer)
new_primPlusNat0(Zero, x0)
new_lt21(x0, x1, app(ty_Ratio, x2))
new_lt22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(x0, x1, app(ty_[], x2))
new_esEs4(x0, x1, ty_Ordering)
new_ltEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs8(x0, x1, ty_Bool)
new_esEs7(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs31(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_primPlusNat0(Succ(x0), x1)
new_ltEs14(Right(x0), Right(x1), x2, ty_Double)
new_ltEs4(x0, x1)
new_compare10(x0, x1, True, x2, x3)
new_compare24(x0, x1, x2, x3, False, x4, x5)
new_esEs34(x0, x1, ty_Integer)
new_esEs31(x0, x1, ty_Ordering)
new_ltEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs6(GT, LT)
new_ltEs6(LT, GT)
new_ltEs14(Left(x0), Left(x1), ty_Char, x2)
new_compare210(x0, x1, True, x2)
new_lt23(x0, x1, app(app(ty_@2, x2), x3))
new_compare0([], [], x0)
new_esEs11(x0, x1, ty_Double)
new_esEs16(:(x0, x1), [], x2)
new_lt19(x0, x1)
new_ltEs23(x0, x1, app(ty_Ratio, x2))
new_compare111(x0, x1, x2, x3, True, x4, x5)
new_esEs4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(x0, x1, ty_Double)
new_compare30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Double)
new_esEs39(x0, x1, ty_Char)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_compare15(EQ, EQ)
new_esEs24(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_lt6(x0, x1, ty_Int)
new_lt5(x0, x1, app(app(ty_@2, x2), x3))
new_lt21(x0, x1, ty_Ordering)
new_esEs24(Left(x0), Left(x1), ty_Bool, x2)
new_esEs28(x0, x1, ty_Ordering)
new_ltEs22(x0, x1, ty_Ordering)
new_ltEs11(x0, x1)
new_esEs16([], :(x0, x1), x2)
new_esEs24(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_lt20(x0, x1, ty_Float)
new_lt21(x0, x1, ty_Integer)
new_esEs32(x0, x1, ty_Bool)
new_esEs39(x0, x1, ty_Float)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt6(x0, x1, ty_Integer)
new_ltEs14(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs10(x0, x1, ty_Double)
new_sr0(x0, x1)
new_esEs23(Just(x0), Just(x1), ty_Integer)
new_esEs24(Left(x0), Left(x1), ty_Integer, x2)
new_esEs20(False, True)
new_esEs20(True, False)
new_lt22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, ty_Bool)
new_ltEs23(x0, x1, ty_Integer)
new_lt22(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs20(False, False)
new_compare12(False, False)
new_ltEs22(x0, x1, app(ty_Ratio, x2))
new_esEs23(Nothing, Nothing, x0)
new_esEs12(LT, EQ)
new_esEs12(EQ, LT)
new_lt21(x0, x1, ty_Int)
new_lt22(x0, x1, ty_Char)
new_esEs31(x0, x1, app(ty_Maybe, x2))
new_compare14(x0, x1, x2, x3, x4, x5, True, x6, x7, x8)
new_esEs31(x0, x1, ty_Float)
new_esEs24(Right(x0), Right(x1), x2, ty_Int)
new_primPlusNat1(Zero, Zero)
new_ltEs21(x0, x1, ty_Bool)
new_esEs34(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs20(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_Float)
new_esEs12(EQ, EQ)
new_compare25(x0, x1, x2, x3, x4, x5, False, x6, x7, x8)
new_esEs23(Just(x0), Just(x1), ty_Bool)
new_esEs27(x0, x1, ty_Char)
new_esEs4(x0, x1, app(app(ty_Either, x2), x3))
new_esEs9(x0, x1, ty_Integer)
new_esEs30(x0, x1, ty_Float)
new_ltEs20(x0, x1, ty_Float)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs28(x0, x1, ty_Double)
new_esEs30(x0, x1, ty_Char)
new_ltEs14(Right(x0), Right(x1), x2, ty_@0)
new_compare30(x0, x1, ty_@0)
new_esEs6(x0, x1, ty_Bool)
new_ltEs5(Nothing, Just(x0), x1)
new_esEs24(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs23(x0, x1, ty_Float)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_lt23(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs7(x0, x1, app(ty_Ratio, x2))
new_compare15(EQ, GT)
new_compare15(GT, EQ)
new_ltEs24(x0, x1, ty_Ordering)
new_compare30(x0, x1, ty_Char)
new_primEqNat0(Succ(x0), Zero)
new_compare15(LT, GT)
new_compare15(GT, LT)
new_esEs24(Right(x0), Right(x1), x2, ty_@0)
new_lt14(x0, x1, x2)
new_esEs36(x0, x1, ty_Double)
new_esEs39(x0, x1, ty_Ordering)
new_esEs4(x0, x1, app(ty_[], x2))
new_ltEs21(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_esEs37(x0, x1, ty_Int)
new_esEs4(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs9(x0, x1, ty_Double)
new_primMulInt(Neg(x0), Neg(x1))
new_compare14(x0, x1, x2, x3, x4, x5, False, x6, x7, x8)
new_ltEs17(x0, x1)
new_compare30(x0, x1, app(ty_Ratio, x2))
new_esEs9(x0, x1, ty_Ordering)
new_esEs8(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, ty_Char)
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_ltEs23(x0, x1, ty_Int)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_esEs8(x0, x1, ty_Int)
new_ltEs5(Just(x0), Just(x1), ty_Int)
new_esEs33(x0, x1, ty_Int)
new_ltEs23(x0, x1, ty_@0)
new_esEs24(Left(x0), Left(x1), ty_Double, x2)
new_lt5(x0, x1, app(app(ty_Either, x2), x3))
new_esEs33(x0, x1, ty_Bool)
new_esEs10(x0, x1, ty_Ordering)
new_ltEs14(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs35(x0, x1, ty_@0)
new_esEs4(x0, x1, ty_Char)
new_ltEs14(Left(x0), Left(x1), ty_Integer, x2)
new_lt23(x0, x1, ty_Int)
new_esEs6(x0, x1, app(ty_[], x2))
new_esEs24(Left(x0), Left(x1), ty_Float, x2)
new_ltEs23(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs34(x0, x1, app(ty_Ratio, x2))
new_ltEs18(x0, x1, ty_Double)
new_lt23(x0, x1, ty_Bool)
new_ltEs14(Left(x0), Left(x1), ty_Float, x2)
new_esEs7(x0, x1, app(ty_Maybe, x2))
new_ltEs24(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_ltEs21(x0, x1, app(ty_Maybe, x2))
new_lt21(x0, x1, ty_Bool)
new_compare18(Float(x0, x1), Float(x2, x3))
new_ltEs5(Just(x0), Just(x1), ty_Float)
new_ltEs22(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_lt22(x0, x1, app(app(ty_Either, x2), x3))
new_compare110(x0, x1, x2, x3, True, x4, x5, x6)
new_esEs26(x0, x1, ty_Bool)
new_lt6(x0, x1, ty_Bool)
new_esEs30(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Integer)
new_ltEs14(Left(x0), Left(x1), ty_Bool, x2)
new_esEs8(x0, x1, ty_Double)
new_lt21(x0, x1, ty_Char)
new_lt5(x0, x1, ty_Float)
new_compare11(Char(x0), Char(x1))
new_compare31(Nothing, Just(x0), x1)
new_compare30(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs30(x0, x1, ty_Integer)
new_esEs7(x0, x1, app(app(ty_@2, x2), x3))
new_esEs33(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, ty_@0)
new_sr(Integer(x0), Integer(x1))
new_esEs16([], [], x0)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs7(x0, x1, ty_@0)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs23(Nothing, Just(x0), x1)
new_esEs11(x0, x1, app(ty_[], x2))
new_esEs34(x0, x1, ty_Char)
new_esEs10(x0, x1, ty_Bool)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs10(x0, x1, ty_@0)
new_compare7(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs39(x0, x1, ty_Double)
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_@0)
new_lt6(x0, x1, app(app(ty_Either, x2), x3))
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_esEs31(x0, x1, ty_Bool)
new_primEqNat0(Zero, Succ(x0))
new_primPlusNat1(Succ(x0), Zero)
new_lt23(x0, x1, ty_Char)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_lt22(x0, x1, app(ty_[], x2))
new_lt12(x0, x1, x2, x3)
new_lt20(x0, x1, ty_Char)
new_lt4(x0, x1, x2, x3, x4)
new_esEs39(x0, x1, app(ty_Maybe, x2))
new_ltEs22(x0, x1, app(ty_[], x2))
new_esEs6(x0, x1, ty_Ordering)
new_esEs33(x0, x1, ty_Char)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt22(x0, x1, app(ty_Maybe, x2))
new_esEs10(x0, x1, app(ty_Ratio, x2))
new_esEs32(x0, x1, ty_Integer)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_esEs33(x0, x1, app(ty_Ratio, x2))
new_pePe(False, x0)
new_ltEs24(x0, x1, ty_Int)
new_ltEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_lt8(x0, x1)
new_ltEs14(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs10(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_lt23(x0, x1, ty_Double)
new_ltEs22(x0, x1, app(ty_Maybe, x2))
new_esEs31(x0, x1, app(app(ty_Either, x2), x3))
new_lt5(x0, x1, app(ty_Maybe, x2))
new_compare110(x0, x1, x2, x3, False, x4, x5, x6)
new_lt20(x0, x1, ty_Bool)
new_esEs29(x0, x1, ty_Int)
new_ltEs14(Left(x0), Left(x1), ty_Double, x2)
new_esEs30(x0, x1, ty_Ordering)
new_lt23(x0, x1, ty_Float)
new_esEs6(x0, x1, app(ty_Ratio, x2))
new_lt6(x0, x1, ty_@0)
new_esEs35(x0, x1, app(app(ty_@2, x2), x3))
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs31(x0, x1, ty_Char)
new_esEs23(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_lt22(x0, x1, ty_Double)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs22(x0, x1, ty_@0)
new_esEs39(x0, x1, ty_Int)
new_esEs30(x0, x1, ty_@0)
new_ltEs16(False, True)
new_ltEs16(True, False)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_ltEs6(GT, GT)
new_compare112(x0, x1, True, x2)
new_esEs10(x0, x1, ty_Int)
new_lt21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs32(x0, x1, ty_Char)
new_lt21(x0, x1, app(ty_Maybe, x2))
new_ltEs18(x0, x1, ty_Int)
new_ltEs5(Just(x0), Just(x1), ty_Ordering)
new_esEs33(x0, x1, app(ty_[], x2))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_ltEs19(x0, x1, ty_Char)
new_ltEs5(Just(x0), Just(x1), ty_Char)
new_esEs27(x0, x1, ty_Int)
new_compare26(x0, x1, False, x2, x3)
new_esEs23(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs21(x0, x1, app(ty_[], x2))
new_ltEs5(Just(x0), Just(x1), ty_Bool)
new_ltEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_lt22(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_@0)
new_ltEs22(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_Integer)
new_esEs33(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Int)
new_primCmpNat0(Zero, Zero)
new_esEs35(x0, x1, ty_Float)
new_asAs(False, x0)
new_ltEs19(x0, x1, app(ty_[], x2))
new_lt5(x0, x1, ty_Integer)
new_ltEs24(x0, x1, ty_@0)
new_esEs6(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs19(x0, x1, ty_Int)
new_lt23(x0, x1, ty_@0)
new_esEs34(x0, x1, ty_Int)
new_ltEs6(LT, LT)
new_compare30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs35(x0, x1, app(app(ty_Either, x2), x3))
new_esEs11(x0, x1, ty_Ordering)
new_esEs28(x0, x1, app(ty_[], x2))
new_ltEs14(Left(x0), Left(x1), ty_Int, x2)
new_ltEs22(x0, x1, ty_Double)
new_esEs9(x0, x1, app(ty_Ratio, x2))
new_ltEs24(x0, x1, ty_Char)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare27(Right(x0), Left(x1), x2, x3)
new_compare27(Left(x0), Right(x1), x2, x3)
new_esEs36(x0, x1, app(ty_[], x2))
new_esEs18(Integer(x0), Integer(x1))
new_esEs32(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Int)
new_esEs34(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(Just(x0), Just(x1), ty_@0)
new_esEs4(x0, x1, app(ty_Maybe, x2))
new_compare24(x0, x1, x2, x3, True, x4, x5)
new_ltEs19(x0, x1, ty_Float)
new_esEs6(x0, x1, ty_Char)
new_lt21(x0, x1, ty_Double)
new_ltEs14(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_compare210(x0, x1, False, x2)
new_esEs30(x0, x1, app(ty_[], x2))
new_esEs24(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_lt5(x0, x1, ty_Bool)
new_esEs23(Just(x0), Just(x1), ty_Char)
new_ltEs13(x0, x1)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs23(x0, x1, ty_Bool)
new_esEs24(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs5(x0, x1, app(ty_[], x2))
new_compare15(LT, EQ)
new_compare15(EQ, LT)
new_compare9(@0, @0)
new_lt13(x0, x1)
new_esEs36(x0, x1, ty_Integer)
new_esEs29(x0, x1, ty_Double)
new_esEs8(x0, x1, app(ty_Maybe, x2))
new_esEs5(x0, x1, app(ty_Ratio, x2))
new_ltEs18(x0, x1, ty_Float)
new_compare25(x0, x1, x2, x3, x4, x5, True, x6, x7, x8)
new_lt18(x0, x1)
new_esEs24(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs8(x0, x1, app(ty_Ratio, x2))
new_lt5(x0, x1, ty_Ordering)
new_esEs5(x0, x1, app(ty_Maybe, x2))
new_lt15(x0, x1)
new_compare8(Integer(x0), Integer(x1))
new_esEs34(x0, x1, app(app(ty_Either, x2), x3))
new_esEs31(x0, x1, app(ty_Ratio, x2))
new_esEs23(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs11(x0, x1, app(ty_Maybe, x2))
new_esEs8(x0, x1, ty_@0)
new_esEs5(x0, x1, ty_Int)
new_not(True)
new_compare30(x0, x1, ty_Float)
new_esEs33(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Ordering)
new_primMulInt(Pos(x0), Pos(x1))
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs4(x0, x1, ty_Bool)
new_esEs32(x0, x1, ty_Float)
new_esEs24(Right(x0), Right(x1), x2, ty_Char)
new_esEs36(x0, x1, ty_Ordering)
new_ltEs5(Just(x0), Just(x1), app(ty_[], x2))
new_esEs9(x0, x1, ty_Bool)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_not(False)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_compare29(Double(x0, x1), Double(x2, x3))
new_esEs6(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(Right(x0), Right(x1), x2, ty_Ordering)
new_compare13(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs24(Left(x0), Left(x1), ty_Int, x2)
new_primCmpNat0(Succ(x0), Succ(x1))
new_esEs7(x0, x1, ty_Ordering)
new_esEs10(x0, x1, app(app(ty_@2, x2), x3))
new_lt23(x0, x1, app(ty_Maybe, x2))
new_ltEs23(x0, x1, ty_Char)
new_esEs8(x0, x1, ty_Ordering)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_lt6(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs39(x0, x1, ty_@0)
new_ltEs21(x0, x1, ty_Char)
new_esEs15(Char(x0), Char(x1))
new_ltEs6(GT, EQ)
new_ltEs6(EQ, GT)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpNat0(Zero, Succ(x0))
new_ltEs24(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Ordering)
new_ltEs24(x0, x1, app(ty_Ratio, x2))
new_ltEs21(x0, x1, app(ty_Ratio, x2))
new_ltEs21(x0, x1, ty_Double)
new_compare6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_compare30(x0, x1, ty_Double)
new_compare27(Left(x0), Left(x1), x2, x3)
new_compare19(x0, x1, True, x2, x3)
new_lt21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt21(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, app(ty_[], x2))
new_ltEs14(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_primCmpNat0(Succ(x0), Zero)
new_lt16(x0, x1, x2, x3)
new_esEs34(x0, x1, ty_Double)
new_compare0([], :(x0, x1), x2)
new_ltEs14(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs22(x0, x1, ty_Int)
new_esEs4(x0, x1, app(ty_Ratio, x2))
new_esEs35(x0, x1, app(ty_Maybe, x2))
new_compare16(x0, x1)
new_ltEs20(x0, x1, ty_Double)
new_esEs22(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs24(x0, x1, ty_Bool)
new_esEs35(x0, x1, ty_Ordering)
new_ltEs18(x0, x1, ty_Integer)
new_esEs35(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs34(x0, x1, ty_@0)
new_esEs5(x0, x1, app(app(ty_@2, x2), x3))
new_esEs37(x0, x1, ty_Integer)
new_ltEs18(x0, x1, ty_Char)
new_esEs7(x0, x1, ty_Double)
new_lt23(x0, x1, ty_Ordering)
new_ltEs24(x0, x1, app(ty_Maybe, x2))
new_esEs24(Left(x0), Right(x1), x2, x3)
new_esEs24(Right(x0), Left(x1), x2, x3)
new_esEs9(x0, x1, ty_Float)
new_esEs32(x0, x1, app(ty_Maybe, x2))
new_esEs23(Just(x0), Just(x1), ty_Ordering)
new_lt6(x0, x1, ty_Char)
new_esEs9(x0, x1, app(app(ty_@2, x2), x3))
new_esEs9(x0, x1, ty_Char)
new_compare31(Just(x0), Nothing, x1)
new_esEs8(x0, x1, ty_Char)
new_esEs35(x0, x1, ty_Int)
new_esEs33(x0, x1, ty_@0)
new_esEs5(x0, x1, ty_Ordering)
new_esEs35(x0, x1, app(ty_Ratio, x2))
new_esEs32(x0, x1, ty_Double)
new_compare111(x0, x1, x2, x3, False, x4, x5)
new_esEs39(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(x0, x1, app(ty_[], x2))
new_esEs14(Float(x0, x1), Float(x2, x3))
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs24(Left(x0), Left(x1), ty_Char, x2)
new_esEs26(x0, x1, ty_Integer)
new_esEs5(x0, x1, ty_@0)
new_esEs5(x0, x1, ty_Char)
new_esEs7(x0, x1, ty_Char)
new_ltEs21(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs9(x0, x1, x2)
new_compare12(True, True)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs36(x0, x1, app(ty_Maybe, x2))
new_esEs5(x0, x1, ty_Integer)
new_esEs33(x0, x1, app(app(ty_@2, x2), x3))
new_primCompAux1(x0, x1, x2, x3)
new_compare30(x0, x1, ty_Ordering)
new_primMulNat0(Zero, Succ(x0))
new_esEs17(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs23(x0, x1, ty_Double)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_compare17(x0, x1, x2, x3, x4, x5, False, x6, x7, x8, x9)
new_esEs9(x0, x1, app(ty_Maybe, x2))
new_esEs24(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs24(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs8(x0, x1, app(app(ty_@2, x2), x3))
new_primCompAux0(x0, GT)
new_esEs39(x0, x1, app(app(ty_@2, x2), x3))
new_lt6(x0, x1, ty_Ordering)
new_primPlusNat1(Zero, Succ(x0))
new_compare0(:(x0, x1), :(x2, x3), x4)
new_esEs36(x0, x1, ty_Float)
new_esEs19(@0, @0)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs36(x0, x1, app(ty_Ratio, x2))
new_esEs24(Right(x0), Right(x1), x2, ty_Integer)
new_esEs31(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs8(x0, x1, x2)
new_esEs36(x0, x1, ty_@0)
new_esEs12(LT, LT)
new_esEs28(x0, x1, ty_Integer)
new_esEs24(Right(x0), Right(x1), x2, ty_Bool)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_ltEs18(x0, x1, ty_Ordering)
new_ltEs16(False, False)
new_compare31(Just(x0), Just(x1), x2)
new_esEs7(x0, x1, app(app(ty_Either, x2), x3))
new_esEs33(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, ty_Ordering)
new_esEs28(x0, x1, ty_@0)
new_esEs11(x0, x1, ty_Float)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_lt10(x0, x1, x2)
new_esEs39(x0, x1, ty_Integer)
new_compare112(x0, x1, False, x2)
new_esEs24(Left(x0), Left(x1), app(ty_Maybe, x2), x3)

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

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



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

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

new_addToFM_C(Branch(:(yvy500, yvy501), yvy51, yvy52, yvy53, yvy54), [], yvy41, h, ba) → new_addToFM_C(yvy53, [], yvy41, h, ba)

The TRS R consists of the following rules:

new_compare210(yvy100, yvy101, False, fee) → new_compare112(yvy100, yvy101, new_ltEs24(yvy100, yvy101, fee), fee)
new_compare7(@2(yvy4000, yvy4001), @2(yvy3000, yvy3001), be, bf) → new_compare24(yvy4000, yvy4001, yvy3000, yvy3001, new_asAs(new_esEs7(yvy4000, yvy3000, be), new_esEs8(yvy4001, yvy3001, bf)), be, bf)
new_esEs24(Left(yvy40000), Left(yvy30000), app(ty_Ratio, def), hf) → new_esEs21(yvy40000, yvy30000, def)
new_ltEs19(yvy1002, yvy1012, app(ty_[], bhh)) → new_ltEs8(yvy1002, yvy1012, bhh)
new_compare112(yvy189, yvy190, True, fgc) → LT
new_lt22(yvy1000, yvy1010, ty_Int) → new_lt17(yvy1000, yvy1010)
new_ltEs22(yvy114, yvy115, app(app(ty_@2, fba), fbb)) → new_ltEs12(yvy114, yvy115, fba, fbb)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Int, hf) → new_esEs25(yvy40000, yvy30000)
new_esEs6(yvy4002, yvy3002, app(app(app(ty_@3, bbe), bbf), bbg)) → new_esEs22(yvy4002, yvy3002, bbe, bbf, bbg)
new_esEs27(yvy1000, yvy1010, app(ty_[], bfd)) → new_esEs16(yvy1000, yvy1010, bfd)
new_esEs20(True, True) → True
new_esEs35(yvy153, yvy156, app(ty_[], dhh)) → new_esEs16(yvy153, yvy156, dhh)
new_compare8(Integer(yvy4000), Integer(yvy3000)) → new_primCmpInt(yvy4000, yvy3000)
new_esEs8(yvy4001, yvy3001, ty_Bool) → new_esEs20(yvy4001, yvy3001)
new_esEs11(yvy4000, yvy3000, ty_Integer) → new_esEs18(yvy4000, yvy3000)
new_esEs27(yvy1000, yvy1010, app(app(ty_@2, bga), bgb)) → new_esEs17(yvy1000, yvy1010, bga, bgb)
new_ltEs20(yvy154, yvy157, app(ty_Ratio, ebc)) → new_ltEs9(yvy154, yvy157, ebc)
new_esEs36(yvy1000, yvy1010, ty_Double) → new_esEs13(yvy1000, yvy1010)
new_esEs28(yvy1001, yvy1011, ty_Float) → new_esEs14(yvy1001, yvy1011)
new_lt6(yvy1000, yvy1010, ty_@0) → new_lt19(yvy1000, yvy1010)
new_compare10(yvy199, yvy200, True, ed, ee) → LT
new_esEs9(yvy4000, yvy3000, ty_Int) → new_esEs25(yvy4000, yvy3000)
new_esEs24(Right(yvy40000), Right(yvy30000), he, ty_Double) → new_esEs13(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, app(app(ty_@2, cgh), cha)) → new_esEs17(yvy40002, yvy30002, cgh, cha)
new_ltEs24(yvy100, yvy101, app(ty_Ratio, cdf)) → new_ltEs9(yvy100, yvy101, cdf)
new_esEs24(Right(yvy40000), Right(yvy30000), he, ty_@0) → new_esEs19(yvy40000, yvy30000)
new_ltEs19(yvy1002, yvy1012, ty_Float) → new_ltEs11(yvy1002, yvy1012)
new_esEs11(yvy4000, yvy3000, app(ty_[], egh)) → new_esEs16(yvy4000, yvy3000, egh)
new_lt23(yvy165, yvy167, app(app(app(ty_@3, fcb), fcc), fcd)) → new_lt4(yvy165, yvy167, fcb, fcc, fcd)
new_esEs7(yvy4000, yvy3000, ty_Double) → new_esEs13(yvy4000, yvy3000)
new_esEs9(yvy4000, yvy3000, ty_Char) → new_esEs15(yvy4000, yvy3000)
new_ltEs23(yvy166, yvy168, ty_Ordering) → new_ltEs6(yvy166, yvy168)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Bool, daa) → new_ltEs16(yvy1000, yvy1010)
new_esEs39(yvy165, yvy167, app(ty_Ratio, fca)) → new_esEs21(yvy165, yvy167, fca)
new_esEs10(yvy4000, yvy3000, ty_@0) → new_esEs19(yvy4000, yvy3000)
new_esEs21(:%(yvy40000, yvy40001), :%(yvy30000, yvy30001), gh) → new_asAs(new_esEs37(yvy40000, yvy30000, gh), new_esEs38(yvy40001, yvy30001, gh))
new_lt5(yvy1001, yvy1011, app(ty_Ratio, bgg)) → new_lt10(yvy1001, yvy1011, bgg)
new_compare13(:%(yvy4000, yvy4001), :%(yvy3000, yvy3001), ty_Integer) → new_compare8(new_sr(yvy4000, yvy3001), new_sr(yvy3000, yvy4001))
new_ltEs22(yvy114, yvy115, app(ty_Ratio, fae)) → new_ltEs9(yvy114, yvy115, fae)
new_ltEs23(yvy166, yvy168, ty_Int) → new_ltEs15(yvy166, yvy168)
new_primMulNat0(Zero, Zero) → Zero
new_ltEs24(yvy100, yvy101, ty_Ordering) → new_ltEs6(yvy100, yvy101)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbd, ty_Float) → new_ltEs11(yvy1000, yvy1010)
new_esEs39(yvy165, yvy167, app(ty_Maybe, fcg)) → new_esEs23(yvy165, yvy167, fcg)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Bool, hf) → new_esEs20(yvy40000, yvy30000)
new_compare15(LT, LT) → EQ
new_esEs6(yvy4002, yvy3002, app(app(ty_@2, bbb), bbc)) → new_esEs17(yvy4002, yvy3002, bbb, bbc)
new_esEs4(yvy4000, yvy3000, ty_Integer) → new_esEs18(yvy4000, yvy3000)
new_esEs26(yvy40000, yvy30000, app(ty_[], bcc)) → new_esEs16(yvy40000, yvy30000, bcc)
new_esEs36(yvy1000, yvy1010, ty_Char) → new_esEs15(yvy1000, yvy1010)
new_esEs28(yvy1001, yvy1011, app(app(ty_Either, bhf), bhg)) → new_esEs24(yvy1001, yvy1011, bhf, bhg)
new_esEs34(yvy152, yvy155, ty_@0) → new_esEs19(yvy152, yvy155)
new_sr(Integer(yvy30000), Integer(yvy40010)) → Integer(new_primMulInt(yvy30000, yvy40010))
new_esEs7(yvy4000, yvy3000, ty_Float) → new_esEs14(yvy4000, yvy3000)
new_compare12(True, False) → GT
new_lt7(yvy152, yvy155) → new_esEs12(new_compare15(yvy152, yvy155), LT)
new_lt22(yvy1000, yvy1010, app(ty_Maybe, edg)) → new_lt14(yvy1000, yvy1010, edg)
new_ltEs24(yvy100, yvy101, app(ty_Maybe, ef)) → new_ltEs5(yvy100, yvy101, ef)
new_esEs35(yvy153, yvy156, app(app(ty_Either, eah), eba)) → new_esEs24(yvy153, yvy156, eah, eba)
new_esEs35(yvy153, yvy156, ty_@0) → new_esEs19(yvy153, yvy156)
new_ltEs15(yvy100, yvy101) → new_fsEs(new_compare16(yvy100, yvy101))
new_esEs6(yvy4002, yvy3002, app(ty_[], bba)) → new_esEs16(yvy4002, yvy3002, bba)
new_esEs26(yvy40000, yvy30000, ty_@0) → new_esEs19(yvy40000, yvy30000)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_@0, hf) → new_esEs19(yvy40000, yvy30000)
new_ltEs16(False, True) → True
new_esEs26(yvy40000, yvy30000, app(app(app(ty_@3, bcg), bch), bda)) → new_esEs22(yvy40000, yvy30000, bcg, bch, bda)
new_esEs10(yvy4000, yvy3000, app(ty_Maybe, ege)) → new_esEs23(yvy4000, yvy3000, ege)
new_ltEs24(yvy100, yvy101, ty_Bool) → new_ltEs16(yvy100, yvy101)
new_compare30(yvy400, yvy300, app(app(ty_@2, be), bf)) → new_compare7(yvy400, yvy300, be, bf)
new_esEs17(@2(yvy40000, yvy40001), @2(yvy30000, yvy30001), gf, gg) → new_asAs(new_esEs29(yvy40000, yvy30000, gf), new_esEs30(yvy40001, yvy30001, gg))
new_esEs11(yvy4000, yvy3000, ty_Char) → new_esEs15(yvy4000, yvy3000)
new_lt20(yvy152, yvy155, app(app(app(ty_@3, bb), bc), bd)) → new_lt4(yvy152, yvy155, bb, bc, bd)
new_esEs27(yvy1000, yvy1010, ty_Bool) → new_esEs20(yvy1000, yvy1010)
new_ltEs23(yvy166, yvy168, app(ty_Ratio, fdc)) → new_ltEs9(yvy166, yvy168, fdc)
new_esEs34(yvy152, yvy155, ty_Double) → new_esEs13(yvy152, yvy155)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Double) → new_esEs13(yvy40000, yvy30000)
new_esEs10(yvy4000, yvy3000, ty_Int) → new_esEs25(yvy4000, yvy3000)
new_esEs26(yvy40000, yvy30000, ty_Char) → new_esEs15(yvy40000, yvy30000)
new_compare30(yvy400, yvy300, ty_Int) → new_compare16(yvy400, yvy300)
new_fsEs(yvy306) → new_not(new_esEs12(yvy306, GT))
new_ltEs16(True, False) → False
new_ltEs14(Right(yvy1000), Right(yvy1010), dbd, ty_Char) → new_ltEs7(yvy1000, yvy1010)
new_esEs7(yvy4000, yvy3000, ty_Int) → new_esEs25(yvy4000, yvy3000)
new_ltEs19(yvy1002, yvy1012, ty_Bool) → new_ltEs16(yvy1002, yvy1012)
new_esEs34(yvy152, yvy155, ty_Ordering) → new_esEs12(yvy152, yvy155)
new_esEs12(GT, LT) → False
new_esEs12(LT, GT) → False
new_esEs27(yvy1000, yvy1010, ty_Char) → new_esEs15(yvy1000, yvy1010)
new_lt5(yvy1001, yvy1011, ty_Integer) → new_lt15(yvy1001, yvy1011)
new_ltEs22(yvy114, yvy115, ty_Ordering) → new_ltEs6(yvy114, yvy115)
new_compare18(Float(yvy4000, yvy4001), Float(yvy3000, yvy3001)) → new_compare16(new_sr0(yvy4000, yvy3000), new_sr0(yvy4001, yvy3001))
new_ltEs18(yvy107, yvy108, app(ty_Ratio, bdh)) → new_ltEs9(yvy107, yvy108, bdh)
new_ltEs23(yvy166, yvy168, ty_Float) → new_ltEs11(yvy166, yvy168)
new_ltEs18(yvy107, yvy108, app(ty_[], bdg)) → new_ltEs8(yvy107, yvy108, bdg)
new_ltEs20(yvy154, yvy157, app(app(ty_@2, ebg), ebh)) → new_ltEs12(yvy154, yvy157, ebg, ebh)
new_esEs31(yvy40000, yvy30000, app(ty_Maybe, cfb)) → new_esEs23(yvy40000, yvy30000, cfb)
new_lt6(yvy1000, yvy1010, app(ty_Ratio, bfe)) → new_lt10(yvy1000, yvy1010, bfe)
new_esEs37(yvy40000, yvy30000, ty_Integer) → new_esEs18(yvy40000, yvy30000)
new_ltEs14(Left(yvy1000), Left(yvy1010), app(app(ty_@2, dag), dah), daa) → new_ltEs12(yvy1000, yvy1010, dag, dah)
new_esEs35(yvy153, yvy156, app(app(ty_@2, eae), eaf)) → new_esEs17(yvy153, yvy156, eae, eaf)
new_esEs5(yvy4001, yvy3001, app(app(app(ty_@3, bac), bad), bae)) → new_esEs22(yvy4001, yvy3001, bac, bad, bae)
new_lt22(yvy1000, yvy1010, ty_Char) → new_lt8(yvy1000, yvy1010)
new_compare110(yvy233, yvy234, yvy235, yvy236, True, yvy238, ecd, ece) → new_compare111(yvy233, yvy234, yvy235, yvy236, True, ecd, ece)
new_ltEs24(yvy100, yvy101, app(app(ty_@2, ecf), ecg)) → new_ltEs12(yvy100, yvy101, ecf, ecg)
new_ltEs13(yvy100, yvy101) → new_fsEs(new_compare29(yvy100, yvy101))
new_esEs5(yvy4001, yvy3001, app(app(ty_Either, bag), bah)) → new_esEs24(yvy4001, yvy3001, bag, bah)
new_esEs24(Right(yvy40000), Right(yvy30000), he, ty_Bool) → new_esEs20(yvy40000, yvy30000)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Float) → new_ltEs11(yvy1000, yvy1010)
new_esEs8(yvy4001, yvy3001, ty_Double) → new_esEs13(yvy4001, yvy3001)
new_esEs31(yvy40000, yvy30000, app(ty_Ratio, cef)) → new_esEs21(yvy40000, yvy30000, cef)
new_esEs29(yvy40000, yvy30000, app(ty_Maybe, cca)) → new_esEs23(yvy40000, yvy30000, cca)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Int) → new_ltEs15(yvy1000, yvy1010)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Double) → new_ltEs13(yvy1000, yvy1010)
new_esEs30(yvy40001, yvy30001, ty_Double) → new_esEs13(yvy40001, yvy30001)
new_ltEs21(yvy1001, yvy1011, app(app(ty_@2, eeg), eeh)) → new_ltEs12(yvy1001, yvy1011, eeg, eeh)
new_esEs10(yvy4000, yvy3000, ty_Bool) → new_esEs20(yvy4000, yvy3000)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Char, daa) → new_ltEs7(yvy1000, yvy1010)
new_ltEs16(True, True) → True
new_lt21(yvy153, yvy156, app(app(ty_@2, eae), eaf)) → new_lt12(yvy153, yvy156, eae, eaf)
new_lt6(yvy1000, yvy1010, ty_Bool) → new_lt18(yvy1000, yvy1010)
new_pePe(False, yvy305) → yvy305
new_compare15(GT, EQ) → GT
new_esEs7(yvy4000, yvy3000, ty_Char) → new_esEs15(yvy4000, yvy3000)
new_esEs31(yvy40000, yvy30000, app(ty_[], cec)) → new_esEs16(yvy40000, yvy30000, cec)
new_esEs39(yvy165, yvy167, ty_@0) → new_esEs19(yvy165, yvy167)
new_esEs23(Just(yvy40000), Just(yvy30000), app(ty_Maybe, ddf)) → new_esEs23(yvy40000, yvy30000, ddf)
new_lt21(yvy153, yvy156, ty_Char) → new_lt8(yvy153, yvy156)
new_esEs26(yvy40000, yvy30000, ty_Bool) → new_esEs20(yvy40000, yvy30000)
new_esEs9(yvy4000, yvy3000, app(app(ty_@2, ffb), ffc)) → new_esEs17(yvy4000, yvy3000, ffb, ffc)
new_compare14(yvy218, yvy219, yvy220, yvy221, yvy222, yvy223, False, cdh, cea, ceb) → GT
new_lt9(yvy152, yvy155, dhd) → new_esEs12(new_compare0(yvy152, yvy155, dhd), LT)
new_esEs28(yvy1001, yvy1011, ty_Integer) → new_esEs18(yvy1001, yvy1011)
new_esEs5(yvy4001, yvy3001, ty_Ordering) → new_esEs12(yvy4001, yvy3001)
new_esEs5(yvy4001, yvy3001, ty_Int) → new_esEs25(yvy4001, yvy3001)
new_esEs4(yvy4000, yvy3000, ty_Float) → new_esEs14(yvy4000, yvy3000)
new_compare15(GT, LT) → GT
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Char, hf) → new_esEs15(yvy40000, yvy30000)
new_esEs29(yvy40000, yvy30000, ty_Int) → new_esEs25(yvy40000, yvy30000)
new_compare30(yvy400, yvy300, app(app(ty_Either, efd), efe)) → new_compare27(yvy400, yvy300, efd, efe)
new_lt22(yvy1000, yvy1010, ty_Double) → new_lt13(yvy1000, yvy1010)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Ordering) → new_esEs12(yvy40000, yvy30000)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Char) → new_esEs15(yvy40000, yvy30000)
new_esEs29(yvy40000, yvy30000, app(app(ty_@2, cbc), cbd)) → new_esEs17(yvy40000, yvy30000, cbc, cbd)
new_esEs24(Right(yvy40000), Right(yvy30000), he, app(app(ty_@2, dff), dfg)) → new_esEs17(yvy40000, yvy30000, dff, dfg)
new_ltEs23(yvy166, yvy168, app(app(ty_Either, feb), fec)) → new_ltEs14(yvy166, yvy168, feb, fec)
new_esEs31(yvy40000, yvy30000, ty_Integer) → new_esEs18(yvy40000, yvy30000)
new_compare12(True, True) → EQ
new_esEs36(yvy1000, yvy1010, app(ty_[], ech)) → new_esEs16(yvy1000, yvy1010, ech)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Ordering, hf) → new_esEs12(yvy40000, yvy30000)
new_ltEs6(GT, EQ) → False
new_ltEs18(yvy107, yvy108, app(app(ty_Either, beg), beh)) → new_ltEs14(yvy107, yvy108, beg, beh)
new_esEs32(yvy40001, yvy30001, app(ty_Maybe, cgd)) → new_esEs23(yvy40001, yvy30001, cgd)
new_esEs35(yvy153, yvy156, ty_Integer) → new_esEs18(yvy153, yvy156)
new_esEs33(yvy40002, yvy30002, ty_Integer) → new_esEs18(yvy40002, yvy30002)
new_esEs31(yvy40000, yvy30000, ty_Double) → new_esEs13(yvy40000, yvy30000)
new_esEs10(yvy4000, yvy3000, ty_Ordering) → new_esEs12(yvy4000, yvy3000)
new_primCompAux1(yvy400, yvy300, yvy51, h) → new_primCompAux0(yvy51, new_compare30(yvy400, yvy300, h))
new_esEs33(yvy40002, yvy30002, ty_Float) → new_esEs14(yvy40002, yvy30002)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbd, app(app(app(ty_@3, dbg), dbh), dca)) → new_ltEs10(yvy1000, yvy1010, dbg, dbh, dca)
new_ltEs23(yvy166, yvy168, app(ty_[], fdb)) → new_ltEs8(yvy166, yvy168, fdb)
new_lt23(yvy165, yvy167, app(app(ty_@2, fce), fcf)) → new_lt12(yvy165, yvy167, fce, fcf)
new_esEs34(yvy152, yvy155, ty_Integer) → new_esEs18(yvy152, yvy155)
new_esEs23(Just(yvy40000), Just(yvy30000), app(app(ty_Either, ddg), ddh)) → new_esEs24(yvy40000, yvy30000, ddg, ddh)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Ordering, daa) → new_ltEs6(yvy1000, yvy1010)
new_lt22(yvy1000, yvy1010, ty_Bool) → new_lt18(yvy1000, yvy1010)
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_esEs39(yvy165, yvy167, ty_Float) → new_esEs14(yvy165, yvy167)
new_ltEs22(yvy114, yvy115, ty_Bool) → new_ltEs16(yvy114, yvy115)
new_ltEs4(yvy100, yvy101) → new_fsEs(new_compare8(yvy100, yvy101))
new_esEs33(yvy40002, yvy30002, app(ty_[], cgg)) → new_esEs16(yvy40002, yvy30002, cgg)
new_ltEs8(yvy100, yvy101, fed) → new_fsEs(new_compare0(yvy100, yvy101, fed))
new_compare30(yvy400, yvy300, ty_Char) → new_compare11(yvy400, yvy300)
new_esEs36(yvy1000, yvy1010, ty_Integer) → new_esEs18(yvy1000, yvy1010)
new_esEs39(yvy165, yvy167, ty_Bool) → new_esEs20(yvy165, yvy167)
new_esEs36(yvy1000, yvy1010, ty_Bool) → new_esEs20(yvy1000, yvy1010)
new_esEs32(yvy40001, yvy30001, app(ty_Ratio, cfh)) → new_esEs21(yvy40001, yvy30001, cfh)
new_compare12(False, True) → LT
new_esEs5(yvy4001, yvy3001, ty_Char) → new_esEs15(yvy4001, yvy3001)
new_esEs34(yvy152, yvy155, ty_Char) → new_esEs15(yvy152, yvy155)
new_esEs31(yvy40000, yvy30000, app(app(ty_@2, ced), cee)) → new_esEs17(yvy40000, yvy30000, ced, cee)
new_ltEs18(yvy107, yvy108, ty_Integer) → new_ltEs4(yvy107, yvy108)
new_lt21(yvy153, yvy156, ty_@0) → new_lt19(yvy153, yvy156)
new_esEs30(yvy40001, yvy30001, ty_@0) → new_esEs19(yvy40001, yvy30001)
new_ltEs18(yvy107, yvy108, app(ty_Maybe, bef)) → new_ltEs5(yvy107, yvy108, bef)
new_esEs12(LT, LT) → True
new_ltEs24(yvy100, yvy101, ty_Char) → new_ltEs7(yvy100, yvy101)
new_esEs31(yvy40000, yvy30000, app(app(ty_Either, cfc), cfd)) → new_esEs24(yvy40000, yvy30000, cfc, cfd)
new_ltEs18(yvy107, yvy108, ty_Double) → new_ltEs13(yvy107, yvy108)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Int, daa) → new_ltEs15(yvy1000, yvy1010)
new_esEs28(yvy1001, yvy1011, app(ty_Maybe, bhe)) → new_esEs23(yvy1001, yvy1011, bhe)
new_lt5(yvy1001, yvy1011, ty_@0) → new_lt19(yvy1001, yvy1011)
new_compare15(EQ, LT) → GT
new_pePe(True, yvy305) → True
new_compare0([], [], fef) → EQ
new_primEqNat0(Zero, Zero) → True
new_ltEs21(yvy1001, yvy1011, ty_Double) → new_ltEs13(yvy1001, yvy1011)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Float) → new_esEs14(yvy40000, yvy30000)
new_esEs6(yvy4002, yvy3002, ty_Double) → new_esEs13(yvy4002, yvy3002)
new_esEs4(yvy4000, yvy3000, app(ty_Maybe, hd)) → new_esEs23(yvy4000, yvy3000, hd)
new_lt5(yvy1001, yvy1011, ty_Bool) → new_lt18(yvy1001, yvy1011)
new_lt23(yvy165, yvy167, ty_Integer) → new_lt15(yvy165, yvy167)
new_esEs5(yvy4001, yvy3001, ty_Float) → new_esEs14(yvy4001, yvy3001)
new_lt21(yvy153, yvy156, app(app(ty_Either, eah), eba)) → new_lt16(yvy153, yvy156, eah, eba)
new_esEs8(yvy4001, yvy3001, app(app(app(ty_@3, df), dg), dh)) → new_esEs22(yvy4001, yvy3001, df, dg, dh)
new_lt11(yvy152, yvy155) → new_esEs12(new_compare18(yvy152, yvy155), LT)
new_lt20(yvy152, yvy155, app(ty_[], dhd)) → new_lt9(yvy152, yvy155, dhd)
new_esEs13(Double(yvy40000, yvy40001), Double(yvy30000, yvy30001)) → new_esEs25(new_sr0(yvy40000, yvy30000), new_sr0(yvy40001, yvy30001))
new_esEs7(yvy4000, yvy3000, ty_Bool) → new_esEs20(yvy4000, yvy3000)
new_compare30(yvy400, yvy300, ty_@0) → new_compare9(yvy400, yvy300)
new_esEs29(yvy40000, yvy30000, ty_@0) → new_esEs19(yvy40000, yvy30000)
new_esEs6(yvy4002, yvy3002, ty_Ordering) → new_esEs12(yvy4002, yvy3002)
new_ltEs18(yvy107, yvy108, app(app(app(ty_@3, bea), beb), bec)) → new_ltEs10(yvy107, yvy108, bea, beb, bec)
new_ltEs22(yvy114, yvy115, ty_@0) → new_ltEs17(yvy114, yvy115)
new_lt5(yvy1001, yvy1011, ty_Char) → new_lt8(yvy1001, yvy1011)
new_lt5(yvy1001, yvy1011, app(app(ty_Either, bhf), bhg)) → new_lt16(yvy1001, yvy1011, bhf, bhg)
new_ltEs19(yvy1002, yvy1012, ty_Ordering) → new_ltEs6(yvy1002, yvy1012)
new_esEs15(Char(yvy40000), Char(yvy30000)) → new_primEqNat0(yvy40000, yvy30000)
new_esEs24(Left(yvy40000), Left(yvy30000), app(app(app(ty_@3, deg), deh), dfa), hf) → new_esEs22(yvy40000, yvy30000, deg, deh, dfa)
new_esEs26(yvy40000, yvy30000, ty_Int) → new_esEs25(yvy40000, yvy30000)
new_esEs32(yvy40001, yvy30001, ty_Integer) → new_esEs18(yvy40001, yvy30001)
new_ltEs23(yvy166, yvy168, ty_Double) → new_ltEs13(yvy166, yvy168)
new_lt22(yvy1000, yvy1010, app(ty_[], ech)) → new_lt9(yvy1000, yvy1010, ech)
new_ltEs23(yvy166, yvy168, ty_Integer) → new_ltEs4(yvy166, yvy168)
new_esEs9(yvy4000, yvy3000, app(ty_[], ffa)) → new_esEs16(yvy4000, yvy3000, ffa)
new_esEs33(yvy40002, yvy30002, ty_Bool) → new_esEs20(yvy40002, yvy30002)
new_esEs11(yvy4000, yvy3000, ty_Double) → new_esEs13(yvy4000, yvy3000)
new_esEs29(yvy40000, yvy30000, ty_Bool) → new_esEs20(yvy40000, yvy30000)
new_lt5(yvy1001, yvy1011, app(ty_[], bgf)) → new_lt9(yvy1001, yvy1011, bgf)
new_ltEs21(yvy1001, yvy1011, ty_Bool) → new_ltEs16(yvy1001, yvy1011)
new_ltEs6(EQ, GT) → True
new_esEs9(yvy4000, yvy3000, ty_Integer) → new_esEs18(yvy4000, yvy3000)
new_esEs11(yvy4000, yvy3000, ty_Ordering) → new_esEs12(yvy4000, yvy3000)
new_esEs23(Just(yvy40000), Nothing, hd) → False
new_esEs23(Nothing, Just(yvy30000), hd) → False
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_ltEs18(yvy107, yvy108, ty_Ordering) → new_ltEs6(yvy107, yvy108)
new_esEs23(Just(yvy40000), Just(yvy30000), app(app(app(ty_@3, ddc), ddd), dde)) → new_esEs22(yvy40000, yvy30000, ddc, ddd, dde)
new_ltEs24(yvy100, yvy101, ty_Double) → new_ltEs13(yvy100, yvy101)
new_esEs10(yvy4000, yvy3000, ty_Double) → new_esEs13(yvy4000, yvy3000)
new_esEs24(Right(yvy40000), Right(yvy30000), he, ty_Float) → new_esEs14(yvy40000, yvy30000)
new_compare110(yvy233, yvy234, yvy235, yvy236, False, yvy238, ecd, ece) → new_compare111(yvy233, yvy234, yvy235, yvy236, yvy238, ecd, ece)
new_ltEs20(yvy154, yvy157, ty_Bool) → new_ltEs16(yvy154, yvy157)
new_ltEs24(yvy100, yvy101, ty_@0) → new_ltEs17(yvy100, yvy101)
new_ltEs5(Just(yvy1000), Just(yvy1010), app(app(ty_@2, fd), ff)) → new_ltEs12(yvy1000, yvy1010, fd, ff)
new_ltEs20(yvy154, yvy157, ty_Int) → new_ltEs15(yvy154, yvy157)
new_esEs8(yvy4001, yvy3001, ty_@0) → new_esEs19(yvy4001, yvy3001)
new_lt22(yvy1000, yvy1010, app(app(ty_Either, edh), eea)) → new_lt16(yvy1000, yvy1010, edh, eea)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Float, daa) → new_ltEs11(yvy1000, yvy1010)
new_compare26(yvy107, yvy108, False, bde, bdf) → new_compare10(yvy107, yvy108, new_ltEs18(yvy107, yvy108, bde), bde, bdf)
new_lt21(yvy153, yvy156, app(ty_Ratio, eaa)) → new_lt10(yvy153, yvy156, eaa)
new_compare30(yvy400, yvy300, ty_Float) → new_compare18(yvy400, yvy300)
new_primEqInt(Neg(Succ(yvy400000)), Neg(Succ(yvy300000))) → new_primEqNat0(yvy400000, yvy300000)
new_esEs23(Nothing, Nothing, hd) → True
new_esEs10(yvy4000, yvy3000, app(app(app(ty_@3, egb), egc), egd)) → new_esEs22(yvy4000, yvy3000, egb, egc, egd)
new_esEs39(yvy165, yvy167, app(app(ty_@2, fce), fcf)) → new_esEs17(yvy165, yvy167, fce, fcf)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbd, app(app(ty_@2, dcb), dcc)) → new_ltEs12(yvy1000, yvy1010, dcb, dcc)
new_ltEs5(Just(yvy1000), Nothing, ef) → False
new_esEs28(yvy1001, yvy1011, ty_Char) → new_esEs15(yvy1001, yvy1011)
new_esEs11(yvy4000, yvy3000, app(ty_Maybe, ehg)) → new_esEs23(yvy4000, yvy3000, ehg)
new_lt14(yvy152, yvy155, dhe) → new_esEs12(new_compare31(yvy152, yvy155, dhe), LT)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbd, ty_@0) → new_ltEs17(yvy1000, yvy1010)
new_ltEs14(Right(yvy1000), Left(yvy1010), dbd, daa) → False
new_esEs12(EQ, LT) → False
new_esEs12(LT, EQ) → False
new_ltEs19(yvy1002, yvy1012, app(ty_Ratio, caa)) → new_ltEs9(yvy1002, yvy1012, caa)
new_lt22(yvy1000, yvy1010, app(app(ty_@2, ede), edf)) → new_lt12(yvy1000, yvy1010, ede, edf)
new_ltEs23(yvy166, yvy168, ty_Bool) → new_ltEs16(yvy166, yvy168)
new_compare111(yvy233, yvy234, yvy235, yvy236, True, ecd, ece) → LT
new_esEs7(yvy4000, yvy3000, app(ty_[], bg)) → new_esEs16(yvy4000, yvy3000, bg)
new_esEs5(yvy4001, yvy3001, ty_Bool) → new_esEs20(yvy4001, yvy3001)
new_lt23(yvy165, yvy167, ty_Int) → new_lt17(yvy165, yvy167)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs30(yvy40001, yvy30001, app(app(app(ty_@3, cch), cda), cdb)) → new_esEs22(yvy40001, yvy30001, cch, cda, cdb)
new_esEs11(yvy4000, yvy3000, app(app(ty_Either, ehh), faa)) → new_esEs24(yvy4000, yvy3000, ehh, faa)
new_esEs35(yvy153, yvy156, app(app(app(ty_@3, eab), eac), ead)) → new_esEs22(yvy153, yvy156, eab, eac, ead)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbd, ty_Int) → new_ltEs15(yvy1000, yvy1010)
new_esEs10(yvy4000, yvy3000, app(app(ty_Either, egf), egg)) → new_esEs24(yvy4000, yvy3000, egf, egg)
new_esEs28(yvy1001, yvy1011, ty_Double) → new_esEs13(yvy1001, yvy1011)
new_lt20(yvy152, yvy155, ty_Ordering) → new_lt7(yvy152, yvy155)
new_ltEs6(EQ, EQ) → True
new_compare31(Just(yvy4000), Nothing, feh) → GT
new_esEs11(yvy4000, yvy3000, app(app(app(ty_@3, ehd), ehe), ehf)) → new_esEs22(yvy4000, yvy3000, ehd, ehe, ehf)
new_ltEs22(yvy114, yvy115, app(app(ty_Either, fbd), fbe)) → new_ltEs14(yvy114, yvy115, fbd, fbe)
new_esEs28(yvy1001, yvy1011, app(app(app(ty_@3, bgh), bha), bhb)) → new_esEs22(yvy1001, yvy1011, bgh, bha, bhb)
new_esEs32(yvy40001, yvy30001, ty_Float) → new_esEs14(yvy40001, yvy30001)
new_esEs27(yvy1000, yvy1010, app(ty_Ratio, bfe)) → new_esEs21(yvy1000, yvy1010, bfe)
new_ltEs19(yvy1002, yvy1012, ty_Integer) → new_ltEs4(yvy1002, yvy1012)
new_primEqInt(Neg(Succ(yvy400000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(yvy300000))) → False
new_primCompAux0(yvy56, GT) → GT
new_compare30(yvy400, yvy300, app(app(app(ty_@3, gb), gc), gd)) → new_compare6(yvy400, yvy300, gb, gc, gd)
new_esEs39(yvy165, yvy167, ty_Integer) → new_esEs18(yvy165, yvy167)
new_compare26(yvy107, yvy108, True, bde, bdf) → EQ
new_esEs23(Just(yvy40000), Just(yvy30000), app(app(ty_@2, dch), dda)) → new_esEs17(yvy40000, yvy30000, dch, dda)
new_esEs24(Right(yvy40000), Right(yvy30000), he, app(app(ty_Either, dge), dgf)) → new_esEs24(yvy40000, yvy30000, dge, dgf)
new_ltEs6(GT, GT) → True
new_ltEs21(yvy1001, yvy1011, app(app(ty_Either, efb), efc)) → new_ltEs14(yvy1001, yvy1011, efb, efc)
new_esEs38(yvy40001, yvy30001, ty_Integer) → new_esEs18(yvy40001, yvy30001)
new_esEs32(yvy40001, yvy30001, app(ty_[], cfe)) → new_esEs16(yvy40001, yvy30001, cfe)
new_esEs34(yvy152, yvy155, ty_Int) → new_esEs25(yvy152, yvy155)
new_compare31(Nothing, Nothing, feh) → EQ
new_esEs29(yvy40000, yvy30000, app(ty_[], cbb)) → new_esEs16(yvy40000, yvy30000, cbb)
new_esEs26(yvy40000, yvy30000, app(ty_Ratio, bcf)) → new_esEs21(yvy40000, yvy30000, bcf)
new_esEs7(yvy4000, yvy3000, app(ty_Maybe, cf)) → new_esEs23(yvy4000, yvy3000, cf)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_@0) → new_ltEs17(yvy1000, yvy1010)
new_lt21(yvy153, yvy156, app(ty_[], dhh)) → new_lt9(yvy153, yvy156, dhh)
new_ltEs20(yvy154, yvy157, app(ty_[], ebb)) → new_ltEs8(yvy154, yvy157, ebb)
new_esEs36(yvy1000, yvy1010, ty_Int) → new_esEs25(yvy1000, yvy1010)
new_esEs19(@0, @0) → True
new_compare6(@3(yvy4000, yvy4001, yvy4002), @3(yvy3000, yvy3001, yvy3002), gb, gc, gd) → new_compare25(yvy4000, yvy4001, yvy4002, yvy3000, yvy3001, yvy3002, new_asAs(new_esEs4(yvy4000, yvy3000, gb), new_asAs(new_esEs5(yvy4001, yvy3001, gc), new_esEs6(yvy4002, yvy3002, gd))), gb, gc, gd)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_esEs7(yvy4000, yvy3000, ty_Integer) → new_esEs18(yvy4000, yvy3000)
new_esEs4(yvy4000, yvy3000, ty_Bool) → new_esEs20(yvy4000, yvy3000)
new_esEs39(yvy165, yvy167, ty_Ordering) → new_esEs12(yvy165, yvy167)
new_lt20(yvy152, yvy155, ty_Char) → new_lt8(yvy152, yvy155)
new_esEs31(yvy40000, yvy30000, ty_Bool) → new_esEs20(yvy40000, yvy30000)
new_lt4(yvy152, yvy155, bb, bc, bd) → new_esEs12(new_compare6(yvy152, yvy155, bb, bc, bd), LT)
new_esEs6(yvy4002, yvy3002, ty_Int) → new_esEs25(yvy4002, yvy3002)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Double, daa) → new_ltEs13(yvy1000, yvy1010)
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_lt6(yvy1000, yvy1010, app(ty_Maybe, bgc)) → new_lt14(yvy1000, yvy1010, bgc)
new_ltEs14(Left(yvy1000), Left(yvy1010), app(ty_Maybe, dba), daa) → new_ltEs5(yvy1000, yvy1010, dba)
new_esEs4(yvy4000, yvy3000, app(ty_Ratio, gh)) → new_esEs21(yvy4000, yvy3000, gh)
new_lt5(yvy1001, yvy1011, app(ty_Maybe, bhe)) → new_lt14(yvy1001, yvy1011, bhe)
new_primEqInt(Pos(Succ(yvy400000)), Pos(Succ(yvy300000))) → new_primEqNat0(yvy400000, yvy300000)
new_compare10(yvy199, yvy200, False, ed, ee) → GT
new_esEs34(yvy152, yvy155, app(ty_Maybe, dhe)) → new_esEs23(yvy152, yvy155, dhe)
new_esEs5(yvy4001, yvy3001, app(ty_[], hg)) → new_esEs16(yvy4001, yvy3001, hg)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbd, ty_Double) → new_ltEs13(yvy1000, yvy1010)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbd, ty_Integer) → new_ltEs4(yvy1000, yvy1010)
new_ltEs21(yvy1001, yvy1011, ty_Float) → new_ltEs11(yvy1001, yvy1011)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbd, app(ty_Maybe, dcd)) → new_ltEs5(yvy1000, yvy1010, dcd)
new_compare13(:%(yvy4000, yvy4001), :%(yvy3000, yvy3001), ty_Int) → new_compare16(new_sr0(yvy4000, yvy3001), new_sr0(yvy3000, yvy4001))
new_esEs26(yvy40000, yvy30000, app(ty_Maybe, bdb)) → new_esEs23(yvy40000, yvy30000, bdb)
new_ltEs24(yvy100, yvy101, ty_Float) → new_ltEs11(yvy100, yvy101)
new_esEs34(yvy152, yvy155, app(app(ty_@2, dea), deb)) → new_esEs17(yvy152, yvy155, dea, deb)
new_esEs8(yvy4001, yvy3001, ty_Integer) → new_esEs18(yvy4001, yvy3001)
new_ltEs22(yvy114, yvy115, app(app(app(ty_@3, faf), fag), fah)) → new_ltEs10(yvy114, yvy115, faf, fag, fah)
new_primEqNat0(Succ(yvy400000), Succ(yvy300000)) → new_primEqNat0(yvy400000, yvy300000)
new_esEs6(yvy4002, yvy3002, ty_Bool) → new_esEs20(yvy4002, yvy3002)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Ordering) → new_ltEs6(yvy1000, yvy1010)
new_ltEs24(yvy100, yvy101, ty_Int) → new_ltEs15(yvy100, yvy101)
new_esEs26(yvy40000, yvy30000, ty_Ordering) → new_esEs12(yvy40000, yvy30000)
new_esEs24(Right(yvy40000), Right(yvy30000), he, app(ty_Ratio, dfh)) → new_esEs21(yvy40000, yvy30000, dfh)
new_esEs11(yvy4000, yvy3000, app(ty_Ratio, ehc)) → new_esEs21(yvy4000, yvy3000, ehc)
new_esEs30(yvy40001, yvy30001, ty_Integer) → new_esEs18(yvy40001, yvy30001)
new_esEs39(yvy165, yvy167, ty_Char) → new_esEs15(yvy165, yvy167)
new_ltEs14(Left(yvy1000), Left(yvy1010), app(ty_Ratio, dac), daa) → new_ltEs9(yvy1000, yvy1010, dac)
new_esEs26(yvy40000, yvy30000, app(app(ty_@2, bcd), bce)) → new_esEs17(yvy40000, yvy30000, bcd, bce)
new_lt5(yvy1001, yvy1011, ty_Float) → new_lt11(yvy1001, yvy1011)
new_esEs32(yvy40001, yvy30001, ty_@0) → new_esEs19(yvy40001, yvy30001)
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_esEs33(yvy40002, yvy30002, app(ty_Maybe, chf)) → new_esEs23(yvy40002, yvy30002, chf)
new_lt6(yvy1000, yvy1010, ty_Int) → new_lt17(yvy1000, yvy1010)
new_esEs24(Right(yvy40000), Right(yvy30000), he, app(app(app(ty_@3, dga), dgb), dgc)) → new_esEs22(yvy40000, yvy30000, dga, dgb, dgc)
new_lt23(yvy165, yvy167, app(app(ty_Either, fch), fda)) → new_lt16(yvy165, yvy167, fch, fda)
new_esEs12(EQ, EQ) → True
new_lt23(yvy165, yvy167, ty_Char) → new_lt8(yvy165, yvy167)
new_ltEs18(yvy107, yvy108, app(app(ty_@2, bed), bee)) → new_ltEs12(yvy107, yvy108, bed, bee)
new_lt21(yvy153, yvy156, ty_Double) → new_lt13(yvy153, yvy156)
new_esEs35(yvy153, yvy156, ty_Ordering) → new_esEs12(yvy153, yvy156)
new_lt5(yvy1001, yvy1011, ty_Int) → new_lt17(yvy1001, yvy1011)
new_esEs10(yvy4000, yvy3000, ty_Char) → new_esEs15(yvy4000, yvy3000)
new_primEqInt(Pos(Succ(yvy400000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(yvy300000))) → False
new_ltEs5(Nothing, Just(yvy1010), ef) → True
new_lt20(yvy152, yvy155, ty_Int) → new_lt17(yvy152, yvy155)
new_esEs35(yvy153, yvy156, app(ty_Maybe, eag)) → new_esEs23(yvy153, yvy156, eag)
new_esEs27(yvy1000, yvy1010, ty_@0) → new_esEs19(yvy1000, yvy1010)
new_ltEs18(yvy107, yvy108, ty_Float) → new_ltEs11(yvy107, yvy108)
new_compare25(yvy152, yvy153, yvy154, yvy155, yvy156, yvy157, True, dha, dhb, dhc) → EQ
new_esEs37(yvy40000, yvy30000, ty_Int) → new_esEs25(yvy40000, yvy30000)
new_primCmpNat0(Zero, Zero) → EQ
new_esEs27(yvy1000, yvy1010, app(app(ty_Either, bgd), bge)) → new_esEs24(yvy1000, yvy1010, bgd, bge)
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_compare27(Left(yvy4000), Right(yvy3000), efd, efe) → LT
new_lt22(yvy1000, yvy1010, ty_@0) → new_lt19(yvy1000, yvy1010)
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_compare9(@0, @0) → EQ
new_esEs28(yvy1001, yvy1011, ty_Int) → new_esEs25(yvy1001, yvy1011)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Float, hf) → new_esEs14(yvy40000, yvy30000)
new_esEs6(yvy4002, yvy3002, ty_Float) → new_esEs14(yvy4002, yvy3002)
new_ltEs9(yvy100, yvy101, cdf) → new_fsEs(new_compare13(yvy100, yvy101, cdf))
new_compare17(yvy218, yvy219, yvy220, yvy221, yvy222, yvy223, True, yvy225, cdh, cea, ceb) → new_compare14(yvy218, yvy219, yvy220, yvy221, yvy222, yvy223, True, cdh, cea, ceb)
new_esEs32(yvy40001, yvy30001, ty_Char) → new_esEs15(yvy40001, yvy30001)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_ltEs14(Left(yvy1000), Left(yvy1010), app(ty_[], dab), daa) → new_ltEs8(yvy1000, yvy1010, dab)
new_ltEs19(yvy1002, yvy1012, app(app(ty_@2, cae), caf)) → new_ltEs12(yvy1002, yvy1012, cae, caf)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Double, hf) → new_esEs13(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, app(app(ty_Either, chg), chh)) → new_esEs24(yvy40002, yvy30002, chg, chh)
new_esEs4(yvy4000, yvy3000, ty_Int) → new_esEs25(yvy4000, yvy3000)
new_compare28(yvy114, yvy115, True, fab, fac) → EQ
new_primEqInt(Pos(Succ(yvy400000)), Neg(yvy30000)) → False
new_primEqInt(Neg(Succ(yvy400000)), Pos(yvy30000)) → False
new_esEs24(Right(yvy40000), Right(yvy30000), he, ty_Int) → new_esEs25(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, ty_Ordering) → new_esEs12(yvy40002, yvy30002)
new_esEs29(yvy40000, yvy30000, app(app(app(ty_@3, cbf), cbg), cbh)) → new_esEs22(yvy40000, yvy30000, cbf, cbg, cbh)
new_esEs26(yvy40000, yvy30000, ty_Double) → new_esEs13(yvy40000, yvy30000)
new_ltEs20(yvy154, yvy157, ty_Integer) → new_ltEs4(yvy154, yvy157)
new_compare210(yvy100, yvy101, True, fee) → EQ
new_lt6(yvy1000, yvy1010, ty_Ordering) → new_lt7(yvy1000, yvy1010)
new_esEs29(yvy40000, yvy30000, app(ty_Ratio, cbe)) → new_esEs21(yvy40000, yvy30000, cbe)
new_esEs20(False, False) → True
new_esEs24(Left(yvy40000), Left(yvy30000), app(ty_[], dec), hf) → new_esEs16(yvy40000, yvy30000, dec)
new_lt23(yvy165, yvy167, app(ty_[], fbh)) → new_lt9(yvy165, yvy167, fbh)
new_ltEs22(yvy114, yvy115, ty_Integer) → new_ltEs4(yvy114, yvy115)
new_ltEs5(Just(yvy1000), Just(yvy1010), app(app(ty_Either, fh), ga)) → new_ltEs14(yvy1000, yvy1010, fh, ga)
new_lt23(yvy165, yvy167, ty_Bool) → new_lt18(yvy165, yvy167)
new_esEs30(yvy40001, yvy30001, ty_Ordering) → new_esEs12(yvy40001, yvy30001)
new_lt6(yvy1000, yvy1010, ty_Integer) → new_lt15(yvy1000, yvy1010)
new_primEqInt(Pos(Zero), Neg(Succ(yvy300000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(yvy300000))) → False
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_compare30(yvy400, yvy300, app(ty_Maybe, feh)) → new_compare31(yvy400, yvy300, feh)
new_esEs9(yvy4000, yvy3000, ty_Ordering) → new_esEs12(yvy4000, yvy3000)
new_esEs7(yvy4000, yvy3000, ty_@0) → new_esEs19(yvy4000, yvy3000)
new_esEs11(yvy4000, yvy3000, ty_Float) → new_esEs14(yvy4000, yvy3000)
new_lt6(yvy1000, yvy1010, app(ty_[], bfd)) → new_lt9(yvy1000, yvy1010, bfd)
new_esEs36(yvy1000, yvy1010, ty_@0) → new_esEs19(yvy1000, yvy1010)
new_esEs5(yvy4001, yvy3001, ty_@0) → new_esEs19(yvy4001, yvy3001)
new_esEs36(yvy1000, yvy1010, app(app(app(ty_@3, edb), edc), edd)) → new_esEs22(yvy1000, yvy1010, edb, edc, edd)
new_esEs28(yvy1001, yvy1011, ty_Ordering) → new_esEs12(yvy1001, yvy1011)
new_esEs10(yvy4000, yvy3000, app(ty_[], eff)) → new_esEs16(yvy4000, yvy3000, eff)
new_primCompAux0(yvy56, LT) → LT
new_esEs6(yvy4002, yvy3002, app(app(ty_Either, bca), bcb)) → new_esEs24(yvy4002, yvy3002, bca, bcb)
new_esEs6(yvy4002, yvy3002, ty_Integer) → new_esEs18(yvy4002, yvy3002)
new_esEs36(yvy1000, yvy1010, app(app(ty_@2, ede), edf)) → new_esEs17(yvy1000, yvy1010, ede, edf)
new_esEs7(yvy4000, yvy3000, app(app(ty_@2, bh), ca)) → new_esEs17(yvy4000, yvy3000, bh, ca)
new_esEs9(yvy4000, yvy3000, ty_Float) → new_esEs14(yvy4000, yvy3000)
new_lt5(yvy1001, yvy1011, ty_Double) → new_lt13(yvy1001, yvy1011)
new_ltEs22(yvy114, yvy115, app(ty_Maybe, fbc)) → new_ltEs5(yvy114, yvy115, fbc)
new_not(False) → True
new_esEs27(yvy1000, yvy1010, ty_Int) → new_esEs25(yvy1000, yvy1010)
new_esEs34(yvy152, yvy155, app(ty_Ratio, cdg)) → new_esEs21(yvy152, yvy155, cdg)
new_compare30(yvy400, yvy300, ty_Bool) → new_compare12(yvy400, yvy300)
new_esEs25(yvy4000, yvy3000) → new_primEqInt(yvy4000, yvy3000)
new_esEs28(yvy1001, yvy1011, app(ty_[], bgf)) → new_esEs16(yvy1001, yvy1011, bgf)
new_esEs31(yvy40000, yvy30000, ty_Char) → new_esEs15(yvy40000, yvy30000)
new_esEs14(Float(yvy40000, yvy40001), Float(yvy30000, yvy30001)) → new_esEs25(new_sr0(yvy40000, yvy30000), new_sr0(yvy40001, yvy30001))
new_esEs11(yvy4000, yvy3000, ty_@0) → new_esEs19(yvy4000, yvy3000)
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_esEs12(GT, EQ) → False
new_esEs12(EQ, GT) → False
new_esEs36(yvy1000, yvy1010, ty_Float) → new_esEs14(yvy1000, yvy1010)
new_esEs4(yvy4000, yvy3000, ty_Ordering) → new_esEs12(yvy4000, yvy3000)
new_esEs9(yvy4000, yvy3000, app(app(ty_Either, fga), fgb)) → new_esEs24(yvy4000, yvy3000, fga, fgb)
new_lt6(yvy1000, yvy1010, app(app(app(ty_@3, bff), bfg), bfh)) → new_lt4(yvy1000, yvy1010, bff, bfg, bfh)
new_esEs4(yvy4000, yvy3000, app(app(ty_@2, gf), gg)) → new_esEs17(yvy4000, yvy3000, gf, gg)
new_esEs24(Right(yvy40000), Right(yvy30000), he, ty_Integer) → new_esEs18(yvy40000, yvy30000)
new_ltEs18(yvy107, yvy108, ty_@0) → new_ltEs17(yvy107, yvy108)
new_esEs39(yvy165, yvy167, ty_Int) → new_esEs25(yvy165, yvy167)
new_compare15(LT, EQ) → LT
new_esEs34(yvy152, yvy155, ty_Float) → new_esEs14(yvy152, yvy155)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbd, app(ty_[], dbe)) → new_ltEs8(yvy1000, yvy1010, dbe)
new_esEs36(yvy1000, yvy1010, app(ty_Ratio, eda)) → new_esEs21(yvy1000, yvy1010, eda)
new_esEs30(yvy40001, yvy30001, app(ty_Ratio, ccg)) → new_esEs21(yvy40001, yvy30001, ccg)
new_compare30(yvy400, yvy300, app(ty_Ratio, feg)) → new_compare13(yvy400, yvy300, feg)
new_esEs24(Left(yvy40000), Right(yvy30000), he, hf) → False
new_esEs24(Right(yvy40000), Left(yvy30000), he, hf) → False
new_lt20(yvy152, yvy155, app(app(ty_Either, dhf), dhg)) → new_lt16(yvy152, yvy155, dhf, dhg)
new_esEs30(yvy40001, yvy30001, app(app(ty_@2, cce), ccf)) → new_esEs17(yvy40001, yvy30001, cce, ccf)
new_esEs32(yvy40001, yvy30001, app(app(ty_Either, cge), cgf)) → new_esEs24(yvy40001, yvy30001, cge, cgf)
new_esEs34(yvy152, yvy155, app(ty_[], dhd)) → new_esEs16(yvy152, yvy155, dhd)
new_lt20(yvy152, yvy155, ty_Double) → new_lt13(yvy152, yvy155)
new_esEs35(yvy153, yvy156, ty_Double) → new_esEs13(yvy153, yvy156)
new_compare0(:(yvy4000, yvy4001), [], fef) → GT
new_lt6(yvy1000, yvy1010, ty_Char) → new_lt8(yvy1000, yvy1010)
new_esEs8(yvy4001, yvy3001, ty_Int) → new_esEs25(yvy4001, yvy3001)
new_esEs38(yvy40001, yvy30001, ty_Int) → new_esEs25(yvy40001, yvy30001)
new_ltEs24(yvy100, yvy101, ty_Integer) → new_ltEs4(yvy100, yvy101)
new_ltEs20(yvy154, yvy157, app(ty_Maybe, eca)) → new_ltEs5(yvy154, yvy157, eca)
new_ltEs20(yvy154, yvy157, ty_@0) → new_ltEs17(yvy154, yvy157)
new_ltEs24(yvy100, yvy101, app(app(ty_Either, dbd), daa)) → new_ltEs14(yvy100, yvy101, dbd, daa)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Int) → new_esEs25(yvy40000, yvy30000)
new_esEs34(yvy152, yvy155, app(app(ty_Either, dhf), dhg)) → new_esEs24(yvy152, yvy155, dhf, dhg)
new_lt13(yvy152, yvy155) → new_esEs12(new_compare29(yvy152, yvy155), LT)
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_esEs30(yvy40001, yvy30001, app(app(ty_Either, cdd), cde)) → new_esEs24(yvy40001, yvy30001, cdd, cde)
new_lt19(yvy152, yvy155) → new_esEs12(new_compare9(yvy152, yvy155), LT)
new_ltEs18(yvy107, yvy108, ty_Char) → new_ltEs7(yvy107, yvy108)
new_esEs4(yvy4000, yvy3000, app(app(ty_Either, he), hf)) → new_esEs24(yvy4000, yvy3000, he, hf)
new_esEs8(yvy4001, yvy3001, app(ty_Ratio, de)) → new_esEs21(yvy4001, yvy3001, de)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Integer) → new_esEs18(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, app(ty_Ratio, chb)) → new_esEs21(yvy40002, yvy30002, chb)
new_lt17(yvy152, yvy155) → new_esEs12(new_compare16(yvy152, yvy155), LT)
new_esEs10(yvy4000, yvy3000, app(app(ty_@2, efg), efh)) → new_esEs17(yvy4000, yvy3000, efg, efh)
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_ltEs7(yvy100, yvy101) → new_fsEs(new_compare11(yvy100, yvy101))
new_esEs31(yvy40000, yvy30000, ty_Float) → new_esEs14(yvy40000, yvy30000)
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_compare15(EQ, GT) → LT
new_esEs32(yvy40001, yvy30001, ty_Int) → new_esEs25(yvy40001, yvy30001)
new_esEs29(yvy40000, yvy30000, ty_Char) → new_esEs15(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, app(app(app(ty_@3, chc), chd), che)) → new_esEs22(yvy40002, yvy30002, chc, chd, che)
new_primEqNat0(Zero, Succ(yvy300000)) → False
new_primEqNat0(Succ(yvy400000), Zero) → False
new_compare15(LT, GT) → LT
new_lt15(yvy152, yvy155) → new_esEs12(new_compare8(yvy152, yvy155), LT)
new_ltEs5(Nothing, Nothing, ef) → True
new_ltEs23(yvy166, yvy168, app(app(app(ty_@3, fdd), fde), fdf)) → new_ltEs10(yvy166, yvy168, fdd, fde, fdf)
new_lt20(yvy152, yvy155, app(app(ty_@2, dea), deb)) → new_lt12(yvy152, yvy155, dea, deb)
new_ltEs6(LT, LT) → True
new_ltEs6(EQ, LT) → False
new_esEs6(yvy4002, yvy3002, app(ty_Ratio, bbd)) → new_esEs21(yvy4002, yvy3002, bbd)
new_ltEs5(Just(yvy1000), Just(yvy1010), app(ty_[], eg)) → new_ltEs8(yvy1000, yvy1010, eg)
new_ltEs19(yvy1002, yvy1012, ty_Char) → new_ltEs7(yvy1002, yvy1012)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_ltEs21(yvy1001, yvy1011, app(ty_Ratio, eec)) → new_ltEs9(yvy1001, yvy1011, eec)
new_esEs9(yvy4000, yvy3000, app(ty_Maybe, ffh)) → new_esEs23(yvy4000, yvy3000, ffh)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Bool) → new_ltEs16(yvy1000, yvy1010)
new_lt21(yvy153, yvy156, app(ty_Maybe, eag)) → new_lt14(yvy153, yvy156, eag)
new_compare15(GT, GT) → EQ
new_esEs11(yvy4000, yvy3000, app(app(ty_@2, eha), ehb)) → new_esEs17(yvy4000, yvy3000, eha, ehb)
new_esEs8(yvy4001, yvy3001, app(app(ty_Either, eb), ec)) → new_esEs24(yvy4001, yvy3001, eb, ec)
new_compare24(yvy165, yvy166, yvy167, yvy168, True, fbf, fbg) → EQ
new_esEs32(yvy40001, yvy30001, ty_Bool) → new_esEs20(yvy40001, yvy30001)
new_lt21(yvy153, yvy156, ty_Float) → new_lt11(yvy153, yvy156)
new_esEs16(:(yvy40000, yvy40001), [], ge) → False
new_esEs16([], :(yvy30000, yvy30001), ge) → False
new_compare31(Just(yvy4000), Just(yvy3000), feh) → new_compare210(yvy4000, yvy3000, new_esEs9(yvy4000, yvy3000, feh), feh)
new_lt21(yvy153, yvy156, ty_Ordering) → new_lt7(yvy153, yvy156)
new_lt20(yvy152, yvy155, ty_Bool) → new_lt18(yvy152, yvy155)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbd, app(ty_Ratio, dbf)) → new_ltEs9(yvy1000, yvy1010, dbf)
new_ltEs19(yvy1002, yvy1012, ty_@0) → new_ltEs17(yvy1002, yvy1012)
new_esEs7(yvy4000, yvy3000, app(app(app(ty_@3, cc), cd), ce)) → new_esEs22(yvy4000, yvy3000, cc, cd, ce)
new_esEs5(yvy4001, yvy3001, ty_Integer) → new_esEs18(yvy4001, yvy3001)
new_esEs31(yvy40000, yvy30000, ty_Int) → new_esEs25(yvy40000, yvy30000)
new_esEs27(yvy1000, yvy1010, app(app(app(ty_@3, bff), bfg), bfh)) → new_esEs22(yvy1000, yvy1010, bff, bfg, bfh)
new_ltEs19(yvy1002, yvy1012, app(ty_Maybe, cag)) → new_ltEs5(yvy1002, yvy1012, cag)
new_lt21(yvy153, yvy156, ty_Integer) → new_lt15(yvy153, yvy156)
new_esEs29(yvy40000, yvy30000, app(app(ty_Either, ccb), ccc)) → new_esEs24(yvy40000, yvy30000, ccb, ccc)
new_esEs10(yvy4000, yvy3000, app(ty_Ratio, ega)) → new_esEs21(yvy4000, yvy3000, ega)
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_ltEs12(@2(yvy1000, yvy1001), @2(yvy1010, yvy1011), ecf, ecg) → new_pePe(new_lt22(yvy1000, yvy1010, ecf), new_asAs(new_esEs36(yvy1000, yvy1010, ecf), new_ltEs21(yvy1001, yvy1011, ecg)))
new_ltEs23(yvy166, yvy168, ty_@0) → new_ltEs17(yvy166, yvy168)
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_esEs5(yvy4001, yvy3001, app(ty_Maybe, baf)) → new_esEs23(yvy4001, yvy3001, baf)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Char) → new_ltEs7(yvy1000, yvy1010)
new_compare0(:(yvy4000, yvy4001), :(yvy3000, yvy3001), fef) → new_primCompAux1(yvy4000, yvy3000, new_compare0(yvy4001, yvy3001, fef), fef)
new_esEs20(False, True) → False
new_esEs20(True, False) → False
new_compare19(yvy206, yvy207, True, dgg, dgh) → LT
new_sr0(yvy3000, yvy4001) → new_primMulInt(yvy3000, yvy4001)
new_esEs28(yvy1001, yvy1011, app(app(ty_@2, bhc), bhd)) → new_esEs17(yvy1001, yvy1011, bhc, bhd)
new_lt6(yvy1000, yvy1010, app(app(ty_Either, bgd), bge)) → new_lt16(yvy1000, yvy1010, bgd, bge)
new_esEs34(yvy152, yvy155, ty_Bool) → new_esEs20(yvy152, yvy155)
new_lt22(yvy1000, yvy1010, ty_Integer) → new_lt15(yvy1000, yvy1010)
new_esEs26(yvy40000, yvy30000, app(app(ty_Either, bdc), bdd)) → new_esEs24(yvy40000, yvy30000, bdc, bdd)
new_compare30(yvy400, yvy300, ty_Ordering) → new_compare15(yvy400, yvy300)
new_esEs30(yvy40001, yvy30001, app(ty_[], ccd)) → new_esEs16(yvy40001, yvy30001, ccd)
new_esEs24(Left(yvy40000), Left(yvy30000), app(app(ty_@2, ded), dee), hf) → new_esEs17(yvy40000, yvy30000, ded, dee)
new_lt23(yvy165, yvy167, ty_@0) → new_lt19(yvy165, yvy167)
new_esEs10(yvy4000, yvy3000, ty_Float) → new_esEs14(yvy4000, yvy3000)
new_compare29(Double(yvy4000, yvy4001), Double(yvy3000, yvy3001)) → new_compare16(new_sr0(yvy4000, yvy3000), new_sr0(yvy4001, yvy3001))
new_ltEs14(Right(yvy1000), Right(yvy1010), dbd, ty_Bool) → new_ltEs16(yvy1000, yvy1010)
new_ltEs22(yvy114, yvy115, app(ty_[], fad)) → new_ltEs8(yvy114, yvy115, fad)
new_esEs39(yvy165, yvy167, app(app(ty_Either, fch), fda)) → new_esEs24(yvy165, yvy167, fch, fda)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs32(yvy40001, yvy30001, ty_Double) → new_esEs13(yvy40001, yvy30001)
new_esEs28(yvy1001, yvy1011, ty_Bool) → new_esEs20(yvy1001, yvy1011)
new_esEs23(Just(yvy40000), Just(yvy30000), app(ty_Ratio, ddb)) → new_esEs21(yvy40000, yvy30000, ddb)
new_esEs5(yvy4001, yvy3001, app(ty_Ratio, bab)) → new_esEs21(yvy4001, yvy3001, bab)
new_ltEs14(Left(yvy1000), Right(yvy1010), dbd, daa) → True
new_compare24(yvy165, yvy166, yvy167, yvy168, False, fbf, fbg) → new_compare110(yvy165, yvy166, yvy167, yvy168, new_lt23(yvy165, yvy167, fbf), new_asAs(new_esEs39(yvy165, yvy167, fbf), new_ltEs23(yvy166, yvy168, fbg)), fbf, fbg)
new_compare30(yvy400, yvy300, app(ty_[], fef)) → new_compare0(yvy400, yvy300, fef)
new_esEs9(yvy4000, yvy3000, app(ty_Ratio, ffd)) → new_esEs21(yvy4000, yvy3000, ffd)
new_ltEs20(yvy154, yvy157, app(app(ty_Either, ecb), ecc)) → new_ltEs14(yvy154, yvy157, ecb, ecc)
new_asAs(False, yvy184) → False
new_compare27(Right(yvy4000), Left(yvy3000), efd, efe) → GT
new_esEs36(yvy1000, yvy1010, app(ty_Maybe, edg)) → new_esEs23(yvy1000, yvy1010, edg)
new_esEs9(yvy4000, yvy3000, ty_Double) → new_esEs13(yvy4000, yvy3000)
new_ltEs19(yvy1002, yvy1012, app(app(ty_Either, cah), cba)) → new_ltEs14(yvy1002, yvy1012, cah, cba)
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_lt20(yvy152, yvy155, ty_@0) → new_lt19(yvy152, yvy155)
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_esEs4(yvy4000, yvy3000, ty_@0) → new_esEs19(yvy4000, yvy3000)
new_esEs27(yvy1000, yvy1010, ty_Double) → new_esEs13(yvy1000, yvy1010)
new_esEs36(yvy1000, yvy1010, ty_Ordering) → new_esEs12(yvy1000, yvy1010)
new_compare16(yvy400, yvy300) → new_primCmpInt(yvy400, yvy300)
new_esEs35(yvy153, yvy156, ty_Bool) → new_esEs20(yvy153, yvy156)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Bool) → new_esEs20(yvy40000, yvy30000)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Integer, daa) → new_ltEs4(yvy1000, yvy1010)
new_compare14(yvy218, yvy219, yvy220, yvy221, yvy222, yvy223, True, cdh, cea, ceb) → LT
new_esEs30(yvy40001, yvy30001, app(ty_Maybe, cdc)) → new_esEs23(yvy40001, yvy30001, cdc)
new_esEs8(yvy4001, yvy3001, ty_Char) → new_esEs15(yvy4001, yvy3001)
new_esEs9(yvy4000, yvy3000, ty_Bool) → new_esEs20(yvy4000, yvy3000)
new_lt5(yvy1001, yvy1011, ty_Ordering) → new_lt7(yvy1001, yvy1011)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbd, ty_Ordering) → new_ltEs6(yvy1000, yvy1010)
new_esEs24(Left(yvy40000), Left(yvy30000), app(app(ty_Either, dfc), dfd), hf) → new_esEs24(yvy40000, yvy30000, dfc, dfd)
new_esEs8(yvy4001, yvy3001, app(ty_[], db)) → new_esEs16(yvy4001, yvy3001, db)
new_compare27(Left(yvy4000), Left(yvy3000), efd, efe) → new_compare26(yvy4000, yvy3000, new_esEs10(yvy4000, yvy3000, efd), efd, efe)
new_esEs29(yvy40000, yvy30000, ty_Double) → new_esEs13(yvy40000, yvy30000)
new_esEs27(yvy1000, yvy1010, ty_Integer) → new_esEs18(yvy1000, yvy1010)
new_esEs18(Integer(yvy40000), Integer(yvy30000)) → new_primEqInt(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, ty_Char) → new_esEs15(yvy40002, yvy30002)
new_ltEs5(Just(yvy1000), Just(yvy1010), app(ty_Maybe, fg)) → new_ltEs5(yvy1000, yvy1010, fg)
new_ltEs11(yvy100, yvy101) → new_fsEs(new_compare18(yvy100, yvy101))
new_ltEs14(Right(yvy1000), Right(yvy1010), dbd, app(app(ty_Either, dce), dcf)) → new_ltEs14(yvy1000, yvy1010, dce, dcf)
new_esEs30(yvy40001, yvy30001, ty_Float) → new_esEs14(yvy40001, yvy30001)
new_lt23(yvy165, yvy167, ty_Float) → new_lt11(yvy165, yvy167)
new_compare12(False, False) → EQ
new_esEs28(yvy1001, yvy1011, ty_@0) → new_esEs19(yvy1001, yvy1011)
new_ltEs23(yvy166, yvy168, ty_Char) → new_ltEs7(yvy166, yvy168)
new_esEs24(Right(yvy40000), Right(yvy30000), he, app(ty_Maybe, dgd)) → new_esEs23(yvy40000, yvy30000, dgd)
new_esEs29(yvy40000, yvy30000, ty_Float) → new_esEs14(yvy40000, yvy30000)
new_esEs7(yvy4000, yvy3000, ty_Ordering) → new_esEs12(yvy4000, yvy3000)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Integer, hf) → new_esEs18(yvy40000, yvy30000)
new_lt20(yvy152, yvy155, app(ty_Maybe, dhe)) → new_lt14(yvy152, yvy155, dhe)
new_esEs39(yvy165, yvy167, app(app(app(ty_@3, fcb), fcc), fcd)) → new_esEs22(yvy165, yvy167, fcb, fcc, fcd)
new_esEs31(yvy40000, yvy30000, ty_@0) → new_esEs19(yvy40000, yvy30000)
new_esEs24(Right(yvy40000), Right(yvy30000), he, app(ty_[], dfe)) → new_esEs16(yvy40000, yvy30000, dfe)
new_compare111(yvy233, yvy234, yvy235, yvy236, False, ecd, ece) → GT
new_lt21(yvy153, yvy156, ty_Bool) → new_lt18(yvy153, yvy156)
new_ltEs6(LT, GT) → True
new_esEs33(yvy40002, yvy30002, ty_Int) → new_esEs25(yvy40002, yvy30002)
new_compare30(yvy400, yvy300, ty_Integer) → new_compare8(yvy400, yvy300)
new_ltEs23(yvy166, yvy168, app(ty_Maybe, fea)) → new_ltEs5(yvy166, yvy168, fea)
new_lt23(yvy165, yvy167, app(ty_Maybe, fcg)) → new_lt14(yvy165, yvy167, fcg)
new_ltEs21(yvy1001, yvy1011, ty_Char) → new_ltEs7(yvy1001, yvy1011)
new_ltEs14(Left(yvy1000), Left(yvy1010), app(app(ty_Either, dbb), dbc), daa) → new_ltEs14(yvy1000, yvy1010, dbb, dbc)
new_ltEs23(yvy166, yvy168, app(app(ty_@2, fdg), fdh)) → new_ltEs12(yvy166, yvy168, fdg, fdh)
new_ltEs21(yvy1001, yvy1011, ty_Ordering) → new_ltEs6(yvy1001, yvy1011)
new_esEs32(yvy40001, yvy30001, app(app(ty_@2, cff), cfg)) → new_esEs17(yvy40001, yvy30001, cff, cfg)
new_esEs24(Left(yvy40000), Left(yvy30000), app(ty_Maybe, dfb), hf) → new_esEs23(yvy40000, yvy30000, dfb)
new_lt22(yvy1000, yvy1010, app(ty_Ratio, eda)) → new_lt10(yvy1000, yvy1010, eda)
new_lt12(yvy152, yvy155, dea, deb) → new_esEs12(new_compare7(yvy152, yvy155, dea, deb), LT)
new_esEs35(yvy153, yvy156, ty_Int) → new_esEs25(yvy153, yvy156)
new_lt10(yvy152, yvy155, cdg) → new_esEs12(new_compare13(yvy152, yvy155, cdg), LT)
new_esEs4(yvy4000, yvy3000, ty_Double) → new_esEs13(yvy4000, yvy3000)
new_esEs8(yvy4001, yvy3001, app(app(ty_@2, dc), dd)) → new_esEs17(yvy4001, yvy3001, dc, dd)
new_esEs5(yvy4001, yvy3001, app(app(ty_@2, hh), baa)) → new_esEs17(yvy4001, yvy3001, hh, baa)
new_esEs16([], [], ge) → True
new_lt22(yvy1000, yvy1010, ty_Float) → new_lt11(yvy1000, yvy1010)
new_esEs32(yvy40001, yvy30001, ty_Ordering) → new_esEs12(yvy40001, yvy30001)
new_ltEs19(yvy1002, yvy1012, ty_Int) → new_ltEs15(yvy1002, yvy1012)
new_ltEs21(yvy1001, yvy1011, ty_Integer) → new_ltEs4(yvy1001, yvy1011)
new_ltEs20(yvy154, yvy157, ty_Float) → new_ltEs11(yvy154, yvy157)
new_lt5(yvy1001, yvy1011, app(app(ty_@2, bhc), bhd)) → new_lt12(yvy1001, yvy1011, bhc, bhd)
new_esEs11(yvy4000, yvy3000, ty_Int) → new_esEs25(yvy4000, yvy3000)
new_esEs32(yvy40001, yvy30001, app(app(app(ty_@3, cga), cgb), cgc)) → new_esEs22(yvy40001, yvy30001, cga, cgb, cgc)
new_lt6(yvy1000, yvy1010, ty_Double) → new_lt13(yvy1000, yvy1010)
new_lt20(yvy152, yvy155, ty_Float) → new_lt11(yvy152, yvy155)
new_ltEs14(Left(yvy1000), Left(yvy1010), app(app(app(ty_@3, dad), dae), daf), daa) → new_ltEs10(yvy1000, yvy1010, dad, dae, daf)
new_esEs26(yvy40000, yvy30000, ty_Integer) → new_esEs18(yvy40000, yvy30000)
new_lt22(yvy1000, yvy1010, app(app(app(ty_@3, edb), edc), edd)) → new_lt4(yvy1000, yvy1010, edb, edc, edd)
new_esEs36(yvy1000, yvy1010, app(app(ty_Either, edh), eea)) → new_esEs24(yvy1000, yvy1010, edh, eea)
new_esEs27(yvy1000, yvy1010, ty_Ordering) → new_esEs12(yvy1000, yvy1010)
new_ltEs19(yvy1002, yvy1012, ty_Double) → new_ltEs13(yvy1002, yvy1012)
new_lt21(yvy153, yvy156, ty_Int) → new_lt17(yvy153, yvy156)
new_lt20(yvy152, yvy155, ty_Integer) → new_lt15(yvy152, yvy155)
new_esEs24(Right(yvy40000), Right(yvy30000), he, ty_Ordering) → new_esEs12(yvy40000, yvy30000)
new_lt8(yvy152, yvy155) → new_esEs12(new_compare11(yvy152, yvy155), LT)
new_ltEs24(yvy100, yvy101, app(ty_[], fed)) → new_ltEs8(yvy100, yvy101, fed)
new_esEs9(yvy4000, yvy3000, ty_@0) → new_esEs19(yvy4000, yvy3000)
new_esEs22(@3(yvy40000, yvy40001, yvy40002), @3(yvy30000, yvy30001, yvy30002), ha, hb, hc) → new_asAs(new_esEs31(yvy40000, yvy30000, ha), new_asAs(new_esEs32(yvy40001, yvy30001, hb), new_esEs33(yvy40002, yvy30002, hc)))
new_esEs8(yvy4001, yvy3001, ty_Float) → new_esEs14(yvy4001, yvy3001)
new_esEs7(yvy4000, yvy3000, app(ty_Ratio, cb)) → new_esEs21(yvy4000, yvy3000, cb)
new_ltEs20(yvy154, yvy157, ty_Double) → new_ltEs13(yvy154, yvy157)
new_ltEs18(yvy107, yvy108, ty_Bool) → new_ltEs16(yvy107, yvy108)
new_compare28(yvy114, yvy115, False, fab, fac) → new_compare19(yvy114, yvy115, new_ltEs22(yvy114, yvy115, fac), fab, fac)
new_esEs6(yvy4002, yvy3002, app(ty_Maybe, bbh)) → new_esEs23(yvy4002, yvy3002, bbh)
new_lt5(yvy1001, yvy1011, app(app(app(ty_@3, bgh), bha), bhb)) → new_lt4(yvy1001, yvy1011, bgh, bha, bhb)
new_esEs31(yvy40000, yvy30000, app(app(app(ty_@3, ceg), ceh), cfa)) → new_esEs22(yvy40000, yvy30000, ceg, ceh, cfa)
new_esEs31(yvy40000, yvy30000, ty_Ordering) → new_esEs12(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, ty_Double) → new_esEs13(yvy40002, yvy30002)
new_lt6(yvy1000, yvy1010, ty_Float) → new_lt11(yvy1000, yvy1010)
new_esEs4(yvy4000, yvy3000, ty_Char) → new_esEs15(yvy4000, yvy3000)
new_esEs7(yvy4000, yvy3000, app(app(ty_Either, cg), da)) → new_esEs24(yvy4000, yvy3000, cg, da)
new_compare112(yvy189, yvy190, False, fgc) → GT
new_esEs12(GT, GT) → True
new_ltEs21(yvy1001, yvy1011, app(app(app(ty_@3, eed), eee), eef)) → new_ltEs10(yvy1001, yvy1011, eed, eee, eef)
new_esEs5(yvy4001, yvy3001, ty_Double) → new_esEs13(yvy4001, yvy3001)
new_compare17(yvy218, yvy219, yvy220, yvy221, yvy222, yvy223, False, yvy225, cdh, cea, ceb) → new_compare14(yvy218, yvy219, yvy220, yvy221, yvy222, yvy223, yvy225, cdh, cea, ceb)
new_esEs8(yvy4001, yvy3001, app(ty_Maybe, ea)) → new_esEs23(yvy4001, yvy3001, ea)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_@0) → new_esEs19(yvy40000, yvy30000)
new_compare25(yvy152, yvy153, yvy154, yvy155, yvy156, yvy157, False, dha, dhb, dhc) → new_compare17(yvy152, yvy153, yvy154, yvy155, yvy156, yvy157, new_lt20(yvy152, yvy155, dha), new_asAs(new_esEs34(yvy152, yvy155, dha), new_pePe(new_lt21(yvy153, yvy156, dhb), new_asAs(new_esEs35(yvy153, yvy156, dhb), new_ltEs20(yvy154, yvy157, dhc)))), dha, dhb, dhc)
new_compare31(Nothing, Just(yvy3000), feh) → LT
new_esEs29(yvy40000, yvy30000, ty_Ordering) → new_esEs12(yvy40000, yvy30000)
new_esEs4(yvy4000, yvy3000, app(ty_[], ge)) → new_esEs16(yvy4000, yvy3000, ge)
new_primPlusNat1(Zero, Zero) → Zero
new_compare0([], :(yvy3000, yvy3001), fef) → LT
new_ltEs6(LT, EQ) → True
new_lt23(yvy165, yvy167, ty_Ordering) → new_lt7(yvy165, yvy167)
new_ltEs21(yvy1001, yvy1011, app(ty_Maybe, efa)) → new_ltEs5(yvy1001, yvy1011, efa)
new_ltEs6(GT, LT) → False
new_lt18(yvy152, yvy155) → new_esEs12(new_compare12(yvy152, yvy155), LT)
new_esEs24(Right(yvy40000), Right(yvy30000), he, ty_Char) → new_esEs15(yvy40000, yvy30000)
new_asAs(True, yvy184) → yvy184
new_esEs26(yvy40000, yvy30000, ty_Float) → new_esEs14(yvy40000, yvy30000)
new_esEs35(yvy153, yvy156, ty_Float) → new_esEs14(yvy153, yvy156)
new_ltEs21(yvy1001, yvy1011, app(ty_[], eeb)) → new_ltEs8(yvy1001, yvy1011, eeb)
new_compare11(Char(yvy4000), Char(yvy3000)) → new_primCmpNat0(yvy4000, yvy3000)
new_ltEs22(yvy114, yvy115, ty_Float) → new_ltEs11(yvy114, yvy115)
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_esEs28(yvy1001, yvy1011, app(ty_Ratio, bgg)) → new_esEs21(yvy1001, yvy1011, bgg)
new_esEs39(yvy165, yvy167, ty_Double) → new_esEs13(yvy165, yvy167)
new_esEs11(yvy4000, yvy3000, ty_Bool) → new_esEs20(yvy4000, yvy3000)
new_ltEs22(yvy114, yvy115, ty_Double) → new_ltEs13(yvy114, yvy115)
new_lt22(yvy1000, yvy1010, ty_Ordering) → new_lt7(yvy1000, yvy1010)
new_esEs4(yvy4000, yvy3000, app(app(app(ty_@3, ha), hb), hc)) → new_esEs22(yvy4000, yvy3000, ha, hb, hc)
new_lt20(yvy152, yvy155, app(ty_Ratio, cdg)) → new_lt10(yvy152, yvy155, cdg)
new_ltEs16(False, False) → True
new_lt23(yvy165, yvy167, ty_Double) → new_lt13(yvy165, yvy167)
new_ltEs17(yvy100, yvy101) → new_fsEs(new_compare9(yvy100, yvy101))
new_esEs29(yvy40000, yvy30000, ty_Integer) → new_esEs18(yvy40000, yvy30000)
new_esEs8(yvy4001, yvy3001, ty_Ordering) → new_esEs12(yvy4001, yvy3001)
new_esEs30(yvy40001, yvy30001, ty_Bool) → new_esEs20(yvy40001, yvy30001)
new_lt23(yvy165, yvy167, app(ty_Ratio, fca)) → new_lt10(yvy165, yvy167, fca)
new_esEs30(yvy40001, yvy30001, ty_Int) → new_esEs25(yvy40001, yvy30001)
new_esEs27(yvy1000, yvy1010, ty_Float) → new_esEs14(yvy1000, yvy1010)
new_ltEs21(yvy1001, yvy1011, ty_Int) → new_ltEs15(yvy1001, yvy1011)
new_ltEs20(yvy154, yvy157, app(app(app(ty_@3, ebd), ebe), ebf)) → new_ltEs10(yvy154, yvy157, ebd, ebe, ebf)
new_esEs23(Just(yvy40000), Just(yvy30000), app(ty_[], dcg)) → new_esEs16(yvy40000, yvy30000, dcg)
new_esEs34(yvy152, yvy155, app(app(app(ty_@3, bb), bc), bd)) → new_esEs22(yvy152, yvy155, bb, bc, bd)
new_esEs16(:(yvy40000, yvy40001), :(yvy30000, yvy30001), ge) → new_asAs(new_esEs26(yvy40000, yvy30000, ge), new_esEs16(yvy40001, yvy30001, ge))
new_esEs9(yvy4000, yvy3000, app(app(app(ty_@3, ffe), fff), ffg)) → new_esEs22(yvy4000, yvy3000, ffe, fff, ffg)
new_ltEs19(yvy1002, yvy1012, app(app(app(ty_@3, cab), cac), cad)) → new_ltEs10(yvy1002, yvy1012, cab, cac, cad)
new_ltEs20(yvy154, yvy157, ty_Ordering) → new_ltEs6(yvy154, yvy157)
new_compare19(yvy206, yvy207, False, dgg, dgh) → GT
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Integer) → new_ltEs4(yvy1000, yvy1010)
new_esEs6(yvy4002, yvy3002, ty_@0) → new_esEs19(yvy4002, yvy3002)
new_ltEs10(@3(yvy1000, yvy1001, yvy1002), @3(yvy1010, yvy1011, yvy1012), bfa, bfb, bfc) → new_pePe(new_lt6(yvy1000, yvy1010, bfa), new_asAs(new_esEs27(yvy1000, yvy1010, bfa), new_pePe(new_lt5(yvy1001, yvy1011, bfb), new_asAs(new_esEs28(yvy1001, yvy1011, bfb), new_ltEs19(yvy1002, yvy1012, bfc)))))
new_esEs33(yvy40002, yvy30002, ty_@0) → new_esEs19(yvy40002, yvy30002)
new_esEs35(yvy153, yvy156, app(ty_Ratio, eaa)) → new_esEs21(yvy153, yvy156, eaa)
new_ltEs22(yvy114, yvy115, ty_Int) → new_ltEs15(yvy114, yvy115)
new_ltEs24(yvy100, yvy101, app(app(app(ty_@3, bfa), bfb), bfc)) → new_ltEs10(yvy100, yvy101, bfa, bfb, bfc)
new_compare27(Right(yvy4000), Right(yvy3000), efd, efe) → new_compare28(yvy4000, yvy3000, new_esEs11(yvy4000, yvy3000, efe), efd, efe)
new_ltEs21(yvy1001, yvy1011, ty_@0) → new_ltEs17(yvy1001, yvy1011)
new_lt16(yvy152, yvy155, dhf, dhg) → new_esEs12(new_compare27(yvy152, yvy155, dhf, dhg), LT)
new_compare15(EQ, EQ) → EQ
new_ltEs22(yvy114, yvy115, ty_Char) → new_ltEs7(yvy114, yvy115)
new_compare30(yvy400, yvy300, ty_Double) → new_compare29(yvy400, yvy300)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCompAux0(yvy56, EQ) → yvy56
new_lt6(yvy1000, yvy1010, app(app(ty_@2, bga), bgb)) → new_lt12(yvy1000, yvy1010, bga, bgb)
new_esEs27(yvy1000, yvy1010, app(ty_Maybe, bgc)) → new_esEs23(yvy1000, yvy1010, bgc)
new_ltEs20(yvy154, yvy157, ty_Char) → new_ltEs7(yvy154, yvy157)
new_esEs10(yvy4000, yvy3000, ty_Integer) → new_esEs18(yvy4000, yvy3000)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_@0, daa) → new_ltEs17(yvy1000, yvy1010)
new_ltEs18(yvy107, yvy108, ty_Int) → new_ltEs15(yvy107, yvy108)
new_lt21(yvy153, yvy156, app(app(app(ty_@3, eab), eac), ead)) → new_lt4(yvy153, yvy156, eab, eac, ead)
new_esEs6(yvy4002, yvy3002, ty_Char) → new_esEs15(yvy4002, yvy3002)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_esEs30(yvy40001, yvy30001, ty_Char) → new_esEs15(yvy40001, yvy30001)
new_ltEs5(Just(yvy1000), Just(yvy1010), app(app(app(ty_@3, fa), fb), fc)) → new_ltEs10(yvy1000, yvy1010, fa, fb, fc)
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_esEs39(yvy165, yvy167, app(ty_[], fbh)) → new_esEs16(yvy165, yvy167, fbh)
new_esEs35(yvy153, yvy156, ty_Char) → new_esEs15(yvy153, yvy156)
new_not(True) → False
new_ltEs5(Just(yvy1000), Just(yvy1010), app(ty_Ratio, eh)) → new_ltEs9(yvy1000, yvy1010, eh)

The set Q consists of the following terms:

new_esEs36(x0, x1, ty_Char)
new_esEs35(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, ty_Float)
new_esEs7(x0, x1, ty_Int)
new_esEs32(x0, x1, app(ty_[], x2))
new_ltEs21(x0, x1, ty_Int)
new_esEs10(x0, x1, ty_Float)
new_ltEs16(True, True)
new_esEs6(x0, x1, ty_Int)
new_lt11(x0, x1)
new_ltEs20(x0, x1, ty_Int)
new_lt5(x0, x1, ty_Char)
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs23(x0, x1, app(ty_Maybe, x2))
new_esEs32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs21(x0, x1, ty_@0)
new_esEs29(x0, x1, ty_Char)
new_ltEs22(x0, x1, ty_Integer)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_compare10(x0, x1, False, x2, x3)
new_esEs32(x0, x1, ty_Int)
new_esEs11(x0, x1, ty_Int)
new_esEs24(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs4(x0, x1, ty_Float)
new_lt23(x0, x1, app(ty_[], x2))
new_esEs33(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Integer)
new_compare30(x0, x1, ty_Int)
new_pePe(True, x0)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs11(x0, x1, ty_@0)
new_esEs35(x0, x1, ty_Integer)
new_esEs11(x0, x1, ty_Char)
new_esEs6(x0, x1, ty_Float)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(x0, x1, ty_Int)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_lt22(x0, x1, ty_@0)
new_compare30(x0, x1, ty_Bool)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_@0)
new_esEs29(x0, x1, ty_Ordering)
new_lt22(x0, x1, ty_Float)
new_lt23(x0, x1, ty_Integer)
new_esEs11(x0, x1, app(ty_Ratio, x2))
new_lt7(x0, x1)
new_esEs8(x0, x1, ty_Integer)
new_esEs23(Just(x0), Just(x1), ty_Float)
new_compare30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs5(Nothing, Nothing, x0)
new_esEs6(x0, x1, ty_Integer)
new_lt5(x0, x1, ty_@0)
new_esEs23(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs11(x0, x1, ty_Bool)
new_lt6(x0, x1, app(app(ty_@2, x2), x3))
new_esEs36(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare12(False, True)
new_compare12(True, False)
new_compare26(x0, x1, True, x2, x3)
new_lt21(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(Left(x0), Left(x1), ty_@0, x2)
new_ltEs7(x0, x1)
new_ltEs18(x0, x1, app(ty_[], x2))
new_primCompAux0(x0, EQ)
new_ltEs14(Right(x0), Right(x1), x2, ty_Char)
new_esEs36(x0, x1, app(app(ty_Either, x2), x3))
new_esEs39(x0, x1, app(ty_Ratio, x2))
new_ltEs14(Right(x0), Right(x1), x2, ty_Float)
new_esEs10(x0, x1, ty_Integer)
new_esEs32(x0, x1, ty_Ordering)
new_ltEs21(x0, x1, ty_Float)
new_ltEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs24(x0, x1, ty_Integer)
new_compare19(x0, x1, False, x2, x3)
new_lt5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs34(x0, x1, ty_Float)
new_ltEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs24(Left(x0), Left(x1), ty_@0, x2)
new_esEs6(x0, x1, ty_@0)
new_lt6(x0, x1, ty_Float)
new_ltEs14(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs9(x0, x1, app(app(ty_Either, x2), x3))
new_esEs9(x0, x1, ty_Int)
new_compare30(x0, x1, ty_Integer)
new_esEs12(GT, EQ)
new_esEs12(EQ, GT)
new_esEs36(x0, x1, ty_Int)
new_ltEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, ty_Bool)
new_esEs11(x0, x1, app(app(ty_@2, x2), x3))
new_esEs10(x0, x1, app(app(ty_Either, x2), x3))
new_lt6(x0, x1, app(ty_Ratio, x2))
new_compare28(x0, x1, False, x2, x3)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt5(x0, x1, ty_Double)
new_lt5(x0, x1, app(ty_[], x2))
new_esEs24(Right(x0), Right(x1), x2, ty_Float)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare15(LT, LT)
new_esEs34(x0, x1, app(ty_Maybe, x2))
new_lt5(x0, x1, app(ty_Ratio, x2))
new_esEs10(x0, x1, ty_Char)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs39(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(Right(x0), Right(x1), x2, ty_Double)
new_esEs34(x0, x1, ty_Ordering)
new_esEs39(x0, x1, app(ty_[], x2))
new_esEs12(GT, GT)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs30(x0, x1, ty_Double)
new_esEs24(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs21(x0, x1, ty_Ordering)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_lt21(x0, x1, ty_Float)
new_esEs11(x0, x1, ty_Integer)
new_compare0(:(x0, x1), [], x2)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(Just(x0), Nothing, x1)
new_esEs23(Just(x0), Just(x1), ty_Double)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs5(Just(x0), Nothing, x1)
new_esEs11(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, ty_Char)
new_esEs38(x0, x1, ty_Integer)
new_esEs27(x0, x1, ty_Bool)
new_esEs10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs6(EQ, EQ)
new_esEs32(x0, x1, ty_@0)
new_esEs7(x0, x1, ty_Float)
new_esEs23(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs22(x0, x1, ty_Char)
new_esEs9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(x0, x1, ty_Double)
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_esEs5(x0, x1, ty_Bool)
new_esEs31(x0, x1, ty_Int)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs32(x0, x1, app(ty_Ratio, x2))
new_esEs33(x0, x1, ty_Double)
new_ltEs14(Right(x0), Right(x1), x2, ty_Int)
new_esEs8(x0, x1, ty_Float)
new_ltEs18(x0, x1, ty_@0)
new_esEs36(x0, x1, app(app(ty_@2, x2), x3))
new_esEs16(:(x0, x1), :(x2, x3), x4)
new_lt9(x0, x1, x2)
new_ltEs5(Just(x0), Just(x1), ty_@0)
new_lt5(x0, x1, ty_Int)
new_ltEs6(LT, EQ)
new_ltEs6(EQ, LT)
new_primCompAux0(x0, LT)
new_esEs38(x0, x1, ty_Int)
new_esEs23(Just(x0), Just(x1), ty_Int)
new_ltEs20(x0, x1, ty_@0)
new_esEs5(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Int)
new_lt17(x0, x1)
new_esEs36(x0, x1, ty_Bool)
new_primEqNat0(Zero, Zero)
new_compare13(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs23(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_@0)
new_compare30(x0, x1, app(ty_[], x2))
new_esEs7(x0, x1, ty_Bool)
new_esEs9(x0, x1, app(ty_[], x2))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs10(x0, x1, app(ty_Maybe, x2))
new_esEs5(x0, x1, ty_Float)
new_ltEs22(x0, x1, ty_Float)
new_compare15(GT, GT)
new_esEs31(x0, x1, ty_Double)
new_compare27(Right(x0), Right(x1), x2, x3)
new_ltEs20(x0, x1, ty_Integer)
new_lt22(x0, x1, ty_Bool)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs34(x0, x1, ty_Bool)
new_esEs31(x0, x1, ty_Integer)
new_esEs6(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, ty_Char)
new_lt20(x0, x1, ty_Double)
new_ltEs22(x0, x1, app(app(ty_Either, x2), x3))
new_compare17(x0, x1, x2, x3, x4, x5, True, x6, x7, x8, x9)
new_ltEs15(x0, x1)
new_esEs4(x0, x1, ty_Integer)
new_esEs31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs39(x0, x1, ty_Bool)
new_ltEs24(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Float)
new_primMulNat0(Zero, Zero)
new_asAs(True, x0)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Double)
new_esEs5(x0, x1, ty_Double)
new_esEs34(x0, x1, app(ty_[], x2))
new_fsEs(x0)
new_esEs6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs8(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(:%(x0, x1), :%(x2, x3), x4)
new_ltEs5(Just(x0), Just(x1), ty_Integer)
new_lt6(x0, x1, ty_Double)
new_compare28(x0, x1, True, x2, x3)
new_esEs35(x0, x1, ty_Double)
new_ltEs18(x0, x1, ty_Bool)
new_lt6(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, ty_Float)
new_ltEs5(Just(x0), Just(x1), ty_Double)
new_lt22(x0, x1, ty_Ordering)
new_esEs9(x0, x1, ty_@0)
new_esEs35(x0, x1, ty_Bool)
new_ltEs14(Left(x0), Right(x1), x2, x3)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(Right(x0), Left(x1), x2, x3)
new_ltEs14(Right(x0), Right(x1), x2, ty_Integer)
new_esEs35(x0, x1, ty_Char)
new_ltEs23(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, ty_Bool)
new_esEs31(x0, x1, ty_@0)
new_esEs24(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs19(x0, x1, ty_Double)
new_ltEs24(x0, x1, ty_Double)
new_esEs13(Double(x0, x1), Double(x2, x3))
new_esEs32(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, ty_Ordering)
new_lt23(x0, x1, app(ty_Ratio, x2))
new_esEs20(True, True)
new_lt20(x0, x1, app(ty_[], x2))
new_lt22(x0, x1, ty_Int)
new_ltEs12(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs7(x0, x1, ty_Integer)
new_esEs30(x0, x1, ty_Bool)
new_lt21(x0, x1, ty_@0)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs33(x0, x1, ty_Float)
new_esEs29(x0, x1, ty_Integer)
new_compare31(Nothing, Nothing, x0)
new_ltEs21(x0, x1, ty_Integer)
new_primPlusNat0(Zero, x0)
new_lt21(x0, x1, app(ty_Ratio, x2))
new_lt22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(x0, x1, app(ty_[], x2))
new_esEs4(x0, x1, ty_Ordering)
new_ltEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs8(x0, x1, ty_Bool)
new_esEs7(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs31(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_primPlusNat0(Succ(x0), x1)
new_ltEs14(Right(x0), Right(x1), x2, ty_Double)
new_ltEs4(x0, x1)
new_compare10(x0, x1, True, x2, x3)
new_compare24(x0, x1, x2, x3, False, x4, x5)
new_esEs34(x0, x1, ty_Integer)
new_esEs31(x0, x1, ty_Ordering)
new_ltEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs6(GT, LT)
new_ltEs6(LT, GT)
new_ltEs14(Left(x0), Left(x1), ty_Char, x2)
new_compare210(x0, x1, True, x2)
new_lt23(x0, x1, app(app(ty_@2, x2), x3))
new_compare0([], [], x0)
new_esEs11(x0, x1, ty_Double)
new_esEs16(:(x0, x1), [], x2)
new_lt19(x0, x1)
new_ltEs23(x0, x1, app(ty_Ratio, x2))
new_compare111(x0, x1, x2, x3, True, x4, x5)
new_esEs4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(x0, x1, ty_Double)
new_compare30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Double)
new_esEs39(x0, x1, ty_Char)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_compare15(EQ, EQ)
new_esEs24(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_lt6(x0, x1, ty_Int)
new_lt5(x0, x1, app(app(ty_@2, x2), x3))
new_lt21(x0, x1, ty_Ordering)
new_esEs24(Left(x0), Left(x1), ty_Bool, x2)
new_esEs28(x0, x1, ty_Ordering)
new_ltEs22(x0, x1, ty_Ordering)
new_ltEs11(x0, x1)
new_esEs16([], :(x0, x1), x2)
new_esEs24(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_lt20(x0, x1, ty_Float)
new_lt21(x0, x1, ty_Integer)
new_esEs32(x0, x1, ty_Bool)
new_esEs39(x0, x1, ty_Float)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt6(x0, x1, ty_Integer)
new_ltEs14(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs10(x0, x1, ty_Double)
new_sr0(x0, x1)
new_esEs23(Just(x0), Just(x1), ty_Integer)
new_esEs24(Left(x0), Left(x1), ty_Integer, x2)
new_esEs20(False, True)
new_esEs20(True, False)
new_lt22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, ty_Bool)
new_ltEs23(x0, x1, ty_Integer)
new_lt22(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs20(False, False)
new_compare12(False, False)
new_ltEs22(x0, x1, app(ty_Ratio, x2))
new_esEs23(Nothing, Nothing, x0)
new_esEs12(LT, EQ)
new_esEs12(EQ, LT)
new_lt21(x0, x1, ty_Int)
new_lt22(x0, x1, ty_Char)
new_esEs31(x0, x1, app(ty_Maybe, x2))
new_compare14(x0, x1, x2, x3, x4, x5, True, x6, x7, x8)
new_esEs31(x0, x1, ty_Float)
new_esEs24(Right(x0), Right(x1), x2, ty_Int)
new_primPlusNat1(Zero, Zero)
new_ltEs21(x0, x1, ty_Bool)
new_esEs34(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs20(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_Float)
new_esEs12(EQ, EQ)
new_compare25(x0, x1, x2, x3, x4, x5, False, x6, x7, x8)
new_esEs23(Just(x0), Just(x1), ty_Bool)
new_esEs27(x0, x1, ty_Char)
new_esEs4(x0, x1, app(app(ty_Either, x2), x3))
new_esEs9(x0, x1, ty_Integer)
new_esEs30(x0, x1, ty_Float)
new_ltEs20(x0, x1, ty_Float)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs28(x0, x1, ty_Double)
new_esEs30(x0, x1, ty_Char)
new_ltEs14(Right(x0), Right(x1), x2, ty_@0)
new_compare30(x0, x1, ty_@0)
new_esEs6(x0, x1, ty_Bool)
new_ltEs5(Nothing, Just(x0), x1)
new_esEs24(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs23(x0, x1, ty_Float)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_lt23(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs7(x0, x1, app(ty_Ratio, x2))
new_compare15(EQ, GT)
new_compare15(GT, EQ)
new_ltEs24(x0, x1, ty_Ordering)
new_compare30(x0, x1, ty_Char)
new_primEqNat0(Succ(x0), Zero)
new_compare15(LT, GT)
new_compare15(GT, LT)
new_esEs24(Right(x0), Right(x1), x2, ty_@0)
new_lt14(x0, x1, x2)
new_esEs36(x0, x1, ty_Double)
new_esEs39(x0, x1, ty_Ordering)
new_esEs4(x0, x1, app(ty_[], x2))
new_ltEs21(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_esEs37(x0, x1, ty_Int)
new_esEs4(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs9(x0, x1, ty_Double)
new_primMulInt(Neg(x0), Neg(x1))
new_compare14(x0, x1, x2, x3, x4, x5, False, x6, x7, x8)
new_ltEs17(x0, x1)
new_compare30(x0, x1, app(ty_Ratio, x2))
new_esEs9(x0, x1, ty_Ordering)
new_esEs8(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, ty_Char)
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_ltEs23(x0, x1, ty_Int)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_esEs8(x0, x1, ty_Int)
new_ltEs5(Just(x0), Just(x1), ty_Int)
new_esEs33(x0, x1, ty_Int)
new_ltEs23(x0, x1, ty_@0)
new_esEs24(Left(x0), Left(x1), ty_Double, x2)
new_lt5(x0, x1, app(app(ty_Either, x2), x3))
new_esEs33(x0, x1, ty_Bool)
new_esEs10(x0, x1, ty_Ordering)
new_ltEs14(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs35(x0, x1, ty_@0)
new_esEs4(x0, x1, ty_Char)
new_ltEs14(Left(x0), Left(x1), ty_Integer, x2)
new_lt23(x0, x1, ty_Int)
new_esEs6(x0, x1, app(ty_[], x2))
new_esEs24(Left(x0), Left(x1), ty_Float, x2)
new_ltEs23(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs34(x0, x1, app(ty_Ratio, x2))
new_ltEs18(x0, x1, ty_Double)
new_lt23(x0, x1, ty_Bool)
new_ltEs14(Left(x0), Left(x1), ty_Float, x2)
new_esEs7(x0, x1, app(ty_Maybe, x2))
new_ltEs24(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_ltEs21(x0, x1, app(ty_Maybe, x2))
new_lt21(x0, x1, ty_Bool)
new_compare18(Float(x0, x1), Float(x2, x3))
new_ltEs5(Just(x0), Just(x1), ty_Float)
new_ltEs22(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_lt22(x0, x1, app(app(ty_Either, x2), x3))
new_compare110(x0, x1, x2, x3, True, x4, x5, x6)
new_esEs26(x0, x1, ty_Bool)
new_lt6(x0, x1, ty_Bool)
new_esEs30(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Integer)
new_ltEs14(Left(x0), Left(x1), ty_Bool, x2)
new_esEs8(x0, x1, ty_Double)
new_lt21(x0, x1, ty_Char)
new_lt5(x0, x1, ty_Float)
new_compare11(Char(x0), Char(x1))
new_compare31(Nothing, Just(x0), x1)
new_compare30(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs30(x0, x1, ty_Integer)
new_esEs7(x0, x1, app(app(ty_@2, x2), x3))
new_esEs33(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, ty_@0)
new_sr(Integer(x0), Integer(x1))
new_esEs16([], [], x0)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs7(x0, x1, ty_@0)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs23(Nothing, Just(x0), x1)
new_esEs11(x0, x1, app(ty_[], x2))
new_esEs34(x0, x1, ty_Char)
new_esEs10(x0, x1, ty_Bool)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs10(x0, x1, ty_@0)
new_compare7(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs39(x0, x1, ty_Double)
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_@0)
new_lt6(x0, x1, app(app(ty_Either, x2), x3))
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_esEs31(x0, x1, ty_Bool)
new_primEqNat0(Zero, Succ(x0))
new_primPlusNat1(Succ(x0), Zero)
new_lt23(x0, x1, ty_Char)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_lt22(x0, x1, app(ty_[], x2))
new_lt12(x0, x1, x2, x3)
new_lt20(x0, x1, ty_Char)
new_lt4(x0, x1, x2, x3, x4)
new_esEs39(x0, x1, app(ty_Maybe, x2))
new_ltEs22(x0, x1, app(ty_[], x2))
new_esEs6(x0, x1, ty_Ordering)
new_esEs33(x0, x1, ty_Char)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt22(x0, x1, app(ty_Maybe, x2))
new_esEs10(x0, x1, app(ty_Ratio, x2))
new_esEs32(x0, x1, ty_Integer)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_esEs33(x0, x1, app(ty_Ratio, x2))
new_pePe(False, x0)
new_ltEs24(x0, x1, ty_Int)
new_ltEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_lt8(x0, x1)
new_ltEs14(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs10(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_lt23(x0, x1, ty_Double)
new_ltEs22(x0, x1, app(ty_Maybe, x2))
new_esEs31(x0, x1, app(app(ty_Either, x2), x3))
new_lt5(x0, x1, app(ty_Maybe, x2))
new_compare110(x0, x1, x2, x3, False, x4, x5, x6)
new_lt20(x0, x1, ty_Bool)
new_esEs29(x0, x1, ty_Int)
new_ltEs14(Left(x0), Left(x1), ty_Double, x2)
new_esEs30(x0, x1, ty_Ordering)
new_lt23(x0, x1, ty_Float)
new_esEs6(x0, x1, app(ty_Ratio, x2))
new_lt6(x0, x1, ty_@0)
new_esEs35(x0, x1, app(app(ty_@2, x2), x3))
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs31(x0, x1, ty_Char)
new_esEs23(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_lt22(x0, x1, ty_Double)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs22(x0, x1, ty_@0)
new_esEs39(x0, x1, ty_Int)
new_esEs30(x0, x1, ty_@0)
new_ltEs16(False, True)
new_ltEs16(True, False)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_ltEs6(GT, GT)
new_compare112(x0, x1, True, x2)
new_esEs10(x0, x1, ty_Int)
new_lt21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs32(x0, x1, ty_Char)
new_lt21(x0, x1, app(ty_Maybe, x2))
new_ltEs18(x0, x1, ty_Int)
new_ltEs5(Just(x0), Just(x1), ty_Ordering)
new_esEs33(x0, x1, app(ty_[], x2))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_ltEs19(x0, x1, ty_Char)
new_ltEs5(Just(x0), Just(x1), ty_Char)
new_esEs27(x0, x1, ty_Int)
new_compare26(x0, x1, False, x2, x3)
new_esEs23(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs21(x0, x1, app(ty_[], x2))
new_ltEs5(Just(x0), Just(x1), ty_Bool)
new_ltEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_lt22(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_@0)
new_ltEs22(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_Integer)
new_esEs33(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Int)
new_primCmpNat0(Zero, Zero)
new_esEs35(x0, x1, ty_Float)
new_asAs(False, x0)
new_ltEs19(x0, x1, app(ty_[], x2))
new_lt5(x0, x1, ty_Integer)
new_ltEs24(x0, x1, ty_@0)
new_esEs6(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs19(x0, x1, ty_Int)
new_lt23(x0, x1, ty_@0)
new_esEs34(x0, x1, ty_Int)
new_ltEs6(LT, LT)
new_compare30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs35(x0, x1, app(app(ty_Either, x2), x3))
new_esEs11(x0, x1, ty_Ordering)
new_esEs28(x0, x1, app(ty_[], x2))
new_ltEs14(Left(x0), Left(x1), ty_Int, x2)
new_ltEs22(x0, x1, ty_Double)
new_esEs9(x0, x1, app(ty_Ratio, x2))
new_ltEs24(x0, x1, ty_Char)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare27(Right(x0), Left(x1), x2, x3)
new_compare27(Left(x0), Right(x1), x2, x3)
new_esEs36(x0, x1, app(ty_[], x2))
new_esEs18(Integer(x0), Integer(x1))
new_esEs32(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Int)
new_esEs34(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(Just(x0), Just(x1), ty_@0)
new_esEs4(x0, x1, app(ty_Maybe, x2))
new_compare24(x0, x1, x2, x3, True, x4, x5)
new_ltEs19(x0, x1, ty_Float)
new_esEs6(x0, x1, ty_Char)
new_lt21(x0, x1, ty_Double)
new_ltEs14(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_compare210(x0, x1, False, x2)
new_esEs30(x0, x1, app(ty_[], x2))
new_esEs24(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_lt5(x0, x1, ty_Bool)
new_esEs23(Just(x0), Just(x1), ty_Char)
new_ltEs13(x0, x1)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs23(x0, x1, ty_Bool)
new_esEs24(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs5(x0, x1, app(ty_[], x2))
new_compare15(LT, EQ)
new_compare15(EQ, LT)
new_compare9(@0, @0)
new_lt13(x0, x1)
new_esEs36(x0, x1, ty_Integer)
new_esEs29(x0, x1, ty_Double)
new_esEs8(x0, x1, app(ty_Maybe, x2))
new_esEs5(x0, x1, app(ty_Ratio, x2))
new_ltEs18(x0, x1, ty_Float)
new_compare25(x0, x1, x2, x3, x4, x5, True, x6, x7, x8)
new_lt18(x0, x1)
new_esEs24(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs8(x0, x1, app(ty_Ratio, x2))
new_lt5(x0, x1, ty_Ordering)
new_esEs5(x0, x1, app(ty_Maybe, x2))
new_lt15(x0, x1)
new_compare8(Integer(x0), Integer(x1))
new_esEs34(x0, x1, app(app(ty_Either, x2), x3))
new_esEs31(x0, x1, app(ty_Ratio, x2))
new_esEs23(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs11(x0, x1, app(ty_Maybe, x2))
new_esEs8(x0, x1, ty_@0)
new_esEs5(x0, x1, ty_Int)
new_not(True)
new_compare30(x0, x1, ty_Float)
new_esEs33(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Ordering)
new_primMulInt(Pos(x0), Pos(x1))
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs4(x0, x1, ty_Bool)
new_esEs32(x0, x1, ty_Float)
new_esEs24(Right(x0), Right(x1), x2, ty_Char)
new_esEs36(x0, x1, ty_Ordering)
new_ltEs5(Just(x0), Just(x1), app(ty_[], x2))
new_esEs9(x0, x1, ty_Bool)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_not(False)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_compare29(Double(x0, x1), Double(x2, x3))
new_esEs6(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(Right(x0), Right(x1), x2, ty_Ordering)
new_compare13(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs24(Left(x0), Left(x1), ty_Int, x2)
new_primCmpNat0(Succ(x0), Succ(x1))
new_esEs7(x0, x1, ty_Ordering)
new_esEs10(x0, x1, app(app(ty_@2, x2), x3))
new_lt23(x0, x1, app(ty_Maybe, x2))
new_ltEs23(x0, x1, ty_Char)
new_esEs8(x0, x1, ty_Ordering)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_lt6(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs39(x0, x1, ty_@0)
new_ltEs21(x0, x1, ty_Char)
new_esEs15(Char(x0), Char(x1))
new_ltEs6(GT, EQ)
new_ltEs6(EQ, GT)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpNat0(Zero, Succ(x0))
new_ltEs24(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Ordering)
new_ltEs24(x0, x1, app(ty_Ratio, x2))
new_ltEs21(x0, x1, app(ty_Ratio, x2))
new_ltEs21(x0, x1, ty_Double)
new_compare6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_compare30(x0, x1, ty_Double)
new_compare27(Left(x0), Left(x1), x2, x3)
new_compare19(x0, x1, True, x2, x3)
new_lt21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt21(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, app(ty_[], x2))
new_ltEs14(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_primCmpNat0(Succ(x0), Zero)
new_lt16(x0, x1, x2, x3)
new_esEs34(x0, x1, ty_Double)
new_compare0([], :(x0, x1), x2)
new_ltEs14(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs22(x0, x1, ty_Int)
new_esEs4(x0, x1, app(ty_Ratio, x2))
new_esEs35(x0, x1, app(ty_Maybe, x2))
new_compare16(x0, x1)
new_ltEs20(x0, x1, ty_Double)
new_esEs22(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs24(x0, x1, ty_Bool)
new_esEs35(x0, x1, ty_Ordering)
new_ltEs18(x0, x1, ty_Integer)
new_esEs35(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs34(x0, x1, ty_@0)
new_esEs5(x0, x1, app(app(ty_@2, x2), x3))
new_esEs37(x0, x1, ty_Integer)
new_ltEs18(x0, x1, ty_Char)
new_esEs7(x0, x1, ty_Double)
new_lt23(x0, x1, ty_Ordering)
new_ltEs24(x0, x1, app(ty_Maybe, x2))
new_esEs24(Left(x0), Right(x1), x2, x3)
new_esEs24(Right(x0), Left(x1), x2, x3)
new_esEs9(x0, x1, ty_Float)
new_esEs32(x0, x1, app(ty_Maybe, x2))
new_esEs23(Just(x0), Just(x1), ty_Ordering)
new_lt6(x0, x1, ty_Char)
new_esEs9(x0, x1, app(app(ty_@2, x2), x3))
new_esEs9(x0, x1, ty_Char)
new_compare31(Just(x0), Nothing, x1)
new_esEs8(x0, x1, ty_Char)
new_esEs35(x0, x1, ty_Int)
new_esEs33(x0, x1, ty_@0)
new_esEs5(x0, x1, ty_Ordering)
new_esEs35(x0, x1, app(ty_Ratio, x2))
new_esEs32(x0, x1, ty_Double)
new_compare111(x0, x1, x2, x3, False, x4, x5)
new_esEs39(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(x0, x1, app(ty_[], x2))
new_esEs14(Float(x0, x1), Float(x2, x3))
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs24(Left(x0), Left(x1), ty_Char, x2)
new_esEs26(x0, x1, ty_Integer)
new_esEs5(x0, x1, ty_@0)
new_esEs5(x0, x1, ty_Char)
new_esEs7(x0, x1, ty_Char)
new_ltEs21(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs9(x0, x1, x2)
new_compare12(True, True)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs36(x0, x1, app(ty_Maybe, x2))
new_esEs5(x0, x1, ty_Integer)
new_esEs33(x0, x1, app(app(ty_@2, x2), x3))
new_primCompAux1(x0, x1, x2, x3)
new_compare30(x0, x1, ty_Ordering)
new_primMulNat0(Zero, Succ(x0))
new_esEs17(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs23(x0, x1, ty_Double)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_compare17(x0, x1, x2, x3, x4, x5, False, x6, x7, x8, x9)
new_esEs9(x0, x1, app(ty_Maybe, x2))
new_esEs24(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs24(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs8(x0, x1, app(app(ty_@2, x2), x3))
new_primCompAux0(x0, GT)
new_esEs39(x0, x1, app(app(ty_@2, x2), x3))
new_lt6(x0, x1, ty_Ordering)
new_primPlusNat1(Zero, Succ(x0))
new_compare0(:(x0, x1), :(x2, x3), x4)
new_esEs36(x0, x1, ty_Float)
new_esEs19(@0, @0)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs36(x0, x1, app(ty_Ratio, x2))
new_esEs24(Right(x0), Right(x1), x2, ty_Integer)
new_esEs31(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs8(x0, x1, x2)
new_esEs36(x0, x1, ty_@0)
new_esEs12(LT, LT)
new_esEs28(x0, x1, ty_Integer)
new_esEs24(Right(x0), Right(x1), x2, ty_Bool)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_ltEs18(x0, x1, ty_Ordering)
new_ltEs16(False, False)
new_compare31(Just(x0), Just(x1), x2)
new_esEs7(x0, x1, app(app(ty_Either, x2), x3))
new_esEs33(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, ty_Ordering)
new_esEs28(x0, x1, ty_@0)
new_esEs11(x0, x1, ty_Float)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_lt10(x0, x1, x2)
new_esEs39(x0, x1, ty_Integer)
new_compare112(x0, x1, False, x2)
new_esEs24(Left(x0), Left(x1), app(ty_Maybe, x2), x3)

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

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

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

new_addToFM_C(Branch(:(yvy500, yvy501), yvy51, yvy52, yvy53, yvy54), [], yvy41, h, ba) → new_addToFM_C(yvy53, [], yvy41, h, ba)

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

new_esEs36(x0, x1, ty_Char)
new_esEs35(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, ty_Float)
new_esEs7(x0, x1, ty_Int)
new_esEs32(x0, x1, app(ty_[], x2))
new_ltEs21(x0, x1, ty_Int)
new_esEs10(x0, x1, ty_Float)
new_ltEs16(True, True)
new_esEs6(x0, x1, ty_Int)
new_lt11(x0, x1)
new_ltEs20(x0, x1, ty_Int)
new_lt5(x0, x1, ty_Char)
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs23(x0, x1, app(ty_Maybe, x2))
new_esEs32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs21(x0, x1, ty_@0)
new_esEs29(x0, x1, ty_Char)
new_ltEs22(x0, x1, ty_Integer)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_compare10(x0, x1, False, x2, x3)
new_esEs32(x0, x1, ty_Int)
new_esEs11(x0, x1, ty_Int)
new_esEs24(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs4(x0, x1, ty_Float)
new_lt23(x0, x1, app(ty_[], x2))
new_esEs33(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Integer)
new_compare30(x0, x1, ty_Int)
new_pePe(True, x0)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs11(x0, x1, ty_@0)
new_esEs35(x0, x1, ty_Integer)
new_esEs11(x0, x1, ty_Char)
new_esEs6(x0, x1, ty_Float)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(x0, x1, ty_Int)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_lt22(x0, x1, ty_@0)
new_compare30(x0, x1, ty_Bool)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_@0)
new_esEs29(x0, x1, ty_Ordering)
new_lt22(x0, x1, ty_Float)
new_lt23(x0, x1, ty_Integer)
new_esEs11(x0, x1, app(ty_Ratio, x2))
new_lt7(x0, x1)
new_esEs8(x0, x1, ty_Integer)
new_esEs23(Just(x0), Just(x1), ty_Float)
new_compare30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs5(Nothing, Nothing, x0)
new_esEs6(x0, x1, ty_Integer)
new_lt5(x0, x1, ty_@0)
new_esEs23(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs11(x0, x1, ty_Bool)
new_lt6(x0, x1, app(app(ty_@2, x2), x3))
new_esEs36(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare12(False, True)
new_compare12(True, False)
new_compare26(x0, x1, True, x2, x3)
new_lt21(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(Left(x0), Left(x1), ty_@0, x2)
new_ltEs7(x0, x1)
new_ltEs18(x0, x1, app(ty_[], x2))
new_primCompAux0(x0, EQ)
new_ltEs14(Right(x0), Right(x1), x2, ty_Char)
new_esEs36(x0, x1, app(app(ty_Either, x2), x3))
new_esEs39(x0, x1, app(ty_Ratio, x2))
new_ltEs14(Right(x0), Right(x1), x2, ty_Float)
new_esEs10(x0, x1, ty_Integer)
new_esEs32(x0, x1, ty_Ordering)
new_ltEs21(x0, x1, ty_Float)
new_ltEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs24(x0, x1, ty_Integer)
new_compare19(x0, x1, False, x2, x3)
new_lt5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs34(x0, x1, ty_Float)
new_ltEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs24(Left(x0), Left(x1), ty_@0, x2)
new_esEs6(x0, x1, ty_@0)
new_lt6(x0, x1, ty_Float)
new_ltEs14(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs9(x0, x1, app(app(ty_Either, x2), x3))
new_esEs9(x0, x1, ty_Int)
new_compare30(x0, x1, ty_Integer)
new_esEs12(GT, EQ)
new_esEs12(EQ, GT)
new_esEs36(x0, x1, ty_Int)
new_ltEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, ty_Bool)
new_esEs11(x0, x1, app(app(ty_@2, x2), x3))
new_esEs10(x0, x1, app(app(ty_Either, x2), x3))
new_lt6(x0, x1, app(ty_Ratio, x2))
new_compare28(x0, x1, False, x2, x3)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt5(x0, x1, ty_Double)
new_lt5(x0, x1, app(ty_[], x2))
new_esEs24(Right(x0), Right(x1), x2, ty_Float)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare15(LT, LT)
new_esEs34(x0, x1, app(ty_Maybe, x2))
new_lt5(x0, x1, app(ty_Ratio, x2))
new_esEs10(x0, x1, ty_Char)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs39(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(Right(x0), Right(x1), x2, ty_Double)
new_esEs34(x0, x1, ty_Ordering)
new_esEs39(x0, x1, app(ty_[], x2))
new_esEs12(GT, GT)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs30(x0, x1, ty_Double)
new_esEs24(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs21(x0, x1, ty_Ordering)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_lt21(x0, x1, ty_Float)
new_esEs11(x0, x1, ty_Integer)
new_compare0(:(x0, x1), [], x2)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(Just(x0), Nothing, x1)
new_esEs23(Just(x0), Just(x1), ty_Double)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs5(Just(x0), Nothing, x1)
new_esEs11(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, ty_Char)
new_esEs38(x0, x1, ty_Integer)
new_esEs27(x0, x1, ty_Bool)
new_esEs10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs6(EQ, EQ)
new_esEs32(x0, x1, ty_@0)
new_esEs7(x0, x1, ty_Float)
new_esEs23(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs22(x0, x1, ty_Char)
new_esEs9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(x0, x1, ty_Double)
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_esEs5(x0, x1, ty_Bool)
new_esEs31(x0, x1, ty_Int)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs32(x0, x1, app(ty_Ratio, x2))
new_esEs33(x0, x1, ty_Double)
new_ltEs14(Right(x0), Right(x1), x2, ty_Int)
new_esEs8(x0, x1, ty_Float)
new_ltEs18(x0, x1, ty_@0)
new_esEs36(x0, x1, app(app(ty_@2, x2), x3))
new_esEs16(:(x0, x1), :(x2, x3), x4)
new_lt9(x0, x1, x2)
new_ltEs5(Just(x0), Just(x1), ty_@0)
new_lt5(x0, x1, ty_Int)
new_ltEs6(LT, EQ)
new_ltEs6(EQ, LT)
new_primCompAux0(x0, LT)
new_esEs38(x0, x1, ty_Int)
new_esEs23(Just(x0), Just(x1), ty_Int)
new_ltEs20(x0, x1, ty_@0)
new_esEs5(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Int)
new_lt17(x0, x1)
new_esEs36(x0, x1, ty_Bool)
new_primEqNat0(Zero, Zero)
new_compare13(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs23(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_@0)
new_compare30(x0, x1, app(ty_[], x2))
new_esEs7(x0, x1, ty_Bool)
new_esEs9(x0, x1, app(ty_[], x2))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs10(x0, x1, app(ty_Maybe, x2))
new_esEs5(x0, x1, ty_Float)
new_ltEs22(x0, x1, ty_Float)
new_compare15(GT, GT)
new_esEs31(x0, x1, ty_Double)
new_compare27(Right(x0), Right(x1), x2, x3)
new_ltEs20(x0, x1, ty_Integer)
new_lt22(x0, x1, ty_Bool)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs34(x0, x1, ty_Bool)
new_esEs31(x0, x1, ty_Integer)
new_esEs6(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, ty_Char)
new_lt20(x0, x1, ty_Double)
new_ltEs22(x0, x1, app(app(ty_Either, x2), x3))
new_compare17(x0, x1, x2, x3, x4, x5, True, x6, x7, x8, x9)
new_ltEs15(x0, x1)
new_esEs4(x0, x1, ty_Integer)
new_esEs31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs39(x0, x1, ty_Bool)
new_ltEs24(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Float)
new_primMulNat0(Zero, Zero)
new_asAs(True, x0)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Double)
new_esEs5(x0, x1, ty_Double)
new_esEs34(x0, x1, app(ty_[], x2))
new_fsEs(x0)
new_esEs6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs8(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(:%(x0, x1), :%(x2, x3), x4)
new_ltEs5(Just(x0), Just(x1), ty_Integer)
new_lt6(x0, x1, ty_Double)
new_compare28(x0, x1, True, x2, x3)
new_esEs35(x0, x1, ty_Double)
new_ltEs18(x0, x1, ty_Bool)
new_lt6(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, ty_Float)
new_ltEs5(Just(x0), Just(x1), ty_Double)
new_lt22(x0, x1, ty_Ordering)
new_esEs9(x0, x1, ty_@0)
new_esEs35(x0, x1, ty_Bool)
new_ltEs14(Left(x0), Right(x1), x2, x3)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(Right(x0), Left(x1), x2, x3)
new_ltEs14(Right(x0), Right(x1), x2, ty_Integer)
new_esEs35(x0, x1, ty_Char)
new_ltEs23(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, ty_Bool)
new_esEs31(x0, x1, ty_@0)
new_esEs24(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs19(x0, x1, ty_Double)
new_ltEs24(x0, x1, ty_Double)
new_esEs13(Double(x0, x1), Double(x2, x3))
new_esEs32(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, ty_Ordering)
new_lt23(x0, x1, app(ty_Ratio, x2))
new_esEs20(True, True)
new_lt20(x0, x1, app(ty_[], x2))
new_lt22(x0, x1, ty_Int)
new_ltEs12(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs7(x0, x1, ty_Integer)
new_esEs30(x0, x1, ty_Bool)
new_lt21(x0, x1, ty_@0)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs33(x0, x1, ty_Float)
new_esEs29(x0, x1, ty_Integer)
new_compare31(Nothing, Nothing, x0)
new_ltEs21(x0, x1, ty_Integer)
new_primPlusNat0(Zero, x0)
new_lt21(x0, x1, app(ty_Ratio, x2))
new_lt22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(x0, x1, app(ty_[], x2))
new_esEs4(x0, x1, ty_Ordering)
new_ltEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs8(x0, x1, ty_Bool)
new_esEs7(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs31(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_primPlusNat0(Succ(x0), x1)
new_ltEs14(Right(x0), Right(x1), x2, ty_Double)
new_ltEs4(x0, x1)
new_compare10(x0, x1, True, x2, x3)
new_compare24(x0, x1, x2, x3, False, x4, x5)
new_esEs34(x0, x1, ty_Integer)
new_esEs31(x0, x1, ty_Ordering)
new_ltEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs6(GT, LT)
new_ltEs6(LT, GT)
new_ltEs14(Left(x0), Left(x1), ty_Char, x2)
new_compare210(x0, x1, True, x2)
new_lt23(x0, x1, app(app(ty_@2, x2), x3))
new_compare0([], [], x0)
new_esEs11(x0, x1, ty_Double)
new_esEs16(:(x0, x1), [], x2)
new_lt19(x0, x1)
new_ltEs23(x0, x1, app(ty_Ratio, x2))
new_compare111(x0, x1, x2, x3, True, x4, x5)
new_esEs4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(x0, x1, ty_Double)
new_compare30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Double)
new_esEs39(x0, x1, ty_Char)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_compare15(EQ, EQ)
new_esEs24(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_lt6(x0, x1, ty_Int)
new_lt5(x0, x1, app(app(ty_@2, x2), x3))
new_lt21(x0, x1, ty_Ordering)
new_esEs24(Left(x0), Left(x1), ty_Bool, x2)
new_esEs28(x0, x1, ty_Ordering)
new_ltEs22(x0, x1, ty_Ordering)
new_ltEs11(x0, x1)
new_esEs16([], :(x0, x1), x2)
new_esEs24(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_lt20(x0, x1, ty_Float)
new_lt21(x0, x1, ty_Integer)
new_esEs32(x0, x1, ty_Bool)
new_esEs39(x0, x1, ty_Float)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt6(x0, x1, ty_Integer)
new_ltEs14(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs10(x0, x1, ty_Double)
new_sr0(x0, x1)
new_esEs23(Just(x0), Just(x1), ty_Integer)
new_esEs24(Left(x0), Left(x1), ty_Integer, x2)
new_esEs20(False, True)
new_esEs20(True, False)
new_lt22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, ty_Bool)
new_ltEs23(x0, x1, ty_Integer)
new_lt22(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs20(False, False)
new_compare12(False, False)
new_ltEs22(x0, x1, app(ty_Ratio, x2))
new_esEs23(Nothing, Nothing, x0)
new_esEs12(LT, EQ)
new_esEs12(EQ, LT)
new_lt21(x0, x1, ty_Int)
new_lt22(x0, x1, ty_Char)
new_esEs31(x0, x1, app(ty_Maybe, x2))
new_compare14(x0, x1, x2, x3, x4, x5, True, x6, x7, x8)
new_esEs31(x0, x1, ty_Float)
new_esEs24(Right(x0), Right(x1), x2, ty_Int)
new_primPlusNat1(Zero, Zero)
new_ltEs21(x0, x1, ty_Bool)
new_esEs34(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs20(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_Float)
new_esEs12(EQ, EQ)
new_compare25(x0, x1, x2, x3, x4, x5, False, x6, x7, x8)
new_esEs23(Just(x0), Just(x1), ty_Bool)
new_esEs27(x0, x1, ty_Char)
new_esEs4(x0, x1, app(app(ty_Either, x2), x3))
new_esEs9(x0, x1, ty_Integer)
new_esEs30(x0, x1, ty_Float)
new_ltEs20(x0, x1, ty_Float)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs28(x0, x1, ty_Double)
new_esEs30(x0, x1, ty_Char)
new_ltEs14(Right(x0), Right(x1), x2, ty_@0)
new_compare30(x0, x1, ty_@0)
new_esEs6(x0, x1, ty_Bool)
new_ltEs5(Nothing, Just(x0), x1)
new_esEs24(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs23(x0, x1, ty_Float)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_lt23(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs7(x0, x1, app(ty_Ratio, x2))
new_compare15(EQ, GT)
new_compare15(GT, EQ)
new_ltEs24(x0, x1, ty_Ordering)
new_compare30(x0, x1, ty_Char)
new_primEqNat0(Succ(x0), Zero)
new_compare15(LT, GT)
new_compare15(GT, LT)
new_esEs24(Right(x0), Right(x1), x2, ty_@0)
new_lt14(x0, x1, x2)
new_esEs36(x0, x1, ty_Double)
new_esEs39(x0, x1, ty_Ordering)
new_esEs4(x0, x1, app(ty_[], x2))
new_ltEs21(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_esEs37(x0, x1, ty_Int)
new_esEs4(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs9(x0, x1, ty_Double)
new_primMulInt(Neg(x0), Neg(x1))
new_compare14(x0, x1, x2, x3, x4, x5, False, x6, x7, x8)
new_ltEs17(x0, x1)
new_compare30(x0, x1, app(ty_Ratio, x2))
new_esEs9(x0, x1, ty_Ordering)
new_esEs8(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, ty_Char)
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_ltEs23(x0, x1, ty_Int)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_esEs8(x0, x1, ty_Int)
new_ltEs5(Just(x0), Just(x1), ty_Int)
new_esEs33(x0, x1, ty_Int)
new_ltEs23(x0, x1, ty_@0)
new_esEs24(Left(x0), Left(x1), ty_Double, x2)
new_lt5(x0, x1, app(app(ty_Either, x2), x3))
new_esEs33(x0, x1, ty_Bool)
new_esEs10(x0, x1, ty_Ordering)
new_ltEs14(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs35(x0, x1, ty_@0)
new_esEs4(x0, x1, ty_Char)
new_ltEs14(Left(x0), Left(x1), ty_Integer, x2)
new_lt23(x0, x1, ty_Int)
new_esEs6(x0, x1, app(ty_[], x2))
new_esEs24(Left(x0), Left(x1), ty_Float, x2)
new_ltEs23(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs34(x0, x1, app(ty_Ratio, x2))
new_ltEs18(x0, x1, ty_Double)
new_lt23(x0, x1, ty_Bool)
new_ltEs14(Left(x0), Left(x1), ty_Float, x2)
new_esEs7(x0, x1, app(ty_Maybe, x2))
new_ltEs24(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_ltEs21(x0, x1, app(ty_Maybe, x2))
new_lt21(x0, x1, ty_Bool)
new_compare18(Float(x0, x1), Float(x2, x3))
new_ltEs5(Just(x0), Just(x1), ty_Float)
new_ltEs22(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_lt22(x0, x1, app(app(ty_Either, x2), x3))
new_compare110(x0, x1, x2, x3, True, x4, x5, x6)
new_esEs26(x0, x1, ty_Bool)
new_lt6(x0, x1, ty_Bool)
new_esEs30(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Integer)
new_ltEs14(Left(x0), Left(x1), ty_Bool, x2)
new_esEs8(x0, x1, ty_Double)
new_lt21(x0, x1, ty_Char)
new_lt5(x0, x1, ty_Float)
new_compare11(Char(x0), Char(x1))
new_compare31(Nothing, Just(x0), x1)
new_compare30(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs30(x0, x1, ty_Integer)
new_esEs7(x0, x1, app(app(ty_@2, x2), x3))
new_esEs33(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, ty_@0)
new_sr(Integer(x0), Integer(x1))
new_esEs16([], [], x0)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs7(x0, x1, ty_@0)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs23(Nothing, Just(x0), x1)
new_esEs11(x0, x1, app(ty_[], x2))
new_esEs34(x0, x1, ty_Char)
new_esEs10(x0, x1, ty_Bool)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs10(x0, x1, ty_@0)
new_compare7(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs39(x0, x1, ty_Double)
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_@0)
new_lt6(x0, x1, app(app(ty_Either, x2), x3))
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_esEs31(x0, x1, ty_Bool)
new_primEqNat0(Zero, Succ(x0))
new_primPlusNat1(Succ(x0), Zero)
new_lt23(x0, x1, ty_Char)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_lt22(x0, x1, app(ty_[], x2))
new_lt12(x0, x1, x2, x3)
new_lt20(x0, x1, ty_Char)
new_lt4(x0, x1, x2, x3, x4)
new_esEs39(x0, x1, app(ty_Maybe, x2))
new_ltEs22(x0, x1, app(ty_[], x2))
new_esEs6(x0, x1, ty_Ordering)
new_esEs33(x0, x1, ty_Char)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt22(x0, x1, app(ty_Maybe, x2))
new_esEs10(x0, x1, app(ty_Ratio, x2))
new_esEs32(x0, x1, ty_Integer)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_esEs33(x0, x1, app(ty_Ratio, x2))
new_pePe(False, x0)
new_ltEs24(x0, x1, ty_Int)
new_ltEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_lt8(x0, x1)
new_ltEs14(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs10(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_lt23(x0, x1, ty_Double)
new_ltEs22(x0, x1, app(ty_Maybe, x2))
new_esEs31(x0, x1, app(app(ty_Either, x2), x3))
new_lt5(x0, x1, app(ty_Maybe, x2))
new_compare110(x0, x1, x2, x3, False, x4, x5, x6)
new_lt20(x0, x1, ty_Bool)
new_esEs29(x0, x1, ty_Int)
new_ltEs14(Left(x0), Left(x1), ty_Double, x2)
new_esEs30(x0, x1, ty_Ordering)
new_lt23(x0, x1, ty_Float)
new_esEs6(x0, x1, app(ty_Ratio, x2))
new_lt6(x0, x1, ty_@0)
new_esEs35(x0, x1, app(app(ty_@2, x2), x3))
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs31(x0, x1, ty_Char)
new_esEs23(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_lt22(x0, x1, ty_Double)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs22(x0, x1, ty_@0)
new_esEs39(x0, x1, ty_Int)
new_esEs30(x0, x1, ty_@0)
new_ltEs16(False, True)
new_ltEs16(True, False)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_ltEs6(GT, GT)
new_compare112(x0, x1, True, x2)
new_esEs10(x0, x1, ty_Int)
new_lt21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs32(x0, x1, ty_Char)
new_lt21(x0, x1, app(ty_Maybe, x2))
new_ltEs18(x0, x1, ty_Int)
new_ltEs5(Just(x0), Just(x1), ty_Ordering)
new_esEs33(x0, x1, app(ty_[], x2))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_ltEs19(x0, x1, ty_Char)
new_ltEs5(Just(x0), Just(x1), ty_Char)
new_esEs27(x0, x1, ty_Int)
new_compare26(x0, x1, False, x2, x3)
new_esEs23(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs21(x0, x1, app(ty_[], x2))
new_ltEs5(Just(x0), Just(x1), ty_Bool)
new_ltEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_lt22(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_@0)
new_ltEs22(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_Integer)
new_esEs33(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Int)
new_primCmpNat0(Zero, Zero)
new_esEs35(x0, x1, ty_Float)
new_asAs(False, x0)
new_ltEs19(x0, x1, app(ty_[], x2))
new_lt5(x0, x1, ty_Integer)
new_ltEs24(x0, x1, ty_@0)
new_esEs6(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs19(x0, x1, ty_Int)
new_lt23(x0, x1, ty_@0)
new_esEs34(x0, x1, ty_Int)
new_ltEs6(LT, LT)
new_compare30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs35(x0, x1, app(app(ty_Either, x2), x3))
new_esEs11(x0, x1, ty_Ordering)
new_esEs28(x0, x1, app(ty_[], x2))
new_ltEs14(Left(x0), Left(x1), ty_Int, x2)
new_ltEs22(x0, x1, ty_Double)
new_esEs9(x0, x1, app(ty_Ratio, x2))
new_ltEs24(x0, x1, ty_Char)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare27(Right(x0), Left(x1), x2, x3)
new_compare27(Left(x0), Right(x1), x2, x3)
new_esEs36(x0, x1, app(ty_[], x2))
new_esEs18(Integer(x0), Integer(x1))
new_esEs32(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Int)
new_esEs34(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(Just(x0), Just(x1), ty_@0)
new_esEs4(x0, x1, app(ty_Maybe, x2))
new_compare24(x0, x1, x2, x3, True, x4, x5)
new_ltEs19(x0, x1, ty_Float)
new_esEs6(x0, x1, ty_Char)
new_lt21(x0, x1, ty_Double)
new_ltEs14(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_compare210(x0, x1, False, x2)
new_esEs30(x0, x1, app(ty_[], x2))
new_esEs24(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_lt5(x0, x1, ty_Bool)
new_esEs23(Just(x0), Just(x1), ty_Char)
new_ltEs13(x0, x1)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs23(x0, x1, ty_Bool)
new_esEs24(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs5(x0, x1, app(ty_[], x2))
new_compare15(LT, EQ)
new_compare15(EQ, LT)
new_compare9(@0, @0)
new_lt13(x0, x1)
new_esEs36(x0, x1, ty_Integer)
new_esEs29(x0, x1, ty_Double)
new_esEs8(x0, x1, app(ty_Maybe, x2))
new_esEs5(x0, x1, app(ty_Ratio, x2))
new_ltEs18(x0, x1, ty_Float)
new_compare25(x0, x1, x2, x3, x4, x5, True, x6, x7, x8)
new_lt18(x0, x1)
new_esEs24(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs8(x0, x1, app(ty_Ratio, x2))
new_lt5(x0, x1, ty_Ordering)
new_esEs5(x0, x1, app(ty_Maybe, x2))
new_lt15(x0, x1)
new_compare8(Integer(x0), Integer(x1))
new_esEs34(x0, x1, app(app(ty_Either, x2), x3))
new_esEs31(x0, x1, app(ty_Ratio, x2))
new_esEs23(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs11(x0, x1, app(ty_Maybe, x2))
new_esEs8(x0, x1, ty_@0)
new_esEs5(x0, x1, ty_Int)
new_not(True)
new_compare30(x0, x1, ty_Float)
new_esEs33(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Ordering)
new_primMulInt(Pos(x0), Pos(x1))
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs4(x0, x1, ty_Bool)
new_esEs32(x0, x1, ty_Float)
new_esEs24(Right(x0), Right(x1), x2, ty_Char)
new_esEs36(x0, x1, ty_Ordering)
new_ltEs5(Just(x0), Just(x1), app(ty_[], x2))
new_esEs9(x0, x1, ty_Bool)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_not(False)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_compare29(Double(x0, x1), Double(x2, x3))
new_esEs6(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(Right(x0), Right(x1), x2, ty_Ordering)
new_compare13(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs24(Left(x0), Left(x1), ty_Int, x2)
new_primCmpNat0(Succ(x0), Succ(x1))
new_esEs7(x0, x1, ty_Ordering)
new_esEs10(x0, x1, app(app(ty_@2, x2), x3))
new_lt23(x0, x1, app(ty_Maybe, x2))
new_ltEs23(x0, x1, ty_Char)
new_esEs8(x0, x1, ty_Ordering)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_lt6(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs39(x0, x1, ty_@0)
new_ltEs21(x0, x1, ty_Char)
new_esEs15(Char(x0), Char(x1))
new_ltEs6(GT, EQ)
new_ltEs6(EQ, GT)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpNat0(Zero, Succ(x0))
new_ltEs24(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Ordering)
new_ltEs24(x0, x1, app(ty_Ratio, x2))
new_ltEs21(x0, x1, app(ty_Ratio, x2))
new_ltEs21(x0, x1, ty_Double)
new_compare6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_compare30(x0, x1, ty_Double)
new_compare27(Left(x0), Left(x1), x2, x3)
new_compare19(x0, x1, True, x2, x3)
new_lt21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt21(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, app(ty_[], x2))
new_ltEs14(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_primCmpNat0(Succ(x0), Zero)
new_lt16(x0, x1, x2, x3)
new_esEs34(x0, x1, ty_Double)
new_compare0([], :(x0, x1), x2)
new_ltEs14(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs22(x0, x1, ty_Int)
new_esEs4(x0, x1, app(ty_Ratio, x2))
new_esEs35(x0, x1, app(ty_Maybe, x2))
new_compare16(x0, x1)
new_ltEs20(x0, x1, ty_Double)
new_esEs22(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs24(x0, x1, ty_Bool)
new_esEs35(x0, x1, ty_Ordering)
new_ltEs18(x0, x1, ty_Integer)
new_esEs35(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs34(x0, x1, ty_@0)
new_esEs5(x0, x1, app(app(ty_@2, x2), x3))
new_esEs37(x0, x1, ty_Integer)
new_ltEs18(x0, x1, ty_Char)
new_esEs7(x0, x1, ty_Double)
new_lt23(x0, x1, ty_Ordering)
new_ltEs24(x0, x1, app(ty_Maybe, x2))
new_esEs24(Left(x0), Right(x1), x2, x3)
new_esEs24(Right(x0), Left(x1), x2, x3)
new_esEs9(x0, x1, ty_Float)
new_esEs32(x0, x1, app(ty_Maybe, x2))
new_esEs23(Just(x0), Just(x1), ty_Ordering)
new_lt6(x0, x1, ty_Char)
new_esEs9(x0, x1, app(app(ty_@2, x2), x3))
new_esEs9(x0, x1, ty_Char)
new_compare31(Just(x0), Nothing, x1)
new_esEs8(x0, x1, ty_Char)
new_esEs35(x0, x1, ty_Int)
new_esEs33(x0, x1, ty_@0)
new_esEs5(x0, x1, ty_Ordering)
new_esEs35(x0, x1, app(ty_Ratio, x2))
new_esEs32(x0, x1, ty_Double)
new_compare111(x0, x1, x2, x3, False, x4, x5)
new_esEs39(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(x0, x1, app(ty_[], x2))
new_esEs14(Float(x0, x1), Float(x2, x3))
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs24(Left(x0), Left(x1), ty_Char, x2)
new_esEs26(x0, x1, ty_Integer)
new_esEs5(x0, x1, ty_@0)
new_esEs5(x0, x1, ty_Char)
new_esEs7(x0, x1, ty_Char)
new_ltEs21(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs9(x0, x1, x2)
new_compare12(True, True)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs36(x0, x1, app(ty_Maybe, x2))
new_esEs5(x0, x1, ty_Integer)
new_esEs33(x0, x1, app(app(ty_@2, x2), x3))
new_primCompAux1(x0, x1, x2, x3)
new_compare30(x0, x1, ty_Ordering)
new_primMulNat0(Zero, Succ(x0))
new_esEs17(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs23(x0, x1, ty_Double)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_compare17(x0, x1, x2, x3, x4, x5, False, x6, x7, x8, x9)
new_esEs9(x0, x1, app(ty_Maybe, x2))
new_esEs24(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs24(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs8(x0, x1, app(app(ty_@2, x2), x3))
new_primCompAux0(x0, GT)
new_esEs39(x0, x1, app(app(ty_@2, x2), x3))
new_lt6(x0, x1, ty_Ordering)
new_primPlusNat1(Zero, Succ(x0))
new_compare0(:(x0, x1), :(x2, x3), x4)
new_esEs36(x0, x1, ty_Float)
new_esEs19(@0, @0)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs36(x0, x1, app(ty_Ratio, x2))
new_esEs24(Right(x0), Right(x1), x2, ty_Integer)
new_esEs31(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs8(x0, x1, x2)
new_esEs36(x0, x1, ty_@0)
new_esEs12(LT, LT)
new_esEs28(x0, x1, ty_Integer)
new_esEs24(Right(x0), Right(x1), x2, ty_Bool)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_ltEs18(x0, x1, ty_Ordering)
new_ltEs16(False, False)
new_compare31(Just(x0), Just(x1), x2)
new_esEs7(x0, x1, app(app(ty_Either, x2), x3))
new_esEs33(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, ty_Ordering)
new_esEs28(x0, x1, ty_@0)
new_esEs11(x0, x1, ty_Float)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_lt10(x0, x1, x2)
new_esEs39(x0, x1, ty_Integer)
new_compare112(x0, x1, False, x2)
new_esEs24(Left(x0), Left(x1), app(ty_Maybe, x2), x3)

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_esEs36(x0, x1, ty_Char)
new_esEs35(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, ty_Float)
new_esEs7(x0, x1, ty_Int)
new_esEs32(x0, x1, app(ty_[], x2))
new_ltEs21(x0, x1, ty_Int)
new_esEs10(x0, x1, ty_Float)
new_ltEs16(True, True)
new_esEs6(x0, x1, ty_Int)
new_lt11(x0, x1)
new_ltEs20(x0, x1, ty_Int)
new_lt5(x0, x1, ty_Char)
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs23(x0, x1, app(ty_Maybe, x2))
new_esEs32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs21(x0, x1, ty_@0)
new_esEs29(x0, x1, ty_Char)
new_ltEs22(x0, x1, ty_Integer)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_compare10(x0, x1, False, x2, x3)
new_esEs32(x0, x1, ty_Int)
new_esEs11(x0, x1, ty_Int)
new_esEs24(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs4(x0, x1, ty_Float)
new_lt23(x0, x1, app(ty_[], x2))
new_esEs33(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Integer)
new_compare30(x0, x1, ty_Int)
new_pePe(True, x0)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs11(x0, x1, ty_@0)
new_esEs35(x0, x1, ty_Integer)
new_esEs11(x0, x1, ty_Char)
new_esEs6(x0, x1, ty_Float)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(x0, x1, ty_Int)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_lt22(x0, x1, ty_@0)
new_compare30(x0, x1, ty_Bool)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_@0)
new_esEs29(x0, x1, ty_Ordering)
new_lt22(x0, x1, ty_Float)
new_lt23(x0, x1, ty_Integer)
new_esEs11(x0, x1, app(ty_Ratio, x2))
new_lt7(x0, x1)
new_esEs8(x0, x1, ty_Integer)
new_esEs23(Just(x0), Just(x1), ty_Float)
new_compare30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs5(Nothing, Nothing, x0)
new_esEs6(x0, x1, ty_Integer)
new_lt5(x0, x1, ty_@0)
new_esEs23(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs11(x0, x1, ty_Bool)
new_lt6(x0, x1, app(app(ty_@2, x2), x3))
new_esEs36(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare12(False, True)
new_compare12(True, False)
new_compare26(x0, x1, True, x2, x3)
new_lt21(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(Left(x0), Left(x1), ty_@0, x2)
new_ltEs7(x0, x1)
new_ltEs18(x0, x1, app(ty_[], x2))
new_primCompAux0(x0, EQ)
new_ltEs14(Right(x0), Right(x1), x2, ty_Char)
new_esEs36(x0, x1, app(app(ty_Either, x2), x3))
new_esEs39(x0, x1, app(ty_Ratio, x2))
new_ltEs14(Right(x0), Right(x1), x2, ty_Float)
new_esEs10(x0, x1, ty_Integer)
new_esEs32(x0, x1, ty_Ordering)
new_ltEs21(x0, x1, ty_Float)
new_ltEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs24(x0, x1, ty_Integer)
new_compare19(x0, x1, False, x2, x3)
new_lt5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs34(x0, x1, ty_Float)
new_ltEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs24(Left(x0), Left(x1), ty_@0, x2)
new_esEs6(x0, x1, ty_@0)
new_lt6(x0, x1, ty_Float)
new_ltEs14(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs9(x0, x1, app(app(ty_Either, x2), x3))
new_esEs9(x0, x1, ty_Int)
new_compare30(x0, x1, ty_Integer)
new_esEs12(GT, EQ)
new_esEs12(EQ, GT)
new_esEs36(x0, x1, ty_Int)
new_ltEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, ty_Bool)
new_esEs11(x0, x1, app(app(ty_@2, x2), x3))
new_esEs10(x0, x1, app(app(ty_Either, x2), x3))
new_lt6(x0, x1, app(ty_Ratio, x2))
new_compare28(x0, x1, False, x2, x3)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt5(x0, x1, ty_Double)
new_lt5(x0, x1, app(ty_[], x2))
new_esEs24(Right(x0), Right(x1), x2, ty_Float)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare15(LT, LT)
new_esEs34(x0, x1, app(ty_Maybe, x2))
new_lt5(x0, x1, app(ty_Ratio, x2))
new_esEs10(x0, x1, ty_Char)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs39(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(Right(x0), Right(x1), x2, ty_Double)
new_esEs34(x0, x1, ty_Ordering)
new_esEs39(x0, x1, app(ty_[], x2))
new_esEs12(GT, GT)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs30(x0, x1, ty_Double)
new_esEs24(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs21(x0, x1, ty_Ordering)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_lt21(x0, x1, ty_Float)
new_esEs11(x0, x1, ty_Integer)
new_compare0(:(x0, x1), [], x2)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(Just(x0), Nothing, x1)
new_esEs23(Just(x0), Just(x1), ty_Double)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs5(Just(x0), Nothing, x1)
new_esEs11(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, ty_Char)
new_esEs38(x0, x1, ty_Integer)
new_esEs27(x0, x1, ty_Bool)
new_esEs10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs6(EQ, EQ)
new_esEs32(x0, x1, ty_@0)
new_esEs7(x0, x1, ty_Float)
new_esEs23(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs22(x0, x1, ty_Char)
new_esEs9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(x0, x1, ty_Double)
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_esEs5(x0, x1, ty_Bool)
new_esEs31(x0, x1, ty_Int)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs32(x0, x1, app(ty_Ratio, x2))
new_esEs33(x0, x1, ty_Double)
new_ltEs14(Right(x0), Right(x1), x2, ty_Int)
new_esEs8(x0, x1, ty_Float)
new_ltEs18(x0, x1, ty_@0)
new_esEs36(x0, x1, app(app(ty_@2, x2), x3))
new_esEs16(:(x0, x1), :(x2, x3), x4)
new_lt9(x0, x1, x2)
new_ltEs5(Just(x0), Just(x1), ty_@0)
new_lt5(x0, x1, ty_Int)
new_ltEs6(LT, EQ)
new_ltEs6(EQ, LT)
new_primCompAux0(x0, LT)
new_esEs38(x0, x1, ty_Int)
new_esEs23(Just(x0), Just(x1), ty_Int)
new_ltEs20(x0, x1, ty_@0)
new_esEs5(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Int)
new_lt17(x0, x1)
new_esEs36(x0, x1, ty_Bool)
new_primEqNat0(Zero, Zero)
new_compare13(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs23(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_@0)
new_compare30(x0, x1, app(ty_[], x2))
new_esEs7(x0, x1, ty_Bool)
new_esEs9(x0, x1, app(ty_[], x2))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs10(x0, x1, app(ty_Maybe, x2))
new_esEs5(x0, x1, ty_Float)
new_ltEs22(x0, x1, ty_Float)
new_compare15(GT, GT)
new_esEs31(x0, x1, ty_Double)
new_compare27(Right(x0), Right(x1), x2, x3)
new_ltEs20(x0, x1, ty_Integer)
new_lt22(x0, x1, ty_Bool)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs34(x0, x1, ty_Bool)
new_esEs31(x0, x1, ty_Integer)
new_esEs6(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, ty_Char)
new_lt20(x0, x1, ty_Double)
new_ltEs22(x0, x1, app(app(ty_Either, x2), x3))
new_compare17(x0, x1, x2, x3, x4, x5, True, x6, x7, x8, x9)
new_ltEs15(x0, x1)
new_esEs4(x0, x1, ty_Integer)
new_esEs31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs39(x0, x1, ty_Bool)
new_ltEs24(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Float)
new_primMulNat0(Zero, Zero)
new_asAs(True, x0)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Double)
new_esEs5(x0, x1, ty_Double)
new_esEs34(x0, x1, app(ty_[], x2))
new_fsEs(x0)
new_esEs6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs8(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(:%(x0, x1), :%(x2, x3), x4)
new_ltEs5(Just(x0), Just(x1), ty_Integer)
new_lt6(x0, x1, ty_Double)
new_compare28(x0, x1, True, x2, x3)
new_esEs35(x0, x1, ty_Double)
new_ltEs18(x0, x1, ty_Bool)
new_lt6(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, ty_Float)
new_ltEs5(Just(x0), Just(x1), ty_Double)
new_lt22(x0, x1, ty_Ordering)
new_esEs9(x0, x1, ty_@0)
new_esEs35(x0, x1, ty_Bool)
new_ltEs14(Left(x0), Right(x1), x2, x3)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(Right(x0), Left(x1), x2, x3)
new_ltEs14(Right(x0), Right(x1), x2, ty_Integer)
new_esEs35(x0, x1, ty_Char)
new_ltEs23(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, ty_Bool)
new_esEs31(x0, x1, ty_@0)
new_esEs24(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs19(x0, x1, ty_Double)
new_ltEs24(x0, x1, ty_Double)
new_esEs13(Double(x0, x1), Double(x2, x3))
new_esEs32(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, ty_Ordering)
new_lt23(x0, x1, app(ty_Ratio, x2))
new_esEs20(True, True)
new_lt20(x0, x1, app(ty_[], x2))
new_lt22(x0, x1, ty_Int)
new_ltEs12(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs7(x0, x1, ty_Integer)
new_esEs30(x0, x1, ty_Bool)
new_lt21(x0, x1, ty_@0)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs33(x0, x1, ty_Float)
new_esEs29(x0, x1, ty_Integer)
new_compare31(Nothing, Nothing, x0)
new_ltEs21(x0, x1, ty_Integer)
new_primPlusNat0(Zero, x0)
new_lt21(x0, x1, app(ty_Ratio, x2))
new_lt22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(x0, x1, app(ty_[], x2))
new_esEs4(x0, x1, ty_Ordering)
new_ltEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs8(x0, x1, ty_Bool)
new_esEs7(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs31(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_primPlusNat0(Succ(x0), x1)
new_ltEs14(Right(x0), Right(x1), x2, ty_Double)
new_ltEs4(x0, x1)
new_compare10(x0, x1, True, x2, x3)
new_compare24(x0, x1, x2, x3, False, x4, x5)
new_esEs34(x0, x1, ty_Integer)
new_esEs31(x0, x1, ty_Ordering)
new_ltEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs6(GT, LT)
new_ltEs6(LT, GT)
new_ltEs14(Left(x0), Left(x1), ty_Char, x2)
new_compare210(x0, x1, True, x2)
new_lt23(x0, x1, app(app(ty_@2, x2), x3))
new_compare0([], [], x0)
new_esEs11(x0, x1, ty_Double)
new_esEs16(:(x0, x1), [], x2)
new_lt19(x0, x1)
new_ltEs23(x0, x1, app(ty_Ratio, x2))
new_compare111(x0, x1, x2, x3, True, x4, x5)
new_esEs4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(x0, x1, ty_Double)
new_compare30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Double)
new_esEs39(x0, x1, ty_Char)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_compare15(EQ, EQ)
new_esEs24(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_lt6(x0, x1, ty_Int)
new_lt5(x0, x1, app(app(ty_@2, x2), x3))
new_lt21(x0, x1, ty_Ordering)
new_esEs24(Left(x0), Left(x1), ty_Bool, x2)
new_esEs28(x0, x1, ty_Ordering)
new_ltEs22(x0, x1, ty_Ordering)
new_ltEs11(x0, x1)
new_esEs16([], :(x0, x1), x2)
new_esEs24(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_lt20(x0, x1, ty_Float)
new_lt21(x0, x1, ty_Integer)
new_esEs32(x0, x1, ty_Bool)
new_esEs39(x0, x1, ty_Float)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt6(x0, x1, ty_Integer)
new_ltEs14(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs10(x0, x1, ty_Double)
new_sr0(x0, x1)
new_esEs23(Just(x0), Just(x1), ty_Integer)
new_esEs24(Left(x0), Left(x1), ty_Integer, x2)
new_esEs20(False, True)
new_esEs20(True, False)
new_lt22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, ty_Bool)
new_ltEs23(x0, x1, ty_Integer)
new_lt22(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs20(False, False)
new_compare12(False, False)
new_ltEs22(x0, x1, app(ty_Ratio, x2))
new_esEs23(Nothing, Nothing, x0)
new_esEs12(LT, EQ)
new_esEs12(EQ, LT)
new_lt21(x0, x1, ty_Int)
new_lt22(x0, x1, ty_Char)
new_esEs31(x0, x1, app(ty_Maybe, x2))
new_compare14(x0, x1, x2, x3, x4, x5, True, x6, x7, x8)
new_esEs31(x0, x1, ty_Float)
new_esEs24(Right(x0), Right(x1), x2, ty_Int)
new_primPlusNat1(Zero, Zero)
new_ltEs21(x0, x1, ty_Bool)
new_esEs34(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs20(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_Float)
new_esEs12(EQ, EQ)
new_compare25(x0, x1, x2, x3, x4, x5, False, x6, x7, x8)
new_esEs23(Just(x0), Just(x1), ty_Bool)
new_esEs27(x0, x1, ty_Char)
new_esEs4(x0, x1, app(app(ty_Either, x2), x3))
new_esEs9(x0, x1, ty_Integer)
new_esEs30(x0, x1, ty_Float)
new_ltEs20(x0, x1, ty_Float)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs28(x0, x1, ty_Double)
new_esEs30(x0, x1, ty_Char)
new_ltEs14(Right(x0), Right(x1), x2, ty_@0)
new_compare30(x0, x1, ty_@0)
new_esEs6(x0, x1, ty_Bool)
new_ltEs5(Nothing, Just(x0), x1)
new_esEs24(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs23(x0, x1, ty_Float)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_lt23(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs7(x0, x1, app(ty_Ratio, x2))
new_compare15(EQ, GT)
new_compare15(GT, EQ)
new_ltEs24(x0, x1, ty_Ordering)
new_compare30(x0, x1, ty_Char)
new_primEqNat0(Succ(x0), Zero)
new_compare15(LT, GT)
new_compare15(GT, LT)
new_esEs24(Right(x0), Right(x1), x2, ty_@0)
new_lt14(x0, x1, x2)
new_esEs36(x0, x1, ty_Double)
new_esEs39(x0, x1, ty_Ordering)
new_esEs4(x0, x1, app(ty_[], x2))
new_ltEs21(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_esEs37(x0, x1, ty_Int)
new_esEs4(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs9(x0, x1, ty_Double)
new_primMulInt(Neg(x0), Neg(x1))
new_compare14(x0, x1, x2, x3, x4, x5, False, x6, x7, x8)
new_ltEs17(x0, x1)
new_compare30(x0, x1, app(ty_Ratio, x2))
new_esEs9(x0, x1, ty_Ordering)
new_esEs8(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, ty_Char)
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_ltEs23(x0, x1, ty_Int)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_esEs8(x0, x1, ty_Int)
new_ltEs5(Just(x0), Just(x1), ty_Int)
new_esEs33(x0, x1, ty_Int)
new_ltEs23(x0, x1, ty_@0)
new_esEs24(Left(x0), Left(x1), ty_Double, x2)
new_lt5(x0, x1, app(app(ty_Either, x2), x3))
new_esEs33(x0, x1, ty_Bool)
new_esEs10(x0, x1, ty_Ordering)
new_ltEs14(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs35(x0, x1, ty_@0)
new_esEs4(x0, x1, ty_Char)
new_ltEs14(Left(x0), Left(x1), ty_Integer, x2)
new_lt23(x0, x1, ty_Int)
new_esEs6(x0, x1, app(ty_[], x2))
new_esEs24(Left(x0), Left(x1), ty_Float, x2)
new_ltEs23(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs34(x0, x1, app(ty_Ratio, x2))
new_ltEs18(x0, x1, ty_Double)
new_lt23(x0, x1, ty_Bool)
new_ltEs14(Left(x0), Left(x1), ty_Float, x2)
new_esEs7(x0, x1, app(ty_Maybe, x2))
new_ltEs24(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_ltEs21(x0, x1, app(ty_Maybe, x2))
new_lt21(x0, x1, ty_Bool)
new_compare18(Float(x0, x1), Float(x2, x3))
new_ltEs5(Just(x0), Just(x1), ty_Float)
new_ltEs22(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_lt22(x0, x1, app(app(ty_Either, x2), x3))
new_compare110(x0, x1, x2, x3, True, x4, x5, x6)
new_esEs26(x0, x1, ty_Bool)
new_lt6(x0, x1, ty_Bool)
new_esEs30(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Integer)
new_ltEs14(Left(x0), Left(x1), ty_Bool, x2)
new_esEs8(x0, x1, ty_Double)
new_lt21(x0, x1, ty_Char)
new_lt5(x0, x1, ty_Float)
new_compare11(Char(x0), Char(x1))
new_compare31(Nothing, Just(x0), x1)
new_compare30(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs30(x0, x1, ty_Integer)
new_esEs7(x0, x1, app(app(ty_@2, x2), x3))
new_esEs33(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, ty_@0)
new_sr(Integer(x0), Integer(x1))
new_esEs16([], [], x0)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs7(x0, x1, ty_@0)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs23(Nothing, Just(x0), x1)
new_esEs11(x0, x1, app(ty_[], x2))
new_esEs34(x0, x1, ty_Char)
new_esEs10(x0, x1, ty_Bool)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs10(x0, x1, ty_@0)
new_compare7(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs39(x0, x1, ty_Double)
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_@0)
new_lt6(x0, x1, app(app(ty_Either, x2), x3))
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_esEs31(x0, x1, ty_Bool)
new_primEqNat0(Zero, Succ(x0))
new_primPlusNat1(Succ(x0), Zero)
new_lt23(x0, x1, ty_Char)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_lt22(x0, x1, app(ty_[], x2))
new_lt12(x0, x1, x2, x3)
new_lt20(x0, x1, ty_Char)
new_lt4(x0, x1, x2, x3, x4)
new_esEs39(x0, x1, app(ty_Maybe, x2))
new_ltEs22(x0, x1, app(ty_[], x2))
new_esEs6(x0, x1, ty_Ordering)
new_esEs33(x0, x1, ty_Char)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt22(x0, x1, app(ty_Maybe, x2))
new_esEs10(x0, x1, app(ty_Ratio, x2))
new_esEs32(x0, x1, ty_Integer)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_esEs33(x0, x1, app(ty_Ratio, x2))
new_pePe(False, x0)
new_ltEs24(x0, x1, ty_Int)
new_ltEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_lt8(x0, x1)
new_ltEs14(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs10(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_lt23(x0, x1, ty_Double)
new_ltEs22(x0, x1, app(ty_Maybe, x2))
new_esEs31(x0, x1, app(app(ty_Either, x2), x3))
new_lt5(x0, x1, app(ty_Maybe, x2))
new_compare110(x0, x1, x2, x3, False, x4, x5, x6)
new_lt20(x0, x1, ty_Bool)
new_esEs29(x0, x1, ty_Int)
new_ltEs14(Left(x0), Left(x1), ty_Double, x2)
new_esEs30(x0, x1, ty_Ordering)
new_lt23(x0, x1, ty_Float)
new_esEs6(x0, x1, app(ty_Ratio, x2))
new_lt6(x0, x1, ty_@0)
new_esEs35(x0, x1, app(app(ty_@2, x2), x3))
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs31(x0, x1, ty_Char)
new_esEs23(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_lt22(x0, x1, ty_Double)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs22(x0, x1, ty_@0)
new_esEs39(x0, x1, ty_Int)
new_esEs30(x0, x1, ty_@0)
new_ltEs16(False, True)
new_ltEs16(True, False)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_ltEs6(GT, GT)
new_compare112(x0, x1, True, x2)
new_esEs10(x0, x1, ty_Int)
new_lt21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs32(x0, x1, ty_Char)
new_lt21(x0, x1, app(ty_Maybe, x2))
new_ltEs18(x0, x1, ty_Int)
new_ltEs5(Just(x0), Just(x1), ty_Ordering)
new_esEs33(x0, x1, app(ty_[], x2))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_ltEs19(x0, x1, ty_Char)
new_ltEs5(Just(x0), Just(x1), ty_Char)
new_esEs27(x0, x1, ty_Int)
new_compare26(x0, x1, False, x2, x3)
new_esEs23(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs21(x0, x1, app(ty_[], x2))
new_ltEs5(Just(x0), Just(x1), ty_Bool)
new_ltEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_lt22(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_@0)
new_ltEs22(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_Integer)
new_esEs33(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Int)
new_primCmpNat0(Zero, Zero)
new_esEs35(x0, x1, ty_Float)
new_asAs(False, x0)
new_ltEs19(x0, x1, app(ty_[], x2))
new_lt5(x0, x1, ty_Integer)
new_ltEs24(x0, x1, ty_@0)
new_esEs6(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs19(x0, x1, ty_Int)
new_lt23(x0, x1, ty_@0)
new_esEs34(x0, x1, ty_Int)
new_ltEs6(LT, LT)
new_compare30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs35(x0, x1, app(app(ty_Either, x2), x3))
new_esEs11(x0, x1, ty_Ordering)
new_esEs28(x0, x1, app(ty_[], x2))
new_ltEs14(Left(x0), Left(x1), ty_Int, x2)
new_ltEs22(x0, x1, ty_Double)
new_esEs9(x0, x1, app(ty_Ratio, x2))
new_ltEs24(x0, x1, ty_Char)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare27(Right(x0), Left(x1), x2, x3)
new_compare27(Left(x0), Right(x1), x2, x3)
new_esEs36(x0, x1, app(ty_[], x2))
new_esEs18(Integer(x0), Integer(x1))
new_esEs32(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Int)
new_esEs34(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(Just(x0), Just(x1), ty_@0)
new_esEs4(x0, x1, app(ty_Maybe, x2))
new_compare24(x0, x1, x2, x3, True, x4, x5)
new_ltEs19(x0, x1, ty_Float)
new_esEs6(x0, x1, ty_Char)
new_lt21(x0, x1, ty_Double)
new_ltEs14(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_compare210(x0, x1, False, x2)
new_esEs30(x0, x1, app(ty_[], x2))
new_esEs24(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_lt5(x0, x1, ty_Bool)
new_esEs23(Just(x0), Just(x1), ty_Char)
new_ltEs13(x0, x1)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs23(x0, x1, ty_Bool)
new_esEs24(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs5(x0, x1, app(ty_[], x2))
new_compare15(LT, EQ)
new_compare15(EQ, LT)
new_compare9(@0, @0)
new_lt13(x0, x1)
new_esEs36(x0, x1, ty_Integer)
new_esEs29(x0, x1, ty_Double)
new_esEs8(x0, x1, app(ty_Maybe, x2))
new_esEs5(x0, x1, app(ty_Ratio, x2))
new_ltEs18(x0, x1, ty_Float)
new_compare25(x0, x1, x2, x3, x4, x5, True, x6, x7, x8)
new_lt18(x0, x1)
new_esEs24(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs8(x0, x1, app(ty_Ratio, x2))
new_lt5(x0, x1, ty_Ordering)
new_esEs5(x0, x1, app(ty_Maybe, x2))
new_lt15(x0, x1)
new_compare8(Integer(x0), Integer(x1))
new_esEs34(x0, x1, app(app(ty_Either, x2), x3))
new_esEs31(x0, x1, app(ty_Ratio, x2))
new_esEs23(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs11(x0, x1, app(ty_Maybe, x2))
new_esEs8(x0, x1, ty_@0)
new_esEs5(x0, x1, ty_Int)
new_not(True)
new_compare30(x0, x1, ty_Float)
new_esEs33(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Ordering)
new_primMulInt(Pos(x0), Pos(x1))
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs4(x0, x1, ty_Bool)
new_esEs32(x0, x1, ty_Float)
new_esEs24(Right(x0), Right(x1), x2, ty_Char)
new_esEs36(x0, x1, ty_Ordering)
new_ltEs5(Just(x0), Just(x1), app(ty_[], x2))
new_esEs9(x0, x1, ty_Bool)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_not(False)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_compare29(Double(x0, x1), Double(x2, x3))
new_esEs6(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(Right(x0), Right(x1), x2, ty_Ordering)
new_compare13(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs24(Left(x0), Left(x1), ty_Int, x2)
new_primCmpNat0(Succ(x0), Succ(x1))
new_esEs7(x0, x1, ty_Ordering)
new_esEs10(x0, x1, app(app(ty_@2, x2), x3))
new_lt23(x0, x1, app(ty_Maybe, x2))
new_ltEs23(x0, x1, ty_Char)
new_esEs8(x0, x1, ty_Ordering)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_lt6(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs39(x0, x1, ty_@0)
new_ltEs21(x0, x1, ty_Char)
new_esEs15(Char(x0), Char(x1))
new_ltEs6(GT, EQ)
new_ltEs6(EQ, GT)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpNat0(Zero, Succ(x0))
new_ltEs24(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Ordering)
new_ltEs24(x0, x1, app(ty_Ratio, x2))
new_ltEs21(x0, x1, app(ty_Ratio, x2))
new_ltEs21(x0, x1, ty_Double)
new_compare6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_compare30(x0, x1, ty_Double)
new_compare27(Left(x0), Left(x1), x2, x3)
new_compare19(x0, x1, True, x2, x3)
new_lt21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt21(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, app(ty_[], x2))
new_ltEs14(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_primCmpNat0(Succ(x0), Zero)
new_lt16(x0, x1, x2, x3)
new_esEs34(x0, x1, ty_Double)
new_compare0([], :(x0, x1), x2)
new_ltEs14(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs22(x0, x1, ty_Int)
new_esEs4(x0, x1, app(ty_Ratio, x2))
new_esEs35(x0, x1, app(ty_Maybe, x2))
new_compare16(x0, x1)
new_ltEs20(x0, x1, ty_Double)
new_esEs22(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs24(x0, x1, ty_Bool)
new_esEs35(x0, x1, ty_Ordering)
new_ltEs18(x0, x1, ty_Integer)
new_esEs35(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs34(x0, x1, ty_@0)
new_esEs5(x0, x1, app(app(ty_@2, x2), x3))
new_esEs37(x0, x1, ty_Integer)
new_ltEs18(x0, x1, ty_Char)
new_esEs7(x0, x1, ty_Double)
new_lt23(x0, x1, ty_Ordering)
new_ltEs24(x0, x1, app(ty_Maybe, x2))
new_esEs24(Left(x0), Right(x1), x2, x3)
new_esEs24(Right(x0), Left(x1), x2, x3)
new_esEs9(x0, x1, ty_Float)
new_esEs32(x0, x1, app(ty_Maybe, x2))
new_esEs23(Just(x0), Just(x1), ty_Ordering)
new_lt6(x0, x1, ty_Char)
new_esEs9(x0, x1, app(app(ty_@2, x2), x3))
new_esEs9(x0, x1, ty_Char)
new_compare31(Just(x0), Nothing, x1)
new_esEs8(x0, x1, ty_Char)
new_esEs35(x0, x1, ty_Int)
new_esEs33(x0, x1, ty_@0)
new_esEs5(x0, x1, ty_Ordering)
new_esEs35(x0, x1, app(ty_Ratio, x2))
new_esEs32(x0, x1, ty_Double)
new_compare111(x0, x1, x2, x3, False, x4, x5)
new_esEs39(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(x0, x1, app(ty_[], x2))
new_esEs14(Float(x0, x1), Float(x2, x3))
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs24(Left(x0), Left(x1), ty_Char, x2)
new_esEs26(x0, x1, ty_Integer)
new_esEs5(x0, x1, ty_@0)
new_esEs5(x0, x1, ty_Char)
new_esEs7(x0, x1, ty_Char)
new_ltEs21(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs9(x0, x1, x2)
new_compare12(True, True)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs36(x0, x1, app(ty_Maybe, x2))
new_esEs5(x0, x1, ty_Integer)
new_esEs33(x0, x1, app(app(ty_@2, x2), x3))
new_primCompAux1(x0, x1, x2, x3)
new_compare30(x0, x1, ty_Ordering)
new_primMulNat0(Zero, Succ(x0))
new_esEs17(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs23(x0, x1, ty_Double)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_compare17(x0, x1, x2, x3, x4, x5, False, x6, x7, x8, x9)
new_esEs9(x0, x1, app(ty_Maybe, x2))
new_esEs24(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs24(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs8(x0, x1, app(app(ty_@2, x2), x3))
new_primCompAux0(x0, GT)
new_esEs39(x0, x1, app(app(ty_@2, x2), x3))
new_lt6(x0, x1, ty_Ordering)
new_primPlusNat1(Zero, Succ(x0))
new_compare0(:(x0, x1), :(x2, x3), x4)
new_esEs36(x0, x1, ty_Float)
new_esEs19(@0, @0)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs36(x0, x1, app(ty_Ratio, x2))
new_esEs24(Right(x0), Right(x1), x2, ty_Integer)
new_esEs31(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs8(x0, x1, x2)
new_esEs36(x0, x1, ty_@0)
new_esEs12(LT, LT)
new_esEs28(x0, x1, ty_Integer)
new_esEs24(Right(x0), Right(x1), x2, ty_Bool)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_ltEs18(x0, x1, ty_Ordering)
new_ltEs16(False, False)
new_compare31(Just(x0), Just(x1), x2)
new_esEs7(x0, x1, app(app(ty_Either, x2), x3))
new_esEs33(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, ty_Ordering)
new_esEs28(x0, x1, ty_@0)
new_esEs11(x0, x1, ty_Float)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_lt10(x0, x1, x2)
new_esEs39(x0, x1, ty_Integer)
new_compare112(x0, x1, False, x2)
new_esEs24(Left(x0), Left(x1), app(ty_Maybe, x2), x3)



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

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

new_addToFM_C(Branch(:(yvy500, yvy501), yvy51, yvy52, yvy53, yvy54), [], yvy41, h, ba) → new_addToFM_C(yvy53, [], yvy41, h, ba)

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

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



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_lt25(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(yvy6200)), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(yvy6200)), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_lt27(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_lt25(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt26(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt26(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt24(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt24(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_lt27(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)

The TRS R consists of the following rules:

new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_esEs12(LT, LT) → True
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_esEs12(GT, GT) → True
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_compare16(yvy400, yvy300) → new_primCmpInt(yvy400, yvy300)
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primPlusNat1(Zero, Zero) → Zero
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_lt24(yvy130, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy130, new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT)
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primMulNat0(Zero, Zero) → Zero
new_lt27(yvy142, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy142, new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_esEs12(GT, EQ) → False
new_esEs12(EQ, GT) → False
new_sr0(yvy3000, yvy4001) → new_primMulInt(yvy3000, yvy4001)
new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_lt26(yvy138, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy138, new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_esEs12(EQ, EQ) → True
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_lt25(yvy134, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy134, new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT)
new_esEs12(GT, LT) → False
new_esEs12(LT, GT) → False
new_esEs12(LT, EQ) → False
new_esEs12(EQ, LT) → False
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(yvy40000), Zero) → GT

The set Q consists of the following terms:

new_lt24(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_compare16(x0, x1)
new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_sr0(x0, x1)
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_lt25(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_lt27(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_lt26(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

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

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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_lt25(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(yvy6200)), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(yvy6200)), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_lt27(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_lt25(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt26(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt26(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt24(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt24(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_lt27(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)

The TRS R consists of the following rules:

new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_sr0(yvy3000, yvy4001) → new_primMulInt(yvy3000, yvy4001)
new_lt25(yvy134, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy134, new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT)
new_compare16(yvy400, yvy300) → new_primCmpInt(yvy400, yvy300)
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_lt24(yvy130, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy130, new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_lt26(yvy138, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy138, new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT)
new_lt27(yvy142, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy142, new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT)

The set Q consists of the following terms:

new_lt24(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_compare16(x0, x1)
new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_sr0(x0, x1)
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_lt25(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_lt27(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_lt26(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_lt25(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), h, ba) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt26(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt24(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(yvy6200)), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(yvy6200)), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_lt27(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_lt25(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt26(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt24(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_lt27(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), h, ba)

The TRS R consists of the following rules:

new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_sr0(yvy3000, yvy4001) → new_primMulInt(yvy3000, yvy4001)
new_lt25(yvy134, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy134, new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT)
new_compare16(yvy400, yvy300) → new_primCmpInt(yvy400, yvy300)
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_lt24(yvy130, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy130, new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_lt26(yvy138, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy138, new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT)
new_lt27(yvy142, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy142, new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT)

The set Q consists of the following terms:

new_lt24(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_compare16(x0, x1)
new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_sr0(x0, x1)
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_lt25(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_lt27(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_lt26(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), h, ba) at position [11,1] we obtained the following new rules:

new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), h, ba)



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

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

new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt26(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt24(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(yvy6200)), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(yvy6200)), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_lt27(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_lt25(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt26(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt24(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_lt27(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), h, ba)

The TRS R consists of the following rules:

new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_sr0(yvy3000, yvy4001) → new_primMulInt(yvy3000, yvy4001)
new_lt25(yvy134, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy134, new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT)
new_compare16(yvy400, yvy300) → new_primCmpInt(yvy400, yvy300)
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_lt24(yvy130, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy130, new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_lt26(yvy138, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy138, new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT)
new_lt27(yvy142, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy142, new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT)

The set Q consists of the following terms:

new_lt24(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_compare16(x0, x1)
new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_sr0(x0, x1)
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_lt25(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_lt27(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_lt26(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(yvy6200)), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba) at position [12,0,0,0] we obtained the following new rules:

new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Zero))), Succ(yvy6200)), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt26(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt24(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(yvy6200)), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Zero))), Succ(yvy6200)), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_lt27(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_lt25(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt26(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt24(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_lt27(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), h, ba)

The TRS R consists of the following rules:

new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_sr0(yvy3000, yvy4001) → new_primMulInt(yvy3000, yvy4001)
new_lt25(yvy134, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy134, new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT)
new_compare16(yvy400, yvy300) → new_primCmpInt(yvy400, yvy300)
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_lt24(yvy130, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy130, new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_lt26(yvy138, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy138, new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT)
new_lt27(yvy142, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy142, new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT)

The set Q consists of the following terms:

new_lt24(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_compare16(x0, x1)
new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_sr0(x0, x1)
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_lt25(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_lt27(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_lt26(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(yvy6200)), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba) at position [12,0,0,0] we obtained the following new rules:

new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Zero))), Succ(yvy6200)), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ 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_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt26(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt24(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Zero))), Succ(yvy6200)), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Zero))), Succ(yvy6200)), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_lt27(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_lt25(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt26(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt24(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_lt27(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), h, ba)

The TRS R consists of the following rules:

new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_sr0(yvy3000, yvy4001) → new_primMulInt(yvy3000, yvy4001)
new_lt25(yvy134, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy134, new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT)
new_compare16(yvy400, yvy300) → new_primCmpInt(yvy400, yvy300)
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_lt24(yvy130, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy130, new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_lt26(yvy138, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy138, new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT)
new_lt27(yvy142, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy142, new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT)

The set Q consists of the following terms:

new_lt24(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_compare16(x0, x1)
new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_sr0(x0, x1)
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_lt25(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_lt27(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_lt26(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_lt27(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), h, ba) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ 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_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt26(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt24(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Zero))), Succ(yvy6200)), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Zero))), Succ(yvy6200)), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_lt25(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt26(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt24(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_lt27(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), h, ba)

The TRS R consists of the following rules:

new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_sr0(yvy3000, yvy4001) → new_primMulInt(yvy3000, yvy4001)
new_lt25(yvy134, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy134, new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT)
new_compare16(yvy400, yvy300) → new_primCmpInt(yvy400, yvy300)
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_lt24(yvy130, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy130, new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_lt26(yvy138, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy138, new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT)
new_lt27(yvy142, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy142, new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT)

The set Q consists of the following terms:

new_lt24(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_compare16(x0, x1)
new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_sr0(x0, x1)
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_lt25(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_lt27(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_lt26(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_lt25(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), h, ba) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)



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

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

new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt26(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt24(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Zero))), Succ(yvy6200)), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Zero))), Succ(yvy6200)), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt26(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt24(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_lt27(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), h, ba)

The TRS R consists of the following rules:

new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_sr0(yvy3000, yvy4001) → new_primMulInt(yvy3000, yvy4001)
new_lt25(yvy134, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy134, new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT)
new_compare16(yvy400, yvy300) → new_primCmpInt(yvy400, yvy300)
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_lt24(yvy130, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy130, new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_lt26(yvy138, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy138, new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT)
new_lt27(yvy142, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy142, new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT)

The set Q consists of the following terms:

new_lt24(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_compare16(x0, x1)
new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_sr0(x0, x1)
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_lt25(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_lt27(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_lt26(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

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

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

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

new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Zero))), Succ(yvy6200)), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Zero))), Succ(yvy6200)), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt26(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt26(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt24(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt24(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_lt27(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)

The TRS R consists of the following rules:

new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_sr0(yvy3000, yvy4001) → new_primMulInt(yvy3000, yvy4001)
new_lt24(yvy130, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy130, new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT)
new_compare16(yvy400, yvy300) → new_primCmpInt(yvy400, yvy300)
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_lt26(yvy138, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy138, new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT)
new_lt27(yvy142, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy142, new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT)

The set Q consists of the following terms:

new_lt24(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_compare16(x0, x1)
new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_sr0(x0, x1)
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_lt25(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_lt27(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_lt26(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

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

new_lt25(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)



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

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

new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Zero))), Succ(yvy6200)), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Zero))), Succ(yvy6200)), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt26(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt26(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt24(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt24(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_lt27(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)

The TRS R consists of the following rules:

new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_sr0(yvy3000, yvy4001) → new_primMulInt(yvy3000, yvy4001)
new_lt24(yvy130, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy130, new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT)
new_compare16(yvy400, yvy300) → new_primCmpInt(yvy400, yvy300)
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_lt26(yvy138, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy138, new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT)
new_lt27(yvy142, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy142, new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT)

The set Q consists of the following terms:

new_lt24(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_compare16(x0, x1)
new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_sr0(x0, x1)
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_lt27(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_lt26(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), h, ba) at position [11,1] we obtained the following new rules:

new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt26(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt24(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Zero))), Succ(yvy6200)), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Zero))), Succ(yvy6200)), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt26(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt24(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_lt27(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), h, ba)

The TRS R consists of the following rules:

new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_sr0(yvy3000, yvy4001) → new_primMulInt(yvy3000, yvy4001)
new_lt24(yvy130, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy130, new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT)
new_compare16(yvy400, yvy300) → new_primCmpInt(yvy400, yvy300)
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_lt26(yvy138, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy138, new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT)
new_lt27(yvy142, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy142, new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT)

The set Q consists of the following terms:

new_lt24(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_compare16(x0, x1)
new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_sr0(x0, x1)
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_lt27(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_lt26(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt26(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt24(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Zero))), Succ(yvy6200)), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Zero))), Succ(yvy6200)), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt26(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt24(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_lt27(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_sr0(yvy3000, yvy4001) → new_primMulInt(yvy3000, yvy4001)
new_lt24(yvy130, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy130, new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT)
new_compare16(yvy400, yvy300) → new_primCmpInt(yvy400, yvy300)
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_lt26(yvy138, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy138, new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT)
new_lt27(yvy142, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy142, new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT)

The set Q consists of the following terms:

new_lt24(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_compare16(x0, x1)
new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_sr0(x0, x1)
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_lt27(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_lt26(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt26(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt24(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Zero))), Succ(yvy6200)), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Zero))), Succ(yvy6200)), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt26(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt24(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_lt27(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_sr0(yvy3000, yvy4001) → new_primMulInt(yvy3000, yvy4001)
new_lt24(yvy130, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy130, new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT)
new_compare16(yvy400, yvy300) → new_primCmpInt(yvy400, yvy300)
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_lt26(yvy138, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy138, new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT)
new_lt27(yvy142, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy142, new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT)

The set Q consists of the following terms:

new_lt24(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_compare16(x0, x1)
new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_sr0(x0, x1)
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_lt27(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_lt26(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Zero))), Succ(yvy6200)), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba) at position [12,0,0,0,0] we obtained the following new rules:

new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Succ(Succ(Zero)), Succ(yvy6200)), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Succ(Succ(Zero)), Succ(yvy6200)), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt26(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt24(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Zero))), Succ(yvy6200)), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt26(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt24(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_lt27(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_sr0(yvy3000, yvy4001) → new_primMulInt(yvy3000, yvy4001)
new_lt24(yvy130, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy130, new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT)
new_compare16(yvy400, yvy300) → new_primCmpInt(yvy400, yvy300)
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_lt26(yvy138, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy138, new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT)
new_lt27(yvy142, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy142, new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT)

The set Q consists of the following terms:

new_lt24(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_compare16(x0, x1)
new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_sr0(x0, x1)
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_lt27(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_lt26(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Zero))), Succ(yvy6200)), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba) at position [12,0,0,0,0] we obtained the following new rules:

new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Succ(Succ(Zero)), Succ(yvy6200)), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Succ(Succ(Zero)), Succ(yvy6200)), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt26(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt24(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Succ(Succ(Zero)), Succ(yvy6200)), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt26(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt24(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_lt27(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_sr0(yvy3000, yvy4001) → new_primMulInt(yvy3000, yvy4001)
new_lt24(yvy130, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy130, new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT)
new_compare16(yvy400, yvy300) → new_primCmpInt(yvy400, yvy300)
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_lt26(yvy138, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy138, new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT)
new_lt27(yvy142, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy142, new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT)

The set Q consists of the following terms:

new_lt24(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_compare16(x0, x1)
new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_sr0(x0, x1)
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_lt27(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_lt26(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt26(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba) at position [12] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Succ(Succ(Zero)), Succ(yvy6200)), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt24(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Succ(Succ(Zero)), Succ(yvy6200)), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt26(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt24(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_lt27(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_sr0(yvy3000, yvy4001) → new_primMulInt(yvy3000, yvy4001)
new_lt24(yvy130, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy130, new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT)
new_compare16(yvy400, yvy300) → new_primCmpInt(yvy400, yvy300)
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_lt26(yvy138, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy138, new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT)
new_lt27(yvy142, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy142, new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT)

The set Q consists of the following terms:

new_lt24(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_compare16(x0, x1)
new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_sr0(x0, x1)
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_lt27(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_lt26(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt26(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba) at position [12] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Succ(Succ(Zero)), Succ(yvy6200)), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt24(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Succ(Succ(Zero)), Succ(yvy6200)), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt24(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_lt27(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_sr0(yvy3000, yvy4001) → new_primMulInt(yvy3000, yvy4001)
new_lt24(yvy130, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy130, new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT)
new_compare16(yvy400, yvy300) → new_primCmpInt(yvy400, yvy300)
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_lt26(yvy138, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy138, new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT)
new_lt27(yvy142, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy142, new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT)

The set Q consists of the following terms:

new_lt24(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_compare16(x0, x1)
new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_sr0(x0, x1)
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_lt27(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_lt26(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

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

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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Succ(Succ(Zero)), Succ(yvy6200)), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Succ(Succ(Zero)), Succ(yvy6200)), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt24(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt24(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_lt27(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_sr0(yvy3000, yvy4001) → new_primMulInt(yvy3000, yvy4001)
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_compare16(yvy400, yvy300) → new_primCmpInt(yvy400, yvy300)
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_lt24(yvy130, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy130, new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT)
new_lt27(yvy142, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy142, new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT)

The set Q consists of the following terms:

new_lt24(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_compare16(x0, x1)
new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_sr0(x0, x1)
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_lt27(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_lt26(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

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

new_lt26(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Succ(Succ(Zero)), Succ(yvy6200)), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Succ(Succ(Zero)), Succ(yvy6200)), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt24(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt24(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_lt27(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_sr0(yvy3000, yvy4001) → new_primMulInt(yvy3000, yvy4001)
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_compare16(yvy400, yvy300) → new_primCmpInt(yvy400, yvy300)
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_lt24(yvy130, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy130, new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT)
new_lt27(yvy142, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy142, new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT)

The set Q consists of the following terms:

new_lt24(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_compare16(x0, x1)
new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_sr0(x0, x1)
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_lt27(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba) at position [11,0,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Succ(Succ(Zero)), Succ(yvy6200)), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt24(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Succ(Succ(Zero)), Succ(yvy6200)), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt24(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_lt27(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_sr0(yvy3000, yvy4001) → new_primMulInt(yvy3000, yvy4001)
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_compare16(yvy400, yvy300) → new_primCmpInt(yvy400, yvy300)
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_lt24(yvy130, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy130, new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT)
new_lt27(yvy142, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy142, new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT)

The set Q consists of the following terms:

new_lt24(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_compare16(x0, x1)
new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_sr0(x0, x1)
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_lt27(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Succ(Succ(Zero)), Succ(yvy6200)), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba) at position [12,0,0,0,0,0] we obtained the following new rules:

new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Succ(Zero), Succ(yvy6200)), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt24(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Succ(Succ(Zero)), Succ(yvy6200)), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Succ(Zero), Succ(yvy6200)), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt24(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_lt27(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_sr0(yvy3000, yvy4001) → new_primMulInt(yvy3000, yvy4001)
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_compare16(yvy400, yvy300) → new_primCmpInt(yvy400, yvy300)
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_lt24(yvy130, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy130, new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT)
new_lt27(yvy142, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy142, new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT)

The set Q consists of the following terms:

new_lt24(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_compare16(x0, x1)
new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_sr0(x0, x1)
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_lt27(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba) at position [12,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ 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_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt24(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Succ(Succ(Zero)), Succ(yvy6200)), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Succ(Zero), Succ(yvy6200)), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt24(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_lt27(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_sr0(yvy3000, yvy4001) → new_primMulInt(yvy3000, yvy4001)
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_compare16(yvy400, yvy300) → new_primCmpInt(yvy400, yvy300)
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_lt24(yvy130, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy130, new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT)
new_lt27(yvy142, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy142, new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT)

The set Q consists of the following terms:

new_lt24(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_compare16(x0, x1)
new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_sr0(x0, x1)
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_lt27(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Succ(Succ(Zero)), Succ(yvy6200)), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba) at position [12,0,0,0,0,0] we obtained the following new rules:

new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Succ(Zero), Succ(yvy6200)), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ 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_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt24(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Succ(Zero), Succ(yvy6200)), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Succ(Zero), Succ(yvy6200)), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt24(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_lt27(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_sr0(yvy3000, yvy4001) → new_primMulInt(yvy3000, yvy4001)
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_compare16(yvy400, yvy300) → new_primCmpInt(yvy400, yvy300)
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_lt24(yvy130, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy130, new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT)
new_lt27(yvy142, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy142, new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT)

The set Q consists of the following terms:

new_lt24(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_compare16(x0, x1)
new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_sr0(x0, x1)
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_lt27(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba) at position [12,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ 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_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt24(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Succ(Zero), Succ(yvy6200)), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Succ(Zero), Succ(yvy6200)), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt24(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_lt27(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_sr0(yvy3000, yvy4001) → new_primMulInt(yvy3000, yvy4001)
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_compare16(yvy400, yvy300) → new_primCmpInt(yvy400, yvy300)
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_lt24(yvy130, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy130, new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT)
new_lt27(yvy142, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy142, new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT)

The set Q consists of the following terms:

new_lt24(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_compare16(x0, x1)
new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_sr0(x0, x1)
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_lt27(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), h, ba) at position [11,1] we obtained the following new rules:

new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), h, ba)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ 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_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt24(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Succ(Zero), Succ(yvy6200)), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Succ(Zero), Succ(yvy6200)), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt24(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_lt27(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_sr0(yvy3000, yvy4001) → new_primMulInt(yvy3000, yvy4001)
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_compare16(yvy400, yvy300) → new_primCmpInt(yvy400, yvy300)
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_lt24(yvy130, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy130, new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT)
new_lt27(yvy142, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy142, new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT)

The set Q consists of the following terms:

new_lt24(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_compare16(x0, x1)
new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_sr0(x0, x1)
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_lt27(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt24(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba) at position [12] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ 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_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt24(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Succ(Zero), Succ(yvy6200)), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Succ(Zero), Succ(yvy6200)), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_lt27(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_sr0(yvy3000, yvy4001) → new_primMulInt(yvy3000, yvy4001)
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_compare16(yvy400, yvy300) → new_primCmpInt(yvy400, yvy300)
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_lt24(yvy130, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy130, new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT)
new_lt27(yvy142, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy142, new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT)

The set Q consists of the following terms:

new_lt24(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_compare16(x0, x1)
new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_sr0(x0, x1)
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_lt27(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt24(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba) at position [12] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Succ(Zero), Succ(yvy6200)), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Succ(Zero), Succ(yvy6200)), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_lt27(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_sr0(yvy3000, yvy4001) → new_primMulInt(yvy3000, yvy4001)
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_compare16(yvy400, yvy300) → new_primCmpInt(yvy400, yvy300)
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_lt24(yvy130, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy130, new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT)
new_lt27(yvy142, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy142, new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT)

The set Q consists of the following terms:

new_lt24(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_compare16(x0, x1)
new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_sr0(x0, x1)
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_lt27(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

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

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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Succ(Zero), Succ(yvy6200)), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Succ(Zero), Succ(yvy6200)), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_lt27(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_sr0(yvy3000, yvy4001) → new_primMulInt(yvy3000, yvy4001)
new_compare16(yvy400, yvy300) → new_primCmpInt(yvy400, yvy300)
new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_lt27(yvy142, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy142, new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT)

The set Q consists of the following terms:

new_lt24(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_compare16(x0, x1)
new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_sr0(x0, x1)
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_lt27(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

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

new_lt24(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Succ(Zero), Succ(yvy6200)), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Succ(Zero), Succ(yvy6200)), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_lt27(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_sr0(yvy3000, yvy4001) → new_primMulInt(yvy3000, yvy4001)
new_compare16(yvy400, yvy300) → new_primCmpInt(yvy400, yvy300)
new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_lt27(yvy142, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy142, new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT)

The set Q consists of the following terms:

new_compare16(x0, x1)
new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_sr0(x0, x1)
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_lt27(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba) at position [12,0,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Succ(Zero), Succ(yvy6200)), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Succ(Zero), Succ(yvy6200)), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_lt27(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_sr0(yvy3000, yvy4001) → new_primMulInt(yvy3000, yvy4001)
new_compare16(yvy400, yvy300) → new_primCmpInt(yvy400, yvy300)
new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_lt27(yvy142, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy142, new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT)

The set Q consists of the following terms:

new_compare16(x0, x1)
new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_sr0(x0, x1)
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_lt27(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba) at position [12,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Succ(Zero), Succ(yvy6200)), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Succ(Zero), Succ(yvy6200)), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_lt27(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_sr0(yvy3000, yvy4001) → new_primMulInt(yvy3000, yvy4001)
new_compare16(yvy400, yvy300) → new_primCmpInt(yvy400, yvy300)
new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_lt27(yvy142, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy142, new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT)

The set Q consists of the following terms:

new_compare16(x0, x1)
new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_sr0(x0, x1)
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_lt27(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), h, ba) at position [11,1] we obtained the following new rules:

new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Succ(Zero), Succ(yvy6200)), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Succ(Zero), Succ(yvy6200)), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_lt27(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_sr0(yvy3000, yvy4001) → new_primMulInt(yvy3000, yvy4001)
new_compare16(yvy400, yvy300) → new_primCmpInt(yvy400, yvy300)
new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_lt27(yvy142, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy142, new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT)

The set Q consists of the following terms:

new_compare16(x0, x1)
new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_sr0(x0, x1)
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_lt27(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba) at position [12,0,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Succ(Zero), Succ(yvy6200)), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Succ(Zero), Succ(yvy6200)), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_lt27(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_sr0(yvy3000, yvy4001) → new_primMulInt(yvy3000, yvy4001)
new_compare16(yvy400, yvy300) → new_primCmpInt(yvy400, yvy300)
new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_lt27(yvy142, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy142, new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT)

The set Q consists of the following terms:

new_compare16(x0, x1)
new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_sr0(x0, x1)
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_lt27(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Succ(Zero), Succ(yvy6200)), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba) at position [12,0,0,0,0,0,0] we obtained the following new rules:

new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Zero, Succ(yvy6200)), yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Zero, Succ(yvy6200)), yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Succ(Zero), Succ(yvy6200)), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_lt27(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_sr0(yvy3000, yvy4001) → new_primMulInt(yvy3000, yvy4001)
new_compare16(yvy400, yvy300) → new_primCmpInt(yvy400, yvy300)
new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_lt27(yvy142, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy142, new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT)

The set Q consists of the following terms:

new_compare16(x0, x1)
new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_sr0(x0, x1)
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_lt27(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Succ(Zero), Succ(yvy6200)), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba) at position [12,0,0,0,0,0,0] we obtained the following new rules:

new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Zero, Succ(yvy6200)), yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Zero, Succ(yvy6200)), yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Zero, Succ(yvy6200)), yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_lt27(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_sr0(yvy3000, yvy4001) → new_primMulInt(yvy3000, yvy4001)
new_compare16(yvy400, yvy300) → new_primCmpInt(yvy400, yvy300)
new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_lt27(yvy142, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy142, new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT)

The set Q consists of the following terms:

new_compare16(x0, x1)
new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_sr0(x0, x1)
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_lt27(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba) at position [12,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Zero, Succ(yvy6200)), yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Zero, Succ(yvy6200)), yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_lt27(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_sr0(yvy3000, yvy4001) → new_primMulInt(yvy3000, yvy4001)
new_compare16(yvy400, yvy300) → new_primCmpInt(yvy400, yvy300)
new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_lt27(yvy142, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy142, new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT)

The set Q consists of the following terms:

new_compare16(x0, x1)
new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_sr0(x0, x1)
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_lt27(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba) at position [11,0,0,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Zero, Succ(yvy6200)), yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Zero, Succ(yvy6200)), yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_lt27(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_sr0(yvy3000, yvy4001) → new_primMulInt(yvy3000, yvy4001)
new_compare16(yvy400, yvy300) → new_primCmpInt(yvy400, yvy300)
new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_lt27(yvy142, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy142, new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT)

The set Q consists of the following terms:

new_compare16(x0, x1)
new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_sr0(x0, x1)
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_lt27(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Zero, Succ(yvy6200)), yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Zero, Succ(yvy6200)), yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_lt27(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_sr0(yvy3000, yvy4001) → new_primMulInt(yvy3000, yvy4001)
new_compare16(yvy400, yvy300) → new_primCmpInt(yvy400, yvy300)
new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_lt27(yvy142, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy142, new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT)

The set Q consists of the following terms:

new_compare16(x0, x1)
new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_sr0(x0, x1)
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_lt27(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_lt27(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), h, ba) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Zero, Succ(yvy6200)), yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Zero, Succ(yvy6200)), yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_sr0(yvy3000, yvy4001) → new_primMulInt(yvy3000, yvy4001)
new_compare16(yvy400, yvy300) → new_primCmpInt(yvy400, yvy300)
new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_lt27(yvy142, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy142, new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT)

The set Q consists of the following terms:

new_compare16(x0, x1)
new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_sr0(x0, x1)
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_lt27(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

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

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

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

new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Zero, Succ(yvy6200)), yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Zero, Succ(yvy6200)), yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)

The TRS R consists of the following rules:

new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_sr0(yvy3000, yvy4001) → new_primMulInt(yvy3000, yvy4001)
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_compare16(yvy400, yvy300) → new_primCmpInt(yvy400, yvy300)

The set Q consists of the following terms:

new_compare16(x0, x1)
new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_sr0(x0, x1)
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_lt27(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

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

new_lt27(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)



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

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

new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Zero, Succ(yvy6200)), yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Zero, Succ(yvy6200)), yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_sr0(yvy3000, yvy4001) → new_primMulInt(yvy3000, yvy4001)
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_compare16(yvy400, yvy300) → new_primCmpInt(yvy400, yvy300)

The set Q consists of the following terms:

new_compare16(x0, x1)
new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_sr0(x0, x1)
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba) at position [11,0,0,1] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Zero, Succ(yvy6200)), yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Zero, Succ(yvy6200)), yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_sr0(yvy3000, yvy4001) → new_primMulInt(yvy3000, yvy4001)
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_compare16(yvy400, yvy300) → new_primCmpInt(yvy400, yvy300)

The set Q consists of the following terms:

new_compare16(x0, x1)
new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_sr0(x0, x1)
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_compare16(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Zero, Succ(yvy6200)), yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Zero, Succ(yvy6200)), yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_sr0(yvy3000, yvy4001) → new_primMulInt(yvy3000, yvy4001)
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_compare16(yvy400, yvy300) → new_primCmpInt(yvy400, yvy300)

The set Q consists of the following terms:

new_compare16(x0, x1)
new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_sr0(x0, x1)
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

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

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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Zero, Succ(yvy6200)), yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Zero, Succ(yvy6200)), yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Zero) → EQ
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_sr0(yvy3000, yvy4001) → new_primMulInt(yvy3000, yvy4001)
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)

The set Q consists of the following terms:

new_compare16(x0, x1)
new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_sr0(x0, x1)
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

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

new_compare16(x0, x1)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
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                                                                              ↳ QDP
                                                                                ↳ Rewriting
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                                                                                        ↳ Rewriting
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                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
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                                                                                                                    ↳ Rewriting
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                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ QReductionProof
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
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                                                                                                                                                                                    ↳ 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_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Zero, Succ(yvy6200)), yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Zero, Succ(yvy6200)), yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)

The TRS R consists of the following rules:

new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Zero) → EQ
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_sr0(yvy3000, yvy4001) → new_primMulInt(yvy3000, yvy4001)
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)

The set Q consists of the following terms:

new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_sr0(x0, x1)
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba) at position [12,0,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Zero, Succ(yvy6200)), yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Zero, Succ(yvy6200)), yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Zero) → EQ
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_sr0(yvy3000, yvy4001) → new_primMulInt(yvy3000, yvy4001)
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)

The set Q consists of the following terms:

new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_sr0(x0, x1)
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba) at position [11,0,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Zero, Succ(yvy6200)), yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Zero, Succ(yvy6200)), yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Zero) → EQ
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_sr0(yvy3000, yvy4001) → new_primMulInt(yvy3000, yvy4001)
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)

The set Q consists of the following terms:

new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_sr0(x0, x1)
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Zero, Succ(yvy6200)), yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba) at position [12,0,0,0,0,0,0,0] we obtained the following new rules:

new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
                                                                                                                                ↳ Rewriting
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ Rewriting
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ QReductionProof
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ QReductionProof
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ 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_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Zero, Succ(yvy6200)), yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Zero) → EQ
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_sr0(yvy3000, yvy4001) → new_primMulInt(yvy3000, yvy4001)
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)

The set Q consists of the following terms:

new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_sr0(x0, x1)
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba) at position [11,0,0,1] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
                                                                                                                                ↳ Rewriting
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ Rewriting
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ QReductionProof
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ QReductionProof
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ 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_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Zero, Succ(yvy6200)), yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Zero) → EQ
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_sr0(yvy3000, yvy4001) → new_primMulInt(yvy3000, yvy4001)
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)

The set Q consists of the following terms:

new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_sr0(x0, x1)
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba) at position [11,0,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
                                                                                                                                ↳ Rewriting
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ Rewriting
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ QReductionProof
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ QReductionProof
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ 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_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Zero, Succ(yvy6200)), yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Zero) → EQ
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_sr0(yvy3000, yvy4001) → new_primMulInt(yvy3000, yvy4001)
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)

The set Q consists of the following terms:

new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_sr0(x0, x1)
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba) at position [12,0,0,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
                                                                                                                                ↳ Rewriting
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ Rewriting
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ QReductionProof
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ QReductionProof
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ 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_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Zero, Succ(yvy6200)), yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Zero) → EQ
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_sr0(yvy3000, yvy4001) → new_primMulInt(yvy3000, yvy4001)
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)

The set Q consists of the following terms:

new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_sr0(x0, x1)
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba) at position [12,0,0,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Zero, Succ(yvy6200)), yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Zero) → EQ
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_sr0(yvy3000, yvy4001) → new_primMulInt(yvy3000, yvy4001)
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)

The set Q consists of the following terms:

new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_sr0(x0, x1)
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(Zero, Succ(yvy6200)), yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba) at position [12,0,0,0,0,0,0,0] we obtained the following new rules:

new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Zero) → EQ
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_sr0(yvy3000, yvy4001) → new_primMulInt(yvy3000, yvy4001)
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)

The set Q consists of the following terms:

new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_sr0(x0, x1)
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba) at position [12,0,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Zero) → EQ
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_sr0(yvy3000, yvy4001) → new_primMulInt(yvy3000, yvy4001)
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)

The set Q consists of the following terms:

new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_sr0(x0, x1)
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba) at position [11,0,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Zero) → EQ
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_sr0(yvy3000, yvy4001) → new_primMulInt(yvy3000, yvy4001)
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)

The set Q consists of the following terms:

new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_sr0(x0, x1)
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

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

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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)

The set Q consists of the following terms:

new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_sr0(x0, x1)
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

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

new_sr0(x0, x1)



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)

The set Q consists of the following terms:

new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba) at position [12,0,0,0,0,0,0] we obtained the following new rules:

new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)

The set Q consists of the following terms:

new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba) at position [12,0,0,1] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)

The set Q consists of the following terms:

new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba) at position [11,0,0,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)

The set Q consists of the following terms:

new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba) at position [12,0,0,0,0,0,0] we obtained the following new rules:

new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)

The set Q consists of the following terms:

new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba) at position [12,0,0,1] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)

The set Q consists of the following terms:

new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba) at position [11,0,1] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
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                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ Rewriting
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ QReductionProof
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
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                                                                                                                                                                                      ↳ 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
                                                                                                                                                                                                                                                            ↳ 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_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)

The set Q consists of the following terms:

new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba) at position [12,0,0,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)

The set Q consists of the following terms:

new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba) at position [11,0,0,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)

The set Q consists of the following terms:

new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba) at position [11,0,0,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)

The set Q consists of the following terms:

new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba) at position [12,0,0,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)

The set Q consists of the following terms:

new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

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

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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)

The TRS R consists of the following rules:

new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)

The set Q consists of the following terms:

new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

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

new_sIZE_RATIO



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)

The TRS R consists of the following rules:

new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)

The set Q consists of the following terms:

new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba) at position [12,0,0,1] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)

The TRS R consists of the following rules:

new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)

The set Q consists of the following terms:

new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba) at position [12,0,0,1] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)

The TRS R consists of the following rules:

new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)

The set Q consists of the following terms:

new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba) at position [12,0,0,0,0,0] we obtained the following new rules:

new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat1(yvy6200, yvy6200))), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat1(yvy6200, yvy6200))), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)

The TRS R consists of the following rules:

new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)

The set Q consists of the following terms:

new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba) at position [11,0,0,1] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat1(yvy6200, yvy6200))), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)

The TRS R consists of the following rules:

new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)

The set Q consists of the following terms:

new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

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

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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat1(yvy6200, yvy6200))), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)

The TRS R consists of the following rules:

new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)

The set Q consists of the following terms:

new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

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

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



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat1(yvy6200, yvy6200))), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)

The TRS R consists of the following rules:

new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)

The set Q consists of the following terms:

new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba) at position [11,0,0,1] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat1(yvy6200, yvy6200))), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)

The TRS R consists of the following rules:

new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)

The set Q consists of the following terms:

new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba) at position [12,0,0,1] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat1(yvy6200, yvy6200))), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)

The TRS R consists of the following rules:

new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)

The set Q consists of the following terms:

new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba) at position [12,0,1] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Succ(yvy6200))), LT), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat1(yvy6200, yvy6200))), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)

The TRS R consists of the following rules:

new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)

The set Q consists of the following terms:

new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba) at position [11,0,0,1] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat1(yvy6200, yvy6200))), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)

The TRS R consists of the following rules:

new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)

The set Q consists of the following terms:

new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba) at position [12,0,0,1] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat1(yvy6200, yvy6200))), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)

The TRS R consists of the following rules:

new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)

The set Q consists of the following terms:

new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba) at position [11,0,0,1] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat1(yvy6200, yvy6200))), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)

The TRS R consists of the following rules:

new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)

The set Q consists of the following terms:

new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

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

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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat1(yvy6200, yvy6200))), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)

The TRS R consists of the following rules:

new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)

The set Q consists of the following terms:

new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

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

new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat1(yvy6200, yvy6200))), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)

The set Q consists of the following terms:

new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba) at position [11,0,0,1] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat1(yvy6200, yvy6200))), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)

The TRS R consists of the following rules:

new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)

The set Q consists of the following terms:

new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT), h, ba) at position [11,0,1] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat1(yvy6200, yvy6200))), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)

The TRS R consists of the following rules:

new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)

The set Q consists of the following terms:

new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba) at position [12,0,1] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Succ(yvy6200))), LT), h, ba)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
                                                                                                                                ↳ Rewriting
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ Rewriting
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ QReductionProof
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ QReductionProof
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ QReductionProof
                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                ↳ QReductionProof
                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                                                              ↳ QDP
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                                                                                                                                                                                                                                                                                            ↳ 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
                                                                                                                                                                                                                                                                                                                                                                    ↳ 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_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat1(yvy6200, yvy6200))), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)

The TRS R consists of the following rules:

new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)

The set Q consists of the following terms:

new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(yvy6200), yvy6200), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba) at position [12,0,0,0,0,0] we obtained the following new rules:

new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat1(yvy6200, yvy6200))), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
                                                                                                                                ↳ Rewriting
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ Rewriting
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ QReductionProof
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
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                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ QReductionProof
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ QReductionProof
                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                              ↳ QDP
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                                                                                                                                                                                                                                  ↳ QDP
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                                                                                                                                                                                                                                      ↳ QDP
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                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                  ↳ QDP
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                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                ↳ QReductionProof
                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                        ↳ Rewriting
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                                                                                                                                                                                                                                                                                                    ↳ 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
                                                                                                                                                                                                                                                                                                                                                                    ↳ 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_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat1(yvy6200, yvy6200))), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat1(yvy6200, yvy6200))), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)

The TRS R consists of the following rules:

new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)

The set Q consists of the following terms:

new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba) at position [12,0,0,1] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat1(yvy6200, yvy6200))), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat1(yvy6200, yvy6200))), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)

The TRS R consists of the following rules:

new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)

The set Q consists of the following terms:

new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba) at position [12,0,0,1] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat1(yvy6200, yvy6200))), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat1(yvy6200, yvy6200))), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)

The TRS R consists of the following rules:

new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)

The set Q consists of the following terms:

new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba) at position [11,0,0,1] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
                                                                                                                                ↳ Rewriting
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ Rewriting
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ QReductionProof
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ QReductionProof
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ QReductionProof
                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                ↳ QReductionProof
                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                                        ↳ 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
                                                                                                                                                                                                                                                                                                                                                                    ↳ 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_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat1(yvy6200, yvy6200))), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat1(yvy6200, yvy6200))), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)

The TRS R consists of the following rules:

new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)

The set Q consists of the following terms:

new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat1(yvy6200, yvy6200))), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba) at position [12,0,0,0,0] we obtained the following new rules:

new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(yvy6200, yvy6200)), yvy6200))), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
                                                                                                                                ↳ Rewriting
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ Rewriting
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ QReductionProof
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
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                                                                                                                                                              ↳ QDP
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                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ QReductionProof
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ QReductionProof
                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                              ↳ QDP
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                                                                                                                                                                                                                                  ↳ QDP
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                                                                                                                                                                                                                                      ↳ QDP
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                                                                                                                                                                                                                                          ↳ QDP
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                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                ↳ QReductionProof
                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                        ↳ Rewriting
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                                                                                                                                                                                                                                                                                                  ↳ 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
                                                                                                                                                                                                                                                                                                                                                                    ↳ 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_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(yvy6200, yvy6200)), yvy6200))), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat1(yvy6200, yvy6200))), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)

The TRS R consists of the following rules:

new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)

The set Q consists of the following terms:

new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba) at position [11,0,1] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Zero)), LT), h, ba)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
                                                                                                                                ↳ Rewriting
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ Rewriting
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ QReductionProof
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ QReductionProof
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ QReductionProof
                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                ↳ QReductionProof
                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                                                  ↳ QDP
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                                                                                                                                                                                                                                                                                      ↳ 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
                                                                                                                                                                                                                                                                                                                                                                    ↳ 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_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(yvy6200, yvy6200)), yvy6200))), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat1(yvy6200, yvy6200))), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)

The TRS R consists of the following rules:

new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)

The set Q consists of the following terms:

new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat1(yvy6200, yvy6200))), yvy6200), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba) at position [12,0,0,0,0] we obtained the following new rules:

new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(yvy6200, yvy6200)), yvy6200))), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(yvy6200, yvy6200)), yvy6200))), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(yvy6200, yvy6200)), yvy6200))), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)

The TRS R consists of the following rules:

new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)

The set Q consists of the following terms:

new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba) at position [12,0,1] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Succ(yvy6200))), LT), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(yvy6200, yvy6200)), yvy6200))), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(yvy6200, yvy6200)), yvy6200))), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)

The TRS R consists of the following rules:

new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)

The set Q consists of the following terms:

new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT), h, ba) at position [12,0,1] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Succ(yvy6200))), LT), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(yvy6200, yvy6200)), yvy6200))), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(yvy6200, yvy6200)), yvy6200))), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)

The TRS R consists of the following rules:

new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)

The set Q consists of the following terms:

new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT), h, ba) at position [11,0,1] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Zero)), LT), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(yvy6200, yvy6200)), yvy6200))), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(yvy6200, yvy6200)), yvy6200))), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)

The TRS R consists of the following rules:

new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)

The set Q consists of the following terms:

new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(yvy6200, yvy6200)), yvy6200))), yvy6200), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba) at position [12,0,0,0] we obtained the following new rules:

new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(yvy6200, yvy6200)), yvy6200)), yvy6200))), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(yvy6200, yvy6200)), yvy6200))), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(yvy6200, yvy6200)), yvy6200)), yvy6200))), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Zero)), LT), h, ba)

The TRS R consists of the following rules:

new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)

The set Q consists of the following terms:

new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(yvy6200, yvy6200)), yvy6200))), yvy6200), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba) at position [12,0,0,0] we obtained the following new rules:

new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(yvy6200, yvy6200)), yvy6200)), yvy6200))), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(yvy6200, yvy6200)), yvy6200)), yvy6200))), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(yvy6200, yvy6200)), yvy6200)), yvy6200))), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)

The TRS R consists of the following rules:

new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)

The set Q consists of the following terms:

new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(yvy6200, yvy6200)), yvy6200)), yvy6200))), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba) at position [12,0,0] we obtained the following new rules:

new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(yvy6200, yvy6200)), yvy6200)), yvy6200)), yvy6200)))), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
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Q DP problem:
The TRS P consists of the following rules:

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(yvy6200, yvy6200)), yvy6200)), yvy6200))), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Zero)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(yvy6200, yvy6200)), yvy6200)), yvy6200)), yvy6200)))), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)

The TRS R consists of the following rules:

new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)

The set Q consists of the following terms:

new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(yvy6200, yvy6200)), yvy6200)), yvy6200))), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba) at position [12,0,0] we obtained the following new rules:

new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(yvy6200, yvy6200)), yvy6200)), yvy6200)), yvy6200)))), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(yvy6200, yvy6200)), yvy6200)), yvy6200)), yvy6200)))), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(yvy6200, yvy6200)), yvy6200)), yvy6200)), yvy6200)))), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)

The TRS R consists of the following rules:

new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)

The set Q consists of the following terms:

new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(yvy6200, yvy6200)), yvy6200)), yvy6200)), yvy6200)))), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba) at position [12,1] we obtained the following new rules:

new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(yvy6200, yvy6200)), yvy6200)), yvy6200)), yvy6200)))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(yvy6200, yvy6200)), yvy6200)), yvy6200)), yvy6200)))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Zero)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(yvy6200, yvy6200)), yvy6200)), yvy6200)), yvy6200)))), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)

The TRS R consists of the following rules:

new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)

The set Q consists of the following terms:

new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

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

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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(yvy6200, yvy6200)), yvy6200)), yvy6200)), yvy6200)))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(yvy6200, yvy6200)), yvy6200)), yvy6200)), yvy6200)))), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)

The TRS R consists of the following rules:

new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ

The set Q consists of the following terms:

new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

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

new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Zero)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(yvy6200, yvy6200)), yvy6200)), yvy6200)), yvy6200)))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Zero)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(yvy6200, yvy6200)), yvy6200)), yvy6200)), yvy6200)))), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)

The TRS R consists of the following rules:

new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ

The set Q consists of the following terms:

new_primMulNat0(Zero, Zero)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(yvy6200, yvy6200)), yvy6200)), yvy6200)), yvy6200)))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), h, ba) at position [12,1] we obtained the following new rules:

new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(yvy6200, yvy6200)), yvy6200)), yvy6200)), yvy6200)))), yvy52), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(yvy6200, yvy6200)), yvy6200)), yvy6200)), yvy6200)))), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(yvy6200, yvy6200)), yvy6200)), yvy6200)), yvy6200)))), yvy52), h, ba)

The TRS R consists of the following rules:

new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ

The set Q consists of the following terms:

new_primMulNat0(Zero, Zero)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(yvy6200, yvy6200)), yvy6200)), yvy6200)), yvy6200)))), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba) at position [12,1] we obtained the following new rules:

new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(yvy6200, yvy6200)), yvy6200)), yvy6200)), yvy6200)))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(yvy6200, yvy6200)), yvy6200)), yvy6200)), yvy6200)))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Zero)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(yvy6200, yvy6200)), yvy6200)), yvy6200)), yvy6200)))), yvy52), h, ba)

The TRS R consists of the following rules:

new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ

The set Q consists of the following terms:

new_primMulNat0(Zero, Zero)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

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

↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
                                                                                                                                ↳ Rewriting
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ Rewriting
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ QReductionProof
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ QReductionProof
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ QReductionProof
                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                ↳ QReductionProof
                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                                        ↳ 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
                                                                                                                                                                                                                                                                                                                                                                    ↳ 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
                                                                                                                                                                                                                                                                                                                                                                                                                                                    ↳ 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_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(yvy6200, yvy6200)), yvy6200)), yvy6200)), yvy6200)))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Zero)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(yvy6200, yvy6200)), yvy6200)), yvy6200)), yvy6200)))), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)

The TRS R consists of the following rules:

new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ

The set Q consists of the following terms:

new_primMulNat0(Zero, Zero)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

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

new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
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                                  ↳ QDP
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                                    ↳ UsableRulesProof
                                      ↳ QDP
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                                                                                                                                                                                                                                                                                                                                                              ↳ 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
                                                                                                                                                                                                                                                                                                                                                                                                                                                    ↳ 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_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(yvy6200, yvy6200)), yvy6200)), yvy6200)), yvy6200)))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(yvy6200, yvy6200)), yvy6200)), yvy6200)), yvy6200)))), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)

The TRS R consists of the following rules:

new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ

The set Q consists of the following terms:

new_primMulNat0(Zero, Zero)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(yvy6200, yvy6200)), yvy6200)), yvy6200)), yvy6200)))), new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)), h, ba) at position [12,1] we obtained the following new rules:

new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(yvy6200, yvy6200)), yvy6200)), yvy6200)), yvy6200)))), yvy52), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(yvy6200, yvy6200)), yvy6200)), yvy6200)), yvy6200)))), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Zero)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(yvy6200, yvy6200)), yvy6200)), yvy6200)), yvy6200)))), yvy52), h, ba)

The TRS R consists of the following rules:

new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Zero) → EQ
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ

The set Q consists of the following terms:

new_primMulNat0(Zero, Zero)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

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

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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(yvy6200, yvy6200)), yvy6200)), yvy6200)), yvy6200)))), yvy52), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(yvy6200, yvy6200)), yvy6200)), yvy6200)), yvy6200)))), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Zero) → EQ
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT

The set Q consists of the following terms:

new_primMulNat0(Zero, Zero)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

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

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



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(yvy6200, yvy6200)), yvy6200)), yvy6200)), yvy6200)))), yvy52), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Zero)), LT), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(yvy6200, yvy6200)), yvy6200)), yvy6200)), yvy6200)))), yvy52), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Zero) → EQ
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT

The set Q consists of the following terms:

new_primMulNat0(Zero, Zero)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

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


The following pairs can be oriented strictly and are deleted.


new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(yvy6200, yvy6200)), yvy6200)), yvy6200)), yvy6200)))), yvy52), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), yvy52), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), yvy52), h, ba)
new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Succ(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(Succ(new_primPlusNat1(yvy6200, yvy6200)), yvy6200)), yvy6200)), yvy6200)))), yvy52), h, ba)
The remaining pairs can at least be oriented weakly.

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
Used ordering: Polynomial interpretation [25]:

POL(Branch(x1, x2, x3, x4, x5)) = 1 + x2 + x4 + x5   
POL(EQ) = 1   
POL(False) = 0   
POL(GT) = 1   
POL(LT) = 1   
POL(Neg(x1)) = 0   
POL(Pos(x1)) = 0   
POL(Succ(x1)) = 0   
POL(True) = 0   
POL(Zero) = 0   
POL(new_esEs12(x1, x2)) = 0   
POL(new_mkVBalBranch(x1, x2, x3, x4, x5, x6)) = x3 + x4   
POL(new_mkVBalBranch3MkVBalBranch1(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15)) = 1 + x10 + x2 + x4 + x5   
POL(new_mkVBalBranch3MkVBalBranch10(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = 1 + x2 + x4 + x5 + x7 + x9   
POL(new_mkVBalBranch3MkVBalBranch11(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15)) = 1 + x10 + x2 + x4 + x5   
POL(new_mkVBalBranch3MkVBalBranch12(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = 1 + x2 + x4 + x5 + x9   
POL(new_mkVBalBranch3MkVBalBranch2(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15)) = 1 + x10 + x2 + x4 + x5 + x7 + x9   
POL(new_mkVBalBranch3MkVBalBranch20(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = 1 + x10 + x2 + x4 + x5 + x7   
POL(new_mkVBalBranch3MkVBalBranch21(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = 1 + x2 + x4 + x5 + x7 + x8 + x9   
POL(new_mkVBalBranch3MkVBalBranch22(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15)) = 1 + x10 + x2 + x4 + x5 + x7 + x9   
POL(new_mkVBalBranch3MkVBalBranch23(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = x12 + x2 + x4 + x5 + x7 + x8 + x9   
POL(new_mkVBalBranch3MkVBalBranch24(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = 1 + x2 + x4 + x5 + x7 + x9   
POL(new_mkVBalBranch3MkVBalBranch25(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = 1 + x10 + x2 + x4 + x5 + x9   
POL(new_mkVBalBranch3MkVBalBranch26(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = 1 + x2 + x4 + x5 + x8 + x9   
POL(new_primCmpInt(x1, x2)) = 1   
POL(new_primCmpNat0(x1, x2)) = 1   
POL(new_primMulInt(x1, x2)) = 1   
POL(new_primMulNat0(x1, x2)) = 1   
POL(new_primPlusNat0(x1, x2)) = 0   
POL(new_primPlusNat1(x1, x2)) = 0   

The following usable rules [17] were oriented:

new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ



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

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

new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch24(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch25(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch21(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch26(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch22(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch11(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Pos(Succ(yvy6200))), LT), h, ba)
new_mkVBalBranch3MkVBalBranch23(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch12(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_esEs12(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy52), Neg(Zero)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkVBalBranch(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba)
new_mkVBalBranch3MkVBalBranch2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch20(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch10(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkVBalBranch(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_primCmpNat0(Zero, Zero) → EQ
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_esEs12(LT, LT) → True
new_esEs12(GT, LT) → False
new_esEs12(EQ, LT) → False
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT

The set Q consists of the following terms:

new_primMulNat0(Zero, Zero)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs12(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_primPlusNat1(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs12(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpNat0(Zero, Zero)
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Zero, x0)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primMulNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(LT, LT)
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat1(Succ(x0), Zero)
new_esEs12(EQ, GT)
new_esEs12(GT, EQ)
new_primCmpNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 0 SCCs with 20 less nodes.

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

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

new_splitLT3(:(yvy300, yvy301), yvy31, yvy32, yvy33, yvy34, :(yvy400, yvy401), bb, bc) → new_splitLT2(yvy300, yvy301, yvy31, yvy32, yvy33, yvy34, yvy400, yvy401, new_primCompAux1(yvy400, yvy300, new_compare0(yvy401, yvy301, bb), bb), bb, bc)
new_splitLT11(yvy36, yvy37, yvy38, yvy39, yvy40, yvy41, yvy42, yvy43, GT, h, ba) → new_splitLT(yvy41, yvy42, yvy43, h, ba)
new_splitLT3(:(yvy300, yvy301), yvy31, yvy32, Branch(yvy330, yvy331, yvy332, yvy333, yvy334), yvy34, [], bb, bc) → new_splitLT3(yvy330, yvy331, yvy332, yvy333, yvy334, [], bb, bc)
new_splitLT3([], yvy31, yvy32, yvy33, yvy34, [], bb, bc) → new_splitLT10(yvy31, yvy32, yvy33, yvy34, new_compare0([], [], bb), bb, bc)
new_splitLT(Branch(yvy400, yvy401, yvy402, yvy403, yvy404), yvy42, yvy43, h, ba) → new_splitLT3(yvy400, yvy401, yvy402, yvy403, yvy404, :(yvy42, yvy43), h, ba)
new_splitLT2(yvy36, yvy37, yvy38, yvy39, Branch(yvy400, yvy401, yvy402, yvy403, yvy404), yvy41, yvy42, yvy43, LT, h, ba) → new_splitLT3(yvy400, yvy401, yvy402, yvy403, yvy404, :(yvy42, yvy43), h, ba)
new_splitLT3([], yvy31, yvy32, yvy33, yvy34, :(yvy400, yvy401), bb, bc) → new_splitLT1(yvy31, yvy32, yvy33, yvy34, yvy400, yvy401, new_compare0(:(yvy400, yvy401), [], bb), bb, bc)
new_splitLT2(yvy36, yvy37, yvy38, yvy39, yvy40, yvy41, yvy42, yvy43, EQ, h, ba) → new_splitLT11(yvy36, yvy37, yvy38, yvy39, yvy40, yvy41, yvy42, yvy43, new_compare0(:(yvy42, yvy43), :(yvy36, yvy37), h), h, ba)
new_splitLT0(Branch(yvy330, yvy331, yvy332, yvy333, yvy334), bb, bc) → new_splitLT3(yvy330, yvy331, yvy332, yvy333, yvy334, [], bb, bc)
new_splitLT20(yvy36, yvy37, yvy38, yvy39, yvy40, yvy41, yvy42, yvy43, h, ba) → new_splitLT11(yvy36, yvy37, yvy38, yvy39, yvy40, yvy41, yvy42, yvy43, new_compare0(:(yvy42, yvy43), :(yvy36, yvy37), h), h, ba)
new_splitLT1(yvy31, yvy32, yvy33, yvy34, yvy400, yvy401, GT, bb, bc) → new_splitLT(yvy34, yvy400, yvy401, bb, bc)
new_splitLT10(yvy31, yvy32, yvy33, yvy34, GT, bb, bc) → new_splitLT0(yvy34, bb, bc)
new_splitLT2(yvy36, yvy37, yvy38, yvy39, yvy40, yvy41, yvy42, yvy43, GT, h, ba) → new_splitLT20(yvy36, yvy37, yvy38, yvy39, yvy40, yvy41, yvy42, yvy43, h, ba)

The TRS R consists of the following rules:

new_compare210(yvy100, yvy101, False, feg) → new_compare112(yvy100, yvy101, new_ltEs24(yvy100, yvy101, feg), feg)
new_compare7(@2(yvy4000, yvy4001), @2(yvy3000, yvy3001), bg, bh) → new_compare24(yvy4000, yvy4001, yvy3000, yvy3001, new_asAs(new_esEs7(yvy4000, yvy3000, bg), new_esEs8(yvy4001, yvy3001, bh)), bg, bh)
new_esEs24(Left(yvy40000), Left(yvy30000), app(ty_Ratio, deh), hh) → new_esEs21(yvy40000, yvy30000, deh)
new_ltEs19(yvy1002, yvy1012, app(ty_[], cab)) → new_ltEs8(yvy1002, yvy1012, cab)
new_compare112(yvy189, yvy190, True, fge) → LT
new_lt22(yvy1000, yvy1010, ty_Int) → new_lt17(yvy1000, yvy1010)
new_ltEs22(yvy114, yvy115, app(app(ty_@2, fbc), fbd)) → new_ltEs12(yvy114, yvy115, fbc, fbd)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Int, hh) → new_esEs25(yvy40000, yvy30000)
new_esEs6(yvy4002, yvy3002, app(app(app(ty_@3, bbg), bbh), bca)) → new_esEs22(yvy4002, yvy3002, bbg, bbh, bca)
new_esEs27(yvy1000, yvy1010, app(ty_[], bff)) → new_esEs16(yvy1000, yvy1010, bff)
new_esEs20(True, True) → True
new_esEs35(yvy153, yvy156, app(ty_[], eab)) → new_esEs16(yvy153, yvy156, eab)
new_compare8(Integer(yvy4000), Integer(yvy3000)) → new_primCmpInt(yvy4000, yvy3000)
new_esEs8(yvy4001, yvy3001, ty_Bool) → new_esEs20(yvy4001, yvy3001)
new_esEs11(yvy4000, yvy3000, ty_Integer) → new_esEs18(yvy4000, yvy3000)
new_esEs27(yvy1000, yvy1010, app(app(ty_@2, bgc), bgd)) → new_esEs17(yvy1000, yvy1010, bgc, bgd)
new_ltEs20(yvy154, yvy157, app(ty_Ratio, ebe)) → new_ltEs9(yvy154, yvy157, ebe)
new_esEs36(yvy1000, yvy1010, ty_Double) → new_esEs13(yvy1000, yvy1010)
new_esEs28(yvy1001, yvy1011, ty_Float) → new_esEs14(yvy1001, yvy1011)
new_lt6(yvy1000, yvy1010, ty_@0) → new_lt19(yvy1000, yvy1010)
new_compare10(yvy199, yvy200, True, ef, eg) → LT
new_esEs9(yvy4000, yvy3000, ty_Int) → new_esEs25(yvy4000, yvy3000)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, ty_Double) → new_esEs13(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, app(app(ty_@2, chb), chc)) → new_esEs17(yvy40002, yvy30002, chb, chc)
new_ltEs24(yvy100, yvy101, app(ty_Ratio, cdh)) → new_ltEs9(yvy100, yvy101, cdh)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, ty_@0) → new_esEs19(yvy40000, yvy30000)
new_ltEs19(yvy1002, yvy1012, ty_Float) → new_ltEs11(yvy1002, yvy1012)
new_esEs11(yvy4000, yvy3000, app(ty_[], ehb)) → new_esEs16(yvy4000, yvy3000, ehb)
new_lt23(yvy165, yvy167, app(app(app(ty_@3, fcd), fce), fcf)) → new_lt4(yvy165, yvy167, fcd, fce, fcf)
new_esEs7(yvy4000, yvy3000, ty_Double) → new_esEs13(yvy4000, yvy3000)
new_esEs9(yvy4000, yvy3000, ty_Char) → new_esEs15(yvy4000, yvy3000)
new_ltEs23(yvy166, yvy168, ty_Ordering) → new_ltEs6(yvy166, yvy168)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Bool, dac) → new_ltEs16(yvy1000, yvy1010)
new_esEs39(yvy165, yvy167, app(ty_Ratio, fcc)) → new_esEs21(yvy165, yvy167, fcc)
new_esEs10(yvy4000, yvy3000, ty_@0) → new_esEs19(yvy4000, yvy3000)
new_esEs21(:%(yvy40000, yvy40001), :%(yvy30000, yvy30001), hb) → new_asAs(new_esEs37(yvy40000, yvy30000, hb), new_esEs38(yvy40001, yvy30001, hb))
new_lt5(yvy1001, yvy1011, app(ty_Ratio, bha)) → new_lt10(yvy1001, yvy1011, bha)
new_compare13(:%(yvy4000, yvy4001), :%(yvy3000, yvy3001), ty_Integer) → new_compare8(new_sr(yvy4000, yvy3001), new_sr(yvy3000, yvy4001))
new_ltEs22(yvy114, yvy115, app(ty_Ratio, fag)) → new_ltEs9(yvy114, yvy115, fag)
new_ltEs23(yvy166, yvy168, ty_Int) → new_ltEs15(yvy166, yvy168)
new_primMulNat0(Zero, Zero) → Zero
new_ltEs24(yvy100, yvy101, ty_Ordering) → new_ltEs6(yvy100, yvy101)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, ty_Float) → new_ltEs11(yvy1000, yvy1010)
new_esEs39(yvy165, yvy167, app(ty_Maybe, fda)) → new_esEs23(yvy165, yvy167, fda)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Bool, hh) → new_esEs20(yvy40000, yvy30000)
new_compare15(LT, LT) → EQ
new_esEs6(yvy4002, yvy3002, app(app(ty_@2, bbd), bbe)) → new_esEs17(yvy4002, yvy3002, bbd, bbe)
new_esEs4(yvy4000, yvy3000, ty_Integer) → new_esEs18(yvy4000, yvy3000)
new_esEs26(yvy40000, yvy30000, app(ty_[], bce)) → new_esEs16(yvy40000, yvy30000, bce)
new_esEs36(yvy1000, yvy1010, ty_Char) → new_esEs15(yvy1000, yvy1010)
new_esEs28(yvy1001, yvy1011, app(app(ty_Either, bhh), caa)) → new_esEs24(yvy1001, yvy1011, bhh, caa)
new_esEs34(yvy152, yvy155, ty_@0) → new_esEs19(yvy152, yvy155)
new_sr(Integer(yvy30000), Integer(yvy40010)) → Integer(new_primMulInt(yvy30000, yvy40010))
new_esEs7(yvy4000, yvy3000, ty_Float) → new_esEs14(yvy4000, yvy3000)
new_compare12(True, False) → GT
new_lt7(yvy152, yvy155) → new_esEs12(new_compare15(yvy152, yvy155), LT)
new_lt22(yvy1000, yvy1010, app(ty_Maybe, eea)) → new_lt14(yvy1000, yvy1010, eea)
new_ltEs24(yvy100, yvy101, app(ty_Maybe, eh)) → new_ltEs5(yvy100, yvy101, eh)
new_esEs35(yvy153, yvy156, app(app(ty_Either, ebb), ebc)) → new_esEs24(yvy153, yvy156, ebb, ebc)
new_esEs35(yvy153, yvy156, ty_@0) → new_esEs19(yvy153, yvy156)
new_ltEs15(yvy100, yvy101) → new_fsEs(new_compare16(yvy100, yvy101))
new_esEs6(yvy4002, yvy3002, app(ty_[], bbc)) → new_esEs16(yvy4002, yvy3002, bbc)
new_esEs26(yvy40000, yvy30000, ty_@0) → new_esEs19(yvy40000, yvy30000)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_@0, hh) → new_esEs19(yvy40000, yvy30000)
new_ltEs16(False, True) → True
new_esEs26(yvy40000, yvy30000, app(app(app(ty_@3, bda), bdb), bdc)) → new_esEs22(yvy40000, yvy30000, bda, bdb, bdc)
new_esEs10(yvy4000, yvy3000, app(ty_Maybe, egg)) → new_esEs23(yvy4000, yvy3000, egg)
new_ltEs24(yvy100, yvy101, ty_Bool) → new_ltEs16(yvy100, yvy101)
new_compare30(yvy400, yvy300, app(app(ty_@2, bg), bh)) → new_compare7(yvy400, yvy300, bg, bh)
new_esEs17(@2(yvy40000, yvy40001), @2(yvy30000, yvy30001), gh, ha) → new_asAs(new_esEs29(yvy40000, yvy30000, gh), new_esEs30(yvy40001, yvy30001, ha))
new_esEs11(yvy4000, yvy3000, ty_Char) → new_esEs15(yvy4000, yvy3000)
new_lt20(yvy152, yvy155, app(app(app(ty_@3, bd), be), bf)) → new_lt4(yvy152, yvy155, bd, be, bf)
new_esEs27(yvy1000, yvy1010, ty_Bool) → new_esEs20(yvy1000, yvy1010)
new_ltEs23(yvy166, yvy168, app(ty_Ratio, fde)) → new_ltEs9(yvy166, yvy168, fde)
new_esEs34(yvy152, yvy155, ty_Double) → new_esEs13(yvy152, yvy155)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Double) → new_esEs13(yvy40000, yvy30000)
new_esEs10(yvy4000, yvy3000, ty_Int) → new_esEs25(yvy4000, yvy3000)
new_esEs26(yvy40000, yvy30000, ty_Char) → new_esEs15(yvy40000, yvy30000)
new_compare30(yvy400, yvy300, ty_Int) → new_compare16(yvy400, yvy300)
new_fsEs(yvy306) → new_not(new_esEs12(yvy306, GT))
new_ltEs16(True, False) → False
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, ty_Char) → new_ltEs7(yvy1000, yvy1010)
new_esEs7(yvy4000, yvy3000, ty_Int) → new_esEs25(yvy4000, yvy3000)
new_ltEs19(yvy1002, yvy1012, ty_Bool) → new_ltEs16(yvy1002, yvy1012)
new_esEs34(yvy152, yvy155, ty_Ordering) → new_esEs12(yvy152, yvy155)
new_esEs12(GT, LT) → False
new_esEs12(LT, GT) → False
new_esEs27(yvy1000, yvy1010, ty_Char) → new_esEs15(yvy1000, yvy1010)
new_lt5(yvy1001, yvy1011, ty_Integer) → new_lt15(yvy1001, yvy1011)
new_ltEs22(yvy114, yvy115, ty_Ordering) → new_ltEs6(yvy114, yvy115)
new_compare18(Float(yvy4000, yvy4001), Float(yvy3000, yvy3001)) → new_compare16(new_sr0(yvy4000, yvy3000), new_sr0(yvy4001, yvy3001))
new_ltEs18(yvy107, yvy108, app(ty_Ratio, beb)) → new_ltEs9(yvy107, yvy108, beb)
new_ltEs23(yvy166, yvy168, ty_Float) → new_ltEs11(yvy166, yvy168)
new_ltEs18(yvy107, yvy108, app(ty_[], bea)) → new_ltEs8(yvy107, yvy108, bea)
new_ltEs20(yvy154, yvy157, app(app(ty_@2, eca), ecb)) → new_ltEs12(yvy154, yvy157, eca, ecb)
new_esEs31(yvy40000, yvy30000, app(ty_Maybe, cfd)) → new_esEs23(yvy40000, yvy30000, cfd)
new_lt6(yvy1000, yvy1010, app(ty_Ratio, bfg)) → new_lt10(yvy1000, yvy1010, bfg)
new_esEs37(yvy40000, yvy30000, ty_Integer) → new_esEs18(yvy40000, yvy30000)
new_ltEs14(Left(yvy1000), Left(yvy1010), app(app(ty_@2, dba), dbb), dac) → new_ltEs12(yvy1000, yvy1010, dba, dbb)
new_esEs35(yvy153, yvy156, app(app(ty_@2, eag), eah)) → new_esEs17(yvy153, yvy156, eag, eah)
new_esEs5(yvy4001, yvy3001, app(app(app(ty_@3, bae), baf), bag)) → new_esEs22(yvy4001, yvy3001, bae, baf, bag)
new_lt22(yvy1000, yvy1010, ty_Char) → new_lt8(yvy1000, yvy1010)
new_compare110(yvy233, yvy234, yvy235, yvy236, True, yvy238, ecf, ecg) → new_compare111(yvy233, yvy234, yvy235, yvy236, True, ecf, ecg)
new_ltEs24(yvy100, yvy101, app(app(ty_@2, ech), eda)) → new_ltEs12(yvy100, yvy101, ech, eda)
new_ltEs13(yvy100, yvy101) → new_fsEs(new_compare29(yvy100, yvy101))
new_esEs5(yvy4001, yvy3001, app(app(ty_Either, bba), bbb)) → new_esEs24(yvy4001, yvy3001, bba, bbb)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, ty_Bool) → new_esEs20(yvy40000, yvy30000)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Float) → new_ltEs11(yvy1000, yvy1010)
new_esEs8(yvy4001, yvy3001, ty_Double) → new_esEs13(yvy4001, yvy3001)
new_esEs31(yvy40000, yvy30000, app(ty_Ratio, ceh)) → new_esEs21(yvy40000, yvy30000, ceh)
new_esEs29(yvy40000, yvy30000, app(ty_Maybe, ccc)) → new_esEs23(yvy40000, yvy30000, ccc)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Int) → new_ltEs15(yvy1000, yvy1010)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Double) → new_ltEs13(yvy1000, yvy1010)
new_esEs30(yvy40001, yvy30001, ty_Double) → new_esEs13(yvy40001, yvy30001)
new_ltEs21(yvy1001, yvy1011, app(app(ty_@2, efa), efb)) → new_ltEs12(yvy1001, yvy1011, efa, efb)
new_esEs10(yvy4000, yvy3000, ty_Bool) → new_esEs20(yvy4000, yvy3000)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Char, dac) → new_ltEs7(yvy1000, yvy1010)
new_ltEs16(True, True) → True
new_lt21(yvy153, yvy156, app(app(ty_@2, eag), eah)) → new_lt12(yvy153, yvy156, eag, eah)
new_lt6(yvy1000, yvy1010, ty_Bool) → new_lt18(yvy1000, yvy1010)
new_pePe(False, yvy305) → yvy305
new_compare15(GT, EQ) → GT
new_esEs7(yvy4000, yvy3000, ty_Char) → new_esEs15(yvy4000, yvy3000)
new_esEs31(yvy40000, yvy30000, app(ty_[], cee)) → new_esEs16(yvy40000, yvy30000, cee)
new_esEs39(yvy165, yvy167, ty_@0) → new_esEs19(yvy165, yvy167)
new_esEs23(Just(yvy40000), Just(yvy30000), app(ty_Maybe, ddh)) → new_esEs23(yvy40000, yvy30000, ddh)
new_lt21(yvy153, yvy156, ty_Char) → new_lt8(yvy153, yvy156)
new_esEs26(yvy40000, yvy30000, ty_Bool) → new_esEs20(yvy40000, yvy30000)
new_esEs9(yvy4000, yvy3000, app(app(ty_@2, ffd), ffe)) → new_esEs17(yvy4000, yvy3000, ffd, ffe)
new_compare14(yvy218, yvy219, yvy220, yvy221, yvy222, yvy223, False, ceb, cec, ced) → GT
new_lt9(yvy152, yvy155, dhf) → new_esEs12(new_compare0(yvy152, yvy155, dhf), LT)
new_esEs28(yvy1001, yvy1011, ty_Integer) → new_esEs18(yvy1001, yvy1011)
new_esEs5(yvy4001, yvy3001, ty_Ordering) → new_esEs12(yvy4001, yvy3001)
new_esEs5(yvy4001, yvy3001, ty_Int) → new_esEs25(yvy4001, yvy3001)
new_esEs4(yvy4000, yvy3000, ty_Float) → new_esEs14(yvy4000, yvy3000)
new_compare15(GT, LT) → GT
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Char, hh) → new_esEs15(yvy40000, yvy30000)
new_esEs29(yvy40000, yvy30000, ty_Int) → new_esEs25(yvy40000, yvy30000)
new_compare30(yvy400, yvy300, app(app(ty_Either, eff), efg)) → new_compare27(yvy400, yvy300, eff, efg)
new_lt22(yvy1000, yvy1010, ty_Double) → new_lt13(yvy1000, yvy1010)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Ordering) → new_esEs12(yvy40000, yvy30000)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Char) → new_esEs15(yvy40000, yvy30000)
new_esEs29(yvy40000, yvy30000, app(app(ty_@2, cbe), cbf)) → new_esEs17(yvy40000, yvy30000, cbe, cbf)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, app(app(ty_@2, dfh), dga)) → new_esEs17(yvy40000, yvy30000, dfh, dga)
new_ltEs23(yvy166, yvy168, app(app(ty_Either, fed), fee)) → new_ltEs14(yvy166, yvy168, fed, fee)
new_esEs31(yvy40000, yvy30000, ty_Integer) → new_esEs18(yvy40000, yvy30000)
new_compare12(True, True) → EQ
new_esEs36(yvy1000, yvy1010, app(ty_[], edb)) → new_esEs16(yvy1000, yvy1010, edb)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Ordering, hh) → new_esEs12(yvy40000, yvy30000)
new_ltEs6(GT, EQ) → False
new_ltEs18(yvy107, yvy108, app(app(ty_Either, bfa), bfb)) → new_ltEs14(yvy107, yvy108, bfa, bfb)
new_esEs32(yvy40001, yvy30001, app(ty_Maybe, cgf)) → new_esEs23(yvy40001, yvy30001, cgf)
new_esEs35(yvy153, yvy156, ty_Integer) → new_esEs18(yvy153, yvy156)
new_esEs33(yvy40002, yvy30002, ty_Integer) → new_esEs18(yvy40002, yvy30002)
new_esEs31(yvy40000, yvy30000, ty_Double) → new_esEs13(yvy40000, yvy30000)
new_esEs10(yvy4000, yvy3000, ty_Ordering) → new_esEs12(yvy4000, yvy3000)
new_primCompAux1(yvy400, yvy300, yvy51, bb) → new_primCompAux0(yvy51, new_compare30(yvy400, yvy300, bb))
new_esEs33(yvy40002, yvy30002, ty_Float) → new_esEs14(yvy40002, yvy30002)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, app(app(app(ty_@3, dca), dcb), dcc)) → new_ltEs10(yvy1000, yvy1010, dca, dcb, dcc)
new_ltEs23(yvy166, yvy168, app(ty_[], fdd)) → new_ltEs8(yvy166, yvy168, fdd)
new_lt23(yvy165, yvy167, app(app(ty_@2, fcg), fch)) → new_lt12(yvy165, yvy167, fcg, fch)
new_esEs34(yvy152, yvy155, ty_Integer) → new_esEs18(yvy152, yvy155)
new_esEs23(Just(yvy40000), Just(yvy30000), app(app(ty_Either, dea), deb)) → new_esEs24(yvy40000, yvy30000, dea, deb)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Ordering, dac) → new_ltEs6(yvy1000, yvy1010)
new_lt22(yvy1000, yvy1010, ty_Bool) → new_lt18(yvy1000, yvy1010)
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_esEs39(yvy165, yvy167, ty_Float) → new_esEs14(yvy165, yvy167)
new_ltEs22(yvy114, yvy115, ty_Bool) → new_ltEs16(yvy114, yvy115)
new_ltEs4(yvy100, yvy101) → new_fsEs(new_compare8(yvy100, yvy101))
new_esEs33(yvy40002, yvy30002, app(ty_[], cha)) → new_esEs16(yvy40002, yvy30002, cha)
new_ltEs8(yvy100, yvy101, fef) → new_fsEs(new_compare0(yvy100, yvy101, fef))
new_compare30(yvy400, yvy300, ty_Char) → new_compare11(yvy400, yvy300)
new_esEs36(yvy1000, yvy1010, ty_Integer) → new_esEs18(yvy1000, yvy1010)
new_esEs39(yvy165, yvy167, ty_Bool) → new_esEs20(yvy165, yvy167)
new_esEs36(yvy1000, yvy1010, ty_Bool) → new_esEs20(yvy1000, yvy1010)
new_esEs32(yvy40001, yvy30001, app(ty_Ratio, cgb)) → new_esEs21(yvy40001, yvy30001, cgb)
new_compare12(False, True) → LT
new_esEs5(yvy4001, yvy3001, ty_Char) → new_esEs15(yvy4001, yvy3001)
new_esEs34(yvy152, yvy155, ty_Char) → new_esEs15(yvy152, yvy155)
new_esEs31(yvy40000, yvy30000, app(app(ty_@2, cef), ceg)) → new_esEs17(yvy40000, yvy30000, cef, ceg)
new_ltEs18(yvy107, yvy108, ty_Integer) → new_ltEs4(yvy107, yvy108)
new_lt21(yvy153, yvy156, ty_@0) → new_lt19(yvy153, yvy156)
new_esEs30(yvy40001, yvy30001, ty_@0) → new_esEs19(yvy40001, yvy30001)
new_ltEs18(yvy107, yvy108, app(ty_Maybe, beh)) → new_ltEs5(yvy107, yvy108, beh)
new_esEs12(LT, LT) → True
new_ltEs24(yvy100, yvy101, ty_Char) → new_ltEs7(yvy100, yvy101)
new_esEs31(yvy40000, yvy30000, app(app(ty_Either, cfe), cff)) → new_esEs24(yvy40000, yvy30000, cfe, cff)
new_ltEs18(yvy107, yvy108, ty_Double) → new_ltEs13(yvy107, yvy108)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Int, dac) → new_ltEs15(yvy1000, yvy1010)
new_esEs28(yvy1001, yvy1011, app(ty_Maybe, bhg)) → new_esEs23(yvy1001, yvy1011, bhg)
new_lt5(yvy1001, yvy1011, ty_@0) → new_lt19(yvy1001, yvy1011)
new_compare15(EQ, LT) → GT
new_pePe(True, yvy305) → True
new_compare0([], [], feh) → EQ
new_primEqNat0(Zero, Zero) → True
new_ltEs21(yvy1001, yvy1011, ty_Double) → new_ltEs13(yvy1001, yvy1011)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Float) → new_esEs14(yvy40000, yvy30000)
new_esEs6(yvy4002, yvy3002, ty_Double) → new_esEs13(yvy4002, yvy3002)
new_esEs4(yvy4000, yvy3000, app(ty_Maybe, hf)) → new_esEs23(yvy4000, yvy3000, hf)
new_lt5(yvy1001, yvy1011, ty_Bool) → new_lt18(yvy1001, yvy1011)
new_lt23(yvy165, yvy167, ty_Integer) → new_lt15(yvy165, yvy167)
new_esEs5(yvy4001, yvy3001, ty_Float) → new_esEs14(yvy4001, yvy3001)
new_lt21(yvy153, yvy156, app(app(ty_Either, ebb), ebc)) → new_lt16(yvy153, yvy156, ebb, ebc)
new_esEs8(yvy4001, yvy3001, app(app(app(ty_@3, dh), ea), eb)) → new_esEs22(yvy4001, yvy3001, dh, ea, eb)
new_lt11(yvy152, yvy155) → new_esEs12(new_compare18(yvy152, yvy155), LT)
new_lt20(yvy152, yvy155, app(ty_[], dhf)) → new_lt9(yvy152, yvy155, dhf)
new_esEs13(Double(yvy40000, yvy40001), Double(yvy30000, yvy30001)) → new_esEs25(new_sr0(yvy40000, yvy30000), new_sr0(yvy40001, yvy30001))
new_esEs7(yvy4000, yvy3000, ty_Bool) → new_esEs20(yvy4000, yvy3000)
new_compare30(yvy400, yvy300, ty_@0) → new_compare9(yvy400, yvy300)
new_esEs29(yvy40000, yvy30000, ty_@0) → new_esEs19(yvy40000, yvy30000)
new_esEs6(yvy4002, yvy3002, ty_Ordering) → new_esEs12(yvy4002, yvy3002)
new_ltEs18(yvy107, yvy108, app(app(app(ty_@3, bec), bed), bee)) → new_ltEs10(yvy107, yvy108, bec, bed, bee)
new_ltEs22(yvy114, yvy115, ty_@0) → new_ltEs17(yvy114, yvy115)
new_lt5(yvy1001, yvy1011, ty_Char) → new_lt8(yvy1001, yvy1011)
new_lt5(yvy1001, yvy1011, app(app(ty_Either, bhh), caa)) → new_lt16(yvy1001, yvy1011, bhh, caa)
new_ltEs19(yvy1002, yvy1012, ty_Ordering) → new_ltEs6(yvy1002, yvy1012)
new_esEs15(Char(yvy40000), Char(yvy30000)) → new_primEqNat0(yvy40000, yvy30000)
new_esEs24(Left(yvy40000), Left(yvy30000), app(app(app(ty_@3, dfa), dfb), dfc), hh) → new_esEs22(yvy40000, yvy30000, dfa, dfb, dfc)
new_esEs26(yvy40000, yvy30000, ty_Int) → new_esEs25(yvy40000, yvy30000)
new_esEs32(yvy40001, yvy30001, ty_Integer) → new_esEs18(yvy40001, yvy30001)
new_ltEs23(yvy166, yvy168, ty_Double) → new_ltEs13(yvy166, yvy168)
new_lt22(yvy1000, yvy1010, app(ty_[], edb)) → new_lt9(yvy1000, yvy1010, edb)
new_ltEs23(yvy166, yvy168, ty_Integer) → new_ltEs4(yvy166, yvy168)
new_esEs9(yvy4000, yvy3000, app(ty_[], ffc)) → new_esEs16(yvy4000, yvy3000, ffc)
new_esEs33(yvy40002, yvy30002, ty_Bool) → new_esEs20(yvy40002, yvy30002)
new_esEs11(yvy4000, yvy3000, ty_Double) → new_esEs13(yvy4000, yvy3000)
new_esEs29(yvy40000, yvy30000, ty_Bool) → new_esEs20(yvy40000, yvy30000)
new_lt5(yvy1001, yvy1011, app(ty_[], bgh)) → new_lt9(yvy1001, yvy1011, bgh)
new_ltEs21(yvy1001, yvy1011, ty_Bool) → new_ltEs16(yvy1001, yvy1011)
new_ltEs6(EQ, GT) → True
new_esEs9(yvy4000, yvy3000, ty_Integer) → new_esEs18(yvy4000, yvy3000)
new_esEs11(yvy4000, yvy3000, ty_Ordering) → new_esEs12(yvy4000, yvy3000)
new_esEs23(Just(yvy40000), Nothing, hf) → False
new_esEs23(Nothing, Just(yvy30000), hf) → False
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_ltEs18(yvy107, yvy108, ty_Ordering) → new_ltEs6(yvy107, yvy108)
new_esEs23(Just(yvy40000), Just(yvy30000), app(app(app(ty_@3, dde), ddf), ddg)) → new_esEs22(yvy40000, yvy30000, dde, ddf, ddg)
new_ltEs24(yvy100, yvy101, ty_Double) → new_ltEs13(yvy100, yvy101)
new_esEs10(yvy4000, yvy3000, ty_Double) → new_esEs13(yvy4000, yvy3000)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, ty_Float) → new_esEs14(yvy40000, yvy30000)
new_compare110(yvy233, yvy234, yvy235, yvy236, False, yvy238, ecf, ecg) → new_compare111(yvy233, yvy234, yvy235, yvy236, yvy238, ecf, ecg)
new_ltEs20(yvy154, yvy157, ty_Bool) → new_ltEs16(yvy154, yvy157)
new_ltEs24(yvy100, yvy101, ty_@0) → new_ltEs17(yvy100, yvy101)
new_ltEs5(Just(yvy1000), Just(yvy1010), app(app(ty_@2, fg), fh)) → new_ltEs12(yvy1000, yvy1010, fg, fh)
new_ltEs20(yvy154, yvy157, ty_Int) → new_ltEs15(yvy154, yvy157)
new_esEs8(yvy4001, yvy3001, ty_@0) → new_esEs19(yvy4001, yvy3001)
new_lt22(yvy1000, yvy1010, app(app(ty_Either, eeb), eec)) → new_lt16(yvy1000, yvy1010, eeb, eec)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Float, dac) → new_ltEs11(yvy1000, yvy1010)
new_compare26(yvy107, yvy108, False, bdg, bdh) → new_compare10(yvy107, yvy108, new_ltEs18(yvy107, yvy108, bdg), bdg, bdh)
new_lt21(yvy153, yvy156, app(ty_Ratio, eac)) → new_lt10(yvy153, yvy156, eac)
new_compare30(yvy400, yvy300, ty_Float) → new_compare18(yvy400, yvy300)
new_primEqInt(Neg(Succ(yvy400000)), Neg(Succ(yvy300000))) → new_primEqNat0(yvy400000, yvy300000)
new_esEs23(Nothing, Nothing, hf) → True
new_esEs10(yvy4000, yvy3000, app(app(app(ty_@3, egd), ege), egf)) → new_esEs22(yvy4000, yvy3000, egd, ege, egf)
new_esEs39(yvy165, yvy167, app(app(ty_@2, fcg), fch)) → new_esEs17(yvy165, yvy167, fcg, fch)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, app(app(ty_@2, dcd), dce)) → new_ltEs12(yvy1000, yvy1010, dcd, dce)
new_ltEs5(Just(yvy1000), Nothing, eh) → False
new_esEs28(yvy1001, yvy1011, ty_Char) → new_esEs15(yvy1001, yvy1011)
new_esEs11(yvy4000, yvy3000, app(ty_Maybe, faa)) → new_esEs23(yvy4000, yvy3000, faa)
new_lt14(yvy152, yvy155, dhg) → new_esEs12(new_compare31(yvy152, yvy155, dhg), LT)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, ty_@0) → new_ltEs17(yvy1000, yvy1010)
new_ltEs14(Right(yvy1000), Left(yvy1010), dbf, dac) → False
new_esEs12(EQ, LT) → False
new_esEs12(LT, EQ) → False
new_ltEs19(yvy1002, yvy1012, app(ty_Ratio, cac)) → new_ltEs9(yvy1002, yvy1012, cac)
new_lt22(yvy1000, yvy1010, app(app(ty_@2, edg), edh)) → new_lt12(yvy1000, yvy1010, edg, edh)
new_ltEs23(yvy166, yvy168, ty_Bool) → new_ltEs16(yvy166, yvy168)
new_compare111(yvy233, yvy234, yvy235, yvy236, True, ecf, ecg) → LT
new_esEs7(yvy4000, yvy3000, app(ty_[], ca)) → new_esEs16(yvy4000, yvy3000, ca)
new_esEs5(yvy4001, yvy3001, ty_Bool) → new_esEs20(yvy4001, yvy3001)
new_lt23(yvy165, yvy167, ty_Int) → new_lt17(yvy165, yvy167)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs30(yvy40001, yvy30001, app(app(app(ty_@3, cdb), cdc), cdd)) → new_esEs22(yvy40001, yvy30001, cdb, cdc, cdd)
new_esEs11(yvy4000, yvy3000, app(app(ty_Either, fab), fac)) → new_esEs24(yvy4000, yvy3000, fab, fac)
new_esEs35(yvy153, yvy156, app(app(app(ty_@3, ead), eae), eaf)) → new_esEs22(yvy153, yvy156, ead, eae, eaf)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, ty_Int) → new_ltEs15(yvy1000, yvy1010)
new_esEs10(yvy4000, yvy3000, app(app(ty_Either, egh), eha)) → new_esEs24(yvy4000, yvy3000, egh, eha)
new_esEs28(yvy1001, yvy1011, ty_Double) → new_esEs13(yvy1001, yvy1011)
new_lt20(yvy152, yvy155, ty_Ordering) → new_lt7(yvy152, yvy155)
new_ltEs6(EQ, EQ) → True
new_compare31(Just(yvy4000), Nothing, ffb) → GT
new_esEs11(yvy4000, yvy3000, app(app(app(ty_@3, ehf), ehg), ehh)) → new_esEs22(yvy4000, yvy3000, ehf, ehg, ehh)
new_ltEs22(yvy114, yvy115, app(app(ty_Either, fbf), fbg)) → new_ltEs14(yvy114, yvy115, fbf, fbg)
new_esEs28(yvy1001, yvy1011, app(app(app(ty_@3, bhb), bhc), bhd)) → new_esEs22(yvy1001, yvy1011, bhb, bhc, bhd)
new_esEs32(yvy40001, yvy30001, ty_Float) → new_esEs14(yvy40001, yvy30001)
new_esEs27(yvy1000, yvy1010, app(ty_Ratio, bfg)) → new_esEs21(yvy1000, yvy1010, bfg)
new_ltEs19(yvy1002, yvy1012, ty_Integer) → new_ltEs4(yvy1002, yvy1012)
new_primEqInt(Neg(Succ(yvy400000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(yvy300000))) → False
new_primCompAux0(yvy56, GT) → GT
new_compare30(yvy400, yvy300, app(app(app(ty_@3, gd), ge), gf)) → new_compare6(yvy400, yvy300, gd, ge, gf)
new_esEs39(yvy165, yvy167, ty_Integer) → new_esEs18(yvy165, yvy167)
new_compare26(yvy107, yvy108, True, bdg, bdh) → EQ
new_esEs23(Just(yvy40000), Just(yvy30000), app(app(ty_@2, ddb), ddc)) → new_esEs17(yvy40000, yvy30000, ddb, ddc)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, app(app(ty_Either, dgg), dgh)) → new_esEs24(yvy40000, yvy30000, dgg, dgh)
new_ltEs6(GT, GT) → True
new_ltEs21(yvy1001, yvy1011, app(app(ty_Either, efd), efe)) → new_ltEs14(yvy1001, yvy1011, efd, efe)
new_esEs38(yvy40001, yvy30001, ty_Integer) → new_esEs18(yvy40001, yvy30001)
new_esEs32(yvy40001, yvy30001, app(ty_[], cfg)) → new_esEs16(yvy40001, yvy30001, cfg)
new_esEs34(yvy152, yvy155, ty_Int) → new_esEs25(yvy152, yvy155)
new_compare31(Nothing, Nothing, ffb) → EQ
new_esEs29(yvy40000, yvy30000, app(ty_[], cbd)) → new_esEs16(yvy40000, yvy30000, cbd)
new_esEs26(yvy40000, yvy30000, app(ty_Ratio, bch)) → new_esEs21(yvy40000, yvy30000, bch)
new_esEs7(yvy4000, yvy3000, app(ty_Maybe, da)) → new_esEs23(yvy4000, yvy3000, da)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_@0) → new_ltEs17(yvy1000, yvy1010)
new_lt21(yvy153, yvy156, app(ty_[], eab)) → new_lt9(yvy153, yvy156, eab)
new_ltEs20(yvy154, yvy157, app(ty_[], ebd)) → new_ltEs8(yvy154, yvy157, ebd)
new_esEs36(yvy1000, yvy1010, ty_Int) → new_esEs25(yvy1000, yvy1010)
new_esEs19(@0, @0) → True
new_compare6(@3(yvy4000, yvy4001, yvy4002), @3(yvy3000, yvy3001, yvy3002), gd, ge, gf) → new_compare25(yvy4000, yvy4001, yvy4002, yvy3000, yvy3001, yvy3002, new_asAs(new_esEs4(yvy4000, yvy3000, gd), new_asAs(new_esEs5(yvy4001, yvy3001, ge), new_esEs6(yvy4002, yvy3002, gf))), gd, ge, gf)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_esEs7(yvy4000, yvy3000, ty_Integer) → new_esEs18(yvy4000, yvy3000)
new_esEs4(yvy4000, yvy3000, ty_Bool) → new_esEs20(yvy4000, yvy3000)
new_esEs39(yvy165, yvy167, ty_Ordering) → new_esEs12(yvy165, yvy167)
new_lt20(yvy152, yvy155, ty_Char) → new_lt8(yvy152, yvy155)
new_esEs31(yvy40000, yvy30000, ty_Bool) → new_esEs20(yvy40000, yvy30000)
new_lt4(yvy152, yvy155, bd, be, bf) → new_esEs12(new_compare6(yvy152, yvy155, bd, be, bf), LT)
new_esEs6(yvy4002, yvy3002, ty_Int) → new_esEs25(yvy4002, yvy3002)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Double, dac) → new_ltEs13(yvy1000, yvy1010)
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_lt6(yvy1000, yvy1010, app(ty_Maybe, bge)) → new_lt14(yvy1000, yvy1010, bge)
new_ltEs14(Left(yvy1000), Left(yvy1010), app(ty_Maybe, dbc), dac) → new_ltEs5(yvy1000, yvy1010, dbc)
new_esEs4(yvy4000, yvy3000, app(ty_Ratio, hb)) → new_esEs21(yvy4000, yvy3000, hb)
new_lt5(yvy1001, yvy1011, app(ty_Maybe, bhg)) → new_lt14(yvy1001, yvy1011, bhg)
new_primEqInt(Pos(Succ(yvy400000)), Pos(Succ(yvy300000))) → new_primEqNat0(yvy400000, yvy300000)
new_compare10(yvy199, yvy200, False, ef, eg) → GT
new_esEs34(yvy152, yvy155, app(ty_Maybe, dhg)) → new_esEs23(yvy152, yvy155, dhg)
new_esEs5(yvy4001, yvy3001, app(ty_[], baa)) → new_esEs16(yvy4001, yvy3001, baa)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, ty_Double) → new_ltEs13(yvy1000, yvy1010)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, ty_Integer) → new_ltEs4(yvy1000, yvy1010)
new_ltEs21(yvy1001, yvy1011, ty_Float) → new_ltEs11(yvy1001, yvy1011)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, app(ty_Maybe, dcf)) → new_ltEs5(yvy1000, yvy1010, dcf)
new_compare13(:%(yvy4000, yvy4001), :%(yvy3000, yvy3001), ty_Int) → new_compare16(new_sr0(yvy4000, yvy3001), new_sr0(yvy3000, yvy4001))
new_esEs26(yvy40000, yvy30000, app(ty_Maybe, bdd)) → new_esEs23(yvy40000, yvy30000, bdd)
new_ltEs24(yvy100, yvy101, ty_Float) → new_ltEs11(yvy100, yvy101)
new_esEs34(yvy152, yvy155, app(app(ty_@2, dec), ded)) → new_esEs17(yvy152, yvy155, dec, ded)
new_esEs8(yvy4001, yvy3001, ty_Integer) → new_esEs18(yvy4001, yvy3001)
new_ltEs22(yvy114, yvy115, app(app(app(ty_@3, fah), fba), fbb)) → new_ltEs10(yvy114, yvy115, fah, fba, fbb)
new_primEqNat0(Succ(yvy400000), Succ(yvy300000)) → new_primEqNat0(yvy400000, yvy300000)
new_esEs6(yvy4002, yvy3002, ty_Bool) → new_esEs20(yvy4002, yvy3002)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Ordering) → new_ltEs6(yvy1000, yvy1010)
new_ltEs24(yvy100, yvy101, ty_Int) → new_ltEs15(yvy100, yvy101)
new_esEs26(yvy40000, yvy30000, ty_Ordering) → new_esEs12(yvy40000, yvy30000)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, app(ty_Ratio, dgb)) → new_esEs21(yvy40000, yvy30000, dgb)
new_esEs11(yvy4000, yvy3000, app(ty_Ratio, ehe)) → new_esEs21(yvy4000, yvy3000, ehe)
new_esEs30(yvy40001, yvy30001, ty_Integer) → new_esEs18(yvy40001, yvy30001)
new_esEs39(yvy165, yvy167, ty_Char) → new_esEs15(yvy165, yvy167)
new_ltEs14(Left(yvy1000), Left(yvy1010), app(ty_Ratio, dae), dac) → new_ltEs9(yvy1000, yvy1010, dae)
new_esEs26(yvy40000, yvy30000, app(app(ty_@2, bcf), bcg)) → new_esEs17(yvy40000, yvy30000, bcf, bcg)
new_lt5(yvy1001, yvy1011, ty_Float) → new_lt11(yvy1001, yvy1011)
new_esEs32(yvy40001, yvy30001, ty_@0) → new_esEs19(yvy40001, yvy30001)
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_esEs33(yvy40002, yvy30002, app(ty_Maybe, chh)) → new_esEs23(yvy40002, yvy30002, chh)
new_lt6(yvy1000, yvy1010, ty_Int) → new_lt17(yvy1000, yvy1010)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, app(app(app(ty_@3, dgc), dgd), dge)) → new_esEs22(yvy40000, yvy30000, dgc, dgd, dge)
new_lt23(yvy165, yvy167, app(app(ty_Either, fdb), fdc)) → new_lt16(yvy165, yvy167, fdb, fdc)
new_esEs12(EQ, EQ) → True
new_lt23(yvy165, yvy167, ty_Char) → new_lt8(yvy165, yvy167)
new_ltEs18(yvy107, yvy108, app(app(ty_@2, bef), beg)) → new_ltEs12(yvy107, yvy108, bef, beg)
new_lt21(yvy153, yvy156, ty_Double) → new_lt13(yvy153, yvy156)
new_esEs35(yvy153, yvy156, ty_Ordering) → new_esEs12(yvy153, yvy156)
new_lt5(yvy1001, yvy1011, ty_Int) → new_lt17(yvy1001, yvy1011)
new_esEs10(yvy4000, yvy3000, ty_Char) → new_esEs15(yvy4000, yvy3000)
new_primEqInt(Pos(Succ(yvy400000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(yvy300000))) → False
new_ltEs5(Nothing, Just(yvy1010), eh) → True
new_lt20(yvy152, yvy155, ty_Int) → new_lt17(yvy152, yvy155)
new_esEs35(yvy153, yvy156, app(ty_Maybe, eba)) → new_esEs23(yvy153, yvy156, eba)
new_esEs27(yvy1000, yvy1010, ty_@0) → new_esEs19(yvy1000, yvy1010)
new_ltEs18(yvy107, yvy108, ty_Float) → new_ltEs11(yvy107, yvy108)
new_compare25(yvy152, yvy153, yvy154, yvy155, yvy156, yvy157, True, dhc, dhd, dhe) → EQ
new_esEs37(yvy40000, yvy30000, ty_Int) → new_esEs25(yvy40000, yvy30000)
new_primCmpNat0(Zero, Zero) → EQ
new_esEs27(yvy1000, yvy1010, app(app(ty_Either, bgf), bgg)) → new_esEs24(yvy1000, yvy1010, bgf, bgg)
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_compare27(Left(yvy4000), Right(yvy3000), eff, efg) → LT
new_lt22(yvy1000, yvy1010, ty_@0) → new_lt19(yvy1000, yvy1010)
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_compare9(@0, @0) → EQ
new_esEs28(yvy1001, yvy1011, ty_Int) → new_esEs25(yvy1001, yvy1011)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Float, hh) → new_esEs14(yvy40000, yvy30000)
new_esEs6(yvy4002, yvy3002, ty_Float) → new_esEs14(yvy4002, yvy3002)
new_ltEs9(yvy100, yvy101, cdh) → new_fsEs(new_compare13(yvy100, yvy101, cdh))
new_compare17(yvy218, yvy219, yvy220, yvy221, yvy222, yvy223, True, yvy225, ceb, cec, ced) → new_compare14(yvy218, yvy219, yvy220, yvy221, yvy222, yvy223, True, ceb, cec, ced)
new_esEs32(yvy40001, yvy30001, ty_Char) → new_esEs15(yvy40001, yvy30001)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_ltEs14(Left(yvy1000), Left(yvy1010), app(ty_[], dad), dac) → new_ltEs8(yvy1000, yvy1010, dad)
new_ltEs19(yvy1002, yvy1012, app(app(ty_@2, cag), cah)) → new_ltEs12(yvy1002, yvy1012, cag, cah)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Double, hh) → new_esEs13(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, app(app(ty_Either, daa), dab)) → new_esEs24(yvy40002, yvy30002, daa, dab)
new_esEs4(yvy4000, yvy3000, ty_Int) → new_esEs25(yvy4000, yvy3000)
new_compare28(yvy114, yvy115, True, fad, fae) → EQ
new_primEqInt(Pos(Succ(yvy400000)), Neg(yvy30000)) → False
new_primEqInt(Neg(Succ(yvy400000)), Pos(yvy30000)) → False
new_esEs24(Right(yvy40000), Right(yvy30000), hg, ty_Int) → new_esEs25(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, ty_Ordering) → new_esEs12(yvy40002, yvy30002)
new_esEs29(yvy40000, yvy30000, app(app(app(ty_@3, cbh), cca), ccb)) → new_esEs22(yvy40000, yvy30000, cbh, cca, ccb)
new_esEs26(yvy40000, yvy30000, ty_Double) → new_esEs13(yvy40000, yvy30000)
new_ltEs20(yvy154, yvy157, ty_Integer) → new_ltEs4(yvy154, yvy157)
new_compare210(yvy100, yvy101, True, feg) → EQ
new_lt6(yvy1000, yvy1010, ty_Ordering) → new_lt7(yvy1000, yvy1010)
new_esEs29(yvy40000, yvy30000, app(ty_Ratio, cbg)) → new_esEs21(yvy40000, yvy30000, cbg)
new_esEs20(False, False) → True
new_esEs24(Left(yvy40000), Left(yvy30000), app(ty_[], dee), hh) → new_esEs16(yvy40000, yvy30000, dee)
new_lt23(yvy165, yvy167, app(ty_[], fcb)) → new_lt9(yvy165, yvy167, fcb)
new_ltEs22(yvy114, yvy115, ty_Integer) → new_ltEs4(yvy114, yvy115)
new_ltEs5(Just(yvy1000), Just(yvy1010), app(app(ty_Either, gb), gc)) → new_ltEs14(yvy1000, yvy1010, gb, gc)
new_lt23(yvy165, yvy167, ty_Bool) → new_lt18(yvy165, yvy167)
new_esEs30(yvy40001, yvy30001, ty_Ordering) → new_esEs12(yvy40001, yvy30001)
new_lt6(yvy1000, yvy1010, ty_Integer) → new_lt15(yvy1000, yvy1010)
new_primEqInt(Pos(Zero), Neg(Succ(yvy300000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(yvy300000))) → False
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_compare30(yvy400, yvy300, app(ty_Maybe, ffb)) → new_compare31(yvy400, yvy300, ffb)
new_esEs9(yvy4000, yvy3000, ty_Ordering) → new_esEs12(yvy4000, yvy3000)
new_esEs7(yvy4000, yvy3000, ty_@0) → new_esEs19(yvy4000, yvy3000)
new_esEs11(yvy4000, yvy3000, ty_Float) → new_esEs14(yvy4000, yvy3000)
new_lt6(yvy1000, yvy1010, app(ty_[], bff)) → new_lt9(yvy1000, yvy1010, bff)
new_esEs36(yvy1000, yvy1010, ty_@0) → new_esEs19(yvy1000, yvy1010)
new_esEs5(yvy4001, yvy3001, ty_@0) → new_esEs19(yvy4001, yvy3001)
new_esEs36(yvy1000, yvy1010, app(app(app(ty_@3, edd), ede), edf)) → new_esEs22(yvy1000, yvy1010, edd, ede, edf)
new_esEs28(yvy1001, yvy1011, ty_Ordering) → new_esEs12(yvy1001, yvy1011)
new_esEs10(yvy4000, yvy3000, app(ty_[], efh)) → new_esEs16(yvy4000, yvy3000, efh)
new_primCompAux0(yvy56, LT) → LT
new_esEs6(yvy4002, yvy3002, app(app(ty_Either, bcc), bcd)) → new_esEs24(yvy4002, yvy3002, bcc, bcd)
new_esEs6(yvy4002, yvy3002, ty_Integer) → new_esEs18(yvy4002, yvy3002)
new_esEs36(yvy1000, yvy1010, app(app(ty_@2, edg), edh)) → new_esEs17(yvy1000, yvy1010, edg, edh)
new_esEs7(yvy4000, yvy3000, app(app(ty_@2, cb), cc)) → new_esEs17(yvy4000, yvy3000, cb, cc)
new_esEs9(yvy4000, yvy3000, ty_Float) → new_esEs14(yvy4000, yvy3000)
new_lt5(yvy1001, yvy1011, ty_Double) → new_lt13(yvy1001, yvy1011)
new_ltEs22(yvy114, yvy115, app(ty_Maybe, fbe)) → new_ltEs5(yvy114, yvy115, fbe)
new_not(False) → True
new_esEs27(yvy1000, yvy1010, ty_Int) → new_esEs25(yvy1000, yvy1010)
new_esEs34(yvy152, yvy155, app(ty_Ratio, cea)) → new_esEs21(yvy152, yvy155, cea)
new_compare30(yvy400, yvy300, ty_Bool) → new_compare12(yvy400, yvy300)
new_esEs25(yvy4000, yvy3000) → new_primEqInt(yvy4000, yvy3000)
new_esEs28(yvy1001, yvy1011, app(ty_[], bgh)) → new_esEs16(yvy1001, yvy1011, bgh)
new_esEs31(yvy40000, yvy30000, ty_Char) → new_esEs15(yvy40000, yvy30000)
new_esEs14(Float(yvy40000, yvy40001), Float(yvy30000, yvy30001)) → new_esEs25(new_sr0(yvy40000, yvy30000), new_sr0(yvy40001, yvy30001))
new_esEs11(yvy4000, yvy3000, ty_@0) → new_esEs19(yvy4000, yvy3000)
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_esEs12(GT, EQ) → False
new_esEs12(EQ, GT) → False
new_esEs36(yvy1000, yvy1010, ty_Float) → new_esEs14(yvy1000, yvy1010)
new_esEs4(yvy4000, yvy3000, ty_Ordering) → new_esEs12(yvy4000, yvy3000)
new_esEs9(yvy4000, yvy3000, app(app(ty_Either, fgc), fgd)) → new_esEs24(yvy4000, yvy3000, fgc, fgd)
new_lt6(yvy1000, yvy1010, app(app(app(ty_@3, bfh), bga), bgb)) → new_lt4(yvy1000, yvy1010, bfh, bga, bgb)
new_esEs4(yvy4000, yvy3000, app(app(ty_@2, gh), ha)) → new_esEs17(yvy4000, yvy3000, gh, ha)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, ty_Integer) → new_esEs18(yvy40000, yvy30000)
new_ltEs18(yvy107, yvy108, ty_@0) → new_ltEs17(yvy107, yvy108)
new_esEs39(yvy165, yvy167, ty_Int) → new_esEs25(yvy165, yvy167)
new_compare15(LT, EQ) → LT
new_esEs34(yvy152, yvy155, ty_Float) → new_esEs14(yvy152, yvy155)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, app(ty_[], dbg)) → new_ltEs8(yvy1000, yvy1010, dbg)
new_esEs36(yvy1000, yvy1010, app(ty_Ratio, edc)) → new_esEs21(yvy1000, yvy1010, edc)
new_esEs30(yvy40001, yvy30001, app(ty_Ratio, cda)) → new_esEs21(yvy40001, yvy30001, cda)
new_compare30(yvy400, yvy300, app(ty_Ratio, ffa)) → new_compare13(yvy400, yvy300, ffa)
new_esEs24(Left(yvy40000), Right(yvy30000), hg, hh) → False
new_esEs24(Right(yvy40000), Left(yvy30000), hg, hh) → False
new_lt20(yvy152, yvy155, app(app(ty_Either, dhh), eaa)) → new_lt16(yvy152, yvy155, dhh, eaa)
new_esEs30(yvy40001, yvy30001, app(app(ty_@2, ccg), cch)) → new_esEs17(yvy40001, yvy30001, ccg, cch)
new_esEs32(yvy40001, yvy30001, app(app(ty_Either, cgg), cgh)) → new_esEs24(yvy40001, yvy30001, cgg, cgh)
new_esEs34(yvy152, yvy155, app(ty_[], dhf)) → new_esEs16(yvy152, yvy155, dhf)
new_lt20(yvy152, yvy155, ty_Double) → new_lt13(yvy152, yvy155)
new_esEs35(yvy153, yvy156, ty_Double) → new_esEs13(yvy153, yvy156)
new_compare0(:(yvy4000, yvy4001), [], feh) → GT
new_lt6(yvy1000, yvy1010, ty_Char) → new_lt8(yvy1000, yvy1010)
new_esEs8(yvy4001, yvy3001, ty_Int) → new_esEs25(yvy4001, yvy3001)
new_esEs38(yvy40001, yvy30001, ty_Int) → new_esEs25(yvy40001, yvy30001)
new_ltEs24(yvy100, yvy101, ty_Integer) → new_ltEs4(yvy100, yvy101)
new_ltEs20(yvy154, yvy157, app(ty_Maybe, ecc)) → new_ltEs5(yvy154, yvy157, ecc)
new_ltEs20(yvy154, yvy157, ty_@0) → new_ltEs17(yvy154, yvy157)
new_ltEs24(yvy100, yvy101, app(app(ty_Either, dbf), dac)) → new_ltEs14(yvy100, yvy101, dbf, dac)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Int) → new_esEs25(yvy40000, yvy30000)
new_esEs34(yvy152, yvy155, app(app(ty_Either, dhh), eaa)) → new_esEs24(yvy152, yvy155, dhh, eaa)
new_lt13(yvy152, yvy155) → new_esEs12(new_compare29(yvy152, yvy155), LT)
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_esEs30(yvy40001, yvy30001, app(app(ty_Either, cdf), cdg)) → new_esEs24(yvy40001, yvy30001, cdf, cdg)
new_lt19(yvy152, yvy155) → new_esEs12(new_compare9(yvy152, yvy155), LT)
new_ltEs18(yvy107, yvy108, ty_Char) → new_ltEs7(yvy107, yvy108)
new_esEs4(yvy4000, yvy3000, app(app(ty_Either, hg), hh)) → new_esEs24(yvy4000, yvy3000, hg, hh)
new_esEs8(yvy4001, yvy3001, app(ty_Ratio, dg)) → new_esEs21(yvy4001, yvy3001, dg)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Integer) → new_esEs18(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, app(ty_Ratio, chd)) → new_esEs21(yvy40002, yvy30002, chd)
new_lt17(yvy152, yvy155) → new_esEs12(new_compare16(yvy152, yvy155), LT)
new_esEs10(yvy4000, yvy3000, app(app(ty_@2, ega), egb)) → new_esEs17(yvy4000, yvy3000, ega, egb)
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_ltEs7(yvy100, yvy101) → new_fsEs(new_compare11(yvy100, yvy101))
new_esEs31(yvy40000, yvy30000, ty_Float) → new_esEs14(yvy40000, yvy30000)
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_compare15(EQ, GT) → LT
new_esEs32(yvy40001, yvy30001, ty_Int) → new_esEs25(yvy40001, yvy30001)
new_esEs29(yvy40000, yvy30000, ty_Char) → new_esEs15(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, app(app(app(ty_@3, che), chf), chg)) → new_esEs22(yvy40002, yvy30002, che, chf, chg)
new_primEqNat0(Zero, Succ(yvy300000)) → False
new_primEqNat0(Succ(yvy400000), Zero) → False
new_compare15(LT, GT) → LT
new_lt15(yvy152, yvy155) → new_esEs12(new_compare8(yvy152, yvy155), LT)
new_ltEs5(Nothing, Nothing, eh) → True
new_ltEs23(yvy166, yvy168, app(app(app(ty_@3, fdf), fdg), fdh)) → new_ltEs10(yvy166, yvy168, fdf, fdg, fdh)
new_lt20(yvy152, yvy155, app(app(ty_@2, dec), ded)) → new_lt12(yvy152, yvy155, dec, ded)
new_ltEs6(LT, LT) → True
new_ltEs6(EQ, LT) → False
new_esEs6(yvy4002, yvy3002, app(ty_Ratio, bbf)) → new_esEs21(yvy4002, yvy3002, bbf)
new_ltEs5(Just(yvy1000), Just(yvy1010), app(ty_[], fa)) → new_ltEs8(yvy1000, yvy1010, fa)
new_ltEs19(yvy1002, yvy1012, ty_Char) → new_ltEs7(yvy1002, yvy1012)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_ltEs21(yvy1001, yvy1011, app(ty_Ratio, eee)) → new_ltEs9(yvy1001, yvy1011, eee)
new_esEs9(yvy4000, yvy3000, app(ty_Maybe, fgb)) → new_esEs23(yvy4000, yvy3000, fgb)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Bool) → new_ltEs16(yvy1000, yvy1010)
new_lt21(yvy153, yvy156, app(ty_Maybe, eba)) → new_lt14(yvy153, yvy156, eba)
new_compare15(GT, GT) → EQ
new_esEs11(yvy4000, yvy3000, app(app(ty_@2, ehc), ehd)) → new_esEs17(yvy4000, yvy3000, ehc, ehd)
new_esEs8(yvy4001, yvy3001, app(app(ty_Either, ed), ee)) → new_esEs24(yvy4001, yvy3001, ed, ee)
new_compare24(yvy165, yvy166, yvy167, yvy168, True, fbh, fca) → EQ
new_esEs32(yvy40001, yvy30001, ty_Bool) → new_esEs20(yvy40001, yvy30001)
new_lt21(yvy153, yvy156, ty_Float) → new_lt11(yvy153, yvy156)
new_esEs16(:(yvy40000, yvy40001), [], gg) → False
new_esEs16([], :(yvy30000, yvy30001), gg) → False
new_compare31(Just(yvy4000), Just(yvy3000), ffb) → new_compare210(yvy4000, yvy3000, new_esEs9(yvy4000, yvy3000, ffb), ffb)
new_lt21(yvy153, yvy156, ty_Ordering) → new_lt7(yvy153, yvy156)
new_lt20(yvy152, yvy155, ty_Bool) → new_lt18(yvy152, yvy155)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, app(ty_Ratio, dbh)) → new_ltEs9(yvy1000, yvy1010, dbh)
new_ltEs19(yvy1002, yvy1012, ty_@0) → new_ltEs17(yvy1002, yvy1012)
new_esEs7(yvy4000, yvy3000, app(app(app(ty_@3, ce), cf), cg)) → new_esEs22(yvy4000, yvy3000, ce, cf, cg)
new_esEs5(yvy4001, yvy3001, ty_Integer) → new_esEs18(yvy4001, yvy3001)
new_esEs31(yvy40000, yvy30000, ty_Int) → new_esEs25(yvy40000, yvy30000)
new_esEs27(yvy1000, yvy1010, app(app(app(ty_@3, bfh), bga), bgb)) → new_esEs22(yvy1000, yvy1010, bfh, bga, bgb)
new_ltEs19(yvy1002, yvy1012, app(ty_Maybe, cba)) → new_ltEs5(yvy1002, yvy1012, cba)
new_lt21(yvy153, yvy156, ty_Integer) → new_lt15(yvy153, yvy156)
new_esEs29(yvy40000, yvy30000, app(app(ty_Either, ccd), cce)) → new_esEs24(yvy40000, yvy30000, ccd, cce)
new_esEs10(yvy4000, yvy3000, app(ty_Ratio, egc)) → new_esEs21(yvy4000, yvy3000, egc)
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_ltEs12(@2(yvy1000, yvy1001), @2(yvy1010, yvy1011), ech, eda) → new_pePe(new_lt22(yvy1000, yvy1010, ech), new_asAs(new_esEs36(yvy1000, yvy1010, ech), new_ltEs21(yvy1001, yvy1011, eda)))
new_ltEs23(yvy166, yvy168, ty_@0) → new_ltEs17(yvy166, yvy168)
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_esEs5(yvy4001, yvy3001, app(ty_Maybe, bah)) → new_esEs23(yvy4001, yvy3001, bah)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Char) → new_ltEs7(yvy1000, yvy1010)
new_compare0(:(yvy4000, yvy4001), :(yvy3000, yvy3001), feh) → new_primCompAux1(yvy4000, yvy3000, new_compare0(yvy4001, yvy3001, feh), feh)
new_esEs20(False, True) → False
new_esEs20(True, False) → False
new_compare19(yvy206, yvy207, True, dha, dhb) → LT
new_sr0(yvy3000, yvy4001) → new_primMulInt(yvy3000, yvy4001)
new_esEs28(yvy1001, yvy1011, app(app(ty_@2, bhe), bhf)) → new_esEs17(yvy1001, yvy1011, bhe, bhf)
new_lt6(yvy1000, yvy1010, app(app(ty_Either, bgf), bgg)) → new_lt16(yvy1000, yvy1010, bgf, bgg)
new_esEs34(yvy152, yvy155, ty_Bool) → new_esEs20(yvy152, yvy155)
new_lt22(yvy1000, yvy1010, ty_Integer) → new_lt15(yvy1000, yvy1010)
new_esEs26(yvy40000, yvy30000, app(app(ty_Either, bde), bdf)) → new_esEs24(yvy40000, yvy30000, bde, bdf)
new_compare30(yvy400, yvy300, ty_Ordering) → new_compare15(yvy400, yvy300)
new_esEs30(yvy40001, yvy30001, app(ty_[], ccf)) → new_esEs16(yvy40001, yvy30001, ccf)
new_esEs24(Left(yvy40000), Left(yvy30000), app(app(ty_@2, def), deg), hh) → new_esEs17(yvy40000, yvy30000, def, deg)
new_lt23(yvy165, yvy167, ty_@0) → new_lt19(yvy165, yvy167)
new_esEs10(yvy4000, yvy3000, ty_Float) → new_esEs14(yvy4000, yvy3000)
new_compare29(Double(yvy4000, yvy4001), Double(yvy3000, yvy3001)) → new_compare16(new_sr0(yvy4000, yvy3000), new_sr0(yvy4001, yvy3001))
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, ty_Bool) → new_ltEs16(yvy1000, yvy1010)
new_ltEs22(yvy114, yvy115, app(ty_[], faf)) → new_ltEs8(yvy114, yvy115, faf)
new_esEs39(yvy165, yvy167, app(app(ty_Either, fdb), fdc)) → new_esEs24(yvy165, yvy167, fdb, fdc)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs32(yvy40001, yvy30001, ty_Double) → new_esEs13(yvy40001, yvy30001)
new_esEs28(yvy1001, yvy1011, ty_Bool) → new_esEs20(yvy1001, yvy1011)
new_esEs23(Just(yvy40000), Just(yvy30000), app(ty_Ratio, ddd)) → new_esEs21(yvy40000, yvy30000, ddd)
new_esEs5(yvy4001, yvy3001, app(ty_Ratio, bad)) → new_esEs21(yvy4001, yvy3001, bad)
new_ltEs14(Left(yvy1000), Right(yvy1010), dbf, dac) → True
new_compare24(yvy165, yvy166, yvy167, yvy168, False, fbh, fca) → new_compare110(yvy165, yvy166, yvy167, yvy168, new_lt23(yvy165, yvy167, fbh), new_asAs(new_esEs39(yvy165, yvy167, fbh), new_ltEs23(yvy166, yvy168, fca)), fbh, fca)
new_compare30(yvy400, yvy300, app(ty_[], feh)) → new_compare0(yvy400, yvy300, feh)
new_esEs9(yvy4000, yvy3000, app(ty_Ratio, fff)) → new_esEs21(yvy4000, yvy3000, fff)
new_ltEs20(yvy154, yvy157, app(app(ty_Either, ecd), ece)) → new_ltEs14(yvy154, yvy157, ecd, ece)
new_asAs(False, yvy184) → False
new_compare27(Right(yvy4000), Left(yvy3000), eff, efg) → GT
new_esEs36(yvy1000, yvy1010, app(ty_Maybe, eea)) → new_esEs23(yvy1000, yvy1010, eea)
new_esEs9(yvy4000, yvy3000, ty_Double) → new_esEs13(yvy4000, yvy3000)
new_ltEs19(yvy1002, yvy1012, app(app(ty_Either, cbb), cbc)) → new_ltEs14(yvy1002, yvy1012, cbb, cbc)
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_lt20(yvy152, yvy155, ty_@0) → new_lt19(yvy152, yvy155)
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_esEs4(yvy4000, yvy3000, ty_@0) → new_esEs19(yvy4000, yvy3000)
new_esEs27(yvy1000, yvy1010, ty_Double) → new_esEs13(yvy1000, yvy1010)
new_esEs36(yvy1000, yvy1010, ty_Ordering) → new_esEs12(yvy1000, yvy1010)
new_compare16(yvy400, yvy300) → new_primCmpInt(yvy400, yvy300)
new_esEs35(yvy153, yvy156, ty_Bool) → new_esEs20(yvy153, yvy156)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Bool) → new_esEs20(yvy40000, yvy30000)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Integer, dac) → new_ltEs4(yvy1000, yvy1010)
new_compare14(yvy218, yvy219, yvy220, yvy221, yvy222, yvy223, True, ceb, cec, ced) → LT
new_esEs30(yvy40001, yvy30001, app(ty_Maybe, cde)) → new_esEs23(yvy40001, yvy30001, cde)
new_esEs8(yvy4001, yvy3001, ty_Char) → new_esEs15(yvy4001, yvy3001)
new_esEs9(yvy4000, yvy3000, ty_Bool) → new_esEs20(yvy4000, yvy3000)
new_lt5(yvy1001, yvy1011, ty_Ordering) → new_lt7(yvy1001, yvy1011)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, ty_Ordering) → new_ltEs6(yvy1000, yvy1010)
new_esEs24(Left(yvy40000), Left(yvy30000), app(app(ty_Either, dfe), dff), hh) → new_esEs24(yvy40000, yvy30000, dfe, dff)
new_esEs8(yvy4001, yvy3001, app(ty_[], dd)) → new_esEs16(yvy4001, yvy3001, dd)
new_compare27(Left(yvy4000), Left(yvy3000), eff, efg) → new_compare26(yvy4000, yvy3000, new_esEs10(yvy4000, yvy3000, eff), eff, efg)
new_esEs29(yvy40000, yvy30000, ty_Double) → new_esEs13(yvy40000, yvy30000)
new_esEs27(yvy1000, yvy1010, ty_Integer) → new_esEs18(yvy1000, yvy1010)
new_esEs18(Integer(yvy40000), Integer(yvy30000)) → new_primEqInt(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, ty_Char) → new_esEs15(yvy40002, yvy30002)
new_ltEs5(Just(yvy1000), Just(yvy1010), app(ty_Maybe, ga)) → new_ltEs5(yvy1000, yvy1010, ga)
new_ltEs11(yvy100, yvy101) → new_fsEs(new_compare18(yvy100, yvy101))
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, app(app(ty_Either, dcg), dch)) → new_ltEs14(yvy1000, yvy1010, dcg, dch)
new_esEs30(yvy40001, yvy30001, ty_Float) → new_esEs14(yvy40001, yvy30001)
new_lt23(yvy165, yvy167, ty_Float) → new_lt11(yvy165, yvy167)
new_compare12(False, False) → EQ
new_esEs28(yvy1001, yvy1011, ty_@0) → new_esEs19(yvy1001, yvy1011)
new_ltEs23(yvy166, yvy168, ty_Char) → new_ltEs7(yvy166, yvy168)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, app(ty_Maybe, dgf)) → new_esEs23(yvy40000, yvy30000, dgf)
new_esEs29(yvy40000, yvy30000, ty_Float) → new_esEs14(yvy40000, yvy30000)
new_esEs7(yvy4000, yvy3000, ty_Ordering) → new_esEs12(yvy4000, yvy3000)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Integer, hh) → new_esEs18(yvy40000, yvy30000)
new_lt20(yvy152, yvy155, app(ty_Maybe, dhg)) → new_lt14(yvy152, yvy155, dhg)
new_esEs39(yvy165, yvy167, app(app(app(ty_@3, fcd), fce), fcf)) → new_esEs22(yvy165, yvy167, fcd, fce, fcf)
new_esEs31(yvy40000, yvy30000, ty_@0) → new_esEs19(yvy40000, yvy30000)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, app(ty_[], dfg)) → new_esEs16(yvy40000, yvy30000, dfg)
new_compare111(yvy233, yvy234, yvy235, yvy236, False, ecf, ecg) → GT
new_lt21(yvy153, yvy156, ty_Bool) → new_lt18(yvy153, yvy156)
new_ltEs6(LT, GT) → True
new_esEs33(yvy40002, yvy30002, ty_Int) → new_esEs25(yvy40002, yvy30002)
new_compare30(yvy400, yvy300, ty_Integer) → new_compare8(yvy400, yvy300)
new_ltEs23(yvy166, yvy168, app(ty_Maybe, fec)) → new_ltEs5(yvy166, yvy168, fec)
new_lt23(yvy165, yvy167, app(ty_Maybe, fda)) → new_lt14(yvy165, yvy167, fda)
new_ltEs21(yvy1001, yvy1011, ty_Char) → new_ltEs7(yvy1001, yvy1011)
new_ltEs14(Left(yvy1000), Left(yvy1010), app(app(ty_Either, dbd), dbe), dac) → new_ltEs14(yvy1000, yvy1010, dbd, dbe)
new_ltEs23(yvy166, yvy168, app(app(ty_@2, fea), feb)) → new_ltEs12(yvy166, yvy168, fea, feb)
new_ltEs21(yvy1001, yvy1011, ty_Ordering) → new_ltEs6(yvy1001, yvy1011)
new_esEs32(yvy40001, yvy30001, app(app(ty_@2, cfh), cga)) → new_esEs17(yvy40001, yvy30001, cfh, cga)
new_esEs24(Left(yvy40000), Left(yvy30000), app(ty_Maybe, dfd), hh) → new_esEs23(yvy40000, yvy30000, dfd)
new_lt22(yvy1000, yvy1010, app(ty_Ratio, edc)) → new_lt10(yvy1000, yvy1010, edc)
new_lt12(yvy152, yvy155, dec, ded) → new_esEs12(new_compare7(yvy152, yvy155, dec, ded), LT)
new_esEs35(yvy153, yvy156, ty_Int) → new_esEs25(yvy153, yvy156)
new_lt10(yvy152, yvy155, cea) → new_esEs12(new_compare13(yvy152, yvy155, cea), LT)
new_esEs4(yvy4000, yvy3000, ty_Double) → new_esEs13(yvy4000, yvy3000)
new_esEs8(yvy4001, yvy3001, app(app(ty_@2, de), df)) → new_esEs17(yvy4001, yvy3001, de, df)
new_esEs5(yvy4001, yvy3001, app(app(ty_@2, bab), bac)) → new_esEs17(yvy4001, yvy3001, bab, bac)
new_esEs16([], [], gg) → True
new_lt22(yvy1000, yvy1010, ty_Float) → new_lt11(yvy1000, yvy1010)
new_esEs32(yvy40001, yvy30001, ty_Ordering) → new_esEs12(yvy40001, yvy30001)
new_ltEs19(yvy1002, yvy1012, ty_Int) → new_ltEs15(yvy1002, yvy1012)
new_ltEs21(yvy1001, yvy1011, ty_Integer) → new_ltEs4(yvy1001, yvy1011)
new_ltEs20(yvy154, yvy157, ty_Float) → new_ltEs11(yvy154, yvy157)
new_lt5(yvy1001, yvy1011, app(app(ty_@2, bhe), bhf)) → new_lt12(yvy1001, yvy1011, bhe, bhf)
new_esEs11(yvy4000, yvy3000, ty_Int) → new_esEs25(yvy4000, yvy3000)
new_esEs32(yvy40001, yvy30001, app(app(app(ty_@3, cgc), cgd), cge)) → new_esEs22(yvy40001, yvy30001, cgc, cgd, cge)
new_lt6(yvy1000, yvy1010, ty_Double) → new_lt13(yvy1000, yvy1010)
new_lt20(yvy152, yvy155, ty_Float) → new_lt11(yvy152, yvy155)
new_ltEs14(Left(yvy1000), Left(yvy1010), app(app(app(ty_@3, daf), dag), dah), dac) → new_ltEs10(yvy1000, yvy1010, daf, dag, dah)
new_esEs26(yvy40000, yvy30000, ty_Integer) → new_esEs18(yvy40000, yvy30000)
new_lt22(yvy1000, yvy1010, app(app(app(ty_@3, edd), ede), edf)) → new_lt4(yvy1000, yvy1010, edd, ede, edf)
new_esEs36(yvy1000, yvy1010, app(app(ty_Either, eeb), eec)) → new_esEs24(yvy1000, yvy1010, eeb, eec)
new_esEs27(yvy1000, yvy1010, ty_Ordering) → new_esEs12(yvy1000, yvy1010)
new_ltEs19(yvy1002, yvy1012, ty_Double) → new_ltEs13(yvy1002, yvy1012)
new_lt21(yvy153, yvy156, ty_Int) → new_lt17(yvy153, yvy156)
new_lt20(yvy152, yvy155, ty_Integer) → new_lt15(yvy152, yvy155)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, ty_Ordering) → new_esEs12(yvy40000, yvy30000)
new_lt8(yvy152, yvy155) → new_esEs12(new_compare11(yvy152, yvy155), LT)
new_ltEs24(yvy100, yvy101, app(ty_[], fef)) → new_ltEs8(yvy100, yvy101, fef)
new_esEs9(yvy4000, yvy3000, ty_@0) → new_esEs19(yvy4000, yvy3000)
new_esEs22(@3(yvy40000, yvy40001, yvy40002), @3(yvy30000, yvy30001, yvy30002), hc, hd, he) → new_asAs(new_esEs31(yvy40000, yvy30000, hc), new_asAs(new_esEs32(yvy40001, yvy30001, hd), new_esEs33(yvy40002, yvy30002, he)))
new_esEs8(yvy4001, yvy3001, ty_Float) → new_esEs14(yvy4001, yvy3001)
new_esEs7(yvy4000, yvy3000, app(ty_Ratio, cd)) → new_esEs21(yvy4000, yvy3000, cd)
new_ltEs20(yvy154, yvy157, ty_Double) → new_ltEs13(yvy154, yvy157)
new_ltEs18(yvy107, yvy108, ty_Bool) → new_ltEs16(yvy107, yvy108)
new_compare28(yvy114, yvy115, False, fad, fae) → new_compare19(yvy114, yvy115, new_ltEs22(yvy114, yvy115, fae), fad, fae)
new_esEs6(yvy4002, yvy3002, app(ty_Maybe, bcb)) → new_esEs23(yvy4002, yvy3002, bcb)
new_lt5(yvy1001, yvy1011, app(app(app(ty_@3, bhb), bhc), bhd)) → new_lt4(yvy1001, yvy1011, bhb, bhc, bhd)
new_esEs31(yvy40000, yvy30000, app(app(app(ty_@3, cfa), cfb), cfc)) → new_esEs22(yvy40000, yvy30000, cfa, cfb, cfc)
new_esEs31(yvy40000, yvy30000, ty_Ordering) → new_esEs12(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, ty_Double) → new_esEs13(yvy40002, yvy30002)
new_lt6(yvy1000, yvy1010, ty_Float) → new_lt11(yvy1000, yvy1010)
new_esEs4(yvy4000, yvy3000, ty_Char) → new_esEs15(yvy4000, yvy3000)
new_esEs7(yvy4000, yvy3000, app(app(ty_Either, db), dc)) → new_esEs24(yvy4000, yvy3000, db, dc)
new_compare112(yvy189, yvy190, False, fge) → GT
new_esEs12(GT, GT) → True
new_ltEs21(yvy1001, yvy1011, app(app(app(ty_@3, eef), eeg), eeh)) → new_ltEs10(yvy1001, yvy1011, eef, eeg, eeh)
new_esEs5(yvy4001, yvy3001, ty_Double) → new_esEs13(yvy4001, yvy3001)
new_compare17(yvy218, yvy219, yvy220, yvy221, yvy222, yvy223, False, yvy225, ceb, cec, ced) → new_compare14(yvy218, yvy219, yvy220, yvy221, yvy222, yvy223, yvy225, ceb, cec, ced)
new_esEs8(yvy4001, yvy3001, app(ty_Maybe, ec)) → new_esEs23(yvy4001, yvy3001, ec)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_@0) → new_esEs19(yvy40000, yvy30000)
new_compare25(yvy152, yvy153, yvy154, yvy155, yvy156, yvy157, False, dhc, dhd, dhe) → new_compare17(yvy152, yvy153, yvy154, yvy155, yvy156, yvy157, new_lt20(yvy152, yvy155, dhc), new_asAs(new_esEs34(yvy152, yvy155, dhc), new_pePe(new_lt21(yvy153, yvy156, dhd), new_asAs(new_esEs35(yvy153, yvy156, dhd), new_ltEs20(yvy154, yvy157, dhe)))), dhc, dhd, dhe)
new_compare31(Nothing, Just(yvy3000), ffb) → LT
new_esEs29(yvy40000, yvy30000, ty_Ordering) → new_esEs12(yvy40000, yvy30000)
new_esEs4(yvy4000, yvy3000, app(ty_[], gg)) → new_esEs16(yvy4000, yvy3000, gg)
new_primPlusNat1(Zero, Zero) → Zero
new_compare0([], :(yvy3000, yvy3001), feh) → LT
new_ltEs6(LT, EQ) → True
new_lt23(yvy165, yvy167, ty_Ordering) → new_lt7(yvy165, yvy167)
new_ltEs21(yvy1001, yvy1011, app(ty_Maybe, efc)) → new_ltEs5(yvy1001, yvy1011, efc)
new_ltEs6(GT, LT) → False
new_lt18(yvy152, yvy155) → new_esEs12(new_compare12(yvy152, yvy155), LT)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, ty_Char) → new_esEs15(yvy40000, yvy30000)
new_asAs(True, yvy184) → yvy184
new_esEs26(yvy40000, yvy30000, ty_Float) → new_esEs14(yvy40000, yvy30000)
new_esEs35(yvy153, yvy156, ty_Float) → new_esEs14(yvy153, yvy156)
new_ltEs21(yvy1001, yvy1011, app(ty_[], eed)) → new_ltEs8(yvy1001, yvy1011, eed)
new_compare11(Char(yvy4000), Char(yvy3000)) → new_primCmpNat0(yvy4000, yvy3000)
new_ltEs22(yvy114, yvy115, ty_Float) → new_ltEs11(yvy114, yvy115)
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_esEs28(yvy1001, yvy1011, app(ty_Ratio, bha)) → new_esEs21(yvy1001, yvy1011, bha)
new_esEs39(yvy165, yvy167, ty_Double) → new_esEs13(yvy165, yvy167)
new_esEs11(yvy4000, yvy3000, ty_Bool) → new_esEs20(yvy4000, yvy3000)
new_ltEs22(yvy114, yvy115, ty_Double) → new_ltEs13(yvy114, yvy115)
new_lt22(yvy1000, yvy1010, ty_Ordering) → new_lt7(yvy1000, yvy1010)
new_esEs4(yvy4000, yvy3000, app(app(app(ty_@3, hc), hd), he)) → new_esEs22(yvy4000, yvy3000, hc, hd, he)
new_lt20(yvy152, yvy155, app(ty_Ratio, cea)) → new_lt10(yvy152, yvy155, cea)
new_ltEs16(False, False) → True
new_lt23(yvy165, yvy167, ty_Double) → new_lt13(yvy165, yvy167)
new_ltEs17(yvy100, yvy101) → new_fsEs(new_compare9(yvy100, yvy101))
new_esEs29(yvy40000, yvy30000, ty_Integer) → new_esEs18(yvy40000, yvy30000)
new_esEs8(yvy4001, yvy3001, ty_Ordering) → new_esEs12(yvy4001, yvy3001)
new_esEs30(yvy40001, yvy30001, ty_Bool) → new_esEs20(yvy40001, yvy30001)
new_lt23(yvy165, yvy167, app(ty_Ratio, fcc)) → new_lt10(yvy165, yvy167, fcc)
new_esEs30(yvy40001, yvy30001, ty_Int) → new_esEs25(yvy40001, yvy30001)
new_esEs27(yvy1000, yvy1010, ty_Float) → new_esEs14(yvy1000, yvy1010)
new_ltEs21(yvy1001, yvy1011, ty_Int) → new_ltEs15(yvy1001, yvy1011)
new_ltEs20(yvy154, yvy157, app(app(app(ty_@3, ebf), ebg), ebh)) → new_ltEs10(yvy154, yvy157, ebf, ebg, ebh)
new_esEs23(Just(yvy40000), Just(yvy30000), app(ty_[], dda)) → new_esEs16(yvy40000, yvy30000, dda)
new_esEs34(yvy152, yvy155, app(app(app(ty_@3, bd), be), bf)) → new_esEs22(yvy152, yvy155, bd, be, bf)
new_esEs16(:(yvy40000, yvy40001), :(yvy30000, yvy30001), gg) → new_asAs(new_esEs26(yvy40000, yvy30000, gg), new_esEs16(yvy40001, yvy30001, gg))
new_esEs9(yvy4000, yvy3000, app(app(app(ty_@3, ffg), ffh), fga)) → new_esEs22(yvy4000, yvy3000, ffg, ffh, fga)
new_ltEs19(yvy1002, yvy1012, app(app(app(ty_@3, cad), cae), caf)) → new_ltEs10(yvy1002, yvy1012, cad, cae, caf)
new_ltEs20(yvy154, yvy157, ty_Ordering) → new_ltEs6(yvy154, yvy157)
new_compare19(yvy206, yvy207, False, dha, dhb) → GT
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Integer) → new_ltEs4(yvy1000, yvy1010)
new_esEs6(yvy4002, yvy3002, ty_@0) → new_esEs19(yvy4002, yvy3002)
new_ltEs10(@3(yvy1000, yvy1001, yvy1002), @3(yvy1010, yvy1011, yvy1012), bfc, bfd, bfe) → new_pePe(new_lt6(yvy1000, yvy1010, bfc), new_asAs(new_esEs27(yvy1000, yvy1010, bfc), new_pePe(new_lt5(yvy1001, yvy1011, bfd), new_asAs(new_esEs28(yvy1001, yvy1011, bfd), new_ltEs19(yvy1002, yvy1012, bfe)))))
new_esEs33(yvy40002, yvy30002, ty_@0) → new_esEs19(yvy40002, yvy30002)
new_esEs35(yvy153, yvy156, app(ty_Ratio, eac)) → new_esEs21(yvy153, yvy156, eac)
new_ltEs22(yvy114, yvy115, ty_Int) → new_ltEs15(yvy114, yvy115)
new_ltEs24(yvy100, yvy101, app(app(app(ty_@3, bfc), bfd), bfe)) → new_ltEs10(yvy100, yvy101, bfc, bfd, bfe)
new_compare27(Right(yvy4000), Right(yvy3000), eff, efg) → new_compare28(yvy4000, yvy3000, new_esEs11(yvy4000, yvy3000, efg), eff, efg)
new_ltEs21(yvy1001, yvy1011, ty_@0) → new_ltEs17(yvy1001, yvy1011)
new_lt16(yvy152, yvy155, dhh, eaa) → new_esEs12(new_compare27(yvy152, yvy155, dhh, eaa), LT)
new_compare15(EQ, EQ) → EQ
new_ltEs22(yvy114, yvy115, ty_Char) → new_ltEs7(yvy114, yvy115)
new_compare30(yvy400, yvy300, ty_Double) → new_compare29(yvy400, yvy300)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCompAux0(yvy56, EQ) → yvy56
new_lt6(yvy1000, yvy1010, app(app(ty_@2, bgc), bgd)) → new_lt12(yvy1000, yvy1010, bgc, bgd)
new_esEs27(yvy1000, yvy1010, app(ty_Maybe, bge)) → new_esEs23(yvy1000, yvy1010, bge)
new_ltEs20(yvy154, yvy157, ty_Char) → new_ltEs7(yvy154, yvy157)
new_esEs10(yvy4000, yvy3000, ty_Integer) → new_esEs18(yvy4000, yvy3000)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_@0, dac) → new_ltEs17(yvy1000, yvy1010)
new_ltEs18(yvy107, yvy108, ty_Int) → new_ltEs15(yvy107, yvy108)
new_lt21(yvy153, yvy156, app(app(app(ty_@3, ead), eae), eaf)) → new_lt4(yvy153, yvy156, ead, eae, eaf)
new_esEs6(yvy4002, yvy3002, ty_Char) → new_esEs15(yvy4002, yvy3002)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_esEs30(yvy40001, yvy30001, ty_Char) → new_esEs15(yvy40001, yvy30001)
new_ltEs5(Just(yvy1000), Just(yvy1010), app(app(app(ty_@3, fc), fd), ff)) → new_ltEs10(yvy1000, yvy1010, fc, fd, ff)
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_esEs39(yvy165, yvy167, app(ty_[], fcb)) → new_esEs16(yvy165, yvy167, fcb)
new_esEs35(yvy153, yvy156, ty_Char) → new_esEs15(yvy153, yvy156)
new_not(True) → False
new_ltEs5(Just(yvy1000), Just(yvy1010), app(ty_Ratio, fb)) → new_ltEs9(yvy1000, yvy1010, fb)

The set Q consists of the following terms:

new_esEs36(x0, x1, ty_Char)
new_esEs29(x0, x1, ty_Float)
new_lt22(x0, x1, app(ty_Maybe, x2))
new_esEs7(x0, x1, ty_Int)
new_ltEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs21(x0, x1, ty_Int)
new_ltEs14(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs10(x0, x1, ty_Float)
new_ltEs16(True, True)
new_esEs6(x0, x1, ty_Int)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs32(x0, x1, app(ty_Maybe, x2))
new_lt11(x0, x1)
new_esEs24(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs20(x0, x1, ty_Int)
new_lt5(x0, x1, ty_Char)
new_esEs5(x0, x1, app(ty_[], x2))
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs36(x0, x1, app(ty_[], x2))
new_lt21(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs21(x0, x1, ty_@0)
new_esEs29(x0, x1, ty_Char)
new_ltEs22(x0, x1, ty_Integer)
new_esEs34(x0, x1, app(ty_[], x2))
new_esEs32(x0, x1, ty_Int)
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs11(x0, x1, ty_Int)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs4(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_Integer)
new_compare30(x0, x1, ty_Int)
new_pePe(True, x0)
new_esEs5(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs11(x0, x1, ty_@0)
new_esEs35(x0, x1, ty_Integer)
new_esEs11(x0, x1, ty_Char)
new_esEs9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(x0, x1, ty_Float)
new_esEs9(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(x0, x1, ty_Int)
new_esEs31(x0, x1, app(app(ty_Either, x2), x3))
new_lt22(x0, x1, ty_@0)
new_compare30(x0, x1, ty_Bool)
new_ltEs5(Nothing, Just(x0), x1)
new_lt20(x0, x1, ty_@0)
new_esEs29(x0, x1, ty_Ordering)
new_lt22(x0, x1, ty_Float)
new_esEs9(x0, x1, app(ty_[], x2))
new_lt23(x0, x1, ty_Integer)
new_ltEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(Right(x0), Right(x1), x2, ty_Bool)
new_lt7(x0, x1)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs8(x0, x1, ty_Integer)
new_esEs23(Just(x0), Just(x1), ty_Float)
new_esEs6(x0, x1, ty_Integer)
new_lt5(x0, x1, ty_@0)
new_esEs33(x0, x1, app(app(ty_@2, x2), x3))
new_esEs11(x0, x1, ty_Bool)
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs24(Right(x0), Right(x1), x2, ty_Integer)
new_compare12(False, True)
new_compare12(True, False)
new_ltEs7(x0, x1)
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_primCompAux0(x0, EQ)
new_esEs32(x0, x1, app(app(ty_@2, x2), x3))
new_lt6(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(x0, x1, ty_Integer)
new_esEs32(x0, x1, ty_Ordering)
new_ltEs21(x0, x1, ty_Float)
new_ltEs24(x0, x1, ty_Integer)
new_esEs34(x0, x1, ty_Float)
new_esEs6(x0, x1, ty_@0)
new_lt6(x0, x1, ty_Float)
new_esEs9(x0, x1, ty_Int)
new_compare30(x0, x1, ty_Integer)
new_esEs12(GT, EQ)
new_esEs12(EQ, GT)
new_esEs36(x0, x1, ty_Int)
new_esEs28(x0, x1, ty_Bool)
new_ltEs14(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs24(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_compare30(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_lt5(x0, x1, ty_Double)
new_compare15(LT, LT)
new_esEs10(x0, x1, ty_Char)
new_esEs23(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primMulNat0(Succ(x0), Zero)
new_ltEs22(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_compare6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs34(x0, x1, ty_Ordering)
new_esEs16([], [], x0)
new_esEs12(GT, GT)
new_esEs30(x0, x1, ty_Double)
new_esEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs21(x0, x1, ty_Ordering)
new_esEs10(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_lt21(x0, x1, ty_Float)
new_esEs11(x0, x1, ty_Integer)
new_esEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs21(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs24(x0, x1, app(ty_Maybe, x2))
new_esEs23(Just(x0), Just(x1), ty_Double)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_Char)
new_esEs34(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(Left(x0), Left(x1), ty_Int, x2)
new_esEs38(x0, x1, ty_Integer)
new_ltEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs27(x0, x1, ty_Bool)
new_esEs24(Right(x0), Right(x1), x2, ty_Char)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs6(EQ, EQ)
new_esEs32(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(x0, x1, ty_Float)
new_esEs8(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs22(x0, x1, ty_Char)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(x0, x1, ty_Double)
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_esEs5(x0, x1, ty_Bool)
new_lt6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs31(x0, x1, ty_Int)
new_compare26(x0, x1, True, x2, x3)
new_compare110(x0, x1, x2, x3, True, x4, x5, x6)
new_ltEs24(x0, x1, app(ty_[], x2))
new_compare27(Right(x0), Left(x1), x2, x3)
new_compare27(Left(x0), Right(x1), x2, x3)
new_esEs33(x0, x1, ty_Double)
new_esEs8(x0, x1, ty_Float)
new_ltEs18(x0, x1, ty_@0)
new_esEs4(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, app(ty_[], x2))
new_ltEs5(Just(x0), Just(x1), ty_@0)
new_lt5(x0, x1, ty_Int)
new_ltEs6(LT, EQ)
new_ltEs6(EQ, LT)
new_esEs24(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_primCompAux0(x0, LT)
new_esEs23(Nothing, Nothing, x0)
new_esEs38(x0, x1, ty_Int)
new_esEs23(Just(x0), Just(x1), ty_Int)
new_ltEs20(x0, x1, ty_@0)
new_lt6(x0, x1, app(ty_Maybe, x2))
new_esEs11(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Int)
new_lt17(x0, x1)
new_esEs8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs36(x0, x1, ty_Bool)
new_primEqNat0(Zero, Zero)
new_compare13(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs26(x0, x1, ty_@0)
new_lt21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(Right(x0), Right(x1), x2, ty_Int)
new_esEs7(x0, x1, ty_Bool)
new_esEs33(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs5(x0, x1, ty_Float)
new_ltEs14(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_compare17(x0, x1, x2, x3, x4, x5, False, x6, x7, x8, x9)
new_ltEs22(x0, x1, ty_Float)
new_compare15(GT, GT)
new_esEs31(x0, x1, ty_Double)
new_ltEs20(x0, x1, ty_Integer)
new_lt22(x0, x1, ty_Bool)
new_compare30(x0, x1, app(ty_[], x2))
new_esEs34(x0, x1, ty_Bool)
new_esEs31(x0, x1, ty_Integer)
new_ltEs20(x0, x1, ty_Char)
new_lt20(x0, x1, ty_Double)
new_esEs35(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_compare28(x0, x1, True, x2, x3)
new_ltEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs21(x0, x1, app(ty_[], x2))
new_ltEs15(x0, x1)
new_esEs4(x0, x1, ty_Integer)
new_esEs39(x0, x1, app(ty_Ratio, x2))
new_esEs6(x0, x1, app(app(ty_Either, x2), x3))
new_esEs39(x0, x1, ty_Bool)
new_esEs6(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs24(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Float)
new_ltEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_primMulNat0(Zero, Zero)
new_asAs(True, x0)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_ltEs14(Left(x0), Right(x1), x2, x3)
new_ltEs14(Right(x0), Left(x1), x2, x3)
new_esEs26(x0, x1, ty_Double)
new_esEs5(x0, x1, ty_Double)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs35(x0, x1, app(app(ty_@2, x2), x3))
new_fsEs(x0)
new_esEs16(:(x0, x1), [], x2)
new_ltEs5(Just(x0), Just(x1), ty_Integer)
new_esEs35(x0, x1, app(ty_Ratio, x2))
new_lt6(x0, x1, ty_Double)
new_esEs35(x0, x1, ty_Double)
new_ltEs18(x0, x1, ty_Bool)
new_esEs23(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Float)
new_ltEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(x0, x1, app(ty_Maybe, x2))
new_compare28(x0, x1, False, x2, x3)
new_ltEs5(Just(x0), Just(x1), ty_Double)
new_lt22(x0, x1, ty_Ordering)
new_lt23(x0, x1, app(ty_Ratio, x2))
new_esEs9(x0, x1, ty_@0)
new_esEs6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare24(x0, x1, x2, x3, False, x4, x5)
new_esEs24(Left(x0), Left(x1), ty_@0, x2)
new_esEs35(x0, x1, ty_Bool)
new_esEs35(x0, x1, ty_Char)
new_ltEs23(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, ty_Bool)
new_ltEs10(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs31(x0, x1, ty_@0)
new_lt10(x0, x1, x2)
new_ltEs19(x0, x1, ty_Double)
new_lt12(x0, x1, x2, x3)
new_ltEs24(x0, x1, ty_Double)
new_esEs13(Double(x0, x1), Double(x2, x3))
new_esEs10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Ordering)
new_esEs5(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(Just(x0), Nothing, x1)
new_ltEs14(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs24(Right(x0), Right(x1), x2, ty_@0)
new_esEs20(True, True)
new_lt22(x0, x1, ty_Int)
new_esEs7(x0, x1, ty_Integer)
new_esEs30(x0, x1, ty_Bool)
new_lt21(x0, x1, ty_@0)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs4(x0, x1, app(ty_Maybe, x2))
new_esEs33(x0, x1, ty_Float)
new_esEs29(x0, x1, ty_Integer)
new_ltEs21(x0, x1, ty_Integer)
new_lt16(x0, x1, x2, x3)
new_primPlusNat0(Zero, x0)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs4(x0, x1, ty_Ordering)
new_esEs8(x0, x1, ty_Bool)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_primPlusNat0(Succ(x0), x1)
new_ltEs4(x0, x1)
new_esEs34(x0, x1, ty_Integer)
new_esEs31(x0, x1, ty_Ordering)
new_ltEs6(GT, LT)
new_ltEs6(LT, GT)
new_compare0([], [], x0)
new_ltEs22(x0, x1, app(ty_Maybe, x2))
new_esEs35(x0, x1, app(ty_Maybe, x2))
new_compare111(x0, x1, x2, x3, True, x4, x5)
new_esEs11(x0, x1, ty_Double)
new_lt19(x0, x1)
new_ltEs14(Left(x0), Left(x1), ty_Double, x2)
new_ltEs8(x0, x1, x2)
new_ltEs14(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs4(x0, x1, ty_Double)
new_esEs36(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, ty_Double)
new_esEs39(x0, x1, ty_Char)
new_ltEs22(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_compare15(EQ, EQ)
new_lt6(x0, x1, ty_Int)
new_lt21(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, ty_Ordering)
new_ltEs14(Right(x0), Right(x1), x2, ty_Double)
new_ltEs22(x0, x1, ty_Ordering)
new_ltEs11(x0, x1)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_compare7(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt20(x0, x1, ty_Float)
new_lt21(x0, x1, ty_Integer)
new_esEs32(x0, x1, ty_Bool)
new_esEs39(x0, x1, ty_Float)
new_compare10(x0, x1, False, x2, x3)
new_lt6(x0, x1, ty_Integer)
new_lt4(x0, x1, x2, x3, x4)
new_esEs10(x0, x1, ty_Double)
new_esEs31(x0, x1, app(ty_[], x2))
new_sr0(x0, x1)
new_esEs23(Just(x0), Just(x1), ty_Integer)
new_esEs24(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs20(False, True)
new_esEs20(True, False)
new_esEs29(x0, x1, ty_Bool)
new_esEs24(Left(x0), Right(x1), x2, x3)
new_esEs24(Right(x0), Left(x1), x2, x3)
new_ltEs23(x0, x1, ty_Integer)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs36(x0, x1, app(ty_Ratio, x2))
new_esEs20(False, False)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare12(False, False)
new_esEs12(LT, EQ)
new_esEs12(EQ, LT)
new_lt21(x0, x1, ty_Int)
new_lt22(x0, x1, ty_Char)
new_ltEs14(Left(x0), Left(x1), ty_Char, x2)
new_ltEs14(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare14(x0, x1, x2, x3, x4, x5, True, x6, x7, x8)
new_esEs31(x0, x1, ty_Float)
new_esEs24(Left(x0), Left(x1), ty_Float, x2)
new_primPlusNat1(Zero, Zero)
new_ltEs21(x0, x1, ty_Bool)
new_esEs24(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs20(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_Float)
new_esEs12(EQ, EQ)
new_esEs23(Just(x0), Just(x1), ty_Bool)
new_esEs27(x0, x1, ty_Char)
new_ltEs14(Right(x0), Right(x1), x2, ty_Int)
new_esEs9(x0, x1, ty_Integer)
new_esEs30(x0, x1, ty_Float)
new_ltEs20(x0, x1, ty_Float)
new_lt22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(Right(x0), Right(x1), x2, ty_Char)
new_esEs9(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Left(x0), Left(x1), ty_Float, x2)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs16(:(x0, x1), :(x2, x3), x4)
new_esEs28(x0, x1, ty_Double)
new_esEs30(x0, x1, ty_Char)
new_compare30(x0, x1, ty_@0)
new_esEs6(x0, x1, ty_Bool)
new_esEs16([], :(x0, x1), x2)
new_ltEs23(x0, x1, ty_Float)
new_esEs9(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs31(x0, x1, app(app(ty_@2, x2), x3))
new_compare15(EQ, GT)
new_compare15(GT, EQ)
new_compare17(x0, x1, x2, x3, x4, x5, True, x6, x7, x8, x9)
new_ltEs9(x0, x1, x2)
new_ltEs24(x0, x1, ty_Ordering)
new_compare30(x0, x1, ty_Char)
new_primEqNat0(Succ(x0), Zero)
new_compare15(LT, GT)
new_compare15(GT, LT)
new_esEs36(x0, x1, ty_Double)
new_esEs39(x0, x1, ty_Ordering)
new_esEs7(x0, x1, app(app(ty_Either, x2), x3))
new_lt21(x0, x1, app(ty_[], x2))
new_esEs37(x0, x1, ty_Int)
new_esEs9(x0, x1, ty_Double)
new_primMulInt(Neg(x0), Neg(x1))
new_ltEs5(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs17(x0, x1)
new_compare0([], :(x0, x1), x2)
new_esEs9(x0, x1, ty_Ordering)
new_ltEs12(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs26(x0, x1, ty_Char)
new_lt23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_lt23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs23(x0, x1, ty_Int)
new_primEqNat0(Succ(x0), Succ(x1))
new_compare210(x0, x1, True, x2)
new_esEs8(x0, x1, ty_Int)
new_ltEs14(Left(x0), Left(x1), ty_Bool, x2)
new_lt21(x0, x1, app(ty_Maybe, x2))
new_ltEs5(Just(x0), Just(x1), ty_Int)
new_esEs33(x0, x1, ty_Int)
new_ltEs23(x0, x1, ty_@0)
new_lt6(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs33(x0, x1, ty_Bool)
new_esEs10(x0, x1, ty_Ordering)
new_esEs24(Left(x0), Left(x1), ty_Double, x2)
new_esEs35(x0, x1, ty_@0)
new_esEs4(x0, x1, ty_Char)
new_compare112(x0, x1, False, x2)
new_esEs24(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_lt23(x0, x1, ty_Int)
new_ltEs14(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs18(x0, x1, ty_Double)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt23(x0, x1, ty_Bool)
new_ltEs14(Left(x0), Left(x1), ty_Integer, x2)
new_esEs24(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_lt9(x0, x1, x2)
new_ltEs18(x0, x1, app(ty_[], x2))
new_esEs33(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, app(ty_[], x2))
new_lt5(x0, x1, app(app(ty_Either, x2), x3))
new_lt21(x0, x1, ty_Bool)
new_esEs24(Left(x0), Left(x1), ty_Char, x2)
new_ltEs5(Nothing, Nothing, x0)
new_compare18(Float(x0, x1), Float(x2, x3))
new_ltEs5(Just(x0), Just(x1), ty_Float)
new_esEs26(x0, x1, ty_Bool)
new_lt6(x0, x1, ty_Bool)
new_esEs30(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Integer)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs8(x0, x1, ty_Double)
new_lt21(x0, x1, ty_Char)
new_lt5(x0, x1, ty_Float)
new_compare11(Char(x0), Char(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs24(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs36(x0, x1, app(app(ty_Either, x2), x3))
new_esEs30(x0, x1, ty_Integer)
new_esEs25(x0, x1)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_compare210(x0, x1, False, x2)
new_esEs29(x0, x1, ty_@0)
new_ltEs14(Left(x0), Left(x1), ty_Int, x2)
new_sr(Integer(x0), Integer(x1))
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs7(x0, x1, ty_@0)
new_esEs39(x0, x1, app(ty_Maybe, x2))
new_primMulNat0(Succ(x0), Succ(x1))
new_ltEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs34(x0, x1, ty_Char)
new_esEs4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs10(x0, x1, ty_Bool)
new_lt5(x0, x1, app(ty_[], x2))
new_esEs10(x0, x1, ty_@0)
new_esEs39(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_@0)
new_esEs31(x0, x1, ty_Bool)
new_primEqNat0(Zero, Succ(x0))
new_primPlusNat1(Succ(x0), Zero)
new_lt23(x0, x1, ty_Char)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs7(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Char)
new_ltEs21(x0, x1, app(ty_Maybe, x2))
new_esEs6(x0, x1, ty_Ordering)
new_esEs33(x0, x1, ty_Char)
new_compare27(Left(x0), Left(x1), x2, x3)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs32(x0, x1, ty_Integer)
new_ltEs14(Left(x0), Left(x1), ty_Ordering, x2)
new_pePe(False, x0)
new_ltEs24(x0, x1, ty_Int)
new_compare24(x0, x1, x2, x3, True, x4, x5)
new_lt8(x0, x1)
new_esEs39(x0, x1, app(app(ty_Either, x2), x3))
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt23(x0, x1, ty_Double)
new_esEs10(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Bool)
new_esEs9(x0, x1, app(app(ty_@2, x2), x3))
new_esEs32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, ty_Int)
new_esEs30(x0, x1, ty_Ordering)
new_lt23(x0, x1, ty_Float)
new_lt6(x0, x1, ty_@0)
new_primPlusNat1(Succ(x0), Succ(x1))
new_compare27(Right(x0), Right(x1), x2, x3)
new_esEs31(x0, x1, ty_Char)
new_lt22(x0, x1, ty_Double)
new_ltEs22(x0, x1, ty_@0)
new_esEs39(x0, x1, ty_Int)
new_esEs30(x0, x1, ty_@0)
new_compare14(x0, x1, x2, x3, x4, x5, False, x6, x7, x8)
new_ltEs16(False, True)
new_ltEs16(True, False)
new_ltEs6(GT, GT)
new_esEs10(x0, x1, ty_Int)
new_compare30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(x0, x1, app(ty_Maybe, x2))
new_esEs31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs32(x0, x1, ty_Char)
new_esEs23(Nothing, Just(x0), x1)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(x0, x1, ty_Int)
new_ltEs5(Just(x0), Just(x1), ty_Ordering)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_ltEs19(x0, x1, ty_Char)
new_ltEs22(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(Just(x0), Just(x1), ty_Char)
new_esEs27(x0, x1, ty_Int)
new_esEs24(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs4(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(Just(x0), Just(x1), ty_Bool)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_Bool)
new_lt22(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_@0)
new_ltEs22(x0, x1, ty_Bool)
new_esEs30(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_Integer)
new_esEs33(x0, x1, ty_Integer)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, ty_Int)
new_primCmpNat0(Zero, Zero)
new_esEs35(x0, x1, ty_Float)
new_asAs(False, x0)
new_lt5(x0, x1, ty_Integer)
new_ltEs24(x0, x1, ty_@0)
new_esEs17(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs19(x0, x1, ty_Int)
new_lt23(x0, x1, ty_@0)
new_esEs34(x0, x1, ty_Int)
new_ltEs6(LT, LT)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs35(x0, x1, app(ty_[], x2))
new_esEs35(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare31(Just(x0), Just(x1), x2)
new_esEs11(x0, x1, ty_Ordering)
new_esEs31(x0, x1, app(ty_Ratio, x2))
new_lt5(x0, x1, app(ty_Ratio, x2))
new_ltEs22(x0, x1, ty_Double)
new_ltEs14(Left(x0), Left(x1), ty_@0, x2)
new_lt23(x0, x1, app(ty_[], x2))
new_compare10(x0, x1, True, x2, x3)
new_ltEs24(x0, x1, ty_Char)
new_esEs21(:%(x0, x1), :%(x2, x3), x4)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs18(Integer(x0), Integer(x1))
new_esEs4(x0, x1, ty_@0)
new_lt22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, ty_Int)
new_ltEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(Just(x0), Just(x1), ty_@0)
new_compare110(x0, x1, x2, x3, False, x4, x5, x6)
new_ltEs14(Right(x0), Right(x1), x2, ty_Integer)
new_compare0(:(x0, x1), [], x2)
new_esEs23(Just(x0), Nothing, x1)
new_ltEs19(x0, x1, ty_Float)
new_esEs6(x0, x1, ty_Char)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_lt21(x0, x1, ty_Double)
new_primCompAux1(x0, x1, x2, x3)
new_esEs32(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs8(x0, x1, app(ty_[], x2))
new_esEs23(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs34(x0, x1, app(app(ty_Either, x2), x3))
new_esEs33(x0, x1, app(ty_[], x2))
new_lt5(x0, x1, ty_Bool)
new_esEs11(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(Just(x0), Just(x1), ty_Char)
new_ltEs13(x0, x1)
new_lt14(x0, x1, x2)
new_ltEs23(x0, x1, ty_Bool)
new_esEs6(x0, x1, app(ty_Ratio, x2))
new_compare15(LT, EQ)
new_compare15(EQ, LT)
new_compare9(@0, @0)
new_lt13(x0, x1)
new_esEs36(x0, x1, ty_Integer)
new_esEs29(x0, x1, ty_Double)
new_ltEs22(x0, x1, app(ty_[], x2))
new_ltEs23(x0, x1, app(ty_Maybe, x2))
new_esEs8(x0, x1, app(ty_Ratio, x2))
new_ltEs18(x0, x1, ty_Float)
new_lt18(x0, x1)
new_lt22(x0, x1, app(ty_Ratio, x2))
new_esEs32(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_Float)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_lt5(x0, x1, ty_Ordering)
new_lt15(x0, x1)
new_compare8(Integer(x0), Integer(x1))
new_lt22(x0, x1, app(ty_[], x2))
new_compare30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs33(x0, x1, app(ty_Ratio, x2))
new_lt5(x0, x1, app(ty_Maybe, x2))
new_esEs36(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs33(x0, x1, app(ty_Maybe, x2))
new_esEs7(x0, x1, app(ty_Maybe, x2))
new_esEs8(x0, x1, ty_@0)
new_lt6(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(x0, x1, ty_Int)
new_not(True)
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_compare30(x0, x1, ty_Float)
new_compare31(Just(x0), Nothing, x1)
new_esEs27(x0, x1, ty_Ordering)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs22(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs23(x0, x1, app(ty_Ratio, x2))
new_ltEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(x0, x1, ty_Bool)
new_esEs32(x0, x1, ty_Float)
new_esEs36(x0, x1, ty_Ordering)
new_esEs9(x0, x1, ty_Bool)
new_esEs23(Just(x0), Just(x1), app(ty_Maybe, x2))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_not(False)
new_esEs24(Left(x0), Left(x1), ty_Ordering, x2)
new_compare29(Double(x0, x1), Double(x2, x3))
new_compare13(:%(x0, x1), :%(x2, x3), ty_Integer)
new_lt6(x0, x1, app(ty_Ratio, x2))
new_primCmpNat0(Succ(x0), Succ(x1))
new_esEs7(x0, x1, ty_Ordering)
new_esEs34(x0, x1, app(ty_Ratio, x2))
new_ltEs23(x0, x1, ty_Char)
new_esEs7(x0, x1, app(ty_[], x2))
new_esEs8(x0, x1, ty_Ordering)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_esEs39(x0, x1, ty_@0)
new_ltEs21(x0, x1, ty_Char)
new_esEs15(Char(x0), Char(x1))
new_esEs7(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(x0, x1, app(ty_Ratio, x2))
new_ltEs6(GT, EQ)
new_ltEs6(EQ, GT)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_esEs7(x0, x1, app(ty_Ratio, x2))
new_esEs32(x0, x1, app(ty_Ratio, x2))
new_primCmpNat0(Zero, Succ(x0))
new_esEs31(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Ordering)
new_lt23(x0, x1, app(ty_Maybe, x2))
new_ltEs21(x0, x1, ty_Double)
new_esEs24(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs8(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs23(x0, x1, app(ty_[], x2))
new_esEs24(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_compare30(x0, x1, ty_Double)
new_compare19(x0, x1, True, x2, x3)
new_esEs36(x0, x1, app(ty_Maybe, x2))
new_esEs24(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs5(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(Right(x0), Right(x1), x2, ty_Double)
new_lt22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(x0, x1, app(ty_[], x2))
new_primCmpNat0(Succ(x0), Zero)
new_compare30(x0, x1, app(ty_Maybe, x2))
new_esEs34(x0, x1, ty_Double)
new_ltEs21(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_@0)
new_esEs11(x0, x1, app(ty_Maybe, x2))
new_esEs6(x0, x1, app(ty_Maybe, x2))
new_ltEs22(x0, x1, ty_Int)
new_compare26(x0, x1, False, x2, x3)
new_compare16(x0, x1)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_esEs23(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs20(x0, x1, ty_Double)
new_ltEs24(x0, x1, ty_Bool)
new_esEs35(x0, x1, ty_Ordering)
new_ltEs18(x0, x1, ty_Integer)
new_esEs39(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs34(x0, x1, ty_@0)
new_compare31(Nothing, Just(x0), x1)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_esEs37(x0, x1, ty_Integer)
new_ltEs18(x0, x1, ty_Char)
new_esEs7(x0, x1, ty_Double)
new_lt23(x0, x1, ty_Ordering)
new_compare112(x0, x1, True, x2)
new_lt21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs34(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs9(x0, x1, ty_Float)
new_esEs23(Just(x0), Just(x1), ty_Ordering)
new_lt6(x0, x1, ty_Char)
new_esEs9(x0, x1, ty_Char)
new_esEs8(x0, x1, ty_Char)
new_esEs35(x0, x1, ty_Int)
new_esEs24(Left(x0), Left(x1), ty_Integer, x2)
new_esEs5(x0, x1, app(ty_Maybe, x2))
new_lt21(x0, x1, app(ty_Ratio, x2))
new_esEs33(x0, x1, ty_@0)
new_esEs24(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs5(x0, x1, ty_Ordering)
new_esEs32(x0, x1, ty_Double)
new_esEs34(x0, x1, app(ty_Maybe, x2))
new_esEs10(x0, x1, app(ty_[], x2))
new_compare30(x0, x1, app(ty_Ratio, x2))
new_ltEs21(x0, x1, app(ty_Ratio, x2))
new_lt23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs24(x0, x1, app(ty_Ratio, x2))
new_esEs14(Float(x0, x1), Float(x2, x3))
new_esEs26(x0, x1, ty_Integer)
new_esEs5(x0, x1, ty_@0)
new_esEs5(x0, x1, ty_Char)
new_esEs7(x0, x1, ty_Char)
new_compare12(True, True)
new_primEqInt(Pos(Zero), Pos(Zero))
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs5(x0, x1, ty_Integer)
new_compare31(Nothing, Nothing, x0)
new_esEs39(x0, x1, app(ty_[], x2))
new_compare30(x0, x1, ty_Ordering)
new_primMulNat0(Zero, Succ(x0))
new_esEs28(x0, x1, app(ty_[], x2))
new_ltEs23(x0, x1, ty_Double)
new_esEs24(Right(x0), Right(x1), x2, ty_Float)
new_esEs11(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_lt5(x0, x1, app(app(ty_@2, x2), x3))
new_primCompAux0(x0, GT)
new_lt6(x0, x1, ty_Ordering)
new_primPlusNat1(Zero, Succ(x0))
new_esEs36(x0, x1, ty_Float)
new_esEs19(@0, @0)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs39(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_compare25(x0, x1, x2, x3, x4, x5, True, x6, x7, x8)
new_esEs36(x0, x1, ty_@0)
new_esEs12(LT, LT)
new_esEs28(x0, x1, ty_Integer)
new_compare19(x0, x1, False, x2, x3)
new_ltEs18(x0, x1, ty_Ordering)
new_ltEs16(False, False)
new_compare111(x0, x1, x2, x3, False, x4, x5)
new_compare25(x0, x1, x2, x3, x4, x5, False, x6, x7, x8)
new_esEs33(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, ty_Ordering)
new_esEs28(x0, x1, ty_@0)
new_esEs11(x0, x1, ty_Float)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs4(x0, x1, app(ty_[], x2))
new_esEs39(x0, x1, ty_Integer)

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

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

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

new_splitLT3(:(yvy300, yvy301), yvy31, yvy32, Branch(yvy330, yvy331, yvy332, yvy333, yvy334), yvy34, [], bb, bc) → new_splitLT3(yvy330, yvy331, yvy332, yvy333, yvy334, [], bb, bc)

The TRS R consists of the following rules:

new_compare210(yvy100, yvy101, False, feg) → new_compare112(yvy100, yvy101, new_ltEs24(yvy100, yvy101, feg), feg)
new_compare7(@2(yvy4000, yvy4001), @2(yvy3000, yvy3001), bg, bh) → new_compare24(yvy4000, yvy4001, yvy3000, yvy3001, new_asAs(new_esEs7(yvy4000, yvy3000, bg), new_esEs8(yvy4001, yvy3001, bh)), bg, bh)
new_esEs24(Left(yvy40000), Left(yvy30000), app(ty_Ratio, deh), hh) → new_esEs21(yvy40000, yvy30000, deh)
new_ltEs19(yvy1002, yvy1012, app(ty_[], cab)) → new_ltEs8(yvy1002, yvy1012, cab)
new_compare112(yvy189, yvy190, True, fge) → LT
new_lt22(yvy1000, yvy1010, ty_Int) → new_lt17(yvy1000, yvy1010)
new_ltEs22(yvy114, yvy115, app(app(ty_@2, fbc), fbd)) → new_ltEs12(yvy114, yvy115, fbc, fbd)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Int, hh) → new_esEs25(yvy40000, yvy30000)
new_esEs6(yvy4002, yvy3002, app(app(app(ty_@3, bbg), bbh), bca)) → new_esEs22(yvy4002, yvy3002, bbg, bbh, bca)
new_esEs27(yvy1000, yvy1010, app(ty_[], bff)) → new_esEs16(yvy1000, yvy1010, bff)
new_esEs20(True, True) → True
new_esEs35(yvy153, yvy156, app(ty_[], eab)) → new_esEs16(yvy153, yvy156, eab)
new_compare8(Integer(yvy4000), Integer(yvy3000)) → new_primCmpInt(yvy4000, yvy3000)
new_esEs8(yvy4001, yvy3001, ty_Bool) → new_esEs20(yvy4001, yvy3001)
new_esEs11(yvy4000, yvy3000, ty_Integer) → new_esEs18(yvy4000, yvy3000)
new_esEs27(yvy1000, yvy1010, app(app(ty_@2, bgc), bgd)) → new_esEs17(yvy1000, yvy1010, bgc, bgd)
new_ltEs20(yvy154, yvy157, app(ty_Ratio, ebe)) → new_ltEs9(yvy154, yvy157, ebe)
new_esEs36(yvy1000, yvy1010, ty_Double) → new_esEs13(yvy1000, yvy1010)
new_esEs28(yvy1001, yvy1011, ty_Float) → new_esEs14(yvy1001, yvy1011)
new_lt6(yvy1000, yvy1010, ty_@0) → new_lt19(yvy1000, yvy1010)
new_compare10(yvy199, yvy200, True, ef, eg) → LT
new_esEs9(yvy4000, yvy3000, ty_Int) → new_esEs25(yvy4000, yvy3000)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, ty_Double) → new_esEs13(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, app(app(ty_@2, chb), chc)) → new_esEs17(yvy40002, yvy30002, chb, chc)
new_ltEs24(yvy100, yvy101, app(ty_Ratio, cdh)) → new_ltEs9(yvy100, yvy101, cdh)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, ty_@0) → new_esEs19(yvy40000, yvy30000)
new_ltEs19(yvy1002, yvy1012, ty_Float) → new_ltEs11(yvy1002, yvy1012)
new_esEs11(yvy4000, yvy3000, app(ty_[], ehb)) → new_esEs16(yvy4000, yvy3000, ehb)
new_lt23(yvy165, yvy167, app(app(app(ty_@3, fcd), fce), fcf)) → new_lt4(yvy165, yvy167, fcd, fce, fcf)
new_esEs7(yvy4000, yvy3000, ty_Double) → new_esEs13(yvy4000, yvy3000)
new_esEs9(yvy4000, yvy3000, ty_Char) → new_esEs15(yvy4000, yvy3000)
new_ltEs23(yvy166, yvy168, ty_Ordering) → new_ltEs6(yvy166, yvy168)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Bool, dac) → new_ltEs16(yvy1000, yvy1010)
new_esEs39(yvy165, yvy167, app(ty_Ratio, fcc)) → new_esEs21(yvy165, yvy167, fcc)
new_esEs10(yvy4000, yvy3000, ty_@0) → new_esEs19(yvy4000, yvy3000)
new_esEs21(:%(yvy40000, yvy40001), :%(yvy30000, yvy30001), hb) → new_asAs(new_esEs37(yvy40000, yvy30000, hb), new_esEs38(yvy40001, yvy30001, hb))
new_lt5(yvy1001, yvy1011, app(ty_Ratio, bha)) → new_lt10(yvy1001, yvy1011, bha)
new_compare13(:%(yvy4000, yvy4001), :%(yvy3000, yvy3001), ty_Integer) → new_compare8(new_sr(yvy4000, yvy3001), new_sr(yvy3000, yvy4001))
new_ltEs22(yvy114, yvy115, app(ty_Ratio, fag)) → new_ltEs9(yvy114, yvy115, fag)
new_ltEs23(yvy166, yvy168, ty_Int) → new_ltEs15(yvy166, yvy168)
new_primMulNat0(Zero, Zero) → Zero
new_ltEs24(yvy100, yvy101, ty_Ordering) → new_ltEs6(yvy100, yvy101)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, ty_Float) → new_ltEs11(yvy1000, yvy1010)
new_esEs39(yvy165, yvy167, app(ty_Maybe, fda)) → new_esEs23(yvy165, yvy167, fda)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Bool, hh) → new_esEs20(yvy40000, yvy30000)
new_compare15(LT, LT) → EQ
new_esEs6(yvy4002, yvy3002, app(app(ty_@2, bbd), bbe)) → new_esEs17(yvy4002, yvy3002, bbd, bbe)
new_esEs4(yvy4000, yvy3000, ty_Integer) → new_esEs18(yvy4000, yvy3000)
new_esEs26(yvy40000, yvy30000, app(ty_[], bce)) → new_esEs16(yvy40000, yvy30000, bce)
new_esEs36(yvy1000, yvy1010, ty_Char) → new_esEs15(yvy1000, yvy1010)
new_esEs28(yvy1001, yvy1011, app(app(ty_Either, bhh), caa)) → new_esEs24(yvy1001, yvy1011, bhh, caa)
new_esEs34(yvy152, yvy155, ty_@0) → new_esEs19(yvy152, yvy155)
new_sr(Integer(yvy30000), Integer(yvy40010)) → Integer(new_primMulInt(yvy30000, yvy40010))
new_esEs7(yvy4000, yvy3000, ty_Float) → new_esEs14(yvy4000, yvy3000)
new_compare12(True, False) → GT
new_lt7(yvy152, yvy155) → new_esEs12(new_compare15(yvy152, yvy155), LT)
new_lt22(yvy1000, yvy1010, app(ty_Maybe, eea)) → new_lt14(yvy1000, yvy1010, eea)
new_ltEs24(yvy100, yvy101, app(ty_Maybe, eh)) → new_ltEs5(yvy100, yvy101, eh)
new_esEs35(yvy153, yvy156, app(app(ty_Either, ebb), ebc)) → new_esEs24(yvy153, yvy156, ebb, ebc)
new_esEs35(yvy153, yvy156, ty_@0) → new_esEs19(yvy153, yvy156)
new_ltEs15(yvy100, yvy101) → new_fsEs(new_compare16(yvy100, yvy101))
new_esEs6(yvy4002, yvy3002, app(ty_[], bbc)) → new_esEs16(yvy4002, yvy3002, bbc)
new_esEs26(yvy40000, yvy30000, ty_@0) → new_esEs19(yvy40000, yvy30000)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_@0, hh) → new_esEs19(yvy40000, yvy30000)
new_ltEs16(False, True) → True
new_esEs26(yvy40000, yvy30000, app(app(app(ty_@3, bda), bdb), bdc)) → new_esEs22(yvy40000, yvy30000, bda, bdb, bdc)
new_esEs10(yvy4000, yvy3000, app(ty_Maybe, egg)) → new_esEs23(yvy4000, yvy3000, egg)
new_ltEs24(yvy100, yvy101, ty_Bool) → new_ltEs16(yvy100, yvy101)
new_compare30(yvy400, yvy300, app(app(ty_@2, bg), bh)) → new_compare7(yvy400, yvy300, bg, bh)
new_esEs17(@2(yvy40000, yvy40001), @2(yvy30000, yvy30001), gh, ha) → new_asAs(new_esEs29(yvy40000, yvy30000, gh), new_esEs30(yvy40001, yvy30001, ha))
new_esEs11(yvy4000, yvy3000, ty_Char) → new_esEs15(yvy4000, yvy3000)
new_lt20(yvy152, yvy155, app(app(app(ty_@3, bd), be), bf)) → new_lt4(yvy152, yvy155, bd, be, bf)
new_esEs27(yvy1000, yvy1010, ty_Bool) → new_esEs20(yvy1000, yvy1010)
new_ltEs23(yvy166, yvy168, app(ty_Ratio, fde)) → new_ltEs9(yvy166, yvy168, fde)
new_esEs34(yvy152, yvy155, ty_Double) → new_esEs13(yvy152, yvy155)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Double) → new_esEs13(yvy40000, yvy30000)
new_esEs10(yvy4000, yvy3000, ty_Int) → new_esEs25(yvy4000, yvy3000)
new_esEs26(yvy40000, yvy30000, ty_Char) → new_esEs15(yvy40000, yvy30000)
new_compare30(yvy400, yvy300, ty_Int) → new_compare16(yvy400, yvy300)
new_fsEs(yvy306) → new_not(new_esEs12(yvy306, GT))
new_ltEs16(True, False) → False
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, ty_Char) → new_ltEs7(yvy1000, yvy1010)
new_esEs7(yvy4000, yvy3000, ty_Int) → new_esEs25(yvy4000, yvy3000)
new_ltEs19(yvy1002, yvy1012, ty_Bool) → new_ltEs16(yvy1002, yvy1012)
new_esEs34(yvy152, yvy155, ty_Ordering) → new_esEs12(yvy152, yvy155)
new_esEs12(GT, LT) → False
new_esEs12(LT, GT) → False
new_esEs27(yvy1000, yvy1010, ty_Char) → new_esEs15(yvy1000, yvy1010)
new_lt5(yvy1001, yvy1011, ty_Integer) → new_lt15(yvy1001, yvy1011)
new_ltEs22(yvy114, yvy115, ty_Ordering) → new_ltEs6(yvy114, yvy115)
new_compare18(Float(yvy4000, yvy4001), Float(yvy3000, yvy3001)) → new_compare16(new_sr0(yvy4000, yvy3000), new_sr0(yvy4001, yvy3001))
new_ltEs18(yvy107, yvy108, app(ty_Ratio, beb)) → new_ltEs9(yvy107, yvy108, beb)
new_ltEs23(yvy166, yvy168, ty_Float) → new_ltEs11(yvy166, yvy168)
new_ltEs18(yvy107, yvy108, app(ty_[], bea)) → new_ltEs8(yvy107, yvy108, bea)
new_ltEs20(yvy154, yvy157, app(app(ty_@2, eca), ecb)) → new_ltEs12(yvy154, yvy157, eca, ecb)
new_esEs31(yvy40000, yvy30000, app(ty_Maybe, cfd)) → new_esEs23(yvy40000, yvy30000, cfd)
new_lt6(yvy1000, yvy1010, app(ty_Ratio, bfg)) → new_lt10(yvy1000, yvy1010, bfg)
new_esEs37(yvy40000, yvy30000, ty_Integer) → new_esEs18(yvy40000, yvy30000)
new_ltEs14(Left(yvy1000), Left(yvy1010), app(app(ty_@2, dba), dbb), dac) → new_ltEs12(yvy1000, yvy1010, dba, dbb)
new_esEs35(yvy153, yvy156, app(app(ty_@2, eag), eah)) → new_esEs17(yvy153, yvy156, eag, eah)
new_esEs5(yvy4001, yvy3001, app(app(app(ty_@3, bae), baf), bag)) → new_esEs22(yvy4001, yvy3001, bae, baf, bag)
new_lt22(yvy1000, yvy1010, ty_Char) → new_lt8(yvy1000, yvy1010)
new_compare110(yvy233, yvy234, yvy235, yvy236, True, yvy238, ecf, ecg) → new_compare111(yvy233, yvy234, yvy235, yvy236, True, ecf, ecg)
new_ltEs24(yvy100, yvy101, app(app(ty_@2, ech), eda)) → new_ltEs12(yvy100, yvy101, ech, eda)
new_ltEs13(yvy100, yvy101) → new_fsEs(new_compare29(yvy100, yvy101))
new_esEs5(yvy4001, yvy3001, app(app(ty_Either, bba), bbb)) → new_esEs24(yvy4001, yvy3001, bba, bbb)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, ty_Bool) → new_esEs20(yvy40000, yvy30000)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Float) → new_ltEs11(yvy1000, yvy1010)
new_esEs8(yvy4001, yvy3001, ty_Double) → new_esEs13(yvy4001, yvy3001)
new_esEs31(yvy40000, yvy30000, app(ty_Ratio, ceh)) → new_esEs21(yvy40000, yvy30000, ceh)
new_esEs29(yvy40000, yvy30000, app(ty_Maybe, ccc)) → new_esEs23(yvy40000, yvy30000, ccc)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Int) → new_ltEs15(yvy1000, yvy1010)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Double) → new_ltEs13(yvy1000, yvy1010)
new_esEs30(yvy40001, yvy30001, ty_Double) → new_esEs13(yvy40001, yvy30001)
new_ltEs21(yvy1001, yvy1011, app(app(ty_@2, efa), efb)) → new_ltEs12(yvy1001, yvy1011, efa, efb)
new_esEs10(yvy4000, yvy3000, ty_Bool) → new_esEs20(yvy4000, yvy3000)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Char, dac) → new_ltEs7(yvy1000, yvy1010)
new_ltEs16(True, True) → True
new_lt21(yvy153, yvy156, app(app(ty_@2, eag), eah)) → new_lt12(yvy153, yvy156, eag, eah)
new_lt6(yvy1000, yvy1010, ty_Bool) → new_lt18(yvy1000, yvy1010)
new_pePe(False, yvy305) → yvy305
new_compare15(GT, EQ) → GT
new_esEs7(yvy4000, yvy3000, ty_Char) → new_esEs15(yvy4000, yvy3000)
new_esEs31(yvy40000, yvy30000, app(ty_[], cee)) → new_esEs16(yvy40000, yvy30000, cee)
new_esEs39(yvy165, yvy167, ty_@0) → new_esEs19(yvy165, yvy167)
new_esEs23(Just(yvy40000), Just(yvy30000), app(ty_Maybe, ddh)) → new_esEs23(yvy40000, yvy30000, ddh)
new_lt21(yvy153, yvy156, ty_Char) → new_lt8(yvy153, yvy156)
new_esEs26(yvy40000, yvy30000, ty_Bool) → new_esEs20(yvy40000, yvy30000)
new_esEs9(yvy4000, yvy3000, app(app(ty_@2, ffd), ffe)) → new_esEs17(yvy4000, yvy3000, ffd, ffe)
new_compare14(yvy218, yvy219, yvy220, yvy221, yvy222, yvy223, False, ceb, cec, ced) → GT
new_lt9(yvy152, yvy155, dhf) → new_esEs12(new_compare0(yvy152, yvy155, dhf), LT)
new_esEs28(yvy1001, yvy1011, ty_Integer) → new_esEs18(yvy1001, yvy1011)
new_esEs5(yvy4001, yvy3001, ty_Ordering) → new_esEs12(yvy4001, yvy3001)
new_esEs5(yvy4001, yvy3001, ty_Int) → new_esEs25(yvy4001, yvy3001)
new_esEs4(yvy4000, yvy3000, ty_Float) → new_esEs14(yvy4000, yvy3000)
new_compare15(GT, LT) → GT
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Char, hh) → new_esEs15(yvy40000, yvy30000)
new_esEs29(yvy40000, yvy30000, ty_Int) → new_esEs25(yvy40000, yvy30000)
new_compare30(yvy400, yvy300, app(app(ty_Either, eff), efg)) → new_compare27(yvy400, yvy300, eff, efg)
new_lt22(yvy1000, yvy1010, ty_Double) → new_lt13(yvy1000, yvy1010)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Ordering) → new_esEs12(yvy40000, yvy30000)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Char) → new_esEs15(yvy40000, yvy30000)
new_esEs29(yvy40000, yvy30000, app(app(ty_@2, cbe), cbf)) → new_esEs17(yvy40000, yvy30000, cbe, cbf)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, app(app(ty_@2, dfh), dga)) → new_esEs17(yvy40000, yvy30000, dfh, dga)
new_ltEs23(yvy166, yvy168, app(app(ty_Either, fed), fee)) → new_ltEs14(yvy166, yvy168, fed, fee)
new_esEs31(yvy40000, yvy30000, ty_Integer) → new_esEs18(yvy40000, yvy30000)
new_compare12(True, True) → EQ
new_esEs36(yvy1000, yvy1010, app(ty_[], edb)) → new_esEs16(yvy1000, yvy1010, edb)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Ordering, hh) → new_esEs12(yvy40000, yvy30000)
new_ltEs6(GT, EQ) → False
new_ltEs18(yvy107, yvy108, app(app(ty_Either, bfa), bfb)) → new_ltEs14(yvy107, yvy108, bfa, bfb)
new_esEs32(yvy40001, yvy30001, app(ty_Maybe, cgf)) → new_esEs23(yvy40001, yvy30001, cgf)
new_esEs35(yvy153, yvy156, ty_Integer) → new_esEs18(yvy153, yvy156)
new_esEs33(yvy40002, yvy30002, ty_Integer) → new_esEs18(yvy40002, yvy30002)
new_esEs31(yvy40000, yvy30000, ty_Double) → new_esEs13(yvy40000, yvy30000)
new_esEs10(yvy4000, yvy3000, ty_Ordering) → new_esEs12(yvy4000, yvy3000)
new_primCompAux1(yvy400, yvy300, yvy51, bb) → new_primCompAux0(yvy51, new_compare30(yvy400, yvy300, bb))
new_esEs33(yvy40002, yvy30002, ty_Float) → new_esEs14(yvy40002, yvy30002)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, app(app(app(ty_@3, dca), dcb), dcc)) → new_ltEs10(yvy1000, yvy1010, dca, dcb, dcc)
new_ltEs23(yvy166, yvy168, app(ty_[], fdd)) → new_ltEs8(yvy166, yvy168, fdd)
new_lt23(yvy165, yvy167, app(app(ty_@2, fcg), fch)) → new_lt12(yvy165, yvy167, fcg, fch)
new_esEs34(yvy152, yvy155, ty_Integer) → new_esEs18(yvy152, yvy155)
new_esEs23(Just(yvy40000), Just(yvy30000), app(app(ty_Either, dea), deb)) → new_esEs24(yvy40000, yvy30000, dea, deb)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Ordering, dac) → new_ltEs6(yvy1000, yvy1010)
new_lt22(yvy1000, yvy1010, ty_Bool) → new_lt18(yvy1000, yvy1010)
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_esEs39(yvy165, yvy167, ty_Float) → new_esEs14(yvy165, yvy167)
new_ltEs22(yvy114, yvy115, ty_Bool) → new_ltEs16(yvy114, yvy115)
new_ltEs4(yvy100, yvy101) → new_fsEs(new_compare8(yvy100, yvy101))
new_esEs33(yvy40002, yvy30002, app(ty_[], cha)) → new_esEs16(yvy40002, yvy30002, cha)
new_ltEs8(yvy100, yvy101, fef) → new_fsEs(new_compare0(yvy100, yvy101, fef))
new_compare30(yvy400, yvy300, ty_Char) → new_compare11(yvy400, yvy300)
new_esEs36(yvy1000, yvy1010, ty_Integer) → new_esEs18(yvy1000, yvy1010)
new_esEs39(yvy165, yvy167, ty_Bool) → new_esEs20(yvy165, yvy167)
new_esEs36(yvy1000, yvy1010, ty_Bool) → new_esEs20(yvy1000, yvy1010)
new_esEs32(yvy40001, yvy30001, app(ty_Ratio, cgb)) → new_esEs21(yvy40001, yvy30001, cgb)
new_compare12(False, True) → LT
new_esEs5(yvy4001, yvy3001, ty_Char) → new_esEs15(yvy4001, yvy3001)
new_esEs34(yvy152, yvy155, ty_Char) → new_esEs15(yvy152, yvy155)
new_esEs31(yvy40000, yvy30000, app(app(ty_@2, cef), ceg)) → new_esEs17(yvy40000, yvy30000, cef, ceg)
new_ltEs18(yvy107, yvy108, ty_Integer) → new_ltEs4(yvy107, yvy108)
new_lt21(yvy153, yvy156, ty_@0) → new_lt19(yvy153, yvy156)
new_esEs30(yvy40001, yvy30001, ty_@0) → new_esEs19(yvy40001, yvy30001)
new_ltEs18(yvy107, yvy108, app(ty_Maybe, beh)) → new_ltEs5(yvy107, yvy108, beh)
new_esEs12(LT, LT) → True
new_ltEs24(yvy100, yvy101, ty_Char) → new_ltEs7(yvy100, yvy101)
new_esEs31(yvy40000, yvy30000, app(app(ty_Either, cfe), cff)) → new_esEs24(yvy40000, yvy30000, cfe, cff)
new_ltEs18(yvy107, yvy108, ty_Double) → new_ltEs13(yvy107, yvy108)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Int, dac) → new_ltEs15(yvy1000, yvy1010)
new_esEs28(yvy1001, yvy1011, app(ty_Maybe, bhg)) → new_esEs23(yvy1001, yvy1011, bhg)
new_lt5(yvy1001, yvy1011, ty_@0) → new_lt19(yvy1001, yvy1011)
new_compare15(EQ, LT) → GT
new_pePe(True, yvy305) → True
new_compare0([], [], feh) → EQ
new_primEqNat0(Zero, Zero) → True
new_ltEs21(yvy1001, yvy1011, ty_Double) → new_ltEs13(yvy1001, yvy1011)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Float) → new_esEs14(yvy40000, yvy30000)
new_esEs6(yvy4002, yvy3002, ty_Double) → new_esEs13(yvy4002, yvy3002)
new_esEs4(yvy4000, yvy3000, app(ty_Maybe, hf)) → new_esEs23(yvy4000, yvy3000, hf)
new_lt5(yvy1001, yvy1011, ty_Bool) → new_lt18(yvy1001, yvy1011)
new_lt23(yvy165, yvy167, ty_Integer) → new_lt15(yvy165, yvy167)
new_esEs5(yvy4001, yvy3001, ty_Float) → new_esEs14(yvy4001, yvy3001)
new_lt21(yvy153, yvy156, app(app(ty_Either, ebb), ebc)) → new_lt16(yvy153, yvy156, ebb, ebc)
new_esEs8(yvy4001, yvy3001, app(app(app(ty_@3, dh), ea), eb)) → new_esEs22(yvy4001, yvy3001, dh, ea, eb)
new_lt11(yvy152, yvy155) → new_esEs12(new_compare18(yvy152, yvy155), LT)
new_lt20(yvy152, yvy155, app(ty_[], dhf)) → new_lt9(yvy152, yvy155, dhf)
new_esEs13(Double(yvy40000, yvy40001), Double(yvy30000, yvy30001)) → new_esEs25(new_sr0(yvy40000, yvy30000), new_sr0(yvy40001, yvy30001))
new_esEs7(yvy4000, yvy3000, ty_Bool) → new_esEs20(yvy4000, yvy3000)
new_compare30(yvy400, yvy300, ty_@0) → new_compare9(yvy400, yvy300)
new_esEs29(yvy40000, yvy30000, ty_@0) → new_esEs19(yvy40000, yvy30000)
new_esEs6(yvy4002, yvy3002, ty_Ordering) → new_esEs12(yvy4002, yvy3002)
new_ltEs18(yvy107, yvy108, app(app(app(ty_@3, bec), bed), bee)) → new_ltEs10(yvy107, yvy108, bec, bed, bee)
new_ltEs22(yvy114, yvy115, ty_@0) → new_ltEs17(yvy114, yvy115)
new_lt5(yvy1001, yvy1011, ty_Char) → new_lt8(yvy1001, yvy1011)
new_lt5(yvy1001, yvy1011, app(app(ty_Either, bhh), caa)) → new_lt16(yvy1001, yvy1011, bhh, caa)
new_ltEs19(yvy1002, yvy1012, ty_Ordering) → new_ltEs6(yvy1002, yvy1012)
new_esEs15(Char(yvy40000), Char(yvy30000)) → new_primEqNat0(yvy40000, yvy30000)
new_esEs24(Left(yvy40000), Left(yvy30000), app(app(app(ty_@3, dfa), dfb), dfc), hh) → new_esEs22(yvy40000, yvy30000, dfa, dfb, dfc)
new_esEs26(yvy40000, yvy30000, ty_Int) → new_esEs25(yvy40000, yvy30000)
new_esEs32(yvy40001, yvy30001, ty_Integer) → new_esEs18(yvy40001, yvy30001)
new_ltEs23(yvy166, yvy168, ty_Double) → new_ltEs13(yvy166, yvy168)
new_lt22(yvy1000, yvy1010, app(ty_[], edb)) → new_lt9(yvy1000, yvy1010, edb)
new_ltEs23(yvy166, yvy168, ty_Integer) → new_ltEs4(yvy166, yvy168)
new_esEs9(yvy4000, yvy3000, app(ty_[], ffc)) → new_esEs16(yvy4000, yvy3000, ffc)
new_esEs33(yvy40002, yvy30002, ty_Bool) → new_esEs20(yvy40002, yvy30002)
new_esEs11(yvy4000, yvy3000, ty_Double) → new_esEs13(yvy4000, yvy3000)
new_esEs29(yvy40000, yvy30000, ty_Bool) → new_esEs20(yvy40000, yvy30000)
new_lt5(yvy1001, yvy1011, app(ty_[], bgh)) → new_lt9(yvy1001, yvy1011, bgh)
new_ltEs21(yvy1001, yvy1011, ty_Bool) → new_ltEs16(yvy1001, yvy1011)
new_ltEs6(EQ, GT) → True
new_esEs9(yvy4000, yvy3000, ty_Integer) → new_esEs18(yvy4000, yvy3000)
new_esEs11(yvy4000, yvy3000, ty_Ordering) → new_esEs12(yvy4000, yvy3000)
new_esEs23(Just(yvy40000), Nothing, hf) → False
new_esEs23(Nothing, Just(yvy30000), hf) → False
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_ltEs18(yvy107, yvy108, ty_Ordering) → new_ltEs6(yvy107, yvy108)
new_esEs23(Just(yvy40000), Just(yvy30000), app(app(app(ty_@3, dde), ddf), ddg)) → new_esEs22(yvy40000, yvy30000, dde, ddf, ddg)
new_ltEs24(yvy100, yvy101, ty_Double) → new_ltEs13(yvy100, yvy101)
new_esEs10(yvy4000, yvy3000, ty_Double) → new_esEs13(yvy4000, yvy3000)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, ty_Float) → new_esEs14(yvy40000, yvy30000)
new_compare110(yvy233, yvy234, yvy235, yvy236, False, yvy238, ecf, ecg) → new_compare111(yvy233, yvy234, yvy235, yvy236, yvy238, ecf, ecg)
new_ltEs20(yvy154, yvy157, ty_Bool) → new_ltEs16(yvy154, yvy157)
new_ltEs24(yvy100, yvy101, ty_@0) → new_ltEs17(yvy100, yvy101)
new_ltEs5(Just(yvy1000), Just(yvy1010), app(app(ty_@2, fg), fh)) → new_ltEs12(yvy1000, yvy1010, fg, fh)
new_ltEs20(yvy154, yvy157, ty_Int) → new_ltEs15(yvy154, yvy157)
new_esEs8(yvy4001, yvy3001, ty_@0) → new_esEs19(yvy4001, yvy3001)
new_lt22(yvy1000, yvy1010, app(app(ty_Either, eeb), eec)) → new_lt16(yvy1000, yvy1010, eeb, eec)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Float, dac) → new_ltEs11(yvy1000, yvy1010)
new_compare26(yvy107, yvy108, False, bdg, bdh) → new_compare10(yvy107, yvy108, new_ltEs18(yvy107, yvy108, bdg), bdg, bdh)
new_lt21(yvy153, yvy156, app(ty_Ratio, eac)) → new_lt10(yvy153, yvy156, eac)
new_compare30(yvy400, yvy300, ty_Float) → new_compare18(yvy400, yvy300)
new_primEqInt(Neg(Succ(yvy400000)), Neg(Succ(yvy300000))) → new_primEqNat0(yvy400000, yvy300000)
new_esEs23(Nothing, Nothing, hf) → True
new_esEs10(yvy4000, yvy3000, app(app(app(ty_@3, egd), ege), egf)) → new_esEs22(yvy4000, yvy3000, egd, ege, egf)
new_esEs39(yvy165, yvy167, app(app(ty_@2, fcg), fch)) → new_esEs17(yvy165, yvy167, fcg, fch)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, app(app(ty_@2, dcd), dce)) → new_ltEs12(yvy1000, yvy1010, dcd, dce)
new_ltEs5(Just(yvy1000), Nothing, eh) → False
new_esEs28(yvy1001, yvy1011, ty_Char) → new_esEs15(yvy1001, yvy1011)
new_esEs11(yvy4000, yvy3000, app(ty_Maybe, faa)) → new_esEs23(yvy4000, yvy3000, faa)
new_lt14(yvy152, yvy155, dhg) → new_esEs12(new_compare31(yvy152, yvy155, dhg), LT)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, ty_@0) → new_ltEs17(yvy1000, yvy1010)
new_ltEs14(Right(yvy1000), Left(yvy1010), dbf, dac) → False
new_esEs12(EQ, LT) → False
new_esEs12(LT, EQ) → False
new_ltEs19(yvy1002, yvy1012, app(ty_Ratio, cac)) → new_ltEs9(yvy1002, yvy1012, cac)
new_lt22(yvy1000, yvy1010, app(app(ty_@2, edg), edh)) → new_lt12(yvy1000, yvy1010, edg, edh)
new_ltEs23(yvy166, yvy168, ty_Bool) → new_ltEs16(yvy166, yvy168)
new_compare111(yvy233, yvy234, yvy235, yvy236, True, ecf, ecg) → LT
new_esEs7(yvy4000, yvy3000, app(ty_[], ca)) → new_esEs16(yvy4000, yvy3000, ca)
new_esEs5(yvy4001, yvy3001, ty_Bool) → new_esEs20(yvy4001, yvy3001)
new_lt23(yvy165, yvy167, ty_Int) → new_lt17(yvy165, yvy167)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs30(yvy40001, yvy30001, app(app(app(ty_@3, cdb), cdc), cdd)) → new_esEs22(yvy40001, yvy30001, cdb, cdc, cdd)
new_esEs11(yvy4000, yvy3000, app(app(ty_Either, fab), fac)) → new_esEs24(yvy4000, yvy3000, fab, fac)
new_esEs35(yvy153, yvy156, app(app(app(ty_@3, ead), eae), eaf)) → new_esEs22(yvy153, yvy156, ead, eae, eaf)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, ty_Int) → new_ltEs15(yvy1000, yvy1010)
new_esEs10(yvy4000, yvy3000, app(app(ty_Either, egh), eha)) → new_esEs24(yvy4000, yvy3000, egh, eha)
new_esEs28(yvy1001, yvy1011, ty_Double) → new_esEs13(yvy1001, yvy1011)
new_lt20(yvy152, yvy155, ty_Ordering) → new_lt7(yvy152, yvy155)
new_ltEs6(EQ, EQ) → True
new_compare31(Just(yvy4000), Nothing, ffb) → GT
new_esEs11(yvy4000, yvy3000, app(app(app(ty_@3, ehf), ehg), ehh)) → new_esEs22(yvy4000, yvy3000, ehf, ehg, ehh)
new_ltEs22(yvy114, yvy115, app(app(ty_Either, fbf), fbg)) → new_ltEs14(yvy114, yvy115, fbf, fbg)
new_esEs28(yvy1001, yvy1011, app(app(app(ty_@3, bhb), bhc), bhd)) → new_esEs22(yvy1001, yvy1011, bhb, bhc, bhd)
new_esEs32(yvy40001, yvy30001, ty_Float) → new_esEs14(yvy40001, yvy30001)
new_esEs27(yvy1000, yvy1010, app(ty_Ratio, bfg)) → new_esEs21(yvy1000, yvy1010, bfg)
new_ltEs19(yvy1002, yvy1012, ty_Integer) → new_ltEs4(yvy1002, yvy1012)
new_primEqInt(Neg(Succ(yvy400000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(yvy300000))) → False
new_primCompAux0(yvy56, GT) → GT
new_compare30(yvy400, yvy300, app(app(app(ty_@3, gd), ge), gf)) → new_compare6(yvy400, yvy300, gd, ge, gf)
new_esEs39(yvy165, yvy167, ty_Integer) → new_esEs18(yvy165, yvy167)
new_compare26(yvy107, yvy108, True, bdg, bdh) → EQ
new_esEs23(Just(yvy40000), Just(yvy30000), app(app(ty_@2, ddb), ddc)) → new_esEs17(yvy40000, yvy30000, ddb, ddc)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, app(app(ty_Either, dgg), dgh)) → new_esEs24(yvy40000, yvy30000, dgg, dgh)
new_ltEs6(GT, GT) → True
new_ltEs21(yvy1001, yvy1011, app(app(ty_Either, efd), efe)) → new_ltEs14(yvy1001, yvy1011, efd, efe)
new_esEs38(yvy40001, yvy30001, ty_Integer) → new_esEs18(yvy40001, yvy30001)
new_esEs32(yvy40001, yvy30001, app(ty_[], cfg)) → new_esEs16(yvy40001, yvy30001, cfg)
new_esEs34(yvy152, yvy155, ty_Int) → new_esEs25(yvy152, yvy155)
new_compare31(Nothing, Nothing, ffb) → EQ
new_esEs29(yvy40000, yvy30000, app(ty_[], cbd)) → new_esEs16(yvy40000, yvy30000, cbd)
new_esEs26(yvy40000, yvy30000, app(ty_Ratio, bch)) → new_esEs21(yvy40000, yvy30000, bch)
new_esEs7(yvy4000, yvy3000, app(ty_Maybe, da)) → new_esEs23(yvy4000, yvy3000, da)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_@0) → new_ltEs17(yvy1000, yvy1010)
new_lt21(yvy153, yvy156, app(ty_[], eab)) → new_lt9(yvy153, yvy156, eab)
new_ltEs20(yvy154, yvy157, app(ty_[], ebd)) → new_ltEs8(yvy154, yvy157, ebd)
new_esEs36(yvy1000, yvy1010, ty_Int) → new_esEs25(yvy1000, yvy1010)
new_esEs19(@0, @0) → True
new_compare6(@3(yvy4000, yvy4001, yvy4002), @3(yvy3000, yvy3001, yvy3002), gd, ge, gf) → new_compare25(yvy4000, yvy4001, yvy4002, yvy3000, yvy3001, yvy3002, new_asAs(new_esEs4(yvy4000, yvy3000, gd), new_asAs(new_esEs5(yvy4001, yvy3001, ge), new_esEs6(yvy4002, yvy3002, gf))), gd, ge, gf)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_esEs7(yvy4000, yvy3000, ty_Integer) → new_esEs18(yvy4000, yvy3000)
new_esEs4(yvy4000, yvy3000, ty_Bool) → new_esEs20(yvy4000, yvy3000)
new_esEs39(yvy165, yvy167, ty_Ordering) → new_esEs12(yvy165, yvy167)
new_lt20(yvy152, yvy155, ty_Char) → new_lt8(yvy152, yvy155)
new_esEs31(yvy40000, yvy30000, ty_Bool) → new_esEs20(yvy40000, yvy30000)
new_lt4(yvy152, yvy155, bd, be, bf) → new_esEs12(new_compare6(yvy152, yvy155, bd, be, bf), LT)
new_esEs6(yvy4002, yvy3002, ty_Int) → new_esEs25(yvy4002, yvy3002)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Double, dac) → new_ltEs13(yvy1000, yvy1010)
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_lt6(yvy1000, yvy1010, app(ty_Maybe, bge)) → new_lt14(yvy1000, yvy1010, bge)
new_ltEs14(Left(yvy1000), Left(yvy1010), app(ty_Maybe, dbc), dac) → new_ltEs5(yvy1000, yvy1010, dbc)
new_esEs4(yvy4000, yvy3000, app(ty_Ratio, hb)) → new_esEs21(yvy4000, yvy3000, hb)
new_lt5(yvy1001, yvy1011, app(ty_Maybe, bhg)) → new_lt14(yvy1001, yvy1011, bhg)
new_primEqInt(Pos(Succ(yvy400000)), Pos(Succ(yvy300000))) → new_primEqNat0(yvy400000, yvy300000)
new_compare10(yvy199, yvy200, False, ef, eg) → GT
new_esEs34(yvy152, yvy155, app(ty_Maybe, dhg)) → new_esEs23(yvy152, yvy155, dhg)
new_esEs5(yvy4001, yvy3001, app(ty_[], baa)) → new_esEs16(yvy4001, yvy3001, baa)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, ty_Double) → new_ltEs13(yvy1000, yvy1010)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, ty_Integer) → new_ltEs4(yvy1000, yvy1010)
new_ltEs21(yvy1001, yvy1011, ty_Float) → new_ltEs11(yvy1001, yvy1011)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, app(ty_Maybe, dcf)) → new_ltEs5(yvy1000, yvy1010, dcf)
new_compare13(:%(yvy4000, yvy4001), :%(yvy3000, yvy3001), ty_Int) → new_compare16(new_sr0(yvy4000, yvy3001), new_sr0(yvy3000, yvy4001))
new_esEs26(yvy40000, yvy30000, app(ty_Maybe, bdd)) → new_esEs23(yvy40000, yvy30000, bdd)
new_ltEs24(yvy100, yvy101, ty_Float) → new_ltEs11(yvy100, yvy101)
new_esEs34(yvy152, yvy155, app(app(ty_@2, dec), ded)) → new_esEs17(yvy152, yvy155, dec, ded)
new_esEs8(yvy4001, yvy3001, ty_Integer) → new_esEs18(yvy4001, yvy3001)
new_ltEs22(yvy114, yvy115, app(app(app(ty_@3, fah), fba), fbb)) → new_ltEs10(yvy114, yvy115, fah, fba, fbb)
new_primEqNat0(Succ(yvy400000), Succ(yvy300000)) → new_primEqNat0(yvy400000, yvy300000)
new_esEs6(yvy4002, yvy3002, ty_Bool) → new_esEs20(yvy4002, yvy3002)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Ordering) → new_ltEs6(yvy1000, yvy1010)
new_ltEs24(yvy100, yvy101, ty_Int) → new_ltEs15(yvy100, yvy101)
new_esEs26(yvy40000, yvy30000, ty_Ordering) → new_esEs12(yvy40000, yvy30000)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, app(ty_Ratio, dgb)) → new_esEs21(yvy40000, yvy30000, dgb)
new_esEs11(yvy4000, yvy3000, app(ty_Ratio, ehe)) → new_esEs21(yvy4000, yvy3000, ehe)
new_esEs30(yvy40001, yvy30001, ty_Integer) → new_esEs18(yvy40001, yvy30001)
new_esEs39(yvy165, yvy167, ty_Char) → new_esEs15(yvy165, yvy167)
new_ltEs14(Left(yvy1000), Left(yvy1010), app(ty_Ratio, dae), dac) → new_ltEs9(yvy1000, yvy1010, dae)
new_esEs26(yvy40000, yvy30000, app(app(ty_@2, bcf), bcg)) → new_esEs17(yvy40000, yvy30000, bcf, bcg)
new_lt5(yvy1001, yvy1011, ty_Float) → new_lt11(yvy1001, yvy1011)
new_esEs32(yvy40001, yvy30001, ty_@0) → new_esEs19(yvy40001, yvy30001)
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_esEs33(yvy40002, yvy30002, app(ty_Maybe, chh)) → new_esEs23(yvy40002, yvy30002, chh)
new_lt6(yvy1000, yvy1010, ty_Int) → new_lt17(yvy1000, yvy1010)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, app(app(app(ty_@3, dgc), dgd), dge)) → new_esEs22(yvy40000, yvy30000, dgc, dgd, dge)
new_lt23(yvy165, yvy167, app(app(ty_Either, fdb), fdc)) → new_lt16(yvy165, yvy167, fdb, fdc)
new_esEs12(EQ, EQ) → True
new_lt23(yvy165, yvy167, ty_Char) → new_lt8(yvy165, yvy167)
new_ltEs18(yvy107, yvy108, app(app(ty_@2, bef), beg)) → new_ltEs12(yvy107, yvy108, bef, beg)
new_lt21(yvy153, yvy156, ty_Double) → new_lt13(yvy153, yvy156)
new_esEs35(yvy153, yvy156, ty_Ordering) → new_esEs12(yvy153, yvy156)
new_lt5(yvy1001, yvy1011, ty_Int) → new_lt17(yvy1001, yvy1011)
new_esEs10(yvy4000, yvy3000, ty_Char) → new_esEs15(yvy4000, yvy3000)
new_primEqInt(Pos(Succ(yvy400000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(yvy300000))) → False
new_ltEs5(Nothing, Just(yvy1010), eh) → True
new_lt20(yvy152, yvy155, ty_Int) → new_lt17(yvy152, yvy155)
new_esEs35(yvy153, yvy156, app(ty_Maybe, eba)) → new_esEs23(yvy153, yvy156, eba)
new_esEs27(yvy1000, yvy1010, ty_@0) → new_esEs19(yvy1000, yvy1010)
new_ltEs18(yvy107, yvy108, ty_Float) → new_ltEs11(yvy107, yvy108)
new_compare25(yvy152, yvy153, yvy154, yvy155, yvy156, yvy157, True, dhc, dhd, dhe) → EQ
new_esEs37(yvy40000, yvy30000, ty_Int) → new_esEs25(yvy40000, yvy30000)
new_primCmpNat0(Zero, Zero) → EQ
new_esEs27(yvy1000, yvy1010, app(app(ty_Either, bgf), bgg)) → new_esEs24(yvy1000, yvy1010, bgf, bgg)
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_compare27(Left(yvy4000), Right(yvy3000), eff, efg) → LT
new_lt22(yvy1000, yvy1010, ty_@0) → new_lt19(yvy1000, yvy1010)
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_compare9(@0, @0) → EQ
new_esEs28(yvy1001, yvy1011, ty_Int) → new_esEs25(yvy1001, yvy1011)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Float, hh) → new_esEs14(yvy40000, yvy30000)
new_esEs6(yvy4002, yvy3002, ty_Float) → new_esEs14(yvy4002, yvy3002)
new_ltEs9(yvy100, yvy101, cdh) → new_fsEs(new_compare13(yvy100, yvy101, cdh))
new_compare17(yvy218, yvy219, yvy220, yvy221, yvy222, yvy223, True, yvy225, ceb, cec, ced) → new_compare14(yvy218, yvy219, yvy220, yvy221, yvy222, yvy223, True, ceb, cec, ced)
new_esEs32(yvy40001, yvy30001, ty_Char) → new_esEs15(yvy40001, yvy30001)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_ltEs14(Left(yvy1000), Left(yvy1010), app(ty_[], dad), dac) → new_ltEs8(yvy1000, yvy1010, dad)
new_ltEs19(yvy1002, yvy1012, app(app(ty_@2, cag), cah)) → new_ltEs12(yvy1002, yvy1012, cag, cah)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Double, hh) → new_esEs13(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, app(app(ty_Either, daa), dab)) → new_esEs24(yvy40002, yvy30002, daa, dab)
new_esEs4(yvy4000, yvy3000, ty_Int) → new_esEs25(yvy4000, yvy3000)
new_compare28(yvy114, yvy115, True, fad, fae) → EQ
new_primEqInt(Pos(Succ(yvy400000)), Neg(yvy30000)) → False
new_primEqInt(Neg(Succ(yvy400000)), Pos(yvy30000)) → False
new_esEs24(Right(yvy40000), Right(yvy30000), hg, ty_Int) → new_esEs25(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, ty_Ordering) → new_esEs12(yvy40002, yvy30002)
new_esEs29(yvy40000, yvy30000, app(app(app(ty_@3, cbh), cca), ccb)) → new_esEs22(yvy40000, yvy30000, cbh, cca, ccb)
new_esEs26(yvy40000, yvy30000, ty_Double) → new_esEs13(yvy40000, yvy30000)
new_ltEs20(yvy154, yvy157, ty_Integer) → new_ltEs4(yvy154, yvy157)
new_compare210(yvy100, yvy101, True, feg) → EQ
new_lt6(yvy1000, yvy1010, ty_Ordering) → new_lt7(yvy1000, yvy1010)
new_esEs29(yvy40000, yvy30000, app(ty_Ratio, cbg)) → new_esEs21(yvy40000, yvy30000, cbg)
new_esEs20(False, False) → True
new_esEs24(Left(yvy40000), Left(yvy30000), app(ty_[], dee), hh) → new_esEs16(yvy40000, yvy30000, dee)
new_lt23(yvy165, yvy167, app(ty_[], fcb)) → new_lt9(yvy165, yvy167, fcb)
new_ltEs22(yvy114, yvy115, ty_Integer) → new_ltEs4(yvy114, yvy115)
new_ltEs5(Just(yvy1000), Just(yvy1010), app(app(ty_Either, gb), gc)) → new_ltEs14(yvy1000, yvy1010, gb, gc)
new_lt23(yvy165, yvy167, ty_Bool) → new_lt18(yvy165, yvy167)
new_esEs30(yvy40001, yvy30001, ty_Ordering) → new_esEs12(yvy40001, yvy30001)
new_lt6(yvy1000, yvy1010, ty_Integer) → new_lt15(yvy1000, yvy1010)
new_primEqInt(Pos(Zero), Neg(Succ(yvy300000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(yvy300000))) → False
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_compare30(yvy400, yvy300, app(ty_Maybe, ffb)) → new_compare31(yvy400, yvy300, ffb)
new_esEs9(yvy4000, yvy3000, ty_Ordering) → new_esEs12(yvy4000, yvy3000)
new_esEs7(yvy4000, yvy3000, ty_@0) → new_esEs19(yvy4000, yvy3000)
new_esEs11(yvy4000, yvy3000, ty_Float) → new_esEs14(yvy4000, yvy3000)
new_lt6(yvy1000, yvy1010, app(ty_[], bff)) → new_lt9(yvy1000, yvy1010, bff)
new_esEs36(yvy1000, yvy1010, ty_@0) → new_esEs19(yvy1000, yvy1010)
new_esEs5(yvy4001, yvy3001, ty_@0) → new_esEs19(yvy4001, yvy3001)
new_esEs36(yvy1000, yvy1010, app(app(app(ty_@3, edd), ede), edf)) → new_esEs22(yvy1000, yvy1010, edd, ede, edf)
new_esEs28(yvy1001, yvy1011, ty_Ordering) → new_esEs12(yvy1001, yvy1011)
new_esEs10(yvy4000, yvy3000, app(ty_[], efh)) → new_esEs16(yvy4000, yvy3000, efh)
new_primCompAux0(yvy56, LT) → LT
new_esEs6(yvy4002, yvy3002, app(app(ty_Either, bcc), bcd)) → new_esEs24(yvy4002, yvy3002, bcc, bcd)
new_esEs6(yvy4002, yvy3002, ty_Integer) → new_esEs18(yvy4002, yvy3002)
new_esEs36(yvy1000, yvy1010, app(app(ty_@2, edg), edh)) → new_esEs17(yvy1000, yvy1010, edg, edh)
new_esEs7(yvy4000, yvy3000, app(app(ty_@2, cb), cc)) → new_esEs17(yvy4000, yvy3000, cb, cc)
new_esEs9(yvy4000, yvy3000, ty_Float) → new_esEs14(yvy4000, yvy3000)
new_lt5(yvy1001, yvy1011, ty_Double) → new_lt13(yvy1001, yvy1011)
new_ltEs22(yvy114, yvy115, app(ty_Maybe, fbe)) → new_ltEs5(yvy114, yvy115, fbe)
new_not(False) → True
new_esEs27(yvy1000, yvy1010, ty_Int) → new_esEs25(yvy1000, yvy1010)
new_esEs34(yvy152, yvy155, app(ty_Ratio, cea)) → new_esEs21(yvy152, yvy155, cea)
new_compare30(yvy400, yvy300, ty_Bool) → new_compare12(yvy400, yvy300)
new_esEs25(yvy4000, yvy3000) → new_primEqInt(yvy4000, yvy3000)
new_esEs28(yvy1001, yvy1011, app(ty_[], bgh)) → new_esEs16(yvy1001, yvy1011, bgh)
new_esEs31(yvy40000, yvy30000, ty_Char) → new_esEs15(yvy40000, yvy30000)
new_esEs14(Float(yvy40000, yvy40001), Float(yvy30000, yvy30001)) → new_esEs25(new_sr0(yvy40000, yvy30000), new_sr0(yvy40001, yvy30001))
new_esEs11(yvy4000, yvy3000, ty_@0) → new_esEs19(yvy4000, yvy3000)
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_esEs12(GT, EQ) → False
new_esEs12(EQ, GT) → False
new_esEs36(yvy1000, yvy1010, ty_Float) → new_esEs14(yvy1000, yvy1010)
new_esEs4(yvy4000, yvy3000, ty_Ordering) → new_esEs12(yvy4000, yvy3000)
new_esEs9(yvy4000, yvy3000, app(app(ty_Either, fgc), fgd)) → new_esEs24(yvy4000, yvy3000, fgc, fgd)
new_lt6(yvy1000, yvy1010, app(app(app(ty_@3, bfh), bga), bgb)) → new_lt4(yvy1000, yvy1010, bfh, bga, bgb)
new_esEs4(yvy4000, yvy3000, app(app(ty_@2, gh), ha)) → new_esEs17(yvy4000, yvy3000, gh, ha)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, ty_Integer) → new_esEs18(yvy40000, yvy30000)
new_ltEs18(yvy107, yvy108, ty_@0) → new_ltEs17(yvy107, yvy108)
new_esEs39(yvy165, yvy167, ty_Int) → new_esEs25(yvy165, yvy167)
new_compare15(LT, EQ) → LT
new_esEs34(yvy152, yvy155, ty_Float) → new_esEs14(yvy152, yvy155)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, app(ty_[], dbg)) → new_ltEs8(yvy1000, yvy1010, dbg)
new_esEs36(yvy1000, yvy1010, app(ty_Ratio, edc)) → new_esEs21(yvy1000, yvy1010, edc)
new_esEs30(yvy40001, yvy30001, app(ty_Ratio, cda)) → new_esEs21(yvy40001, yvy30001, cda)
new_compare30(yvy400, yvy300, app(ty_Ratio, ffa)) → new_compare13(yvy400, yvy300, ffa)
new_esEs24(Left(yvy40000), Right(yvy30000), hg, hh) → False
new_esEs24(Right(yvy40000), Left(yvy30000), hg, hh) → False
new_lt20(yvy152, yvy155, app(app(ty_Either, dhh), eaa)) → new_lt16(yvy152, yvy155, dhh, eaa)
new_esEs30(yvy40001, yvy30001, app(app(ty_@2, ccg), cch)) → new_esEs17(yvy40001, yvy30001, ccg, cch)
new_esEs32(yvy40001, yvy30001, app(app(ty_Either, cgg), cgh)) → new_esEs24(yvy40001, yvy30001, cgg, cgh)
new_esEs34(yvy152, yvy155, app(ty_[], dhf)) → new_esEs16(yvy152, yvy155, dhf)
new_lt20(yvy152, yvy155, ty_Double) → new_lt13(yvy152, yvy155)
new_esEs35(yvy153, yvy156, ty_Double) → new_esEs13(yvy153, yvy156)
new_compare0(:(yvy4000, yvy4001), [], feh) → GT
new_lt6(yvy1000, yvy1010, ty_Char) → new_lt8(yvy1000, yvy1010)
new_esEs8(yvy4001, yvy3001, ty_Int) → new_esEs25(yvy4001, yvy3001)
new_esEs38(yvy40001, yvy30001, ty_Int) → new_esEs25(yvy40001, yvy30001)
new_ltEs24(yvy100, yvy101, ty_Integer) → new_ltEs4(yvy100, yvy101)
new_ltEs20(yvy154, yvy157, app(ty_Maybe, ecc)) → new_ltEs5(yvy154, yvy157, ecc)
new_ltEs20(yvy154, yvy157, ty_@0) → new_ltEs17(yvy154, yvy157)
new_ltEs24(yvy100, yvy101, app(app(ty_Either, dbf), dac)) → new_ltEs14(yvy100, yvy101, dbf, dac)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Int) → new_esEs25(yvy40000, yvy30000)
new_esEs34(yvy152, yvy155, app(app(ty_Either, dhh), eaa)) → new_esEs24(yvy152, yvy155, dhh, eaa)
new_lt13(yvy152, yvy155) → new_esEs12(new_compare29(yvy152, yvy155), LT)
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_esEs30(yvy40001, yvy30001, app(app(ty_Either, cdf), cdg)) → new_esEs24(yvy40001, yvy30001, cdf, cdg)
new_lt19(yvy152, yvy155) → new_esEs12(new_compare9(yvy152, yvy155), LT)
new_ltEs18(yvy107, yvy108, ty_Char) → new_ltEs7(yvy107, yvy108)
new_esEs4(yvy4000, yvy3000, app(app(ty_Either, hg), hh)) → new_esEs24(yvy4000, yvy3000, hg, hh)
new_esEs8(yvy4001, yvy3001, app(ty_Ratio, dg)) → new_esEs21(yvy4001, yvy3001, dg)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Integer) → new_esEs18(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, app(ty_Ratio, chd)) → new_esEs21(yvy40002, yvy30002, chd)
new_lt17(yvy152, yvy155) → new_esEs12(new_compare16(yvy152, yvy155), LT)
new_esEs10(yvy4000, yvy3000, app(app(ty_@2, ega), egb)) → new_esEs17(yvy4000, yvy3000, ega, egb)
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_ltEs7(yvy100, yvy101) → new_fsEs(new_compare11(yvy100, yvy101))
new_esEs31(yvy40000, yvy30000, ty_Float) → new_esEs14(yvy40000, yvy30000)
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_compare15(EQ, GT) → LT
new_esEs32(yvy40001, yvy30001, ty_Int) → new_esEs25(yvy40001, yvy30001)
new_esEs29(yvy40000, yvy30000, ty_Char) → new_esEs15(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, app(app(app(ty_@3, che), chf), chg)) → new_esEs22(yvy40002, yvy30002, che, chf, chg)
new_primEqNat0(Zero, Succ(yvy300000)) → False
new_primEqNat0(Succ(yvy400000), Zero) → False
new_compare15(LT, GT) → LT
new_lt15(yvy152, yvy155) → new_esEs12(new_compare8(yvy152, yvy155), LT)
new_ltEs5(Nothing, Nothing, eh) → True
new_ltEs23(yvy166, yvy168, app(app(app(ty_@3, fdf), fdg), fdh)) → new_ltEs10(yvy166, yvy168, fdf, fdg, fdh)
new_lt20(yvy152, yvy155, app(app(ty_@2, dec), ded)) → new_lt12(yvy152, yvy155, dec, ded)
new_ltEs6(LT, LT) → True
new_ltEs6(EQ, LT) → False
new_esEs6(yvy4002, yvy3002, app(ty_Ratio, bbf)) → new_esEs21(yvy4002, yvy3002, bbf)
new_ltEs5(Just(yvy1000), Just(yvy1010), app(ty_[], fa)) → new_ltEs8(yvy1000, yvy1010, fa)
new_ltEs19(yvy1002, yvy1012, ty_Char) → new_ltEs7(yvy1002, yvy1012)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_ltEs21(yvy1001, yvy1011, app(ty_Ratio, eee)) → new_ltEs9(yvy1001, yvy1011, eee)
new_esEs9(yvy4000, yvy3000, app(ty_Maybe, fgb)) → new_esEs23(yvy4000, yvy3000, fgb)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Bool) → new_ltEs16(yvy1000, yvy1010)
new_lt21(yvy153, yvy156, app(ty_Maybe, eba)) → new_lt14(yvy153, yvy156, eba)
new_compare15(GT, GT) → EQ
new_esEs11(yvy4000, yvy3000, app(app(ty_@2, ehc), ehd)) → new_esEs17(yvy4000, yvy3000, ehc, ehd)
new_esEs8(yvy4001, yvy3001, app(app(ty_Either, ed), ee)) → new_esEs24(yvy4001, yvy3001, ed, ee)
new_compare24(yvy165, yvy166, yvy167, yvy168, True, fbh, fca) → EQ
new_esEs32(yvy40001, yvy30001, ty_Bool) → new_esEs20(yvy40001, yvy30001)
new_lt21(yvy153, yvy156, ty_Float) → new_lt11(yvy153, yvy156)
new_esEs16(:(yvy40000, yvy40001), [], gg) → False
new_esEs16([], :(yvy30000, yvy30001), gg) → False
new_compare31(Just(yvy4000), Just(yvy3000), ffb) → new_compare210(yvy4000, yvy3000, new_esEs9(yvy4000, yvy3000, ffb), ffb)
new_lt21(yvy153, yvy156, ty_Ordering) → new_lt7(yvy153, yvy156)
new_lt20(yvy152, yvy155, ty_Bool) → new_lt18(yvy152, yvy155)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, app(ty_Ratio, dbh)) → new_ltEs9(yvy1000, yvy1010, dbh)
new_ltEs19(yvy1002, yvy1012, ty_@0) → new_ltEs17(yvy1002, yvy1012)
new_esEs7(yvy4000, yvy3000, app(app(app(ty_@3, ce), cf), cg)) → new_esEs22(yvy4000, yvy3000, ce, cf, cg)
new_esEs5(yvy4001, yvy3001, ty_Integer) → new_esEs18(yvy4001, yvy3001)
new_esEs31(yvy40000, yvy30000, ty_Int) → new_esEs25(yvy40000, yvy30000)
new_esEs27(yvy1000, yvy1010, app(app(app(ty_@3, bfh), bga), bgb)) → new_esEs22(yvy1000, yvy1010, bfh, bga, bgb)
new_ltEs19(yvy1002, yvy1012, app(ty_Maybe, cba)) → new_ltEs5(yvy1002, yvy1012, cba)
new_lt21(yvy153, yvy156, ty_Integer) → new_lt15(yvy153, yvy156)
new_esEs29(yvy40000, yvy30000, app(app(ty_Either, ccd), cce)) → new_esEs24(yvy40000, yvy30000, ccd, cce)
new_esEs10(yvy4000, yvy3000, app(ty_Ratio, egc)) → new_esEs21(yvy4000, yvy3000, egc)
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_ltEs12(@2(yvy1000, yvy1001), @2(yvy1010, yvy1011), ech, eda) → new_pePe(new_lt22(yvy1000, yvy1010, ech), new_asAs(new_esEs36(yvy1000, yvy1010, ech), new_ltEs21(yvy1001, yvy1011, eda)))
new_ltEs23(yvy166, yvy168, ty_@0) → new_ltEs17(yvy166, yvy168)
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_esEs5(yvy4001, yvy3001, app(ty_Maybe, bah)) → new_esEs23(yvy4001, yvy3001, bah)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Char) → new_ltEs7(yvy1000, yvy1010)
new_compare0(:(yvy4000, yvy4001), :(yvy3000, yvy3001), feh) → new_primCompAux1(yvy4000, yvy3000, new_compare0(yvy4001, yvy3001, feh), feh)
new_esEs20(False, True) → False
new_esEs20(True, False) → False
new_compare19(yvy206, yvy207, True, dha, dhb) → LT
new_sr0(yvy3000, yvy4001) → new_primMulInt(yvy3000, yvy4001)
new_esEs28(yvy1001, yvy1011, app(app(ty_@2, bhe), bhf)) → new_esEs17(yvy1001, yvy1011, bhe, bhf)
new_lt6(yvy1000, yvy1010, app(app(ty_Either, bgf), bgg)) → new_lt16(yvy1000, yvy1010, bgf, bgg)
new_esEs34(yvy152, yvy155, ty_Bool) → new_esEs20(yvy152, yvy155)
new_lt22(yvy1000, yvy1010, ty_Integer) → new_lt15(yvy1000, yvy1010)
new_esEs26(yvy40000, yvy30000, app(app(ty_Either, bde), bdf)) → new_esEs24(yvy40000, yvy30000, bde, bdf)
new_compare30(yvy400, yvy300, ty_Ordering) → new_compare15(yvy400, yvy300)
new_esEs30(yvy40001, yvy30001, app(ty_[], ccf)) → new_esEs16(yvy40001, yvy30001, ccf)
new_esEs24(Left(yvy40000), Left(yvy30000), app(app(ty_@2, def), deg), hh) → new_esEs17(yvy40000, yvy30000, def, deg)
new_lt23(yvy165, yvy167, ty_@0) → new_lt19(yvy165, yvy167)
new_esEs10(yvy4000, yvy3000, ty_Float) → new_esEs14(yvy4000, yvy3000)
new_compare29(Double(yvy4000, yvy4001), Double(yvy3000, yvy3001)) → new_compare16(new_sr0(yvy4000, yvy3000), new_sr0(yvy4001, yvy3001))
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, ty_Bool) → new_ltEs16(yvy1000, yvy1010)
new_ltEs22(yvy114, yvy115, app(ty_[], faf)) → new_ltEs8(yvy114, yvy115, faf)
new_esEs39(yvy165, yvy167, app(app(ty_Either, fdb), fdc)) → new_esEs24(yvy165, yvy167, fdb, fdc)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs32(yvy40001, yvy30001, ty_Double) → new_esEs13(yvy40001, yvy30001)
new_esEs28(yvy1001, yvy1011, ty_Bool) → new_esEs20(yvy1001, yvy1011)
new_esEs23(Just(yvy40000), Just(yvy30000), app(ty_Ratio, ddd)) → new_esEs21(yvy40000, yvy30000, ddd)
new_esEs5(yvy4001, yvy3001, app(ty_Ratio, bad)) → new_esEs21(yvy4001, yvy3001, bad)
new_ltEs14(Left(yvy1000), Right(yvy1010), dbf, dac) → True
new_compare24(yvy165, yvy166, yvy167, yvy168, False, fbh, fca) → new_compare110(yvy165, yvy166, yvy167, yvy168, new_lt23(yvy165, yvy167, fbh), new_asAs(new_esEs39(yvy165, yvy167, fbh), new_ltEs23(yvy166, yvy168, fca)), fbh, fca)
new_compare30(yvy400, yvy300, app(ty_[], feh)) → new_compare0(yvy400, yvy300, feh)
new_esEs9(yvy4000, yvy3000, app(ty_Ratio, fff)) → new_esEs21(yvy4000, yvy3000, fff)
new_ltEs20(yvy154, yvy157, app(app(ty_Either, ecd), ece)) → new_ltEs14(yvy154, yvy157, ecd, ece)
new_asAs(False, yvy184) → False
new_compare27(Right(yvy4000), Left(yvy3000), eff, efg) → GT
new_esEs36(yvy1000, yvy1010, app(ty_Maybe, eea)) → new_esEs23(yvy1000, yvy1010, eea)
new_esEs9(yvy4000, yvy3000, ty_Double) → new_esEs13(yvy4000, yvy3000)
new_ltEs19(yvy1002, yvy1012, app(app(ty_Either, cbb), cbc)) → new_ltEs14(yvy1002, yvy1012, cbb, cbc)
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_lt20(yvy152, yvy155, ty_@0) → new_lt19(yvy152, yvy155)
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_esEs4(yvy4000, yvy3000, ty_@0) → new_esEs19(yvy4000, yvy3000)
new_esEs27(yvy1000, yvy1010, ty_Double) → new_esEs13(yvy1000, yvy1010)
new_esEs36(yvy1000, yvy1010, ty_Ordering) → new_esEs12(yvy1000, yvy1010)
new_compare16(yvy400, yvy300) → new_primCmpInt(yvy400, yvy300)
new_esEs35(yvy153, yvy156, ty_Bool) → new_esEs20(yvy153, yvy156)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Bool) → new_esEs20(yvy40000, yvy30000)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Integer, dac) → new_ltEs4(yvy1000, yvy1010)
new_compare14(yvy218, yvy219, yvy220, yvy221, yvy222, yvy223, True, ceb, cec, ced) → LT
new_esEs30(yvy40001, yvy30001, app(ty_Maybe, cde)) → new_esEs23(yvy40001, yvy30001, cde)
new_esEs8(yvy4001, yvy3001, ty_Char) → new_esEs15(yvy4001, yvy3001)
new_esEs9(yvy4000, yvy3000, ty_Bool) → new_esEs20(yvy4000, yvy3000)
new_lt5(yvy1001, yvy1011, ty_Ordering) → new_lt7(yvy1001, yvy1011)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, ty_Ordering) → new_ltEs6(yvy1000, yvy1010)
new_esEs24(Left(yvy40000), Left(yvy30000), app(app(ty_Either, dfe), dff), hh) → new_esEs24(yvy40000, yvy30000, dfe, dff)
new_esEs8(yvy4001, yvy3001, app(ty_[], dd)) → new_esEs16(yvy4001, yvy3001, dd)
new_compare27(Left(yvy4000), Left(yvy3000), eff, efg) → new_compare26(yvy4000, yvy3000, new_esEs10(yvy4000, yvy3000, eff), eff, efg)
new_esEs29(yvy40000, yvy30000, ty_Double) → new_esEs13(yvy40000, yvy30000)
new_esEs27(yvy1000, yvy1010, ty_Integer) → new_esEs18(yvy1000, yvy1010)
new_esEs18(Integer(yvy40000), Integer(yvy30000)) → new_primEqInt(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, ty_Char) → new_esEs15(yvy40002, yvy30002)
new_ltEs5(Just(yvy1000), Just(yvy1010), app(ty_Maybe, ga)) → new_ltEs5(yvy1000, yvy1010, ga)
new_ltEs11(yvy100, yvy101) → new_fsEs(new_compare18(yvy100, yvy101))
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, app(app(ty_Either, dcg), dch)) → new_ltEs14(yvy1000, yvy1010, dcg, dch)
new_esEs30(yvy40001, yvy30001, ty_Float) → new_esEs14(yvy40001, yvy30001)
new_lt23(yvy165, yvy167, ty_Float) → new_lt11(yvy165, yvy167)
new_compare12(False, False) → EQ
new_esEs28(yvy1001, yvy1011, ty_@0) → new_esEs19(yvy1001, yvy1011)
new_ltEs23(yvy166, yvy168, ty_Char) → new_ltEs7(yvy166, yvy168)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, app(ty_Maybe, dgf)) → new_esEs23(yvy40000, yvy30000, dgf)
new_esEs29(yvy40000, yvy30000, ty_Float) → new_esEs14(yvy40000, yvy30000)
new_esEs7(yvy4000, yvy3000, ty_Ordering) → new_esEs12(yvy4000, yvy3000)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Integer, hh) → new_esEs18(yvy40000, yvy30000)
new_lt20(yvy152, yvy155, app(ty_Maybe, dhg)) → new_lt14(yvy152, yvy155, dhg)
new_esEs39(yvy165, yvy167, app(app(app(ty_@3, fcd), fce), fcf)) → new_esEs22(yvy165, yvy167, fcd, fce, fcf)
new_esEs31(yvy40000, yvy30000, ty_@0) → new_esEs19(yvy40000, yvy30000)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, app(ty_[], dfg)) → new_esEs16(yvy40000, yvy30000, dfg)
new_compare111(yvy233, yvy234, yvy235, yvy236, False, ecf, ecg) → GT
new_lt21(yvy153, yvy156, ty_Bool) → new_lt18(yvy153, yvy156)
new_ltEs6(LT, GT) → True
new_esEs33(yvy40002, yvy30002, ty_Int) → new_esEs25(yvy40002, yvy30002)
new_compare30(yvy400, yvy300, ty_Integer) → new_compare8(yvy400, yvy300)
new_ltEs23(yvy166, yvy168, app(ty_Maybe, fec)) → new_ltEs5(yvy166, yvy168, fec)
new_lt23(yvy165, yvy167, app(ty_Maybe, fda)) → new_lt14(yvy165, yvy167, fda)
new_ltEs21(yvy1001, yvy1011, ty_Char) → new_ltEs7(yvy1001, yvy1011)
new_ltEs14(Left(yvy1000), Left(yvy1010), app(app(ty_Either, dbd), dbe), dac) → new_ltEs14(yvy1000, yvy1010, dbd, dbe)
new_ltEs23(yvy166, yvy168, app(app(ty_@2, fea), feb)) → new_ltEs12(yvy166, yvy168, fea, feb)
new_ltEs21(yvy1001, yvy1011, ty_Ordering) → new_ltEs6(yvy1001, yvy1011)
new_esEs32(yvy40001, yvy30001, app(app(ty_@2, cfh), cga)) → new_esEs17(yvy40001, yvy30001, cfh, cga)
new_esEs24(Left(yvy40000), Left(yvy30000), app(ty_Maybe, dfd), hh) → new_esEs23(yvy40000, yvy30000, dfd)
new_lt22(yvy1000, yvy1010, app(ty_Ratio, edc)) → new_lt10(yvy1000, yvy1010, edc)
new_lt12(yvy152, yvy155, dec, ded) → new_esEs12(new_compare7(yvy152, yvy155, dec, ded), LT)
new_esEs35(yvy153, yvy156, ty_Int) → new_esEs25(yvy153, yvy156)
new_lt10(yvy152, yvy155, cea) → new_esEs12(new_compare13(yvy152, yvy155, cea), LT)
new_esEs4(yvy4000, yvy3000, ty_Double) → new_esEs13(yvy4000, yvy3000)
new_esEs8(yvy4001, yvy3001, app(app(ty_@2, de), df)) → new_esEs17(yvy4001, yvy3001, de, df)
new_esEs5(yvy4001, yvy3001, app(app(ty_@2, bab), bac)) → new_esEs17(yvy4001, yvy3001, bab, bac)
new_esEs16([], [], gg) → True
new_lt22(yvy1000, yvy1010, ty_Float) → new_lt11(yvy1000, yvy1010)
new_esEs32(yvy40001, yvy30001, ty_Ordering) → new_esEs12(yvy40001, yvy30001)
new_ltEs19(yvy1002, yvy1012, ty_Int) → new_ltEs15(yvy1002, yvy1012)
new_ltEs21(yvy1001, yvy1011, ty_Integer) → new_ltEs4(yvy1001, yvy1011)
new_ltEs20(yvy154, yvy157, ty_Float) → new_ltEs11(yvy154, yvy157)
new_lt5(yvy1001, yvy1011, app(app(ty_@2, bhe), bhf)) → new_lt12(yvy1001, yvy1011, bhe, bhf)
new_esEs11(yvy4000, yvy3000, ty_Int) → new_esEs25(yvy4000, yvy3000)
new_esEs32(yvy40001, yvy30001, app(app(app(ty_@3, cgc), cgd), cge)) → new_esEs22(yvy40001, yvy30001, cgc, cgd, cge)
new_lt6(yvy1000, yvy1010, ty_Double) → new_lt13(yvy1000, yvy1010)
new_lt20(yvy152, yvy155, ty_Float) → new_lt11(yvy152, yvy155)
new_ltEs14(Left(yvy1000), Left(yvy1010), app(app(app(ty_@3, daf), dag), dah), dac) → new_ltEs10(yvy1000, yvy1010, daf, dag, dah)
new_esEs26(yvy40000, yvy30000, ty_Integer) → new_esEs18(yvy40000, yvy30000)
new_lt22(yvy1000, yvy1010, app(app(app(ty_@3, edd), ede), edf)) → new_lt4(yvy1000, yvy1010, edd, ede, edf)
new_esEs36(yvy1000, yvy1010, app(app(ty_Either, eeb), eec)) → new_esEs24(yvy1000, yvy1010, eeb, eec)
new_esEs27(yvy1000, yvy1010, ty_Ordering) → new_esEs12(yvy1000, yvy1010)
new_ltEs19(yvy1002, yvy1012, ty_Double) → new_ltEs13(yvy1002, yvy1012)
new_lt21(yvy153, yvy156, ty_Int) → new_lt17(yvy153, yvy156)
new_lt20(yvy152, yvy155, ty_Integer) → new_lt15(yvy152, yvy155)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, ty_Ordering) → new_esEs12(yvy40000, yvy30000)
new_lt8(yvy152, yvy155) → new_esEs12(new_compare11(yvy152, yvy155), LT)
new_ltEs24(yvy100, yvy101, app(ty_[], fef)) → new_ltEs8(yvy100, yvy101, fef)
new_esEs9(yvy4000, yvy3000, ty_@0) → new_esEs19(yvy4000, yvy3000)
new_esEs22(@3(yvy40000, yvy40001, yvy40002), @3(yvy30000, yvy30001, yvy30002), hc, hd, he) → new_asAs(new_esEs31(yvy40000, yvy30000, hc), new_asAs(new_esEs32(yvy40001, yvy30001, hd), new_esEs33(yvy40002, yvy30002, he)))
new_esEs8(yvy4001, yvy3001, ty_Float) → new_esEs14(yvy4001, yvy3001)
new_esEs7(yvy4000, yvy3000, app(ty_Ratio, cd)) → new_esEs21(yvy4000, yvy3000, cd)
new_ltEs20(yvy154, yvy157, ty_Double) → new_ltEs13(yvy154, yvy157)
new_ltEs18(yvy107, yvy108, ty_Bool) → new_ltEs16(yvy107, yvy108)
new_compare28(yvy114, yvy115, False, fad, fae) → new_compare19(yvy114, yvy115, new_ltEs22(yvy114, yvy115, fae), fad, fae)
new_esEs6(yvy4002, yvy3002, app(ty_Maybe, bcb)) → new_esEs23(yvy4002, yvy3002, bcb)
new_lt5(yvy1001, yvy1011, app(app(app(ty_@3, bhb), bhc), bhd)) → new_lt4(yvy1001, yvy1011, bhb, bhc, bhd)
new_esEs31(yvy40000, yvy30000, app(app(app(ty_@3, cfa), cfb), cfc)) → new_esEs22(yvy40000, yvy30000, cfa, cfb, cfc)
new_esEs31(yvy40000, yvy30000, ty_Ordering) → new_esEs12(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, ty_Double) → new_esEs13(yvy40002, yvy30002)
new_lt6(yvy1000, yvy1010, ty_Float) → new_lt11(yvy1000, yvy1010)
new_esEs4(yvy4000, yvy3000, ty_Char) → new_esEs15(yvy4000, yvy3000)
new_esEs7(yvy4000, yvy3000, app(app(ty_Either, db), dc)) → new_esEs24(yvy4000, yvy3000, db, dc)
new_compare112(yvy189, yvy190, False, fge) → GT
new_esEs12(GT, GT) → True
new_ltEs21(yvy1001, yvy1011, app(app(app(ty_@3, eef), eeg), eeh)) → new_ltEs10(yvy1001, yvy1011, eef, eeg, eeh)
new_esEs5(yvy4001, yvy3001, ty_Double) → new_esEs13(yvy4001, yvy3001)
new_compare17(yvy218, yvy219, yvy220, yvy221, yvy222, yvy223, False, yvy225, ceb, cec, ced) → new_compare14(yvy218, yvy219, yvy220, yvy221, yvy222, yvy223, yvy225, ceb, cec, ced)
new_esEs8(yvy4001, yvy3001, app(ty_Maybe, ec)) → new_esEs23(yvy4001, yvy3001, ec)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_@0) → new_esEs19(yvy40000, yvy30000)
new_compare25(yvy152, yvy153, yvy154, yvy155, yvy156, yvy157, False, dhc, dhd, dhe) → new_compare17(yvy152, yvy153, yvy154, yvy155, yvy156, yvy157, new_lt20(yvy152, yvy155, dhc), new_asAs(new_esEs34(yvy152, yvy155, dhc), new_pePe(new_lt21(yvy153, yvy156, dhd), new_asAs(new_esEs35(yvy153, yvy156, dhd), new_ltEs20(yvy154, yvy157, dhe)))), dhc, dhd, dhe)
new_compare31(Nothing, Just(yvy3000), ffb) → LT
new_esEs29(yvy40000, yvy30000, ty_Ordering) → new_esEs12(yvy40000, yvy30000)
new_esEs4(yvy4000, yvy3000, app(ty_[], gg)) → new_esEs16(yvy4000, yvy3000, gg)
new_primPlusNat1(Zero, Zero) → Zero
new_compare0([], :(yvy3000, yvy3001), feh) → LT
new_ltEs6(LT, EQ) → True
new_lt23(yvy165, yvy167, ty_Ordering) → new_lt7(yvy165, yvy167)
new_ltEs21(yvy1001, yvy1011, app(ty_Maybe, efc)) → new_ltEs5(yvy1001, yvy1011, efc)
new_ltEs6(GT, LT) → False
new_lt18(yvy152, yvy155) → new_esEs12(new_compare12(yvy152, yvy155), LT)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, ty_Char) → new_esEs15(yvy40000, yvy30000)
new_asAs(True, yvy184) → yvy184
new_esEs26(yvy40000, yvy30000, ty_Float) → new_esEs14(yvy40000, yvy30000)
new_esEs35(yvy153, yvy156, ty_Float) → new_esEs14(yvy153, yvy156)
new_ltEs21(yvy1001, yvy1011, app(ty_[], eed)) → new_ltEs8(yvy1001, yvy1011, eed)
new_compare11(Char(yvy4000), Char(yvy3000)) → new_primCmpNat0(yvy4000, yvy3000)
new_ltEs22(yvy114, yvy115, ty_Float) → new_ltEs11(yvy114, yvy115)
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_esEs28(yvy1001, yvy1011, app(ty_Ratio, bha)) → new_esEs21(yvy1001, yvy1011, bha)
new_esEs39(yvy165, yvy167, ty_Double) → new_esEs13(yvy165, yvy167)
new_esEs11(yvy4000, yvy3000, ty_Bool) → new_esEs20(yvy4000, yvy3000)
new_ltEs22(yvy114, yvy115, ty_Double) → new_ltEs13(yvy114, yvy115)
new_lt22(yvy1000, yvy1010, ty_Ordering) → new_lt7(yvy1000, yvy1010)
new_esEs4(yvy4000, yvy3000, app(app(app(ty_@3, hc), hd), he)) → new_esEs22(yvy4000, yvy3000, hc, hd, he)
new_lt20(yvy152, yvy155, app(ty_Ratio, cea)) → new_lt10(yvy152, yvy155, cea)
new_ltEs16(False, False) → True
new_lt23(yvy165, yvy167, ty_Double) → new_lt13(yvy165, yvy167)
new_ltEs17(yvy100, yvy101) → new_fsEs(new_compare9(yvy100, yvy101))
new_esEs29(yvy40000, yvy30000, ty_Integer) → new_esEs18(yvy40000, yvy30000)
new_esEs8(yvy4001, yvy3001, ty_Ordering) → new_esEs12(yvy4001, yvy3001)
new_esEs30(yvy40001, yvy30001, ty_Bool) → new_esEs20(yvy40001, yvy30001)
new_lt23(yvy165, yvy167, app(ty_Ratio, fcc)) → new_lt10(yvy165, yvy167, fcc)
new_esEs30(yvy40001, yvy30001, ty_Int) → new_esEs25(yvy40001, yvy30001)
new_esEs27(yvy1000, yvy1010, ty_Float) → new_esEs14(yvy1000, yvy1010)
new_ltEs21(yvy1001, yvy1011, ty_Int) → new_ltEs15(yvy1001, yvy1011)
new_ltEs20(yvy154, yvy157, app(app(app(ty_@3, ebf), ebg), ebh)) → new_ltEs10(yvy154, yvy157, ebf, ebg, ebh)
new_esEs23(Just(yvy40000), Just(yvy30000), app(ty_[], dda)) → new_esEs16(yvy40000, yvy30000, dda)
new_esEs34(yvy152, yvy155, app(app(app(ty_@3, bd), be), bf)) → new_esEs22(yvy152, yvy155, bd, be, bf)
new_esEs16(:(yvy40000, yvy40001), :(yvy30000, yvy30001), gg) → new_asAs(new_esEs26(yvy40000, yvy30000, gg), new_esEs16(yvy40001, yvy30001, gg))
new_esEs9(yvy4000, yvy3000, app(app(app(ty_@3, ffg), ffh), fga)) → new_esEs22(yvy4000, yvy3000, ffg, ffh, fga)
new_ltEs19(yvy1002, yvy1012, app(app(app(ty_@3, cad), cae), caf)) → new_ltEs10(yvy1002, yvy1012, cad, cae, caf)
new_ltEs20(yvy154, yvy157, ty_Ordering) → new_ltEs6(yvy154, yvy157)
new_compare19(yvy206, yvy207, False, dha, dhb) → GT
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Integer) → new_ltEs4(yvy1000, yvy1010)
new_esEs6(yvy4002, yvy3002, ty_@0) → new_esEs19(yvy4002, yvy3002)
new_ltEs10(@3(yvy1000, yvy1001, yvy1002), @3(yvy1010, yvy1011, yvy1012), bfc, bfd, bfe) → new_pePe(new_lt6(yvy1000, yvy1010, bfc), new_asAs(new_esEs27(yvy1000, yvy1010, bfc), new_pePe(new_lt5(yvy1001, yvy1011, bfd), new_asAs(new_esEs28(yvy1001, yvy1011, bfd), new_ltEs19(yvy1002, yvy1012, bfe)))))
new_esEs33(yvy40002, yvy30002, ty_@0) → new_esEs19(yvy40002, yvy30002)
new_esEs35(yvy153, yvy156, app(ty_Ratio, eac)) → new_esEs21(yvy153, yvy156, eac)
new_ltEs22(yvy114, yvy115, ty_Int) → new_ltEs15(yvy114, yvy115)
new_ltEs24(yvy100, yvy101, app(app(app(ty_@3, bfc), bfd), bfe)) → new_ltEs10(yvy100, yvy101, bfc, bfd, bfe)
new_compare27(Right(yvy4000), Right(yvy3000), eff, efg) → new_compare28(yvy4000, yvy3000, new_esEs11(yvy4000, yvy3000, efg), eff, efg)
new_ltEs21(yvy1001, yvy1011, ty_@0) → new_ltEs17(yvy1001, yvy1011)
new_lt16(yvy152, yvy155, dhh, eaa) → new_esEs12(new_compare27(yvy152, yvy155, dhh, eaa), LT)
new_compare15(EQ, EQ) → EQ
new_ltEs22(yvy114, yvy115, ty_Char) → new_ltEs7(yvy114, yvy115)
new_compare30(yvy400, yvy300, ty_Double) → new_compare29(yvy400, yvy300)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCompAux0(yvy56, EQ) → yvy56
new_lt6(yvy1000, yvy1010, app(app(ty_@2, bgc), bgd)) → new_lt12(yvy1000, yvy1010, bgc, bgd)
new_esEs27(yvy1000, yvy1010, app(ty_Maybe, bge)) → new_esEs23(yvy1000, yvy1010, bge)
new_ltEs20(yvy154, yvy157, ty_Char) → new_ltEs7(yvy154, yvy157)
new_esEs10(yvy4000, yvy3000, ty_Integer) → new_esEs18(yvy4000, yvy3000)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_@0, dac) → new_ltEs17(yvy1000, yvy1010)
new_ltEs18(yvy107, yvy108, ty_Int) → new_ltEs15(yvy107, yvy108)
new_lt21(yvy153, yvy156, app(app(app(ty_@3, ead), eae), eaf)) → new_lt4(yvy153, yvy156, ead, eae, eaf)
new_esEs6(yvy4002, yvy3002, ty_Char) → new_esEs15(yvy4002, yvy3002)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_esEs30(yvy40001, yvy30001, ty_Char) → new_esEs15(yvy40001, yvy30001)
new_ltEs5(Just(yvy1000), Just(yvy1010), app(app(app(ty_@3, fc), fd), ff)) → new_ltEs10(yvy1000, yvy1010, fc, fd, ff)
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_esEs39(yvy165, yvy167, app(ty_[], fcb)) → new_esEs16(yvy165, yvy167, fcb)
new_esEs35(yvy153, yvy156, ty_Char) → new_esEs15(yvy153, yvy156)
new_not(True) → False
new_ltEs5(Just(yvy1000), Just(yvy1010), app(ty_Ratio, fb)) → new_ltEs9(yvy1000, yvy1010, fb)

The set Q consists of the following terms:

new_esEs36(x0, x1, ty_Char)
new_esEs29(x0, x1, ty_Float)
new_lt22(x0, x1, app(ty_Maybe, x2))
new_esEs7(x0, x1, ty_Int)
new_ltEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs21(x0, x1, ty_Int)
new_ltEs14(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs10(x0, x1, ty_Float)
new_ltEs16(True, True)
new_esEs6(x0, x1, ty_Int)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs32(x0, x1, app(ty_Maybe, x2))
new_lt11(x0, x1)
new_esEs24(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs20(x0, x1, ty_Int)
new_lt5(x0, x1, ty_Char)
new_esEs5(x0, x1, app(ty_[], x2))
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs36(x0, x1, app(ty_[], x2))
new_lt21(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs21(x0, x1, ty_@0)
new_esEs29(x0, x1, ty_Char)
new_ltEs22(x0, x1, ty_Integer)
new_esEs34(x0, x1, app(ty_[], x2))
new_esEs32(x0, x1, ty_Int)
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs11(x0, x1, ty_Int)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs4(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_Integer)
new_compare30(x0, x1, ty_Int)
new_pePe(True, x0)
new_esEs5(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs11(x0, x1, ty_@0)
new_esEs35(x0, x1, ty_Integer)
new_esEs11(x0, x1, ty_Char)
new_esEs9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(x0, x1, ty_Float)
new_esEs9(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(x0, x1, ty_Int)
new_esEs31(x0, x1, app(app(ty_Either, x2), x3))
new_lt22(x0, x1, ty_@0)
new_compare30(x0, x1, ty_Bool)
new_ltEs5(Nothing, Just(x0), x1)
new_lt20(x0, x1, ty_@0)
new_esEs29(x0, x1, ty_Ordering)
new_lt22(x0, x1, ty_Float)
new_esEs9(x0, x1, app(ty_[], x2))
new_lt23(x0, x1, ty_Integer)
new_ltEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(Right(x0), Right(x1), x2, ty_Bool)
new_lt7(x0, x1)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs8(x0, x1, ty_Integer)
new_esEs23(Just(x0), Just(x1), ty_Float)
new_esEs6(x0, x1, ty_Integer)
new_lt5(x0, x1, ty_@0)
new_esEs33(x0, x1, app(app(ty_@2, x2), x3))
new_esEs11(x0, x1, ty_Bool)
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs24(Right(x0), Right(x1), x2, ty_Integer)
new_compare12(False, True)
new_compare12(True, False)
new_ltEs7(x0, x1)
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_primCompAux0(x0, EQ)
new_esEs32(x0, x1, app(app(ty_@2, x2), x3))
new_lt6(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(x0, x1, ty_Integer)
new_esEs32(x0, x1, ty_Ordering)
new_ltEs21(x0, x1, ty_Float)
new_ltEs24(x0, x1, ty_Integer)
new_esEs34(x0, x1, ty_Float)
new_esEs6(x0, x1, ty_@0)
new_lt6(x0, x1, ty_Float)
new_esEs9(x0, x1, ty_Int)
new_compare30(x0, x1, ty_Integer)
new_esEs12(GT, EQ)
new_esEs12(EQ, GT)
new_esEs36(x0, x1, ty_Int)
new_esEs28(x0, x1, ty_Bool)
new_ltEs14(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs24(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_compare30(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_lt5(x0, x1, ty_Double)
new_compare15(LT, LT)
new_esEs10(x0, x1, ty_Char)
new_esEs23(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primMulNat0(Succ(x0), Zero)
new_ltEs22(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_compare6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs34(x0, x1, ty_Ordering)
new_esEs16([], [], x0)
new_esEs12(GT, GT)
new_esEs30(x0, x1, ty_Double)
new_esEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs21(x0, x1, ty_Ordering)
new_esEs10(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_lt21(x0, x1, ty_Float)
new_esEs11(x0, x1, ty_Integer)
new_esEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs21(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs24(x0, x1, app(ty_Maybe, x2))
new_esEs23(Just(x0), Just(x1), ty_Double)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_Char)
new_esEs34(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(Left(x0), Left(x1), ty_Int, x2)
new_esEs38(x0, x1, ty_Integer)
new_ltEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs27(x0, x1, ty_Bool)
new_esEs24(Right(x0), Right(x1), x2, ty_Char)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs6(EQ, EQ)
new_esEs32(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(x0, x1, ty_Float)
new_esEs8(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs22(x0, x1, ty_Char)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(x0, x1, ty_Double)
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_esEs5(x0, x1, ty_Bool)
new_lt6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs31(x0, x1, ty_Int)
new_compare26(x0, x1, True, x2, x3)
new_compare110(x0, x1, x2, x3, True, x4, x5, x6)
new_ltEs24(x0, x1, app(ty_[], x2))
new_compare27(Right(x0), Left(x1), x2, x3)
new_compare27(Left(x0), Right(x1), x2, x3)
new_esEs33(x0, x1, ty_Double)
new_esEs8(x0, x1, ty_Float)
new_ltEs18(x0, x1, ty_@0)
new_esEs4(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, app(ty_[], x2))
new_ltEs5(Just(x0), Just(x1), ty_@0)
new_lt5(x0, x1, ty_Int)
new_ltEs6(LT, EQ)
new_ltEs6(EQ, LT)
new_esEs24(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_primCompAux0(x0, LT)
new_esEs23(Nothing, Nothing, x0)
new_esEs38(x0, x1, ty_Int)
new_esEs23(Just(x0), Just(x1), ty_Int)
new_ltEs20(x0, x1, ty_@0)
new_lt6(x0, x1, app(ty_Maybe, x2))
new_esEs11(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Int)
new_lt17(x0, x1)
new_esEs8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs36(x0, x1, ty_Bool)
new_primEqNat0(Zero, Zero)
new_compare13(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs26(x0, x1, ty_@0)
new_lt21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(Right(x0), Right(x1), x2, ty_Int)
new_esEs7(x0, x1, ty_Bool)
new_esEs33(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs5(x0, x1, ty_Float)
new_ltEs14(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_compare17(x0, x1, x2, x3, x4, x5, False, x6, x7, x8, x9)
new_ltEs22(x0, x1, ty_Float)
new_compare15(GT, GT)
new_esEs31(x0, x1, ty_Double)
new_ltEs20(x0, x1, ty_Integer)
new_lt22(x0, x1, ty_Bool)
new_compare30(x0, x1, app(ty_[], x2))
new_esEs34(x0, x1, ty_Bool)
new_esEs31(x0, x1, ty_Integer)
new_ltEs20(x0, x1, ty_Char)
new_lt20(x0, x1, ty_Double)
new_esEs35(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_compare28(x0, x1, True, x2, x3)
new_ltEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs21(x0, x1, app(ty_[], x2))
new_ltEs15(x0, x1)
new_esEs4(x0, x1, ty_Integer)
new_esEs39(x0, x1, app(ty_Ratio, x2))
new_esEs6(x0, x1, app(app(ty_Either, x2), x3))
new_esEs39(x0, x1, ty_Bool)
new_esEs6(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs24(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Float)
new_ltEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_primMulNat0(Zero, Zero)
new_asAs(True, x0)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_ltEs14(Left(x0), Right(x1), x2, x3)
new_ltEs14(Right(x0), Left(x1), x2, x3)
new_esEs26(x0, x1, ty_Double)
new_esEs5(x0, x1, ty_Double)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs35(x0, x1, app(app(ty_@2, x2), x3))
new_fsEs(x0)
new_esEs16(:(x0, x1), [], x2)
new_ltEs5(Just(x0), Just(x1), ty_Integer)
new_esEs35(x0, x1, app(ty_Ratio, x2))
new_lt6(x0, x1, ty_Double)
new_esEs35(x0, x1, ty_Double)
new_ltEs18(x0, x1, ty_Bool)
new_esEs23(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Float)
new_ltEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(x0, x1, app(ty_Maybe, x2))
new_compare28(x0, x1, False, x2, x3)
new_ltEs5(Just(x0), Just(x1), ty_Double)
new_lt22(x0, x1, ty_Ordering)
new_lt23(x0, x1, app(ty_Ratio, x2))
new_esEs9(x0, x1, ty_@0)
new_esEs6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare24(x0, x1, x2, x3, False, x4, x5)
new_esEs24(Left(x0), Left(x1), ty_@0, x2)
new_esEs35(x0, x1, ty_Bool)
new_esEs35(x0, x1, ty_Char)
new_ltEs23(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, ty_Bool)
new_ltEs10(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs31(x0, x1, ty_@0)
new_lt10(x0, x1, x2)
new_ltEs19(x0, x1, ty_Double)
new_lt12(x0, x1, x2, x3)
new_ltEs24(x0, x1, ty_Double)
new_esEs13(Double(x0, x1), Double(x2, x3))
new_esEs10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Ordering)
new_esEs5(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(Just(x0), Nothing, x1)
new_ltEs14(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs24(Right(x0), Right(x1), x2, ty_@0)
new_esEs20(True, True)
new_lt22(x0, x1, ty_Int)
new_esEs7(x0, x1, ty_Integer)
new_esEs30(x0, x1, ty_Bool)
new_lt21(x0, x1, ty_@0)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs4(x0, x1, app(ty_Maybe, x2))
new_esEs33(x0, x1, ty_Float)
new_esEs29(x0, x1, ty_Integer)
new_ltEs21(x0, x1, ty_Integer)
new_lt16(x0, x1, x2, x3)
new_primPlusNat0(Zero, x0)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs4(x0, x1, ty_Ordering)
new_esEs8(x0, x1, ty_Bool)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_primPlusNat0(Succ(x0), x1)
new_ltEs4(x0, x1)
new_esEs34(x0, x1, ty_Integer)
new_esEs31(x0, x1, ty_Ordering)
new_ltEs6(GT, LT)
new_ltEs6(LT, GT)
new_compare0([], [], x0)
new_ltEs22(x0, x1, app(ty_Maybe, x2))
new_esEs35(x0, x1, app(ty_Maybe, x2))
new_compare111(x0, x1, x2, x3, True, x4, x5)
new_esEs11(x0, x1, ty_Double)
new_lt19(x0, x1)
new_ltEs14(Left(x0), Left(x1), ty_Double, x2)
new_ltEs8(x0, x1, x2)
new_ltEs14(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs4(x0, x1, ty_Double)
new_esEs36(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, ty_Double)
new_esEs39(x0, x1, ty_Char)
new_ltEs22(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_compare15(EQ, EQ)
new_lt6(x0, x1, ty_Int)
new_lt21(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, ty_Ordering)
new_ltEs14(Right(x0), Right(x1), x2, ty_Double)
new_ltEs22(x0, x1, ty_Ordering)
new_ltEs11(x0, x1)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_compare7(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt20(x0, x1, ty_Float)
new_lt21(x0, x1, ty_Integer)
new_esEs32(x0, x1, ty_Bool)
new_esEs39(x0, x1, ty_Float)
new_compare10(x0, x1, False, x2, x3)
new_lt6(x0, x1, ty_Integer)
new_lt4(x0, x1, x2, x3, x4)
new_esEs10(x0, x1, ty_Double)
new_esEs31(x0, x1, app(ty_[], x2))
new_sr0(x0, x1)
new_esEs23(Just(x0), Just(x1), ty_Integer)
new_esEs24(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs20(False, True)
new_esEs20(True, False)
new_esEs29(x0, x1, ty_Bool)
new_esEs24(Left(x0), Right(x1), x2, x3)
new_esEs24(Right(x0), Left(x1), x2, x3)
new_ltEs23(x0, x1, ty_Integer)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs36(x0, x1, app(ty_Ratio, x2))
new_esEs20(False, False)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare12(False, False)
new_esEs12(LT, EQ)
new_esEs12(EQ, LT)
new_lt21(x0, x1, ty_Int)
new_lt22(x0, x1, ty_Char)
new_ltEs14(Left(x0), Left(x1), ty_Char, x2)
new_ltEs14(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare14(x0, x1, x2, x3, x4, x5, True, x6, x7, x8)
new_esEs31(x0, x1, ty_Float)
new_esEs24(Left(x0), Left(x1), ty_Float, x2)
new_primPlusNat1(Zero, Zero)
new_ltEs21(x0, x1, ty_Bool)
new_esEs24(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs20(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_Float)
new_esEs12(EQ, EQ)
new_esEs23(Just(x0), Just(x1), ty_Bool)
new_esEs27(x0, x1, ty_Char)
new_ltEs14(Right(x0), Right(x1), x2, ty_Int)
new_esEs9(x0, x1, ty_Integer)
new_esEs30(x0, x1, ty_Float)
new_ltEs20(x0, x1, ty_Float)
new_lt22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(Right(x0), Right(x1), x2, ty_Char)
new_esEs9(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Left(x0), Left(x1), ty_Float, x2)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs16(:(x0, x1), :(x2, x3), x4)
new_esEs28(x0, x1, ty_Double)
new_esEs30(x0, x1, ty_Char)
new_compare30(x0, x1, ty_@0)
new_esEs6(x0, x1, ty_Bool)
new_esEs16([], :(x0, x1), x2)
new_ltEs23(x0, x1, ty_Float)
new_esEs9(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs31(x0, x1, app(app(ty_@2, x2), x3))
new_compare15(EQ, GT)
new_compare15(GT, EQ)
new_compare17(x0, x1, x2, x3, x4, x5, True, x6, x7, x8, x9)
new_ltEs9(x0, x1, x2)
new_ltEs24(x0, x1, ty_Ordering)
new_compare30(x0, x1, ty_Char)
new_primEqNat0(Succ(x0), Zero)
new_compare15(LT, GT)
new_compare15(GT, LT)
new_esEs36(x0, x1, ty_Double)
new_esEs39(x0, x1, ty_Ordering)
new_esEs7(x0, x1, app(app(ty_Either, x2), x3))
new_lt21(x0, x1, app(ty_[], x2))
new_esEs37(x0, x1, ty_Int)
new_esEs9(x0, x1, ty_Double)
new_primMulInt(Neg(x0), Neg(x1))
new_ltEs5(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs17(x0, x1)
new_compare0([], :(x0, x1), x2)
new_esEs9(x0, x1, ty_Ordering)
new_ltEs12(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs26(x0, x1, ty_Char)
new_lt23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_lt23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs23(x0, x1, ty_Int)
new_primEqNat0(Succ(x0), Succ(x1))
new_compare210(x0, x1, True, x2)
new_esEs8(x0, x1, ty_Int)
new_ltEs14(Left(x0), Left(x1), ty_Bool, x2)
new_lt21(x0, x1, app(ty_Maybe, x2))
new_ltEs5(Just(x0), Just(x1), ty_Int)
new_esEs33(x0, x1, ty_Int)
new_ltEs23(x0, x1, ty_@0)
new_lt6(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs33(x0, x1, ty_Bool)
new_esEs10(x0, x1, ty_Ordering)
new_esEs24(Left(x0), Left(x1), ty_Double, x2)
new_esEs35(x0, x1, ty_@0)
new_esEs4(x0, x1, ty_Char)
new_compare112(x0, x1, False, x2)
new_esEs24(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_lt23(x0, x1, ty_Int)
new_ltEs14(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs18(x0, x1, ty_Double)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt23(x0, x1, ty_Bool)
new_ltEs14(Left(x0), Left(x1), ty_Integer, x2)
new_esEs24(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_lt9(x0, x1, x2)
new_ltEs18(x0, x1, app(ty_[], x2))
new_esEs33(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, app(ty_[], x2))
new_lt5(x0, x1, app(app(ty_Either, x2), x3))
new_lt21(x0, x1, ty_Bool)
new_esEs24(Left(x0), Left(x1), ty_Char, x2)
new_ltEs5(Nothing, Nothing, x0)
new_compare18(Float(x0, x1), Float(x2, x3))
new_ltEs5(Just(x0), Just(x1), ty_Float)
new_esEs26(x0, x1, ty_Bool)
new_lt6(x0, x1, ty_Bool)
new_esEs30(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Integer)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs8(x0, x1, ty_Double)
new_lt21(x0, x1, ty_Char)
new_lt5(x0, x1, ty_Float)
new_compare11(Char(x0), Char(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs24(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs36(x0, x1, app(app(ty_Either, x2), x3))
new_esEs30(x0, x1, ty_Integer)
new_esEs25(x0, x1)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_compare210(x0, x1, False, x2)
new_esEs29(x0, x1, ty_@0)
new_ltEs14(Left(x0), Left(x1), ty_Int, x2)
new_sr(Integer(x0), Integer(x1))
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs7(x0, x1, ty_@0)
new_esEs39(x0, x1, app(ty_Maybe, x2))
new_primMulNat0(Succ(x0), Succ(x1))
new_ltEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs34(x0, x1, ty_Char)
new_esEs4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs10(x0, x1, ty_Bool)
new_lt5(x0, x1, app(ty_[], x2))
new_esEs10(x0, x1, ty_@0)
new_esEs39(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_@0)
new_esEs31(x0, x1, ty_Bool)
new_primEqNat0(Zero, Succ(x0))
new_primPlusNat1(Succ(x0), Zero)
new_lt23(x0, x1, ty_Char)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs7(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Char)
new_ltEs21(x0, x1, app(ty_Maybe, x2))
new_esEs6(x0, x1, ty_Ordering)
new_esEs33(x0, x1, ty_Char)
new_compare27(Left(x0), Left(x1), x2, x3)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs32(x0, x1, ty_Integer)
new_ltEs14(Left(x0), Left(x1), ty_Ordering, x2)
new_pePe(False, x0)
new_ltEs24(x0, x1, ty_Int)
new_compare24(x0, x1, x2, x3, True, x4, x5)
new_lt8(x0, x1)
new_esEs39(x0, x1, app(app(ty_Either, x2), x3))
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt23(x0, x1, ty_Double)
new_esEs10(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Bool)
new_esEs9(x0, x1, app(app(ty_@2, x2), x3))
new_esEs32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, ty_Int)
new_esEs30(x0, x1, ty_Ordering)
new_lt23(x0, x1, ty_Float)
new_lt6(x0, x1, ty_@0)
new_primPlusNat1(Succ(x0), Succ(x1))
new_compare27(Right(x0), Right(x1), x2, x3)
new_esEs31(x0, x1, ty_Char)
new_lt22(x0, x1, ty_Double)
new_ltEs22(x0, x1, ty_@0)
new_esEs39(x0, x1, ty_Int)
new_esEs30(x0, x1, ty_@0)
new_compare14(x0, x1, x2, x3, x4, x5, False, x6, x7, x8)
new_ltEs16(False, True)
new_ltEs16(True, False)
new_ltEs6(GT, GT)
new_esEs10(x0, x1, ty_Int)
new_compare30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(x0, x1, app(ty_Maybe, x2))
new_esEs31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs32(x0, x1, ty_Char)
new_esEs23(Nothing, Just(x0), x1)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(x0, x1, ty_Int)
new_ltEs5(Just(x0), Just(x1), ty_Ordering)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_ltEs19(x0, x1, ty_Char)
new_ltEs22(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(Just(x0), Just(x1), ty_Char)
new_esEs27(x0, x1, ty_Int)
new_esEs24(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs4(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(Just(x0), Just(x1), ty_Bool)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_Bool)
new_lt22(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_@0)
new_ltEs22(x0, x1, ty_Bool)
new_esEs30(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_Integer)
new_esEs33(x0, x1, ty_Integer)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, ty_Int)
new_primCmpNat0(Zero, Zero)
new_esEs35(x0, x1, ty_Float)
new_asAs(False, x0)
new_lt5(x0, x1, ty_Integer)
new_ltEs24(x0, x1, ty_@0)
new_esEs17(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs19(x0, x1, ty_Int)
new_lt23(x0, x1, ty_@0)
new_esEs34(x0, x1, ty_Int)
new_ltEs6(LT, LT)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs35(x0, x1, app(ty_[], x2))
new_esEs35(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare31(Just(x0), Just(x1), x2)
new_esEs11(x0, x1, ty_Ordering)
new_esEs31(x0, x1, app(ty_Ratio, x2))
new_lt5(x0, x1, app(ty_Ratio, x2))
new_ltEs22(x0, x1, ty_Double)
new_ltEs14(Left(x0), Left(x1), ty_@0, x2)
new_lt23(x0, x1, app(ty_[], x2))
new_compare10(x0, x1, True, x2, x3)
new_ltEs24(x0, x1, ty_Char)
new_esEs21(:%(x0, x1), :%(x2, x3), x4)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs18(Integer(x0), Integer(x1))
new_esEs4(x0, x1, ty_@0)
new_lt22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, ty_Int)
new_ltEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(Just(x0), Just(x1), ty_@0)
new_compare110(x0, x1, x2, x3, False, x4, x5, x6)
new_ltEs14(Right(x0), Right(x1), x2, ty_Integer)
new_compare0(:(x0, x1), [], x2)
new_esEs23(Just(x0), Nothing, x1)
new_ltEs19(x0, x1, ty_Float)
new_esEs6(x0, x1, ty_Char)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_lt21(x0, x1, ty_Double)
new_primCompAux1(x0, x1, x2, x3)
new_esEs32(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs8(x0, x1, app(ty_[], x2))
new_esEs23(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs34(x0, x1, app(app(ty_Either, x2), x3))
new_esEs33(x0, x1, app(ty_[], x2))
new_lt5(x0, x1, ty_Bool)
new_esEs11(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(Just(x0), Just(x1), ty_Char)
new_ltEs13(x0, x1)
new_lt14(x0, x1, x2)
new_ltEs23(x0, x1, ty_Bool)
new_esEs6(x0, x1, app(ty_Ratio, x2))
new_compare15(LT, EQ)
new_compare15(EQ, LT)
new_compare9(@0, @0)
new_lt13(x0, x1)
new_esEs36(x0, x1, ty_Integer)
new_esEs29(x0, x1, ty_Double)
new_ltEs22(x0, x1, app(ty_[], x2))
new_ltEs23(x0, x1, app(ty_Maybe, x2))
new_esEs8(x0, x1, app(ty_Ratio, x2))
new_ltEs18(x0, x1, ty_Float)
new_lt18(x0, x1)
new_lt22(x0, x1, app(ty_Ratio, x2))
new_esEs32(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_Float)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_lt5(x0, x1, ty_Ordering)
new_lt15(x0, x1)
new_compare8(Integer(x0), Integer(x1))
new_lt22(x0, x1, app(ty_[], x2))
new_compare30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs33(x0, x1, app(ty_Ratio, x2))
new_lt5(x0, x1, app(ty_Maybe, x2))
new_esEs36(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs33(x0, x1, app(ty_Maybe, x2))
new_esEs7(x0, x1, app(ty_Maybe, x2))
new_esEs8(x0, x1, ty_@0)
new_lt6(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(x0, x1, ty_Int)
new_not(True)
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_compare30(x0, x1, ty_Float)
new_compare31(Just(x0), Nothing, x1)
new_esEs27(x0, x1, ty_Ordering)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs22(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs23(x0, x1, app(ty_Ratio, x2))
new_ltEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(x0, x1, ty_Bool)
new_esEs32(x0, x1, ty_Float)
new_esEs36(x0, x1, ty_Ordering)
new_esEs9(x0, x1, ty_Bool)
new_esEs23(Just(x0), Just(x1), app(ty_Maybe, x2))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_not(False)
new_esEs24(Left(x0), Left(x1), ty_Ordering, x2)
new_compare29(Double(x0, x1), Double(x2, x3))
new_compare13(:%(x0, x1), :%(x2, x3), ty_Integer)
new_lt6(x0, x1, app(ty_Ratio, x2))
new_primCmpNat0(Succ(x0), Succ(x1))
new_esEs7(x0, x1, ty_Ordering)
new_esEs34(x0, x1, app(ty_Ratio, x2))
new_ltEs23(x0, x1, ty_Char)
new_esEs7(x0, x1, app(ty_[], x2))
new_esEs8(x0, x1, ty_Ordering)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_esEs39(x0, x1, ty_@0)
new_ltEs21(x0, x1, ty_Char)
new_esEs15(Char(x0), Char(x1))
new_esEs7(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(x0, x1, app(ty_Ratio, x2))
new_ltEs6(GT, EQ)
new_ltEs6(EQ, GT)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_esEs7(x0, x1, app(ty_Ratio, x2))
new_esEs32(x0, x1, app(ty_Ratio, x2))
new_primCmpNat0(Zero, Succ(x0))
new_esEs31(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Ordering)
new_lt23(x0, x1, app(ty_Maybe, x2))
new_ltEs21(x0, x1, ty_Double)
new_esEs24(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs8(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs23(x0, x1, app(ty_[], x2))
new_esEs24(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_compare30(x0, x1, ty_Double)
new_compare19(x0, x1, True, x2, x3)
new_esEs36(x0, x1, app(ty_Maybe, x2))
new_esEs24(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs5(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(Right(x0), Right(x1), x2, ty_Double)
new_lt22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(x0, x1, app(ty_[], x2))
new_primCmpNat0(Succ(x0), Zero)
new_compare30(x0, x1, app(ty_Maybe, x2))
new_esEs34(x0, x1, ty_Double)
new_ltEs21(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_@0)
new_esEs11(x0, x1, app(ty_Maybe, x2))
new_esEs6(x0, x1, app(ty_Maybe, x2))
new_ltEs22(x0, x1, ty_Int)
new_compare26(x0, x1, False, x2, x3)
new_compare16(x0, x1)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_esEs23(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs20(x0, x1, ty_Double)
new_ltEs24(x0, x1, ty_Bool)
new_esEs35(x0, x1, ty_Ordering)
new_ltEs18(x0, x1, ty_Integer)
new_esEs39(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs34(x0, x1, ty_@0)
new_compare31(Nothing, Just(x0), x1)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_esEs37(x0, x1, ty_Integer)
new_ltEs18(x0, x1, ty_Char)
new_esEs7(x0, x1, ty_Double)
new_lt23(x0, x1, ty_Ordering)
new_compare112(x0, x1, True, x2)
new_lt21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs34(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs9(x0, x1, ty_Float)
new_esEs23(Just(x0), Just(x1), ty_Ordering)
new_lt6(x0, x1, ty_Char)
new_esEs9(x0, x1, ty_Char)
new_esEs8(x0, x1, ty_Char)
new_esEs35(x0, x1, ty_Int)
new_esEs24(Left(x0), Left(x1), ty_Integer, x2)
new_esEs5(x0, x1, app(ty_Maybe, x2))
new_lt21(x0, x1, app(ty_Ratio, x2))
new_esEs33(x0, x1, ty_@0)
new_esEs24(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs5(x0, x1, ty_Ordering)
new_esEs32(x0, x1, ty_Double)
new_esEs34(x0, x1, app(ty_Maybe, x2))
new_esEs10(x0, x1, app(ty_[], x2))
new_compare30(x0, x1, app(ty_Ratio, x2))
new_ltEs21(x0, x1, app(ty_Ratio, x2))
new_lt23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs24(x0, x1, app(ty_Ratio, x2))
new_esEs14(Float(x0, x1), Float(x2, x3))
new_esEs26(x0, x1, ty_Integer)
new_esEs5(x0, x1, ty_@0)
new_esEs5(x0, x1, ty_Char)
new_esEs7(x0, x1, ty_Char)
new_compare12(True, True)
new_primEqInt(Pos(Zero), Pos(Zero))
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs5(x0, x1, ty_Integer)
new_compare31(Nothing, Nothing, x0)
new_esEs39(x0, x1, app(ty_[], x2))
new_compare30(x0, x1, ty_Ordering)
new_primMulNat0(Zero, Succ(x0))
new_esEs28(x0, x1, app(ty_[], x2))
new_ltEs23(x0, x1, ty_Double)
new_esEs24(Right(x0), Right(x1), x2, ty_Float)
new_esEs11(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_lt5(x0, x1, app(app(ty_@2, x2), x3))
new_primCompAux0(x0, GT)
new_lt6(x0, x1, ty_Ordering)
new_primPlusNat1(Zero, Succ(x0))
new_esEs36(x0, x1, ty_Float)
new_esEs19(@0, @0)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs39(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_compare25(x0, x1, x2, x3, x4, x5, True, x6, x7, x8)
new_esEs36(x0, x1, ty_@0)
new_esEs12(LT, LT)
new_esEs28(x0, x1, ty_Integer)
new_compare19(x0, x1, False, x2, x3)
new_ltEs18(x0, x1, ty_Ordering)
new_ltEs16(False, False)
new_compare111(x0, x1, x2, x3, False, x4, x5)
new_compare25(x0, x1, x2, x3, x4, x5, False, x6, x7, x8)
new_esEs33(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, ty_Ordering)
new_esEs28(x0, x1, ty_@0)
new_esEs11(x0, x1, ty_Float)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs4(x0, x1, app(ty_[], x2))
new_esEs39(x0, x1, ty_Integer)

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

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

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

new_splitLT3(:(yvy300, yvy301), yvy31, yvy32, Branch(yvy330, yvy331, yvy332, yvy333, yvy334), yvy34, [], bb, bc) → new_splitLT3(yvy330, yvy331, yvy332, yvy333, yvy334, [], bb, bc)

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

new_esEs36(x0, x1, ty_Char)
new_esEs29(x0, x1, ty_Float)
new_lt22(x0, x1, app(ty_Maybe, x2))
new_esEs7(x0, x1, ty_Int)
new_ltEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs21(x0, x1, ty_Int)
new_ltEs14(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs10(x0, x1, ty_Float)
new_ltEs16(True, True)
new_esEs6(x0, x1, ty_Int)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs32(x0, x1, app(ty_Maybe, x2))
new_lt11(x0, x1)
new_esEs24(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs20(x0, x1, ty_Int)
new_lt5(x0, x1, ty_Char)
new_esEs5(x0, x1, app(ty_[], x2))
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs36(x0, x1, app(ty_[], x2))
new_lt21(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs21(x0, x1, ty_@0)
new_esEs29(x0, x1, ty_Char)
new_ltEs22(x0, x1, ty_Integer)
new_esEs34(x0, x1, app(ty_[], x2))
new_esEs32(x0, x1, ty_Int)
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs11(x0, x1, ty_Int)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs4(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_Integer)
new_compare30(x0, x1, ty_Int)
new_pePe(True, x0)
new_esEs5(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs11(x0, x1, ty_@0)
new_esEs35(x0, x1, ty_Integer)
new_esEs11(x0, x1, ty_Char)
new_esEs9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(x0, x1, ty_Float)
new_esEs9(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(x0, x1, ty_Int)
new_esEs31(x0, x1, app(app(ty_Either, x2), x3))
new_lt22(x0, x1, ty_@0)
new_compare30(x0, x1, ty_Bool)
new_ltEs5(Nothing, Just(x0), x1)
new_lt20(x0, x1, ty_@0)
new_esEs29(x0, x1, ty_Ordering)
new_lt22(x0, x1, ty_Float)
new_esEs9(x0, x1, app(ty_[], x2))
new_lt23(x0, x1, ty_Integer)
new_ltEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(Right(x0), Right(x1), x2, ty_Bool)
new_lt7(x0, x1)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs8(x0, x1, ty_Integer)
new_esEs23(Just(x0), Just(x1), ty_Float)
new_esEs6(x0, x1, ty_Integer)
new_lt5(x0, x1, ty_@0)
new_esEs33(x0, x1, app(app(ty_@2, x2), x3))
new_esEs11(x0, x1, ty_Bool)
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs24(Right(x0), Right(x1), x2, ty_Integer)
new_compare12(False, True)
new_compare12(True, False)
new_ltEs7(x0, x1)
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_primCompAux0(x0, EQ)
new_esEs32(x0, x1, app(app(ty_@2, x2), x3))
new_lt6(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(x0, x1, ty_Integer)
new_esEs32(x0, x1, ty_Ordering)
new_ltEs21(x0, x1, ty_Float)
new_ltEs24(x0, x1, ty_Integer)
new_esEs34(x0, x1, ty_Float)
new_esEs6(x0, x1, ty_@0)
new_lt6(x0, x1, ty_Float)
new_esEs9(x0, x1, ty_Int)
new_compare30(x0, x1, ty_Integer)
new_esEs12(GT, EQ)
new_esEs12(EQ, GT)
new_esEs36(x0, x1, ty_Int)
new_esEs28(x0, x1, ty_Bool)
new_ltEs14(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs24(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_compare30(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_lt5(x0, x1, ty_Double)
new_compare15(LT, LT)
new_esEs10(x0, x1, ty_Char)
new_esEs23(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primMulNat0(Succ(x0), Zero)
new_ltEs22(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_compare6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs34(x0, x1, ty_Ordering)
new_esEs16([], [], x0)
new_esEs12(GT, GT)
new_esEs30(x0, x1, ty_Double)
new_esEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs21(x0, x1, ty_Ordering)
new_esEs10(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_lt21(x0, x1, ty_Float)
new_esEs11(x0, x1, ty_Integer)
new_esEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs21(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs24(x0, x1, app(ty_Maybe, x2))
new_esEs23(Just(x0), Just(x1), ty_Double)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_Char)
new_esEs34(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(Left(x0), Left(x1), ty_Int, x2)
new_esEs38(x0, x1, ty_Integer)
new_ltEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs27(x0, x1, ty_Bool)
new_esEs24(Right(x0), Right(x1), x2, ty_Char)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs6(EQ, EQ)
new_esEs32(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(x0, x1, ty_Float)
new_esEs8(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs22(x0, x1, ty_Char)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(x0, x1, ty_Double)
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_esEs5(x0, x1, ty_Bool)
new_lt6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs31(x0, x1, ty_Int)
new_compare26(x0, x1, True, x2, x3)
new_compare110(x0, x1, x2, x3, True, x4, x5, x6)
new_ltEs24(x0, x1, app(ty_[], x2))
new_compare27(Right(x0), Left(x1), x2, x3)
new_compare27(Left(x0), Right(x1), x2, x3)
new_esEs33(x0, x1, ty_Double)
new_esEs8(x0, x1, ty_Float)
new_ltEs18(x0, x1, ty_@0)
new_esEs4(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, app(ty_[], x2))
new_ltEs5(Just(x0), Just(x1), ty_@0)
new_lt5(x0, x1, ty_Int)
new_ltEs6(LT, EQ)
new_ltEs6(EQ, LT)
new_esEs24(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_primCompAux0(x0, LT)
new_esEs23(Nothing, Nothing, x0)
new_esEs38(x0, x1, ty_Int)
new_esEs23(Just(x0), Just(x1), ty_Int)
new_ltEs20(x0, x1, ty_@0)
new_lt6(x0, x1, app(ty_Maybe, x2))
new_esEs11(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Int)
new_lt17(x0, x1)
new_esEs8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs36(x0, x1, ty_Bool)
new_primEqNat0(Zero, Zero)
new_compare13(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs26(x0, x1, ty_@0)
new_lt21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(Right(x0), Right(x1), x2, ty_Int)
new_esEs7(x0, x1, ty_Bool)
new_esEs33(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs5(x0, x1, ty_Float)
new_ltEs14(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_compare17(x0, x1, x2, x3, x4, x5, False, x6, x7, x8, x9)
new_ltEs22(x0, x1, ty_Float)
new_compare15(GT, GT)
new_esEs31(x0, x1, ty_Double)
new_ltEs20(x0, x1, ty_Integer)
new_lt22(x0, x1, ty_Bool)
new_compare30(x0, x1, app(ty_[], x2))
new_esEs34(x0, x1, ty_Bool)
new_esEs31(x0, x1, ty_Integer)
new_ltEs20(x0, x1, ty_Char)
new_lt20(x0, x1, ty_Double)
new_esEs35(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_compare28(x0, x1, True, x2, x3)
new_ltEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs21(x0, x1, app(ty_[], x2))
new_ltEs15(x0, x1)
new_esEs4(x0, x1, ty_Integer)
new_esEs39(x0, x1, app(ty_Ratio, x2))
new_esEs6(x0, x1, app(app(ty_Either, x2), x3))
new_esEs39(x0, x1, ty_Bool)
new_esEs6(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs24(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Float)
new_ltEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_primMulNat0(Zero, Zero)
new_asAs(True, x0)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_ltEs14(Left(x0), Right(x1), x2, x3)
new_ltEs14(Right(x0), Left(x1), x2, x3)
new_esEs26(x0, x1, ty_Double)
new_esEs5(x0, x1, ty_Double)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs35(x0, x1, app(app(ty_@2, x2), x3))
new_fsEs(x0)
new_esEs16(:(x0, x1), [], x2)
new_ltEs5(Just(x0), Just(x1), ty_Integer)
new_esEs35(x0, x1, app(ty_Ratio, x2))
new_lt6(x0, x1, ty_Double)
new_esEs35(x0, x1, ty_Double)
new_ltEs18(x0, x1, ty_Bool)
new_esEs23(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Float)
new_ltEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(x0, x1, app(ty_Maybe, x2))
new_compare28(x0, x1, False, x2, x3)
new_ltEs5(Just(x0), Just(x1), ty_Double)
new_lt22(x0, x1, ty_Ordering)
new_lt23(x0, x1, app(ty_Ratio, x2))
new_esEs9(x0, x1, ty_@0)
new_esEs6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare24(x0, x1, x2, x3, False, x4, x5)
new_esEs24(Left(x0), Left(x1), ty_@0, x2)
new_esEs35(x0, x1, ty_Bool)
new_esEs35(x0, x1, ty_Char)
new_ltEs23(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, ty_Bool)
new_ltEs10(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs31(x0, x1, ty_@0)
new_lt10(x0, x1, x2)
new_ltEs19(x0, x1, ty_Double)
new_lt12(x0, x1, x2, x3)
new_ltEs24(x0, x1, ty_Double)
new_esEs13(Double(x0, x1), Double(x2, x3))
new_esEs10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Ordering)
new_esEs5(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(Just(x0), Nothing, x1)
new_ltEs14(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs24(Right(x0), Right(x1), x2, ty_@0)
new_esEs20(True, True)
new_lt22(x0, x1, ty_Int)
new_esEs7(x0, x1, ty_Integer)
new_esEs30(x0, x1, ty_Bool)
new_lt21(x0, x1, ty_@0)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs4(x0, x1, app(ty_Maybe, x2))
new_esEs33(x0, x1, ty_Float)
new_esEs29(x0, x1, ty_Integer)
new_ltEs21(x0, x1, ty_Integer)
new_lt16(x0, x1, x2, x3)
new_primPlusNat0(Zero, x0)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs4(x0, x1, ty_Ordering)
new_esEs8(x0, x1, ty_Bool)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_primPlusNat0(Succ(x0), x1)
new_ltEs4(x0, x1)
new_esEs34(x0, x1, ty_Integer)
new_esEs31(x0, x1, ty_Ordering)
new_ltEs6(GT, LT)
new_ltEs6(LT, GT)
new_compare0([], [], x0)
new_ltEs22(x0, x1, app(ty_Maybe, x2))
new_esEs35(x0, x1, app(ty_Maybe, x2))
new_compare111(x0, x1, x2, x3, True, x4, x5)
new_esEs11(x0, x1, ty_Double)
new_lt19(x0, x1)
new_ltEs14(Left(x0), Left(x1), ty_Double, x2)
new_ltEs8(x0, x1, x2)
new_ltEs14(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs4(x0, x1, ty_Double)
new_esEs36(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, ty_Double)
new_esEs39(x0, x1, ty_Char)
new_ltEs22(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_compare15(EQ, EQ)
new_lt6(x0, x1, ty_Int)
new_lt21(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, ty_Ordering)
new_ltEs14(Right(x0), Right(x1), x2, ty_Double)
new_ltEs22(x0, x1, ty_Ordering)
new_ltEs11(x0, x1)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_compare7(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt20(x0, x1, ty_Float)
new_lt21(x0, x1, ty_Integer)
new_esEs32(x0, x1, ty_Bool)
new_esEs39(x0, x1, ty_Float)
new_compare10(x0, x1, False, x2, x3)
new_lt6(x0, x1, ty_Integer)
new_lt4(x0, x1, x2, x3, x4)
new_esEs10(x0, x1, ty_Double)
new_esEs31(x0, x1, app(ty_[], x2))
new_sr0(x0, x1)
new_esEs23(Just(x0), Just(x1), ty_Integer)
new_esEs24(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs20(False, True)
new_esEs20(True, False)
new_esEs29(x0, x1, ty_Bool)
new_esEs24(Left(x0), Right(x1), x2, x3)
new_esEs24(Right(x0), Left(x1), x2, x3)
new_ltEs23(x0, x1, ty_Integer)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs36(x0, x1, app(ty_Ratio, x2))
new_esEs20(False, False)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare12(False, False)
new_esEs12(LT, EQ)
new_esEs12(EQ, LT)
new_lt21(x0, x1, ty_Int)
new_lt22(x0, x1, ty_Char)
new_ltEs14(Left(x0), Left(x1), ty_Char, x2)
new_ltEs14(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare14(x0, x1, x2, x3, x4, x5, True, x6, x7, x8)
new_esEs31(x0, x1, ty_Float)
new_esEs24(Left(x0), Left(x1), ty_Float, x2)
new_primPlusNat1(Zero, Zero)
new_ltEs21(x0, x1, ty_Bool)
new_esEs24(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs20(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_Float)
new_esEs12(EQ, EQ)
new_esEs23(Just(x0), Just(x1), ty_Bool)
new_esEs27(x0, x1, ty_Char)
new_ltEs14(Right(x0), Right(x1), x2, ty_Int)
new_esEs9(x0, x1, ty_Integer)
new_esEs30(x0, x1, ty_Float)
new_ltEs20(x0, x1, ty_Float)
new_lt22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(Right(x0), Right(x1), x2, ty_Char)
new_esEs9(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Left(x0), Left(x1), ty_Float, x2)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs16(:(x0, x1), :(x2, x3), x4)
new_esEs28(x0, x1, ty_Double)
new_esEs30(x0, x1, ty_Char)
new_compare30(x0, x1, ty_@0)
new_esEs6(x0, x1, ty_Bool)
new_esEs16([], :(x0, x1), x2)
new_ltEs23(x0, x1, ty_Float)
new_esEs9(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs31(x0, x1, app(app(ty_@2, x2), x3))
new_compare15(EQ, GT)
new_compare15(GT, EQ)
new_compare17(x0, x1, x2, x3, x4, x5, True, x6, x7, x8, x9)
new_ltEs9(x0, x1, x2)
new_ltEs24(x0, x1, ty_Ordering)
new_compare30(x0, x1, ty_Char)
new_primEqNat0(Succ(x0), Zero)
new_compare15(LT, GT)
new_compare15(GT, LT)
new_esEs36(x0, x1, ty_Double)
new_esEs39(x0, x1, ty_Ordering)
new_esEs7(x0, x1, app(app(ty_Either, x2), x3))
new_lt21(x0, x1, app(ty_[], x2))
new_esEs37(x0, x1, ty_Int)
new_esEs9(x0, x1, ty_Double)
new_primMulInt(Neg(x0), Neg(x1))
new_ltEs5(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs17(x0, x1)
new_compare0([], :(x0, x1), x2)
new_esEs9(x0, x1, ty_Ordering)
new_ltEs12(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs26(x0, x1, ty_Char)
new_lt23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_lt23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs23(x0, x1, ty_Int)
new_primEqNat0(Succ(x0), Succ(x1))
new_compare210(x0, x1, True, x2)
new_esEs8(x0, x1, ty_Int)
new_ltEs14(Left(x0), Left(x1), ty_Bool, x2)
new_lt21(x0, x1, app(ty_Maybe, x2))
new_ltEs5(Just(x0), Just(x1), ty_Int)
new_esEs33(x0, x1, ty_Int)
new_ltEs23(x0, x1, ty_@0)
new_lt6(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs33(x0, x1, ty_Bool)
new_esEs10(x0, x1, ty_Ordering)
new_esEs24(Left(x0), Left(x1), ty_Double, x2)
new_esEs35(x0, x1, ty_@0)
new_esEs4(x0, x1, ty_Char)
new_compare112(x0, x1, False, x2)
new_esEs24(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_lt23(x0, x1, ty_Int)
new_ltEs14(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs18(x0, x1, ty_Double)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt23(x0, x1, ty_Bool)
new_ltEs14(Left(x0), Left(x1), ty_Integer, x2)
new_esEs24(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_lt9(x0, x1, x2)
new_ltEs18(x0, x1, app(ty_[], x2))
new_esEs33(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, app(ty_[], x2))
new_lt5(x0, x1, app(app(ty_Either, x2), x3))
new_lt21(x0, x1, ty_Bool)
new_esEs24(Left(x0), Left(x1), ty_Char, x2)
new_ltEs5(Nothing, Nothing, x0)
new_compare18(Float(x0, x1), Float(x2, x3))
new_ltEs5(Just(x0), Just(x1), ty_Float)
new_esEs26(x0, x1, ty_Bool)
new_lt6(x0, x1, ty_Bool)
new_esEs30(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Integer)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs8(x0, x1, ty_Double)
new_lt21(x0, x1, ty_Char)
new_lt5(x0, x1, ty_Float)
new_compare11(Char(x0), Char(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs24(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs36(x0, x1, app(app(ty_Either, x2), x3))
new_esEs30(x0, x1, ty_Integer)
new_esEs25(x0, x1)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_compare210(x0, x1, False, x2)
new_esEs29(x0, x1, ty_@0)
new_ltEs14(Left(x0), Left(x1), ty_Int, x2)
new_sr(Integer(x0), Integer(x1))
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs7(x0, x1, ty_@0)
new_esEs39(x0, x1, app(ty_Maybe, x2))
new_primMulNat0(Succ(x0), Succ(x1))
new_ltEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs34(x0, x1, ty_Char)
new_esEs4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs10(x0, x1, ty_Bool)
new_lt5(x0, x1, app(ty_[], x2))
new_esEs10(x0, x1, ty_@0)
new_esEs39(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_@0)
new_esEs31(x0, x1, ty_Bool)
new_primEqNat0(Zero, Succ(x0))
new_primPlusNat1(Succ(x0), Zero)
new_lt23(x0, x1, ty_Char)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs7(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Char)
new_ltEs21(x0, x1, app(ty_Maybe, x2))
new_esEs6(x0, x1, ty_Ordering)
new_esEs33(x0, x1, ty_Char)
new_compare27(Left(x0), Left(x1), x2, x3)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs32(x0, x1, ty_Integer)
new_ltEs14(Left(x0), Left(x1), ty_Ordering, x2)
new_pePe(False, x0)
new_ltEs24(x0, x1, ty_Int)
new_compare24(x0, x1, x2, x3, True, x4, x5)
new_lt8(x0, x1)
new_esEs39(x0, x1, app(app(ty_Either, x2), x3))
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt23(x0, x1, ty_Double)
new_esEs10(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Bool)
new_esEs9(x0, x1, app(app(ty_@2, x2), x3))
new_esEs32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, ty_Int)
new_esEs30(x0, x1, ty_Ordering)
new_lt23(x0, x1, ty_Float)
new_lt6(x0, x1, ty_@0)
new_primPlusNat1(Succ(x0), Succ(x1))
new_compare27(Right(x0), Right(x1), x2, x3)
new_esEs31(x0, x1, ty_Char)
new_lt22(x0, x1, ty_Double)
new_ltEs22(x0, x1, ty_@0)
new_esEs39(x0, x1, ty_Int)
new_esEs30(x0, x1, ty_@0)
new_compare14(x0, x1, x2, x3, x4, x5, False, x6, x7, x8)
new_ltEs16(False, True)
new_ltEs16(True, False)
new_ltEs6(GT, GT)
new_esEs10(x0, x1, ty_Int)
new_compare30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(x0, x1, app(ty_Maybe, x2))
new_esEs31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs32(x0, x1, ty_Char)
new_esEs23(Nothing, Just(x0), x1)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(x0, x1, ty_Int)
new_ltEs5(Just(x0), Just(x1), ty_Ordering)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_ltEs19(x0, x1, ty_Char)
new_ltEs22(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(Just(x0), Just(x1), ty_Char)
new_esEs27(x0, x1, ty_Int)
new_esEs24(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs4(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(Just(x0), Just(x1), ty_Bool)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_Bool)
new_lt22(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_@0)
new_ltEs22(x0, x1, ty_Bool)
new_esEs30(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_Integer)
new_esEs33(x0, x1, ty_Integer)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, ty_Int)
new_primCmpNat0(Zero, Zero)
new_esEs35(x0, x1, ty_Float)
new_asAs(False, x0)
new_lt5(x0, x1, ty_Integer)
new_ltEs24(x0, x1, ty_@0)
new_esEs17(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs19(x0, x1, ty_Int)
new_lt23(x0, x1, ty_@0)
new_esEs34(x0, x1, ty_Int)
new_ltEs6(LT, LT)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs35(x0, x1, app(ty_[], x2))
new_esEs35(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare31(Just(x0), Just(x1), x2)
new_esEs11(x0, x1, ty_Ordering)
new_esEs31(x0, x1, app(ty_Ratio, x2))
new_lt5(x0, x1, app(ty_Ratio, x2))
new_ltEs22(x0, x1, ty_Double)
new_ltEs14(Left(x0), Left(x1), ty_@0, x2)
new_lt23(x0, x1, app(ty_[], x2))
new_compare10(x0, x1, True, x2, x3)
new_ltEs24(x0, x1, ty_Char)
new_esEs21(:%(x0, x1), :%(x2, x3), x4)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs18(Integer(x0), Integer(x1))
new_esEs4(x0, x1, ty_@0)
new_lt22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, ty_Int)
new_ltEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(Just(x0), Just(x1), ty_@0)
new_compare110(x0, x1, x2, x3, False, x4, x5, x6)
new_ltEs14(Right(x0), Right(x1), x2, ty_Integer)
new_compare0(:(x0, x1), [], x2)
new_esEs23(Just(x0), Nothing, x1)
new_ltEs19(x0, x1, ty_Float)
new_esEs6(x0, x1, ty_Char)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_lt21(x0, x1, ty_Double)
new_primCompAux1(x0, x1, x2, x3)
new_esEs32(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs8(x0, x1, app(ty_[], x2))
new_esEs23(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs34(x0, x1, app(app(ty_Either, x2), x3))
new_esEs33(x0, x1, app(ty_[], x2))
new_lt5(x0, x1, ty_Bool)
new_esEs11(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(Just(x0), Just(x1), ty_Char)
new_ltEs13(x0, x1)
new_lt14(x0, x1, x2)
new_ltEs23(x0, x1, ty_Bool)
new_esEs6(x0, x1, app(ty_Ratio, x2))
new_compare15(LT, EQ)
new_compare15(EQ, LT)
new_compare9(@0, @0)
new_lt13(x0, x1)
new_esEs36(x0, x1, ty_Integer)
new_esEs29(x0, x1, ty_Double)
new_ltEs22(x0, x1, app(ty_[], x2))
new_ltEs23(x0, x1, app(ty_Maybe, x2))
new_esEs8(x0, x1, app(ty_Ratio, x2))
new_ltEs18(x0, x1, ty_Float)
new_lt18(x0, x1)
new_lt22(x0, x1, app(ty_Ratio, x2))
new_esEs32(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_Float)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_lt5(x0, x1, ty_Ordering)
new_lt15(x0, x1)
new_compare8(Integer(x0), Integer(x1))
new_lt22(x0, x1, app(ty_[], x2))
new_compare30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs33(x0, x1, app(ty_Ratio, x2))
new_lt5(x0, x1, app(ty_Maybe, x2))
new_esEs36(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs33(x0, x1, app(ty_Maybe, x2))
new_esEs7(x0, x1, app(ty_Maybe, x2))
new_esEs8(x0, x1, ty_@0)
new_lt6(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(x0, x1, ty_Int)
new_not(True)
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_compare30(x0, x1, ty_Float)
new_compare31(Just(x0), Nothing, x1)
new_esEs27(x0, x1, ty_Ordering)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs22(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs23(x0, x1, app(ty_Ratio, x2))
new_ltEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(x0, x1, ty_Bool)
new_esEs32(x0, x1, ty_Float)
new_esEs36(x0, x1, ty_Ordering)
new_esEs9(x0, x1, ty_Bool)
new_esEs23(Just(x0), Just(x1), app(ty_Maybe, x2))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_not(False)
new_esEs24(Left(x0), Left(x1), ty_Ordering, x2)
new_compare29(Double(x0, x1), Double(x2, x3))
new_compare13(:%(x0, x1), :%(x2, x3), ty_Integer)
new_lt6(x0, x1, app(ty_Ratio, x2))
new_primCmpNat0(Succ(x0), Succ(x1))
new_esEs7(x0, x1, ty_Ordering)
new_esEs34(x0, x1, app(ty_Ratio, x2))
new_ltEs23(x0, x1, ty_Char)
new_esEs7(x0, x1, app(ty_[], x2))
new_esEs8(x0, x1, ty_Ordering)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_esEs39(x0, x1, ty_@0)
new_ltEs21(x0, x1, ty_Char)
new_esEs15(Char(x0), Char(x1))
new_esEs7(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(x0, x1, app(ty_Ratio, x2))
new_ltEs6(GT, EQ)
new_ltEs6(EQ, GT)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_esEs7(x0, x1, app(ty_Ratio, x2))
new_esEs32(x0, x1, app(ty_Ratio, x2))
new_primCmpNat0(Zero, Succ(x0))
new_esEs31(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Ordering)
new_lt23(x0, x1, app(ty_Maybe, x2))
new_ltEs21(x0, x1, ty_Double)
new_esEs24(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs8(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs23(x0, x1, app(ty_[], x2))
new_esEs24(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_compare30(x0, x1, ty_Double)
new_compare19(x0, x1, True, x2, x3)
new_esEs36(x0, x1, app(ty_Maybe, x2))
new_esEs24(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs5(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(Right(x0), Right(x1), x2, ty_Double)
new_lt22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(x0, x1, app(ty_[], x2))
new_primCmpNat0(Succ(x0), Zero)
new_compare30(x0, x1, app(ty_Maybe, x2))
new_esEs34(x0, x1, ty_Double)
new_ltEs21(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_@0)
new_esEs11(x0, x1, app(ty_Maybe, x2))
new_esEs6(x0, x1, app(ty_Maybe, x2))
new_ltEs22(x0, x1, ty_Int)
new_compare26(x0, x1, False, x2, x3)
new_compare16(x0, x1)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_esEs23(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs20(x0, x1, ty_Double)
new_ltEs24(x0, x1, ty_Bool)
new_esEs35(x0, x1, ty_Ordering)
new_ltEs18(x0, x1, ty_Integer)
new_esEs39(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs34(x0, x1, ty_@0)
new_compare31(Nothing, Just(x0), x1)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_esEs37(x0, x1, ty_Integer)
new_ltEs18(x0, x1, ty_Char)
new_esEs7(x0, x1, ty_Double)
new_lt23(x0, x1, ty_Ordering)
new_compare112(x0, x1, True, x2)
new_lt21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs34(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs9(x0, x1, ty_Float)
new_esEs23(Just(x0), Just(x1), ty_Ordering)
new_lt6(x0, x1, ty_Char)
new_esEs9(x0, x1, ty_Char)
new_esEs8(x0, x1, ty_Char)
new_esEs35(x0, x1, ty_Int)
new_esEs24(Left(x0), Left(x1), ty_Integer, x2)
new_esEs5(x0, x1, app(ty_Maybe, x2))
new_lt21(x0, x1, app(ty_Ratio, x2))
new_esEs33(x0, x1, ty_@0)
new_esEs24(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs5(x0, x1, ty_Ordering)
new_esEs32(x0, x1, ty_Double)
new_esEs34(x0, x1, app(ty_Maybe, x2))
new_esEs10(x0, x1, app(ty_[], x2))
new_compare30(x0, x1, app(ty_Ratio, x2))
new_ltEs21(x0, x1, app(ty_Ratio, x2))
new_lt23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs24(x0, x1, app(ty_Ratio, x2))
new_esEs14(Float(x0, x1), Float(x2, x3))
new_esEs26(x0, x1, ty_Integer)
new_esEs5(x0, x1, ty_@0)
new_esEs5(x0, x1, ty_Char)
new_esEs7(x0, x1, ty_Char)
new_compare12(True, True)
new_primEqInt(Pos(Zero), Pos(Zero))
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs5(x0, x1, ty_Integer)
new_compare31(Nothing, Nothing, x0)
new_esEs39(x0, x1, app(ty_[], x2))
new_compare30(x0, x1, ty_Ordering)
new_primMulNat0(Zero, Succ(x0))
new_esEs28(x0, x1, app(ty_[], x2))
new_ltEs23(x0, x1, ty_Double)
new_esEs24(Right(x0), Right(x1), x2, ty_Float)
new_esEs11(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_lt5(x0, x1, app(app(ty_@2, x2), x3))
new_primCompAux0(x0, GT)
new_lt6(x0, x1, ty_Ordering)
new_primPlusNat1(Zero, Succ(x0))
new_esEs36(x0, x1, ty_Float)
new_esEs19(@0, @0)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs39(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_compare25(x0, x1, x2, x3, x4, x5, True, x6, x7, x8)
new_esEs36(x0, x1, ty_@0)
new_esEs12(LT, LT)
new_esEs28(x0, x1, ty_Integer)
new_compare19(x0, x1, False, x2, x3)
new_ltEs18(x0, x1, ty_Ordering)
new_ltEs16(False, False)
new_compare111(x0, x1, x2, x3, False, x4, x5)
new_compare25(x0, x1, x2, x3, x4, x5, False, x6, x7, x8)
new_esEs33(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, ty_Ordering)
new_esEs28(x0, x1, ty_@0)
new_esEs11(x0, x1, ty_Float)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs4(x0, x1, app(ty_[], x2))
new_esEs39(x0, x1, ty_Integer)

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_esEs36(x0, x1, ty_Char)
new_esEs29(x0, x1, ty_Float)
new_lt22(x0, x1, app(ty_Maybe, x2))
new_esEs7(x0, x1, ty_Int)
new_ltEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs21(x0, x1, ty_Int)
new_ltEs14(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs10(x0, x1, ty_Float)
new_ltEs16(True, True)
new_esEs6(x0, x1, ty_Int)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs32(x0, x1, app(ty_Maybe, x2))
new_lt11(x0, x1)
new_esEs24(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs20(x0, x1, ty_Int)
new_lt5(x0, x1, ty_Char)
new_esEs5(x0, x1, app(ty_[], x2))
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs36(x0, x1, app(ty_[], x2))
new_lt21(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs21(x0, x1, ty_@0)
new_esEs29(x0, x1, ty_Char)
new_ltEs22(x0, x1, ty_Integer)
new_esEs34(x0, x1, app(ty_[], x2))
new_esEs32(x0, x1, ty_Int)
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs11(x0, x1, ty_Int)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs4(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_Integer)
new_compare30(x0, x1, ty_Int)
new_pePe(True, x0)
new_esEs5(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs11(x0, x1, ty_@0)
new_esEs35(x0, x1, ty_Integer)
new_esEs11(x0, x1, ty_Char)
new_esEs9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(x0, x1, ty_Float)
new_esEs9(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(x0, x1, ty_Int)
new_esEs31(x0, x1, app(app(ty_Either, x2), x3))
new_lt22(x0, x1, ty_@0)
new_compare30(x0, x1, ty_Bool)
new_ltEs5(Nothing, Just(x0), x1)
new_lt20(x0, x1, ty_@0)
new_esEs29(x0, x1, ty_Ordering)
new_lt22(x0, x1, ty_Float)
new_esEs9(x0, x1, app(ty_[], x2))
new_lt23(x0, x1, ty_Integer)
new_ltEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(Right(x0), Right(x1), x2, ty_Bool)
new_lt7(x0, x1)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs8(x0, x1, ty_Integer)
new_esEs23(Just(x0), Just(x1), ty_Float)
new_esEs6(x0, x1, ty_Integer)
new_lt5(x0, x1, ty_@0)
new_esEs33(x0, x1, app(app(ty_@2, x2), x3))
new_esEs11(x0, x1, ty_Bool)
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs24(Right(x0), Right(x1), x2, ty_Integer)
new_compare12(False, True)
new_compare12(True, False)
new_ltEs7(x0, x1)
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_primCompAux0(x0, EQ)
new_esEs32(x0, x1, app(app(ty_@2, x2), x3))
new_lt6(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(x0, x1, ty_Integer)
new_esEs32(x0, x1, ty_Ordering)
new_ltEs21(x0, x1, ty_Float)
new_ltEs24(x0, x1, ty_Integer)
new_esEs34(x0, x1, ty_Float)
new_esEs6(x0, x1, ty_@0)
new_lt6(x0, x1, ty_Float)
new_esEs9(x0, x1, ty_Int)
new_compare30(x0, x1, ty_Integer)
new_esEs12(GT, EQ)
new_esEs12(EQ, GT)
new_esEs36(x0, x1, ty_Int)
new_esEs28(x0, x1, ty_Bool)
new_ltEs14(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs24(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_compare30(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_lt5(x0, x1, ty_Double)
new_compare15(LT, LT)
new_esEs10(x0, x1, ty_Char)
new_esEs23(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primMulNat0(Succ(x0), Zero)
new_ltEs22(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_compare6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs34(x0, x1, ty_Ordering)
new_esEs16([], [], x0)
new_esEs12(GT, GT)
new_esEs30(x0, x1, ty_Double)
new_esEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs21(x0, x1, ty_Ordering)
new_esEs10(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_lt21(x0, x1, ty_Float)
new_esEs11(x0, x1, ty_Integer)
new_esEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs21(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs24(x0, x1, app(ty_Maybe, x2))
new_esEs23(Just(x0), Just(x1), ty_Double)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_Char)
new_esEs34(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(Left(x0), Left(x1), ty_Int, x2)
new_esEs38(x0, x1, ty_Integer)
new_ltEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs27(x0, x1, ty_Bool)
new_esEs24(Right(x0), Right(x1), x2, ty_Char)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs6(EQ, EQ)
new_esEs32(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(x0, x1, ty_Float)
new_esEs8(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs22(x0, x1, ty_Char)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(x0, x1, ty_Double)
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_esEs5(x0, x1, ty_Bool)
new_lt6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs31(x0, x1, ty_Int)
new_compare26(x0, x1, True, x2, x3)
new_compare110(x0, x1, x2, x3, True, x4, x5, x6)
new_ltEs24(x0, x1, app(ty_[], x2))
new_compare27(Right(x0), Left(x1), x2, x3)
new_compare27(Left(x0), Right(x1), x2, x3)
new_esEs33(x0, x1, ty_Double)
new_esEs8(x0, x1, ty_Float)
new_ltEs18(x0, x1, ty_@0)
new_esEs4(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, app(ty_[], x2))
new_ltEs5(Just(x0), Just(x1), ty_@0)
new_lt5(x0, x1, ty_Int)
new_ltEs6(LT, EQ)
new_ltEs6(EQ, LT)
new_esEs24(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_primCompAux0(x0, LT)
new_esEs23(Nothing, Nothing, x0)
new_esEs38(x0, x1, ty_Int)
new_esEs23(Just(x0), Just(x1), ty_Int)
new_ltEs20(x0, x1, ty_@0)
new_lt6(x0, x1, app(ty_Maybe, x2))
new_esEs11(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Int)
new_lt17(x0, x1)
new_esEs8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs36(x0, x1, ty_Bool)
new_primEqNat0(Zero, Zero)
new_compare13(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs26(x0, x1, ty_@0)
new_lt21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(Right(x0), Right(x1), x2, ty_Int)
new_esEs7(x0, x1, ty_Bool)
new_esEs33(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs5(x0, x1, ty_Float)
new_ltEs14(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_compare17(x0, x1, x2, x3, x4, x5, False, x6, x7, x8, x9)
new_ltEs22(x0, x1, ty_Float)
new_compare15(GT, GT)
new_esEs31(x0, x1, ty_Double)
new_ltEs20(x0, x1, ty_Integer)
new_lt22(x0, x1, ty_Bool)
new_compare30(x0, x1, app(ty_[], x2))
new_esEs34(x0, x1, ty_Bool)
new_esEs31(x0, x1, ty_Integer)
new_ltEs20(x0, x1, ty_Char)
new_lt20(x0, x1, ty_Double)
new_esEs35(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_compare28(x0, x1, True, x2, x3)
new_ltEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs21(x0, x1, app(ty_[], x2))
new_ltEs15(x0, x1)
new_esEs4(x0, x1, ty_Integer)
new_esEs39(x0, x1, app(ty_Ratio, x2))
new_esEs6(x0, x1, app(app(ty_Either, x2), x3))
new_esEs39(x0, x1, ty_Bool)
new_esEs6(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs24(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Float)
new_ltEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_primMulNat0(Zero, Zero)
new_asAs(True, x0)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_ltEs14(Left(x0), Right(x1), x2, x3)
new_ltEs14(Right(x0), Left(x1), x2, x3)
new_esEs26(x0, x1, ty_Double)
new_esEs5(x0, x1, ty_Double)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs35(x0, x1, app(app(ty_@2, x2), x3))
new_fsEs(x0)
new_esEs16(:(x0, x1), [], x2)
new_ltEs5(Just(x0), Just(x1), ty_Integer)
new_esEs35(x0, x1, app(ty_Ratio, x2))
new_lt6(x0, x1, ty_Double)
new_esEs35(x0, x1, ty_Double)
new_ltEs18(x0, x1, ty_Bool)
new_esEs23(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Float)
new_ltEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(x0, x1, app(ty_Maybe, x2))
new_compare28(x0, x1, False, x2, x3)
new_ltEs5(Just(x0), Just(x1), ty_Double)
new_lt22(x0, x1, ty_Ordering)
new_lt23(x0, x1, app(ty_Ratio, x2))
new_esEs9(x0, x1, ty_@0)
new_esEs6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare24(x0, x1, x2, x3, False, x4, x5)
new_esEs24(Left(x0), Left(x1), ty_@0, x2)
new_esEs35(x0, x1, ty_Bool)
new_esEs35(x0, x1, ty_Char)
new_ltEs23(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, ty_Bool)
new_ltEs10(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs31(x0, x1, ty_@0)
new_lt10(x0, x1, x2)
new_ltEs19(x0, x1, ty_Double)
new_lt12(x0, x1, x2, x3)
new_ltEs24(x0, x1, ty_Double)
new_esEs13(Double(x0, x1), Double(x2, x3))
new_esEs10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Ordering)
new_esEs5(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(Just(x0), Nothing, x1)
new_ltEs14(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs24(Right(x0), Right(x1), x2, ty_@0)
new_esEs20(True, True)
new_lt22(x0, x1, ty_Int)
new_esEs7(x0, x1, ty_Integer)
new_esEs30(x0, x1, ty_Bool)
new_lt21(x0, x1, ty_@0)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs4(x0, x1, app(ty_Maybe, x2))
new_esEs33(x0, x1, ty_Float)
new_esEs29(x0, x1, ty_Integer)
new_ltEs21(x0, x1, ty_Integer)
new_lt16(x0, x1, x2, x3)
new_primPlusNat0(Zero, x0)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs4(x0, x1, ty_Ordering)
new_esEs8(x0, x1, ty_Bool)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_primPlusNat0(Succ(x0), x1)
new_ltEs4(x0, x1)
new_esEs34(x0, x1, ty_Integer)
new_esEs31(x0, x1, ty_Ordering)
new_ltEs6(GT, LT)
new_ltEs6(LT, GT)
new_compare0([], [], x0)
new_ltEs22(x0, x1, app(ty_Maybe, x2))
new_esEs35(x0, x1, app(ty_Maybe, x2))
new_compare111(x0, x1, x2, x3, True, x4, x5)
new_esEs11(x0, x1, ty_Double)
new_lt19(x0, x1)
new_ltEs14(Left(x0), Left(x1), ty_Double, x2)
new_ltEs8(x0, x1, x2)
new_ltEs14(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs4(x0, x1, ty_Double)
new_esEs36(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, ty_Double)
new_esEs39(x0, x1, ty_Char)
new_ltEs22(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_compare15(EQ, EQ)
new_lt6(x0, x1, ty_Int)
new_lt21(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, ty_Ordering)
new_ltEs14(Right(x0), Right(x1), x2, ty_Double)
new_ltEs22(x0, x1, ty_Ordering)
new_ltEs11(x0, x1)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_compare7(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt20(x0, x1, ty_Float)
new_lt21(x0, x1, ty_Integer)
new_esEs32(x0, x1, ty_Bool)
new_esEs39(x0, x1, ty_Float)
new_compare10(x0, x1, False, x2, x3)
new_lt6(x0, x1, ty_Integer)
new_lt4(x0, x1, x2, x3, x4)
new_esEs10(x0, x1, ty_Double)
new_esEs31(x0, x1, app(ty_[], x2))
new_sr0(x0, x1)
new_esEs23(Just(x0), Just(x1), ty_Integer)
new_esEs24(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs20(False, True)
new_esEs20(True, False)
new_esEs29(x0, x1, ty_Bool)
new_esEs24(Left(x0), Right(x1), x2, x3)
new_esEs24(Right(x0), Left(x1), x2, x3)
new_ltEs23(x0, x1, ty_Integer)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs36(x0, x1, app(ty_Ratio, x2))
new_esEs20(False, False)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare12(False, False)
new_esEs12(LT, EQ)
new_esEs12(EQ, LT)
new_lt21(x0, x1, ty_Int)
new_lt22(x0, x1, ty_Char)
new_ltEs14(Left(x0), Left(x1), ty_Char, x2)
new_ltEs14(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare14(x0, x1, x2, x3, x4, x5, True, x6, x7, x8)
new_esEs31(x0, x1, ty_Float)
new_esEs24(Left(x0), Left(x1), ty_Float, x2)
new_primPlusNat1(Zero, Zero)
new_ltEs21(x0, x1, ty_Bool)
new_esEs24(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs20(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_Float)
new_esEs12(EQ, EQ)
new_esEs23(Just(x0), Just(x1), ty_Bool)
new_esEs27(x0, x1, ty_Char)
new_ltEs14(Right(x0), Right(x1), x2, ty_Int)
new_esEs9(x0, x1, ty_Integer)
new_esEs30(x0, x1, ty_Float)
new_ltEs20(x0, x1, ty_Float)
new_lt22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(Right(x0), Right(x1), x2, ty_Char)
new_esEs9(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Left(x0), Left(x1), ty_Float, x2)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs16(:(x0, x1), :(x2, x3), x4)
new_esEs28(x0, x1, ty_Double)
new_esEs30(x0, x1, ty_Char)
new_compare30(x0, x1, ty_@0)
new_esEs6(x0, x1, ty_Bool)
new_esEs16([], :(x0, x1), x2)
new_ltEs23(x0, x1, ty_Float)
new_esEs9(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs31(x0, x1, app(app(ty_@2, x2), x3))
new_compare15(EQ, GT)
new_compare15(GT, EQ)
new_compare17(x0, x1, x2, x3, x4, x5, True, x6, x7, x8, x9)
new_ltEs9(x0, x1, x2)
new_ltEs24(x0, x1, ty_Ordering)
new_compare30(x0, x1, ty_Char)
new_primEqNat0(Succ(x0), Zero)
new_compare15(LT, GT)
new_compare15(GT, LT)
new_esEs36(x0, x1, ty_Double)
new_esEs39(x0, x1, ty_Ordering)
new_esEs7(x0, x1, app(app(ty_Either, x2), x3))
new_lt21(x0, x1, app(ty_[], x2))
new_esEs37(x0, x1, ty_Int)
new_esEs9(x0, x1, ty_Double)
new_primMulInt(Neg(x0), Neg(x1))
new_ltEs5(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs17(x0, x1)
new_compare0([], :(x0, x1), x2)
new_esEs9(x0, x1, ty_Ordering)
new_ltEs12(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs26(x0, x1, ty_Char)
new_lt23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_lt23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs23(x0, x1, ty_Int)
new_primEqNat0(Succ(x0), Succ(x1))
new_compare210(x0, x1, True, x2)
new_esEs8(x0, x1, ty_Int)
new_ltEs14(Left(x0), Left(x1), ty_Bool, x2)
new_lt21(x0, x1, app(ty_Maybe, x2))
new_ltEs5(Just(x0), Just(x1), ty_Int)
new_esEs33(x0, x1, ty_Int)
new_ltEs23(x0, x1, ty_@0)
new_lt6(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs33(x0, x1, ty_Bool)
new_esEs10(x0, x1, ty_Ordering)
new_esEs24(Left(x0), Left(x1), ty_Double, x2)
new_esEs35(x0, x1, ty_@0)
new_esEs4(x0, x1, ty_Char)
new_compare112(x0, x1, False, x2)
new_esEs24(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_lt23(x0, x1, ty_Int)
new_ltEs14(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs18(x0, x1, ty_Double)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt23(x0, x1, ty_Bool)
new_ltEs14(Left(x0), Left(x1), ty_Integer, x2)
new_esEs24(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_lt9(x0, x1, x2)
new_ltEs18(x0, x1, app(ty_[], x2))
new_esEs33(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, app(ty_[], x2))
new_lt5(x0, x1, app(app(ty_Either, x2), x3))
new_lt21(x0, x1, ty_Bool)
new_esEs24(Left(x0), Left(x1), ty_Char, x2)
new_ltEs5(Nothing, Nothing, x0)
new_compare18(Float(x0, x1), Float(x2, x3))
new_ltEs5(Just(x0), Just(x1), ty_Float)
new_esEs26(x0, x1, ty_Bool)
new_lt6(x0, x1, ty_Bool)
new_esEs30(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Integer)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs8(x0, x1, ty_Double)
new_lt21(x0, x1, ty_Char)
new_lt5(x0, x1, ty_Float)
new_compare11(Char(x0), Char(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs24(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs36(x0, x1, app(app(ty_Either, x2), x3))
new_esEs30(x0, x1, ty_Integer)
new_esEs25(x0, x1)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_compare210(x0, x1, False, x2)
new_esEs29(x0, x1, ty_@0)
new_ltEs14(Left(x0), Left(x1), ty_Int, x2)
new_sr(Integer(x0), Integer(x1))
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs7(x0, x1, ty_@0)
new_esEs39(x0, x1, app(ty_Maybe, x2))
new_primMulNat0(Succ(x0), Succ(x1))
new_ltEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs34(x0, x1, ty_Char)
new_esEs4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs10(x0, x1, ty_Bool)
new_lt5(x0, x1, app(ty_[], x2))
new_esEs10(x0, x1, ty_@0)
new_esEs39(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_@0)
new_esEs31(x0, x1, ty_Bool)
new_primEqNat0(Zero, Succ(x0))
new_primPlusNat1(Succ(x0), Zero)
new_lt23(x0, x1, ty_Char)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs7(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Char)
new_ltEs21(x0, x1, app(ty_Maybe, x2))
new_esEs6(x0, x1, ty_Ordering)
new_esEs33(x0, x1, ty_Char)
new_compare27(Left(x0), Left(x1), x2, x3)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs32(x0, x1, ty_Integer)
new_ltEs14(Left(x0), Left(x1), ty_Ordering, x2)
new_pePe(False, x0)
new_ltEs24(x0, x1, ty_Int)
new_compare24(x0, x1, x2, x3, True, x4, x5)
new_lt8(x0, x1)
new_esEs39(x0, x1, app(app(ty_Either, x2), x3))
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt23(x0, x1, ty_Double)
new_esEs10(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Bool)
new_esEs9(x0, x1, app(app(ty_@2, x2), x3))
new_esEs32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, ty_Int)
new_esEs30(x0, x1, ty_Ordering)
new_lt23(x0, x1, ty_Float)
new_lt6(x0, x1, ty_@0)
new_primPlusNat1(Succ(x0), Succ(x1))
new_compare27(Right(x0), Right(x1), x2, x3)
new_esEs31(x0, x1, ty_Char)
new_lt22(x0, x1, ty_Double)
new_ltEs22(x0, x1, ty_@0)
new_esEs39(x0, x1, ty_Int)
new_esEs30(x0, x1, ty_@0)
new_compare14(x0, x1, x2, x3, x4, x5, False, x6, x7, x8)
new_ltEs16(False, True)
new_ltEs16(True, False)
new_ltEs6(GT, GT)
new_esEs10(x0, x1, ty_Int)
new_compare30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(x0, x1, app(ty_Maybe, x2))
new_esEs31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs32(x0, x1, ty_Char)
new_esEs23(Nothing, Just(x0), x1)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(x0, x1, ty_Int)
new_ltEs5(Just(x0), Just(x1), ty_Ordering)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_ltEs19(x0, x1, ty_Char)
new_ltEs22(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(Just(x0), Just(x1), ty_Char)
new_esEs27(x0, x1, ty_Int)
new_esEs24(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs4(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(Just(x0), Just(x1), ty_Bool)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_Bool)
new_lt22(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_@0)
new_ltEs22(x0, x1, ty_Bool)
new_esEs30(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_Integer)
new_esEs33(x0, x1, ty_Integer)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, ty_Int)
new_primCmpNat0(Zero, Zero)
new_esEs35(x0, x1, ty_Float)
new_asAs(False, x0)
new_lt5(x0, x1, ty_Integer)
new_ltEs24(x0, x1, ty_@0)
new_esEs17(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs19(x0, x1, ty_Int)
new_lt23(x0, x1, ty_@0)
new_esEs34(x0, x1, ty_Int)
new_ltEs6(LT, LT)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs35(x0, x1, app(ty_[], x2))
new_esEs35(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare31(Just(x0), Just(x1), x2)
new_esEs11(x0, x1, ty_Ordering)
new_esEs31(x0, x1, app(ty_Ratio, x2))
new_lt5(x0, x1, app(ty_Ratio, x2))
new_ltEs22(x0, x1, ty_Double)
new_ltEs14(Left(x0), Left(x1), ty_@0, x2)
new_lt23(x0, x1, app(ty_[], x2))
new_compare10(x0, x1, True, x2, x3)
new_ltEs24(x0, x1, ty_Char)
new_esEs21(:%(x0, x1), :%(x2, x3), x4)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs18(Integer(x0), Integer(x1))
new_esEs4(x0, x1, ty_@0)
new_lt22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, ty_Int)
new_ltEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(Just(x0), Just(x1), ty_@0)
new_compare110(x0, x1, x2, x3, False, x4, x5, x6)
new_ltEs14(Right(x0), Right(x1), x2, ty_Integer)
new_compare0(:(x0, x1), [], x2)
new_esEs23(Just(x0), Nothing, x1)
new_ltEs19(x0, x1, ty_Float)
new_esEs6(x0, x1, ty_Char)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_lt21(x0, x1, ty_Double)
new_primCompAux1(x0, x1, x2, x3)
new_esEs32(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs8(x0, x1, app(ty_[], x2))
new_esEs23(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs34(x0, x1, app(app(ty_Either, x2), x3))
new_esEs33(x0, x1, app(ty_[], x2))
new_lt5(x0, x1, ty_Bool)
new_esEs11(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(Just(x0), Just(x1), ty_Char)
new_ltEs13(x0, x1)
new_lt14(x0, x1, x2)
new_ltEs23(x0, x1, ty_Bool)
new_esEs6(x0, x1, app(ty_Ratio, x2))
new_compare15(LT, EQ)
new_compare15(EQ, LT)
new_compare9(@0, @0)
new_lt13(x0, x1)
new_esEs36(x0, x1, ty_Integer)
new_esEs29(x0, x1, ty_Double)
new_ltEs22(x0, x1, app(ty_[], x2))
new_ltEs23(x0, x1, app(ty_Maybe, x2))
new_esEs8(x0, x1, app(ty_Ratio, x2))
new_ltEs18(x0, x1, ty_Float)
new_lt18(x0, x1)
new_lt22(x0, x1, app(ty_Ratio, x2))
new_esEs32(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_Float)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_lt5(x0, x1, ty_Ordering)
new_lt15(x0, x1)
new_compare8(Integer(x0), Integer(x1))
new_lt22(x0, x1, app(ty_[], x2))
new_compare30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs33(x0, x1, app(ty_Ratio, x2))
new_lt5(x0, x1, app(ty_Maybe, x2))
new_esEs36(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs33(x0, x1, app(ty_Maybe, x2))
new_esEs7(x0, x1, app(ty_Maybe, x2))
new_esEs8(x0, x1, ty_@0)
new_lt6(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(x0, x1, ty_Int)
new_not(True)
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_compare30(x0, x1, ty_Float)
new_compare31(Just(x0), Nothing, x1)
new_esEs27(x0, x1, ty_Ordering)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs22(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs23(x0, x1, app(ty_Ratio, x2))
new_ltEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(x0, x1, ty_Bool)
new_esEs32(x0, x1, ty_Float)
new_esEs36(x0, x1, ty_Ordering)
new_esEs9(x0, x1, ty_Bool)
new_esEs23(Just(x0), Just(x1), app(ty_Maybe, x2))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_not(False)
new_esEs24(Left(x0), Left(x1), ty_Ordering, x2)
new_compare29(Double(x0, x1), Double(x2, x3))
new_compare13(:%(x0, x1), :%(x2, x3), ty_Integer)
new_lt6(x0, x1, app(ty_Ratio, x2))
new_primCmpNat0(Succ(x0), Succ(x1))
new_esEs7(x0, x1, ty_Ordering)
new_esEs34(x0, x1, app(ty_Ratio, x2))
new_ltEs23(x0, x1, ty_Char)
new_esEs7(x0, x1, app(ty_[], x2))
new_esEs8(x0, x1, ty_Ordering)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_esEs39(x0, x1, ty_@0)
new_ltEs21(x0, x1, ty_Char)
new_esEs15(Char(x0), Char(x1))
new_esEs7(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(x0, x1, app(ty_Ratio, x2))
new_ltEs6(GT, EQ)
new_ltEs6(EQ, GT)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_esEs7(x0, x1, app(ty_Ratio, x2))
new_esEs32(x0, x1, app(ty_Ratio, x2))
new_primCmpNat0(Zero, Succ(x0))
new_esEs31(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Ordering)
new_lt23(x0, x1, app(ty_Maybe, x2))
new_ltEs21(x0, x1, ty_Double)
new_esEs24(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs8(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs23(x0, x1, app(ty_[], x2))
new_esEs24(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_compare30(x0, x1, ty_Double)
new_compare19(x0, x1, True, x2, x3)
new_esEs36(x0, x1, app(ty_Maybe, x2))
new_esEs24(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs5(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(Right(x0), Right(x1), x2, ty_Double)
new_lt22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(x0, x1, app(ty_[], x2))
new_primCmpNat0(Succ(x0), Zero)
new_compare30(x0, x1, app(ty_Maybe, x2))
new_esEs34(x0, x1, ty_Double)
new_ltEs21(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_@0)
new_esEs11(x0, x1, app(ty_Maybe, x2))
new_esEs6(x0, x1, app(ty_Maybe, x2))
new_ltEs22(x0, x1, ty_Int)
new_compare26(x0, x1, False, x2, x3)
new_compare16(x0, x1)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_esEs23(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs20(x0, x1, ty_Double)
new_ltEs24(x0, x1, ty_Bool)
new_esEs35(x0, x1, ty_Ordering)
new_ltEs18(x0, x1, ty_Integer)
new_esEs39(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs34(x0, x1, ty_@0)
new_compare31(Nothing, Just(x0), x1)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_esEs37(x0, x1, ty_Integer)
new_ltEs18(x0, x1, ty_Char)
new_esEs7(x0, x1, ty_Double)
new_lt23(x0, x1, ty_Ordering)
new_compare112(x0, x1, True, x2)
new_lt21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs34(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs9(x0, x1, ty_Float)
new_esEs23(Just(x0), Just(x1), ty_Ordering)
new_lt6(x0, x1, ty_Char)
new_esEs9(x0, x1, ty_Char)
new_esEs8(x0, x1, ty_Char)
new_esEs35(x0, x1, ty_Int)
new_esEs24(Left(x0), Left(x1), ty_Integer, x2)
new_esEs5(x0, x1, app(ty_Maybe, x2))
new_lt21(x0, x1, app(ty_Ratio, x2))
new_esEs33(x0, x1, ty_@0)
new_esEs24(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs5(x0, x1, ty_Ordering)
new_esEs32(x0, x1, ty_Double)
new_esEs34(x0, x1, app(ty_Maybe, x2))
new_esEs10(x0, x1, app(ty_[], x2))
new_compare30(x0, x1, app(ty_Ratio, x2))
new_ltEs21(x0, x1, app(ty_Ratio, x2))
new_lt23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs24(x0, x1, app(ty_Ratio, x2))
new_esEs14(Float(x0, x1), Float(x2, x3))
new_esEs26(x0, x1, ty_Integer)
new_esEs5(x0, x1, ty_@0)
new_esEs5(x0, x1, ty_Char)
new_esEs7(x0, x1, ty_Char)
new_compare12(True, True)
new_primEqInt(Pos(Zero), Pos(Zero))
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs5(x0, x1, ty_Integer)
new_compare31(Nothing, Nothing, x0)
new_esEs39(x0, x1, app(ty_[], x2))
new_compare30(x0, x1, ty_Ordering)
new_primMulNat0(Zero, Succ(x0))
new_esEs28(x0, x1, app(ty_[], x2))
new_ltEs23(x0, x1, ty_Double)
new_esEs24(Right(x0), Right(x1), x2, ty_Float)
new_esEs11(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_lt5(x0, x1, app(app(ty_@2, x2), x3))
new_primCompAux0(x0, GT)
new_lt6(x0, x1, ty_Ordering)
new_primPlusNat1(Zero, Succ(x0))
new_esEs36(x0, x1, ty_Float)
new_esEs19(@0, @0)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs39(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_compare25(x0, x1, x2, x3, x4, x5, True, x6, x7, x8)
new_esEs36(x0, x1, ty_@0)
new_esEs12(LT, LT)
new_esEs28(x0, x1, ty_Integer)
new_compare19(x0, x1, False, x2, x3)
new_ltEs18(x0, x1, ty_Ordering)
new_ltEs16(False, False)
new_compare111(x0, x1, x2, x3, False, x4, x5)
new_compare25(x0, x1, x2, x3, x4, x5, False, x6, x7, x8)
new_esEs33(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, ty_Ordering)
new_esEs28(x0, x1, ty_@0)
new_esEs11(x0, x1, ty_Float)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs4(x0, x1, app(ty_[], x2))
new_esEs39(x0, x1, ty_Integer)



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

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

new_splitLT3(:(yvy300, yvy301), yvy31, yvy32, Branch(yvy330, yvy331, yvy332, yvy333, yvy334), yvy34, [], bb, bc) → new_splitLT3(yvy330, yvy331, yvy332, yvy333, yvy334, [], bb, bc)

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

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



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

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

new_splitLT3([], yvy31, yvy32, yvy33, yvy34, :(yvy400, yvy401), bb, bc) → new_splitLT1(yvy31, yvy32, yvy33, yvy34, yvy400, yvy401, new_compare0(:(yvy400, yvy401), [], bb), bb, bc)
new_splitLT2(yvy36, yvy37, yvy38, yvy39, yvy40, yvy41, yvy42, yvy43, EQ, h, ba) → new_splitLT11(yvy36, yvy37, yvy38, yvy39, yvy40, yvy41, yvy42, yvy43, new_compare0(:(yvy42, yvy43), :(yvy36, yvy37), h), h, ba)
new_splitLT11(yvy36, yvy37, yvy38, yvy39, yvy40, yvy41, yvy42, yvy43, GT, h, ba) → new_splitLT(yvy41, yvy42, yvy43, h, ba)
new_splitLT3(:(yvy300, yvy301), yvy31, yvy32, yvy33, yvy34, :(yvy400, yvy401), bb, bc) → new_splitLT2(yvy300, yvy301, yvy31, yvy32, yvy33, yvy34, yvy400, yvy401, new_primCompAux1(yvy400, yvy300, new_compare0(yvy401, yvy301, bb), bb), bb, bc)
new_splitLT20(yvy36, yvy37, yvy38, yvy39, yvy40, yvy41, yvy42, yvy43, h, ba) → new_splitLT11(yvy36, yvy37, yvy38, yvy39, yvy40, yvy41, yvy42, yvy43, new_compare0(:(yvy42, yvy43), :(yvy36, yvy37), h), h, ba)
new_splitLT1(yvy31, yvy32, yvy33, yvy34, yvy400, yvy401, GT, bb, bc) → new_splitLT(yvy34, yvy400, yvy401, bb, bc)
new_splitLT2(yvy36, yvy37, yvy38, yvy39, yvy40, yvy41, yvy42, yvy43, GT, h, ba) → new_splitLT20(yvy36, yvy37, yvy38, yvy39, yvy40, yvy41, yvy42, yvy43, h, ba)
new_splitLT(Branch(yvy400, yvy401, yvy402, yvy403, yvy404), yvy42, yvy43, h, ba) → new_splitLT3(yvy400, yvy401, yvy402, yvy403, yvy404, :(yvy42, yvy43), h, ba)
new_splitLT2(yvy36, yvy37, yvy38, yvy39, Branch(yvy400, yvy401, yvy402, yvy403, yvy404), yvy41, yvy42, yvy43, LT, h, ba) → new_splitLT3(yvy400, yvy401, yvy402, yvy403, yvy404, :(yvy42, yvy43), h, ba)

The TRS R consists of the following rules:

new_compare210(yvy100, yvy101, False, feg) → new_compare112(yvy100, yvy101, new_ltEs24(yvy100, yvy101, feg), feg)
new_compare7(@2(yvy4000, yvy4001), @2(yvy3000, yvy3001), bg, bh) → new_compare24(yvy4000, yvy4001, yvy3000, yvy3001, new_asAs(new_esEs7(yvy4000, yvy3000, bg), new_esEs8(yvy4001, yvy3001, bh)), bg, bh)
new_esEs24(Left(yvy40000), Left(yvy30000), app(ty_Ratio, deh), hh) → new_esEs21(yvy40000, yvy30000, deh)
new_ltEs19(yvy1002, yvy1012, app(ty_[], cab)) → new_ltEs8(yvy1002, yvy1012, cab)
new_compare112(yvy189, yvy190, True, fge) → LT
new_lt22(yvy1000, yvy1010, ty_Int) → new_lt17(yvy1000, yvy1010)
new_ltEs22(yvy114, yvy115, app(app(ty_@2, fbc), fbd)) → new_ltEs12(yvy114, yvy115, fbc, fbd)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Int, hh) → new_esEs25(yvy40000, yvy30000)
new_esEs6(yvy4002, yvy3002, app(app(app(ty_@3, bbg), bbh), bca)) → new_esEs22(yvy4002, yvy3002, bbg, bbh, bca)
new_esEs27(yvy1000, yvy1010, app(ty_[], bff)) → new_esEs16(yvy1000, yvy1010, bff)
new_esEs20(True, True) → True
new_esEs35(yvy153, yvy156, app(ty_[], eab)) → new_esEs16(yvy153, yvy156, eab)
new_compare8(Integer(yvy4000), Integer(yvy3000)) → new_primCmpInt(yvy4000, yvy3000)
new_esEs8(yvy4001, yvy3001, ty_Bool) → new_esEs20(yvy4001, yvy3001)
new_esEs11(yvy4000, yvy3000, ty_Integer) → new_esEs18(yvy4000, yvy3000)
new_esEs27(yvy1000, yvy1010, app(app(ty_@2, bgc), bgd)) → new_esEs17(yvy1000, yvy1010, bgc, bgd)
new_ltEs20(yvy154, yvy157, app(ty_Ratio, ebe)) → new_ltEs9(yvy154, yvy157, ebe)
new_esEs36(yvy1000, yvy1010, ty_Double) → new_esEs13(yvy1000, yvy1010)
new_esEs28(yvy1001, yvy1011, ty_Float) → new_esEs14(yvy1001, yvy1011)
new_lt6(yvy1000, yvy1010, ty_@0) → new_lt19(yvy1000, yvy1010)
new_compare10(yvy199, yvy200, True, ef, eg) → LT
new_esEs9(yvy4000, yvy3000, ty_Int) → new_esEs25(yvy4000, yvy3000)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, ty_Double) → new_esEs13(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, app(app(ty_@2, chb), chc)) → new_esEs17(yvy40002, yvy30002, chb, chc)
new_ltEs24(yvy100, yvy101, app(ty_Ratio, cdh)) → new_ltEs9(yvy100, yvy101, cdh)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, ty_@0) → new_esEs19(yvy40000, yvy30000)
new_ltEs19(yvy1002, yvy1012, ty_Float) → new_ltEs11(yvy1002, yvy1012)
new_esEs11(yvy4000, yvy3000, app(ty_[], ehb)) → new_esEs16(yvy4000, yvy3000, ehb)
new_lt23(yvy165, yvy167, app(app(app(ty_@3, fcd), fce), fcf)) → new_lt4(yvy165, yvy167, fcd, fce, fcf)
new_esEs7(yvy4000, yvy3000, ty_Double) → new_esEs13(yvy4000, yvy3000)
new_esEs9(yvy4000, yvy3000, ty_Char) → new_esEs15(yvy4000, yvy3000)
new_ltEs23(yvy166, yvy168, ty_Ordering) → new_ltEs6(yvy166, yvy168)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Bool, dac) → new_ltEs16(yvy1000, yvy1010)
new_esEs39(yvy165, yvy167, app(ty_Ratio, fcc)) → new_esEs21(yvy165, yvy167, fcc)
new_esEs10(yvy4000, yvy3000, ty_@0) → new_esEs19(yvy4000, yvy3000)
new_esEs21(:%(yvy40000, yvy40001), :%(yvy30000, yvy30001), hb) → new_asAs(new_esEs37(yvy40000, yvy30000, hb), new_esEs38(yvy40001, yvy30001, hb))
new_lt5(yvy1001, yvy1011, app(ty_Ratio, bha)) → new_lt10(yvy1001, yvy1011, bha)
new_compare13(:%(yvy4000, yvy4001), :%(yvy3000, yvy3001), ty_Integer) → new_compare8(new_sr(yvy4000, yvy3001), new_sr(yvy3000, yvy4001))
new_ltEs22(yvy114, yvy115, app(ty_Ratio, fag)) → new_ltEs9(yvy114, yvy115, fag)
new_ltEs23(yvy166, yvy168, ty_Int) → new_ltEs15(yvy166, yvy168)
new_primMulNat0(Zero, Zero) → Zero
new_ltEs24(yvy100, yvy101, ty_Ordering) → new_ltEs6(yvy100, yvy101)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, ty_Float) → new_ltEs11(yvy1000, yvy1010)
new_esEs39(yvy165, yvy167, app(ty_Maybe, fda)) → new_esEs23(yvy165, yvy167, fda)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Bool, hh) → new_esEs20(yvy40000, yvy30000)
new_compare15(LT, LT) → EQ
new_esEs6(yvy4002, yvy3002, app(app(ty_@2, bbd), bbe)) → new_esEs17(yvy4002, yvy3002, bbd, bbe)
new_esEs4(yvy4000, yvy3000, ty_Integer) → new_esEs18(yvy4000, yvy3000)
new_esEs26(yvy40000, yvy30000, app(ty_[], bce)) → new_esEs16(yvy40000, yvy30000, bce)
new_esEs36(yvy1000, yvy1010, ty_Char) → new_esEs15(yvy1000, yvy1010)
new_esEs28(yvy1001, yvy1011, app(app(ty_Either, bhh), caa)) → new_esEs24(yvy1001, yvy1011, bhh, caa)
new_esEs34(yvy152, yvy155, ty_@0) → new_esEs19(yvy152, yvy155)
new_sr(Integer(yvy30000), Integer(yvy40010)) → Integer(new_primMulInt(yvy30000, yvy40010))
new_esEs7(yvy4000, yvy3000, ty_Float) → new_esEs14(yvy4000, yvy3000)
new_compare12(True, False) → GT
new_lt7(yvy152, yvy155) → new_esEs12(new_compare15(yvy152, yvy155), LT)
new_lt22(yvy1000, yvy1010, app(ty_Maybe, eea)) → new_lt14(yvy1000, yvy1010, eea)
new_ltEs24(yvy100, yvy101, app(ty_Maybe, eh)) → new_ltEs5(yvy100, yvy101, eh)
new_esEs35(yvy153, yvy156, app(app(ty_Either, ebb), ebc)) → new_esEs24(yvy153, yvy156, ebb, ebc)
new_esEs35(yvy153, yvy156, ty_@0) → new_esEs19(yvy153, yvy156)
new_ltEs15(yvy100, yvy101) → new_fsEs(new_compare16(yvy100, yvy101))
new_esEs6(yvy4002, yvy3002, app(ty_[], bbc)) → new_esEs16(yvy4002, yvy3002, bbc)
new_esEs26(yvy40000, yvy30000, ty_@0) → new_esEs19(yvy40000, yvy30000)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_@0, hh) → new_esEs19(yvy40000, yvy30000)
new_ltEs16(False, True) → True
new_esEs26(yvy40000, yvy30000, app(app(app(ty_@3, bda), bdb), bdc)) → new_esEs22(yvy40000, yvy30000, bda, bdb, bdc)
new_esEs10(yvy4000, yvy3000, app(ty_Maybe, egg)) → new_esEs23(yvy4000, yvy3000, egg)
new_ltEs24(yvy100, yvy101, ty_Bool) → new_ltEs16(yvy100, yvy101)
new_compare30(yvy400, yvy300, app(app(ty_@2, bg), bh)) → new_compare7(yvy400, yvy300, bg, bh)
new_esEs17(@2(yvy40000, yvy40001), @2(yvy30000, yvy30001), gh, ha) → new_asAs(new_esEs29(yvy40000, yvy30000, gh), new_esEs30(yvy40001, yvy30001, ha))
new_esEs11(yvy4000, yvy3000, ty_Char) → new_esEs15(yvy4000, yvy3000)
new_lt20(yvy152, yvy155, app(app(app(ty_@3, bd), be), bf)) → new_lt4(yvy152, yvy155, bd, be, bf)
new_esEs27(yvy1000, yvy1010, ty_Bool) → new_esEs20(yvy1000, yvy1010)
new_ltEs23(yvy166, yvy168, app(ty_Ratio, fde)) → new_ltEs9(yvy166, yvy168, fde)
new_esEs34(yvy152, yvy155, ty_Double) → new_esEs13(yvy152, yvy155)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Double) → new_esEs13(yvy40000, yvy30000)
new_esEs10(yvy4000, yvy3000, ty_Int) → new_esEs25(yvy4000, yvy3000)
new_esEs26(yvy40000, yvy30000, ty_Char) → new_esEs15(yvy40000, yvy30000)
new_compare30(yvy400, yvy300, ty_Int) → new_compare16(yvy400, yvy300)
new_fsEs(yvy306) → new_not(new_esEs12(yvy306, GT))
new_ltEs16(True, False) → False
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, ty_Char) → new_ltEs7(yvy1000, yvy1010)
new_esEs7(yvy4000, yvy3000, ty_Int) → new_esEs25(yvy4000, yvy3000)
new_ltEs19(yvy1002, yvy1012, ty_Bool) → new_ltEs16(yvy1002, yvy1012)
new_esEs34(yvy152, yvy155, ty_Ordering) → new_esEs12(yvy152, yvy155)
new_esEs12(GT, LT) → False
new_esEs12(LT, GT) → False
new_esEs27(yvy1000, yvy1010, ty_Char) → new_esEs15(yvy1000, yvy1010)
new_lt5(yvy1001, yvy1011, ty_Integer) → new_lt15(yvy1001, yvy1011)
new_ltEs22(yvy114, yvy115, ty_Ordering) → new_ltEs6(yvy114, yvy115)
new_compare18(Float(yvy4000, yvy4001), Float(yvy3000, yvy3001)) → new_compare16(new_sr0(yvy4000, yvy3000), new_sr0(yvy4001, yvy3001))
new_ltEs18(yvy107, yvy108, app(ty_Ratio, beb)) → new_ltEs9(yvy107, yvy108, beb)
new_ltEs23(yvy166, yvy168, ty_Float) → new_ltEs11(yvy166, yvy168)
new_ltEs18(yvy107, yvy108, app(ty_[], bea)) → new_ltEs8(yvy107, yvy108, bea)
new_ltEs20(yvy154, yvy157, app(app(ty_@2, eca), ecb)) → new_ltEs12(yvy154, yvy157, eca, ecb)
new_esEs31(yvy40000, yvy30000, app(ty_Maybe, cfd)) → new_esEs23(yvy40000, yvy30000, cfd)
new_lt6(yvy1000, yvy1010, app(ty_Ratio, bfg)) → new_lt10(yvy1000, yvy1010, bfg)
new_esEs37(yvy40000, yvy30000, ty_Integer) → new_esEs18(yvy40000, yvy30000)
new_ltEs14(Left(yvy1000), Left(yvy1010), app(app(ty_@2, dba), dbb), dac) → new_ltEs12(yvy1000, yvy1010, dba, dbb)
new_esEs35(yvy153, yvy156, app(app(ty_@2, eag), eah)) → new_esEs17(yvy153, yvy156, eag, eah)
new_esEs5(yvy4001, yvy3001, app(app(app(ty_@3, bae), baf), bag)) → new_esEs22(yvy4001, yvy3001, bae, baf, bag)
new_lt22(yvy1000, yvy1010, ty_Char) → new_lt8(yvy1000, yvy1010)
new_compare110(yvy233, yvy234, yvy235, yvy236, True, yvy238, ecf, ecg) → new_compare111(yvy233, yvy234, yvy235, yvy236, True, ecf, ecg)
new_ltEs24(yvy100, yvy101, app(app(ty_@2, ech), eda)) → new_ltEs12(yvy100, yvy101, ech, eda)
new_ltEs13(yvy100, yvy101) → new_fsEs(new_compare29(yvy100, yvy101))
new_esEs5(yvy4001, yvy3001, app(app(ty_Either, bba), bbb)) → new_esEs24(yvy4001, yvy3001, bba, bbb)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, ty_Bool) → new_esEs20(yvy40000, yvy30000)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Float) → new_ltEs11(yvy1000, yvy1010)
new_esEs8(yvy4001, yvy3001, ty_Double) → new_esEs13(yvy4001, yvy3001)
new_esEs31(yvy40000, yvy30000, app(ty_Ratio, ceh)) → new_esEs21(yvy40000, yvy30000, ceh)
new_esEs29(yvy40000, yvy30000, app(ty_Maybe, ccc)) → new_esEs23(yvy40000, yvy30000, ccc)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Int) → new_ltEs15(yvy1000, yvy1010)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Double) → new_ltEs13(yvy1000, yvy1010)
new_esEs30(yvy40001, yvy30001, ty_Double) → new_esEs13(yvy40001, yvy30001)
new_ltEs21(yvy1001, yvy1011, app(app(ty_@2, efa), efb)) → new_ltEs12(yvy1001, yvy1011, efa, efb)
new_esEs10(yvy4000, yvy3000, ty_Bool) → new_esEs20(yvy4000, yvy3000)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Char, dac) → new_ltEs7(yvy1000, yvy1010)
new_ltEs16(True, True) → True
new_lt21(yvy153, yvy156, app(app(ty_@2, eag), eah)) → new_lt12(yvy153, yvy156, eag, eah)
new_lt6(yvy1000, yvy1010, ty_Bool) → new_lt18(yvy1000, yvy1010)
new_pePe(False, yvy305) → yvy305
new_compare15(GT, EQ) → GT
new_esEs7(yvy4000, yvy3000, ty_Char) → new_esEs15(yvy4000, yvy3000)
new_esEs31(yvy40000, yvy30000, app(ty_[], cee)) → new_esEs16(yvy40000, yvy30000, cee)
new_esEs39(yvy165, yvy167, ty_@0) → new_esEs19(yvy165, yvy167)
new_esEs23(Just(yvy40000), Just(yvy30000), app(ty_Maybe, ddh)) → new_esEs23(yvy40000, yvy30000, ddh)
new_lt21(yvy153, yvy156, ty_Char) → new_lt8(yvy153, yvy156)
new_esEs26(yvy40000, yvy30000, ty_Bool) → new_esEs20(yvy40000, yvy30000)
new_esEs9(yvy4000, yvy3000, app(app(ty_@2, ffd), ffe)) → new_esEs17(yvy4000, yvy3000, ffd, ffe)
new_compare14(yvy218, yvy219, yvy220, yvy221, yvy222, yvy223, False, ceb, cec, ced) → GT
new_lt9(yvy152, yvy155, dhf) → new_esEs12(new_compare0(yvy152, yvy155, dhf), LT)
new_esEs28(yvy1001, yvy1011, ty_Integer) → new_esEs18(yvy1001, yvy1011)
new_esEs5(yvy4001, yvy3001, ty_Ordering) → new_esEs12(yvy4001, yvy3001)
new_esEs5(yvy4001, yvy3001, ty_Int) → new_esEs25(yvy4001, yvy3001)
new_esEs4(yvy4000, yvy3000, ty_Float) → new_esEs14(yvy4000, yvy3000)
new_compare15(GT, LT) → GT
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Char, hh) → new_esEs15(yvy40000, yvy30000)
new_esEs29(yvy40000, yvy30000, ty_Int) → new_esEs25(yvy40000, yvy30000)
new_compare30(yvy400, yvy300, app(app(ty_Either, eff), efg)) → new_compare27(yvy400, yvy300, eff, efg)
new_lt22(yvy1000, yvy1010, ty_Double) → new_lt13(yvy1000, yvy1010)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Ordering) → new_esEs12(yvy40000, yvy30000)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Char) → new_esEs15(yvy40000, yvy30000)
new_esEs29(yvy40000, yvy30000, app(app(ty_@2, cbe), cbf)) → new_esEs17(yvy40000, yvy30000, cbe, cbf)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, app(app(ty_@2, dfh), dga)) → new_esEs17(yvy40000, yvy30000, dfh, dga)
new_ltEs23(yvy166, yvy168, app(app(ty_Either, fed), fee)) → new_ltEs14(yvy166, yvy168, fed, fee)
new_esEs31(yvy40000, yvy30000, ty_Integer) → new_esEs18(yvy40000, yvy30000)
new_compare12(True, True) → EQ
new_esEs36(yvy1000, yvy1010, app(ty_[], edb)) → new_esEs16(yvy1000, yvy1010, edb)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Ordering, hh) → new_esEs12(yvy40000, yvy30000)
new_ltEs6(GT, EQ) → False
new_ltEs18(yvy107, yvy108, app(app(ty_Either, bfa), bfb)) → new_ltEs14(yvy107, yvy108, bfa, bfb)
new_esEs32(yvy40001, yvy30001, app(ty_Maybe, cgf)) → new_esEs23(yvy40001, yvy30001, cgf)
new_esEs35(yvy153, yvy156, ty_Integer) → new_esEs18(yvy153, yvy156)
new_esEs33(yvy40002, yvy30002, ty_Integer) → new_esEs18(yvy40002, yvy30002)
new_esEs31(yvy40000, yvy30000, ty_Double) → new_esEs13(yvy40000, yvy30000)
new_esEs10(yvy4000, yvy3000, ty_Ordering) → new_esEs12(yvy4000, yvy3000)
new_primCompAux1(yvy400, yvy300, yvy51, bb) → new_primCompAux0(yvy51, new_compare30(yvy400, yvy300, bb))
new_esEs33(yvy40002, yvy30002, ty_Float) → new_esEs14(yvy40002, yvy30002)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, app(app(app(ty_@3, dca), dcb), dcc)) → new_ltEs10(yvy1000, yvy1010, dca, dcb, dcc)
new_ltEs23(yvy166, yvy168, app(ty_[], fdd)) → new_ltEs8(yvy166, yvy168, fdd)
new_lt23(yvy165, yvy167, app(app(ty_@2, fcg), fch)) → new_lt12(yvy165, yvy167, fcg, fch)
new_esEs34(yvy152, yvy155, ty_Integer) → new_esEs18(yvy152, yvy155)
new_esEs23(Just(yvy40000), Just(yvy30000), app(app(ty_Either, dea), deb)) → new_esEs24(yvy40000, yvy30000, dea, deb)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Ordering, dac) → new_ltEs6(yvy1000, yvy1010)
new_lt22(yvy1000, yvy1010, ty_Bool) → new_lt18(yvy1000, yvy1010)
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_esEs39(yvy165, yvy167, ty_Float) → new_esEs14(yvy165, yvy167)
new_ltEs22(yvy114, yvy115, ty_Bool) → new_ltEs16(yvy114, yvy115)
new_ltEs4(yvy100, yvy101) → new_fsEs(new_compare8(yvy100, yvy101))
new_esEs33(yvy40002, yvy30002, app(ty_[], cha)) → new_esEs16(yvy40002, yvy30002, cha)
new_ltEs8(yvy100, yvy101, fef) → new_fsEs(new_compare0(yvy100, yvy101, fef))
new_compare30(yvy400, yvy300, ty_Char) → new_compare11(yvy400, yvy300)
new_esEs36(yvy1000, yvy1010, ty_Integer) → new_esEs18(yvy1000, yvy1010)
new_esEs39(yvy165, yvy167, ty_Bool) → new_esEs20(yvy165, yvy167)
new_esEs36(yvy1000, yvy1010, ty_Bool) → new_esEs20(yvy1000, yvy1010)
new_esEs32(yvy40001, yvy30001, app(ty_Ratio, cgb)) → new_esEs21(yvy40001, yvy30001, cgb)
new_compare12(False, True) → LT
new_esEs5(yvy4001, yvy3001, ty_Char) → new_esEs15(yvy4001, yvy3001)
new_esEs34(yvy152, yvy155, ty_Char) → new_esEs15(yvy152, yvy155)
new_esEs31(yvy40000, yvy30000, app(app(ty_@2, cef), ceg)) → new_esEs17(yvy40000, yvy30000, cef, ceg)
new_ltEs18(yvy107, yvy108, ty_Integer) → new_ltEs4(yvy107, yvy108)
new_lt21(yvy153, yvy156, ty_@0) → new_lt19(yvy153, yvy156)
new_esEs30(yvy40001, yvy30001, ty_@0) → new_esEs19(yvy40001, yvy30001)
new_ltEs18(yvy107, yvy108, app(ty_Maybe, beh)) → new_ltEs5(yvy107, yvy108, beh)
new_esEs12(LT, LT) → True
new_ltEs24(yvy100, yvy101, ty_Char) → new_ltEs7(yvy100, yvy101)
new_esEs31(yvy40000, yvy30000, app(app(ty_Either, cfe), cff)) → new_esEs24(yvy40000, yvy30000, cfe, cff)
new_ltEs18(yvy107, yvy108, ty_Double) → new_ltEs13(yvy107, yvy108)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Int, dac) → new_ltEs15(yvy1000, yvy1010)
new_esEs28(yvy1001, yvy1011, app(ty_Maybe, bhg)) → new_esEs23(yvy1001, yvy1011, bhg)
new_lt5(yvy1001, yvy1011, ty_@0) → new_lt19(yvy1001, yvy1011)
new_compare15(EQ, LT) → GT
new_pePe(True, yvy305) → True
new_compare0([], [], feh) → EQ
new_primEqNat0(Zero, Zero) → True
new_ltEs21(yvy1001, yvy1011, ty_Double) → new_ltEs13(yvy1001, yvy1011)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Float) → new_esEs14(yvy40000, yvy30000)
new_esEs6(yvy4002, yvy3002, ty_Double) → new_esEs13(yvy4002, yvy3002)
new_esEs4(yvy4000, yvy3000, app(ty_Maybe, hf)) → new_esEs23(yvy4000, yvy3000, hf)
new_lt5(yvy1001, yvy1011, ty_Bool) → new_lt18(yvy1001, yvy1011)
new_lt23(yvy165, yvy167, ty_Integer) → new_lt15(yvy165, yvy167)
new_esEs5(yvy4001, yvy3001, ty_Float) → new_esEs14(yvy4001, yvy3001)
new_lt21(yvy153, yvy156, app(app(ty_Either, ebb), ebc)) → new_lt16(yvy153, yvy156, ebb, ebc)
new_esEs8(yvy4001, yvy3001, app(app(app(ty_@3, dh), ea), eb)) → new_esEs22(yvy4001, yvy3001, dh, ea, eb)
new_lt11(yvy152, yvy155) → new_esEs12(new_compare18(yvy152, yvy155), LT)
new_lt20(yvy152, yvy155, app(ty_[], dhf)) → new_lt9(yvy152, yvy155, dhf)
new_esEs13(Double(yvy40000, yvy40001), Double(yvy30000, yvy30001)) → new_esEs25(new_sr0(yvy40000, yvy30000), new_sr0(yvy40001, yvy30001))
new_esEs7(yvy4000, yvy3000, ty_Bool) → new_esEs20(yvy4000, yvy3000)
new_compare30(yvy400, yvy300, ty_@0) → new_compare9(yvy400, yvy300)
new_esEs29(yvy40000, yvy30000, ty_@0) → new_esEs19(yvy40000, yvy30000)
new_esEs6(yvy4002, yvy3002, ty_Ordering) → new_esEs12(yvy4002, yvy3002)
new_ltEs18(yvy107, yvy108, app(app(app(ty_@3, bec), bed), bee)) → new_ltEs10(yvy107, yvy108, bec, bed, bee)
new_ltEs22(yvy114, yvy115, ty_@0) → new_ltEs17(yvy114, yvy115)
new_lt5(yvy1001, yvy1011, ty_Char) → new_lt8(yvy1001, yvy1011)
new_lt5(yvy1001, yvy1011, app(app(ty_Either, bhh), caa)) → new_lt16(yvy1001, yvy1011, bhh, caa)
new_ltEs19(yvy1002, yvy1012, ty_Ordering) → new_ltEs6(yvy1002, yvy1012)
new_esEs15(Char(yvy40000), Char(yvy30000)) → new_primEqNat0(yvy40000, yvy30000)
new_esEs24(Left(yvy40000), Left(yvy30000), app(app(app(ty_@3, dfa), dfb), dfc), hh) → new_esEs22(yvy40000, yvy30000, dfa, dfb, dfc)
new_esEs26(yvy40000, yvy30000, ty_Int) → new_esEs25(yvy40000, yvy30000)
new_esEs32(yvy40001, yvy30001, ty_Integer) → new_esEs18(yvy40001, yvy30001)
new_ltEs23(yvy166, yvy168, ty_Double) → new_ltEs13(yvy166, yvy168)
new_lt22(yvy1000, yvy1010, app(ty_[], edb)) → new_lt9(yvy1000, yvy1010, edb)
new_ltEs23(yvy166, yvy168, ty_Integer) → new_ltEs4(yvy166, yvy168)
new_esEs9(yvy4000, yvy3000, app(ty_[], ffc)) → new_esEs16(yvy4000, yvy3000, ffc)
new_esEs33(yvy40002, yvy30002, ty_Bool) → new_esEs20(yvy40002, yvy30002)
new_esEs11(yvy4000, yvy3000, ty_Double) → new_esEs13(yvy4000, yvy3000)
new_esEs29(yvy40000, yvy30000, ty_Bool) → new_esEs20(yvy40000, yvy30000)
new_lt5(yvy1001, yvy1011, app(ty_[], bgh)) → new_lt9(yvy1001, yvy1011, bgh)
new_ltEs21(yvy1001, yvy1011, ty_Bool) → new_ltEs16(yvy1001, yvy1011)
new_ltEs6(EQ, GT) → True
new_esEs9(yvy4000, yvy3000, ty_Integer) → new_esEs18(yvy4000, yvy3000)
new_esEs11(yvy4000, yvy3000, ty_Ordering) → new_esEs12(yvy4000, yvy3000)
new_esEs23(Just(yvy40000), Nothing, hf) → False
new_esEs23(Nothing, Just(yvy30000), hf) → False
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_ltEs18(yvy107, yvy108, ty_Ordering) → new_ltEs6(yvy107, yvy108)
new_esEs23(Just(yvy40000), Just(yvy30000), app(app(app(ty_@3, dde), ddf), ddg)) → new_esEs22(yvy40000, yvy30000, dde, ddf, ddg)
new_ltEs24(yvy100, yvy101, ty_Double) → new_ltEs13(yvy100, yvy101)
new_esEs10(yvy4000, yvy3000, ty_Double) → new_esEs13(yvy4000, yvy3000)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, ty_Float) → new_esEs14(yvy40000, yvy30000)
new_compare110(yvy233, yvy234, yvy235, yvy236, False, yvy238, ecf, ecg) → new_compare111(yvy233, yvy234, yvy235, yvy236, yvy238, ecf, ecg)
new_ltEs20(yvy154, yvy157, ty_Bool) → new_ltEs16(yvy154, yvy157)
new_ltEs24(yvy100, yvy101, ty_@0) → new_ltEs17(yvy100, yvy101)
new_ltEs5(Just(yvy1000), Just(yvy1010), app(app(ty_@2, fg), fh)) → new_ltEs12(yvy1000, yvy1010, fg, fh)
new_ltEs20(yvy154, yvy157, ty_Int) → new_ltEs15(yvy154, yvy157)
new_esEs8(yvy4001, yvy3001, ty_@0) → new_esEs19(yvy4001, yvy3001)
new_lt22(yvy1000, yvy1010, app(app(ty_Either, eeb), eec)) → new_lt16(yvy1000, yvy1010, eeb, eec)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Float, dac) → new_ltEs11(yvy1000, yvy1010)
new_compare26(yvy107, yvy108, False, bdg, bdh) → new_compare10(yvy107, yvy108, new_ltEs18(yvy107, yvy108, bdg), bdg, bdh)
new_lt21(yvy153, yvy156, app(ty_Ratio, eac)) → new_lt10(yvy153, yvy156, eac)
new_compare30(yvy400, yvy300, ty_Float) → new_compare18(yvy400, yvy300)
new_primEqInt(Neg(Succ(yvy400000)), Neg(Succ(yvy300000))) → new_primEqNat0(yvy400000, yvy300000)
new_esEs23(Nothing, Nothing, hf) → True
new_esEs10(yvy4000, yvy3000, app(app(app(ty_@3, egd), ege), egf)) → new_esEs22(yvy4000, yvy3000, egd, ege, egf)
new_esEs39(yvy165, yvy167, app(app(ty_@2, fcg), fch)) → new_esEs17(yvy165, yvy167, fcg, fch)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, app(app(ty_@2, dcd), dce)) → new_ltEs12(yvy1000, yvy1010, dcd, dce)
new_ltEs5(Just(yvy1000), Nothing, eh) → False
new_esEs28(yvy1001, yvy1011, ty_Char) → new_esEs15(yvy1001, yvy1011)
new_esEs11(yvy4000, yvy3000, app(ty_Maybe, faa)) → new_esEs23(yvy4000, yvy3000, faa)
new_lt14(yvy152, yvy155, dhg) → new_esEs12(new_compare31(yvy152, yvy155, dhg), LT)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, ty_@0) → new_ltEs17(yvy1000, yvy1010)
new_ltEs14(Right(yvy1000), Left(yvy1010), dbf, dac) → False
new_esEs12(EQ, LT) → False
new_esEs12(LT, EQ) → False
new_ltEs19(yvy1002, yvy1012, app(ty_Ratio, cac)) → new_ltEs9(yvy1002, yvy1012, cac)
new_lt22(yvy1000, yvy1010, app(app(ty_@2, edg), edh)) → new_lt12(yvy1000, yvy1010, edg, edh)
new_ltEs23(yvy166, yvy168, ty_Bool) → new_ltEs16(yvy166, yvy168)
new_compare111(yvy233, yvy234, yvy235, yvy236, True, ecf, ecg) → LT
new_esEs7(yvy4000, yvy3000, app(ty_[], ca)) → new_esEs16(yvy4000, yvy3000, ca)
new_esEs5(yvy4001, yvy3001, ty_Bool) → new_esEs20(yvy4001, yvy3001)
new_lt23(yvy165, yvy167, ty_Int) → new_lt17(yvy165, yvy167)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs30(yvy40001, yvy30001, app(app(app(ty_@3, cdb), cdc), cdd)) → new_esEs22(yvy40001, yvy30001, cdb, cdc, cdd)
new_esEs11(yvy4000, yvy3000, app(app(ty_Either, fab), fac)) → new_esEs24(yvy4000, yvy3000, fab, fac)
new_esEs35(yvy153, yvy156, app(app(app(ty_@3, ead), eae), eaf)) → new_esEs22(yvy153, yvy156, ead, eae, eaf)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, ty_Int) → new_ltEs15(yvy1000, yvy1010)
new_esEs10(yvy4000, yvy3000, app(app(ty_Either, egh), eha)) → new_esEs24(yvy4000, yvy3000, egh, eha)
new_esEs28(yvy1001, yvy1011, ty_Double) → new_esEs13(yvy1001, yvy1011)
new_lt20(yvy152, yvy155, ty_Ordering) → new_lt7(yvy152, yvy155)
new_ltEs6(EQ, EQ) → True
new_compare31(Just(yvy4000), Nothing, ffb) → GT
new_esEs11(yvy4000, yvy3000, app(app(app(ty_@3, ehf), ehg), ehh)) → new_esEs22(yvy4000, yvy3000, ehf, ehg, ehh)
new_ltEs22(yvy114, yvy115, app(app(ty_Either, fbf), fbg)) → new_ltEs14(yvy114, yvy115, fbf, fbg)
new_esEs28(yvy1001, yvy1011, app(app(app(ty_@3, bhb), bhc), bhd)) → new_esEs22(yvy1001, yvy1011, bhb, bhc, bhd)
new_esEs32(yvy40001, yvy30001, ty_Float) → new_esEs14(yvy40001, yvy30001)
new_esEs27(yvy1000, yvy1010, app(ty_Ratio, bfg)) → new_esEs21(yvy1000, yvy1010, bfg)
new_ltEs19(yvy1002, yvy1012, ty_Integer) → new_ltEs4(yvy1002, yvy1012)
new_primEqInt(Neg(Succ(yvy400000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(yvy300000))) → False
new_primCompAux0(yvy56, GT) → GT
new_compare30(yvy400, yvy300, app(app(app(ty_@3, gd), ge), gf)) → new_compare6(yvy400, yvy300, gd, ge, gf)
new_esEs39(yvy165, yvy167, ty_Integer) → new_esEs18(yvy165, yvy167)
new_compare26(yvy107, yvy108, True, bdg, bdh) → EQ
new_esEs23(Just(yvy40000), Just(yvy30000), app(app(ty_@2, ddb), ddc)) → new_esEs17(yvy40000, yvy30000, ddb, ddc)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, app(app(ty_Either, dgg), dgh)) → new_esEs24(yvy40000, yvy30000, dgg, dgh)
new_ltEs6(GT, GT) → True
new_ltEs21(yvy1001, yvy1011, app(app(ty_Either, efd), efe)) → new_ltEs14(yvy1001, yvy1011, efd, efe)
new_esEs38(yvy40001, yvy30001, ty_Integer) → new_esEs18(yvy40001, yvy30001)
new_esEs32(yvy40001, yvy30001, app(ty_[], cfg)) → new_esEs16(yvy40001, yvy30001, cfg)
new_esEs34(yvy152, yvy155, ty_Int) → new_esEs25(yvy152, yvy155)
new_compare31(Nothing, Nothing, ffb) → EQ
new_esEs29(yvy40000, yvy30000, app(ty_[], cbd)) → new_esEs16(yvy40000, yvy30000, cbd)
new_esEs26(yvy40000, yvy30000, app(ty_Ratio, bch)) → new_esEs21(yvy40000, yvy30000, bch)
new_esEs7(yvy4000, yvy3000, app(ty_Maybe, da)) → new_esEs23(yvy4000, yvy3000, da)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_@0) → new_ltEs17(yvy1000, yvy1010)
new_lt21(yvy153, yvy156, app(ty_[], eab)) → new_lt9(yvy153, yvy156, eab)
new_ltEs20(yvy154, yvy157, app(ty_[], ebd)) → new_ltEs8(yvy154, yvy157, ebd)
new_esEs36(yvy1000, yvy1010, ty_Int) → new_esEs25(yvy1000, yvy1010)
new_esEs19(@0, @0) → True
new_compare6(@3(yvy4000, yvy4001, yvy4002), @3(yvy3000, yvy3001, yvy3002), gd, ge, gf) → new_compare25(yvy4000, yvy4001, yvy4002, yvy3000, yvy3001, yvy3002, new_asAs(new_esEs4(yvy4000, yvy3000, gd), new_asAs(new_esEs5(yvy4001, yvy3001, ge), new_esEs6(yvy4002, yvy3002, gf))), gd, ge, gf)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_esEs7(yvy4000, yvy3000, ty_Integer) → new_esEs18(yvy4000, yvy3000)
new_esEs4(yvy4000, yvy3000, ty_Bool) → new_esEs20(yvy4000, yvy3000)
new_esEs39(yvy165, yvy167, ty_Ordering) → new_esEs12(yvy165, yvy167)
new_lt20(yvy152, yvy155, ty_Char) → new_lt8(yvy152, yvy155)
new_esEs31(yvy40000, yvy30000, ty_Bool) → new_esEs20(yvy40000, yvy30000)
new_lt4(yvy152, yvy155, bd, be, bf) → new_esEs12(new_compare6(yvy152, yvy155, bd, be, bf), LT)
new_esEs6(yvy4002, yvy3002, ty_Int) → new_esEs25(yvy4002, yvy3002)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Double, dac) → new_ltEs13(yvy1000, yvy1010)
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_lt6(yvy1000, yvy1010, app(ty_Maybe, bge)) → new_lt14(yvy1000, yvy1010, bge)
new_ltEs14(Left(yvy1000), Left(yvy1010), app(ty_Maybe, dbc), dac) → new_ltEs5(yvy1000, yvy1010, dbc)
new_esEs4(yvy4000, yvy3000, app(ty_Ratio, hb)) → new_esEs21(yvy4000, yvy3000, hb)
new_lt5(yvy1001, yvy1011, app(ty_Maybe, bhg)) → new_lt14(yvy1001, yvy1011, bhg)
new_primEqInt(Pos(Succ(yvy400000)), Pos(Succ(yvy300000))) → new_primEqNat0(yvy400000, yvy300000)
new_compare10(yvy199, yvy200, False, ef, eg) → GT
new_esEs34(yvy152, yvy155, app(ty_Maybe, dhg)) → new_esEs23(yvy152, yvy155, dhg)
new_esEs5(yvy4001, yvy3001, app(ty_[], baa)) → new_esEs16(yvy4001, yvy3001, baa)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, ty_Double) → new_ltEs13(yvy1000, yvy1010)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, ty_Integer) → new_ltEs4(yvy1000, yvy1010)
new_ltEs21(yvy1001, yvy1011, ty_Float) → new_ltEs11(yvy1001, yvy1011)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, app(ty_Maybe, dcf)) → new_ltEs5(yvy1000, yvy1010, dcf)
new_compare13(:%(yvy4000, yvy4001), :%(yvy3000, yvy3001), ty_Int) → new_compare16(new_sr0(yvy4000, yvy3001), new_sr0(yvy3000, yvy4001))
new_esEs26(yvy40000, yvy30000, app(ty_Maybe, bdd)) → new_esEs23(yvy40000, yvy30000, bdd)
new_ltEs24(yvy100, yvy101, ty_Float) → new_ltEs11(yvy100, yvy101)
new_esEs34(yvy152, yvy155, app(app(ty_@2, dec), ded)) → new_esEs17(yvy152, yvy155, dec, ded)
new_esEs8(yvy4001, yvy3001, ty_Integer) → new_esEs18(yvy4001, yvy3001)
new_ltEs22(yvy114, yvy115, app(app(app(ty_@3, fah), fba), fbb)) → new_ltEs10(yvy114, yvy115, fah, fba, fbb)
new_primEqNat0(Succ(yvy400000), Succ(yvy300000)) → new_primEqNat0(yvy400000, yvy300000)
new_esEs6(yvy4002, yvy3002, ty_Bool) → new_esEs20(yvy4002, yvy3002)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Ordering) → new_ltEs6(yvy1000, yvy1010)
new_ltEs24(yvy100, yvy101, ty_Int) → new_ltEs15(yvy100, yvy101)
new_esEs26(yvy40000, yvy30000, ty_Ordering) → new_esEs12(yvy40000, yvy30000)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, app(ty_Ratio, dgb)) → new_esEs21(yvy40000, yvy30000, dgb)
new_esEs11(yvy4000, yvy3000, app(ty_Ratio, ehe)) → new_esEs21(yvy4000, yvy3000, ehe)
new_esEs30(yvy40001, yvy30001, ty_Integer) → new_esEs18(yvy40001, yvy30001)
new_esEs39(yvy165, yvy167, ty_Char) → new_esEs15(yvy165, yvy167)
new_ltEs14(Left(yvy1000), Left(yvy1010), app(ty_Ratio, dae), dac) → new_ltEs9(yvy1000, yvy1010, dae)
new_esEs26(yvy40000, yvy30000, app(app(ty_@2, bcf), bcg)) → new_esEs17(yvy40000, yvy30000, bcf, bcg)
new_lt5(yvy1001, yvy1011, ty_Float) → new_lt11(yvy1001, yvy1011)
new_esEs32(yvy40001, yvy30001, ty_@0) → new_esEs19(yvy40001, yvy30001)
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_esEs33(yvy40002, yvy30002, app(ty_Maybe, chh)) → new_esEs23(yvy40002, yvy30002, chh)
new_lt6(yvy1000, yvy1010, ty_Int) → new_lt17(yvy1000, yvy1010)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, app(app(app(ty_@3, dgc), dgd), dge)) → new_esEs22(yvy40000, yvy30000, dgc, dgd, dge)
new_lt23(yvy165, yvy167, app(app(ty_Either, fdb), fdc)) → new_lt16(yvy165, yvy167, fdb, fdc)
new_esEs12(EQ, EQ) → True
new_lt23(yvy165, yvy167, ty_Char) → new_lt8(yvy165, yvy167)
new_ltEs18(yvy107, yvy108, app(app(ty_@2, bef), beg)) → new_ltEs12(yvy107, yvy108, bef, beg)
new_lt21(yvy153, yvy156, ty_Double) → new_lt13(yvy153, yvy156)
new_esEs35(yvy153, yvy156, ty_Ordering) → new_esEs12(yvy153, yvy156)
new_lt5(yvy1001, yvy1011, ty_Int) → new_lt17(yvy1001, yvy1011)
new_esEs10(yvy4000, yvy3000, ty_Char) → new_esEs15(yvy4000, yvy3000)
new_primEqInt(Pos(Succ(yvy400000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(yvy300000))) → False
new_ltEs5(Nothing, Just(yvy1010), eh) → True
new_lt20(yvy152, yvy155, ty_Int) → new_lt17(yvy152, yvy155)
new_esEs35(yvy153, yvy156, app(ty_Maybe, eba)) → new_esEs23(yvy153, yvy156, eba)
new_esEs27(yvy1000, yvy1010, ty_@0) → new_esEs19(yvy1000, yvy1010)
new_ltEs18(yvy107, yvy108, ty_Float) → new_ltEs11(yvy107, yvy108)
new_compare25(yvy152, yvy153, yvy154, yvy155, yvy156, yvy157, True, dhc, dhd, dhe) → EQ
new_esEs37(yvy40000, yvy30000, ty_Int) → new_esEs25(yvy40000, yvy30000)
new_primCmpNat0(Zero, Zero) → EQ
new_esEs27(yvy1000, yvy1010, app(app(ty_Either, bgf), bgg)) → new_esEs24(yvy1000, yvy1010, bgf, bgg)
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_compare27(Left(yvy4000), Right(yvy3000), eff, efg) → LT
new_lt22(yvy1000, yvy1010, ty_@0) → new_lt19(yvy1000, yvy1010)
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_compare9(@0, @0) → EQ
new_esEs28(yvy1001, yvy1011, ty_Int) → new_esEs25(yvy1001, yvy1011)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Float, hh) → new_esEs14(yvy40000, yvy30000)
new_esEs6(yvy4002, yvy3002, ty_Float) → new_esEs14(yvy4002, yvy3002)
new_ltEs9(yvy100, yvy101, cdh) → new_fsEs(new_compare13(yvy100, yvy101, cdh))
new_compare17(yvy218, yvy219, yvy220, yvy221, yvy222, yvy223, True, yvy225, ceb, cec, ced) → new_compare14(yvy218, yvy219, yvy220, yvy221, yvy222, yvy223, True, ceb, cec, ced)
new_esEs32(yvy40001, yvy30001, ty_Char) → new_esEs15(yvy40001, yvy30001)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_ltEs14(Left(yvy1000), Left(yvy1010), app(ty_[], dad), dac) → new_ltEs8(yvy1000, yvy1010, dad)
new_ltEs19(yvy1002, yvy1012, app(app(ty_@2, cag), cah)) → new_ltEs12(yvy1002, yvy1012, cag, cah)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Double, hh) → new_esEs13(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, app(app(ty_Either, daa), dab)) → new_esEs24(yvy40002, yvy30002, daa, dab)
new_esEs4(yvy4000, yvy3000, ty_Int) → new_esEs25(yvy4000, yvy3000)
new_compare28(yvy114, yvy115, True, fad, fae) → EQ
new_primEqInt(Pos(Succ(yvy400000)), Neg(yvy30000)) → False
new_primEqInt(Neg(Succ(yvy400000)), Pos(yvy30000)) → False
new_esEs24(Right(yvy40000), Right(yvy30000), hg, ty_Int) → new_esEs25(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, ty_Ordering) → new_esEs12(yvy40002, yvy30002)
new_esEs29(yvy40000, yvy30000, app(app(app(ty_@3, cbh), cca), ccb)) → new_esEs22(yvy40000, yvy30000, cbh, cca, ccb)
new_esEs26(yvy40000, yvy30000, ty_Double) → new_esEs13(yvy40000, yvy30000)
new_ltEs20(yvy154, yvy157, ty_Integer) → new_ltEs4(yvy154, yvy157)
new_compare210(yvy100, yvy101, True, feg) → EQ
new_lt6(yvy1000, yvy1010, ty_Ordering) → new_lt7(yvy1000, yvy1010)
new_esEs29(yvy40000, yvy30000, app(ty_Ratio, cbg)) → new_esEs21(yvy40000, yvy30000, cbg)
new_esEs20(False, False) → True
new_esEs24(Left(yvy40000), Left(yvy30000), app(ty_[], dee), hh) → new_esEs16(yvy40000, yvy30000, dee)
new_lt23(yvy165, yvy167, app(ty_[], fcb)) → new_lt9(yvy165, yvy167, fcb)
new_ltEs22(yvy114, yvy115, ty_Integer) → new_ltEs4(yvy114, yvy115)
new_ltEs5(Just(yvy1000), Just(yvy1010), app(app(ty_Either, gb), gc)) → new_ltEs14(yvy1000, yvy1010, gb, gc)
new_lt23(yvy165, yvy167, ty_Bool) → new_lt18(yvy165, yvy167)
new_esEs30(yvy40001, yvy30001, ty_Ordering) → new_esEs12(yvy40001, yvy30001)
new_lt6(yvy1000, yvy1010, ty_Integer) → new_lt15(yvy1000, yvy1010)
new_primEqInt(Pos(Zero), Neg(Succ(yvy300000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(yvy300000))) → False
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_compare30(yvy400, yvy300, app(ty_Maybe, ffb)) → new_compare31(yvy400, yvy300, ffb)
new_esEs9(yvy4000, yvy3000, ty_Ordering) → new_esEs12(yvy4000, yvy3000)
new_esEs7(yvy4000, yvy3000, ty_@0) → new_esEs19(yvy4000, yvy3000)
new_esEs11(yvy4000, yvy3000, ty_Float) → new_esEs14(yvy4000, yvy3000)
new_lt6(yvy1000, yvy1010, app(ty_[], bff)) → new_lt9(yvy1000, yvy1010, bff)
new_esEs36(yvy1000, yvy1010, ty_@0) → new_esEs19(yvy1000, yvy1010)
new_esEs5(yvy4001, yvy3001, ty_@0) → new_esEs19(yvy4001, yvy3001)
new_esEs36(yvy1000, yvy1010, app(app(app(ty_@3, edd), ede), edf)) → new_esEs22(yvy1000, yvy1010, edd, ede, edf)
new_esEs28(yvy1001, yvy1011, ty_Ordering) → new_esEs12(yvy1001, yvy1011)
new_esEs10(yvy4000, yvy3000, app(ty_[], efh)) → new_esEs16(yvy4000, yvy3000, efh)
new_primCompAux0(yvy56, LT) → LT
new_esEs6(yvy4002, yvy3002, app(app(ty_Either, bcc), bcd)) → new_esEs24(yvy4002, yvy3002, bcc, bcd)
new_esEs6(yvy4002, yvy3002, ty_Integer) → new_esEs18(yvy4002, yvy3002)
new_esEs36(yvy1000, yvy1010, app(app(ty_@2, edg), edh)) → new_esEs17(yvy1000, yvy1010, edg, edh)
new_esEs7(yvy4000, yvy3000, app(app(ty_@2, cb), cc)) → new_esEs17(yvy4000, yvy3000, cb, cc)
new_esEs9(yvy4000, yvy3000, ty_Float) → new_esEs14(yvy4000, yvy3000)
new_lt5(yvy1001, yvy1011, ty_Double) → new_lt13(yvy1001, yvy1011)
new_ltEs22(yvy114, yvy115, app(ty_Maybe, fbe)) → new_ltEs5(yvy114, yvy115, fbe)
new_not(False) → True
new_esEs27(yvy1000, yvy1010, ty_Int) → new_esEs25(yvy1000, yvy1010)
new_esEs34(yvy152, yvy155, app(ty_Ratio, cea)) → new_esEs21(yvy152, yvy155, cea)
new_compare30(yvy400, yvy300, ty_Bool) → new_compare12(yvy400, yvy300)
new_esEs25(yvy4000, yvy3000) → new_primEqInt(yvy4000, yvy3000)
new_esEs28(yvy1001, yvy1011, app(ty_[], bgh)) → new_esEs16(yvy1001, yvy1011, bgh)
new_esEs31(yvy40000, yvy30000, ty_Char) → new_esEs15(yvy40000, yvy30000)
new_esEs14(Float(yvy40000, yvy40001), Float(yvy30000, yvy30001)) → new_esEs25(new_sr0(yvy40000, yvy30000), new_sr0(yvy40001, yvy30001))
new_esEs11(yvy4000, yvy3000, ty_@0) → new_esEs19(yvy4000, yvy3000)
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_esEs12(GT, EQ) → False
new_esEs12(EQ, GT) → False
new_esEs36(yvy1000, yvy1010, ty_Float) → new_esEs14(yvy1000, yvy1010)
new_esEs4(yvy4000, yvy3000, ty_Ordering) → new_esEs12(yvy4000, yvy3000)
new_esEs9(yvy4000, yvy3000, app(app(ty_Either, fgc), fgd)) → new_esEs24(yvy4000, yvy3000, fgc, fgd)
new_lt6(yvy1000, yvy1010, app(app(app(ty_@3, bfh), bga), bgb)) → new_lt4(yvy1000, yvy1010, bfh, bga, bgb)
new_esEs4(yvy4000, yvy3000, app(app(ty_@2, gh), ha)) → new_esEs17(yvy4000, yvy3000, gh, ha)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, ty_Integer) → new_esEs18(yvy40000, yvy30000)
new_ltEs18(yvy107, yvy108, ty_@0) → new_ltEs17(yvy107, yvy108)
new_esEs39(yvy165, yvy167, ty_Int) → new_esEs25(yvy165, yvy167)
new_compare15(LT, EQ) → LT
new_esEs34(yvy152, yvy155, ty_Float) → new_esEs14(yvy152, yvy155)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, app(ty_[], dbg)) → new_ltEs8(yvy1000, yvy1010, dbg)
new_esEs36(yvy1000, yvy1010, app(ty_Ratio, edc)) → new_esEs21(yvy1000, yvy1010, edc)
new_esEs30(yvy40001, yvy30001, app(ty_Ratio, cda)) → new_esEs21(yvy40001, yvy30001, cda)
new_compare30(yvy400, yvy300, app(ty_Ratio, ffa)) → new_compare13(yvy400, yvy300, ffa)
new_esEs24(Left(yvy40000), Right(yvy30000), hg, hh) → False
new_esEs24(Right(yvy40000), Left(yvy30000), hg, hh) → False
new_lt20(yvy152, yvy155, app(app(ty_Either, dhh), eaa)) → new_lt16(yvy152, yvy155, dhh, eaa)
new_esEs30(yvy40001, yvy30001, app(app(ty_@2, ccg), cch)) → new_esEs17(yvy40001, yvy30001, ccg, cch)
new_esEs32(yvy40001, yvy30001, app(app(ty_Either, cgg), cgh)) → new_esEs24(yvy40001, yvy30001, cgg, cgh)
new_esEs34(yvy152, yvy155, app(ty_[], dhf)) → new_esEs16(yvy152, yvy155, dhf)
new_lt20(yvy152, yvy155, ty_Double) → new_lt13(yvy152, yvy155)
new_esEs35(yvy153, yvy156, ty_Double) → new_esEs13(yvy153, yvy156)
new_compare0(:(yvy4000, yvy4001), [], feh) → GT
new_lt6(yvy1000, yvy1010, ty_Char) → new_lt8(yvy1000, yvy1010)
new_esEs8(yvy4001, yvy3001, ty_Int) → new_esEs25(yvy4001, yvy3001)
new_esEs38(yvy40001, yvy30001, ty_Int) → new_esEs25(yvy40001, yvy30001)
new_ltEs24(yvy100, yvy101, ty_Integer) → new_ltEs4(yvy100, yvy101)
new_ltEs20(yvy154, yvy157, app(ty_Maybe, ecc)) → new_ltEs5(yvy154, yvy157, ecc)
new_ltEs20(yvy154, yvy157, ty_@0) → new_ltEs17(yvy154, yvy157)
new_ltEs24(yvy100, yvy101, app(app(ty_Either, dbf), dac)) → new_ltEs14(yvy100, yvy101, dbf, dac)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Int) → new_esEs25(yvy40000, yvy30000)
new_esEs34(yvy152, yvy155, app(app(ty_Either, dhh), eaa)) → new_esEs24(yvy152, yvy155, dhh, eaa)
new_lt13(yvy152, yvy155) → new_esEs12(new_compare29(yvy152, yvy155), LT)
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_esEs30(yvy40001, yvy30001, app(app(ty_Either, cdf), cdg)) → new_esEs24(yvy40001, yvy30001, cdf, cdg)
new_lt19(yvy152, yvy155) → new_esEs12(new_compare9(yvy152, yvy155), LT)
new_ltEs18(yvy107, yvy108, ty_Char) → new_ltEs7(yvy107, yvy108)
new_esEs4(yvy4000, yvy3000, app(app(ty_Either, hg), hh)) → new_esEs24(yvy4000, yvy3000, hg, hh)
new_esEs8(yvy4001, yvy3001, app(ty_Ratio, dg)) → new_esEs21(yvy4001, yvy3001, dg)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Integer) → new_esEs18(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, app(ty_Ratio, chd)) → new_esEs21(yvy40002, yvy30002, chd)
new_lt17(yvy152, yvy155) → new_esEs12(new_compare16(yvy152, yvy155), LT)
new_esEs10(yvy4000, yvy3000, app(app(ty_@2, ega), egb)) → new_esEs17(yvy4000, yvy3000, ega, egb)
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_ltEs7(yvy100, yvy101) → new_fsEs(new_compare11(yvy100, yvy101))
new_esEs31(yvy40000, yvy30000, ty_Float) → new_esEs14(yvy40000, yvy30000)
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_compare15(EQ, GT) → LT
new_esEs32(yvy40001, yvy30001, ty_Int) → new_esEs25(yvy40001, yvy30001)
new_esEs29(yvy40000, yvy30000, ty_Char) → new_esEs15(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, app(app(app(ty_@3, che), chf), chg)) → new_esEs22(yvy40002, yvy30002, che, chf, chg)
new_primEqNat0(Zero, Succ(yvy300000)) → False
new_primEqNat0(Succ(yvy400000), Zero) → False
new_compare15(LT, GT) → LT
new_lt15(yvy152, yvy155) → new_esEs12(new_compare8(yvy152, yvy155), LT)
new_ltEs5(Nothing, Nothing, eh) → True
new_ltEs23(yvy166, yvy168, app(app(app(ty_@3, fdf), fdg), fdh)) → new_ltEs10(yvy166, yvy168, fdf, fdg, fdh)
new_lt20(yvy152, yvy155, app(app(ty_@2, dec), ded)) → new_lt12(yvy152, yvy155, dec, ded)
new_ltEs6(LT, LT) → True
new_ltEs6(EQ, LT) → False
new_esEs6(yvy4002, yvy3002, app(ty_Ratio, bbf)) → new_esEs21(yvy4002, yvy3002, bbf)
new_ltEs5(Just(yvy1000), Just(yvy1010), app(ty_[], fa)) → new_ltEs8(yvy1000, yvy1010, fa)
new_ltEs19(yvy1002, yvy1012, ty_Char) → new_ltEs7(yvy1002, yvy1012)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_ltEs21(yvy1001, yvy1011, app(ty_Ratio, eee)) → new_ltEs9(yvy1001, yvy1011, eee)
new_esEs9(yvy4000, yvy3000, app(ty_Maybe, fgb)) → new_esEs23(yvy4000, yvy3000, fgb)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Bool) → new_ltEs16(yvy1000, yvy1010)
new_lt21(yvy153, yvy156, app(ty_Maybe, eba)) → new_lt14(yvy153, yvy156, eba)
new_compare15(GT, GT) → EQ
new_esEs11(yvy4000, yvy3000, app(app(ty_@2, ehc), ehd)) → new_esEs17(yvy4000, yvy3000, ehc, ehd)
new_esEs8(yvy4001, yvy3001, app(app(ty_Either, ed), ee)) → new_esEs24(yvy4001, yvy3001, ed, ee)
new_compare24(yvy165, yvy166, yvy167, yvy168, True, fbh, fca) → EQ
new_esEs32(yvy40001, yvy30001, ty_Bool) → new_esEs20(yvy40001, yvy30001)
new_lt21(yvy153, yvy156, ty_Float) → new_lt11(yvy153, yvy156)
new_esEs16(:(yvy40000, yvy40001), [], gg) → False
new_esEs16([], :(yvy30000, yvy30001), gg) → False
new_compare31(Just(yvy4000), Just(yvy3000), ffb) → new_compare210(yvy4000, yvy3000, new_esEs9(yvy4000, yvy3000, ffb), ffb)
new_lt21(yvy153, yvy156, ty_Ordering) → new_lt7(yvy153, yvy156)
new_lt20(yvy152, yvy155, ty_Bool) → new_lt18(yvy152, yvy155)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, app(ty_Ratio, dbh)) → new_ltEs9(yvy1000, yvy1010, dbh)
new_ltEs19(yvy1002, yvy1012, ty_@0) → new_ltEs17(yvy1002, yvy1012)
new_esEs7(yvy4000, yvy3000, app(app(app(ty_@3, ce), cf), cg)) → new_esEs22(yvy4000, yvy3000, ce, cf, cg)
new_esEs5(yvy4001, yvy3001, ty_Integer) → new_esEs18(yvy4001, yvy3001)
new_esEs31(yvy40000, yvy30000, ty_Int) → new_esEs25(yvy40000, yvy30000)
new_esEs27(yvy1000, yvy1010, app(app(app(ty_@3, bfh), bga), bgb)) → new_esEs22(yvy1000, yvy1010, bfh, bga, bgb)
new_ltEs19(yvy1002, yvy1012, app(ty_Maybe, cba)) → new_ltEs5(yvy1002, yvy1012, cba)
new_lt21(yvy153, yvy156, ty_Integer) → new_lt15(yvy153, yvy156)
new_esEs29(yvy40000, yvy30000, app(app(ty_Either, ccd), cce)) → new_esEs24(yvy40000, yvy30000, ccd, cce)
new_esEs10(yvy4000, yvy3000, app(ty_Ratio, egc)) → new_esEs21(yvy4000, yvy3000, egc)
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_ltEs12(@2(yvy1000, yvy1001), @2(yvy1010, yvy1011), ech, eda) → new_pePe(new_lt22(yvy1000, yvy1010, ech), new_asAs(new_esEs36(yvy1000, yvy1010, ech), new_ltEs21(yvy1001, yvy1011, eda)))
new_ltEs23(yvy166, yvy168, ty_@0) → new_ltEs17(yvy166, yvy168)
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_esEs5(yvy4001, yvy3001, app(ty_Maybe, bah)) → new_esEs23(yvy4001, yvy3001, bah)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Char) → new_ltEs7(yvy1000, yvy1010)
new_compare0(:(yvy4000, yvy4001), :(yvy3000, yvy3001), feh) → new_primCompAux1(yvy4000, yvy3000, new_compare0(yvy4001, yvy3001, feh), feh)
new_esEs20(False, True) → False
new_esEs20(True, False) → False
new_compare19(yvy206, yvy207, True, dha, dhb) → LT
new_sr0(yvy3000, yvy4001) → new_primMulInt(yvy3000, yvy4001)
new_esEs28(yvy1001, yvy1011, app(app(ty_@2, bhe), bhf)) → new_esEs17(yvy1001, yvy1011, bhe, bhf)
new_lt6(yvy1000, yvy1010, app(app(ty_Either, bgf), bgg)) → new_lt16(yvy1000, yvy1010, bgf, bgg)
new_esEs34(yvy152, yvy155, ty_Bool) → new_esEs20(yvy152, yvy155)
new_lt22(yvy1000, yvy1010, ty_Integer) → new_lt15(yvy1000, yvy1010)
new_esEs26(yvy40000, yvy30000, app(app(ty_Either, bde), bdf)) → new_esEs24(yvy40000, yvy30000, bde, bdf)
new_compare30(yvy400, yvy300, ty_Ordering) → new_compare15(yvy400, yvy300)
new_esEs30(yvy40001, yvy30001, app(ty_[], ccf)) → new_esEs16(yvy40001, yvy30001, ccf)
new_esEs24(Left(yvy40000), Left(yvy30000), app(app(ty_@2, def), deg), hh) → new_esEs17(yvy40000, yvy30000, def, deg)
new_lt23(yvy165, yvy167, ty_@0) → new_lt19(yvy165, yvy167)
new_esEs10(yvy4000, yvy3000, ty_Float) → new_esEs14(yvy4000, yvy3000)
new_compare29(Double(yvy4000, yvy4001), Double(yvy3000, yvy3001)) → new_compare16(new_sr0(yvy4000, yvy3000), new_sr0(yvy4001, yvy3001))
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, ty_Bool) → new_ltEs16(yvy1000, yvy1010)
new_ltEs22(yvy114, yvy115, app(ty_[], faf)) → new_ltEs8(yvy114, yvy115, faf)
new_esEs39(yvy165, yvy167, app(app(ty_Either, fdb), fdc)) → new_esEs24(yvy165, yvy167, fdb, fdc)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs32(yvy40001, yvy30001, ty_Double) → new_esEs13(yvy40001, yvy30001)
new_esEs28(yvy1001, yvy1011, ty_Bool) → new_esEs20(yvy1001, yvy1011)
new_esEs23(Just(yvy40000), Just(yvy30000), app(ty_Ratio, ddd)) → new_esEs21(yvy40000, yvy30000, ddd)
new_esEs5(yvy4001, yvy3001, app(ty_Ratio, bad)) → new_esEs21(yvy4001, yvy3001, bad)
new_ltEs14(Left(yvy1000), Right(yvy1010), dbf, dac) → True
new_compare24(yvy165, yvy166, yvy167, yvy168, False, fbh, fca) → new_compare110(yvy165, yvy166, yvy167, yvy168, new_lt23(yvy165, yvy167, fbh), new_asAs(new_esEs39(yvy165, yvy167, fbh), new_ltEs23(yvy166, yvy168, fca)), fbh, fca)
new_compare30(yvy400, yvy300, app(ty_[], feh)) → new_compare0(yvy400, yvy300, feh)
new_esEs9(yvy4000, yvy3000, app(ty_Ratio, fff)) → new_esEs21(yvy4000, yvy3000, fff)
new_ltEs20(yvy154, yvy157, app(app(ty_Either, ecd), ece)) → new_ltEs14(yvy154, yvy157, ecd, ece)
new_asAs(False, yvy184) → False
new_compare27(Right(yvy4000), Left(yvy3000), eff, efg) → GT
new_esEs36(yvy1000, yvy1010, app(ty_Maybe, eea)) → new_esEs23(yvy1000, yvy1010, eea)
new_esEs9(yvy4000, yvy3000, ty_Double) → new_esEs13(yvy4000, yvy3000)
new_ltEs19(yvy1002, yvy1012, app(app(ty_Either, cbb), cbc)) → new_ltEs14(yvy1002, yvy1012, cbb, cbc)
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_lt20(yvy152, yvy155, ty_@0) → new_lt19(yvy152, yvy155)
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_esEs4(yvy4000, yvy3000, ty_@0) → new_esEs19(yvy4000, yvy3000)
new_esEs27(yvy1000, yvy1010, ty_Double) → new_esEs13(yvy1000, yvy1010)
new_esEs36(yvy1000, yvy1010, ty_Ordering) → new_esEs12(yvy1000, yvy1010)
new_compare16(yvy400, yvy300) → new_primCmpInt(yvy400, yvy300)
new_esEs35(yvy153, yvy156, ty_Bool) → new_esEs20(yvy153, yvy156)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Bool) → new_esEs20(yvy40000, yvy30000)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Integer, dac) → new_ltEs4(yvy1000, yvy1010)
new_compare14(yvy218, yvy219, yvy220, yvy221, yvy222, yvy223, True, ceb, cec, ced) → LT
new_esEs30(yvy40001, yvy30001, app(ty_Maybe, cde)) → new_esEs23(yvy40001, yvy30001, cde)
new_esEs8(yvy4001, yvy3001, ty_Char) → new_esEs15(yvy4001, yvy3001)
new_esEs9(yvy4000, yvy3000, ty_Bool) → new_esEs20(yvy4000, yvy3000)
new_lt5(yvy1001, yvy1011, ty_Ordering) → new_lt7(yvy1001, yvy1011)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, ty_Ordering) → new_ltEs6(yvy1000, yvy1010)
new_esEs24(Left(yvy40000), Left(yvy30000), app(app(ty_Either, dfe), dff), hh) → new_esEs24(yvy40000, yvy30000, dfe, dff)
new_esEs8(yvy4001, yvy3001, app(ty_[], dd)) → new_esEs16(yvy4001, yvy3001, dd)
new_compare27(Left(yvy4000), Left(yvy3000), eff, efg) → new_compare26(yvy4000, yvy3000, new_esEs10(yvy4000, yvy3000, eff), eff, efg)
new_esEs29(yvy40000, yvy30000, ty_Double) → new_esEs13(yvy40000, yvy30000)
new_esEs27(yvy1000, yvy1010, ty_Integer) → new_esEs18(yvy1000, yvy1010)
new_esEs18(Integer(yvy40000), Integer(yvy30000)) → new_primEqInt(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, ty_Char) → new_esEs15(yvy40002, yvy30002)
new_ltEs5(Just(yvy1000), Just(yvy1010), app(ty_Maybe, ga)) → new_ltEs5(yvy1000, yvy1010, ga)
new_ltEs11(yvy100, yvy101) → new_fsEs(new_compare18(yvy100, yvy101))
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, app(app(ty_Either, dcg), dch)) → new_ltEs14(yvy1000, yvy1010, dcg, dch)
new_esEs30(yvy40001, yvy30001, ty_Float) → new_esEs14(yvy40001, yvy30001)
new_lt23(yvy165, yvy167, ty_Float) → new_lt11(yvy165, yvy167)
new_compare12(False, False) → EQ
new_esEs28(yvy1001, yvy1011, ty_@0) → new_esEs19(yvy1001, yvy1011)
new_ltEs23(yvy166, yvy168, ty_Char) → new_ltEs7(yvy166, yvy168)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, app(ty_Maybe, dgf)) → new_esEs23(yvy40000, yvy30000, dgf)
new_esEs29(yvy40000, yvy30000, ty_Float) → new_esEs14(yvy40000, yvy30000)
new_esEs7(yvy4000, yvy3000, ty_Ordering) → new_esEs12(yvy4000, yvy3000)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Integer, hh) → new_esEs18(yvy40000, yvy30000)
new_lt20(yvy152, yvy155, app(ty_Maybe, dhg)) → new_lt14(yvy152, yvy155, dhg)
new_esEs39(yvy165, yvy167, app(app(app(ty_@3, fcd), fce), fcf)) → new_esEs22(yvy165, yvy167, fcd, fce, fcf)
new_esEs31(yvy40000, yvy30000, ty_@0) → new_esEs19(yvy40000, yvy30000)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, app(ty_[], dfg)) → new_esEs16(yvy40000, yvy30000, dfg)
new_compare111(yvy233, yvy234, yvy235, yvy236, False, ecf, ecg) → GT
new_lt21(yvy153, yvy156, ty_Bool) → new_lt18(yvy153, yvy156)
new_ltEs6(LT, GT) → True
new_esEs33(yvy40002, yvy30002, ty_Int) → new_esEs25(yvy40002, yvy30002)
new_compare30(yvy400, yvy300, ty_Integer) → new_compare8(yvy400, yvy300)
new_ltEs23(yvy166, yvy168, app(ty_Maybe, fec)) → new_ltEs5(yvy166, yvy168, fec)
new_lt23(yvy165, yvy167, app(ty_Maybe, fda)) → new_lt14(yvy165, yvy167, fda)
new_ltEs21(yvy1001, yvy1011, ty_Char) → new_ltEs7(yvy1001, yvy1011)
new_ltEs14(Left(yvy1000), Left(yvy1010), app(app(ty_Either, dbd), dbe), dac) → new_ltEs14(yvy1000, yvy1010, dbd, dbe)
new_ltEs23(yvy166, yvy168, app(app(ty_@2, fea), feb)) → new_ltEs12(yvy166, yvy168, fea, feb)
new_ltEs21(yvy1001, yvy1011, ty_Ordering) → new_ltEs6(yvy1001, yvy1011)
new_esEs32(yvy40001, yvy30001, app(app(ty_@2, cfh), cga)) → new_esEs17(yvy40001, yvy30001, cfh, cga)
new_esEs24(Left(yvy40000), Left(yvy30000), app(ty_Maybe, dfd), hh) → new_esEs23(yvy40000, yvy30000, dfd)
new_lt22(yvy1000, yvy1010, app(ty_Ratio, edc)) → new_lt10(yvy1000, yvy1010, edc)
new_lt12(yvy152, yvy155, dec, ded) → new_esEs12(new_compare7(yvy152, yvy155, dec, ded), LT)
new_esEs35(yvy153, yvy156, ty_Int) → new_esEs25(yvy153, yvy156)
new_lt10(yvy152, yvy155, cea) → new_esEs12(new_compare13(yvy152, yvy155, cea), LT)
new_esEs4(yvy4000, yvy3000, ty_Double) → new_esEs13(yvy4000, yvy3000)
new_esEs8(yvy4001, yvy3001, app(app(ty_@2, de), df)) → new_esEs17(yvy4001, yvy3001, de, df)
new_esEs5(yvy4001, yvy3001, app(app(ty_@2, bab), bac)) → new_esEs17(yvy4001, yvy3001, bab, bac)
new_esEs16([], [], gg) → True
new_lt22(yvy1000, yvy1010, ty_Float) → new_lt11(yvy1000, yvy1010)
new_esEs32(yvy40001, yvy30001, ty_Ordering) → new_esEs12(yvy40001, yvy30001)
new_ltEs19(yvy1002, yvy1012, ty_Int) → new_ltEs15(yvy1002, yvy1012)
new_ltEs21(yvy1001, yvy1011, ty_Integer) → new_ltEs4(yvy1001, yvy1011)
new_ltEs20(yvy154, yvy157, ty_Float) → new_ltEs11(yvy154, yvy157)
new_lt5(yvy1001, yvy1011, app(app(ty_@2, bhe), bhf)) → new_lt12(yvy1001, yvy1011, bhe, bhf)
new_esEs11(yvy4000, yvy3000, ty_Int) → new_esEs25(yvy4000, yvy3000)
new_esEs32(yvy40001, yvy30001, app(app(app(ty_@3, cgc), cgd), cge)) → new_esEs22(yvy40001, yvy30001, cgc, cgd, cge)
new_lt6(yvy1000, yvy1010, ty_Double) → new_lt13(yvy1000, yvy1010)
new_lt20(yvy152, yvy155, ty_Float) → new_lt11(yvy152, yvy155)
new_ltEs14(Left(yvy1000), Left(yvy1010), app(app(app(ty_@3, daf), dag), dah), dac) → new_ltEs10(yvy1000, yvy1010, daf, dag, dah)
new_esEs26(yvy40000, yvy30000, ty_Integer) → new_esEs18(yvy40000, yvy30000)
new_lt22(yvy1000, yvy1010, app(app(app(ty_@3, edd), ede), edf)) → new_lt4(yvy1000, yvy1010, edd, ede, edf)
new_esEs36(yvy1000, yvy1010, app(app(ty_Either, eeb), eec)) → new_esEs24(yvy1000, yvy1010, eeb, eec)
new_esEs27(yvy1000, yvy1010, ty_Ordering) → new_esEs12(yvy1000, yvy1010)
new_ltEs19(yvy1002, yvy1012, ty_Double) → new_ltEs13(yvy1002, yvy1012)
new_lt21(yvy153, yvy156, ty_Int) → new_lt17(yvy153, yvy156)
new_lt20(yvy152, yvy155, ty_Integer) → new_lt15(yvy152, yvy155)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, ty_Ordering) → new_esEs12(yvy40000, yvy30000)
new_lt8(yvy152, yvy155) → new_esEs12(new_compare11(yvy152, yvy155), LT)
new_ltEs24(yvy100, yvy101, app(ty_[], fef)) → new_ltEs8(yvy100, yvy101, fef)
new_esEs9(yvy4000, yvy3000, ty_@0) → new_esEs19(yvy4000, yvy3000)
new_esEs22(@3(yvy40000, yvy40001, yvy40002), @3(yvy30000, yvy30001, yvy30002), hc, hd, he) → new_asAs(new_esEs31(yvy40000, yvy30000, hc), new_asAs(new_esEs32(yvy40001, yvy30001, hd), new_esEs33(yvy40002, yvy30002, he)))
new_esEs8(yvy4001, yvy3001, ty_Float) → new_esEs14(yvy4001, yvy3001)
new_esEs7(yvy4000, yvy3000, app(ty_Ratio, cd)) → new_esEs21(yvy4000, yvy3000, cd)
new_ltEs20(yvy154, yvy157, ty_Double) → new_ltEs13(yvy154, yvy157)
new_ltEs18(yvy107, yvy108, ty_Bool) → new_ltEs16(yvy107, yvy108)
new_compare28(yvy114, yvy115, False, fad, fae) → new_compare19(yvy114, yvy115, new_ltEs22(yvy114, yvy115, fae), fad, fae)
new_esEs6(yvy4002, yvy3002, app(ty_Maybe, bcb)) → new_esEs23(yvy4002, yvy3002, bcb)
new_lt5(yvy1001, yvy1011, app(app(app(ty_@3, bhb), bhc), bhd)) → new_lt4(yvy1001, yvy1011, bhb, bhc, bhd)
new_esEs31(yvy40000, yvy30000, app(app(app(ty_@3, cfa), cfb), cfc)) → new_esEs22(yvy40000, yvy30000, cfa, cfb, cfc)
new_esEs31(yvy40000, yvy30000, ty_Ordering) → new_esEs12(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, ty_Double) → new_esEs13(yvy40002, yvy30002)
new_lt6(yvy1000, yvy1010, ty_Float) → new_lt11(yvy1000, yvy1010)
new_esEs4(yvy4000, yvy3000, ty_Char) → new_esEs15(yvy4000, yvy3000)
new_esEs7(yvy4000, yvy3000, app(app(ty_Either, db), dc)) → new_esEs24(yvy4000, yvy3000, db, dc)
new_compare112(yvy189, yvy190, False, fge) → GT
new_esEs12(GT, GT) → True
new_ltEs21(yvy1001, yvy1011, app(app(app(ty_@3, eef), eeg), eeh)) → new_ltEs10(yvy1001, yvy1011, eef, eeg, eeh)
new_esEs5(yvy4001, yvy3001, ty_Double) → new_esEs13(yvy4001, yvy3001)
new_compare17(yvy218, yvy219, yvy220, yvy221, yvy222, yvy223, False, yvy225, ceb, cec, ced) → new_compare14(yvy218, yvy219, yvy220, yvy221, yvy222, yvy223, yvy225, ceb, cec, ced)
new_esEs8(yvy4001, yvy3001, app(ty_Maybe, ec)) → new_esEs23(yvy4001, yvy3001, ec)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_@0) → new_esEs19(yvy40000, yvy30000)
new_compare25(yvy152, yvy153, yvy154, yvy155, yvy156, yvy157, False, dhc, dhd, dhe) → new_compare17(yvy152, yvy153, yvy154, yvy155, yvy156, yvy157, new_lt20(yvy152, yvy155, dhc), new_asAs(new_esEs34(yvy152, yvy155, dhc), new_pePe(new_lt21(yvy153, yvy156, dhd), new_asAs(new_esEs35(yvy153, yvy156, dhd), new_ltEs20(yvy154, yvy157, dhe)))), dhc, dhd, dhe)
new_compare31(Nothing, Just(yvy3000), ffb) → LT
new_esEs29(yvy40000, yvy30000, ty_Ordering) → new_esEs12(yvy40000, yvy30000)
new_esEs4(yvy4000, yvy3000, app(ty_[], gg)) → new_esEs16(yvy4000, yvy3000, gg)
new_primPlusNat1(Zero, Zero) → Zero
new_compare0([], :(yvy3000, yvy3001), feh) → LT
new_ltEs6(LT, EQ) → True
new_lt23(yvy165, yvy167, ty_Ordering) → new_lt7(yvy165, yvy167)
new_ltEs21(yvy1001, yvy1011, app(ty_Maybe, efc)) → new_ltEs5(yvy1001, yvy1011, efc)
new_ltEs6(GT, LT) → False
new_lt18(yvy152, yvy155) → new_esEs12(new_compare12(yvy152, yvy155), LT)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, ty_Char) → new_esEs15(yvy40000, yvy30000)
new_asAs(True, yvy184) → yvy184
new_esEs26(yvy40000, yvy30000, ty_Float) → new_esEs14(yvy40000, yvy30000)
new_esEs35(yvy153, yvy156, ty_Float) → new_esEs14(yvy153, yvy156)
new_ltEs21(yvy1001, yvy1011, app(ty_[], eed)) → new_ltEs8(yvy1001, yvy1011, eed)
new_compare11(Char(yvy4000), Char(yvy3000)) → new_primCmpNat0(yvy4000, yvy3000)
new_ltEs22(yvy114, yvy115, ty_Float) → new_ltEs11(yvy114, yvy115)
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_esEs28(yvy1001, yvy1011, app(ty_Ratio, bha)) → new_esEs21(yvy1001, yvy1011, bha)
new_esEs39(yvy165, yvy167, ty_Double) → new_esEs13(yvy165, yvy167)
new_esEs11(yvy4000, yvy3000, ty_Bool) → new_esEs20(yvy4000, yvy3000)
new_ltEs22(yvy114, yvy115, ty_Double) → new_ltEs13(yvy114, yvy115)
new_lt22(yvy1000, yvy1010, ty_Ordering) → new_lt7(yvy1000, yvy1010)
new_esEs4(yvy4000, yvy3000, app(app(app(ty_@3, hc), hd), he)) → new_esEs22(yvy4000, yvy3000, hc, hd, he)
new_lt20(yvy152, yvy155, app(ty_Ratio, cea)) → new_lt10(yvy152, yvy155, cea)
new_ltEs16(False, False) → True
new_lt23(yvy165, yvy167, ty_Double) → new_lt13(yvy165, yvy167)
new_ltEs17(yvy100, yvy101) → new_fsEs(new_compare9(yvy100, yvy101))
new_esEs29(yvy40000, yvy30000, ty_Integer) → new_esEs18(yvy40000, yvy30000)
new_esEs8(yvy4001, yvy3001, ty_Ordering) → new_esEs12(yvy4001, yvy3001)
new_esEs30(yvy40001, yvy30001, ty_Bool) → new_esEs20(yvy40001, yvy30001)
new_lt23(yvy165, yvy167, app(ty_Ratio, fcc)) → new_lt10(yvy165, yvy167, fcc)
new_esEs30(yvy40001, yvy30001, ty_Int) → new_esEs25(yvy40001, yvy30001)
new_esEs27(yvy1000, yvy1010, ty_Float) → new_esEs14(yvy1000, yvy1010)
new_ltEs21(yvy1001, yvy1011, ty_Int) → new_ltEs15(yvy1001, yvy1011)
new_ltEs20(yvy154, yvy157, app(app(app(ty_@3, ebf), ebg), ebh)) → new_ltEs10(yvy154, yvy157, ebf, ebg, ebh)
new_esEs23(Just(yvy40000), Just(yvy30000), app(ty_[], dda)) → new_esEs16(yvy40000, yvy30000, dda)
new_esEs34(yvy152, yvy155, app(app(app(ty_@3, bd), be), bf)) → new_esEs22(yvy152, yvy155, bd, be, bf)
new_esEs16(:(yvy40000, yvy40001), :(yvy30000, yvy30001), gg) → new_asAs(new_esEs26(yvy40000, yvy30000, gg), new_esEs16(yvy40001, yvy30001, gg))
new_esEs9(yvy4000, yvy3000, app(app(app(ty_@3, ffg), ffh), fga)) → new_esEs22(yvy4000, yvy3000, ffg, ffh, fga)
new_ltEs19(yvy1002, yvy1012, app(app(app(ty_@3, cad), cae), caf)) → new_ltEs10(yvy1002, yvy1012, cad, cae, caf)
new_ltEs20(yvy154, yvy157, ty_Ordering) → new_ltEs6(yvy154, yvy157)
new_compare19(yvy206, yvy207, False, dha, dhb) → GT
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Integer) → new_ltEs4(yvy1000, yvy1010)
new_esEs6(yvy4002, yvy3002, ty_@0) → new_esEs19(yvy4002, yvy3002)
new_ltEs10(@3(yvy1000, yvy1001, yvy1002), @3(yvy1010, yvy1011, yvy1012), bfc, bfd, bfe) → new_pePe(new_lt6(yvy1000, yvy1010, bfc), new_asAs(new_esEs27(yvy1000, yvy1010, bfc), new_pePe(new_lt5(yvy1001, yvy1011, bfd), new_asAs(new_esEs28(yvy1001, yvy1011, bfd), new_ltEs19(yvy1002, yvy1012, bfe)))))
new_esEs33(yvy40002, yvy30002, ty_@0) → new_esEs19(yvy40002, yvy30002)
new_esEs35(yvy153, yvy156, app(ty_Ratio, eac)) → new_esEs21(yvy153, yvy156, eac)
new_ltEs22(yvy114, yvy115, ty_Int) → new_ltEs15(yvy114, yvy115)
new_ltEs24(yvy100, yvy101, app(app(app(ty_@3, bfc), bfd), bfe)) → new_ltEs10(yvy100, yvy101, bfc, bfd, bfe)
new_compare27(Right(yvy4000), Right(yvy3000), eff, efg) → new_compare28(yvy4000, yvy3000, new_esEs11(yvy4000, yvy3000, efg), eff, efg)
new_ltEs21(yvy1001, yvy1011, ty_@0) → new_ltEs17(yvy1001, yvy1011)
new_lt16(yvy152, yvy155, dhh, eaa) → new_esEs12(new_compare27(yvy152, yvy155, dhh, eaa), LT)
new_compare15(EQ, EQ) → EQ
new_ltEs22(yvy114, yvy115, ty_Char) → new_ltEs7(yvy114, yvy115)
new_compare30(yvy400, yvy300, ty_Double) → new_compare29(yvy400, yvy300)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCompAux0(yvy56, EQ) → yvy56
new_lt6(yvy1000, yvy1010, app(app(ty_@2, bgc), bgd)) → new_lt12(yvy1000, yvy1010, bgc, bgd)
new_esEs27(yvy1000, yvy1010, app(ty_Maybe, bge)) → new_esEs23(yvy1000, yvy1010, bge)
new_ltEs20(yvy154, yvy157, ty_Char) → new_ltEs7(yvy154, yvy157)
new_esEs10(yvy4000, yvy3000, ty_Integer) → new_esEs18(yvy4000, yvy3000)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_@0, dac) → new_ltEs17(yvy1000, yvy1010)
new_ltEs18(yvy107, yvy108, ty_Int) → new_ltEs15(yvy107, yvy108)
new_lt21(yvy153, yvy156, app(app(app(ty_@3, ead), eae), eaf)) → new_lt4(yvy153, yvy156, ead, eae, eaf)
new_esEs6(yvy4002, yvy3002, ty_Char) → new_esEs15(yvy4002, yvy3002)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_esEs30(yvy40001, yvy30001, ty_Char) → new_esEs15(yvy40001, yvy30001)
new_ltEs5(Just(yvy1000), Just(yvy1010), app(app(app(ty_@3, fc), fd), ff)) → new_ltEs10(yvy1000, yvy1010, fc, fd, ff)
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_esEs39(yvy165, yvy167, app(ty_[], fcb)) → new_esEs16(yvy165, yvy167, fcb)
new_esEs35(yvy153, yvy156, ty_Char) → new_esEs15(yvy153, yvy156)
new_not(True) → False
new_ltEs5(Just(yvy1000), Just(yvy1010), app(ty_Ratio, fb)) → new_ltEs9(yvy1000, yvy1010, fb)

The set Q consists of the following terms:

new_esEs36(x0, x1, ty_Char)
new_esEs29(x0, x1, ty_Float)
new_lt22(x0, x1, app(ty_Maybe, x2))
new_esEs7(x0, x1, ty_Int)
new_ltEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs21(x0, x1, ty_Int)
new_ltEs14(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs10(x0, x1, ty_Float)
new_ltEs16(True, True)
new_esEs6(x0, x1, ty_Int)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs32(x0, x1, app(ty_Maybe, x2))
new_lt11(x0, x1)
new_esEs24(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs20(x0, x1, ty_Int)
new_lt5(x0, x1, ty_Char)
new_esEs5(x0, x1, app(ty_[], x2))
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs36(x0, x1, app(ty_[], x2))
new_lt21(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs21(x0, x1, ty_@0)
new_esEs29(x0, x1, ty_Char)
new_ltEs22(x0, x1, ty_Integer)
new_esEs34(x0, x1, app(ty_[], x2))
new_esEs32(x0, x1, ty_Int)
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs11(x0, x1, ty_Int)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs4(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_Integer)
new_compare30(x0, x1, ty_Int)
new_pePe(True, x0)
new_esEs5(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs11(x0, x1, ty_@0)
new_esEs35(x0, x1, ty_Integer)
new_esEs11(x0, x1, ty_Char)
new_esEs9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(x0, x1, ty_Float)
new_esEs9(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(x0, x1, ty_Int)
new_esEs31(x0, x1, app(app(ty_Either, x2), x3))
new_lt22(x0, x1, ty_@0)
new_compare30(x0, x1, ty_Bool)
new_ltEs5(Nothing, Just(x0), x1)
new_lt20(x0, x1, ty_@0)
new_esEs29(x0, x1, ty_Ordering)
new_lt22(x0, x1, ty_Float)
new_esEs9(x0, x1, app(ty_[], x2))
new_lt23(x0, x1, ty_Integer)
new_ltEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(Right(x0), Right(x1), x2, ty_Bool)
new_lt7(x0, x1)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs8(x0, x1, ty_Integer)
new_esEs23(Just(x0), Just(x1), ty_Float)
new_esEs6(x0, x1, ty_Integer)
new_lt5(x0, x1, ty_@0)
new_esEs33(x0, x1, app(app(ty_@2, x2), x3))
new_esEs11(x0, x1, ty_Bool)
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs24(Right(x0), Right(x1), x2, ty_Integer)
new_compare12(False, True)
new_compare12(True, False)
new_ltEs7(x0, x1)
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_primCompAux0(x0, EQ)
new_esEs32(x0, x1, app(app(ty_@2, x2), x3))
new_lt6(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(x0, x1, ty_Integer)
new_esEs32(x0, x1, ty_Ordering)
new_ltEs21(x0, x1, ty_Float)
new_ltEs24(x0, x1, ty_Integer)
new_esEs34(x0, x1, ty_Float)
new_esEs6(x0, x1, ty_@0)
new_lt6(x0, x1, ty_Float)
new_esEs9(x0, x1, ty_Int)
new_compare30(x0, x1, ty_Integer)
new_esEs12(GT, EQ)
new_esEs12(EQ, GT)
new_esEs36(x0, x1, ty_Int)
new_esEs28(x0, x1, ty_Bool)
new_ltEs14(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs24(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_compare30(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_lt5(x0, x1, ty_Double)
new_compare15(LT, LT)
new_esEs10(x0, x1, ty_Char)
new_esEs23(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primMulNat0(Succ(x0), Zero)
new_ltEs22(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_compare6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs34(x0, x1, ty_Ordering)
new_esEs16([], [], x0)
new_esEs12(GT, GT)
new_esEs30(x0, x1, ty_Double)
new_esEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs21(x0, x1, ty_Ordering)
new_esEs10(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_lt21(x0, x1, ty_Float)
new_esEs11(x0, x1, ty_Integer)
new_esEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs21(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs24(x0, x1, app(ty_Maybe, x2))
new_esEs23(Just(x0), Just(x1), ty_Double)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_Char)
new_esEs34(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(Left(x0), Left(x1), ty_Int, x2)
new_esEs38(x0, x1, ty_Integer)
new_ltEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs27(x0, x1, ty_Bool)
new_esEs24(Right(x0), Right(x1), x2, ty_Char)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs6(EQ, EQ)
new_esEs32(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(x0, x1, ty_Float)
new_esEs8(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs22(x0, x1, ty_Char)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(x0, x1, ty_Double)
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_esEs5(x0, x1, ty_Bool)
new_lt6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs31(x0, x1, ty_Int)
new_compare26(x0, x1, True, x2, x3)
new_compare110(x0, x1, x2, x3, True, x4, x5, x6)
new_ltEs24(x0, x1, app(ty_[], x2))
new_compare27(Right(x0), Left(x1), x2, x3)
new_compare27(Left(x0), Right(x1), x2, x3)
new_esEs33(x0, x1, ty_Double)
new_esEs8(x0, x1, ty_Float)
new_ltEs18(x0, x1, ty_@0)
new_esEs4(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, app(ty_[], x2))
new_ltEs5(Just(x0), Just(x1), ty_@0)
new_lt5(x0, x1, ty_Int)
new_ltEs6(LT, EQ)
new_ltEs6(EQ, LT)
new_esEs24(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_primCompAux0(x0, LT)
new_esEs23(Nothing, Nothing, x0)
new_esEs38(x0, x1, ty_Int)
new_esEs23(Just(x0), Just(x1), ty_Int)
new_ltEs20(x0, x1, ty_@0)
new_lt6(x0, x1, app(ty_Maybe, x2))
new_esEs11(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Int)
new_lt17(x0, x1)
new_esEs8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs36(x0, x1, ty_Bool)
new_primEqNat0(Zero, Zero)
new_compare13(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs26(x0, x1, ty_@0)
new_lt21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(Right(x0), Right(x1), x2, ty_Int)
new_esEs7(x0, x1, ty_Bool)
new_esEs33(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs5(x0, x1, ty_Float)
new_ltEs14(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_compare17(x0, x1, x2, x3, x4, x5, False, x6, x7, x8, x9)
new_ltEs22(x0, x1, ty_Float)
new_compare15(GT, GT)
new_esEs31(x0, x1, ty_Double)
new_ltEs20(x0, x1, ty_Integer)
new_lt22(x0, x1, ty_Bool)
new_compare30(x0, x1, app(ty_[], x2))
new_esEs34(x0, x1, ty_Bool)
new_esEs31(x0, x1, ty_Integer)
new_ltEs20(x0, x1, ty_Char)
new_lt20(x0, x1, ty_Double)
new_esEs35(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_compare28(x0, x1, True, x2, x3)
new_ltEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs21(x0, x1, app(ty_[], x2))
new_ltEs15(x0, x1)
new_esEs4(x0, x1, ty_Integer)
new_esEs39(x0, x1, app(ty_Ratio, x2))
new_esEs6(x0, x1, app(app(ty_Either, x2), x3))
new_esEs39(x0, x1, ty_Bool)
new_esEs6(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs24(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Float)
new_ltEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_primMulNat0(Zero, Zero)
new_asAs(True, x0)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_ltEs14(Left(x0), Right(x1), x2, x3)
new_ltEs14(Right(x0), Left(x1), x2, x3)
new_esEs26(x0, x1, ty_Double)
new_esEs5(x0, x1, ty_Double)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs35(x0, x1, app(app(ty_@2, x2), x3))
new_fsEs(x0)
new_esEs16(:(x0, x1), [], x2)
new_ltEs5(Just(x0), Just(x1), ty_Integer)
new_esEs35(x0, x1, app(ty_Ratio, x2))
new_lt6(x0, x1, ty_Double)
new_esEs35(x0, x1, ty_Double)
new_ltEs18(x0, x1, ty_Bool)
new_esEs23(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Float)
new_ltEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(x0, x1, app(ty_Maybe, x2))
new_compare28(x0, x1, False, x2, x3)
new_ltEs5(Just(x0), Just(x1), ty_Double)
new_lt22(x0, x1, ty_Ordering)
new_lt23(x0, x1, app(ty_Ratio, x2))
new_esEs9(x0, x1, ty_@0)
new_esEs6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare24(x0, x1, x2, x3, False, x4, x5)
new_esEs24(Left(x0), Left(x1), ty_@0, x2)
new_esEs35(x0, x1, ty_Bool)
new_esEs35(x0, x1, ty_Char)
new_ltEs23(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, ty_Bool)
new_ltEs10(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs31(x0, x1, ty_@0)
new_lt10(x0, x1, x2)
new_ltEs19(x0, x1, ty_Double)
new_lt12(x0, x1, x2, x3)
new_ltEs24(x0, x1, ty_Double)
new_esEs13(Double(x0, x1), Double(x2, x3))
new_esEs10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Ordering)
new_esEs5(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(Just(x0), Nothing, x1)
new_ltEs14(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs24(Right(x0), Right(x1), x2, ty_@0)
new_esEs20(True, True)
new_lt22(x0, x1, ty_Int)
new_esEs7(x0, x1, ty_Integer)
new_esEs30(x0, x1, ty_Bool)
new_lt21(x0, x1, ty_@0)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs4(x0, x1, app(ty_Maybe, x2))
new_esEs33(x0, x1, ty_Float)
new_esEs29(x0, x1, ty_Integer)
new_ltEs21(x0, x1, ty_Integer)
new_lt16(x0, x1, x2, x3)
new_primPlusNat0(Zero, x0)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs4(x0, x1, ty_Ordering)
new_esEs8(x0, x1, ty_Bool)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_primPlusNat0(Succ(x0), x1)
new_ltEs4(x0, x1)
new_esEs34(x0, x1, ty_Integer)
new_esEs31(x0, x1, ty_Ordering)
new_ltEs6(GT, LT)
new_ltEs6(LT, GT)
new_compare0([], [], x0)
new_ltEs22(x0, x1, app(ty_Maybe, x2))
new_esEs35(x0, x1, app(ty_Maybe, x2))
new_compare111(x0, x1, x2, x3, True, x4, x5)
new_esEs11(x0, x1, ty_Double)
new_lt19(x0, x1)
new_ltEs14(Left(x0), Left(x1), ty_Double, x2)
new_ltEs8(x0, x1, x2)
new_ltEs14(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs4(x0, x1, ty_Double)
new_esEs36(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, ty_Double)
new_esEs39(x0, x1, ty_Char)
new_ltEs22(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_compare15(EQ, EQ)
new_lt6(x0, x1, ty_Int)
new_lt21(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, ty_Ordering)
new_ltEs14(Right(x0), Right(x1), x2, ty_Double)
new_ltEs22(x0, x1, ty_Ordering)
new_ltEs11(x0, x1)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_compare7(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt20(x0, x1, ty_Float)
new_lt21(x0, x1, ty_Integer)
new_esEs32(x0, x1, ty_Bool)
new_esEs39(x0, x1, ty_Float)
new_compare10(x0, x1, False, x2, x3)
new_lt6(x0, x1, ty_Integer)
new_lt4(x0, x1, x2, x3, x4)
new_esEs10(x0, x1, ty_Double)
new_esEs31(x0, x1, app(ty_[], x2))
new_sr0(x0, x1)
new_esEs23(Just(x0), Just(x1), ty_Integer)
new_esEs24(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs20(False, True)
new_esEs20(True, False)
new_esEs29(x0, x1, ty_Bool)
new_esEs24(Left(x0), Right(x1), x2, x3)
new_esEs24(Right(x0), Left(x1), x2, x3)
new_ltEs23(x0, x1, ty_Integer)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs36(x0, x1, app(ty_Ratio, x2))
new_esEs20(False, False)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare12(False, False)
new_esEs12(LT, EQ)
new_esEs12(EQ, LT)
new_lt21(x0, x1, ty_Int)
new_lt22(x0, x1, ty_Char)
new_ltEs14(Left(x0), Left(x1), ty_Char, x2)
new_ltEs14(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare14(x0, x1, x2, x3, x4, x5, True, x6, x7, x8)
new_esEs31(x0, x1, ty_Float)
new_esEs24(Left(x0), Left(x1), ty_Float, x2)
new_primPlusNat1(Zero, Zero)
new_ltEs21(x0, x1, ty_Bool)
new_esEs24(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs20(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_Float)
new_esEs12(EQ, EQ)
new_esEs23(Just(x0), Just(x1), ty_Bool)
new_esEs27(x0, x1, ty_Char)
new_ltEs14(Right(x0), Right(x1), x2, ty_Int)
new_esEs9(x0, x1, ty_Integer)
new_esEs30(x0, x1, ty_Float)
new_ltEs20(x0, x1, ty_Float)
new_lt22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(Right(x0), Right(x1), x2, ty_Char)
new_esEs9(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Left(x0), Left(x1), ty_Float, x2)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs16(:(x0, x1), :(x2, x3), x4)
new_esEs28(x0, x1, ty_Double)
new_esEs30(x0, x1, ty_Char)
new_compare30(x0, x1, ty_@0)
new_esEs6(x0, x1, ty_Bool)
new_esEs16([], :(x0, x1), x2)
new_ltEs23(x0, x1, ty_Float)
new_esEs9(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs31(x0, x1, app(app(ty_@2, x2), x3))
new_compare15(EQ, GT)
new_compare15(GT, EQ)
new_compare17(x0, x1, x2, x3, x4, x5, True, x6, x7, x8, x9)
new_ltEs9(x0, x1, x2)
new_ltEs24(x0, x1, ty_Ordering)
new_compare30(x0, x1, ty_Char)
new_primEqNat0(Succ(x0), Zero)
new_compare15(LT, GT)
new_compare15(GT, LT)
new_esEs36(x0, x1, ty_Double)
new_esEs39(x0, x1, ty_Ordering)
new_esEs7(x0, x1, app(app(ty_Either, x2), x3))
new_lt21(x0, x1, app(ty_[], x2))
new_esEs37(x0, x1, ty_Int)
new_esEs9(x0, x1, ty_Double)
new_primMulInt(Neg(x0), Neg(x1))
new_ltEs5(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs17(x0, x1)
new_compare0([], :(x0, x1), x2)
new_esEs9(x0, x1, ty_Ordering)
new_ltEs12(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs26(x0, x1, ty_Char)
new_lt23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_lt23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs23(x0, x1, ty_Int)
new_primEqNat0(Succ(x0), Succ(x1))
new_compare210(x0, x1, True, x2)
new_esEs8(x0, x1, ty_Int)
new_ltEs14(Left(x0), Left(x1), ty_Bool, x2)
new_lt21(x0, x1, app(ty_Maybe, x2))
new_ltEs5(Just(x0), Just(x1), ty_Int)
new_esEs33(x0, x1, ty_Int)
new_ltEs23(x0, x1, ty_@0)
new_lt6(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs33(x0, x1, ty_Bool)
new_esEs10(x0, x1, ty_Ordering)
new_esEs24(Left(x0), Left(x1), ty_Double, x2)
new_esEs35(x0, x1, ty_@0)
new_esEs4(x0, x1, ty_Char)
new_compare112(x0, x1, False, x2)
new_esEs24(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_lt23(x0, x1, ty_Int)
new_ltEs14(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs18(x0, x1, ty_Double)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt23(x0, x1, ty_Bool)
new_ltEs14(Left(x0), Left(x1), ty_Integer, x2)
new_esEs24(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_lt9(x0, x1, x2)
new_ltEs18(x0, x1, app(ty_[], x2))
new_esEs33(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, app(ty_[], x2))
new_lt5(x0, x1, app(app(ty_Either, x2), x3))
new_lt21(x0, x1, ty_Bool)
new_esEs24(Left(x0), Left(x1), ty_Char, x2)
new_ltEs5(Nothing, Nothing, x0)
new_compare18(Float(x0, x1), Float(x2, x3))
new_ltEs5(Just(x0), Just(x1), ty_Float)
new_esEs26(x0, x1, ty_Bool)
new_lt6(x0, x1, ty_Bool)
new_esEs30(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Integer)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs8(x0, x1, ty_Double)
new_lt21(x0, x1, ty_Char)
new_lt5(x0, x1, ty_Float)
new_compare11(Char(x0), Char(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs24(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs36(x0, x1, app(app(ty_Either, x2), x3))
new_esEs30(x0, x1, ty_Integer)
new_esEs25(x0, x1)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_compare210(x0, x1, False, x2)
new_esEs29(x0, x1, ty_@0)
new_ltEs14(Left(x0), Left(x1), ty_Int, x2)
new_sr(Integer(x0), Integer(x1))
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs7(x0, x1, ty_@0)
new_esEs39(x0, x1, app(ty_Maybe, x2))
new_primMulNat0(Succ(x0), Succ(x1))
new_ltEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs34(x0, x1, ty_Char)
new_esEs4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs10(x0, x1, ty_Bool)
new_lt5(x0, x1, app(ty_[], x2))
new_esEs10(x0, x1, ty_@0)
new_esEs39(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_@0)
new_esEs31(x0, x1, ty_Bool)
new_primEqNat0(Zero, Succ(x0))
new_primPlusNat1(Succ(x0), Zero)
new_lt23(x0, x1, ty_Char)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs7(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Char)
new_ltEs21(x0, x1, app(ty_Maybe, x2))
new_esEs6(x0, x1, ty_Ordering)
new_esEs33(x0, x1, ty_Char)
new_compare27(Left(x0), Left(x1), x2, x3)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs32(x0, x1, ty_Integer)
new_ltEs14(Left(x0), Left(x1), ty_Ordering, x2)
new_pePe(False, x0)
new_ltEs24(x0, x1, ty_Int)
new_compare24(x0, x1, x2, x3, True, x4, x5)
new_lt8(x0, x1)
new_esEs39(x0, x1, app(app(ty_Either, x2), x3))
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt23(x0, x1, ty_Double)
new_esEs10(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Bool)
new_esEs9(x0, x1, app(app(ty_@2, x2), x3))
new_esEs32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, ty_Int)
new_esEs30(x0, x1, ty_Ordering)
new_lt23(x0, x1, ty_Float)
new_lt6(x0, x1, ty_@0)
new_primPlusNat1(Succ(x0), Succ(x1))
new_compare27(Right(x0), Right(x1), x2, x3)
new_esEs31(x0, x1, ty_Char)
new_lt22(x0, x1, ty_Double)
new_ltEs22(x0, x1, ty_@0)
new_esEs39(x0, x1, ty_Int)
new_esEs30(x0, x1, ty_@0)
new_compare14(x0, x1, x2, x3, x4, x5, False, x6, x7, x8)
new_ltEs16(False, True)
new_ltEs16(True, False)
new_ltEs6(GT, GT)
new_esEs10(x0, x1, ty_Int)
new_compare30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(x0, x1, app(ty_Maybe, x2))
new_esEs31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs32(x0, x1, ty_Char)
new_esEs23(Nothing, Just(x0), x1)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(x0, x1, ty_Int)
new_ltEs5(Just(x0), Just(x1), ty_Ordering)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_ltEs19(x0, x1, ty_Char)
new_ltEs22(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(Just(x0), Just(x1), ty_Char)
new_esEs27(x0, x1, ty_Int)
new_esEs24(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs4(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(Just(x0), Just(x1), ty_Bool)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_Bool)
new_lt22(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_@0)
new_ltEs22(x0, x1, ty_Bool)
new_esEs30(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_Integer)
new_esEs33(x0, x1, ty_Integer)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, ty_Int)
new_primCmpNat0(Zero, Zero)
new_esEs35(x0, x1, ty_Float)
new_asAs(False, x0)
new_lt5(x0, x1, ty_Integer)
new_ltEs24(x0, x1, ty_@0)
new_esEs17(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs19(x0, x1, ty_Int)
new_lt23(x0, x1, ty_@0)
new_esEs34(x0, x1, ty_Int)
new_ltEs6(LT, LT)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs35(x0, x1, app(ty_[], x2))
new_esEs35(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare31(Just(x0), Just(x1), x2)
new_esEs11(x0, x1, ty_Ordering)
new_esEs31(x0, x1, app(ty_Ratio, x2))
new_lt5(x0, x1, app(ty_Ratio, x2))
new_ltEs22(x0, x1, ty_Double)
new_ltEs14(Left(x0), Left(x1), ty_@0, x2)
new_lt23(x0, x1, app(ty_[], x2))
new_compare10(x0, x1, True, x2, x3)
new_ltEs24(x0, x1, ty_Char)
new_esEs21(:%(x0, x1), :%(x2, x3), x4)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs18(Integer(x0), Integer(x1))
new_esEs4(x0, x1, ty_@0)
new_lt22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, ty_Int)
new_ltEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(Just(x0), Just(x1), ty_@0)
new_compare110(x0, x1, x2, x3, False, x4, x5, x6)
new_ltEs14(Right(x0), Right(x1), x2, ty_Integer)
new_compare0(:(x0, x1), [], x2)
new_esEs23(Just(x0), Nothing, x1)
new_ltEs19(x0, x1, ty_Float)
new_esEs6(x0, x1, ty_Char)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_lt21(x0, x1, ty_Double)
new_primCompAux1(x0, x1, x2, x3)
new_esEs32(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs8(x0, x1, app(ty_[], x2))
new_esEs23(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs34(x0, x1, app(app(ty_Either, x2), x3))
new_esEs33(x0, x1, app(ty_[], x2))
new_lt5(x0, x1, ty_Bool)
new_esEs11(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(Just(x0), Just(x1), ty_Char)
new_ltEs13(x0, x1)
new_lt14(x0, x1, x2)
new_ltEs23(x0, x1, ty_Bool)
new_esEs6(x0, x1, app(ty_Ratio, x2))
new_compare15(LT, EQ)
new_compare15(EQ, LT)
new_compare9(@0, @0)
new_lt13(x0, x1)
new_esEs36(x0, x1, ty_Integer)
new_esEs29(x0, x1, ty_Double)
new_ltEs22(x0, x1, app(ty_[], x2))
new_ltEs23(x0, x1, app(ty_Maybe, x2))
new_esEs8(x0, x1, app(ty_Ratio, x2))
new_ltEs18(x0, x1, ty_Float)
new_lt18(x0, x1)
new_lt22(x0, x1, app(ty_Ratio, x2))
new_esEs32(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_Float)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_lt5(x0, x1, ty_Ordering)
new_lt15(x0, x1)
new_compare8(Integer(x0), Integer(x1))
new_lt22(x0, x1, app(ty_[], x2))
new_compare30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs33(x0, x1, app(ty_Ratio, x2))
new_lt5(x0, x1, app(ty_Maybe, x2))
new_esEs36(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs33(x0, x1, app(ty_Maybe, x2))
new_esEs7(x0, x1, app(ty_Maybe, x2))
new_esEs8(x0, x1, ty_@0)
new_lt6(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(x0, x1, ty_Int)
new_not(True)
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_compare30(x0, x1, ty_Float)
new_compare31(Just(x0), Nothing, x1)
new_esEs27(x0, x1, ty_Ordering)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs22(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs23(x0, x1, app(ty_Ratio, x2))
new_ltEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(x0, x1, ty_Bool)
new_esEs32(x0, x1, ty_Float)
new_esEs36(x0, x1, ty_Ordering)
new_esEs9(x0, x1, ty_Bool)
new_esEs23(Just(x0), Just(x1), app(ty_Maybe, x2))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_not(False)
new_esEs24(Left(x0), Left(x1), ty_Ordering, x2)
new_compare29(Double(x0, x1), Double(x2, x3))
new_compare13(:%(x0, x1), :%(x2, x3), ty_Integer)
new_lt6(x0, x1, app(ty_Ratio, x2))
new_primCmpNat0(Succ(x0), Succ(x1))
new_esEs7(x0, x1, ty_Ordering)
new_esEs34(x0, x1, app(ty_Ratio, x2))
new_ltEs23(x0, x1, ty_Char)
new_esEs7(x0, x1, app(ty_[], x2))
new_esEs8(x0, x1, ty_Ordering)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_esEs39(x0, x1, ty_@0)
new_ltEs21(x0, x1, ty_Char)
new_esEs15(Char(x0), Char(x1))
new_esEs7(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(x0, x1, app(ty_Ratio, x2))
new_ltEs6(GT, EQ)
new_ltEs6(EQ, GT)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_esEs7(x0, x1, app(ty_Ratio, x2))
new_esEs32(x0, x1, app(ty_Ratio, x2))
new_primCmpNat0(Zero, Succ(x0))
new_esEs31(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Ordering)
new_lt23(x0, x1, app(ty_Maybe, x2))
new_ltEs21(x0, x1, ty_Double)
new_esEs24(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs8(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs23(x0, x1, app(ty_[], x2))
new_esEs24(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_compare30(x0, x1, ty_Double)
new_compare19(x0, x1, True, x2, x3)
new_esEs36(x0, x1, app(ty_Maybe, x2))
new_esEs24(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs5(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(Right(x0), Right(x1), x2, ty_Double)
new_lt22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(x0, x1, app(ty_[], x2))
new_primCmpNat0(Succ(x0), Zero)
new_compare30(x0, x1, app(ty_Maybe, x2))
new_esEs34(x0, x1, ty_Double)
new_ltEs21(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_@0)
new_esEs11(x0, x1, app(ty_Maybe, x2))
new_esEs6(x0, x1, app(ty_Maybe, x2))
new_ltEs22(x0, x1, ty_Int)
new_compare26(x0, x1, False, x2, x3)
new_compare16(x0, x1)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_esEs23(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs20(x0, x1, ty_Double)
new_ltEs24(x0, x1, ty_Bool)
new_esEs35(x0, x1, ty_Ordering)
new_ltEs18(x0, x1, ty_Integer)
new_esEs39(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs34(x0, x1, ty_@0)
new_compare31(Nothing, Just(x0), x1)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_esEs37(x0, x1, ty_Integer)
new_ltEs18(x0, x1, ty_Char)
new_esEs7(x0, x1, ty_Double)
new_lt23(x0, x1, ty_Ordering)
new_compare112(x0, x1, True, x2)
new_lt21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs34(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs9(x0, x1, ty_Float)
new_esEs23(Just(x0), Just(x1), ty_Ordering)
new_lt6(x0, x1, ty_Char)
new_esEs9(x0, x1, ty_Char)
new_esEs8(x0, x1, ty_Char)
new_esEs35(x0, x1, ty_Int)
new_esEs24(Left(x0), Left(x1), ty_Integer, x2)
new_esEs5(x0, x1, app(ty_Maybe, x2))
new_lt21(x0, x1, app(ty_Ratio, x2))
new_esEs33(x0, x1, ty_@0)
new_esEs24(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs5(x0, x1, ty_Ordering)
new_esEs32(x0, x1, ty_Double)
new_esEs34(x0, x1, app(ty_Maybe, x2))
new_esEs10(x0, x1, app(ty_[], x2))
new_compare30(x0, x1, app(ty_Ratio, x2))
new_ltEs21(x0, x1, app(ty_Ratio, x2))
new_lt23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs24(x0, x1, app(ty_Ratio, x2))
new_esEs14(Float(x0, x1), Float(x2, x3))
new_esEs26(x0, x1, ty_Integer)
new_esEs5(x0, x1, ty_@0)
new_esEs5(x0, x1, ty_Char)
new_esEs7(x0, x1, ty_Char)
new_compare12(True, True)
new_primEqInt(Pos(Zero), Pos(Zero))
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs5(x0, x1, ty_Integer)
new_compare31(Nothing, Nothing, x0)
new_esEs39(x0, x1, app(ty_[], x2))
new_compare30(x0, x1, ty_Ordering)
new_primMulNat0(Zero, Succ(x0))
new_esEs28(x0, x1, app(ty_[], x2))
new_ltEs23(x0, x1, ty_Double)
new_esEs24(Right(x0), Right(x1), x2, ty_Float)
new_esEs11(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_lt5(x0, x1, app(app(ty_@2, x2), x3))
new_primCompAux0(x0, GT)
new_lt6(x0, x1, ty_Ordering)
new_primPlusNat1(Zero, Succ(x0))
new_esEs36(x0, x1, ty_Float)
new_esEs19(@0, @0)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs39(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_compare25(x0, x1, x2, x3, x4, x5, True, x6, x7, x8)
new_esEs36(x0, x1, ty_@0)
new_esEs12(LT, LT)
new_esEs28(x0, x1, ty_Integer)
new_compare19(x0, x1, False, x2, x3)
new_ltEs18(x0, x1, ty_Ordering)
new_ltEs16(False, False)
new_compare111(x0, x1, x2, x3, False, x4, x5)
new_compare25(x0, x1, x2, x3, x4, x5, False, x6, x7, x8)
new_esEs33(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, ty_Ordering)
new_esEs28(x0, x1, ty_@0)
new_esEs11(x0, x1, ty_Float)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs4(x0, x1, app(ty_[], x2))
new_esEs39(x0, x1, ty_Integer)

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

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



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

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

new_splitGT1(yvy300, yvy301, yvy31, yvy32, Branch(yvy330, yvy331, yvy332, yvy333, yvy334), yvy34, LT, h, ba) → new_splitGT3(yvy330, yvy331, yvy332, yvy333, yvy334, [], h, ba)
new_splitGT10(yvy31, yvy32, yvy33, yvy34, LT, h, ba) → new_splitGT0(yvy33, h, ba)
new_splitGT3(:(yvy300, yvy301), yvy31, yvy32, yvy33, yvy34, [], h, ba) → new_splitGT1(yvy300, yvy301, yvy31, yvy32, yvy33, yvy34, new_compare0([], :(yvy300, yvy301), h), h, ba)
new_splitGT(Branch(yvy340, yvy341, yvy342, yvy343, yvy344), yvy400, yvy401, h, ba) → new_splitGT3(yvy340, yvy341, yvy342, yvy343, yvy344, :(yvy400, yvy401), h, ba)
new_splitGT2(yvy17, yvy18, yvy19, yvy20, yvy21, yvy22, yvy23, yvy24, EQ, bb, bc) → new_splitGT20(yvy17, yvy18, yvy19, yvy20, yvy21, yvy22, yvy23, yvy24, bb, bc)
new_splitGT11(yvy17, yvy18, yvy19, yvy20, yvy21, yvy22, yvy23, yvy24, LT, bb, bc) → new_splitGT(yvy21, yvy23, yvy24, bb, bc)
new_splitGT2(yvy17, yvy18, yvy19, yvy20, yvy21, yvy22, yvy23, yvy24, GT, bb, bc) → new_splitGT(yvy22, yvy23, yvy24, bb, bc)
new_splitGT0(Branch(yvy330, yvy331, yvy332, yvy333, yvy334), h, ba) → new_splitGT3(yvy330, yvy331, yvy332, yvy333, yvy334, [], h, ba)
new_splitGT2(yvy17, yvy18, yvy19, yvy20, yvy21, yvy22, yvy23, yvy24, LT, bb, bc) → new_splitGT11(yvy17, yvy18, yvy19, yvy20, yvy21, yvy22, yvy23, yvy24, new_compare0(:(yvy23, yvy24), :(yvy17, yvy18), bb), bb, bc)
new_splitGT20(yvy17, yvy18, yvy19, yvy20, yvy21, yvy22, yvy23, yvy24, bb, bc) → new_splitGT11(yvy17, yvy18, yvy19, yvy20, yvy21, yvy22, yvy23, yvy24, new_compare0(:(yvy23, yvy24), :(yvy17, yvy18), bb), bb, bc)
new_splitGT3(:(yvy300, yvy301), yvy31, yvy32, yvy33, yvy34, :(yvy400, yvy401), h, ba) → new_splitGT2(yvy300, yvy301, yvy31, yvy32, yvy33, yvy34, yvy400, yvy401, new_primCompAux1(yvy400, yvy300, new_compare0(yvy401, yvy301, h), h), h, ba)
new_splitGT3([], yvy31, yvy32, yvy33, Branch(yvy340, yvy341, yvy342, yvy343, yvy344), :(yvy400, yvy401), h, ba) → new_splitGT3(yvy340, yvy341, yvy342, yvy343, yvy344, :(yvy400, yvy401), h, ba)
new_splitGT3([], yvy31, yvy32, yvy33, yvy34, [], h, ba) → new_splitGT10(yvy31, yvy32, yvy33, yvy34, new_compare0([], [], h), h, ba)

The TRS R consists of the following rules:

new_compare210(yvy100, yvy101, False, feg) → new_compare112(yvy100, yvy101, new_ltEs24(yvy100, yvy101, feg), feg)
new_compare7(@2(yvy4000, yvy4001), @2(yvy3000, yvy3001), bg, bh) → new_compare24(yvy4000, yvy4001, yvy3000, yvy3001, new_asAs(new_esEs7(yvy4000, yvy3000, bg), new_esEs8(yvy4001, yvy3001, bh)), bg, bh)
new_esEs24(Left(yvy40000), Left(yvy30000), app(ty_Ratio, deh), hh) → new_esEs21(yvy40000, yvy30000, deh)
new_ltEs19(yvy1002, yvy1012, app(ty_[], cab)) → new_ltEs8(yvy1002, yvy1012, cab)
new_compare112(yvy189, yvy190, True, fge) → LT
new_lt22(yvy1000, yvy1010, ty_Int) → new_lt17(yvy1000, yvy1010)
new_ltEs22(yvy114, yvy115, app(app(ty_@2, fbc), fbd)) → new_ltEs12(yvy114, yvy115, fbc, fbd)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Int, hh) → new_esEs25(yvy40000, yvy30000)
new_esEs6(yvy4002, yvy3002, app(app(app(ty_@3, bbg), bbh), bca)) → new_esEs22(yvy4002, yvy3002, bbg, bbh, bca)
new_esEs27(yvy1000, yvy1010, app(ty_[], bff)) → new_esEs16(yvy1000, yvy1010, bff)
new_esEs20(True, True) → True
new_esEs35(yvy153, yvy156, app(ty_[], eab)) → new_esEs16(yvy153, yvy156, eab)
new_compare8(Integer(yvy4000), Integer(yvy3000)) → new_primCmpInt(yvy4000, yvy3000)
new_esEs8(yvy4001, yvy3001, ty_Bool) → new_esEs20(yvy4001, yvy3001)
new_esEs11(yvy4000, yvy3000, ty_Integer) → new_esEs18(yvy4000, yvy3000)
new_esEs27(yvy1000, yvy1010, app(app(ty_@2, bgc), bgd)) → new_esEs17(yvy1000, yvy1010, bgc, bgd)
new_ltEs20(yvy154, yvy157, app(ty_Ratio, ebe)) → new_ltEs9(yvy154, yvy157, ebe)
new_esEs36(yvy1000, yvy1010, ty_Double) → new_esEs13(yvy1000, yvy1010)
new_esEs28(yvy1001, yvy1011, ty_Float) → new_esEs14(yvy1001, yvy1011)
new_lt6(yvy1000, yvy1010, ty_@0) → new_lt19(yvy1000, yvy1010)
new_compare10(yvy199, yvy200, True, ef, eg) → LT
new_esEs9(yvy4000, yvy3000, ty_Int) → new_esEs25(yvy4000, yvy3000)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, ty_Double) → new_esEs13(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, app(app(ty_@2, chb), chc)) → new_esEs17(yvy40002, yvy30002, chb, chc)
new_ltEs24(yvy100, yvy101, app(ty_Ratio, cdh)) → new_ltEs9(yvy100, yvy101, cdh)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, ty_@0) → new_esEs19(yvy40000, yvy30000)
new_ltEs19(yvy1002, yvy1012, ty_Float) → new_ltEs11(yvy1002, yvy1012)
new_esEs11(yvy4000, yvy3000, app(ty_[], ehb)) → new_esEs16(yvy4000, yvy3000, ehb)
new_lt23(yvy165, yvy167, app(app(app(ty_@3, fcd), fce), fcf)) → new_lt4(yvy165, yvy167, fcd, fce, fcf)
new_esEs7(yvy4000, yvy3000, ty_Double) → new_esEs13(yvy4000, yvy3000)
new_esEs9(yvy4000, yvy3000, ty_Char) → new_esEs15(yvy4000, yvy3000)
new_ltEs23(yvy166, yvy168, ty_Ordering) → new_ltEs6(yvy166, yvy168)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Bool, dac) → new_ltEs16(yvy1000, yvy1010)
new_esEs39(yvy165, yvy167, app(ty_Ratio, fcc)) → new_esEs21(yvy165, yvy167, fcc)
new_esEs10(yvy4000, yvy3000, ty_@0) → new_esEs19(yvy4000, yvy3000)
new_esEs21(:%(yvy40000, yvy40001), :%(yvy30000, yvy30001), hb) → new_asAs(new_esEs37(yvy40000, yvy30000, hb), new_esEs38(yvy40001, yvy30001, hb))
new_lt5(yvy1001, yvy1011, app(ty_Ratio, bha)) → new_lt10(yvy1001, yvy1011, bha)
new_compare13(:%(yvy4000, yvy4001), :%(yvy3000, yvy3001), ty_Integer) → new_compare8(new_sr(yvy4000, yvy3001), new_sr(yvy3000, yvy4001))
new_ltEs22(yvy114, yvy115, app(ty_Ratio, fag)) → new_ltEs9(yvy114, yvy115, fag)
new_ltEs23(yvy166, yvy168, ty_Int) → new_ltEs15(yvy166, yvy168)
new_primMulNat0(Zero, Zero) → Zero
new_ltEs24(yvy100, yvy101, ty_Ordering) → new_ltEs6(yvy100, yvy101)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, ty_Float) → new_ltEs11(yvy1000, yvy1010)
new_esEs39(yvy165, yvy167, app(ty_Maybe, fda)) → new_esEs23(yvy165, yvy167, fda)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Bool, hh) → new_esEs20(yvy40000, yvy30000)
new_compare15(LT, LT) → EQ
new_esEs6(yvy4002, yvy3002, app(app(ty_@2, bbd), bbe)) → new_esEs17(yvy4002, yvy3002, bbd, bbe)
new_esEs4(yvy4000, yvy3000, ty_Integer) → new_esEs18(yvy4000, yvy3000)
new_esEs26(yvy40000, yvy30000, app(ty_[], bce)) → new_esEs16(yvy40000, yvy30000, bce)
new_esEs36(yvy1000, yvy1010, ty_Char) → new_esEs15(yvy1000, yvy1010)
new_esEs28(yvy1001, yvy1011, app(app(ty_Either, bhh), caa)) → new_esEs24(yvy1001, yvy1011, bhh, caa)
new_esEs34(yvy152, yvy155, ty_@0) → new_esEs19(yvy152, yvy155)
new_sr(Integer(yvy30000), Integer(yvy40010)) → Integer(new_primMulInt(yvy30000, yvy40010))
new_esEs7(yvy4000, yvy3000, ty_Float) → new_esEs14(yvy4000, yvy3000)
new_compare12(True, False) → GT
new_lt7(yvy152, yvy155) → new_esEs12(new_compare15(yvy152, yvy155), LT)
new_lt22(yvy1000, yvy1010, app(ty_Maybe, eea)) → new_lt14(yvy1000, yvy1010, eea)
new_ltEs24(yvy100, yvy101, app(ty_Maybe, eh)) → new_ltEs5(yvy100, yvy101, eh)
new_esEs35(yvy153, yvy156, app(app(ty_Either, ebb), ebc)) → new_esEs24(yvy153, yvy156, ebb, ebc)
new_esEs35(yvy153, yvy156, ty_@0) → new_esEs19(yvy153, yvy156)
new_ltEs15(yvy100, yvy101) → new_fsEs(new_compare16(yvy100, yvy101))
new_esEs6(yvy4002, yvy3002, app(ty_[], bbc)) → new_esEs16(yvy4002, yvy3002, bbc)
new_esEs26(yvy40000, yvy30000, ty_@0) → new_esEs19(yvy40000, yvy30000)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_@0, hh) → new_esEs19(yvy40000, yvy30000)
new_ltEs16(False, True) → True
new_esEs26(yvy40000, yvy30000, app(app(app(ty_@3, bda), bdb), bdc)) → new_esEs22(yvy40000, yvy30000, bda, bdb, bdc)
new_esEs10(yvy4000, yvy3000, app(ty_Maybe, egg)) → new_esEs23(yvy4000, yvy3000, egg)
new_ltEs24(yvy100, yvy101, ty_Bool) → new_ltEs16(yvy100, yvy101)
new_compare30(yvy400, yvy300, app(app(ty_@2, bg), bh)) → new_compare7(yvy400, yvy300, bg, bh)
new_esEs17(@2(yvy40000, yvy40001), @2(yvy30000, yvy30001), gh, ha) → new_asAs(new_esEs29(yvy40000, yvy30000, gh), new_esEs30(yvy40001, yvy30001, ha))
new_esEs11(yvy4000, yvy3000, ty_Char) → new_esEs15(yvy4000, yvy3000)
new_lt20(yvy152, yvy155, app(app(app(ty_@3, bd), be), bf)) → new_lt4(yvy152, yvy155, bd, be, bf)
new_esEs27(yvy1000, yvy1010, ty_Bool) → new_esEs20(yvy1000, yvy1010)
new_ltEs23(yvy166, yvy168, app(ty_Ratio, fde)) → new_ltEs9(yvy166, yvy168, fde)
new_esEs34(yvy152, yvy155, ty_Double) → new_esEs13(yvy152, yvy155)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Double) → new_esEs13(yvy40000, yvy30000)
new_esEs10(yvy4000, yvy3000, ty_Int) → new_esEs25(yvy4000, yvy3000)
new_esEs26(yvy40000, yvy30000, ty_Char) → new_esEs15(yvy40000, yvy30000)
new_compare30(yvy400, yvy300, ty_Int) → new_compare16(yvy400, yvy300)
new_fsEs(yvy306) → new_not(new_esEs12(yvy306, GT))
new_ltEs16(True, False) → False
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, ty_Char) → new_ltEs7(yvy1000, yvy1010)
new_esEs7(yvy4000, yvy3000, ty_Int) → new_esEs25(yvy4000, yvy3000)
new_ltEs19(yvy1002, yvy1012, ty_Bool) → new_ltEs16(yvy1002, yvy1012)
new_esEs34(yvy152, yvy155, ty_Ordering) → new_esEs12(yvy152, yvy155)
new_esEs12(GT, LT) → False
new_esEs12(LT, GT) → False
new_esEs27(yvy1000, yvy1010, ty_Char) → new_esEs15(yvy1000, yvy1010)
new_lt5(yvy1001, yvy1011, ty_Integer) → new_lt15(yvy1001, yvy1011)
new_ltEs22(yvy114, yvy115, ty_Ordering) → new_ltEs6(yvy114, yvy115)
new_compare18(Float(yvy4000, yvy4001), Float(yvy3000, yvy3001)) → new_compare16(new_sr0(yvy4000, yvy3000), new_sr0(yvy4001, yvy3001))
new_ltEs18(yvy107, yvy108, app(ty_Ratio, beb)) → new_ltEs9(yvy107, yvy108, beb)
new_ltEs23(yvy166, yvy168, ty_Float) → new_ltEs11(yvy166, yvy168)
new_ltEs18(yvy107, yvy108, app(ty_[], bea)) → new_ltEs8(yvy107, yvy108, bea)
new_ltEs20(yvy154, yvy157, app(app(ty_@2, eca), ecb)) → new_ltEs12(yvy154, yvy157, eca, ecb)
new_esEs31(yvy40000, yvy30000, app(ty_Maybe, cfd)) → new_esEs23(yvy40000, yvy30000, cfd)
new_lt6(yvy1000, yvy1010, app(ty_Ratio, bfg)) → new_lt10(yvy1000, yvy1010, bfg)
new_esEs37(yvy40000, yvy30000, ty_Integer) → new_esEs18(yvy40000, yvy30000)
new_ltEs14(Left(yvy1000), Left(yvy1010), app(app(ty_@2, dba), dbb), dac) → new_ltEs12(yvy1000, yvy1010, dba, dbb)
new_esEs35(yvy153, yvy156, app(app(ty_@2, eag), eah)) → new_esEs17(yvy153, yvy156, eag, eah)
new_esEs5(yvy4001, yvy3001, app(app(app(ty_@3, bae), baf), bag)) → new_esEs22(yvy4001, yvy3001, bae, baf, bag)
new_lt22(yvy1000, yvy1010, ty_Char) → new_lt8(yvy1000, yvy1010)
new_compare110(yvy233, yvy234, yvy235, yvy236, True, yvy238, ecf, ecg) → new_compare111(yvy233, yvy234, yvy235, yvy236, True, ecf, ecg)
new_ltEs24(yvy100, yvy101, app(app(ty_@2, ech), eda)) → new_ltEs12(yvy100, yvy101, ech, eda)
new_ltEs13(yvy100, yvy101) → new_fsEs(new_compare29(yvy100, yvy101))
new_esEs5(yvy4001, yvy3001, app(app(ty_Either, bba), bbb)) → new_esEs24(yvy4001, yvy3001, bba, bbb)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, ty_Bool) → new_esEs20(yvy40000, yvy30000)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Float) → new_ltEs11(yvy1000, yvy1010)
new_esEs8(yvy4001, yvy3001, ty_Double) → new_esEs13(yvy4001, yvy3001)
new_esEs31(yvy40000, yvy30000, app(ty_Ratio, ceh)) → new_esEs21(yvy40000, yvy30000, ceh)
new_esEs29(yvy40000, yvy30000, app(ty_Maybe, ccc)) → new_esEs23(yvy40000, yvy30000, ccc)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Int) → new_ltEs15(yvy1000, yvy1010)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Double) → new_ltEs13(yvy1000, yvy1010)
new_esEs30(yvy40001, yvy30001, ty_Double) → new_esEs13(yvy40001, yvy30001)
new_ltEs21(yvy1001, yvy1011, app(app(ty_@2, efa), efb)) → new_ltEs12(yvy1001, yvy1011, efa, efb)
new_esEs10(yvy4000, yvy3000, ty_Bool) → new_esEs20(yvy4000, yvy3000)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Char, dac) → new_ltEs7(yvy1000, yvy1010)
new_ltEs16(True, True) → True
new_lt21(yvy153, yvy156, app(app(ty_@2, eag), eah)) → new_lt12(yvy153, yvy156, eag, eah)
new_lt6(yvy1000, yvy1010, ty_Bool) → new_lt18(yvy1000, yvy1010)
new_pePe(False, yvy305) → yvy305
new_compare15(GT, EQ) → GT
new_esEs7(yvy4000, yvy3000, ty_Char) → new_esEs15(yvy4000, yvy3000)
new_esEs31(yvy40000, yvy30000, app(ty_[], cee)) → new_esEs16(yvy40000, yvy30000, cee)
new_esEs39(yvy165, yvy167, ty_@0) → new_esEs19(yvy165, yvy167)
new_esEs23(Just(yvy40000), Just(yvy30000), app(ty_Maybe, ddh)) → new_esEs23(yvy40000, yvy30000, ddh)
new_lt21(yvy153, yvy156, ty_Char) → new_lt8(yvy153, yvy156)
new_esEs26(yvy40000, yvy30000, ty_Bool) → new_esEs20(yvy40000, yvy30000)
new_esEs9(yvy4000, yvy3000, app(app(ty_@2, ffd), ffe)) → new_esEs17(yvy4000, yvy3000, ffd, ffe)
new_compare14(yvy218, yvy219, yvy220, yvy221, yvy222, yvy223, False, ceb, cec, ced) → GT
new_lt9(yvy152, yvy155, dhf) → new_esEs12(new_compare0(yvy152, yvy155, dhf), LT)
new_esEs28(yvy1001, yvy1011, ty_Integer) → new_esEs18(yvy1001, yvy1011)
new_esEs5(yvy4001, yvy3001, ty_Ordering) → new_esEs12(yvy4001, yvy3001)
new_esEs5(yvy4001, yvy3001, ty_Int) → new_esEs25(yvy4001, yvy3001)
new_esEs4(yvy4000, yvy3000, ty_Float) → new_esEs14(yvy4000, yvy3000)
new_compare15(GT, LT) → GT
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Char, hh) → new_esEs15(yvy40000, yvy30000)
new_esEs29(yvy40000, yvy30000, ty_Int) → new_esEs25(yvy40000, yvy30000)
new_compare30(yvy400, yvy300, app(app(ty_Either, eff), efg)) → new_compare27(yvy400, yvy300, eff, efg)
new_lt22(yvy1000, yvy1010, ty_Double) → new_lt13(yvy1000, yvy1010)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Ordering) → new_esEs12(yvy40000, yvy30000)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Char) → new_esEs15(yvy40000, yvy30000)
new_esEs29(yvy40000, yvy30000, app(app(ty_@2, cbe), cbf)) → new_esEs17(yvy40000, yvy30000, cbe, cbf)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, app(app(ty_@2, dfh), dga)) → new_esEs17(yvy40000, yvy30000, dfh, dga)
new_ltEs23(yvy166, yvy168, app(app(ty_Either, fed), fee)) → new_ltEs14(yvy166, yvy168, fed, fee)
new_esEs31(yvy40000, yvy30000, ty_Integer) → new_esEs18(yvy40000, yvy30000)
new_compare12(True, True) → EQ
new_esEs36(yvy1000, yvy1010, app(ty_[], edb)) → new_esEs16(yvy1000, yvy1010, edb)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Ordering, hh) → new_esEs12(yvy40000, yvy30000)
new_ltEs6(GT, EQ) → False
new_ltEs18(yvy107, yvy108, app(app(ty_Either, bfa), bfb)) → new_ltEs14(yvy107, yvy108, bfa, bfb)
new_esEs32(yvy40001, yvy30001, app(ty_Maybe, cgf)) → new_esEs23(yvy40001, yvy30001, cgf)
new_esEs35(yvy153, yvy156, ty_Integer) → new_esEs18(yvy153, yvy156)
new_esEs33(yvy40002, yvy30002, ty_Integer) → new_esEs18(yvy40002, yvy30002)
new_esEs31(yvy40000, yvy30000, ty_Double) → new_esEs13(yvy40000, yvy30000)
new_esEs10(yvy4000, yvy3000, ty_Ordering) → new_esEs12(yvy4000, yvy3000)
new_primCompAux1(yvy400, yvy300, yvy51, h) → new_primCompAux0(yvy51, new_compare30(yvy400, yvy300, h))
new_esEs33(yvy40002, yvy30002, ty_Float) → new_esEs14(yvy40002, yvy30002)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, app(app(app(ty_@3, dca), dcb), dcc)) → new_ltEs10(yvy1000, yvy1010, dca, dcb, dcc)
new_ltEs23(yvy166, yvy168, app(ty_[], fdd)) → new_ltEs8(yvy166, yvy168, fdd)
new_lt23(yvy165, yvy167, app(app(ty_@2, fcg), fch)) → new_lt12(yvy165, yvy167, fcg, fch)
new_esEs34(yvy152, yvy155, ty_Integer) → new_esEs18(yvy152, yvy155)
new_esEs23(Just(yvy40000), Just(yvy30000), app(app(ty_Either, dea), deb)) → new_esEs24(yvy40000, yvy30000, dea, deb)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Ordering, dac) → new_ltEs6(yvy1000, yvy1010)
new_lt22(yvy1000, yvy1010, ty_Bool) → new_lt18(yvy1000, yvy1010)
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_esEs39(yvy165, yvy167, ty_Float) → new_esEs14(yvy165, yvy167)
new_ltEs22(yvy114, yvy115, ty_Bool) → new_ltEs16(yvy114, yvy115)
new_ltEs4(yvy100, yvy101) → new_fsEs(new_compare8(yvy100, yvy101))
new_esEs33(yvy40002, yvy30002, app(ty_[], cha)) → new_esEs16(yvy40002, yvy30002, cha)
new_ltEs8(yvy100, yvy101, fef) → new_fsEs(new_compare0(yvy100, yvy101, fef))
new_compare30(yvy400, yvy300, ty_Char) → new_compare11(yvy400, yvy300)
new_esEs36(yvy1000, yvy1010, ty_Integer) → new_esEs18(yvy1000, yvy1010)
new_esEs39(yvy165, yvy167, ty_Bool) → new_esEs20(yvy165, yvy167)
new_esEs36(yvy1000, yvy1010, ty_Bool) → new_esEs20(yvy1000, yvy1010)
new_esEs32(yvy40001, yvy30001, app(ty_Ratio, cgb)) → new_esEs21(yvy40001, yvy30001, cgb)
new_compare12(False, True) → LT
new_esEs5(yvy4001, yvy3001, ty_Char) → new_esEs15(yvy4001, yvy3001)
new_esEs34(yvy152, yvy155, ty_Char) → new_esEs15(yvy152, yvy155)
new_esEs31(yvy40000, yvy30000, app(app(ty_@2, cef), ceg)) → new_esEs17(yvy40000, yvy30000, cef, ceg)
new_ltEs18(yvy107, yvy108, ty_Integer) → new_ltEs4(yvy107, yvy108)
new_lt21(yvy153, yvy156, ty_@0) → new_lt19(yvy153, yvy156)
new_esEs30(yvy40001, yvy30001, ty_@0) → new_esEs19(yvy40001, yvy30001)
new_ltEs18(yvy107, yvy108, app(ty_Maybe, beh)) → new_ltEs5(yvy107, yvy108, beh)
new_esEs12(LT, LT) → True
new_ltEs24(yvy100, yvy101, ty_Char) → new_ltEs7(yvy100, yvy101)
new_esEs31(yvy40000, yvy30000, app(app(ty_Either, cfe), cff)) → new_esEs24(yvy40000, yvy30000, cfe, cff)
new_ltEs18(yvy107, yvy108, ty_Double) → new_ltEs13(yvy107, yvy108)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Int, dac) → new_ltEs15(yvy1000, yvy1010)
new_esEs28(yvy1001, yvy1011, app(ty_Maybe, bhg)) → new_esEs23(yvy1001, yvy1011, bhg)
new_lt5(yvy1001, yvy1011, ty_@0) → new_lt19(yvy1001, yvy1011)
new_compare15(EQ, LT) → GT
new_pePe(True, yvy305) → True
new_compare0([], [], feh) → EQ
new_primEqNat0(Zero, Zero) → True
new_ltEs21(yvy1001, yvy1011, ty_Double) → new_ltEs13(yvy1001, yvy1011)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Float) → new_esEs14(yvy40000, yvy30000)
new_esEs6(yvy4002, yvy3002, ty_Double) → new_esEs13(yvy4002, yvy3002)
new_esEs4(yvy4000, yvy3000, app(ty_Maybe, hf)) → new_esEs23(yvy4000, yvy3000, hf)
new_lt5(yvy1001, yvy1011, ty_Bool) → new_lt18(yvy1001, yvy1011)
new_lt23(yvy165, yvy167, ty_Integer) → new_lt15(yvy165, yvy167)
new_esEs5(yvy4001, yvy3001, ty_Float) → new_esEs14(yvy4001, yvy3001)
new_lt21(yvy153, yvy156, app(app(ty_Either, ebb), ebc)) → new_lt16(yvy153, yvy156, ebb, ebc)
new_esEs8(yvy4001, yvy3001, app(app(app(ty_@3, dh), ea), eb)) → new_esEs22(yvy4001, yvy3001, dh, ea, eb)
new_lt11(yvy152, yvy155) → new_esEs12(new_compare18(yvy152, yvy155), LT)
new_lt20(yvy152, yvy155, app(ty_[], dhf)) → new_lt9(yvy152, yvy155, dhf)
new_esEs13(Double(yvy40000, yvy40001), Double(yvy30000, yvy30001)) → new_esEs25(new_sr0(yvy40000, yvy30000), new_sr0(yvy40001, yvy30001))
new_esEs7(yvy4000, yvy3000, ty_Bool) → new_esEs20(yvy4000, yvy3000)
new_compare30(yvy400, yvy300, ty_@0) → new_compare9(yvy400, yvy300)
new_esEs29(yvy40000, yvy30000, ty_@0) → new_esEs19(yvy40000, yvy30000)
new_esEs6(yvy4002, yvy3002, ty_Ordering) → new_esEs12(yvy4002, yvy3002)
new_ltEs18(yvy107, yvy108, app(app(app(ty_@3, bec), bed), bee)) → new_ltEs10(yvy107, yvy108, bec, bed, bee)
new_ltEs22(yvy114, yvy115, ty_@0) → new_ltEs17(yvy114, yvy115)
new_lt5(yvy1001, yvy1011, ty_Char) → new_lt8(yvy1001, yvy1011)
new_lt5(yvy1001, yvy1011, app(app(ty_Either, bhh), caa)) → new_lt16(yvy1001, yvy1011, bhh, caa)
new_ltEs19(yvy1002, yvy1012, ty_Ordering) → new_ltEs6(yvy1002, yvy1012)
new_esEs15(Char(yvy40000), Char(yvy30000)) → new_primEqNat0(yvy40000, yvy30000)
new_esEs24(Left(yvy40000), Left(yvy30000), app(app(app(ty_@3, dfa), dfb), dfc), hh) → new_esEs22(yvy40000, yvy30000, dfa, dfb, dfc)
new_esEs26(yvy40000, yvy30000, ty_Int) → new_esEs25(yvy40000, yvy30000)
new_esEs32(yvy40001, yvy30001, ty_Integer) → new_esEs18(yvy40001, yvy30001)
new_ltEs23(yvy166, yvy168, ty_Double) → new_ltEs13(yvy166, yvy168)
new_lt22(yvy1000, yvy1010, app(ty_[], edb)) → new_lt9(yvy1000, yvy1010, edb)
new_ltEs23(yvy166, yvy168, ty_Integer) → new_ltEs4(yvy166, yvy168)
new_esEs9(yvy4000, yvy3000, app(ty_[], ffc)) → new_esEs16(yvy4000, yvy3000, ffc)
new_esEs33(yvy40002, yvy30002, ty_Bool) → new_esEs20(yvy40002, yvy30002)
new_esEs11(yvy4000, yvy3000, ty_Double) → new_esEs13(yvy4000, yvy3000)
new_esEs29(yvy40000, yvy30000, ty_Bool) → new_esEs20(yvy40000, yvy30000)
new_lt5(yvy1001, yvy1011, app(ty_[], bgh)) → new_lt9(yvy1001, yvy1011, bgh)
new_ltEs21(yvy1001, yvy1011, ty_Bool) → new_ltEs16(yvy1001, yvy1011)
new_ltEs6(EQ, GT) → True
new_esEs9(yvy4000, yvy3000, ty_Integer) → new_esEs18(yvy4000, yvy3000)
new_esEs11(yvy4000, yvy3000, ty_Ordering) → new_esEs12(yvy4000, yvy3000)
new_esEs23(Just(yvy40000), Nothing, hf) → False
new_esEs23(Nothing, Just(yvy30000), hf) → False
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_ltEs18(yvy107, yvy108, ty_Ordering) → new_ltEs6(yvy107, yvy108)
new_esEs23(Just(yvy40000), Just(yvy30000), app(app(app(ty_@3, dde), ddf), ddg)) → new_esEs22(yvy40000, yvy30000, dde, ddf, ddg)
new_ltEs24(yvy100, yvy101, ty_Double) → new_ltEs13(yvy100, yvy101)
new_esEs10(yvy4000, yvy3000, ty_Double) → new_esEs13(yvy4000, yvy3000)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, ty_Float) → new_esEs14(yvy40000, yvy30000)
new_compare110(yvy233, yvy234, yvy235, yvy236, False, yvy238, ecf, ecg) → new_compare111(yvy233, yvy234, yvy235, yvy236, yvy238, ecf, ecg)
new_ltEs20(yvy154, yvy157, ty_Bool) → new_ltEs16(yvy154, yvy157)
new_ltEs24(yvy100, yvy101, ty_@0) → new_ltEs17(yvy100, yvy101)
new_ltEs5(Just(yvy1000), Just(yvy1010), app(app(ty_@2, fg), fh)) → new_ltEs12(yvy1000, yvy1010, fg, fh)
new_ltEs20(yvy154, yvy157, ty_Int) → new_ltEs15(yvy154, yvy157)
new_esEs8(yvy4001, yvy3001, ty_@0) → new_esEs19(yvy4001, yvy3001)
new_lt22(yvy1000, yvy1010, app(app(ty_Either, eeb), eec)) → new_lt16(yvy1000, yvy1010, eeb, eec)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Float, dac) → new_ltEs11(yvy1000, yvy1010)
new_compare26(yvy107, yvy108, False, bdg, bdh) → new_compare10(yvy107, yvy108, new_ltEs18(yvy107, yvy108, bdg), bdg, bdh)
new_lt21(yvy153, yvy156, app(ty_Ratio, eac)) → new_lt10(yvy153, yvy156, eac)
new_compare30(yvy400, yvy300, ty_Float) → new_compare18(yvy400, yvy300)
new_primEqInt(Neg(Succ(yvy400000)), Neg(Succ(yvy300000))) → new_primEqNat0(yvy400000, yvy300000)
new_esEs23(Nothing, Nothing, hf) → True
new_esEs10(yvy4000, yvy3000, app(app(app(ty_@3, egd), ege), egf)) → new_esEs22(yvy4000, yvy3000, egd, ege, egf)
new_esEs39(yvy165, yvy167, app(app(ty_@2, fcg), fch)) → new_esEs17(yvy165, yvy167, fcg, fch)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, app(app(ty_@2, dcd), dce)) → new_ltEs12(yvy1000, yvy1010, dcd, dce)
new_ltEs5(Just(yvy1000), Nothing, eh) → False
new_esEs28(yvy1001, yvy1011, ty_Char) → new_esEs15(yvy1001, yvy1011)
new_esEs11(yvy4000, yvy3000, app(ty_Maybe, faa)) → new_esEs23(yvy4000, yvy3000, faa)
new_lt14(yvy152, yvy155, dhg) → new_esEs12(new_compare31(yvy152, yvy155, dhg), LT)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, ty_@0) → new_ltEs17(yvy1000, yvy1010)
new_ltEs14(Right(yvy1000), Left(yvy1010), dbf, dac) → False
new_esEs12(EQ, LT) → False
new_esEs12(LT, EQ) → False
new_ltEs19(yvy1002, yvy1012, app(ty_Ratio, cac)) → new_ltEs9(yvy1002, yvy1012, cac)
new_lt22(yvy1000, yvy1010, app(app(ty_@2, edg), edh)) → new_lt12(yvy1000, yvy1010, edg, edh)
new_ltEs23(yvy166, yvy168, ty_Bool) → new_ltEs16(yvy166, yvy168)
new_compare111(yvy233, yvy234, yvy235, yvy236, True, ecf, ecg) → LT
new_esEs7(yvy4000, yvy3000, app(ty_[], ca)) → new_esEs16(yvy4000, yvy3000, ca)
new_esEs5(yvy4001, yvy3001, ty_Bool) → new_esEs20(yvy4001, yvy3001)
new_lt23(yvy165, yvy167, ty_Int) → new_lt17(yvy165, yvy167)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs30(yvy40001, yvy30001, app(app(app(ty_@3, cdb), cdc), cdd)) → new_esEs22(yvy40001, yvy30001, cdb, cdc, cdd)
new_esEs11(yvy4000, yvy3000, app(app(ty_Either, fab), fac)) → new_esEs24(yvy4000, yvy3000, fab, fac)
new_esEs35(yvy153, yvy156, app(app(app(ty_@3, ead), eae), eaf)) → new_esEs22(yvy153, yvy156, ead, eae, eaf)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, ty_Int) → new_ltEs15(yvy1000, yvy1010)
new_esEs10(yvy4000, yvy3000, app(app(ty_Either, egh), eha)) → new_esEs24(yvy4000, yvy3000, egh, eha)
new_esEs28(yvy1001, yvy1011, ty_Double) → new_esEs13(yvy1001, yvy1011)
new_lt20(yvy152, yvy155, ty_Ordering) → new_lt7(yvy152, yvy155)
new_ltEs6(EQ, EQ) → True
new_compare31(Just(yvy4000), Nothing, ffb) → GT
new_esEs11(yvy4000, yvy3000, app(app(app(ty_@3, ehf), ehg), ehh)) → new_esEs22(yvy4000, yvy3000, ehf, ehg, ehh)
new_ltEs22(yvy114, yvy115, app(app(ty_Either, fbf), fbg)) → new_ltEs14(yvy114, yvy115, fbf, fbg)
new_esEs28(yvy1001, yvy1011, app(app(app(ty_@3, bhb), bhc), bhd)) → new_esEs22(yvy1001, yvy1011, bhb, bhc, bhd)
new_esEs32(yvy40001, yvy30001, ty_Float) → new_esEs14(yvy40001, yvy30001)
new_esEs27(yvy1000, yvy1010, app(ty_Ratio, bfg)) → new_esEs21(yvy1000, yvy1010, bfg)
new_ltEs19(yvy1002, yvy1012, ty_Integer) → new_ltEs4(yvy1002, yvy1012)
new_primEqInt(Neg(Succ(yvy400000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(yvy300000))) → False
new_primCompAux0(yvy56, GT) → GT
new_compare30(yvy400, yvy300, app(app(app(ty_@3, gd), ge), gf)) → new_compare6(yvy400, yvy300, gd, ge, gf)
new_esEs39(yvy165, yvy167, ty_Integer) → new_esEs18(yvy165, yvy167)
new_compare26(yvy107, yvy108, True, bdg, bdh) → EQ
new_esEs23(Just(yvy40000), Just(yvy30000), app(app(ty_@2, ddb), ddc)) → new_esEs17(yvy40000, yvy30000, ddb, ddc)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, app(app(ty_Either, dgg), dgh)) → new_esEs24(yvy40000, yvy30000, dgg, dgh)
new_ltEs6(GT, GT) → True
new_ltEs21(yvy1001, yvy1011, app(app(ty_Either, efd), efe)) → new_ltEs14(yvy1001, yvy1011, efd, efe)
new_esEs38(yvy40001, yvy30001, ty_Integer) → new_esEs18(yvy40001, yvy30001)
new_esEs32(yvy40001, yvy30001, app(ty_[], cfg)) → new_esEs16(yvy40001, yvy30001, cfg)
new_esEs34(yvy152, yvy155, ty_Int) → new_esEs25(yvy152, yvy155)
new_compare31(Nothing, Nothing, ffb) → EQ
new_esEs29(yvy40000, yvy30000, app(ty_[], cbd)) → new_esEs16(yvy40000, yvy30000, cbd)
new_esEs26(yvy40000, yvy30000, app(ty_Ratio, bch)) → new_esEs21(yvy40000, yvy30000, bch)
new_esEs7(yvy4000, yvy3000, app(ty_Maybe, da)) → new_esEs23(yvy4000, yvy3000, da)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_@0) → new_ltEs17(yvy1000, yvy1010)
new_lt21(yvy153, yvy156, app(ty_[], eab)) → new_lt9(yvy153, yvy156, eab)
new_ltEs20(yvy154, yvy157, app(ty_[], ebd)) → new_ltEs8(yvy154, yvy157, ebd)
new_esEs36(yvy1000, yvy1010, ty_Int) → new_esEs25(yvy1000, yvy1010)
new_esEs19(@0, @0) → True
new_compare6(@3(yvy4000, yvy4001, yvy4002), @3(yvy3000, yvy3001, yvy3002), gd, ge, gf) → new_compare25(yvy4000, yvy4001, yvy4002, yvy3000, yvy3001, yvy3002, new_asAs(new_esEs4(yvy4000, yvy3000, gd), new_asAs(new_esEs5(yvy4001, yvy3001, ge), new_esEs6(yvy4002, yvy3002, gf))), gd, ge, gf)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_esEs7(yvy4000, yvy3000, ty_Integer) → new_esEs18(yvy4000, yvy3000)
new_esEs4(yvy4000, yvy3000, ty_Bool) → new_esEs20(yvy4000, yvy3000)
new_esEs39(yvy165, yvy167, ty_Ordering) → new_esEs12(yvy165, yvy167)
new_lt20(yvy152, yvy155, ty_Char) → new_lt8(yvy152, yvy155)
new_esEs31(yvy40000, yvy30000, ty_Bool) → new_esEs20(yvy40000, yvy30000)
new_lt4(yvy152, yvy155, bd, be, bf) → new_esEs12(new_compare6(yvy152, yvy155, bd, be, bf), LT)
new_esEs6(yvy4002, yvy3002, ty_Int) → new_esEs25(yvy4002, yvy3002)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Double, dac) → new_ltEs13(yvy1000, yvy1010)
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_lt6(yvy1000, yvy1010, app(ty_Maybe, bge)) → new_lt14(yvy1000, yvy1010, bge)
new_ltEs14(Left(yvy1000), Left(yvy1010), app(ty_Maybe, dbc), dac) → new_ltEs5(yvy1000, yvy1010, dbc)
new_esEs4(yvy4000, yvy3000, app(ty_Ratio, hb)) → new_esEs21(yvy4000, yvy3000, hb)
new_lt5(yvy1001, yvy1011, app(ty_Maybe, bhg)) → new_lt14(yvy1001, yvy1011, bhg)
new_primEqInt(Pos(Succ(yvy400000)), Pos(Succ(yvy300000))) → new_primEqNat0(yvy400000, yvy300000)
new_compare10(yvy199, yvy200, False, ef, eg) → GT
new_esEs34(yvy152, yvy155, app(ty_Maybe, dhg)) → new_esEs23(yvy152, yvy155, dhg)
new_esEs5(yvy4001, yvy3001, app(ty_[], baa)) → new_esEs16(yvy4001, yvy3001, baa)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, ty_Double) → new_ltEs13(yvy1000, yvy1010)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, ty_Integer) → new_ltEs4(yvy1000, yvy1010)
new_ltEs21(yvy1001, yvy1011, ty_Float) → new_ltEs11(yvy1001, yvy1011)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, app(ty_Maybe, dcf)) → new_ltEs5(yvy1000, yvy1010, dcf)
new_compare13(:%(yvy4000, yvy4001), :%(yvy3000, yvy3001), ty_Int) → new_compare16(new_sr0(yvy4000, yvy3001), new_sr0(yvy3000, yvy4001))
new_esEs26(yvy40000, yvy30000, app(ty_Maybe, bdd)) → new_esEs23(yvy40000, yvy30000, bdd)
new_ltEs24(yvy100, yvy101, ty_Float) → new_ltEs11(yvy100, yvy101)
new_esEs34(yvy152, yvy155, app(app(ty_@2, dec), ded)) → new_esEs17(yvy152, yvy155, dec, ded)
new_esEs8(yvy4001, yvy3001, ty_Integer) → new_esEs18(yvy4001, yvy3001)
new_ltEs22(yvy114, yvy115, app(app(app(ty_@3, fah), fba), fbb)) → new_ltEs10(yvy114, yvy115, fah, fba, fbb)
new_primEqNat0(Succ(yvy400000), Succ(yvy300000)) → new_primEqNat0(yvy400000, yvy300000)
new_esEs6(yvy4002, yvy3002, ty_Bool) → new_esEs20(yvy4002, yvy3002)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Ordering) → new_ltEs6(yvy1000, yvy1010)
new_ltEs24(yvy100, yvy101, ty_Int) → new_ltEs15(yvy100, yvy101)
new_esEs26(yvy40000, yvy30000, ty_Ordering) → new_esEs12(yvy40000, yvy30000)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, app(ty_Ratio, dgb)) → new_esEs21(yvy40000, yvy30000, dgb)
new_esEs11(yvy4000, yvy3000, app(ty_Ratio, ehe)) → new_esEs21(yvy4000, yvy3000, ehe)
new_esEs30(yvy40001, yvy30001, ty_Integer) → new_esEs18(yvy40001, yvy30001)
new_esEs39(yvy165, yvy167, ty_Char) → new_esEs15(yvy165, yvy167)
new_ltEs14(Left(yvy1000), Left(yvy1010), app(ty_Ratio, dae), dac) → new_ltEs9(yvy1000, yvy1010, dae)
new_esEs26(yvy40000, yvy30000, app(app(ty_@2, bcf), bcg)) → new_esEs17(yvy40000, yvy30000, bcf, bcg)
new_lt5(yvy1001, yvy1011, ty_Float) → new_lt11(yvy1001, yvy1011)
new_esEs32(yvy40001, yvy30001, ty_@0) → new_esEs19(yvy40001, yvy30001)
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_esEs33(yvy40002, yvy30002, app(ty_Maybe, chh)) → new_esEs23(yvy40002, yvy30002, chh)
new_lt6(yvy1000, yvy1010, ty_Int) → new_lt17(yvy1000, yvy1010)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, app(app(app(ty_@3, dgc), dgd), dge)) → new_esEs22(yvy40000, yvy30000, dgc, dgd, dge)
new_lt23(yvy165, yvy167, app(app(ty_Either, fdb), fdc)) → new_lt16(yvy165, yvy167, fdb, fdc)
new_esEs12(EQ, EQ) → True
new_lt23(yvy165, yvy167, ty_Char) → new_lt8(yvy165, yvy167)
new_ltEs18(yvy107, yvy108, app(app(ty_@2, bef), beg)) → new_ltEs12(yvy107, yvy108, bef, beg)
new_lt21(yvy153, yvy156, ty_Double) → new_lt13(yvy153, yvy156)
new_esEs35(yvy153, yvy156, ty_Ordering) → new_esEs12(yvy153, yvy156)
new_lt5(yvy1001, yvy1011, ty_Int) → new_lt17(yvy1001, yvy1011)
new_esEs10(yvy4000, yvy3000, ty_Char) → new_esEs15(yvy4000, yvy3000)
new_primEqInt(Pos(Succ(yvy400000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(yvy300000))) → False
new_ltEs5(Nothing, Just(yvy1010), eh) → True
new_lt20(yvy152, yvy155, ty_Int) → new_lt17(yvy152, yvy155)
new_esEs35(yvy153, yvy156, app(ty_Maybe, eba)) → new_esEs23(yvy153, yvy156, eba)
new_esEs27(yvy1000, yvy1010, ty_@0) → new_esEs19(yvy1000, yvy1010)
new_ltEs18(yvy107, yvy108, ty_Float) → new_ltEs11(yvy107, yvy108)
new_compare25(yvy152, yvy153, yvy154, yvy155, yvy156, yvy157, True, dhc, dhd, dhe) → EQ
new_esEs37(yvy40000, yvy30000, ty_Int) → new_esEs25(yvy40000, yvy30000)
new_primCmpNat0(Zero, Zero) → EQ
new_esEs27(yvy1000, yvy1010, app(app(ty_Either, bgf), bgg)) → new_esEs24(yvy1000, yvy1010, bgf, bgg)
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_compare27(Left(yvy4000), Right(yvy3000), eff, efg) → LT
new_lt22(yvy1000, yvy1010, ty_@0) → new_lt19(yvy1000, yvy1010)
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_compare9(@0, @0) → EQ
new_esEs28(yvy1001, yvy1011, ty_Int) → new_esEs25(yvy1001, yvy1011)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Float, hh) → new_esEs14(yvy40000, yvy30000)
new_esEs6(yvy4002, yvy3002, ty_Float) → new_esEs14(yvy4002, yvy3002)
new_ltEs9(yvy100, yvy101, cdh) → new_fsEs(new_compare13(yvy100, yvy101, cdh))
new_compare17(yvy218, yvy219, yvy220, yvy221, yvy222, yvy223, True, yvy225, ceb, cec, ced) → new_compare14(yvy218, yvy219, yvy220, yvy221, yvy222, yvy223, True, ceb, cec, ced)
new_esEs32(yvy40001, yvy30001, ty_Char) → new_esEs15(yvy40001, yvy30001)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_ltEs14(Left(yvy1000), Left(yvy1010), app(ty_[], dad), dac) → new_ltEs8(yvy1000, yvy1010, dad)
new_ltEs19(yvy1002, yvy1012, app(app(ty_@2, cag), cah)) → new_ltEs12(yvy1002, yvy1012, cag, cah)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Double, hh) → new_esEs13(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, app(app(ty_Either, daa), dab)) → new_esEs24(yvy40002, yvy30002, daa, dab)
new_esEs4(yvy4000, yvy3000, ty_Int) → new_esEs25(yvy4000, yvy3000)
new_compare28(yvy114, yvy115, True, fad, fae) → EQ
new_primEqInt(Pos(Succ(yvy400000)), Neg(yvy30000)) → False
new_primEqInt(Neg(Succ(yvy400000)), Pos(yvy30000)) → False
new_esEs24(Right(yvy40000), Right(yvy30000), hg, ty_Int) → new_esEs25(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, ty_Ordering) → new_esEs12(yvy40002, yvy30002)
new_esEs29(yvy40000, yvy30000, app(app(app(ty_@3, cbh), cca), ccb)) → new_esEs22(yvy40000, yvy30000, cbh, cca, ccb)
new_esEs26(yvy40000, yvy30000, ty_Double) → new_esEs13(yvy40000, yvy30000)
new_ltEs20(yvy154, yvy157, ty_Integer) → new_ltEs4(yvy154, yvy157)
new_compare210(yvy100, yvy101, True, feg) → EQ
new_lt6(yvy1000, yvy1010, ty_Ordering) → new_lt7(yvy1000, yvy1010)
new_esEs29(yvy40000, yvy30000, app(ty_Ratio, cbg)) → new_esEs21(yvy40000, yvy30000, cbg)
new_esEs20(False, False) → True
new_esEs24(Left(yvy40000), Left(yvy30000), app(ty_[], dee), hh) → new_esEs16(yvy40000, yvy30000, dee)
new_lt23(yvy165, yvy167, app(ty_[], fcb)) → new_lt9(yvy165, yvy167, fcb)
new_ltEs22(yvy114, yvy115, ty_Integer) → new_ltEs4(yvy114, yvy115)
new_ltEs5(Just(yvy1000), Just(yvy1010), app(app(ty_Either, gb), gc)) → new_ltEs14(yvy1000, yvy1010, gb, gc)
new_lt23(yvy165, yvy167, ty_Bool) → new_lt18(yvy165, yvy167)
new_esEs30(yvy40001, yvy30001, ty_Ordering) → new_esEs12(yvy40001, yvy30001)
new_lt6(yvy1000, yvy1010, ty_Integer) → new_lt15(yvy1000, yvy1010)
new_primEqInt(Pos(Zero), Neg(Succ(yvy300000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(yvy300000))) → False
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_compare30(yvy400, yvy300, app(ty_Maybe, ffb)) → new_compare31(yvy400, yvy300, ffb)
new_esEs9(yvy4000, yvy3000, ty_Ordering) → new_esEs12(yvy4000, yvy3000)
new_esEs7(yvy4000, yvy3000, ty_@0) → new_esEs19(yvy4000, yvy3000)
new_esEs11(yvy4000, yvy3000, ty_Float) → new_esEs14(yvy4000, yvy3000)
new_lt6(yvy1000, yvy1010, app(ty_[], bff)) → new_lt9(yvy1000, yvy1010, bff)
new_esEs36(yvy1000, yvy1010, ty_@0) → new_esEs19(yvy1000, yvy1010)
new_esEs5(yvy4001, yvy3001, ty_@0) → new_esEs19(yvy4001, yvy3001)
new_esEs36(yvy1000, yvy1010, app(app(app(ty_@3, edd), ede), edf)) → new_esEs22(yvy1000, yvy1010, edd, ede, edf)
new_esEs28(yvy1001, yvy1011, ty_Ordering) → new_esEs12(yvy1001, yvy1011)
new_esEs10(yvy4000, yvy3000, app(ty_[], efh)) → new_esEs16(yvy4000, yvy3000, efh)
new_primCompAux0(yvy56, LT) → LT
new_esEs6(yvy4002, yvy3002, app(app(ty_Either, bcc), bcd)) → new_esEs24(yvy4002, yvy3002, bcc, bcd)
new_esEs6(yvy4002, yvy3002, ty_Integer) → new_esEs18(yvy4002, yvy3002)
new_esEs36(yvy1000, yvy1010, app(app(ty_@2, edg), edh)) → new_esEs17(yvy1000, yvy1010, edg, edh)
new_esEs7(yvy4000, yvy3000, app(app(ty_@2, cb), cc)) → new_esEs17(yvy4000, yvy3000, cb, cc)
new_esEs9(yvy4000, yvy3000, ty_Float) → new_esEs14(yvy4000, yvy3000)
new_lt5(yvy1001, yvy1011, ty_Double) → new_lt13(yvy1001, yvy1011)
new_ltEs22(yvy114, yvy115, app(ty_Maybe, fbe)) → new_ltEs5(yvy114, yvy115, fbe)
new_not(False) → True
new_esEs27(yvy1000, yvy1010, ty_Int) → new_esEs25(yvy1000, yvy1010)
new_esEs34(yvy152, yvy155, app(ty_Ratio, cea)) → new_esEs21(yvy152, yvy155, cea)
new_compare30(yvy400, yvy300, ty_Bool) → new_compare12(yvy400, yvy300)
new_esEs25(yvy4000, yvy3000) → new_primEqInt(yvy4000, yvy3000)
new_esEs28(yvy1001, yvy1011, app(ty_[], bgh)) → new_esEs16(yvy1001, yvy1011, bgh)
new_esEs31(yvy40000, yvy30000, ty_Char) → new_esEs15(yvy40000, yvy30000)
new_esEs14(Float(yvy40000, yvy40001), Float(yvy30000, yvy30001)) → new_esEs25(new_sr0(yvy40000, yvy30000), new_sr0(yvy40001, yvy30001))
new_esEs11(yvy4000, yvy3000, ty_@0) → new_esEs19(yvy4000, yvy3000)
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_esEs12(GT, EQ) → False
new_esEs12(EQ, GT) → False
new_esEs36(yvy1000, yvy1010, ty_Float) → new_esEs14(yvy1000, yvy1010)
new_esEs4(yvy4000, yvy3000, ty_Ordering) → new_esEs12(yvy4000, yvy3000)
new_esEs9(yvy4000, yvy3000, app(app(ty_Either, fgc), fgd)) → new_esEs24(yvy4000, yvy3000, fgc, fgd)
new_lt6(yvy1000, yvy1010, app(app(app(ty_@3, bfh), bga), bgb)) → new_lt4(yvy1000, yvy1010, bfh, bga, bgb)
new_esEs4(yvy4000, yvy3000, app(app(ty_@2, gh), ha)) → new_esEs17(yvy4000, yvy3000, gh, ha)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, ty_Integer) → new_esEs18(yvy40000, yvy30000)
new_ltEs18(yvy107, yvy108, ty_@0) → new_ltEs17(yvy107, yvy108)
new_esEs39(yvy165, yvy167, ty_Int) → new_esEs25(yvy165, yvy167)
new_compare15(LT, EQ) → LT
new_esEs34(yvy152, yvy155, ty_Float) → new_esEs14(yvy152, yvy155)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, app(ty_[], dbg)) → new_ltEs8(yvy1000, yvy1010, dbg)
new_esEs36(yvy1000, yvy1010, app(ty_Ratio, edc)) → new_esEs21(yvy1000, yvy1010, edc)
new_esEs30(yvy40001, yvy30001, app(ty_Ratio, cda)) → new_esEs21(yvy40001, yvy30001, cda)
new_compare30(yvy400, yvy300, app(ty_Ratio, ffa)) → new_compare13(yvy400, yvy300, ffa)
new_esEs24(Left(yvy40000), Right(yvy30000), hg, hh) → False
new_esEs24(Right(yvy40000), Left(yvy30000), hg, hh) → False
new_lt20(yvy152, yvy155, app(app(ty_Either, dhh), eaa)) → new_lt16(yvy152, yvy155, dhh, eaa)
new_esEs30(yvy40001, yvy30001, app(app(ty_@2, ccg), cch)) → new_esEs17(yvy40001, yvy30001, ccg, cch)
new_esEs32(yvy40001, yvy30001, app(app(ty_Either, cgg), cgh)) → new_esEs24(yvy40001, yvy30001, cgg, cgh)
new_esEs34(yvy152, yvy155, app(ty_[], dhf)) → new_esEs16(yvy152, yvy155, dhf)
new_lt20(yvy152, yvy155, ty_Double) → new_lt13(yvy152, yvy155)
new_esEs35(yvy153, yvy156, ty_Double) → new_esEs13(yvy153, yvy156)
new_compare0(:(yvy4000, yvy4001), [], feh) → GT
new_lt6(yvy1000, yvy1010, ty_Char) → new_lt8(yvy1000, yvy1010)
new_esEs8(yvy4001, yvy3001, ty_Int) → new_esEs25(yvy4001, yvy3001)
new_esEs38(yvy40001, yvy30001, ty_Int) → new_esEs25(yvy40001, yvy30001)
new_ltEs24(yvy100, yvy101, ty_Integer) → new_ltEs4(yvy100, yvy101)
new_ltEs20(yvy154, yvy157, app(ty_Maybe, ecc)) → new_ltEs5(yvy154, yvy157, ecc)
new_ltEs20(yvy154, yvy157, ty_@0) → new_ltEs17(yvy154, yvy157)
new_ltEs24(yvy100, yvy101, app(app(ty_Either, dbf), dac)) → new_ltEs14(yvy100, yvy101, dbf, dac)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Int) → new_esEs25(yvy40000, yvy30000)
new_esEs34(yvy152, yvy155, app(app(ty_Either, dhh), eaa)) → new_esEs24(yvy152, yvy155, dhh, eaa)
new_lt13(yvy152, yvy155) → new_esEs12(new_compare29(yvy152, yvy155), LT)
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_esEs30(yvy40001, yvy30001, app(app(ty_Either, cdf), cdg)) → new_esEs24(yvy40001, yvy30001, cdf, cdg)
new_lt19(yvy152, yvy155) → new_esEs12(new_compare9(yvy152, yvy155), LT)
new_ltEs18(yvy107, yvy108, ty_Char) → new_ltEs7(yvy107, yvy108)
new_esEs4(yvy4000, yvy3000, app(app(ty_Either, hg), hh)) → new_esEs24(yvy4000, yvy3000, hg, hh)
new_esEs8(yvy4001, yvy3001, app(ty_Ratio, dg)) → new_esEs21(yvy4001, yvy3001, dg)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Integer) → new_esEs18(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, app(ty_Ratio, chd)) → new_esEs21(yvy40002, yvy30002, chd)
new_lt17(yvy152, yvy155) → new_esEs12(new_compare16(yvy152, yvy155), LT)
new_esEs10(yvy4000, yvy3000, app(app(ty_@2, ega), egb)) → new_esEs17(yvy4000, yvy3000, ega, egb)
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_ltEs7(yvy100, yvy101) → new_fsEs(new_compare11(yvy100, yvy101))
new_esEs31(yvy40000, yvy30000, ty_Float) → new_esEs14(yvy40000, yvy30000)
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_compare15(EQ, GT) → LT
new_esEs32(yvy40001, yvy30001, ty_Int) → new_esEs25(yvy40001, yvy30001)
new_esEs29(yvy40000, yvy30000, ty_Char) → new_esEs15(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, app(app(app(ty_@3, che), chf), chg)) → new_esEs22(yvy40002, yvy30002, che, chf, chg)
new_primEqNat0(Zero, Succ(yvy300000)) → False
new_primEqNat0(Succ(yvy400000), Zero) → False
new_compare15(LT, GT) → LT
new_lt15(yvy152, yvy155) → new_esEs12(new_compare8(yvy152, yvy155), LT)
new_ltEs5(Nothing, Nothing, eh) → True
new_ltEs23(yvy166, yvy168, app(app(app(ty_@3, fdf), fdg), fdh)) → new_ltEs10(yvy166, yvy168, fdf, fdg, fdh)
new_lt20(yvy152, yvy155, app(app(ty_@2, dec), ded)) → new_lt12(yvy152, yvy155, dec, ded)
new_ltEs6(LT, LT) → True
new_ltEs6(EQ, LT) → False
new_esEs6(yvy4002, yvy3002, app(ty_Ratio, bbf)) → new_esEs21(yvy4002, yvy3002, bbf)
new_ltEs5(Just(yvy1000), Just(yvy1010), app(ty_[], fa)) → new_ltEs8(yvy1000, yvy1010, fa)
new_ltEs19(yvy1002, yvy1012, ty_Char) → new_ltEs7(yvy1002, yvy1012)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_ltEs21(yvy1001, yvy1011, app(ty_Ratio, eee)) → new_ltEs9(yvy1001, yvy1011, eee)
new_esEs9(yvy4000, yvy3000, app(ty_Maybe, fgb)) → new_esEs23(yvy4000, yvy3000, fgb)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Bool) → new_ltEs16(yvy1000, yvy1010)
new_lt21(yvy153, yvy156, app(ty_Maybe, eba)) → new_lt14(yvy153, yvy156, eba)
new_compare15(GT, GT) → EQ
new_esEs11(yvy4000, yvy3000, app(app(ty_@2, ehc), ehd)) → new_esEs17(yvy4000, yvy3000, ehc, ehd)
new_esEs8(yvy4001, yvy3001, app(app(ty_Either, ed), ee)) → new_esEs24(yvy4001, yvy3001, ed, ee)
new_compare24(yvy165, yvy166, yvy167, yvy168, True, fbh, fca) → EQ
new_esEs32(yvy40001, yvy30001, ty_Bool) → new_esEs20(yvy40001, yvy30001)
new_lt21(yvy153, yvy156, ty_Float) → new_lt11(yvy153, yvy156)
new_esEs16(:(yvy40000, yvy40001), [], gg) → False
new_esEs16([], :(yvy30000, yvy30001), gg) → False
new_compare31(Just(yvy4000), Just(yvy3000), ffb) → new_compare210(yvy4000, yvy3000, new_esEs9(yvy4000, yvy3000, ffb), ffb)
new_lt21(yvy153, yvy156, ty_Ordering) → new_lt7(yvy153, yvy156)
new_lt20(yvy152, yvy155, ty_Bool) → new_lt18(yvy152, yvy155)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, app(ty_Ratio, dbh)) → new_ltEs9(yvy1000, yvy1010, dbh)
new_ltEs19(yvy1002, yvy1012, ty_@0) → new_ltEs17(yvy1002, yvy1012)
new_esEs7(yvy4000, yvy3000, app(app(app(ty_@3, ce), cf), cg)) → new_esEs22(yvy4000, yvy3000, ce, cf, cg)
new_esEs5(yvy4001, yvy3001, ty_Integer) → new_esEs18(yvy4001, yvy3001)
new_esEs31(yvy40000, yvy30000, ty_Int) → new_esEs25(yvy40000, yvy30000)
new_esEs27(yvy1000, yvy1010, app(app(app(ty_@3, bfh), bga), bgb)) → new_esEs22(yvy1000, yvy1010, bfh, bga, bgb)
new_ltEs19(yvy1002, yvy1012, app(ty_Maybe, cba)) → new_ltEs5(yvy1002, yvy1012, cba)
new_lt21(yvy153, yvy156, ty_Integer) → new_lt15(yvy153, yvy156)
new_esEs29(yvy40000, yvy30000, app(app(ty_Either, ccd), cce)) → new_esEs24(yvy40000, yvy30000, ccd, cce)
new_esEs10(yvy4000, yvy3000, app(ty_Ratio, egc)) → new_esEs21(yvy4000, yvy3000, egc)
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_ltEs12(@2(yvy1000, yvy1001), @2(yvy1010, yvy1011), ech, eda) → new_pePe(new_lt22(yvy1000, yvy1010, ech), new_asAs(new_esEs36(yvy1000, yvy1010, ech), new_ltEs21(yvy1001, yvy1011, eda)))
new_ltEs23(yvy166, yvy168, ty_@0) → new_ltEs17(yvy166, yvy168)
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_esEs5(yvy4001, yvy3001, app(ty_Maybe, bah)) → new_esEs23(yvy4001, yvy3001, bah)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Char) → new_ltEs7(yvy1000, yvy1010)
new_compare0(:(yvy4000, yvy4001), :(yvy3000, yvy3001), feh) → new_primCompAux1(yvy4000, yvy3000, new_compare0(yvy4001, yvy3001, feh), feh)
new_esEs20(False, True) → False
new_esEs20(True, False) → False
new_compare19(yvy206, yvy207, True, dha, dhb) → LT
new_sr0(yvy3000, yvy4001) → new_primMulInt(yvy3000, yvy4001)
new_esEs28(yvy1001, yvy1011, app(app(ty_@2, bhe), bhf)) → new_esEs17(yvy1001, yvy1011, bhe, bhf)
new_lt6(yvy1000, yvy1010, app(app(ty_Either, bgf), bgg)) → new_lt16(yvy1000, yvy1010, bgf, bgg)
new_esEs34(yvy152, yvy155, ty_Bool) → new_esEs20(yvy152, yvy155)
new_lt22(yvy1000, yvy1010, ty_Integer) → new_lt15(yvy1000, yvy1010)
new_esEs26(yvy40000, yvy30000, app(app(ty_Either, bde), bdf)) → new_esEs24(yvy40000, yvy30000, bde, bdf)
new_compare30(yvy400, yvy300, ty_Ordering) → new_compare15(yvy400, yvy300)
new_esEs30(yvy40001, yvy30001, app(ty_[], ccf)) → new_esEs16(yvy40001, yvy30001, ccf)
new_esEs24(Left(yvy40000), Left(yvy30000), app(app(ty_@2, def), deg), hh) → new_esEs17(yvy40000, yvy30000, def, deg)
new_lt23(yvy165, yvy167, ty_@0) → new_lt19(yvy165, yvy167)
new_esEs10(yvy4000, yvy3000, ty_Float) → new_esEs14(yvy4000, yvy3000)
new_compare29(Double(yvy4000, yvy4001), Double(yvy3000, yvy3001)) → new_compare16(new_sr0(yvy4000, yvy3000), new_sr0(yvy4001, yvy3001))
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, ty_Bool) → new_ltEs16(yvy1000, yvy1010)
new_ltEs22(yvy114, yvy115, app(ty_[], faf)) → new_ltEs8(yvy114, yvy115, faf)
new_esEs39(yvy165, yvy167, app(app(ty_Either, fdb), fdc)) → new_esEs24(yvy165, yvy167, fdb, fdc)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs32(yvy40001, yvy30001, ty_Double) → new_esEs13(yvy40001, yvy30001)
new_esEs28(yvy1001, yvy1011, ty_Bool) → new_esEs20(yvy1001, yvy1011)
new_esEs23(Just(yvy40000), Just(yvy30000), app(ty_Ratio, ddd)) → new_esEs21(yvy40000, yvy30000, ddd)
new_esEs5(yvy4001, yvy3001, app(ty_Ratio, bad)) → new_esEs21(yvy4001, yvy3001, bad)
new_ltEs14(Left(yvy1000), Right(yvy1010), dbf, dac) → True
new_compare24(yvy165, yvy166, yvy167, yvy168, False, fbh, fca) → new_compare110(yvy165, yvy166, yvy167, yvy168, new_lt23(yvy165, yvy167, fbh), new_asAs(new_esEs39(yvy165, yvy167, fbh), new_ltEs23(yvy166, yvy168, fca)), fbh, fca)
new_compare30(yvy400, yvy300, app(ty_[], feh)) → new_compare0(yvy400, yvy300, feh)
new_esEs9(yvy4000, yvy3000, app(ty_Ratio, fff)) → new_esEs21(yvy4000, yvy3000, fff)
new_ltEs20(yvy154, yvy157, app(app(ty_Either, ecd), ece)) → new_ltEs14(yvy154, yvy157, ecd, ece)
new_asAs(False, yvy184) → False
new_compare27(Right(yvy4000), Left(yvy3000), eff, efg) → GT
new_esEs36(yvy1000, yvy1010, app(ty_Maybe, eea)) → new_esEs23(yvy1000, yvy1010, eea)
new_esEs9(yvy4000, yvy3000, ty_Double) → new_esEs13(yvy4000, yvy3000)
new_ltEs19(yvy1002, yvy1012, app(app(ty_Either, cbb), cbc)) → new_ltEs14(yvy1002, yvy1012, cbb, cbc)
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_lt20(yvy152, yvy155, ty_@0) → new_lt19(yvy152, yvy155)
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_esEs4(yvy4000, yvy3000, ty_@0) → new_esEs19(yvy4000, yvy3000)
new_esEs27(yvy1000, yvy1010, ty_Double) → new_esEs13(yvy1000, yvy1010)
new_esEs36(yvy1000, yvy1010, ty_Ordering) → new_esEs12(yvy1000, yvy1010)
new_compare16(yvy400, yvy300) → new_primCmpInt(yvy400, yvy300)
new_esEs35(yvy153, yvy156, ty_Bool) → new_esEs20(yvy153, yvy156)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Bool) → new_esEs20(yvy40000, yvy30000)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Integer, dac) → new_ltEs4(yvy1000, yvy1010)
new_compare14(yvy218, yvy219, yvy220, yvy221, yvy222, yvy223, True, ceb, cec, ced) → LT
new_esEs30(yvy40001, yvy30001, app(ty_Maybe, cde)) → new_esEs23(yvy40001, yvy30001, cde)
new_esEs8(yvy4001, yvy3001, ty_Char) → new_esEs15(yvy4001, yvy3001)
new_esEs9(yvy4000, yvy3000, ty_Bool) → new_esEs20(yvy4000, yvy3000)
new_lt5(yvy1001, yvy1011, ty_Ordering) → new_lt7(yvy1001, yvy1011)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, ty_Ordering) → new_ltEs6(yvy1000, yvy1010)
new_esEs24(Left(yvy40000), Left(yvy30000), app(app(ty_Either, dfe), dff), hh) → new_esEs24(yvy40000, yvy30000, dfe, dff)
new_esEs8(yvy4001, yvy3001, app(ty_[], dd)) → new_esEs16(yvy4001, yvy3001, dd)
new_compare27(Left(yvy4000), Left(yvy3000), eff, efg) → new_compare26(yvy4000, yvy3000, new_esEs10(yvy4000, yvy3000, eff), eff, efg)
new_esEs29(yvy40000, yvy30000, ty_Double) → new_esEs13(yvy40000, yvy30000)
new_esEs27(yvy1000, yvy1010, ty_Integer) → new_esEs18(yvy1000, yvy1010)
new_esEs18(Integer(yvy40000), Integer(yvy30000)) → new_primEqInt(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, ty_Char) → new_esEs15(yvy40002, yvy30002)
new_ltEs5(Just(yvy1000), Just(yvy1010), app(ty_Maybe, ga)) → new_ltEs5(yvy1000, yvy1010, ga)
new_ltEs11(yvy100, yvy101) → new_fsEs(new_compare18(yvy100, yvy101))
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, app(app(ty_Either, dcg), dch)) → new_ltEs14(yvy1000, yvy1010, dcg, dch)
new_esEs30(yvy40001, yvy30001, ty_Float) → new_esEs14(yvy40001, yvy30001)
new_lt23(yvy165, yvy167, ty_Float) → new_lt11(yvy165, yvy167)
new_compare12(False, False) → EQ
new_esEs28(yvy1001, yvy1011, ty_@0) → new_esEs19(yvy1001, yvy1011)
new_ltEs23(yvy166, yvy168, ty_Char) → new_ltEs7(yvy166, yvy168)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, app(ty_Maybe, dgf)) → new_esEs23(yvy40000, yvy30000, dgf)
new_esEs29(yvy40000, yvy30000, ty_Float) → new_esEs14(yvy40000, yvy30000)
new_esEs7(yvy4000, yvy3000, ty_Ordering) → new_esEs12(yvy4000, yvy3000)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Integer, hh) → new_esEs18(yvy40000, yvy30000)
new_lt20(yvy152, yvy155, app(ty_Maybe, dhg)) → new_lt14(yvy152, yvy155, dhg)
new_esEs39(yvy165, yvy167, app(app(app(ty_@3, fcd), fce), fcf)) → new_esEs22(yvy165, yvy167, fcd, fce, fcf)
new_esEs31(yvy40000, yvy30000, ty_@0) → new_esEs19(yvy40000, yvy30000)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, app(ty_[], dfg)) → new_esEs16(yvy40000, yvy30000, dfg)
new_compare111(yvy233, yvy234, yvy235, yvy236, False, ecf, ecg) → GT
new_lt21(yvy153, yvy156, ty_Bool) → new_lt18(yvy153, yvy156)
new_ltEs6(LT, GT) → True
new_esEs33(yvy40002, yvy30002, ty_Int) → new_esEs25(yvy40002, yvy30002)
new_compare30(yvy400, yvy300, ty_Integer) → new_compare8(yvy400, yvy300)
new_ltEs23(yvy166, yvy168, app(ty_Maybe, fec)) → new_ltEs5(yvy166, yvy168, fec)
new_lt23(yvy165, yvy167, app(ty_Maybe, fda)) → new_lt14(yvy165, yvy167, fda)
new_ltEs21(yvy1001, yvy1011, ty_Char) → new_ltEs7(yvy1001, yvy1011)
new_ltEs14(Left(yvy1000), Left(yvy1010), app(app(ty_Either, dbd), dbe), dac) → new_ltEs14(yvy1000, yvy1010, dbd, dbe)
new_ltEs23(yvy166, yvy168, app(app(ty_@2, fea), feb)) → new_ltEs12(yvy166, yvy168, fea, feb)
new_ltEs21(yvy1001, yvy1011, ty_Ordering) → new_ltEs6(yvy1001, yvy1011)
new_esEs32(yvy40001, yvy30001, app(app(ty_@2, cfh), cga)) → new_esEs17(yvy40001, yvy30001, cfh, cga)
new_esEs24(Left(yvy40000), Left(yvy30000), app(ty_Maybe, dfd), hh) → new_esEs23(yvy40000, yvy30000, dfd)
new_lt22(yvy1000, yvy1010, app(ty_Ratio, edc)) → new_lt10(yvy1000, yvy1010, edc)
new_lt12(yvy152, yvy155, dec, ded) → new_esEs12(new_compare7(yvy152, yvy155, dec, ded), LT)
new_esEs35(yvy153, yvy156, ty_Int) → new_esEs25(yvy153, yvy156)
new_lt10(yvy152, yvy155, cea) → new_esEs12(new_compare13(yvy152, yvy155, cea), LT)
new_esEs4(yvy4000, yvy3000, ty_Double) → new_esEs13(yvy4000, yvy3000)
new_esEs8(yvy4001, yvy3001, app(app(ty_@2, de), df)) → new_esEs17(yvy4001, yvy3001, de, df)
new_esEs5(yvy4001, yvy3001, app(app(ty_@2, bab), bac)) → new_esEs17(yvy4001, yvy3001, bab, bac)
new_esEs16([], [], gg) → True
new_lt22(yvy1000, yvy1010, ty_Float) → new_lt11(yvy1000, yvy1010)
new_esEs32(yvy40001, yvy30001, ty_Ordering) → new_esEs12(yvy40001, yvy30001)
new_ltEs19(yvy1002, yvy1012, ty_Int) → new_ltEs15(yvy1002, yvy1012)
new_ltEs21(yvy1001, yvy1011, ty_Integer) → new_ltEs4(yvy1001, yvy1011)
new_ltEs20(yvy154, yvy157, ty_Float) → new_ltEs11(yvy154, yvy157)
new_lt5(yvy1001, yvy1011, app(app(ty_@2, bhe), bhf)) → new_lt12(yvy1001, yvy1011, bhe, bhf)
new_esEs11(yvy4000, yvy3000, ty_Int) → new_esEs25(yvy4000, yvy3000)
new_esEs32(yvy40001, yvy30001, app(app(app(ty_@3, cgc), cgd), cge)) → new_esEs22(yvy40001, yvy30001, cgc, cgd, cge)
new_lt6(yvy1000, yvy1010, ty_Double) → new_lt13(yvy1000, yvy1010)
new_lt20(yvy152, yvy155, ty_Float) → new_lt11(yvy152, yvy155)
new_ltEs14(Left(yvy1000), Left(yvy1010), app(app(app(ty_@3, daf), dag), dah), dac) → new_ltEs10(yvy1000, yvy1010, daf, dag, dah)
new_esEs26(yvy40000, yvy30000, ty_Integer) → new_esEs18(yvy40000, yvy30000)
new_lt22(yvy1000, yvy1010, app(app(app(ty_@3, edd), ede), edf)) → new_lt4(yvy1000, yvy1010, edd, ede, edf)
new_esEs36(yvy1000, yvy1010, app(app(ty_Either, eeb), eec)) → new_esEs24(yvy1000, yvy1010, eeb, eec)
new_esEs27(yvy1000, yvy1010, ty_Ordering) → new_esEs12(yvy1000, yvy1010)
new_ltEs19(yvy1002, yvy1012, ty_Double) → new_ltEs13(yvy1002, yvy1012)
new_lt21(yvy153, yvy156, ty_Int) → new_lt17(yvy153, yvy156)
new_lt20(yvy152, yvy155, ty_Integer) → new_lt15(yvy152, yvy155)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, ty_Ordering) → new_esEs12(yvy40000, yvy30000)
new_lt8(yvy152, yvy155) → new_esEs12(new_compare11(yvy152, yvy155), LT)
new_ltEs24(yvy100, yvy101, app(ty_[], fef)) → new_ltEs8(yvy100, yvy101, fef)
new_esEs9(yvy4000, yvy3000, ty_@0) → new_esEs19(yvy4000, yvy3000)
new_esEs22(@3(yvy40000, yvy40001, yvy40002), @3(yvy30000, yvy30001, yvy30002), hc, hd, he) → new_asAs(new_esEs31(yvy40000, yvy30000, hc), new_asAs(new_esEs32(yvy40001, yvy30001, hd), new_esEs33(yvy40002, yvy30002, he)))
new_esEs8(yvy4001, yvy3001, ty_Float) → new_esEs14(yvy4001, yvy3001)
new_esEs7(yvy4000, yvy3000, app(ty_Ratio, cd)) → new_esEs21(yvy4000, yvy3000, cd)
new_ltEs20(yvy154, yvy157, ty_Double) → new_ltEs13(yvy154, yvy157)
new_ltEs18(yvy107, yvy108, ty_Bool) → new_ltEs16(yvy107, yvy108)
new_compare28(yvy114, yvy115, False, fad, fae) → new_compare19(yvy114, yvy115, new_ltEs22(yvy114, yvy115, fae), fad, fae)
new_esEs6(yvy4002, yvy3002, app(ty_Maybe, bcb)) → new_esEs23(yvy4002, yvy3002, bcb)
new_lt5(yvy1001, yvy1011, app(app(app(ty_@3, bhb), bhc), bhd)) → new_lt4(yvy1001, yvy1011, bhb, bhc, bhd)
new_esEs31(yvy40000, yvy30000, app(app(app(ty_@3, cfa), cfb), cfc)) → new_esEs22(yvy40000, yvy30000, cfa, cfb, cfc)
new_esEs31(yvy40000, yvy30000, ty_Ordering) → new_esEs12(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, ty_Double) → new_esEs13(yvy40002, yvy30002)
new_lt6(yvy1000, yvy1010, ty_Float) → new_lt11(yvy1000, yvy1010)
new_esEs4(yvy4000, yvy3000, ty_Char) → new_esEs15(yvy4000, yvy3000)
new_esEs7(yvy4000, yvy3000, app(app(ty_Either, db), dc)) → new_esEs24(yvy4000, yvy3000, db, dc)
new_compare112(yvy189, yvy190, False, fge) → GT
new_esEs12(GT, GT) → True
new_ltEs21(yvy1001, yvy1011, app(app(app(ty_@3, eef), eeg), eeh)) → new_ltEs10(yvy1001, yvy1011, eef, eeg, eeh)
new_esEs5(yvy4001, yvy3001, ty_Double) → new_esEs13(yvy4001, yvy3001)
new_compare17(yvy218, yvy219, yvy220, yvy221, yvy222, yvy223, False, yvy225, ceb, cec, ced) → new_compare14(yvy218, yvy219, yvy220, yvy221, yvy222, yvy223, yvy225, ceb, cec, ced)
new_esEs8(yvy4001, yvy3001, app(ty_Maybe, ec)) → new_esEs23(yvy4001, yvy3001, ec)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_@0) → new_esEs19(yvy40000, yvy30000)
new_compare25(yvy152, yvy153, yvy154, yvy155, yvy156, yvy157, False, dhc, dhd, dhe) → new_compare17(yvy152, yvy153, yvy154, yvy155, yvy156, yvy157, new_lt20(yvy152, yvy155, dhc), new_asAs(new_esEs34(yvy152, yvy155, dhc), new_pePe(new_lt21(yvy153, yvy156, dhd), new_asAs(new_esEs35(yvy153, yvy156, dhd), new_ltEs20(yvy154, yvy157, dhe)))), dhc, dhd, dhe)
new_compare31(Nothing, Just(yvy3000), ffb) → LT
new_esEs29(yvy40000, yvy30000, ty_Ordering) → new_esEs12(yvy40000, yvy30000)
new_esEs4(yvy4000, yvy3000, app(ty_[], gg)) → new_esEs16(yvy4000, yvy3000, gg)
new_primPlusNat1(Zero, Zero) → Zero
new_compare0([], :(yvy3000, yvy3001), feh) → LT
new_ltEs6(LT, EQ) → True
new_lt23(yvy165, yvy167, ty_Ordering) → new_lt7(yvy165, yvy167)
new_ltEs21(yvy1001, yvy1011, app(ty_Maybe, efc)) → new_ltEs5(yvy1001, yvy1011, efc)
new_ltEs6(GT, LT) → False
new_lt18(yvy152, yvy155) → new_esEs12(new_compare12(yvy152, yvy155), LT)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, ty_Char) → new_esEs15(yvy40000, yvy30000)
new_asAs(True, yvy184) → yvy184
new_esEs26(yvy40000, yvy30000, ty_Float) → new_esEs14(yvy40000, yvy30000)
new_esEs35(yvy153, yvy156, ty_Float) → new_esEs14(yvy153, yvy156)
new_ltEs21(yvy1001, yvy1011, app(ty_[], eed)) → new_ltEs8(yvy1001, yvy1011, eed)
new_compare11(Char(yvy4000), Char(yvy3000)) → new_primCmpNat0(yvy4000, yvy3000)
new_ltEs22(yvy114, yvy115, ty_Float) → new_ltEs11(yvy114, yvy115)
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_esEs28(yvy1001, yvy1011, app(ty_Ratio, bha)) → new_esEs21(yvy1001, yvy1011, bha)
new_esEs39(yvy165, yvy167, ty_Double) → new_esEs13(yvy165, yvy167)
new_esEs11(yvy4000, yvy3000, ty_Bool) → new_esEs20(yvy4000, yvy3000)
new_ltEs22(yvy114, yvy115, ty_Double) → new_ltEs13(yvy114, yvy115)
new_lt22(yvy1000, yvy1010, ty_Ordering) → new_lt7(yvy1000, yvy1010)
new_esEs4(yvy4000, yvy3000, app(app(app(ty_@3, hc), hd), he)) → new_esEs22(yvy4000, yvy3000, hc, hd, he)
new_lt20(yvy152, yvy155, app(ty_Ratio, cea)) → new_lt10(yvy152, yvy155, cea)
new_ltEs16(False, False) → True
new_lt23(yvy165, yvy167, ty_Double) → new_lt13(yvy165, yvy167)
new_ltEs17(yvy100, yvy101) → new_fsEs(new_compare9(yvy100, yvy101))
new_esEs29(yvy40000, yvy30000, ty_Integer) → new_esEs18(yvy40000, yvy30000)
new_esEs8(yvy4001, yvy3001, ty_Ordering) → new_esEs12(yvy4001, yvy3001)
new_esEs30(yvy40001, yvy30001, ty_Bool) → new_esEs20(yvy40001, yvy30001)
new_lt23(yvy165, yvy167, app(ty_Ratio, fcc)) → new_lt10(yvy165, yvy167, fcc)
new_esEs30(yvy40001, yvy30001, ty_Int) → new_esEs25(yvy40001, yvy30001)
new_esEs27(yvy1000, yvy1010, ty_Float) → new_esEs14(yvy1000, yvy1010)
new_ltEs21(yvy1001, yvy1011, ty_Int) → new_ltEs15(yvy1001, yvy1011)
new_ltEs20(yvy154, yvy157, app(app(app(ty_@3, ebf), ebg), ebh)) → new_ltEs10(yvy154, yvy157, ebf, ebg, ebh)
new_esEs23(Just(yvy40000), Just(yvy30000), app(ty_[], dda)) → new_esEs16(yvy40000, yvy30000, dda)
new_esEs34(yvy152, yvy155, app(app(app(ty_@3, bd), be), bf)) → new_esEs22(yvy152, yvy155, bd, be, bf)
new_esEs16(:(yvy40000, yvy40001), :(yvy30000, yvy30001), gg) → new_asAs(new_esEs26(yvy40000, yvy30000, gg), new_esEs16(yvy40001, yvy30001, gg))
new_esEs9(yvy4000, yvy3000, app(app(app(ty_@3, ffg), ffh), fga)) → new_esEs22(yvy4000, yvy3000, ffg, ffh, fga)
new_ltEs19(yvy1002, yvy1012, app(app(app(ty_@3, cad), cae), caf)) → new_ltEs10(yvy1002, yvy1012, cad, cae, caf)
new_ltEs20(yvy154, yvy157, ty_Ordering) → new_ltEs6(yvy154, yvy157)
new_compare19(yvy206, yvy207, False, dha, dhb) → GT
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Integer) → new_ltEs4(yvy1000, yvy1010)
new_esEs6(yvy4002, yvy3002, ty_@0) → new_esEs19(yvy4002, yvy3002)
new_ltEs10(@3(yvy1000, yvy1001, yvy1002), @3(yvy1010, yvy1011, yvy1012), bfc, bfd, bfe) → new_pePe(new_lt6(yvy1000, yvy1010, bfc), new_asAs(new_esEs27(yvy1000, yvy1010, bfc), new_pePe(new_lt5(yvy1001, yvy1011, bfd), new_asAs(new_esEs28(yvy1001, yvy1011, bfd), new_ltEs19(yvy1002, yvy1012, bfe)))))
new_esEs33(yvy40002, yvy30002, ty_@0) → new_esEs19(yvy40002, yvy30002)
new_esEs35(yvy153, yvy156, app(ty_Ratio, eac)) → new_esEs21(yvy153, yvy156, eac)
new_ltEs22(yvy114, yvy115, ty_Int) → new_ltEs15(yvy114, yvy115)
new_ltEs24(yvy100, yvy101, app(app(app(ty_@3, bfc), bfd), bfe)) → new_ltEs10(yvy100, yvy101, bfc, bfd, bfe)
new_compare27(Right(yvy4000), Right(yvy3000), eff, efg) → new_compare28(yvy4000, yvy3000, new_esEs11(yvy4000, yvy3000, efg), eff, efg)
new_ltEs21(yvy1001, yvy1011, ty_@0) → new_ltEs17(yvy1001, yvy1011)
new_lt16(yvy152, yvy155, dhh, eaa) → new_esEs12(new_compare27(yvy152, yvy155, dhh, eaa), LT)
new_compare15(EQ, EQ) → EQ
new_ltEs22(yvy114, yvy115, ty_Char) → new_ltEs7(yvy114, yvy115)
new_compare30(yvy400, yvy300, ty_Double) → new_compare29(yvy400, yvy300)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCompAux0(yvy56, EQ) → yvy56
new_lt6(yvy1000, yvy1010, app(app(ty_@2, bgc), bgd)) → new_lt12(yvy1000, yvy1010, bgc, bgd)
new_esEs27(yvy1000, yvy1010, app(ty_Maybe, bge)) → new_esEs23(yvy1000, yvy1010, bge)
new_ltEs20(yvy154, yvy157, ty_Char) → new_ltEs7(yvy154, yvy157)
new_esEs10(yvy4000, yvy3000, ty_Integer) → new_esEs18(yvy4000, yvy3000)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_@0, dac) → new_ltEs17(yvy1000, yvy1010)
new_ltEs18(yvy107, yvy108, ty_Int) → new_ltEs15(yvy107, yvy108)
new_lt21(yvy153, yvy156, app(app(app(ty_@3, ead), eae), eaf)) → new_lt4(yvy153, yvy156, ead, eae, eaf)
new_esEs6(yvy4002, yvy3002, ty_Char) → new_esEs15(yvy4002, yvy3002)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_esEs30(yvy40001, yvy30001, ty_Char) → new_esEs15(yvy40001, yvy30001)
new_ltEs5(Just(yvy1000), Just(yvy1010), app(app(app(ty_@3, fc), fd), ff)) → new_ltEs10(yvy1000, yvy1010, fc, fd, ff)
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_esEs39(yvy165, yvy167, app(ty_[], fcb)) → new_esEs16(yvy165, yvy167, fcb)
new_esEs35(yvy153, yvy156, ty_Char) → new_esEs15(yvy153, yvy156)
new_not(True) → False
new_ltEs5(Just(yvy1000), Just(yvy1010), app(ty_Ratio, fb)) → new_ltEs9(yvy1000, yvy1010, fb)

The set Q consists of the following terms:

new_esEs36(x0, x1, ty_Char)
new_esEs29(x0, x1, ty_Float)
new_lt22(x0, x1, app(ty_Maybe, x2))
new_esEs7(x0, x1, ty_Int)
new_ltEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs21(x0, x1, ty_Int)
new_ltEs14(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs10(x0, x1, ty_Float)
new_ltEs16(True, True)
new_esEs6(x0, x1, ty_Int)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs32(x0, x1, app(ty_Maybe, x2))
new_lt11(x0, x1)
new_esEs24(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs20(x0, x1, ty_Int)
new_lt5(x0, x1, ty_Char)
new_esEs5(x0, x1, app(ty_[], x2))
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs36(x0, x1, app(ty_[], x2))
new_lt21(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs21(x0, x1, ty_@0)
new_esEs29(x0, x1, ty_Char)
new_ltEs22(x0, x1, ty_Integer)
new_esEs34(x0, x1, app(ty_[], x2))
new_esEs32(x0, x1, ty_Int)
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs11(x0, x1, ty_Int)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs4(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_Integer)
new_compare30(x0, x1, ty_Int)
new_pePe(True, x0)
new_esEs5(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs11(x0, x1, ty_@0)
new_esEs35(x0, x1, ty_Integer)
new_esEs11(x0, x1, ty_Char)
new_esEs9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(x0, x1, ty_Float)
new_esEs9(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(x0, x1, ty_Int)
new_esEs31(x0, x1, app(app(ty_Either, x2), x3))
new_lt22(x0, x1, ty_@0)
new_compare30(x0, x1, ty_Bool)
new_ltEs5(Nothing, Just(x0), x1)
new_lt20(x0, x1, ty_@0)
new_esEs29(x0, x1, ty_Ordering)
new_lt22(x0, x1, ty_Float)
new_esEs9(x0, x1, app(ty_[], x2))
new_lt23(x0, x1, ty_Integer)
new_ltEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(Right(x0), Right(x1), x2, ty_Bool)
new_lt7(x0, x1)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs8(x0, x1, ty_Integer)
new_esEs23(Just(x0), Just(x1), ty_Float)
new_esEs6(x0, x1, ty_Integer)
new_lt5(x0, x1, ty_@0)
new_esEs33(x0, x1, app(app(ty_@2, x2), x3))
new_esEs11(x0, x1, ty_Bool)
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs24(Right(x0), Right(x1), x2, ty_Integer)
new_compare12(False, True)
new_compare12(True, False)
new_ltEs7(x0, x1)
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_primCompAux0(x0, EQ)
new_esEs32(x0, x1, app(app(ty_@2, x2), x3))
new_lt6(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(x0, x1, ty_Integer)
new_esEs32(x0, x1, ty_Ordering)
new_ltEs21(x0, x1, ty_Float)
new_ltEs24(x0, x1, ty_Integer)
new_esEs34(x0, x1, ty_Float)
new_esEs6(x0, x1, ty_@0)
new_lt6(x0, x1, ty_Float)
new_esEs9(x0, x1, ty_Int)
new_compare30(x0, x1, ty_Integer)
new_esEs12(GT, EQ)
new_esEs12(EQ, GT)
new_esEs36(x0, x1, ty_Int)
new_esEs28(x0, x1, ty_Bool)
new_ltEs14(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs24(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_compare30(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_lt5(x0, x1, ty_Double)
new_compare15(LT, LT)
new_esEs10(x0, x1, ty_Char)
new_esEs23(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primMulNat0(Succ(x0), Zero)
new_ltEs22(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_compare6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs34(x0, x1, ty_Ordering)
new_esEs16([], [], x0)
new_esEs12(GT, GT)
new_esEs30(x0, x1, ty_Double)
new_esEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs21(x0, x1, ty_Ordering)
new_esEs10(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_lt21(x0, x1, ty_Float)
new_esEs11(x0, x1, ty_Integer)
new_esEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs21(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs24(x0, x1, app(ty_Maybe, x2))
new_esEs23(Just(x0), Just(x1), ty_Double)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_Char)
new_esEs34(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(Left(x0), Left(x1), ty_Int, x2)
new_esEs38(x0, x1, ty_Integer)
new_ltEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs27(x0, x1, ty_Bool)
new_esEs24(Right(x0), Right(x1), x2, ty_Char)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs6(EQ, EQ)
new_esEs32(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(x0, x1, ty_Float)
new_esEs8(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs22(x0, x1, ty_Char)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(x0, x1, ty_Double)
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_esEs5(x0, x1, ty_Bool)
new_lt6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs31(x0, x1, ty_Int)
new_compare26(x0, x1, True, x2, x3)
new_compare110(x0, x1, x2, x3, True, x4, x5, x6)
new_ltEs24(x0, x1, app(ty_[], x2))
new_compare27(Right(x0), Left(x1), x2, x3)
new_compare27(Left(x0), Right(x1), x2, x3)
new_esEs33(x0, x1, ty_Double)
new_esEs8(x0, x1, ty_Float)
new_ltEs18(x0, x1, ty_@0)
new_esEs4(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, app(ty_[], x2))
new_ltEs5(Just(x0), Just(x1), ty_@0)
new_lt5(x0, x1, ty_Int)
new_ltEs6(LT, EQ)
new_ltEs6(EQ, LT)
new_esEs24(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_primCompAux0(x0, LT)
new_esEs23(Nothing, Nothing, x0)
new_esEs38(x0, x1, ty_Int)
new_esEs23(Just(x0), Just(x1), ty_Int)
new_ltEs20(x0, x1, ty_@0)
new_lt6(x0, x1, app(ty_Maybe, x2))
new_esEs11(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Int)
new_lt17(x0, x1)
new_esEs8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs36(x0, x1, ty_Bool)
new_primEqNat0(Zero, Zero)
new_compare13(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs26(x0, x1, ty_@0)
new_lt21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(Right(x0), Right(x1), x2, ty_Int)
new_esEs7(x0, x1, ty_Bool)
new_esEs33(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs5(x0, x1, ty_Float)
new_ltEs14(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_compare17(x0, x1, x2, x3, x4, x5, False, x6, x7, x8, x9)
new_ltEs22(x0, x1, ty_Float)
new_compare15(GT, GT)
new_esEs31(x0, x1, ty_Double)
new_ltEs20(x0, x1, ty_Integer)
new_lt22(x0, x1, ty_Bool)
new_compare30(x0, x1, app(ty_[], x2))
new_esEs34(x0, x1, ty_Bool)
new_esEs31(x0, x1, ty_Integer)
new_ltEs20(x0, x1, ty_Char)
new_lt20(x0, x1, ty_Double)
new_esEs35(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_compare28(x0, x1, True, x2, x3)
new_ltEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs21(x0, x1, app(ty_[], x2))
new_ltEs15(x0, x1)
new_esEs4(x0, x1, ty_Integer)
new_esEs39(x0, x1, app(ty_Ratio, x2))
new_esEs6(x0, x1, app(app(ty_Either, x2), x3))
new_esEs39(x0, x1, ty_Bool)
new_esEs6(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs24(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Float)
new_ltEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_primMulNat0(Zero, Zero)
new_asAs(True, x0)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_ltEs14(Left(x0), Right(x1), x2, x3)
new_ltEs14(Right(x0), Left(x1), x2, x3)
new_esEs26(x0, x1, ty_Double)
new_esEs5(x0, x1, ty_Double)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs35(x0, x1, app(app(ty_@2, x2), x3))
new_fsEs(x0)
new_esEs16(:(x0, x1), [], x2)
new_ltEs5(Just(x0), Just(x1), ty_Integer)
new_esEs35(x0, x1, app(ty_Ratio, x2))
new_lt6(x0, x1, ty_Double)
new_esEs35(x0, x1, ty_Double)
new_ltEs18(x0, x1, ty_Bool)
new_esEs23(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Float)
new_ltEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(x0, x1, app(ty_Maybe, x2))
new_compare28(x0, x1, False, x2, x3)
new_ltEs5(Just(x0), Just(x1), ty_Double)
new_lt22(x0, x1, ty_Ordering)
new_lt23(x0, x1, app(ty_Ratio, x2))
new_esEs9(x0, x1, ty_@0)
new_esEs6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare24(x0, x1, x2, x3, False, x4, x5)
new_esEs24(Left(x0), Left(x1), ty_@0, x2)
new_esEs35(x0, x1, ty_Bool)
new_esEs35(x0, x1, ty_Char)
new_ltEs23(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, ty_Bool)
new_ltEs10(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs31(x0, x1, ty_@0)
new_lt10(x0, x1, x2)
new_ltEs19(x0, x1, ty_Double)
new_lt12(x0, x1, x2, x3)
new_ltEs24(x0, x1, ty_Double)
new_esEs13(Double(x0, x1), Double(x2, x3))
new_esEs10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Ordering)
new_esEs5(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(Just(x0), Nothing, x1)
new_ltEs14(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs24(Right(x0), Right(x1), x2, ty_@0)
new_esEs20(True, True)
new_lt22(x0, x1, ty_Int)
new_esEs7(x0, x1, ty_Integer)
new_esEs30(x0, x1, ty_Bool)
new_lt21(x0, x1, ty_@0)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs4(x0, x1, app(ty_Maybe, x2))
new_esEs33(x0, x1, ty_Float)
new_esEs29(x0, x1, ty_Integer)
new_ltEs21(x0, x1, ty_Integer)
new_lt16(x0, x1, x2, x3)
new_primPlusNat0(Zero, x0)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs4(x0, x1, ty_Ordering)
new_esEs8(x0, x1, ty_Bool)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_primPlusNat0(Succ(x0), x1)
new_ltEs4(x0, x1)
new_esEs34(x0, x1, ty_Integer)
new_esEs31(x0, x1, ty_Ordering)
new_ltEs6(GT, LT)
new_ltEs6(LT, GT)
new_compare0([], [], x0)
new_ltEs22(x0, x1, app(ty_Maybe, x2))
new_esEs35(x0, x1, app(ty_Maybe, x2))
new_compare111(x0, x1, x2, x3, True, x4, x5)
new_esEs11(x0, x1, ty_Double)
new_lt19(x0, x1)
new_ltEs14(Left(x0), Left(x1), ty_Double, x2)
new_ltEs8(x0, x1, x2)
new_ltEs14(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs4(x0, x1, ty_Double)
new_esEs36(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, ty_Double)
new_esEs39(x0, x1, ty_Char)
new_ltEs22(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_compare15(EQ, EQ)
new_lt6(x0, x1, ty_Int)
new_lt21(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, ty_Ordering)
new_ltEs14(Right(x0), Right(x1), x2, ty_Double)
new_ltEs22(x0, x1, ty_Ordering)
new_ltEs11(x0, x1)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_compare7(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt20(x0, x1, ty_Float)
new_lt21(x0, x1, ty_Integer)
new_esEs32(x0, x1, ty_Bool)
new_esEs39(x0, x1, ty_Float)
new_compare10(x0, x1, False, x2, x3)
new_lt6(x0, x1, ty_Integer)
new_lt4(x0, x1, x2, x3, x4)
new_esEs10(x0, x1, ty_Double)
new_esEs31(x0, x1, app(ty_[], x2))
new_sr0(x0, x1)
new_esEs23(Just(x0), Just(x1), ty_Integer)
new_esEs24(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs20(False, True)
new_esEs20(True, False)
new_esEs29(x0, x1, ty_Bool)
new_esEs24(Left(x0), Right(x1), x2, x3)
new_esEs24(Right(x0), Left(x1), x2, x3)
new_ltEs23(x0, x1, ty_Integer)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs36(x0, x1, app(ty_Ratio, x2))
new_esEs20(False, False)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare12(False, False)
new_esEs12(LT, EQ)
new_esEs12(EQ, LT)
new_lt21(x0, x1, ty_Int)
new_lt22(x0, x1, ty_Char)
new_ltEs14(Left(x0), Left(x1), ty_Char, x2)
new_ltEs14(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare14(x0, x1, x2, x3, x4, x5, True, x6, x7, x8)
new_esEs31(x0, x1, ty_Float)
new_esEs24(Left(x0), Left(x1), ty_Float, x2)
new_primPlusNat1(Zero, Zero)
new_ltEs21(x0, x1, ty_Bool)
new_esEs24(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs20(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_Float)
new_esEs12(EQ, EQ)
new_esEs23(Just(x0), Just(x1), ty_Bool)
new_esEs27(x0, x1, ty_Char)
new_ltEs14(Right(x0), Right(x1), x2, ty_Int)
new_esEs9(x0, x1, ty_Integer)
new_esEs30(x0, x1, ty_Float)
new_ltEs20(x0, x1, ty_Float)
new_lt22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(Right(x0), Right(x1), x2, ty_Char)
new_esEs9(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Left(x0), Left(x1), ty_Float, x2)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs16(:(x0, x1), :(x2, x3), x4)
new_esEs28(x0, x1, ty_Double)
new_esEs30(x0, x1, ty_Char)
new_compare30(x0, x1, ty_@0)
new_esEs6(x0, x1, ty_Bool)
new_esEs16([], :(x0, x1), x2)
new_ltEs23(x0, x1, ty_Float)
new_esEs9(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs31(x0, x1, app(app(ty_@2, x2), x3))
new_compare15(EQ, GT)
new_compare15(GT, EQ)
new_compare17(x0, x1, x2, x3, x4, x5, True, x6, x7, x8, x9)
new_ltEs9(x0, x1, x2)
new_ltEs24(x0, x1, ty_Ordering)
new_compare30(x0, x1, ty_Char)
new_primEqNat0(Succ(x0), Zero)
new_compare15(LT, GT)
new_compare15(GT, LT)
new_esEs36(x0, x1, ty_Double)
new_esEs39(x0, x1, ty_Ordering)
new_esEs7(x0, x1, app(app(ty_Either, x2), x3))
new_lt21(x0, x1, app(ty_[], x2))
new_esEs37(x0, x1, ty_Int)
new_esEs9(x0, x1, ty_Double)
new_primMulInt(Neg(x0), Neg(x1))
new_ltEs5(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs17(x0, x1)
new_compare0([], :(x0, x1), x2)
new_esEs9(x0, x1, ty_Ordering)
new_ltEs12(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs26(x0, x1, ty_Char)
new_lt23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_lt23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs23(x0, x1, ty_Int)
new_primEqNat0(Succ(x0), Succ(x1))
new_compare210(x0, x1, True, x2)
new_esEs8(x0, x1, ty_Int)
new_ltEs14(Left(x0), Left(x1), ty_Bool, x2)
new_lt21(x0, x1, app(ty_Maybe, x2))
new_ltEs5(Just(x0), Just(x1), ty_Int)
new_esEs33(x0, x1, ty_Int)
new_ltEs23(x0, x1, ty_@0)
new_lt6(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs33(x0, x1, ty_Bool)
new_esEs10(x0, x1, ty_Ordering)
new_esEs24(Left(x0), Left(x1), ty_Double, x2)
new_esEs35(x0, x1, ty_@0)
new_esEs4(x0, x1, ty_Char)
new_compare112(x0, x1, False, x2)
new_esEs24(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_lt23(x0, x1, ty_Int)
new_ltEs14(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs18(x0, x1, ty_Double)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt23(x0, x1, ty_Bool)
new_ltEs14(Left(x0), Left(x1), ty_Integer, x2)
new_esEs24(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_lt9(x0, x1, x2)
new_ltEs18(x0, x1, app(ty_[], x2))
new_esEs33(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, app(ty_[], x2))
new_lt5(x0, x1, app(app(ty_Either, x2), x3))
new_lt21(x0, x1, ty_Bool)
new_esEs24(Left(x0), Left(x1), ty_Char, x2)
new_ltEs5(Nothing, Nothing, x0)
new_compare18(Float(x0, x1), Float(x2, x3))
new_ltEs5(Just(x0), Just(x1), ty_Float)
new_esEs26(x0, x1, ty_Bool)
new_lt6(x0, x1, ty_Bool)
new_esEs30(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Integer)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs8(x0, x1, ty_Double)
new_lt21(x0, x1, ty_Char)
new_lt5(x0, x1, ty_Float)
new_compare11(Char(x0), Char(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs24(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs36(x0, x1, app(app(ty_Either, x2), x3))
new_esEs30(x0, x1, ty_Integer)
new_esEs25(x0, x1)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_compare210(x0, x1, False, x2)
new_esEs29(x0, x1, ty_@0)
new_ltEs14(Left(x0), Left(x1), ty_Int, x2)
new_sr(Integer(x0), Integer(x1))
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs7(x0, x1, ty_@0)
new_esEs39(x0, x1, app(ty_Maybe, x2))
new_primMulNat0(Succ(x0), Succ(x1))
new_ltEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs34(x0, x1, ty_Char)
new_esEs4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs10(x0, x1, ty_Bool)
new_lt5(x0, x1, app(ty_[], x2))
new_esEs10(x0, x1, ty_@0)
new_esEs39(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_@0)
new_esEs31(x0, x1, ty_Bool)
new_primEqNat0(Zero, Succ(x0))
new_primPlusNat1(Succ(x0), Zero)
new_lt23(x0, x1, ty_Char)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs7(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Char)
new_ltEs21(x0, x1, app(ty_Maybe, x2))
new_esEs6(x0, x1, ty_Ordering)
new_esEs33(x0, x1, ty_Char)
new_compare27(Left(x0), Left(x1), x2, x3)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs32(x0, x1, ty_Integer)
new_ltEs14(Left(x0), Left(x1), ty_Ordering, x2)
new_pePe(False, x0)
new_ltEs24(x0, x1, ty_Int)
new_compare24(x0, x1, x2, x3, True, x4, x5)
new_lt8(x0, x1)
new_esEs39(x0, x1, app(app(ty_Either, x2), x3))
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt23(x0, x1, ty_Double)
new_esEs10(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Bool)
new_esEs9(x0, x1, app(app(ty_@2, x2), x3))
new_esEs32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, ty_Int)
new_esEs30(x0, x1, ty_Ordering)
new_lt23(x0, x1, ty_Float)
new_lt6(x0, x1, ty_@0)
new_primPlusNat1(Succ(x0), Succ(x1))
new_compare27(Right(x0), Right(x1), x2, x3)
new_esEs31(x0, x1, ty_Char)
new_lt22(x0, x1, ty_Double)
new_ltEs22(x0, x1, ty_@0)
new_esEs39(x0, x1, ty_Int)
new_esEs30(x0, x1, ty_@0)
new_compare14(x0, x1, x2, x3, x4, x5, False, x6, x7, x8)
new_ltEs16(False, True)
new_ltEs16(True, False)
new_ltEs6(GT, GT)
new_esEs10(x0, x1, ty_Int)
new_compare30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(x0, x1, app(ty_Maybe, x2))
new_esEs31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs32(x0, x1, ty_Char)
new_esEs23(Nothing, Just(x0), x1)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(x0, x1, ty_Int)
new_ltEs5(Just(x0), Just(x1), ty_Ordering)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_ltEs19(x0, x1, ty_Char)
new_ltEs22(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(Just(x0), Just(x1), ty_Char)
new_esEs27(x0, x1, ty_Int)
new_esEs24(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs4(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(Just(x0), Just(x1), ty_Bool)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_Bool)
new_lt22(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_@0)
new_ltEs22(x0, x1, ty_Bool)
new_esEs30(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_Integer)
new_esEs33(x0, x1, ty_Integer)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, ty_Int)
new_primCmpNat0(Zero, Zero)
new_esEs35(x0, x1, ty_Float)
new_asAs(False, x0)
new_lt5(x0, x1, ty_Integer)
new_ltEs24(x0, x1, ty_@0)
new_esEs17(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs19(x0, x1, ty_Int)
new_lt23(x0, x1, ty_@0)
new_esEs34(x0, x1, ty_Int)
new_ltEs6(LT, LT)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs35(x0, x1, app(ty_[], x2))
new_esEs35(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare31(Just(x0), Just(x1), x2)
new_esEs11(x0, x1, ty_Ordering)
new_esEs31(x0, x1, app(ty_Ratio, x2))
new_lt5(x0, x1, app(ty_Ratio, x2))
new_ltEs22(x0, x1, ty_Double)
new_ltEs14(Left(x0), Left(x1), ty_@0, x2)
new_lt23(x0, x1, app(ty_[], x2))
new_compare10(x0, x1, True, x2, x3)
new_ltEs24(x0, x1, ty_Char)
new_esEs21(:%(x0, x1), :%(x2, x3), x4)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs18(Integer(x0), Integer(x1))
new_esEs4(x0, x1, ty_@0)
new_lt22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, ty_Int)
new_ltEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(Just(x0), Just(x1), ty_@0)
new_compare110(x0, x1, x2, x3, False, x4, x5, x6)
new_ltEs14(Right(x0), Right(x1), x2, ty_Integer)
new_compare0(:(x0, x1), [], x2)
new_esEs23(Just(x0), Nothing, x1)
new_ltEs19(x0, x1, ty_Float)
new_esEs6(x0, x1, ty_Char)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_lt21(x0, x1, ty_Double)
new_esEs32(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs8(x0, x1, app(ty_[], x2))
new_esEs23(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs34(x0, x1, app(app(ty_Either, x2), x3))
new_esEs33(x0, x1, app(ty_[], x2))
new_lt5(x0, x1, ty_Bool)
new_esEs11(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(Just(x0), Just(x1), ty_Char)
new_ltEs13(x0, x1)
new_lt14(x0, x1, x2)
new_ltEs23(x0, x1, ty_Bool)
new_esEs6(x0, x1, app(ty_Ratio, x2))
new_compare15(LT, EQ)
new_compare15(EQ, LT)
new_compare9(@0, @0)
new_lt13(x0, x1)
new_esEs36(x0, x1, ty_Integer)
new_esEs29(x0, x1, ty_Double)
new_ltEs22(x0, x1, app(ty_[], x2))
new_ltEs23(x0, x1, app(ty_Maybe, x2))
new_esEs8(x0, x1, app(ty_Ratio, x2))
new_ltEs18(x0, x1, ty_Float)
new_lt18(x0, x1)
new_lt22(x0, x1, app(ty_Ratio, x2))
new_esEs32(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_Float)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_lt5(x0, x1, ty_Ordering)
new_lt15(x0, x1)
new_compare8(Integer(x0), Integer(x1))
new_lt22(x0, x1, app(ty_[], x2))
new_compare30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs33(x0, x1, app(ty_Ratio, x2))
new_lt5(x0, x1, app(ty_Maybe, x2))
new_esEs36(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs33(x0, x1, app(ty_Maybe, x2))
new_esEs7(x0, x1, app(ty_Maybe, x2))
new_esEs8(x0, x1, ty_@0)
new_lt6(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(x0, x1, ty_Int)
new_not(True)
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_compare30(x0, x1, ty_Float)
new_compare31(Just(x0), Nothing, x1)
new_esEs27(x0, x1, ty_Ordering)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs22(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs23(x0, x1, app(ty_Ratio, x2))
new_ltEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(x0, x1, ty_Bool)
new_esEs32(x0, x1, ty_Float)
new_esEs36(x0, x1, ty_Ordering)
new_esEs9(x0, x1, ty_Bool)
new_esEs23(Just(x0), Just(x1), app(ty_Maybe, x2))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_not(False)
new_esEs24(Left(x0), Left(x1), ty_Ordering, x2)
new_compare29(Double(x0, x1), Double(x2, x3))
new_compare13(:%(x0, x1), :%(x2, x3), ty_Integer)
new_lt6(x0, x1, app(ty_Ratio, x2))
new_primCmpNat0(Succ(x0), Succ(x1))
new_esEs7(x0, x1, ty_Ordering)
new_esEs34(x0, x1, app(ty_Ratio, x2))
new_ltEs23(x0, x1, ty_Char)
new_esEs7(x0, x1, app(ty_[], x2))
new_esEs8(x0, x1, ty_Ordering)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_esEs39(x0, x1, ty_@0)
new_ltEs21(x0, x1, ty_Char)
new_esEs15(Char(x0), Char(x1))
new_esEs7(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(x0, x1, app(ty_Ratio, x2))
new_ltEs6(GT, EQ)
new_ltEs6(EQ, GT)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_esEs7(x0, x1, app(ty_Ratio, x2))
new_esEs32(x0, x1, app(ty_Ratio, x2))
new_primCmpNat0(Zero, Succ(x0))
new_esEs31(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Ordering)
new_lt23(x0, x1, app(ty_Maybe, x2))
new_ltEs21(x0, x1, ty_Double)
new_esEs24(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs8(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs23(x0, x1, app(ty_[], x2))
new_esEs24(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_compare30(x0, x1, ty_Double)
new_compare19(x0, x1, True, x2, x3)
new_esEs36(x0, x1, app(ty_Maybe, x2))
new_esEs24(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs5(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(Right(x0), Right(x1), x2, ty_Double)
new_lt22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(x0, x1, app(ty_[], x2))
new_primCmpNat0(Succ(x0), Zero)
new_compare30(x0, x1, app(ty_Maybe, x2))
new_esEs34(x0, x1, ty_Double)
new_ltEs21(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_@0)
new_esEs11(x0, x1, app(ty_Maybe, x2))
new_esEs6(x0, x1, app(ty_Maybe, x2))
new_ltEs22(x0, x1, ty_Int)
new_compare26(x0, x1, False, x2, x3)
new_compare16(x0, x1)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_esEs23(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs20(x0, x1, ty_Double)
new_ltEs24(x0, x1, ty_Bool)
new_esEs35(x0, x1, ty_Ordering)
new_ltEs18(x0, x1, ty_Integer)
new_esEs39(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs34(x0, x1, ty_@0)
new_compare31(Nothing, Just(x0), x1)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_esEs37(x0, x1, ty_Integer)
new_ltEs18(x0, x1, ty_Char)
new_esEs7(x0, x1, ty_Double)
new_lt23(x0, x1, ty_Ordering)
new_compare112(x0, x1, True, x2)
new_lt21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs34(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs9(x0, x1, ty_Float)
new_esEs23(Just(x0), Just(x1), ty_Ordering)
new_lt6(x0, x1, ty_Char)
new_esEs9(x0, x1, ty_Char)
new_esEs8(x0, x1, ty_Char)
new_esEs35(x0, x1, ty_Int)
new_esEs24(Left(x0), Left(x1), ty_Integer, x2)
new_esEs5(x0, x1, app(ty_Maybe, x2))
new_lt21(x0, x1, app(ty_Ratio, x2))
new_esEs33(x0, x1, ty_@0)
new_esEs24(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs5(x0, x1, ty_Ordering)
new_esEs32(x0, x1, ty_Double)
new_esEs34(x0, x1, app(ty_Maybe, x2))
new_esEs10(x0, x1, app(ty_[], x2))
new_compare30(x0, x1, app(ty_Ratio, x2))
new_ltEs21(x0, x1, app(ty_Ratio, x2))
new_lt23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs24(x0, x1, app(ty_Ratio, x2))
new_esEs14(Float(x0, x1), Float(x2, x3))
new_esEs26(x0, x1, ty_Integer)
new_esEs5(x0, x1, ty_@0)
new_esEs5(x0, x1, ty_Char)
new_esEs7(x0, x1, ty_Char)
new_compare12(True, True)
new_primEqInt(Pos(Zero), Pos(Zero))
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs5(x0, x1, ty_Integer)
new_primCompAux1(x0, x1, x2, x3)
new_compare31(Nothing, Nothing, x0)
new_esEs39(x0, x1, app(ty_[], x2))
new_compare30(x0, x1, ty_Ordering)
new_primMulNat0(Zero, Succ(x0))
new_esEs28(x0, x1, app(ty_[], x2))
new_ltEs23(x0, x1, ty_Double)
new_esEs24(Right(x0), Right(x1), x2, ty_Float)
new_esEs11(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_lt5(x0, x1, app(app(ty_@2, x2), x3))
new_primCompAux0(x0, GT)
new_lt6(x0, x1, ty_Ordering)
new_primPlusNat1(Zero, Succ(x0))
new_esEs36(x0, x1, ty_Float)
new_esEs19(@0, @0)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs39(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_compare25(x0, x1, x2, x3, x4, x5, True, x6, x7, x8)
new_esEs36(x0, x1, ty_@0)
new_esEs12(LT, LT)
new_esEs28(x0, x1, ty_Integer)
new_compare19(x0, x1, False, x2, x3)
new_ltEs18(x0, x1, ty_Ordering)
new_ltEs16(False, False)
new_compare111(x0, x1, x2, x3, False, x4, x5)
new_compare25(x0, x1, x2, x3, x4, x5, False, x6, x7, x8)
new_esEs33(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, ty_Ordering)
new_esEs28(x0, x1, ty_@0)
new_esEs11(x0, x1, ty_Float)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs4(x0, x1, app(ty_[], x2))
new_esEs39(x0, x1, ty_Integer)

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

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

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

new_splitGT(Branch(yvy340, yvy341, yvy342, yvy343, yvy344), yvy400, yvy401, h, ba) → new_splitGT3(yvy340, yvy341, yvy342, yvy343, yvy344, :(yvy400, yvy401), h, ba)
new_splitGT2(yvy17, yvy18, yvy19, yvy20, yvy21, yvy22, yvy23, yvy24, EQ, bb, bc) → new_splitGT20(yvy17, yvy18, yvy19, yvy20, yvy21, yvy22, yvy23, yvy24, bb, bc)
new_splitGT11(yvy17, yvy18, yvy19, yvy20, yvy21, yvy22, yvy23, yvy24, LT, bb, bc) → new_splitGT(yvy21, yvy23, yvy24, bb, bc)
new_splitGT2(yvy17, yvy18, yvy19, yvy20, yvy21, yvy22, yvy23, yvy24, GT, bb, bc) → new_splitGT(yvy22, yvy23, yvy24, bb, bc)
new_splitGT2(yvy17, yvy18, yvy19, yvy20, yvy21, yvy22, yvy23, yvy24, LT, bb, bc) → new_splitGT11(yvy17, yvy18, yvy19, yvy20, yvy21, yvy22, yvy23, yvy24, new_compare0(:(yvy23, yvy24), :(yvy17, yvy18), bb), bb, bc)
new_splitGT20(yvy17, yvy18, yvy19, yvy20, yvy21, yvy22, yvy23, yvy24, bb, bc) → new_splitGT11(yvy17, yvy18, yvy19, yvy20, yvy21, yvy22, yvy23, yvy24, new_compare0(:(yvy23, yvy24), :(yvy17, yvy18), bb), bb, bc)
new_splitGT3([], yvy31, yvy32, yvy33, Branch(yvy340, yvy341, yvy342, yvy343, yvy344), :(yvy400, yvy401), h, ba) → new_splitGT3(yvy340, yvy341, yvy342, yvy343, yvy344, :(yvy400, yvy401), h, ba)
new_splitGT3(:(yvy300, yvy301), yvy31, yvy32, yvy33, yvy34, :(yvy400, yvy401), h, ba) → new_splitGT2(yvy300, yvy301, yvy31, yvy32, yvy33, yvy34, yvy400, yvy401, new_primCompAux1(yvy400, yvy300, new_compare0(yvy401, yvy301, h), h), h, ba)

The TRS R consists of the following rules:

new_compare210(yvy100, yvy101, False, feg) → new_compare112(yvy100, yvy101, new_ltEs24(yvy100, yvy101, feg), feg)
new_compare7(@2(yvy4000, yvy4001), @2(yvy3000, yvy3001), bg, bh) → new_compare24(yvy4000, yvy4001, yvy3000, yvy3001, new_asAs(new_esEs7(yvy4000, yvy3000, bg), new_esEs8(yvy4001, yvy3001, bh)), bg, bh)
new_esEs24(Left(yvy40000), Left(yvy30000), app(ty_Ratio, deh), hh) → new_esEs21(yvy40000, yvy30000, deh)
new_ltEs19(yvy1002, yvy1012, app(ty_[], cab)) → new_ltEs8(yvy1002, yvy1012, cab)
new_compare112(yvy189, yvy190, True, fge) → LT
new_lt22(yvy1000, yvy1010, ty_Int) → new_lt17(yvy1000, yvy1010)
new_ltEs22(yvy114, yvy115, app(app(ty_@2, fbc), fbd)) → new_ltEs12(yvy114, yvy115, fbc, fbd)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Int, hh) → new_esEs25(yvy40000, yvy30000)
new_esEs6(yvy4002, yvy3002, app(app(app(ty_@3, bbg), bbh), bca)) → new_esEs22(yvy4002, yvy3002, bbg, bbh, bca)
new_esEs27(yvy1000, yvy1010, app(ty_[], bff)) → new_esEs16(yvy1000, yvy1010, bff)
new_esEs20(True, True) → True
new_esEs35(yvy153, yvy156, app(ty_[], eab)) → new_esEs16(yvy153, yvy156, eab)
new_compare8(Integer(yvy4000), Integer(yvy3000)) → new_primCmpInt(yvy4000, yvy3000)
new_esEs8(yvy4001, yvy3001, ty_Bool) → new_esEs20(yvy4001, yvy3001)
new_esEs11(yvy4000, yvy3000, ty_Integer) → new_esEs18(yvy4000, yvy3000)
new_esEs27(yvy1000, yvy1010, app(app(ty_@2, bgc), bgd)) → new_esEs17(yvy1000, yvy1010, bgc, bgd)
new_ltEs20(yvy154, yvy157, app(ty_Ratio, ebe)) → new_ltEs9(yvy154, yvy157, ebe)
new_esEs36(yvy1000, yvy1010, ty_Double) → new_esEs13(yvy1000, yvy1010)
new_esEs28(yvy1001, yvy1011, ty_Float) → new_esEs14(yvy1001, yvy1011)
new_lt6(yvy1000, yvy1010, ty_@0) → new_lt19(yvy1000, yvy1010)
new_compare10(yvy199, yvy200, True, ef, eg) → LT
new_esEs9(yvy4000, yvy3000, ty_Int) → new_esEs25(yvy4000, yvy3000)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, ty_Double) → new_esEs13(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, app(app(ty_@2, chb), chc)) → new_esEs17(yvy40002, yvy30002, chb, chc)
new_ltEs24(yvy100, yvy101, app(ty_Ratio, cdh)) → new_ltEs9(yvy100, yvy101, cdh)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, ty_@0) → new_esEs19(yvy40000, yvy30000)
new_ltEs19(yvy1002, yvy1012, ty_Float) → new_ltEs11(yvy1002, yvy1012)
new_esEs11(yvy4000, yvy3000, app(ty_[], ehb)) → new_esEs16(yvy4000, yvy3000, ehb)
new_lt23(yvy165, yvy167, app(app(app(ty_@3, fcd), fce), fcf)) → new_lt4(yvy165, yvy167, fcd, fce, fcf)
new_esEs7(yvy4000, yvy3000, ty_Double) → new_esEs13(yvy4000, yvy3000)
new_esEs9(yvy4000, yvy3000, ty_Char) → new_esEs15(yvy4000, yvy3000)
new_ltEs23(yvy166, yvy168, ty_Ordering) → new_ltEs6(yvy166, yvy168)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Bool, dac) → new_ltEs16(yvy1000, yvy1010)
new_esEs39(yvy165, yvy167, app(ty_Ratio, fcc)) → new_esEs21(yvy165, yvy167, fcc)
new_esEs10(yvy4000, yvy3000, ty_@0) → new_esEs19(yvy4000, yvy3000)
new_esEs21(:%(yvy40000, yvy40001), :%(yvy30000, yvy30001), hb) → new_asAs(new_esEs37(yvy40000, yvy30000, hb), new_esEs38(yvy40001, yvy30001, hb))
new_lt5(yvy1001, yvy1011, app(ty_Ratio, bha)) → new_lt10(yvy1001, yvy1011, bha)
new_compare13(:%(yvy4000, yvy4001), :%(yvy3000, yvy3001), ty_Integer) → new_compare8(new_sr(yvy4000, yvy3001), new_sr(yvy3000, yvy4001))
new_ltEs22(yvy114, yvy115, app(ty_Ratio, fag)) → new_ltEs9(yvy114, yvy115, fag)
new_ltEs23(yvy166, yvy168, ty_Int) → new_ltEs15(yvy166, yvy168)
new_primMulNat0(Zero, Zero) → Zero
new_ltEs24(yvy100, yvy101, ty_Ordering) → new_ltEs6(yvy100, yvy101)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, ty_Float) → new_ltEs11(yvy1000, yvy1010)
new_esEs39(yvy165, yvy167, app(ty_Maybe, fda)) → new_esEs23(yvy165, yvy167, fda)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Bool, hh) → new_esEs20(yvy40000, yvy30000)
new_compare15(LT, LT) → EQ
new_esEs6(yvy4002, yvy3002, app(app(ty_@2, bbd), bbe)) → new_esEs17(yvy4002, yvy3002, bbd, bbe)
new_esEs4(yvy4000, yvy3000, ty_Integer) → new_esEs18(yvy4000, yvy3000)
new_esEs26(yvy40000, yvy30000, app(ty_[], bce)) → new_esEs16(yvy40000, yvy30000, bce)
new_esEs36(yvy1000, yvy1010, ty_Char) → new_esEs15(yvy1000, yvy1010)
new_esEs28(yvy1001, yvy1011, app(app(ty_Either, bhh), caa)) → new_esEs24(yvy1001, yvy1011, bhh, caa)
new_esEs34(yvy152, yvy155, ty_@0) → new_esEs19(yvy152, yvy155)
new_sr(Integer(yvy30000), Integer(yvy40010)) → Integer(new_primMulInt(yvy30000, yvy40010))
new_esEs7(yvy4000, yvy3000, ty_Float) → new_esEs14(yvy4000, yvy3000)
new_compare12(True, False) → GT
new_lt7(yvy152, yvy155) → new_esEs12(new_compare15(yvy152, yvy155), LT)
new_lt22(yvy1000, yvy1010, app(ty_Maybe, eea)) → new_lt14(yvy1000, yvy1010, eea)
new_ltEs24(yvy100, yvy101, app(ty_Maybe, eh)) → new_ltEs5(yvy100, yvy101, eh)
new_esEs35(yvy153, yvy156, app(app(ty_Either, ebb), ebc)) → new_esEs24(yvy153, yvy156, ebb, ebc)
new_esEs35(yvy153, yvy156, ty_@0) → new_esEs19(yvy153, yvy156)
new_ltEs15(yvy100, yvy101) → new_fsEs(new_compare16(yvy100, yvy101))
new_esEs6(yvy4002, yvy3002, app(ty_[], bbc)) → new_esEs16(yvy4002, yvy3002, bbc)
new_esEs26(yvy40000, yvy30000, ty_@0) → new_esEs19(yvy40000, yvy30000)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_@0, hh) → new_esEs19(yvy40000, yvy30000)
new_ltEs16(False, True) → True
new_esEs26(yvy40000, yvy30000, app(app(app(ty_@3, bda), bdb), bdc)) → new_esEs22(yvy40000, yvy30000, bda, bdb, bdc)
new_esEs10(yvy4000, yvy3000, app(ty_Maybe, egg)) → new_esEs23(yvy4000, yvy3000, egg)
new_ltEs24(yvy100, yvy101, ty_Bool) → new_ltEs16(yvy100, yvy101)
new_compare30(yvy400, yvy300, app(app(ty_@2, bg), bh)) → new_compare7(yvy400, yvy300, bg, bh)
new_esEs17(@2(yvy40000, yvy40001), @2(yvy30000, yvy30001), gh, ha) → new_asAs(new_esEs29(yvy40000, yvy30000, gh), new_esEs30(yvy40001, yvy30001, ha))
new_esEs11(yvy4000, yvy3000, ty_Char) → new_esEs15(yvy4000, yvy3000)
new_lt20(yvy152, yvy155, app(app(app(ty_@3, bd), be), bf)) → new_lt4(yvy152, yvy155, bd, be, bf)
new_esEs27(yvy1000, yvy1010, ty_Bool) → new_esEs20(yvy1000, yvy1010)
new_ltEs23(yvy166, yvy168, app(ty_Ratio, fde)) → new_ltEs9(yvy166, yvy168, fde)
new_esEs34(yvy152, yvy155, ty_Double) → new_esEs13(yvy152, yvy155)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Double) → new_esEs13(yvy40000, yvy30000)
new_esEs10(yvy4000, yvy3000, ty_Int) → new_esEs25(yvy4000, yvy3000)
new_esEs26(yvy40000, yvy30000, ty_Char) → new_esEs15(yvy40000, yvy30000)
new_compare30(yvy400, yvy300, ty_Int) → new_compare16(yvy400, yvy300)
new_fsEs(yvy306) → new_not(new_esEs12(yvy306, GT))
new_ltEs16(True, False) → False
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, ty_Char) → new_ltEs7(yvy1000, yvy1010)
new_esEs7(yvy4000, yvy3000, ty_Int) → new_esEs25(yvy4000, yvy3000)
new_ltEs19(yvy1002, yvy1012, ty_Bool) → new_ltEs16(yvy1002, yvy1012)
new_esEs34(yvy152, yvy155, ty_Ordering) → new_esEs12(yvy152, yvy155)
new_esEs12(GT, LT) → False
new_esEs12(LT, GT) → False
new_esEs27(yvy1000, yvy1010, ty_Char) → new_esEs15(yvy1000, yvy1010)
new_lt5(yvy1001, yvy1011, ty_Integer) → new_lt15(yvy1001, yvy1011)
new_ltEs22(yvy114, yvy115, ty_Ordering) → new_ltEs6(yvy114, yvy115)
new_compare18(Float(yvy4000, yvy4001), Float(yvy3000, yvy3001)) → new_compare16(new_sr0(yvy4000, yvy3000), new_sr0(yvy4001, yvy3001))
new_ltEs18(yvy107, yvy108, app(ty_Ratio, beb)) → new_ltEs9(yvy107, yvy108, beb)
new_ltEs23(yvy166, yvy168, ty_Float) → new_ltEs11(yvy166, yvy168)
new_ltEs18(yvy107, yvy108, app(ty_[], bea)) → new_ltEs8(yvy107, yvy108, bea)
new_ltEs20(yvy154, yvy157, app(app(ty_@2, eca), ecb)) → new_ltEs12(yvy154, yvy157, eca, ecb)
new_esEs31(yvy40000, yvy30000, app(ty_Maybe, cfd)) → new_esEs23(yvy40000, yvy30000, cfd)
new_lt6(yvy1000, yvy1010, app(ty_Ratio, bfg)) → new_lt10(yvy1000, yvy1010, bfg)
new_esEs37(yvy40000, yvy30000, ty_Integer) → new_esEs18(yvy40000, yvy30000)
new_ltEs14(Left(yvy1000), Left(yvy1010), app(app(ty_@2, dba), dbb), dac) → new_ltEs12(yvy1000, yvy1010, dba, dbb)
new_esEs35(yvy153, yvy156, app(app(ty_@2, eag), eah)) → new_esEs17(yvy153, yvy156, eag, eah)
new_esEs5(yvy4001, yvy3001, app(app(app(ty_@3, bae), baf), bag)) → new_esEs22(yvy4001, yvy3001, bae, baf, bag)
new_lt22(yvy1000, yvy1010, ty_Char) → new_lt8(yvy1000, yvy1010)
new_compare110(yvy233, yvy234, yvy235, yvy236, True, yvy238, ecf, ecg) → new_compare111(yvy233, yvy234, yvy235, yvy236, True, ecf, ecg)
new_ltEs24(yvy100, yvy101, app(app(ty_@2, ech), eda)) → new_ltEs12(yvy100, yvy101, ech, eda)
new_ltEs13(yvy100, yvy101) → new_fsEs(new_compare29(yvy100, yvy101))
new_esEs5(yvy4001, yvy3001, app(app(ty_Either, bba), bbb)) → new_esEs24(yvy4001, yvy3001, bba, bbb)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, ty_Bool) → new_esEs20(yvy40000, yvy30000)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Float) → new_ltEs11(yvy1000, yvy1010)
new_esEs8(yvy4001, yvy3001, ty_Double) → new_esEs13(yvy4001, yvy3001)
new_esEs31(yvy40000, yvy30000, app(ty_Ratio, ceh)) → new_esEs21(yvy40000, yvy30000, ceh)
new_esEs29(yvy40000, yvy30000, app(ty_Maybe, ccc)) → new_esEs23(yvy40000, yvy30000, ccc)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Int) → new_ltEs15(yvy1000, yvy1010)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Double) → new_ltEs13(yvy1000, yvy1010)
new_esEs30(yvy40001, yvy30001, ty_Double) → new_esEs13(yvy40001, yvy30001)
new_ltEs21(yvy1001, yvy1011, app(app(ty_@2, efa), efb)) → new_ltEs12(yvy1001, yvy1011, efa, efb)
new_esEs10(yvy4000, yvy3000, ty_Bool) → new_esEs20(yvy4000, yvy3000)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Char, dac) → new_ltEs7(yvy1000, yvy1010)
new_ltEs16(True, True) → True
new_lt21(yvy153, yvy156, app(app(ty_@2, eag), eah)) → new_lt12(yvy153, yvy156, eag, eah)
new_lt6(yvy1000, yvy1010, ty_Bool) → new_lt18(yvy1000, yvy1010)
new_pePe(False, yvy305) → yvy305
new_compare15(GT, EQ) → GT
new_esEs7(yvy4000, yvy3000, ty_Char) → new_esEs15(yvy4000, yvy3000)
new_esEs31(yvy40000, yvy30000, app(ty_[], cee)) → new_esEs16(yvy40000, yvy30000, cee)
new_esEs39(yvy165, yvy167, ty_@0) → new_esEs19(yvy165, yvy167)
new_esEs23(Just(yvy40000), Just(yvy30000), app(ty_Maybe, ddh)) → new_esEs23(yvy40000, yvy30000, ddh)
new_lt21(yvy153, yvy156, ty_Char) → new_lt8(yvy153, yvy156)
new_esEs26(yvy40000, yvy30000, ty_Bool) → new_esEs20(yvy40000, yvy30000)
new_esEs9(yvy4000, yvy3000, app(app(ty_@2, ffd), ffe)) → new_esEs17(yvy4000, yvy3000, ffd, ffe)
new_compare14(yvy218, yvy219, yvy220, yvy221, yvy222, yvy223, False, ceb, cec, ced) → GT
new_lt9(yvy152, yvy155, dhf) → new_esEs12(new_compare0(yvy152, yvy155, dhf), LT)
new_esEs28(yvy1001, yvy1011, ty_Integer) → new_esEs18(yvy1001, yvy1011)
new_esEs5(yvy4001, yvy3001, ty_Ordering) → new_esEs12(yvy4001, yvy3001)
new_esEs5(yvy4001, yvy3001, ty_Int) → new_esEs25(yvy4001, yvy3001)
new_esEs4(yvy4000, yvy3000, ty_Float) → new_esEs14(yvy4000, yvy3000)
new_compare15(GT, LT) → GT
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Char, hh) → new_esEs15(yvy40000, yvy30000)
new_esEs29(yvy40000, yvy30000, ty_Int) → new_esEs25(yvy40000, yvy30000)
new_compare30(yvy400, yvy300, app(app(ty_Either, eff), efg)) → new_compare27(yvy400, yvy300, eff, efg)
new_lt22(yvy1000, yvy1010, ty_Double) → new_lt13(yvy1000, yvy1010)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Ordering) → new_esEs12(yvy40000, yvy30000)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Char) → new_esEs15(yvy40000, yvy30000)
new_esEs29(yvy40000, yvy30000, app(app(ty_@2, cbe), cbf)) → new_esEs17(yvy40000, yvy30000, cbe, cbf)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, app(app(ty_@2, dfh), dga)) → new_esEs17(yvy40000, yvy30000, dfh, dga)
new_ltEs23(yvy166, yvy168, app(app(ty_Either, fed), fee)) → new_ltEs14(yvy166, yvy168, fed, fee)
new_esEs31(yvy40000, yvy30000, ty_Integer) → new_esEs18(yvy40000, yvy30000)
new_compare12(True, True) → EQ
new_esEs36(yvy1000, yvy1010, app(ty_[], edb)) → new_esEs16(yvy1000, yvy1010, edb)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Ordering, hh) → new_esEs12(yvy40000, yvy30000)
new_ltEs6(GT, EQ) → False
new_ltEs18(yvy107, yvy108, app(app(ty_Either, bfa), bfb)) → new_ltEs14(yvy107, yvy108, bfa, bfb)
new_esEs32(yvy40001, yvy30001, app(ty_Maybe, cgf)) → new_esEs23(yvy40001, yvy30001, cgf)
new_esEs35(yvy153, yvy156, ty_Integer) → new_esEs18(yvy153, yvy156)
new_esEs33(yvy40002, yvy30002, ty_Integer) → new_esEs18(yvy40002, yvy30002)
new_esEs31(yvy40000, yvy30000, ty_Double) → new_esEs13(yvy40000, yvy30000)
new_esEs10(yvy4000, yvy3000, ty_Ordering) → new_esEs12(yvy4000, yvy3000)
new_primCompAux1(yvy400, yvy300, yvy51, h) → new_primCompAux0(yvy51, new_compare30(yvy400, yvy300, h))
new_esEs33(yvy40002, yvy30002, ty_Float) → new_esEs14(yvy40002, yvy30002)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, app(app(app(ty_@3, dca), dcb), dcc)) → new_ltEs10(yvy1000, yvy1010, dca, dcb, dcc)
new_ltEs23(yvy166, yvy168, app(ty_[], fdd)) → new_ltEs8(yvy166, yvy168, fdd)
new_lt23(yvy165, yvy167, app(app(ty_@2, fcg), fch)) → new_lt12(yvy165, yvy167, fcg, fch)
new_esEs34(yvy152, yvy155, ty_Integer) → new_esEs18(yvy152, yvy155)
new_esEs23(Just(yvy40000), Just(yvy30000), app(app(ty_Either, dea), deb)) → new_esEs24(yvy40000, yvy30000, dea, deb)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Ordering, dac) → new_ltEs6(yvy1000, yvy1010)
new_lt22(yvy1000, yvy1010, ty_Bool) → new_lt18(yvy1000, yvy1010)
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_esEs39(yvy165, yvy167, ty_Float) → new_esEs14(yvy165, yvy167)
new_ltEs22(yvy114, yvy115, ty_Bool) → new_ltEs16(yvy114, yvy115)
new_ltEs4(yvy100, yvy101) → new_fsEs(new_compare8(yvy100, yvy101))
new_esEs33(yvy40002, yvy30002, app(ty_[], cha)) → new_esEs16(yvy40002, yvy30002, cha)
new_ltEs8(yvy100, yvy101, fef) → new_fsEs(new_compare0(yvy100, yvy101, fef))
new_compare30(yvy400, yvy300, ty_Char) → new_compare11(yvy400, yvy300)
new_esEs36(yvy1000, yvy1010, ty_Integer) → new_esEs18(yvy1000, yvy1010)
new_esEs39(yvy165, yvy167, ty_Bool) → new_esEs20(yvy165, yvy167)
new_esEs36(yvy1000, yvy1010, ty_Bool) → new_esEs20(yvy1000, yvy1010)
new_esEs32(yvy40001, yvy30001, app(ty_Ratio, cgb)) → new_esEs21(yvy40001, yvy30001, cgb)
new_compare12(False, True) → LT
new_esEs5(yvy4001, yvy3001, ty_Char) → new_esEs15(yvy4001, yvy3001)
new_esEs34(yvy152, yvy155, ty_Char) → new_esEs15(yvy152, yvy155)
new_esEs31(yvy40000, yvy30000, app(app(ty_@2, cef), ceg)) → new_esEs17(yvy40000, yvy30000, cef, ceg)
new_ltEs18(yvy107, yvy108, ty_Integer) → new_ltEs4(yvy107, yvy108)
new_lt21(yvy153, yvy156, ty_@0) → new_lt19(yvy153, yvy156)
new_esEs30(yvy40001, yvy30001, ty_@0) → new_esEs19(yvy40001, yvy30001)
new_ltEs18(yvy107, yvy108, app(ty_Maybe, beh)) → new_ltEs5(yvy107, yvy108, beh)
new_esEs12(LT, LT) → True
new_ltEs24(yvy100, yvy101, ty_Char) → new_ltEs7(yvy100, yvy101)
new_esEs31(yvy40000, yvy30000, app(app(ty_Either, cfe), cff)) → new_esEs24(yvy40000, yvy30000, cfe, cff)
new_ltEs18(yvy107, yvy108, ty_Double) → new_ltEs13(yvy107, yvy108)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Int, dac) → new_ltEs15(yvy1000, yvy1010)
new_esEs28(yvy1001, yvy1011, app(ty_Maybe, bhg)) → new_esEs23(yvy1001, yvy1011, bhg)
new_lt5(yvy1001, yvy1011, ty_@0) → new_lt19(yvy1001, yvy1011)
new_compare15(EQ, LT) → GT
new_pePe(True, yvy305) → True
new_compare0([], [], feh) → EQ
new_primEqNat0(Zero, Zero) → True
new_ltEs21(yvy1001, yvy1011, ty_Double) → new_ltEs13(yvy1001, yvy1011)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Float) → new_esEs14(yvy40000, yvy30000)
new_esEs6(yvy4002, yvy3002, ty_Double) → new_esEs13(yvy4002, yvy3002)
new_esEs4(yvy4000, yvy3000, app(ty_Maybe, hf)) → new_esEs23(yvy4000, yvy3000, hf)
new_lt5(yvy1001, yvy1011, ty_Bool) → new_lt18(yvy1001, yvy1011)
new_lt23(yvy165, yvy167, ty_Integer) → new_lt15(yvy165, yvy167)
new_esEs5(yvy4001, yvy3001, ty_Float) → new_esEs14(yvy4001, yvy3001)
new_lt21(yvy153, yvy156, app(app(ty_Either, ebb), ebc)) → new_lt16(yvy153, yvy156, ebb, ebc)
new_esEs8(yvy4001, yvy3001, app(app(app(ty_@3, dh), ea), eb)) → new_esEs22(yvy4001, yvy3001, dh, ea, eb)
new_lt11(yvy152, yvy155) → new_esEs12(new_compare18(yvy152, yvy155), LT)
new_lt20(yvy152, yvy155, app(ty_[], dhf)) → new_lt9(yvy152, yvy155, dhf)
new_esEs13(Double(yvy40000, yvy40001), Double(yvy30000, yvy30001)) → new_esEs25(new_sr0(yvy40000, yvy30000), new_sr0(yvy40001, yvy30001))
new_esEs7(yvy4000, yvy3000, ty_Bool) → new_esEs20(yvy4000, yvy3000)
new_compare30(yvy400, yvy300, ty_@0) → new_compare9(yvy400, yvy300)
new_esEs29(yvy40000, yvy30000, ty_@0) → new_esEs19(yvy40000, yvy30000)
new_esEs6(yvy4002, yvy3002, ty_Ordering) → new_esEs12(yvy4002, yvy3002)
new_ltEs18(yvy107, yvy108, app(app(app(ty_@3, bec), bed), bee)) → new_ltEs10(yvy107, yvy108, bec, bed, bee)
new_ltEs22(yvy114, yvy115, ty_@0) → new_ltEs17(yvy114, yvy115)
new_lt5(yvy1001, yvy1011, ty_Char) → new_lt8(yvy1001, yvy1011)
new_lt5(yvy1001, yvy1011, app(app(ty_Either, bhh), caa)) → new_lt16(yvy1001, yvy1011, bhh, caa)
new_ltEs19(yvy1002, yvy1012, ty_Ordering) → new_ltEs6(yvy1002, yvy1012)
new_esEs15(Char(yvy40000), Char(yvy30000)) → new_primEqNat0(yvy40000, yvy30000)
new_esEs24(Left(yvy40000), Left(yvy30000), app(app(app(ty_@3, dfa), dfb), dfc), hh) → new_esEs22(yvy40000, yvy30000, dfa, dfb, dfc)
new_esEs26(yvy40000, yvy30000, ty_Int) → new_esEs25(yvy40000, yvy30000)
new_esEs32(yvy40001, yvy30001, ty_Integer) → new_esEs18(yvy40001, yvy30001)
new_ltEs23(yvy166, yvy168, ty_Double) → new_ltEs13(yvy166, yvy168)
new_lt22(yvy1000, yvy1010, app(ty_[], edb)) → new_lt9(yvy1000, yvy1010, edb)
new_ltEs23(yvy166, yvy168, ty_Integer) → new_ltEs4(yvy166, yvy168)
new_esEs9(yvy4000, yvy3000, app(ty_[], ffc)) → new_esEs16(yvy4000, yvy3000, ffc)
new_esEs33(yvy40002, yvy30002, ty_Bool) → new_esEs20(yvy40002, yvy30002)
new_esEs11(yvy4000, yvy3000, ty_Double) → new_esEs13(yvy4000, yvy3000)
new_esEs29(yvy40000, yvy30000, ty_Bool) → new_esEs20(yvy40000, yvy30000)
new_lt5(yvy1001, yvy1011, app(ty_[], bgh)) → new_lt9(yvy1001, yvy1011, bgh)
new_ltEs21(yvy1001, yvy1011, ty_Bool) → new_ltEs16(yvy1001, yvy1011)
new_ltEs6(EQ, GT) → True
new_esEs9(yvy4000, yvy3000, ty_Integer) → new_esEs18(yvy4000, yvy3000)
new_esEs11(yvy4000, yvy3000, ty_Ordering) → new_esEs12(yvy4000, yvy3000)
new_esEs23(Just(yvy40000), Nothing, hf) → False
new_esEs23(Nothing, Just(yvy30000), hf) → False
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_ltEs18(yvy107, yvy108, ty_Ordering) → new_ltEs6(yvy107, yvy108)
new_esEs23(Just(yvy40000), Just(yvy30000), app(app(app(ty_@3, dde), ddf), ddg)) → new_esEs22(yvy40000, yvy30000, dde, ddf, ddg)
new_ltEs24(yvy100, yvy101, ty_Double) → new_ltEs13(yvy100, yvy101)
new_esEs10(yvy4000, yvy3000, ty_Double) → new_esEs13(yvy4000, yvy3000)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, ty_Float) → new_esEs14(yvy40000, yvy30000)
new_compare110(yvy233, yvy234, yvy235, yvy236, False, yvy238, ecf, ecg) → new_compare111(yvy233, yvy234, yvy235, yvy236, yvy238, ecf, ecg)
new_ltEs20(yvy154, yvy157, ty_Bool) → new_ltEs16(yvy154, yvy157)
new_ltEs24(yvy100, yvy101, ty_@0) → new_ltEs17(yvy100, yvy101)
new_ltEs5(Just(yvy1000), Just(yvy1010), app(app(ty_@2, fg), fh)) → new_ltEs12(yvy1000, yvy1010, fg, fh)
new_ltEs20(yvy154, yvy157, ty_Int) → new_ltEs15(yvy154, yvy157)
new_esEs8(yvy4001, yvy3001, ty_@0) → new_esEs19(yvy4001, yvy3001)
new_lt22(yvy1000, yvy1010, app(app(ty_Either, eeb), eec)) → new_lt16(yvy1000, yvy1010, eeb, eec)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Float, dac) → new_ltEs11(yvy1000, yvy1010)
new_compare26(yvy107, yvy108, False, bdg, bdh) → new_compare10(yvy107, yvy108, new_ltEs18(yvy107, yvy108, bdg), bdg, bdh)
new_lt21(yvy153, yvy156, app(ty_Ratio, eac)) → new_lt10(yvy153, yvy156, eac)
new_compare30(yvy400, yvy300, ty_Float) → new_compare18(yvy400, yvy300)
new_primEqInt(Neg(Succ(yvy400000)), Neg(Succ(yvy300000))) → new_primEqNat0(yvy400000, yvy300000)
new_esEs23(Nothing, Nothing, hf) → True
new_esEs10(yvy4000, yvy3000, app(app(app(ty_@3, egd), ege), egf)) → new_esEs22(yvy4000, yvy3000, egd, ege, egf)
new_esEs39(yvy165, yvy167, app(app(ty_@2, fcg), fch)) → new_esEs17(yvy165, yvy167, fcg, fch)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, app(app(ty_@2, dcd), dce)) → new_ltEs12(yvy1000, yvy1010, dcd, dce)
new_ltEs5(Just(yvy1000), Nothing, eh) → False
new_esEs28(yvy1001, yvy1011, ty_Char) → new_esEs15(yvy1001, yvy1011)
new_esEs11(yvy4000, yvy3000, app(ty_Maybe, faa)) → new_esEs23(yvy4000, yvy3000, faa)
new_lt14(yvy152, yvy155, dhg) → new_esEs12(new_compare31(yvy152, yvy155, dhg), LT)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, ty_@0) → new_ltEs17(yvy1000, yvy1010)
new_ltEs14(Right(yvy1000), Left(yvy1010), dbf, dac) → False
new_esEs12(EQ, LT) → False
new_esEs12(LT, EQ) → False
new_ltEs19(yvy1002, yvy1012, app(ty_Ratio, cac)) → new_ltEs9(yvy1002, yvy1012, cac)
new_lt22(yvy1000, yvy1010, app(app(ty_@2, edg), edh)) → new_lt12(yvy1000, yvy1010, edg, edh)
new_ltEs23(yvy166, yvy168, ty_Bool) → new_ltEs16(yvy166, yvy168)
new_compare111(yvy233, yvy234, yvy235, yvy236, True, ecf, ecg) → LT
new_esEs7(yvy4000, yvy3000, app(ty_[], ca)) → new_esEs16(yvy4000, yvy3000, ca)
new_esEs5(yvy4001, yvy3001, ty_Bool) → new_esEs20(yvy4001, yvy3001)
new_lt23(yvy165, yvy167, ty_Int) → new_lt17(yvy165, yvy167)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs30(yvy40001, yvy30001, app(app(app(ty_@3, cdb), cdc), cdd)) → new_esEs22(yvy40001, yvy30001, cdb, cdc, cdd)
new_esEs11(yvy4000, yvy3000, app(app(ty_Either, fab), fac)) → new_esEs24(yvy4000, yvy3000, fab, fac)
new_esEs35(yvy153, yvy156, app(app(app(ty_@3, ead), eae), eaf)) → new_esEs22(yvy153, yvy156, ead, eae, eaf)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, ty_Int) → new_ltEs15(yvy1000, yvy1010)
new_esEs10(yvy4000, yvy3000, app(app(ty_Either, egh), eha)) → new_esEs24(yvy4000, yvy3000, egh, eha)
new_esEs28(yvy1001, yvy1011, ty_Double) → new_esEs13(yvy1001, yvy1011)
new_lt20(yvy152, yvy155, ty_Ordering) → new_lt7(yvy152, yvy155)
new_ltEs6(EQ, EQ) → True
new_compare31(Just(yvy4000), Nothing, ffb) → GT
new_esEs11(yvy4000, yvy3000, app(app(app(ty_@3, ehf), ehg), ehh)) → new_esEs22(yvy4000, yvy3000, ehf, ehg, ehh)
new_ltEs22(yvy114, yvy115, app(app(ty_Either, fbf), fbg)) → new_ltEs14(yvy114, yvy115, fbf, fbg)
new_esEs28(yvy1001, yvy1011, app(app(app(ty_@3, bhb), bhc), bhd)) → new_esEs22(yvy1001, yvy1011, bhb, bhc, bhd)
new_esEs32(yvy40001, yvy30001, ty_Float) → new_esEs14(yvy40001, yvy30001)
new_esEs27(yvy1000, yvy1010, app(ty_Ratio, bfg)) → new_esEs21(yvy1000, yvy1010, bfg)
new_ltEs19(yvy1002, yvy1012, ty_Integer) → new_ltEs4(yvy1002, yvy1012)
new_primEqInt(Neg(Succ(yvy400000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(yvy300000))) → False
new_primCompAux0(yvy56, GT) → GT
new_compare30(yvy400, yvy300, app(app(app(ty_@3, gd), ge), gf)) → new_compare6(yvy400, yvy300, gd, ge, gf)
new_esEs39(yvy165, yvy167, ty_Integer) → new_esEs18(yvy165, yvy167)
new_compare26(yvy107, yvy108, True, bdg, bdh) → EQ
new_esEs23(Just(yvy40000), Just(yvy30000), app(app(ty_@2, ddb), ddc)) → new_esEs17(yvy40000, yvy30000, ddb, ddc)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, app(app(ty_Either, dgg), dgh)) → new_esEs24(yvy40000, yvy30000, dgg, dgh)
new_ltEs6(GT, GT) → True
new_ltEs21(yvy1001, yvy1011, app(app(ty_Either, efd), efe)) → new_ltEs14(yvy1001, yvy1011, efd, efe)
new_esEs38(yvy40001, yvy30001, ty_Integer) → new_esEs18(yvy40001, yvy30001)
new_esEs32(yvy40001, yvy30001, app(ty_[], cfg)) → new_esEs16(yvy40001, yvy30001, cfg)
new_esEs34(yvy152, yvy155, ty_Int) → new_esEs25(yvy152, yvy155)
new_compare31(Nothing, Nothing, ffb) → EQ
new_esEs29(yvy40000, yvy30000, app(ty_[], cbd)) → new_esEs16(yvy40000, yvy30000, cbd)
new_esEs26(yvy40000, yvy30000, app(ty_Ratio, bch)) → new_esEs21(yvy40000, yvy30000, bch)
new_esEs7(yvy4000, yvy3000, app(ty_Maybe, da)) → new_esEs23(yvy4000, yvy3000, da)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_@0) → new_ltEs17(yvy1000, yvy1010)
new_lt21(yvy153, yvy156, app(ty_[], eab)) → new_lt9(yvy153, yvy156, eab)
new_ltEs20(yvy154, yvy157, app(ty_[], ebd)) → new_ltEs8(yvy154, yvy157, ebd)
new_esEs36(yvy1000, yvy1010, ty_Int) → new_esEs25(yvy1000, yvy1010)
new_esEs19(@0, @0) → True
new_compare6(@3(yvy4000, yvy4001, yvy4002), @3(yvy3000, yvy3001, yvy3002), gd, ge, gf) → new_compare25(yvy4000, yvy4001, yvy4002, yvy3000, yvy3001, yvy3002, new_asAs(new_esEs4(yvy4000, yvy3000, gd), new_asAs(new_esEs5(yvy4001, yvy3001, ge), new_esEs6(yvy4002, yvy3002, gf))), gd, ge, gf)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_esEs7(yvy4000, yvy3000, ty_Integer) → new_esEs18(yvy4000, yvy3000)
new_esEs4(yvy4000, yvy3000, ty_Bool) → new_esEs20(yvy4000, yvy3000)
new_esEs39(yvy165, yvy167, ty_Ordering) → new_esEs12(yvy165, yvy167)
new_lt20(yvy152, yvy155, ty_Char) → new_lt8(yvy152, yvy155)
new_esEs31(yvy40000, yvy30000, ty_Bool) → new_esEs20(yvy40000, yvy30000)
new_lt4(yvy152, yvy155, bd, be, bf) → new_esEs12(new_compare6(yvy152, yvy155, bd, be, bf), LT)
new_esEs6(yvy4002, yvy3002, ty_Int) → new_esEs25(yvy4002, yvy3002)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Double, dac) → new_ltEs13(yvy1000, yvy1010)
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_lt6(yvy1000, yvy1010, app(ty_Maybe, bge)) → new_lt14(yvy1000, yvy1010, bge)
new_ltEs14(Left(yvy1000), Left(yvy1010), app(ty_Maybe, dbc), dac) → new_ltEs5(yvy1000, yvy1010, dbc)
new_esEs4(yvy4000, yvy3000, app(ty_Ratio, hb)) → new_esEs21(yvy4000, yvy3000, hb)
new_lt5(yvy1001, yvy1011, app(ty_Maybe, bhg)) → new_lt14(yvy1001, yvy1011, bhg)
new_primEqInt(Pos(Succ(yvy400000)), Pos(Succ(yvy300000))) → new_primEqNat0(yvy400000, yvy300000)
new_compare10(yvy199, yvy200, False, ef, eg) → GT
new_esEs34(yvy152, yvy155, app(ty_Maybe, dhg)) → new_esEs23(yvy152, yvy155, dhg)
new_esEs5(yvy4001, yvy3001, app(ty_[], baa)) → new_esEs16(yvy4001, yvy3001, baa)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, ty_Double) → new_ltEs13(yvy1000, yvy1010)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, ty_Integer) → new_ltEs4(yvy1000, yvy1010)
new_ltEs21(yvy1001, yvy1011, ty_Float) → new_ltEs11(yvy1001, yvy1011)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, app(ty_Maybe, dcf)) → new_ltEs5(yvy1000, yvy1010, dcf)
new_compare13(:%(yvy4000, yvy4001), :%(yvy3000, yvy3001), ty_Int) → new_compare16(new_sr0(yvy4000, yvy3001), new_sr0(yvy3000, yvy4001))
new_esEs26(yvy40000, yvy30000, app(ty_Maybe, bdd)) → new_esEs23(yvy40000, yvy30000, bdd)
new_ltEs24(yvy100, yvy101, ty_Float) → new_ltEs11(yvy100, yvy101)
new_esEs34(yvy152, yvy155, app(app(ty_@2, dec), ded)) → new_esEs17(yvy152, yvy155, dec, ded)
new_esEs8(yvy4001, yvy3001, ty_Integer) → new_esEs18(yvy4001, yvy3001)
new_ltEs22(yvy114, yvy115, app(app(app(ty_@3, fah), fba), fbb)) → new_ltEs10(yvy114, yvy115, fah, fba, fbb)
new_primEqNat0(Succ(yvy400000), Succ(yvy300000)) → new_primEqNat0(yvy400000, yvy300000)
new_esEs6(yvy4002, yvy3002, ty_Bool) → new_esEs20(yvy4002, yvy3002)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Ordering) → new_ltEs6(yvy1000, yvy1010)
new_ltEs24(yvy100, yvy101, ty_Int) → new_ltEs15(yvy100, yvy101)
new_esEs26(yvy40000, yvy30000, ty_Ordering) → new_esEs12(yvy40000, yvy30000)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, app(ty_Ratio, dgb)) → new_esEs21(yvy40000, yvy30000, dgb)
new_esEs11(yvy4000, yvy3000, app(ty_Ratio, ehe)) → new_esEs21(yvy4000, yvy3000, ehe)
new_esEs30(yvy40001, yvy30001, ty_Integer) → new_esEs18(yvy40001, yvy30001)
new_esEs39(yvy165, yvy167, ty_Char) → new_esEs15(yvy165, yvy167)
new_ltEs14(Left(yvy1000), Left(yvy1010), app(ty_Ratio, dae), dac) → new_ltEs9(yvy1000, yvy1010, dae)
new_esEs26(yvy40000, yvy30000, app(app(ty_@2, bcf), bcg)) → new_esEs17(yvy40000, yvy30000, bcf, bcg)
new_lt5(yvy1001, yvy1011, ty_Float) → new_lt11(yvy1001, yvy1011)
new_esEs32(yvy40001, yvy30001, ty_@0) → new_esEs19(yvy40001, yvy30001)
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_esEs33(yvy40002, yvy30002, app(ty_Maybe, chh)) → new_esEs23(yvy40002, yvy30002, chh)
new_lt6(yvy1000, yvy1010, ty_Int) → new_lt17(yvy1000, yvy1010)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, app(app(app(ty_@3, dgc), dgd), dge)) → new_esEs22(yvy40000, yvy30000, dgc, dgd, dge)
new_lt23(yvy165, yvy167, app(app(ty_Either, fdb), fdc)) → new_lt16(yvy165, yvy167, fdb, fdc)
new_esEs12(EQ, EQ) → True
new_lt23(yvy165, yvy167, ty_Char) → new_lt8(yvy165, yvy167)
new_ltEs18(yvy107, yvy108, app(app(ty_@2, bef), beg)) → new_ltEs12(yvy107, yvy108, bef, beg)
new_lt21(yvy153, yvy156, ty_Double) → new_lt13(yvy153, yvy156)
new_esEs35(yvy153, yvy156, ty_Ordering) → new_esEs12(yvy153, yvy156)
new_lt5(yvy1001, yvy1011, ty_Int) → new_lt17(yvy1001, yvy1011)
new_esEs10(yvy4000, yvy3000, ty_Char) → new_esEs15(yvy4000, yvy3000)
new_primEqInt(Pos(Succ(yvy400000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(yvy300000))) → False
new_ltEs5(Nothing, Just(yvy1010), eh) → True
new_lt20(yvy152, yvy155, ty_Int) → new_lt17(yvy152, yvy155)
new_esEs35(yvy153, yvy156, app(ty_Maybe, eba)) → new_esEs23(yvy153, yvy156, eba)
new_esEs27(yvy1000, yvy1010, ty_@0) → new_esEs19(yvy1000, yvy1010)
new_ltEs18(yvy107, yvy108, ty_Float) → new_ltEs11(yvy107, yvy108)
new_compare25(yvy152, yvy153, yvy154, yvy155, yvy156, yvy157, True, dhc, dhd, dhe) → EQ
new_esEs37(yvy40000, yvy30000, ty_Int) → new_esEs25(yvy40000, yvy30000)
new_primCmpNat0(Zero, Zero) → EQ
new_esEs27(yvy1000, yvy1010, app(app(ty_Either, bgf), bgg)) → new_esEs24(yvy1000, yvy1010, bgf, bgg)
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_compare27(Left(yvy4000), Right(yvy3000), eff, efg) → LT
new_lt22(yvy1000, yvy1010, ty_@0) → new_lt19(yvy1000, yvy1010)
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_compare9(@0, @0) → EQ
new_esEs28(yvy1001, yvy1011, ty_Int) → new_esEs25(yvy1001, yvy1011)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Float, hh) → new_esEs14(yvy40000, yvy30000)
new_esEs6(yvy4002, yvy3002, ty_Float) → new_esEs14(yvy4002, yvy3002)
new_ltEs9(yvy100, yvy101, cdh) → new_fsEs(new_compare13(yvy100, yvy101, cdh))
new_compare17(yvy218, yvy219, yvy220, yvy221, yvy222, yvy223, True, yvy225, ceb, cec, ced) → new_compare14(yvy218, yvy219, yvy220, yvy221, yvy222, yvy223, True, ceb, cec, ced)
new_esEs32(yvy40001, yvy30001, ty_Char) → new_esEs15(yvy40001, yvy30001)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_ltEs14(Left(yvy1000), Left(yvy1010), app(ty_[], dad), dac) → new_ltEs8(yvy1000, yvy1010, dad)
new_ltEs19(yvy1002, yvy1012, app(app(ty_@2, cag), cah)) → new_ltEs12(yvy1002, yvy1012, cag, cah)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Double, hh) → new_esEs13(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, app(app(ty_Either, daa), dab)) → new_esEs24(yvy40002, yvy30002, daa, dab)
new_esEs4(yvy4000, yvy3000, ty_Int) → new_esEs25(yvy4000, yvy3000)
new_compare28(yvy114, yvy115, True, fad, fae) → EQ
new_primEqInt(Pos(Succ(yvy400000)), Neg(yvy30000)) → False
new_primEqInt(Neg(Succ(yvy400000)), Pos(yvy30000)) → False
new_esEs24(Right(yvy40000), Right(yvy30000), hg, ty_Int) → new_esEs25(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, ty_Ordering) → new_esEs12(yvy40002, yvy30002)
new_esEs29(yvy40000, yvy30000, app(app(app(ty_@3, cbh), cca), ccb)) → new_esEs22(yvy40000, yvy30000, cbh, cca, ccb)
new_esEs26(yvy40000, yvy30000, ty_Double) → new_esEs13(yvy40000, yvy30000)
new_ltEs20(yvy154, yvy157, ty_Integer) → new_ltEs4(yvy154, yvy157)
new_compare210(yvy100, yvy101, True, feg) → EQ
new_lt6(yvy1000, yvy1010, ty_Ordering) → new_lt7(yvy1000, yvy1010)
new_esEs29(yvy40000, yvy30000, app(ty_Ratio, cbg)) → new_esEs21(yvy40000, yvy30000, cbg)
new_esEs20(False, False) → True
new_esEs24(Left(yvy40000), Left(yvy30000), app(ty_[], dee), hh) → new_esEs16(yvy40000, yvy30000, dee)
new_lt23(yvy165, yvy167, app(ty_[], fcb)) → new_lt9(yvy165, yvy167, fcb)
new_ltEs22(yvy114, yvy115, ty_Integer) → new_ltEs4(yvy114, yvy115)
new_ltEs5(Just(yvy1000), Just(yvy1010), app(app(ty_Either, gb), gc)) → new_ltEs14(yvy1000, yvy1010, gb, gc)
new_lt23(yvy165, yvy167, ty_Bool) → new_lt18(yvy165, yvy167)
new_esEs30(yvy40001, yvy30001, ty_Ordering) → new_esEs12(yvy40001, yvy30001)
new_lt6(yvy1000, yvy1010, ty_Integer) → new_lt15(yvy1000, yvy1010)
new_primEqInt(Pos(Zero), Neg(Succ(yvy300000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(yvy300000))) → False
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_compare30(yvy400, yvy300, app(ty_Maybe, ffb)) → new_compare31(yvy400, yvy300, ffb)
new_esEs9(yvy4000, yvy3000, ty_Ordering) → new_esEs12(yvy4000, yvy3000)
new_esEs7(yvy4000, yvy3000, ty_@0) → new_esEs19(yvy4000, yvy3000)
new_esEs11(yvy4000, yvy3000, ty_Float) → new_esEs14(yvy4000, yvy3000)
new_lt6(yvy1000, yvy1010, app(ty_[], bff)) → new_lt9(yvy1000, yvy1010, bff)
new_esEs36(yvy1000, yvy1010, ty_@0) → new_esEs19(yvy1000, yvy1010)
new_esEs5(yvy4001, yvy3001, ty_@0) → new_esEs19(yvy4001, yvy3001)
new_esEs36(yvy1000, yvy1010, app(app(app(ty_@3, edd), ede), edf)) → new_esEs22(yvy1000, yvy1010, edd, ede, edf)
new_esEs28(yvy1001, yvy1011, ty_Ordering) → new_esEs12(yvy1001, yvy1011)
new_esEs10(yvy4000, yvy3000, app(ty_[], efh)) → new_esEs16(yvy4000, yvy3000, efh)
new_primCompAux0(yvy56, LT) → LT
new_esEs6(yvy4002, yvy3002, app(app(ty_Either, bcc), bcd)) → new_esEs24(yvy4002, yvy3002, bcc, bcd)
new_esEs6(yvy4002, yvy3002, ty_Integer) → new_esEs18(yvy4002, yvy3002)
new_esEs36(yvy1000, yvy1010, app(app(ty_@2, edg), edh)) → new_esEs17(yvy1000, yvy1010, edg, edh)
new_esEs7(yvy4000, yvy3000, app(app(ty_@2, cb), cc)) → new_esEs17(yvy4000, yvy3000, cb, cc)
new_esEs9(yvy4000, yvy3000, ty_Float) → new_esEs14(yvy4000, yvy3000)
new_lt5(yvy1001, yvy1011, ty_Double) → new_lt13(yvy1001, yvy1011)
new_ltEs22(yvy114, yvy115, app(ty_Maybe, fbe)) → new_ltEs5(yvy114, yvy115, fbe)
new_not(False) → True
new_esEs27(yvy1000, yvy1010, ty_Int) → new_esEs25(yvy1000, yvy1010)
new_esEs34(yvy152, yvy155, app(ty_Ratio, cea)) → new_esEs21(yvy152, yvy155, cea)
new_compare30(yvy400, yvy300, ty_Bool) → new_compare12(yvy400, yvy300)
new_esEs25(yvy4000, yvy3000) → new_primEqInt(yvy4000, yvy3000)
new_esEs28(yvy1001, yvy1011, app(ty_[], bgh)) → new_esEs16(yvy1001, yvy1011, bgh)
new_esEs31(yvy40000, yvy30000, ty_Char) → new_esEs15(yvy40000, yvy30000)
new_esEs14(Float(yvy40000, yvy40001), Float(yvy30000, yvy30001)) → new_esEs25(new_sr0(yvy40000, yvy30000), new_sr0(yvy40001, yvy30001))
new_esEs11(yvy4000, yvy3000, ty_@0) → new_esEs19(yvy4000, yvy3000)
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_esEs12(GT, EQ) → False
new_esEs12(EQ, GT) → False
new_esEs36(yvy1000, yvy1010, ty_Float) → new_esEs14(yvy1000, yvy1010)
new_esEs4(yvy4000, yvy3000, ty_Ordering) → new_esEs12(yvy4000, yvy3000)
new_esEs9(yvy4000, yvy3000, app(app(ty_Either, fgc), fgd)) → new_esEs24(yvy4000, yvy3000, fgc, fgd)
new_lt6(yvy1000, yvy1010, app(app(app(ty_@3, bfh), bga), bgb)) → new_lt4(yvy1000, yvy1010, bfh, bga, bgb)
new_esEs4(yvy4000, yvy3000, app(app(ty_@2, gh), ha)) → new_esEs17(yvy4000, yvy3000, gh, ha)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, ty_Integer) → new_esEs18(yvy40000, yvy30000)
new_ltEs18(yvy107, yvy108, ty_@0) → new_ltEs17(yvy107, yvy108)
new_esEs39(yvy165, yvy167, ty_Int) → new_esEs25(yvy165, yvy167)
new_compare15(LT, EQ) → LT
new_esEs34(yvy152, yvy155, ty_Float) → new_esEs14(yvy152, yvy155)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, app(ty_[], dbg)) → new_ltEs8(yvy1000, yvy1010, dbg)
new_esEs36(yvy1000, yvy1010, app(ty_Ratio, edc)) → new_esEs21(yvy1000, yvy1010, edc)
new_esEs30(yvy40001, yvy30001, app(ty_Ratio, cda)) → new_esEs21(yvy40001, yvy30001, cda)
new_compare30(yvy400, yvy300, app(ty_Ratio, ffa)) → new_compare13(yvy400, yvy300, ffa)
new_esEs24(Left(yvy40000), Right(yvy30000), hg, hh) → False
new_esEs24(Right(yvy40000), Left(yvy30000), hg, hh) → False
new_lt20(yvy152, yvy155, app(app(ty_Either, dhh), eaa)) → new_lt16(yvy152, yvy155, dhh, eaa)
new_esEs30(yvy40001, yvy30001, app(app(ty_@2, ccg), cch)) → new_esEs17(yvy40001, yvy30001, ccg, cch)
new_esEs32(yvy40001, yvy30001, app(app(ty_Either, cgg), cgh)) → new_esEs24(yvy40001, yvy30001, cgg, cgh)
new_esEs34(yvy152, yvy155, app(ty_[], dhf)) → new_esEs16(yvy152, yvy155, dhf)
new_lt20(yvy152, yvy155, ty_Double) → new_lt13(yvy152, yvy155)
new_esEs35(yvy153, yvy156, ty_Double) → new_esEs13(yvy153, yvy156)
new_compare0(:(yvy4000, yvy4001), [], feh) → GT
new_lt6(yvy1000, yvy1010, ty_Char) → new_lt8(yvy1000, yvy1010)
new_esEs8(yvy4001, yvy3001, ty_Int) → new_esEs25(yvy4001, yvy3001)
new_esEs38(yvy40001, yvy30001, ty_Int) → new_esEs25(yvy40001, yvy30001)
new_ltEs24(yvy100, yvy101, ty_Integer) → new_ltEs4(yvy100, yvy101)
new_ltEs20(yvy154, yvy157, app(ty_Maybe, ecc)) → new_ltEs5(yvy154, yvy157, ecc)
new_ltEs20(yvy154, yvy157, ty_@0) → new_ltEs17(yvy154, yvy157)
new_ltEs24(yvy100, yvy101, app(app(ty_Either, dbf), dac)) → new_ltEs14(yvy100, yvy101, dbf, dac)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Int) → new_esEs25(yvy40000, yvy30000)
new_esEs34(yvy152, yvy155, app(app(ty_Either, dhh), eaa)) → new_esEs24(yvy152, yvy155, dhh, eaa)
new_lt13(yvy152, yvy155) → new_esEs12(new_compare29(yvy152, yvy155), LT)
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_esEs30(yvy40001, yvy30001, app(app(ty_Either, cdf), cdg)) → new_esEs24(yvy40001, yvy30001, cdf, cdg)
new_lt19(yvy152, yvy155) → new_esEs12(new_compare9(yvy152, yvy155), LT)
new_ltEs18(yvy107, yvy108, ty_Char) → new_ltEs7(yvy107, yvy108)
new_esEs4(yvy4000, yvy3000, app(app(ty_Either, hg), hh)) → new_esEs24(yvy4000, yvy3000, hg, hh)
new_esEs8(yvy4001, yvy3001, app(ty_Ratio, dg)) → new_esEs21(yvy4001, yvy3001, dg)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Integer) → new_esEs18(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, app(ty_Ratio, chd)) → new_esEs21(yvy40002, yvy30002, chd)
new_lt17(yvy152, yvy155) → new_esEs12(new_compare16(yvy152, yvy155), LT)
new_esEs10(yvy4000, yvy3000, app(app(ty_@2, ega), egb)) → new_esEs17(yvy4000, yvy3000, ega, egb)
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_ltEs7(yvy100, yvy101) → new_fsEs(new_compare11(yvy100, yvy101))
new_esEs31(yvy40000, yvy30000, ty_Float) → new_esEs14(yvy40000, yvy30000)
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_compare15(EQ, GT) → LT
new_esEs32(yvy40001, yvy30001, ty_Int) → new_esEs25(yvy40001, yvy30001)
new_esEs29(yvy40000, yvy30000, ty_Char) → new_esEs15(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, app(app(app(ty_@3, che), chf), chg)) → new_esEs22(yvy40002, yvy30002, che, chf, chg)
new_primEqNat0(Zero, Succ(yvy300000)) → False
new_primEqNat0(Succ(yvy400000), Zero) → False
new_compare15(LT, GT) → LT
new_lt15(yvy152, yvy155) → new_esEs12(new_compare8(yvy152, yvy155), LT)
new_ltEs5(Nothing, Nothing, eh) → True
new_ltEs23(yvy166, yvy168, app(app(app(ty_@3, fdf), fdg), fdh)) → new_ltEs10(yvy166, yvy168, fdf, fdg, fdh)
new_lt20(yvy152, yvy155, app(app(ty_@2, dec), ded)) → new_lt12(yvy152, yvy155, dec, ded)
new_ltEs6(LT, LT) → True
new_ltEs6(EQ, LT) → False
new_esEs6(yvy4002, yvy3002, app(ty_Ratio, bbf)) → new_esEs21(yvy4002, yvy3002, bbf)
new_ltEs5(Just(yvy1000), Just(yvy1010), app(ty_[], fa)) → new_ltEs8(yvy1000, yvy1010, fa)
new_ltEs19(yvy1002, yvy1012, ty_Char) → new_ltEs7(yvy1002, yvy1012)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_ltEs21(yvy1001, yvy1011, app(ty_Ratio, eee)) → new_ltEs9(yvy1001, yvy1011, eee)
new_esEs9(yvy4000, yvy3000, app(ty_Maybe, fgb)) → new_esEs23(yvy4000, yvy3000, fgb)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Bool) → new_ltEs16(yvy1000, yvy1010)
new_lt21(yvy153, yvy156, app(ty_Maybe, eba)) → new_lt14(yvy153, yvy156, eba)
new_compare15(GT, GT) → EQ
new_esEs11(yvy4000, yvy3000, app(app(ty_@2, ehc), ehd)) → new_esEs17(yvy4000, yvy3000, ehc, ehd)
new_esEs8(yvy4001, yvy3001, app(app(ty_Either, ed), ee)) → new_esEs24(yvy4001, yvy3001, ed, ee)
new_compare24(yvy165, yvy166, yvy167, yvy168, True, fbh, fca) → EQ
new_esEs32(yvy40001, yvy30001, ty_Bool) → new_esEs20(yvy40001, yvy30001)
new_lt21(yvy153, yvy156, ty_Float) → new_lt11(yvy153, yvy156)
new_esEs16(:(yvy40000, yvy40001), [], gg) → False
new_esEs16([], :(yvy30000, yvy30001), gg) → False
new_compare31(Just(yvy4000), Just(yvy3000), ffb) → new_compare210(yvy4000, yvy3000, new_esEs9(yvy4000, yvy3000, ffb), ffb)
new_lt21(yvy153, yvy156, ty_Ordering) → new_lt7(yvy153, yvy156)
new_lt20(yvy152, yvy155, ty_Bool) → new_lt18(yvy152, yvy155)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, app(ty_Ratio, dbh)) → new_ltEs9(yvy1000, yvy1010, dbh)
new_ltEs19(yvy1002, yvy1012, ty_@0) → new_ltEs17(yvy1002, yvy1012)
new_esEs7(yvy4000, yvy3000, app(app(app(ty_@3, ce), cf), cg)) → new_esEs22(yvy4000, yvy3000, ce, cf, cg)
new_esEs5(yvy4001, yvy3001, ty_Integer) → new_esEs18(yvy4001, yvy3001)
new_esEs31(yvy40000, yvy30000, ty_Int) → new_esEs25(yvy40000, yvy30000)
new_esEs27(yvy1000, yvy1010, app(app(app(ty_@3, bfh), bga), bgb)) → new_esEs22(yvy1000, yvy1010, bfh, bga, bgb)
new_ltEs19(yvy1002, yvy1012, app(ty_Maybe, cba)) → new_ltEs5(yvy1002, yvy1012, cba)
new_lt21(yvy153, yvy156, ty_Integer) → new_lt15(yvy153, yvy156)
new_esEs29(yvy40000, yvy30000, app(app(ty_Either, ccd), cce)) → new_esEs24(yvy40000, yvy30000, ccd, cce)
new_esEs10(yvy4000, yvy3000, app(ty_Ratio, egc)) → new_esEs21(yvy4000, yvy3000, egc)
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_ltEs12(@2(yvy1000, yvy1001), @2(yvy1010, yvy1011), ech, eda) → new_pePe(new_lt22(yvy1000, yvy1010, ech), new_asAs(new_esEs36(yvy1000, yvy1010, ech), new_ltEs21(yvy1001, yvy1011, eda)))
new_ltEs23(yvy166, yvy168, ty_@0) → new_ltEs17(yvy166, yvy168)
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_esEs5(yvy4001, yvy3001, app(ty_Maybe, bah)) → new_esEs23(yvy4001, yvy3001, bah)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Char) → new_ltEs7(yvy1000, yvy1010)
new_compare0(:(yvy4000, yvy4001), :(yvy3000, yvy3001), feh) → new_primCompAux1(yvy4000, yvy3000, new_compare0(yvy4001, yvy3001, feh), feh)
new_esEs20(False, True) → False
new_esEs20(True, False) → False
new_compare19(yvy206, yvy207, True, dha, dhb) → LT
new_sr0(yvy3000, yvy4001) → new_primMulInt(yvy3000, yvy4001)
new_esEs28(yvy1001, yvy1011, app(app(ty_@2, bhe), bhf)) → new_esEs17(yvy1001, yvy1011, bhe, bhf)
new_lt6(yvy1000, yvy1010, app(app(ty_Either, bgf), bgg)) → new_lt16(yvy1000, yvy1010, bgf, bgg)
new_esEs34(yvy152, yvy155, ty_Bool) → new_esEs20(yvy152, yvy155)
new_lt22(yvy1000, yvy1010, ty_Integer) → new_lt15(yvy1000, yvy1010)
new_esEs26(yvy40000, yvy30000, app(app(ty_Either, bde), bdf)) → new_esEs24(yvy40000, yvy30000, bde, bdf)
new_compare30(yvy400, yvy300, ty_Ordering) → new_compare15(yvy400, yvy300)
new_esEs30(yvy40001, yvy30001, app(ty_[], ccf)) → new_esEs16(yvy40001, yvy30001, ccf)
new_esEs24(Left(yvy40000), Left(yvy30000), app(app(ty_@2, def), deg), hh) → new_esEs17(yvy40000, yvy30000, def, deg)
new_lt23(yvy165, yvy167, ty_@0) → new_lt19(yvy165, yvy167)
new_esEs10(yvy4000, yvy3000, ty_Float) → new_esEs14(yvy4000, yvy3000)
new_compare29(Double(yvy4000, yvy4001), Double(yvy3000, yvy3001)) → new_compare16(new_sr0(yvy4000, yvy3000), new_sr0(yvy4001, yvy3001))
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, ty_Bool) → new_ltEs16(yvy1000, yvy1010)
new_ltEs22(yvy114, yvy115, app(ty_[], faf)) → new_ltEs8(yvy114, yvy115, faf)
new_esEs39(yvy165, yvy167, app(app(ty_Either, fdb), fdc)) → new_esEs24(yvy165, yvy167, fdb, fdc)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs32(yvy40001, yvy30001, ty_Double) → new_esEs13(yvy40001, yvy30001)
new_esEs28(yvy1001, yvy1011, ty_Bool) → new_esEs20(yvy1001, yvy1011)
new_esEs23(Just(yvy40000), Just(yvy30000), app(ty_Ratio, ddd)) → new_esEs21(yvy40000, yvy30000, ddd)
new_esEs5(yvy4001, yvy3001, app(ty_Ratio, bad)) → new_esEs21(yvy4001, yvy3001, bad)
new_ltEs14(Left(yvy1000), Right(yvy1010), dbf, dac) → True
new_compare24(yvy165, yvy166, yvy167, yvy168, False, fbh, fca) → new_compare110(yvy165, yvy166, yvy167, yvy168, new_lt23(yvy165, yvy167, fbh), new_asAs(new_esEs39(yvy165, yvy167, fbh), new_ltEs23(yvy166, yvy168, fca)), fbh, fca)
new_compare30(yvy400, yvy300, app(ty_[], feh)) → new_compare0(yvy400, yvy300, feh)
new_esEs9(yvy4000, yvy3000, app(ty_Ratio, fff)) → new_esEs21(yvy4000, yvy3000, fff)
new_ltEs20(yvy154, yvy157, app(app(ty_Either, ecd), ece)) → new_ltEs14(yvy154, yvy157, ecd, ece)
new_asAs(False, yvy184) → False
new_compare27(Right(yvy4000), Left(yvy3000), eff, efg) → GT
new_esEs36(yvy1000, yvy1010, app(ty_Maybe, eea)) → new_esEs23(yvy1000, yvy1010, eea)
new_esEs9(yvy4000, yvy3000, ty_Double) → new_esEs13(yvy4000, yvy3000)
new_ltEs19(yvy1002, yvy1012, app(app(ty_Either, cbb), cbc)) → new_ltEs14(yvy1002, yvy1012, cbb, cbc)
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_lt20(yvy152, yvy155, ty_@0) → new_lt19(yvy152, yvy155)
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_esEs4(yvy4000, yvy3000, ty_@0) → new_esEs19(yvy4000, yvy3000)
new_esEs27(yvy1000, yvy1010, ty_Double) → new_esEs13(yvy1000, yvy1010)
new_esEs36(yvy1000, yvy1010, ty_Ordering) → new_esEs12(yvy1000, yvy1010)
new_compare16(yvy400, yvy300) → new_primCmpInt(yvy400, yvy300)
new_esEs35(yvy153, yvy156, ty_Bool) → new_esEs20(yvy153, yvy156)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Bool) → new_esEs20(yvy40000, yvy30000)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Integer, dac) → new_ltEs4(yvy1000, yvy1010)
new_compare14(yvy218, yvy219, yvy220, yvy221, yvy222, yvy223, True, ceb, cec, ced) → LT
new_esEs30(yvy40001, yvy30001, app(ty_Maybe, cde)) → new_esEs23(yvy40001, yvy30001, cde)
new_esEs8(yvy4001, yvy3001, ty_Char) → new_esEs15(yvy4001, yvy3001)
new_esEs9(yvy4000, yvy3000, ty_Bool) → new_esEs20(yvy4000, yvy3000)
new_lt5(yvy1001, yvy1011, ty_Ordering) → new_lt7(yvy1001, yvy1011)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, ty_Ordering) → new_ltEs6(yvy1000, yvy1010)
new_esEs24(Left(yvy40000), Left(yvy30000), app(app(ty_Either, dfe), dff), hh) → new_esEs24(yvy40000, yvy30000, dfe, dff)
new_esEs8(yvy4001, yvy3001, app(ty_[], dd)) → new_esEs16(yvy4001, yvy3001, dd)
new_compare27(Left(yvy4000), Left(yvy3000), eff, efg) → new_compare26(yvy4000, yvy3000, new_esEs10(yvy4000, yvy3000, eff), eff, efg)
new_esEs29(yvy40000, yvy30000, ty_Double) → new_esEs13(yvy40000, yvy30000)
new_esEs27(yvy1000, yvy1010, ty_Integer) → new_esEs18(yvy1000, yvy1010)
new_esEs18(Integer(yvy40000), Integer(yvy30000)) → new_primEqInt(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, ty_Char) → new_esEs15(yvy40002, yvy30002)
new_ltEs5(Just(yvy1000), Just(yvy1010), app(ty_Maybe, ga)) → new_ltEs5(yvy1000, yvy1010, ga)
new_ltEs11(yvy100, yvy101) → new_fsEs(new_compare18(yvy100, yvy101))
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, app(app(ty_Either, dcg), dch)) → new_ltEs14(yvy1000, yvy1010, dcg, dch)
new_esEs30(yvy40001, yvy30001, ty_Float) → new_esEs14(yvy40001, yvy30001)
new_lt23(yvy165, yvy167, ty_Float) → new_lt11(yvy165, yvy167)
new_compare12(False, False) → EQ
new_esEs28(yvy1001, yvy1011, ty_@0) → new_esEs19(yvy1001, yvy1011)
new_ltEs23(yvy166, yvy168, ty_Char) → new_ltEs7(yvy166, yvy168)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, app(ty_Maybe, dgf)) → new_esEs23(yvy40000, yvy30000, dgf)
new_esEs29(yvy40000, yvy30000, ty_Float) → new_esEs14(yvy40000, yvy30000)
new_esEs7(yvy4000, yvy3000, ty_Ordering) → new_esEs12(yvy4000, yvy3000)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Integer, hh) → new_esEs18(yvy40000, yvy30000)
new_lt20(yvy152, yvy155, app(ty_Maybe, dhg)) → new_lt14(yvy152, yvy155, dhg)
new_esEs39(yvy165, yvy167, app(app(app(ty_@3, fcd), fce), fcf)) → new_esEs22(yvy165, yvy167, fcd, fce, fcf)
new_esEs31(yvy40000, yvy30000, ty_@0) → new_esEs19(yvy40000, yvy30000)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, app(ty_[], dfg)) → new_esEs16(yvy40000, yvy30000, dfg)
new_compare111(yvy233, yvy234, yvy235, yvy236, False, ecf, ecg) → GT
new_lt21(yvy153, yvy156, ty_Bool) → new_lt18(yvy153, yvy156)
new_ltEs6(LT, GT) → True
new_esEs33(yvy40002, yvy30002, ty_Int) → new_esEs25(yvy40002, yvy30002)
new_compare30(yvy400, yvy300, ty_Integer) → new_compare8(yvy400, yvy300)
new_ltEs23(yvy166, yvy168, app(ty_Maybe, fec)) → new_ltEs5(yvy166, yvy168, fec)
new_lt23(yvy165, yvy167, app(ty_Maybe, fda)) → new_lt14(yvy165, yvy167, fda)
new_ltEs21(yvy1001, yvy1011, ty_Char) → new_ltEs7(yvy1001, yvy1011)
new_ltEs14(Left(yvy1000), Left(yvy1010), app(app(ty_Either, dbd), dbe), dac) → new_ltEs14(yvy1000, yvy1010, dbd, dbe)
new_ltEs23(yvy166, yvy168, app(app(ty_@2, fea), feb)) → new_ltEs12(yvy166, yvy168, fea, feb)
new_ltEs21(yvy1001, yvy1011, ty_Ordering) → new_ltEs6(yvy1001, yvy1011)
new_esEs32(yvy40001, yvy30001, app(app(ty_@2, cfh), cga)) → new_esEs17(yvy40001, yvy30001, cfh, cga)
new_esEs24(Left(yvy40000), Left(yvy30000), app(ty_Maybe, dfd), hh) → new_esEs23(yvy40000, yvy30000, dfd)
new_lt22(yvy1000, yvy1010, app(ty_Ratio, edc)) → new_lt10(yvy1000, yvy1010, edc)
new_lt12(yvy152, yvy155, dec, ded) → new_esEs12(new_compare7(yvy152, yvy155, dec, ded), LT)
new_esEs35(yvy153, yvy156, ty_Int) → new_esEs25(yvy153, yvy156)
new_lt10(yvy152, yvy155, cea) → new_esEs12(new_compare13(yvy152, yvy155, cea), LT)
new_esEs4(yvy4000, yvy3000, ty_Double) → new_esEs13(yvy4000, yvy3000)
new_esEs8(yvy4001, yvy3001, app(app(ty_@2, de), df)) → new_esEs17(yvy4001, yvy3001, de, df)
new_esEs5(yvy4001, yvy3001, app(app(ty_@2, bab), bac)) → new_esEs17(yvy4001, yvy3001, bab, bac)
new_esEs16([], [], gg) → True
new_lt22(yvy1000, yvy1010, ty_Float) → new_lt11(yvy1000, yvy1010)
new_esEs32(yvy40001, yvy30001, ty_Ordering) → new_esEs12(yvy40001, yvy30001)
new_ltEs19(yvy1002, yvy1012, ty_Int) → new_ltEs15(yvy1002, yvy1012)
new_ltEs21(yvy1001, yvy1011, ty_Integer) → new_ltEs4(yvy1001, yvy1011)
new_ltEs20(yvy154, yvy157, ty_Float) → new_ltEs11(yvy154, yvy157)
new_lt5(yvy1001, yvy1011, app(app(ty_@2, bhe), bhf)) → new_lt12(yvy1001, yvy1011, bhe, bhf)
new_esEs11(yvy4000, yvy3000, ty_Int) → new_esEs25(yvy4000, yvy3000)
new_esEs32(yvy40001, yvy30001, app(app(app(ty_@3, cgc), cgd), cge)) → new_esEs22(yvy40001, yvy30001, cgc, cgd, cge)
new_lt6(yvy1000, yvy1010, ty_Double) → new_lt13(yvy1000, yvy1010)
new_lt20(yvy152, yvy155, ty_Float) → new_lt11(yvy152, yvy155)
new_ltEs14(Left(yvy1000), Left(yvy1010), app(app(app(ty_@3, daf), dag), dah), dac) → new_ltEs10(yvy1000, yvy1010, daf, dag, dah)
new_esEs26(yvy40000, yvy30000, ty_Integer) → new_esEs18(yvy40000, yvy30000)
new_lt22(yvy1000, yvy1010, app(app(app(ty_@3, edd), ede), edf)) → new_lt4(yvy1000, yvy1010, edd, ede, edf)
new_esEs36(yvy1000, yvy1010, app(app(ty_Either, eeb), eec)) → new_esEs24(yvy1000, yvy1010, eeb, eec)
new_esEs27(yvy1000, yvy1010, ty_Ordering) → new_esEs12(yvy1000, yvy1010)
new_ltEs19(yvy1002, yvy1012, ty_Double) → new_ltEs13(yvy1002, yvy1012)
new_lt21(yvy153, yvy156, ty_Int) → new_lt17(yvy153, yvy156)
new_lt20(yvy152, yvy155, ty_Integer) → new_lt15(yvy152, yvy155)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, ty_Ordering) → new_esEs12(yvy40000, yvy30000)
new_lt8(yvy152, yvy155) → new_esEs12(new_compare11(yvy152, yvy155), LT)
new_ltEs24(yvy100, yvy101, app(ty_[], fef)) → new_ltEs8(yvy100, yvy101, fef)
new_esEs9(yvy4000, yvy3000, ty_@0) → new_esEs19(yvy4000, yvy3000)
new_esEs22(@3(yvy40000, yvy40001, yvy40002), @3(yvy30000, yvy30001, yvy30002), hc, hd, he) → new_asAs(new_esEs31(yvy40000, yvy30000, hc), new_asAs(new_esEs32(yvy40001, yvy30001, hd), new_esEs33(yvy40002, yvy30002, he)))
new_esEs8(yvy4001, yvy3001, ty_Float) → new_esEs14(yvy4001, yvy3001)
new_esEs7(yvy4000, yvy3000, app(ty_Ratio, cd)) → new_esEs21(yvy4000, yvy3000, cd)
new_ltEs20(yvy154, yvy157, ty_Double) → new_ltEs13(yvy154, yvy157)
new_ltEs18(yvy107, yvy108, ty_Bool) → new_ltEs16(yvy107, yvy108)
new_compare28(yvy114, yvy115, False, fad, fae) → new_compare19(yvy114, yvy115, new_ltEs22(yvy114, yvy115, fae), fad, fae)
new_esEs6(yvy4002, yvy3002, app(ty_Maybe, bcb)) → new_esEs23(yvy4002, yvy3002, bcb)
new_lt5(yvy1001, yvy1011, app(app(app(ty_@3, bhb), bhc), bhd)) → new_lt4(yvy1001, yvy1011, bhb, bhc, bhd)
new_esEs31(yvy40000, yvy30000, app(app(app(ty_@3, cfa), cfb), cfc)) → new_esEs22(yvy40000, yvy30000, cfa, cfb, cfc)
new_esEs31(yvy40000, yvy30000, ty_Ordering) → new_esEs12(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, ty_Double) → new_esEs13(yvy40002, yvy30002)
new_lt6(yvy1000, yvy1010, ty_Float) → new_lt11(yvy1000, yvy1010)
new_esEs4(yvy4000, yvy3000, ty_Char) → new_esEs15(yvy4000, yvy3000)
new_esEs7(yvy4000, yvy3000, app(app(ty_Either, db), dc)) → new_esEs24(yvy4000, yvy3000, db, dc)
new_compare112(yvy189, yvy190, False, fge) → GT
new_esEs12(GT, GT) → True
new_ltEs21(yvy1001, yvy1011, app(app(app(ty_@3, eef), eeg), eeh)) → new_ltEs10(yvy1001, yvy1011, eef, eeg, eeh)
new_esEs5(yvy4001, yvy3001, ty_Double) → new_esEs13(yvy4001, yvy3001)
new_compare17(yvy218, yvy219, yvy220, yvy221, yvy222, yvy223, False, yvy225, ceb, cec, ced) → new_compare14(yvy218, yvy219, yvy220, yvy221, yvy222, yvy223, yvy225, ceb, cec, ced)
new_esEs8(yvy4001, yvy3001, app(ty_Maybe, ec)) → new_esEs23(yvy4001, yvy3001, ec)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_@0) → new_esEs19(yvy40000, yvy30000)
new_compare25(yvy152, yvy153, yvy154, yvy155, yvy156, yvy157, False, dhc, dhd, dhe) → new_compare17(yvy152, yvy153, yvy154, yvy155, yvy156, yvy157, new_lt20(yvy152, yvy155, dhc), new_asAs(new_esEs34(yvy152, yvy155, dhc), new_pePe(new_lt21(yvy153, yvy156, dhd), new_asAs(new_esEs35(yvy153, yvy156, dhd), new_ltEs20(yvy154, yvy157, dhe)))), dhc, dhd, dhe)
new_compare31(Nothing, Just(yvy3000), ffb) → LT
new_esEs29(yvy40000, yvy30000, ty_Ordering) → new_esEs12(yvy40000, yvy30000)
new_esEs4(yvy4000, yvy3000, app(ty_[], gg)) → new_esEs16(yvy4000, yvy3000, gg)
new_primPlusNat1(Zero, Zero) → Zero
new_compare0([], :(yvy3000, yvy3001), feh) → LT
new_ltEs6(LT, EQ) → True
new_lt23(yvy165, yvy167, ty_Ordering) → new_lt7(yvy165, yvy167)
new_ltEs21(yvy1001, yvy1011, app(ty_Maybe, efc)) → new_ltEs5(yvy1001, yvy1011, efc)
new_ltEs6(GT, LT) → False
new_lt18(yvy152, yvy155) → new_esEs12(new_compare12(yvy152, yvy155), LT)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, ty_Char) → new_esEs15(yvy40000, yvy30000)
new_asAs(True, yvy184) → yvy184
new_esEs26(yvy40000, yvy30000, ty_Float) → new_esEs14(yvy40000, yvy30000)
new_esEs35(yvy153, yvy156, ty_Float) → new_esEs14(yvy153, yvy156)
new_ltEs21(yvy1001, yvy1011, app(ty_[], eed)) → new_ltEs8(yvy1001, yvy1011, eed)
new_compare11(Char(yvy4000), Char(yvy3000)) → new_primCmpNat0(yvy4000, yvy3000)
new_ltEs22(yvy114, yvy115, ty_Float) → new_ltEs11(yvy114, yvy115)
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_esEs28(yvy1001, yvy1011, app(ty_Ratio, bha)) → new_esEs21(yvy1001, yvy1011, bha)
new_esEs39(yvy165, yvy167, ty_Double) → new_esEs13(yvy165, yvy167)
new_esEs11(yvy4000, yvy3000, ty_Bool) → new_esEs20(yvy4000, yvy3000)
new_ltEs22(yvy114, yvy115, ty_Double) → new_ltEs13(yvy114, yvy115)
new_lt22(yvy1000, yvy1010, ty_Ordering) → new_lt7(yvy1000, yvy1010)
new_esEs4(yvy4000, yvy3000, app(app(app(ty_@3, hc), hd), he)) → new_esEs22(yvy4000, yvy3000, hc, hd, he)
new_lt20(yvy152, yvy155, app(ty_Ratio, cea)) → new_lt10(yvy152, yvy155, cea)
new_ltEs16(False, False) → True
new_lt23(yvy165, yvy167, ty_Double) → new_lt13(yvy165, yvy167)
new_ltEs17(yvy100, yvy101) → new_fsEs(new_compare9(yvy100, yvy101))
new_esEs29(yvy40000, yvy30000, ty_Integer) → new_esEs18(yvy40000, yvy30000)
new_esEs8(yvy4001, yvy3001, ty_Ordering) → new_esEs12(yvy4001, yvy3001)
new_esEs30(yvy40001, yvy30001, ty_Bool) → new_esEs20(yvy40001, yvy30001)
new_lt23(yvy165, yvy167, app(ty_Ratio, fcc)) → new_lt10(yvy165, yvy167, fcc)
new_esEs30(yvy40001, yvy30001, ty_Int) → new_esEs25(yvy40001, yvy30001)
new_esEs27(yvy1000, yvy1010, ty_Float) → new_esEs14(yvy1000, yvy1010)
new_ltEs21(yvy1001, yvy1011, ty_Int) → new_ltEs15(yvy1001, yvy1011)
new_ltEs20(yvy154, yvy157, app(app(app(ty_@3, ebf), ebg), ebh)) → new_ltEs10(yvy154, yvy157, ebf, ebg, ebh)
new_esEs23(Just(yvy40000), Just(yvy30000), app(ty_[], dda)) → new_esEs16(yvy40000, yvy30000, dda)
new_esEs34(yvy152, yvy155, app(app(app(ty_@3, bd), be), bf)) → new_esEs22(yvy152, yvy155, bd, be, bf)
new_esEs16(:(yvy40000, yvy40001), :(yvy30000, yvy30001), gg) → new_asAs(new_esEs26(yvy40000, yvy30000, gg), new_esEs16(yvy40001, yvy30001, gg))
new_esEs9(yvy4000, yvy3000, app(app(app(ty_@3, ffg), ffh), fga)) → new_esEs22(yvy4000, yvy3000, ffg, ffh, fga)
new_ltEs19(yvy1002, yvy1012, app(app(app(ty_@3, cad), cae), caf)) → new_ltEs10(yvy1002, yvy1012, cad, cae, caf)
new_ltEs20(yvy154, yvy157, ty_Ordering) → new_ltEs6(yvy154, yvy157)
new_compare19(yvy206, yvy207, False, dha, dhb) → GT
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Integer) → new_ltEs4(yvy1000, yvy1010)
new_esEs6(yvy4002, yvy3002, ty_@0) → new_esEs19(yvy4002, yvy3002)
new_ltEs10(@3(yvy1000, yvy1001, yvy1002), @3(yvy1010, yvy1011, yvy1012), bfc, bfd, bfe) → new_pePe(new_lt6(yvy1000, yvy1010, bfc), new_asAs(new_esEs27(yvy1000, yvy1010, bfc), new_pePe(new_lt5(yvy1001, yvy1011, bfd), new_asAs(new_esEs28(yvy1001, yvy1011, bfd), new_ltEs19(yvy1002, yvy1012, bfe)))))
new_esEs33(yvy40002, yvy30002, ty_@0) → new_esEs19(yvy40002, yvy30002)
new_esEs35(yvy153, yvy156, app(ty_Ratio, eac)) → new_esEs21(yvy153, yvy156, eac)
new_ltEs22(yvy114, yvy115, ty_Int) → new_ltEs15(yvy114, yvy115)
new_ltEs24(yvy100, yvy101, app(app(app(ty_@3, bfc), bfd), bfe)) → new_ltEs10(yvy100, yvy101, bfc, bfd, bfe)
new_compare27(Right(yvy4000), Right(yvy3000), eff, efg) → new_compare28(yvy4000, yvy3000, new_esEs11(yvy4000, yvy3000, efg), eff, efg)
new_ltEs21(yvy1001, yvy1011, ty_@0) → new_ltEs17(yvy1001, yvy1011)
new_lt16(yvy152, yvy155, dhh, eaa) → new_esEs12(new_compare27(yvy152, yvy155, dhh, eaa), LT)
new_compare15(EQ, EQ) → EQ
new_ltEs22(yvy114, yvy115, ty_Char) → new_ltEs7(yvy114, yvy115)
new_compare30(yvy400, yvy300, ty_Double) → new_compare29(yvy400, yvy300)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCompAux0(yvy56, EQ) → yvy56
new_lt6(yvy1000, yvy1010, app(app(ty_@2, bgc), bgd)) → new_lt12(yvy1000, yvy1010, bgc, bgd)
new_esEs27(yvy1000, yvy1010, app(ty_Maybe, bge)) → new_esEs23(yvy1000, yvy1010, bge)
new_ltEs20(yvy154, yvy157, ty_Char) → new_ltEs7(yvy154, yvy157)
new_esEs10(yvy4000, yvy3000, ty_Integer) → new_esEs18(yvy4000, yvy3000)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_@0, dac) → new_ltEs17(yvy1000, yvy1010)
new_ltEs18(yvy107, yvy108, ty_Int) → new_ltEs15(yvy107, yvy108)
new_lt21(yvy153, yvy156, app(app(app(ty_@3, ead), eae), eaf)) → new_lt4(yvy153, yvy156, ead, eae, eaf)
new_esEs6(yvy4002, yvy3002, ty_Char) → new_esEs15(yvy4002, yvy3002)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_esEs30(yvy40001, yvy30001, ty_Char) → new_esEs15(yvy40001, yvy30001)
new_ltEs5(Just(yvy1000), Just(yvy1010), app(app(app(ty_@3, fc), fd), ff)) → new_ltEs10(yvy1000, yvy1010, fc, fd, ff)
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_esEs39(yvy165, yvy167, app(ty_[], fcb)) → new_esEs16(yvy165, yvy167, fcb)
new_esEs35(yvy153, yvy156, ty_Char) → new_esEs15(yvy153, yvy156)
new_not(True) → False
new_ltEs5(Just(yvy1000), Just(yvy1010), app(ty_Ratio, fb)) → new_ltEs9(yvy1000, yvy1010, fb)

The set Q consists of the following terms:

new_esEs36(x0, x1, ty_Char)
new_esEs29(x0, x1, ty_Float)
new_lt22(x0, x1, app(ty_Maybe, x2))
new_esEs7(x0, x1, ty_Int)
new_ltEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs21(x0, x1, ty_Int)
new_ltEs14(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs10(x0, x1, ty_Float)
new_ltEs16(True, True)
new_esEs6(x0, x1, ty_Int)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs32(x0, x1, app(ty_Maybe, x2))
new_lt11(x0, x1)
new_esEs24(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs20(x0, x1, ty_Int)
new_lt5(x0, x1, ty_Char)
new_esEs5(x0, x1, app(ty_[], x2))
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs36(x0, x1, app(ty_[], x2))
new_lt21(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs21(x0, x1, ty_@0)
new_esEs29(x0, x1, ty_Char)
new_ltEs22(x0, x1, ty_Integer)
new_esEs34(x0, x1, app(ty_[], x2))
new_esEs32(x0, x1, ty_Int)
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs11(x0, x1, ty_Int)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs4(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_Integer)
new_compare30(x0, x1, ty_Int)
new_pePe(True, x0)
new_esEs5(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs11(x0, x1, ty_@0)
new_esEs35(x0, x1, ty_Integer)
new_esEs11(x0, x1, ty_Char)
new_esEs9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(x0, x1, ty_Float)
new_esEs9(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(x0, x1, ty_Int)
new_esEs31(x0, x1, app(app(ty_Either, x2), x3))
new_lt22(x0, x1, ty_@0)
new_compare30(x0, x1, ty_Bool)
new_ltEs5(Nothing, Just(x0), x1)
new_lt20(x0, x1, ty_@0)
new_esEs29(x0, x1, ty_Ordering)
new_lt22(x0, x1, ty_Float)
new_esEs9(x0, x1, app(ty_[], x2))
new_lt23(x0, x1, ty_Integer)
new_ltEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(Right(x0), Right(x1), x2, ty_Bool)
new_lt7(x0, x1)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs8(x0, x1, ty_Integer)
new_esEs23(Just(x0), Just(x1), ty_Float)
new_esEs6(x0, x1, ty_Integer)
new_lt5(x0, x1, ty_@0)
new_esEs33(x0, x1, app(app(ty_@2, x2), x3))
new_esEs11(x0, x1, ty_Bool)
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs24(Right(x0), Right(x1), x2, ty_Integer)
new_compare12(False, True)
new_compare12(True, False)
new_ltEs7(x0, x1)
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_primCompAux0(x0, EQ)
new_esEs32(x0, x1, app(app(ty_@2, x2), x3))
new_lt6(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(x0, x1, ty_Integer)
new_esEs32(x0, x1, ty_Ordering)
new_ltEs21(x0, x1, ty_Float)
new_ltEs24(x0, x1, ty_Integer)
new_esEs34(x0, x1, ty_Float)
new_esEs6(x0, x1, ty_@0)
new_lt6(x0, x1, ty_Float)
new_esEs9(x0, x1, ty_Int)
new_compare30(x0, x1, ty_Integer)
new_esEs12(GT, EQ)
new_esEs12(EQ, GT)
new_esEs36(x0, x1, ty_Int)
new_esEs28(x0, x1, ty_Bool)
new_ltEs14(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs24(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_compare30(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_lt5(x0, x1, ty_Double)
new_compare15(LT, LT)
new_esEs10(x0, x1, ty_Char)
new_esEs23(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primMulNat0(Succ(x0), Zero)
new_ltEs22(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_compare6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs34(x0, x1, ty_Ordering)
new_esEs16([], [], x0)
new_esEs12(GT, GT)
new_esEs30(x0, x1, ty_Double)
new_esEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs21(x0, x1, ty_Ordering)
new_esEs10(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_lt21(x0, x1, ty_Float)
new_esEs11(x0, x1, ty_Integer)
new_esEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs21(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs24(x0, x1, app(ty_Maybe, x2))
new_esEs23(Just(x0), Just(x1), ty_Double)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_Char)
new_esEs34(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(Left(x0), Left(x1), ty_Int, x2)
new_esEs38(x0, x1, ty_Integer)
new_ltEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs27(x0, x1, ty_Bool)
new_esEs24(Right(x0), Right(x1), x2, ty_Char)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs6(EQ, EQ)
new_esEs32(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(x0, x1, ty_Float)
new_esEs8(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs22(x0, x1, ty_Char)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(x0, x1, ty_Double)
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_esEs5(x0, x1, ty_Bool)
new_lt6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs31(x0, x1, ty_Int)
new_compare26(x0, x1, True, x2, x3)
new_compare110(x0, x1, x2, x3, True, x4, x5, x6)
new_ltEs24(x0, x1, app(ty_[], x2))
new_compare27(Right(x0), Left(x1), x2, x3)
new_compare27(Left(x0), Right(x1), x2, x3)
new_esEs33(x0, x1, ty_Double)
new_esEs8(x0, x1, ty_Float)
new_ltEs18(x0, x1, ty_@0)
new_esEs4(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, app(ty_[], x2))
new_ltEs5(Just(x0), Just(x1), ty_@0)
new_lt5(x0, x1, ty_Int)
new_ltEs6(LT, EQ)
new_ltEs6(EQ, LT)
new_esEs24(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_primCompAux0(x0, LT)
new_esEs23(Nothing, Nothing, x0)
new_esEs38(x0, x1, ty_Int)
new_esEs23(Just(x0), Just(x1), ty_Int)
new_ltEs20(x0, x1, ty_@0)
new_lt6(x0, x1, app(ty_Maybe, x2))
new_esEs11(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Int)
new_lt17(x0, x1)
new_esEs8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs36(x0, x1, ty_Bool)
new_primEqNat0(Zero, Zero)
new_compare13(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs26(x0, x1, ty_@0)
new_lt21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(Right(x0), Right(x1), x2, ty_Int)
new_esEs7(x0, x1, ty_Bool)
new_esEs33(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs5(x0, x1, ty_Float)
new_ltEs14(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_compare17(x0, x1, x2, x3, x4, x5, False, x6, x7, x8, x9)
new_ltEs22(x0, x1, ty_Float)
new_compare15(GT, GT)
new_esEs31(x0, x1, ty_Double)
new_ltEs20(x0, x1, ty_Integer)
new_lt22(x0, x1, ty_Bool)
new_compare30(x0, x1, app(ty_[], x2))
new_esEs34(x0, x1, ty_Bool)
new_esEs31(x0, x1, ty_Integer)
new_ltEs20(x0, x1, ty_Char)
new_lt20(x0, x1, ty_Double)
new_esEs35(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_compare28(x0, x1, True, x2, x3)
new_ltEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs21(x0, x1, app(ty_[], x2))
new_ltEs15(x0, x1)
new_esEs4(x0, x1, ty_Integer)
new_esEs39(x0, x1, app(ty_Ratio, x2))
new_esEs6(x0, x1, app(app(ty_Either, x2), x3))
new_esEs39(x0, x1, ty_Bool)
new_esEs6(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs24(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Float)
new_ltEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_primMulNat0(Zero, Zero)
new_asAs(True, x0)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_ltEs14(Left(x0), Right(x1), x2, x3)
new_ltEs14(Right(x0), Left(x1), x2, x3)
new_esEs26(x0, x1, ty_Double)
new_esEs5(x0, x1, ty_Double)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs35(x0, x1, app(app(ty_@2, x2), x3))
new_fsEs(x0)
new_esEs16(:(x0, x1), [], x2)
new_ltEs5(Just(x0), Just(x1), ty_Integer)
new_esEs35(x0, x1, app(ty_Ratio, x2))
new_lt6(x0, x1, ty_Double)
new_esEs35(x0, x1, ty_Double)
new_ltEs18(x0, x1, ty_Bool)
new_esEs23(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Float)
new_ltEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(x0, x1, app(ty_Maybe, x2))
new_compare28(x0, x1, False, x2, x3)
new_ltEs5(Just(x0), Just(x1), ty_Double)
new_lt22(x0, x1, ty_Ordering)
new_lt23(x0, x1, app(ty_Ratio, x2))
new_esEs9(x0, x1, ty_@0)
new_esEs6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare24(x0, x1, x2, x3, False, x4, x5)
new_esEs24(Left(x0), Left(x1), ty_@0, x2)
new_esEs35(x0, x1, ty_Bool)
new_esEs35(x0, x1, ty_Char)
new_ltEs23(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, ty_Bool)
new_ltEs10(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs31(x0, x1, ty_@0)
new_lt10(x0, x1, x2)
new_ltEs19(x0, x1, ty_Double)
new_lt12(x0, x1, x2, x3)
new_ltEs24(x0, x1, ty_Double)
new_esEs13(Double(x0, x1), Double(x2, x3))
new_esEs10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Ordering)
new_esEs5(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(Just(x0), Nothing, x1)
new_ltEs14(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs24(Right(x0), Right(x1), x2, ty_@0)
new_esEs20(True, True)
new_lt22(x0, x1, ty_Int)
new_esEs7(x0, x1, ty_Integer)
new_esEs30(x0, x1, ty_Bool)
new_lt21(x0, x1, ty_@0)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs4(x0, x1, app(ty_Maybe, x2))
new_esEs33(x0, x1, ty_Float)
new_esEs29(x0, x1, ty_Integer)
new_ltEs21(x0, x1, ty_Integer)
new_lt16(x0, x1, x2, x3)
new_primPlusNat0(Zero, x0)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs4(x0, x1, ty_Ordering)
new_esEs8(x0, x1, ty_Bool)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_primPlusNat0(Succ(x0), x1)
new_ltEs4(x0, x1)
new_esEs34(x0, x1, ty_Integer)
new_esEs31(x0, x1, ty_Ordering)
new_ltEs6(GT, LT)
new_ltEs6(LT, GT)
new_compare0([], [], x0)
new_ltEs22(x0, x1, app(ty_Maybe, x2))
new_esEs35(x0, x1, app(ty_Maybe, x2))
new_compare111(x0, x1, x2, x3, True, x4, x5)
new_esEs11(x0, x1, ty_Double)
new_lt19(x0, x1)
new_ltEs14(Left(x0), Left(x1), ty_Double, x2)
new_ltEs8(x0, x1, x2)
new_ltEs14(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs4(x0, x1, ty_Double)
new_esEs36(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, ty_Double)
new_esEs39(x0, x1, ty_Char)
new_ltEs22(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_compare15(EQ, EQ)
new_lt6(x0, x1, ty_Int)
new_lt21(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, ty_Ordering)
new_ltEs14(Right(x0), Right(x1), x2, ty_Double)
new_ltEs22(x0, x1, ty_Ordering)
new_ltEs11(x0, x1)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_compare7(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt20(x0, x1, ty_Float)
new_lt21(x0, x1, ty_Integer)
new_esEs32(x0, x1, ty_Bool)
new_esEs39(x0, x1, ty_Float)
new_compare10(x0, x1, False, x2, x3)
new_lt6(x0, x1, ty_Integer)
new_lt4(x0, x1, x2, x3, x4)
new_esEs10(x0, x1, ty_Double)
new_esEs31(x0, x1, app(ty_[], x2))
new_sr0(x0, x1)
new_esEs23(Just(x0), Just(x1), ty_Integer)
new_esEs24(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs20(False, True)
new_esEs20(True, False)
new_esEs29(x0, x1, ty_Bool)
new_esEs24(Left(x0), Right(x1), x2, x3)
new_esEs24(Right(x0), Left(x1), x2, x3)
new_ltEs23(x0, x1, ty_Integer)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs36(x0, x1, app(ty_Ratio, x2))
new_esEs20(False, False)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare12(False, False)
new_esEs12(LT, EQ)
new_esEs12(EQ, LT)
new_lt21(x0, x1, ty_Int)
new_lt22(x0, x1, ty_Char)
new_ltEs14(Left(x0), Left(x1), ty_Char, x2)
new_ltEs14(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare14(x0, x1, x2, x3, x4, x5, True, x6, x7, x8)
new_esEs31(x0, x1, ty_Float)
new_esEs24(Left(x0), Left(x1), ty_Float, x2)
new_primPlusNat1(Zero, Zero)
new_ltEs21(x0, x1, ty_Bool)
new_esEs24(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs20(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_Float)
new_esEs12(EQ, EQ)
new_esEs23(Just(x0), Just(x1), ty_Bool)
new_esEs27(x0, x1, ty_Char)
new_ltEs14(Right(x0), Right(x1), x2, ty_Int)
new_esEs9(x0, x1, ty_Integer)
new_esEs30(x0, x1, ty_Float)
new_ltEs20(x0, x1, ty_Float)
new_lt22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(Right(x0), Right(x1), x2, ty_Char)
new_esEs9(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Left(x0), Left(x1), ty_Float, x2)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs16(:(x0, x1), :(x2, x3), x4)
new_esEs28(x0, x1, ty_Double)
new_esEs30(x0, x1, ty_Char)
new_compare30(x0, x1, ty_@0)
new_esEs6(x0, x1, ty_Bool)
new_esEs16([], :(x0, x1), x2)
new_ltEs23(x0, x1, ty_Float)
new_esEs9(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs31(x0, x1, app(app(ty_@2, x2), x3))
new_compare15(EQ, GT)
new_compare15(GT, EQ)
new_compare17(x0, x1, x2, x3, x4, x5, True, x6, x7, x8, x9)
new_ltEs9(x0, x1, x2)
new_ltEs24(x0, x1, ty_Ordering)
new_compare30(x0, x1, ty_Char)
new_primEqNat0(Succ(x0), Zero)
new_compare15(LT, GT)
new_compare15(GT, LT)
new_esEs36(x0, x1, ty_Double)
new_esEs39(x0, x1, ty_Ordering)
new_esEs7(x0, x1, app(app(ty_Either, x2), x3))
new_lt21(x0, x1, app(ty_[], x2))
new_esEs37(x0, x1, ty_Int)
new_esEs9(x0, x1, ty_Double)
new_primMulInt(Neg(x0), Neg(x1))
new_ltEs5(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs17(x0, x1)
new_compare0([], :(x0, x1), x2)
new_esEs9(x0, x1, ty_Ordering)
new_ltEs12(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs26(x0, x1, ty_Char)
new_lt23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_lt23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs23(x0, x1, ty_Int)
new_primEqNat0(Succ(x0), Succ(x1))
new_compare210(x0, x1, True, x2)
new_esEs8(x0, x1, ty_Int)
new_ltEs14(Left(x0), Left(x1), ty_Bool, x2)
new_lt21(x0, x1, app(ty_Maybe, x2))
new_ltEs5(Just(x0), Just(x1), ty_Int)
new_esEs33(x0, x1, ty_Int)
new_ltEs23(x0, x1, ty_@0)
new_lt6(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs33(x0, x1, ty_Bool)
new_esEs10(x0, x1, ty_Ordering)
new_esEs24(Left(x0), Left(x1), ty_Double, x2)
new_esEs35(x0, x1, ty_@0)
new_esEs4(x0, x1, ty_Char)
new_compare112(x0, x1, False, x2)
new_esEs24(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_lt23(x0, x1, ty_Int)
new_ltEs14(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs18(x0, x1, ty_Double)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt23(x0, x1, ty_Bool)
new_ltEs14(Left(x0), Left(x1), ty_Integer, x2)
new_esEs24(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_lt9(x0, x1, x2)
new_ltEs18(x0, x1, app(ty_[], x2))
new_esEs33(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, app(ty_[], x2))
new_lt5(x0, x1, app(app(ty_Either, x2), x3))
new_lt21(x0, x1, ty_Bool)
new_esEs24(Left(x0), Left(x1), ty_Char, x2)
new_ltEs5(Nothing, Nothing, x0)
new_compare18(Float(x0, x1), Float(x2, x3))
new_ltEs5(Just(x0), Just(x1), ty_Float)
new_esEs26(x0, x1, ty_Bool)
new_lt6(x0, x1, ty_Bool)
new_esEs30(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Integer)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs8(x0, x1, ty_Double)
new_lt21(x0, x1, ty_Char)
new_lt5(x0, x1, ty_Float)
new_compare11(Char(x0), Char(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs24(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs36(x0, x1, app(app(ty_Either, x2), x3))
new_esEs30(x0, x1, ty_Integer)
new_esEs25(x0, x1)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_compare210(x0, x1, False, x2)
new_esEs29(x0, x1, ty_@0)
new_ltEs14(Left(x0), Left(x1), ty_Int, x2)
new_sr(Integer(x0), Integer(x1))
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs7(x0, x1, ty_@0)
new_esEs39(x0, x1, app(ty_Maybe, x2))
new_primMulNat0(Succ(x0), Succ(x1))
new_ltEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs34(x0, x1, ty_Char)
new_esEs4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs10(x0, x1, ty_Bool)
new_lt5(x0, x1, app(ty_[], x2))
new_esEs10(x0, x1, ty_@0)
new_esEs39(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_@0)
new_esEs31(x0, x1, ty_Bool)
new_primEqNat0(Zero, Succ(x0))
new_primPlusNat1(Succ(x0), Zero)
new_lt23(x0, x1, ty_Char)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs7(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Char)
new_ltEs21(x0, x1, app(ty_Maybe, x2))
new_esEs6(x0, x1, ty_Ordering)
new_esEs33(x0, x1, ty_Char)
new_compare27(Left(x0), Left(x1), x2, x3)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs32(x0, x1, ty_Integer)
new_ltEs14(Left(x0), Left(x1), ty_Ordering, x2)
new_pePe(False, x0)
new_ltEs24(x0, x1, ty_Int)
new_compare24(x0, x1, x2, x3, True, x4, x5)
new_lt8(x0, x1)
new_esEs39(x0, x1, app(app(ty_Either, x2), x3))
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt23(x0, x1, ty_Double)
new_esEs10(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Bool)
new_esEs9(x0, x1, app(app(ty_@2, x2), x3))
new_esEs32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, ty_Int)
new_esEs30(x0, x1, ty_Ordering)
new_lt23(x0, x1, ty_Float)
new_lt6(x0, x1, ty_@0)
new_primPlusNat1(Succ(x0), Succ(x1))
new_compare27(Right(x0), Right(x1), x2, x3)
new_esEs31(x0, x1, ty_Char)
new_lt22(x0, x1, ty_Double)
new_ltEs22(x0, x1, ty_@0)
new_esEs39(x0, x1, ty_Int)
new_esEs30(x0, x1, ty_@0)
new_compare14(x0, x1, x2, x3, x4, x5, False, x6, x7, x8)
new_ltEs16(False, True)
new_ltEs16(True, False)
new_ltEs6(GT, GT)
new_esEs10(x0, x1, ty_Int)
new_compare30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(x0, x1, app(ty_Maybe, x2))
new_esEs31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs32(x0, x1, ty_Char)
new_esEs23(Nothing, Just(x0), x1)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(x0, x1, ty_Int)
new_ltEs5(Just(x0), Just(x1), ty_Ordering)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_ltEs19(x0, x1, ty_Char)
new_ltEs22(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(Just(x0), Just(x1), ty_Char)
new_esEs27(x0, x1, ty_Int)
new_esEs24(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs4(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(Just(x0), Just(x1), ty_Bool)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_Bool)
new_lt22(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_@0)
new_ltEs22(x0, x1, ty_Bool)
new_esEs30(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_Integer)
new_esEs33(x0, x1, ty_Integer)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, ty_Int)
new_primCmpNat0(Zero, Zero)
new_esEs35(x0, x1, ty_Float)
new_asAs(False, x0)
new_lt5(x0, x1, ty_Integer)
new_ltEs24(x0, x1, ty_@0)
new_esEs17(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs19(x0, x1, ty_Int)
new_lt23(x0, x1, ty_@0)
new_esEs34(x0, x1, ty_Int)
new_ltEs6(LT, LT)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs35(x0, x1, app(ty_[], x2))
new_esEs35(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare31(Just(x0), Just(x1), x2)
new_esEs11(x0, x1, ty_Ordering)
new_esEs31(x0, x1, app(ty_Ratio, x2))
new_lt5(x0, x1, app(ty_Ratio, x2))
new_ltEs22(x0, x1, ty_Double)
new_ltEs14(Left(x0), Left(x1), ty_@0, x2)
new_lt23(x0, x1, app(ty_[], x2))
new_compare10(x0, x1, True, x2, x3)
new_ltEs24(x0, x1, ty_Char)
new_esEs21(:%(x0, x1), :%(x2, x3), x4)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs18(Integer(x0), Integer(x1))
new_esEs4(x0, x1, ty_@0)
new_lt22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, ty_Int)
new_ltEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(Just(x0), Just(x1), ty_@0)
new_compare110(x0, x1, x2, x3, False, x4, x5, x6)
new_ltEs14(Right(x0), Right(x1), x2, ty_Integer)
new_compare0(:(x0, x1), [], x2)
new_esEs23(Just(x0), Nothing, x1)
new_ltEs19(x0, x1, ty_Float)
new_esEs6(x0, x1, ty_Char)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_lt21(x0, x1, ty_Double)
new_esEs32(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs8(x0, x1, app(ty_[], x2))
new_esEs23(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs34(x0, x1, app(app(ty_Either, x2), x3))
new_esEs33(x0, x1, app(ty_[], x2))
new_lt5(x0, x1, ty_Bool)
new_esEs11(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(Just(x0), Just(x1), ty_Char)
new_ltEs13(x0, x1)
new_lt14(x0, x1, x2)
new_ltEs23(x0, x1, ty_Bool)
new_esEs6(x0, x1, app(ty_Ratio, x2))
new_compare15(LT, EQ)
new_compare15(EQ, LT)
new_compare9(@0, @0)
new_lt13(x0, x1)
new_esEs36(x0, x1, ty_Integer)
new_esEs29(x0, x1, ty_Double)
new_ltEs22(x0, x1, app(ty_[], x2))
new_ltEs23(x0, x1, app(ty_Maybe, x2))
new_esEs8(x0, x1, app(ty_Ratio, x2))
new_ltEs18(x0, x1, ty_Float)
new_lt18(x0, x1)
new_lt22(x0, x1, app(ty_Ratio, x2))
new_esEs32(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_Float)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_lt5(x0, x1, ty_Ordering)
new_lt15(x0, x1)
new_compare8(Integer(x0), Integer(x1))
new_lt22(x0, x1, app(ty_[], x2))
new_compare30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs33(x0, x1, app(ty_Ratio, x2))
new_lt5(x0, x1, app(ty_Maybe, x2))
new_esEs36(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs33(x0, x1, app(ty_Maybe, x2))
new_esEs7(x0, x1, app(ty_Maybe, x2))
new_esEs8(x0, x1, ty_@0)
new_lt6(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(x0, x1, ty_Int)
new_not(True)
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_compare30(x0, x1, ty_Float)
new_compare31(Just(x0), Nothing, x1)
new_esEs27(x0, x1, ty_Ordering)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs22(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs23(x0, x1, app(ty_Ratio, x2))
new_ltEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(x0, x1, ty_Bool)
new_esEs32(x0, x1, ty_Float)
new_esEs36(x0, x1, ty_Ordering)
new_esEs9(x0, x1, ty_Bool)
new_esEs23(Just(x0), Just(x1), app(ty_Maybe, x2))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_not(False)
new_esEs24(Left(x0), Left(x1), ty_Ordering, x2)
new_compare29(Double(x0, x1), Double(x2, x3))
new_compare13(:%(x0, x1), :%(x2, x3), ty_Integer)
new_lt6(x0, x1, app(ty_Ratio, x2))
new_primCmpNat0(Succ(x0), Succ(x1))
new_esEs7(x0, x1, ty_Ordering)
new_esEs34(x0, x1, app(ty_Ratio, x2))
new_ltEs23(x0, x1, ty_Char)
new_esEs7(x0, x1, app(ty_[], x2))
new_esEs8(x0, x1, ty_Ordering)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_esEs39(x0, x1, ty_@0)
new_ltEs21(x0, x1, ty_Char)
new_esEs15(Char(x0), Char(x1))
new_esEs7(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(x0, x1, app(ty_Ratio, x2))
new_ltEs6(GT, EQ)
new_ltEs6(EQ, GT)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_esEs7(x0, x1, app(ty_Ratio, x2))
new_esEs32(x0, x1, app(ty_Ratio, x2))
new_primCmpNat0(Zero, Succ(x0))
new_esEs31(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Ordering)
new_lt23(x0, x1, app(ty_Maybe, x2))
new_ltEs21(x0, x1, ty_Double)
new_esEs24(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs8(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs23(x0, x1, app(ty_[], x2))
new_esEs24(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_compare30(x0, x1, ty_Double)
new_compare19(x0, x1, True, x2, x3)
new_esEs36(x0, x1, app(ty_Maybe, x2))
new_esEs24(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs5(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(Right(x0), Right(x1), x2, ty_Double)
new_lt22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(x0, x1, app(ty_[], x2))
new_primCmpNat0(Succ(x0), Zero)
new_compare30(x0, x1, app(ty_Maybe, x2))
new_esEs34(x0, x1, ty_Double)
new_ltEs21(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_@0)
new_esEs11(x0, x1, app(ty_Maybe, x2))
new_esEs6(x0, x1, app(ty_Maybe, x2))
new_ltEs22(x0, x1, ty_Int)
new_compare26(x0, x1, False, x2, x3)
new_compare16(x0, x1)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_esEs23(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs20(x0, x1, ty_Double)
new_ltEs24(x0, x1, ty_Bool)
new_esEs35(x0, x1, ty_Ordering)
new_ltEs18(x0, x1, ty_Integer)
new_esEs39(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs34(x0, x1, ty_@0)
new_compare31(Nothing, Just(x0), x1)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_esEs37(x0, x1, ty_Integer)
new_ltEs18(x0, x1, ty_Char)
new_esEs7(x0, x1, ty_Double)
new_lt23(x0, x1, ty_Ordering)
new_compare112(x0, x1, True, x2)
new_lt21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs34(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs9(x0, x1, ty_Float)
new_esEs23(Just(x0), Just(x1), ty_Ordering)
new_lt6(x0, x1, ty_Char)
new_esEs9(x0, x1, ty_Char)
new_esEs8(x0, x1, ty_Char)
new_esEs35(x0, x1, ty_Int)
new_esEs24(Left(x0), Left(x1), ty_Integer, x2)
new_esEs5(x0, x1, app(ty_Maybe, x2))
new_lt21(x0, x1, app(ty_Ratio, x2))
new_esEs33(x0, x1, ty_@0)
new_esEs24(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs5(x0, x1, ty_Ordering)
new_esEs32(x0, x1, ty_Double)
new_esEs34(x0, x1, app(ty_Maybe, x2))
new_esEs10(x0, x1, app(ty_[], x2))
new_compare30(x0, x1, app(ty_Ratio, x2))
new_ltEs21(x0, x1, app(ty_Ratio, x2))
new_lt23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs24(x0, x1, app(ty_Ratio, x2))
new_esEs14(Float(x0, x1), Float(x2, x3))
new_esEs26(x0, x1, ty_Integer)
new_esEs5(x0, x1, ty_@0)
new_esEs5(x0, x1, ty_Char)
new_esEs7(x0, x1, ty_Char)
new_compare12(True, True)
new_primEqInt(Pos(Zero), Pos(Zero))
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs5(x0, x1, ty_Integer)
new_primCompAux1(x0, x1, x2, x3)
new_compare31(Nothing, Nothing, x0)
new_esEs39(x0, x1, app(ty_[], x2))
new_compare30(x0, x1, ty_Ordering)
new_primMulNat0(Zero, Succ(x0))
new_esEs28(x0, x1, app(ty_[], x2))
new_ltEs23(x0, x1, ty_Double)
new_esEs24(Right(x0), Right(x1), x2, ty_Float)
new_esEs11(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_lt5(x0, x1, app(app(ty_@2, x2), x3))
new_primCompAux0(x0, GT)
new_lt6(x0, x1, ty_Ordering)
new_primPlusNat1(Zero, Succ(x0))
new_esEs36(x0, x1, ty_Float)
new_esEs19(@0, @0)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs39(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_compare25(x0, x1, x2, x3, x4, x5, True, x6, x7, x8)
new_esEs36(x0, x1, ty_@0)
new_esEs12(LT, LT)
new_esEs28(x0, x1, ty_Integer)
new_compare19(x0, x1, False, x2, x3)
new_ltEs18(x0, x1, ty_Ordering)
new_ltEs16(False, False)
new_compare111(x0, x1, x2, x3, False, x4, x5)
new_compare25(x0, x1, x2, x3, x4, x5, False, x6, x7, x8)
new_esEs33(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, ty_Ordering)
new_esEs28(x0, x1, ty_@0)
new_esEs11(x0, x1, ty_Float)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs4(x0, x1, app(ty_[], x2))
new_esEs39(x0, x1, ty_Integer)

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

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



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

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

new_splitGT3(:(yvy300, yvy301), yvy31, yvy32, yvy33, yvy34, [], h, ba) → new_splitGT1(yvy300, yvy301, yvy31, yvy32, yvy33, yvy34, new_compare0([], :(yvy300, yvy301), h), h, ba)
new_splitGT1(yvy300, yvy301, yvy31, yvy32, Branch(yvy330, yvy331, yvy332, yvy333, yvy334), yvy34, LT, h, ba) → new_splitGT3(yvy330, yvy331, yvy332, yvy333, yvy334, [], h, ba)

The TRS R consists of the following rules:

new_compare210(yvy100, yvy101, False, feg) → new_compare112(yvy100, yvy101, new_ltEs24(yvy100, yvy101, feg), feg)
new_compare7(@2(yvy4000, yvy4001), @2(yvy3000, yvy3001), bg, bh) → new_compare24(yvy4000, yvy4001, yvy3000, yvy3001, new_asAs(new_esEs7(yvy4000, yvy3000, bg), new_esEs8(yvy4001, yvy3001, bh)), bg, bh)
new_esEs24(Left(yvy40000), Left(yvy30000), app(ty_Ratio, deh), hh) → new_esEs21(yvy40000, yvy30000, deh)
new_ltEs19(yvy1002, yvy1012, app(ty_[], cab)) → new_ltEs8(yvy1002, yvy1012, cab)
new_compare112(yvy189, yvy190, True, fge) → LT
new_lt22(yvy1000, yvy1010, ty_Int) → new_lt17(yvy1000, yvy1010)
new_ltEs22(yvy114, yvy115, app(app(ty_@2, fbc), fbd)) → new_ltEs12(yvy114, yvy115, fbc, fbd)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Int, hh) → new_esEs25(yvy40000, yvy30000)
new_esEs6(yvy4002, yvy3002, app(app(app(ty_@3, bbg), bbh), bca)) → new_esEs22(yvy4002, yvy3002, bbg, bbh, bca)
new_esEs27(yvy1000, yvy1010, app(ty_[], bff)) → new_esEs16(yvy1000, yvy1010, bff)
new_esEs20(True, True) → True
new_esEs35(yvy153, yvy156, app(ty_[], eab)) → new_esEs16(yvy153, yvy156, eab)
new_compare8(Integer(yvy4000), Integer(yvy3000)) → new_primCmpInt(yvy4000, yvy3000)
new_esEs8(yvy4001, yvy3001, ty_Bool) → new_esEs20(yvy4001, yvy3001)
new_esEs11(yvy4000, yvy3000, ty_Integer) → new_esEs18(yvy4000, yvy3000)
new_esEs27(yvy1000, yvy1010, app(app(ty_@2, bgc), bgd)) → new_esEs17(yvy1000, yvy1010, bgc, bgd)
new_ltEs20(yvy154, yvy157, app(ty_Ratio, ebe)) → new_ltEs9(yvy154, yvy157, ebe)
new_esEs36(yvy1000, yvy1010, ty_Double) → new_esEs13(yvy1000, yvy1010)
new_esEs28(yvy1001, yvy1011, ty_Float) → new_esEs14(yvy1001, yvy1011)
new_lt6(yvy1000, yvy1010, ty_@0) → new_lt19(yvy1000, yvy1010)
new_compare10(yvy199, yvy200, True, ef, eg) → LT
new_esEs9(yvy4000, yvy3000, ty_Int) → new_esEs25(yvy4000, yvy3000)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, ty_Double) → new_esEs13(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, app(app(ty_@2, chb), chc)) → new_esEs17(yvy40002, yvy30002, chb, chc)
new_ltEs24(yvy100, yvy101, app(ty_Ratio, cdh)) → new_ltEs9(yvy100, yvy101, cdh)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, ty_@0) → new_esEs19(yvy40000, yvy30000)
new_ltEs19(yvy1002, yvy1012, ty_Float) → new_ltEs11(yvy1002, yvy1012)
new_esEs11(yvy4000, yvy3000, app(ty_[], ehb)) → new_esEs16(yvy4000, yvy3000, ehb)
new_lt23(yvy165, yvy167, app(app(app(ty_@3, fcd), fce), fcf)) → new_lt4(yvy165, yvy167, fcd, fce, fcf)
new_esEs7(yvy4000, yvy3000, ty_Double) → new_esEs13(yvy4000, yvy3000)
new_esEs9(yvy4000, yvy3000, ty_Char) → new_esEs15(yvy4000, yvy3000)
new_ltEs23(yvy166, yvy168, ty_Ordering) → new_ltEs6(yvy166, yvy168)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Bool, dac) → new_ltEs16(yvy1000, yvy1010)
new_esEs39(yvy165, yvy167, app(ty_Ratio, fcc)) → new_esEs21(yvy165, yvy167, fcc)
new_esEs10(yvy4000, yvy3000, ty_@0) → new_esEs19(yvy4000, yvy3000)
new_esEs21(:%(yvy40000, yvy40001), :%(yvy30000, yvy30001), hb) → new_asAs(new_esEs37(yvy40000, yvy30000, hb), new_esEs38(yvy40001, yvy30001, hb))
new_lt5(yvy1001, yvy1011, app(ty_Ratio, bha)) → new_lt10(yvy1001, yvy1011, bha)
new_compare13(:%(yvy4000, yvy4001), :%(yvy3000, yvy3001), ty_Integer) → new_compare8(new_sr(yvy4000, yvy3001), new_sr(yvy3000, yvy4001))
new_ltEs22(yvy114, yvy115, app(ty_Ratio, fag)) → new_ltEs9(yvy114, yvy115, fag)
new_ltEs23(yvy166, yvy168, ty_Int) → new_ltEs15(yvy166, yvy168)
new_primMulNat0(Zero, Zero) → Zero
new_ltEs24(yvy100, yvy101, ty_Ordering) → new_ltEs6(yvy100, yvy101)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, ty_Float) → new_ltEs11(yvy1000, yvy1010)
new_esEs39(yvy165, yvy167, app(ty_Maybe, fda)) → new_esEs23(yvy165, yvy167, fda)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Bool, hh) → new_esEs20(yvy40000, yvy30000)
new_compare15(LT, LT) → EQ
new_esEs6(yvy4002, yvy3002, app(app(ty_@2, bbd), bbe)) → new_esEs17(yvy4002, yvy3002, bbd, bbe)
new_esEs4(yvy4000, yvy3000, ty_Integer) → new_esEs18(yvy4000, yvy3000)
new_esEs26(yvy40000, yvy30000, app(ty_[], bce)) → new_esEs16(yvy40000, yvy30000, bce)
new_esEs36(yvy1000, yvy1010, ty_Char) → new_esEs15(yvy1000, yvy1010)
new_esEs28(yvy1001, yvy1011, app(app(ty_Either, bhh), caa)) → new_esEs24(yvy1001, yvy1011, bhh, caa)
new_esEs34(yvy152, yvy155, ty_@0) → new_esEs19(yvy152, yvy155)
new_sr(Integer(yvy30000), Integer(yvy40010)) → Integer(new_primMulInt(yvy30000, yvy40010))
new_esEs7(yvy4000, yvy3000, ty_Float) → new_esEs14(yvy4000, yvy3000)
new_compare12(True, False) → GT
new_lt7(yvy152, yvy155) → new_esEs12(new_compare15(yvy152, yvy155), LT)
new_lt22(yvy1000, yvy1010, app(ty_Maybe, eea)) → new_lt14(yvy1000, yvy1010, eea)
new_ltEs24(yvy100, yvy101, app(ty_Maybe, eh)) → new_ltEs5(yvy100, yvy101, eh)
new_esEs35(yvy153, yvy156, app(app(ty_Either, ebb), ebc)) → new_esEs24(yvy153, yvy156, ebb, ebc)
new_esEs35(yvy153, yvy156, ty_@0) → new_esEs19(yvy153, yvy156)
new_ltEs15(yvy100, yvy101) → new_fsEs(new_compare16(yvy100, yvy101))
new_esEs6(yvy4002, yvy3002, app(ty_[], bbc)) → new_esEs16(yvy4002, yvy3002, bbc)
new_esEs26(yvy40000, yvy30000, ty_@0) → new_esEs19(yvy40000, yvy30000)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_@0, hh) → new_esEs19(yvy40000, yvy30000)
new_ltEs16(False, True) → True
new_esEs26(yvy40000, yvy30000, app(app(app(ty_@3, bda), bdb), bdc)) → new_esEs22(yvy40000, yvy30000, bda, bdb, bdc)
new_esEs10(yvy4000, yvy3000, app(ty_Maybe, egg)) → new_esEs23(yvy4000, yvy3000, egg)
new_ltEs24(yvy100, yvy101, ty_Bool) → new_ltEs16(yvy100, yvy101)
new_compare30(yvy400, yvy300, app(app(ty_@2, bg), bh)) → new_compare7(yvy400, yvy300, bg, bh)
new_esEs17(@2(yvy40000, yvy40001), @2(yvy30000, yvy30001), gh, ha) → new_asAs(new_esEs29(yvy40000, yvy30000, gh), new_esEs30(yvy40001, yvy30001, ha))
new_esEs11(yvy4000, yvy3000, ty_Char) → new_esEs15(yvy4000, yvy3000)
new_lt20(yvy152, yvy155, app(app(app(ty_@3, bd), be), bf)) → new_lt4(yvy152, yvy155, bd, be, bf)
new_esEs27(yvy1000, yvy1010, ty_Bool) → new_esEs20(yvy1000, yvy1010)
new_ltEs23(yvy166, yvy168, app(ty_Ratio, fde)) → new_ltEs9(yvy166, yvy168, fde)
new_esEs34(yvy152, yvy155, ty_Double) → new_esEs13(yvy152, yvy155)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Double) → new_esEs13(yvy40000, yvy30000)
new_esEs10(yvy4000, yvy3000, ty_Int) → new_esEs25(yvy4000, yvy3000)
new_esEs26(yvy40000, yvy30000, ty_Char) → new_esEs15(yvy40000, yvy30000)
new_compare30(yvy400, yvy300, ty_Int) → new_compare16(yvy400, yvy300)
new_fsEs(yvy306) → new_not(new_esEs12(yvy306, GT))
new_ltEs16(True, False) → False
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, ty_Char) → new_ltEs7(yvy1000, yvy1010)
new_esEs7(yvy4000, yvy3000, ty_Int) → new_esEs25(yvy4000, yvy3000)
new_ltEs19(yvy1002, yvy1012, ty_Bool) → new_ltEs16(yvy1002, yvy1012)
new_esEs34(yvy152, yvy155, ty_Ordering) → new_esEs12(yvy152, yvy155)
new_esEs12(GT, LT) → False
new_esEs12(LT, GT) → False
new_esEs27(yvy1000, yvy1010, ty_Char) → new_esEs15(yvy1000, yvy1010)
new_lt5(yvy1001, yvy1011, ty_Integer) → new_lt15(yvy1001, yvy1011)
new_ltEs22(yvy114, yvy115, ty_Ordering) → new_ltEs6(yvy114, yvy115)
new_compare18(Float(yvy4000, yvy4001), Float(yvy3000, yvy3001)) → new_compare16(new_sr0(yvy4000, yvy3000), new_sr0(yvy4001, yvy3001))
new_ltEs18(yvy107, yvy108, app(ty_Ratio, beb)) → new_ltEs9(yvy107, yvy108, beb)
new_ltEs23(yvy166, yvy168, ty_Float) → new_ltEs11(yvy166, yvy168)
new_ltEs18(yvy107, yvy108, app(ty_[], bea)) → new_ltEs8(yvy107, yvy108, bea)
new_ltEs20(yvy154, yvy157, app(app(ty_@2, eca), ecb)) → new_ltEs12(yvy154, yvy157, eca, ecb)
new_esEs31(yvy40000, yvy30000, app(ty_Maybe, cfd)) → new_esEs23(yvy40000, yvy30000, cfd)
new_lt6(yvy1000, yvy1010, app(ty_Ratio, bfg)) → new_lt10(yvy1000, yvy1010, bfg)
new_esEs37(yvy40000, yvy30000, ty_Integer) → new_esEs18(yvy40000, yvy30000)
new_ltEs14(Left(yvy1000), Left(yvy1010), app(app(ty_@2, dba), dbb), dac) → new_ltEs12(yvy1000, yvy1010, dba, dbb)
new_esEs35(yvy153, yvy156, app(app(ty_@2, eag), eah)) → new_esEs17(yvy153, yvy156, eag, eah)
new_esEs5(yvy4001, yvy3001, app(app(app(ty_@3, bae), baf), bag)) → new_esEs22(yvy4001, yvy3001, bae, baf, bag)
new_lt22(yvy1000, yvy1010, ty_Char) → new_lt8(yvy1000, yvy1010)
new_compare110(yvy233, yvy234, yvy235, yvy236, True, yvy238, ecf, ecg) → new_compare111(yvy233, yvy234, yvy235, yvy236, True, ecf, ecg)
new_ltEs24(yvy100, yvy101, app(app(ty_@2, ech), eda)) → new_ltEs12(yvy100, yvy101, ech, eda)
new_ltEs13(yvy100, yvy101) → new_fsEs(new_compare29(yvy100, yvy101))
new_esEs5(yvy4001, yvy3001, app(app(ty_Either, bba), bbb)) → new_esEs24(yvy4001, yvy3001, bba, bbb)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, ty_Bool) → new_esEs20(yvy40000, yvy30000)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Float) → new_ltEs11(yvy1000, yvy1010)
new_esEs8(yvy4001, yvy3001, ty_Double) → new_esEs13(yvy4001, yvy3001)
new_esEs31(yvy40000, yvy30000, app(ty_Ratio, ceh)) → new_esEs21(yvy40000, yvy30000, ceh)
new_esEs29(yvy40000, yvy30000, app(ty_Maybe, ccc)) → new_esEs23(yvy40000, yvy30000, ccc)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Int) → new_ltEs15(yvy1000, yvy1010)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Double) → new_ltEs13(yvy1000, yvy1010)
new_esEs30(yvy40001, yvy30001, ty_Double) → new_esEs13(yvy40001, yvy30001)
new_ltEs21(yvy1001, yvy1011, app(app(ty_@2, efa), efb)) → new_ltEs12(yvy1001, yvy1011, efa, efb)
new_esEs10(yvy4000, yvy3000, ty_Bool) → new_esEs20(yvy4000, yvy3000)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Char, dac) → new_ltEs7(yvy1000, yvy1010)
new_ltEs16(True, True) → True
new_lt21(yvy153, yvy156, app(app(ty_@2, eag), eah)) → new_lt12(yvy153, yvy156, eag, eah)
new_lt6(yvy1000, yvy1010, ty_Bool) → new_lt18(yvy1000, yvy1010)
new_pePe(False, yvy305) → yvy305
new_compare15(GT, EQ) → GT
new_esEs7(yvy4000, yvy3000, ty_Char) → new_esEs15(yvy4000, yvy3000)
new_esEs31(yvy40000, yvy30000, app(ty_[], cee)) → new_esEs16(yvy40000, yvy30000, cee)
new_esEs39(yvy165, yvy167, ty_@0) → new_esEs19(yvy165, yvy167)
new_esEs23(Just(yvy40000), Just(yvy30000), app(ty_Maybe, ddh)) → new_esEs23(yvy40000, yvy30000, ddh)
new_lt21(yvy153, yvy156, ty_Char) → new_lt8(yvy153, yvy156)
new_esEs26(yvy40000, yvy30000, ty_Bool) → new_esEs20(yvy40000, yvy30000)
new_esEs9(yvy4000, yvy3000, app(app(ty_@2, ffd), ffe)) → new_esEs17(yvy4000, yvy3000, ffd, ffe)
new_compare14(yvy218, yvy219, yvy220, yvy221, yvy222, yvy223, False, ceb, cec, ced) → GT
new_lt9(yvy152, yvy155, dhf) → new_esEs12(new_compare0(yvy152, yvy155, dhf), LT)
new_esEs28(yvy1001, yvy1011, ty_Integer) → new_esEs18(yvy1001, yvy1011)
new_esEs5(yvy4001, yvy3001, ty_Ordering) → new_esEs12(yvy4001, yvy3001)
new_esEs5(yvy4001, yvy3001, ty_Int) → new_esEs25(yvy4001, yvy3001)
new_esEs4(yvy4000, yvy3000, ty_Float) → new_esEs14(yvy4000, yvy3000)
new_compare15(GT, LT) → GT
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Char, hh) → new_esEs15(yvy40000, yvy30000)
new_esEs29(yvy40000, yvy30000, ty_Int) → new_esEs25(yvy40000, yvy30000)
new_compare30(yvy400, yvy300, app(app(ty_Either, eff), efg)) → new_compare27(yvy400, yvy300, eff, efg)
new_lt22(yvy1000, yvy1010, ty_Double) → new_lt13(yvy1000, yvy1010)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Ordering) → new_esEs12(yvy40000, yvy30000)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Char) → new_esEs15(yvy40000, yvy30000)
new_esEs29(yvy40000, yvy30000, app(app(ty_@2, cbe), cbf)) → new_esEs17(yvy40000, yvy30000, cbe, cbf)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, app(app(ty_@2, dfh), dga)) → new_esEs17(yvy40000, yvy30000, dfh, dga)
new_ltEs23(yvy166, yvy168, app(app(ty_Either, fed), fee)) → new_ltEs14(yvy166, yvy168, fed, fee)
new_esEs31(yvy40000, yvy30000, ty_Integer) → new_esEs18(yvy40000, yvy30000)
new_compare12(True, True) → EQ
new_esEs36(yvy1000, yvy1010, app(ty_[], edb)) → new_esEs16(yvy1000, yvy1010, edb)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Ordering, hh) → new_esEs12(yvy40000, yvy30000)
new_ltEs6(GT, EQ) → False
new_ltEs18(yvy107, yvy108, app(app(ty_Either, bfa), bfb)) → new_ltEs14(yvy107, yvy108, bfa, bfb)
new_esEs32(yvy40001, yvy30001, app(ty_Maybe, cgf)) → new_esEs23(yvy40001, yvy30001, cgf)
new_esEs35(yvy153, yvy156, ty_Integer) → new_esEs18(yvy153, yvy156)
new_esEs33(yvy40002, yvy30002, ty_Integer) → new_esEs18(yvy40002, yvy30002)
new_esEs31(yvy40000, yvy30000, ty_Double) → new_esEs13(yvy40000, yvy30000)
new_esEs10(yvy4000, yvy3000, ty_Ordering) → new_esEs12(yvy4000, yvy3000)
new_primCompAux1(yvy400, yvy300, yvy51, h) → new_primCompAux0(yvy51, new_compare30(yvy400, yvy300, h))
new_esEs33(yvy40002, yvy30002, ty_Float) → new_esEs14(yvy40002, yvy30002)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, app(app(app(ty_@3, dca), dcb), dcc)) → new_ltEs10(yvy1000, yvy1010, dca, dcb, dcc)
new_ltEs23(yvy166, yvy168, app(ty_[], fdd)) → new_ltEs8(yvy166, yvy168, fdd)
new_lt23(yvy165, yvy167, app(app(ty_@2, fcg), fch)) → new_lt12(yvy165, yvy167, fcg, fch)
new_esEs34(yvy152, yvy155, ty_Integer) → new_esEs18(yvy152, yvy155)
new_esEs23(Just(yvy40000), Just(yvy30000), app(app(ty_Either, dea), deb)) → new_esEs24(yvy40000, yvy30000, dea, deb)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Ordering, dac) → new_ltEs6(yvy1000, yvy1010)
new_lt22(yvy1000, yvy1010, ty_Bool) → new_lt18(yvy1000, yvy1010)
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_esEs39(yvy165, yvy167, ty_Float) → new_esEs14(yvy165, yvy167)
new_ltEs22(yvy114, yvy115, ty_Bool) → new_ltEs16(yvy114, yvy115)
new_ltEs4(yvy100, yvy101) → new_fsEs(new_compare8(yvy100, yvy101))
new_esEs33(yvy40002, yvy30002, app(ty_[], cha)) → new_esEs16(yvy40002, yvy30002, cha)
new_ltEs8(yvy100, yvy101, fef) → new_fsEs(new_compare0(yvy100, yvy101, fef))
new_compare30(yvy400, yvy300, ty_Char) → new_compare11(yvy400, yvy300)
new_esEs36(yvy1000, yvy1010, ty_Integer) → new_esEs18(yvy1000, yvy1010)
new_esEs39(yvy165, yvy167, ty_Bool) → new_esEs20(yvy165, yvy167)
new_esEs36(yvy1000, yvy1010, ty_Bool) → new_esEs20(yvy1000, yvy1010)
new_esEs32(yvy40001, yvy30001, app(ty_Ratio, cgb)) → new_esEs21(yvy40001, yvy30001, cgb)
new_compare12(False, True) → LT
new_esEs5(yvy4001, yvy3001, ty_Char) → new_esEs15(yvy4001, yvy3001)
new_esEs34(yvy152, yvy155, ty_Char) → new_esEs15(yvy152, yvy155)
new_esEs31(yvy40000, yvy30000, app(app(ty_@2, cef), ceg)) → new_esEs17(yvy40000, yvy30000, cef, ceg)
new_ltEs18(yvy107, yvy108, ty_Integer) → new_ltEs4(yvy107, yvy108)
new_lt21(yvy153, yvy156, ty_@0) → new_lt19(yvy153, yvy156)
new_esEs30(yvy40001, yvy30001, ty_@0) → new_esEs19(yvy40001, yvy30001)
new_ltEs18(yvy107, yvy108, app(ty_Maybe, beh)) → new_ltEs5(yvy107, yvy108, beh)
new_esEs12(LT, LT) → True
new_ltEs24(yvy100, yvy101, ty_Char) → new_ltEs7(yvy100, yvy101)
new_esEs31(yvy40000, yvy30000, app(app(ty_Either, cfe), cff)) → new_esEs24(yvy40000, yvy30000, cfe, cff)
new_ltEs18(yvy107, yvy108, ty_Double) → new_ltEs13(yvy107, yvy108)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Int, dac) → new_ltEs15(yvy1000, yvy1010)
new_esEs28(yvy1001, yvy1011, app(ty_Maybe, bhg)) → new_esEs23(yvy1001, yvy1011, bhg)
new_lt5(yvy1001, yvy1011, ty_@0) → new_lt19(yvy1001, yvy1011)
new_compare15(EQ, LT) → GT
new_pePe(True, yvy305) → True
new_compare0([], [], feh) → EQ
new_primEqNat0(Zero, Zero) → True
new_ltEs21(yvy1001, yvy1011, ty_Double) → new_ltEs13(yvy1001, yvy1011)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Float) → new_esEs14(yvy40000, yvy30000)
new_esEs6(yvy4002, yvy3002, ty_Double) → new_esEs13(yvy4002, yvy3002)
new_esEs4(yvy4000, yvy3000, app(ty_Maybe, hf)) → new_esEs23(yvy4000, yvy3000, hf)
new_lt5(yvy1001, yvy1011, ty_Bool) → new_lt18(yvy1001, yvy1011)
new_lt23(yvy165, yvy167, ty_Integer) → new_lt15(yvy165, yvy167)
new_esEs5(yvy4001, yvy3001, ty_Float) → new_esEs14(yvy4001, yvy3001)
new_lt21(yvy153, yvy156, app(app(ty_Either, ebb), ebc)) → new_lt16(yvy153, yvy156, ebb, ebc)
new_esEs8(yvy4001, yvy3001, app(app(app(ty_@3, dh), ea), eb)) → new_esEs22(yvy4001, yvy3001, dh, ea, eb)
new_lt11(yvy152, yvy155) → new_esEs12(new_compare18(yvy152, yvy155), LT)
new_lt20(yvy152, yvy155, app(ty_[], dhf)) → new_lt9(yvy152, yvy155, dhf)
new_esEs13(Double(yvy40000, yvy40001), Double(yvy30000, yvy30001)) → new_esEs25(new_sr0(yvy40000, yvy30000), new_sr0(yvy40001, yvy30001))
new_esEs7(yvy4000, yvy3000, ty_Bool) → new_esEs20(yvy4000, yvy3000)
new_compare30(yvy400, yvy300, ty_@0) → new_compare9(yvy400, yvy300)
new_esEs29(yvy40000, yvy30000, ty_@0) → new_esEs19(yvy40000, yvy30000)
new_esEs6(yvy4002, yvy3002, ty_Ordering) → new_esEs12(yvy4002, yvy3002)
new_ltEs18(yvy107, yvy108, app(app(app(ty_@3, bec), bed), bee)) → new_ltEs10(yvy107, yvy108, bec, bed, bee)
new_ltEs22(yvy114, yvy115, ty_@0) → new_ltEs17(yvy114, yvy115)
new_lt5(yvy1001, yvy1011, ty_Char) → new_lt8(yvy1001, yvy1011)
new_lt5(yvy1001, yvy1011, app(app(ty_Either, bhh), caa)) → new_lt16(yvy1001, yvy1011, bhh, caa)
new_ltEs19(yvy1002, yvy1012, ty_Ordering) → new_ltEs6(yvy1002, yvy1012)
new_esEs15(Char(yvy40000), Char(yvy30000)) → new_primEqNat0(yvy40000, yvy30000)
new_esEs24(Left(yvy40000), Left(yvy30000), app(app(app(ty_@3, dfa), dfb), dfc), hh) → new_esEs22(yvy40000, yvy30000, dfa, dfb, dfc)
new_esEs26(yvy40000, yvy30000, ty_Int) → new_esEs25(yvy40000, yvy30000)
new_esEs32(yvy40001, yvy30001, ty_Integer) → new_esEs18(yvy40001, yvy30001)
new_ltEs23(yvy166, yvy168, ty_Double) → new_ltEs13(yvy166, yvy168)
new_lt22(yvy1000, yvy1010, app(ty_[], edb)) → new_lt9(yvy1000, yvy1010, edb)
new_ltEs23(yvy166, yvy168, ty_Integer) → new_ltEs4(yvy166, yvy168)
new_esEs9(yvy4000, yvy3000, app(ty_[], ffc)) → new_esEs16(yvy4000, yvy3000, ffc)
new_esEs33(yvy40002, yvy30002, ty_Bool) → new_esEs20(yvy40002, yvy30002)
new_esEs11(yvy4000, yvy3000, ty_Double) → new_esEs13(yvy4000, yvy3000)
new_esEs29(yvy40000, yvy30000, ty_Bool) → new_esEs20(yvy40000, yvy30000)
new_lt5(yvy1001, yvy1011, app(ty_[], bgh)) → new_lt9(yvy1001, yvy1011, bgh)
new_ltEs21(yvy1001, yvy1011, ty_Bool) → new_ltEs16(yvy1001, yvy1011)
new_ltEs6(EQ, GT) → True
new_esEs9(yvy4000, yvy3000, ty_Integer) → new_esEs18(yvy4000, yvy3000)
new_esEs11(yvy4000, yvy3000, ty_Ordering) → new_esEs12(yvy4000, yvy3000)
new_esEs23(Just(yvy40000), Nothing, hf) → False
new_esEs23(Nothing, Just(yvy30000), hf) → False
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_ltEs18(yvy107, yvy108, ty_Ordering) → new_ltEs6(yvy107, yvy108)
new_esEs23(Just(yvy40000), Just(yvy30000), app(app(app(ty_@3, dde), ddf), ddg)) → new_esEs22(yvy40000, yvy30000, dde, ddf, ddg)
new_ltEs24(yvy100, yvy101, ty_Double) → new_ltEs13(yvy100, yvy101)
new_esEs10(yvy4000, yvy3000, ty_Double) → new_esEs13(yvy4000, yvy3000)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, ty_Float) → new_esEs14(yvy40000, yvy30000)
new_compare110(yvy233, yvy234, yvy235, yvy236, False, yvy238, ecf, ecg) → new_compare111(yvy233, yvy234, yvy235, yvy236, yvy238, ecf, ecg)
new_ltEs20(yvy154, yvy157, ty_Bool) → new_ltEs16(yvy154, yvy157)
new_ltEs24(yvy100, yvy101, ty_@0) → new_ltEs17(yvy100, yvy101)
new_ltEs5(Just(yvy1000), Just(yvy1010), app(app(ty_@2, fg), fh)) → new_ltEs12(yvy1000, yvy1010, fg, fh)
new_ltEs20(yvy154, yvy157, ty_Int) → new_ltEs15(yvy154, yvy157)
new_esEs8(yvy4001, yvy3001, ty_@0) → new_esEs19(yvy4001, yvy3001)
new_lt22(yvy1000, yvy1010, app(app(ty_Either, eeb), eec)) → new_lt16(yvy1000, yvy1010, eeb, eec)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Float, dac) → new_ltEs11(yvy1000, yvy1010)
new_compare26(yvy107, yvy108, False, bdg, bdh) → new_compare10(yvy107, yvy108, new_ltEs18(yvy107, yvy108, bdg), bdg, bdh)
new_lt21(yvy153, yvy156, app(ty_Ratio, eac)) → new_lt10(yvy153, yvy156, eac)
new_compare30(yvy400, yvy300, ty_Float) → new_compare18(yvy400, yvy300)
new_primEqInt(Neg(Succ(yvy400000)), Neg(Succ(yvy300000))) → new_primEqNat0(yvy400000, yvy300000)
new_esEs23(Nothing, Nothing, hf) → True
new_esEs10(yvy4000, yvy3000, app(app(app(ty_@3, egd), ege), egf)) → new_esEs22(yvy4000, yvy3000, egd, ege, egf)
new_esEs39(yvy165, yvy167, app(app(ty_@2, fcg), fch)) → new_esEs17(yvy165, yvy167, fcg, fch)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, app(app(ty_@2, dcd), dce)) → new_ltEs12(yvy1000, yvy1010, dcd, dce)
new_ltEs5(Just(yvy1000), Nothing, eh) → False
new_esEs28(yvy1001, yvy1011, ty_Char) → new_esEs15(yvy1001, yvy1011)
new_esEs11(yvy4000, yvy3000, app(ty_Maybe, faa)) → new_esEs23(yvy4000, yvy3000, faa)
new_lt14(yvy152, yvy155, dhg) → new_esEs12(new_compare31(yvy152, yvy155, dhg), LT)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, ty_@0) → new_ltEs17(yvy1000, yvy1010)
new_ltEs14(Right(yvy1000), Left(yvy1010), dbf, dac) → False
new_esEs12(EQ, LT) → False
new_esEs12(LT, EQ) → False
new_ltEs19(yvy1002, yvy1012, app(ty_Ratio, cac)) → new_ltEs9(yvy1002, yvy1012, cac)
new_lt22(yvy1000, yvy1010, app(app(ty_@2, edg), edh)) → new_lt12(yvy1000, yvy1010, edg, edh)
new_ltEs23(yvy166, yvy168, ty_Bool) → new_ltEs16(yvy166, yvy168)
new_compare111(yvy233, yvy234, yvy235, yvy236, True, ecf, ecg) → LT
new_esEs7(yvy4000, yvy3000, app(ty_[], ca)) → new_esEs16(yvy4000, yvy3000, ca)
new_esEs5(yvy4001, yvy3001, ty_Bool) → new_esEs20(yvy4001, yvy3001)
new_lt23(yvy165, yvy167, ty_Int) → new_lt17(yvy165, yvy167)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs30(yvy40001, yvy30001, app(app(app(ty_@3, cdb), cdc), cdd)) → new_esEs22(yvy40001, yvy30001, cdb, cdc, cdd)
new_esEs11(yvy4000, yvy3000, app(app(ty_Either, fab), fac)) → new_esEs24(yvy4000, yvy3000, fab, fac)
new_esEs35(yvy153, yvy156, app(app(app(ty_@3, ead), eae), eaf)) → new_esEs22(yvy153, yvy156, ead, eae, eaf)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, ty_Int) → new_ltEs15(yvy1000, yvy1010)
new_esEs10(yvy4000, yvy3000, app(app(ty_Either, egh), eha)) → new_esEs24(yvy4000, yvy3000, egh, eha)
new_esEs28(yvy1001, yvy1011, ty_Double) → new_esEs13(yvy1001, yvy1011)
new_lt20(yvy152, yvy155, ty_Ordering) → new_lt7(yvy152, yvy155)
new_ltEs6(EQ, EQ) → True
new_compare31(Just(yvy4000), Nothing, ffb) → GT
new_esEs11(yvy4000, yvy3000, app(app(app(ty_@3, ehf), ehg), ehh)) → new_esEs22(yvy4000, yvy3000, ehf, ehg, ehh)
new_ltEs22(yvy114, yvy115, app(app(ty_Either, fbf), fbg)) → new_ltEs14(yvy114, yvy115, fbf, fbg)
new_esEs28(yvy1001, yvy1011, app(app(app(ty_@3, bhb), bhc), bhd)) → new_esEs22(yvy1001, yvy1011, bhb, bhc, bhd)
new_esEs32(yvy40001, yvy30001, ty_Float) → new_esEs14(yvy40001, yvy30001)
new_esEs27(yvy1000, yvy1010, app(ty_Ratio, bfg)) → new_esEs21(yvy1000, yvy1010, bfg)
new_ltEs19(yvy1002, yvy1012, ty_Integer) → new_ltEs4(yvy1002, yvy1012)
new_primEqInt(Neg(Succ(yvy400000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(yvy300000))) → False
new_primCompAux0(yvy56, GT) → GT
new_compare30(yvy400, yvy300, app(app(app(ty_@3, gd), ge), gf)) → new_compare6(yvy400, yvy300, gd, ge, gf)
new_esEs39(yvy165, yvy167, ty_Integer) → new_esEs18(yvy165, yvy167)
new_compare26(yvy107, yvy108, True, bdg, bdh) → EQ
new_esEs23(Just(yvy40000), Just(yvy30000), app(app(ty_@2, ddb), ddc)) → new_esEs17(yvy40000, yvy30000, ddb, ddc)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, app(app(ty_Either, dgg), dgh)) → new_esEs24(yvy40000, yvy30000, dgg, dgh)
new_ltEs6(GT, GT) → True
new_ltEs21(yvy1001, yvy1011, app(app(ty_Either, efd), efe)) → new_ltEs14(yvy1001, yvy1011, efd, efe)
new_esEs38(yvy40001, yvy30001, ty_Integer) → new_esEs18(yvy40001, yvy30001)
new_esEs32(yvy40001, yvy30001, app(ty_[], cfg)) → new_esEs16(yvy40001, yvy30001, cfg)
new_esEs34(yvy152, yvy155, ty_Int) → new_esEs25(yvy152, yvy155)
new_compare31(Nothing, Nothing, ffb) → EQ
new_esEs29(yvy40000, yvy30000, app(ty_[], cbd)) → new_esEs16(yvy40000, yvy30000, cbd)
new_esEs26(yvy40000, yvy30000, app(ty_Ratio, bch)) → new_esEs21(yvy40000, yvy30000, bch)
new_esEs7(yvy4000, yvy3000, app(ty_Maybe, da)) → new_esEs23(yvy4000, yvy3000, da)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_@0) → new_ltEs17(yvy1000, yvy1010)
new_lt21(yvy153, yvy156, app(ty_[], eab)) → new_lt9(yvy153, yvy156, eab)
new_ltEs20(yvy154, yvy157, app(ty_[], ebd)) → new_ltEs8(yvy154, yvy157, ebd)
new_esEs36(yvy1000, yvy1010, ty_Int) → new_esEs25(yvy1000, yvy1010)
new_esEs19(@0, @0) → True
new_compare6(@3(yvy4000, yvy4001, yvy4002), @3(yvy3000, yvy3001, yvy3002), gd, ge, gf) → new_compare25(yvy4000, yvy4001, yvy4002, yvy3000, yvy3001, yvy3002, new_asAs(new_esEs4(yvy4000, yvy3000, gd), new_asAs(new_esEs5(yvy4001, yvy3001, ge), new_esEs6(yvy4002, yvy3002, gf))), gd, ge, gf)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_esEs7(yvy4000, yvy3000, ty_Integer) → new_esEs18(yvy4000, yvy3000)
new_esEs4(yvy4000, yvy3000, ty_Bool) → new_esEs20(yvy4000, yvy3000)
new_esEs39(yvy165, yvy167, ty_Ordering) → new_esEs12(yvy165, yvy167)
new_lt20(yvy152, yvy155, ty_Char) → new_lt8(yvy152, yvy155)
new_esEs31(yvy40000, yvy30000, ty_Bool) → new_esEs20(yvy40000, yvy30000)
new_lt4(yvy152, yvy155, bd, be, bf) → new_esEs12(new_compare6(yvy152, yvy155, bd, be, bf), LT)
new_esEs6(yvy4002, yvy3002, ty_Int) → new_esEs25(yvy4002, yvy3002)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Double, dac) → new_ltEs13(yvy1000, yvy1010)
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_lt6(yvy1000, yvy1010, app(ty_Maybe, bge)) → new_lt14(yvy1000, yvy1010, bge)
new_ltEs14(Left(yvy1000), Left(yvy1010), app(ty_Maybe, dbc), dac) → new_ltEs5(yvy1000, yvy1010, dbc)
new_esEs4(yvy4000, yvy3000, app(ty_Ratio, hb)) → new_esEs21(yvy4000, yvy3000, hb)
new_lt5(yvy1001, yvy1011, app(ty_Maybe, bhg)) → new_lt14(yvy1001, yvy1011, bhg)
new_primEqInt(Pos(Succ(yvy400000)), Pos(Succ(yvy300000))) → new_primEqNat0(yvy400000, yvy300000)
new_compare10(yvy199, yvy200, False, ef, eg) → GT
new_esEs34(yvy152, yvy155, app(ty_Maybe, dhg)) → new_esEs23(yvy152, yvy155, dhg)
new_esEs5(yvy4001, yvy3001, app(ty_[], baa)) → new_esEs16(yvy4001, yvy3001, baa)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, ty_Double) → new_ltEs13(yvy1000, yvy1010)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, ty_Integer) → new_ltEs4(yvy1000, yvy1010)
new_ltEs21(yvy1001, yvy1011, ty_Float) → new_ltEs11(yvy1001, yvy1011)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, app(ty_Maybe, dcf)) → new_ltEs5(yvy1000, yvy1010, dcf)
new_compare13(:%(yvy4000, yvy4001), :%(yvy3000, yvy3001), ty_Int) → new_compare16(new_sr0(yvy4000, yvy3001), new_sr0(yvy3000, yvy4001))
new_esEs26(yvy40000, yvy30000, app(ty_Maybe, bdd)) → new_esEs23(yvy40000, yvy30000, bdd)
new_ltEs24(yvy100, yvy101, ty_Float) → new_ltEs11(yvy100, yvy101)
new_esEs34(yvy152, yvy155, app(app(ty_@2, dec), ded)) → new_esEs17(yvy152, yvy155, dec, ded)
new_esEs8(yvy4001, yvy3001, ty_Integer) → new_esEs18(yvy4001, yvy3001)
new_ltEs22(yvy114, yvy115, app(app(app(ty_@3, fah), fba), fbb)) → new_ltEs10(yvy114, yvy115, fah, fba, fbb)
new_primEqNat0(Succ(yvy400000), Succ(yvy300000)) → new_primEqNat0(yvy400000, yvy300000)
new_esEs6(yvy4002, yvy3002, ty_Bool) → new_esEs20(yvy4002, yvy3002)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Ordering) → new_ltEs6(yvy1000, yvy1010)
new_ltEs24(yvy100, yvy101, ty_Int) → new_ltEs15(yvy100, yvy101)
new_esEs26(yvy40000, yvy30000, ty_Ordering) → new_esEs12(yvy40000, yvy30000)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, app(ty_Ratio, dgb)) → new_esEs21(yvy40000, yvy30000, dgb)
new_esEs11(yvy4000, yvy3000, app(ty_Ratio, ehe)) → new_esEs21(yvy4000, yvy3000, ehe)
new_esEs30(yvy40001, yvy30001, ty_Integer) → new_esEs18(yvy40001, yvy30001)
new_esEs39(yvy165, yvy167, ty_Char) → new_esEs15(yvy165, yvy167)
new_ltEs14(Left(yvy1000), Left(yvy1010), app(ty_Ratio, dae), dac) → new_ltEs9(yvy1000, yvy1010, dae)
new_esEs26(yvy40000, yvy30000, app(app(ty_@2, bcf), bcg)) → new_esEs17(yvy40000, yvy30000, bcf, bcg)
new_lt5(yvy1001, yvy1011, ty_Float) → new_lt11(yvy1001, yvy1011)
new_esEs32(yvy40001, yvy30001, ty_@0) → new_esEs19(yvy40001, yvy30001)
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_esEs33(yvy40002, yvy30002, app(ty_Maybe, chh)) → new_esEs23(yvy40002, yvy30002, chh)
new_lt6(yvy1000, yvy1010, ty_Int) → new_lt17(yvy1000, yvy1010)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, app(app(app(ty_@3, dgc), dgd), dge)) → new_esEs22(yvy40000, yvy30000, dgc, dgd, dge)
new_lt23(yvy165, yvy167, app(app(ty_Either, fdb), fdc)) → new_lt16(yvy165, yvy167, fdb, fdc)
new_esEs12(EQ, EQ) → True
new_lt23(yvy165, yvy167, ty_Char) → new_lt8(yvy165, yvy167)
new_ltEs18(yvy107, yvy108, app(app(ty_@2, bef), beg)) → new_ltEs12(yvy107, yvy108, bef, beg)
new_lt21(yvy153, yvy156, ty_Double) → new_lt13(yvy153, yvy156)
new_esEs35(yvy153, yvy156, ty_Ordering) → new_esEs12(yvy153, yvy156)
new_lt5(yvy1001, yvy1011, ty_Int) → new_lt17(yvy1001, yvy1011)
new_esEs10(yvy4000, yvy3000, ty_Char) → new_esEs15(yvy4000, yvy3000)
new_primEqInt(Pos(Succ(yvy400000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(yvy300000))) → False
new_ltEs5(Nothing, Just(yvy1010), eh) → True
new_lt20(yvy152, yvy155, ty_Int) → new_lt17(yvy152, yvy155)
new_esEs35(yvy153, yvy156, app(ty_Maybe, eba)) → new_esEs23(yvy153, yvy156, eba)
new_esEs27(yvy1000, yvy1010, ty_@0) → new_esEs19(yvy1000, yvy1010)
new_ltEs18(yvy107, yvy108, ty_Float) → new_ltEs11(yvy107, yvy108)
new_compare25(yvy152, yvy153, yvy154, yvy155, yvy156, yvy157, True, dhc, dhd, dhe) → EQ
new_esEs37(yvy40000, yvy30000, ty_Int) → new_esEs25(yvy40000, yvy30000)
new_primCmpNat0(Zero, Zero) → EQ
new_esEs27(yvy1000, yvy1010, app(app(ty_Either, bgf), bgg)) → new_esEs24(yvy1000, yvy1010, bgf, bgg)
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_compare27(Left(yvy4000), Right(yvy3000), eff, efg) → LT
new_lt22(yvy1000, yvy1010, ty_@0) → new_lt19(yvy1000, yvy1010)
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_compare9(@0, @0) → EQ
new_esEs28(yvy1001, yvy1011, ty_Int) → new_esEs25(yvy1001, yvy1011)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Float, hh) → new_esEs14(yvy40000, yvy30000)
new_esEs6(yvy4002, yvy3002, ty_Float) → new_esEs14(yvy4002, yvy3002)
new_ltEs9(yvy100, yvy101, cdh) → new_fsEs(new_compare13(yvy100, yvy101, cdh))
new_compare17(yvy218, yvy219, yvy220, yvy221, yvy222, yvy223, True, yvy225, ceb, cec, ced) → new_compare14(yvy218, yvy219, yvy220, yvy221, yvy222, yvy223, True, ceb, cec, ced)
new_esEs32(yvy40001, yvy30001, ty_Char) → new_esEs15(yvy40001, yvy30001)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_ltEs14(Left(yvy1000), Left(yvy1010), app(ty_[], dad), dac) → new_ltEs8(yvy1000, yvy1010, dad)
new_ltEs19(yvy1002, yvy1012, app(app(ty_@2, cag), cah)) → new_ltEs12(yvy1002, yvy1012, cag, cah)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Double, hh) → new_esEs13(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, app(app(ty_Either, daa), dab)) → new_esEs24(yvy40002, yvy30002, daa, dab)
new_esEs4(yvy4000, yvy3000, ty_Int) → new_esEs25(yvy4000, yvy3000)
new_compare28(yvy114, yvy115, True, fad, fae) → EQ
new_primEqInt(Pos(Succ(yvy400000)), Neg(yvy30000)) → False
new_primEqInt(Neg(Succ(yvy400000)), Pos(yvy30000)) → False
new_esEs24(Right(yvy40000), Right(yvy30000), hg, ty_Int) → new_esEs25(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, ty_Ordering) → new_esEs12(yvy40002, yvy30002)
new_esEs29(yvy40000, yvy30000, app(app(app(ty_@3, cbh), cca), ccb)) → new_esEs22(yvy40000, yvy30000, cbh, cca, ccb)
new_esEs26(yvy40000, yvy30000, ty_Double) → new_esEs13(yvy40000, yvy30000)
new_ltEs20(yvy154, yvy157, ty_Integer) → new_ltEs4(yvy154, yvy157)
new_compare210(yvy100, yvy101, True, feg) → EQ
new_lt6(yvy1000, yvy1010, ty_Ordering) → new_lt7(yvy1000, yvy1010)
new_esEs29(yvy40000, yvy30000, app(ty_Ratio, cbg)) → new_esEs21(yvy40000, yvy30000, cbg)
new_esEs20(False, False) → True
new_esEs24(Left(yvy40000), Left(yvy30000), app(ty_[], dee), hh) → new_esEs16(yvy40000, yvy30000, dee)
new_lt23(yvy165, yvy167, app(ty_[], fcb)) → new_lt9(yvy165, yvy167, fcb)
new_ltEs22(yvy114, yvy115, ty_Integer) → new_ltEs4(yvy114, yvy115)
new_ltEs5(Just(yvy1000), Just(yvy1010), app(app(ty_Either, gb), gc)) → new_ltEs14(yvy1000, yvy1010, gb, gc)
new_lt23(yvy165, yvy167, ty_Bool) → new_lt18(yvy165, yvy167)
new_esEs30(yvy40001, yvy30001, ty_Ordering) → new_esEs12(yvy40001, yvy30001)
new_lt6(yvy1000, yvy1010, ty_Integer) → new_lt15(yvy1000, yvy1010)
new_primEqInt(Pos(Zero), Neg(Succ(yvy300000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(yvy300000))) → False
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_compare30(yvy400, yvy300, app(ty_Maybe, ffb)) → new_compare31(yvy400, yvy300, ffb)
new_esEs9(yvy4000, yvy3000, ty_Ordering) → new_esEs12(yvy4000, yvy3000)
new_esEs7(yvy4000, yvy3000, ty_@0) → new_esEs19(yvy4000, yvy3000)
new_esEs11(yvy4000, yvy3000, ty_Float) → new_esEs14(yvy4000, yvy3000)
new_lt6(yvy1000, yvy1010, app(ty_[], bff)) → new_lt9(yvy1000, yvy1010, bff)
new_esEs36(yvy1000, yvy1010, ty_@0) → new_esEs19(yvy1000, yvy1010)
new_esEs5(yvy4001, yvy3001, ty_@0) → new_esEs19(yvy4001, yvy3001)
new_esEs36(yvy1000, yvy1010, app(app(app(ty_@3, edd), ede), edf)) → new_esEs22(yvy1000, yvy1010, edd, ede, edf)
new_esEs28(yvy1001, yvy1011, ty_Ordering) → new_esEs12(yvy1001, yvy1011)
new_esEs10(yvy4000, yvy3000, app(ty_[], efh)) → new_esEs16(yvy4000, yvy3000, efh)
new_primCompAux0(yvy56, LT) → LT
new_esEs6(yvy4002, yvy3002, app(app(ty_Either, bcc), bcd)) → new_esEs24(yvy4002, yvy3002, bcc, bcd)
new_esEs6(yvy4002, yvy3002, ty_Integer) → new_esEs18(yvy4002, yvy3002)
new_esEs36(yvy1000, yvy1010, app(app(ty_@2, edg), edh)) → new_esEs17(yvy1000, yvy1010, edg, edh)
new_esEs7(yvy4000, yvy3000, app(app(ty_@2, cb), cc)) → new_esEs17(yvy4000, yvy3000, cb, cc)
new_esEs9(yvy4000, yvy3000, ty_Float) → new_esEs14(yvy4000, yvy3000)
new_lt5(yvy1001, yvy1011, ty_Double) → new_lt13(yvy1001, yvy1011)
new_ltEs22(yvy114, yvy115, app(ty_Maybe, fbe)) → new_ltEs5(yvy114, yvy115, fbe)
new_not(False) → True
new_esEs27(yvy1000, yvy1010, ty_Int) → new_esEs25(yvy1000, yvy1010)
new_esEs34(yvy152, yvy155, app(ty_Ratio, cea)) → new_esEs21(yvy152, yvy155, cea)
new_compare30(yvy400, yvy300, ty_Bool) → new_compare12(yvy400, yvy300)
new_esEs25(yvy4000, yvy3000) → new_primEqInt(yvy4000, yvy3000)
new_esEs28(yvy1001, yvy1011, app(ty_[], bgh)) → new_esEs16(yvy1001, yvy1011, bgh)
new_esEs31(yvy40000, yvy30000, ty_Char) → new_esEs15(yvy40000, yvy30000)
new_esEs14(Float(yvy40000, yvy40001), Float(yvy30000, yvy30001)) → new_esEs25(new_sr0(yvy40000, yvy30000), new_sr0(yvy40001, yvy30001))
new_esEs11(yvy4000, yvy3000, ty_@0) → new_esEs19(yvy4000, yvy3000)
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_esEs12(GT, EQ) → False
new_esEs12(EQ, GT) → False
new_esEs36(yvy1000, yvy1010, ty_Float) → new_esEs14(yvy1000, yvy1010)
new_esEs4(yvy4000, yvy3000, ty_Ordering) → new_esEs12(yvy4000, yvy3000)
new_esEs9(yvy4000, yvy3000, app(app(ty_Either, fgc), fgd)) → new_esEs24(yvy4000, yvy3000, fgc, fgd)
new_lt6(yvy1000, yvy1010, app(app(app(ty_@3, bfh), bga), bgb)) → new_lt4(yvy1000, yvy1010, bfh, bga, bgb)
new_esEs4(yvy4000, yvy3000, app(app(ty_@2, gh), ha)) → new_esEs17(yvy4000, yvy3000, gh, ha)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, ty_Integer) → new_esEs18(yvy40000, yvy30000)
new_ltEs18(yvy107, yvy108, ty_@0) → new_ltEs17(yvy107, yvy108)
new_esEs39(yvy165, yvy167, ty_Int) → new_esEs25(yvy165, yvy167)
new_compare15(LT, EQ) → LT
new_esEs34(yvy152, yvy155, ty_Float) → new_esEs14(yvy152, yvy155)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, app(ty_[], dbg)) → new_ltEs8(yvy1000, yvy1010, dbg)
new_esEs36(yvy1000, yvy1010, app(ty_Ratio, edc)) → new_esEs21(yvy1000, yvy1010, edc)
new_esEs30(yvy40001, yvy30001, app(ty_Ratio, cda)) → new_esEs21(yvy40001, yvy30001, cda)
new_compare30(yvy400, yvy300, app(ty_Ratio, ffa)) → new_compare13(yvy400, yvy300, ffa)
new_esEs24(Left(yvy40000), Right(yvy30000), hg, hh) → False
new_esEs24(Right(yvy40000), Left(yvy30000), hg, hh) → False
new_lt20(yvy152, yvy155, app(app(ty_Either, dhh), eaa)) → new_lt16(yvy152, yvy155, dhh, eaa)
new_esEs30(yvy40001, yvy30001, app(app(ty_@2, ccg), cch)) → new_esEs17(yvy40001, yvy30001, ccg, cch)
new_esEs32(yvy40001, yvy30001, app(app(ty_Either, cgg), cgh)) → new_esEs24(yvy40001, yvy30001, cgg, cgh)
new_esEs34(yvy152, yvy155, app(ty_[], dhf)) → new_esEs16(yvy152, yvy155, dhf)
new_lt20(yvy152, yvy155, ty_Double) → new_lt13(yvy152, yvy155)
new_esEs35(yvy153, yvy156, ty_Double) → new_esEs13(yvy153, yvy156)
new_compare0(:(yvy4000, yvy4001), [], feh) → GT
new_lt6(yvy1000, yvy1010, ty_Char) → new_lt8(yvy1000, yvy1010)
new_esEs8(yvy4001, yvy3001, ty_Int) → new_esEs25(yvy4001, yvy3001)
new_esEs38(yvy40001, yvy30001, ty_Int) → new_esEs25(yvy40001, yvy30001)
new_ltEs24(yvy100, yvy101, ty_Integer) → new_ltEs4(yvy100, yvy101)
new_ltEs20(yvy154, yvy157, app(ty_Maybe, ecc)) → new_ltEs5(yvy154, yvy157, ecc)
new_ltEs20(yvy154, yvy157, ty_@0) → new_ltEs17(yvy154, yvy157)
new_ltEs24(yvy100, yvy101, app(app(ty_Either, dbf), dac)) → new_ltEs14(yvy100, yvy101, dbf, dac)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Int) → new_esEs25(yvy40000, yvy30000)
new_esEs34(yvy152, yvy155, app(app(ty_Either, dhh), eaa)) → new_esEs24(yvy152, yvy155, dhh, eaa)
new_lt13(yvy152, yvy155) → new_esEs12(new_compare29(yvy152, yvy155), LT)
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_esEs30(yvy40001, yvy30001, app(app(ty_Either, cdf), cdg)) → new_esEs24(yvy40001, yvy30001, cdf, cdg)
new_lt19(yvy152, yvy155) → new_esEs12(new_compare9(yvy152, yvy155), LT)
new_ltEs18(yvy107, yvy108, ty_Char) → new_ltEs7(yvy107, yvy108)
new_esEs4(yvy4000, yvy3000, app(app(ty_Either, hg), hh)) → new_esEs24(yvy4000, yvy3000, hg, hh)
new_esEs8(yvy4001, yvy3001, app(ty_Ratio, dg)) → new_esEs21(yvy4001, yvy3001, dg)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Integer) → new_esEs18(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, app(ty_Ratio, chd)) → new_esEs21(yvy40002, yvy30002, chd)
new_lt17(yvy152, yvy155) → new_esEs12(new_compare16(yvy152, yvy155), LT)
new_esEs10(yvy4000, yvy3000, app(app(ty_@2, ega), egb)) → new_esEs17(yvy4000, yvy3000, ega, egb)
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_ltEs7(yvy100, yvy101) → new_fsEs(new_compare11(yvy100, yvy101))
new_esEs31(yvy40000, yvy30000, ty_Float) → new_esEs14(yvy40000, yvy30000)
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_compare15(EQ, GT) → LT
new_esEs32(yvy40001, yvy30001, ty_Int) → new_esEs25(yvy40001, yvy30001)
new_esEs29(yvy40000, yvy30000, ty_Char) → new_esEs15(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, app(app(app(ty_@3, che), chf), chg)) → new_esEs22(yvy40002, yvy30002, che, chf, chg)
new_primEqNat0(Zero, Succ(yvy300000)) → False
new_primEqNat0(Succ(yvy400000), Zero) → False
new_compare15(LT, GT) → LT
new_lt15(yvy152, yvy155) → new_esEs12(new_compare8(yvy152, yvy155), LT)
new_ltEs5(Nothing, Nothing, eh) → True
new_ltEs23(yvy166, yvy168, app(app(app(ty_@3, fdf), fdg), fdh)) → new_ltEs10(yvy166, yvy168, fdf, fdg, fdh)
new_lt20(yvy152, yvy155, app(app(ty_@2, dec), ded)) → new_lt12(yvy152, yvy155, dec, ded)
new_ltEs6(LT, LT) → True
new_ltEs6(EQ, LT) → False
new_esEs6(yvy4002, yvy3002, app(ty_Ratio, bbf)) → new_esEs21(yvy4002, yvy3002, bbf)
new_ltEs5(Just(yvy1000), Just(yvy1010), app(ty_[], fa)) → new_ltEs8(yvy1000, yvy1010, fa)
new_ltEs19(yvy1002, yvy1012, ty_Char) → new_ltEs7(yvy1002, yvy1012)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_ltEs21(yvy1001, yvy1011, app(ty_Ratio, eee)) → new_ltEs9(yvy1001, yvy1011, eee)
new_esEs9(yvy4000, yvy3000, app(ty_Maybe, fgb)) → new_esEs23(yvy4000, yvy3000, fgb)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Bool) → new_ltEs16(yvy1000, yvy1010)
new_lt21(yvy153, yvy156, app(ty_Maybe, eba)) → new_lt14(yvy153, yvy156, eba)
new_compare15(GT, GT) → EQ
new_esEs11(yvy4000, yvy3000, app(app(ty_@2, ehc), ehd)) → new_esEs17(yvy4000, yvy3000, ehc, ehd)
new_esEs8(yvy4001, yvy3001, app(app(ty_Either, ed), ee)) → new_esEs24(yvy4001, yvy3001, ed, ee)
new_compare24(yvy165, yvy166, yvy167, yvy168, True, fbh, fca) → EQ
new_esEs32(yvy40001, yvy30001, ty_Bool) → new_esEs20(yvy40001, yvy30001)
new_lt21(yvy153, yvy156, ty_Float) → new_lt11(yvy153, yvy156)
new_esEs16(:(yvy40000, yvy40001), [], gg) → False
new_esEs16([], :(yvy30000, yvy30001), gg) → False
new_compare31(Just(yvy4000), Just(yvy3000), ffb) → new_compare210(yvy4000, yvy3000, new_esEs9(yvy4000, yvy3000, ffb), ffb)
new_lt21(yvy153, yvy156, ty_Ordering) → new_lt7(yvy153, yvy156)
new_lt20(yvy152, yvy155, ty_Bool) → new_lt18(yvy152, yvy155)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, app(ty_Ratio, dbh)) → new_ltEs9(yvy1000, yvy1010, dbh)
new_ltEs19(yvy1002, yvy1012, ty_@0) → new_ltEs17(yvy1002, yvy1012)
new_esEs7(yvy4000, yvy3000, app(app(app(ty_@3, ce), cf), cg)) → new_esEs22(yvy4000, yvy3000, ce, cf, cg)
new_esEs5(yvy4001, yvy3001, ty_Integer) → new_esEs18(yvy4001, yvy3001)
new_esEs31(yvy40000, yvy30000, ty_Int) → new_esEs25(yvy40000, yvy30000)
new_esEs27(yvy1000, yvy1010, app(app(app(ty_@3, bfh), bga), bgb)) → new_esEs22(yvy1000, yvy1010, bfh, bga, bgb)
new_ltEs19(yvy1002, yvy1012, app(ty_Maybe, cba)) → new_ltEs5(yvy1002, yvy1012, cba)
new_lt21(yvy153, yvy156, ty_Integer) → new_lt15(yvy153, yvy156)
new_esEs29(yvy40000, yvy30000, app(app(ty_Either, ccd), cce)) → new_esEs24(yvy40000, yvy30000, ccd, cce)
new_esEs10(yvy4000, yvy3000, app(ty_Ratio, egc)) → new_esEs21(yvy4000, yvy3000, egc)
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_ltEs12(@2(yvy1000, yvy1001), @2(yvy1010, yvy1011), ech, eda) → new_pePe(new_lt22(yvy1000, yvy1010, ech), new_asAs(new_esEs36(yvy1000, yvy1010, ech), new_ltEs21(yvy1001, yvy1011, eda)))
new_ltEs23(yvy166, yvy168, ty_@0) → new_ltEs17(yvy166, yvy168)
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_esEs5(yvy4001, yvy3001, app(ty_Maybe, bah)) → new_esEs23(yvy4001, yvy3001, bah)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Char) → new_ltEs7(yvy1000, yvy1010)
new_compare0(:(yvy4000, yvy4001), :(yvy3000, yvy3001), feh) → new_primCompAux1(yvy4000, yvy3000, new_compare0(yvy4001, yvy3001, feh), feh)
new_esEs20(False, True) → False
new_esEs20(True, False) → False
new_compare19(yvy206, yvy207, True, dha, dhb) → LT
new_sr0(yvy3000, yvy4001) → new_primMulInt(yvy3000, yvy4001)
new_esEs28(yvy1001, yvy1011, app(app(ty_@2, bhe), bhf)) → new_esEs17(yvy1001, yvy1011, bhe, bhf)
new_lt6(yvy1000, yvy1010, app(app(ty_Either, bgf), bgg)) → new_lt16(yvy1000, yvy1010, bgf, bgg)
new_esEs34(yvy152, yvy155, ty_Bool) → new_esEs20(yvy152, yvy155)
new_lt22(yvy1000, yvy1010, ty_Integer) → new_lt15(yvy1000, yvy1010)
new_esEs26(yvy40000, yvy30000, app(app(ty_Either, bde), bdf)) → new_esEs24(yvy40000, yvy30000, bde, bdf)
new_compare30(yvy400, yvy300, ty_Ordering) → new_compare15(yvy400, yvy300)
new_esEs30(yvy40001, yvy30001, app(ty_[], ccf)) → new_esEs16(yvy40001, yvy30001, ccf)
new_esEs24(Left(yvy40000), Left(yvy30000), app(app(ty_@2, def), deg), hh) → new_esEs17(yvy40000, yvy30000, def, deg)
new_lt23(yvy165, yvy167, ty_@0) → new_lt19(yvy165, yvy167)
new_esEs10(yvy4000, yvy3000, ty_Float) → new_esEs14(yvy4000, yvy3000)
new_compare29(Double(yvy4000, yvy4001), Double(yvy3000, yvy3001)) → new_compare16(new_sr0(yvy4000, yvy3000), new_sr0(yvy4001, yvy3001))
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, ty_Bool) → new_ltEs16(yvy1000, yvy1010)
new_ltEs22(yvy114, yvy115, app(ty_[], faf)) → new_ltEs8(yvy114, yvy115, faf)
new_esEs39(yvy165, yvy167, app(app(ty_Either, fdb), fdc)) → new_esEs24(yvy165, yvy167, fdb, fdc)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs32(yvy40001, yvy30001, ty_Double) → new_esEs13(yvy40001, yvy30001)
new_esEs28(yvy1001, yvy1011, ty_Bool) → new_esEs20(yvy1001, yvy1011)
new_esEs23(Just(yvy40000), Just(yvy30000), app(ty_Ratio, ddd)) → new_esEs21(yvy40000, yvy30000, ddd)
new_esEs5(yvy4001, yvy3001, app(ty_Ratio, bad)) → new_esEs21(yvy4001, yvy3001, bad)
new_ltEs14(Left(yvy1000), Right(yvy1010), dbf, dac) → True
new_compare24(yvy165, yvy166, yvy167, yvy168, False, fbh, fca) → new_compare110(yvy165, yvy166, yvy167, yvy168, new_lt23(yvy165, yvy167, fbh), new_asAs(new_esEs39(yvy165, yvy167, fbh), new_ltEs23(yvy166, yvy168, fca)), fbh, fca)
new_compare30(yvy400, yvy300, app(ty_[], feh)) → new_compare0(yvy400, yvy300, feh)
new_esEs9(yvy4000, yvy3000, app(ty_Ratio, fff)) → new_esEs21(yvy4000, yvy3000, fff)
new_ltEs20(yvy154, yvy157, app(app(ty_Either, ecd), ece)) → new_ltEs14(yvy154, yvy157, ecd, ece)
new_asAs(False, yvy184) → False
new_compare27(Right(yvy4000), Left(yvy3000), eff, efg) → GT
new_esEs36(yvy1000, yvy1010, app(ty_Maybe, eea)) → new_esEs23(yvy1000, yvy1010, eea)
new_esEs9(yvy4000, yvy3000, ty_Double) → new_esEs13(yvy4000, yvy3000)
new_ltEs19(yvy1002, yvy1012, app(app(ty_Either, cbb), cbc)) → new_ltEs14(yvy1002, yvy1012, cbb, cbc)
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_lt20(yvy152, yvy155, ty_@0) → new_lt19(yvy152, yvy155)
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_esEs4(yvy4000, yvy3000, ty_@0) → new_esEs19(yvy4000, yvy3000)
new_esEs27(yvy1000, yvy1010, ty_Double) → new_esEs13(yvy1000, yvy1010)
new_esEs36(yvy1000, yvy1010, ty_Ordering) → new_esEs12(yvy1000, yvy1010)
new_compare16(yvy400, yvy300) → new_primCmpInt(yvy400, yvy300)
new_esEs35(yvy153, yvy156, ty_Bool) → new_esEs20(yvy153, yvy156)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Bool) → new_esEs20(yvy40000, yvy30000)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Integer, dac) → new_ltEs4(yvy1000, yvy1010)
new_compare14(yvy218, yvy219, yvy220, yvy221, yvy222, yvy223, True, ceb, cec, ced) → LT
new_esEs30(yvy40001, yvy30001, app(ty_Maybe, cde)) → new_esEs23(yvy40001, yvy30001, cde)
new_esEs8(yvy4001, yvy3001, ty_Char) → new_esEs15(yvy4001, yvy3001)
new_esEs9(yvy4000, yvy3000, ty_Bool) → new_esEs20(yvy4000, yvy3000)
new_lt5(yvy1001, yvy1011, ty_Ordering) → new_lt7(yvy1001, yvy1011)
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, ty_Ordering) → new_ltEs6(yvy1000, yvy1010)
new_esEs24(Left(yvy40000), Left(yvy30000), app(app(ty_Either, dfe), dff), hh) → new_esEs24(yvy40000, yvy30000, dfe, dff)
new_esEs8(yvy4001, yvy3001, app(ty_[], dd)) → new_esEs16(yvy4001, yvy3001, dd)
new_compare27(Left(yvy4000), Left(yvy3000), eff, efg) → new_compare26(yvy4000, yvy3000, new_esEs10(yvy4000, yvy3000, eff), eff, efg)
new_esEs29(yvy40000, yvy30000, ty_Double) → new_esEs13(yvy40000, yvy30000)
new_esEs27(yvy1000, yvy1010, ty_Integer) → new_esEs18(yvy1000, yvy1010)
new_esEs18(Integer(yvy40000), Integer(yvy30000)) → new_primEqInt(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, ty_Char) → new_esEs15(yvy40002, yvy30002)
new_ltEs5(Just(yvy1000), Just(yvy1010), app(ty_Maybe, ga)) → new_ltEs5(yvy1000, yvy1010, ga)
new_ltEs11(yvy100, yvy101) → new_fsEs(new_compare18(yvy100, yvy101))
new_ltEs14(Right(yvy1000), Right(yvy1010), dbf, app(app(ty_Either, dcg), dch)) → new_ltEs14(yvy1000, yvy1010, dcg, dch)
new_esEs30(yvy40001, yvy30001, ty_Float) → new_esEs14(yvy40001, yvy30001)
new_lt23(yvy165, yvy167, ty_Float) → new_lt11(yvy165, yvy167)
new_compare12(False, False) → EQ
new_esEs28(yvy1001, yvy1011, ty_@0) → new_esEs19(yvy1001, yvy1011)
new_ltEs23(yvy166, yvy168, ty_Char) → new_ltEs7(yvy166, yvy168)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, app(ty_Maybe, dgf)) → new_esEs23(yvy40000, yvy30000, dgf)
new_esEs29(yvy40000, yvy30000, ty_Float) → new_esEs14(yvy40000, yvy30000)
new_esEs7(yvy4000, yvy3000, ty_Ordering) → new_esEs12(yvy4000, yvy3000)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Integer, hh) → new_esEs18(yvy40000, yvy30000)
new_lt20(yvy152, yvy155, app(ty_Maybe, dhg)) → new_lt14(yvy152, yvy155, dhg)
new_esEs39(yvy165, yvy167, app(app(app(ty_@3, fcd), fce), fcf)) → new_esEs22(yvy165, yvy167, fcd, fce, fcf)
new_esEs31(yvy40000, yvy30000, ty_@0) → new_esEs19(yvy40000, yvy30000)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, app(ty_[], dfg)) → new_esEs16(yvy40000, yvy30000, dfg)
new_compare111(yvy233, yvy234, yvy235, yvy236, False, ecf, ecg) → GT
new_lt21(yvy153, yvy156, ty_Bool) → new_lt18(yvy153, yvy156)
new_ltEs6(LT, GT) → True
new_esEs33(yvy40002, yvy30002, ty_Int) → new_esEs25(yvy40002, yvy30002)
new_compare30(yvy400, yvy300, ty_Integer) → new_compare8(yvy400, yvy300)
new_ltEs23(yvy166, yvy168, app(ty_Maybe, fec)) → new_ltEs5(yvy166, yvy168, fec)
new_lt23(yvy165, yvy167, app(ty_Maybe, fda)) → new_lt14(yvy165, yvy167, fda)
new_ltEs21(yvy1001, yvy1011, ty_Char) → new_ltEs7(yvy1001, yvy1011)
new_ltEs14(Left(yvy1000), Left(yvy1010), app(app(ty_Either, dbd), dbe), dac) → new_ltEs14(yvy1000, yvy1010, dbd, dbe)
new_ltEs23(yvy166, yvy168, app(app(ty_@2, fea), feb)) → new_ltEs12(yvy166, yvy168, fea, feb)
new_ltEs21(yvy1001, yvy1011, ty_Ordering) → new_ltEs6(yvy1001, yvy1011)
new_esEs32(yvy40001, yvy30001, app(app(ty_@2, cfh), cga)) → new_esEs17(yvy40001, yvy30001, cfh, cga)
new_esEs24(Left(yvy40000), Left(yvy30000), app(ty_Maybe, dfd), hh) → new_esEs23(yvy40000, yvy30000, dfd)
new_lt22(yvy1000, yvy1010, app(ty_Ratio, edc)) → new_lt10(yvy1000, yvy1010, edc)
new_lt12(yvy152, yvy155, dec, ded) → new_esEs12(new_compare7(yvy152, yvy155, dec, ded), LT)
new_esEs35(yvy153, yvy156, ty_Int) → new_esEs25(yvy153, yvy156)
new_lt10(yvy152, yvy155, cea) → new_esEs12(new_compare13(yvy152, yvy155, cea), LT)
new_esEs4(yvy4000, yvy3000, ty_Double) → new_esEs13(yvy4000, yvy3000)
new_esEs8(yvy4001, yvy3001, app(app(ty_@2, de), df)) → new_esEs17(yvy4001, yvy3001, de, df)
new_esEs5(yvy4001, yvy3001, app(app(ty_@2, bab), bac)) → new_esEs17(yvy4001, yvy3001, bab, bac)
new_esEs16([], [], gg) → True
new_lt22(yvy1000, yvy1010, ty_Float) → new_lt11(yvy1000, yvy1010)
new_esEs32(yvy40001, yvy30001, ty_Ordering) → new_esEs12(yvy40001, yvy30001)
new_ltEs19(yvy1002, yvy1012, ty_Int) → new_ltEs15(yvy1002, yvy1012)
new_ltEs21(yvy1001, yvy1011, ty_Integer) → new_ltEs4(yvy1001, yvy1011)
new_ltEs20(yvy154, yvy157, ty_Float) → new_ltEs11(yvy154, yvy157)
new_lt5(yvy1001, yvy1011, app(app(ty_@2, bhe), bhf)) → new_lt12(yvy1001, yvy1011, bhe, bhf)
new_esEs11(yvy4000, yvy3000, ty_Int) → new_esEs25(yvy4000, yvy3000)
new_esEs32(yvy40001, yvy30001, app(app(app(ty_@3, cgc), cgd), cge)) → new_esEs22(yvy40001, yvy30001, cgc, cgd, cge)
new_lt6(yvy1000, yvy1010, ty_Double) → new_lt13(yvy1000, yvy1010)
new_lt20(yvy152, yvy155, ty_Float) → new_lt11(yvy152, yvy155)
new_ltEs14(Left(yvy1000), Left(yvy1010), app(app(app(ty_@3, daf), dag), dah), dac) → new_ltEs10(yvy1000, yvy1010, daf, dag, dah)
new_esEs26(yvy40000, yvy30000, ty_Integer) → new_esEs18(yvy40000, yvy30000)
new_lt22(yvy1000, yvy1010, app(app(app(ty_@3, edd), ede), edf)) → new_lt4(yvy1000, yvy1010, edd, ede, edf)
new_esEs36(yvy1000, yvy1010, app(app(ty_Either, eeb), eec)) → new_esEs24(yvy1000, yvy1010, eeb, eec)
new_esEs27(yvy1000, yvy1010, ty_Ordering) → new_esEs12(yvy1000, yvy1010)
new_ltEs19(yvy1002, yvy1012, ty_Double) → new_ltEs13(yvy1002, yvy1012)
new_lt21(yvy153, yvy156, ty_Int) → new_lt17(yvy153, yvy156)
new_lt20(yvy152, yvy155, ty_Integer) → new_lt15(yvy152, yvy155)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, ty_Ordering) → new_esEs12(yvy40000, yvy30000)
new_lt8(yvy152, yvy155) → new_esEs12(new_compare11(yvy152, yvy155), LT)
new_ltEs24(yvy100, yvy101, app(ty_[], fef)) → new_ltEs8(yvy100, yvy101, fef)
new_esEs9(yvy4000, yvy3000, ty_@0) → new_esEs19(yvy4000, yvy3000)
new_esEs22(@3(yvy40000, yvy40001, yvy40002), @3(yvy30000, yvy30001, yvy30002), hc, hd, he) → new_asAs(new_esEs31(yvy40000, yvy30000, hc), new_asAs(new_esEs32(yvy40001, yvy30001, hd), new_esEs33(yvy40002, yvy30002, he)))
new_esEs8(yvy4001, yvy3001, ty_Float) → new_esEs14(yvy4001, yvy3001)
new_esEs7(yvy4000, yvy3000, app(ty_Ratio, cd)) → new_esEs21(yvy4000, yvy3000, cd)
new_ltEs20(yvy154, yvy157, ty_Double) → new_ltEs13(yvy154, yvy157)
new_ltEs18(yvy107, yvy108, ty_Bool) → new_ltEs16(yvy107, yvy108)
new_compare28(yvy114, yvy115, False, fad, fae) → new_compare19(yvy114, yvy115, new_ltEs22(yvy114, yvy115, fae), fad, fae)
new_esEs6(yvy4002, yvy3002, app(ty_Maybe, bcb)) → new_esEs23(yvy4002, yvy3002, bcb)
new_lt5(yvy1001, yvy1011, app(app(app(ty_@3, bhb), bhc), bhd)) → new_lt4(yvy1001, yvy1011, bhb, bhc, bhd)
new_esEs31(yvy40000, yvy30000, app(app(app(ty_@3, cfa), cfb), cfc)) → new_esEs22(yvy40000, yvy30000, cfa, cfb, cfc)
new_esEs31(yvy40000, yvy30000, ty_Ordering) → new_esEs12(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, ty_Double) → new_esEs13(yvy40002, yvy30002)
new_lt6(yvy1000, yvy1010, ty_Float) → new_lt11(yvy1000, yvy1010)
new_esEs4(yvy4000, yvy3000, ty_Char) → new_esEs15(yvy4000, yvy3000)
new_esEs7(yvy4000, yvy3000, app(app(ty_Either, db), dc)) → new_esEs24(yvy4000, yvy3000, db, dc)
new_compare112(yvy189, yvy190, False, fge) → GT
new_esEs12(GT, GT) → True
new_ltEs21(yvy1001, yvy1011, app(app(app(ty_@3, eef), eeg), eeh)) → new_ltEs10(yvy1001, yvy1011, eef, eeg, eeh)
new_esEs5(yvy4001, yvy3001, ty_Double) → new_esEs13(yvy4001, yvy3001)
new_compare17(yvy218, yvy219, yvy220, yvy221, yvy222, yvy223, False, yvy225, ceb, cec, ced) → new_compare14(yvy218, yvy219, yvy220, yvy221, yvy222, yvy223, yvy225, ceb, cec, ced)
new_esEs8(yvy4001, yvy3001, app(ty_Maybe, ec)) → new_esEs23(yvy4001, yvy3001, ec)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_@0) → new_esEs19(yvy40000, yvy30000)
new_compare25(yvy152, yvy153, yvy154, yvy155, yvy156, yvy157, False, dhc, dhd, dhe) → new_compare17(yvy152, yvy153, yvy154, yvy155, yvy156, yvy157, new_lt20(yvy152, yvy155, dhc), new_asAs(new_esEs34(yvy152, yvy155, dhc), new_pePe(new_lt21(yvy153, yvy156, dhd), new_asAs(new_esEs35(yvy153, yvy156, dhd), new_ltEs20(yvy154, yvy157, dhe)))), dhc, dhd, dhe)
new_compare31(Nothing, Just(yvy3000), ffb) → LT
new_esEs29(yvy40000, yvy30000, ty_Ordering) → new_esEs12(yvy40000, yvy30000)
new_esEs4(yvy4000, yvy3000, app(ty_[], gg)) → new_esEs16(yvy4000, yvy3000, gg)
new_primPlusNat1(Zero, Zero) → Zero
new_compare0([], :(yvy3000, yvy3001), feh) → LT
new_ltEs6(LT, EQ) → True
new_lt23(yvy165, yvy167, ty_Ordering) → new_lt7(yvy165, yvy167)
new_ltEs21(yvy1001, yvy1011, app(ty_Maybe, efc)) → new_ltEs5(yvy1001, yvy1011, efc)
new_ltEs6(GT, LT) → False
new_lt18(yvy152, yvy155) → new_esEs12(new_compare12(yvy152, yvy155), LT)
new_esEs24(Right(yvy40000), Right(yvy30000), hg, ty_Char) → new_esEs15(yvy40000, yvy30000)
new_asAs(True, yvy184) → yvy184
new_esEs26(yvy40000, yvy30000, ty_Float) → new_esEs14(yvy40000, yvy30000)
new_esEs35(yvy153, yvy156, ty_Float) → new_esEs14(yvy153, yvy156)
new_ltEs21(yvy1001, yvy1011, app(ty_[], eed)) → new_ltEs8(yvy1001, yvy1011, eed)
new_compare11(Char(yvy4000), Char(yvy3000)) → new_primCmpNat0(yvy4000, yvy3000)
new_ltEs22(yvy114, yvy115, ty_Float) → new_ltEs11(yvy114, yvy115)
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_esEs28(yvy1001, yvy1011, app(ty_Ratio, bha)) → new_esEs21(yvy1001, yvy1011, bha)
new_esEs39(yvy165, yvy167, ty_Double) → new_esEs13(yvy165, yvy167)
new_esEs11(yvy4000, yvy3000, ty_Bool) → new_esEs20(yvy4000, yvy3000)
new_ltEs22(yvy114, yvy115, ty_Double) → new_ltEs13(yvy114, yvy115)
new_lt22(yvy1000, yvy1010, ty_Ordering) → new_lt7(yvy1000, yvy1010)
new_esEs4(yvy4000, yvy3000, app(app(app(ty_@3, hc), hd), he)) → new_esEs22(yvy4000, yvy3000, hc, hd, he)
new_lt20(yvy152, yvy155, app(ty_Ratio, cea)) → new_lt10(yvy152, yvy155, cea)
new_ltEs16(False, False) → True
new_lt23(yvy165, yvy167, ty_Double) → new_lt13(yvy165, yvy167)
new_ltEs17(yvy100, yvy101) → new_fsEs(new_compare9(yvy100, yvy101))
new_esEs29(yvy40000, yvy30000, ty_Integer) → new_esEs18(yvy40000, yvy30000)
new_esEs8(yvy4001, yvy3001, ty_Ordering) → new_esEs12(yvy4001, yvy3001)
new_esEs30(yvy40001, yvy30001, ty_Bool) → new_esEs20(yvy40001, yvy30001)
new_lt23(yvy165, yvy167, app(ty_Ratio, fcc)) → new_lt10(yvy165, yvy167, fcc)
new_esEs30(yvy40001, yvy30001, ty_Int) → new_esEs25(yvy40001, yvy30001)
new_esEs27(yvy1000, yvy1010, ty_Float) → new_esEs14(yvy1000, yvy1010)
new_ltEs21(yvy1001, yvy1011, ty_Int) → new_ltEs15(yvy1001, yvy1011)
new_ltEs20(yvy154, yvy157, app(app(app(ty_@3, ebf), ebg), ebh)) → new_ltEs10(yvy154, yvy157, ebf, ebg, ebh)
new_esEs23(Just(yvy40000), Just(yvy30000), app(ty_[], dda)) → new_esEs16(yvy40000, yvy30000, dda)
new_esEs34(yvy152, yvy155, app(app(app(ty_@3, bd), be), bf)) → new_esEs22(yvy152, yvy155, bd, be, bf)
new_esEs16(:(yvy40000, yvy40001), :(yvy30000, yvy30001), gg) → new_asAs(new_esEs26(yvy40000, yvy30000, gg), new_esEs16(yvy40001, yvy30001, gg))
new_esEs9(yvy4000, yvy3000, app(app(app(ty_@3, ffg), ffh), fga)) → new_esEs22(yvy4000, yvy3000, ffg, ffh, fga)
new_ltEs19(yvy1002, yvy1012, app(app(app(ty_@3, cad), cae), caf)) → new_ltEs10(yvy1002, yvy1012, cad, cae, caf)
new_ltEs20(yvy154, yvy157, ty_Ordering) → new_ltEs6(yvy154, yvy157)
new_compare19(yvy206, yvy207, False, dha, dhb) → GT
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Integer) → new_ltEs4(yvy1000, yvy1010)
new_esEs6(yvy4002, yvy3002, ty_@0) → new_esEs19(yvy4002, yvy3002)
new_ltEs10(@3(yvy1000, yvy1001, yvy1002), @3(yvy1010, yvy1011, yvy1012), bfc, bfd, bfe) → new_pePe(new_lt6(yvy1000, yvy1010, bfc), new_asAs(new_esEs27(yvy1000, yvy1010, bfc), new_pePe(new_lt5(yvy1001, yvy1011, bfd), new_asAs(new_esEs28(yvy1001, yvy1011, bfd), new_ltEs19(yvy1002, yvy1012, bfe)))))
new_esEs33(yvy40002, yvy30002, ty_@0) → new_esEs19(yvy40002, yvy30002)
new_esEs35(yvy153, yvy156, app(ty_Ratio, eac)) → new_esEs21(yvy153, yvy156, eac)
new_ltEs22(yvy114, yvy115, ty_Int) → new_ltEs15(yvy114, yvy115)
new_ltEs24(yvy100, yvy101, app(app(app(ty_@3, bfc), bfd), bfe)) → new_ltEs10(yvy100, yvy101, bfc, bfd, bfe)
new_compare27(Right(yvy4000), Right(yvy3000), eff, efg) → new_compare28(yvy4000, yvy3000, new_esEs11(yvy4000, yvy3000, efg), eff, efg)
new_ltEs21(yvy1001, yvy1011, ty_@0) → new_ltEs17(yvy1001, yvy1011)
new_lt16(yvy152, yvy155, dhh, eaa) → new_esEs12(new_compare27(yvy152, yvy155, dhh, eaa), LT)
new_compare15(EQ, EQ) → EQ
new_ltEs22(yvy114, yvy115, ty_Char) → new_ltEs7(yvy114, yvy115)
new_compare30(yvy400, yvy300, ty_Double) → new_compare29(yvy400, yvy300)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCompAux0(yvy56, EQ) → yvy56
new_lt6(yvy1000, yvy1010, app(app(ty_@2, bgc), bgd)) → new_lt12(yvy1000, yvy1010, bgc, bgd)
new_esEs27(yvy1000, yvy1010, app(ty_Maybe, bge)) → new_esEs23(yvy1000, yvy1010, bge)
new_ltEs20(yvy154, yvy157, ty_Char) → new_ltEs7(yvy154, yvy157)
new_esEs10(yvy4000, yvy3000, ty_Integer) → new_esEs18(yvy4000, yvy3000)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_@0, dac) → new_ltEs17(yvy1000, yvy1010)
new_ltEs18(yvy107, yvy108, ty_Int) → new_ltEs15(yvy107, yvy108)
new_lt21(yvy153, yvy156, app(app(app(ty_@3, ead), eae), eaf)) → new_lt4(yvy153, yvy156, ead, eae, eaf)
new_esEs6(yvy4002, yvy3002, ty_Char) → new_esEs15(yvy4002, yvy3002)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_esEs30(yvy40001, yvy30001, ty_Char) → new_esEs15(yvy40001, yvy30001)
new_ltEs5(Just(yvy1000), Just(yvy1010), app(app(app(ty_@3, fc), fd), ff)) → new_ltEs10(yvy1000, yvy1010, fc, fd, ff)
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_esEs39(yvy165, yvy167, app(ty_[], fcb)) → new_esEs16(yvy165, yvy167, fcb)
new_esEs35(yvy153, yvy156, ty_Char) → new_esEs15(yvy153, yvy156)
new_not(True) → False
new_ltEs5(Just(yvy1000), Just(yvy1010), app(ty_Ratio, fb)) → new_ltEs9(yvy1000, yvy1010, fb)

The set Q consists of the following terms:

new_esEs36(x0, x1, ty_Char)
new_esEs29(x0, x1, ty_Float)
new_lt22(x0, x1, app(ty_Maybe, x2))
new_esEs7(x0, x1, ty_Int)
new_ltEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs21(x0, x1, ty_Int)
new_ltEs14(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs10(x0, x1, ty_Float)
new_ltEs16(True, True)
new_esEs6(x0, x1, ty_Int)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs32(x0, x1, app(ty_Maybe, x2))
new_lt11(x0, x1)
new_esEs24(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs20(x0, x1, ty_Int)
new_lt5(x0, x1, ty_Char)
new_esEs5(x0, x1, app(ty_[], x2))
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs36(x0, x1, app(ty_[], x2))
new_lt21(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs21(x0, x1, ty_@0)
new_esEs29(x0, x1, ty_Char)
new_ltEs22(x0, x1, ty_Integer)
new_esEs34(x0, x1, app(ty_[], x2))
new_esEs32(x0, x1, ty_Int)
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs11(x0, x1, ty_Int)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs4(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_Integer)
new_compare30(x0, x1, ty_Int)
new_pePe(True, x0)
new_esEs5(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs11(x0, x1, ty_@0)
new_esEs35(x0, x1, ty_Integer)
new_esEs11(x0, x1, ty_Char)
new_esEs9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(x0, x1, ty_Float)
new_esEs9(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(x0, x1, ty_Int)
new_esEs31(x0, x1, app(app(ty_Either, x2), x3))
new_lt22(x0, x1, ty_@0)
new_compare30(x0, x1, ty_Bool)
new_ltEs5(Nothing, Just(x0), x1)
new_lt20(x0, x1, ty_@0)
new_esEs29(x0, x1, ty_Ordering)
new_lt22(x0, x1, ty_Float)
new_esEs9(x0, x1, app(ty_[], x2))
new_lt23(x0, x1, ty_Integer)
new_ltEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(Right(x0), Right(x1), x2, ty_Bool)
new_lt7(x0, x1)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs8(x0, x1, ty_Integer)
new_esEs23(Just(x0), Just(x1), ty_Float)
new_esEs6(x0, x1, ty_Integer)
new_lt5(x0, x1, ty_@0)
new_esEs33(x0, x1, app(app(ty_@2, x2), x3))
new_esEs11(x0, x1, ty_Bool)
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs24(Right(x0), Right(x1), x2, ty_Integer)
new_compare12(False, True)
new_compare12(True, False)
new_ltEs7(x0, x1)
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_primCompAux0(x0, EQ)
new_esEs32(x0, x1, app(app(ty_@2, x2), x3))
new_lt6(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(x0, x1, ty_Integer)
new_esEs32(x0, x1, ty_Ordering)
new_ltEs21(x0, x1, ty_Float)
new_ltEs24(x0, x1, ty_Integer)
new_esEs34(x0, x1, ty_Float)
new_esEs6(x0, x1, ty_@0)
new_lt6(x0, x1, ty_Float)
new_esEs9(x0, x1, ty_Int)
new_compare30(x0, x1, ty_Integer)
new_esEs12(GT, EQ)
new_esEs12(EQ, GT)
new_esEs36(x0, x1, ty_Int)
new_esEs28(x0, x1, ty_Bool)
new_ltEs14(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs24(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_compare30(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_lt5(x0, x1, ty_Double)
new_compare15(LT, LT)
new_esEs10(x0, x1, ty_Char)
new_esEs23(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primMulNat0(Succ(x0), Zero)
new_ltEs22(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_compare6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs34(x0, x1, ty_Ordering)
new_esEs16([], [], x0)
new_esEs12(GT, GT)
new_esEs30(x0, x1, ty_Double)
new_esEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs21(x0, x1, ty_Ordering)
new_esEs10(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_lt21(x0, x1, ty_Float)
new_esEs11(x0, x1, ty_Integer)
new_esEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs21(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs24(x0, x1, app(ty_Maybe, x2))
new_esEs23(Just(x0), Just(x1), ty_Double)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_Char)
new_esEs34(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(Left(x0), Left(x1), ty_Int, x2)
new_esEs38(x0, x1, ty_Integer)
new_ltEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs27(x0, x1, ty_Bool)
new_esEs24(Right(x0), Right(x1), x2, ty_Char)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs6(EQ, EQ)
new_esEs32(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(x0, x1, ty_Float)
new_esEs8(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs22(x0, x1, ty_Char)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(x0, x1, ty_Double)
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_esEs5(x0, x1, ty_Bool)
new_lt6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs31(x0, x1, ty_Int)
new_compare26(x0, x1, True, x2, x3)
new_compare110(x0, x1, x2, x3, True, x4, x5, x6)
new_ltEs24(x0, x1, app(ty_[], x2))
new_compare27(Right(x0), Left(x1), x2, x3)
new_compare27(Left(x0), Right(x1), x2, x3)
new_esEs33(x0, x1, ty_Double)
new_esEs8(x0, x1, ty_Float)
new_ltEs18(x0, x1, ty_@0)
new_esEs4(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, app(ty_[], x2))
new_ltEs5(Just(x0), Just(x1), ty_@0)
new_lt5(x0, x1, ty_Int)
new_ltEs6(LT, EQ)
new_ltEs6(EQ, LT)
new_esEs24(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_primCompAux0(x0, LT)
new_esEs23(Nothing, Nothing, x0)
new_esEs38(x0, x1, ty_Int)
new_esEs23(Just(x0), Just(x1), ty_Int)
new_ltEs20(x0, x1, ty_@0)
new_lt6(x0, x1, app(ty_Maybe, x2))
new_esEs11(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Int)
new_lt17(x0, x1)
new_esEs8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs36(x0, x1, ty_Bool)
new_primEqNat0(Zero, Zero)
new_compare13(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs26(x0, x1, ty_@0)
new_lt21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(Right(x0), Right(x1), x2, ty_Int)
new_esEs7(x0, x1, ty_Bool)
new_esEs33(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs5(x0, x1, ty_Float)
new_ltEs14(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_compare17(x0, x1, x2, x3, x4, x5, False, x6, x7, x8, x9)
new_ltEs22(x0, x1, ty_Float)
new_compare15(GT, GT)
new_esEs31(x0, x1, ty_Double)
new_ltEs20(x0, x1, ty_Integer)
new_lt22(x0, x1, ty_Bool)
new_compare30(x0, x1, app(ty_[], x2))
new_esEs34(x0, x1, ty_Bool)
new_esEs31(x0, x1, ty_Integer)
new_ltEs20(x0, x1, ty_Char)
new_lt20(x0, x1, ty_Double)
new_esEs35(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_compare28(x0, x1, True, x2, x3)
new_ltEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs21(x0, x1, app(ty_[], x2))
new_ltEs15(x0, x1)
new_esEs4(x0, x1, ty_Integer)
new_esEs39(x0, x1, app(ty_Ratio, x2))
new_esEs6(x0, x1, app(app(ty_Either, x2), x3))
new_esEs39(x0, x1, ty_Bool)
new_esEs6(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs24(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Float)
new_ltEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_primMulNat0(Zero, Zero)
new_asAs(True, x0)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_ltEs14(Left(x0), Right(x1), x2, x3)
new_ltEs14(Right(x0), Left(x1), x2, x3)
new_esEs26(x0, x1, ty_Double)
new_esEs5(x0, x1, ty_Double)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs35(x0, x1, app(app(ty_@2, x2), x3))
new_fsEs(x0)
new_esEs16(:(x0, x1), [], x2)
new_ltEs5(Just(x0), Just(x1), ty_Integer)
new_esEs35(x0, x1, app(ty_Ratio, x2))
new_lt6(x0, x1, ty_Double)
new_esEs35(x0, x1, ty_Double)
new_ltEs18(x0, x1, ty_Bool)
new_esEs23(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Float)
new_ltEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(x0, x1, app(ty_Maybe, x2))
new_compare28(x0, x1, False, x2, x3)
new_ltEs5(Just(x0), Just(x1), ty_Double)
new_lt22(x0, x1, ty_Ordering)
new_lt23(x0, x1, app(ty_Ratio, x2))
new_esEs9(x0, x1, ty_@0)
new_esEs6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare24(x0, x1, x2, x3, False, x4, x5)
new_esEs24(Left(x0), Left(x1), ty_@0, x2)
new_esEs35(x0, x1, ty_Bool)
new_esEs35(x0, x1, ty_Char)
new_ltEs23(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, ty_Bool)
new_ltEs10(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs31(x0, x1, ty_@0)
new_lt10(x0, x1, x2)
new_ltEs19(x0, x1, ty_Double)
new_lt12(x0, x1, x2, x3)
new_ltEs24(x0, x1, ty_Double)
new_esEs13(Double(x0, x1), Double(x2, x3))
new_esEs10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Ordering)
new_esEs5(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(Just(x0), Nothing, x1)
new_ltEs14(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs24(Right(x0), Right(x1), x2, ty_@0)
new_esEs20(True, True)
new_lt22(x0, x1, ty_Int)
new_esEs7(x0, x1, ty_Integer)
new_esEs30(x0, x1, ty_Bool)
new_lt21(x0, x1, ty_@0)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs4(x0, x1, app(ty_Maybe, x2))
new_esEs33(x0, x1, ty_Float)
new_esEs29(x0, x1, ty_Integer)
new_ltEs21(x0, x1, ty_Integer)
new_lt16(x0, x1, x2, x3)
new_primPlusNat0(Zero, x0)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs4(x0, x1, ty_Ordering)
new_esEs8(x0, x1, ty_Bool)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_primPlusNat0(Succ(x0), x1)
new_ltEs4(x0, x1)
new_esEs34(x0, x1, ty_Integer)
new_esEs31(x0, x1, ty_Ordering)
new_ltEs6(GT, LT)
new_ltEs6(LT, GT)
new_compare0([], [], x0)
new_ltEs22(x0, x1, app(ty_Maybe, x2))
new_esEs35(x0, x1, app(ty_Maybe, x2))
new_compare111(x0, x1, x2, x3, True, x4, x5)
new_esEs11(x0, x1, ty_Double)
new_lt19(x0, x1)
new_ltEs14(Left(x0), Left(x1), ty_Double, x2)
new_ltEs8(x0, x1, x2)
new_ltEs14(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs4(x0, x1, ty_Double)
new_esEs36(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, ty_Double)
new_esEs39(x0, x1, ty_Char)
new_ltEs22(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_compare15(EQ, EQ)
new_lt6(x0, x1, ty_Int)
new_lt21(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, ty_Ordering)
new_ltEs14(Right(x0), Right(x1), x2, ty_Double)
new_ltEs22(x0, x1, ty_Ordering)
new_ltEs11(x0, x1)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_compare7(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt20(x0, x1, ty_Float)
new_lt21(x0, x1, ty_Integer)
new_esEs32(x0, x1, ty_Bool)
new_esEs39(x0, x1, ty_Float)
new_compare10(x0, x1, False, x2, x3)
new_lt6(x0, x1, ty_Integer)
new_lt4(x0, x1, x2, x3, x4)
new_esEs10(x0, x1, ty_Double)
new_esEs31(x0, x1, app(ty_[], x2))
new_sr0(x0, x1)
new_esEs23(Just(x0), Just(x1), ty_Integer)
new_esEs24(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs20(False, True)
new_esEs20(True, False)
new_esEs29(x0, x1, ty_Bool)
new_esEs24(Left(x0), Right(x1), x2, x3)
new_esEs24(Right(x0), Left(x1), x2, x3)
new_ltEs23(x0, x1, ty_Integer)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs36(x0, x1, app(ty_Ratio, x2))
new_esEs20(False, False)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare12(False, False)
new_esEs12(LT, EQ)
new_esEs12(EQ, LT)
new_lt21(x0, x1, ty_Int)
new_lt22(x0, x1, ty_Char)
new_ltEs14(Left(x0), Left(x1), ty_Char, x2)
new_ltEs14(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare14(x0, x1, x2, x3, x4, x5, True, x6, x7, x8)
new_esEs31(x0, x1, ty_Float)
new_esEs24(Left(x0), Left(x1), ty_Float, x2)
new_primPlusNat1(Zero, Zero)
new_ltEs21(x0, x1, ty_Bool)
new_esEs24(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs20(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_Float)
new_esEs12(EQ, EQ)
new_esEs23(Just(x0), Just(x1), ty_Bool)
new_esEs27(x0, x1, ty_Char)
new_ltEs14(Right(x0), Right(x1), x2, ty_Int)
new_esEs9(x0, x1, ty_Integer)
new_esEs30(x0, x1, ty_Float)
new_ltEs20(x0, x1, ty_Float)
new_lt22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(Right(x0), Right(x1), x2, ty_Char)
new_esEs9(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Left(x0), Left(x1), ty_Float, x2)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs16(:(x0, x1), :(x2, x3), x4)
new_esEs28(x0, x1, ty_Double)
new_esEs30(x0, x1, ty_Char)
new_compare30(x0, x1, ty_@0)
new_esEs6(x0, x1, ty_Bool)
new_esEs16([], :(x0, x1), x2)
new_ltEs23(x0, x1, ty_Float)
new_esEs9(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs31(x0, x1, app(app(ty_@2, x2), x3))
new_compare15(EQ, GT)
new_compare15(GT, EQ)
new_compare17(x0, x1, x2, x3, x4, x5, True, x6, x7, x8, x9)
new_ltEs9(x0, x1, x2)
new_ltEs24(x0, x1, ty_Ordering)
new_compare30(x0, x1, ty_Char)
new_primEqNat0(Succ(x0), Zero)
new_compare15(LT, GT)
new_compare15(GT, LT)
new_esEs36(x0, x1, ty_Double)
new_esEs39(x0, x1, ty_Ordering)
new_esEs7(x0, x1, app(app(ty_Either, x2), x3))
new_lt21(x0, x1, app(ty_[], x2))
new_esEs37(x0, x1, ty_Int)
new_esEs9(x0, x1, ty_Double)
new_primMulInt(Neg(x0), Neg(x1))
new_ltEs5(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs17(x0, x1)
new_compare0([], :(x0, x1), x2)
new_esEs9(x0, x1, ty_Ordering)
new_ltEs12(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs26(x0, x1, ty_Char)
new_lt23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_lt23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs23(x0, x1, ty_Int)
new_primEqNat0(Succ(x0), Succ(x1))
new_compare210(x0, x1, True, x2)
new_esEs8(x0, x1, ty_Int)
new_ltEs14(Left(x0), Left(x1), ty_Bool, x2)
new_lt21(x0, x1, app(ty_Maybe, x2))
new_ltEs5(Just(x0), Just(x1), ty_Int)
new_esEs33(x0, x1, ty_Int)
new_ltEs23(x0, x1, ty_@0)
new_lt6(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs33(x0, x1, ty_Bool)
new_esEs10(x0, x1, ty_Ordering)
new_esEs24(Left(x0), Left(x1), ty_Double, x2)
new_esEs35(x0, x1, ty_@0)
new_esEs4(x0, x1, ty_Char)
new_compare112(x0, x1, False, x2)
new_esEs24(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_lt23(x0, x1, ty_Int)
new_ltEs14(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs18(x0, x1, ty_Double)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt23(x0, x1, ty_Bool)
new_ltEs14(Left(x0), Left(x1), ty_Integer, x2)
new_esEs24(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_lt9(x0, x1, x2)
new_ltEs18(x0, x1, app(ty_[], x2))
new_esEs33(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, app(ty_[], x2))
new_lt5(x0, x1, app(app(ty_Either, x2), x3))
new_lt21(x0, x1, ty_Bool)
new_esEs24(Left(x0), Left(x1), ty_Char, x2)
new_ltEs5(Nothing, Nothing, x0)
new_compare18(Float(x0, x1), Float(x2, x3))
new_ltEs5(Just(x0), Just(x1), ty_Float)
new_esEs26(x0, x1, ty_Bool)
new_lt6(x0, x1, ty_Bool)
new_esEs30(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Integer)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs8(x0, x1, ty_Double)
new_lt21(x0, x1, ty_Char)
new_lt5(x0, x1, ty_Float)
new_compare11(Char(x0), Char(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs24(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs36(x0, x1, app(app(ty_Either, x2), x3))
new_esEs30(x0, x1, ty_Integer)
new_esEs25(x0, x1)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_compare210(x0, x1, False, x2)
new_esEs29(x0, x1, ty_@0)
new_ltEs14(Left(x0), Left(x1), ty_Int, x2)
new_sr(Integer(x0), Integer(x1))
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs7(x0, x1, ty_@0)
new_esEs39(x0, x1, app(ty_Maybe, x2))
new_primMulNat0(Succ(x0), Succ(x1))
new_ltEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs34(x0, x1, ty_Char)
new_esEs4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs10(x0, x1, ty_Bool)
new_lt5(x0, x1, app(ty_[], x2))
new_esEs10(x0, x1, ty_@0)
new_esEs39(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_@0)
new_esEs31(x0, x1, ty_Bool)
new_primEqNat0(Zero, Succ(x0))
new_primPlusNat1(Succ(x0), Zero)
new_lt23(x0, x1, ty_Char)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs7(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Char)
new_ltEs21(x0, x1, app(ty_Maybe, x2))
new_esEs6(x0, x1, ty_Ordering)
new_esEs33(x0, x1, ty_Char)
new_compare27(Left(x0), Left(x1), x2, x3)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs32(x0, x1, ty_Integer)
new_ltEs14(Left(x0), Left(x1), ty_Ordering, x2)
new_pePe(False, x0)
new_ltEs24(x0, x1, ty_Int)
new_compare24(x0, x1, x2, x3, True, x4, x5)
new_lt8(x0, x1)
new_esEs39(x0, x1, app(app(ty_Either, x2), x3))
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt23(x0, x1, ty_Double)
new_esEs10(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Bool)
new_esEs9(x0, x1, app(app(ty_@2, x2), x3))
new_esEs32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, ty_Int)
new_esEs30(x0, x1, ty_Ordering)
new_lt23(x0, x1, ty_Float)
new_lt6(x0, x1, ty_@0)
new_primPlusNat1(Succ(x0), Succ(x1))
new_compare27(Right(x0), Right(x1), x2, x3)
new_esEs31(x0, x1, ty_Char)
new_lt22(x0, x1, ty_Double)
new_ltEs22(x0, x1, ty_@0)
new_esEs39(x0, x1, ty_Int)
new_esEs30(x0, x1, ty_@0)
new_compare14(x0, x1, x2, x3, x4, x5, False, x6, x7, x8)
new_ltEs16(False, True)
new_ltEs16(True, False)
new_ltEs6(GT, GT)
new_esEs10(x0, x1, ty_Int)
new_compare30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(x0, x1, app(ty_Maybe, x2))
new_esEs31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs32(x0, x1, ty_Char)
new_esEs23(Nothing, Just(x0), x1)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(x0, x1, ty_Int)
new_ltEs5(Just(x0), Just(x1), ty_Ordering)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_ltEs19(x0, x1, ty_Char)
new_ltEs22(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(Just(x0), Just(x1), ty_Char)
new_esEs27(x0, x1, ty_Int)
new_esEs24(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs4(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(Just(x0), Just(x1), ty_Bool)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_Bool)
new_lt22(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_@0)
new_ltEs22(x0, x1, ty_Bool)
new_esEs30(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_Integer)
new_esEs33(x0, x1, ty_Integer)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, ty_Int)
new_primCmpNat0(Zero, Zero)
new_esEs35(x0, x1, ty_Float)
new_asAs(False, x0)
new_lt5(x0, x1, ty_Integer)
new_ltEs24(x0, x1, ty_@0)
new_esEs17(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs19(x0, x1, ty_Int)
new_lt23(x0, x1, ty_@0)
new_esEs34(x0, x1, ty_Int)
new_ltEs6(LT, LT)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs35(x0, x1, app(ty_[], x2))
new_esEs35(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare31(Just(x0), Just(x1), x2)
new_esEs11(x0, x1, ty_Ordering)
new_esEs31(x0, x1, app(ty_Ratio, x2))
new_lt5(x0, x1, app(ty_Ratio, x2))
new_ltEs22(x0, x1, ty_Double)
new_ltEs14(Left(x0), Left(x1), ty_@0, x2)
new_lt23(x0, x1, app(ty_[], x2))
new_compare10(x0, x1, True, x2, x3)
new_ltEs24(x0, x1, ty_Char)
new_esEs21(:%(x0, x1), :%(x2, x3), x4)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs18(Integer(x0), Integer(x1))
new_esEs4(x0, x1, ty_@0)
new_lt22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, ty_Int)
new_ltEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(Just(x0), Just(x1), ty_@0)
new_compare110(x0, x1, x2, x3, False, x4, x5, x6)
new_ltEs14(Right(x0), Right(x1), x2, ty_Integer)
new_compare0(:(x0, x1), [], x2)
new_esEs23(Just(x0), Nothing, x1)
new_ltEs19(x0, x1, ty_Float)
new_esEs6(x0, x1, ty_Char)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_lt21(x0, x1, ty_Double)
new_esEs32(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs8(x0, x1, app(ty_[], x2))
new_esEs23(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs34(x0, x1, app(app(ty_Either, x2), x3))
new_esEs33(x0, x1, app(ty_[], x2))
new_lt5(x0, x1, ty_Bool)
new_esEs11(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(Just(x0), Just(x1), ty_Char)
new_ltEs13(x0, x1)
new_lt14(x0, x1, x2)
new_ltEs23(x0, x1, ty_Bool)
new_esEs6(x0, x1, app(ty_Ratio, x2))
new_compare15(LT, EQ)
new_compare15(EQ, LT)
new_compare9(@0, @0)
new_lt13(x0, x1)
new_esEs36(x0, x1, ty_Integer)
new_esEs29(x0, x1, ty_Double)
new_ltEs22(x0, x1, app(ty_[], x2))
new_ltEs23(x0, x1, app(ty_Maybe, x2))
new_esEs8(x0, x1, app(ty_Ratio, x2))
new_ltEs18(x0, x1, ty_Float)
new_lt18(x0, x1)
new_lt22(x0, x1, app(ty_Ratio, x2))
new_esEs32(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_Float)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_lt5(x0, x1, ty_Ordering)
new_lt15(x0, x1)
new_compare8(Integer(x0), Integer(x1))
new_lt22(x0, x1, app(ty_[], x2))
new_compare30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs33(x0, x1, app(ty_Ratio, x2))
new_lt5(x0, x1, app(ty_Maybe, x2))
new_esEs36(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs33(x0, x1, app(ty_Maybe, x2))
new_esEs7(x0, x1, app(ty_Maybe, x2))
new_esEs8(x0, x1, ty_@0)
new_lt6(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(x0, x1, ty_Int)
new_not(True)
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_compare30(x0, x1, ty_Float)
new_compare31(Just(x0), Nothing, x1)
new_esEs27(x0, x1, ty_Ordering)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs22(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs23(x0, x1, app(ty_Ratio, x2))
new_ltEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(x0, x1, ty_Bool)
new_esEs32(x0, x1, ty_Float)
new_esEs36(x0, x1, ty_Ordering)
new_esEs9(x0, x1, ty_Bool)
new_esEs23(Just(x0), Just(x1), app(ty_Maybe, x2))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_not(False)
new_esEs24(Left(x0), Left(x1), ty_Ordering, x2)
new_compare29(Double(x0, x1), Double(x2, x3))
new_compare13(:%(x0, x1), :%(x2, x3), ty_Integer)
new_lt6(x0, x1, app(ty_Ratio, x2))
new_primCmpNat0(Succ(x0), Succ(x1))
new_esEs7(x0, x1, ty_Ordering)
new_esEs34(x0, x1, app(ty_Ratio, x2))
new_ltEs23(x0, x1, ty_Char)
new_esEs7(x0, x1, app(ty_[], x2))
new_esEs8(x0, x1, ty_Ordering)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_esEs39(x0, x1, ty_@0)
new_ltEs21(x0, x1, ty_Char)
new_esEs15(Char(x0), Char(x1))
new_esEs7(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(x0, x1, app(ty_Ratio, x2))
new_ltEs6(GT, EQ)
new_ltEs6(EQ, GT)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_esEs7(x0, x1, app(ty_Ratio, x2))
new_esEs32(x0, x1, app(ty_Ratio, x2))
new_primCmpNat0(Zero, Succ(x0))
new_esEs31(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Ordering)
new_lt23(x0, x1, app(ty_Maybe, x2))
new_ltEs21(x0, x1, ty_Double)
new_esEs24(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs8(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs23(x0, x1, app(ty_[], x2))
new_esEs24(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_compare30(x0, x1, ty_Double)
new_compare19(x0, x1, True, x2, x3)
new_esEs36(x0, x1, app(ty_Maybe, x2))
new_esEs24(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs5(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(Right(x0), Right(x1), x2, ty_Double)
new_lt22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(x0, x1, app(ty_[], x2))
new_primCmpNat0(Succ(x0), Zero)
new_compare30(x0, x1, app(ty_Maybe, x2))
new_esEs34(x0, x1, ty_Double)
new_ltEs21(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_@0)
new_esEs11(x0, x1, app(ty_Maybe, x2))
new_esEs6(x0, x1, app(ty_Maybe, x2))
new_ltEs22(x0, x1, ty_Int)
new_compare26(x0, x1, False, x2, x3)
new_compare16(x0, x1)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_esEs23(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs20(x0, x1, ty_Double)
new_ltEs24(x0, x1, ty_Bool)
new_esEs35(x0, x1, ty_Ordering)
new_ltEs18(x0, x1, ty_Integer)
new_esEs39(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs34(x0, x1, ty_@0)
new_compare31(Nothing, Just(x0), x1)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_esEs37(x0, x1, ty_Integer)
new_ltEs18(x0, x1, ty_Char)
new_esEs7(x0, x1, ty_Double)
new_lt23(x0, x1, ty_Ordering)
new_compare112(x0, x1, True, x2)
new_lt21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs34(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs9(x0, x1, ty_Float)
new_esEs23(Just(x0), Just(x1), ty_Ordering)
new_lt6(x0, x1, ty_Char)
new_esEs9(x0, x1, ty_Char)
new_esEs8(x0, x1, ty_Char)
new_esEs35(x0, x1, ty_Int)
new_esEs24(Left(x0), Left(x1), ty_Integer, x2)
new_esEs5(x0, x1, app(ty_Maybe, x2))
new_lt21(x0, x1, app(ty_Ratio, x2))
new_esEs33(x0, x1, ty_@0)
new_esEs24(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs5(x0, x1, ty_Ordering)
new_esEs32(x0, x1, ty_Double)
new_esEs34(x0, x1, app(ty_Maybe, x2))
new_esEs10(x0, x1, app(ty_[], x2))
new_compare30(x0, x1, app(ty_Ratio, x2))
new_ltEs21(x0, x1, app(ty_Ratio, x2))
new_lt23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs24(x0, x1, app(ty_Ratio, x2))
new_esEs14(Float(x0, x1), Float(x2, x3))
new_esEs26(x0, x1, ty_Integer)
new_esEs5(x0, x1, ty_@0)
new_esEs5(x0, x1, ty_Char)
new_esEs7(x0, x1, ty_Char)
new_compare12(True, True)
new_primEqInt(Pos(Zero), Pos(Zero))
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs5(x0, x1, ty_Integer)
new_primCompAux1(x0, x1, x2, x3)
new_compare31(Nothing, Nothing, x0)
new_esEs39(x0, x1, app(ty_[], x2))
new_compare30(x0, x1, ty_Ordering)
new_primMulNat0(Zero, Succ(x0))
new_esEs28(x0, x1, app(ty_[], x2))
new_ltEs23(x0, x1, ty_Double)
new_esEs24(Right(x0), Right(x1), x2, ty_Float)
new_esEs11(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_lt5(x0, x1, app(app(ty_@2, x2), x3))
new_primCompAux0(x0, GT)
new_lt6(x0, x1, ty_Ordering)
new_primPlusNat1(Zero, Succ(x0))
new_esEs36(x0, x1, ty_Float)
new_esEs19(@0, @0)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs39(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_compare25(x0, x1, x2, x3, x4, x5, True, x6, x7, x8)
new_esEs36(x0, x1, ty_@0)
new_esEs12(LT, LT)
new_esEs28(x0, x1, ty_Integer)
new_compare19(x0, x1, False, x2, x3)
new_ltEs18(x0, x1, ty_Ordering)
new_ltEs16(False, False)
new_compare111(x0, x1, x2, x3, False, x4, x5)
new_compare25(x0, x1, x2, x3, x4, x5, False, x6, x7, x8)
new_esEs33(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, ty_Ordering)
new_esEs28(x0, x1, ty_@0)
new_esEs11(x0, x1, ty_Float)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs4(x0, x1, app(ty_[], x2))
new_esEs39(x0, x1, ty_Integer)

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

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

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

new_splitGT3(:(yvy300, yvy301), yvy31, yvy32, yvy33, yvy34, [], h, ba) → new_splitGT1(yvy300, yvy301, yvy31, yvy32, yvy33, yvy34, new_compare0([], :(yvy300, yvy301), h), h, ba)
new_splitGT1(yvy300, yvy301, yvy31, yvy32, Branch(yvy330, yvy331, yvy332, yvy333, yvy334), yvy34, LT, h, ba) → new_splitGT3(yvy330, yvy331, yvy332, yvy333, yvy334, [], h, ba)

The TRS R consists of the following rules:

new_compare0([], :(yvy3000, yvy3001), feh) → LT

The set Q consists of the following terms:

new_esEs36(x0, x1, ty_Char)
new_esEs29(x0, x1, ty_Float)
new_lt22(x0, x1, app(ty_Maybe, x2))
new_esEs7(x0, x1, ty_Int)
new_ltEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs21(x0, x1, ty_Int)
new_ltEs14(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs10(x0, x1, ty_Float)
new_ltEs16(True, True)
new_esEs6(x0, x1, ty_Int)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs32(x0, x1, app(ty_Maybe, x2))
new_lt11(x0, x1)
new_esEs24(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs20(x0, x1, ty_Int)
new_lt5(x0, x1, ty_Char)
new_esEs5(x0, x1, app(ty_[], x2))
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs36(x0, x1, app(ty_[], x2))
new_lt21(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs21(x0, x1, ty_@0)
new_esEs29(x0, x1, ty_Char)
new_ltEs22(x0, x1, ty_Integer)
new_esEs34(x0, x1, app(ty_[], x2))
new_esEs32(x0, x1, ty_Int)
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs11(x0, x1, ty_Int)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs4(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_Integer)
new_compare30(x0, x1, ty_Int)
new_pePe(True, x0)
new_esEs5(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs11(x0, x1, ty_@0)
new_esEs35(x0, x1, ty_Integer)
new_esEs11(x0, x1, ty_Char)
new_esEs9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(x0, x1, ty_Float)
new_esEs9(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(x0, x1, ty_Int)
new_esEs31(x0, x1, app(app(ty_Either, x2), x3))
new_lt22(x0, x1, ty_@0)
new_compare30(x0, x1, ty_Bool)
new_ltEs5(Nothing, Just(x0), x1)
new_lt20(x0, x1, ty_@0)
new_esEs29(x0, x1, ty_Ordering)
new_lt22(x0, x1, ty_Float)
new_esEs9(x0, x1, app(ty_[], x2))
new_lt23(x0, x1, ty_Integer)
new_ltEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(Right(x0), Right(x1), x2, ty_Bool)
new_lt7(x0, x1)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs8(x0, x1, ty_Integer)
new_esEs23(Just(x0), Just(x1), ty_Float)
new_esEs6(x0, x1, ty_Integer)
new_lt5(x0, x1, ty_@0)
new_esEs33(x0, x1, app(app(ty_@2, x2), x3))
new_esEs11(x0, x1, ty_Bool)
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs24(Right(x0), Right(x1), x2, ty_Integer)
new_compare12(False, True)
new_compare12(True, False)
new_ltEs7(x0, x1)
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_primCompAux0(x0, EQ)
new_esEs32(x0, x1, app(app(ty_@2, x2), x3))
new_lt6(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(x0, x1, ty_Integer)
new_esEs32(x0, x1, ty_Ordering)
new_ltEs21(x0, x1, ty_Float)
new_ltEs24(x0, x1, ty_Integer)
new_esEs34(x0, x1, ty_Float)
new_esEs6(x0, x1, ty_@0)
new_lt6(x0, x1, ty_Float)
new_esEs9(x0, x1, ty_Int)
new_compare30(x0, x1, ty_Integer)
new_esEs12(GT, EQ)
new_esEs12(EQ, GT)
new_esEs36(x0, x1, ty_Int)
new_esEs28(x0, x1, ty_Bool)
new_ltEs14(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs24(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_compare30(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_lt5(x0, x1, ty_Double)
new_compare15(LT, LT)
new_esEs10(x0, x1, ty_Char)
new_esEs23(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primMulNat0(Succ(x0), Zero)
new_ltEs22(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_compare6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs34(x0, x1, ty_Ordering)
new_esEs16([], [], x0)
new_esEs12(GT, GT)
new_esEs30(x0, x1, ty_Double)
new_esEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs21(x0, x1, ty_Ordering)
new_esEs10(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_lt21(x0, x1, ty_Float)
new_esEs11(x0, x1, ty_Integer)
new_esEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs21(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs24(x0, x1, app(ty_Maybe, x2))
new_esEs23(Just(x0), Just(x1), ty_Double)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_Char)
new_esEs34(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(Left(x0), Left(x1), ty_Int, x2)
new_esEs38(x0, x1, ty_Integer)
new_ltEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs27(x0, x1, ty_Bool)
new_esEs24(Right(x0), Right(x1), x2, ty_Char)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs6(EQ, EQ)
new_esEs32(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(x0, x1, ty_Float)
new_esEs8(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs22(x0, x1, ty_Char)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(x0, x1, ty_Double)
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_esEs5(x0, x1, ty_Bool)
new_lt6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs31(x0, x1, ty_Int)
new_compare26(x0, x1, True, x2, x3)
new_compare110(x0, x1, x2, x3, True, x4, x5, x6)
new_ltEs24(x0, x1, app(ty_[], x2))
new_compare27(Right(x0), Left(x1), x2, x3)
new_compare27(Left(x0), Right(x1), x2, x3)
new_esEs33(x0, x1, ty_Double)
new_esEs8(x0, x1, ty_Float)
new_ltEs18(x0, x1, ty_@0)
new_esEs4(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, app(ty_[], x2))
new_ltEs5(Just(x0), Just(x1), ty_@0)
new_lt5(x0, x1, ty_Int)
new_ltEs6(LT, EQ)
new_ltEs6(EQ, LT)
new_esEs24(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_primCompAux0(x0, LT)
new_esEs23(Nothing, Nothing, x0)
new_esEs38(x0, x1, ty_Int)
new_esEs23(Just(x0), Just(x1), ty_Int)
new_ltEs20(x0, x1, ty_@0)
new_lt6(x0, x1, app(ty_Maybe, x2))
new_esEs11(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Int)
new_lt17(x0, x1)
new_esEs8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs36(x0, x1, ty_Bool)
new_primEqNat0(Zero, Zero)
new_compare13(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs26(x0, x1, ty_@0)
new_lt21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(Right(x0), Right(x1), x2, ty_Int)
new_esEs7(x0, x1, ty_Bool)
new_esEs33(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs5(x0, x1, ty_Float)
new_ltEs14(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_compare17(x0, x1, x2, x3, x4, x5, False, x6, x7, x8, x9)
new_ltEs22(x0, x1, ty_Float)
new_compare15(GT, GT)
new_esEs31(x0, x1, ty_Double)
new_ltEs20(x0, x1, ty_Integer)
new_lt22(x0, x1, ty_Bool)
new_compare30(x0, x1, app(ty_[], x2))
new_esEs34(x0, x1, ty_Bool)
new_esEs31(x0, x1, ty_Integer)
new_ltEs20(x0, x1, ty_Char)
new_lt20(x0, x1, ty_Double)
new_esEs35(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_compare28(x0, x1, True, x2, x3)
new_ltEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs21(x0, x1, app(ty_[], x2))
new_ltEs15(x0, x1)
new_esEs4(x0, x1, ty_Integer)
new_esEs39(x0, x1, app(ty_Ratio, x2))
new_esEs6(x0, x1, app(app(ty_Either, x2), x3))
new_esEs39(x0, x1, ty_Bool)
new_esEs6(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs24(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Float)
new_ltEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_primMulNat0(Zero, Zero)
new_asAs(True, x0)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_ltEs14(Left(x0), Right(x1), x2, x3)
new_ltEs14(Right(x0), Left(x1), x2, x3)
new_esEs26(x0, x1, ty_Double)
new_esEs5(x0, x1, ty_Double)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs35(x0, x1, app(app(ty_@2, x2), x3))
new_fsEs(x0)
new_esEs16(:(x0, x1), [], x2)
new_ltEs5(Just(x0), Just(x1), ty_Integer)
new_esEs35(x0, x1, app(ty_Ratio, x2))
new_lt6(x0, x1, ty_Double)
new_esEs35(x0, x1, ty_Double)
new_ltEs18(x0, x1, ty_Bool)
new_esEs23(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Float)
new_ltEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(x0, x1, app(ty_Maybe, x2))
new_compare28(x0, x1, False, x2, x3)
new_ltEs5(Just(x0), Just(x1), ty_Double)
new_lt22(x0, x1, ty_Ordering)
new_lt23(x0, x1, app(ty_Ratio, x2))
new_esEs9(x0, x1, ty_@0)
new_esEs6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare24(x0, x1, x2, x3, False, x4, x5)
new_esEs24(Left(x0), Left(x1), ty_@0, x2)
new_esEs35(x0, x1, ty_Bool)
new_esEs35(x0, x1, ty_Char)
new_ltEs23(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, ty_Bool)
new_ltEs10(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs31(x0, x1, ty_@0)
new_lt10(x0, x1, x2)
new_ltEs19(x0, x1, ty_Double)
new_lt12(x0, x1, x2, x3)
new_ltEs24(x0, x1, ty_Double)
new_esEs13(Double(x0, x1), Double(x2, x3))
new_esEs10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Ordering)
new_esEs5(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(Just(x0), Nothing, x1)
new_ltEs14(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs24(Right(x0), Right(x1), x2, ty_@0)
new_esEs20(True, True)
new_lt22(x0, x1, ty_Int)
new_esEs7(x0, x1, ty_Integer)
new_esEs30(x0, x1, ty_Bool)
new_lt21(x0, x1, ty_@0)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs4(x0, x1, app(ty_Maybe, x2))
new_esEs33(x0, x1, ty_Float)
new_esEs29(x0, x1, ty_Integer)
new_ltEs21(x0, x1, ty_Integer)
new_lt16(x0, x1, x2, x3)
new_primPlusNat0(Zero, x0)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs4(x0, x1, ty_Ordering)
new_esEs8(x0, x1, ty_Bool)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_primPlusNat0(Succ(x0), x1)
new_ltEs4(x0, x1)
new_esEs34(x0, x1, ty_Integer)
new_esEs31(x0, x1, ty_Ordering)
new_ltEs6(GT, LT)
new_ltEs6(LT, GT)
new_compare0([], [], x0)
new_ltEs22(x0, x1, app(ty_Maybe, x2))
new_esEs35(x0, x1, app(ty_Maybe, x2))
new_compare111(x0, x1, x2, x3, True, x4, x5)
new_esEs11(x0, x1, ty_Double)
new_lt19(x0, x1)
new_ltEs14(Left(x0), Left(x1), ty_Double, x2)
new_ltEs8(x0, x1, x2)
new_ltEs14(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs4(x0, x1, ty_Double)
new_esEs36(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, ty_Double)
new_esEs39(x0, x1, ty_Char)
new_ltEs22(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_compare15(EQ, EQ)
new_lt6(x0, x1, ty_Int)
new_lt21(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, ty_Ordering)
new_ltEs14(Right(x0), Right(x1), x2, ty_Double)
new_ltEs22(x0, x1, ty_Ordering)
new_ltEs11(x0, x1)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_compare7(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt20(x0, x1, ty_Float)
new_lt21(x0, x1, ty_Integer)
new_esEs32(x0, x1, ty_Bool)
new_esEs39(x0, x1, ty_Float)
new_compare10(x0, x1, False, x2, x3)
new_lt6(x0, x1, ty_Integer)
new_lt4(x0, x1, x2, x3, x4)
new_esEs10(x0, x1, ty_Double)
new_esEs31(x0, x1, app(ty_[], x2))
new_sr0(x0, x1)
new_esEs23(Just(x0), Just(x1), ty_Integer)
new_esEs24(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs20(False, True)
new_esEs20(True, False)
new_esEs29(x0, x1, ty_Bool)
new_esEs24(Left(x0), Right(x1), x2, x3)
new_esEs24(Right(x0), Left(x1), x2, x3)
new_ltEs23(x0, x1, ty_Integer)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs36(x0, x1, app(ty_Ratio, x2))
new_esEs20(False, False)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare12(False, False)
new_esEs12(LT, EQ)
new_esEs12(EQ, LT)
new_lt21(x0, x1, ty_Int)
new_lt22(x0, x1, ty_Char)
new_ltEs14(Left(x0), Left(x1), ty_Char, x2)
new_ltEs14(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare14(x0, x1, x2, x3, x4, x5, True, x6, x7, x8)
new_esEs31(x0, x1, ty_Float)
new_esEs24(Left(x0), Left(x1), ty_Float, x2)
new_primPlusNat1(Zero, Zero)
new_ltEs21(x0, x1, ty_Bool)
new_esEs24(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs20(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_Float)
new_esEs12(EQ, EQ)
new_esEs23(Just(x0), Just(x1), ty_Bool)
new_esEs27(x0, x1, ty_Char)
new_ltEs14(Right(x0), Right(x1), x2, ty_Int)
new_esEs9(x0, x1, ty_Integer)
new_esEs30(x0, x1, ty_Float)
new_ltEs20(x0, x1, ty_Float)
new_lt22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(Right(x0), Right(x1), x2, ty_Char)
new_esEs9(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Left(x0), Left(x1), ty_Float, x2)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs16(:(x0, x1), :(x2, x3), x4)
new_esEs28(x0, x1, ty_Double)
new_esEs30(x0, x1, ty_Char)
new_compare30(x0, x1, ty_@0)
new_esEs6(x0, x1, ty_Bool)
new_esEs16([], :(x0, x1), x2)
new_ltEs23(x0, x1, ty_Float)
new_esEs9(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs31(x0, x1, app(app(ty_@2, x2), x3))
new_compare15(EQ, GT)
new_compare15(GT, EQ)
new_compare17(x0, x1, x2, x3, x4, x5, True, x6, x7, x8, x9)
new_ltEs9(x0, x1, x2)
new_ltEs24(x0, x1, ty_Ordering)
new_compare30(x0, x1, ty_Char)
new_primEqNat0(Succ(x0), Zero)
new_compare15(LT, GT)
new_compare15(GT, LT)
new_esEs36(x0, x1, ty_Double)
new_esEs39(x0, x1, ty_Ordering)
new_esEs7(x0, x1, app(app(ty_Either, x2), x3))
new_lt21(x0, x1, app(ty_[], x2))
new_esEs37(x0, x1, ty_Int)
new_esEs9(x0, x1, ty_Double)
new_primMulInt(Neg(x0), Neg(x1))
new_ltEs5(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs17(x0, x1)
new_compare0([], :(x0, x1), x2)
new_esEs9(x0, x1, ty_Ordering)
new_ltEs12(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs26(x0, x1, ty_Char)
new_lt23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_lt23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs23(x0, x1, ty_Int)
new_primEqNat0(Succ(x0), Succ(x1))
new_compare210(x0, x1, True, x2)
new_esEs8(x0, x1, ty_Int)
new_ltEs14(Left(x0), Left(x1), ty_Bool, x2)
new_lt21(x0, x1, app(ty_Maybe, x2))
new_ltEs5(Just(x0), Just(x1), ty_Int)
new_esEs33(x0, x1, ty_Int)
new_ltEs23(x0, x1, ty_@0)
new_lt6(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs33(x0, x1, ty_Bool)
new_esEs10(x0, x1, ty_Ordering)
new_esEs24(Left(x0), Left(x1), ty_Double, x2)
new_esEs35(x0, x1, ty_@0)
new_esEs4(x0, x1, ty_Char)
new_compare112(x0, x1, False, x2)
new_esEs24(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_lt23(x0, x1, ty_Int)
new_ltEs14(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs18(x0, x1, ty_Double)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt23(x0, x1, ty_Bool)
new_ltEs14(Left(x0), Left(x1), ty_Integer, x2)
new_esEs24(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_lt9(x0, x1, x2)
new_ltEs18(x0, x1, app(ty_[], x2))
new_esEs33(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, app(ty_[], x2))
new_lt5(x0, x1, app(app(ty_Either, x2), x3))
new_lt21(x0, x1, ty_Bool)
new_esEs24(Left(x0), Left(x1), ty_Char, x2)
new_ltEs5(Nothing, Nothing, x0)
new_compare18(Float(x0, x1), Float(x2, x3))
new_ltEs5(Just(x0), Just(x1), ty_Float)
new_esEs26(x0, x1, ty_Bool)
new_lt6(x0, x1, ty_Bool)
new_esEs30(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Integer)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs8(x0, x1, ty_Double)
new_lt21(x0, x1, ty_Char)
new_lt5(x0, x1, ty_Float)
new_compare11(Char(x0), Char(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs24(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs36(x0, x1, app(app(ty_Either, x2), x3))
new_esEs30(x0, x1, ty_Integer)
new_esEs25(x0, x1)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_compare210(x0, x1, False, x2)
new_esEs29(x0, x1, ty_@0)
new_ltEs14(Left(x0), Left(x1), ty_Int, x2)
new_sr(Integer(x0), Integer(x1))
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs7(x0, x1, ty_@0)
new_esEs39(x0, x1, app(ty_Maybe, x2))
new_primMulNat0(Succ(x0), Succ(x1))
new_ltEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs34(x0, x1, ty_Char)
new_esEs4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs10(x0, x1, ty_Bool)
new_lt5(x0, x1, app(ty_[], x2))
new_esEs10(x0, x1, ty_@0)
new_esEs39(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_@0)
new_esEs31(x0, x1, ty_Bool)
new_primEqNat0(Zero, Succ(x0))
new_primPlusNat1(Succ(x0), Zero)
new_lt23(x0, x1, ty_Char)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs7(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Char)
new_ltEs21(x0, x1, app(ty_Maybe, x2))
new_esEs6(x0, x1, ty_Ordering)
new_esEs33(x0, x1, ty_Char)
new_compare27(Left(x0), Left(x1), x2, x3)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs32(x0, x1, ty_Integer)
new_ltEs14(Left(x0), Left(x1), ty_Ordering, x2)
new_pePe(False, x0)
new_ltEs24(x0, x1, ty_Int)
new_compare24(x0, x1, x2, x3, True, x4, x5)
new_lt8(x0, x1)
new_esEs39(x0, x1, app(app(ty_Either, x2), x3))
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt23(x0, x1, ty_Double)
new_esEs10(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Bool)
new_esEs9(x0, x1, app(app(ty_@2, x2), x3))
new_esEs32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, ty_Int)
new_esEs30(x0, x1, ty_Ordering)
new_lt23(x0, x1, ty_Float)
new_lt6(x0, x1, ty_@0)
new_primPlusNat1(Succ(x0), Succ(x1))
new_compare27(Right(x0), Right(x1), x2, x3)
new_esEs31(x0, x1, ty_Char)
new_lt22(x0, x1, ty_Double)
new_ltEs22(x0, x1, ty_@0)
new_esEs39(x0, x1, ty_Int)
new_esEs30(x0, x1, ty_@0)
new_compare14(x0, x1, x2, x3, x4, x5, False, x6, x7, x8)
new_ltEs16(False, True)
new_ltEs16(True, False)
new_ltEs6(GT, GT)
new_esEs10(x0, x1, ty_Int)
new_compare30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(x0, x1, app(ty_Maybe, x2))
new_esEs31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs32(x0, x1, ty_Char)
new_esEs23(Nothing, Just(x0), x1)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(x0, x1, ty_Int)
new_ltEs5(Just(x0), Just(x1), ty_Ordering)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_ltEs19(x0, x1, ty_Char)
new_ltEs22(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(Just(x0), Just(x1), ty_Char)
new_esEs27(x0, x1, ty_Int)
new_esEs24(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs4(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(Just(x0), Just(x1), ty_Bool)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_Bool)
new_lt22(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_@0)
new_ltEs22(x0, x1, ty_Bool)
new_esEs30(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_Integer)
new_esEs33(x0, x1, ty_Integer)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, ty_Int)
new_primCmpNat0(Zero, Zero)
new_esEs35(x0, x1, ty_Float)
new_asAs(False, x0)
new_lt5(x0, x1, ty_Integer)
new_ltEs24(x0, x1, ty_@0)
new_esEs17(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs19(x0, x1, ty_Int)
new_lt23(x0, x1, ty_@0)
new_esEs34(x0, x1, ty_Int)
new_ltEs6(LT, LT)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs35(x0, x1, app(ty_[], x2))
new_esEs35(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare31(Just(x0), Just(x1), x2)
new_esEs11(x0, x1, ty_Ordering)
new_esEs31(x0, x1, app(ty_Ratio, x2))
new_lt5(x0, x1, app(ty_Ratio, x2))
new_ltEs22(x0, x1, ty_Double)
new_ltEs14(Left(x0), Left(x1), ty_@0, x2)
new_lt23(x0, x1, app(ty_[], x2))
new_compare10(x0, x1, True, x2, x3)
new_ltEs24(x0, x1, ty_Char)
new_esEs21(:%(x0, x1), :%(x2, x3), x4)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs18(Integer(x0), Integer(x1))
new_esEs4(x0, x1, ty_@0)
new_lt22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, ty_Int)
new_ltEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(Just(x0), Just(x1), ty_@0)
new_compare110(x0, x1, x2, x3, False, x4, x5, x6)
new_ltEs14(Right(x0), Right(x1), x2, ty_Integer)
new_compare0(:(x0, x1), [], x2)
new_esEs23(Just(x0), Nothing, x1)
new_ltEs19(x0, x1, ty_Float)
new_esEs6(x0, x1, ty_Char)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_lt21(x0, x1, ty_Double)
new_esEs32(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs8(x0, x1, app(ty_[], x2))
new_esEs23(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs34(x0, x1, app(app(ty_Either, x2), x3))
new_esEs33(x0, x1, app(ty_[], x2))
new_lt5(x0, x1, ty_Bool)
new_esEs11(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(Just(x0), Just(x1), ty_Char)
new_ltEs13(x0, x1)
new_lt14(x0, x1, x2)
new_ltEs23(x0, x1, ty_Bool)
new_esEs6(x0, x1, app(ty_Ratio, x2))
new_compare15(LT, EQ)
new_compare15(EQ, LT)
new_compare9(@0, @0)
new_lt13(x0, x1)
new_esEs36(x0, x1, ty_Integer)
new_esEs29(x0, x1, ty_Double)
new_ltEs22(x0, x1, app(ty_[], x2))
new_ltEs23(x0, x1, app(ty_Maybe, x2))
new_esEs8(x0, x1, app(ty_Ratio, x2))
new_ltEs18(x0, x1, ty_Float)
new_lt18(x0, x1)
new_lt22(x0, x1, app(ty_Ratio, x2))
new_esEs32(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_Float)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_lt5(x0, x1, ty_Ordering)
new_lt15(x0, x1)
new_compare8(Integer(x0), Integer(x1))
new_lt22(x0, x1, app(ty_[], x2))
new_compare30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs33(x0, x1, app(ty_Ratio, x2))
new_lt5(x0, x1, app(ty_Maybe, x2))
new_esEs36(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs33(x0, x1, app(ty_Maybe, x2))
new_esEs7(x0, x1, app(ty_Maybe, x2))
new_esEs8(x0, x1, ty_@0)
new_lt6(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(x0, x1, ty_Int)
new_not(True)
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_compare30(x0, x1, ty_Float)
new_compare31(Just(x0), Nothing, x1)
new_esEs27(x0, x1, ty_Ordering)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs22(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs23(x0, x1, app(ty_Ratio, x2))
new_ltEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(x0, x1, ty_Bool)
new_esEs32(x0, x1, ty_Float)
new_esEs36(x0, x1, ty_Ordering)
new_esEs9(x0, x1, ty_Bool)
new_esEs23(Just(x0), Just(x1), app(ty_Maybe, x2))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_not(False)
new_esEs24(Left(x0), Left(x1), ty_Ordering, x2)
new_compare29(Double(x0, x1), Double(x2, x3))
new_compare13(:%(x0, x1), :%(x2, x3), ty_Integer)
new_lt6(x0, x1, app(ty_Ratio, x2))
new_primCmpNat0(Succ(x0), Succ(x1))
new_esEs7(x0, x1, ty_Ordering)
new_esEs34(x0, x1, app(ty_Ratio, x2))
new_ltEs23(x0, x1, ty_Char)
new_esEs7(x0, x1, app(ty_[], x2))
new_esEs8(x0, x1, ty_Ordering)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_esEs39(x0, x1, ty_@0)
new_ltEs21(x0, x1, ty_Char)
new_esEs15(Char(x0), Char(x1))
new_esEs7(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(x0, x1, app(ty_Ratio, x2))
new_ltEs6(GT, EQ)
new_ltEs6(EQ, GT)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_esEs7(x0, x1, app(ty_Ratio, x2))
new_esEs32(x0, x1, app(ty_Ratio, x2))
new_primCmpNat0(Zero, Succ(x0))
new_esEs31(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Ordering)
new_lt23(x0, x1, app(ty_Maybe, x2))
new_ltEs21(x0, x1, ty_Double)
new_esEs24(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs8(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs23(x0, x1, app(ty_[], x2))
new_esEs24(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_compare30(x0, x1, ty_Double)
new_compare19(x0, x1, True, x2, x3)
new_esEs36(x0, x1, app(ty_Maybe, x2))
new_esEs24(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs5(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(Right(x0), Right(x1), x2, ty_Double)
new_lt22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(x0, x1, app(ty_[], x2))
new_primCmpNat0(Succ(x0), Zero)
new_compare30(x0, x1, app(ty_Maybe, x2))
new_esEs34(x0, x1, ty_Double)
new_ltEs21(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_@0)
new_esEs11(x0, x1, app(ty_Maybe, x2))
new_esEs6(x0, x1, app(ty_Maybe, x2))
new_ltEs22(x0, x1, ty_Int)
new_compare26(x0, x1, False, x2, x3)
new_compare16(x0, x1)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_esEs23(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs20(x0, x1, ty_Double)
new_ltEs24(x0, x1, ty_Bool)
new_esEs35(x0, x1, ty_Ordering)
new_ltEs18(x0, x1, ty_Integer)
new_esEs39(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs34(x0, x1, ty_@0)
new_compare31(Nothing, Just(x0), x1)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_esEs37(x0, x1, ty_Integer)
new_ltEs18(x0, x1, ty_Char)
new_esEs7(x0, x1, ty_Double)
new_lt23(x0, x1, ty_Ordering)
new_compare112(x0, x1, True, x2)
new_lt21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs34(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs9(x0, x1, ty_Float)
new_esEs23(Just(x0), Just(x1), ty_Ordering)
new_lt6(x0, x1, ty_Char)
new_esEs9(x0, x1, ty_Char)
new_esEs8(x0, x1, ty_Char)
new_esEs35(x0, x1, ty_Int)
new_esEs24(Left(x0), Left(x1), ty_Integer, x2)
new_esEs5(x0, x1, app(ty_Maybe, x2))
new_lt21(x0, x1, app(ty_Ratio, x2))
new_esEs33(x0, x1, ty_@0)
new_esEs24(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs5(x0, x1, ty_Ordering)
new_esEs32(x0, x1, ty_Double)
new_esEs34(x0, x1, app(ty_Maybe, x2))
new_esEs10(x0, x1, app(ty_[], x2))
new_compare30(x0, x1, app(ty_Ratio, x2))
new_ltEs21(x0, x1, app(ty_Ratio, x2))
new_lt23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs24(x0, x1, app(ty_Ratio, x2))
new_esEs14(Float(x0, x1), Float(x2, x3))
new_esEs26(x0, x1, ty_Integer)
new_esEs5(x0, x1, ty_@0)
new_esEs5(x0, x1, ty_Char)
new_esEs7(x0, x1, ty_Char)
new_compare12(True, True)
new_primEqInt(Pos(Zero), Pos(Zero))
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs5(x0, x1, ty_Integer)
new_primCompAux1(x0, x1, x2, x3)
new_compare31(Nothing, Nothing, x0)
new_esEs39(x0, x1, app(ty_[], x2))
new_compare30(x0, x1, ty_Ordering)
new_primMulNat0(Zero, Succ(x0))
new_esEs28(x0, x1, app(ty_[], x2))
new_ltEs23(x0, x1, ty_Double)
new_esEs24(Right(x0), Right(x1), x2, ty_Float)
new_esEs11(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_lt5(x0, x1, app(app(ty_@2, x2), x3))
new_primCompAux0(x0, GT)
new_lt6(x0, x1, ty_Ordering)
new_primPlusNat1(Zero, Succ(x0))
new_esEs36(x0, x1, ty_Float)
new_esEs19(@0, @0)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs39(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_compare25(x0, x1, x2, x3, x4, x5, True, x6, x7, x8)
new_esEs36(x0, x1, ty_@0)
new_esEs12(LT, LT)
new_esEs28(x0, x1, ty_Integer)
new_compare19(x0, x1, False, x2, x3)
new_ltEs18(x0, x1, ty_Ordering)
new_ltEs16(False, False)
new_compare111(x0, x1, x2, x3, False, x4, x5)
new_compare25(x0, x1, x2, x3, x4, x5, False, x6, x7, x8)
new_esEs33(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, ty_Ordering)
new_esEs28(x0, x1, ty_@0)
new_esEs11(x0, x1, ty_Float)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs4(x0, x1, app(ty_[], x2))
new_esEs39(x0, x1, ty_Integer)

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_esEs36(x0, x1, ty_Char)
new_esEs29(x0, x1, ty_Float)
new_lt22(x0, x1, app(ty_Maybe, x2))
new_esEs7(x0, x1, ty_Int)
new_ltEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs21(x0, x1, ty_Int)
new_ltEs14(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs10(x0, x1, ty_Float)
new_ltEs16(True, True)
new_esEs6(x0, x1, ty_Int)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs32(x0, x1, app(ty_Maybe, x2))
new_lt11(x0, x1)
new_esEs24(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs20(x0, x1, ty_Int)
new_lt5(x0, x1, ty_Char)
new_esEs5(x0, x1, app(ty_[], x2))
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs36(x0, x1, app(ty_[], x2))
new_lt21(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs21(x0, x1, ty_@0)
new_esEs29(x0, x1, ty_Char)
new_ltEs22(x0, x1, ty_Integer)
new_esEs34(x0, x1, app(ty_[], x2))
new_esEs32(x0, x1, ty_Int)
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs11(x0, x1, ty_Int)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs4(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_Integer)
new_compare30(x0, x1, ty_Int)
new_pePe(True, x0)
new_esEs5(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs11(x0, x1, ty_@0)
new_esEs35(x0, x1, ty_Integer)
new_esEs11(x0, x1, ty_Char)
new_esEs9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(x0, x1, ty_Float)
new_esEs9(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(x0, x1, ty_Int)
new_esEs31(x0, x1, app(app(ty_Either, x2), x3))
new_lt22(x0, x1, ty_@0)
new_compare30(x0, x1, ty_Bool)
new_ltEs5(Nothing, Just(x0), x1)
new_lt20(x0, x1, ty_@0)
new_esEs29(x0, x1, ty_Ordering)
new_lt22(x0, x1, ty_Float)
new_esEs9(x0, x1, app(ty_[], x2))
new_lt23(x0, x1, ty_Integer)
new_ltEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(Right(x0), Right(x1), x2, ty_Bool)
new_lt7(x0, x1)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs8(x0, x1, ty_Integer)
new_esEs23(Just(x0), Just(x1), ty_Float)
new_esEs6(x0, x1, ty_Integer)
new_lt5(x0, x1, ty_@0)
new_esEs33(x0, x1, app(app(ty_@2, x2), x3))
new_esEs11(x0, x1, ty_Bool)
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs24(Right(x0), Right(x1), x2, ty_Integer)
new_compare12(False, True)
new_compare12(True, False)
new_ltEs7(x0, x1)
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_primCompAux0(x0, EQ)
new_esEs32(x0, x1, app(app(ty_@2, x2), x3))
new_lt6(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(x0, x1, ty_Integer)
new_esEs32(x0, x1, ty_Ordering)
new_ltEs21(x0, x1, ty_Float)
new_ltEs24(x0, x1, ty_Integer)
new_esEs34(x0, x1, ty_Float)
new_esEs6(x0, x1, ty_@0)
new_lt6(x0, x1, ty_Float)
new_esEs9(x0, x1, ty_Int)
new_compare30(x0, x1, ty_Integer)
new_esEs12(GT, EQ)
new_esEs12(EQ, GT)
new_esEs36(x0, x1, ty_Int)
new_esEs28(x0, x1, ty_Bool)
new_ltEs14(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs24(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_compare30(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_lt5(x0, x1, ty_Double)
new_compare15(LT, LT)
new_esEs10(x0, x1, ty_Char)
new_esEs23(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primMulNat0(Succ(x0), Zero)
new_ltEs22(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_compare6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs34(x0, x1, ty_Ordering)
new_esEs16([], [], x0)
new_esEs12(GT, GT)
new_esEs30(x0, x1, ty_Double)
new_esEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs21(x0, x1, ty_Ordering)
new_esEs10(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_lt21(x0, x1, ty_Float)
new_esEs11(x0, x1, ty_Integer)
new_esEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs21(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs24(x0, x1, app(ty_Maybe, x2))
new_esEs23(Just(x0), Just(x1), ty_Double)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_Char)
new_esEs34(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(Left(x0), Left(x1), ty_Int, x2)
new_esEs38(x0, x1, ty_Integer)
new_ltEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs27(x0, x1, ty_Bool)
new_esEs24(Right(x0), Right(x1), x2, ty_Char)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs6(EQ, EQ)
new_esEs32(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(x0, x1, ty_Float)
new_esEs8(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs22(x0, x1, ty_Char)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(x0, x1, ty_Double)
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_esEs5(x0, x1, ty_Bool)
new_lt6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs31(x0, x1, ty_Int)
new_compare26(x0, x1, True, x2, x3)
new_compare110(x0, x1, x2, x3, True, x4, x5, x6)
new_ltEs24(x0, x1, app(ty_[], x2))
new_compare27(Right(x0), Left(x1), x2, x3)
new_compare27(Left(x0), Right(x1), x2, x3)
new_esEs33(x0, x1, ty_Double)
new_esEs8(x0, x1, ty_Float)
new_ltEs18(x0, x1, ty_@0)
new_esEs4(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, app(ty_[], x2))
new_ltEs5(Just(x0), Just(x1), ty_@0)
new_lt5(x0, x1, ty_Int)
new_ltEs6(LT, EQ)
new_ltEs6(EQ, LT)
new_esEs24(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_primCompAux0(x0, LT)
new_esEs23(Nothing, Nothing, x0)
new_esEs38(x0, x1, ty_Int)
new_esEs23(Just(x0), Just(x1), ty_Int)
new_ltEs20(x0, x1, ty_@0)
new_lt6(x0, x1, app(ty_Maybe, x2))
new_esEs11(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Int)
new_lt17(x0, x1)
new_esEs8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs36(x0, x1, ty_Bool)
new_primEqNat0(Zero, Zero)
new_compare13(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs26(x0, x1, ty_@0)
new_lt21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(Right(x0), Right(x1), x2, ty_Int)
new_esEs7(x0, x1, ty_Bool)
new_esEs33(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs5(x0, x1, ty_Float)
new_ltEs14(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_compare17(x0, x1, x2, x3, x4, x5, False, x6, x7, x8, x9)
new_ltEs22(x0, x1, ty_Float)
new_compare15(GT, GT)
new_esEs31(x0, x1, ty_Double)
new_ltEs20(x0, x1, ty_Integer)
new_lt22(x0, x1, ty_Bool)
new_compare30(x0, x1, app(ty_[], x2))
new_esEs34(x0, x1, ty_Bool)
new_esEs31(x0, x1, ty_Integer)
new_ltEs20(x0, x1, ty_Char)
new_lt20(x0, x1, ty_Double)
new_esEs35(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_compare28(x0, x1, True, x2, x3)
new_ltEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs21(x0, x1, app(ty_[], x2))
new_ltEs15(x0, x1)
new_esEs4(x0, x1, ty_Integer)
new_esEs39(x0, x1, app(ty_Ratio, x2))
new_esEs6(x0, x1, app(app(ty_Either, x2), x3))
new_esEs39(x0, x1, ty_Bool)
new_esEs6(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs24(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Float)
new_ltEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_primMulNat0(Zero, Zero)
new_asAs(True, x0)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_ltEs14(Left(x0), Right(x1), x2, x3)
new_ltEs14(Right(x0), Left(x1), x2, x3)
new_esEs26(x0, x1, ty_Double)
new_esEs5(x0, x1, ty_Double)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs35(x0, x1, app(app(ty_@2, x2), x3))
new_fsEs(x0)
new_esEs16(:(x0, x1), [], x2)
new_ltEs5(Just(x0), Just(x1), ty_Integer)
new_esEs35(x0, x1, app(ty_Ratio, x2))
new_lt6(x0, x1, ty_Double)
new_esEs35(x0, x1, ty_Double)
new_ltEs18(x0, x1, ty_Bool)
new_esEs23(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Float)
new_ltEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(x0, x1, app(ty_Maybe, x2))
new_compare28(x0, x1, False, x2, x3)
new_ltEs5(Just(x0), Just(x1), ty_Double)
new_lt22(x0, x1, ty_Ordering)
new_lt23(x0, x1, app(ty_Ratio, x2))
new_esEs9(x0, x1, ty_@0)
new_esEs6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare24(x0, x1, x2, x3, False, x4, x5)
new_esEs24(Left(x0), Left(x1), ty_@0, x2)
new_esEs35(x0, x1, ty_Bool)
new_esEs35(x0, x1, ty_Char)
new_ltEs23(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, ty_Bool)
new_ltEs10(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs31(x0, x1, ty_@0)
new_lt10(x0, x1, x2)
new_ltEs19(x0, x1, ty_Double)
new_lt12(x0, x1, x2, x3)
new_ltEs24(x0, x1, ty_Double)
new_esEs13(Double(x0, x1), Double(x2, x3))
new_esEs10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Ordering)
new_esEs5(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(Just(x0), Nothing, x1)
new_ltEs14(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs24(Right(x0), Right(x1), x2, ty_@0)
new_esEs20(True, True)
new_lt22(x0, x1, ty_Int)
new_esEs7(x0, x1, ty_Integer)
new_esEs30(x0, x1, ty_Bool)
new_lt21(x0, x1, ty_@0)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs4(x0, x1, app(ty_Maybe, x2))
new_esEs33(x0, x1, ty_Float)
new_esEs29(x0, x1, ty_Integer)
new_ltEs21(x0, x1, ty_Integer)
new_lt16(x0, x1, x2, x3)
new_primPlusNat0(Zero, x0)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs4(x0, x1, ty_Ordering)
new_esEs8(x0, x1, ty_Bool)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_primPlusNat0(Succ(x0), x1)
new_ltEs4(x0, x1)
new_esEs34(x0, x1, ty_Integer)
new_esEs31(x0, x1, ty_Ordering)
new_ltEs6(GT, LT)
new_ltEs6(LT, GT)
new_ltEs22(x0, x1, app(ty_Maybe, x2))
new_esEs35(x0, x1, app(ty_Maybe, x2))
new_compare111(x0, x1, x2, x3, True, x4, x5)
new_esEs11(x0, x1, ty_Double)
new_lt19(x0, x1)
new_ltEs14(Left(x0), Left(x1), ty_Double, x2)
new_ltEs8(x0, x1, x2)
new_ltEs14(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs4(x0, x1, ty_Double)
new_esEs36(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, ty_Double)
new_esEs39(x0, x1, ty_Char)
new_ltEs22(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_compare15(EQ, EQ)
new_lt6(x0, x1, ty_Int)
new_lt21(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, ty_Ordering)
new_ltEs14(Right(x0), Right(x1), x2, ty_Double)
new_ltEs22(x0, x1, ty_Ordering)
new_ltEs11(x0, x1)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_compare7(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt20(x0, x1, ty_Float)
new_lt21(x0, x1, ty_Integer)
new_esEs32(x0, x1, ty_Bool)
new_esEs39(x0, x1, ty_Float)
new_compare10(x0, x1, False, x2, x3)
new_lt6(x0, x1, ty_Integer)
new_lt4(x0, x1, x2, x3, x4)
new_esEs10(x0, x1, ty_Double)
new_esEs31(x0, x1, app(ty_[], x2))
new_sr0(x0, x1)
new_esEs23(Just(x0), Just(x1), ty_Integer)
new_esEs24(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs20(False, True)
new_esEs20(True, False)
new_esEs29(x0, x1, ty_Bool)
new_esEs24(Left(x0), Right(x1), x2, x3)
new_esEs24(Right(x0), Left(x1), x2, x3)
new_ltEs23(x0, x1, ty_Integer)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs36(x0, x1, app(ty_Ratio, x2))
new_esEs20(False, False)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare12(False, False)
new_esEs12(LT, EQ)
new_esEs12(EQ, LT)
new_lt21(x0, x1, ty_Int)
new_lt22(x0, x1, ty_Char)
new_ltEs14(Left(x0), Left(x1), ty_Char, x2)
new_ltEs14(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare14(x0, x1, x2, x3, x4, x5, True, x6, x7, x8)
new_esEs31(x0, x1, ty_Float)
new_esEs24(Left(x0), Left(x1), ty_Float, x2)
new_primPlusNat1(Zero, Zero)
new_ltEs21(x0, x1, ty_Bool)
new_esEs24(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs20(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_Float)
new_esEs12(EQ, EQ)
new_esEs23(Just(x0), Just(x1), ty_Bool)
new_esEs27(x0, x1, ty_Char)
new_ltEs14(Right(x0), Right(x1), x2, ty_Int)
new_esEs9(x0, x1, ty_Integer)
new_esEs30(x0, x1, ty_Float)
new_ltEs20(x0, x1, ty_Float)
new_lt22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(Right(x0), Right(x1), x2, ty_Char)
new_esEs9(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Left(x0), Left(x1), ty_Float, x2)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs16(:(x0, x1), :(x2, x3), x4)
new_esEs28(x0, x1, ty_Double)
new_esEs30(x0, x1, ty_Char)
new_compare30(x0, x1, ty_@0)
new_esEs6(x0, x1, ty_Bool)
new_esEs16([], :(x0, x1), x2)
new_ltEs23(x0, x1, ty_Float)
new_esEs9(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs31(x0, x1, app(app(ty_@2, x2), x3))
new_compare15(EQ, GT)
new_compare15(GT, EQ)
new_compare17(x0, x1, x2, x3, x4, x5, True, x6, x7, x8, x9)
new_ltEs9(x0, x1, x2)
new_ltEs24(x0, x1, ty_Ordering)
new_compare30(x0, x1, ty_Char)
new_primEqNat0(Succ(x0), Zero)
new_compare15(LT, GT)
new_compare15(GT, LT)
new_esEs36(x0, x1, ty_Double)
new_esEs39(x0, x1, ty_Ordering)
new_esEs7(x0, x1, app(app(ty_Either, x2), x3))
new_lt21(x0, x1, app(ty_[], x2))
new_esEs37(x0, x1, ty_Int)
new_esEs9(x0, x1, ty_Double)
new_primMulInt(Neg(x0), Neg(x1))
new_ltEs5(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs17(x0, x1)
new_esEs9(x0, x1, ty_Ordering)
new_ltEs12(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs26(x0, x1, ty_Char)
new_lt23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_lt23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs23(x0, x1, ty_Int)
new_primEqNat0(Succ(x0), Succ(x1))
new_compare210(x0, x1, True, x2)
new_esEs8(x0, x1, ty_Int)
new_ltEs14(Left(x0), Left(x1), ty_Bool, x2)
new_lt21(x0, x1, app(ty_Maybe, x2))
new_ltEs5(Just(x0), Just(x1), ty_Int)
new_esEs33(x0, x1, ty_Int)
new_ltEs23(x0, x1, ty_@0)
new_lt6(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs33(x0, x1, ty_Bool)
new_esEs10(x0, x1, ty_Ordering)
new_esEs24(Left(x0), Left(x1), ty_Double, x2)
new_esEs35(x0, x1, ty_@0)
new_esEs4(x0, x1, ty_Char)
new_compare112(x0, x1, False, x2)
new_esEs24(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_lt23(x0, x1, ty_Int)
new_ltEs14(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs18(x0, x1, ty_Double)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt23(x0, x1, ty_Bool)
new_ltEs14(Left(x0), Left(x1), ty_Integer, x2)
new_esEs24(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_lt9(x0, x1, x2)
new_ltEs18(x0, x1, app(ty_[], x2))
new_esEs33(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, app(ty_[], x2))
new_lt5(x0, x1, app(app(ty_Either, x2), x3))
new_lt21(x0, x1, ty_Bool)
new_esEs24(Left(x0), Left(x1), ty_Char, x2)
new_ltEs5(Nothing, Nothing, x0)
new_compare18(Float(x0, x1), Float(x2, x3))
new_ltEs5(Just(x0), Just(x1), ty_Float)
new_esEs26(x0, x1, ty_Bool)
new_lt6(x0, x1, ty_Bool)
new_esEs30(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Integer)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs8(x0, x1, ty_Double)
new_lt21(x0, x1, ty_Char)
new_lt5(x0, x1, ty_Float)
new_compare11(Char(x0), Char(x1))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs24(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs36(x0, x1, app(app(ty_Either, x2), x3))
new_esEs30(x0, x1, ty_Integer)
new_esEs25(x0, x1)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_compare210(x0, x1, False, x2)
new_esEs29(x0, x1, ty_@0)
new_ltEs14(Left(x0), Left(x1), ty_Int, x2)
new_sr(Integer(x0), Integer(x1))
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs7(x0, x1, ty_@0)
new_esEs39(x0, x1, app(ty_Maybe, x2))
new_primMulNat0(Succ(x0), Succ(x1))
new_ltEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs34(x0, x1, ty_Char)
new_esEs4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs10(x0, x1, ty_Bool)
new_lt5(x0, x1, app(ty_[], x2))
new_esEs10(x0, x1, ty_@0)
new_esEs39(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_@0)
new_esEs31(x0, x1, ty_Bool)
new_primEqNat0(Zero, Succ(x0))
new_primPlusNat1(Succ(x0), Zero)
new_lt23(x0, x1, ty_Char)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs7(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Char)
new_ltEs21(x0, x1, app(ty_Maybe, x2))
new_esEs6(x0, x1, ty_Ordering)
new_esEs33(x0, x1, ty_Char)
new_compare27(Left(x0), Left(x1), x2, x3)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs32(x0, x1, ty_Integer)
new_ltEs14(Left(x0), Left(x1), ty_Ordering, x2)
new_pePe(False, x0)
new_ltEs24(x0, x1, ty_Int)
new_compare24(x0, x1, x2, x3, True, x4, x5)
new_lt8(x0, x1)
new_esEs39(x0, x1, app(app(ty_Either, x2), x3))
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt23(x0, x1, ty_Double)
new_esEs10(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Bool)
new_esEs9(x0, x1, app(app(ty_@2, x2), x3))
new_esEs32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, ty_Int)
new_esEs30(x0, x1, ty_Ordering)
new_lt23(x0, x1, ty_Float)
new_lt6(x0, x1, ty_@0)
new_primPlusNat1(Succ(x0), Succ(x1))
new_compare27(Right(x0), Right(x1), x2, x3)
new_esEs31(x0, x1, ty_Char)
new_lt22(x0, x1, ty_Double)
new_ltEs22(x0, x1, ty_@0)
new_esEs39(x0, x1, ty_Int)
new_esEs30(x0, x1, ty_@0)
new_compare14(x0, x1, x2, x3, x4, x5, False, x6, x7, x8)
new_ltEs16(False, True)
new_ltEs16(True, False)
new_ltEs6(GT, GT)
new_esEs10(x0, x1, ty_Int)
new_compare30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(x0, x1, app(ty_Maybe, x2))
new_esEs31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs32(x0, x1, ty_Char)
new_esEs23(Nothing, Just(x0), x1)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(x0, x1, ty_Int)
new_ltEs5(Just(x0), Just(x1), ty_Ordering)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_ltEs19(x0, x1, ty_Char)
new_ltEs22(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(Just(x0), Just(x1), ty_Char)
new_esEs27(x0, x1, ty_Int)
new_esEs24(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs4(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(Just(x0), Just(x1), ty_Bool)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_Bool)
new_lt22(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_@0)
new_ltEs22(x0, x1, ty_Bool)
new_esEs30(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_Integer)
new_esEs33(x0, x1, ty_Integer)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, ty_Int)
new_primCmpNat0(Zero, Zero)
new_esEs35(x0, x1, ty_Float)
new_asAs(False, x0)
new_lt5(x0, x1, ty_Integer)
new_ltEs24(x0, x1, ty_@0)
new_esEs17(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs19(x0, x1, ty_Int)
new_lt23(x0, x1, ty_@0)
new_esEs34(x0, x1, ty_Int)
new_ltEs6(LT, LT)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs35(x0, x1, app(ty_[], x2))
new_esEs35(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare31(Just(x0), Just(x1), x2)
new_esEs11(x0, x1, ty_Ordering)
new_esEs31(x0, x1, app(ty_Ratio, x2))
new_lt5(x0, x1, app(ty_Ratio, x2))
new_ltEs22(x0, x1, ty_Double)
new_ltEs14(Left(x0), Left(x1), ty_@0, x2)
new_lt23(x0, x1, app(ty_[], x2))
new_compare10(x0, x1, True, x2, x3)
new_ltEs24(x0, x1, ty_Char)
new_esEs21(:%(x0, x1), :%(x2, x3), x4)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs18(Integer(x0), Integer(x1))
new_esEs4(x0, x1, ty_@0)
new_lt22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, ty_Int)
new_ltEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(Just(x0), Just(x1), ty_@0)
new_compare110(x0, x1, x2, x3, False, x4, x5, x6)
new_ltEs14(Right(x0), Right(x1), x2, ty_Integer)
new_esEs23(Just(x0), Nothing, x1)
new_ltEs19(x0, x1, ty_Float)
new_esEs6(x0, x1, ty_Char)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_lt21(x0, x1, ty_Double)
new_esEs32(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs8(x0, x1, app(ty_[], x2))
new_esEs23(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs34(x0, x1, app(app(ty_Either, x2), x3))
new_esEs33(x0, x1, app(ty_[], x2))
new_lt5(x0, x1, ty_Bool)
new_esEs11(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(Just(x0), Just(x1), ty_Char)
new_ltEs13(x0, x1)
new_lt14(x0, x1, x2)
new_ltEs23(x0, x1, ty_Bool)
new_esEs6(x0, x1, app(ty_Ratio, x2))
new_compare15(LT, EQ)
new_compare15(EQ, LT)
new_compare9(@0, @0)
new_lt13(x0, x1)
new_esEs36(x0, x1, ty_Integer)
new_esEs29(x0, x1, ty_Double)
new_ltEs22(x0, x1, app(ty_[], x2))
new_ltEs23(x0, x1, app(ty_Maybe, x2))
new_esEs8(x0, x1, app(ty_Ratio, x2))
new_ltEs18(x0, x1, ty_Float)
new_lt18(x0, x1)
new_lt22(x0, x1, app(ty_Ratio, x2))
new_esEs32(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_Float)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_lt5(x0, x1, ty_Ordering)
new_lt15(x0, x1)
new_compare8(Integer(x0), Integer(x1))
new_lt22(x0, x1, app(ty_[], x2))
new_compare30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs33(x0, x1, app(ty_Ratio, x2))
new_lt5(x0, x1, app(ty_Maybe, x2))
new_esEs36(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs33(x0, x1, app(ty_Maybe, x2))
new_esEs7(x0, x1, app(ty_Maybe, x2))
new_esEs8(x0, x1, ty_@0)
new_lt6(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(x0, x1, ty_Int)
new_not(True)
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_compare30(x0, x1, ty_Float)
new_compare31(Just(x0), Nothing, x1)
new_esEs27(x0, x1, ty_Ordering)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs22(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs23(x0, x1, app(ty_Ratio, x2))
new_ltEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(x0, x1, ty_Bool)
new_esEs32(x0, x1, ty_Float)
new_esEs36(x0, x1, ty_Ordering)
new_esEs9(x0, x1, ty_Bool)
new_esEs23(Just(x0), Just(x1), app(ty_Maybe, x2))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_not(False)
new_esEs24(Left(x0), Left(x1), ty_Ordering, x2)
new_compare29(Double(x0, x1), Double(x2, x3))
new_compare13(:%(x0, x1), :%(x2, x3), ty_Integer)
new_lt6(x0, x1, app(ty_Ratio, x2))
new_primCmpNat0(Succ(x0), Succ(x1))
new_esEs7(x0, x1, ty_Ordering)
new_esEs34(x0, x1, app(ty_Ratio, x2))
new_ltEs23(x0, x1, ty_Char)
new_esEs7(x0, x1, app(ty_[], x2))
new_esEs8(x0, x1, ty_Ordering)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_esEs39(x0, x1, ty_@0)
new_ltEs21(x0, x1, ty_Char)
new_esEs15(Char(x0), Char(x1))
new_esEs7(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(x0, x1, app(ty_Ratio, x2))
new_ltEs6(GT, EQ)
new_ltEs6(EQ, GT)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_esEs7(x0, x1, app(ty_Ratio, x2))
new_esEs32(x0, x1, app(ty_Ratio, x2))
new_primCmpNat0(Zero, Succ(x0))
new_esEs31(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Ordering)
new_lt23(x0, x1, app(ty_Maybe, x2))
new_ltEs21(x0, x1, ty_Double)
new_esEs24(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs8(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs23(x0, x1, app(ty_[], x2))
new_esEs24(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_compare30(x0, x1, ty_Double)
new_compare19(x0, x1, True, x2, x3)
new_esEs36(x0, x1, app(ty_Maybe, x2))
new_esEs24(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs5(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(Right(x0), Right(x1), x2, ty_Double)
new_lt22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(x0, x1, app(ty_[], x2))
new_primCmpNat0(Succ(x0), Zero)
new_compare30(x0, x1, app(ty_Maybe, x2))
new_esEs34(x0, x1, ty_Double)
new_ltEs21(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_@0)
new_esEs11(x0, x1, app(ty_Maybe, x2))
new_esEs6(x0, x1, app(ty_Maybe, x2))
new_ltEs22(x0, x1, ty_Int)
new_compare26(x0, x1, False, x2, x3)
new_compare16(x0, x1)
new_esEs23(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs20(x0, x1, ty_Double)
new_ltEs24(x0, x1, ty_Bool)
new_esEs35(x0, x1, ty_Ordering)
new_ltEs18(x0, x1, ty_Integer)
new_esEs39(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs34(x0, x1, ty_@0)
new_compare31(Nothing, Just(x0), x1)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_esEs37(x0, x1, ty_Integer)
new_ltEs18(x0, x1, ty_Char)
new_esEs7(x0, x1, ty_Double)
new_lt23(x0, x1, ty_Ordering)
new_compare112(x0, x1, True, x2)
new_lt21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs34(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs9(x0, x1, ty_Float)
new_esEs23(Just(x0), Just(x1), ty_Ordering)
new_lt6(x0, x1, ty_Char)
new_esEs9(x0, x1, ty_Char)
new_esEs8(x0, x1, ty_Char)
new_esEs35(x0, x1, ty_Int)
new_esEs24(Left(x0), Left(x1), ty_Integer, x2)
new_esEs5(x0, x1, app(ty_Maybe, x2))
new_lt21(x0, x1, app(ty_Ratio, x2))
new_esEs33(x0, x1, ty_@0)
new_esEs24(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs5(x0, x1, ty_Ordering)
new_esEs32(x0, x1, ty_Double)
new_esEs34(x0, x1, app(ty_Maybe, x2))
new_esEs10(x0, x1, app(ty_[], x2))
new_compare30(x0, x1, app(ty_Ratio, x2))
new_ltEs21(x0, x1, app(ty_Ratio, x2))
new_lt23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs24(x0, x1, app(ty_Ratio, x2))
new_esEs14(Float(x0, x1), Float(x2, x3))
new_esEs26(x0, x1, ty_Integer)
new_esEs5(x0, x1, ty_@0)
new_esEs5(x0, x1, ty_Char)
new_esEs7(x0, x1, ty_Char)
new_compare12(True, True)
new_primEqInt(Pos(Zero), Pos(Zero))
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs5(x0, x1, ty_Integer)
new_primCompAux1(x0, x1, x2, x3)
new_compare31(Nothing, Nothing, x0)
new_esEs39(x0, x1, app(ty_[], x2))
new_compare30(x0, x1, ty_Ordering)
new_primMulNat0(Zero, Succ(x0))
new_esEs28(x0, x1, app(ty_[], x2))
new_ltEs23(x0, x1, ty_Double)
new_esEs24(Right(x0), Right(x1), x2, ty_Float)
new_esEs11(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_lt5(x0, x1, app(app(ty_@2, x2), x3))
new_primCompAux0(x0, GT)
new_lt6(x0, x1, ty_Ordering)
new_primPlusNat1(Zero, Succ(x0))
new_esEs36(x0, x1, ty_Float)
new_esEs19(@0, @0)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs39(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_compare25(x0, x1, x2, x3, x4, x5, True, x6, x7, x8)
new_esEs36(x0, x1, ty_@0)
new_esEs12(LT, LT)
new_esEs28(x0, x1, ty_Integer)
new_compare19(x0, x1, False, x2, x3)
new_ltEs18(x0, x1, ty_Ordering)
new_ltEs16(False, False)
new_compare111(x0, x1, x2, x3, False, x4, x5)
new_compare25(x0, x1, x2, x3, x4, x5, False, x6, x7, x8)
new_esEs33(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, ty_Ordering)
new_esEs28(x0, x1, ty_@0)
new_esEs11(x0, x1, ty_Float)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs4(x0, x1, app(ty_[], x2))
new_esEs39(x0, x1, ty_Integer)



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

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

new_splitGT3(:(yvy300, yvy301), yvy31, yvy32, yvy33, yvy34, [], h, ba) → new_splitGT1(yvy300, yvy301, yvy31, yvy32, yvy33, yvy34, new_compare0([], :(yvy300, yvy301), h), h, ba)
new_splitGT1(yvy300, yvy301, yvy31, yvy32, Branch(yvy330, yvy331, yvy332, yvy333, yvy334), yvy34, LT, h, ba) → new_splitGT3(yvy330, yvy331, yvy332, yvy333, yvy334, [], h, ba)

The TRS R consists of the following rules:

new_compare0([], :(yvy3000, yvy3001), feh) → LT

The set Q consists of the following terms:

new_compare0([], [], x0)
new_compare0([], :(x0, x1), x2)
new_compare0(:(x0, x1), [], x2)
new_compare0(:(x0, x1), :(x2, x3), x4)

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

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



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

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

new_plusFM(Branch(yvy30, yvy31, yvy32, yvy33, yvy34), Branch(yvy40, yvy41, yvy42, yvy43, yvy44), h, ba) → new_plusFM(new_splitGT30(yvy30, yvy31, yvy32, yvy33, yvy34, yvy40, h, ba), yvy44, h, ba)
new_plusFM(Branch(yvy30, yvy31, yvy32, yvy33, yvy34), Branch(yvy40, yvy41, yvy42, yvy43, yvy44), h, ba) → new_plusFM(new_splitLT30(yvy30, yvy31, yvy32, yvy33, yvy34, yvy40, h, ba), yvy43, h, ba)

The TRS R consists of the following rules:

new_compare210(yvy100, yvy101, False, fff) → new_compare112(yvy100, yvy101, new_ltEs24(yvy100, yvy101, fff), fff)
new_compare7(@2(yvy4000, yvy4001), @2(yvy3000, yvy3001), cgg, cgh) → new_compare24(yvy4000, yvy4001, yvy3000, yvy3001, new_asAs(new_esEs7(yvy4000, yvy3000, cgg), new_esEs8(yvy4001, yvy3001, cgh)), cgg, cgh)
new_mkVBalBranch3MkVBalBranch16(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkBalBranch(yvy60, yvy61, yvy63, new_mkVBalBranch0(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba), h, ba)
new_lt22(yvy1000, yvy1010, ty_Int) → new_lt17(yvy1000, yvy1010)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Int, ddg) → new_esEs25(yvy40000, yvy30000)
new_splitGT17(yvy31, yvy32, yvy33, yvy34, EQ, h, ba) → new_splitGT14(yvy31, yvy32, yvy33, yvy34, h, ba)
new_esEs6(yvy4002, yvy3002, app(app(app(ty_@3, dff), dfg), dfh)) → new_esEs22(yvy4002, yvy3002, dff, dfg, dfh)
new_esEs35(yvy153, yvy156, app(ty_[], efh)) → new_esEs16(yvy153, yvy156, efh)
new_compare8(Integer(yvy4000), Integer(yvy3000)) → new_primCmpInt(yvy4000, yvy3000)
new_mkBalBranch6MkBalBranch4(yvy50, yvy51, Branch(yvy540, yvy541, yvy542, yvy543, yvy544), yvy118, True, h, ba) → new_mkBalBranch6MkBalBranch01(yvy50, yvy51, yvy540, yvy541, yvy542, yvy543, yvy544, yvy118, new_lt17(new_sizeFM1(yvy543, h, ba), new_sr0(Pos(Succ(Succ(Zero))), new_sizeFM1(yvy544, h, ba))), h, ba)
new_esEs28(yvy1001, yvy1011, ty_Float) → new_esEs14(yvy1001, yvy1011)
new_lt6(yvy1000, yvy1010, ty_@0) → new_lt19(yvy1000, yvy1010)
new_esEs9(yvy4000, yvy3000, ty_Int) → new_esEs25(yvy4000, yvy3000)
new_esEs24(Right(yvy40000), Right(yvy30000), ddf, ty_Double) → new_esEs13(yvy40000, yvy30000)
new_mkVBalBranch0(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch210(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(Zero), new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), h, ba)
new_ltEs24(yvy100, yvy101, app(ty_Ratio, ecd)) → new_ltEs9(yvy100, yvy101, ecd)
new_ltEs19(yvy1002, yvy1012, ty_Float) → new_ltEs11(yvy1002, yvy1012)
new_primMinusNat1(Zero, Succ(yvy54200)) → Neg(Succ(yvy54200))
new_ltEs23(yvy166, yvy168, ty_Ordering) → new_ltEs6(yvy166, yvy168)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Bool, bfd) → new_ltEs16(yvy1000, yvy1010)
new_esEs39(yvy165, yvy167, app(ty_Ratio, fdc)) → new_esEs21(yvy165, yvy167, fdc)
new_esEs10(yvy4000, yvy3000, ty_@0) → new_esEs19(yvy4000, yvy3000)
new_esEs21(:%(yvy40000, yvy40001), :%(yvy30000, yvy30001), dde) → new_asAs(new_esEs37(yvy40000, yvy30000, dde), new_esEs38(yvy40001, yvy30001, dde))
new_lt5(yvy1001, yvy1011, app(ty_Ratio, ge)) → new_lt10(yvy1001, yvy1011, ge)
new_compare13(:%(yvy4000, yvy4001), :%(yvy3000, yvy3001), ty_Integer) → new_compare8(new_sr(yvy4000, yvy3001), new_sr(yvy3000, yvy4001))
new_ltEs14(Right(yvy1000), Right(yvy1010), bgg, ty_Float) → new_ltEs11(yvy1000, yvy1010)
new_esEs39(yvy165, yvy167, app(ty_Maybe, fea)) → new_esEs23(yvy165, yvy167, fea)
new_esEs4(yvy4000, yvy3000, ty_Integer) → new_esEs18(yvy4000, yvy3000)
new_compare15(LT, LT) → EQ
new_addToFM_C22(yvy500, yvy501, yvy51, yvy52, yvy53, yvy54, yvy400, yvy401, yvy41, LT, h, ba) → new_mkBalBranch(:(yvy500, yvy501), yvy51, new_addToFM_C0(yvy53, :(yvy400, yvy401), yvy41, h, ba), yvy54, h, ba)
new_compare12(True, False) → GT
new_sr(Integer(yvy30000), Integer(yvy40010)) → Integer(new_primMulInt(yvy30000, yvy40010))
new_addToFM_C22(yvy500, yvy501, yvy51, yvy52, yvy53, yvy54, yvy400, yvy401, yvy41, EQ, h, ba) → new_addToFM_C21(yvy500, yvy501, yvy51, yvy52, yvy53, yvy54, yvy400, yvy401, yvy41, h, ba)
new_ltEs24(yvy100, yvy101, app(ty_Maybe, bd)) → new_ltEs5(yvy100, yvy101, bd)
new_esEs35(yvy153, yvy156, app(app(ty_Either, egh), eha)) → new_esEs24(yvy153, yvy156, egh, eha)
new_esEs26(yvy40000, yvy30000, ty_@0) → new_esEs19(yvy40000, yvy30000)
new_esEs6(yvy4002, yvy3002, app(ty_[], dfb)) → new_esEs16(yvy4002, yvy3002, dfb)
new_ltEs16(False, True) → True
new_esEs26(yvy40000, yvy30000, app(app(app(ty_@3, dhb), dhc), dhd)) → new_esEs22(yvy40000, yvy30000, dhb, dhc, dhd)
new_ltEs24(yvy100, yvy101, ty_Bool) → new_ltEs16(yvy100, yvy101)
new_lt20(yvy152, yvy155, app(app(app(ty_@3, dac), dad), dae)) → new_lt4(yvy152, yvy155, dac, dad, dae)
new_esEs27(yvy1000, yvy1010, ty_Bool) → new_esEs20(yvy1000, yvy1010)
new_esEs34(yvy152, yvy155, ty_Double) → new_esEs13(yvy152, yvy155)
new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_esEs10(yvy4000, yvy3000, ty_Int) → new_esEs25(yvy4000, yvy3000)
new_compare30(yvy400, yvy300, ty_Int) → new_compare16(yvy400, yvy300)
new_ltEs16(True, False) → False
new_ltEs19(yvy1002, yvy1012, ty_Bool) → new_ltEs16(yvy1002, yvy1012)
new_addToFM_C21(yvy500, yvy501, yvy51, yvy52, yvy53, yvy54, yvy400, yvy401, yvy41, h, ba) → new_addToFM_C12(yvy500, yvy501, yvy51, yvy52, yvy53, yvy54, yvy400, yvy401, yvy41, new_compare0(:(yvy400, yvy401), :(yvy500, yvy501), h), h, ba)
new_lt5(yvy1001, yvy1011, ty_Integer) → new_lt15(yvy1001, yvy1011)
new_esEs27(yvy1000, yvy1010, ty_Char) → new_esEs15(yvy1000, yvy1010)
new_esEs12(LT, GT) → False
new_esEs12(GT, LT) → False
new_ltEs22(yvy114, yvy115, ty_Ordering) → new_ltEs6(yvy114, yvy115)
new_ltEs18(yvy107, yvy108, app(ty_Ratio, de)) → new_ltEs9(yvy107, yvy108, de)
new_ltEs23(yvy166, yvy168, ty_Float) → new_ltEs11(yvy166, yvy168)
new_ltEs20(yvy154, yvy157, app(app(ty_@2, ehg), ehh)) → new_ltEs12(yvy154, yvy157, ehg, ehh)
new_esEs31(yvy40000, yvy30000, app(ty_Maybe, bce)) → new_esEs23(yvy40000, yvy30000, bce)
new_mkBalBranch6MkBalBranch11(yvy50, yvy51, yvy54, yvy1180, yvy1181, yvy1182, yvy1183, Branch(yvy11840, yvy11841, yvy11842, yvy11843, yvy11844), False, h, ba) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))), yvy11840, yvy11841, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), yvy1180, yvy1181, yvy1183, yvy11843, app(ty_[], h), ba), new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), yvy50, yvy51, yvy11844, yvy54, app(ty_[], h), ba), app(ty_[], h), ba)
new_splitLT21(yvy36, yvy37, yvy38, yvy39, yvy40, yvy41, yvy42, yvy43, LT, cg, da) → new_splitLT4(yvy40, yvy42, yvy43, cg, da)
new_compare110(yvy233, yvy234, yvy235, yvy236, True, yvy238, chg, chh) → new_compare111(yvy233, yvy234, yvy235, yvy236, True, chg, chh)
new_ltEs24(yvy100, yvy101, app(app(ty_@2, cbg), cbh)) → new_ltEs12(yvy100, yvy101, cbg, cbh)
new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_ltEs13(yvy100, yvy101) → new_fsEs(new_compare29(yvy100, yvy101))
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Float) → new_ltEs11(yvy1000, yvy1010)
new_addToFM_C0(Branch([], yvy51, yvy52, yvy53, yvy54), :(yvy400, yvy401), yvy41, h, ba) → new_addToFM_C17(yvy51, yvy52, yvy53, yvy54, yvy400, yvy401, yvy41, new_compare0(:(yvy400, yvy401), [], h), h, ba)
new_esEs8(yvy4001, yvy3001, ty_Double) → new_esEs13(yvy4001, yvy3001)
new_esEs31(yvy40000, yvy30000, app(ty_Ratio, bca)) → new_esEs21(yvy40000, yvy30000, bca)
new_esEs29(yvy40000, yvy30000, app(ty_Maybe, eag)) → new_esEs23(yvy40000, yvy30000, eag)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Int) → new_ltEs15(yvy1000, yvy1010)
new_mkBalBranch6MkBalBranch50(yvy50, yvy51, yvy54, yvy118, LT, h, ba) → new_mkBranch(Zero, yvy50, yvy51, yvy118, yvy54, app(ty_[], h), ba)
new_mkVBalBranch3MkVBalBranch13(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), app(ty_[], h), ba)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Double) → new_ltEs13(yvy1000, yvy1010)
new_esEs30(yvy40001, yvy30001, ty_Double) → new_esEs13(yvy40001, yvy30001)
new_esEs10(yvy4000, yvy3000, ty_Bool) → new_esEs20(yvy4000, yvy3000)
new_splitLT4(Branch(yvy400, yvy401, yvy402, yvy403, yvy404), yvy42, yvy43, cg, da) → new_splitLT30(yvy400, yvy401, yvy402, yvy403, yvy404, :(yvy42, yvy43), cg, da)
new_mkVBalBranch3MkVBalBranch27(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch14(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt24(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_pePe(False, yvy305) → yvy305
new_esEs31(yvy40000, yvy30000, app(ty_[], bbf)) → new_esEs16(yvy40000, yvy30000, bbf)
new_esEs39(yvy165, yvy167, ty_@0) → new_esEs19(yvy165, yvy167)
new_esEs26(yvy40000, yvy30000, ty_Bool) → new_esEs20(yvy40000, yvy30000)
new_esEs9(yvy4000, yvy3000, app(app(ty_@2, ffh), fga)) → new_esEs17(yvy4000, yvy3000, ffh, fga)
new_primPlusInt0(yvy11820, Neg(yvy5420)) → new_primMinusNat1(yvy11820, yvy5420)
new_lt9(yvy152, yvy155, chd) → new_esEs12(new_compare0(yvy152, yvy155, chd), LT)
new_esEs28(yvy1001, yvy1011, ty_Integer) → new_esEs18(yvy1001, yvy1011)
new_esEs5(yvy4001, yvy3001, ty_Ordering) → new_esEs12(yvy4001, yvy3001)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Char, ddg) → new_esEs15(yvy40000, yvy30000)
new_compare15(GT, LT) → GT
new_lt22(yvy1000, yvy1010, ty_Double) → new_lt13(yvy1000, yvy1010)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Char) → new_esEs15(yvy40000, yvy30000)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Ordering) → new_esEs12(yvy40000, yvy30000)
new_addToFM_C16(yvy51, yvy52, yvy53, yvy54, yvy400, yvy401, yvy41, h, ba) → Branch(:(yvy400, yvy401), new_addToFM0(yvy51, yvy41, ba), yvy52, yvy53, yvy54)
new_ltEs23(yvy166, yvy168, app(app(ty_Either, ffd), ffe)) → new_ltEs14(yvy166, yvy168, ffd, ffe)
new_esEs36(yvy1000, yvy1010, app(ty_[], cca)) → new_esEs16(yvy1000, yvy1010, cca)
new_ltEs6(GT, EQ) → False
new_ltEs18(yvy107, yvy108, app(app(ty_Either, ed), ee)) → new_ltEs14(yvy107, yvy108, ed, ee)
new_esEs32(yvy40001, yvy30001, app(ty_Maybe, bdg)) → new_esEs23(yvy40001, yvy30001, bdg)
new_addToFM_C14(yvy51, yvy52, yvy53, yvy54, yvy41, EQ, h, ba) → new_addToFM_C15(yvy51, yvy52, yvy53, yvy54, yvy41, h, ba)
new_esEs33(yvy40002, yvy30002, ty_Integer) → new_esEs18(yvy40002, yvy30002)
new_esEs31(yvy40000, yvy30000, ty_Double) → new_esEs13(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, ty_Float) → new_esEs14(yvy40002, yvy30002)
new_ltEs14(Right(yvy1000), Right(yvy1010), bgg, app(app(app(ty_@3, bhb), bhc), bhd)) → new_ltEs10(yvy1000, yvy1010, bhb, bhc, bhd)
new_ltEs23(yvy166, yvy168, app(ty_[], fed)) → new_ltEs8(yvy166, yvy168, fed)
new_esEs34(yvy152, yvy155, ty_Integer) → new_esEs18(yvy152, yvy155)
new_mkVBalBranch0(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch213(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(Zero), new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), h, ba)
new_mkBalBranch6MkBalBranch3(yvy50, yvy51, yvy54, Branch(yvy1180, yvy1181, yvy1182, yvy1183, yvy1184), True, h, ba) → new_mkBalBranch6MkBalBranch11(yvy50, yvy51, yvy54, yvy1180, yvy1181, yvy1182, yvy1183, yvy1184, new_lt17(new_sizeFM1(yvy1184, h, ba), new_sr0(Pos(Succ(Succ(Zero))), new_sizeFM1(yvy1183, h, ba))), h, ba)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Ordering, bfd) → new_ltEs6(yvy1000, yvy1010)
new_addToFM(yvy5, yvy40, yvy41, h, ba) → new_addToFM_C0(yvy5, yvy40, yvy41, h, ba)
new_ltEs4(yvy100, yvy101) → new_fsEs(new_compare8(yvy100, yvy101))
new_esEs33(yvy40002, yvy30002, app(ty_[], beb)) → new_esEs16(yvy40002, yvy30002, beb)
new_ltEs8(yvy100, yvy101, cga) → new_fsEs(new_compare0(yvy100, yvy101, cga))
new_splitLT5(EmptyFM, h, ba) → new_emptyFM(h, ba)
new_esEs36(yvy1000, yvy1010, ty_Integer) → new_esEs18(yvy1000, yvy1010)
new_addToFM_C0(Branch([], yvy51, yvy52, yvy53, yvy54), [], yvy41, h, ba) → new_addToFM_C14(yvy51, yvy52, yvy53, yvy54, yvy41, new_compare0([], [], h), h, ba)
new_esEs32(yvy40001, yvy30001, app(ty_Ratio, bdc)) → new_esEs21(yvy40001, yvy30001, bdc)
new_compare12(False, True) → LT
new_esEs5(yvy4001, yvy3001, ty_Char) → new_esEs15(yvy4001, yvy3001)
new_esEs31(yvy40000, yvy30000, app(app(ty_@2, bbg), bbh)) → new_esEs17(yvy40000, yvy30000, bbg, bbh)
new_lt21(yvy153, yvy156, ty_@0) → new_lt19(yvy153, yvy156)
new_ltEs18(yvy107, yvy108, ty_Integer) → new_ltEs4(yvy107, yvy108)
new_splitLT21(yvy36, yvy37, yvy38, yvy39, yvy40, yvy41, yvy42, yvy43, EQ, cg, da) → new_splitLT22(yvy36, yvy37, yvy38, yvy39, yvy40, yvy41, yvy42, yvy43, cg, da)
new_esEs12(LT, LT) → True
new_esEs28(yvy1001, yvy1011, app(ty_Maybe, hc)) → new_esEs23(yvy1001, yvy1011, hc)
new_compare15(EQ, LT) → GT
new_pePe(True, yvy305) → True
new_compare0([], [], cgb) → EQ
new_primEqNat0(Zero, Zero) → True
new_esEs6(yvy4002, yvy3002, ty_Double) → new_esEs13(yvy4002, yvy3002)
new_esEs4(yvy4000, yvy3000, app(ty_Maybe, cab)) → new_esEs23(yvy4000, yvy3000, cab)
new_lt5(yvy1001, yvy1011, ty_Bool) → new_lt18(yvy1001, yvy1011)
new_mkVBalBranch0(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch28(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Neg(new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(yvy6200)), yvy6200)), new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_esEs5(yvy4001, yvy3001, ty_Float) → new_esEs14(yvy4001, yvy3001)
new_lt21(yvy153, yvy156, app(app(ty_Either, egh), eha)) → new_lt16(yvy153, yvy156, egh, eha)
new_splitGT21(yvy17, yvy18, yvy19, yvy20, yvy21, yvy22, yvy23, yvy24, dgd, dge) → new_splitGT15(yvy17, yvy18, yvy19, yvy20, yvy21, yvy22, yvy23, yvy24, new_compare0(:(yvy23, yvy24), :(yvy17, yvy18), dgd), dgd, dge)
new_esEs8(yvy4001, yvy3001, app(app(app(ty_@3, dcd), dce), dcf)) → new_esEs22(yvy4001, yvy3001, dcd, dce, dcf)
new_lt20(yvy152, yvy155, app(ty_[], chd)) → new_lt9(yvy152, yvy155, chd)
new_primPlusInt1(yvy11820, Neg(yvy5420)) → Neg(new_primPlusNat1(yvy11820, yvy5420))
new_esEs13(Double(yvy40000, yvy40001), Double(yvy30000, yvy30001)) → new_esEs25(new_sr0(yvy40000, yvy30000), new_sr0(yvy40001, yvy30001))
new_esEs7(yvy4000, yvy3000, ty_Bool) → new_esEs20(yvy4000, yvy3000)
new_compare30(yvy400, yvy300, ty_@0) → new_compare9(yvy400, yvy300)
new_esEs29(yvy40000, yvy30000, ty_@0) → new_esEs19(yvy40000, yvy30000)
new_esEs6(yvy4002, yvy3002, ty_Ordering) → new_esEs12(yvy4002, yvy3002)
new_esEs15(Char(yvy40000), Char(yvy30000)) → new_primEqNat0(yvy40000, yvy30000)
new_esEs26(yvy40000, yvy30000, ty_Int) → new_esEs25(yvy40000, yvy30000)
new_esEs32(yvy40001, yvy30001, ty_Integer) → new_esEs18(yvy40001, yvy30001)
new_lt22(yvy1000, yvy1010, app(ty_[], cca)) → new_lt9(yvy1000, yvy1010, cca)
new_esEs11(yvy4000, yvy3000, ty_Double) → new_esEs13(yvy4000, yvy3000)
new_splitGT12(yvy300, yvy301, yvy31, yvy32, yvy33, yvy34, LT, h, ba) → new_mkVBalBranch0(:(yvy300, yvy301), yvy31, new_splitGT4(yvy33, h, ba), yvy34, h, ba)
new_esEs29(yvy40000, yvy30000, ty_Bool) → new_esEs20(yvy40000, yvy30000)
new_lt5(yvy1001, yvy1011, app(ty_[], gd)) → new_lt9(yvy1001, yvy1011, gd)
new_ltEs21(yvy1001, yvy1011, ty_Bool) → new_ltEs16(yvy1001, yvy1011)
new_ltEs6(EQ, GT) → True
new_esEs9(yvy4000, yvy3000, ty_Integer) → new_esEs18(yvy4000, yvy3000)
new_primPlusNat0(Succ(yvy3070), yvy400100) → Succ(Succ(new_primPlusNat1(yvy3070, yvy400100)))
new_esEs23(Nothing, Just(yvy30000), cab) → False
new_esEs23(Just(yvy40000), Nothing, cab) → False
new_splitGT15(yvy17, yvy18, yvy19, yvy20, yvy21, yvy22, yvy23, yvy24, LT, dgd, dge) → new_mkVBalBranch0(:(yvy17, yvy18), yvy19, new_splitGT5(yvy21, yvy23, yvy24, dgd, dge), yvy22, dgd, dge)
new_esEs24(Right(yvy40000), Right(yvy30000), ddf, ty_Float) → new_esEs14(yvy40000, yvy30000)
new_addToFM_C17(yvy51, yvy52, yvy53, yvy54, yvy400, yvy401, yvy41, GT, h, ba) → new_mkBalBranch([], yvy51, yvy53, new_addToFM_C0(yvy54, :(yvy400, yvy401), yvy41, h, ba), h, ba)
new_ltEs20(yvy154, yvy157, ty_Bool) → new_ltEs16(yvy154, yvy157)
new_ltEs5(Just(yvy1000), Just(yvy1010), app(app(ty_@2, cb), cc)) → new_ltEs12(yvy1000, yvy1010, cb, cc)
new_ltEs20(yvy154, yvy157, ty_Int) → new_ltEs15(yvy154, yvy157)
new_addToFM_C17(yvy51, yvy52, yvy53, yvy54, yvy400, yvy401, yvy41, EQ, h, ba) → new_addToFM_C16(yvy51, yvy52, yvy53, yvy54, yvy400, yvy401, yvy41, h, ba)
new_esEs8(yvy4001, yvy3001, ty_@0) → new_esEs19(yvy4001, yvy3001)
new_splitGT22(yvy17, yvy18, yvy19, yvy20, yvy21, yvy22, yvy23, yvy24, EQ, dgd, dge) → new_splitGT21(yvy17, yvy18, yvy19, yvy20, yvy21, yvy22, yvy23, yvy24, dgd, dge)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Float, bfd) → new_ltEs11(yvy1000, yvy1010)
new_lt21(yvy153, yvy156, app(ty_Ratio, ega)) → new_lt10(yvy153, yvy156, ega)
new_primEqInt(Neg(Succ(yvy400000)), Neg(Succ(yvy300000))) → new_primEqNat0(yvy400000, yvy300000)
new_esEs10(yvy4000, yvy3000, app(app(app(ty_@3, fah), fba), fbb)) → new_esEs22(yvy4000, yvy3000, fah, fba, fbb)
new_ltEs14(Right(yvy1000), Right(yvy1010), bgg, app(app(ty_@2, bhe), bhf)) → new_ltEs12(yvy1000, yvy1010, bhe, bhf)
new_sizeFM1(Branch(yvy540, yvy541, yvy542, yvy543, yvy544), h, ba) → yvy542
new_ltEs5(Just(yvy1000), Nothing, bd) → False
new_esEs28(yvy1001, yvy1011, ty_Char) → new_esEs15(yvy1001, yvy1011)
new_primPlusNat1(Succ(yvy30700), Zero) → Succ(yvy30700)
new_primPlusNat1(Zero, Succ(yvy4001000)) → Succ(yvy4001000)
new_lt25(yvy134, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy134, new_sizeFM(yvy60, yvy61, Pos(Zero), yvy63, yvy64, h, ba)), LT)
new_ltEs14(Right(yvy1000), Left(yvy1010), bgg, bfd) → False
new_esEs12(LT, EQ) → False
new_esEs12(EQ, LT) → False
new_lt22(yvy1000, yvy1010, app(app(ty_@2, ccf), ccg)) → new_lt12(yvy1000, yvy1010, ccf, ccg)
new_mkVBalBranch3MkVBalBranch213(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch214(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_mkVBalBranch3MkVBalBranch14(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkBalBranch(yvy60, yvy61, yvy63, new_mkVBalBranch0(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba), h, ba)
new_esEs5(yvy4001, yvy3001, ty_Bool) → new_esEs20(yvy4001, yvy3001)
new_lt23(yvy165, yvy167, ty_Int) → new_lt17(yvy165, yvy167)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs30(yvy40001, yvy30001, app(app(app(ty_@3, ebf), ebg), ebh)) → new_esEs22(yvy40001, yvy30001, ebf, ebg, ebh)
new_esEs35(yvy153, yvy156, app(app(app(ty_@3, egb), egc), egd)) → new_esEs22(yvy153, yvy156, egb, egc, egd)
new_esEs28(yvy1001, yvy1011, ty_Double) → new_esEs13(yvy1001, yvy1011)
new_compare31(Just(yvy4000), Nothing, cha) → GT
new_esEs11(yvy4000, yvy3000, app(app(app(ty_@3, fcb), fcc), fcd)) → new_esEs22(yvy4000, yvy3000, fcb, fcc, fcd)
new_esEs28(yvy1001, yvy1011, app(app(app(ty_@3, gf), gg), gh)) → new_esEs22(yvy1001, yvy1011, gf, gg, gh)
new_splitGT12(yvy300, yvy301, yvy31, yvy32, yvy33, yvy34, EQ, h, ba) → new_splitGT13(yvy300, yvy301, yvy31, yvy32, yvy33, yvy34, h, ba)
new_esEs27(yvy1000, yvy1010, app(ty_Ratio, fb)) → new_esEs21(yvy1000, yvy1010, fb)
new_compare30(yvy400, yvy300, app(app(app(ty_@3, cgd), cge), cgf)) → new_compare6(yvy400, yvy300, cgd, cge, cgf)
new_primCompAux0(yvy56, GT) → GT
new_esEs39(yvy165, yvy167, ty_Integer) → new_esEs18(yvy165, yvy167)
new_compare26(yvy107, yvy108, True, db, dc) → EQ
new_esEs24(Right(yvy40000), Right(yvy30000), ddf, app(app(ty_Either, efb), efc)) → new_esEs24(yvy40000, yvy30000, efb, efc)
new_ltEs6(GT, GT) → True
new_ltEs21(yvy1001, yvy1011, app(app(ty_Either, cec), ced)) → new_ltEs14(yvy1001, yvy1011, cec, ced)
new_mkVBalBranch3MkVBalBranch212(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkBalBranch(yvy50, yvy51, new_mkVBalBranch0(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba), yvy54, h, ba)
new_esEs34(yvy152, yvy155, ty_Int) → new_esEs25(yvy152, yvy155)
new_esEs29(yvy40000, yvy30000, app(ty_[], dhh)) → new_esEs16(yvy40000, yvy30000, dhh)
new_esEs7(yvy4000, yvy3000, app(ty_Maybe, dbe)) → new_esEs23(yvy4000, yvy3000, dbe)
new_esEs36(yvy1000, yvy1010, ty_Int) → new_esEs25(yvy1000, yvy1010)
new_esEs19(@0, @0) → True
new_compare6(@3(yvy4000, yvy4001, yvy4002), @3(yvy3000, yvy3001, yvy3002), cgd, cge, cgf) → new_compare25(yvy4000, yvy4001, yvy4002, yvy3000, yvy3001, yvy3002, new_asAs(new_esEs4(yvy4000, yvy3000, cgd), new_asAs(new_esEs5(yvy4001, yvy3001, cge), new_esEs6(yvy4002, yvy3002, cgf))), cgd, cge, cgf)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_esEs4(yvy4000, yvy3000, ty_Bool) → new_esEs20(yvy4000, yvy3000)
new_lt20(yvy152, yvy155, ty_Char) → new_lt8(yvy152, yvy155)
new_esEs31(yvy40000, yvy30000, ty_Bool) → new_esEs20(yvy40000, yvy30000)
new_esEs6(yvy4002, yvy3002, ty_Int) → new_esEs25(yvy4002, yvy3002)
new_mkBalBranch6Size_r(yvy50, yvy51, yvy54, yvy118, h, ba) → new_sizeFM1(yvy54, h, ba)
new_ltEs14(Left(yvy1000), Left(yvy1010), app(ty_Maybe, bgd), bfd) → new_ltEs5(yvy1000, yvy1010, bgd)
new_esEs4(yvy4000, yvy3000, app(ty_Ratio, dde)) → new_esEs21(yvy4000, yvy3000, dde)
new_lt5(yvy1001, yvy1011, app(ty_Maybe, hc)) → new_lt14(yvy1001, yvy1011, hc)
new_primEqInt(Pos(Succ(yvy400000)), Pos(Succ(yvy300000))) → new_primEqNat0(yvy400000, yvy300000)
new_ltEs14(Right(yvy1000), Right(yvy1010), bgg, ty_Double) → new_ltEs13(yvy1000, yvy1010)
new_ltEs14(Right(yvy1000), Right(yvy1010), bgg, ty_Integer) → new_ltEs4(yvy1000, yvy1010)
new_ltEs21(yvy1001, yvy1011, ty_Float) → new_ltEs11(yvy1001, yvy1011)
new_esEs26(yvy40000, yvy30000, app(ty_Maybe, dhe)) → new_esEs23(yvy40000, yvy30000, dhe)
new_ltEs24(yvy100, yvy101, ty_Float) → new_ltEs11(yvy100, yvy101)
new_esEs34(yvy152, yvy155, app(app(ty_@2, ecf), ecg)) → new_esEs17(yvy152, yvy155, ecf, ecg)
new_primEqNat0(Succ(yvy400000), Succ(yvy300000)) → new_primEqNat0(yvy400000, yvy300000)
new_splitGT5(EmptyFM, yvy400, yvy401, h, ba) → new_emptyFM(h, ba)
new_mkVBalBranch3MkVBalBranch213(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch214(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_esEs24(Right(yvy40000), Right(yvy30000), ddf, app(ty_Ratio, eee)) → new_esEs21(yvy40000, yvy30000, eee)
new_esEs26(yvy40000, yvy30000, ty_Ordering) → new_esEs12(yvy40000, yvy30000)
new_esEs11(yvy4000, yvy3000, app(ty_Ratio, fca)) → new_esEs21(yvy4000, yvy3000, fca)
new_esEs30(yvy40001, yvy30001, ty_Integer) → new_esEs18(yvy40001, yvy30001)
new_esEs39(yvy165, yvy167, ty_Char) → new_esEs15(yvy165, yvy167)
new_splitLT15(yvy36, yvy37, yvy38, yvy39, yvy40, yvy41, yvy42, yvy43, LT, cg, da) → new_splitLT12(yvy36, yvy37, yvy38, yvy39, yvy40, yvy41, yvy42, yvy43, cg, da)
new_splitLT16(yvy31, yvy32, yvy33, yvy34, LT, h, ba) → new_splitLT17(yvy31, yvy32, yvy33, yvy34, h, ba)
new_lt5(yvy1001, yvy1011, ty_Float) → new_lt11(yvy1001, yvy1011)
new_primCmpInt(Neg(Succ(yvy40000)), Neg(yvy3000)) → new_primCmpNat0(yvy3000, Succ(yvy40000))
new_esEs33(yvy40002, yvy30002, app(ty_Maybe, bfa)) → new_esEs23(yvy40002, yvy30002, bfa)
new_lt6(yvy1000, yvy1010, ty_Int) → new_lt17(yvy1000, yvy1010)
new_esEs24(Right(yvy40000), Right(yvy30000), ddf, app(app(app(ty_@3, eef), eeg), eeh)) → new_esEs22(yvy40000, yvy30000, eef, eeg, eeh)
new_lt23(yvy165, yvy167, app(app(ty_Either, feb), fec)) → new_lt16(yvy165, yvy167, feb, fec)
new_lt23(yvy165, yvy167, ty_Char) → new_lt8(yvy165, yvy167)
new_lt21(yvy153, yvy156, ty_Double) → new_lt13(yvy153, yvy156)
new_addToFM_C12(yvy500, yvy501, yvy51, yvy52, yvy53, yvy54, yvy400, yvy401, yvy41, EQ, h, ba) → new_addToFM_C13(yvy500, yvy501, yvy51, yvy52, yvy53, yvy54, yvy400, yvy401, yvy41, h, ba)
new_esEs10(yvy4000, yvy3000, ty_Char) → new_esEs15(yvy4000, yvy3000)
new_esEs27(yvy1000, yvy1010, ty_@0) → new_esEs19(yvy1000, yvy1010)
new_ltEs18(yvy107, yvy108, ty_Float) → new_ltEs11(yvy107, yvy108)
new_esEs27(yvy1000, yvy1010, app(app(ty_Either, gb), gc)) → new_esEs24(yvy1000, yvy1010, gb, gc)
new_compare27(Left(yvy4000), Right(yvy3000), chb, chc) → LT
new_splitGT14(yvy31, yvy32, yvy33, yvy34, h, ba) → yvy34
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Float, ddg) → new_esEs14(yvy40000, yvy30000)
new_esEs28(yvy1001, yvy1011, ty_Int) → new_esEs25(yvy1001, yvy1011)
new_esEs6(yvy4002, yvy3002, ty_Float) → new_esEs14(yvy4002, yvy3002)
new_splitGT12(yvy300, yvy301, yvy31, yvy32, yvy33, yvy34, GT, h, ba) → new_splitGT13(yvy300, yvy301, yvy31, yvy32, yvy33, yvy34, h, ba)
new_compare17(yvy218, yvy219, yvy220, yvy221, yvy222, yvy223, True, yvy225, bah, bba, bbb) → new_compare14(yvy218, yvy219, yvy220, yvy221, yvy222, yvy223, True, bah, bba, bbb)
new_primPlusNat1(Succ(yvy30700), Succ(yvy4001000)) → Succ(Succ(new_primPlusNat1(yvy30700, yvy4001000)))
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Double, ddg) → new_esEs13(yvy40000, yvy30000)
new_ltEs19(yvy1002, yvy1012, app(app(ty_@2, bac), bad)) → new_ltEs12(yvy1002, yvy1012, bac, bad)
new_esEs33(yvy40002, yvy30002, app(app(ty_Either, bfb), bfc)) → new_esEs24(yvy40002, yvy30002, bfb, bfc)
new_esEs24(Right(yvy40000), Right(yvy30000), ddf, ty_Int) → new_esEs25(yvy40000, yvy30000)
new_esEs29(yvy40000, yvy30000, app(app(app(ty_@3, ead), eae), eaf)) → new_esEs22(yvy40000, yvy30000, ead, eae, eaf)
new_esEs26(yvy40000, yvy30000, ty_Double) → new_esEs13(yvy40000, yvy30000)
new_compare210(yvy100, yvy101, True, fff) → EQ
new_splitGT15(yvy17, yvy18, yvy19, yvy20, yvy21, yvy22, yvy23, yvy24, GT, dgd, dge) → new_splitGT16(yvy17, yvy18, yvy19, yvy20, yvy21, yvy22, yvy23, yvy24, dgd, dge)
new_esEs24(Left(yvy40000), Left(yvy30000), app(ty_[], ech), ddg) → new_esEs16(yvy40000, yvy30000, ech)
new_ltEs5(Just(yvy1000), Just(yvy1010), app(app(ty_Either, ce), cf)) → new_ltEs14(yvy1000, yvy1010, ce, cf)
new_lt23(yvy165, yvy167, ty_Bool) → new_lt18(yvy165, yvy167)
new_primEqInt(Pos(Zero), Neg(Succ(yvy300000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(yvy300000))) → False
new_primCmpInt(Pos(Zero), Pos(Succ(yvy30000))) → new_primCmpNat0(Zero, Succ(yvy30000))
new_esEs9(yvy4000, yvy3000, ty_Ordering) → new_esEs12(yvy4000, yvy3000)
new_esEs36(yvy1000, yvy1010, app(app(app(ty_@3, ccc), ccd), cce)) → new_esEs22(yvy1000, yvy1010, ccc, ccd, cce)
new_emptyFM(h, ba) → EmptyFM
new_addToFM_C12(yvy500, yvy501, yvy51, yvy52, yvy53, yvy54, yvy400, yvy401, yvy41, LT, h, ba) → new_addToFM_C13(yvy500, yvy501, yvy51, yvy52, yvy53, yvy54, yvy400, yvy401, yvy41, h, ba)
new_esEs28(yvy1001, yvy1011, ty_Ordering) → new_esEs12(yvy1001, yvy1011)
new_esEs10(yvy4000, yvy3000, app(ty_[], fad)) → new_esEs16(yvy4000, yvy3000, fad)
new_esEs6(yvy4002, yvy3002, app(app(ty_Either, dgb), dgc)) → new_esEs24(yvy4002, yvy3002, dgb, dgc)
new_primCompAux0(yvy56, LT) → LT
new_esEs6(yvy4002, yvy3002, ty_Integer) → new_esEs18(yvy4002, yvy3002)
new_esEs36(yvy1000, yvy1010, app(app(ty_@2, ccf), ccg)) → new_esEs17(yvy1000, yvy1010, ccf, ccg)
new_ltEs22(yvy114, yvy115, app(ty_Maybe, cff)) → new_ltEs5(yvy114, yvy115, cff)
new_not(False) → True
new_esEs34(yvy152, yvy155, app(ty_Ratio, ece)) → new_esEs21(yvy152, yvy155, ece)
new_compare30(yvy400, yvy300, ty_Bool) → new_compare12(yvy400, yvy300)
new_esEs28(yvy1001, yvy1011, app(ty_[], gd)) → new_esEs16(yvy1001, yvy1011, gd)
new_esEs11(yvy4000, yvy3000, ty_@0) → new_esEs19(yvy4000, yvy3000)
new_esEs36(yvy1000, yvy1010, ty_Float) → new_esEs14(yvy1000, yvy1010)
new_esEs4(yvy4000, yvy3000, ty_Ordering) → new_esEs12(yvy4000, yvy3000)
new_splitLT16(yvy31, yvy32, yvy33, yvy34, GT, h, ba) → new_mkVBalBranch0([], yvy31, yvy33, new_splitLT5(yvy34, h, ba), h, ba)
new_ltEs18(yvy107, yvy108, ty_@0) → new_ltEs17(yvy107, yvy108)
new_esEs39(yvy165, yvy167, ty_Int) → new_esEs25(yvy165, yvy167)
new_compare15(LT, EQ) → LT
new_primPlusInt(Branch(yvy1180, yvy1181, Neg(yvy11820), yvy1183, yvy1184), yvy50, yvy51, EmptyFM, h, ba) → new_primMinusNat0(yvy11820)
new_splitGT4(EmptyFM, h, ba) → new_emptyFM(h, ba)
new_esEs36(yvy1000, yvy1010, app(ty_Ratio, ccb)) → new_esEs21(yvy1000, yvy1010, ccb)
new_esEs24(Right(yvy40000), Left(yvy30000), ddf, ddg) → False
new_esEs24(Left(yvy40000), Right(yvy30000), ddf, ddg) → False
new_splitLT4(EmptyFM, yvy42, yvy43, cg, da) → new_emptyFM(cg, da)
new_lt20(yvy152, yvy155, app(app(ty_Either, daa), dab)) → new_lt16(yvy152, yvy155, daa, dab)
new_esEs30(yvy40001, yvy30001, app(app(ty_@2, ebc), ebd)) → new_esEs17(yvy40001, yvy30001, ebc, ebd)
new_esEs34(yvy152, yvy155, app(ty_[], chd)) → new_esEs16(yvy152, yvy155, chd)
new_lt20(yvy152, yvy155, ty_Double) → new_lt13(yvy152, yvy155)
new_compare0(:(yvy4000, yvy4001), [], cgb) → GT
new_primPlusInt(EmptyFM, yvy50, yvy51, EmptyFM, h, ba) → Pos(new_primPlusNat1(Zero, Zero))
new_esEs8(yvy4001, yvy3001, ty_Int) → new_esEs25(yvy4001, yvy3001)
new_esEs38(yvy40001, yvy30001, ty_Int) → new_esEs25(yvy40001, yvy30001)
new_splitGT30([], yvy31, yvy32, yvy33, yvy34, :(yvy400, yvy401), h, ba) → new_splitGT5(yvy34, yvy400, yvy401, h, ba)
new_ltEs24(yvy100, yvy101, ty_Integer) → new_ltEs4(yvy100, yvy101)
new_ltEs20(yvy154, yvy157, app(ty_Maybe, faa)) → new_ltEs5(yvy154, yvy157, faa)
new_primMinusNat0(Succ(yvy54200)) → Neg(Succ(yvy54200))
new_esEs34(yvy152, yvy155, app(app(ty_Either, daa), dab)) → new_esEs24(yvy152, yvy155, daa, dab)
new_lt13(yvy152, yvy155) → new_esEs12(new_compare29(yvy152, yvy155), LT)
new_esEs30(yvy40001, yvy30001, app(app(ty_Either, ecb), ecc)) → new_esEs24(yvy40001, yvy30001, ecb, ecc)
new_lt19(yvy152, yvy155) → new_esEs12(new_compare9(yvy152, yvy155), LT)
new_esEs8(yvy4001, yvy3001, app(ty_Ratio, dcc)) → new_esEs21(yvy4001, yvy3001, dcc)
new_esEs33(yvy40002, yvy30002, app(ty_Ratio, bee)) → new_esEs21(yvy40002, yvy30002, bee)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Integer) → new_esEs18(yvy40000, yvy30000)
new_mkVBalBranch3MkVBalBranch28(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch29(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_splitGT13(yvy300, yvy301, yvy31, yvy32, yvy33, yvy34, h, ba) → yvy34
new_esEs31(yvy40000, yvy30000, ty_Float) → new_esEs14(yvy40000, yvy30000)
new_primMulInt(Neg(yvy30000), Neg(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_esEs32(yvy40001, yvy30001, ty_Int) → new_esEs25(yvy40001, yvy30001)
new_esEs33(yvy40002, yvy30002, app(app(app(ty_@3, bef), beg), beh)) → new_esEs22(yvy40002, yvy30002, bef, beg, beh)
new_primEqNat0(Zero, Succ(yvy300000)) → False
new_primEqNat0(Succ(yvy400000), Zero) → False
new_compare15(LT, GT) → LT
new_ltEs5(Nothing, Nothing, bd) → True
new_ltEs23(yvy166, yvy168, app(app(app(ty_@3, fef), feg), feh)) → new_ltEs10(yvy166, yvy168, fef, feg, feh)
new_lt20(yvy152, yvy155, app(app(ty_@2, ecf), ecg)) → new_lt12(yvy152, yvy155, ecf, ecg)
new_mkVBalBranch0(yvy40, yvy41, Branch(yvy60, yvy61, yvy62, yvy63, yvy64), EmptyFM, h, ba) → new_addToFM(Branch(yvy60, yvy61, yvy62, yvy63, yvy64), yvy40, yvy41, h, ba)
new_ltEs6(EQ, LT) → False
new_esEs9(yvy4000, yvy3000, app(ty_Maybe, fgf)) → new_esEs23(yvy4000, yvy3000, fgf)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Bool) → new_ltEs16(yvy1000, yvy1010)
new_lt21(yvy153, yvy156, app(ty_Maybe, egg)) → new_lt14(yvy153, yvy156, egg)
new_esEs11(yvy4000, yvy3000, app(app(ty_@2, fbg), fbh)) → new_esEs17(yvy4000, yvy3000, fbg, fbh)
new_lt21(yvy153, yvy156, ty_Float) → new_lt11(yvy153, yvy156)
new_esEs32(yvy40001, yvy30001, ty_Bool) → new_esEs20(yvy40001, yvy30001)
new_compare31(Just(yvy4000), Just(yvy3000), cha) → new_compare210(yvy4000, yvy3000, new_esEs9(yvy4000, yvy3000, cha), cha)
new_lt20(yvy152, yvy155, ty_Bool) → new_lt18(yvy152, yvy155)
new_ltEs19(yvy1002, yvy1012, ty_@0) → new_ltEs17(yvy1002, yvy1012)
new_ltEs14(Right(yvy1000), Right(yvy1010), bgg, app(ty_Ratio, bha)) → new_ltEs9(yvy1000, yvy1010, bha)
new_esEs5(yvy4001, yvy3001, ty_Integer) → new_esEs18(yvy4001, yvy3001)
new_esEs31(yvy40000, yvy30000, ty_Int) → new_esEs25(yvy40000, yvy30000)
new_esEs27(yvy1000, yvy1010, app(app(app(ty_@3, fc), fd), ff)) → new_esEs22(yvy1000, yvy1010, fc, fd, ff)
new_esEs29(yvy40000, yvy30000, app(app(ty_Either, eah), eba)) → new_esEs24(yvy40000, yvy30000, eah, eba)
new_primCmpInt(Pos(Zero), Neg(Succ(yvy30000))) → GT
new_esEs5(yvy4001, yvy3001, app(ty_Maybe, deg)) → new_esEs23(yvy4001, yvy3001, deg)
new_compare0(:(yvy4000, yvy4001), :(yvy3000, yvy3001), cgb) → new_primCompAux1(yvy4000, yvy3000, new_compare0(yvy4001, yvy3001, cgb), cgb)
new_esEs20(False, True) → False
new_esEs20(True, False) → False
new_compare19(yvy206, yvy207, True, cbe, cbf) → LT
new_esEs28(yvy1001, yvy1011, app(app(ty_@2, ha), hb)) → new_esEs17(yvy1001, yvy1011, ha, hb)
new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkBalBranch6MkBalBranch4(yvy50, yvy51, EmptyFM, yvy118, True, h, ba) → error([])
new_lt22(yvy1000, yvy1010, ty_Integer) → new_lt15(yvy1000, yvy1010)
new_lt26(yvy138, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy138, new_sizeFM(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT)
new_esEs30(yvy40001, yvy30001, app(ty_[], ebb)) → new_esEs16(yvy40001, yvy30001, ebb)
new_esEs24(Left(yvy40000), Left(yvy30000), app(app(ty_@2, eda), edb), ddg) → new_esEs17(yvy40000, yvy30000, eda, edb)
new_esEs10(yvy4000, yvy3000, ty_Float) → new_esEs14(yvy4000, yvy3000)
new_compare29(Double(yvy4000, yvy4001), Double(yvy3000, yvy3001)) → new_compare16(new_sr0(yvy4000, yvy3000), new_sr0(yvy4001, yvy3001))
new_mkVBalBranch3MkVBalBranch213(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkBalBranch(yvy50, yvy51, new_mkVBalBranch0(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), yvy53, h, ba), yvy54, h, ba)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs32(yvy40001, yvy30001, ty_Double) → new_esEs13(yvy40001, yvy30001)
new_esEs23(Just(yvy40000), Just(yvy30000), app(ty_Ratio, caf)) → new_esEs21(yvy40000, yvy30000, caf)
new_ltEs14(Left(yvy1000), Right(yvy1010), bgg, bfd) → True
new_compare30(yvy400, yvy300, app(ty_[], cgb)) → new_compare0(yvy400, yvy300, cgb)
new_asAs(False, yvy184) → False
new_compare27(Right(yvy4000), Left(yvy3000), chb, chc) → GT
new_esEs36(yvy1000, yvy1010, app(ty_Maybe, cch)) → new_esEs23(yvy1000, yvy1010, cch)
new_primMulInt(Pos(yvy30000), Neg(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_primMulInt(Neg(yvy30000), Pos(yvy40010)) → Neg(new_primMulNat0(yvy30000, yvy40010))
new_sizeFM1(EmptyFM, h, ba) → Pos(Zero)
new_lt20(yvy152, yvy155, ty_@0) → new_lt19(yvy152, yvy155)
new_compare16(yvy400, yvy300) → new_primCmpInt(yvy400, yvy300)
new_esEs27(yvy1000, yvy1010, ty_Double) → new_esEs13(yvy1000, yvy1010)
new_esEs36(yvy1000, yvy1010, ty_Ordering) → new_esEs12(yvy1000, yvy1010)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Bool) → new_esEs20(yvy40000, yvy30000)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Integer, bfd) → new_ltEs4(yvy1000, yvy1010)
new_esEs30(yvy40001, yvy30001, app(ty_Maybe, eca)) → new_esEs23(yvy40001, yvy30001, eca)
new_compare14(yvy218, yvy219, yvy220, yvy221, yvy222, yvy223, True, bah, bba, bbb) → LT
new_esEs9(yvy4000, yvy3000, ty_Bool) → new_esEs20(yvy4000, yvy3000)
new_lt5(yvy1001, yvy1011, ty_Ordering) → new_lt7(yvy1001, yvy1011)
new_compare27(Left(yvy4000), Left(yvy3000), chb, chc) → new_compare26(yvy4000, yvy3000, new_esEs10(yvy4000, yvy3000, chb), chb, chc)
new_esEs27(yvy1000, yvy1010, ty_Integer) → new_esEs18(yvy1000, yvy1010)
new_esEs18(Integer(yvy40000), Integer(yvy30000)) → new_primEqInt(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, ty_Char) → new_esEs15(yvy40002, yvy30002)
new_ltEs5(Just(yvy1000), Just(yvy1010), app(ty_Maybe, cd)) → new_ltEs5(yvy1000, yvy1010, cd)
new_splitLT30([], yvy31, yvy32, yvy33, yvy34, [], h, ba) → new_splitLT16(yvy31, yvy32, yvy33, yvy34, new_compare0([], [], h), h, ba)
new_ltEs11(yvy100, yvy101) → new_fsEs(new_compare18(yvy100, yvy101))
new_ltEs14(Right(yvy1000), Right(yvy1010), bgg, app(app(ty_Either, bhh), caa)) → new_ltEs14(yvy1000, yvy1010, bhh, caa)
new_esEs28(yvy1001, yvy1011, ty_@0) → new_esEs19(yvy1001, yvy1011)
new_esEs24(Right(yvy40000), Right(yvy30000), ddf, app(ty_Maybe, efa)) → new_esEs23(yvy40000, yvy30000, efa)
new_esEs7(yvy4000, yvy3000, ty_Ordering) → new_esEs12(yvy4000, yvy3000)
new_mkBalBranch6MkBalBranch01(yvy50, yvy51, yvy540, yvy541, yvy542, yvy543, yvy544, yvy118, True, h, ba) → new_mkBranch(Succ(Succ(Zero)), yvy540, yvy541, new_mkBranch(Succ(Succ(Succ(Zero))), yvy50, yvy51, yvy118, yvy543, app(ty_[], h), ba), yvy544, app(ty_[], h), ba)
new_esEs24(Right(yvy40000), Right(yvy30000), ddf, app(ty_[], eeb)) → new_esEs16(yvy40000, yvy30000, eeb)
new_compare111(yvy233, yvy234, yvy235, yvy236, False, chg, chh) → GT
new_ltEs6(LT, GT) → True
new_ltEs23(yvy166, yvy168, app(ty_Maybe, ffc)) → new_ltEs5(yvy166, yvy168, ffc)
new_lt23(yvy165, yvy167, app(ty_Maybe, fea)) → new_lt14(yvy165, yvy167, fea)
new_mkVBalBranch3MkVBalBranch15(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), yvy40, yvy41, Branch(yvy60, yvy61, Pos(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), app(ty_[], h), ba)
new_ltEs14(Left(yvy1000), Left(yvy1010), app(app(ty_Either, bge), bgf), bfd) → new_ltEs14(yvy1000, yvy1010, bge, bgf)
new_ltEs23(yvy166, yvy168, app(app(ty_@2, ffa), ffb)) → new_ltEs12(yvy166, yvy168, ffa, ffb)
new_ltEs21(yvy1001, yvy1011, ty_Ordering) → new_ltEs6(yvy1001, yvy1011)
new_esEs24(Left(yvy40000), Left(yvy30000), app(ty_Maybe, edg), ddg) → new_esEs23(yvy40000, yvy30000, edg)
new_lt12(yvy152, yvy155, ecf, ecg) → new_esEs12(new_compare7(yvy152, yvy155, ecf, ecg), LT)
new_lt10(yvy152, yvy155, ece) → new_esEs12(new_compare13(yvy152, yvy155, ece), LT)
new_esEs8(yvy4001, yvy3001, app(app(ty_@2, dca), dcb)) → new_esEs17(yvy4001, yvy3001, dca, dcb)
new_lt22(yvy1000, yvy1010, ty_Float) → new_lt11(yvy1000, yvy1010)
new_mkVBalBranch3MkVBalBranch214(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch15(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_lt25(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r0(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), h, ba)
new_lt20(yvy152, yvy155, ty_Float) → new_lt11(yvy152, yvy155)
new_lt6(yvy1000, yvy1010, ty_Double) → new_lt13(yvy1000, yvy1010)
new_ltEs14(Left(yvy1000), Left(yvy1010), app(app(app(ty_@3, bfg), bfh), bga), bfd) → new_ltEs10(yvy1000, yvy1010, bfg, bfh, bga)
new_esEs26(yvy40000, yvy30000, ty_Integer) → new_esEs18(yvy40000, yvy30000)
new_ltEs19(yvy1002, yvy1012, ty_Double) → new_ltEs13(yvy1002, yvy1012)
new_lt20(yvy152, yvy155, ty_Integer) → new_lt15(yvy152, yvy155)
new_esEs22(@3(yvy40000, yvy40001, yvy40002), @3(yvy30000, yvy30001, yvy30002), bbc, bbd, bbe) → new_asAs(new_esEs31(yvy40000, yvy30000, bbc), new_asAs(new_esEs32(yvy40001, yvy30001, bbd), new_esEs33(yvy40002, yvy30002, bbe)))
new_esEs8(yvy4001, yvy3001, ty_Float) → new_esEs14(yvy4001, yvy3001)
new_splitLT21(yvy36, yvy37, yvy38, yvy39, yvy40, yvy41, yvy42, yvy43, GT, cg, da) → new_splitLT22(yvy36, yvy37, yvy38, yvy39, yvy40, yvy41, yvy42, yvy43, cg, da)
new_mkVBalBranch3MkVBalBranch15(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkBalBranch(yvy60, yvy61, yvy63, new_mkVBalBranch0(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba), h, ba)
new_lt5(yvy1001, yvy1011, app(app(app(ty_@3, gf), gg), gh)) → new_lt4(yvy1001, yvy1011, gf, gg, gh)
new_esEs31(yvy40000, yvy30000, ty_Ordering) → new_esEs12(yvy40000, yvy30000)
new_esEs33(yvy40002, yvy30002, ty_Double) → new_esEs13(yvy40002, yvy30002)
new_addToFM_C12(yvy500, yvy501, yvy51, yvy52, yvy53, yvy54, yvy400, yvy401, yvy41, GT, h, ba) → new_mkBalBranch(:(yvy500, yvy501), yvy51, yvy53, new_addToFM_C0(yvy54, :(yvy400, yvy401), yvy41, h, ba), h, ba)
new_primMinusNat1(Succ(yvy118200), Zero) → Pos(Succ(yvy118200))
new_esEs5(yvy4001, yvy3001, ty_Double) → new_esEs13(yvy4001, yvy3001)
new_esEs8(yvy4001, yvy3001, app(ty_Maybe, dcg)) → new_esEs23(yvy4001, yvy3001, dcg)
new_esEs29(yvy40000, yvy30000, ty_Ordering) → new_esEs12(yvy40000, yvy30000)
new_esEs4(yvy4000, yvy3000, app(ty_[], ddb)) → new_esEs16(yvy4000, yvy3000, ddb)
new_primPlusNat1(Zero, Zero) → Zero
new_compare0([], :(yvy3000, yvy3001), cgb) → LT
new_ltEs6(LT, EQ) → True
new_lt23(yvy165, yvy167, ty_Ordering) → new_lt7(yvy165, yvy167)
new_addToFM_C0(EmptyFM, yvy40, yvy41, h, ba) → Branch(yvy40, yvy41, Pos(Succ(Zero)), new_emptyFM(h, ba), new_emptyFM(h, ba))
new_ltEs21(yvy1001, yvy1011, app(ty_Maybe, ceb)) → new_ltEs5(yvy1001, yvy1011, ceb)
new_ltEs6(GT, LT) → False
new_asAs(True, yvy184) → yvy184
new_esEs35(yvy153, yvy156, ty_Float) → new_esEs14(yvy153, yvy156)
new_esEs26(yvy40000, yvy30000, ty_Float) → new_esEs14(yvy40000, yvy30000)
new_compare11(Char(yvy4000), Char(yvy3000)) → new_primCmpNat0(yvy4000, yvy3000)
new_ltEs22(yvy114, yvy115, ty_Float) → new_ltEs11(yvy114, yvy115)
new_mkVBalBranch3MkVBalBranch211(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch16(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, new_lt27(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba), h, ba)
new_lt20(yvy152, yvy155, app(ty_Ratio, ece)) → new_lt10(yvy152, yvy155, ece)
new_esEs4(yvy4000, yvy3000, app(app(app(ty_@3, bbc), bbd), bbe)) → new_esEs22(yvy4000, yvy3000, bbc, bbd, bbe)
new_ltEs16(False, False) → True
new_esEs29(yvy40000, yvy30000, ty_Integer) → new_esEs18(yvy40000, yvy30000)
new_esEs8(yvy4001, yvy3001, ty_Ordering) → new_esEs12(yvy4001, yvy3001)
new_gt(yvy311, yvy310) → new_esEs12(new_compare16(yvy311, yvy310), GT)
new_esEs30(yvy40001, yvy30001, ty_Bool) → new_esEs20(yvy40001, yvy30001)
new_esEs30(yvy40001, yvy30001, ty_Int) → new_esEs25(yvy40001, yvy30001)
new_ltEs21(yvy1001, yvy1011, ty_Int) → new_ltEs15(yvy1001, yvy1011)
new_ltEs20(yvy154, yvy157, app(app(app(ty_@3, ehd), ehe), ehf)) → new_ltEs10(yvy154, yvy157, ehd, ehe, ehf)
new_esEs23(Just(yvy40000), Just(yvy30000), app(ty_[], cac)) → new_esEs16(yvy40000, yvy30000, cac)
new_esEs34(yvy152, yvy155, app(app(app(ty_@3, dac), dad), dae)) → new_esEs22(yvy152, yvy155, dac, dad, dae)
new_esEs9(yvy4000, yvy3000, app(app(app(ty_@3, fgc), fgd), fge)) → new_esEs22(yvy4000, yvy3000, fgc, fgd, fge)
new_ltEs20(yvy154, yvy157, ty_Ordering) → new_ltEs6(yvy154, yvy157)
new_esEs6(yvy4002, yvy3002, ty_@0) → new_esEs19(yvy4002, yvy3002)
new_splitGT17(yvy31, yvy32, yvy33, yvy34, GT, h, ba) → new_splitGT14(yvy31, yvy32, yvy33, yvy34, h, ba)
new_ltEs10(@3(yvy1000, yvy1001, yvy1002), @3(yvy1010, yvy1011, yvy1012), ef, eg, eh) → new_pePe(new_lt6(yvy1000, yvy1010, ef), new_asAs(new_esEs27(yvy1000, yvy1010, ef), new_pePe(new_lt5(yvy1001, yvy1011, eg), new_asAs(new_esEs28(yvy1001, yvy1011, eg), new_ltEs19(yvy1002, yvy1012, eh)))))
new_esEs33(yvy40002, yvy30002, ty_@0) → new_esEs19(yvy40002, yvy30002)
new_ltEs22(yvy114, yvy115, ty_Int) → new_ltEs15(yvy114, yvy115)
new_mkBalBranch6MkBalBranch5(yvy50, yvy51, yvy54, yvy118, h, ba) → new_mkBalBranch6MkBalBranch4(yvy50, yvy51, yvy54, yvy118, new_gt(new_mkBalBranch6Size_r(yvy50, yvy51, yvy54, yvy118, h, ba), new_sr0(new_sIZE_RATIO, new_mkBalBranch6Size_l(yvy50, yvy51, yvy54, yvy118, h, ba))), h, ba)
new_compare27(Right(yvy4000), Right(yvy3000), chb, chc) → new_compare28(yvy4000, yvy3000, new_esEs11(yvy4000, yvy3000, chc), chb, chc)
new_addToFM_C14(yvy51, yvy52, yvy53, yvy54, yvy41, GT, h, ba) → new_mkBalBranch([], yvy51, yvy53, new_addToFM_C0(yvy54, [], yvy41, h, ba), h, ba)
new_ltEs21(yvy1001, yvy1011, ty_@0) → new_ltEs17(yvy1001, yvy1011)
new_ltEs20(yvy154, yvy157, ty_Char) → new_ltEs7(yvy154, yvy157)
new_primCompAux0(yvy56, EQ) → yvy56
new_addToFM_C14(yvy51, yvy52, yvy53, yvy54, yvy41, LT, h, ba) → new_addToFM_C15(yvy51, yvy52, yvy53, yvy54, yvy41, h, ba)
new_splitGT15(yvy17, yvy18, yvy19, yvy20, yvy21, yvy22, yvy23, yvy24, EQ, dgd, dge) → new_splitGT16(yvy17, yvy18, yvy19, yvy20, yvy21, yvy22, yvy23, yvy24, dgd, dge)
new_ltEs18(yvy107, yvy108, ty_Int) → new_ltEs15(yvy107, yvy108)
new_lt21(yvy153, yvy156, app(app(app(ty_@3, egb), egc), egd)) → new_lt4(yvy153, yvy156, egb, egc, egd)
new_esEs6(yvy4002, yvy3002, ty_Char) → new_esEs15(yvy4002, yvy3002)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_ltEs5(Just(yvy1000), Just(yvy1010), app(app(app(ty_@3, bg), bh), ca)) → new_ltEs10(yvy1000, yvy1010, bg, bh, ca)
new_esEs39(yvy165, yvy167, app(ty_[], fdb)) → new_esEs16(yvy165, yvy167, fdb)
new_splitGT30([], yvy31, yvy32, yvy33, yvy34, [], h, ba) → new_splitGT17(yvy31, yvy32, yvy33, yvy34, new_compare0([], [], h), h, ba)
new_not(True) → False
new_ltEs5(Just(yvy1000), Just(yvy1010), app(ty_Ratio, bf)) → new_ltEs9(yvy1000, yvy1010, bf)
new_esEs24(Left(yvy40000), Left(yvy30000), app(ty_Ratio, edc), ddg) → new_esEs21(yvy40000, yvy30000, edc)
new_ltEs19(yvy1002, yvy1012, app(ty_[], hf)) → new_ltEs8(yvy1002, yvy1012, hf)
new_compare112(yvy189, yvy190, True, fha) → LT
new_ltEs22(yvy114, yvy115, app(app(ty_@2, cfd), cfe)) → new_ltEs12(yvy114, yvy115, cfd, cfe)
new_esEs27(yvy1000, yvy1010, app(ty_[], fa)) → new_esEs16(yvy1000, yvy1010, fa)
new_esEs20(True, True) → True
new_esEs8(yvy4001, yvy3001, ty_Bool) → new_esEs20(yvy4001, yvy3001)
new_esEs11(yvy4000, yvy3000, ty_Integer) → new_esEs18(yvy4000, yvy3000)
new_ltEs20(yvy154, yvy157, app(ty_Ratio, ehc)) → new_ltEs9(yvy154, yvy157, ehc)
new_esEs27(yvy1000, yvy1010, app(app(ty_@2, fg), fh)) → new_esEs17(yvy1000, yvy1010, fg, fh)
new_esEs36(yvy1000, yvy1010, ty_Double) → new_esEs13(yvy1000, yvy1010)
new_compare10(yvy199, yvy200, True, bb, bc) → LT
new_esEs33(yvy40002, yvy30002, app(app(ty_@2, bec), bed)) → new_esEs17(yvy40002, yvy30002, bec, bed)
new_esEs24(Right(yvy40000), Right(yvy30000), ddf, ty_@0) → new_esEs19(yvy40000, yvy30000)
new_esEs11(yvy4000, yvy3000, app(ty_[], fbf)) → new_esEs16(yvy4000, yvy3000, fbf)
new_lt23(yvy165, yvy167, app(app(app(ty_@3, fdd), fde), fdf)) → new_lt4(yvy165, yvy167, fdd, fde, fdf)
new_esEs7(yvy4000, yvy3000, ty_Double) → new_esEs13(yvy4000, yvy3000)
new_esEs9(yvy4000, yvy3000, ty_Char) → new_esEs15(yvy4000, yvy3000)
new_addToFM_C0(Branch(:(yvy500, yvy501), yvy51, yvy52, yvy53, yvy54), [], yvy41, h, ba) → new_mkBalBranch(:(yvy500, yvy501), yvy51, new_addToFM_C0(yvy53, [], yvy41, h, ba), yvy54, h, ba)
new_sizeFM0(Branch(yvy3630, yvy3631, yvy3632, yvy3633, yvy3634), che, chf) → yvy3632
new_splitGT17(yvy31, yvy32, yvy33, yvy34, LT, h, ba) → new_mkVBalBranch0([], yvy31, new_splitGT4(yvy33, h, ba), yvy34, h, ba)
new_splitGT22(yvy17, yvy18, yvy19, yvy20, yvy21, yvy22, yvy23, yvy24, LT, dgd, dge) → new_splitGT21(yvy17, yvy18, yvy19, yvy20, yvy21, yvy22, yvy23, yvy24, dgd, dge)
new_ltEs22(yvy114, yvy115, app(ty_Ratio, ceh)) → new_ltEs9(yvy114, yvy115, ceh)
new_ltEs23(yvy166, yvy168, ty_Int) → new_ltEs15(yvy166, yvy168)
new_primMulNat0(Zero, Zero) → Zero
new_ltEs24(yvy100, yvy101, ty_Ordering) → new_ltEs6(yvy100, yvy101)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Bool, ddg) → new_esEs20(yvy40000, yvy30000)
new_mkVBalBranch3MkVBalBranch210(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch211(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_primPlusInt0(yvy11820, Pos(yvy5420)) → Pos(new_primPlusNat1(yvy11820, yvy5420))
new_esEs6(yvy4002, yvy3002, app(app(ty_@2, dfc), dfd)) → new_esEs17(yvy4002, yvy3002, dfc, dfd)
new_esEs26(yvy40000, yvy30000, app(ty_[], dgf)) → new_esEs16(yvy40000, yvy30000, dgf)
new_esEs36(yvy1000, yvy1010, ty_Char) → new_esEs15(yvy1000, yvy1010)
new_esEs28(yvy1001, yvy1011, app(app(ty_Either, hd), he)) → new_esEs24(yvy1001, yvy1011, hd, he)
new_esEs34(yvy152, yvy155, ty_@0) → new_esEs19(yvy152, yvy155)
new_esEs7(yvy4000, yvy3000, ty_Float) → new_esEs14(yvy4000, yvy3000)
new_lt7(yvy152, yvy155) → new_esEs12(new_compare15(yvy152, yvy155), LT)
new_lt22(yvy1000, yvy1010, app(ty_Maybe, cch)) → new_lt14(yvy1000, yvy1010, cch)
new_esEs35(yvy153, yvy156, ty_@0) → new_esEs19(yvy153, yvy156)
new_mkBranch(yvy360, yvy361, yvy362, yvy363, yvy364, che, chf) → Branch(yvy361, yvy362, new_primPlusInt2(new_primPlusInt0(Succ(Zero), new_sizeFM0(yvy363, che, chf)), yvy363, yvy364, yvy361, che, chf), yvy363, yvy364)
new_ltEs15(yvy100, yvy101) → new_fsEs(new_compare16(yvy100, yvy101))
new_esEs24(Left(yvy40000), Left(yvy30000), ty_@0, ddg) → new_esEs19(yvy40000, yvy30000)
new_esEs10(yvy4000, yvy3000, app(ty_Maybe, fbc)) → new_esEs23(yvy4000, yvy3000, fbc)
new_compare30(yvy400, yvy300, app(app(ty_@2, cgg), cgh)) → new_compare7(yvy400, yvy300, cgg, cgh)
new_esEs11(yvy4000, yvy3000, ty_Char) → new_esEs15(yvy4000, yvy3000)
new_esEs17(@2(yvy40000, yvy40001), @2(yvy30000, yvy30001), ddc, ddd) → new_asAs(new_esEs29(yvy40000, yvy30000, ddc), new_esEs30(yvy40001, yvy30001, ddd))
new_splitLT13(yvy31, yvy32, yvy33, yvy34, yvy400, yvy401, GT, h, ba) → new_mkVBalBranch0([], yvy31, yvy33, new_splitLT4(yvy34, yvy400, yvy401, h, ba), h, ba)
new_ltEs23(yvy166, yvy168, app(ty_Ratio, fee)) → new_ltEs9(yvy166, yvy168, fee)
new_mkVBalBranch3MkVBalBranch13(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, True, h, ba) → new_mkBalBranch(yvy60, yvy61, yvy63, new_mkVBalBranch0(yvy40, yvy41, yvy64, Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba), h, ba)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Double) → new_esEs13(yvy40000, yvy30000)
new_esEs26(yvy40000, yvy30000, ty_Char) → new_esEs15(yvy40000, yvy30000)
new_fsEs(yvy306) → new_not(new_esEs12(yvy306, GT))
new_ltEs14(Right(yvy1000), Right(yvy1010), bgg, ty_Char) → new_ltEs7(yvy1000, yvy1010)
new_esEs7(yvy4000, yvy3000, ty_Int) → new_esEs25(yvy4000, yvy3000)
new_esEs34(yvy152, yvy155, ty_Ordering) → new_esEs12(yvy152, yvy155)
new_compare18(Float(yvy4000, yvy4001), Float(yvy3000, yvy3001)) → new_compare16(new_sr0(yvy4000, yvy3000), new_sr0(yvy4001, yvy3001))
new_ltEs18(yvy107, yvy108, app(ty_[], dd)) → new_ltEs8(yvy107, yvy108, dd)
new_lt6(yvy1000, yvy1010, app(ty_Ratio, fb)) → new_lt10(yvy1000, yvy1010, fb)
new_esEs37(yvy40000, yvy30000, ty_Integer) → new_esEs18(yvy40000, yvy30000)
new_ltEs14(Left(yvy1000), Left(yvy1010), app(app(ty_@2, bgb), bgc), bfd) → new_ltEs12(yvy1000, yvy1010, bgb, bgc)
new_esEs35(yvy153, yvy156, app(app(ty_@2, ege), egf)) → new_esEs17(yvy153, yvy156, ege, egf)
new_esEs5(yvy4001, yvy3001, app(app(app(ty_@3, ded), dee), def)) → new_esEs22(yvy4001, yvy3001, ded, dee, def)
new_mkVBalBranch3MkVBalBranch14(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), app(ty_[], h), ba)
new_lt22(yvy1000, yvy1010, ty_Char) → new_lt8(yvy1000, yvy1010)
new_esEs5(yvy4001, yvy3001, app(app(ty_Either, deh), dfa)) → new_esEs24(yvy4001, yvy3001, deh, dfa)
new_esEs24(Right(yvy40000), Right(yvy30000), ddf, ty_Bool) → new_esEs20(yvy40000, yvy30000)
new_ltEs21(yvy1001, yvy1011, app(app(ty_@2, cdh), cea)) → new_ltEs12(yvy1001, yvy1011, cdh, cea)
new_splitGT30(:(yvy300, yvy301), yvy31, yvy32, yvy33, yvy34, [], h, ba) → new_splitGT12(yvy300, yvy301, yvy31, yvy32, yvy33, yvy34, new_compare0([], :(yvy300, yvy301), h), h, ba)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Char, bfd) → new_ltEs7(yvy1000, yvy1010)
new_primPlusInt(EmptyFM, yvy50, yvy51, Branch(yvy540, yvy541, Neg(yvy5420), yvy543, yvy544), h, ba) → new_primMinusNat0(yvy5420)
new_ltEs16(True, True) → True
new_splitLT12(yvy36, yvy37, yvy38, yvy39, yvy40, yvy41, yvy42, yvy43, cg, da) → yvy40
new_lt21(yvy153, yvy156, app(app(ty_@2, ege), egf)) → new_lt12(yvy153, yvy156, ege, egf)
new_lt6(yvy1000, yvy1010, ty_Bool) → new_lt18(yvy1000, yvy1010)
new_compare15(GT, EQ) → GT
new_esEs7(yvy4000, yvy3000, ty_Char) → new_esEs15(yvy4000, yvy3000)
new_mkBalBranch6MkBalBranch50(yvy50, yvy51, yvy54, yvy118, EQ, h, ba) → new_mkBalBranch6MkBalBranch5(yvy50, yvy51, yvy54, yvy118, h, ba)
new_lt21(yvy153, yvy156, ty_Char) → new_lt8(yvy153, yvy156)
new_esEs23(Just(yvy40000), Just(yvy30000), app(ty_Maybe, cbb)) → new_esEs23(yvy40000, yvy30000, cbb)
new_compare14(yvy218, yvy219, yvy220, yvy221, yvy222, yvy223, False, bah, bba, bbb) → GT
new_mkVBalBranch3MkVBalBranch212(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch27(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_esEs5(yvy4001, yvy3001, ty_Int) → new_esEs25(yvy4001, yvy3001)
new_esEs4(yvy4000, yvy3000, ty_Float) → new_esEs14(yvy4000, yvy3000)
new_esEs29(yvy40000, yvy30000, ty_Int) → new_esEs25(yvy40000, yvy30000)
new_compare30(yvy400, yvy300, app(app(ty_Either, chb), chc)) → new_compare27(yvy400, yvy300, chb, chc)
new_lt27(yvy142, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy142, new_sizeFM(yvy60, yvy61, Neg(Zero), yvy63, yvy64, h, ba)), LT)
new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_esEs24(Right(yvy40000), Right(yvy30000), ddf, app(app(ty_@2, eec), eed)) → new_esEs17(yvy40000, yvy30000, eec, eed)
new_esEs29(yvy40000, yvy30000, app(app(ty_@2, eaa), eab)) → new_esEs17(yvy40000, yvy30000, eaa, eab)
new_compare12(True, True) → EQ
new_esEs31(yvy40000, yvy30000, ty_Integer) → new_esEs18(yvy40000, yvy30000)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Ordering, ddg) → new_esEs12(yvy40000, yvy30000)
new_esEs35(yvy153, yvy156, ty_Integer) → new_esEs18(yvy153, yvy156)
new_esEs10(yvy4000, yvy3000, ty_Ordering) → new_esEs12(yvy4000, yvy3000)
new_primCompAux1(yvy400, yvy300, yvy51, h) → new_primCompAux0(yvy51, new_compare30(yvy400, yvy300, h))
new_addToFM_C22(yvy500, yvy501, yvy51, yvy52, yvy53, yvy54, yvy400, yvy401, yvy41, GT, h, ba) → new_addToFM_C21(yvy500, yvy501, yvy51, yvy52, yvy53, yvy54, yvy400, yvy401, yvy41, h, ba)
new_lt23(yvy165, yvy167, app(app(ty_@2, fdg), fdh)) → new_lt12(yvy165, yvy167, fdg, fdh)
new_mkVBalBranch3MkVBalBranch210(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, EQ, h, ba) → new_mkVBalBranch3MkVBalBranch211(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, h, ba)
new_esEs23(Just(yvy40000), Just(yvy30000), app(app(ty_Either, cbc), cbd)) → new_esEs24(yvy40000, yvy30000, cbc, cbd)
new_lt22(yvy1000, yvy1010, ty_Bool) → new_lt18(yvy1000, yvy1010)
new_primCmpNat0(Zero, Succ(yvy30000)) → LT
new_addToFM_C13(yvy500, yvy501, yvy51, yvy52, yvy53, yvy54, yvy400, yvy401, yvy41, h, ba) → Branch(:(yvy400, yvy401), new_addToFM0(yvy51, yvy41, ba), yvy52, yvy53, yvy54)
new_esEs39(yvy165, yvy167, ty_Float) → new_esEs14(yvy165, yvy167)
new_ltEs22(yvy114, yvy115, ty_Bool) → new_ltEs16(yvy114, yvy115)
new_splitGT16(yvy17, yvy18, yvy19, yvy20, yvy21, yvy22, yvy23, yvy24, dgd, dge) → yvy22
new_compare30(yvy400, yvy300, ty_Char) → new_compare11(yvy400, yvy300)
new_esEs39(yvy165, yvy167, ty_Bool) → new_esEs20(yvy165, yvy167)
new_esEs36(yvy1000, yvy1010, ty_Bool) → new_esEs20(yvy1000, yvy1010)
new_esEs34(yvy152, yvy155, ty_Char) → new_esEs15(yvy152, yvy155)
new_mkBalBranch6MkBalBranch4(yvy50, yvy51, yvy54, yvy118, False, h, ba) → new_mkBalBranch6MkBalBranch3(yvy50, yvy51, yvy54, yvy118, new_gt(new_mkBalBranch6Size_l(yvy50, yvy51, yvy54, yvy118, h, ba), new_sr0(new_sIZE_RATIO, new_mkBalBranch6Size_r(yvy50, yvy51, yvy54, yvy118, h, ba))), h, ba)
new_esEs30(yvy40001, yvy30001, ty_@0) → new_esEs19(yvy40001, yvy30001)
new_ltEs18(yvy107, yvy108, app(ty_Maybe, ec)) → new_ltEs5(yvy107, yvy108, ec)
new_splitLT13(yvy31, yvy32, yvy33, yvy34, yvy400, yvy401, EQ, h, ba) → new_splitLT14(yvy31, yvy32, yvy33, yvy34, yvy400, yvy401, h, ba)
new_ltEs24(yvy100, yvy101, ty_Char) → new_ltEs7(yvy100, yvy101)
new_esEs31(yvy40000, yvy30000, app(app(ty_Either, bcf), bcg)) → new_esEs24(yvy40000, yvy30000, bcf, bcg)
new_ltEs18(yvy107, yvy108, ty_Double) → new_ltEs13(yvy107, yvy108)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Int, bfd) → new_ltEs15(yvy1000, yvy1010)
new_lt5(yvy1001, yvy1011, ty_@0) → new_lt19(yvy1001, yvy1011)
new_mkVBalBranch0(yvy40, yvy41, EmptyFM, yvy5, h, ba) → new_addToFM(yvy5, yvy40, yvy41, h, ba)
new_ltEs21(yvy1001, yvy1011, ty_Double) → new_ltEs13(yvy1001, yvy1011)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Float) → new_esEs14(yvy40000, yvy30000)
new_lt23(yvy165, yvy167, ty_Integer) → new_lt15(yvy165, yvy167)
new_lt11(yvy152, yvy155) → new_esEs12(new_compare18(yvy152, yvy155), LT)
new_addToFM_C0(Branch(:(yvy500, yvy501), yvy51, yvy52, yvy53, yvy54), :(yvy400, yvy401), yvy41, h, ba) → new_addToFM_C22(yvy500, yvy501, yvy51, yvy52, yvy53, yvy54, yvy400, yvy401, yvy41, new_primCompAux1(yvy400, yvy500, new_compare0(yvy401, yvy501, h), h), h, ba)
new_ltEs18(yvy107, yvy108, app(app(app(ty_@3, df), dg), dh)) → new_ltEs10(yvy107, yvy108, df, dg, dh)
new_ltEs22(yvy114, yvy115, ty_@0) → new_ltEs17(yvy114, yvy115)
new_mkVBalBranch3Size_r2(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, h, ba) → new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba)
new_lt5(yvy1001, yvy1011, app(app(ty_Either, hd), he)) → new_lt16(yvy1001, yvy1011, hd, he)
new_lt5(yvy1001, yvy1011, ty_Char) → new_lt8(yvy1001, yvy1011)
new_ltEs19(yvy1002, yvy1012, ty_Ordering) → new_ltEs6(yvy1002, yvy1012)
new_esEs24(Left(yvy40000), Left(yvy30000), app(app(app(ty_@3, edd), ede), edf), ddg) → new_esEs22(yvy40000, yvy30000, edd, ede, edf)
new_ltEs23(yvy166, yvy168, ty_Double) → new_ltEs13(yvy166, yvy168)
new_ltEs23(yvy166, yvy168, ty_Integer) → new_ltEs4(yvy166, yvy168)
new_esEs9(yvy4000, yvy3000, app(ty_[], ffg)) → new_esEs16(yvy4000, yvy3000, ffg)
new_esEs33(yvy40002, yvy30002, ty_Bool) → new_esEs20(yvy40002, yvy30002)
new_esEs11(yvy4000, yvy3000, ty_Ordering) → new_esEs12(yvy4000, yvy3000)
new_splitLT30(:(yvy300, yvy301), yvy31, yvy32, yvy33, yvy34, :(yvy400, yvy401), h, ba) → new_splitLT21(yvy300, yvy301, yvy31, yvy32, yvy33, yvy34, yvy400, yvy401, new_primCompAux1(yvy400, yvy300, new_compare0(yvy401, yvy301, h), h), h, ba)
new_ltEs18(yvy107, yvy108, ty_Ordering) → new_ltEs6(yvy107, yvy108)
new_esEs23(Just(yvy40000), Just(yvy30000), app(app(app(ty_@3, cag), cah), cba)) → new_esEs22(yvy40000, yvy30000, cag, cah, cba)
new_ltEs24(yvy100, yvy101, ty_Double) → new_ltEs13(yvy100, yvy101)
new_esEs10(yvy4000, yvy3000, ty_Double) → new_esEs13(yvy4000, yvy3000)
new_compare110(yvy233, yvy234, yvy235, yvy236, False, yvy238, chg, chh) → new_compare111(yvy233, yvy234, yvy235, yvy236, yvy238, chg, chh)
new_ltEs24(yvy100, yvy101, ty_@0) → new_ltEs17(yvy100, yvy101)
new_mkBalBranch6MkBalBranch11(yvy50, yvy51, yvy54, yvy1180, yvy1181, yvy1182, yvy1183, yvy1184, True, h, ba) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), yvy1180, yvy1181, yvy1183, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), yvy50, yvy51, yvy1184, yvy54, app(ty_[], h), ba), app(ty_[], h), ba)
new_lt22(yvy1000, yvy1010, app(app(ty_Either, cda), cdb)) → new_lt16(yvy1000, yvy1010, cda, cdb)
new_compare26(yvy107, yvy108, False, db, dc) → new_compare10(yvy107, yvy108, new_ltEs18(yvy107, yvy108, db), db, dc)
new_compare30(yvy400, yvy300, ty_Float) → new_compare18(yvy400, yvy300)
new_esEs23(Nothing, Nothing, cab) → True
new_esEs39(yvy165, yvy167, app(app(ty_@2, fdg), fdh)) → new_esEs17(yvy165, yvy167, fdg, fdh)
new_splitLT16(yvy31, yvy32, yvy33, yvy34, EQ, h, ba) → new_splitLT17(yvy31, yvy32, yvy33, yvy34, h, ba)
new_esEs11(yvy4000, yvy3000, app(ty_Maybe, fce)) → new_esEs23(yvy4000, yvy3000, fce)
new_lt14(yvy152, yvy155, efg) → new_esEs12(new_compare31(yvy152, yvy155, efg), LT)
new_addToFM0(yvy51, yvy41, ba) → yvy41
new_ltEs14(Right(yvy1000), Right(yvy1010), bgg, ty_@0) → new_ltEs17(yvy1000, yvy1010)
new_ltEs19(yvy1002, yvy1012, app(ty_Ratio, hg)) → new_ltEs9(yvy1002, yvy1012, hg)
new_mkBalBranch(yvy50, yvy51, yvy118, yvy54, h, ba) → new_mkBalBranch6MkBalBranch50(yvy50, yvy51, yvy54, yvy118, new_compare16(new_primPlusInt(yvy118, yvy50, yvy51, yvy54, h, ba), Pos(Succ(Succ(Zero)))), h, ba)
new_compare111(yvy233, yvy234, yvy235, yvy236, True, chg, chh) → LT
new_ltEs23(yvy166, yvy168, ty_Bool) → new_ltEs16(yvy166, yvy168)
new_esEs7(yvy4000, yvy3000, app(ty_[], daf)) → new_esEs16(yvy4000, yvy3000, daf)
new_esEs11(yvy4000, yvy3000, app(app(ty_Either, fcf), fcg)) → new_esEs24(yvy4000, yvy3000, fcf, fcg)
new_ltEs14(Right(yvy1000), Right(yvy1010), bgg, ty_Int) → new_ltEs15(yvy1000, yvy1010)
new_esEs10(yvy4000, yvy3000, app(app(ty_Either, fbd), fbe)) → new_esEs24(yvy4000, yvy3000, fbd, fbe)
new_ltEs6(EQ, EQ) → True
new_lt20(yvy152, yvy155, ty_Ordering) → new_lt7(yvy152, yvy155)
new_ltEs22(yvy114, yvy115, app(app(ty_Either, cfg), cfh)) → new_ltEs14(yvy114, yvy115, cfg, cfh)
new_mkVBalBranch3MkVBalBranch210(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkBalBranch(yvy50, yvy51, new_mkVBalBranch0(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), yvy53, h, ba), yvy54, h, ba)
new_esEs32(yvy40001, yvy30001, ty_Float) → new_esEs14(yvy40001, yvy30001)
new_ltEs19(yvy1002, yvy1012, ty_Integer) → new_ltEs4(yvy1002, yvy1012)
new_primEqInt(Neg(Succ(yvy400000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(yvy300000))) → False
new_mkBalBranch6MkBalBranch50(yvy50, yvy51, yvy54, yvy118, GT, h, ba) → new_mkBalBranch6MkBalBranch5(yvy50, yvy51, yvy54, yvy118, h, ba)
new_esEs23(Just(yvy40000), Just(yvy30000), app(app(ty_@2, cad), cae)) → new_esEs17(yvy40000, yvy30000, cad, cae)
new_esEs38(yvy40001, yvy30001, ty_Integer) → new_esEs18(yvy40001, yvy30001)
new_esEs32(yvy40001, yvy30001, app(ty_[], bch)) → new_esEs16(yvy40001, yvy30001, bch)
new_compare31(Nothing, Nothing, cha) → EQ
new_esEs26(yvy40000, yvy30000, app(ty_Ratio, dha)) → new_esEs21(yvy40000, yvy30000, dha)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_@0) → new_ltEs17(yvy1000, yvy1010)
new_lt21(yvy153, yvy156, app(ty_[], efh)) → new_lt9(yvy153, yvy156, efh)
new_ltEs20(yvy154, yvy157, app(ty_[], ehb)) → new_ltEs8(yvy154, yvy157, ehb)
new_esEs7(yvy4000, yvy3000, ty_Integer) → new_esEs18(yvy4000, yvy3000)
new_esEs39(yvy165, yvy167, ty_Ordering) → new_esEs12(yvy165, yvy167)
new_mkVBalBranch3MkVBalBranch28(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, LT, h, ba) → new_mkBalBranch(yvy50, yvy51, new_mkVBalBranch0(yvy40, yvy41, Branch(yvy60, yvy61, Neg(Succ(yvy6200)), yvy63, yvy64), yvy53, h, ba), yvy54, h, ba)
new_lt4(yvy152, yvy155, dac, dad, dae) → new_esEs12(new_compare6(yvy152, yvy155, dac, dad, dae), LT)
new_mkBalBranch6Size_l(yvy50, yvy51, yvy54, yvy118, h, ba) → new_sizeFM1(yvy118, h, ba)
new_primCmpNat0(Succ(yvy40000), Succ(yvy30000)) → new_primCmpNat0(yvy40000, yvy30000)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_Double, bfd) → new_ltEs13(yvy1000, yvy1010)
new_lt6(yvy1000, yvy1010, app(ty_Maybe, ga)) → new_lt14(yvy1000, yvy1010, ga)
new_compare10(yvy199, yvy200, False, bb, bc) → GT
new_esEs34(yvy152, yvy155, app(ty_Maybe, efg)) → new_esEs23(yvy152, yvy155, efg)
new_esEs5(yvy4001, yvy3001, app(ty_[], ddh)) → new_esEs16(yvy4001, yvy3001, ddh)
new_ltEs14(Right(yvy1000), Right(yvy1010), bgg, app(ty_Maybe, bhg)) → new_ltEs5(yvy1000, yvy1010, bhg)
new_compare13(:%(yvy4000, yvy4001), :%(yvy3000, yvy3001), ty_Int) → new_compare16(new_sr0(yvy4000, yvy3001), new_sr0(yvy3000, yvy4001))
new_primMinusNat0(Zero) → Pos(Zero)
new_esEs8(yvy4001, yvy3001, ty_Integer) → new_esEs18(yvy4001, yvy3001)
new_ltEs22(yvy114, yvy115, app(app(app(ty_@3, cfa), cfb), cfc)) → new_ltEs10(yvy114, yvy115, cfa, cfb, cfc)
new_esEs6(yvy4002, yvy3002, ty_Bool) → new_esEs20(yvy4002, yvy3002)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Ordering) → new_ltEs6(yvy1000, yvy1010)
new_ltEs24(yvy100, yvy101, ty_Int) → new_ltEs15(yvy100, yvy101)
new_mkVBalBranch0(yvy40, yvy41, Branch(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), h, ba) → new_mkVBalBranch3MkVBalBranch212(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_primCmpInt(Pos(new_primPlusNat0(new_primMulNat0(Succ(Succ(Succ(Succ(Zero)))), Succ(yvy6200)), yvy6200)), new_mkVBalBranch3Size_r(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), h, ba)
new_esEs26(yvy40000, yvy30000, app(app(ty_@2, dgg), dgh)) → new_esEs17(yvy40000, yvy30000, dgg, dgh)
new_ltEs14(Left(yvy1000), Left(yvy1010), app(ty_Ratio, bff), bfd) → new_ltEs9(yvy1000, yvy1010, bff)
new_esEs32(yvy40001, yvy30001, ty_@0) → new_esEs19(yvy40001, yvy30001)
new_esEs12(EQ, EQ) → True
new_sizeFM(yvy50, yvy51, yvy52, yvy53, yvy54, h, ba) → yvy52
new_ltEs18(yvy107, yvy108, app(app(ty_@2, ea), eb)) → new_ltEs12(yvy107, yvy108, ea, eb)
new_esEs35(yvy153, yvy156, ty_Ordering) → new_esEs12(yvy153, yvy156)
new_lt5(yvy1001, yvy1011, ty_Int) → new_lt17(yvy1001, yvy1011)
new_primEqInt(Pos(Succ(yvy400000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(yvy300000))) → False
new_esEs35(yvy153, yvy156, app(ty_Maybe, egg)) → new_esEs23(yvy153, yvy156, egg)
new_lt20(yvy152, yvy155, ty_Int) → new_lt17(yvy152, yvy155)
new_ltEs5(Nothing, Just(yvy1010), bd) → True
new_compare25(yvy152, yvy153, yvy154, yvy155, yvy156, yvy157, True, efd, efe, eff) → EQ
new_primCmpNat0(Zero, Zero) → EQ
new_esEs37(yvy40000, yvy30000, ty_Int) → new_esEs25(yvy40000, yvy30000)
new_primCmpNat0(Succ(yvy40000), Zero) → GT
new_mkVBalBranch3MkVBalBranch29(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba) → new_mkVBalBranch3MkVBalBranch13(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, new_lt26(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r1(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba)), yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch16(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy63, yvy64, yvy40, yvy41, False, h, ba) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), yvy40, yvy41, Branch(yvy60, yvy61, Neg(Zero), yvy63, yvy64), Branch(yvy50, yvy51, yvy52, yvy53, yvy54), app(ty_[], h), ba)
new_lt22(yvy1000, yvy1010, ty_@0) → new_lt19(yvy1000, yvy1010)
new_primCmpInt(Neg(Zero), Pos(Succ(yvy30000))) → LT
new_compare9(@0, @0) → EQ
new_ltEs9(yvy100, yvy101, ecd) → new_fsEs(new_compare13(yvy100, yvy101, ecd))
new_esEs32(yvy40001, yvy30001, ty_Char) → new_esEs15(yvy40001, yvy30001)
new_splitLT14(yvy31, yvy32, yvy33, yvy34, yvy400, yvy401, h, ba) → yvy33
new_ltEs14(Left(yvy1000), Left(yvy1010), app(ty_[], bfe), bfd) → new_ltEs8(yvy1000, yvy1010, bfe)
new_esEs4(yvy4000, yvy3000, ty_Int) → new_esEs25(yvy4000, yvy3000)
new_compare28(yvy114, yvy115, True, cee, cef) → EQ
new_primEqInt(Pos(Succ(yvy400000)), Neg(yvy30000)) → False
new_primEqInt(Neg(Succ(yvy400000)), Pos(yvy30000)) → False
new_primPlusInt(Branch(yvy1180, yvy1181, Pos(yvy11820), yvy1183, yvy1184), yvy50, yvy51, EmptyFM, h, ba) → Pos(new_primPlusNat1(yvy11820, Zero))
new_esEs33(yvy40002, yvy30002, ty_Ordering) → new_esEs12(yvy40002, yvy30002)
new_ltEs20(yvy154, yvy157, ty_Integer) → new_ltEs4(yvy154, yvy157)
new_lt6(yvy1000, yvy1010, ty_Ordering) → new_lt7(yvy1000, yvy1010)
new_splitGT30(:(yvy300, yvy301), yvy31, yvy32, yvy33, yvy34, :(yvy400, yvy401), h, ba) → new_splitGT22(yvy300, yvy301, yvy31, yvy32, yvy33, yvy34, yvy400, yvy401, new_primCompAux1(yvy400, yvy300, new_compare0(yvy401, yvy301, h), h), h, ba)
new_esEs29(yvy40000, yvy30000, app(ty_Ratio, eac)) → new_esEs21(yvy40000, yvy30000, eac)
new_esEs20(False, False) → True
new_lt23(yvy165, yvy167, app(ty_[], fdb)) → new_lt9(yvy165, yvy167, fdb)
new_mkBalBranch6MkBalBranch3(yvy50, yvy51, yvy54, EmptyFM, True, h, ba) → error([])
new_ltEs22(yvy114, yvy115, ty_Integer) → new_ltEs4(yvy114, yvy115)
new_esEs30(yvy40001, yvy30001, ty_Ordering) → new_esEs12(yvy40001, yvy30001)
new_lt6(yvy1000, yvy1010, ty_Integer) → new_lt15(yvy1000, yvy1010)
new_compare30(yvy400, yvy300, app(ty_Maybe, cha)) → new_compare31(yvy400, yvy300, cha)
new_esEs7(yvy4000, yvy3000, ty_@0) → new_esEs19(yvy4000, yvy3000)
new_esEs11(yvy4000, yvy3000, ty_Float) → new_esEs14(yvy4000, yvy3000)
new_lt6(yvy1000, yvy1010, app(ty_[], fa)) → new_lt9(yvy1000, yvy1010, fa)
new_esEs36(yvy1000, yvy1010, ty_@0) → new_esEs19(yvy1000, yvy1010)
new_esEs5(yvy4001, yvy3001, ty_@0) → new_esEs19(yvy4001, yvy3001)
new_mkBalBranch6MkBalBranch3(yvy50, yvy51, yvy54, yvy118, False, h, ba) → new_mkBranch(Succ(Zero), yvy50, yvy51, yvy118, yvy54, app(ty_[], h), ba)
new_splitLT15(yvy36, yvy37, yvy38, yvy39, yvy40, yvy41, yvy42, yvy43, GT, cg, da) → new_mkVBalBranch0(:(yvy36, yvy37), yvy38, yvy40, new_splitLT4(yvy41, yvy42, yvy43, cg, da), cg, da)
new_esEs7(yvy4000, yvy3000, app(app(ty_@2, dag), dah)) → new_esEs17(yvy4000, yvy3000, dag, dah)
new_esEs9(yvy4000, yvy3000, ty_Float) → new_esEs14(yvy4000, yvy3000)
new_lt5(yvy1001, yvy1011, ty_Double) → new_lt13(yvy1001, yvy1011)
new_esEs27(yvy1000, yvy1010, ty_Int) → new_esEs25(yvy1000, yvy1010)
new_esEs25(yvy4000, yvy3000) → new_primEqInt(yvy4000, yvy3000)
new_esEs31(yvy40000, yvy30000, ty_Char) → new_esEs15(yvy40000, yvy30000)
new_esEs14(Float(yvy40000, yvy40001), Float(yvy30000, yvy30001)) → new_esEs25(new_sr0(yvy40000, yvy30000), new_sr0(yvy40001, yvy30001))
new_primPlusNat0(Zero, yvy400100) → Succ(yvy400100)
new_primCmpInt(Pos(Succ(yvy40000)), Pos(yvy3000)) → new_primCmpNat0(Succ(yvy40000), yvy3000)
new_esEs12(EQ, GT) → False
new_esEs12(GT, EQ) → False
new_esEs9(yvy4000, yvy3000, app(app(ty_Either, fgg), fgh)) → new_esEs24(yvy4000, yvy3000, fgg, fgh)
new_lt6(yvy1000, yvy1010, app(app(app(ty_@3, fc), fd), ff)) → new_lt4(yvy1000, yvy1010, fc, fd, ff)
new_esEs24(Right(yvy40000), Right(yvy30000), ddf, ty_Integer) → new_esEs18(yvy40000, yvy30000)
new_esEs4(yvy4000, yvy3000, app(app(ty_@2, ddc), ddd)) → new_esEs17(yvy4000, yvy3000, ddc, ddd)
new_esEs34(yvy152, yvy155, ty_Float) → new_esEs14(yvy152, yvy155)
new_ltEs14(Right(yvy1000), Right(yvy1010), bgg, app(ty_[], bgh)) → new_ltEs8(yvy1000, yvy1010, bgh)
new_esEs30(yvy40001, yvy30001, app(ty_Ratio, ebe)) → new_esEs21(yvy40001, yvy30001, ebe)
new_compare30(yvy400, yvy300, app(ty_Ratio, cgc)) → new_compare13(yvy400, yvy300, cgc)
new_esEs32(yvy40001, yvy30001, app(app(ty_Either, bdh), bea)) → new_esEs24(yvy40001, yvy30001, bdh, bea)
new_esEs35(yvy153, yvy156, ty_Double) → new_esEs13(yvy153, yvy156)
new_lt6(yvy1000, yvy1010, ty_Char) → new_lt8(yvy1000, yvy1010)
new_splitGT22(yvy17, yvy18, yvy19, yvy20, yvy21, yvy22, yvy23, yvy24, GT, dgd, dge) → new_splitGT5(yvy22, yvy23, yvy24, dgd, dge)
new_splitLT22(yvy36, yvy37, yvy38, yvy39, yvy40, yvy41, yvy42, yvy43, cg, da) → new_splitLT15(yvy36, yvy37, yvy38, yvy39, yvy40, yvy41, yvy42, yvy43, new_compare0(:(yvy42, yvy43), :(yvy36, yvy37), cg), cg, da)
new_ltEs20(yvy154, yvy157, ty_@0) → new_ltEs17(yvy154, yvy157)
new_ltEs24(yvy100, yvy101, app(app(ty_Either, bgg), bfd)) → new_ltEs14(yvy100, yvy101, bgg, bfd)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_Int) → new_esEs25(yvy40000, yvy30000)
new_primCmpInt(Pos(Succ(yvy40000)), Neg(yvy3000)) → GT
new_ltEs18(yvy107, yvy108, ty_Char) → new_ltEs7(yvy107, yvy108)
new_esEs4(yvy4000, yvy3000, app(app(ty_Either, ddf), ddg)) → new_esEs24(yvy4000, yvy3000, ddf, ddg)
new_esEs10(yvy4000, yvy3000, app(app(ty_@2, fae), faf)) → new_esEs17(yvy4000, yvy3000, fae, faf)
new_lt17(yvy152, yvy155) → new_esEs12(new_compare16(yvy152, yvy155), LT)
new_primMulInt(Pos(yvy30000), Pos(yvy40010)) → Pos(new_primMulNat0(yvy30000, yvy40010))
new_primPlusInt1(yvy11820, Pos(yvy5420)) → new_primMinusNat1(yvy5420, yvy11820)
new_ltEs7(yvy100, yvy101) → new_fsEs(new_compare11(yvy100, yvy101))
new_splitLT30([], yvy31, yvy32, yvy33, yvy34, :(yvy400, yvy401), h, ba) → new_splitLT13(yvy31, yvy32, yvy33, yvy34, yvy400, yvy401, new_compare0(:(yvy400, yvy401), [], h), h, ba)
new_splitLT17(yvy31, yvy32, yvy33, yvy34, h, ba) → yvy33
new_compare15(EQ, GT) → LT
new_esEs29(yvy40000, yvy30000, ty_Char) → new_esEs15(yvy40000, yvy30000)
new_lt15(yvy152, yvy155) → new_esEs12(new_compare8(yvy152, yvy155), LT)
new_ltEs6(LT, LT) → True
new_esEs6(yvy4002, yvy3002, app(ty_Ratio, dfe)) → new_esEs21(yvy4002, yvy3002, dfe)
new_ltEs5(Just(yvy1000), Just(yvy1010), app(ty_[], be)) → new_ltEs8(yvy1000, yvy1010, be)
new_ltEs19(yvy1002, yvy1012, ty_Char) → new_ltEs7(yvy1002, yvy1012)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_ltEs21(yvy1001, yvy1011, app(ty_Ratio, cdd)) → new_ltEs9(yvy1001, yvy1011, cdd)
new_compare15(GT, GT) → EQ
new_esEs8(yvy4001, yvy3001, app(app(ty_Either, dch), dda)) → new_esEs24(yvy4001, yvy3001, dch, dda)
new_compare24(yvy165, yvy166, yvy167, yvy168, True, fch, fda) → EQ
new_esEs16([], :(yvy30000, yvy30001), ddb) → False
new_esEs16(:(yvy40000, yvy40001), [], ddb) → False
new_lt21(yvy153, yvy156, ty_Ordering) → new_lt7(yvy153, yvy156)
new_primPlusInt(Branch(yvy1180, yvy1181, Neg(yvy11820), yvy1183, yvy1184), yvy50, yvy51, Branch(yvy540, yvy541, yvy542, yvy543, yvy544), h, ba) → new_primPlusInt1(yvy11820, yvy542)
new_splitLT5(Branch(yvy330, yvy331, yvy332, yvy333, yvy334), h, ba) → new_splitLT30(yvy330, yvy331, yvy332, yvy333, yvy334, [], h, ba)
new_sizeFM0(EmptyFM, che, chf) → Pos(Zero)
new_primPlusInt(EmptyFM, yvy50, yvy51, Branch(yvy540, yvy541, Pos(yvy5420), yvy543, yvy544), h, ba) → Pos(new_primPlusNat1(Zero, yvy5420))
new_esEs7(yvy4000, yvy3000, app(app(app(ty_@3, dbb), dbc), dbd)) → new_esEs22(yvy4000, yvy3000, dbb, dbc, dbd)
new_lt21(yvy153, yvy156, ty_Integer) → new_lt15(yvy153, yvy156)
new_ltEs19(yvy1002, yvy1012, app(ty_Maybe, bae)) → new_ltEs5(yvy1002, yvy1012, bae)
new_esEs10(yvy4000, yvy3000, app(ty_Ratio, fag)) → new_esEs21(yvy4000, yvy3000, fag)
new_splitLT13(yvy31, yvy32, yvy33, yvy34, yvy400, yvy401, LT, h, ba) → new_splitLT14(yvy31, yvy32, yvy33, yvy34, yvy400, yvy401, h, ba)
new_primCmpInt(Neg(Zero), Neg(Succ(yvy30000))) → new_primCmpNat0(Succ(yvy30000), Zero)
new_ltEs12(@2(yvy1000, yvy1001), @2(yvy1010, yvy1011), cbg, cbh) → new_pePe(new_lt22(yvy1000, yvy1010, cbg), new_asAs(new_esEs36(yvy1000, yvy1010, cbg), new_ltEs21(yvy1001, yvy1011, cbh)))
new_ltEs23(yvy166, yvy168, ty_@0) → new_ltEs17(yvy166, yvy168)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Char) → new_ltEs7(yvy1000, yvy1010)
new_sr0(yvy3000, yvy4001) → new_primMulInt(yvy3000, yvy4001)
new_esEs34(yvy152, yvy155, ty_Bool) → new_esEs20(yvy152, yvy155)
new_lt6(yvy1000, yvy1010, app(app(ty_Either, gb), gc)) → new_lt16(yvy1000, yvy1010, gb, gc)
new_esEs26(yvy40000, yvy30000, app(app(ty_Either, dhf), dhg)) → new_esEs24(yvy40000, yvy30000, dhf, dhg)
new_compare30(yvy400, yvy300, ty_Ordering) → new_compare15(yvy400, yvy300)
new_lt23(yvy165, yvy167, ty_@0) → new_lt19(yvy165, yvy167)
new_splitLT30(:(yvy300, yvy301), yvy31, yvy32, yvy33, yvy34, [], h, ba) → new_splitLT5(yvy33, h, ba)
new_ltEs14(Right(yvy1000), Right(yvy1010), bgg, ty_Bool) → new_ltEs16(yvy1000, yvy1010)
new_ltEs22(yvy114, yvy115, app(ty_[], ceg)) → new_ltEs8(yvy114, yvy115, ceg)
new_esEs39(yvy165, yvy167, app(app(ty_Either, feb), fec)) → new_esEs24(yvy165, yvy167, feb, fec)
new_esEs28(yvy1001, yvy1011, ty_Bool) → new_esEs20(yvy1001, yvy1011)
new_esEs5(yvy4001, yvy3001, app(ty_Ratio, dec)) → new_esEs21(yvy4001, yvy3001, dec)
new_compare24(yvy165, yvy166, yvy167, yvy168, False, fch, fda) → new_compare110(yvy165, yvy166, yvy167, yvy168, new_lt23(yvy165, yvy167, fch), new_asAs(new_esEs39(yvy165, yvy167, fch), new_ltEs23(yvy166, yvy168, fda)), fch, fda)
new_esEs9(yvy4000, yvy3000, app(ty_Ratio, fgb)) → new_esEs21(yvy4000, yvy3000, fgb)
new_ltEs20(yvy154, yvy157, app(app(ty_Either, fab), fac)) → new_ltEs14(yvy154, yvy157, fab, fac)
new_esEs9(yvy4000, yvy3000, ty_Double) → new_esEs13(yvy4000, yvy3000)
new_ltEs19(yvy1002, yvy1012, app(app(ty_Either, baf), bag)) → new_ltEs14(yvy1002, yvy1012, baf, bag)
new_esEs4(yvy4000, yvy3000, ty_@0) → new_esEs19(yvy4000, yvy3000)
new_primMulNat0(Succ(yvy300000), Zero) → Zero
new_primMulNat0(Zero, Succ(yvy400100)) → Zero
new_esEs35(yvy153, yvy156, ty_Bool) → new_esEs20(yvy153, yvy156)
new_esEs8(yvy4001, yvy3001, ty_Char) → new_esEs15(yvy4001, yvy3001)
new_esEs24(Left(yvy40000), Left(yvy30000), app(app(ty_Either, edh), eea), ddg) → new_esEs24(yvy40000, yvy30000, edh, eea)
new_ltEs14(Right(yvy1000), Right(yvy1010), bgg, ty_Ordering) → new_ltEs6(yvy1000, yvy1010)
new_esEs8(yvy4001, yvy3001, app(ty_[], dbh)) → new_esEs16(yvy4001, yvy3001, dbh)
new_esEs29(yvy40000, yvy30000, ty_Double) → new_esEs13(yvy40000, yvy30000)
new_lt24(yvy130, yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, h, ba) → new_esEs12(new_compare16(yvy130, new_sizeFM(yvy60, yvy61, Pos(Succ(yvy6200)), yvy63, yvy64, h, ba)), LT)
new_primPlusInt(Branch(yvy1180, yvy1181, Pos(yvy11820), yvy1183, yvy1184), yvy50, yvy51, Branch(yvy540, yvy541, yvy542, yvy543, yvy544), h, ba) → new_primPlusInt0(yvy11820, yvy542)
new_splitGT5(Branch(yvy340, yvy341, yvy342, yvy343, yvy344), yvy400, yvy401, h, ba) → new_splitGT30(yvy340, yvy341, yvy342, yvy343, yvy344, :(yvy400, yvy401), h, ba)
new_mkVBalBranch3MkVBalBranch28(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch29(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_esEs30(yvy40001, yvy30001, ty_Float) → new_esEs14(yvy40001, yvy30001)
new_lt23(yvy165, yvy167, ty_Float) → new_lt11(yvy165, yvy167)
new_compare12(False, False) → EQ
new_ltEs23(yvy166, yvy168, ty_Char) → new_ltEs7(yvy166, yvy168)
new_esEs29(yvy40000, yvy30000, ty_Float) → new_esEs14(yvy40000, yvy30000)
new_lt20(yvy152, yvy155, app(ty_Maybe, efg)) → new_lt14(yvy152, yvy155, efg)
new_esEs24(Left(yvy40000), Left(yvy30000), ty_Integer, ddg) → new_esEs18(yvy40000, yvy30000)
new_esEs39(yvy165, yvy167, app(app(app(ty_@3, fdd), fde), fdf)) → new_esEs22(yvy165, yvy167, fdd, fde, fdf)
new_esEs31(yvy40000, yvy30000, ty_@0) → new_esEs19(yvy40000, yvy30000)
new_mkBalBranch6MkBalBranch01(yvy50, yvy51, yvy540, yvy541, yvy542, EmptyFM, yvy544, yvy118, False, h, ba) → error([])
new_lt21(yvy153, yvy156, ty_Bool) → new_lt18(yvy153, yvy156)
new_esEs33(yvy40002, yvy30002, ty_Int) → new_esEs25(yvy40002, yvy30002)
new_compare30(yvy400, yvy300, ty_Integer) → new_compare8(yvy400, yvy300)
new_ltEs21(yvy1001, yvy1011, ty_Char) → new_ltEs7(yvy1001, yvy1011)
new_esEs32(yvy40001, yvy30001, app(app(ty_@2, bda), bdb)) → new_esEs17(yvy40001, yvy30001, bda, bdb)
new_lt22(yvy1000, yvy1010, app(ty_Ratio, ccb)) → new_lt10(yvy1000, yvy1010, ccb)
new_esEs35(yvy153, yvy156, ty_Int) → new_esEs25(yvy153, yvy156)
new_esEs4(yvy4000, yvy3000, ty_Double) → new_esEs13(yvy4000, yvy3000)
new_mkVBalBranch3MkVBalBranch212(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, GT, h, ba) → new_mkVBalBranch3MkVBalBranch27(yvy50, yvy51, yvy52, yvy53, yvy54, yvy60, yvy61, yvy6200, yvy63, yvy64, yvy40, yvy41, h, ba)
new_esEs5(yvy4001, yvy3001, app(app(ty_@2, dea), deb)) → new_esEs17(yvy4001, yvy3001, dea, deb)
new_esEs16([], [], ddb) → True
new_esEs32(yvy40001, yvy30001, ty_Ordering) → new_esEs12(yvy40001, yvy30001)
new_ltEs19(yvy1002, yvy1012, ty_Int) → new_ltEs15(yvy1002, yvy1012)
new_ltEs21(yvy1001, yvy1011, ty_Integer) → new_ltEs4(yvy1001, yvy1011)
new_ltEs20(yvy154, yvy157, ty_Float) → new_ltEs11(yvy154, yvy157)
new_lt5(yvy1001, yvy1011, app(app(ty_@2, ha), hb)) → new_lt12(yvy1001, yvy1011, ha, hb)
new_primMinusNat1(Succ(yvy118200), Succ(yvy54200)) → new_primMinusNat1(yvy118200, yvy54200)
new_esEs11(yvy4000, yvy3000, ty_Int) → new_esEs25(yvy4000, yvy3000)
new_esEs32(yvy40001, yvy30001, app(app(app(ty_@3, bdd), bde), bdf)) → new_esEs22(yvy40001, yvy30001, bdd, bde, bdf)
new_primPlusInt2(Pos(yvy3650), yvy363, yvy364, yvy361, che, chf) → new_primPlusInt0(yvy3650, new_sizeFM0(yvy364, che, chf))
new_lt22(yvy1000, yvy1010, app(app(app(ty_@3, ccc), ccd), cce)) → new_lt4(yvy1000, yvy1010, ccc, ccd, cce)
new_esEs36(yvy1000, yvy1010, app(app(ty_Either, cda), cdb)) → new_esEs24(yvy1000, yvy1010, cda, cdb)
new_lt21(yvy153, yvy156, ty_Int) → new_lt17(yvy153, yvy156)
new_esEs27(yvy1000, yvy1010, ty_Ordering) → new_esEs12(yvy1000, yvy1010)
new_esEs24(Right(yvy40000), Right(yvy30000), ddf, ty_Ordering) → new_esEs12(yvy40000, yvy30000)
new_lt8(yvy152, yvy155) → new_esEs12(new_compare11(yvy152, yvy155), LT)
new_ltEs24(yvy100, yvy101, app(ty_[], cga)) → new_ltEs8(yvy100, yvy101, cga)
new_esEs9(yvy4000, yvy3000, ty_@0) → new_esEs19(yvy4000, yvy3000)
new_esEs7(yvy4000, yvy3000, app(ty_Ratio, dba)) → new_esEs21(yvy4000, yvy3000, dba)
new_ltEs20(yvy154, yvy157, ty_Double) → new_ltEs13(yvy154, yvy157)
new_ltEs18(yvy107, yvy108, ty_Bool) → new_ltEs16(yvy107, yvy108)
new_compare28(yvy114, yvy115, False, cee, cef) → new_compare19(yvy114, yvy115, new_ltEs22(yvy114, yvy115, cef), cee, cef)
new_esEs6(yvy4002, yvy3002, app(ty_Maybe, dga)) → new_esEs23(yvy4002, yvy3002, dga)
new_esEs31(yvy40000, yvy30000, app(app(app(ty_@3, bcb), bcc), bcd)) → new_esEs22(yvy40000, yvy30000, bcb, bcc, bcd)
new_esEs4(yvy4000, yvy3000, ty_Char) → new_esEs15(yvy4000, yvy3000)
new_esEs7(yvy4000, yvy3000, app(app(ty_Either, dbf), dbg)) → new_esEs24(yvy4000, yvy3000, dbf, dbg)
new_lt6(yvy1000, yvy1010, ty_Float) → new_lt11(yvy1000, yvy1010)
new_compare112(yvy189, yvy190, False, fha) → GT
new_esEs12(GT, GT) → True
new_ltEs21(yvy1001, yvy1011, app(app(app(ty_@3, cde), cdf), cdg)) → new_ltEs10(yvy1001, yvy1011, cde, cdf, cdg)
new_mkBalBranch6MkBalBranch11(yvy50, yvy51, yvy54, yvy1180, yvy1181, yvy1182, yvy1183, EmptyFM, False, h, ba) → error([])
new_compare17(yvy218, yvy219, yvy220, yvy221, yvy222, yvy223, False, yvy225, bah, bba, bbb) → new_compare14(yvy218, yvy219, yvy220, yvy221, yvy222, yvy223, yvy225, bah, bba, bbb)
new_esEs23(Just(yvy40000), Just(yvy30000), ty_@0) → new_esEs19(yvy40000, yvy30000)
new_mkBalBranch6MkBalBranch01(yvy50, yvy51, yvy540, yvy541, yvy542, Branch(yvy5430, yvy5431, yvy5432, yvy5433, yvy5434), yvy544, yvy118, False, h, ba) → new_mkBranch(Succ(Succ(Succ(Succ(Zero)))), yvy5430, yvy5431, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Zero))))), yvy50, yvy51, yvy118, yvy5433, app(ty_[], h), ba), new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))), yvy540, yvy541, yvy5434, yvy544, app(ty_[], h), ba), app(ty_[], h), ba)
new_compare25(yvy152, yvy153, yvy154, yvy155, yvy156, yvy157, False, efd, efe, eff) → new_compare17(yvy152, yvy153, yvy154, yvy155, yvy156, yvy157, new_lt20(yvy152, yvy155, efd), new_asAs(new_esEs34(yvy152, yvy155, efd), new_pePe(new_lt21(yvy153, yvy156, efe), new_asAs(new_esEs35(yvy153, yvy156, efe), new_ltEs20(yvy154, yvy157, eff)))), efd, efe, eff)
new_compare31(Nothing, Just(yvy3000), cha) → LT
new_esEs24(Right(yvy40000), Right(yvy30000), ddf, ty_Char) → new_esEs15(yvy40000, yvy30000)
new_lt18(yvy152, yvy155) → new_esEs12(new_compare12(yvy152, yvy155), LT)
new_ltEs21(yvy1001, yvy1011, app(ty_[], cdc)) → new_ltEs8(yvy1001, yvy1011, cdc)
new_splitGT4(Branch(yvy330, yvy331, yvy332, yvy333, yvy334), h, ba) → new_splitGT30(yvy330, yvy331, yvy332, yvy333, yvy334, [], h, ba)
new_primMulNat0(Succ(yvy300000), Succ(yvy400100)) → new_primPlusNat0(new_primMulNat0(yvy300000, Succ(yvy400100)), yvy400100)
new_esEs28(yvy1001, yvy1011, app(ty_Ratio, ge)) → new_esEs21(yvy1001, yvy1011, ge)
new_esEs39(yvy165, yvy167, ty_Double) → new_esEs13(yvy165, yvy167)
new_esEs11(yvy4000, yvy3000, ty_Bool) → new_esEs20(yvy4000, yvy3000)
new_ltEs22(yvy114, yvy115, ty_Double) → new_ltEs13(yvy114, yvy115)
new_lt22(yvy1000, yvy1010, ty_Ordering) → new_lt7(yvy1000, yvy1010)
new_lt23(yvy165, yvy167, ty_Double) → new_lt13(yvy165, yvy167)
new_splitLT15(yvy36, yvy37, yvy38, yvy39, yvy40, yvy41, yvy42, yvy43, EQ, cg, da) → new_splitLT12(yvy36, yvy37, yvy38, yvy39, yvy40, yvy41, yvy42, yvy43, cg, da)
new_ltEs17(yvy100, yvy101) → new_fsEs(new_compare9(yvy100, yvy101))
new_primMinusNat1(Zero, Zero) → Pos(Zero)
new_lt23(yvy165, yvy167, app(ty_Ratio, fdc)) → new_lt10(yvy165, yvy167, fdc)
new_esEs27(yvy1000, yvy1010, ty_Float) → new_esEs14(yvy1000, yvy1010)
new_esEs16(:(yvy40000, yvy40001), :(yvy30000, yvy30001), ddb) → new_asAs(new_esEs26(yvy40000, yvy30000, ddb), new_esEs16(yvy40001, yvy30001, ddb))
new_ltEs19(yvy1002, yvy1012, app(app(app(ty_@3, hh), baa), bab)) → new_ltEs10(yvy1002, yvy1012, hh, baa, bab)
new_compare19(yvy206, yvy207, False, cbe, cbf) → GT
new_addToFM_C17(yvy51, yvy52, yvy53, yvy54, yvy400, yvy401, yvy41, LT, h, ba) → new_addToFM_C16(yvy51, yvy52, yvy53, yvy54, yvy400, yvy401, yvy41, h, ba)
new_ltEs5(Just(yvy1000), Just(yvy1010), ty_Integer) → new_ltEs4(yvy1000, yvy1010)
new_addToFM_C15(yvy51, yvy52, yvy53, yvy54, yvy41, h, ba) → Branch([], new_addToFM0(yvy51, yvy41, ba), yvy52, yvy53, yvy54)
new_esEs35(yvy153, yvy156, app(ty_Ratio, ega)) → new_esEs21(yvy153, yvy156, ega)
new_ltEs24(yvy100, yvy101, app(app(app(ty_@3, ef), eg), eh)) → new_ltEs10(yvy100, yvy101, ef, eg, eh)
new_lt16(yvy152, yvy155, daa, dab) → new_esEs12(new_compare27(yvy152, yvy155, daa, dab), LT)
new_compare30(yvy400, yvy300, ty_Double) → new_compare29(yvy400, yvy300)
new_compare15(EQ, EQ) → EQ
new_ltEs22(yvy114, yvy115, ty_Char) → new_ltEs7(yvy114, yvy115)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_lt6(yvy1000, yvy1010, app(app(ty_@2, fg), fh)) → new_lt12(yvy1000, yvy1010, fg, fh)
new_esEs27(yvy1000, yvy1010, app(ty_Maybe, ga)) → new_esEs23(yvy1000, yvy1010, ga)
new_esEs10(yvy4000, yvy3000, ty_Integer) → new_esEs18(yvy4000, yvy3000)
new_ltEs14(Left(yvy1000), Left(yvy1010), ty_@0, bfd) → new_ltEs17(yvy1000, yvy1010)
new_esEs30(yvy40001, yvy30001, ty_Char) → new_esEs15(yvy40001, yvy30001)
new_primCmpInt(Neg(Succ(yvy40000)), Pos(yvy3000)) → LT
new_esEs35(yvy153, yvy156, ty_Char) → new_esEs15(yvy153, yvy156)
new_primPlusInt2(Neg(yvy3650), yvy363, yvy364, yvy361, che, chf) → new_primPlusInt1(yvy3650, new_sizeFM0(yvy364, che, chf))

The set Q consists of the following terms:

new_esEs29(x0, x1, ty_Float)
new_esEs7(x0, x1, ty_Int)
new_esEs6(x0, x1, ty_Int)
new_splitGT21(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_ltEs16(True, True)
new_ltEs24(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(Left(x0), Left(x1), ty_Float, x2)
new_lt5(x0, x1, ty_Char)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_splitLT16(x0, x1, x2, x3, GT, x4, x5)
new_esEs29(x0, x1, ty_Char)
new_mkVBalBranch3MkVBalBranch212(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, EQ, x12, x13)
new_esEs32(x0, x1, ty_Int)
new_ltEs22(x0, x1, app(ty_Maybe, x2))
new_esEs11(x0, x1, ty_Int)
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_esEs36(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, ty_Integer)
new_compare30(x0, x1, ty_Int)
new_esEs24(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs35(x0, x1, ty_Integer)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(x0, x1, app(app(ty_@2, x2), x3))
new_esEs32(x0, x1, app(ty_Ratio, x2))
new_esEs4(x0, x1, ty_Int)
new_primPlusInt(Branch(x0, x1, Neg(x2), x3, x4), x5, x6, EmptyFM, x7, x8)
new_compare30(x0, x1, ty_Bool)
new_esEs6(x0, x1, app(ty_Maybe, x2))
new_splitLT30(:(x0, x1), x2, x3, x4, x5, [], x6, x7)
new_lt23(x0, x1, ty_Integer)
new_lt7(x0, x1)
new_esEs8(x0, x1, ty_Integer)
new_esEs6(x0, x1, ty_Integer)
new_addToFM_C13(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs16(:(x0, x1), :(x2, x3), x4)
new_esEs24(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare19(x0, x1, False, x2, x3)
new_compare27(Right(x0), Right(x1), x2, x3)
new_ltEs7(x0, x1)
new_compare112(x0, x1, True, x2)
new_mkVBalBranch0(x0, x1, Branch(x2, x3, Pos(Zero), x4, x5), Branch(x6, x7, x8, x9, x10), x11, x12)
new_esEs10(x0, x1, ty_Integer)
new_esEs7(x0, x1, app(ty_Ratio, x2))
new_compare19(x0, x1, True, x2, x3)
new_esEs32(x0, x1, ty_Ordering)
new_ltEs24(x0, x1, ty_Integer)
new_addToFM_C0(Branch([], x0, x1, x2, x3), [], x4, x5, x6)
new_esEs34(x0, x1, ty_Float)
new_esEs6(x0, x1, ty_@0)
new_esEs9(x0, x1, ty_Int)
new_compare30(x0, x1, ty_Integer)
new_esEs36(x0, x1, ty_Int)
new_esEs12(GT, EQ)
new_esEs12(EQ, GT)
new_esEs24(Right(x0), Right(x1), x2, ty_Integer)
new_esEs28(x0, x1, ty_Bool)
new_esEs24(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_compare30(x0, x1, app(app(ty_Either, x2), x3))
new_compare110(x0, x1, x2, x3, False, x4, x5, x6)
new_mkVBalBranch3MkVBalBranch214(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_addToFM_C12(x0, x1, x2, x3, x4, x5, x6, x7, x8, EQ, x9, x10)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_mkBalBranch6MkBalBranch50(x0, x1, x2, x3, LT, x4, x5)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_lt21(x0, x1, ty_Float)
new_esEs11(x0, x1, ty_Integer)
new_lt22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(Just(x0), Just(x1), ty_Double)
new_mkVBalBranch3MkVBalBranch27(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_splitGT15(x0, x1, x2, x3, x4, x5, x6, x7, GT, x8, x9)
new_esEs28(x0, x1, ty_Char)
new_primPlusInt(Branch(x0, x1, Pos(x2), x3, x4), x5, x6, Branch(x7, x8, x9, x10, x11), x12, x13)
new_esEs38(x0, x1, ty_Integer)
new_esEs27(x0, x1, ty_Bool)
new_ltEs6(EQ, EQ)
new_esEs32(x0, x1, ty_@0)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs39(x0, x1, app(ty_Ratio, x2))
new_esEs7(x0, x1, ty_Float)
new_esEs24(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs6(x0, x1, ty_Double)
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_ltEs14(Right(x0), Right(x1), x2, ty_Bool)
new_esEs5(x0, x1, app(ty_Maybe, x2))
new_esEs6(x0, x1, app(app(ty_Either, x2), x3))
new_esEs39(x0, x1, app(app(ty_@2, x2), x3))
new_esEs31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs33(x0, x1, ty_Double)
new_esEs8(x0, x1, ty_Float)
new_ltEs5(Just(x0), Just(x1), ty_@0)
new_lt5(x0, x1, ty_Int)
new_ltEs6(EQ, LT)
new_ltEs6(LT, EQ)
new_ltEs14(Right(x0), Right(x1), x2, ty_Char)
new_esEs38(x0, x1, ty_Int)
new_esEs24(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs20(x0, x1, ty_@0)
new_lt20(x0, x1, ty_Int)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_lt17(x0, x1)
new_primEqNat0(Zero, Zero)
new_esEs36(x0, x1, ty_Bool)
new_compare13(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs26(x0, x1, ty_@0)
new_esEs33(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_ltEs20(x0, x1, ty_Integer)
new_lt22(x0, x1, ty_Bool)
new_esEs35(x0, x1, app(ty_Maybe, x2))
new_lt14(x0, x1, x2)
new_compare28(x0, x1, False, x2, x3)
new_esEs4(x0, x1, ty_Integer)
new_esEs39(x0, x1, ty_Bool)
new_lt23(x0, x1, app(ty_Maybe, x2))
new_ltEs24(x0, x1, ty_Float)
new_addToFM_C14(x0, x1, x2, x3, x4, EQ, x5, x6)
new_primMulNat0(Zero, Zero)
new_asAs(True, x0)
new_esEs26(x0, x1, ty_Double)
new_esEs5(x0, x1, ty_Double)
new_esEs23(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs5(Just(x0), Just(x1), ty_Integer)
new_lt6(x0, x1, ty_Double)
new_ltEs5(Just(x0), Just(x1), ty_Double)
new_ltEs21(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs35(x0, x1, ty_Char)
new_lt21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare30(x0, x1, app(ty_Maybe, x2))
new_ltEs23(x0, x1, ty_Ordering)
new_esEs5(x0, x1, app(ty_[], x2))
new_ltEs21(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, ty_Double)
new_esEs31(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs24(x0, x1, ty_Double)
new_esEs13(Double(x0, x1), Double(x2, x3))
new_esEs26(x0, x1, ty_Ordering)
new_splitGT13(x0, x1, x2, x3, x4, x5, x6, x7)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs20(True, True)
new_esEs7(x0, x1, ty_Integer)
new_mkVBalBranch3MkVBalBranch213(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, LT, x11, x12)
new_lt21(x0, x1, ty_@0)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs8(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs21(x0, x1, ty_Integer)
new_primPlusNat0(Zero, x0)
new_ltEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(x0, x1, ty_Ordering)
new_esEs8(x0, x1, app(ty_[], x2))
new_esEs32(x0, x1, app(ty_[], x2))
new_mkVBalBranch3MkVBalBranch213(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, EQ, x11, x12)
new_esEs23(Just(x0), Just(x1), app(ty_[], x2))
new_esEs27(x0, x1, ty_Double)
new_esEs39(x0, x1, ty_Char)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_compare15(EQ, EQ)
new_addToFM_C0(Branch(:(x0, x1), x2, x3, x4, x5), [], x6, x7, x8)
new_splitLT14(x0, x1, x2, x3, x4, x5, x6, x7)
new_splitGT12(x0, x1, x2, x3, x4, x5, GT, x6, x7)
new_esEs28(x0, x1, ty_Ordering)
new_ltEs5(Nothing, Nothing, x0)
new_ltEs11(x0, x1)
new_lt20(x0, x1, ty_Float)
new_esEs32(x0, x1, ty_Bool)
new_splitLT5(EmptyFM, x0, x1)
new_addToFM_C17(x0, x1, x2, x3, x4, x5, x6, EQ, x7, x8)
new_esEs10(x0, x1, ty_Double)
new_ltEs14(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs23(x0, x1, ty_Integer)
new_esEs4(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs20(False, False)
new_compare12(False, False)
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_lt22(x0, x1, ty_Char)
new_ltEs22(x0, x1, app(app(ty_Either, x2), x3))
new_compare30(x0, x1, app(ty_Ratio, x2))
new_mkVBalBranch3MkVBalBranch16(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, True, x11, x12)
new_addToFM_C22(x0, x1, x2, x3, x4, x5, x6, x7, x8, EQ, x9, x10)
new_esEs27(x0, x1, ty_Float)
new_esEs23(Just(x0), Just(x1), ty_Bool)
new_esEs27(x0, x1, ty_Char)
new_esEs9(x0, x1, ty_Integer)
new_ltEs20(x0, x1, ty_Float)
new_esEs34(x0, x1, app(ty_[], x2))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, ty_Double)
new_compare6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs6(x0, x1, ty_Bool)
new_esEs7(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(Left(x0), Left(x1), ty_@0, x2)
new_sizeFM0(EmptyFM, x0, x1)
new_mkVBalBranch3MkVBalBranch29(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_esEs24(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs24(x0, x1, ty_Ordering)
new_addToFM_C0(Branch([], x0, x1, x2, x3), :(x4, x5), x6, x7, x8)
new_lt27(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs37(x0, x1, ty_Int)
new_mkBalBranch6MkBalBranch4(x0, x1, EmptyFM, x2, True, x3, x4)
new_primMulInt(Neg(x0), Neg(x1))
new_compare111(x0, x1, x2, x3, False, x4, x5)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs9(x0, x1, ty_Ordering)
new_splitLT22(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_esEs26(x0, x1, ty_Char)
new_esEs7(x0, x1, app(ty_[], x2))
new_esEs10(x0, x1, app(ty_[], x2))
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs36(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs5(Just(x0), Just(x1), ty_Int)
new_mkBalBranch6MkBalBranch11(x0, x1, x2, x3, x4, x5, x6, EmptyFM, False, x7, x8)
new_ltEs23(x0, x1, ty_@0)
new_esEs10(x0, x1, ty_Ordering)
new_addToFM_C17(x0, x1, x2, x3, x4, x5, x6, LT, x7, x8)
new_esEs4(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(x0, x1, ty_Char)
new_addToFM0(x0, x1, x2)
new_lt22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt6(x0, x1, app(ty_Ratio, x2))
new_ltEs9(x0, x1, x2)
new_lt23(x0, x1, ty_Bool)
new_ltEs5(Just(x0), Just(x1), ty_Float)
new_esEs24(Left(x0), Left(x1), ty_Int, x2)
new_lt6(x0, x1, ty_Bool)
new_mkBalBranch6Size_l(x0, x1, x2, x3, x4, x5)
new_lt20(x0, x1, ty_Integer)
new_esEs30(x0, x1, ty_Int)
new_compare10(x0, x1, False, x2, x3)
new_lt5(x0, x1, ty_Float)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare11(Char(x0), Char(x1))
new_ltEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs30(x0, x1, ty_Integer)
new_esEs25(x0, x1)
new_ltEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, ty_@0)
new_compare110(x0, x1, x2, x3, True, x4, x5, x6)
new_sr(Integer(x0), Integer(x1))
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs7(x0, x1, ty_@0)
new_splitLT4(EmptyFM, x0, x1, x2, x3)
new_primPlusInt(Branch(x0, x1, Neg(x2), x3, x4), x5, x6, Branch(x7, x8, x9, x10, x11), x12, x13)
new_esEs10(x0, x1, ty_Bool)
new_compare210(x0, x1, True, x2)
new_ltEs14(Left(x0), Right(x1), x2, x3)
new_ltEs14(Right(x0), Left(x1), x2, x3)
new_esEs6(x0, x1, app(ty_[], x2))
new_ltEs14(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs31(x0, x1, ty_Bool)
new_primPlusNat1(Succ(x0), Zero)
new_esEs6(x0, x1, ty_Ordering)
new_mkVBalBranch0(x0, x1, Branch(x2, x3, Neg(Succ(x4)), x5, x6), Branch(x7, x8, x9, x10, x11), x12, x13)
new_splitLT16(x0, x1, x2, x3, EQ, x4, x5)
new_splitGT12(x0, x1, x2, x3, x4, x5, LT, x6, x7)
new_pePe(False, x0)
new_lt23(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Bool)
new_esEs29(x0, x1, ty_Int)
new_esEs30(x0, x1, ty_Ordering)
new_lt23(x0, x1, ty_Float)
new_ltEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_primPlusNat1(Succ(x0), Succ(x1))
new_lt22(x0, x1, app(ty_[], x2))
new_mkVBalBranch3MkVBalBranch213(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, GT, x11, x12)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_lt5(x0, x1, app(ty_Ratio, x2))
new_esEs31(x0, x1, ty_Char)
new_lt22(x0, x1, ty_Double)
new_ltEs16(False, True)
new_ltEs16(True, False)
new_lt6(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(x0, x1, ty_Int)
new_splitLT15(x0, x1, x2, x3, x4, x5, x6, x7, GT, x8, x9)
new_esEs33(x0, x1, app(ty_[], x2))
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_mkVBalBranch0(x0, x1, Branch(x2, x3, Neg(Zero), x4, x5), Branch(x6, x7, x8, x9, x10), x11, x12)
new_splitLT30([], x0, x1, x2, x3, :(x4, x5), x6, x7)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_ltEs5(Just(x0), Just(x1), ty_Char)
new_esEs27(x0, x1, ty_Int)
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_ltEs5(Just(x0), Just(x1), ty_Bool)
new_ltEs23(x0, x1, app(ty_Ratio, x2))
new_esEs35(x0, x1, app(app(ty_@2, x2), x3))
new_mkBalBranch6MkBalBranch01(x0, x1, x2, x3, x4, x5, x6, x7, True, x8, x9)
new_lt22(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_@0)
new_ltEs22(x0, x1, ty_Bool)
new_esEs24(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs27(x0, x1, ty_Integer)
new_esEs33(x0, x1, ty_Integer)
new_esEs35(x0, x1, ty_Float)
new_lt5(x0, x1, ty_Integer)
new_lt23(x0, x1, ty_@0)
new_ltEs6(LT, LT)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs21(x0, x1, app(ty_Ratio, x2))
new_compare17(x0, x1, x2, x3, x4, x5, False, x6, x7, x8, x9)
new_mkVBalBranch3MkVBalBranch210(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, EQ, x11, x12)
new_ltEs24(x0, x1, ty_Char)
new_splitLT21(x0, x1, x2, x3, x4, x5, x6, x7, LT, x8, x9)
new_esEs28(x0, x1, ty_Int)
new_mkVBalBranch3MkVBalBranch28(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, LT, x12, x13)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs23(Just(x0), Just(x1), ty_@0)
new_lt21(x0, x1, ty_Double)
new_esEs6(x0, x1, ty_Char)
new_esEs31(x0, x1, app(ty_[], x2))
new_compare0([], [], x0)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_esEs33(x0, x1, app(app(ty_@2, x2), x3))
new_esEs33(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare25(x0, x1, x2, x3, x4, x5, False, x6, x7, x8)
new_compare31(Just(x0), Just(x1), x2)
new_lt5(x0, x1, ty_Bool)
new_splitLT13(x0, x1, x2, x3, x4, x5, LT, x6, x7)
new_ltEs23(x0, x1, ty_Bool)
new_primPlusInt2(Pos(x0), x1, x2, x3, x4, x5)
new_esEs29(x0, x1, ty_Double)
new_esEs35(x0, x1, app(ty_Ratio, x2))
new_compare30(x0, x1, app(app(ty_@2, x2), x3))
new_compare28(x0, x1, True, x2, x3)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_addToFM_C12(x0, x1, x2, x3, x4, x5, x6, x7, x8, LT, x9, x10)
new_mkVBalBranch3MkVBalBranch16(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, False, x11, x12)
new_lt5(x0, x1, ty_Ordering)
new_addToFM_C14(x0, x1, x2, x3, x4, GT, x5, x6)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_addToFM(x0, x1, x2, x3, x4)
new_esEs31(x0, x1, app(ty_Ratio, x2))
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_not(True)
new_lt5(x0, x1, app(app(ty_Either, x2), x3))
new_esEs32(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Right(x0), Right(x1), x2, ty_Float)
new_splitGT15(x0, x1, x2, x3, x4, x5, x6, x7, EQ, x8, x9)
new_primMulInt(Pos(x0), Pos(x1))
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(x0, x1, ty_Bool)
new_ltEs24(x0, x1, app(ty_Maybe, x2))
new_splitGT22(x0, x1, x2, x3, x4, x5, x6, x7, GT, x8, x9)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_not(False)
new_compare29(Double(x0, x1), Double(x2, x3))
new_esEs16(:(x0, x1), [], x2)
new_esEs7(x0, x1, ty_Ordering)
new_esEs8(x0, x1, ty_Ordering)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_ltEs14(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs21(x0, x1, ty_Char)
new_compare25(x0, x1, x2, x3, x4, x5, True, x6, x7, x8)
new_esEs24(Left(x0), Left(x1), ty_Char, x2)
new_splitLT13(x0, x1, x2, x3, x4, x5, GT, x6, x7)
new_esEs39(x0, x1, app(ty_Maybe, x2))
new_esEs11(x0, x1, app(ty_Ratio, x2))
new_ltEs14(Right(x0), Right(x1), x2, ty_Double)
new_ltEs6(GT, EQ)
new_ltEs6(EQ, GT)
new_esEs17(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs23(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs10(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs21(x0, x1, ty_Double)
new_compare30(x0, x1, ty_Double)
new_mkBalBranch6MkBalBranch3(x0, x1, x2, x3, False, x4, x5)
new_splitLT5(Branch(x0, x1, x2, x3, x4), x5, x6)
new_esEs33(x0, x1, app(ty_Ratio, x2))
new_ltEs22(x0, x1, app(ty_Ratio, x2))
new_addToFM_C22(x0, x1, x2, x3, x4, x5, x6, x7, x8, LT, x9, x10)
new_ltEs5(Just(x0), Nothing, x1)
new_addToFM_C15(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3MkVBalBranch212(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, LT, x12, x13)
new_ltEs22(x0, x1, ty_Int)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_compare16(x0, x1)
new_compare10(x0, x1, True, x2, x3)
new_ltEs20(x0, x1, ty_Double)
new_ltEs24(x0, x1, ty_Bool)
new_esEs35(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Left(x0), Left(x1), ty_@0, x2)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs34(x0, x1, ty_@0)
new_esEs37(x0, x1, ty_Integer)
new_compare17(x0, x1, x2, x3, x4, x5, True, x6, x7, x8, x9)
new_esEs7(x0, x1, ty_Double)
new_ltEs18(x0, x1, ty_Char)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt23(x0, x1, ty_Ordering)
new_esEs9(x0, x1, app(ty_[], x2))
new_esEs9(x0, x1, ty_Float)
new_lt6(x0, x1, ty_Char)
new_esEs36(x0, x1, app(app(ty_Either, x2), x3))
new_lt25(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs33(x0, x1, ty_@0)
new_splitGT30([], x0, x1, x2, x3, [], x4, x5)
new_esEs24(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs5(x0, x1, ty_Ordering)
new_esEs32(x0, x1, ty_Double)
new_esEs14(Float(x0, x1), Float(x2, x3))
new_ltEs14(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs5(x0, x1, ty_@0)
new_compare12(True, True)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs23(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_primCompAux1(x0, x1, x2, x3)
new_lt6(x0, x1, ty_Ordering)
new_lt5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs19(@0, @0)
new_splitLT12(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_compare24(x0, x1, x2, x3, False, x4, x5)
new_mkVBalBranch0(x0, x1, Branch(x2, x3, x4, x5, x6), EmptyFM, x7, x8)
new_esEs28(x0, x1, ty_Integer)
new_esEs12(LT, LT)
new_ltEs18(x0, x1, ty_Ordering)
new_esEs10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_lt21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs39(x0, x1, ty_Integer)
new_mkVBalBranch3Size_r2(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_esEs36(x0, x1, ty_Char)
new_mkBalBranch6MkBalBranch50(x0, x1, x2, x3, EQ, x4, x5)
new_ltEs21(x0, x1, ty_Int)
new_esEs10(x0, x1, ty_Float)
new_lt11(x0, x1)
new_ltEs20(x0, x1, ty_Int)
new_lt20(x0, x1, app(ty_[], x2))
new_ltEs21(x0, x1, ty_@0)
new_ltEs22(x0, x1, ty_Integer)
new_addToFM_C0(Branch(:(x0, x1), x2, x3, x4, x5), :(x6, x7), x8, x9, x10)
new_esEs23(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_mkBalBranch6MkBalBranch01(x0, x1, x2, x3, x4, EmptyFM, x5, x6, False, x7, x8)
new_primPlusInt1(x0, Neg(x1))
new_ltEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(x0, x1, ty_Float)
new_pePe(True, x0)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs11(x0, x1, ty_@0)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs11(x0, x1, ty_Char)
new_esEs34(x0, x1, app(ty_Maybe, x2))
new_ltEs5(Just(x0), Just(x1), app(ty_[], x2))
new_esEs6(x0, x1, ty_Float)
new_esEs6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt22(x0, x1, ty_@0)
new_esEs7(x0, x1, app(ty_Maybe, x2))
new_esEs4(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_@0)
new_esEs29(x0, x1, ty_Ordering)
new_lt22(x0, x1, ty_Float)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs23(Just(x0), Just(x1), ty_Float)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(x0, x1, app(ty_Ratio, x2))
new_lt5(x0, x1, ty_@0)
new_mkBalBranch6Size_r(x0, x1, x2, x3, x4, x5)
new_esEs11(x0, x1, ty_Bool)
new_compare30(x0, x1, app(ty_[], x2))
new_mkBalBranch6MkBalBranch4(x0, x1, Branch(x2, x3, x4, x5, x6), x7, True, x8, x9)
new_primPlusInt(EmptyFM, x0, x1, Branch(x2, x3, Neg(x4), x5, x6), x7, x8)
new_compare12(True, False)
new_compare12(False, True)
new_ltEs14(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs14(Left(x0), Left(x1), ty_Int, x2)
new_primCompAux0(x0, EQ)
new_esEs24(Right(x0), Right(x1), x2, ty_Float)
new_ltEs21(x0, x1, ty_Float)
new_primMinusNat1(Zero, Succ(x0))
new_lt6(x0, x1, ty_Float)
new_esEs16([], [], x0)
new_esEs24(Right(x0), Right(x1), x2, ty_Double)
new_sizeFM1(Branch(x0, x1, x2, x3, x4), x5, x6)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare210(x0, x1, False, x2)
new_lt5(x0, x1, ty_Double)
new_lt21(x0, x1, app(ty_Maybe, x2))
new_compare15(LT, LT)
new_esEs32(x0, x1, app(app(ty_Either, x2), x3))
new_lt6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs10(x0, x1, ty_Char)
new_ltEs8(x0, x1, x2)
new_mkVBalBranch3Size_r1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs34(x0, x1, ty_Ordering)
new_mkBalBranch6MkBalBranch50(x0, x1, x2, x3, GT, x4, x5)
new_esEs12(GT, GT)
new_addToFM_C14(x0, x1, x2, x3, x4, LT, x5, x6)
new_addToFM_C16(x0, x1, x2, x3, x4, x5, x6, x7, x8)
new_esEs30(x0, x1, ty_Double)
new_mkBranch(x0, x1, x2, x3, x4, x5, x6)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs21(x0, x1, ty_Ordering)
new_splitLT4(Branch(x0, x1, x2, x3, x4), x5, x6, x7, x8)
new_esEs23(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(Left(x0), Left(x1), ty_Double, x2)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs5(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs12(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_mkVBalBranch3MkVBalBranch211(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primMinusNat0(Zero)
new_ltEs14(Right(x0), Right(x1), x2, ty_Int)
new_ltEs22(x0, x1, ty_Char)
new_esEs24(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_lt22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(x0, x1, ty_Bool)
new_esEs31(x0, x1, ty_Int)
new_compare30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs22(x0, x1, app(ty_[], x2))
new_ltEs18(x0, x1, ty_@0)
new_esEs9(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, app(ty_[], x2))
new_primCompAux0(x0, LT)
new_esEs23(Just(x0), Just(x1), ty_Int)
new_lt10(x0, x1, x2)
new_esEs10(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(x0, x1, app(ty_Maybe, x2))
new_splitGT12(x0, x1, x2, x3, x4, x5, EQ, x6, x7)
new_esEs7(x0, x1, ty_Bool)
new_esEs5(x0, x1, ty_Float)
new_ltEs22(x0, x1, ty_Float)
new_compare15(GT, GT)
new_splitLT30([], x0, x1, x2, x3, [], x4, x5)
new_esEs31(x0, x1, ty_Double)
new_ltEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs32(x0, x1, app(app(ty_@2, x2), x3))
new_esEs34(x0, x1, ty_Bool)
new_esEs31(x0, x1, ty_Integer)
new_lt20(x0, x1, ty_Double)
new_ltEs20(x0, x1, ty_Char)
new_ltEs14(Left(x0), Left(x1), app(ty_[], x2), x3)
new_mkVBalBranch3MkVBalBranch13(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, True, x12, x13)
new_ltEs15(x0, x1)
new_esEs28(x0, x1, ty_Float)
new_esEs31(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs24(x0, x1, app(app(ty_@2, x2), x3))
new_mkBalBranch6MkBalBranch3(x0, x1, x2, Branch(x3, x4, x5, x6, x7), True, x8, x9)
new_fsEs(x0)
new_ltEs14(Right(x0), Right(x1), x2, ty_Integer)
new_compare112(x0, x1, False, x2)
new_esEs35(x0, x1, ty_Double)
new_ltEs18(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_Float)
new_lt22(x0, x1, ty_Ordering)
new_esEs9(x0, x1, ty_@0)
new_lt23(x0, x1, app(ty_Ratio, x2))
new_esEs35(x0, x1, ty_Bool)
new_ltEs14(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_addToFM_C17(x0, x1, x2, x3, x4, x5, x6, GT, x7, x8)
new_esEs34(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, ty_Bool)
new_esEs31(x0, x1, ty_@0)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs11(x0, x1, app(app(ty_@2, x2), x3))
new_esEs11(x0, x1, app(app(ty_Either, x2), x3))
new_lt12(x0, x1, x2, x3)
new_sIZE_RATIO
new_esEs21(:%(x0, x1), :%(x2, x3), x4)
new_lt22(x0, x1, ty_Int)
new_splitGT4(Branch(x0, x1, x2, x3, x4), x5, x6)
new_esEs30(x0, x1, ty_Bool)
new_esEs33(x0, x1, ty_Float)
new_esEs29(x0, x1, ty_Integer)
new_esEs23(Just(x0), Nothing, x1)
new_esEs6(x0, x1, app(ty_Ratio, x2))
new_compare31(Nothing, Nothing, x0)
new_esEs7(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs8(x0, x1, ty_Bool)
new_gt(x0, x1)
new_primPlusNat0(Succ(x0), x1)
new_ltEs4(x0, x1)
new_splitLT15(x0, x1, x2, x3, x4, x5, x6, x7, EQ, x8, x9)
new_compare14(x0, x1, x2, x3, x4, x5, False, x6, x7, x8)
new_esEs34(x0, x1, ty_Integer)
new_esEs31(x0, x1, ty_Ordering)
new_ltEs6(LT, GT)
new_ltEs6(GT, LT)
new_esEs11(x0, x1, ty_Double)
new_esEs23(Nothing, Just(x0), x1)
new_lt21(x0, x1, app(ty_[], x2))
new_lt19(x0, x1)
new_lt21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_splitGT17(x0, x1, x2, x3, LT, x4, x5)
new_esEs23(Nothing, Nothing, x0)
new_esEs32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(x0, x1, ty_Double)
new_emptyFM(x0, x1)
new_esEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt6(x0, x1, ty_Int)
new_lt21(x0, x1, ty_Ordering)
new_ltEs22(x0, x1, ty_Ordering)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_lt23(x0, x1, app(app(ty_@2, x2), x3))
new_lt21(x0, x1, ty_Integer)
new_esEs39(x0, x1, ty_Float)
new_lt6(x0, x1, ty_Integer)
new_esEs24(Right(x0), Right(x1), x2, ty_Ordering)
new_sr0(x0, x1)
new_esEs23(Just(x0), Just(x1), ty_Integer)
new_esEs20(False, True)
new_esEs20(True, False)
new_esEs29(x0, x1, ty_Bool)
new_lt21(x0, x1, ty_Int)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs39(x0, x1, app(ty_[], x2))
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_esEs31(x0, x1, ty_Float)
new_primPlusNat1(Zero, Zero)
new_ltEs21(x0, x1, ty_Bool)
new_ltEs20(x0, x1, ty_Bool)
new_mkVBalBranch3MkVBalBranch28(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, GT, x12, x13)
new_esEs22(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs12(EQ, EQ)
new_esEs30(x0, x1, ty_Float)
new_primMinusNat1(Zero, Zero)
new_esEs30(x0, x1, ty_Char)
new_compare30(x0, x1, ty_@0)
new_esEs36(x0, x1, app(ty_Maybe, x2))
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs24(Left(x0), Left(x1), app(ty_[], x2), x3)
new_mkVBalBranch3MkVBalBranch14(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, False, x12, x13)
new_ltEs23(x0, x1, ty_Float)
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt4(x0, x1, x2, x3, x4)
new_addToFM_C0(EmptyFM, x0, x1, x2, x3)
new_compare15(GT, EQ)
new_compare15(EQ, GT)
new_esEs8(x0, x1, app(app(ty_@2, x2), x3))
new_compare30(x0, x1, ty_Char)
new_primEqNat0(Succ(x0), Zero)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_compare15(LT, GT)
new_compare15(GT, LT)
new_esEs24(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs5(Nothing, Just(x0), x1)
new_esEs36(x0, x1, ty_Double)
new_esEs39(x0, x1, ty_Ordering)
new_esEs34(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs9(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, app(ty_[], x2))
new_ltEs14(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs9(x0, x1, ty_Double)
new_lt23(x0, x1, app(ty_[], x2))
new_splitLT13(x0, x1, x2, x3, x4, x5, EQ, x6, x7)
new_ltEs17(x0, x1)
new_compare0(:(x0, x1), [], x2)
new_lt5(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs9(x0, x1, app(ty_Maybe, x2))
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_lt5(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs23(x0, x1, ty_Int)
new_splitGT15(x0, x1, x2, x3, x4, x5, x6, x7, LT, x8, x9)
new_primPlusInt(EmptyFM, x0, x1, EmptyFM, x2, x3)
new_esEs24(Right(x0), Right(x1), x2, ty_Bool)
new_primMinusNat1(Succ(x0), Succ(x1))
new_esEs8(x0, x1, ty_Int)
new_lt6(x0, x1, app(ty_[], x2))
new_esEs33(x0, x1, ty_Int)
new_mkVBalBranch3MkVBalBranch28(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, EQ, x12, x13)
new_esEs39(x0, x1, app(app(ty_Either, x2), x3))
new_esEs36(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs33(x0, x1, ty_Bool)
new_lt9(x0, x1, x2)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs35(x0, x1, ty_@0)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_lt23(x0, x1, ty_Int)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs39(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare31(Just(x0), Nothing, x1)
new_ltEs18(x0, x1, ty_Double)
new_splitLT15(x0, x1, x2, x3, x4, x5, x6, x7, LT, x8, x9)
new_primMinusNat1(Succ(x0), Zero)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_lt21(x0, x1, ty_Bool)
new_compare18(Float(x0, x1), Float(x2, x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_@0)
new_esEs8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs33(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Bool)
new_esEs24(Right(x0), Left(x1), x2, x3)
new_esEs24(Left(x0), Right(x1), x2, x3)
new_esEs35(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(x0, x1, ty_Double)
new_lt21(x0, x1, ty_Char)
new_mkVBalBranch3MkVBalBranch15(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, False, x11, x12)
new_primPlusInt(Branch(x0, x1, Pos(x2), x3, x4), x5, x6, EmptyFM, x7, x8)
new_esEs24(Right(x0), Right(x1), x2, ty_Char)
new_esEs36(x0, x1, app(ty_Ratio, x2))
new_esEs11(x0, x1, app(ty_Maybe, x2))
new_splitGT5(Branch(x0, x1, x2, x3, x4), x5, x6, x7, x8)
new_splitGT22(x0, x1, x2, x3, x4, x5, x6, x7, EQ, x8, x9)
new_primPlusInt(EmptyFM, x0, x1, Branch(x2, x3, Pos(x4), x5, x6), x7, x8)
new_primMulNat0(Succ(x0), Succ(x1))
new_splitLT16(x0, x1, x2, x3, LT, x4, x5)
new_esEs34(x0, x1, ty_Char)
new_esEs4(x0, x1, app(ty_[], x2))
new_esEs10(x0, x1, ty_@0)
new_esEs39(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_@0)
new_ltEs23(x0, x1, app(ty_Maybe, x2))
new_esEs35(x0, x1, app(ty_[], x2))
new_mkBalBranch6MkBalBranch4(x0, x1, x2, x3, False, x4, x5)
new_primEqNat0(Zero, Succ(x0))
new_lt23(x0, x1, ty_Char)
new_splitLT21(x0, x1, x2, x3, x4, x5, x6, x7, EQ, x8, x9)
new_lt20(x0, x1, ty_Char)
new_esEs34(x0, x1, app(app(ty_Either, x2), x3))
new_splitGT14(x0, x1, x2, x3, x4, x5)
new_esEs30(x0, x1, app(ty_[], x2))
new_esEs34(x0, x1, app(app(ty_@2, x2), x3))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_ltEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs33(x0, x1, ty_Char)
new_esEs32(x0, x1, ty_Integer)
new_splitGT17(x0, x1, x2, x3, GT, x4, x5)
new_ltEs24(x0, x1, ty_Int)
new_lt8(x0, x1)
new_esEs11(x0, x1, app(ty_[], x2))
new_lt6(x0, x1, ty_@0)
new_esEs35(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs31(x0, x1, app(ty_Maybe, x2))
new_esEs24(Right(x0), Right(x1), x2, ty_Int)
new_ltEs18(x0, x1, app(ty_[], x2))
new_esEs4(x0, x1, app(ty_Ratio, x2))
new_ltEs22(x0, x1, ty_@0)
new_esEs39(x0, x1, ty_Int)
new_esEs30(x0, x1, ty_@0)
new_mkBalBranch6MkBalBranch11(x0, x1, x2, x3, x4, x5, x6, Branch(x7, x8, x9, x10, x11), False, x12, x13)
new_ltEs6(GT, GT)
new_primPlusInt1(x0, Pos(x1))
new_esEs32(x0, x1, ty_Char)
new_ltEs18(x0, x1, ty_Int)
new_ltEs5(Just(x0), Just(x1), ty_Ordering)
new_esEs24(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs19(x0, x1, ty_Char)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs24(Right(x0), Right(x1), x2, ty_@0)
new_esEs26(x0, x1, ty_Int)
new_primCmpNat0(Zero, Zero)
new_asAs(False, x0)
new_ltEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_lt6(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs24(x0, x1, ty_@0)
new_ltEs19(x0, x1, ty_Int)
new_esEs34(x0, x1, ty_Int)
new_addToFM_C12(x0, x1, x2, x3, x4, x5, x6, x7, x8, GT, x9, x10)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_compare26(x0, x1, True, x2, x3)
new_mkVBalBranch3MkVBalBranch210(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, LT, x11, x12)
new_ltEs14(Left(x0), Left(x1), ty_Double, x2)
new_primPlusInt0(x0, Pos(x1))
new_esEs11(x0, x1, ty_Ordering)
new_mkBalBranch6MkBalBranch01(x0, x1, x2, x3, x4, Branch(x5, x6, x7, x8, x9), x10, x11, False, x12, x13)
new_ltEs14(Left(x0), Left(x1), ty_Char, x2)
new_ltEs22(x0, x1, ty_Double)
new_esEs18(Integer(x0), Integer(x1))
new_esEs7(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(x0, x1, ty_@0)
new_splitGT30(:(x0, x1), x2, x3, x4, x5, [], x6, x7)
new_splitLT30(:(x0, x1), x2, x3, x4, x5, :(x6, x7), x8, x9)
new_lt23(x0, x1, app(app(ty_Either, x2), x3))
new_mkVBalBranch3MkVBalBranch13(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, False, x12, x13)
new_ltEs19(x0, x1, ty_Float)
new_ltEs24(x0, x1, app(ty_[], x2))
new_esEs24(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_lt24(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkBalBranch6MkBalBranch5(x0, x1, x2, x3, x4, x5)
new_esEs23(Just(x0), Just(x1), ty_Char)
new_ltEs13(x0, x1)
new_compare15(LT, EQ)
new_compare15(EQ, LT)
new_lt6(x0, x1, app(ty_Maybe, x2))
new_compare9(@0, @0)
new_lt13(x0, x1)
new_esEs36(x0, x1, ty_Integer)
new_compare24(x0, x1, x2, x3, True, x4, x5)
new_mkBalBranch6MkBalBranch3(x0, x1, x2, EmptyFM, True, x3, x4)
new_ltEs18(x0, x1, ty_Float)
new_compare0([], :(x0, x1), x2)
new_lt18(x0, x1)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_compare8(Integer(x0), Integer(x1))
new_lt15(x0, x1)
new_mkVBalBranch0(x0, x1, Branch(x2, x3, Pos(Succ(x4)), x5, x6), Branch(x7, x8, x9, x10, x11), x12, x13)
new_compare7(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs8(x0, x1, ty_@0)
new_lt16(x0, x1, x2, x3)
new_esEs5(x0, x1, ty_Int)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_splitGT22(x0, x1, x2, x3, x4, x5, x6, x7, LT, x8, x9)
new_compare30(x0, x1, ty_Float)
new_splitLT17(x0, x1, x2, x3, x4, x5)
new_esEs27(x0, x1, ty_Ordering)
new_lt23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_splitGT16(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_esEs10(x0, x1, app(ty_Ratio, x2))
new_ltEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs32(x0, x1, ty_Float)
new_esEs36(x0, x1, ty_Ordering)
new_esEs9(x0, x1, ty_Bool)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_primMinusNat0(Succ(x0))
new_compare13(:%(x0, x1), :%(x2, x3), ty_Integer)
new_primCmpNat0(Succ(x0), Succ(x1))
new_ltEs23(x0, x1, ty_Char)
new_esEs39(x0, x1, ty_@0)
new_esEs15(Char(x0), Char(x1))
new_lt21(x0, x1, app(ty_Ratio, x2))
new_mkBalBranch6MkBalBranch11(x0, x1, x2, x3, x4, x5, x6, x7, True, x8, x9)
new_ltEs21(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpNat0(Zero, Succ(x0))
new_ltEs14(Right(x0), Right(x1), x2, ty_Ordering)
new_lt20(x0, x1, ty_Ordering)
new_compare111(x0, x1, x2, x3, True, x4, x5)
new_esEs5(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, app(ty_[], x2))
new_splitGT30(:(x0, x1), x2, x3, x4, x5, :(x6, x7), x8, x9)
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_addToFM_C22(x0, x1, x2, x3, x4, x5, x6, x7, x8, GT, x9, x10)
new_primCmpNat0(Succ(x0), Zero)
new_esEs34(x0, x1, ty_Double)
new_lt22(x0, x1, app(ty_Maybe, x2))
new_compare31(Nothing, Just(x0), x1)
new_compare26(x0, x1, False, x2, x3)
new_primPlusInt0(x0, Neg(x1))
new_esEs24(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs18(x0, x1, ty_Integer)
new_esEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt22(x0, x1, app(ty_Ratio, x2))
new_compare27(Left(x0), Left(x1), x2, x3)
new_mkBalBranch(x0, x1, x2, x3, x4, x5)
new_esEs23(Just(x0), Just(x1), ty_Ordering)
new_esEs10(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_esEs9(x0, x1, ty_Char)
new_esEs8(x0, x1, ty_Char)
new_ltEs14(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs35(x0, x1, ty_Int)
new_esEs8(x0, x1, app(ty_Ratio, x2))
new_lt5(x0, x1, app(ty_Maybe, x2))
new_compare27(Right(x0), Left(x1), x2, x3)
new_compare27(Left(x0), Right(x1), x2, x3)
new_esEs9(x0, x1, app(app(ty_@2, x2), x3))
new_addToFM_C21(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusInt2(Neg(x0), x1, x2, x3, x4, x5)
new_esEs26(x0, x1, ty_Integer)
new_esEs5(x0, x1, ty_Char)
new_esEs7(x0, x1, ty_Char)
new_mkVBalBranch3MkVBalBranch210(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, GT, x11, x12)
new_esEs24(Left(x0), Left(x1), ty_Float, x2)
new_splitGT5(EmptyFM, x0, x1, x2, x3)
new_splitGT4(EmptyFM, x0, x1)
new_compare14(x0, x1, x2, x3, x4, x5, True, x6, x7, x8)
new_esEs5(x0, x1, ty_Integer)
new_compare30(x0, x1, ty_Ordering)
new_primMulNat0(Zero, Succ(x0))
new_ltEs23(x0, x1, ty_Double)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_ltEs23(x0, x1, app(ty_[], x2))
new_mkVBalBranch3MkVBalBranch212(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, GT, x12, x13)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_splitLT21(x0, x1, x2, x3, x4, x5, x6, x7, GT, x8, x9)
new_primCompAux0(x0, GT)
new_ltEs14(Left(x0), Left(x1), ty_Integer, x2)
new_primPlusNat1(Zero, Succ(x0))
new_splitGT17(x0, x1, x2, x3, EQ, x4, x5)
new_esEs36(x0, x1, ty_Float)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_splitGT30([], x0, x1, x2, x3, :(x4, x5), x6, x7)
new_esEs9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs36(x0, x1, ty_@0)
new_ltEs16(False, False)
new_esEs16([], :(x0, x1), x2)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs24(x0, x1, app(ty_Ratio, x2))
new_mkVBalBranch3MkVBalBranch14(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, True, x12, x13)
new_mkVBalBranch3MkVBalBranch15(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, True, x11, x12)
new_esEs33(x0, x1, ty_Ordering)
new_esEs28(x0, x1, ty_@0)
new_ltEs20(x0, x1, ty_Ordering)
new_esEs11(x0, x1, ty_Float)
new_lt26(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs10(x0, x1, app(ty_Maybe, x2))
new_sizeFM1(EmptyFM, x0, x1)
new_mkVBalBranch0(x0, x1, EmptyFM, x2, x3, x4)

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: