YES 33.69 H-Termination proof of /home/matraf/haskell/eval_FullyBlown_Fast/FiniteMap.hs
H-Termination of the given Haskell-Program with start terms could successfully be proven:



↳ HASKELL
  ↳ LR

mainModule FiniteMap
  ((minusFM :: (Ord b, Ord c) => FiniteMap (Either b c) d  ->  FiniteMap (Either b c) a  ->  FiniteMap (Either b c) d) :: (Ord b, Ord c) => FiniteMap (Either b c) d  ->  FiniteMap (Either b c) a  ->  FiniteMap (Either b c) d)

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 (\old new ->new) fm key elt

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

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

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

  emptyFM :: FiniteMap a b
emptyFM = EmptyFM

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

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

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

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

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

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

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

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

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

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

  sIZE_RATIO :: Int
sIZE_RATIO = 5

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

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

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


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

is transformed to
mid_key10 (mid_key1,_) = mid_key1

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

is transformed to
mid_elt10 (_,mid_elt1) = mid_elt1

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

is transformed to
mid_key20 (mid_key2,_) = mid_key2

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

is transformed to
mid_elt20 (_,mid_elt2) = mid_elt2

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

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

The following Lambda expression
\oldnew→new

is transformed to
addToFM0 old new = new



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR

mainModule FiniteMap
  ((minusFM :: (Ord b, Ord d) => FiniteMap (Either d b) a  ->  FiniteMap (Either d b) c  ->  FiniteMap (Either d b) a) :: (Ord d, Ord b) => FiniteMap (Either d b) a  ->  FiniteMap (Either d b) c  ->  FiniteMap (Either d 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_r) new_key new_elt 
 | new_key < key = 
mkBalBranch key elt (addToFM_C combiner fm_l new_key new_elt) fm_r
 | new_key > key = 
mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt)
 | otherwise = 
Branch new_key (combiner elt new_elt) size fm_l fm_r

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

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

  emptyFM :: FiniteMap a b
emptyFM = EmptyFM

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

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

  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_r) = foldFM k (k key elt (foldFM k z fm_r)) fm_l

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

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

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

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

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

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

  sIZE_RATIO :: Int
sIZE_RATIO = 5

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

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

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


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
  ((minusFM :: (Ord a, Ord b) => FiniteMap (Either b a) d  ->  FiniteMap (Either b a) c  ->  FiniteMap (Either b a) d) :: (Ord b, Ord a) => FiniteMap (Either b a) d  ->  FiniteMap (Either b a) c  ->  FiniteMap (Either b a) d)

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

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

  
addToFM0 old new = new

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

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

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

  emptyFM :: FiniteMap a b
emptyFM = EmptyFM

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

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

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

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

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

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

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

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

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

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

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

  sIZE_RATIO :: Int
sIZE_RATIO = 5

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

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

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


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
  ((minusFM :: (Ord c, Ord a) => FiniteMap (Either a c) d  ->  FiniteMap (Either a c) b  ->  FiniteMap (Either a c) d) :: (Ord c, Ord a) => FiniteMap (Either a c) d  ->  FiniteMap (Either a c) b  ->  FiniteMap (Either a c) d)

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 = unitFM key elt
addToFM_C combiner (Branch key elt size fm_l fm_r) new_key new_elt 
 | new_key < key = 
mkBalBranch key elt (addToFM_C combiner fm_l new_key new_elt) fm_r
 | new_key > key = 
mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt)
 | otherwise = 
Branch new_key (combiner elt new_elt) size fm_l fm_r

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

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

  emptyFM :: FiniteMap b a
emptyFM = EmptyFM

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

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

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

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

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

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

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

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

  sIZE_RATIO :: Int
sIZE_RATIO = 5

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

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

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


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

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

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

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

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

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

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

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



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

mainModule FiniteMap
  ((minusFM :: (Ord b, Ord d) => FiniteMap (Either b d) c  ->  FiniteMap (Either b d) a  ->  FiniteMap (Either b d) c) :: (Ord d, Ord b) => FiniteMap (Either b d) c  ->  FiniteMap (Either b d) a  ->  FiniteMap (Either b d) c)

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

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

  
addToFM0 old new = new

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

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

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

  emptyFM :: FiniteMap b a
emptyFM = EmptyFM

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

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

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

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

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

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

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

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

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

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

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

  sIZE_RATIO :: Int
sIZE_RATIO = 5

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

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

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


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

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

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)

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

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

splitLT4 EmptyFM split_key = emptyFM
splitLT4 wzx wzy = splitLT3 wzx wzy

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

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

splitGT0 key elt xy fm_l fm_r split_key True = fm_r

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

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

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

splitGT4 EmptyFM split_key = emptyFM
splitGT4 xuv xuw = splitGT3 xuv xuw

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

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

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

glueVBal4 fm1 EmptyFM = fm1
glueVBal4 xvu xvv = glueVBal3 xvu xvv

glueVBal5 EmptyFM fm2 = fm2
glueVBal5 xvx xvy = glueVBal4 xvx xvy

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

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

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

mkVBalBranch4 key elt fm_l EmptyFM = addToFM fm_l key elt
mkVBalBranch4 xww xwx xwy xwz = mkVBalBranch3 xww xwx xwy xwz

mkVBalBranch5 key elt EmptyFM fm_r = addToFM fm_r key elt
mkVBalBranch5 xxv xxw xxx xxy = mkVBalBranch4 xxv xxw xxx xxy

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

addToFM_C4 combiner EmptyFM key elt = unitFM key elt
addToFM_C4 xyx xyy xyz xzu = addToFM_C3 xyx xyy xyz xzu

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

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

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

glueBal3 fm1 EmptyFM = fm1
glueBal3 xzw xzx = glueBal2 xzw xzx

glueBal4 EmptyFM fm2 = fm2
glueBal4 xzz yuu = glueBal3 xzz yuu

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 yuv = gcd'2 x yuv
gcd' x y = gcd'0 x y

gcd'0 x y = gcd' y (x `rem` y)

gcd'1 True x yuv = x
gcd'1 yuw yux yuy = gcd'0 yux yuy

gcd'2 x yuv = gcd'1 (yuv == 0) x yuv
gcd'2 yuz yvu = gcd'0 yuz yvu

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 yvv yvw = gcd3 yvv yvw
gcd x y = gcd0 x y

gcd0 x y = 
gcd' (abs x) (abs y)
where 
gcd' x yuv = gcd'2 x yuv
gcd' x y = gcd'0 x y
gcd'0 x y = gcd' y (x `rem` y)
gcd'1 True x yuv = x
gcd'1 yuw yux yuy = gcd'0 yux yuy
gcd'2 x yuv = gcd'1 (yuv == 0) x yuv
gcd'2 yuz yvu = gcd'0 yuz yvu

gcd1 True yvv yvw = error []
gcd1 yvx yvy yvz = gcd0 yvy yvz

gcd2 True yvv yvw = gcd1 (yvw == 0) yvv yvw
gcd2 ywu ywv yww = gcd0 ywv yww

gcd3 yvv yvw = gcd2 (yvv == 0) yvv yvw
gcd3 ywx ywy = gcd0 ywx ywy

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
  ((minusFM :: (Ord c, Ord a) => FiniteMap (Either c a) b  ->  FiniteMap (Either c a) d  ->  FiniteMap (Either c a) b) :: (Ord a, Ord c) => FiniteMap (Either c a) b  ->  FiniteMap (Either c a) d  ->  FiniteMap (Either c 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 a b) where 
   
(==) fm_1 fm_2 = sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2

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

  
addToFM0 old new = new

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

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

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

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

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

  
addToFM_C4 combiner EmptyFM key elt = unitFM key elt
addToFM_C4 xyx xyy xyz xzu = addToFM_C3 xyx xyy xyz xzu

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

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

  emptyFM :: FiniteMap b a
emptyFM = EmptyFM

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

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

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

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

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

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

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

  
glueBal3 fm1 EmptyFM = fm1
glueBal3 xzw xzx = glueBal2 xzw xzx

  
glueBal4 EmptyFM fm2 = fm2
glueBal4 xzz yuu = glueBal3 xzz yuu

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

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

  
glueVBal4 fm1 EmptyFM = fm1
glueVBal4 xvu xvv = glueVBal3 xvu xvv

  
glueVBal5 EmptyFM fm2 = fm2
glueVBal5 xvx xvy = glueVBal4 xvx xvy

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

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

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

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

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

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

  
mkVBalBranch4 key elt fm_l EmptyFM = addToFM fm_l key elt
mkVBalBranch4 xww xwx xwy xwz = mkVBalBranch3 xww xwx xwy xwz

  
mkVBalBranch5 key elt EmptyFM fm_r = addToFM fm_r key elt
mkVBalBranch5 xxv xxw xxx xxy = mkVBalBranch4 xxv xxw xxx xxy

  sIZE_RATIO :: Int
sIZE_RATIO = 5

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

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

  
splitGT0 key elt xy fm_l fm_r split_key True = fm_r

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

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

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

  
splitGT4 EmptyFM split_key = emptyFM
splitGT4 xuv xuw = splitGT3 xuv xuw

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

  
splitLT0 key elt xx fm_l fm_r split_key True = fm_l

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

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

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

  
splitLT4 EmptyFM split_key = emptyFM
splitLT4 wzx wzy = splitLT3 wzx wzy

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


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

are unpacked to the following functions on top level
mkBalBranch6MkBalBranch3 ywz yxu yxv yxw key elt fm_L fm_R True = mkBalBranch6MkBalBranch1 ywz yxu yxv yxw fm_L fm_R fm_L
mkBalBranch6MkBalBranch3 ywz yxu yxv yxw key elt fm_L fm_R False = mkBalBranch6MkBalBranch2 ywz yxu yxv yxw key elt fm_L fm_R otherwise

mkBalBranch6Single_L ywz yxu yxv yxw fm_l (Branch key_r elt_r vyy fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 ywz yxu fm_l fm_rl) fm_rr

mkBalBranch6MkBalBranch11 ywz yxu yxv yxw fm_L fm_R vxw vxx vxy fm_ll fm_lr True = mkBalBranch6Single_R ywz yxu yxv yxw fm_L fm_R
mkBalBranch6MkBalBranch11 ywz yxu yxv yxw fm_L fm_R vxw vxx vxy fm_ll fm_lr False = mkBalBranch6MkBalBranch10 ywz yxu yxv yxw fm_L fm_R vxw vxx vxy fm_ll fm_lr otherwise

mkBalBranch6MkBalBranch1 ywz yxu yxv yxw fm_L fm_R (Branch vxw vxx vxy fm_ll fm_lr) = mkBalBranch6MkBalBranch12 ywz yxu yxv yxw fm_L fm_R (Branch vxw vxx vxy fm_ll fm_lr)

mkBalBranch6MkBalBranch02 ywz yxu yxv yxw fm_L fm_R (Branch vyv vyw vyx fm_rl fm_rr) = mkBalBranch6MkBalBranch01 ywz yxu yxv yxw fm_L fm_R vyv vyw vyx fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr)

mkBalBranch6MkBalBranch12 ywz yxu yxv yxw fm_L fm_R (Branch vxw vxx vxy fm_ll fm_lr) = mkBalBranch6MkBalBranch11 ywz yxu yxv yxw fm_L fm_R vxw vxx vxy fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll)

mkBalBranch6MkBalBranch00 ywz yxu yxv yxw fm_L fm_R vyv vyw vyx fm_rl fm_rr True = mkBalBranch6Double_L ywz yxu yxv yxw fm_L fm_R

mkBalBranch6Double_L ywz yxu yxv yxw fm_l (Branch key_r elt_r vxz (Branch key_rl elt_rl vyu fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 ywz yxu fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr)

mkBalBranch6Size_l ywz yxu yxv yxw = sizeFM yxv

mkBalBranch6MkBalBranch4 ywz yxu yxv yxw key elt fm_L fm_R True = mkBalBranch6MkBalBranch0 ywz yxu yxv yxw fm_L fm_R fm_R
mkBalBranch6MkBalBranch4 ywz yxu yxv yxw key elt fm_L fm_R False = mkBalBranch6MkBalBranch3 ywz yxu yxv yxw key elt fm_L fm_R (mkBalBranch6Size_l ywz yxu yxv yxw > sIZE_RATIO * mkBalBranch6Size_r ywz yxu yxv yxw)

mkBalBranch6MkBalBranch5 ywz yxu yxv yxw key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R
mkBalBranch6MkBalBranch5 ywz yxu yxv yxw key elt fm_L fm_R False = mkBalBranch6MkBalBranch4 ywz yxu yxv yxw key elt fm_L fm_R (mkBalBranch6Size_r ywz yxu yxv yxw > sIZE_RATIO * mkBalBranch6Size_l ywz yxu yxv yxw)

mkBalBranch6MkBalBranch2 ywz yxu yxv yxw key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R

mkBalBranch6Size_r ywz yxu yxv yxw = sizeFM yxw

mkBalBranch6Double_R ywz yxu yxv yxw (Branch key_l elt_l vxu fm_ll (Branch key_lr elt_lr vxv fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 ywz yxu fm_lrr fm_r)

mkBalBranch6MkBalBranch10 ywz yxu yxv yxw fm_L fm_R vxw vxx vxy fm_ll fm_lr True = mkBalBranch6Double_R ywz yxu yxv yxw fm_L fm_R

mkBalBranch6MkBalBranch0 ywz yxu yxv yxw fm_L fm_R (Branch vyv vyw vyx fm_rl fm_rr) = mkBalBranch6MkBalBranch02 ywz yxu yxv yxw fm_L fm_R (Branch vyv vyw vyx fm_rl fm_rr)

mkBalBranch6Single_R ywz yxu yxv yxw (Branch key_l elt_l vwz fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 ywz yxu fm_lr fm_r)

mkBalBranch6MkBalBranch01 ywz yxu yxv yxw fm_L fm_R vyv vyw vyx fm_rl fm_rr True = mkBalBranch6Single_L ywz yxu yxv yxw fm_L fm_R
mkBalBranch6MkBalBranch01 ywz yxu yxv yxw fm_L fm_R vyv vyw vyx fm_rl fm_rr False = mkBalBranch6MkBalBranch00 ywz yxu yxv yxw fm_L fm_R vyv vyw vyx fm_rl fm_rr otherwise

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

are unpacked to the following functions on top level
glueVBal3Size_r yxx yxy yxz yyu yyv yyw yyx yyy yyz yzu = sizeFM (Branch yxx yxy yxz yyu yyv)

glueVBal3GlueVBal2 yxx yxy yxz yyu yyv yyw yyx yyy yyz yzu yy yz zu zv zw zy zz vuu vuv vuw True = mkBalBranch zy zz (glueVBal (Branch yy yz zu zv zw) vuv) vuw
glueVBal3GlueVBal2 yxx yxy yxz yyu yyv yyw yyx yyy yyz yzu yy yz zu zv zw zy zz vuu vuv vuw False = glueVBal3GlueVBal1 yxx yxy yxz yyu yyv yyw yyx yyy yyz yzu yy yz zu zv zw zy zz vuu vuv vuw (sIZE_RATIO * glueVBal3Size_r yxx yxy yxz yyu yyv yyw yyx yyy yyz yzu < glueVBal3Size_l yxx yxy yxz yyu yyv yyw yyx yyy yyz yzu)

glueVBal3GlueVBal1 yxx yxy yxz yyu yyv yyw yyx yyy yyz yzu yy yz zu zv zw zy zz vuu vuv vuw True = mkBalBranch yy yz zv (glueVBal zw (Branch zy zz vuu vuv vuw))
glueVBal3GlueVBal1 yxx yxy yxz yyu yyv yyw yyx yyy yyz yzu yy yz zu zv zw zy zz vuu vuv vuw False = glueVBal3GlueVBal0 yxx yxy yxz yyu yyv yyw yyx yyy yyz yzu yy yz zu zv zw zy zz vuu vuv vuw otherwise

glueVBal3GlueVBal0 yxx yxy yxz yyu yyv yyw yyx yyy yyz yzu yy yz zu zv zw zy zz vuu vuv vuw True = glueBal (Branch yy yz zu zv zw) (Branch zy zz vuu vuv vuw)

glueVBal3Size_l yxx yxy yxz yyu yyv yyw yyx yyy yyz yzu = sizeFM (Branch yyw yyx yyy yyz yzu)

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

are unpacked to the following functions on top level
minusFMLts yzv yzw = splitLT yzv yzw

minusFMGts yzv yzw = splitGT yzv yzw

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
mkBranchUnbox yzx yzy yzz x = x

mkBranchRight_ok yzx yzy yzz = mkBranchRight_ok0 yzx yzy yzz yzx yzy yzx

mkBranchBalance_ok yzx yzy yzz = True

mkBranchRight_ok0 yzx yzy yzz fm_r key EmptyFM = True
mkBranchRight_ok0 yzx yzy yzz fm_r key (Branch right_key wu wv ww wx) = key < mkBranchRight_ok0Smallest_right_key fm_r

mkBranchLeft_ok0 yzx yzy yzz fm_l key EmptyFM = True
mkBranchLeft_ok0 yzx yzy yzz fm_l key (Branch left_key vw vx vy vz) = mkBranchLeft_ok0Biggest_left_key fm_l < key

mkBranchRight_size yzx yzy yzz = sizeFM yzx

mkBranchLeft_size yzx yzy yzz = sizeFM yzz

mkBranchLeft_ok yzx yzy yzz = mkBranchLeft_ok0 yzx yzy yzz yzz yzy yzz

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 zuu zuv zuw zux = Branch zuu zuv (mkBranchUnbox zuw zuu zux (1 + mkBranchLeft_size zuw zuu zux + mkBranchRight_size zuw zuu zux)) zux zuw

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

are unpacked to the following functions on top level
glueBal2Mid_key10 zuy zuz (mid_key1,vzz) = mid_key1

glueBal2Mid_key2 zuy zuz = glueBal2Mid_key20 zuy zuz (glueBal2Vv3 zuy zuz)

glueBal2GlueBal0 zuy zuz fm1 fm2 True = mkBalBranch (glueBal2Mid_key1 zuy zuz) (glueBal2Mid_elt1 zuy zuz) (deleteMax fm1) fm2

glueBal2Mid_elt2 zuy zuz = glueBal2Mid_elt20 zuy zuz (glueBal2Vv3 zuy zuz)

glueBal2GlueBal1 zuy zuz fm1 fm2 True = mkBalBranch (glueBal2Mid_key2 zuy zuz) (glueBal2Mid_elt2 zuy zuz) fm1 (deleteMin fm2)
glueBal2GlueBal1 zuy zuz fm1 fm2 False = glueBal2GlueBal0 zuy zuz fm1 fm2 otherwise

glueBal2Mid_elt1 zuy zuz = glueBal2Mid_elt10 zuy zuz (glueBal2Vv2 zuy zuz)

glueBal2Mid_elt20 zuy zuz (vzy,mid_elt2) = mid_elt2

glueBal2Mid_elt10 zuy zuz (vzx,mid_elt1) = mid_elt1

glueBal2Vv2 zuy zuz = findMax zuy

glueBal2Mid_key1 zuy zuz = glueBal2Mid_key10 zuy zuz (glueBal2Vv2 zuy zuz)

glueBal2Mid_key20 zuy zuz (mid_key2,wuu) = mid_key2

glueBal2Vv3 zuy zuz = findMin zuz

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

are unpacked to the following functions on top level
mkVBalBranch3Size_r zvu zvv zvw zvx zvy zvz zwu zwv zww zwx = sizeFM (Branch zvu zvv zvw zvx zvy)

mkVBalBranch3MkVBalBranch1 zvu zvv zvw zvx zvy zvz zwu zwv zww zwx key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww True = mkBalBranch vuy vuz vvv (mkVBalBranch key elt vvw (Branch vvy vvz vwu vwv vww))
mkVBalBranch3MkVBalBranch1 zvu zvv zvw zvx zvy zvz zwu zwv zww zwx key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww False = mkVBalBranch3MkVBalBranch0 zvu zvv zvw zvx zvy zvz zwu zwv zww zwx key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww otherwise

mkVBalBranch3MkVBalBranch2 zvu zvv zvw zvx zvy zvz zwu zwv zww zwx key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww True = mkBalBranch vvy vvz (mkVBalBranch key elt (Branch vuy vuz vvu vvv vvw) vwv) vww
mkVBalBranch3MkVBalBranch2 zvu zvv zvw zvx zvy zvz zwu zwv zww zwx key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww False = mkVBalBranch3MkVBalBranch1 zvu zvv zvw zvx zvy zvz zwu zwv zww zwx key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww (sIZE_RATIO * mkVBalBranch3Size_r zvu zvv zvw zvx zvy zvz zwu zwv zww zwx < mkVBalBranch3Size_l zvu zvv zvw zvx zvy zvz zwu zwv zww zwx)

mkVBalBranch3MkVBalBranch0 zvu zvv zvw zvx zvy zvz zwu zwv zww zwx key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww True = mkBranch 13 key elt (Branch vuy vuz vvu vvv vvw) (Branch vvy vvz vwu vwv vww)

mkVBalBranch3Size_l zvu zvv zvw zvx zvy zvz zwu zwv zww zwx = sizeFM (Branch zvz zwu zwv zww zwx)

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 zwy = fst (findMin zwy)

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 zwz = fst (findMax zwz)

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 zxu zxv x y True = x `quot` reduce2D zxu zxv :% (y `quot` reduce2D zxu zxv)

reduce2Reduce1 zxu zxv x y True = error []
reduce2Reduce1 zxu zxv x y False = reduce2Reduce0 zxu zxv x y otherwise

reduce2D zxu zxv = gcd zxu zxv

The bindings of the following Let/Where expression
gcd' (abs x) (abs y)
where 
gcd' x yuv = gcd'2 x yuv
gcd' x y = gcd'0 x y
gcd'0 x y = gcd' y (x `rem` y)
gcd'1 True x yuv = x
gcd'1 yuw yux yuy = gcd'0 yux yuy
gcd'2 x yuv = gcd'1 (yuv == 0) x yuv
gcd'2 yuz yvu = gcd'0 yuz yvu

are unpacked to the following functions on top level
gcd0Gcd' x yuv = gcd0Gcd'2 x yuv
gcd0Gcd' x y = gcd0Gcd'0 x y

gcd0Gcd'2 x yuv = gcd0Gcd'1 (yuv == 0) x yuv
gcd0Gcd'2 yuz yvu = gcd0Gcd'0 yuz yvu

gcd0Gcd'1 True x yuv = x
gcd0Gcd'1 yuw yux yuy = gcd0Gcd'0 yux yuy

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



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

mainModule FiniteMap
  ((minusFM :: (Ord c, Ord b) => FiniteMap (Either b c) a  ->  FiniteMap (Either b c) d  ->  FiniteMap (Either b c) a) :: (Ord b, Ord c) => FiniteMap (Either b c) a  ->  FiniteMap (Either b c) d  ->  FiniteMap (Either b c) a)

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

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

  
addToFM0 old new = new

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

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

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

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

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

  
addToFM_C4 combiner EmptyFM key elt = unitFM key elt
addToFM_C4 xyx xyy xyz xzu = addToFM_C3 xyx xyy xyz xzu

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

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

  emptyFM :: FiniteMap a b
emptyFM = EmptyFM

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

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

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

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

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

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

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

  
glueBal2GlueBal0 zuy zuz fm1 fm2 True = mkBalBranch (glueBal2Mid_key1 zuy zuz) (glueBal2Mid_elt1 zuy zuz) (deleteMax fm1) fm2

  
glueBal2GlueBal1 zuy zuz fm1 fm2 True = mkBalBranch (glueBal2Mid_key2 zuy zuz) (glueBal2Mid_elt2 zuy zuz) fm1 (deleteMin fm2)
glueBal2GlueBal1 zuy zuz fm1 fm2 False = glueBal2GlueBal0 zuy zuz fm1 fm2 otherwise

  
glueBal2Mid_elt1 zuy zuz = glueBal2Mid_elt10 zuy zuz (glueBal2Vv2 zuy zuz)

  
glueBal2Mid_elt10 zuy zuz (vzx,mid_elt1) = mid_elt1

  
glueBal2Mid_elt2 zuy zuz = glueBal2Mid_elt20 zuy zuz (glueBal2Vv3 zuy zuz)

  
glueBal2Mid_elt20 zuy zuz (vzy,mid_elt2) = mid_elt2

  
glueBal2Mid_key1 zuy zuz = glueBal2Mid_key10 zuy zuz (glueBal2Vv2 zuy zuz)

  
glueBal2Mid_key10 zuy zuz (mid_key1,vzz) = mid_key1

  
glueBal2Mid_key2 zuy zuz = glueBal2Mid_key20 zuy zuz (glueBal2Vv3 zuy zuz)

  
glueBal2Mid_key20 zuy zuz (mid_key2,wuu) = mid_key2

  
glueBal2Vv2 zuy zuz = findMax zuy

  
glueBal2Vv3 zuy zuz = findMin zuz

  
glueBal3 fm1 EmptyFM = fm1
glueBal3 xzw xzx = glueBal2 xzw xzx

  
glueBal4 EmptyFM fm2 = fm2
glueBal4 xzz yuu = glueBal3 xzz yuu

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

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

  
glueVBal3GlueVBal0 yxx yxy yxz yyu yyv yyw yyx yyy yyz yzu yy yz zu zv zw zy zz vuu vuv vuw True = glueBal (Branch yy yz zu zv zw) (Branch zy zz vuu vuv vuw)

  
glueVBal3GlueVBal1 yxx yxy yxz yyu yyv yyw yyx yyy yyz yzu yy yz zu zv zw zy zz vuu vuv vuw True = mkBalBranch yy yz zv (glueVBal zw (Branch zy zz vuu vuv vuw))
glueVBal3GlueVBal1 yxx yxy yxz yyu yyv yyw yyx yyy yyz yzu yy yz zu zv zw zy zz vuu vuv vuw False = glueVBal3GlueVBal0 yxx yxy yxz yyu yyv yyw yyx yyy yyz yzu yy yz zu zv zw zy zz vuu vuv vuw otherwise

  
glueVBal3GlueVBal2 yxx yxy yxz yyu yyv yyw yyx yyy yyz yzu yy yz zu zv zw zy zz vuu vuv vuw True = mkBalBranch zy zz (glueVBal (Branch yy yz zu zv zw) vuv) vuw
glueVBal3GlueVBal2 yxx yxy yxz yyu yyv yyw yyx yyy yyz yzu yy yz zu zv zw zy zz vuu vuv vuw False = glueVBal3GlueVBal1 yxx yxy yxz yyu yyv yyw yyx yyy yyz yzu yy yz zu zv zw zy zz vuu vuv vuw (sIZE_RATIO * glueVBal3Size_r yxx yxy yxz yyu yyv yyw yyx yyy yyz yzu < glueVBal3Size_l yxx yxy yxz yyu yyv yyw yyx yyy yyz yzu)

  
glueVBal3Size_l yxx yxy yxz yyu yyv yyw yyx yyy yyz yzu = sizeFM (Branch yyw yyx yyy yyz yzu)

  
glueVBal3Size_r yxx yxy yxz yyu yyv yyw yyx yyy yyz yzu = sizeFM (Branch yxx yxy yxz yyu yyv)

  
glueVBal4 fm1 EmptyFM = fm1
glueVBal4 xvu xvv = glueVBal3 xvu xvv

  
glueVBal5 EmptyFM fm2 = fm2
glueVBal5 xvx xvy = glueVBal4 xvx xvy

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

  
minusFMGts yzv yzw = splitGT yzv yzw

  
minusFMLts yzv yzw = splitLT yzv yzw

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

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

  
mkBalBranch6Double_L ywz yxu yxv yxw fm_l (Branch key_r elt_r vxz (Branch key_rl elt_rl vyu fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 ywz yxu fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr)

  
mkBalBranch6Double_R ywz yxu yxv yxw (Branch key_l elt_l vxu fm_ll (Branch key_lr elt_lr vxv fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 ywz yxu fm_lrr fm_r)

  
mkBalBranch6MkBalBranch0 ywz yxu yxv yxw fm_L fm_R (Branch vyv vyw vyx fm_rl fm_rr) = mkBalBranch6MkBalBranch02 ywz yxu yxv yxw fm_L fm_R (Branch vyv vyw vyx fm_rl fm_rr)

  
mkBalBranch6MkBalBranch00 ywz yxu yxv yxw fm_L fm_R vyv vyw vyx fm_rl fm_rr True = mkBalBranch6Double_L ywz yxu yxv yxw fm_L fm_R

  
mkBalBranch6MkBalBranch01 ywz yxu yxv yxw fm_L fm_R vyv vyw vyx fm_rl fm_rr True = mkBalBranch6Single_L ywz yxu yxv yxw fm_L fm_R
mkBalBranch6MkBalBranch01 ywz yxu yxv yxw fm_L fm_R vyv vyw vyx fm_rl fm_rr False = mkBalBranch6MkBalBranch00 ywz yxu yxv yxw fm_L fm_R vyv vyw vyx fm_rl fm_rr otherwise

  
mkBalBranch6MkBalBranch02 ywz yxu yxv yxw fm_L fm_R (Branch vyv vyw vyx fm_rl fm_rr) = mkBalBranch6MkBalBranch01 ywz yxu yxv yxw fm_L fm_R vyv vyw vyx fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr)

  
mkBalBranch6MkBalBranch1 ywz yxu yxv yxw fm_L fm_R (Branch vxw vxx vxy fm_ll fm_lr) = mkBalBranch6MkBalBranch12 ywz yxu yxv yxw fm_L fm_R (Branch vxw vxx vxy fm_ll fm_lr)

  
mkBalBranch6MkBalBranch10 ywz yxu yxv yxw fm_L fm_R vxw vxx vxy fm_ll fm_lr True = mkBalBranch6Double_R ywz yxu yxv yxw fm_L fm_R

  
mkBalBranch6MkBalBranch11 ywz yxu yxv yxw fm_L fm_R vxw vxx vxy fm_ll fm_lr True = mkBalBranch6Single_R ywz yxu yxv yxw fm_L fm_R
mkBalBranch6MkBalBranch11 ywz yxu yxv yxw fm_L fm_R vxw vxx vxy fm_ll fm_lr False = mkBalBranch6MkBalBranch10 ywz yxu yxv yxw fm_L fm_R vxw vxx vxy fm_ll fm_lr otherwise

  
mkBalBranch6MkBalBranch12 ywz yxu yxv yxw fm_L fm_R (Branch vxw vxx vxy fm_ll fm_lr) = mkBalBranch6MkBalBranch11 ywz yxu yxv yxw fm_L fm_R vxw vxx vxy fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll)

  
mkBalBranch6MkBalBranch2 ywz yxu yxv yxw key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R

  
mkBalBranch6MkBalBranch3 ywz yxu yxv yxw key elt fm_L fm_R True = mkBalBranch6MkBalBranch1 ywz yxu yxv yxw fm_L fm_R fm_L
mkBalBranch6MkBalBranch3 ywz yxu yxv yxw key elt fm_L fm_R False = mkBalBranch6MkBalBranch2 ywz yxu yxv yxw key elt fm_L fm_R otherwise

  
mkBalBranch6MkBalBranch4 ywz yxu yxv yxw key elt fm_L fm_R True = mkBalBranch6MkBalBranch0 ywz yxu yxv yxw fm_L fm_R fm_R
mkBalBranch6MkBalBranch4 ywz yxu yxv yxw key elt fm_L fm_R False = mkBalBranch6MkBalBranch3 ywz yxu yxv yxw key elt fm_L fm_R (mkBalBranch6Size_l ywz yxu yxv yxw > sIZE_RATIO * mkBalBranch6Size_r ywz yxu yxv yxw)

  
mkBalBranch6MkBalBranch5 ywz yxu yxv yxw key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R
mkBalBranch6MkBalBranch5 ywz yxu yxv yxw key elt fm_L fm_R False = mkBalBranch6MkBalBranch4 ywz yxu yxv yxw key elt fm_L fm_R (mkBalBranch6Size_r ywz yxu yxv yxw > sIZE_RATIO * mkBalBranch6Size_l ywz yxu yxv yxw)

  
mkBalBranch6Single_L ywz yxu yxv yxw fm_l (Branch key_r elt_r vyy fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 ywz yxu fm_l fm_rl) fm_rr

  
mkBalBranch6Single_R ywz yxu yxv yxw (Branch key_l elt_l vwz fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 ywz yxu fm_lr fm_r)

  
mkBalBranch6Size_l ywz yxu yxv yxw = sizeFM yxv

  
mkBalBranch6Size_r ywz yxu yxv yxw = sizeFM yxw

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

  
mkBranchBalance_ok yzx yzy yzz = True

  
mkBranchLeft_ok yzx yzy yzz = mkBranchLeft_ok0 yzx yzy yzz yzz yzy yzz

  
mkBranchLeft_ok0 yzx yzy yzz fm_l key EmptyFM = True
mkBranchLeft_ok0 yzx yzy yzz fm_l key (Branch left_key vw vx vy vz) = mkBranchLeft_ok0Biggest_left_key fm_l < key

  
mkBranchLeft_ok0Biggest_left_key zwz = fst (findMax zwz)

  
mkBranchLeft_size yzx yzy yzz = sizeFM yzz

  
mkBranchResult zuu zuv zuw zux = Branch zuu zuv (mkBranchUnbox zuw zuu zux (1 + mkBranchLeft_size zuw zuu zux + mkBranchRight_size zuw zuu zux)) zux zuw

  
mkBranchRight_ok yzx yzy yzz = mkBranchRight_ok0 yzx yzy yzz yzx yzy yzx

  
mkBranchRight_ok0 yzx yzy yzz fm_r key EmptyFM = True
mkBranchRight_ok0 yzx yzy yzz fm_r key (Branch right_key wu wv ww wx) = key < mkBranchRight_ok0Smallest_right_key fm_r

  
mkBranchRight_ok0Smallest_right_key zwy = fst (findMin zwy)

  
mkBranchRight_size yzx yzy yzz = sizeFM yzx

  mkBranchUnbox :: Ord a =>  ->  (FiniteMap a b) ( ->  a ( ->  (FiniteMap a b) (Int  ->  Int)))
mkBranchUnbox yzx yzy yzz x = x

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

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

  
mkVBalBranch3MkVBalBranch0 zvu zvv zvw zvx zvy zvz zwu zwv zww zwx key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww True = mkBranch 13 key elt (Branch vuy vuz vvu vvv vvw) (Branch vvy vvz vwu vwv vww)

  
mkVBalBranch3MkVBalBranch1 zvu zvv zvw zvx zvy zvz zwu zwv zww zwx key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww True = mkBalBranch vuy vuz vvv (mkVBalBranch key elt vvw (Branch vvy vvz vwu vwv vww))
mkVBalBranch3MkVBalBranch1 zvu zvv zvw zvx zvy zvz zwu zwv zww zwx key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww False = mkVBalBranch3MkVBalBranch0 zvu zvv zvw zvx zvy zvz zwu zwv zww zwx key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww otherwise

  
mkVBalBranch3MkVBalBranch2 zvu zvv zvw zvx zvy zvz zwu zwv zww zwx key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww True = mkBalBranch vvy vvz (mkVBalBranch key elt (Branch vuy vuz vvu vvv vvw) vwv) vww
mkVBalBranch3MkVBalBranch2 zvu zvv zvw zvx zvy zvz zwu zwv zww zwx key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww False = mkVBalBranch3MkVBalBranch1 zvu zvv zvw zvx zvy zvz zwu zwv zww zwx key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww (sIZE_RATIO * mkVBalBranch3Size_r zvu zvv zvw zvx zvy zvz zwu zwv zww zwx < mkVBalBranch3Size_l zvu zvv zvw zvx zvy zvz zwu zwv zww zwx)

  
mkVBalBranch3Size_l zvu zvv zvw zvx zvy zvz zwu zwv zww zwx = sizeFM (Branch zvz zwu zwv zww zwx)

  
mkVBalBranch3Size_r zvu zvv zvw zvx zvy zvz zwu zwv zww zwx = sizeFM (Branch zvu zvv zvw zvx zvy)

  
mkVBalBranch4 key elt fm_l EmptyFM = addToFM fm_l key elt
mkVBalBranch4 xww xwx xwy xwz = mkVBalBranch3 xww xwx xwy xwz

  
mkVBalBranch5 key elt EmptyFM fm_r = addToFM fm_r key elt
mkVBalBranch5 xxv xxw xxx xxy = mkVBalBranch4 xxv xxw xxx xxy

  sIZE_RATIO :: Int
sIZE_RATIO = 5

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

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

  
splitGT0 key elt xy fm_l fm_r split_key True = fm_r

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

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

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

  
splitGT4 EmptyFM split_key = emptyFM
splitGT4 xuv xuw = splitGT3 xuv xuw

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

  
splitLT0 key elt xx fm_l fm_r split_key True = fm_l

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

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

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

  
splitLT4 EmptyFM split_key = emptyFM
splitLT4 wzx wzy = splitLT3 wzx wzy

  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
  (minusFM :: (Ord a, Ord d) => FiniteMap (Either a d) c  ->  FiniteMap (Either a d) b  ->  FiniteMap (Either a d) c)

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

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

  
addToFM0 old new = new

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

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

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

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

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

  
addToFM_C4 combiner EmptyFM key elt = unitFM key elt
addToFM_C4 xyx xyy xyz xzu = addToFM_C3 xyx xyy xyz xzu

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

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

  emptyFM :: FiniteMap b a
emptyFM = EmptyFM

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

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

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

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

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

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

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

  
glueBal2GlueBal0 zuy zuz fm1 fm2 True = mkBalBranch (glueBal2Mid_key1 zuy zuz) (glueBal2Mid_elt1 zuy zuz) (deleteMax fm1) fm2

  
glueBal2GlueBal1 zuy zuz fm1 fm2 True = mkBalBranch (glueBal2Mid_key2 zuy zuz) (glueBal2Mid_elt2 zuy zuz) fm1 (deleteMin fm2)
glueBal2GlueBal1 zuy zuz fm1 fm2 False = glueBal2GlueBal0 zuy zuz fm1 fm2 otherwise

  
glueBal2Mid_elt1 zuy zuz = glueBal2Mid_elt10 zuy zuz (glueBal2Vv2 zuy zuz)

  
glueBal2Mid_elt10 zuy zuz (vzx,mid_elt1) = mid_elt1

  
glueBal2Mid_elt2 zuy zuz = glueBal2Mid_elt20 zuy zuz (glueBal2Vv3 zuy zuz)

  
glueBal2Mid_elt20 zuy zuz (vzy,mid_elt2) = mid_elt2

  
glueBal2Mid_key1 zuy zuz = glueBal2Mid_key10 zuy zuz (glueBal2Vv2 zuy zuz)

  
glueBal2Mid_key10 zuy zuz (mid_key1,vzz) = mid_key1

  
glueBal2Mid_key2 zuy zuz = glueBal2Mid_key20 zuy zuz (glueBal2Vv3 zuy zuz)

  
glueBal2Mid_key20 zuy zuz (mid_key2,wuu) = mid_key2

  
glueBal2Vv2 zuy zuz = findMax zuy

  
glueBal2Vv3 zuy zuz = findMin zuz

  
glueBal3 fm1 EmptyFM = fm1
glueBal3 xzw xzx = glueBal2 xzw xzx

  
glueBal4 EmptyFM fm2 = fm2
glueBal4 xzz yuu = glueBal3 xzz yuu

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

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

  
glueVBal3GlueVBal0 yxx yxy yxz yyu yyv yyw yyx yyy yyz yzu yy yz zu zv zw zy zz vuu vuv vuw True = glueBal (Branch yy yz zu zv zw) (Branch zy zz vuu vuv vuw)

  
glueVBal3GlueVBal1 yxx yxy yxz yyu yyv yyw yyx yyy yyz yzu yy yz zu zv zw zy zz vuu vuv vuw True = mkBalBranch yy yz zv (glueVBal zw (Branch zy zz vuu vuv vuw))
glueVBal3GlueVBal1 yxx yxy yxz yyu yyv yyw yyx yyy yyz yzu yy yz zu zv zw zy zz vuu vuv vuw False = glueVBal3GlueVBal0 yxx yxy yxz yyu yyv yyw yyx yyy yyz yzu yy yz zu zv zw zy zz vuu vuv vuw otherwise

  
glueVBal3GlueVBal2 yxx yxy yxz yyu yyv yyw yyx yyy yyz yzu yy yz zu zv zw zy zz vuu vuv vuw True = mkBalBranch zy zz (glueVBal (Branch yy yz zu zv zw) vuv) vuw
glueVBal3GlueVBal2 yxx yxy yxz yyu yyv yyw yyx yyy yyz yzu yy yz zu zv zw zy zz vuu vuv vuw False = glueVBal3GlueVBal1 yxx yxy yxz yyu yyv yyw yyx yyy yyz yzu yy yz zu zv zw zy zz vuu vuv vuw (sIZE_RATIO * glueVBal3Size_r yxx yxy yxz yyu yyv yyw yyx yyy yyz yzu < glueVBal3Size_l yxx yxy yxz yyu yyv yyw yyx yyy yyz yzu)

  
glueVBal3Size_l yxx yxy yxz yyu yyv yyw yyx yyy yyz yzu = sizeFM (Branch yyw yyx yyy yyz yzu)

  
glueVBal3Size_r yxx yxy yxz yyu yyv yyw yyx yyy yyz yzu = sizeFM (Branch yxx yxy yxz yyu yyv)

  
glueVBal4 fm1 EmptyFM = fm1
glueVBal4 xvu xvv = glueVBal3 xvu xvv

  
glueVBal5 EmptyFM fm2 = fm2
glueVBal5 xvx xvy = glueVBal4 xvx xvy

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

  
minusFMGts yzv yzw = splitGT yzv yzw

  
minusFMLts yzv yzw = splitLT yzv yzw

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

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

  
mkBalBranch6Double_L ywz yxu yxv yxw fm_l (Branch key_r elt_r vxz (Branch key_rl elt_rl vyu fm_rll fm_rlr) fm_rr) = mkBranch (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) key_rl elt_rl (mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))) ywz yxu fm_l fm_rll) (mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) key_r elt_r fm_rlr fm_rr)

  
mkBalBranch6Double_R ywz yxu yxv yxw (Branch key_l elt_l vxu fm_ll (Branch key_lr elt_lr vxv fm_lrl fm_lrr)) fm_r = mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))) key_lr elt_lr (mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))) key_l elt_l fm_ll fm_lrl) (mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))) ywz yxu fm_lrr fm_r)

  
mkBalBranch6MkBalBranch0 ywz yxu yxv yxw fm_L fm_R (Branch vyv vyw vyx fm_rl fm_rr) = mkBalBranch6MkBalBranch02 ywz yxu yxv yxw fm_L fm_R (Branch vyv vyw vyx fm_rl fm_rr)

  
mkBalBranch6MkBalBranch00 ywz yxu yxv yxw fm_L fm_R vyv vyw vyx fm_rl fm_rr True = mkBalBranch6Double_L ywz yxu yxv yxw fm_L fm_R

  
mkBalBranch6MkBalBranch01 ywz yxu yxv yxw fm_L fm_R vyv vyw vyx fm_rl fm_rr True = mkBalBranch6Single_L ywz yxu yxv yxw fm_L fm_R
mkBalBranch6MkBalBranch01 ywz yxu yxv yxw fm_L fm_R vyv vyw vyx fm_rl fm_rr False = mkBalBranch6MkBalBranch00 ywz yxu yxv yxw fm_L fm_R vyv vyw vyx fm_rl fm_rr otherwise

  
mkBalBranch6MkBalBranch02 ywz yxu yxv yxw fm_L fm_R (Branch vyv vyw vyx fm_rl fm_rr) = mkBalBranch6MkBalBranch01 ywz yxu yxv yxw fm_L fm_R vyv vyw vyx fm_rl fm_rr (sizeFM fm_rl < Pos (Succ (Succ Zero)) * sizeFM fm_rr)

  
mkBalBranch6MkBalBranch1 ywz yxu yxv yxw fm_L fm_R (Branch vxw vxx vxy fm_ll fm_lr) = mkBalBranch6MkBalBranch12 ywz yxu yxv yxw fm_L fm_R (Branch vxw vxx vxy fm_ll fm_lr)

  
mkBalBranch6MkBalBranch10 ywz yxu yxv yxw fm_L fm_R vxw vxx vxy fm_ll fm_lr True = mkBalBranch6Double_R ywz yxu yxv yxw fm_L fm_R

  
mkBalBranch6MkBalBranch11 ywz yxu yxv yxw fm_L fm_R vxw vxx vxy fm_ll fm_lr True = mkBalBranch6Single_R ywz yxu yxv yxw fm_L fm_R
mkBalBranch6MkBalBranch11 ywz yxu yxv yxw fm_L fm_R vxw vxx vxy fm_ll fm_lr False = mkBalBranch6MkBalBranch10 ywz yxu yxv yxw fm_L fm_R vxw vxx vxy fm_ll fm_lr otherwise

  
mkBalBranch6MkBalBranch12 ywz yxu yxv yxw fm_L fm_R (Branch vxw vxx vxy fm_ll fm_lr) = mkBalBranch6MkBalBranch11 ywz yxu yxv yxw fm_L fm_R vxw vxx vxy fm_ll fm_lr (sizeFM fm_lr < Pos (Succ (Succ Zero)) * sizeFM fm_ll)

  
mkBalBranch6MkBalBranch2 ywz yxu yxv yxw key elt fm_L fm_R True = mkBranch (Pos (Succ (Succ Zero))) key elt fm_L fm_R

  
mkBalBranch6MkBalBranch3 ywz yxu yxv yxw key elt fm_L fm_R True = mkBalBranch6MkBalBranch1 ywz yxu yxv yxw fm_L fm_R fm_L
mkBalBranch6MkBalBranch3 ywz yxu yxv yxw key elt fm_L fm_R False = mkBalBranch6MkBalBranch2 ywz yxu yxv yxw key elt fm_L fm_R otherwise

  
mkBalBranch6MkBalBranch4 ywz yxu yxv yxw key elt fm_L fm_R True = mkBalBranch6MkBalBranch0 ywz yxu yxv yxw fm_L fm_R fm_R
mkBalBranch6MkBalBranch4 ywz yxu yxv yxw key elt fm_L fm_R False = mkBalBranch6MkBalBranch3 ywz yxu yxv yxw key elt fm_L fm_R (mkBalBranch6Size_l ywz yxu yxv yxw > sIZE_RATIO * mkBalBranch6Size_r ywz yxu yxv yxw)

  
mkBalBranch6MkBalBranch5 ywz yxu yxv yxw key elt fm_L fm_R True = mkBranch (Pos (Succ Zero)) key elt fm_L fm_R
mkBalBranch6MkBalBranch5 ywz yxu yxv yxw key elt fm_L fm_R False = mkBalBranch6MkBalBranch4 ywz yxu yxv yxw key elt fm_L fm_R (mkBalBranch6Size_r ywz yxu yxv yxw > sIZE_RATIO * mkBalBranch6Size_l ywz yxu yxv yxw)

  
mkBalBranch6Single_L ywz yxu yxv yxw fm_l (Branch key_r elt_r vyy fm_rl fm_rr) = mkBranch (Pos (Succ (Succ (Succ Zero)))) key_r elt_r (mkBranch (Pos (Succ (Succ (Succ (Succ Zero))))) ywz yxu fm_l fm_rl) fm_rr

  
mkBalBranch6Single_R ywz yxu yxv yxw (Branch key_l elt_l vwz fm_ll fm_lr) fm_r = mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))) key_l elt_l fm_ll (mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))) ywz yxu fm_lr fm_r)

  
mkBalBranch6Size_l ywz yxu yxv yxw = sizeFM yxv

  
mkBalBranch6Size_r ywz yxu yxv yxw = sizeFM yxw

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

  
mkBranchBalance_ok yzx yzy yzz = True

  
mkBranchLeft_ok yzx yzy yzz = mkBranchLeft_ok0 yzx yzy yzz yzz yzy yzz

  
mkBranchLeft_ok0 yzx yzy yzz fm_l key EmptyFM = True
mkBranchLeft_ok0 yzx yzy yzz fm_l key (Branch left_key vw vx vy vz) = mkBranchLeft_ok0Biggest_left_key fm_l < key

  
mkBranchLeft_ok0Biggest_left_key zwz = fst (findMax zwz)

  
mkBranchLeft_size yzx yzy yzz = sizeFM yzz

  
mkBranchResult zuu zuv zuw zux = Branch zuu zuv (mkBranchUnbox zuw zuu zux (Pos (Succ Zero) + mkBranchLeft_size zuw zuu zux + mkBranchRight_size zuw zuu zux)) zux zuw

  
mkBranchRight_ok yzx yzy yzz = mkBranchRight_ok0 yzx yzy yzz yzx yzy yzx

  
mkBranchRight_ok0 yzx yzy yzz fm_r key EmptyFM = True
mkBranchRight_ok0 yzx yzy yzz fm_r key (Branch right_key wu wv ww wx) = key < mkBranchRight_ok0Smallest_right_key fm_r

  
mkBranchRight_ok0Smallest_right_key zwy = fst (findMin zwy)

  
mkBranchRight_size yzx yzy yzz = sizeFM yzx

  mkBranchUnbox :: Ord a =>  ->  (FiniteMap a b) ( ->  a ( ->  (FiniteMap a b) (Int  ->  Int)))
mkBranchUnbox yzx yzy yzz x = x

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

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

  
mkVBalBranch3MkVBalBranch0 zvu zvv zvw zvx zvy zvz zwu zwv zww zwx key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww True = mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))) key elt (Branch vuy vuz vvu vvv vvw) (Branch vvy vvz vwu vwv vww)

  
mkVBalBranch3MkVBalBranch1 zvu zvv zvw zvx zvy zvz zwu zwv zww zwx key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww True = mkBalBranch vuy vuz vvv (mkVBalBranch key elt vvw (Branch vvy vvz vwu vwv vww))
mkVBalBranch3MkVBalBranch1 zvu zvv zvw zvx zvy zvz zwu zwv zww zwx key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww False = mkVBalBranch3MkVBalBranch0 zvu zvv zvw zvx zvy zvz zwu zwv zww zwx key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww otherwise

  
mkVBalBranch3MkVBalBranch2 zvu zvv zvw zvx zvy zvz zwu zwv zww zwx key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww True = mkBalBranch vvy vvz (mkVBalBranch key elt (Branch vuy vuz vvu vvv vvw) vwv) vww
mkVBalBranch3MkVBalBranch2 zvu zvv zvw zvx zvy zvz zwu zwv zww zwx key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww False = mkVBalBranch3MkVBalBranch1 zvu zvv zvw zvx zvy zvz zwu zwv zww zwx key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww (sIZE_RATIO * mkVBalBranch3Size_r zvu zvv zvw zvx zvy zvz zwu zwv zww zwx < mkVBalBranch3Size_l zvu zvv zvw zvx zvy zvz zwu zwv zww zwx)

  
mkVBalBranch3Size_l zvu zvv zvw zvx zvy zvz zwu zwv zww zwx = sizeFM (Branch zvz zwu zwv zww zwx)

  
mkVBalBranch3Size_r zvu zvv zvw zvx zvy zvz zwu zwv zww zwx = sizeFM (Branch zvu zvv zvw zvx zvy)

  
mkVBalBranch4 key elt fm_l EmptyFM = addToFM fm_l key elt
mkVBalBranch4 xww xwx xwy xwz = mkVBalBranch3 xww xwx xwy xwz

  
mkVBalBranch5 key elt EmptyFM fm_r = addToFM fm_r key elt
mkVBalBranch5 xxv xxw xxx xxy = mkVBalBranch4 xxv xxw xxx xxy

  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 yw) = size

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

  
splitGT0 key elt xy fm_l fm_r split_key True = fm_r

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

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

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

  
splitGT4 EmptyFM split_key = emptyFM
splitGT4 xuv xuw = splitGT3 xuv xuw

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

  
splitLT0 key elt xx fm_l fm_r split_key True = fm_l

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

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

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

  
splitLT4 EmptyFM split_key = emptyFM
splitLT4 wzx wzy = splitLT3 wzx wzy

  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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_primEqNat(Succ(zxw40000), Succ(zxw30000)) → new_primEqNat(zxw40000, zxw30000)

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

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



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

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

new_glueBal2Mid_key20(zxw374, zxw375, zxw376, zxw377, zxw378, zxw379, zxw380, zxw381, zxw382, zxw383, zxw384, zxw385, zxw386, Branch(zxw3870, zxw3871, zxw3872, zxw3873, zxw3874), zxw388, h, ba) → new_glueBal2Mid_key20(zxw374, zxw375, zxw376, zxw377, zxw378, zxw379, zxw380, zxw381, zxw382, zxw383, zxw3870, zxw3871, zxw3872, zxw3873, zxw3874, h, ba)

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

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



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

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

new_glueBal2Mid_elt20(zxw358, zxw359, zxw360, zxw361, zxw362, zxw363, zxw364, zxw365, zxw366, zxw367, zxw368, zxw369, zxw370, Branch(zxw3710, zxw3711, zxw3712, zxw3713, zxw3714), zxw372, h, ba) → new_glueBal2Mid_elt20(zxw358, zxw359, zxw360, zxw361, zxw362, zxw363, zxw364, zxw365, zxw366, zxw367, zxw3710, zxw3711, zxw3712, zxw3713, zxw3714, h, ba)

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

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



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

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

new_glueBal2Mid_key10(zxw438, zxw439, zxw440, zxw441, zxw442, zxw443, zxw444, zxw445, zxw446, zxw447, zxw448, zxw449, zxw450, zxw451, Branch(zxw4520, zxw4521, zxw4522, zxw4523, zxw4524), h, ba) → new_glueBal2Mid_key10(zxw438, zxw439, zxw440, zxw441, zxw442, zxw443, zxw444, zxw445, zxw446, zxw447, zxw4520, zxw4521, zxw4522, zxw4523, zxw4524, h, ba)

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

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



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

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

new_glueBal2Mid_elt10(zxw422, zxw423, zxw424, zxw425, zxw426, zxw427, zxw428, zxw429, zxw430, zxw431, zxw432, zxw433, zxw434, zxw435, Branch(zxw4360, zxw4361, zxw4362, zxw4363, zxw4364), h, ba) → new_glueBal2Mid_elt10(zxw422, zxw423, zxw424, zxw425, zxw426, zxw427, zxw428, zxw429, zxw430, zxw431, zxw4360, zxw4361, zxw4362, zxw4363, zxw4364, h, ba)

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

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



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

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

new_glueBal2Mid_key200(zxw336, zxw337, zxw338, zxw339, zxw340, zxw341, zxw342, zxw343, zxw344, zxw345, zxw346, zxw347, zxw348, Branch(zxw3490, zxw3491, zxw3492, zxw3493, zxw3494), zxw350, h, ba) → new_glueBal2Mid_key200(zxw336, zxw337, zxw338, zxw339, zxw340, zxw341, zxw342, zxw343, zxw344, zxw345, zxw3490, zxw3491, zxw3492, zxw3493, zxw3494, h, ba)

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

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



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

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

new_glueBal2Mid_elt200(zxw320, zxw321, zxw322, zxw323, zxw324, zxw325, zxw326, zxw327, zxw328, zxw329, zxw330, zxw331, zxw332, Branch(zxw3330, zxw3331, zxw3332, zxw3333, zxw3334), zxw334, h, ba) → new_glueBal2Mid_elt200(zxw320, zxw321, zxw322, zxw323, zxw324, zxw325, zxw326, zxw327, zxw328, zxw329, zxw3330, zxw3331, zxw3332, zxw3333, zxw3334, h, ba)

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

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



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

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

new_glueBal2Mid_key100(zxw406, zxw407, zxw408, zxw409, zxw410, zxw411, zxw412, zxw413, zxw414, zxw415, zxw416, zxw417, zxw418, zxw419, Branch(zxw4200, zxw4201, zxw4202, zxw4203, zxw4204), h, ba) → new_glueBal2Mid_key100(zxw406, zxw407, zxw408, zxw409, zxw410, zxw411, zxw412, zxw413, zxw414, zxw415, zxw4200, zxw4201, zxw4202, zxw4203, zxw4204, h, ba)

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

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



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

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

new_glueBal2Mid_elt100(zxw390, zxw391, zxw392, zxw393, zxw394, zxw395, zxw396, zxw397, zxw398, zxw399, zxw400, zxw401, zxw402, zxw403, Branch(zxw4040, zxw4041, zxw4042, zxw4043, zxw4044), h, ba) → new_glueBal2Mid_elt100(zxw390, zxw391, zxw392, zxw393, zxw394, zxw395, zxw396, zxw397, zxw398, zxw399, zxw4040, zxw4041, zxw4042, zxw4043, zxw4044, h, ba)

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

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



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

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

new_primCmpNat(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat(zxw79000, zxw80000)

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

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



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

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

new_primMinusNat(Succ(zxw18900), Succ(zxw18000)) → new_primMinusNat(zxw18900, zxw18000)

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

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



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

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

new_primPlusNat(Succ(zxw19000), Succ(zxw3000000)) → new_primPlusNat(zxw19000, zxw3000000)

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

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



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

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

new_primMulNat(Succ(zxw400000), Succ(zxw300000)) → new_primMulNat(zxw400000, Succ(zxw300000))

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

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



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

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

new_esEs2(Left(zxw4000), Left(zxw3000), app(ty_[], ga), gb) → new_esEs(zxw4000, zxw3000, ga)
new_esEs1(@2(zxw4000, zxw4001), @2(zxw3000, zxw3001), app(ty_Maybe, eh), eg) → new_esEs0(zxw4000, zxw3000, eh)
new_esEs3(@3(zxw4000, zxw4001, zxw4002), @3(zxw3000, zxw3001, zxw3002), bae, app(app(ty_@2, bcc), bcd), bca) → new_esEs1(zxw4001, zxw3001, bcc, bcd)
new_esEs1(@2(zxw4000, zxw4001), @2(zxw3000, zxw3001), app(app(ty_Either, fc), fd), eg) → new_esEs2(zxw4000, zxw3000, fc, fd)
new_esEs1(@2(zxw4000, zxw4001), @2(zxw3000, zxw3001), dd, app(app(app(ty_@3, ec), ed), ee)) → new_esEs3(zxw4001, zxw3001, ec, ed, ee)
new_esEs2(Right(zxw4000), Right(zxw3000), hc, app(ty_[], hd)) → new_esEs(zxw4000, zxw3000, hd)
new_esEs3(@3(zxw4000, zxw4001, zxw4002), @3(zxw3000, zxw3001, zxw3002), app(app(ty_Either, bdf), bdg), baf, bca) → new_esEs2(zxw4000, zxw3000, bdf, bdg)
new_esEs3(@3(zxw4000, zxw4001, zxw4002), @3(zxw3000, zxw3001, zxw3002), bae, baf, app(app(app(ty_@3, bbe), bbf), bbg)) → new_esEs3(zxw4002, zxw3002, bbe, bbf, bbg)
new_esEs3(@3(zxw4000, zxw4001, zxw4002), @3(zxw3000, zxw3001, zxw3002), bae, baf, app(ty_[], bag)) → new_esEs(zxw4002, zxw3002, bag)
new_esEs3(@3(zxw4000, zxw4001, zxw4002), @3(zxw3000, zxw3001, zxw3002), bae, app(ty_Maybe, bcb), bca) → new_esEs0(zxw4001, zxw3001, bcb)
new_esEs3(@3(zxw4000, zxw4001, zxw4002), @3(zxw3000, zxw3001, zxw3002), app(app(ty_@2, bdd), bde), baf, bca) → new_esEs1(zxw4000, zxw3000, bdd, bde)
new_esEs(:(zxw4000, zxw4001), :(zxw3000, zxw3001), app(app(app(ty_@3, bg), bh), ca)) → new_esEs3(zxw4000, zxw3000, bg, bh, ca)
new_esEs3(@3(zxw4000, zxw4001, zxw4002), @3(zxw3000, zxw3001, zxw3002), app(ty_[], bdb), baf, bca) → new_esEs(zxw4000, zxw3000, bdb)
new_esEs3(@3(zxw4000, zxw4001, zxw4002), @3(zxw3000, zxw3001, zxw3002), bae, baf, app(ty_Maybe, bah)) → new_esEs0(zxw4002, zxw3002, bah)
new_esEs2(Right(zxw4000), Right(zxw3000), hc, app(app(ty_@2, hf), hg)) → new_esEs1(zxw4000, zxw3000, hf, hg)
new_esEs0(Just(zxw4000), Just(zxw3000), app(ty_Maybe, cc)) → new_esEs0(zxw4000, zxw3000, cc)
new_esEs3(@3(zxw4000, zxw4001, zxw4002), @3(zxw3000, zxw3001, zxw3002), bae, app(app(ty_Either, bce), bcf), bca) → new_esEs2(zxw4001, zxw3001, bce, bcf)
new_esEs0(Just(zxw4000), Just(zxw3000), app(ty_[], cb)) → new_esEs(zxw4000, zxw3000, cb)
new_esEs3(@3(zxw4000, zxw4001, zxw4002), @3(zxw3000, zxw3001, zxw3002), bae, app(ty_[], bbh), bca) → new_esEs(zxw4001, zxw3001, bbh)
new_esEs2(Left(zxw4000), Left(zxw3000), app(app(ty_Either, gf), gg), gb) → new_esEs2(zxw4000, zxw3000, gf, gg)
new_esEs2(Left(zxw4000), Left(zxw3000), app(app(app(ty_@3, gh), ha), hb), gb) → new_esEs3(zxw4000, zxw3000, gh, ha, hb)
new_esEs1(@2(zxw4000, zxw4001), @2(zxw3000, zxw3001), dd, app(ty_[], de)) → new_esEs(zxw4001, zxw3001, de)
new_esEs1(@2(zxw4000, zxw4001), @2(zxw3000, zxw3001), app(ty_[], ef), eg) → new_esEs(zxw4000, zxw3000, ef)
new_esEs3(@3(zxw4000, zxw4001, zxw4002), @3(zxw3000, zxw3001, zxw3002), bae, baf, app(app(ty_Either, bbc), bbd)) → new_esEs2(zxw4002, zxw3002, bbc, bbd)
new_esEs(:(zxw4000, zxw4001), :(zxw3000, zxw3001), app(ty_Maybe, bb)) → new_esEs0(zxw4000, zxw3000, bb)
new_esEs1(@2(zxw4000, zxw4001), @2(zxw3000, zxw3001), dd, app(app(ty_@2, dg), dh)) → new_esEs1(zxw4001, zxw3001, dg, dh)
new_esEs(:(zxw4000, zxw4001), :(zxw3000, zxw3001), app(app(ty_@2, bc), bd)) → new_esEs1(zxw4000, zxw3000, bc, bd)
new_esEs3(@3(zxw4000, zxw4001, zxw4002), @3(zxw3000, zxw3001, zxw3002), bae, app(app(app(ty_@3, bcg), bch), bda), bca) → new_esEs3(zxw4001, zxw3001, bcg, bch, bda)
new_esEs0(Just(zxw4000), Just(zxw3000), app(app(app(ty_@3, da), db), dc)) → new_esEs3(zxw4000, zxw3000, da, db, dc)
new_esEs(:(zxw4000, zxw4001), :(zxw3000, zxw3001), h) → new_esEs(zxw4001, zxw3001, h)
new_esEs(:(zxw4000, zxw4001), :(zxw3000, zxw3001), app(app(ty_Either, be), bf)) → new_esEs2(zxw4000, zxw3000, be, bf)
new_esEs3(@3(zxw4000, zxw4001, zxw4002), @3(zxw3000, zxw3001, zxw3002), bae, baf, app(app(ty_@2, bba), bbb)) → new_esEs1(zxw4002, zxw3002, bba, bbb)
new_esEs1(@2(zxw4000, zxw4001), @2(zxw3000, zxw3001), app(app(app(ty_@3, ff), fg), fh), eg) → new_esEs3(zxw4000, zxw3000, ff, fg, fh)
new_esEs1(@2(zxw4000, zxw4001), @2(zxw3000, zxw3001), app(app(ty_@2, fa), fb), eg) → new_esEs1(zxw4000, zxw3000, fa, fb)
new_esEs2(Right(zxw4000), Right(zxw3000), hc, app(app(ty_Either, hh), baa)) → new_esEs2(zxw4000, zxw3000, hh, baa)
new_esEs1(@2(zxw4000, zxw4001), @2(zxw3000, zxw3001), dd, app(app(ty_Either, ea), eb)) → new_esEs2(zxw4001, zxw3001, ea, eb)
new_esEs3(@3(zxw4000, zxw4001, zxw4002), @3(zxw3000, zxw3001, zxw3002), app(ty_Maybe, bdc), baf, bca) → new_esEs0(zxw4000, zxw3000, bdc)
new_esEs2(Left(zxw4000), Left(zxw3000), app(ty_Maybe, gc), gb) → new_esEs0(zxw4000, zxw3000, gc)
new_esEs1(@2(zxw4000, zxw4001), @2(zxw3000, zxw3001), dd, app(ty_Maybe, df)) → new_esEs0(zxw4001, zxw3001, df)
new_esEs2(Right(zxw4000), Right(zxw3000), hc, app(ty_Maybe, he)) → new_esEs0(zxw4000, zxw3000, he)
new_esEs2(Right(zxw4000), Right(zxw3000), hc, app(app(app(ty_@3, bab), bac), bad)) → new_esEs3(zxw4000, zxw3000, bab, bac, bad)
new_esEs0(Just(zxw4000), Just(zxw3000), app(app(ty_@2, cd), ce)) → new_esEs1(zxw4000, zxw3000, cd, ce)
new_esEs2(Left(zxw4000), Left(zxw3000), app(app(ty_@2, gd), ge), gb) → new_esEs1(zxw4000, zxw3000, gd, ge)
new_esEs(:(zxw4000, zxw4001), :(zxw3000, zxw3001), app(ty_[], ba)) → new_esEs(zxw4000, zxw3000, ba)
new_esEs0(Just(zxw4000), Just(zxw3000), app(app(ty_Either, cf), cg)) → new_esEs2(zxw4000, zxw3000, cf, cg)
new_esEs3(@3(zxw4000, zxw4001, zxw4002), @3(zxw3000, zxw3001, zxw3002), app(app(app(ty_@3, bdh), bea), beb), baf, bca) → new_esEs3(zxw4000, zxw3000, bdh, bea, beb)

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

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



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

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

new_compare22(Left(@3(zxw79000, zxw79001, zxw79002)), Left(@3(zxw80000, zxw80001, zxw80002)), False, app(app(app(ty_@3, cc), app(ty_Maybe, de)), bd), bag) → new_lt3(zxw79001, zxw80001, de)
new_compare(:(zxw79000, zxw79001), :(zxw80000, zxw80001), eg) → new_primCompAux(zxw79000, zxw80000, new_compare1(zxw79001, zxw80001, eg), eg)
new_ltEs1(@2(zxw79000, zxw79001), @2(zxw80000, zxw80001), hd, app(app(ty_@2, baa), bab)) → new_ltEs1(zxw79001, zxw80001, baa, bab)
new_ltEs2(Left(zxw79000), Left(zxw80000), app(app(ty_Either, bbg), bbh), bbc) → new_ltEs2(zxw79000, zxw80000, bbg, bbh)
new_compare22(Left(Left(zxw79000)), Left(Left(zxw80000)), False, app(app(ty_Either, app(app(ty_Either, bbg), bbh)), bbc), bag) → new_ltEs2(zxw79000, zxw80000, bbg, bbh)
new_compare20(zxw79000, zxw80000, False, bf, bg) → new_ltEs1(zxw79000, zxw80000, bf, bg)
new_ltEs(@3(zxw79000, zxw79001, zxw79002), @3(zxw80000, zxw80001, zxw80002), app(ty_Maybe, cb), bc, bd) → new_compare21(zxw79000, zxw80000, new_esEs6(zxw79000, zxw80000, cb), cb)
new_compare22(Left(:(zxw79000, zxw79001)), Left(:(zxw80000, zxw80001)), False, app(ty_[], eg), bag) → new_compare(zxw79001, zxw80001, eg)
new_ltEs(@3(zxw79000, zxw79001, zxw79002), @3(zxw80000, zxw80001, zxw80002), cc, bc, app(ty_[], ea)) → new_ltEs0(zxw79002, zxw80002, ea)
new_compare22(Left(@2(zxw79000, zxw79001)), Left(@2(zxw80000, zxw80001)), False, app(app(ty_@2, hd), app(ty_Maybe, bae)), bag) → new_ltEs3(zxw79001, zxw80001, bae)
new_ltEs(@3(zxw79000, zxw79001, zxw79002), @3(zxw80000, zxw80001, zxw80002), cc, bc, app(app(ty_@2, eb), ec)) → new_ltEs1(zxw79002, zxw80002, eb, ec)
new_compare22(Left(Left(zxw79000)), Left(Left(zxw80000)), False, app(app(ty_Either, app(ty_[], bbd)), bbc), bag) → new_ltEs0(zxw79000, zxw80000, bbd)
new_compare22(Left(@3(zxw79000, zxw79001, zxw79002)), Left(@3(zxw80000, zxw80001, zxw80002)), False, app(app(app(ty_@3, cc), app(ty_[], cg)), bd), bag) → new_lt1(zxw79001, zxw80001, cg)
new_primCompAux(zxw79000, zxw80000, zxw272, app(ty_[], fc)) → new_compare(zxw79000, zxw80000, fc)
new_compare22(Left(Right(zxw79000)), Left(Right(zxw80000)), False, app(app(ty_Either, bcb), app(app(ty_Either, bda), bdb)), bag) → new_ltEs2(zxw79000, zxw80000, bda, bdb)
new_compare22(Left(Left(zxw79000)), Left(Left(zxw80000)), False, app(app(ty_Either, app(ty_Maybe, bca)), bbc), bag) → new_ltEs3(zxw79000, zxw80000, bca)
new_ltEs1(@2(zxw79000, zxw79001), @2(zxw80000, zxw80001), hd, app(ty_Maybe, bae)) → new_ltEs3(zxw79001, zxw80001, bae)
new_ltEs(@3(zxw79000, zxw79001, zxw79002), @3(zxw80000, zxw80001, zxw80002), cc, bc, app(app(ty_Either, ed), ee)) → new_ltEs2(zxw79002, zxw80002, ed, ee)
new_compare22(Left(Just(zxw79000)), Left(Just(zxw80000)), False, app(ty_Maybe, app(ty_Maybe, bed)), bag) → new_ltEs3(zxw79000, zxw80000, bed)
new_lt3(zxw79000, zxw80000, cb) → new_compare21(zxw79000, zxw80000, new_esEs6(zxw79000, zxw80000, cb), cb)
new_compare22(Left(Right(zxw79000)), Left(Right(zxw80000)), False, app(app(ty_Either, bcb), app(app(app(ty_@3, bcc), bcd), bce)), bag) → new_ltEs(zxw79000, zxw80000, bcc, bcd, bce)
new_compare22(Left(@3(zxw79000, zxw79001, zxw79002)), Left(@3(zxw80000, zxw80001, zxw80002)), False, app(app(app(ty_@3, cc), app(app(ty_Either, dc), dd)), bd), bag) → new_lt(zxw79001, zxw80001, dc, dd)
new_ltEs2(Left(zxw79000), Left(zxw80000), app(app(app(ty_@3, bah), bba), bbb), bbc) → new_ltEs(zxw79000, zxw80000, bah, bba, bbb)
new_ltEs3(Just(zxw79000), Just(zxw80000), app(app(app(ty_@3, bdd), bde), bdf)) → new_ltEs(zxw79000, zxw80000, bdd, bde, bdf)
new_compare22(Left(@2(zxw79000, zxw79001)), Left(@2(zxw80000, zxw80001)), False, app(app(ty_@2, hd), app(app(app(ty_@3, he), hf), hg)), bag) → new_ltEs(zxw79001, zxw80001, he, hf, hg)
new_ltEs2(Right(zxw79000), Right(zxw80000), bcb, app(ty_[], bcf)) → new_ltEs0(zxw79000, zxw80000, bcf)
new_ltEs1(@2(zxw79000, zxw79001), @2(zxw80000, zxw80001), app(ty_[], gf), ge) → new_lt1(zxw79000, zxw80000, gf)
new_ltEs1(@2(zxw79000, zxw79001), @2(zxw80000, zxw80001), hd, app(app(app(ty_@3, he), hf), hg)) → new_ltEs(zxw79001, zxw80001, he, hf, hg)
new_ltEs(@3(zxw79000, zxw79001, zxw79002), @3(zxw80000, zxw80001, zxw80002), cc, app(app(app(ty_@3, cd), ce), cf), bd) → new_lt0(zxw79001, zxw80001, cd, ce, cf)
new_compare4(zxw790, zxw800, baf, bag) → new_compare22(zxw790, zxw800, new_esEs7(zxw790, zxw800, baf, bag), baf, bag)
new_ltEs1(@2(zxw79000, zxw79001), @2(zxw80000, zxw80001), app(app(ty_@2, gg), gh), ge) → new_lt2(zxw79000, zxw80000, gg, gh)
new_ltEs(@3(zxw79000, zxw79001, zxw79002), @3(zxw80000, zxw80001, zxw80002), cc, bc, app(ty_Maybe, ef)) → new_ltEs3(zxw79002, zxw80002, ef)
new_ltEs3(Just(zxw79000), Just(zxw80000), app(ty_[], bdg)) → new_ltEs0(zxw79000, zxw80000, bdg)
new_compare22(Left(@3(zxw79000, zxw79001, zxw79002)), Left(@3(zxw80000, zxw80001, zxw80002)), False, app(app(app(ty_@3, app(app(ty_Either, bh), ca)), bc), bd), bag) → new_lt(zxw79000, zxw80000, bh, ca)
new_compare2(zxw79000, zxw80000, False, h, ba, bb) → new_ltEs(zxw79000, zxw80000, h, ba, bb)
new_ltEs(@3(zxw79000, zxw79001, zxw79002), @3(zxw80000, zxw80001, zxw80002), app(ty_[], be), bc, bd) → new_compare(zxw79000, zxw80000, be)
new_compare22(Left(@3(zxw79000, zxw79001, zxw79002)), Left(@3(zxw80000, zxw80001, zxw80002)), False, app(app(app(ty_@3, app(app(app(ty_@3, h), ba), bb)), bc), bd), bag) → new_compare2(zxw79000, zxw80000, new_esEs4(zxw79000, zxw80000, h, ba, bb), h, ba, bb)
new_ltEs(@3(zxw79000, zxw79001, zxw79002), @3(zxw80000, zxw80001, zxw80002), app(app(app(ty_@3, h), ba), bb), bc, bd) → new_compare2(zxw79000, zxw80000, new_esEs4(zxw79000, zxw80000, h, ba, bb), h, ba, bb)
new_compare22(Right(zxw7900), Right(zxw8000), False, baf, app(ty_[], beh)) → new_ltEs0(zxw7900, zxw8000, beh)
new_compare22(Left(@2(zxw79000, zxw79001)), Left(@2(zxw80000, zxw80001)), False, app(app(ty_@2, hd), app(app(ty_Either, bac), bad)), bag) → new_ltEs2(zxw79001, zxw80001, bac, bad)
new_ltEs(@3(zxw79000, zxw79001, zxw79002), @3(zxw80000, zxw80001, zxw80002), cc, app(ty_[], cg), bd) → new_lt1(zxw79001, zxw80001, cg)
new_compare22(Left(@3(zxw79000, zxw79001, zxw79002)), Left(@3(zxw80000, zxw80001, zxw80002)), False, app(app(app(ty_@3, app(app(ty_@2, bf), bg)), bc), bd), bag) → new_compare20(zxw79000, zxw80000, new_esEs5(zxw79000, zxw80000, bf, bg), bf, bg)
new_ltEs(@3(zxw79000, zxw79001, zxw79002), @3(zxw80000, zxw80001, zxw80002), cc, bc, app(app(app(ty_@3, df), dg), dh)) → new_ltEs(zxw79002, zxw80002, df, dg, dh)
new_compare22(Left(@2(zxw79000, zxw79001)), Left(@2(zxw80000, zxw80001)), False, app(app(ty_@2, hd), app(ty_[], hh)), bag) → new_ltEs0(zxw79001, zxw80001, hh)
new_ltEs3(Just(zxw79000), Just(zxw80000), app(ty_Maybe, bed)) → new_ltEs3(zxw79000, zxw80000, bed)
new_compare5(zxw79000, zxw80000, cb) → new_compare21(zxw79000, zxw80000, new_esEs6(zxw79000, zxw80000, cb), cb)
new_compare21(zxw79000, zxw80000, False, cb) → new_ltEs3(zxw79000, zxw80000, cb)
new_compare22(Left(@3(zxw79000, zxw79001, zxw79002)), Left(@3(zxw80000, zxw80001, zxw80002)), False, app(app(app(ty_@3, cc), bc), app(app(ty_Either, ed), ee)), bag) → new_ltEs2(zxw79002, zxw80002, ed, ee)
new_ltEs2(Left(zxw79000), Left(zxw80000), app(ty_[], bbd), bbc) → new_ltEs0(zxw79000, zxw80000, bbd)
new_compare22(Left(@2(zxw79000, zxw79001)), Left(@2(zxw80000, zxw80001)), False, app(app(ty_@2, hd), app(app(ty_@2, baa), bab)), bag) → new_ltEs1(zxw79001, zxw80001, baa, bab)
new_compare0(zxw79000, zxw80000, h, ba, bb) → new_compare2(zxw79000, zxw80000, new_esEs4(zxw79000, zxw80000, h, ba, bb), h, ba, bb)
new_compare22(Left(Just(zxw79000)), Left(Just(zxw80000)), False, app(ty_Maybe, app(app(app(ty_@3, bdd), bde), bdf)), bag) → new_ltEs(zxw79000, zxw80000, bdd, bde, bdf)
new_ltEs0(:(zxw79000, zxw79001), :(zxw80000, zxw80001), eg) → new_compare(zxw79001, zxw80001, eg)
new_compare22(Left(Left(zxw79000)), Left(Left(zxw80000)), False, app(app(ty_Either, app(app(app(ty_@3, bah), bba), bbb)), bbc), bag) → new_ltEs(zxw79000, zxw80000, bah, bba, bbb)
new_ltEs(@3(zxw79000, zxw79001, zxw79002), @3(zxw80000, zxw80001, zxw80002), cc, app(app(ty_Either, dc), dd), bd) → new_lt(zxw79001, zxw80001, dc, dd)
new_primCompAux(zxw79000, zxw80000, zxw272, app(app(ty_@2, fd), ff)) → new_compare3(zxw79000, zxw80000, fd, ff)
new_ltEs(@3(zxw79000, zxw79001, zxw79002), @3(zxw80000, zxw80001, zxw80002), app(app(ty_@2, bf), bg), bc, bd) → new_compare20(zxw79000, zxw80000, new_esEs5(zxw79000, zxw80000, bf, bg), bf, bg)
new_lt2(zxw79000, zxw80000, bf, bg) → new_compare20(zxw79000, zxw80000, new_esEs5(zxw79000, zxw80000, bf, bg), bf, bg)
new_compare22(Left(@2(zxw79000, zxw79001)), Left(@2(zxw80000, zxw80001)), False, app(app(ty_@2, app(app(ty_Either, ha), hb)), ge), bag) → new_lt(zxw79000, zxw80000, ha, hb)
new_primCompAux(zxw79000, zxw80000, zxw272, app(app(app(ty_@3, eh), fa), fb)) → new_compare0(zxw79000, zxw80000, eh, fa, fb)
new_ltEs1(@2(zxw79000, zxw79001), @2(zxw80000, zxw80001), app(ty_Maybe, hc), ge) → new_lt3(zxw79000, zxw80000, hc)
new_compare22(Left(@2(zxw79000, zxw79001)), Left(@2(zxw80000, zxw80001)), False, app(app(ty_@2, app(app(app(ty_@3, gb), gc), gd)), ge), bag) → new_lt0(zxw79000, zxw80000, gb, gc, gd)
new_compare3(zxw79000, zxw80000, bf, bg) → new_compare20(zxw79000, zxw80000, new_esEs5(zxw79000, zxw80000, bf, bg), bf, bg)
new_ltEs2(Right(zxw79000), Right(zxw80000), bcb, app(app(ty_@2, bcg), bch)) → new_ltEs1(zxw79000, zxw80000, bcg, bch)
new_compare22(Left(@3(zxw79000, zxw79001, zxw79002)), Left(@3(zxw80000, zxw80001, zxw80002)), False, app(app(app(ty_@3, cc), bc), app(app(ty_@2, eb), ec)), bag) → new_ltEs1(zxw79002, zxw80002, eb, ec)
new_compare22(Right(zxw7900), Right(zxw8000), False, baf, app(app(ty_Either, bfc), bfd)) → new_ltEs2(zxw7900, zxw8000, bfc, bfd)
new_compare22(Left(Right(zxw79000)), Left(Right(zxw80000)), False, app(app(ty_Either, bcb), app(app(ty_@2, bcg), bch)), bag) → new_ltEs1(zxw79000, zxw80000, bcg, bch)
new_compare22(Left(:(zxw79000, zxw79001)), Left(:(zxw80000, zxw80001)), False, app(ty_[], eg), bag) → new_primCompAux(zxw79000, zxw80000, new_compare1(zxw79001, zxw80001, eg), eg)
new_ltEs2(Left(zxw79000), Left(zxw80000), app(ty_Maybe, bca), bbc) → new_ltEs3(zxw79000, zxw80000, bca)
new_compare22(Left(Right(zxw79000)), Left(Right(zxw80000)), False, app(app(ty_Either, bcb), app(ty_[], bcf)), bag) → new_ltEs0(zxw79000, zxw80000, bcf)
new_compare22(Left(Right(zxw79000)), Left(Right(zxw80000)), False, app(app(ty_Either, bcb), app(ty_Maybe, bdc)), bag) → new_ltEs3(zxw79000, zxw80000, bdc)
new_ltEs1(@2(zxw79000, zxw79001), @2(zxw80000, zxw80001), app(app(ty_Either, ha), hb), ge) → new_lt(zxw79000, zxw80000, ha, hb)
new_ltEs3(Just(zxw79000), Just(zxw80000), app(app(ty_Either, beb), bec)) → new_ltEs2(zxw79000, zxw80000, beb, bec)
new_compare22(Left(@2(zxw79000, zxw79001)), Left(@2(zxw80000, zxw80001)), False, app(app(ty_@2, app(ty_Maybe, hc)), ge), bag) → new_lt3(zxw79000, zxw80000, hc)
new_compare22(Left(@3(zxw79000, zxw79001, zxw79002)), Left(@3(zxw80000, zxw80001, zxw80002)), False, app(app(app(ty_@3, app(ty_[], be)), bc), bd), bag) → new_compare(zxw79000, zxw80000, be)
new_ltEs3(Just(zxw79000), Just(zxw80000), app(app(ty_@2, bdh), bea)) → new_ltEs1(zxw79000, zxw80000, bdh, bea)
new_ltEs2(Right(zxw79000), Right(zxw80000), bcb, app(app(app(ty_@3, bcc), bcd), bce)) → new_ltEs(zxw79000, zxw80000, bcc, bcd, bce)
new_primCompAux(zxw79000, zxw80000, zxw272, app(app(ty_Either, fg), fh)) → new_compare4(zxw79000, zxw80000, fg, fh)
new_ltEs1(@2(zxw79000, zxw79001), @2(zxw80000, zxw80001), hd, app(ty_[], hh)) → new_ltEs0(zxw79001, zxw80001, hh)
new_ltEs2(Right(zxw79000), Right(zxw80000), bcb, app(app(ty_Either, bda), bdb)) → new_ltEs2(zxw79000, zxw80000, bda, bdb)
new_lt0(zxw79000, zxw80000, h, ba, bb) → new_compare2(zxw79000, zxw80000, new_esEs4(zxw79000, zxw80000, h, ba, bb), h, ba, bb)
new_compare22(Left(@3(zxw79000, zxw79001, zxw79002)), Left(@3(zxw80000, zxw80001, zxw80002)), False, app(app(app(ty_@3, cc), bc), app(app(app(ty_@3, df), dg), dh)), bag) → new_ltEs(zxw79002, zxw80002, df, dg, dh)
new_compare22(Left(Just(zxw79000)), Left(Just(zxw80000)), False, app(ty_Maybe, app(ty_[], bdg)), bag) → new_ltEs0(zxw79000, zxw80000, bdg)
new_ltEs(@3(zxw79000, zxw79001, zxw79002), @3(zxw80000, zxw80001, zxw80002), cc, app(app(ty_@2, da), db), bd) → new_lt2(zxw79001, zxw80001, da, db)
new_lt(zxw790, zxw800, baf, bag) → new_compare22(zxw790, zxw800, new_esEs7(zxw790, zxw800, baf, bag), baf, bag)
new_compare22(Left(Left(zxw79000)), Left(Left(zxw80000)), False, app(app(ty_Either, app(app(ty_@2, bbe), bbf)), bbc), bag) → new_ltEs1(zxw79000, zxw80000, bbe, bbf)
new_lt1(zxw79000, zxw80000, be) → new_compare(zxw79000, zxw80000, be)
new_compare22(Right(zxw7900), Right(zxw8000), False, baf, app(app(app(ty_@3, bee), bef), beg)) → new_ltEs(zxw7900, zxw8000, bee, bef, beg)
new_compare(:(zxw79000, zxw79001), :(zxw80000, zxw80001), eg) → new_compare(zxw79001, zxw80001, eg)
new_compare22(Right(zxw7900), Right(zxw8000), False, baf, app(ty_Maybe, bfe)) → new_ltEs3(zxw7900, zxw8000, bfe)
new_compare22(Left(@3(zxw79000, zxw79001, zxw79002)), Left(@3(zxw80000, zxw80001, zxw80002)), False, app(app(app(ty_@3, cc), app(app(app(ty_@3, cd), ce), cf)), bd), bag) → new_lt0(zxw79001, zxw80001, cd, ce, cf)
new_ltEs1(@2(zxw79000, zxw79001), @2(zxw80000, zxw80001), app(app(app(ty_@3, gb), gc), gd), ge) → new_lt0(zxw79000, zxw80000, gb, gc, gd)
new_compare22(Left(@3(zxw79000, zxw79001, zxw79002)), Left(@3(zxw80000, zxw80001, zxw80002)), False, app(app(app(ty_@3, cc), bc), app(ty_[], ea)), bag) → new_ltEs0(zxw79002, zxw80002, ea)
new_ltEs0(:(zxw79000, zxw79001), :(zxw80000, zxw80001), eg) → new_primCompAux(zxw79000, zxw80000, new_compare1(zxw79001, zxw80001, eg), eg)
new_ltEs(@3(zxw79000, zxw79001, zxw79002), @3(zxw80000, zxw80001, zxw80002), app(app(ty_Either, bh), ca), bc, bd) → new_lt(zxw79000, zxw80000, bh, ca)
new_compare22(Left(@3(zxw79000, zxw79001, zxw79002)), Left(@3(zxw80000, zxw80001, zxw80002)), False, app(app(app(ty_@3, cc), app(app(ty_@2, da), db)), bd), bag) → new_lt2(zxw79001, zxw80001, da, db)
new_compare22(Left(Just(zxw79000)), Left(Just(zxw80000)), False, app(ty_Maybe, app(app(ty_@2, bdh), bea)), bag) → new_ltEs1(zxw79000, zxw80000, bdh, bea)
new_primCompAux(zxw79000, zxw80000, zxw272, app(ty_Maybe, ga)) → new_compare5(zxw79000, zxw80000, ga)
new_compare22(Left(@3(zxw79000, zxw79001, zxw79002)), Left(@3(zxw80000, zxw80001, zxw80002)), False, app(app(app(ty_@3, app(ty_Maybe, cb)), bc), bd), bag) → new_compare21(zxw79000, zxw80000, new_esEs6(zxw79000, zxw80000, cb), cb)
new_compare22(Left(@2(zxw79000, zxw79001)), Left(@2(zxw80000, zxw80001)), False, app(app(ty_@2, app(app(ty_@2, gg), gh)), ge), bag) → new_lt2(zxw79000, zxw80000, gg, gh)
new_ltEs2(Left(zxw79000), Left(zxw80000), app(app(ty_@2, bbe), bbf), bbc) → new_ltEs1(zxw79000, zxw80000, bbe, bbf)
new_compare22(Left(@2(zxw79000, zxw79001)), Left(@2(zxw80000, zxw80001)), False, app(app(ty_@2, app(ty_[], gf)), ge), bag) → new_lt1(zxw79000, zxw80000, gf)
new_ltEs2(Right(zxw79000), Right(zxw80000), bcb, app(ty_Maybe, bdc)) → new_ltEs3(zxw79000, zxw80000, bdc)
new_ltEs(@3(zxw79000, zxw79001, zxw79002), @3(zxw80000, zxw80001, zxw80002), cc, app(ty_Maybe, de), bd) → new_lt3(zxw79001, zxw80001, de)
new_compare22(Left(@3(zxw79000, zxw79001, zxw79002)), Left(@3(zxw80000, zxw80001, zxw80002)), False, app(app(app(ty_@3, cc), bc), app(ty_Maybe, ef)), bag) → new_ltEs3(zxw79002, zxw80002, ef)
new_compare22(Right(zxw7900), Right(zxw8000), False, baf, app(app(ty_@2, bfa), bfb)) → new_ltEs1(zxw7900, zxw8000, bfa, bfb)
new_ltEs1(@2(zxw79000, zxw79001), @2(zxw80000, zxw80001), hd, app(app(ty_Either, bac), bad)) → new_ltEs2(zxw79001, zxw80001, bac, bad)
new_compare22(Left(Just(zxw79000)), Left(Just(zxw80000)), False, app(ty_Maybe, app(app(ty_Either, beb), bec)), bag) → new_ltEs2(zxw79000, zxw80000, beb, bec)

The TRS R consists of the following rules:

new_ltEs15(zxw7900, zxw8000) → new_fsEs(new_compare6(zxw7900, zxw8000))
new_ltEs14(Right(zxw79000), Right(zxw80000), bcb, ty_Bool) → new_ltEs12(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Char) → new_ltEs10(zxw79000, zxw80000)
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, app(ty_Maybe, bfe)) → new_ltEs18(zxw7900, zxw8000, bfe)
new_esEs28(zxw4000, zxw3000, app(ty_[], dda)) → new_esEs13(zxw4000, zxw3000, dda)
new_esEs23(zxw4000, zxw3000, app(app(ty_Either, cha), chb)) → new_esEs7(zxw4000, zxw3000, cha, chb)
new_esEs6(Just(zxw4000), Just(zxw3000), app(app(ty_@2, bgd), bge)) → new_esEs5(zxw4000, zxw3000, bgd, bge)
new_lt4(zxw79000, zxw80000, app(app(app(ty_@3, gb), gc), gd)) → new_lt5(zxw79000, zxw80000, gb, gc, gd)
new_esEs7(Left(zxw4000), Left(zxw3000), app(app(ty_Either, cag), cah), cab) → new_esEs7(zxw4000, zxw3000, cag, cah)
new_ltEs20(zxw7900, zxw8000, ty_Int) → new_ltEs9(zxw7900, zxw8000)
new_lt19(zxw79000, zxw80000, app(app(ty_Either, bh), ca)) → new_lt14(zxw79000, zxw80000, bh, ca)
new_esEs9(GT, LT) → False
new_esEs9(LT, GT) → False
new_esEs13([], [], cgc) → True
new_lt4(zxw79000, zxw80000, app(ty_[], gf)) → new_lt10(zxw79000, zxw80000, gf)
new_compare110(zxw79000, zxw80000, True, bf, bg) → LT
new_esEs27(zxw4001, zxw3001, app(ty_Ratio, dbf)) → new_esEs18(zxw4001, zxw3001, dbf)
new_compare29(zxw79000, zxw80000, ty_Char) → new_compare17(zxw79000, zxw80000)
new_ltEs7(LT, EQ) → True
new_ltEs18(Just(zxw79000), Just(zxw80000), app(ty_Maybe, bed)) → new_ltEs18(zxw79000, zxw80000, bed)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Integer) → new_ltEs13(zxw79000, zxw80000)
new_ltEs20(zxw7900, zxw8000, ty_@0) → new_ltEs8(zxw7900, zxw8000)
new_lt20(zxw79001, zxw80001, app(app(ty_Either, dc), dd)) → new_lt14(zxw79001, zxw80001, dc, dd)
new_esEs23(zxw4000, zxw3000, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_ltEs8(zxw7900, zxw8000) → new_fsEs(new_compare30(zxw7900, zxw8000))
new_lt19(zxw79000, zxw80000, ty_Double) → new_lt15(zxw79000, zxw80000)
new_esEs22(zxw4000, zxw3000, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_ltEs14(Right(zxw79000), Right(zxw80000), bcb, app(ty_[], bcf)) → new_ltEs11(zxw79000, zxw80000, bcf)
new_ltEs21(zxw79002, zxw80002, ty_Char) → new_ltEs10(zxw79002, zxw80002)
new_esEs23(zxw4000, zxw3000, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Bool, bbc) → new_ltEs12(zxw79000, zxw80000)
new_compare8(:%(zxw79000, zxw79001), :%(zxw80000, zxw80001), ty_Integer) → new_compare32(new_sr0(zxw79000, zxw80001), new_sr0(zxw80000, zxw79001))
new_esEs26(zxw4002, zxw3002, ty_Float) → new_esEs17(zxw4002, zxw3002)
new_esEs19(zxw79001, zxw80001, app(ty_Ratio, ccg)) → new_esEs18(zxw79001, zxw80001, ccg)
new_primMulNat0(Zero, Zero) → Zero
new_esEs20(zxw79000, zxw80000, app(ty_[], be)) → new_esEs13(zxw79000, zxw80000, be)
new_esEs7(Right(zxw4000), Right(zxw3000), cbd, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_lt20(zxw79001, zxw80001, ty_@0) → new_lt7(zxw79001, zxw80001)
new_esEs27(zxw4001, zxw3001, app(app(app(ty_@3, dce), dcf), dcg)) → new_esEs4(zxw4001, zxw3001, dce, dcf, dcg)
new_esEs19(zxw79001, zxw80001, ty_Ordering) → new_esEs9(zxw79001, zxw80001)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(ty_Ratio, cdb)) → new_ltEs17(zxw79000, zxw80000, cdb)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Bool, cab) → new_esEs14(zxw4000, zxw3000)
new_esEs24(zxw4001, zxw3001, ty_Integer) → new_esEs15(zxw4001, zxw3001)
new_lt19(zxw79000, zxw80000, ty_Ordering) → new_lt6(zxw79000, zxw80000)
new_lt20(zxw79001, zxw80001, app(app(ty_@2, da), db)) → new_lt11(zxw79001, zxw80001, da, db)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(ty_Ratio, cdc), bbc) → new_ltEs17(zxw79000, zxw80000, cdc)
new_compare9(zxw79000, zxw80000, h, ba, bb) → new_compare25(zxw79000, zxw80000, new_esEs4(zxw79000, zxw80000, h, ba, bb), h, ba, bb)
new_lt11(zxw79000, zxw80000, bf, bg) → new_esEs9(new_compare19(zxw79000, zxw80000, bf, bg), LT)
new_compare1([], :(zxw80000, zxw80001), eg) → LT
new_lt18(zxw79000, zxw80000, cb) → new_esEs9(new_compare27(zxw79000, zxw80000, cb), LT)
new_esEs8(zxw79000, zxw80000, ty_Int) → new_esEs11(zxw79000, zxw80000)
new_compare32(Integer(zxw79000), Integer(zxw80000)) → new_primCmpInt(zxw79000, zxw80000)
new_ltEs5(zxw79001, zxw80001, ty_Char) → new_ltEs10(zxw79001, zxw80001)
new_lt4(zxw79000, zxw80000, ty_Bool) → new_lt12(zxw79000, zxw80000)
new_compare27(zxw79000, zxw80000, cb) → new_compare28(zxw79000, zxw80000, new_esEs6(zxw79000, zxw80000, cb), cb)
new_lt4(zxw79000, zxw80000, app(ty_Maybe, hc)) → new_lt18(zxw79000, zxw80000, hc)
new_compare29(zxw79000, zxw80000, ty_Bool) → new_compare31(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, ty_Double) → new_esEs16(zxw79000, zxw80000)
new_esEs22(zxw4000, zxw3000, app(app(ty_@2, cfd), cfe)) → new_esEs5(zxw4000, zxw3000, cfd, cfe)
new_lt4(zxw79000, zxw80000, ty_Ordering) → new_lt6(zxw79000, zxw80000)
new_esEs22(zxw4000, zxw3000, app(ty_Maybe, cfc)) → new_esEs6(zxw4000, zxw3000, cfc)
new_ltEs14(Right(zxw79000), Right(zxw80000), bcb, app(app(app(ty_@3, bcc), bcd), bce)) → new_ltEs6(zxw79000, zxw80000, bcc, bcd, bce)
new_esEs27(zxw4001, zxw3001, app(ty_Maybe, dbh)) → new_esEs6(zxw4001, zxw3001, dbh)
new_esEs8(zxw79000, zxw80000, app(app(app(ty_@3, gb), gc), gd)) → new_esEs4(zxw79000, zxw80000, gb, gc, gd)
new_esEs15(Integer(zxw4000), Integer(zxw3000)) → new_primEqInt(zxw4000, zxw3000)
new_ltEs21(zxw79002, zxw80002, app(app(ty_@2, eb), ec)) → new_ltEs4(zxw79002, zxw80002, eb, ec)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Float, bbc) → new_ltEs16(zxw79000, zxw80000)
new_lt5(zxw79000, zxw80000, h, ba, bb) → new_esEs9(new_compare9(zxw79000, zxw80000, h, ba, bb), LT)
new_esEs22(zxw4000, zxw3000, app(ty_Ratio, cfa)) → new_esEs18(zxw4000, zxw3000, cfa)
new_esEs22(zxw4000, zxw3000, app(app(ty_Either, cff), cfg)) → new_esEs7(zxw4000, zxw3000, cff, cfg)
new_ltEs19(zxw7900, zxw8000, ty_Float) → new_ltEs16(zxw7900, zxw8000)
new_esEs7(Right(zxw4000), Right(zxw3000), cbd, app(ty_Maybe, cbg)) → new_esEs6(zxw4000, zxw3000, cbg)
new_pePe(False, zxw271) → zxw271
new_esEs7(Left(zxw4000), Right(zxw3000), cbd, cab) → False
new_esEs7(Right(zxw4000), Left(zxw3000), cbd, cab) → False
new_lt15(zxw79000, zxw80000) → new_esEs9(new_compare6(zxw79000, zxw80000), LT)
new_compare15(zxw790, zxw800, baf, bag) → new_compare26(zxw790, zxw800, new_esEs7(zxw790, zxw800, baf, bag), baf, bag)
new_ltEs14(Right(zxw79000), Right(zxw80000), bcb, ty_Float) → new_ltEs16(zxw79000, zxw80000)
new_ltEs12(True, False) → False
new_esEs20(zxw79000, zxw80000, ty_Double) → new_esEs16(zxw79000, zxw80000)
new_ltEs19(zxw7900, zxw8000, app(app(ty_@2, hd), ge)) → new_ltEs4(zxw7900, zxw8000, hd, ge)
new_compare23(zxw79000, zxw80000, True) → EQ
new_esEs27(zxw4001, zxw3001, app(app(ty_Either, dcc), dcd)) → new_esEs7(zxw4001, zxw3001, dcc, dcd)
new_esEs27(zxw4001, zxw3001, ty_Ordering) → new_esEs9(zxw4001, zxw3001)
new_esEs27(zxw4001, zxw3001, ty_Float) → new_esEs17(zxw4001, zxw3001)
new_esEs19(zxw79001, zxw80001, app(ty_Maybe, de)) → new_esEs6(zxw79001, zxw80001, de)
new_lt10(zxw79000, zxw80000, be) → new_esEs9(new_compare1(zxw79000, zxw80000, be), LT)
new_esEs26(zxw4002, zxw3002, ty_Char) → new_esEs12(zxw4002, zxw3002)
new_ltEs19(zxw7900, zxw8000, app(ty_[], eg)) → new_ltEs11(zxw7900, zxw8000, eg)
new_esEs26(zxw4002, zxw3002, ty_Int) → new_esEs11(zxw4002, zxw3002)
new_ltEs5(zxw79001, zxw80001, app(app(ty_@2, baa), bab)) → new_ltEs4(zxw79001, zxw80001, baa, bab)
new_lt19(zxw79000, zxw80000, app(ty_Ratio, bhc)) → new_lt17(zxw79000, zxw80000, bhc)
new_esEs22(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, app(app(app(ty_@3, ddg), ddh), dea)) → new_esEs4(zxw4000, zxw3000, ddg, ddh, dea)
new_compare29(zxw79000, zxw80000, app(app(ty_@2, fd), ff)) → new_compare19(zxw79000, zxw80000, fd, ff)
new_ltEs21(zxw79002, zxw80002, ty_Int) → new_ltEs9(zxw79002, zxw80002)
new_esEs20(zxw79000, zxw80000, ty_Char) → new_esEs12(zxw79000, zxw80000)
new_compare13(zxw235, zxw236, False, bhg, bhh) → GT
new_esEs9(GT, EQ) → False
new_esEs9(EQ, GT) → False
new_esEs19(zxw79001, zxw80001, app(app(ty_Either, dc), dd)) → new_esEs7(zxw79001, zxw80001, dc, dd)
new_esEs20(zxw79000, zxw80000, app(app(ty_@2, bf), bg)) → new_esEs5(zxw79000, zxw80000, bf, bg)
new_ltEs7(GT, GT) → True
new_ltEs20(zxw7900, zxw8000, app(app(ty_@2, bfa), bfb)) → new_ltEs4(zxw7900, zxw8000, bfa, bfb)
new_esEs7(Right(zxw4000), Right(zxw3000), cbd, app(app(ty_@2, cbh), cca)) → new_esEs5(zxw4000, zxw3000, cbh, cca)
new_esEs21(zxw4001, zxw3001, ty_Bool) → new_esEs14(zxw4001, zxw3001)
new_primCompAux0(zxw79000, zxw80000, zxw272, eg) → new_primCompAux00(zxw272, new_compare29(zxw79000, zxw80000, eg))
new_ltEs21(zxw79002, zxw80002, ty_Ordering) → new_ltEs7(zxw79002, zxw80002)
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_compare29(zxw79000, zxw80000, app(ty_[], fc)) → new_compare1(zxw79000, zxw80000, fc)
new_lt20(zxw79001, zxw80001, ty_Ordering) → new_lt6(zxw79001, zxw80001)
new_esEs8(zxw79000, zxw80000, app(ty_[], gf)) → new_esEs13(zxw79000, zxw80000, gf)
new_esEs7(Right(zxw4000), Right(zxw3000), cbd, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_esEs27(zxw4001, zxw3001, ty_@0) → new_esEs10(zxw4001, zxw3001)
new_compare25(zxw79000, zxw80000, True, h, ba, bb) → EQ
new_esEs19(zxw79001, zxw80001, ty_Float) → new_esEs17(zxw79001, zxw80001)
new_ltEs5(zxw79001, zxw80001, ty_Ordering) → new_ltEs7(zxw79001, zxw80001)
new_lt4(zxw79000, zxw80000, app(ty_Ratio, bff)) → new_lt17(zxw79000, zxw80000, bff)
new_esEs28(zxw4000, zxw3000, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Int, cab) → new_esEs11(zxw4000, zxw3000)
new_ltEs21(zxw79002, zxw80002, ty_Float) → new_ltEs16(zxw79002, zxw80002)
new_esEs28(zxw4000, zxw3000, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(app(app(ty_@3, bdd), bde), bdf)) → new_ltEs6(zxw79000, zxw80000, bdd, bde, bdf)
new_compare29(zxw79000, zxw80000, app(app(app(ty_@3, eh), fa), fb)) → new_compare9(zxw79000, zxw80000, eh, fa, fb)
new_lt19(zxw79000, zxw80000, app(app(ty_@2, bf), bg)) → new_lt11(zxw79000, zxw80000, bf, bg)
new_pePe(True, zxw271) → True
new_primEqNat0(Zero, Zero) → True
new_compare14(zxw242, zxw243, False, chg, chh) → GT
new_ltEs14(Right(zxw79000), Right(zxw80000), bcb, ty_Double) → new_ltEs15(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, ty_Int) → new_esEs11(zxw79000, zxw80000)
new_ltEs21(zxw79002, zxw80002, ty_Bool) → new_ltEs12(zxw79002, zxw80002)
new_lt9(zxw79000, zxw80000) → new_esEs9(new_compare17(zxw79000, zxw80000), LT)
new_ltEs12(False, False) → True
new_esEs7(Left(zxw4000), Left(zxw3000), app(app(ty_@2, cae), caf), cab) → new_esEs5(zxw4000, zxw3000, cae, caf)
new_esEs26(zxw4002, zxw3002, app(ty_Maybe, daf)) → new_esEs6(zxw4002, zxw3002, daf)
new_compare8(:%(zxw79000, zxw79001), :%(zxw80000, zxw80001), ty_Int) → new_compare16(new_sr(zxw79000, zxw80001), new_sr(zxw80000, zxw79001))
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Ordering, cab) → new_esEs9(zxw4000, zxw3000)
new_esEs27(zxw4001, zxw3001, ty_Char) → new_esEs12(zxw4001, zxw3001)
new_lt7(zxw79000, zxw80000) → new_esEs9(new_compare30(zxw79000, zxw80000), LT)
new_compare110(zxw79000, zxw80000, False, bf, bg) → GT
new_sr(zxw4000, zxw3000) → new_primMulInt(zxw4000, zxw3000)
new_compare12(zxw79000, zxw80000, True, h, ba, bb) → LT
new_lt19(zxw79000, zxw80000, ty_Int) → new_lt8(zxw79000, zxw80000)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_ltEs14(Right(zxw79000), Right(zxw80000), bcb, app(app(ty_@2, bcg), bch)) → new_ltEs4(zxw79000, zxw80000, bcg, bch)
new_ltEs19(zxw7900, zxw8000, ty_Char) → new_ltEs10(zxw7900, zxw8000)
new_esEs21(zxw4001, zxw3001, ty_Double) → new_esEs16(zxw4001, zxw3001)
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_esEs7(Right(zxw4000), Right(zxw3000), cbd, app(app(ty_Either, ccb), ccc)) → new_esEs7(zxw4000, zxw3000, ccb, ccc)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Double, bbc) → new_ltEs15(zxw79000, zxw80000)
new_ltEs19(zxw7900, zxw8000, ty_Bool) → new_ltEs12(zxw7900, zxw8000)
new_esEs26(zxw4002, zxw3002, app(app(app(ty_@3, dbc), dbd), dbe)) → new_esEs4(zxw4002, zxw3002, dbc, dbd, dbe)
new_esEs7(Right(zxw4000), Right(zxw3000), cbd, app(ty_[], cbf)) → new_esEs13(zxw4000, zxw3000, cbf)
new_ltEs11(zxw7900, zxw8000, eg) → new_fsEs(new_compare1(zxw7900, zxw8000, eg))
new_ltEs20(zxw7900, zxw8000, ty_Float) → new_ltEs16(zxw7900, zxw8000)
new_esEs21(zxw4001, zxw3001, ty_Ordering) → new_esEs9(zxw4001, zxw3001)
new_esEs7(Right(zxw4000), Right(zxw3000), cbd, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_esEs9(EQ, EQ) → True
new_fsEs(zxw259) → new_not(new_esEs9(zxw259, GT))
new_esEs8(zxw79000, zxw80000, ty_Char) → new_esEs12(zxw79000, zxw80000)
new_primEqInt(Neg(Succ(zxw40000)), Neg(Succ(zxw30000))) → new_primEqNat0(zxw40000, zxw30000)
new_esEs8(zxw79000, zxw80000, app(app(ty_@2, gg), gh)) → new_esEs5(zxw79000, zxw80000, gg, gh)
new_compare13(zxw235, zxw236, True, bhg, bhh) → LT
new_compare26(Left(zxw7900), Right(zxw8000), False, baf, bag) → LT
new_esEs13(:(zxw4000, zxw4001), :(zxw3000, zxw3001), cgc) → new_asAs(new_esEs23(zxw4000, zxw3000, cgc), new_esEs13(zxw4001, zxw3001, cgc))
new_esEs26(zxw4002, zxw3002, app(ty_[], dae)) → new_esEs13(zxw4002, zxw3002, dae)
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_ltEs19(zxw7900, zxw8000, app(ty_Ratio, bhd)) → new_ltEs17(zxw7900, zxw8000, bhd)
new_ltEs20(zxw7900, zxw8000, ty_Bool) → new_ltEs12(zxw7900, zxw8000)
new_esEs21(zxw4001, zxw3001, ty_Char) → new_esEs12(zxw4001, zxw3001)
new_compare23(zxw79000, zxw80000, False) → new_compare10(zxw79000, zxw80000, new_ltEs12(zxw79000, zxw80000))
new_ltEs14(Right(zxw79000), Left(zxw80000), bcb, bbc) → False
new_compare210(zxw79000, zxw80000, False, bf, bg) → new_compare110(zxw79000, zxw80000, new_ltEs4(zxw79000, zxw80000, bf, bg), bf, bg)
new_primCmpNat1(Zero, zxw7900) → LT
new_compare7(Float(zxw79000, zxw79001), Float(zxw80000, zxw80001)) → new_compare16(new_sr(zxw79000, zxw80000), new_sr(zxw79001, zxw80001))
new_ltEs21(zxw79002, zxw80002, ty_Integer) → new_ltEs13(zxw79002, zxw80002)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_lt20(zxw79001, zxw80001, app(ty_Maybe, de)) → new_lt18(zxw79001, zxw80001, de)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Integer, cab) → new_esEs15(zxw4000, zxw3000)
new_ltEs5(zxw79001, zxw80001, ty_Bool) → new_ltEs12(zxw79001, zxw80001)
new_esEs19(zxw79001, zxw80001, ty_Bool) → new_esEs14(zxw79001, zxw80001)
new_ltEs7(EQ, EQ) → True
new_ltEs20(zxw7900, zxw8000, app(ty_Ratio, bhf)) → new_ltEs17(zxw7900, zxw8000, bhf)
new_primEqInt(Neg(Zero), Neg(Succ(zxw30000))) → False
new_primEqInt(Neg(Succ(zxw40000)), Neg(Zero)) → False
new_ltEs5(zxw79001, zxw80001, ty_Integer) → new_ltEs13(zxw79001, zxw80001)
new_compare26(zxw790, zxw800, True, baf, bag) → EQ
new_compare111(zxw79000, zxw80000, True, cb) → LT
new_esEs20(zxw79000, zxw80000, ty_@0) → new_esEs10(zxw79000, zxw80000)
new_ltEs21(zxw79002, zxw80002, app(app(ty_Either, ed), ee)) → new_ltEs14(zxw79002, zxw80002, ed, ee)
new_esEs8(zxw79000, zxw80000, ty_Float) → new_esEs17(zxw79000, zxw80000)
new_esEs23(zxw4000, zxw3000, app(app(app(ty_@3, chc), chd), che)) → new_esEs4(zxw4000, zxw3000, chc, chd, che)
new_ltEs21(zxw79002, zxw80002, app(ty_[], ea)) → new_ltEs11(zxw79002, zxw80002, ea)
new_esEs21(zxw4001, zxw3001, ty_Float) → new_esEs17(zxw4001, zxw3001)
new_compare24(zxw79000, zxw80000, False) → new_compare11(zxw79000, zxw80000, new_ltEs7(zxw79000, zxw80000))
new_ltEs5(zxw79001, zxw80001, app(ty_Ratio, bfg)) → new_ltEs17(zxw79001, zxw80001, bfg)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_esEs26(zxw4002, zxw3002, app(app(ty_Either, dba), dbb)) → new_esEs7(zxw4002, zxw3002, dba, dbb)
new_lt20(zxw79001, zxw80001, ty_Int) → new_lt8(zxw79001, zxw80001)
new_lt4(zxw79000, zxw80000, ty_Int) → new_lt8(zxw79000, zxw80000)
new_ltEs20(zxw7900, zxw8000, ty_Double) → new_ltEs15(zxw7900, zxw8000)
new_lt12(zxw79000, zxw80000) → new_esEs9(new_compare31(zxw79000, zxw80000), LT)
new_ltEs7(GT, LT) → False
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Int, bbc) → new_ltEs9(zxw79000, zxw80000)
new_lt20(zxw79001, zxw80001, ty_Integer) → new_lt13(zxw79001, zxw80001)
new_ltEs7(GT, EQ) → False
new_esEs6(Nothing, Nothing, bfh) → True
new_primEqInt(Pos(Succ(zxw40000)), Pos(Succ(zxw30000))) → new_primEqNat0(zxw40000, zxw30000)
new_lt8(zxw790, zxw800) → new_esEs9(new_compare16(zxw790, zxw800), LT)
new_esEs21(zxw4001, zxw3001, app(ty_Maybe, cea)) → new_esEs6(zxw4001, zxw3001, cea)
new_lt6(zxw79000, zxw80000) → new_esEs9(new_compare18(zxw79000, zxw80000), LT)
new_esEs14(False, True) → False
new_esEs14(True, False) → False
new_esEs26(zxw4002, zxw3002, ty_Integer) → new_esEs15(zxw4002, zxw3002)
new_esEs7(Right(zxw4000), Right(zxw3000), cbd, app(app(app(ty_@3, ccd), cce), ccf)) → new_esEs4(zxw4000, zxw3000, ccd, cce, ccf)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs6(Nothing, Just(zxw3000), bfh) → False
new_esEs6(Just(zxw4000), Nothing, bfh) → False
new_primEqNat0(Succ(zxw40000), Succ(zxw30000)) → new_primEqNat0(zxw40000, zxw30000)
new_esEs16(Double(zxw4000, zxw4001), Double(zxw3000, zxw3001)) → new_esEs11(new_sr(zxw4000, zxw3000), new_sr(zxw4001, zxw3001))
new_lt19(zxw79000, zxw80000, ty_@0) → new_lt7(zxw79000, zxw80000)
new_ltEs5(zxw79001, zxw80001, app(ty_Maybe, bae)) → new_ltEs18(zxw79001, zxw80001, bae)
new_esEs17(Float(zxw4000, zxw4001), Float(zxw3000, zxw3001)) → new_esEs11(new_sr(zxw4000, zxw3000), new_sr(zxw4001, zxw3001))
new_primCompAux00(zxw276, LT) → LT
new_esEs28(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), app(ty_Ratio, caa), cab) → new_esEs18(zxw4000, zxw3000, caa)
new_esEs21(zxw4001, zxw3001, ty_Int) → new_esEs11(zxw4001, zxw3001)
new_compare1(:(zxw79000, zxw79001), :(zxw80000, zxw80001), eg) → new_primCompAux0(zxw79000, zxw80000, new_compare1(zxw79001, zxw80001, eg), eg)
new_primEqInt(Pos(Zero), Pos(Succ(zxw30000))) → False
new_primEqInt(Pos(Succ(zxw40000)), Pos(Zero)) → False
new_compare29(zxw79000, zxw80000, ty_Int) → new_compare16(zxw79000, zxw80000)
new_lt20(zxw79001, zxw80001, app(ty_Ratio, ccg)) → new_lt17(zxw79001, zxw80001, ccg)
new_ltEs20(zxw7900, zxw8000, ty_Integer) → new_ltEs13(zxw7900, zxw8000)
new_esEs5(@2(zxw4000, zxw4001), @2(zxw3000, zxw3001), cde, cdf) → new_asAs(new_esEs22(zxw4000, zxw3000, cde), new_esEs21(zxw4001, zxw3001, cdf))
new_ltEs18(Nothing, Nothing, bhe) → True
new_ltEs21(zxw79002, zxw80002, app(ty_Ratio, cch)) → new_ltEs17(zxw79002, zxw80002, cch)
new_esEs23(zxw4000, zxw3000, app(app(ty_@2, cgg), cgh)) → new_esEs5(zxw4000, zxw3000, cgg, cgh)
new_esEs20(zxw79000, zxw80000, app(app(app(ty_@3, h), ba), bb)) → new_esEs4(zxw79000, zxw80000, h, ba, bb)
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_ltEs21(zxw79002, zxw80002, app(app(app(ty_@3, df), dg), dh)) → new_ltEs6(zxw79002, zxw80002, df, dg, dh)
new_ltEs10(zxw7900, zxw8000) → new_fsEs(new_compare17(zxw7900, zxw8000))
new_compare17(Char(zxw79000), Char(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_sr0(Integer(zxw800000), Integer(zxw790010)) → Integer(new_primMulInt(zxw800000, zxw790010))
new_ltEs5(zxw79001, zxw80001, ty_Double) → new_ltEs15(zxw79001, zxw80001)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_esEs8(zxw79000, zxw80000, app(app(ty_Either, ha), hb)) → new_esEs7(zxw79000, zxw80000, ha, hb)
new_primEqInt(Neg(Succ(zxw40000)), Pos(zxw3000)) → False
new_primEqInt(Pos(Succ(zxw40000)), Neg(zxw3000)) → False
new_compare29(zxw79000, zxw80000, ty_Integer) → new_compare32(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), bcb, ty_Char) → new_ltEs10(zxw79000, zxw80000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_@0, cab) → new_esEs10(zxw4000, zxw3000)
new_lt19(zxw79000, zxw80000, app(app(app(ty_@3, h), ba), bb)) → new_lt5(zxw79000, zxw80000, h, ba, bb)
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_esEs28(zxw4000, zxw3000, app(ty_Maybe, ddb)) → new_esEs6(zxw4000, zxw3000, ddb)
new_esEs21(zxw4001, zxw3001, app(ty_[], cdh)) → new_esEs13(zxw4001, zxw3001, cdh)
new_ltEs21(zxw79002, zxw80002, ty_@0) → new_ltEs8(zxw79002, zxw80002)
new_primEqInt(Neg(Zero), Pos(Succ(zxw30000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(zxw30000))) → False
new_ltEs7(EQ, GT) → True
new_lt4(zxw79000, zxw80000, ty_Double) → new_lt15(zxw79000, zxw80000)
new_esEs21(zxw4001, zxw3001, ty_Integer) → new_esEs15(zxw4001, zxw3001)
new_primCompAux00(zxw276, EQ) → zxw276
new_esEs28(zxw4000, zxw3000, app(app(ty_Either, dde), ddf)) → new_esEs7(zxw4000, zxw3000, dde, ddf)
new_compare24(zxw79000, zxw80000, True) → EQ
new_compare6(Double(zxw79000, zxw79001), Double(zxw80000, zxw80001)) → new_compare16(new_sr(zxw79000, zxw80000), new_sr(zxw79001, zxw80001))
new_esEs8(zxw79000, zxw80000, ty_@0) → new_esEs10(zxw79000, zxw80000)
new_ltEs5(zxw79001, zxw80001, app(app(ty_Either, bac), bad)) → new_ltEs14(zxw79001, zxw80001, bac, bad)
new_lt13(zxw79000, zxw80000) → new_esEs9(new_compare32(zxw79000, zxw80000), LT)
new_esEs27(zxw4001, zxw3001, ty_Double) → new_esEs16(zxw4001, zxw3001)
new_esEs7(Left(zxw4000), Left(zxw3000), app(app(app(ty_@3, cba), cbb), cbc), cab) → new_esEs4(zxw4000, zxw3000, cba, cbb, cbc)
new_esEs26(zxw4002, zxw3002, app(app(ty_@2, dag), dah)) → new_esEs5(zxw4002, zxw3002, dag, dah)
new_esEs21(zxw4001, zxw3001, app(app(ty_@2, ceb), cec)) → new_esEs5(zxw4001, zxw3001, ceb, cec)
new_lt19(zxw79000, zxw80000, app(ty_Maybe, cb)) → new_lt18(zxw79000, zxw80000, cb)
new_esEs12(Char(zxw4000), Char(zxw3000)) → new_primEqNat0(zxw4000, zxw3000)
new_ltEs20(zxw7900, zxw8000, app(app(app(ty_@3, bee), bef), beg)) → new_ltEs6(zxw7900, zxw8000, bee, bef, beg)
new_not(False) → True
new_lt20(zxw79001, zxw80001, ty_Char) → new_lt9(zxw79001, zxw80001)
new_esEs11(zxw400, zxw300) → new_primEqInt(zxw400, zxw300)
new_ltEs14(Right(zxw79000), Right(zxw80000), bcb, app(ty_Maybe, bdc)) → new_ltEs18(zxw79000, zxw80000, bdc)
new_ltEs18(Just(zxw79000), Nothing, bhe) → False
new_esEs8(zxw79000, zxw80000, app(ty_Maybe, hc)) → new_esEs6(zxw79000, zxw80000, hc)
new_esEs7(Left(zxw4000), Left(zxw3000), app(ty_Maybe, cad), cab) → new_esEs6(zxw4000, zxw3000, cad)
new_compare210(zxw79000, zxw80000, True, bf, bg) → EQ
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Double, cab) → new_esEs16(zxw4000, zxw3000)
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_esEs19(zxw79001, zxw80001, ty_Int) → new_esEs11(zxw79001, zxw80001)
new_compare12(zxw79000, zxw80000, False, h, ba, bb) → GT
new_ltEs16(zxw7900, zxw8000) → new_fsEs(new_compare7(zxw7900, zxw8000))
new_esEs9(GT, GT) → True
new_esEs26(zxw4002, zxw3002, app(ty_Ratio, dad)) → new_esEs18(zxw4002, zxw3002, dad)
new_esEs25(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_lt20(zxw79001, zxw80001, app(ty_[], cg)) → new_lt10(zxw79001, zxw80001, cg)
new_lt4(zxw79000, zxw80000, app(app(ty_Either, ha), hb)) → new_lt14(zxw79000, zxw80000, ha, hb)
new_esEs26(zxw4002, zxw3002, ty_Bool) → new_esEs14(zxw4002, zxw3002)
new_compare19(zxw79000, zxw80000, bf, bg) → new_compare210(zxw79000, zxw80000, new_esEs5(zxw79000, zxw80000, bf, bg), bf, bg)
new_esEs8(zxw79000, zxw80000, ty_Bool) → new_esEs14(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Double) → new_ltEs15(zxw79000, zxw80000)
new_esEs28(zxw4000, zxw3000, app(app(ty_@2, ddc), ddd)) → new_esEs5(zxw4000, zxw3000, ddc, ddd)
new_ltEs19(zxw7900, zxw8000, app(app(app(ty_@3, cc), bc), bd)) → new_ltEs6(zxw7900, zxw8000, cc, bc, bd)
new_lt4(zxw79000, zxw80000, ty_Char) → new_lt9(zxw79000, zxw80000)
new_esEs22(zxw4000, zxw3000, app(app(app(ty_@3, cfh), cga), cgb)) → new_esEs4(zxw4000, zxw3000, cfh, cga, cgb)
new_esEs22(zxw4000, zxw3000, app(ty_[], cfb)) → new_esEs13(zxw4000, zxw3000, cfb)
new_ltEs14(Right(zxw79000), Right(zxw80000), bcb, ty_@0) → new_ltEs8(zxw79000, zxw80000)
new_esEs23(zxw4000, zxw3000, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Float, cab) → new_esEs17(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_esEs27(zxw4001, zxw3001, ty_Int) → new_esEs11(zxw4001, zxw3001)
new_esEs19(zxw79001, zxw80001, app(app(app(ty_@3, cd), ce), cf)) → new_esEs4(zxw79001, zxw80001, cd, ce, cf)
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_esEs7(Right(zxw4000), Right(zxw3000), cbd, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(app(app(ty_@3, bah), bba), bbb), bbc) → new_ltEs6(zxw79000, zxw80000, bah, bba, bbb)
new_ltEs19(zxw7900, zxw8000, ty_Int) → new_ltEs9(zxw7900, zxw8000)
new_lt4(zxw79000, zxw80000, ty_@0) → new_lt7(zxw79000, zxw80000)
new_lt20(zxw79001, zxw80001, ty_Double) → new_lt15(zxw79001, zxw80001)
new_lt19(zxw79000, zxw80000, ty_Float) → new_lt16(zxw79000, zxw80000)
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_esEs26(zxw4002, zxw3002, ty_@0) → new_esEs10(zxw4002, zxw3002)
new_lt19(zxw79000, zxw80000, ty_Bool) → new_lt12(zxw79000, zxw80000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Char, cab) → new_esEs12(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(ty_[], bdg)) → new_ltEs11(zxw79000, zxw80000, bdg)
new_lt4(zxw79000, zxw80000, ty_Float) → new_lt16(zxw79000, zxw80000)
new_primMulInt(Neg(zxw40000), Neg(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_ltEs5(zxw79001, zxw80001, app(app(app(ty_@3, he), hf), hg)) → new_ltEs6(zxw79001, zxw80001, he, hf, hg)
new_primCmpNat2(Zero, Zero) → EQ
new_esEs20(zxw79000, zxw80000, ty_Integer) → new_esEs15(zxw79000, zxw80000)
new_primEqNat0(Zero, Succ(zxw30000)) → False
new_primEqNat0(Succ(zxw40000), Zero) → False
new_esEs21(zxw4001, zxw3001, ty_@0) → new_esEs10(zxw4001, zxw3001)
new_esEs22(zxw4000, zxw3000, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_esEs20(zxw79000, zxw80000, ty_Bool) → new_esEs14(zxw79000, zxw80000)
new_ltEs5(zxw79001, zxw80001, app(ty_[], hh)) → new_ltEs11(zxw79001, zxw80001, hh)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs23(zxw4000, zxw3000, app(ty_Ratio, cgd)) → new_esEs18(zxw4000, zxw3000, cgd)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(app(ty_@2, bdh), bea)) → new_ltEs4(zxw79000, zxw80000, bdh, bea)
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_ltEs5(zxw79001, zxw80001, ty_Int) → new_ltEs9(zxw79001, zxw80001)
new_esEs27(zxw4001, zxw3001, app(app(ty_@2, dca), dcb)) → new_esEs5(zxw4001, zxw3001, dca, dcb)
new_primCmpNat0(zxw7900, Zero) → GT
new_compare26(Right(zxw7900), Left(zxw8000), False, baf, bag) → GT
new_esEs23(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_@0, bbc) → new_ltEs8(zxw79000, zxw80000)
new_ltEs21(zxw79002, zxw80002, app(ty_Maybe, ef)) → new_ltEs18(zxw79002, zxw80002, ef)
new_esEs21(zxw4001, zxw3001, app(app(ty_Either, ced), cee)) → new_esEs7(zxw4001, zxw3001, ced, cee)
new_esEs22(zxw4000, zxw3000, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Bool) → new_ltEs12(zxw79000, zxw80000)
new_compare29(zxw79000, zxw80000, app(ty_Maybe, ga)) → new_compare27(zxw79000, zxw80000, ga)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_ltEs14(Left(zxw79000), Left(zxw80000), app(ty_Maybe, bca), bbc) → new_ltEs18(zxw79000, zxw80000, bca)
new_lt20(zxw79001, zxw80001, ty_Float) → new_lt16(zxw79001, zxw80001)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Ordering) → new_ltEs7(zxw79000, zxw80000)
new_lt17(zxw79000, zxw80000, bhc) → new_esEs9(new_compare8(zxw79000, zxw80000, bhc), LT)
new_compare30(@0, @0) → EQ
new_lt19(zxw79000, zxw80000, app(ty_[], be)) → new_lt10(zxw79000, zxw80000, be)
new_esEs21(zxw4001, zxw3001, app(app(app(ty_@3, cef), ceg), ceh)) → new_esEs4(zxw4001, zxw3001, cef, ceg, ceh)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_esEs20(zxw79000, zxw80000, app(ty_Ratio, bhc)) → new_esEs18(zxw79000, zxw80000, bhc)
new_esEs6(Just(zxw4000), Just(zxw3000), app(app(app(ty_@3, bgh), bha), bhb)) → new_esEs4(zxw4000, zxw3000, bgh, bha, bhb)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(app(ty_Either, beb), bec)) → new_ltEs14(zxw79000, zxw80000, beb, bec)
new_esEs24(zxw4001, zxw3001, ty_Int) → new_esEs11(zxw4001, zxw3001)
new_esEs8(zxw79000, zxw80000, ty_Ordering) → new_esEs9(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), bcb, ty_Ordering) → new_ltEs7(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, app(app(ty_Either, bh), ca)) → new_esEs7(zxw79000, zxw80000, bh, ca)
new_compare29(zxw79000, zxw80000, app(ty_Ratio, cda)) → new_compare8(zxw79000, zxw80000, cda)
new_lt4(zxw79000, zxw80000, app(app(ty_@2, gg), gh)) → new_lt11(zxw79000, zxw80000, gg, gh)
new_compare29(zxw79000, zxw80000, ty_Float) → new_compare7(zxw79000, zxw80000)
new_esEs19(zxw79001, zxw80001, app(app(ty_@2, da), db)) → new_esEs5(zxw79001, zxw80001, da, db)
new_esEs10(@0, @0) → True
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_compare29(zxw79000, zxw80000, ty_Double) → new_compare6(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, app(ty_Maybe, cb)) → new_esEs6(zxw79000, zxw80000, cb)
new_ltEs14(Left(zxw79000), Right(zxw80000), bcb, bbc) → True
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Float) → new_ltEs16(zxw79000, zxw80000)
new_esEs28(zxw4000, zxw3000, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_compare29(zxw79000, zxw80000, app(app(ty_Either, fg), fh)) → new_compare15(zxw79000, zxw80000, fg, fh)
new_esEs19(zxw79001, zxw80001, ty_Double) → new_esEs16(zxw79001, zxw80001)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_ltEs20(zxw7900, zxw8000, app(app(ty_Either, bfc), bfd)) → new_ltEs14(zxw7900, zxw8000, bfc, bfd)
new_asAs(False, zxw230) → False
new_ltEs13(zxw7900, zxw8000) → new_fsEs(new_compare32(zxw7900, zxw8000))
new_ltEs19(zxw7900, zxw8000, app(app(ty_Either, bcb), bbc)) → new_ltEs14(zxw7900, zxw8000, bcb, bbc)
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Pos(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_ltEs20(zxw7900, zxw8000, app(ty_[], beh)) → new_ltEs11(zxw7900, zxw8000, beh)
new_compare16(zxw79, zxw80) → new_primCmpInt(zxw79, zxw80)
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_esEs13(:(zxw4000, zxw4001), [], cgc) → False
new_esEs13([], :(zxw3000, zxw3001), cgc) → False
new_compare25(zxw79000, zxw80000, False, h, ba, bb) → new_compare12(zxw79000, zxw80000, new_ltEs6(zxw79000, zxw80000, h, ba, bb), h, ba, bb)
new_esEs7(Right(zxw4000), Right(zxw3000), cbd, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(app(ty_@2, bbe), bbf), bbc) → new_ltEs4(zxw79000, zxw80000, bbe, bbf)
new_esEs6(Just(zxw4000), Just(zxw3000), app(ty_Maybe, bgc)) → new_esEs6(zxw4000, zxw3000, bgc)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_@0) → new_esEs10(zxw4000, zxw3000)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(ty_[], bbd), bbc) → new_ltEs11(zxw79000, zxw80000, bbd)
new_esEs7(Left(zxw4000), Left(zxw3000), app(ty_[], cac), cab) → new_esEs13(zxw4000, zxw3000, cac)
new_esEs7(Right(zxw4000), Right(zxw3000), cbd, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_compare31(zxw79000, zxw80000) → new_compare23(zxw79000, zxw80000, new_esEs14(zxw79000, zxw80000))
new_ltEs18(Nothing, Just(zxw80000), bhe) → True
new_esEs28(zxw4000, zxw3000, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_ltEs21(zxw79002, zxw80002, ty_Double) → new_ltEs15(zxw79002, zxw80002)
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_ltEs12(True, True) → True
new_esEs23(zxw4000, zxw3000, app(ty_Maybe, cgf)) → new_esEs6(zxw4000, zxw3000, cgf)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_ltEs14(Right(zxw79000), Right(zxw80000), bcb, app(app(ty_Either, bda), bdb)) → new_ltEs14(zxw79000, zxw80000, bda, bdb)
new_esEs8(zxw79000, zxw80000, ty_Integer) → new_esEs15(zxw79000, zxw80000)
new_ltEs6(@3(zxw79000, zxw79001, zxw79002), @3(zxw80000, zxw80001, zxw80002), cc, bc, bd) → new_pePe(new_lt19(zxw79000, zxw80000, cc), new_asAs(new_esEs20(zxw79000, zxw80000, cc), new_pePe(new_lt20(zxw79001, zxw80001, bc), new_asAs(new_esEs19(zxw79001, zxw80001, bc), new_ltEs21(zxw79002, zxw80002, bd)))))
new_esEs28(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_lt16(zxw79000, zxw80000) → new_esEs9(new_compare7(zxw79000, zxw80000), LT)
new_esEs23(zxw4000, zxw3000, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Integer, bbc) → new_ltEs13(zxw79000, zxw80000)
new_ltEs12(False, True) → True
new_esEs23(zxw4000, zxw3000, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs8(zxw79000, zxw80000, app(ty_Ratio, bff)) → new_esEs18(zxw79000, zxw80000, bff)
new_esEs23(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs14(True, True) → True
new_compare111(zxw79000, zxw80000, False, cb) → GT
new_esEs27(zxw4001, zxw3001, ty_Bool) → new_esEs14(zxw4001, zxw3001)
new_esEs20(zxw79000, zxw80000, ty_Ordering) → new_esEs9(zxw79000, zxw80000)
new_ltEs19(zxw7900, zxw8000, ty_@0) → new_ltEs8(zxw7900, zxw8000)
new_ltEs14(Right(zxw79000), Right(zxw80000), bcb, ty_Int) → new_ltEs9(zxw79000, zxw80000)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(app(ty_Either, bbg), bbh), bbc) → new_ltEs14(zxw79000, zxw80000, bbg, bbh)
new_lt19(zxw79000, zxw80000, ty_Integer) → new_lt13(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, ty_Float) → new_esEs17(zxw79000, zxw80000)
new_esEs7(Right(zxw4000), Right(zxw3000), cbd, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Ordering, bbc) → new_ltEs7(zxw79000, zxw80000)
new_compare11(zxw79000, zxw80000, False) → GT
new_esEs4(@3(zxw4000, zxw4001, zxw4002), @3(zxw3000, zxw3001, zxw3002), daa, dab, dac) → new_asAs(new_esEs28(zxw4000, zxw3000, daa), new_asAs(new_esEs27(zxw4001, zxw3001, dab), new_esEs26(zxw4002, zxw3002, dac)))
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Int) → new_ltEs9(zxw79000, zxw80000)
new_esEs6(Just(zxw4000), Just(zxw3000), app(ty_[], bgb)) → new_esEs13(zxw4000, zxw3000, bgb)
new_esEs9(EQ, LT) → False
new_esEs9(LT, EQ) → False
new_compare26(Right(zxw7900), Right(zxw8000), False, baf, bag) → new_compare14(zxw7900, zxw8000, new_ltEs20(zxw7900, zxw8000, bag), baf, bag)
new_compare11(zxw79000, zxw80000, True) → LT
new_ltEs5(zxw79001, zxw80001, ty_@0) → new_ltEs8(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, ty_Bool) → new_lt12(zxw79001, zxw80001)
new_compare14(zxw242, zxw243, True, chg, chh) → LT
new_esEs14(False, False) → True
new_esEs18(:%(zxw4000, zxw4001), :%(zxw3000, zxw3001), chf) → new_asAs(new_esEs25(zxw4000, zxw3000, chf), new_esEs24(zxw4001, zxw3001, chf))
new_compare26(Left(zxw7900), Left(zxw8000), False, baf, bag) → new_compare13(zxw7900, zxw8000, new_ltEs19(zxw7900, zxw8000, baf), baf, bag)
new_ltEs19(zxw7900, zxw8000, ty_Double) → new_ltEs15(zxw7900, zxw8000)
new_ltEs7(EQ, LT) → False
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Char) → new_esEs12(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_ltEs7(LT, LT) → True
new_lt20(zxw79001, zxw80001, app(app(app(ty_@3, cd), ce), cf)) → new_lt5(zxw79001, zxw80001, cd, ce, cf)
new_lt14(zxw790, zxw800, baf, bag) → new_esEs9(new_compare15(zxw790, zxw800, baf, bag), LT)
new_esEs22(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_ltEs9(zxw7900, zxw8000) → new_fsEs(new_compare16(zxw7900, zxw8000))
new_compare29(zxw79000, zxw80000, ty_Ordering) → new_compare18(zxw79000, zxw80000)
new_primPlusNat1(Zero, Zero) → Zero
new_esEs26(zxw4002, zxw3002, ty_Ordering) → new_esEs9(zxw4002, zxw3002)
new_esEs19(zxw79001, zxw80001, ty_Integer) → new_esEs15(zxw79001, zxw80001)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Char, bbc) → new_ltEs10(zxw79000, zxw80000)
new_asAs(True, zxw230) → zxw230
new_esEs25(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_ltEs7(LT, GT) → True
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Float) → new_esEs17(zxw4000, zxw3000)
new_ltEs5(zxw79001, zxw80001, ty_Float) → new_ltEs16(zxw79001, zxw80001)
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_esEs7(Right(zxw4000), Right(zxw3000), cbd, app(ty_Ratio, cbe)) → new_esEs18(zxw4000, zxw3000, cbe)
new_esEs27(zxw4001, zxw3001, app(ty_[], dbg)) → new_esEs13(zxw4001, zxw3001, dbg)
new_esEs6(Just(zxw4000), Just(zxw3000), app(app(ty_Either, bgf), bgg)) → new_esEs7(zxw4000, zxw3000, bgf, bgg)
new_compare28(zxw79000, zxw80000, False, cb) → new_compare111(zxw79000, zxw80000, new_ltEs18(zxw79000, zxw80000, cb), cb)
new_compare1(:(zxw79000, zxw79001), [], eg) → GT
new_esEs28(zxw4000, zxw3000, app(ty_Ratio, dch)) → new_esEs18(zxw4000, zxw3000, dch)
new_lt4(zxw79000, zxw80000, ty_Integer) → new_lt13(zxw79000, zxw80000)
new_esEs19(zxw79001, zxw80001, ty_@0) → new_esEs10(zxw79001, zxw80001)
new_compare29(zxw79000, zxw80000, ty_@0) → new_compare30(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), bcb, app(ty_Ratio, cdd)) → new_ltEs17(zxw79000, zxw80000, cdd)
new_ltEs19(zxw7900, zxw8000, ty_Integer) → new_ltEs13(zxw7900, zxw8000)
new_ltEs14(Right(zxw79000), Right(zxw80000), bcb, ty_Integer) → new_ltEs13(zxw79000, zxw80000)
new_ltEs19(zxw7900, zxw8000, ty_Ordering) → new_ltEs7(zxw7900, zxw8000)
new_compare28(zxw79000, zxw80000, True, cb) → EQ
new_esEs26(zxw4002, zxw3002, ty_Double) → new_esEs16(zxw4002, zxw3002)
new_compare10(zxw79000, zxw80000, True) → LT
new_esEs19(zxw79001, zxw80001, app(ty_[], cg)) → new_esEs13(zxw79001, zxw80001, cg)
new_compare10(zxw79000, zxw80000, False) → GT
new_esEs9(LT, LT) → True
new_ltEs20(zxw7900, zxw8000, ty_Char) → new_ltEs10(zxw7900, zxw8000)
new_primCompAux00(zxw276, GT) → GT
new_ltEs20(zxw7900, zxw8000, ty_Ordering) → new_ltEs7(zxw7900, zxw8000)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_@0) → new_ltEs8(zxw79000, zxw80000)
new_compare18(zxw79000, zxw80000) → new_compare24(zxw79000, zxw80000, new_esEs9(zxw79000, zxw80000))
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs7(Right(zxw4000), Right(zxw3000), cbd, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_lt19(zxw79000, zxw80000, ty_Char) → new_lt9(zxw79000, zxw80000)
new_esEs28(zxw4000, zxw3000, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_ltEs19(zxw7900, zxw8000, app(ty_Maybe, bhe)) → new_ltEs18(zxw7900, zxw8000, bhe)
new_esEs27(zxw4001, zxw3001, ty_Integer) → new_esEs15(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, app(ty_Ratio, cdg)) → new_esEs18(zxw4001, zxw3001, cdg)
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_esEs19(zxw79001, zxw80001, ty_Char) → new_esEs12(zxw79001, zxw80001)
new_esEs23(zxw4000, zxw3000, app(ty_[], cge)) → new_esEs13(zxw4000, zxw3000, cge)
new_ltEs17(zxw7900, zxw8000, bhd) → new_fsEs(new_compare8(zxw7900, zxw8000, bhd))
new_not(True) → False
new_ltEs4(@2(zxw79000, zxw79001), @2(zxw80000, zxw80001), hd, ge) → new_pePe(new_lt4(zxw79000, zxw80000, hd), new_asAs(new_esEs8(zxw79000, zxw80000, hd), new_ltEs5(zxw79001, zxw80001, ge)))
new_compare1([], [], eg) → EQ
new_esEs6(Just(zxw4000), Just(zxw3000), app(ty_Ratio, bga)) → new_esEs18(zxw4000, zxw3000, bga)

The set Q consists of the following terms:

new_compare23(x0, x1, True)
new_lt6(x0, x1)
new_lt18(x0, x1, x2)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_[], x3))
new_lt19(x0, x1, ty_Integer)
new_ltEs18(Just(x0), Just(x1), ty_@0)
new_compare16(x0, x1)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Double)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs19(x0, x1, ty_Bool)
new_esEs7(Right(x0), Right(x1), x2, ty_Int)
new_lt4(x0, x1, app(ty_Ratio, x2))
new_compare30(@0, @0)
new_primCompAux00(x0, GT)
new_esEs8(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1, ty_Char)
new_esEs7(Right(x0), Right(x1), x2, ty_@0)
new_ltEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs5(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_Ordering)
new_compare17(Char(x0), Char(x1))
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs13(:(x0, x1), [], x2)
new_esEs28(x0, x1, ty_Int)
new_ltEs21(x0, x1, ty_Ordering)
new_lt11(x0, x1, x2, x3)
new_ltEs15(x0, x1)
new_primPlusNat1(Zero, Succ(x0))
new_esEs7(Right(x0), Left(x1), x2, x3)
new_esEs7(Left(x0), Right(x1), x2, x3)
new_compare24(x0, x1, False)
new_esEs6(Just(x0), Just(x1), ty_Double)
new_esEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt20(x0, x1, ty_Char)
new_compare26(Left(x0), Left(x1), False, x2, x3)
new_esEs23(x0, x1, ty_Bool)
new_ltEs21(x0, x1, app(app(ty_@2, x2), x3))
new_sr0(Integer(x0), Integer(x1))
new_ltEs5(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_compare19(x0, x1, x2, x3)
new_ltEs7(EQ, EQ)
new_esEs19(x0, x1, ty_Integer)
new_compare110(x0, x1, True, x2, x3)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs20(x0, x1, ty_Bool)
new_ltEs18(Just(x0), Just(x1), app(ty_[], x2))
new_esEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs14(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Integer)
new_ltEs5(x0, x1, ty_Integer)
new_ltEs14(Right(x0), Right(x1), x2, ty_Char)
new_ltEs7(EQ, LT)
new_ltEs7(LT, EQ)
new_esEs7(Left(x0), Left(x1), ty_Float, x2)
new_esEs20(x0, x1, ty_Ordering)
new_esEs17(Float(x0, x1), Float(x2, x3))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_ltEs14(Left(x0), Left(x1), ty_Double, x2)
new_lt19(x0, x1, ty_Ordering)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs6(Nothing, Nothing, x0)
new_esEs7(Left(x0), Left(x1), ty_Int, x2)
new_compare29(x0, x1, app(app(ty_Either, x2), x3))
new_compare210(x0, x1, False, x2, x3)
new_ltEs16(x0, x1)
new_compare26(Right(x0), Right(x1), False, x2, x3)
new_sr(x0, x1)
new_ltEs19(x0, x1, ty_Double)
new_compare7(Float(x0, x1), Float(x2, x3))
new_ltEs9(x0, x1)
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_compare12(x0, x1, True, x2, x3, x4)
new_lt7(x0, x1)
new_esEs25(x0, x1, ty_Int)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat0(Zero, x0)
new_ltEs14(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs7(LT, LT)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Bool)
new_ltEs14(Left(x0), Left(x1), ty_Bool, x2)
new_lt4(x0, x1, ty_Ordering)
new_primEqNat0(Zero, Succ(x0))
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, ty_Int)
new_ltEs14(Right(x0), Right(x1), x2, ty_Double)
new_esEs15(Integer(x0), Integer(x1))
new_esEs26(x0, x1, ty_Int)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, ty_Double)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs18(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, ty_@0)
new_esEs7(Left(x0), Left(x1), ty_Integer, x2)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_primPlusNat1(Succ(x0), Zero)
new_esEs22(x0, x1, ty_Integer)
new_primMulInt(Neg(x0), Neg(x1))
new_ltEs19(x0, x1, ty_Int)
new_lt19(x0, x1, app(ty_[], x2))
new_ltEs14(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs23(x0, x1, app(ty_[], x2))
new_ltEs18(Just(x0), Nothing, x1)
new_compare29(x0, x1, ty_Integer)
new_esEs14(True, True)
new_esEs7(Right(x0), Right(x1), x2, ty_Float)
new_esEs21(x0, x1, ty_Char)
new_esEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Int)
new_ltEs18(Just(x0), Just(x1), ty_Integer)
new_compare26(x0, x1, True, x2, x3)
new_esEs24(x0, x1, ty_Int)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_primEqNat0(Zero, Zero)
new_esEs16(Double(x0, x1), Double(x2, x3))
new_esEs12(Char(x0), Char(x1))
new_lt4(x0, x1, ty_Char)
new_esEs7(Right(x0), Right(x1), x2, ty_Integer)
new_esEs20(x0, x1, ty_Bool)
new_esEs8(x0, x1, ty_Float)
new_esEs23(x0, x1, ty_Integer)
new_primCompAux00(x0, LT)
new_esEs27(x0, x1, ty_Integer)
new_esEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt14(x0, x1, x2, x3)
new_ltEs5(x0, x1, ty_Double)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(Just(x0), Just(x1), ty_Char)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_primMulNat0(Zero, Zero)
new_lt9(x0, x1)
new_compare29(x0, x1, ty_Double)
new_ltEs5(x0, x1, ty_@0)
new_compare110(x0, x1, False, x2, x3)
new_ltEs14(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_compare25(x0, x1, False, x2, x3, x4)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(x0, x1, ty_Ordering)
new_compare10(x0, x1, True)
new_ltEs19(x0, x1, ty_Ordering)
new_primEqNat0(Succ(x0), Succ(x1))
new_compare28(x0, x1, True, x2)
new_ltEs19(x0, x1, ty_Bool)
new_esEs28(x0, x1, ty_Double)
new_ltEs20(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_@0)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_pePe(True, x0)
new_ltEs14(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs19(x0, x1, ty_Float)
new_compare29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_lt16(x0, x1)
new_compare29(x0, x1, ty_Bool)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_compare11(x0, x1, True)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs6(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_Float)
new_lt19(x0, x1, ty_@0)
new_esEs6(Just(x0), Just(x1), ty_Ordering)
new_ltEs14(Right(x0), Left(x1), x2, x3)
new_esEs23(x0, x1, ty_@0)
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(Left(x0), Right(x1), x2, x3)
new_ltEs14(Left(x0), Left(x1), ty_Char, x2)
new_ltEs5(x0, x1, ty_Char)
new_ltEs21(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Float)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs7(Left(x0), Left(x1), ty_Double, x2)
new_compare29(x0, x1, ty_Ordering)
new_compare14(x0, x1, True, x2, x3)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs21(x0, x1, ty_@0)
new_esEs8(x0, x1, ty_Int)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs12(False, False)
new_ltEs14(Left(x0), Left(x1), ty_@0, x2)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs6(Just(x0), Just(x1), ty_Bool)
new_compare32(Integer(x0), Integer(x1))
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs21(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_Int)
new_primMulNat0(Succ(x0), Succ(x1))
new_ltEs21(x0, x1, ty_Integer)
new_compare29(x0, x1, ty_Float)
new_compare26(Left(x0), Right(x1), False, x2, x3)
new_compare26(Right(x0), Left(x1), False, x2, x3)
new_esEs6(Just(x0), Just(x1), ty_Float)
new_ltEs5(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(Nothing, Just(x0), x1)
new_ltEs5(x0, x1, ty_Float)
new_ltEs18(Just(x0), Just(x1), ty_Float)
new_compare15(x0, x1, x2, x3)
new_esEs26(x0, x1, ty_Bool)
new_primCmpNat1(Zero, x0)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs8(x0, x1)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs18(:%(x0, x1), :%(x2, x3), x4)
new_esEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs18(Just(x0), Just(x1), app(ty_Ratio, x2))
new_primPlusNat1(Zero, Zero)
new_esEs23(x0, x1, ty_Double)
new_primCmpNat2(Zero, Zero)
new_ltEs18(Just(x0), Just(x1), ty_Ordering)
new_compare111(x0, x1, False, x2)
new_ltEs5(x0, x1, ty_Bool)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_asAs(False, x0)
new_ltEs20(x0, x1, ty_Char)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs8(x0, x1, ty_Integer)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(Just(x0), Just(x1), ty_Bool)
new_primCmpNat1(Succ(x0), x1)
new_primCompAux0(x0, x1, x2, x3)
new_compare25(x0, x1, True, x2, x3, x4)
new_lt4(x0, x1, app(app(ty_Either, x2), x3))
new_compare29(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, ty_Integer)
new_esEs27(x0, x1, ty_@0)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_lt4(x0, x1, ty_Float)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs19(x0, x1, ty_Char)
new_lt4(x0, x1, ty_Double)
new_esEs19(x0, x1, ty_Ordering)
new_esEs8(x0, x1, app(ty_[], x2))
new_compare12(x0, x1, False, x2, x3, x4)
new_esEs10(@0, @0)
new_esEs11(x0, x1)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs21(x0, x1, app(ty_Maybe, x2))
new_esEs20(x0, x1, ty_Float)
new_esEs9(GT, GT)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs27(x0, x1, ty_Char)
new_compare11(x0, x1, False)
new_compare23(x0, x1, False)
new_esEs8(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, ty_Bool)
new_compare24(x0, x1, True)
new_lt4(x0, x1, app(ty_[], x2))
new_esEs6(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primEqNat0(Succ(x0), Zero)
new_esEs23(x0, x1, ty_Ordering)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_esEs19(x0, x1, app(ty_[], x2))
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_ltEs14(Right(x0), Right(x1), x2, ty_Int)
new_esEs7(Right(x0), Right(x1), x2, ty_Bool)
new_esEs8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Int)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs21(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Integer)
new_esEs23(x0, x1, ty_Int)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_lt4(x0, x1, ty_@0)
new_esEs23(x0, x1, ty_Char)
new_esEs28(x0, x1, ty_Ordering)
new_ltEs18(Just(x0), Just(x1), ty_Double)
new_ltEs20(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_lt20(x0, x1, ty_@0)
new_esEs9(EQ, EQ)
new_pePe(False, x0)
new_esEs20(x0, x1, app(ty_[], x2))
new_primEqInt(Neg(Zero), Neg(Zero))
new_compare27(x0, x1, x2)
new_esEs6(Just(x0), Just(x1), ty_Char)
new_esEs25(x0, x1, ty_Integer)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Integer)
new_compare1(:(x0, x1), [], x2)
new_primCompAux00(x0, EQ)
new_esEs8(x0, x1, app(app(ty_Either, x2), x3))
new_esEs19(x0, x1, ty_Int)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs14(True, False)
new_esEs14(False, True)
new_ltEs18(Just(x0), Just(x1), app(ty_Maybe, x2))
new_lt4(x0, x1, ty_Integer)
new_esEs6(Nothing, Just(x0), x1)
new_fsEs(x0)
new_esEs22(x0, x1, ty_Float)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare9(x0, x1, x2, x3, x4)
new_lt4(x0, x1, ty_Bool)
new_primCmpNat2(Succ(x0), Succ(x1))
new_asAs(True, x0)
new_ltEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Bool)
new_ltEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs13([], :(x0, x1), x2)
new_compare1(:(x0, x1), :(x2, x3), x4)
new_ltEs14(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs6(Just(x0), Nothing, x1)
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs8(x0, x1, ty_Char)
new_esEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_lt19(x0, x1, ty_Float)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, ty_@0)
new_compare13(x0, x1, True, x2, x3)
new_compare29(x0, x1, app(ty_[], x2))
new_ltEs5(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, ty_Char)
new_compare1([], :(x0, x1), x2)
new_ltEs12(False, True)
new_ltEs12(True, False)
new_compare6(Double(x0, x1), Double(x2, x3))
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs20(x0, x1, ty_@0)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs21(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_@0)
new_ltEs17(x0, x1, x2)
new_lt19(x0, x1, ty_Double)
new_lt19(x0, x1, ty_Bool)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, ty_Char)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs5(x0, x1, ty_Int)
new_esEs8(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Left(x0), Left(x1), ty_Float, x2)
new_esEs20(x0, x1, ty_Double)
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs19(x0, x1, ty_@0)
new_esEs4(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs14(Right(x0), Right(x1), x2, ty_@0)
new_lt5(x0, x1, x2, x3, x4)
new_esEs13([], [], x0)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs21(x0, x1, ty_Bool)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs21(x0, x1, ty_Double)
new_lt12(x0, x1)
new_esEs8(x0, x1, ty_Bool)
new_ltEs21(x0, x1, ty_Char)
new_lt13(x0, x1)
new_lt4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs7(Right(x0), Right(x1), x2, ty_Char)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_compare10(x0, x1, False)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_primMulNat0(Succ(x0), Zero)
new_esEs26(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, ty_Float)
new_esEs23(x0, x1, ty_Float)
new_compare29(x0, x1, ty_Int)
new_esEs22(x0, x1, ty_Int)
new_lt10(x0, x1, x2)
new_esEs20(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Float)
new_compare31(x0, x1)
new_esEs6(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs5(x0, x1, app(ty_Maybe, x2))
new_esEs6(Just(x0), Just(x1), ty_Int)
new_ltEs7(LT, GT)
new_ltEs7(GT, LT)
new_esEs21(x0, x1, ty_Integer)
new_compare28(x0, x1, False, x2)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, ty_Double)
new_esEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs7(Left(x0), Left(x1), ty_Char, x2)
new_ltEs13(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, ty_Double)
new_lt4(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Float)
new_not(True)
new_esEs20(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Ordering)
new_compare29(x0, x1, app(ty_Maybe, x2))
new_esEs6(Just(x0), Just(x1), ty_Integer)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_not(False)
new_lt8(x0, x1)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_compare1([], [], x0)
new_compare14(x0, x1, False, x2, x3)
new_ltEs14(Left(x0), Left(x1), ty_Int, x2)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, ty_Char)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Integer)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs22(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_Integer)
new_esEs8(x0, x1, ty_@0)
new_lt4(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_compare13(x0, x1, False, x2, x3)
new_ltEs18(Nothing, Nothing, x0)
new_ltEs12(True, True)
new_lt15(x0, x1)
new_esEs27(x0, x1, ty_Float)
new_esEs26(x0, x1, ty_Ordering)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs27(x0, x1, ty_Double)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_lt20(x0, x1, ty_Ordering)
new_esEs27(x0, x1, app(ty_[], x2))
new_ltEs21(x0, x1, app(ty_Ratio, x2))
new_lt17(x0, x1, x2)
new_esEs7(Left(x0), Left(x1), ty_Bool, x2)
new_esEs22(x0, x1, ty_Char)
new_lt20(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Bool)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_ltEs21(x0, x1, ty_Float)
new_ltEs10(x0, x1)
new_compare29(x0, x1, app(ty_Ratio, x2))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(x0, x1, ty_Ordering)
new_ltEs11(x0, x1, x2)
new_ltEs14(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs8(x0, x1, ty_Double)
new_compare29(x0, x1, ty_Char)
new_esEs6(Just(x0), Just(x1), ty_@0)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs19(x0, x1, ty_Double)
new_esEs14(False, False)
new_primEqInt(Pos(Zero), Pos(Zero))
new_ltEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_compare111(x0, x1, True, x2)
new_ltEs21(x0, x1, ty_Double)
new_primCmpNat2(Succ(x0), Zero)
new_compare18(x0, x1)
new_compare210(x0, x1, True, x2, x3)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_ltEs18(Just(x0), Just(x1), ty_Int)
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs13(:(x0, x1), :(x2, x3), x4)
new_ltEs21(x0, x1, app(app(ty_Either, x2), x3))
new_primPlusNat0(Succ(x0), x1)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_ltEs14(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs20(x0, x1, ty_Integer)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primCmpNat0(x0, Zero)
new_lt4(x0, x1, app(ty_Maybe, x2))
new_esEs6(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs7(GT, EQ)
new_ltEs7(EQ, GT)
new_ltEs14(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs14(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs7(GT, GT)
new_esEs9(LT, LT)
new_ltEs14(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Left(x0), Left(x1), ty_@0, x2)
new_compare29(x0, x1, ty_@0)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_primCmpNat0(x0, Succ(x1))
new_esEs27(x0, x1, ty_Ordering)

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

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



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

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

new_deleteMin(zxw50, zxw51, zxw52, Branch(zxw530, zxw531, zxw532, zxw533, zxw534), zxw54, h, ba, bb) → new_deleteMin(zxw530, zxw531, zxw532, zxw533, zxw534, h, ba, bb)

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

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



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

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

new_deleteMax(zxw640, zxw641, zxw642, zxw643, Branch(zxw6440, zxw6441, zxw6442, zxw6443, zxw6444), h, ba, bb) → new_deleteMax(zxw6440, zxw6441, zxw6442, zxw6443, zxw6444, h, ba, bb)

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

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



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

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

new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb)
new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), zxw53, h, ba, bb)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), zxw53, h, ba, bb)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba, bb) → new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt0(new_sr(new_sIZE_RATIO, new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)
new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba, bb) → new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt3(new_sr(new_sIZE_RATIO, new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)
new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb)
new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb) → new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt1(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)
new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb) → new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt2(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)

The TRS R consists of the following rules:

new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Pos(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_esEs9(GT, LT) → False
new_esEs9(LT, GT) → False
new_primCmpInt3(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Zero), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba, bb))
new_primMulInt(Neg(zxw40000), Neg(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primCmpNat2(Zero, Zero) → EQ
new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb)
new_primPlusNat1(Zero, Zero) → Zero
new_primCmpInt1(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → new_primCmpInt5(zxw6200, new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba, bb))
new_primCmpInt3(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Zero), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba, bb))
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → LT
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt0(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_sr(zxw4000, zxw3000) → new_primMulInt(zxw4000, zxw3000)
new_primCmpNat0(zxw7900, Zero) → GT
new_primMulNat0(Zero, Zero) → Zero
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt2(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primCmpInt0(Pos(Succ(zxw13500)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Succ(zxw13500)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt0(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt3(Pos(Succ(zxw13700)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Succ(zxw13700)), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba, bb))
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → GT
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt0(Neg(Succ(zxw13500)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Succ(zxw13500)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_esEs9(GT, EQ) → False
new_esEs9(EQ, GT) → False
new_esEs9(EQ, EQ) → True
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → GT
new_sizeFM0(EmptyFM, h, ba, bb) → Pos(Zero)
new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_primCmpInt2(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → LT
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_esEs9(GT, GT) → True
new_esEs9(LT, LT) → True
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba, bb) → zxw542
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb) → zxw52
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primCmpInt4(zxw6200, zxw153) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw153)
new_primCmpInt2(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → new_primCmpInt4(zxw6200, new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba, bb))
new_primCmpNat1(Zero, zxw7900) → LT
new_esEs9(EQ, LT) → False
new_esEs9(LT, EQ) → False
new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb)
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt3(Neg(Succ(zxw13700)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Succ(zxw13700)), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba, bb))
new_primCmpInt5(zxw6200, zxw150) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw150)

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt2(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_sr(x0, x1)
new_primCmpNat1(Zero, x0)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt0(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat0(Zero, x0)
new_primCmpInt2(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt4(x0, x1)
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt0(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt3(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_sizeFM0(EmptyFM, x0, x1, x2)
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_sIZE_RATIO
new_primCmpInt2(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt3(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_glueVBal3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpInt0(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt5(x0, x1)
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt2(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt0(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs9(LT, LT)
new_primCmpInt3(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt2(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt3(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

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

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

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

new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb)
new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), zxw53, h, ba, bb)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), zxw53, h, ba, bb)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba, bb) → new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt0(new_sr(new_sIZE_RATIO, new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)
new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba, bb) → new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt3(new_sr(new_sIZE_RATIO, new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)
new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb)
new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb) → new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt1(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)
new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb) → new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt2(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)

The TRS R consists of the following rules:

new_primCmpInt2(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → GT
new_primCmpInt2(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → LT
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt2(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → new_primCmpInt4(zxw6200, new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba, bb))
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb)
new_primCmpInt4(zxw6200, zxw153) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw153)
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb) → zxw52
new_primCmpInt1(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → new_primCmpInt5(zxw6200, new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba, bb))
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → LT
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → GT
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb)
new_primCmpInt5(zxw6200, zxw150) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw150)
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_sr(zxw4000, zxw3000) → new_primMulInt(zxw4000, zxw3000)
new_primCmpInt0(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_primCmpInt0(Pos(Succ(zxw13500)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Succ(zxw13500)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_primCmpInt0(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_primCmpInt0(Neg(Succ(zxw13500)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Succ(zxw13500)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Pos(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Neg(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primCmpInt3(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Zero), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba, bb))
new_primCmpInt3(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Zero), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba, bb))
new_primCmpInt3(Pos(Succ(zxw13700)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Succ(zxw13700)), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba, bb))
new_primCmpInt3(Neg(Succ(zxw13700)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Succ(zxw13700)), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba, bb))
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba, bb) → zxw542

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt2(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_sr(x0, x1)
new_primCmpNat1(Zero, x0)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt0(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat0(Zero, x0)
new_primCmpInt2(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt4(x0, x1)
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt0(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt3(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_sizeFM0(EmptyFM, x0, x1, x2)
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_sIZE_RATIO
new_primCmpInt2(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt3(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_glueVBal3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpInt0(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt5(x0, x1)
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt2(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt0(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs9(LT, LT)
new_primCmpInt3(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt2(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt3(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba, bb) → new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt0(new_sr(new_sIZE_RATIO, new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb), LT), h, ba, bb) at position [10,0,0] we obtained the following new rules:

new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba, bb) → new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt0(new_primMulInt(new_sIZE_RATIO, new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)



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

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

new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), zxw53, h, ba, bb)
new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), zxw53, h, ba, bb)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba, bb) → new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt0(new_primMulInt(new_sIZE_RATIO, new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)
new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba, bb) → new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt3(new_sr(new_sIZE_RATIO, new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)
new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb)
new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb) → new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt1(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)
new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb) → new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt2(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)

The TRS R consists of the following rules:

new_primCmpInt2(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → GT
new_primCmpInt2(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → LT
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt2(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → new_primCmpInt4(zxw6200, new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba, bb))
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb)
new_primCmpInt4(zxw6200, zxw153) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw153)
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb) → zxw52
new_primCmpInt1(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → new_primCmpInt5(zxw6200, new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba, bb))
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → LT
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → GT
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb)
new_primCmpInt5(zxw6200, zxw150) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw150)
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_sr(zxw4000, zxw3000) → new_primMulInt(zxw4000, zxw3000)
new_primCmpInt0(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_primCmpInt0(Pos(Succ(zxw13500)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Succ(zxw13500)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_primCmpInt0(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_primCmpInt0(Neg(Succ(zxw13500)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Succ(zxw13500)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Pos(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Neg(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primCmpInt3(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Zero), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba, bb))
new_primCmpInt3(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Zero), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba, bb))
new_primCmpInt3(Pos(Succ(zxw13700)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Succ(zxw13700)), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba, bb))
new_primCmpInt3(Neg(Succ(zxw13700)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Succ(zxw13700)), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba, bb))
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba, bb) → zxw542

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt2(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_sr(x0, x1)
new_primCmpNat1(Zero, x0)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt0(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat0(Zero, x0)
new_primCmpInt2(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt4(x0, x1)
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt0(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt3(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_sizeFM0(EmptyFM, x0, x1, x2)
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_sIZE_RATIO
new_primCmpInt2(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt3(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_glueVBal3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpInt0(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt5(x0, x1)
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt2(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt0(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs9(LT, LT)
new_primCmpInt3(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt2(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt3(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba, bb) → new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt3(new_sr(new_sIZE_RATIO, new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb), LT), h, ba, bb) at position [10,0,0] we obtained the following new rules:

new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba, bb) → new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt3(new_primMulInt(new_sIZE_RATIO, new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)



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

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

new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb)
new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), zxw53, h, ba, bb)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), zxw53, h, ba, bb)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba, bb) → new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt0(new_primMulInt(new_sIZE_RATIO, new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)
new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba, bb) → new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt3(new_primMulInt(new_sIZE_RATIO, new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)
new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb)
new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb) → new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt1(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)
new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb) → new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt2(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)

The TRS R consists of the following rules:

new_primCmpInt2(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → GT
new_primCmpInt2(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → LT
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt2(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → new_primCmpInt4(zxw6200, new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba, bb))
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb)
new_primCmpInt4(zxw6200, zxw153) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw153)
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb) → zxw52
new_primCmpInt1(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → new_primCmpInt5(zxw6200, new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba, bb))
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → LT
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → GT
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb)
new_primCmpInt5(zxw6200, zxw150) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw150)
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_sr(zxw4000, zxw3000) → new_primMulInt(zxw4000, zxw3000)
new_primCmpInt0(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_primCmpInt0(Pos(Succ(zxw13500)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Succ(zxw13500)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_primCmpInt0(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_primCmpInt0(Neg(Succ(zxw13500)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Succ(zxw13500)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Pos(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Neg(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primCmpInt3(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Zero), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba, bb))
new_primCmpInt3(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Zero), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba, bb))
new_primCmpInt3(Pos(Succ(zxw13700)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Succ(zxw13700)), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba, bb))
new_primCmpInt3(Neg(Succ(zxw13700)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Succ(zxw13700)), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba, bb))
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba, bb) → zxw542

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt2(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_sr(x0, x1)
new_primCmpNat1(Zero, x0)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt0(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat0(Zero, x0)
new_primCmpInt2(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt4(x0, x1)
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt0(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt3(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_sizeFM0(EmptyFM, x0, x1, x2)
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_sIZE_RATIO
new_primCmpInt2(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt3(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_glueVBal3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpInt0(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt5(x0, x1)
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt2(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt0(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs9(LT, LT)
new_primCmpInt3(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt2(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt3(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

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

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

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

new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb)
new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), zxw53, h, ba, bb)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), zxw53, h, ba, bb)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba, bb) → new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt0(new_primMulInt(new_sIZE_RATIO, new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)
new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba, bb) → new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt3(new_primMulInt(new_sIZE_RATIO, new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)
new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb)
new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb) → new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt1(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)
new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb) → new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt2(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb)
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Pos(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Neg(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primCmpInt0(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_primCmpInt0(Pos(Succ(zxw13500)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Succ(zxw13500)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_primCmpInt0(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_primCmpInt0(Neg(Succ(zxw13500)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Succ(zxw13500)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb) → zxw52
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primCmpInt2(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → GT
new_primCmpInt2(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → LT
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt2(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → new_primCmpInt4(zxw6200, new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba, bb))
new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb)
new_primCmpInt4(zxw6200, zxw153) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw153)
new_primCmpInt1(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → new_primCmpInt5(zxw6200, new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba, bb))
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → LT
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → GT
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt5(zxw6200, zxw150) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw150)
new_primCmpInt3(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Zero), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba, bb))
new_primCmpInt3(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Zero), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba, bb))
new_primCmpInt3(Pos(Succ(zxw13700)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Succ(zxw13700)), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba, bb))
new_primCmpInt3(Neg(Succ(zxw13700)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Succ(zxw13700)), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba, bb))
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba, bb) → zxw542

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt2(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_sr(x0, x1)
new_primCmpNat1(Zero, x0)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt0(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat0(Zero, x0)
new_primCmpInt2(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt4(x0, x1)
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt0(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt3(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_sizeFM0(EmptyFM, x0, x1, x2)
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_sIZE_RATIO
new_primCmpInt2(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt3(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_glueVBal3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpInt0(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt5(x0, x1)
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt2(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt0(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs9(LT, LT)
new_primCmpInt3(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt2(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt3(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(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_sr(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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ UsableRulesProof
                                                  ↳ QDP
                                                    ↳ QReductionProof
                                                      ↳ QDP
                                                        ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), zxw53, h, ba, bb)
new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), zxw53, h, ba, bb)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba, bb) → new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt0(new_primMulInt(new_sIZE_RATIO, new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)
new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba, bb) → new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt3(new_primMulInt(new_sIZE_RATIO, new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)
new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb)
new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb) → new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt1(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)
new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb) → new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt2(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb)
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Pos(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Neg(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primCmpInt0(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_primCmpInt0(Pos(Succ(zxw13500)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Succ(zxw13500)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_primCmpInt0(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_primCmpInt0(Neg(Succ(zxw13500)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Succ(zxw13500)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb) → zxw52
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primCmpInt2(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → GT
new_primCmpInt2(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → LT
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt2(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → new_primCmpInt4(zxw6200, new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba, bb))
new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb)
new_primCmpInt4(zxw6200, zxw153) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw153)
new_primCmpInt1(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → new_primCmpInt5(zxw6200, new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba, bb))
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → LT
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → GT
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt5(zxw6200, zxw150) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw150)
new_primCmpInt3(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Zero), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba, bb))
new_primCmpInt3(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Zero), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba, bb))
new_primCmpInt3(Pos(Succ(zxw13700)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Succ(zxw13700)), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba, bb))
new_primCmpInt3(Neg(Succ(zxw13700)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Succ(zxw13700)), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba, bb))
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba, bb) → zxw542

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt2(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpNat1(Zero, x0)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt0(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat0(Zero, x0)
new_primCmpInt2(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt4(x0, x1)
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt0(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt3(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_sizeFM0(EmptyFM, x0, x1, x2)
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_sIZE_RATIO
new_primCmpInt2(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt3(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_glueVBal3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpInt0(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt5(x0, x1)
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt2(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt0(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs9(LT, LT)
new_primCmpInt3(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt2(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt3(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba, bb) → new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt0(new_primMulInt(new_sIZE_RATIO, new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb), LT), h, ba, bb) at position [10,0,0,0] we obtained the following new rules:

new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba, bb) → new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt0(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)



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

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

new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb)
new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), zxw53, h, ba, bb)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), zxw53, h, ba, bb)
new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba, bb) → new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt3(new_primMulInt(new_sIZE_RATIO, new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)
new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb)
new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb) → new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt1(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba, bb) → new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt0(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)
new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb) → new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt2(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb)
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Pos(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Neg(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primCmpInt0(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_primCmpInt0(Pos(Succ(zxw13500)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Succ(zxw13500)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_primCmpInt0(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_primCmpInt0(Neg(Succ(zxw13500)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Succ(zxw13500)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb) → zxw52
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primCmpInt2(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → GT
new_primCmpInt2(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → LT
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt2(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → new_primCmpInt4(zxw6200, new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba, bb))
new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb)
new_primCmpInt4(zxw6200, zxw153) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw153)
new_primCmpInt1(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → new_primCmpInt5(zxw6200, new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba, bb))
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → LT
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → GT
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt5(zxw6200, zxw150) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw150)
new_primCmpInt3(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Zero), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba, bb))
new_primCmpInt3(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Zero), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba, bb))
new_primCmpInt3(Pos(Succ(zxw13700)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Succ(zxw13700)), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba, bb))
new_primCmpInt3(Neg(Succ(zxw13700)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Succ(zxw13700)), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba, bb))
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba, bb) → zxw542

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt2(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpNat1(Zero, x0)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt0(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat0(Zero, x0)
new_primCmpInt2(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt4(x0, x1)
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt0(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt3(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_sizeFM0(EmptyFM, x0, x1, x2)
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_sIZE_RATIO
new_primCmpInt2(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt3(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_glueVBal3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpInt0(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt5(x0, x1)
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt2(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt0(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs9(LT, LT)
new_primCmpInt3(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt2(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt3(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba, bb) → new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt3(new_primMulInt(new_sIZE_RATIO, new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb), LT), h, ba, bb) at position [10,0,0,0] we obtained the following new rules:

new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba, bb) → new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt3(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)



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

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

new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), zxw53, h, ba, bb)
new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), zxw53, h, ba, bb)
new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb)
new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba, bb) → new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt3(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)
new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb) → new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt1(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)
new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb) → new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt2(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba, bb) → new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt0(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb)
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Pos(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Neg(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primCmpInt0(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_primCmpInt0(Pos(Succ(zxw13500)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Succ(zxw13500)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_primCmpInt0(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_primCmpInt0(Neg(Succ(zxw13500)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Succ(zxw13500)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb) → zxw52
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primCmpInt2(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → GT
new_primCmpInt2(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → LT
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt2(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → new_primCmpInt4(zxw6200, new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba, bb))
new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb)
new_primCmpInt4(zxw6200, zxw153) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw153)
new_primCmpInt1(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → new_primCmpInt5(zxw6200, new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba, bb))
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → LT
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → GT
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt5(zxw6200, zxw150) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw150)
new_primCmpInt3(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Zero), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba, bb))
new_primCmpInt3(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Zero), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba, bb))
new_primCmpInt3(Pos(Succ(zxw13700)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Succ(zxw13700)), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba, bb))
new_primCmpInt3(Neg(Succ(zxw13700)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Succ(zxw13700)), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba, bb))
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba, bb) → zxw542

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt2(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpNat1(Zero, x0)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt0(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat0(Zero, x0)
new_primCmpInt2(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt4(x0, x1)
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt0(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt3(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_sizeFM0(EmptyFM, x0, x1, x2)
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_sIZE_RATIO
new_primCmpInt2(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt3(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_glueVBal3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpInt0(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt5(x0, x1)
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt2(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt0(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs9(LT, LT)
new_primCmpInt3(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt2(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt3(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

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

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

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

new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), zxw53, h, ba, bb)
new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), zxw53, h, ba, bb)
new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb)
new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba, bb) → new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt3(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)
new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb) → new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt1(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba, bb) → new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt0(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)
new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb) → new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt2(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)

The TRS R consists of the following rules:

new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb)
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primCmpInt0(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_primCmpInt0(Pos(Succ(zxw13500)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Succ(zxw13500)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_primCmpInt0(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_primCmpInt0(Neg(Succ(zxw13500)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Succ(zxw13500)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb) → zxw52
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primCmpInt2(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → GT
new_primCmpInt2(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → LT
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt2(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → new_primCmpInt4(zxw6200, new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba, bb))
new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb)
new_primCmpInt4(zxw6200, zxw153) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw153)
new_primCmpInt3(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Zero), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba, bb))
new_primCmpInt3(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Zero), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba, bb))
new_primCmpInt3(Pos(Succ(zxw13700)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Succ(zxw13700)), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba, bb))
new_primCmpInt3(Neg(Succ(zxw13700)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Succ(zxw13700)), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba, bb))
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba, bb) → zxw542
new_primCmpInt1(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → new_primCmpInt5(zxw6200, new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba, bb))
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → LT
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → GT
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt5(zxw6200, zxw150) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw150)

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt2(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpNat1(Zero, x0)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt0(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat0(Zero, x0)
new_primCmpInt2(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt4(x0, x1)
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt0(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt3(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_sizeFM0(EmptyFM, x0, x1, x2)
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_sIZE_RATIO
new_primCmpInt2(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt3(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_glueVBal3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpInt0(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt5(x0, x1)
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt2(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt0(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs9(LT, LT)
new_primCmpInt3(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt2(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt3(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ UsableRulesProof
                                                  ↳ QDP
                                                    ↳ QReductionProof
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb)
new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), zxw53, h, ba, bb)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), zxw53, h, ba, bb)
new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb)
new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb) → new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt1(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)
new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba, bb) → new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt3(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)
new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb) → new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt2(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba, bb) → new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt0(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)

The TRS R consists of the following rules:

new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb)
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primCmpInt0(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_primCmpInt0(Pos(Succ(zxw13500)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Succ(zxw13500)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_primCmpInt0(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_primCmpInt0(Neg(Succ(zxw13500)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Succ(zxw13500)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb) → zxw52
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primCmpInt2(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → GT
new_primCmpInt2(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → LT
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt2(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → new_primCmpInt4(zxw6200, new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba, bb))
new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb)
new_primCmpInt4(zxw6200, zxw153) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw153)
new_primCmpInt3(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Zero), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba, bb))
new_primCmpInt3(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Zero), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba, bb))
new_primCmpInt3(Pos(Succ(zxw13700)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Succ(zxw13700)), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba, bb))
new_primCmpInt3(Neg(Succ(zxw13700)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Succ(zxw13700)), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba, bb))
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba, bb) → zxw542
new_primCmpInt1(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → new_primCmpInt5(zxw6200, new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba, bb))
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → LT
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → GT
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt5(zxw6200, zxw150) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw150)

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt2(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpNat1(Zero, x0)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt0(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat0(Zero, x0)
new_primCmpInt2(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt4(x0, x1)
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt0(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt3(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_sizeFM0(EmptyFM, x0, x1, x2)
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpInt2(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt3(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_glueVBal3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpInt0(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt5(x0, x1)
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt2(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt0(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs9(LT, LT)
new_primCmpInt3(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt2(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt3(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba, bb) → new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt3(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb), LT), h, ba, bb) at position [10,0,0,1] we obtained the following new rules:

new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba, bb) → new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt3(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)



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

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

new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), zxw53, h, ba, bb)
new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), zxw53, h, ba, bb)
new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba, bb) → new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt3(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)
new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb)
new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb) → new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt1(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba, bb) → new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt0(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)
new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb) → new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt2(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)

The TRS R consists of the following rules:

new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb)
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primCmpInt0(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_primCmpInt0(Pos(Succ(zxw13500)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Succ(zxw13500)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_primCmpInt0(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_primCmpInt0(Neg(Succ(zxw13500)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Succ(zxw13500)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb) → zxw52
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primCmpInt2(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → GT
new_primCmpInt2(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → LT
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt2(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → new_primCmpInt4(zxw6200, new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba, bb))
new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb)
new_primCmpInt4(zxw6200, zxw153) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw153)
new_primCmpInt3(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Zero), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba, bb))
new_primCmpInt3(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Zero), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba, bb))
new_primCmpInt3(Pos(Succ(zxw13700)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Succ(zxw13700)), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba, bb))
new_primCmpInt3(Neg(Succ(zxw13700)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Succ(zxw13700)), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba, bb))
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba, bb) → zxw542
new_primCmpInt1(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → new_primCmpInt5(zxw6200, new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba, bb))
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → LT
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → GT
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt5(zxw6200, zxw150) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw150)

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt2(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpNat1(Zero, x0)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt0(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat0(Zero, x0)
new_primCmpInt2(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt4(x0, x1)
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt0(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt3(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_sizeFM0(EmptyFM, x0, x1, x2)
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpInt2(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt3(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_glueVBal3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpInt0(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt5(x0, x1)
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt2(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt0(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs9(LT, LT)
new_primCmpInt3(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt2(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt3(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba, bb) → new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt0(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb), LT), h, ba, bb) at position [10,0,0,1] we obtained the following new rules:

new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba, bb) → new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt0(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)



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

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

new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb)
new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), zxw53, h, ba, bb)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), zxw53, h, ba, bb)
new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba, bb) → new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt3(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba, bb) → new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt0(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)
new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb)
new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb) → new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt1(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)
new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb) → new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt2(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)

The TRS R consists of the following rules:

new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb)
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primCmpInt0(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_primCmpInt0(Pos(Succ(zxw13500)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Succ(zxw13500)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_primCmpInt0(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_primCmpInt0(Neg(Succ(zxw13500)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Succ(zxw13500)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb) → zxw52
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primCmpInt2(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → GT
new_primCmpInt2(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → LT
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt2(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → new_primCmpInt4(zxw6200, new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba, bb))
new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb)
new_primCmpInt4(zxw6200, zxw153) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw153)
new_primCmpInt3(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Zero), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba, bb))
new_primCmpInt3(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Zero), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba, bb))
new_primCmpInt3(Pos(Succ(zxw13700)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Succ(zxw13700)), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba, bb))
new_primCmpInt3(Neg(Succ(zxw13700)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Succ(zxw13700)), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba, bb))
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba, bb) → zxw542
new_primCmpInt1(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → new_primCmpInt5(zxw6200, new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba, bb))
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → LT
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → GT
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt5(zxw6200, zxw150) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw150)

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt2(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpNat1(Zero, x0)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt0(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat0(Zero, x0)
new_primCmpInt2(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt4(x0, x1)
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt0(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt3(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_sizeFM0(EmptyFM, x0, x1, x2)
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpInt2(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt3(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_glueVBal3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpInt0(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt5(x0, x1)
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt2(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt0(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs9(LT, LT)
new_primCmpInt3(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt2(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt3(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba, bb) → new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt3(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb), LT), h, ba, bb) at position [10,0,0,1] we obtained the following new rules:

new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba, bb) → new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt3(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw52), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)



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

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

new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), zxw53, h, ba, bb)
new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), zxw53, h, ba, bb)
new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba, bb) → new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt3(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw52), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba, bb) → new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt0(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)
new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb)
new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb) → new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt1(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)
new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb) → new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt2(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)

The TRS R consists of the following rules:

new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb)
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primCmpInt0(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_primCmpInt0(Pos(Succ(zxw13500)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Succ(zxw13500)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_primCmpInt0(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_primCmpInt0(Neg(Succ(zxw13500)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Succ(zxw13500)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb) → zxw52
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primCmpInt2(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → GT
new_primCmpInt2(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → LT
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt2(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → new_primCmpInt4(zxw6200, new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba, bb))
new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb)
new_primCmpInt4(zxw6200, zxw153) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw153)
new_primCmpInt3(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Zero), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba, bb))
new_primCmpInt3(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Zero), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba, bb))
new_primCmpInt3(Pos(Succ(zxw13700)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Succ(zxw13700)), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba, bb))
new_primCmpInt3(Neg(Succ(zxw13700)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Succ(zxw13700)), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba, bb))
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba, bb) → zxw542
new_primCmpInt1(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → new_primCmpInt5(zxw6200, new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba, bb))
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → LT
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → GT
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt5(zxw6200, zxw150) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw150)

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt2(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpNat1(Zero, x0)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt0(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat0(Zero, x0)
new_primCmpInt2(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt4(x0, x1)
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt0(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt3(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_sizeFM0(EmptyFM, x0, x1, x2)
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpInt2(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt3(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_glueVBal3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpInt0(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt5(x0, x1)
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt2(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt0(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs9(LT, LT)
new_primCmpInt3(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt2(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt3(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba, bb) → new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt0(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb), LT), h, ba, bb) at position [10,0,0,1] we obtained the following new rules:

new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba, bb) → new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt0(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw52), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)



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

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

new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb)
new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), zxw53, h, ba, bb)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), zxw53, h, ba, bb)
new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba, bb) → new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt3(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw52), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)
new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb)
new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb) → new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt1(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)
new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb) → new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt2(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba, bb) → new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt0(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw52), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)

The TRS R consists of the following rules:

new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb)
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primCmpInt0(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_primCmpInt0(Pos(Succ(zxw13500)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Succ(zxw13500)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_primCmpInt0(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_primCmpInt0(Neg(Succ(zxw13500)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Succ(zxw13500)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb) → zxw52
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primCmpInt2(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → GT
new_primCmpInt2(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → LT
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt2(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → new_primCmpInt4(zxw6200, new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba, bb))
new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb)
new_primCmpInt4(zxw6200, zxw153) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw153)
new_primCmpInt3(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Zero), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba, bb))
new_primCmpInt3(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Zero), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba, bb))
new_primCmpInt3(Pos(Succ(zxw13700)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Succ(zxw13700)), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba, bb))
new_primCmpInt3(Neg(Succ(zxw13700)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Succ(zxw13700)), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba, bb))
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba, bb) → zxw542
new_primCmpInt1(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → new_primCmpInt5(zxw6200, new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba, bb))
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → LT
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → GT
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt5(zxw6200, zxw150) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw150)

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt2(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpNat1(Zero, x0)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt0(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat0(Zero, x0)
new_primCmpInt2(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt4(x0, x1)
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt0(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt3(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_sizeFM0(EmptyFM, x0, x1, x2)
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpInt2(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt3(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_glueVBal3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpInt0(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt5(x0, x1)
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt2(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt0(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs9(LT, LT)
new_primCmpInt3(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt2(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt3(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(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_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba, bb) → new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt3(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw52), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)
The remaining pairs can at least be oriented weakly.

new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb)
new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), zxw53, h, ba, bb)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), zxw53, h, ba, bb)
new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb)
new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb) → new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt1(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)
new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb) → new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt2(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba, bb) → new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt0(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw52), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)
Used ordering: Polynomial interpretation [25]:

POL(Branch(x1, x2, x3, x4, x5)) = x3 + x5   
POL(EQ) = 1   
POL(False) = 1   
POL(GT) = 1   
POL(LT) = 1   
POL(Neg(x1)) = 1   
POL(Pos(x1)) = 0   
POL(Succ(x1)) = 0   
POL(True) = 1   
POL(Zero) = 0   
POL(new_esEs9(x1, x2)) = x2   
POL(new_glueVBal(x1, x2, x3, x4, x5)) = x1   
POL(new_glueVBal3GlueVBal1(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = x10   
POL(new_glueVBal3GlueVBal10(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = x10   
POL(new_glueVBal3GlueVBal2(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = x10   
POL(new_glueVBal3GlueVBal20(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = x10 + x11   
POL(new_glueVBal3Size_r(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = 0   
POL(new_glueVBal3Size_r0(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = x1 + x11 + x9   
POL(new_primCmpInt(x1, x2)) = 0   
POL(new_primCmpInt0(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = 0   
POL(new_primCmpInt1(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = 0   
POL(new_primCmpInt2(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = 1 + x11 + x2 + x3 + x4 + x5 + x6 + x7 + x9   
POL(new_primCmpInt3(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = 0   
POL(new_primCmpInt4(x1, x2)) = x2   
POL(new_primCmpInt5(x1, x2)) = 0   
POL(new_primCmpNat0(x1, x2)) = 0   
POL(new_primCmpNat1(x1, x2)) = 0   
POL(new_primCmpNat2(x1, x2)) = 0   
POL(new_primMulInt(x1, x2)) = x2   
POL(new_primMulNat0(x1, x2)) = 0   
POL(new_primPlusNat0(x1, x2)) = 1 + x2   
POL(new_primPlusNat1(x1, x2)) = 1   
POL(new_sizeFM(x1, x2, x3, x4, x5, x6, x7, x8)) = x1   
POL(new_sizeFM0(x1, x2, x3, x4)) = 0   

The following usable rules [17] were oriented:

new_esEs9(LT, LT) → True
new_esEs9(GT, LT) → False
new_esEs9(EQ, LT) → False



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

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

new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), zxw53, h, ba, bb)
new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), zxw53, h, ba, bb)
new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb)
new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb) → new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt1(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)
new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb) → new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt2(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba, bb) → new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt0(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw52), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)

The TRS R consists of the following rules:

new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb)
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primCmpInt0(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_primCmpInt0(Pos(Succ(zxw13500)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Succ(zxw13500)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_primCmpInt0(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_primCmpInt0(Neg(Succ(zxw13500)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Succ(zxw13500)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb) → zxw52
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primCmpInt2(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → GT
new_primCmpInt2(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → LT
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt2(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → new_primCmpInt4(zxw6200, new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba, bb))
new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb)
new_primCmpInt4(zxw6200, zxw153) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw153)
new_primCmpInt3(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Zero), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba, bb))
new_primCmpInt3(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Zero), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba, bb))
new_primCmpInt3(Pos(Succ(zxw13700)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Succ(zxw13700)), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba, bb))
new_primCmpInt3(Neg(Succ(zxw13700)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Succ(zxw13700)), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba, bb))
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba, bb) → zxw542
new_primCmpInt1(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → new_primCmpInt5(zxw6200, new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba, bb))
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → LT
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → GT
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt5(zxw6200, zxw150) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw150)

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt2(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpNat1(Zero, x0)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt0(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat0(Zero, x0)
new_primCmpInt2(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt4(x0, x1)
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt0(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt3(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_sizeFM0(EmptyFM, x0, x1, x2)
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpInt2(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt3(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_glueVBal3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpInt0(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt5(x0, x1)
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt2(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt0(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs9(LT, LT)
new_primCmpInt3(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt2(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt3(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

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

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

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

new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), zxw53, h, ba, bb)
new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb) → new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt2(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)

The TRS R consists of the following rules:

new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb)
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primCmpInt0(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_primCmpInt0(Pos(Succ(zxw13500)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Succ(zxw13500)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_primCmpInt0(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_primCmpInt0(Neg(Succ(zxw13500)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Succ(zxw13500)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb) → zxw52
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primCmpInt2(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → GT
new_primCmpInt2(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → LT
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt2(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → new_primCmpInt4(zxw6200, new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba, bb))
new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb)
new_primCmpInt4(zxw6200, zxw153) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw153)
new_primCmpInt3(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Zero), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba, bb))
new_primCmpInt3(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Zero), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba, bb))
new_primCmpInt3(Pos(Succ(zxw13700)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Succ(zxw13700)), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba, bb))
new_primCmpInt3(Neg(Succ(zxw13700)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Succ(zxw13700)), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba, bb))
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba, bb) → zxw542
new_primCmpInt1(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → new_primCmpInt5(zxw6200, new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba, bb))
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → LT
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → GT
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt5(zxw6200, zxw150) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw150)

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt2(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpNat1(Zero, x0)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt0(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat0(Zero, x0)
new_primCmpInt2(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt4(x0, x1)
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt0(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt3(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_sizeFM0(EmptyFM, x0, x1, x2)
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpInt2(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt3(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_glueVBal3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpInt0(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt5(x0, x1)
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt2(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt0(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs9(LT, LT)
new_primCmpInt3(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt2(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt3(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

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

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

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

new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), zxw53, h, ba, bb)
new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb) → new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt2(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)

The TRS R consists of the following rules:

new_primCmpInt2(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → GT
new_primCmpInt2(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → LT
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt2(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → new_primCmpInt4(zxw6200, new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba, bb))
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb)
new_primCmpInt4(zxw6200, zxw153) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw153)
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb) → zxw52

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt2(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpNat1(Zero, x0)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt0(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat0(Zero, x0)
new_primCmpInt2(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt4(x0, x1)
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt0(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt3(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_sizeFM0(EmptyFM, x0, x1, x2)
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpInt2(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt3(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_glueVBal3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpInt0(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt5(x0, x1)
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt2(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt0(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs9(LT, LT)
new_primCmpInt3(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt2(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt3(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

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

new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulNat0(Zero, Zero)
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt0(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt0(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt3(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_sizeFM0(EmptyFM, x0, x1, x2)
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpInt3(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_primMulInt(Neg(x0), Neg(x1))
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt0(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt5(x0, x1)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt0(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpInt3(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_primCmpInt3(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primMulNat0(Succ(x0), Zero)



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

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

new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), zxw53, h, ba, bb)
new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb) → new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt2(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)

The TRS R consists of the following rules:

new_primCmpInt2(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → GT
new_primCmpInt2(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → LT
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt2(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → new_primCmpInt4(zxw6200, new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba, bb))
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb)
new_primCmpInt4(zxw6200, zxw153) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw153)
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb) → zxw52

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primCmpInt2(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpNat1(Zero, x0)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primCmpInt2(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt4(x0, x1)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt2(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_glueVBal3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primPlusNat1(Succ(x0), Zero)
new_primCmpNat2(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat1(Succ(x0), x1)
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primCmpInt2(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt2(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat0(x0, Succ(x1))

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

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



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

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

new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), zxw53, h, ba, bb)
new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb) → new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt1(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba, bb) → new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt0(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw52), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)

The TRS R consists of the following rules:

new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb)
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primCmpInt0(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_primCmpInt0(Pos(Succ(zxw13500)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Succ(zxw13500)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_primCmpInt0(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_primCmpInt0(Neg(Succ(zxw13500)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Succ(zxw13500)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb) → zxw52
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primCmpInt2(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → GT
new_primCmpInt2(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → LT
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt2(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → new_primCmpInt4(zxw6200, new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba, bb))
new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb)
new_primCmpInt4(zxw6200, zxw153) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw153)
new_primCmpInt3(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Zero), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba, bb))
new_primCmpInt3(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Zero), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba, bb))
new_primCmpInt3(Pos(Succ(zxw13700)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Succ(zxw13700)), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba, bb))
new_primCmpInt3(Neg(Succ(zxw13700)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Succ(zxw13700)), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba, bb))
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba, bb) → zxw542
new_primCmpInt1(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → new_primCmpInt5(zxw6200, new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba, bb))
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → LT
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → GT
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt5(zxw6200, zxw150) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw150)

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt2(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpNat1(Zero, x0)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt0(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat0(Zero, x0)
new_primCmpInt2(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt4(x0, x1)
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt0(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt3(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_sizeFM0(EmptyFM, x0, x1, x2)
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpInt2(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt3(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_glueVBal3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpInt0(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt5(x0, x1)
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt2(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt0(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs9(LT, LT)
new_primCmpInt3(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt2(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt3(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

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

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

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

new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), zxw53, h, ba, bb)
new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb) → new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt1(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba, bb) → new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt0(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw52), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)

The TRS R consists of the following rules:

new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primCmpInt0(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_primCmpInt0(Pos(Succ(zxw13500)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Succ(zxw13500)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_primCmpInt0(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_primCmpInt0(Neg(Succ(zxw13500)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Succ(zxw13500)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb) → zxw52
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primCmpInt1(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → new_primCmpInt5(zxw6200, new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba, bb))
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → LT
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → GT
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb)
new_primCmpInt5(zxw6200, zxw150) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw150)

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt2(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpNat1(Zero, x0)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt0(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat0(Zero, x0)
new_primCmpInt2(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat1(Zero, Zero)
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt4(x0, x1)
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt0(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt3(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_sizeFM0(EmptyFM, x0, x1, x2)
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpInt2(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt3(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_glueVBal3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpInt0(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt5(x0, x1)
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt2(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt0(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs9(LT, LT)
new_primCmpInt3(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt2(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt3(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(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_primCmpInt2(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpInt2(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpInt4(x0, x1)
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt3(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_sizeFM0(EmptyFM, x0, x1, x2)
new_primCmpInt2(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt3(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_glueVBal3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt2(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt3(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_primCmpInt2(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt3(Pos(Zero), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ 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
                                                                                        ↳ QDPOrderProof
                                                                                          ↳ QDP
                                                                                            ↳ DependencyGraphProof
                                                                                              ↳ AND
                                                                                                ↳ QDP
                                                                                                ↳ QDP
                                                                                                  ↳ UsableRulesProof
                                                                                                    ↳ QDP
                                                                                                      ↳ QReductionProof
                                                                                                        ↳ QDP
                                                                                                          ↳ QDPOrderProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), zxw53, h, ba, bb)
new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb) → new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt1(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba, bb) → new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt0(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw52), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)

The TRS R consists of the following rules:

new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primCmpInt0(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_primCmpInt0(Pos(Succ(zxw13500)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Succ(zxw13500)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_primCmpInt0(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_primCmpInt0(Neg(Succ(zxw13500)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Succ(zxw13500)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb) → zxw52
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primCmpInt1(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → new_primCmpInt5(zxw6200, new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba, bb))
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → LT
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → GT
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb)
new_primCmpInt5(zxw6200, zxw150) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw150)

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpNat1(Zero, x0)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt0(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt0(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpInt0(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt5(x0, x1)
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt0(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(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_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba, bb) → new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt0(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw52), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)
The remaining pairs can at least be oriented weakly.

new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), zxw53, h, ba, bb)
new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb) → new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt1(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)
Used ordering: Polynomial interpretation [25]:

POL(Branch(x1, x2, x3, x4, x5)) = 1 + x1 + x2 + x4 + x5   
POL(EQ) = 0   
POL(False) = 1   
POL(GT) = 0   
POL(LT) = 0   
POL(Neg(x1)) = 0   
POL(Pos(x1)) = 0   
POL(Succ(x1)) = 0   
POL(True) = 1   
POL(Zero) = 0   
POL(new_esEs9(x1, x2)) = 1   
POL(new_glueVBal(x1, x2, x3, x4, x5)) = 1 + x1   
POL(new_glueVBal3GlueVBal1(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = 1 + x10 + x7   
POL(new_glueVBal3GlueVBal2(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = 1 + x10 + x11 + x6 + x7 + x9   
POL(new_glueVBal3Size_r(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = x1 + x11 + x12 + x13 + x2 + x3 + x4 + x5   
POL(new_primCmpInt(x1, x2)) = 1   
POL(new_primCmpInt0(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = 0   
POL(new_primCmpInt1(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = 1 + x10 + x11 + x12 + x13 + x2 + x3 + x4 + x5 + x7 + x8 + x9   
POL(new_primCmpInt5(x1, x2)) = 1   
POL(new_primCmpNat0(x1, x2)) = 0   
POL(new_primCmpNat1(x1, x2)) = 1   
POL(new_primCmpNat2(x1, x2)) = 0   
POL(new_primMulInt(x1, x2)) = 1   
POL(new_primMulNat0(x1, x2)) = 1   
POL(new_primPlusNat0(x1, x2)) = 0   
POL(new_primPlusNat1(x1, x2)) = 0   
POL(new_sizeFM(x1, x2, x3, x4, x5, x6, x7, x8)) = x2 + x6   

The following usable rules [17] were oriented:

new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_esEs9(GT, LT) → False



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

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

new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), zxw53, h, ba, bb)
new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb) → new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt1(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)

The TRS R consists of the following rules:

new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primCmpInt0(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_primCmpInt0(Pos(Succ(zxw13500)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Succ(zxw13500)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_primCmpInt0(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_primCmpInt0(Neg(Succ(zxw13500)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Succ(zxw13500)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb) → zxw52
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primCmpInt1(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → new_primCmpInt5(zxw6200, new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba, bb))
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → LT
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → GT
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb)
new_primCmpInt5(zxw6200, zxw150) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw150)

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpNat1(Zero, x0)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt0(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt0(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpInt0(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt5(x0, x1)
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt0(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

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

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

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

new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), zxw53, h, ba, bb)
new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb) → new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt1(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)

The TRS R consists of the following rules:

new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primCmpInt0(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_primCmpInt0(Pos(Succ(zxw13500)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Succ(zxw13500)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_primCmpInt0(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Pos(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_primCmpInt0(Neg(Succ(zxw13500)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_primCmpInt(Neg(Succ(zxw13500)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba, bb))
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb) → zxw52
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primCmpInt1(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → new_primCmpInt5(zxw6200, new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba, bb))
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → LT
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → GT
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb)
new_primCmpInt5(zxw6200, zxw150) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw150)

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpNat1(Zero, x0)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt0(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt0(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpInt0(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt5(x0, x1)
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt0(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

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

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

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

new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), zxw53, h, ba, bb)
new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb) → new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt1(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)

The TRS R consists of the following rules:

new_primCmpInt1(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → new_primCmpInt5(zxw6200, new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba, bb))
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → LT
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → GT
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb)
new_primCmpInt5(zxw6200, zxw150) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw150)
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat1(Zero, zxw7900) → LT
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb) → zxw52

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpNat1(Zero, x0)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt0(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt0(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpInt0(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt5(x0, x1)
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt0(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

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

new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulNat0(Zero, Zero)
new_primCmpInt0(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_primCmpInt0(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primMulInt(Neg(x0), Neg(x1))
new_primMulNat0(Zero, Succ(x0))
new_primCmpInt0(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt0(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primMulNat0(Succ(x0), Zero)



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

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

new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba, bb) → new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), zxw53, h, ba, bb)
new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba, bb) → new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs9(new_primCmpInt1(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb), LT), h, ba, bb)

The TRS R consists of the following rules:

new_primCmpInt1(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → new_primCmpInt5(zxw6200, new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba, bb))
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → LT
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → GT
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba, bb) → EQ
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba, bb) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb)
new_primCmpInt5(zxw6200, zxw150) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw150)
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat1(Zero, zxw7900) → LT
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb) → zxw52

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpNat1(Zero, x0)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primPlusNat1(Succ(x0), Zero)
new_primCmpNat2(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat1(Succ(x0), x1)
new_primCmpInt5(x0, x1)
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))

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

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



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

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

new_addToFM_C(Branch(zxw340, zxw341, zxw342, zxw343, zxw344), zxw300, zxw31, h, ba, bb) → new_addToFM_C2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw300, zxw31, new_lt14(Right(zxw300), zxw340, h, ba), h, ba, bb)
new_addToFM_C1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw300, zxw31, True, h, ba, bb) → new_addToFM_C(zxw344, zxw300, zxw31, h, ba, bb)
new_addToFM_C2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw300, zxw31, False, h, ba, bb) → new_addToFM_C1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw300, zxw31, new_esEs9(new_compare15(Right(zxw300), zxw340, h, ba), GT), h, ba, bb)
new_addToFM_C2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw300, zxw31, True, h, ba, bb) → new_addToFM_C(zxw343, zxw300, zxw31, h, ba, bb)

The TRS R consists of the following rules:

new_ltEs15(zxw7900, zxw8000) → new_fsEs(new_compare6(zxw7900, zxw8000))
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Char) → new_ltEs10(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), gh, ty_Bool) → new_ltEs12(zxw79000, zxw80000)
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, app(ty_Maybe, bae)) → new_ltEs18(zxw7900, zxw8000, bae)
new_esEs28(zxw4000, zxw3000, app(ty_[], ddd)) → new_esEs13(zxw4000, zxw3000, ddd)
new_esEs23(zxw4000, zxw3000, app(app(ty_Either, chd), che)) → new_esEs7(zxw4000, zxw3000, chd, che)
new_esEs6(Just(zxw4000), Just(zxw3000), app(app(ty_@2, ef), eg)) → new_esEs5(zxw4000, zxw3000, ef, eg)
new_lt4(zxw79000, zxw80000, app(app(app(ty_@3, be), bf), bg)) → new_lt5(zxw79000, zxw80000, be, bf, bg)
new_esEs7(Left(zxw4000), Left(zxw3000), app(app(ty_Either, bca), bcb), bbd) → new_esEs7(zxw4000, zxw3000, bca, bcb)
new_ltEs20(zxw7900, zxw8000, ty_Int) → new_ltEs9(zxw7900, zxw8000)
new_lt19(zxw79000, zxw80000, app(app(ty_Either, beb), bec)) → new_lt14(zxw79000, zxw80000, beb, bec)
new_esEs9(GT, LT) → False
new_esEs9(LT, GT) → False
new_esEs13([], [], cgf) → True
new_lt4(zxw79000, zxw80000, app(ty_[], bh)) → new_lt10(zxw79000, zxw80000, bh)
new_compare110(zxw79000, zxw80000, True, baf, bag) → LT
new_esEs27(zxw4001, zxw3001, app(ty_Ratio, dca)) → new_esEs18(zxw4001, zxw3001, dca)
new_compare29(zxw79000, zxw80000, ty_Char) → new_compare17(zxw79000, zxw80000)
new_ltEs7(LT, EQ) → True
new_ltEs18(Just(zxw79000), Just(zxw80000), app(ty_Maybe, cdg)) → new_ltEs18(zxw79000, zxw80000, cdg)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Integer) → new_ltEs13(zxw79000, zxw80000)
new_ltEs20(zxw7900, zxw8000, ty_@0) → new_ltEs8(zxw7900, zxw8000)
new_lt20(zxw79001, zxw80001, app(app(ty_Either, bfb), bfc)) → new_lt14(zxw79001, zxw80001, bfb, bfc)
new_esEs23(zxw4000, zxw3000, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_ltEs8(zxw7900, zxw8000) → new_fsEs(new_compare30(zxw7900, zxw8000))
new_lt19(zxw79000, zxw80000, ty_Double) → new_lt15(zxw79000, zxw80000)
new_esEs22(zxw4000, zxw3000, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_ltEs14(Right(zxw79000), Right(zxw80000), gh, app(ty_[], cbg)) → new_ltEs11(zxw79000, zxw80000, cbg)
new_ltEs21(zxw79002, zxw80002, ty_Char) → new_ltEs10(zxw79002, zxw80002)
new_esEs23(zxw4000, zxw3000, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Bool, ha) → new_ltEs12(zxw79000, zxw80000)
new_compare8(:%(zxw79000, zxw79001), :%(zxw80000, zxw80001), ty_Integer) → new_compare32(new_sr0(zxw79000, zxw80001), new_sr0(zxw80000, zxw79001))
new_esEs26(zxw4002, zxw3002, ty_Float) → new_esEs17(zxw4002, zxw3002)
new_esEs19(zxw79001, zxw80001, app(ty_Ratio, bfd)) → new_esEs18(zxw79001, zxw80001, bfd)
new_primMulNat0(Zero, Zero) → Zero
new_esEs20(zxw79000, zxw80000, app(ty_[], bea)) → new_esEs13(zxw79000, zxw80000, bea)
new_esEs7(Right(zxw4000), Right(zxw3000), bcf, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_lt20(zxw79001, zxw80001, ty_@0) → new_lt7(zxw79001, zxw80001)
new_esEs27(zxw4001, zxw3001, app(app(app(ty_@3, dch), dda), ddb)) → new_esEs4(zxw4001, zxw3001, dch, dda, ddb)
new_esEs19(zxw79001, zxw80001, ty_Ordering) → new_esEs9(zxw79001, zxw80001)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(ty_Ratio, cdf)) → new_ltEs17(zxw79000, zxw80000, cdf)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Bool, bbd) → new_esEs14(zxw4000, zxw3000)
new_esEs24(zxw4001, zxw3001, ty_Integer) → new_esEs15(zxw4001, zxw3001)
new_lt19(zxw79000, zxw80000, ty_Ordering) → new_lt6(zxw79000, zxw80000)
new_lt20(zxw79001, zxw80001, app(app(ty_@2, beh), bfa)) → new_lt11(zxw79001, zxw80001, beh, bfa)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(ty_Ratio, cbb), ha) → new_ltEs17(zxw79000, zxw80000, cbb)
new_compare9(zxw79000, zxw80000, ff, fg, fh) → new_compare25(zxw79000, zxw80000, new_esEs4(zxw79000, zxw80000, ff, fg, fh), ff, fg, fh)
new_lt11(zxw79000, zxw80000, baf, bag) → new_esEs9(new_compare19(zxw79000, zxw80000, baf, bag), LT)
new_compare1([], :(zxw80000, zxw80001), gg) → LT
new_lt18(zxw79000, zxw80000, bbb) → new_esEs9(new_compare27(zxw79000, zxw80000, bbb), LT)
new_esEs8(zxw79000, zxw80000, ty_Int) → new_esEs11(zxw79000, zxw80000)
new_compare32(Integer(zxw79000), Integer(zxw80000)) → new_primCmpInt(zxw79000, zxw80000)
new_ltEs5(zxw79001, zxw80001, ty_Char) → new_ltEs10(zxw79001, zxw80001)
new_lt4(zxw79000, zxw80000, ty_Bool) → new_lt12(zxw79000, zxw80000)
new_compare27(zxw79000, zxw80000, bbb) → new_compare28(zxw79000, zxw80000, new_esEs6(zxw79000, zxw80000, bbb), bbb)
new_lt4(zxw79000, zxw80000, app(ty_Maybe, cf)) → new_lt18(zxw79000, zxw80000, cf)
new_compare29(zxw79000, zxw80000, ty_Bool) → new_compare31(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, ty_Double) → new_esEs16(zxw79000, zxw80000)
new_esEs22(zxw4000, zxw3000, app(app(ty_@2, cfg), cfh)) → new_esEs5(zxw4000, zxw3000, cfg, cfh)
new_lt4(zxw79000, zxw80000, ty_Ordering) → new_lt6(zxw79000, zxw80000)
new_esEs22(zxw4000, zxw3000, app(ty_Maybe, cff)) → new_esEs6(zxw4000, zxw3000, cff)
new_ltEs14(Right(zxw79000), Right(zxw80000), gh, app(app(app(ty_@3, cbd), cbe), cbf)) → new_ltEs6(zxw79000, zxw80000, cbd, cbe, cbf)
new_esEs27(zxw4001, zxw3001, app(ty_Maybe, dcc)) → new_esEs6(zxw4001, zxw3001, dcc)
new_esEs8(zxw79000, zxw80000, app(app(app(ty_@3, be), bf), bg)) → new_esEs4(zxw79000, zxw80000, be, bf, bg)
new_esEs15(Integer(zxw4000), Integer(zxw3000)) → new_primEqInt(zxw4000, zxw3000)
new_ltEs21(zxw79002, zxw80002, app(app(ty_@2, bgb), bgc)) → new_ltEs4(zxw79002, zxw80002, bgb, bgc)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Float, ha) → new_ltEs16(zxw79000, zxw80000)
new_lt5(zxw79000, zxw80000, ff, fg, fh) → new_esEs9(new_compare9(zxw79000, zxw80000, ff, fg, fh), LT)
new_esEs22(zxw4000, zxw3000, app(ty_Ratio, cfd)) → new_esEs18(zxw4000, zxw3000, cfd)
new_esEs22(zxw4000, zxw3000, app(app(ty_Either, cga), cgb)) → new_esEs7(zxw4000, zxw3000, cga, cgb)
new_ltEs19(zxw7900, zxw8000, ty_Float) → new_ltEs16(zxw7900, zxw8000)
new_esEs7(Right(zxw4000), Right(zxw3000), bcf, app(ty_Maybe, bda)) → new_esEs6(zxw4000, zxw3000, bda)
new_pePe(False, zxw271) → zxw271
new_esEs7(Left(zxw4000), Right(zxw3000), bcf, bbd) → False
new_esEs7(Right(zxw4000), Left(zxw3000), bcf, bbd) → False
new_lt15(zxw79000, zxw80000) → new_esEs9(new_compare6(zxw79000, zxw80000), LT)
new_compare15(zxw790, zxw800, gb, gc) → new_compare26(zxw790, zxw800, new_esEs7(zxw790, zxw800, gb, gc), gb, gc)
new_ltEs14(Right(zxw79000), Right(zxw80000), gh, ty_Float) → new_ltEs16(zxw79000, zxw80000)
new_ltEs12(True, False) → False
new_esEs20(zxw79000, zxw80000, ty_Double) → new_esEs16(zxw79000, zxw80000)
new_ltEs19(zxw7900, zxw8000, app(app(ty_@2, bc), bd)) → new_ltEs4(zxw7900, zxw8000, bc, bd)
new_compare23(zxw79000, zxw80000, True) → EQ
new_esEs27(zxw4001, zxw3001, app(app(ty_Either, dcf), dcg)) → new_esEs7(zxw4001, zxw3001, dcf, dcg)
new_esEs27(zxw4001, zxw3001, ty_Ordering) → new_esEs9(zxw4001, zxw3001)
new_esEs27(zxw4001, zxw3001, ty_Float) → new_esEs17(zxw4001, zxw3001)
new_esEs19(zxw79001, zxw80001, app(ty_Maybe, bfe)) → new_esEs6(zxw79001, zxw80001, bfe)
new_lt10(zxw79000, zxw80000, bea) → new_esEs9(new_compare1(zxw79000, zxw80000, bea), LT)
new_esEs26(zxw4002, zxw3002, ty_Char) → new_esEs12(zxw4002, zxw3002)
new_ltEs19(zxw7900, zxw8000, app(ty_[], gg)) → new_ltEs11(zxw7900, zxw8000, gg)
new_esEs26(zxw4002, zxw3002, ty_Int) → new_esEs11(zxw4002, zxw3002)
new_ltEs5(zxw79001, zxw80001, app(app(ty_@2, dd), de)) → new_ltEs4(zxw79001, zxw80001, dd, de)
new_lt19(zxw79000, zxw80000, app(ty_Ratio, ga)) → new_lt17(zxw79000, zxw80000, ga)
new_esEs22(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, app(app(app(ty_@3, deb), dec), ded)) → new_esEs4(zxw4000, zxw3000, deb, dec, ded)
new_compare29(zxw79000, zxw80000, app(app(ty_@2, bhd), bhe)) → new_compare19(zxw79000, zxw80000, bhd, bhe)
new_ltEs21(zxw79002, zxw80002, ty_Int) → new_ltEs9(zxw79002, zxw80002)
new_esEs20(zxw79000, zxw80000, ty_Char) → new_esEs12(zxw79000, zxw80000)
new_compare13(zxw235, zxw236, False, bah, bba) → GT
new_esEs9(GT, EQ) → False
new_esEs9(EQ, GT) → False
new_esEs19(zxw79001, zxw80001, app(app(ty_Either, bfb), bfc)) → new_esEs7(zxw79001, zxw80001, bfb, bfc)
new_esEs20(zxw79000, zxw80000, app(app(ty_@2, baf), bag)) → new_esEs5(zxw79000, zxw80000, baf, bag)
new_ltEs7(GT, GT) → True
new_ltEs20(zxw7900, zxw8000, app(app(ty_@2, hh), baa)) → new_ltEs4(zxw7900, zxw8000, hh, baa)
new_esEs7(Right(zxw4000), Right(zxw3000), bcf, app(app(ty_@2, bdb), bdc)) → new_esEs5(zxw4000, zxw3000, bdb, bdc)
new_esEs21(zxw4001, zxw3001, ty_Bool) → new_esEs14(zxw4001, zxw3001)
new_primCompAux0(zxw79000, zxw80000, zxw272, gg) → new_primCompAux00(zxw272, new_compare29(zxw79000, zxw80000, gg))
new_ltEs21(zxw79002, zxw80002, ty_Ordering) → new_ltEs7(zxw79002, zxw80002)
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_compare29(zxw79000, zxw80000, app(ty_[], bhc)) → new_compare1(zxw79000, zxw80000, bhc)
new_lt20(zxw79001, zxw80001, ty_Ordering) → new_lt6(zxw79001, zxw80001)
new_esEs8(zxw79000, zxw80000, app(ty_[], bh)) → new_esEs13(zxw79000, zxw80000, bh)
new_esEs7(Right(zxw4000), Right(zxw3000), bcf, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_esEs27(zxw4001, zxw3001, ty_@0) → new_esEs10(zxw4001, zxw3001)
new_compare25(zxw79000, zxw80000, True, ff, fg, fh) → EQ
new_esEs19(zxw79001, zxw80001, ty_Float) → new_esEs17(zxw79001, zxw80001)
new_ltEs5(zxw79001, zxw80001, ty_Ordering) → new_ltEs7(zxw79001, zxw80001)
new_lt4(zxw79000, zxw80000, app(ty_Ratio, ce)) → new_lt17(zxw79000, zxw80000, ce)
new_esEs28(zxw4000, zxw3000, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Int, bbd) → new_esEs11(zxw4000, zxw3000)
new_ltEs21(zxw79002, zxw80002, ty_Float) → new_ltEs16(zxw79002, zxw80002)
new_esEs28(zxw4000, zxw3000, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(app(app(ty_@3, ccf), ccg), cch)) → new_ltEs6(zxw79000, zxw80000, ccf, ccg, cch)
new_compare29(zxw79000, zxw80000, app(app(app(ty_@3, bgh), bha), bhb)) → new_compare9(zxw79000, zxw80000, bgh, bha, bhb)
new_lt19(zxw79000, zxw80000, app(app(ty_@2, baf), bag)) → new_lt11(zxw79000, zxw80000, baf, bag)
new_pePe(True, zxw271) → True
new_primEqNat0(Zero, Zero) → True
new_compare14(zxw242, zxw243, False, dab, dac) → GT
new_ltEs14(Right(zxw79000), Right(zxw80000), gh, ty_Double) → new_ltEs15(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, ty_Int) → new_esEs11(zxw79000, zxw80000)
new_ltEs21(zxw79002, zxw80002, ty_Bool) → new_ltEs12(zxw79002, zxw80002)
new_lt9(zxw79000, zxw80000) → new_esEs9(new_compare17(zxw79000, zxw80000), LT)
new_ltEs12(False, False) → True
new_esEs7(Left(zxw4000), Left(zxw3000), app(app(ty_@2, bbg), bbh), bbd) → new_esEs5(zxw4000, zxw3000, bbg, bbh)
new_esEs26(zxw4002, zxw3002, app(ty_Maybe, dba)) → new_esEs6(zxw4002, zxw3002, dba)
new_compare8(:%(zxw79000, zxw79001), :%(zxw80000, zxw80001), ty_Int) → new_compare16(new_sr(zxw79000, zxw80001), new_sr(zxw80000, zxw79001))
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Ordering, bbd) → new_esEs9(zxw4000, zxw3000)
new_esEs27(zxw4001, zxw3001, ty_Char) → new_esEs12(zxw4001, zxw3001)
new_lt7(zxw79000, zxw80000) → new_esEs9(new_compare30(zxw79000, zxw80000), LT)
new_compare110(zxw79000, zxw80000, False, baf, bag) → GT
new_sr(zxw4000, zxw3000) → new_primMulInt(zxw4000, zxw3000)
new_compare12(zxw79000, zxw80000, True, ff, fg, fh) → LT
new_lt19(zxw79000, zxw80000, ty_Int) → new_lt8(zxw79000, zxw80000)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_ltEs14(Right(zxw79000), Right(zxw80000), gh, app(app(ty_@2, cbh), cca)) → new_ltEs4(zxw79000, zxw80000, cbh, cca)
new_ltEs19(zxw7900, zxw8000, ty_Char) → new_ltEs10(zxw7900, zxw8000)
new_esEs21(zxw4001, zxw3001, ty_Double) → new_esEs16(zxw4001, zxw3001)
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_esEs7(Right(zxw4000), Right(zxw3000), bcf, app(app(ty_Either, bdd), bde)) → new_esEs7(zxw4000, zxw3000, bdd, bde)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Double, ha) → new_ltEs15(zxw79000, zxw80000)
new_ltEs19(zxw7900, zxw8000, ty_Bool) → new_ltEs12(zxw7900, zxw8000)
new_esEs26(zxw4002, zxw3002, app(app(app(ty_@3, dbf), dbg), dbh)) → new_esEs4(zxw4002, zxw3002, dbf, dbg, dbh)
new_esEs7(Right(zxw4000), Right(zxw3000), bcf, app(ty_[], bch)) → new_esEs13(zxw4000, zxw3000, bch)
new_ltEs11(zxw7900, zxw8000, gg) → new_fsEs(new_compare1(zxw7900, zxw8000, gg))
new_ltEs20(zxw7900, zxw8000, ty_Float) → new_ltEs16(zxw7900, zxw8000)
new_esEs21(zxw4001, zxw3001, ty_Ordering) → new_esEs9(zxw4001, zxw3001)
new_esEs7(Right(zxw4000), Right(zxw3000), bcf, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_esEs9(EQ, EQ) → True
new_fsEs(zxw259) → new_not(new_esEs9(zxw259, GT))
new_esEs8(zxw79000, zxw80000, ty_Char) → new_esEs12(zxw79000, zxw80000)
new_primEqInt(Neg(Succ(zxw40000)), Neg(Succ(zxw30000))) → new_primEqNat0(zxw40000, zxw30000)
new_esEs8(zxw79000, zxw80000, app(app(ty_@2, ca), cb)) → new_esEs5(zxw79000, zxw80000, ca, cb)
new_compare13(zxw235, zxw236, True, bah, bba) → LT
new_compare26(Left(zxw7900), Right(zxw8000), False, gb, gc) → LT
new_esEs13(:(zxw4000, zxw4001), :(zxw3000, zxw3001), cgf) → new_asAs(new_esEs23(zxw4000, zxw3000, cgf), new_esEs13(zxw4001, zxw3001, cgf))
new_esEs26(zxw4002, zxw3002, app(ty_[], dah)) → new_esEs13(zxw4002, zxw3002, dah)
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_ltEs19(zxw7900, zxw8000, app(ty_Ratio, hb)) → new_ltEs17(zxw7900, zxw8000, hb)
new_ltEs20(zxw7900, zxw8000, ty_Bool) → new_ltEs12(zxw7900, zxw8000)
new_esEs21(zxw4001, zxw3001, ty_Char) → new_esEs12(zxw4001, zxw3001)
new_compare23(zxw79000, zxw80000, False) → new_compare10(zxw79000, zxw80000, new_ltEs12(zxw79000, zxw80000))
new_ltEs14(Right(zxw79000), Left(zxw80000), gh, ha) → False
new_compare210(zxw79000, zxw80000, False, baf, bag) → new_compare110(zxw79000, zxw80000, new_ltEs4(zxw79000, zxw80000, baf, bag), baf, bag)
new_primCmpNat1(Zero, zxw7900) → LT
new_compare7(Float(zxw79000, zxw79001), Float(zxw80000, zxw80001)) → new_compare16(new_sr(zxw79000, zxw80000), new_sr(zxw79001, zxw80001))
new_ltEs21(zxw79002, zxw80002, ty_Integer) → new_ltEs13(zxw79002, zxw80002)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_lt20(zxw79001, zxw80001, app(ty_Maybe, bfe)) → new_lt18(zxw79001, zxw80001, bfe)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Integer, bbd) → new_esEs15(zxw4000, zxw3000)
new_ltEs5(zxw79001, zxw80001, ty_Bool) → new_ltEs12(zxw79001, zxw80001)
new_esEs19(zxw79001, zxw80001, ty_Bool) → new_esEs14(zxw79001, zxw80001)
new_ltEs7(EQ, EQ) → True
new_ltEs20(zxw7900, zxw8000, app(ty_Ratio, bad)) → new_ltEs17(zxw7900, zxw8000, bad)
new_primEqInt(Neg(Zero), Neg(Succ(zxw30000))) → False
new_primEqInt(Neg(Succ(zxw40000)), Neg(Zero)) → False
new_ltEs5(zxw79001, zxw80001, ty_Integer) → new_ltEs13(zxw79001, zxw80001)
new_compare26(zxw790, zxw800, True, gb, gc) → EQ
new_compare111(zxw79000, zxw80000, True, bbb) → LT
new_esEs20(zxw79000, zxw80000, ty_@0) → new_esEs10(zxw79000, zxw80000)
new_ltEs21(zxw79002, zxw80002, app(app(ty_Either, bgd), bge)) → new_ltEs14(zxw79002, zxw80002, bgd, bge)
new_esEs8(zxw79000, zxw80000, ty_Float) → new_esEs17(zxw79000, zxw80000)
new_esEs23(zxw4000, zxw3000, app(app(app(ty_@3, chf), chg), chh)) → new_esEs4(zxw4000, zxw3000, chf, chg, chh)
new_ltEs21(zxw79002, zxw80002, app(ty_[], bga)) → new_ltEs11(zxw79002, zxw80002, bga)
new_esEs21(zxw4001, zxw3001, ty_Float) → new_esEs17(zxw4001, zxw3001)
new_compare24(zxw79000, zxw80000, False) → new_compare11(zxw79000, zxw80000, new_ltEs7(zxw79000, zxw80000))
new_ltEs5(zxw79001, zxw80001, app(ty_Ratio, dh)) → new_ltEs17(zxw79001, zxw80001, dh)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_esEs26(zxw4002, zxw3002, app(app(ty_Either, dbd), dbe)) → new_esEs7(zxw4002, zxw3002, dbd, dbe)
new_lt20(zxw79001, zxw80001, ty_Int) → new_lt8(zxw79001, zxw80001)
new_lt4(zxw79000, zxw80000, ty_Int) → new_lt8(zxw79000, zxw80000)
new_ltEs20(zxw7900, zxw8000, ty_Double) → new_ltEs15(zxw7900, zxw8000)
new_lt12(zxw79000, zxw80000) → new_esEs9(new_compare31(zxw79000, zxw80000), LT)
new_ltEs7(GT, LT) → False
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Int, ha) → new_ltEs9(zxw79000, zxw80000)
new_lt20(zxw79001, zxw80001, ty_Integer) → new_lt13(zxw79001, zxw80001)
new_ltEs7(GT, EQ) → False
new_esEs6(Nothing, Nothing, eb) → True
new_primEqInt(Pos(Succ(zxw40000)), Pos(Succ(zxw30000))) → new_primEqNat0(zxw40000, zxw30000)
new_lt8(zxw790, zxw800) → new_esEs9(new_compare16(zxw790, zxw800), LT)
new_esEs21(zxw4001, zxw3001, app(ty_Maybe, ced)) → new_esEs6(zxw4001, zxw3001, ced)
new_lt6(zxw79000, zxw80000) → new_esEs9(new_compare18(zxw79000, zxw80000), LT)
new_esEs14(False, True) → False
new_esEs14(True, False) → False
new_esEs26(zxw4002, zxw3002, ty_Integer) → new_esEs15(zxw4002, zxw3002)
new_esEs7(Right(zxw4000), Right(zxw3000), bcf, app(app(app(ty_@3, bdf), bdg), bdh)) → new_esEs4(zxw4000, zxw3000, bdf, bdg, bdh)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs6(Nothing, Just(zxw3000), eb) → False
new_esEs6(Just(zxw4000), Nothing, eb) → False
new_primEqNat0(Succ(zxw40000), Succ(zxw30000)) → new_primEqNat0(zxw40000, zxw30000)
new_esEs16(Double(zxw4000, zxw4001), Double(zxw3000, zxw3001)) → new_esEs11(new_sr(zxw4000, zxw3000), new_sr(zxw4001, zxw3001))
new_lt19(zxw79000, zxw80000, ty_@0) → new_lt7(zxw79000, zxw80000)
new_ltEs5(zxw79001, zxw80001, app(ty_Maybe, ea)) → new_ltEs18(zxw79001, zxw80001, ea)
new_esEs17(Float(zxw4000, zxw4001), Float(zxw3000, zxw3001)) → new_esEs11(new_sr(zxw4000, zxw3000), new_sr(zxw4001, zxw3001))
new_primCompAux00(zxw276, LT) → LT
new_esEs28(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), app(ty_Ratio, bbc), bbd) → new_esEs18(zxw4000, zxw3000, bbc)
new_esEs21(zxw4001, zxw3001, ty_Int) → new_esEs11(zxw4001, zxw3001)
new_compare1(:(zxw79000, zxw79001), :(zxw80000, zxw80001), gg) → new_primCompAux0(zxw79000, zxw80000, new_compare1(zxw79001, zxw80001, gg), gg)
new_primEqInt(Pos(Zero), Pos(Succ(zxw30000))) → False
new_primEqInt(Pos(Succ(zxw40000)), Pos(Zero)) → False
new_compare29(zxw79000, zxw80000, ty_Int) → new_compare16(zxw79000, zxw80000)
new_lt20(zxw79001, zxw80001, app(ty_Ratio, bfd)) → new_lt17(zxw79001, zxw80001, bfd)
new_ltEs20(zxw7900, zxw8000, ty_Integer) → new_ltEs13(zxw7900, zxw8000)
new_esEs5(@2(zxw4000, zxw4001), @2(zxw3000, zxw3001), cdh, cea) → new_asAs(new_esEs22(zxw4000, zxw3000, cdh), new_esEs21(zxw4001, zxw3001, cea))
new_ltEs18(Nothing, Nothing, hc) → True
new_ltEs21(zxw79002, zxw80002, app(ty_Ratio, bgf)) → new_ltEs17(zxw79002, zxw80002, bgf)
new_esEs23(zxw4000, zxw3000, app(app(ty_@2, chb), chc)) → new_esEs5(zxw4000, zxw3000, chb, chc)
new_esEs20(zxw79000, zxw80000, app(app(app(ty_@3, ff), fg), fh)) → new_esEs4(zxw79000, zxw80000, ff, fg, fh)
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_ltEs21(zxw79002, zxw80002, app(app(app(ty_@3, bff), bfg), bfh)) → new_ltEs6(zxw79002, zxw80002, bff, bfg, bfh)
new_ltEs10(zxw7900, zxw8000) → new_fsEs(new_compare17(zxw7900, zxw8000))
new_compare17(Char(zxw79000), Char(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_sr0(Integer(zxw800000), Integer(zxw790010)) → Integer(new_primMulInt(zxw800000, zxw790010))
new_ltEs5(zxw79001, zxw80001, ty_Double) → new_ltEs15(zxw79001, zxw80001)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_esEs8(zxw79000, zxw80000, app(app(ty_Either, cc), cd)) → new_esEs7(zxw79000, zxw80000, cc, cd)
new_primEqInt(Neg(Succ(zxw40000)), Pos(zxw3000)) → False
new_primEqInt(Pos(Succ(zxw40000)), Neg(zxw3000)) → False
new_compare29(zxw79000, zxw80000, ty_Integer) → new_compare32(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), gh, ty_Char) → new_ltEs10(zxw79000, zxw80000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_@0, bbd) → new_esEs10(zxw4000, zxw3000)
new_lt19(zxw79000, zxw80000, app(app(app(ty_@3, ff), fg), fh)) → new_lt5(zxw79000, zxw80000, ff, fg, fh)
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_esEs28(zxw4000, zxw3000, app(ty_Maybe, dde)) → new_esEs6(zxw4000, zxw3000, dde)
new_esEs21(zxw4001, zxw3001, app(ty_[], cec)) → new_esEs13(zxw4001, zxw3001, cec)
new_ltEs21(zxw79002, zxw80002, ty_@0) → new_ltEs8(zxw79002, zxw80002)
new_primEqInt(Neg(Zero), Pos(Succ(zxw30000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(zxw30000))) → False
new_ltEs7(EQ, GT) → True
new_lt4(zxw79000, zxw80000, ty_Double) → new_lt15(zxw79000, zxw80000)
new_esEs21(zxw4001, zxw3001, ty_Integer) → new_esEs15(zxw4001, zxw3001)
new_primCompAux00(zxw276, EQ) → zxw276
new_esEs28(zxw4000, zxw3000, app(app(ty_Either, ddh), dea)) → new_esEs7(zxw4000, zxw3000, ddh, dea)
new_compare24(zxw79000, zxw80000, True) → EQ
new_compare6(Double(zxw79000, zxw79001), Double(zxw80000, zxw80001)) → new_compare16(new_sr(zxw79000, zxw80000), new_sr(zxw79001, zxw80001))
new_esEs8(zxw79000, zxw80000, ty_@0) → new_esEs10(zxw79000, zxw80000)
new_ltEs5(zxw79001, zxw80001, app(app(ty_Either, df), dg)) → new_ltEs14(zxw79001, zxw80001, df, dg)
new_lt13(zxw79000, zxw80000) → new_esEs9(new_compare32(zxw79000, zxw80000), LT)
new_esEs27(zxw4001, zxw3001, ty_Double) → new_esEs16(zxw4001, zxw3001)
new_esEs7(Left(zxw4000), Left(zxw3000), app(app(app(ty_@3, bcc), bcd), bce), bbd) → new_esEs4(zxw4000, zxw3000, bcc, bcd, bce)
new_esEs26(zxw4002, zxw3002, app(app(ty_@2, dbb), dbc)) → new_esEs5(zxw4002, zxw3002, dbb, dbc)
new_esEs21(zxw4001, zxw3001, app(app(ty_@2, cee), cef)) → new_esEs5(zxw4001, zxw3001, cee, cef)
new_lt19(zxw79000, zxw80000, app(ty_Maybe, bbb)) → new_lt18(zxw79000, zxw80000, bbb)
new_esEs12(Char(zxw4000), Char(zxw3000)) → new_primEqNat0(zxw4000, zxw3000)
new_ltEs20(zxw7900, zxw8000, app(app(app(ty_@3, hd), he), hf)) → new_ltEs6(zxw7900, zxw8000, hd, he, hf)
new_not(False) → True
new_lt20(zxw79001, zxw80001, ty_Char) → new_lt9(zxw79001, zxw80001)
new_esEs11(zxw400, zxw300) → new_primEqInt(zxw400, zxw300)
new_ltEs14(Right(zxw79000), Right(zxw80000), gh, app(ty_Maybe, cce)) → new_ltEs18(zxw79000, zxw80000, cce)
new_ltEs18(Just(zxw79000), Nothing, hc) → False
new_esEs8(zxw79000, zxw80000, app(ty_Maybe, cf)) → new_esEs6(zxw79000, zxw80000, cf)
new_esEs7(Left(zxw4000), Left(zxw3000), app(ty_Maybe, bbf), bbd) → new_esEs6(zxw4000, zxw3000, bbf)
new_compare210(zxw79000, zxw80000, True, baf, bag) → EQ
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Double, bbd) → new_esEs16(zxw4000, zxw3000)
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_esEs19(zxw79001, zxw80001, ty_Int) → new_esEs11(zxw79001, zxw80001)
new_compare12(zxw79000, zxw80000, False, ff, fg, fh) → GT
new_ltEs16(zxw7900, zxw8000) → new_fsEs(new_compare7(zxw7900, zxw8000))
new_esEs9(GT, GT) → True
new_esEs26(zxw4002, zxw3002, app(ty_Ratio, dag)) → new_esEs18(zxw4002, zxw3002, dag)
new_esEs25(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_lt20(zxw79001, zxw80001, app(ty_[], beg)) → new_lt10(zxw79001, zxw80001, beg)
new_lt4(zxw79000, zxw80000, app(app(ty_Either, cc), cd)) → new_lt14(zxw79000, zxw80000, cc, cd)
new_esEs26(zxw4002, zxw3002, ty_Bool) → new_esEs14(zxw4002, zxw3002)
new_compare19(zxw79000, zxw80000, baf, bag) → new_compare210(zxw79000, zxw80000, new_esEs5(zxw79000, zxw80000, baf, bag), baf, bag)
new_esEs8(zxw79000, zxw80000, ty_Bool) → new_esEs14(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Double) → new_ltEs15(zxw79000, zxw80000)
new_esEs28(zxw4000, zxw3000, app(app(ty_@2, ddf), ddg)) → new_esEs5(zxw4000, zxw3000, ddf, ddg)
new_ltEs19(zxw7900, zxw8000, app(app(app(ty_@3, gd), ge), gf)) → new_ltEs6(zxw7900, zxw8000, gd, ge, gf)
new_lt4(zxw79000, zxw80000, ty_Char) → new_lt9(zxw79000, zxw80000)
new_esEs22(zxw4000, zxw3000, app(app(app(ty_@3, cgc), cgd), cge)) → new_esEs4(zxw4000, zxw3000, cgc, cgd, cge)
new_esEs22(zxw4000, zxw3000, app(ty_[], cfe)) → new_esEs13(zxw4000, zxw3000, cfe)
new_ltEs14(Right(zxw79000), Right(zxw80000), gh, ty_@0) → new_ltEs8(zxw79000, zxw80000)
new_esEs23(zxw4000, zxw3000, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Float, bbd) → new_esEs17(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_esEs27(zxw4001, zxw3001, ty_Int) → new_esEs11(zxw4001, zxw3001)
new_esEs19(zxw79001, zxw80001, app(app(app(ty_@3, bed), bee), bef)) → new_esEs4(zxw79001, zxw80001, bed, bee, bef)
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_esEs7(Right(zxw4000), Right(zxw3000), bcf, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(app(app(ty_@3, cab), cac), cad), ha) → new_ltEs6(zxw79000, zxw80000, cab, cac, cad)
new_ltEs19(zxw7900, zxw8000, ty_Int) → new_ltEs9(zxw7900, zxw8000)
new_lt4(zxw79000, zxw80000, ty_@0) → new_lt7(zxw79000, zxw80000)
new_lt20(zxw79001, zxw80001, ty_Double) → new_lt15(zxw79001, zxw80001)
new_lt19(zxw79000, zxw80000, ty_Float) → new_lt16(zxw79000, zxw80000)
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_esEs26(zxw4002, zxw3002, ty_@0) → new_esEs10(zxw4002, zxw3002)
new_lt19(zxw79000, zxw80000, ty_Bool) → new_lt12(zxw79000, zxw80000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Char, bbd) → new_esEs12(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(ty_[], cda)) → new_ltEs11(zxw79000, zxw80000, cda)
new_lt4(zxw79000, zxw80000, ty_Float) → new_lt16(zxw79000, zxw80000)
new_primMulInt(Neg(zxw40000), Neg(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_ltEs5(zxw79001, zxw80001, app(app(app(ty_@3, cg), da), db)) → new_ltEs6(zxw79001, zxw80001, cg, da, db)
new_primCmpNat2(Zero, Zero) → EQ
new_esEs20(zxw79000, zxw80000, ty_Integer) → new_esEs15(zxw79000, zxw80000)
new_primEqNat0(Zero, Succ(zxw30000)) → False
new_primEqNat0(Succ(zxw40000), Zero) → False
new_esEs21(zxw4001, zxw3001, ty_@0) → new_esEs10(zxw4001, zxw3001)
new_esEs22(zxw4000, zxw3000, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_esEs20(zxw79000, zxw80000, ty_Bool) → new_esEs14(zxw79000, zxw80000)
new_ltEs5(zxw79001, zxw80001, app(ty_[], dc)) → new_ltEs11(zxw79001, zxw80001, dc)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs23(zxw4000, zxw3000, app(ty_Ratio, cgg)) → new_esEs18(zxw4000, zxw3000, cgg)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(app(ty_@2, cdb), cdc)) → new_ltEs4(zxw79000, zxw80000, cdb, cdc)
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_ltEs5(zxw79001, zxw80001, ty_Int) → new_ltEs9(zxw79001, zxw80001)
new_esEs27(zxw4001, zxw3001, app(app(ty_@2, dcd), dce)) → new_esEs5(zxw4001, zxw3001, dcd, dce)
new_primCmpNat0(zxw7900, Zero) → GT
new_compare26(Right(zxw7900), Left(zxw8000), False, gb, gc) → GT
new_esEs23(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_@0, ha) → new_ltEs8(zxw79000, zxw80000)
new_ltEs21(zxw79002, zxw80002, app(ty_Maybe, bgg)) → new_ltEs18(zxw79002, zxw80002, bgg)
new_esEs21(zxw4001, zxw3001, app(app(ty_Either, ceg), ceh)) → new_esEs7(zxw4001, zxw3001, ceg, ceh)
new_esEs22(zxw4000, zxw3000, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Bool) → new_ltEs12(zxw79000, zxw80000)
new_compare29(zxw79000, zxw80000, app(ty_Maybe, caa)) → new_compare27(zxw79000, zxw80000, caa)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_ltEs14(Left(zxw79000), Left(zxw80000), app(ty_Maybe, cbc), ha) → new_ltEs18(zxw79000, zxw80000, cbc)
new_lt20(zxw79001, zxw80001, ty_Float) → new_lt16(zxw79001, zxw80001)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Ordering) → new_ltEs7(zxw79000, zxw80000)
new_lt17(zxw79000, zxw80000, ga) → new_esEs9(new_compare8(zxw79000, zxw80000, ga), LT)
new_compare30(@0, @0) → EQ
new_lt19(zxw79000, zxw80000, app(ty_[], bea)) → new_lt10(zxw79000, zxw80000, bea)
new_esEs21(zxw4001, zxw3001, app(app(app(ty_@3, cfa), cfb), cfc)) → new_esEs4(zxw4001, zxw3001, cfa, cfb, cfc)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_esEs20(zxw79000, zxw80000, app(ty_Ratio, ga)) → new_esEs18(zxw79000, zxw80000, ga)
new_esEs6(Just(zxw4000), Just(zxw3000), app(app(app(ty_@3, fb), fc), fd)) → new_esEs4(zxw4000, zxw3000, fb, fc, fd)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(app(ty_Either, cdd), cde)) → new_ltEs14(zxw79000, zxw80000, cdd, cde)
new_esEs24(zxw4001, zxw3001, ty_Int) → new_esEs11(zxw4001, zxw3001)
new_esEs8(zxw79000, zxw80000, ty_Ordering) → new_esEs9(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), gh, ty_Ordering) → new_ltEs7(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, app(app(ty_Either, beb), bec)) → new_esEs7(zxw79000, zxw80000, beb, bec)
new_compare29(zxw79000, zxw80000, app(ty_Ratio, bhh)) → new_compare8(zxw79000, zxw80000, bhh)
new_lt4(zxw79000, zxw80000, app(app(ty_@2, ca), cb)) → new_lt11(zxw79000, zxw80000, ca, cb)
new_compare29(zxw79000, zxw80000, ty_Float) → new_compare7(zxw79000, zxw80000)
new_esEs19(zxw79001, zxw80001, app(app(ty_@2, beh), bfa)) → new_esEs5(zxw79001, zxw80001, beh, bfa)
new_esEs10(@0, @0) → True
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_compare29(zxw79000, zxw80000, ty_Double) → new_compare6(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, app(ty_Maybe, bbb)) → new_esEs6(zxw79000, zxw80000, bbb)
new_ltEs14(Left(zxw79000), Right(zxw80000), gh, ha) → True
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Float) → new_ltEs16(zxw79000, zxw80000)
new_esEs28(zxw4000, zxw3000, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_compare29(zxw79000, zxw80000, app(app(ty_Either, bhf), bhg)) → new_compare15(zxw79000, zxw80000, bhf, bhg)
new_esEs19(zxw79001, zxw80001, ty_Double) → new_esEs16(zxw79001, zxw80001)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_ltEs20(zxw7900, zxw8000, app(app(ty_Either, bab), bac)) → new_ltEs14(zxw7900, zxw8000, bab, bac)
new_asAs(False, zxw230) → False
new_ltEs13(zxw7900, zxw8000) → new_fsEs(new_compare32(zxw7900, zxw8000))
new_ltEs19(zxw7900, zxw8000, app(app(ty_Either, gh), ha)) → new_ltEs14(zxw7900, zxw8000, gh, ha)
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Pos(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_ltEs20(zxw7900, zxw8000, app(ty_[], hg)) → new_ltEs11(zxw7900, zxw8000, hg)
new_compare16(zxw79, zxw80) → new_primCmpInt(zxw79, zxw80)
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_esEs13(:(zxw4000, zxw4001), [], cgf) → False
new_esEs13([], :(zxw3000, zxw3001), cgf) → False
new_compare25(zxw79000, zxw80000, False, ff, fg, fh) → new_compare12(zxw79000, zxw80000, new_ltEs6(zxw79000, zxw80000, ff, fg, fh), ff, fg, fh)
new_esEs7(Right(zxw4000), Right(zxw3000), bcf, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(app(ty_@2, caf), cag), ha) → new_ltEs4(zxw79000, zxw80000, caf, cag)
new_esEs6(Just(zxw4000), Just(zxw3000), app(ty_Maybe, ee)) → new_esEs6(zxw4000, zxw3000, ee)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_@0) → new_esEs10(zxw4000, zxw3000)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(ty_[], cae), ha) → new_ltEs11(zxw79000, zxw80000, cae)
new_esEs7(Left(zxw4000), Left(zxw3000), app(ty_[], bbe), bbd) → new_esEs13(zxw4000, zxw3000, bbe)
new_esEs7(Right(zxw4000), Right(zxw3000), bcf, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_compare31(zxw79000, zxw80000) → new_compare23(zxw79000, zxw80000, new_esEs14(zxw79000, zxw80000))
new_ltEs18(Nothing, Just(zxw80000), hc) → True
new_esEs28(zxw4000, zxw3000, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_ltEs21(zxw79002, zxw80002, ty_Double) → new_ltEs15(zxw79002, zxw80002)
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_ltEs12(True, True) → True
new_esEs23(zxw4000, zxw3000, app(ty_Maybe, cha)) → new_esEs6(zxw4000, zxw3000, cha)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_ltEs14(Right(zxw79000), Right(zxw80000), gh, app(app(ty_Either, ccb), ccc)) → new_ltEs14(zxw79000, zxw80000, ccb, ccc)
new_esEs8(zxw79000, zxw80000, ty_Integer) → new_esEs15(zxw79000, zxw80000)
new_ltEs6(@3(zxw79000, zxw79001, zxw79002), @3(zxw80000, zxw80001, zxw80002), gd, ge, gf) → new_pePe(new_lt19(zxw79000, zxw80000, gd), new_asAs(new_esEs20(zxw79000, zxw80000, gd), new_pePe(new_lt20(zxw79001, zxw80001, ge), new_asAs(new_esEs19(zxw79001, zxw80001, ge), new_ltEs21(zxw79002, zxw80002, gf)))))
new_esEs28(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_lt16(zxw79000, zxw80000) → new_esEs9(new_compare7(zxw79000, zxw80000), LT)
new_esEs23(zxw4000, zxw3000, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Integer, ha) → new_ltEs13(zxw79000, zxw80000)
new_ltEs12(False, True) → True
new_esEs23(zxw4000, zxw3000, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs8(zxw79000, zxw80000, app(ty_Ratio, ce)) → new_esEs18(zxw79000, zxw80000, ce)
new_esEs23(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs14(True, True) → True
new_compare111(zxw79000, zxw80000, False, bbb) → GT
new_esEs27(zxw4001, zxw3001, ty_Bool) → new_esEs14(zxw4001, zxw3001)
new_esEs20(zxw79000, zxw80000, ty_Ordering) → new_esEs9(zxw79000, zxw80000)
new_ltEs19(zxw7900, zxw8000, ty_@0) → new_ltEs8(zxw7900, zxw8000)
new_ltEs14(Right(zxw79000), Right(zxw80000), gh, ty_Int) → new_ltEs9(zxw79000, zxw80000)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(app(ty_Either, cah), cba), ha) → new_ltEs14(zxw79000, zxw80000, cah, cba)
new_lt19(zxw79000, zxw80000, ty_Integer) → new_lt13(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, ty_Float) → new_esEs17(zxw79000, zxw80000)
new_esEs7(Right(zxw4000), Right(zxw3000), bcf, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Ordering, ha) → new_ltEs7(zxw79000, zxw80000)
new_compare11(zxw79000, zxw80000, False) → GT
new_esEs4(@3(zxw4000, zxw4001, zxw4002), @3(zxw3000, zxw3001, zxw3002), dad, dae, daf) → new_asAs(new_esEs28(zxw4000, zxw3000, dad), new_asAs(new_esEs27(zxw4001, zxw3001, dae), new_esEs26(zxw4002, zxw3002, daf)))
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Int) → new_ltEs9(zxw79000, zxw80000)
new_esEs6(Just(zxw4000), Just(zxw3000), app(ty_[], ed)) → new_esEs13(zxw4000, zxw3000, ed)
new_esEs9(EQ, LT) → False
new_esEs9(LT, EQ) → False
new_compare26(Right(zxw7900), Right(zxw8000), False, gb, gc) → new_compare14(zxw7900, zxw8000, new_ltEs20(zxw7900, zxw8000, gc), gb, gc)
new_compare11(zxw79000, zxw80000, True) → LT
new_ltEs5(zxw79001, zxw80001, ty_@0) → new_ltEs8(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, ty_Bool) → new_lt12(zxw79001, zxw80001)
new_compare14(zxw242, zxw243, True, dab, dac) → LT
new_esEs14(False, False) → True
new_esEs18(:%(zxw4000, zxw4001), :%(zxw3000, zxw3001), daa) → new_asAs(new_esEs25(zxw4000, zxw3000, daa), new_esEs24(zxw4001, zxw3001, daa))
new_compare26(Left(zxw7900), Left(zxw8000), False, gb, gc) → new_compare13(zxw7900, zxw8000, new_ltEs19(zxw7900, zxw8000, gb), gb, gc)
new_ltEs19(zxw7900, zxw8000, ty_Double) → new_ltEs15(zxw7900, zxw8000)
new_ltEs7(EQ, LT) → False
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Char) → new_esEs12(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_ltEs7(LT, LT) → True
new_lt20(zxw79001, zxw80001, app(app(app(ty_@3, bed), bee), bef)) → new_lt5(zxw79001, zxw80001, bed, bee, bef)
new_lt14(zxw790, zxw800, gb, gc) → new_esEs9(new_compare15(zxw790, zxw800, gb, gc), LT)
new_esEs22(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_ltEs9(zxw7900, zxw8000) → new_fsEs(new_compare16(zxw7900, zxw8000))
new_compare29(zxw79000, zxw80000, ty_Ordering) → new_compare18(zxw79000, zxw80000)
new_primPlusNat1(Zero, Zero) → Zero
new_esEs26(zxw4002, zxw3002, ty_Ordering) → new_esEs9(zxw4002, zxw3002)
new_esEs19(zxw79001, zxw80001, ty_Integer) → new_esEs15(zxw79001, zxw80001)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Char, ha) → new_ltEs10(zxw79000, zxw80000)
new_asAs(True, zxw230) → zxw230
new_esEs25(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_ltEs7(LT, GT) → True
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Float) → new_esEs17(zxw4000, zxw3000)
new_ltEs5(zxw79001, zxw80001, ty_Float) → new_ltEs16(zxw79001, zxw80001)
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_esEs7(Right(zxw4000), Right(zxw3000), bcf, app(ty_Ratio, bcg)) → new_esEs18(zxw4000, zxw3000, bcg)
new_esEs27(zxw4001, zxw3001, app(ty_[], dcb)) → new_esEs13(zxw4001, zxw3001, dcb)
new_esEs6(Just(zxw4000), Just(zxw3000), app(app(ty_Either, eh), fa)) → new_esEs7(zxw4000, zxw3000, eh, fa)
new_compare28(zxw79000, zxw80000, False, bbb) → new_compare111(zxw79000, zxw80000, new_ltEs18(zxw79000, zxw80000, bbb), bbb)
new_compare1(:(zxw79000, zxw79001), [], gg) → GT
new_esEs28(zxw4000, zxw3000, app(ty_Ratio, ddc)) → new_esEs18(zxw4000, zxw3000, ddc)
new_lt4(zxw79000, zxw80000, ty_Integer) → new_lt13(zxw79000, zxw80000)
new_esEs19(zxw79001, zxw80001, ty_@0) → new_esEs10(zxw79001, zxw80001)
new_compare29(zxw79000, zxw80000, ty_@0) → new_compare30(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), gh, app(ty_Ratio, ccd)) → new_ltEs17(zxw79000, zxw80000, ccd)
new_ltEs19(zxw7900, zxw8000, ty_Integer) → new_ltEs13(zxw7900, zxw8000)
new_ltEs14(Right(zxw79000), Right(zxw80000), gh, ty_Integer) → new_ltEs13(zxw79000, zxw80000)
new_ltEs19(zxw7900, zxw8000, ty_Ordering) → new_ltEs7(zxw7900, zxw8000)
new_compare28(zxw79000, zxw80000, True, bbb) → EQ
new_esEs26(zxw4002, zxw3002, ty_Double) → new_esEs16(zxw4002, zxw3002)
new_compare10(zxw79000, zxw80000, True) → LT
new_esEs19(zxw79001, zxw80001, app(ty_[], beg)) → new_esEs13(zxw79001, zxw80001, beg)
new_compare10(zxw79000, zxw80000, False) → GT
new_esEs9(LT, LT) → True
new_ltEs20(zxw7900, zxw8000, ty_Char) → new_ltEs10(zxw7900, zxw8000)
new_primCompAux00(zxw276, GT) → GT
new_ltEs20(zxw7900, zxw8000, ty_Ordering) → new_ltEs7(zxw7900, zxw8000)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_@0) → new_ltEs8(zxw79000, zxw80000)
new_compare18(zxw79000, zxw80000) → new_compare24(zxw79000, zxw80000, new_esEs9(zxw79000, zxw80000))
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs7(Right(zxw4000), Right(zxw3000), bcf, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_lt19(zxw79000, zxw80000, ty_Char) → new_lt9(zxw79000, zxw80000)
new_esEs28(zxw4000, zxw3000, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_ltEs19(zxw7900, zxw8000, app(ty_Maybe, hc)) → new_ltEs18(zxw7900, zxw8000, hc)
new_esEs27(zxw4001, zxw3001, ty_Integer) → new_esEs15(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, app(ty_Ratio, ceb)) → new_esEs18(zxw4001, zxw3001, ceb)
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_esEs19(zxw79001, zxw80001, ty_Char) → new_esEs12(zxw79001, zxw80001)
new_esEs23(zxw4000, zxw3000, app(ty_[], cgh)) → new_esEs13(zxw4000, zxw3000, cgh)
new_ltEs17(zxw7900, zxw8000, hb) → new_fsEs(new_compare8(zxw7900, zxw8000, hb))
new_not(True) → False
new_ltEs4(@2(zxw79000, zxw79001), @2(zxw80000, zxw80001), bc, bd) → new_pePe(new_lt4(zxw79000, zxw80000, bc), new_asAs(new_esEs8(zxw79000, zxw80000, bc), new_ltEs5(zxw79001, zxw80001, bd)))
new_compare1([], [], gg) → EQ
new_esEs6(Just(zxw4000), Just(zxw3000), app(ty_Ratio, ec)) → new_esEs18(zxw4000, zxw3000, ec)

The set Q consists of the following terms:

new_compare23(x0, x1, True)
new_lt6(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_lt19(x0, x1, ty_Integer)
new_ltEs18(Just(x0), Just(x1), ty_@0)
new_compare16(x0, x1)
new_ltEs18(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs13(:(x0, x1), :(x2, x3), x4)
new_esEs7(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs20(x0, x1, ty_Double)
new_esEs19(x0, x1, ty_Bool)
new_compare30(@0, @0)
new_primCompAux00(x0, GT)
new_lt5(x0, x1, x2, x3, x4)
new_lt19(x0, x1, ty_Char)
new_lt19(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_Int)
new_compare29(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, ty_Ordering)
new_compare17(Char(x0), Char(x1))
new_esEs28(x0, x1, ty_Int)
new_compare27(x0, x1, x2)
new_ltEs21(x0, x1, ty_Ordering)
new_compare12(x0, x1, True, x2, x3, x4)
new_ltEs15(x0, x1)
new_primPlusNat1(Zero, Succ(x0))
new_compare24(x0, x1, False)
new_esEs6(Just(x0), Just(x1), ty_Double)
new_lt20(x0, x1, ty_Char)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs5(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_Bool)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_sr0(Integer(x0), Integer(x1))
new_ltEs14(Right(x0), Right(x1), x2, ty_Double)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs13([], :(x0, x1), x2)
new_compare26(x0, x1, True, x2, x3)
new_ltEs7(EQ, EQ)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs19(x0, x1, ty_Integer)
new_compare14(x0, x1, True, x2, x3)
new_ltEs20(x0, x1, ty_Bool)
new_ltEs14(Right(x0), Right(x1), x2, ty_Ordering)
new_compare110(x0, x1, False, x2, x3)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_ltEs19(x0, x1, ty_Integer)
new_ltEs5(x0, x1, ty_Integer)
new_ltEs7(EQ, LT)
new_ltEs7(LT, EQ)
new_esEs20(x0, x1, ty_Ordering)
new_esEs17(Float(x0, x1), Float(x2, x3))
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_lt19(x0, x1, ty_Ordering)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs16(x0, x1)
new_ltEs18(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_sr(x0, x1)
new_ltEs19(x0, x1, ty_Double)
new_compare7(Float(x0, x1), Float(x2, x3))
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_ltEs14(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs9(x0, x1)
new_esEs6(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_lt7(x0, x1)
new_ltEs5(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Int)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat0(Zero, x0)
new_ltEs7(LT, LT)
new_esEs27(x0, x1, ty_Bool)
new_ltEs18(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_lt4(x0, x1, ty_Ordering)
new_ltEs14(Left(x0), Left(x1), ty_Int, x2)
new_primEqNat0(Zero, Succ(x0))
new_lt19(x0, x1, ty_Int)
new_esEs15(Integer(x0), Integer(x1))
new_esEs26(x0, x1, ty_Int)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Double)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs28(x0, x1, ty_@0)
new_primPlusNat1(Succ(x0), Zero)
new_esEs22(x0, x1, ty_Integer)
new_primMulInt(Neg(x0), Neg(x1))
new_lt4(x0, x1, app(ty_Maybe, x2))
new_esEs7(Left(x0), Left(x1), ty_Float, x2)
new_ltEs19(x0, x1, ty_Int)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_compare29(x0, x1, ty_Integer)
new_esEs14(True, True)
new_esEs21(x0, x1, ty_Char)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Int)
new_ltEs18(Just(x0), Just(x1), ty_Integer)
new_esEs7(Right(x0), Right(x1), x2, ty_Char)
new_esEs24(x0, x1, ty_Int)
new_compare14(x0, x1, False, x2, x3)
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_primEqNat0(Zero, Zero)
new_esEs16(Double(x0, x1), Double(x2, x3))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs12(Char(x0), Char(x1))
new_esEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_lt4(x0, x1, ty_Char)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_compare1(:(x0, x1), :(x2, x3), x4)
new_esEs20(x0, x1, ty_Bool)
new_esEs8(x0, x1, ty_Float)
new_ltEs14(Right(x0), Right(x1), x2, ty_Integer)
new_lt10(x0, x1, x2)
new_ltEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Integer)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_compare111(x0, x1, True, x2)
new_compare28(x0, x1, False, x2)
new_primCompAux00(x0, LT)
new_esEs27(x0, x1, ty_Integer)
new_ltEs14(Right(x0), Right(x1), x2, ty_Float)
new_ltEs5(x0, x1, ty_Double)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs7(Right(x0), Right(x1), x2, ty_Double)
new_ltEs18(Just(x0), Just(x1), ty_Char)
new_ltEs14(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_primMulNat0(Zero, Zero)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_compare1(:(x0, x1), [], x2)
new_lt9(x0, x1)
new_compare29(x0, x1, ty_Double)
new_ltEs5(x0, x1, ty_@0)
new_compare29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare29(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Right(x0), Right(x1), x2, ty_Bool)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs8(x0, x1, app(app(ty_@2, x2), x3))
new_lt4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_ltEs14(Right(x0), Right(x1), x2, ty_@0)
new_esEs8(x0, x1, ty_Ordering)
new_esEs6(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_compare10(x0, x1, True)
new_esEs22(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, ty_Ordering)
new_primEqNat0(Succ(x0), Succ(x1))
new_ltEs19(x0, x1, ty_Bool)
new_esEs28(x0, x1, ty_Double)
new_ltEs20(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_@0)
new_pePe(True, x0)
new_esEs19(x0, x1, ty_Float)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_primCmpNat2(Zero, Succ(x0))
new_compare25(x0, x1, False, x2, x3, x4)
new_primMulNat0(Zero, Succ(x0))
new_lt16(x0, x1)
new_compare29(x0, x1, ty_Bool)
new_lt4(x0, x1, app(app(ty_Either, x2), x3))
new_compare11(x0, x1, True)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1, ty_@0)
new_esEs6(Just(x0), Just(x1), ty_Ordering)
new_esEs23(x0, x1, ty_@0)
new_ltEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs5(x0, x1, ty_Char)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_ltEs21(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Float)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_compare29(x0, x1, ty_Ordering)
new_ltEs21(x0, x1, ty_@0)
new_esEs8(x0, x1, ty_Int)
new_ltEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs12(False, False)
new_esEs6(Just(x0), Just(x1), ty_Bool)
new_compare32(Integer(x0), Integer(x1))
new_esEs21(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_Int)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_primMulNat0(Succ(x0), Succ(x1))
new_ltEs21(x0, x1, ty_Integer)
new_compare29(x0, x1, ty_Float)
new_esEs7(Right(x0), Right(x1), x2, ty_Bool)
new_esEs6(Just(x0), Just(x1), ty_Float)
new_ltEs5(x0, x1, ty_Float)
new_ltEs5(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, app(ty_[], x2))
new_ltEs18(Just(x0), Just(x1), ty_Float)
new_esEs26(x0, x1, ty_Bool)
new_primCmpNat1(Zero, x0)
new_ltEs8(x0, x1)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primPlusNat1(Zero, Zero)
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Double)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_compare210(x0, x1, True, x2, x3)
new_primCmpNat2(Zero, Zero)
new_ltEs18(Just(x0), Just(x1), ty_Ordering)
new_esEs7(Left(x0), Left(x1), ty_Int, x2)
new_ltEs5(x0, x1, ty_Bool)
new_esEs13(:(x0, x1), [], x2)
new_ltEs14(Left(x0), Left(x1), ty_Char, x2)
new_asAs(False, x0)
new_ltEs20(x0, x1, ty_Char)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_compare26(Right(x0), Right(x1), False, x2, x3)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs8(x0, x1, ty_Integer)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs18(Just(x0), Just(x1), ty_Bool)
new_ltEs14(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_esEs19(x0, x1, app(ty_[], x2))
new_primCmpNat1(Succ(x0), x1)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, ty_Integer)
new_lt4(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_@0)
new_ltEs14(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_lt4(x0, x1, ty_Float)
new_esEs19(x0, x1, ty_Char)
new_ltEs14(Right(x0), Left(x1), x2, x3)
new_ltEs14(Left(x0), Right(x1), x2, x3)
new_lt4(x0, x1, ty_Double)
new_esEs19(x0, x1, ty_Ordering)
new_esEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs10(@0, @0)
new_esEs8(x0, x1, app(ty_Maybe, x2))
new_esEs11(x0, x1)
new_ltEs14(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs20(x0, x1, ty_Float)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs9(GT, GT)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs27(x0, x1, ty_Char)
new_compare11(x0, x1, False)
new_compare23(x0, x1, False)
new_compare13(x0, x1, False, x2, x3)
new_esEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt18(x0, x1, x2)
new_esEs28(x0, x1, ty_Bool)
new_compare24(x0, x1, True)
new_ltEs19(x0, x1, app(ty_[], x2))
new_primEqNat0(Succ(x0), Zero)
new_esEs23(x0, x1, ty_Ordering)
new_primPlusNat1(Succ(x0), Succ(x1))
new_ltEs14(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Int)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs7(Left(x0), Left(x1), ty_Char, x2)
new_esEs21(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Integer)
new_esEs23(x0, x1, ty_Int)
new_esEs13([], [], x0)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs14(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_lt4(x0, x1, ty_@0)
new_esEs23(x0, x1, ty_Char)
new_esEs28(x0, x1, ty_Ordering)
new_esEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs18(Just(x0), Just(x1), ty_Double)
new_ltEs20(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_@0)
new_esEs9(EQ, EQ)
new_pePe(False, x0)
new_esEs6(Nothing, Nothing, x0)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Just(x0), Just(x1), ty_Char)
new_esEs25(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Integer)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs6(Just(x0), Just(x1), app(ty_[], x2))
new_compare19(x0, x1, x2, x3)
new_primCompAux00(x0, EQ)
new_esEs19(x0, x1, ty_Int)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs14(True, False)
new_esEs14(False, True)
new_lt4(x0, x1, ty_Integer)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_fsEs(x0)
new_esEs7(Left(x0), Left(x1), ty_@0, x2)
new_esEs22(x0, x1, ty_Float)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs21(x0, x1, app(ty_[], x2))
new_lt4(x0, x1, ty_Bool)
new_primCmpNat2(Succ(x0), Succ(x1))
new_esEs7(Right(x0), Right(x1), x2, ty_Float)
new_asAs(True, x0)
new_ltEs14(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_compare9(x0, x1, x2, x3, x4)
new_esEs21(x0, x1, ty_Bool)
new_esEs6(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare13(x0, x1, True, x2, x3)
new_compare25(x0, x1, True, x2, x3, x4)
new_esEs7(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs21(x0, x1, app(ty_Maybe, x2))
new_esEs8(x0, x1, ty_Char)
new_lt19(x0, x1, ty_Float)
new_compare111(x0, x1, False, x2)
new_esEs22(x0, x1, ty_@0)
new_esEs8(x0, x1, app(ty_Ratio, x2))
new_esEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs20(x0, x1, ty_Char)
new_ltEs12(False, True)
new_ltEs12(True, False)
new_compare6(Double(x0, x1), Double(x2, x3))
new_ltEs20(x0, x1, ty_@0)
new_esEs22(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_@0)
new_ltEs11(x0, x1, x2)
new_lt19(x0, x1, ty_Double)
new_lt19(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_Char)
new_ltEs5(x0, x1, ty_Int)
new_compare12(x0, x1, False, x2, x3, x4)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, ty_Double)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs19(x0, x1, ty_@0)
new_ltEs21(x0, x1, ty_Bool)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs21(x0, x1, ty_Double)
new_compare110(x0, x1, True, x2, x3)
new_lt17(x0, x1, x2)
new_lt12(x0, x1)
new_esEs6(Just(x0), Nothing, x1)
new_ltEs18(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs8(x0, x1, ty_Bool)
new_ltEs21(x0, x1, ty_Char)
new_lt13(x0, x1)
new_lt4(x0, x1, app(ty_[], x2))
new_compare15(x0, x1, x2, x3)
new_ltEs14(Right(x0), Right(x1), x2, ty_Int)
new_esEs6(Nothing, Just(x0), x1)
new_esEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_compare10(x0, x1, False)
new_primMulNat0(Succ(x0), Zero)
new_ltEs19(x0, x1, ty_Float)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_Float)
new_compare29(x0, x1, ty_Int)
new_esEs22(x0, x1, ty_Int)
new_compare1([], :(x0, x1), x2)
new_compare1([], [], x0)
new_esEs20(x0, x1, ty_Int)
new_esEs8(x0, x1, app(ty_[], x2))
new_ltEs14(Left(x0), Left(x1), ty_Float, x2)
new_esEs21(x0, x1, ty_Float)
new_esEs6(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_compare31(x0, x1)
new_esEs6(Just(x0), Just(x1), ty_Int)
new_ltEs7(LT, GT)
new_ltEs7(GT, LT)
new_esEs21(x0, x1, ty_Integer)
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs18(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs18(Nothing, Nothing, x0)
new_esEs22(x0, x1, ty_Double)
new_esEs26(x0, x1, app(ty_[], x2))
new_primCompAux0(x0, x1, x2, x3)
new_ltEs13(x0, x1)
new_compare29(x0, x1, app(app(ty_@2, x2), x3))
new_lt4(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Float)
new_not(True)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs20(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Float)
new_ltEs17(x0, x1, x2)
new_compare28(x0, x1, True, x2)
new_esEs28(x0, x1, ty_Char)
new_esEs6(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Ordering)
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs7(Right(x0), Right(x1), x2, ty_@0)
new_esEs6(Just(x0), Just(x1), ty_Integer)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_not(False)
new_lt8(x0, x1)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt4(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs20(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, ty_Char)
new_esEs4(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Integer)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primMulInt(Pos(x0), Pos(x1))
new_esEs22(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(x0, x1, ty_@0)
new_ltEs18(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs20(x0, x1, app(ty_[], x2))
new_ltEs12(True, True)
new_lt15(x0, x1)
new_esEs27(x0, x1, ty_Float)
new_esEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_lt14(x0, x1, x2, x3)
new_esEs26(x0, x1, ty_Ordering)
new_esEs18(:%(x0, x1), :%(x2, x3), x4)
new_esEs27(x0, x1, ty_Double)
new_ltEs18(Just(x0), Nothing, x1)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_lt20(x0, x1, ty_Ordering)
new_compare29(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, ty_Char)
new_lt20(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Bool)
new_esEs7(Left(x0), Left(x1), ty_Double, x2)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_ltEs21(x0, x1, ty_Float)
new_compare29(x0, x1, app(ty_[], x2))
new_ltEs10(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs14(Left(x0), Left(x1), ty_Integer, x2)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs5(x0, x1, ty_Ordering)
new_compare26(Left(x0), Right(x1), False, x2, x3)
new_compare26(Right(x0), Left(x1), False, x2, x3)
new_ltEs14(Left(x0), Left(x1), ty_Bool, x2)
new_esEs8(x0, x1, ty_Double)
new_compare29(x0, x1, ty_Char)
new_ltEs18(Nothing, Just(x0), x1)
new_esEs6(Just(x0), Just(x1), ty_@0)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs7(Right(x0), Left(x1), x2, x3)
new_esEs7(Left(x0), Right(x1), x2, x3)
new_lt11(x0, x1, x2, x3)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs14(Left(x0), Left(x1), ty_@0, x2)
new_esEs8(x0, x1, app(app(ty_Either, x2), x3))
new_esEs19(x0, x1, ty_Double)
new_esEs14(False, False)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Zero), Pos(Zero))
new_compare210(x0, x1, False, x2, x3)
new_ltEs21(x0, x1, ty_Double)
new_primCmpNat2(Succ(x0), Zero)
new_esEs7(Right(x0), Right(x1), x2, ty_Int)
new_compare18(x0, x1)
new_esEs27(x0, x1, app(ty_[], x2))
new_compare26(Left(x0), Left(x1), False, x2, x3)
new_ltEs18(Just(x0), Just(x1), ty_Int)
new_ltEs21(x0, x1, app(ty_Ratio, x2))
new_primPlusNat0(Succ(x0), x1)
new_ltEs5(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, ty_Integer)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primCmpNat0(x0, Zero)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs7(GT, EQ)
new_ltEs7(EQ, GT)
new_ltEs7(GT, GT)
new_ltEs5(x0, x1, app(ty_Ratio, x2))
new_esEs9(LT, LT)
new_esEs8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare29(x0, x1, ty_@0)
new_ltEs14(Left(x0), Left(x1), ty_Double, x2)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(Right(x0), Right(x1), x2, ty_Char)
new_primCmpNat0(x0, Succ(x1))
new_esEs27(x0, x1, ty_Ordering)

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

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



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

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

new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), zxw343, h, ba, bb)
new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, zxw1084, Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_lt8(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), new_mkVBalBranch3Size_l(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), h, ba, bb)
new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_lt8(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), new_mkVBalBranch3Size_r(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), h, ba, bb)

The TRS R consists of the following rules:

new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Pos(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_compare16(zxw79, zxw80) → new_primCmpInt(zxw79, zxw80)
new_esEs9(GT, LT) → False
new_esEs9(LT, GT) → False
new_primMulInt(Neg(zxw40000), Neg(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primCmpNat2(Zero, Zero) → EQ
new_primPlusNat1(Zero, Zero) → Zero
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_sr(zxw4000, zxw3000) → new_primMulInt(zxw4000, zxw3000)
new_lt8(zxw790, zxw800) → new_esEs9(new_compare16(zxw790, zxw800), LT)
new_primCmpNat0(zxw7900, Zero) → GT
new_primMulNat0(Zero, Zero) → Zero
new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, bc, bd, be) → new_sizeFM0(Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), bc, bd, be)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, bc, bd, be) → new_sizeFM(zxw190, zxw191, zxw192, zxw193, zxw194, bc, bd, be)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_esEs9(GT, EQ) → False
new_esEs9(EQ, GT) → False
new_esEs9(EQ, EQ) → True
new_sizeFM0(EmptyFM, h, ba, bb) → Pos(Zero)
new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_esEs9(GT, GT) → True
new_esEs9(LT, LT) → True
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba, bb) → zxw542
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb) → zxw52
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_esEs9(EQ, LT) → False
new_esEs9(LT, EQ) → False
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_compare16(x0, x1)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_sr(x0, x1)
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM0(EmptyFM, x0, x1, x2)
new_sIZE_RATIO
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_lt8(x0, x1)
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

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

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

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

new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), zxw343, h, ba, bb)
new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, zxw1084, Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_lt8(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), new_mkVBalBranch3Size_l(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), h, ba, bb)
new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_lt8(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), new_mkVBalBranch3Size_r(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), h, ba, bb)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, bc, bd, be) → new_sizeFM0(Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), bc, bd, be)
new_sr(zxw4000, zxw3000) → new_primMulInt(zxw4000, zxw3000)
new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, bc, bd, be) → new_sizeFM(zxw190, zxw191, zxw192, zxw193, zxw194, bc, bd, be)
new_lt8(zxw790, zxw800) → new_esEs9(new_compare16(zxw790, zxw800), LT)
new_compare16(zxw79, zxw80) → new_primCmpInt(zxw79, zxw80)
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb) → zxw52
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Pos(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Neg(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba, bb) → zxw542

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_compare16(x0, x1)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_sr(x0, x1)
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM0(EmptyFM, x0, x1, x2)
new_sIZE_RATIO
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_lt8(x0, x1)
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_lt8(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), new_mkVBalBranch3Size_l(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), h, ba, bb) at position [12] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_compare16(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), new_mkVBalBranch3Size_l(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), LT), h, ba, bb)



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

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

new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), zxw343, h, ba, bb)
new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, zxw1084, Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_compare16(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), new_mkVBalBranch3Size_l(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_lt8(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), new_mkVBalBranch3Size_r(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), h, ba, bb)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, bc, bd, be) → new_sizeFM0(Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), bc, bd, be)
new_sr(zxw4000, zxw3000) → new_primMulInt(zxw4000, zxw3000)
new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, bc, bd, be) → new_sizeFM(zxw190, zxw191, zxw192, zxw193, zxw194, bc, bd, be)
new_lt8(zxw790, zxw800) → new_esEs9(new_compare16(zxw790, zxw800), LT)
new_compare16(zxw79, zxw80) → new_primCmpInt(zxw79, zxw80)
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb) → zxw52
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Pos(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Neg(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba, bb) → zxw542

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_compare16(x0, x1)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_sr(x0, x1)
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM0(EmptyFM, x0, x1, x2)
new_sIZE_RATIO
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_lt8(x0, x1)
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_lt8(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), new_mkVBalBranch3Size_r(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), h, ba, bb) at position [12] we obtained the following new rules:

new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_compare16(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), new_mkVBalBranch3Size_r(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), LT), h, ba, bb)



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

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

new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), zxw343, h, ba, bb)
new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, zxw1084, Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb)
new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_compare16(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), new_mkVBalBranch3Size_r(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_compare16(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), new_mkVBalBranch3Size_l(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, bc, bd, be) → new_sizeFM0(Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), bc, bd, be)
new_sr(zxw4000, zxw3000) → new_primMulInt(zxw4000, zxw3000)
new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, bc, bd, be) → new_sizeFM(zxw190, zxw191, zxw192, zxw193, zxw194, bc, bd, be)
new_lt8(zxw790, zxw800) → new_esEs9(new_compare16(zxw790, zxw800), LT)
new_compare16(zxw79, zxw80) → new_primCmpInt(zxw79, zxw80)
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb) → zxw52
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Pos(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Neg(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba, bb) → zxw542

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_compare16(x0, x1)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_sr(x0, x1)
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM0(EmptyFM, x0, x1, x2)
new_sIZE_RATIO
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_lt8(x0, x1)
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

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

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

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

new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), zxw343, h, ba, bb)
new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, zxw1084, Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb)
new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_compare16(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), new_mkVBalBranch3Size_r(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_compare16(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), new_mkVBalBranch3Size_l(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, bc, bd, be) → new_sizeFM0(Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), bc, bd, be)
new_sr(zxw4000, zxw3000) → new_primMulInt(zxw4000, zxw3000)
new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, bc, bd, be) → new_sizeFM(zxw190, zxw191, zxw192, zxw193, zxw194, bc, bd, be)
new_compare16(zxw79, zxw80) → new_primCmpInt(zxw79, zxw80)
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb) → zxw52
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Pos(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Neg(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba, bb) → zxw542

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_compare16(x0, x1)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_sr(x0, x1)
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM0(EmptyFM, x0, x1, x2)
new_sIZE_RATIO
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_lt8(x0, x1)
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(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_lt8(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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ UsableRulesProof
                                                  ↳ QDP
                                                    ↳ QReductionProof
                                                      ↳ QDP
                                                        ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), zxw343, h, ba, bb)
new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, zxw1084, Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb)
new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_compare16(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), new_mkVBalBranch3Size_r(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_compare16(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), new_mkVBalBranch3Size_l(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, bc, bd, be) → new_sizeFM0(Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), bc, bd, be)
new_sr(zxw4000, zxw3000) → new_primMulInt(zxw4000, zxw3000)
new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, bc, bd, be) → new_sizeFM(zxw190, zxw191, zxw192, zxw193, zxw194, bc, bd, be)
new_compare16(zxw79, zxw80) → new_primCmpInt(zxw79, zxw80)
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb) → zxw52
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Pos(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Neg(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba, bb) → zxw542

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_compare16(x0, x1)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_sr(x0, x1)
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM0(EmptyFM, x0, x1, x2)
new_sIZE_RATIO
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_compare16(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), new_mkVBalBranch3Size_r(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), LT), h, ba, bb) at position [12,0] we obtained the following new rules:

new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), new_mkVBalBranch3Size_r(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), LT), h, ba, bb)



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

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

new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), zxw343, h, ba, bb)
new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, zxw1084, Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb)
new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), new_mkVBalBranch3Size_r(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_compare16(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), new_mkVBalBranch3Size_l(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, bc, bd, be) → new_sizeFM0(Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), bc, bd, be)
new_sr(zxw4000, zxw3000) → new_primMulInt(zxw4000, zxw3000)
new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, bc, bd, be) → new_sizeFM(zxw190, zxw191, zxw192, zxw193, zxw194, bc, bd, be)
new_compare16(zxw79, zxw80) → new_primCmpInt(zxw79, zxw80)
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb) → zxw52
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Pos(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Neg(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba, bb) → zxw542

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_compare16(x0, x1)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_sr(x0, x1)
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM0(EmptyFM, x0, x1, x2)
new_sIZE_RATIO
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_compare16(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), new_mkVBalBranch3Size_l(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), LT), h, ba, bb) at position [12,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), new_mkVBalBranch3Size_l(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), LT), h, ba, bb)



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

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

new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), zxw343, h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), new_mkVBalBranch3Size_l(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, zxw1084, Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb)
new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), new_mkVBalBranch3Size_r(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, bc, bd, be) → new_sizeFM0(Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), bc, bd, be)
new_sr(zxw4000, zxw3000) → new_primMulInt(zxw4000, zxw3000)
new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, bc, bd, be) → new_sizeFM(zxw190, zxw191, zxw192, zxw193, zxw194, bc, bd, be)
new_compare16(zxw79, zxw80) → new_primCmpInt(zxw79, zxw80)
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb) → zxw52
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Pos(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Neg(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba, bb) → zxw542

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_compare16(x0, x1)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_sr(x0, x1)
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM0(EmptyFM, x0, x1, x2)
new_sIZE_RATIO
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

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

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

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

new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), zxw343, h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), new_mkVBalBranch3Size_l(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, zxw1084, Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb)
new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), new_mkVBalBranch3Size_r(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, bc, bd, be) → new_sizeFM0(Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), bc, bd, be)
new_sr(zxw4000, zxw3000) → new_primMulInt(zxw4000, zxw3000)
new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, bc, bd, be) → new_sizeFM(zxw190, zxw191, zxw192, zxw193, zxw194, bc, bd, be)
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb) → zxw52
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Pos(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Neg(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba, bb) → zxw542

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_compare16(x0, x1)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_sr(x0, x1)
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM0(EmptyFM, x0, x1, x2)
new_sIZE_RATIO
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ UsableRulesProof
                                                  ↳ QDP
                                                    ↳ QReductionProof
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), zxw343, h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), new_mkVBalBranch3Size_l(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, zxw1084, Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb)
new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), new_mkVBalBranch3Size_r(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, bc, bd, be) → new_sizeFM0(Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), bc, bd, be)
new_sr(zxw4000, zxw3000) → new_primMulInt(zxw4000, zxw3000)
new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, bc, bd, be) → new_sizeFM(zxw190, zxw191, zxw192, zxw193, zxw194, bc, bd, be)
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb) → zxw52
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Pos(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Neg(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba, bb) → zxw542

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_sr(x0, x1)
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM0(EmptyFM, x0, x1, x2)
new_sIZE_RATIO
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), new_mkVBalBranch3Size_l(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), LT), h, ba, bb) at position [12,0,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), new_mkVBalBranch3Size_l(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), LT), h, ba, bb)



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

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

new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), zxw343, h, ba, bb)
new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, zxw1084, Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb)
new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), new_mkVBalBranch3Size_r(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), new_mkVBalBranch3Size_l(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, bc, bd, be) → new_sizeFM0(Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), bc, bd, be)
new_sr(zxw4000, zxw3000) → new_primMulInt(zxw4000, zxw3000)
new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, bc, bd, be) → new_sizeFM(zxw190, zxw191, zxw192, zxw193, zxw194, bc, bd, be)
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb) → zxw52
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Pos(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Neg(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba, bb) → zxw542

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_sr(x0, x1)
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM0(EmptyFM, x0, x1, x2)
new_sIZE_RATIO
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), new_mkVBalBranch3Size_r(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), LT), h, ba, bb) at position [12,0,0] we obtained the following new rules:

new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), new_mkVBalBranch3Size_r(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), LT), h, ba, bb)



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

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

new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), new_mkVBalBranch3Size_r(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), zxw343, h, ba, bb)
new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, zxw1084, Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), new_mkVBalBranch3Size_l(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, bc, bd, be) → new_sizeFM0(Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), bc, bd, be)
new_sr(zxw4000, zxw3000) → new_primMulInt(zxw4000, zxw3000)
new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, bc, bd, be) → new_sizeFM(zxw190, zxw191, zxw192, zxw193, zxw194, bc, bd, be)
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb) → zxw52
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Pos(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Neg(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba, bb) → zxw542

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_sr(x0, x1)
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM0(EmptyFM, x0, x1, x2)
new_sIZE_RATIO
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

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

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

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

new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), new_mkVBalBranch3Size_r(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), zxw343, h, ba, bb)
new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, zxw1084, Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), new_mkVBalBranch3Size_l(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, bc, bd, be) → new_sizeFM(zxw190, zxw191, zxw192, zxw193, zxw194, bc, bd, be)
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Pos(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Neg(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, bc, bd, be) → new_sizeFM0(Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), bc, bd, be)
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba, bb) → zxw542
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb) → zxw52

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_sr(x0, x1)
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM0(EmptyFM, x0, x1, x2)
new_sIZE_RATIO
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(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_sr(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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ UsableRulesProof
                                                  ↳ QDP
                                                    ↳ QReductionProof
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), zxw343, h, ba, bb)
new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), new_mkVBalBranch3Size_r(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, zxw1084, Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), new_mkVBalBranch3Size_l(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, bc, bd, be) → new_sizeFM(zxw190, zxw191, zxw192, zxw193, zxw194, bc, bd, be)
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Pos(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Neg(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, bc, bd, be) → new_sizeFM0(Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), bc, bd, be)
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba, bb) → zxw542
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb) → zxw52

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM0(EmptyFM, x0, x1, x2)
new_sIZE_RATIO
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), new_mkVBalBranch3Size_r(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), LT), h, ba, bb) at position [12,0,0,0] we obtained the following new rules:

new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_l(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), new_mkVBalBranch3Size_r(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), LT), h, ba, bb)



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

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

new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_l(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), new_mkVBalBranch3Size_r(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), zxw343, h, ba, bb)
new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, zxw1084, Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), new_mkVBalBranch3Size_l(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, bc, bd, be) → new_sizeFM(zxw190, zxw191, zxw192, zxw193, zxw194, bc, bd, be)
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Pos(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Neg(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, bc, bd, be) → new_sizeFM0(Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), bc, bd, be)
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba, bb) → zxw542
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb) → zxw52

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM0(EmptyFM, x0, x1, x2)
new_sIZE_RATIO
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), new_mkVBalBranch3Size_l(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), LT), h, ba, bb) at position [12,0,0,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), new_mkVBalBranch3Size_l(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), LT), h, ba, bb)



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

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

new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), zxw343, h, ba, bb)
new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_l(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), new_mkVBalBranch3Size_r(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, zxw1084, Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), new_mkVBalBranch3Size_l(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, bc, bd, be) → new_sizeFM(zxw190, zxw191, zxw192, zxw193, zxw194, bc, bd, be)
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Pos(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Neg(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, bc, bd, be) → new_sizeFM0(Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), bc, bd, be)
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba, bb) → zxw542
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb) → zxw52

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM0(EmptyFM, x0, x1, x2)
new_sIZE_RATIO
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

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

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

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

new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_l(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), new_mkVBalBranch3Size_r(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), zxw343, h, ba, bb)
new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, zxw1084, Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), new_mkVBalBranch3Size_l(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, bc, bd, be) → new_sizeFM(zxw190, zxw191, zxw192, zxw193, zxw194, bc, bd, be)
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, bc, bd, be) → new_sizeFM0(Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), bc, bd, be)
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba, bb) → zxw542
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb) → zxw52

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM0(EmptyFM, x0, x1, x2)
new_sIZE_RATIO
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ UsableRulesProof
                                                  ↳ QDP
                                                    ↳ QReductionProof
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ UsableRulesProof
                                                                                                  ↳ QDP
                                                                                                    ↳ QReductionProof
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), zxw343, h, ba, bb)
new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_l(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), new_mkVBalBranch3Size_r(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, zxw1084, Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), new_mkVBalBranch3Size_l(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, bc, bd, be) → new_sizeFM(zxw190, zxw191, zxw192, zxw193, zxw194, bc, bd, be)
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, bc, bd, be) → new_sizeFM0(Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), bc, bd, be)
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba, bb) → zxw542
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb) → zxw52

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM0(EmptyFM, x0, x1, x2)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_l(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), new_mkVBalBranch3Size_r(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), LT), h, ba, bb) at position [12,0,0,1] we obtained the following new rules:

new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM0(Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), h, ba, bb)), new_mkVBalBranch3Size_r(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), LT), h, ba, bb)



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

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

new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), zxw343, h, ba, bb)
new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, zxw1084, Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), new_mkVBalBranch3Size_l(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM0(Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), h, ba, bb)), new_mkVBalBranch3Size_r(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, bc, bd, be) → new_sizeFM(zxw190, zxw191, zxw192, zxw193, zxw194, bc, bd, be)
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, bc, bd, be) → new_sizeFM0(Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), bc, bd, be)
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba, bb) → zxw542
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb) → zxw52

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM0(EmptyFM, x0, x1, x2)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), new_mkVBalBranch3Size_l(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), LT), h, ba, bb) at position [12,0,0,1] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(zxw340, zxw341, zxw342, zxw343, zxw344, h, ba, bb)), new_mkVBalBranch3Size_l(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), LT), h, ba, bb)



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

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

new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), zxw343, h, ba, bb)
new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, zxw1084, Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb)
new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM0(Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), h, ba, bb)), new_mkVBalBranch3Size_r(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(zxw340, zxw341, zxw342, zxw343, zxw344, h, ba, bb)), new_mkVBalBranch3Size_l(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, bc, bd, be) → new_sizeFM(zxw190, zxw191, zxw192, zxw193, zxw194, bc, bd, be)
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, bc, bd, be) → new_sizeFM0(Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), bc, bd, be)
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba, bb) → zxw542
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb) → zxw52

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM0(EmptyFM, x0, x1, x2)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM0(Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), h, ba, bb)), new_mkVBalBranch3Size_r(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), LT), h, ba, bb) at position [12,0,0,1] we obtained the following new rules:

new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw1082), new_mkVBalBranch3Size_r(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), LT), h, ba, bb)



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

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

new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), zxw343, h, ba, bb)
new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, zxw1084, Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb)
new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw1082), new_mkVBalBranch3Size_r(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(zxw340, zxw341, zxw342, zxw343, zxw344, h, ba, bb)), new_mkVBalBranch3Size_l(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, bc, bd, be) → new_sizeFM(zxw190, zxw191, zxw192, zxw193, zxw194, bc, bd, be)
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, bc, bd, be) → new_sizeFM0(Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), bc, bd, be)
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba, bb) → zxw542
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb) → zxw52

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM0(EmptyFM, x0, x1, x2)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(zxw340, zxw341, zxw342, zxw343, zxw344, h, ba, bb)), new_mkVBalBranch3Size_l(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), LT), h, ba, bb) at position [12,0,0,1] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw342), new_mkVBalBranch3Size_l(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), LT), h, ba, bb)



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

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

new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), zxw343, h, ba, bb)
new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, zxw1084, Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb)
new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw1082), new_mkVBalBranch3Size_r(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw342), new_mkVBalBranch3Size_l(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, bc, bd, be) → new_sizeFM(zxw190, zxw191, zxw192, zxw193, zxw194, bc, bd, be)
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, bc, bd, be) → new_sizeFM0(Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), bc, bd, be)
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba, bb) → zxw542
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb) → zxw52

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM0(EmptyFM, x0, x1, x2)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw1082), new_mkVBalBranch3Size_r(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), LT), h, ba, bb) at position [12,0,1] we obtained the following new rules:

new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw1082), new_sizeFM(zxw340, zxw341, zxw342, zxw343, zxw344, h, ba, bb)), LT), h, ba, bb)



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

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

new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), zxw343, h, ba, bb)
new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw1082), new_sizeFM(zxw340, zxw341, zxw342, zxw343, zxw344, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, zxw1084, Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw342), new_mkVBalBranch3Size_l(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, bc, bd, be) → new_sizeFM(zxw190, zxw191, zxw192, zxw193, zxw194, bc, bd, be)
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, bc, bd, be) → new_sizeFM0(Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), bc, bd, be)
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba, bb) → zxw542
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb) → zxw52

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM0(EmptyFM, x0, x1, x2)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

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

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

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

new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), zxw343, h, ba, bb)
new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw1082), new_sizeFM(zxw340, zxw341, zxw342, zxw343, zxw344, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, zxw1084, Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw342), new_mkVBalBranch3Size_l(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, bc, bd, be) → new_sizeFM0(Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), bc, bd, be)
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba, bb) → zxw542
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb) → zxw52

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM0(EmptyFM, x0, x1, x2)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(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, 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ UsableRulesProof
                                                  ↳ QDP
                                                    ↳ QReductionProof
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ UsableRulesProof
                                                                                                  ↳ QDP
                                                                                                    ↳ QReductionProof
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ UsableRulesProof
                                                                                                                              ↳ QDP
                                                                                                                                ↳ QReductionProof
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), zxw343, h, ba, bb)
new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, zxw1084, Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb)
new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw1082), new_sizeFM(zxw340, zxw341, zxw342, zxw343, zxw344, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw342), new_mkVBalBranch3Size_l(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, bc, bd, be) → new_sizeFM0(Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), bc, bd, be)
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba, bb) → zxw542
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb) → zxw52

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM0(EmptyFM, x0, x1, x2)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw1082), new_sizeFM(zxw340, zxw341, zxw342, zxw343, zxw344, h, ba, bb)), LT), h, ba, bb) at position [12,0,1] we obtained the following new rules:

new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw1082), zxw342), LT), h, ba, bb)



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

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

new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), zxw343, h, ba, bb)
new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, zxw1084, Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw342), new_mkVBalBranch3Size_l(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw1082), zxw342), LT), h, ba, bb)

The TRS R consists of the following rules:

new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, bc, bd, be) → new_sizeFM0(Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), bc, bd, be)
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba, bb) → zxw542
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb) → zxw52

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM0(EmptyFM, x0, x1, x2)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

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

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

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

new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), zxw343, h, ba, bb)
new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, zxw1084, Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw342), new_mkVBalBranch3Size_l(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw1082), zxw342), LT), h, ba, bb)

The TRS R consists of the following rules:

new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, bc, bd, be) → new_sizeFM0(Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), bc, bd, be)
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba, bb) → zxw542
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM0(EmptyFM, x0, x1, x2)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(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, x7)



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

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

new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), zxw343, h, ba, bb)
new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, zxw1084, Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw342), new_mkVBalBranch3Size_l(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw1082), zxw342), LT), h, ba, bb)

The TRS R consists of the following rules:

new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, bc, bd, be) → new_sizeFM0(Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), bc, bd, be)
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba, bb) → zxw542
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM0(EmptyFM, x0, x1, x2)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw342), new_mkVBalBranch3Size_l(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), LT), h, ba, bb) at position [12,0,1] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw342), new_sizeFM0(Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), h, ba, bb)), LT), h, ba, bb)



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

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

new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), zxw343, h, ba, bb)
new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, zxw1084, Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw342), new_sizeFM0(Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw1082), zxw342), LT), h, ba, bb)

The TRS R consists of the following rules:

new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, bc, bd, be) → new_sizeFM0(Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), bc, bd, be)
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba, bb) → zxw542
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM0(EmptyFM, x0, x1, x2)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

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

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

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

new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), zxw343, h, ba, bb)
new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, zxw1084, Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw342), new_sizeFM0(Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw1082), zxw342), LT), h, ba, bb)

The TRS R consists of the following rules:

new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba, bb) → zxw542
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM0(EmptyFM, x0, x1, x2)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(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_l(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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ UsableRulesProof
                                                  ↳ QDP
                                                    ↳ QReductionProof
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ UsableRulesProof
                                                                                                  ↳ QDP
                                                                                                    ↳ QReductionProof
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ UsableRulesProof
                                                                                                                              ↳ QDP
                                                                                                                                ↳ QReductionProof
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ UsableRulesProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ QReductionProof
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ UsableRulesProof
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ QReductionProof
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), zxw343, h, ba, bb)
new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, zxw1084, Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw342), new_sizeFM0(Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw1082), zxw342), LT), h, ba, bb)

The TRS R consists of the following rules:

new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba, bb) → zxw542
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM0(EmptyFM, x0, x1, x2)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw342), new_sizeFM0(Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), h, ba, bb)), LT), h, ba, bb) at position [12,0,1] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw342), zxw1082), LT), h, ba, bb)



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

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

new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), zxw343, h, ba, bb)
new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, zxw1084, Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw342), zxw1082), LT), h, ba, bb)
new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw1082), zxw342), LT), h, ba, bb)

The TRS R consists of the following rules:

new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba, bb) → zxw542
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM0(EmptyFM, x0, x1, x2)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

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

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

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

new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), zxw343, h, ba, bb)
new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, zxw1084, Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw342), zxw1082), LT), h, ba, bb)
new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw1082), zxw342), LT), h, ba, bb)

The TRS R consists of the following rules:

new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM0(EmptyFM, x0, x1, x2)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(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_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_sizeFM0(EmptyFM, x0, x1, x2)



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

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

new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), zxw343, h, ba, bb)
new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, zxw1084, Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb)
new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw342), zxw1082), LT), h, ba, bb)
new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw1082), zxw342), LT), h, ba, bb)

The TRS R consists of the following rules:

new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(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_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw342), zxw1082), LT), h, ba, bb)
The remaining pairs can at least be oriented weakly.

new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), zxw343, h, ba, bb)
new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, zxw1084, Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb)
new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw1082), zxw342), LT), h, ba, bb)
Used ordering: Polynomial interpretation [25]:

POL(Branch(x1, x2, x3, x4, x5)) = 1 + x1 + x5   
POL(EQ) = 0   
POL(False) = 0   
POL(GT) = 0   
POL(LT) = 0   
POL(Neg(x1)) = 0   
POL(Pos(x1)) = 0   
POL(Succ(x1)) = 0   
POL(True) = 0   
POL(Zero) = 0   
POL(new_esEs9(x1, x2)) = 0   
POL(new_mkVBalBranch(x1, x2, x3, x4, x5, x6, x7)) = x3   
POL(new_mkVBalBranch3MkVBalBranch1(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16)) = x10   
POL(new_mkVBalBranch3MkVBalBranch2(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16)) = 1 + x10 + x6   
POL(new_primCmpInt(x1, x2)) = 0   
POL(new_primCmpNat0(x1, x2)) = 0   
POL(new_primCmpNat1(x1, x2)) = 0   
POL(new_primCmpNat2(x1, x2)) = 0   
POL(new_primMulInt(x1, x2)) = 0   
POL(new_primMulNat0(x1, x2)) = 0   
POL(new_primPlusNat0(x1, x2)) = 0   
POL(new_primPlusNat1(x1, x2)) = 0   

The following usable rules [17] were oriented: none



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

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

new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), zxw343, h, ba, bb)
new_mkVBalBranch3MkVBalBranch1(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, zxw1084, Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb)
new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw1082), zxw342), LT), h, ba, bb)

The TRS R consists of the following rules:

new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

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

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

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

new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), zxw343, h, ba, bb)
new_mkVBalBranch(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb) → new_mkVBalBranch3MkVBalBranch2(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw1082), zxw342), LT), h, ba, bb)

The TRS R consists of the following rules:

new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

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

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



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

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

new_addToFM_C20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw15, zxw16, False, h, ba, bb) → new_addToFM_C10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw15, zxw16, new_esEs9(new_compare15(Left(zxw15), zxw190, h, ba), GT), h, ba, bb)
new_addToFM_C20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw15, zxw16, True, h, ba, bb) → new_addToFM_C0(zxw193, zxw15, zxw16, h, ba, bb)
new_addToFM_C0(Branch(zxw190, zxw191, zxw192, zxw193, zxw194), zxw15, zxw16, h, ba, bb) → new_addToFM_C20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw15, zxw16, new_lt14(Left(zxw15), zxw190, h, ba), h, ba, bb)
new_addToFM_C10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw15, zxw16, True, h, ba, bb) → new_addToFM_C0(zxw194, zxw15, zxw16, h, ba, bb)

The TRS R consists of the following rules:

new_ltEs15(zxw7900, zxw8000) → new_fsEs(new_compare6(zxw7900, zxw8000))
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Char) → new_ltEs10(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), gh, ty_Bool) → new_ltEs12(zxw79000, zxw80000)
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, app(ty_Maybe, bae)) → new_ltEs18(zxw7900, zxw8000, bae)
new_esEs28(zxw4000, zxw3000, app(ty_[], ddd)) → new_esEs13(zxw4000, zxw3000, ddd)
new_esEs23(zxw4000, zxw3000, app(app(ty_Either, chd), che)) → new_esEs7(zxw4000, zxw3000, chd, che)
new_esEs6(Just(zxw4000), Just(zxw3000), app(app(ty_@2, ef), eg)) → new_esEs5(zxw4000, zxw3000, ef, eg)
new_lt4(zxw79000, zxw80000, app(app(app(ty_@3, be), bf), bg)) → new_lt5(zxw79000, zxw80000, be, bf, bg)
new_esEs7(Left(zxw4000), Left(zxw3000), app(app(ty_Either, bca), bcb), bbd) → new_esEs7(zxw4000, zxw3000, bca, bcb)
new_ltEs20(zxw7900, zxw8000, ty_Int) → new_ltEs9(zxw7900, zxw8000)
new_lt19(zxw79000, zxw80000, app(app(ty_Either, beb), bec)) → new_lt14(zxw79000, zxw80000, beb, bec)
new_esEs9(GT, LT) → False
new_esEs9(LT, GT) → False
new_esEs13([], [], cgf) → True
new_lt4(zxw79000, zxw80000, app(ty_[], bh)) → new_lt10(zxw79000, zxw80000, bh)
new_compare110(zxw79000, zxw80000, True, baf, bag) → LT
new_esEs27(zxw4001, zxw3001, app(ty_Ratio, dca)) → new_esEs18(zxw4001, zxw3001, dca)
new_compare29(zxw79000, zxw80000, ty_Char) → new_compare17(zxw79000, zxw80000)
new_ltEs7(LT, EQ) → True
new_ltEs18(Just(zxw79000), Just(zxw80000), app(ty_Maybe, cdg)) → new_ltEs18(zxw79000, zxw80000, cdg)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Integer) → new_ltEs13(zxw79000, zxw80000)
new_ltEs20(zxw7900, zxw8000, ty_@0) → new_ltEs8(zxw7900, zxw8000)
new_lt20(zxw79001, zxw80001, app(app(ty_Either, bfb), bfc)) → new_lt14(zxw79001, zxw80001, bfb, bfc)
new_esEs23(zxw4000, zxw3000, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_ltEs8(zxw7900, zxw8000) → new_fsEs(new_compare30(zxw7900, zxw8000))
new_lt19(zxw79000, zxw80000, ty_Double) → new_lt15(zxw79000, zxw80000)
new_esEs22(zxw4000, zxw3000, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_ltEs14(Right(zxw79000), Right(zxw80000), gh, app(ty_[], cbg)) → new_ltEs11(zxw79000, zxw80000, cbg)
new_ltEs21(zxw79002, zxw80002, ty_Char) → new_ltEs10(zxw79002, zxw80002)
new_esEs23(zxw4000, zxw3000, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Bool, ha) → new_ltEs12(zxw79000, zxw80000)
new_compare8(:%(zxw79000, zxw79001), :%(zxw80000, zxw80001), ty_Integer) → new_compare32(new_sr0(zxw79000, zxw80001), new_sr0(zxw80000, zxw79001))
new_esEs26(zxw4002, zxw3002, ty_Float) → new_esEs17(zxw4002, zxw3002)
new_esEs19(zxw79001, zxw80001, app(ty_Ratio, bfd)) → new_esEs18(zxw79001, zxw80001, bfd)
new_primMulNat0(Zero, Zero) → Zero
new_esEs20(zxw79000, zxw80000, app(ty_[], bea)) → new_esEs13(zxw79000, zxw80000, bea)
new_esEs7(Right(zxw4000), Right(zxw3000), bcf, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_lt20(zxw79001, zxw80001, ty_@0) → new_lt7(zxw79001, zxw80001)
new_esEs27(zxw4001, zxw3001, app(app(app(ty_@3, dch), dda), ddb)) → new_esEs4(zxw4001, zxw3001, dch, dda, ddb)
new_esEs19(zxw79001, zxw80001, ty_Ordering) → new_esEs9(zxw79001, zxw80001)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(ty_Ratio, cdf)) → new_ltEs17(zxw79000, zxw80000, cdf)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Bool, bbd) → new_esEs14(zxw4000, zxw3000)
new_esEs24(zxw4001, zxw3001, ty_Integer) → new_esEs15(zxw4001, zxw3001)
new_lt19(zxw79000, zxw80000, ty_Ordering) → new_lt6(zxw79000, zxw80000)
new_lt20(zxw79001, zxw80001, app(app(ty_@2, beh), bfa)) → new_lt11(zxw79001, zxw80001, beh, bfa)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(ty_Ratio, cbb), ha) → new_ltEs17(zxw79000, zxw80000, cbb)
new_compare9(zxw79000, zxw80000, ff, fg, fh) → new_compare25(zxw79000, zxw80000, new_esEs4(zxw79000, zxw80000, ff, fg, fh), ff, fg, fh)
new_lt11(zxw79000, zxw80000, baf, bag) → new_esEs9(new_compare19(zxw79000, zxw80000, baf, bag), LT)
new_compare1([], :(zxw80000, zxw80001), gg) → LT
new_lt18(zxw79000, zxw80000, bbb) → new_esEs9(new_compare27(zxw79000, zxw80000, bbb), LT)
new_esEs8(zxw79000, zxw80000, ty_Int) → new_esEs11(zxw79000, zxw80000)
new_compare32(Integer(zxw79000), Integer(zxw80000)) → new_primCmpInt(zxw79000, zxw80000)
new_ltEs5(zxw79001, zxw80001, ty_Char) → new_ltEs10(zxw79001, zxw80001)
new_lt4(zxw79000, zxw80000, ty_Bool) → new_lt12(zxw79000, zxw80000)
new_compare27(zxw79000, zxw80000, bbb) → new_compare28(zxw79000, zxw80000, new_esEs6(zxw79000, zxw80000, bbb), bbb)
new_lt4(zxw79000, zxw80000, app(ty_Maybe, cf)) → new_lt18(zxw79000, zxw80000, cf)
new_compare29(zxw79000, zxw80000, ty_Bool) → new_compare31(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, ty_Double) → new_esEs16(zxw79000, zxw80000)
new_esEs22(zxw4000, zxw3000, app(app(ty_@2, cfg), cfh)) → new_esEs5(zxw4000, zxw3000, cfg, cfh)
new_lt4(zxw79000, zxw80000, ty_Ordering) → new_lt6(zxw79000, zxw80000)
new_esEs22(zxw4000, zxw3000, app(ty_Maybe, cff)) → new_esEs6(zxw4000, zxw3000, cff)
new_ltEs14(Right(zxw79000), Right(zxw80000), gh, app(app(app(ty_@3, cbd), cbe), cbf)) → new_ltEs6(zxw79000, zxw80000, cbd, cbe, cbf)
new_esEs27(zxw4001, zxw3001, app(ty_Maybe, dcc)) → new_esEs6(zxw4001, zxw3001, dcc)
new_esEs8(zxw79000, zxw80000, app(app(app(ty_@3, be), bf), bg)) → new_esEs4(zxw79000, zxw80000, be, bf, bg)
new_esEs15(Integer(zxw4000), Integer(zxw3000)) → new_primEqInt(zxw4000, zxw3000)
new_ltEs21(zxw79002, zxw80002, app(app(ty_@2, bgb), bgc)) → new_ltEs4(zxw79002, zxw80002, bgb, bgc)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Float, ha) → new_ltEs16(zxw79000, zxw80000)
new_lt5(zxw79000, zxw80000, ff, fg, fh) → new_esEs9(new_compare9(zxw79000, zxw80000, ff, fg, fh), LT)
new_esEs22(zxw4000, zxw3000, app(ty_Ratio, cfd)) → new_esEs18(zxw4000, zxw3000, cfd)
new_esEs22(zxw4000, zxw3000, app(app(ty_Either, cga), cgb)) → new_esEs7(zxw4000, zxw3000, cga, cgb)
new_ltEs19(zxw7900, zxw8000, ty_Float) → new_ltEs16(zxw7900, zxw8000)
new_esEs7(Right(zxw4000), Right(zxw3000), bcf, app(ty_Maybe, bda)) → new_esEs6(zxw4000, zxw3000, bda)
new_pePe(False, zxw271) → zxw271
new_esEs7(Left(zxw4000), Right(zxw3000), bcf, bbd) → False
new_esEs7(Right(zxw4000), Left(zxw3000), bcf, bbd) → False
new_lt15(zxw79000, zxw80000) → new_esEs9(new_compare6(zxw79000, zxw80000), LT)
new_compare15(zxw790, zxw800, gb, gc) → new_compare26(zxw790, zxw800, new_esEs7(zxw790, zxw800, gb, gc), gb, gc)
new_ltEs14(Right(zxw79000), Right(zxw80000), gh, ty_Float) → new_ltEs16(zxw79000, zxw80000)
new_ltEs12(True, False) → False
new_esEs20(zxw79000, zxw80000, ty_Double) → new_esEs16(zxw79000, zxw80000)
new_ltEs19(zxw7900, zxw8000, app(app(ty_@2, bc), bd)) → new_ltEs4(zxw7900, zxw8000, bc, bd)
new_compare23(zxw79000, zxw80000, True) → EQ
new_esEs27(zxw4001, zxw3001, app(app(ty_Either, dcf), dcg)) → new_esEs7(zxw4001, zxw3001, dcf, dcg)
new_esEs27(zxw4001, zxw3001, ty_Ordering) → new_esEs9(zxw4001, zxw3001)
new_esEs27(zxw4001, zxw3001, ty_Float) → new_esEs17(zxw4001, zxw3001)
new_esEs19(zxw79001, zxw80001, app(ty_Maybe, bfe)) → new_esEs6(zxw79001, zxw80001, bfe)
new_lt10(zxw79000, zxw80000, bea) → new_esEs9(new_compare1(zxw79000, zxw80000, bea), LT)
new_esEs26(zxw4002, zxw3002, ty_Char) → new_esEs12(zxw4002, zxw3002)
new_ltEs19(zxw7900, zxw8000, app(ty_[], gg)) → new_ltEs11(zxw7900, zxw8000, gg)
new_esEs26(zxw4002, zxw3002, ty_Int) → new_esEs11(zxw4002, zxw3002)
new_ltEs5(zxw79001, zxw80001, app(app(ty_@2, dd), de)) → new_ltEs4(zxw79001, zxw80001, dd, de)
new_lt19(zxw79000, zxw80000, app(ty_Ratio, ga)) → new_lt17(zxw79000, zxw80000, ga)
new_esEs22(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, app(app(app(ty_@3, deb), dec), ded)) → new_esEs4(zxw4000, zxw3000, deb, dec, ded)
new_compare29(zxw79000, zxw80000, app(app(ty_@2, bhd), bhe)) → new_compare19(zxw79000, zxw80000, bhd, bhe)
new_ltEs21(zxw79002, zxw80002, ty_Int) → new_ltEs9(zxw79002, zxw80002)
new_esEs20(zxw79000, zxw80000, ty_Char) → new_esEs12(zxw79000, zxw80000)
new_compare13(zxw235, zxw236, False, bah, bba) → GT
new_esEs9(GT, EQ) → False
new_esEs9(EQ, GT) → False
new_esEs19(zxw79001, zxw80001, app(app(ty_Either, bfb), bfc)) → new_esEs7(zxw79001, zxw80001, bfb, bfc)
new_esEs20(zxw79000, zxw80000, app(app(ty_@2, baf), bag)) → new_esEs5(zxw79000, zxw80000, baf, bag)
new_ltEs7(GT, GT) → True
new_ltEs20(zxw7900, zxw8000, app(app(ty_@2, hh), baa)) → new_ltEs4(zxw7900, zxw8000, hh, baa)
new_esEs7(Right(zxw4000), Right(zxw3000), bcf, app(app(ty_@2, bdb), bdc)) → new_esEs5(zxw4000, zxw3000, bdb, bdc)
new_esEs21(zxw4001, zxw3001, ty_Bool) → new_esEs14(zxw4001, zxw3001)
new_primCompAux0(zxw79000, zxw80000, zxw272, gg) → new_primCompAux00(zxw272, new_compare29(zxw79000, zxw80000, gg))
new_ltEs21(zxw79002, zxw80002, ty_Ordering) → new_ltEs7(zxw79002, zxw80002)
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_compare29(zxw79000, zxw80000, app(ty_[], bhc)) → new_compare1(zxw79000, zxw80000, bhc)
new_lt20(zxw79001, zxw80001, ty_Ordering) → new_lt6(zxw79001, zxw80001)
new_esEs8(zxw79000, zxw80000, app(ty_[], bh)) → new_esEs13(zxw79000, zxw80000, bh)
new_esEs7(Right(zxw4000), Right(zxw3000), bcf, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_esEs27(zxw4001, zxw3001, ty_@0) → new_esEs10(zxw4001, zxw3001)
new_compare25(zxw79000, zxw80000, True, ff, fg, fh) → EQ
new_esEs19(zxw79001, zxw80001, ty_Float) → new_esEs17(zxw79001, zxw80001)
new_ltEs5(zxw79001, zxw80001, ty_Ordering) → new_ltEs7(zxw79001, zxw80001)
new_lt4(zxw79000, zxw80000, app(ty_Ratio, ce)) → new_lt17(zxw79000, zxw80000, ce)
new_esEs28(zxw4000, zxw3000, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Int, bbd) → new_esEs11(zxw4000, zxw3000)
new_ltEs21(zxw79002, zxw80002, ty_Float) → new_ltEs16(zxw79002, zxw80002)
new_esEs28(zxw4000, zxw3000, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(app(app(ty_@3, ccf), ccg), cch)) → new_ltEs6(zxw79000, zxw80000, ccf, ccg, cch)
new_compare29(zxw79000, zxw80000, app(app(app(ty_@3, bgh), bha), bhb)) → new_compare9(zxw79000, zxw80000, bgh, bha, bhb)
new_lt19(zxw79000, zxw80000, app(app(ty_@2, baf), bag)) → new_lt11(zxw79000, zxw80000, baf, bag)
new_pePe(True, zxw271) → True
new_primEqNat0(Zero, Zero) → True
new_compare14(zxw242, zxw243, False, dab, dac) → GT
new_ltEs14(Right(zxw79000), Right(zxw80000), gh, ty_Double) → new_ltEs15(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, ty_Int) → new_esEs11(zxw79000, zxw80000)
new_ltEs21(zxw79002, zxw80002, ty_Bool) → new_ltEs12(zxw79002, zxw80002)
new_lt9(zxw79000, zxw80000) → new_esEs9(new_compare17(zxw79000, zxw80000), LT)
new_ltEs12(False, False) → True
new_esEs7(Left(zxw4000), Left(zxw3000), app(app(ty_@2, bbg), bbh), bbd) → new_esEs5(zxw4000, zxw3000, bbg, bbh)
new_esEs26(zxw4002, zxw3002, app(ty_Maybe, dba)) → new_esEs6(zxw4002, zxw3002, dba)
new_compare8(:%(zxw79000, zxw79001), :%(zxw80000, zxw80001), ty_Int) → new_compare16(new_sr(zxw79000, zxw80001), new_sr(zxw80000, zxw79001))
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Ordering, bbd) → new_esEs9(zxw4000, zxw3000)
new_esEs27(zxw4001, zxw3001, ty_Char) → new_esEs12(zxw4001, zxw3001)
new_lt7(zxw79000, zxw80000) → new_esEs9(new_compare30(zxw79000, zxw80000), LT)
new_compare110(zxw79000, zxw80000, False, baf, bag) → GT
new_sr(zxw4000, zxw3000) → new_primMulInt(zxw4000, zxw3000)
new_compare12(zxw79000, zxw80000, True, ff, fg, fh) → LT
new_lt19(zxw79000, zxw80000, ty_Int) → new_lt8(zxw79000, zxw80000)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_ltEs14(Right(zxw79000), Right(zxw80000), gh, app(app(ty_@2, cbh), cca)) → new_ltEs4(zxw79000, zxw80000, cbh, cca)
new_ltEs19(zxw7900, zxw8000, ty_Char) → new_ltEs10(zxw7900, zxw8000)
new_esEs21(zxw4001, zxw3001, ty_Double) → new_esEs16(zxw4001, zxw3001)
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_esEs7(Right(zxw4000), Right(zxw3000), bcf, app(app(ty_Either, bdd), bde)) → new_esEs7(zxw4000, zxw3000, bdd, bde)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Double, ha) → new_ltEs15(zxw79000, zxw80000)
new_ltEs19(zxw7900, zxw8000, ty_Bool) → new_ltEs12(zxw7900, zxw8000)
new_esEs26(zxw4002, zxw3002, app(app(app(ty_@3, dbf), dbg), dbh)) → new_esEs4(zxw4002, zxw3002, dbf, dbg, dbh)
new_esEs7(Right(zxw4000), Right(zxw3000), bcf, app(ty_[], bch)) → new_esEs13(zxw4000, zxw3000, bch)
new_ltEs11(zxw7900, zxw8000, gg) → new_fsEs(new_compare1(zxw7900, zxw8000, gg))
new_ltEs20(zxw7900, zxw8000, ty_Float) → new_ltEs16(zxw7900, zxw8000)
new_esEs21(zxw4001, zxw3001, ty_Ordering) → new_esEs9(zxw4001, zxw3001)
new_esEs7(Right(zxw4000), Right(zxw3000), bcf, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_esEs9(EQ, EQ) → True
new_fsEs(zxw259) → new_not(new_esEs9(zxw259, GT))
new_esEs8(zxw79000, zxw80000, ty_Char) → new_esEs12(zxw79000, zxw80000)
new_primEqInt(Neg(Succ(zxw40000)), Neg(Succ(zxw30000))) → new_primEqNat0(zxw40000, zxw30000)
new_esEs8(zxw79000, zxw80000, app(app(ty_@2, ca), cb)) → new_esEs5(zxw79000, zxw80000, ca, cb)
new_compare13(zxw235, zxw236, True, bah, bba) → LT
new_compare26(Left(zxw7900), Right(zxw8000), False, gb, gc) → LT
new_esEs13(:(zxw4000, zxw4001), :(zxw3000, zxw3001), cgf) → new_asAs(new_esEs23(zxw4000, zxw3000, cgf), new_esEs13(zxw4001, zxw3001, cgf))
new_esEs26(zxw4002, zxw3002, app(ty_[], dah)) → new_esEs13(zxw4002, zxw3002, dah)
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_ltEs19(zxw7900, zxw8000, app(ty_Ratio, hb)) → new_ltEs17(zxw7900, zxw8000, hb)
new_ltEs20(zxw7900, zxw8000, ty_Bool) → new_ltEs12(zxw7900, zxw8000)
new_esEs21(zxw4001, zxw3001, ty_Char) → new_esEs12(zxw4001, zxw3001)
new_compare23(zxw79000, zxw80000, False) → new_compare10(zxw79000, zxw80000, new_ltEs12(zxw79000, zxw80000))
new_ltEs14(Right(zxw79000), Left(zxw80000), gh, ha) → False
new_compare210(zxw79000, zxw80000, False, baf, bag) → new_compare110(zxw79000, zxw80000, new_ltEs4(zxw79000, zxw80000, baf, bag), baf, bag)
new_primCmpNat1(Zero, zxw7900) → LT
new_compare7(Float(zxw79000, zxw79001), Float(zxw80000, zxw80001)) → new_compare16(new_sr(zxw79000, zxw80000), new_sr(zxw79001, zxw80001))
new_ltEs21(zxw79002, zxw80002, ty_Integer) → new_ltEs13(zxw79002, zxw80002)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_lt20(zxw79001, zxw80001, app(ty_Maybe, bfe)) → new_lt18(zxw79001, zxw80001, bfe)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Integer, bbd) → new_esEs15(zxw4000, zxw3000)
new_ltEs5(zxw79001, zxw80001, ty_Bool) → new_ltEs12(zxw79001, zxw80001)
new_esEs19(zxw79001, zxw80001, ty_Bool) → new_esEs14(zxw79001, zxw80001)
new_ltEs7(EQ, EQ) → True
new_ltEs20(zxw7900, zxw8000, app(ty_Ratio, bad)) → new_ltEs17(zxw7900, zxw8000, bad)
new_primEqInt(Neg(Zero), Neg(Succ(zxw30000))) → False
new_primEqInt(Neg(Succ(zxw40000)), Neg(Zero)) → False
new_ltEs5(zxw79001, zxw80001, ty_Integer) → new_ltEs13(zxw79001, zxw80001)
new_compare26(zxw790, zxw800, True, gb, gc) → EQ
new_compare111(zxw79000, zxw80000, True, bbb) → LT
new_esEs20(zxw79000, zxw80000, ty_@0) → new_esEs10(zxw79000, zxw80000)
new_ltEs21(zxw79002, zxw80002, app(app(ty_Either, bgd), bge)) → new_ltEs14(zxw79002, zxw80002, bgd, bge)
new_esEs8(zxw79000, zxw80000, ty_Float) → new_esEs17(zxw79000, zxw80000)
new_esEs23(zxw4000, zxw3000, app(app(app(ty_@3, chf), chg), chh)) → new_esEs4(zxw4000, zxw3000, chf, chg, chh)
new_ltEs21(zxw79002, zxw80002, app(ty_[], bga)) → new_ltEs11(zxw79002, zxw80002, bga)
new_esEs21(zxw4001, zxw3001, ty_Float) → new_esEs17(zxw4001, zxw3001)
new_compare24(zxw79000, zxw80000, False) → new_compare11(zxw79000, zxw80000, new_ltEs7(zxw79000, zxw80000))
new_ltEs5(zxw79001, zxw80001, app(ty_Ratio, dh)) → new_ltEs17(zxw79001, zxw80001, dh)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_esEs26(zxw4002, zxw3002, app(app(ty_Either, dbd), dbe)) → new_esEs7(zxw4002, zxw3002, dbd, dbe)
new_lt20(zxw79001, zxw80001, ty_Int) → new_lt8(zxw79001, zxw80001)
new_lt4(zxw79000, zxw80000, ty_Int) → new_lt8(zxw79000, zxw80000)
new_ltEs20(zxw7900, zxw8000, ty_Double) → new_ltEs15(zxw7900, zxw8000)
new_lt12(zxw79000, zxw80000) → new_esEs9(new_compare31(zxw79000, zxw80000), LT)
new_ltEs7(GT, LT) → False
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Int, ha) → new_ltEs9(zxw79000, zxw80000)
new_lt20(zxw79001, zxw80001, ty_Integer) → new_lt13(zxw79001, zxw80001)
new_ltEs7(GT, EQ) → False
new_esEs6(Nothing, Nothing, eb) → True
new_primEqInt(Pos(Succ(zxw40000)), Pos(Succ(zxw30000))) → new_primEqNat0(zxw40000, zxw30000)
new_lt8(zxw790, zxw800) → new_esEs9(new_compare16(zxw790, zxw800), LT)
new_esEs21(zxw4001, zxw3001, app(ty_Maybe, ced)) → new_esEs6(zxw4001, zxw3001, ced)
new_lt6(zxw79000, zxw80000) → new_esEs9(new_compare18(zxw79000, zxw80000), LT)
new_esEs14(False, True) → False
new_esEs14(True, False) → False
new_esEs26(zxw4002, zxw3002, ty_Integer) → new_esEs15(zxw4002, zxw3002)
new_esEs7(Right(zxw4000), Right(zxw3000), bcf, app(app(app(ty_@3, bdf), bdg), bdh)) → new_esEs4(zxw4000, zxw3000, bdf, bdg, bdh)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs6(Nothing, Just(zxw3000), eb) → False
new_esEs6(Just(zxw4000), Nothing, eb) → False
new_primEqNat0(Succ(zxw40000), Succ(zxw30000)) → new_primEqNat0(zxw40000, zxw30000)
new_esEs16(Double(zxw4000, zxw4001), Double(zxw3000, zxw3001)) → new_esEs11(new_sr(zxw4000, zxw3000), new_sr(zxw4001, zxw3001))
new_lt19(zxw79000, zxw80000, ty_@0) → new_lt7(zxw79000, zxw80000)
new_ltEs5(zxw79001, zxw80001, app(ty_Maybe, ea)) → new_ltEs18(zxw79001, zxw80001, ea)
new_esEs17(Float(zxw4000, zxw4001), Float(zxw3000, zxw3001)) → new_esEs11(new_sr(zxw4000, zxw3000), new_sr(zxw4001, zxw3001))
new_primCompAux00(zxw276, LT) → LT
new_esEs28(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), app(ty_Ratio, bbc), bbd) → new_esEs18(zxw4000, zxw3000, bbc)
new_esEs21(zxw4001, zxw3001, ty_Int) → new_esEs11(zxw4001, zxw3001)
new_compare1(:(zxw79000, zxw79001), :(zxw80000, zxw80001), gg) → new_primCompAux0(zxw79000, zxw80000, new_compare1(zxw79001, zxw80001, gg), gg)
new_primEqInt(Pos(Zero), Pos(Succ(zxw30000))) → False
new_primEqInt(Pos(Succ(zxw40000)), Pos(Zero)) → False
new_compare29(zxw79000, zxw80000, ty_Int) → new_compare16(zxw79000, zxw80000)
new_lt20(zxw79001, zxw80001, app(ty_Ratio, bfd)) → new_lt17(zxw79001, zxw80001, bfd)
new_ltEs20(zxw7900, zxw8000, ty_Integer) → new_ltEs13(zxw7900, zxw8000)
new_esEs5(@2(zxw4000, zxw4001), @2(zxw3000, zxw3001), cdh, cea) → new_asAs(new_esEs22(zxw4000, zxw3000, cdh), new_esEs21(zxw4001, zxw3001, cea))
new_ltEs18(Nothing, Nothing, hc) → True
new_ltEs21(zxw79002, zxw80002, app(ty_Ratio, bgf)) → new_ltEs17(zxw79002, zxw80002, bgf)
new_esEs23(zxw4000, zxw3000, app(app(ty_@2, chb), chc)) → new_esEs5(zxw4000, zxw3000, chb, chc)
new_esEs20(zxw79000, zxw80000, app(app(app(ty_@3, ff), fg), fh)) → new_esEs4(zxw79000, zxw80000, ff, fg, fh)
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_ltEs21(zxw79002, zxw80002, app(app(app(ty_@3, bff), bfg), bfh)) → new_ltEs6(zxw79002, zxw80002, bff, bfg, bfh)
new_ltEs10(zxw7900, zxw8000) → new_fsEs(new_compare17(zxw7900, zxw8000))
new_compare17(Char(zxw79000), Char(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_sr0(Integer(zxw800000), Integer(zxw790010)) → Integer(new_primMulInt(zxw800000, zxw790010))
new_ltEs5(zxw79001, zxw80001, ty_Double) → new_ltEs15(zxw79001, zxw80001)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_esEs8(zxw79000, zxw80000, app(app(ty_Either, cc), cd)) → new_esEs7(zxw79000, zxw80000, cc, cd)
new_primEqInt(Neg(Succ(zxw40000)), Pos(zxw3000)) → False
new_primEqInt(Pos(Succ(zxw40000)), Neg(zxw3000)) → False
new_compare29(zxw79000, zxw80000, ty_Integer) → new_compare32(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), gh, ty_Char) → new_ltEs10(zxw79000, zxw80000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_@0, bbd) → new_esEs10(zxw4000, zxw3000)
new_lt19(zxw79000, zxw80000, app(app(app(ty_@3, ff), fg), fh)) → new_lt5(zxw79000, zxw80000, ff, fg, fh)
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_esEs28(zxw4000, zxw3000, app(ty_Maybe, dde)) → new_esEs6(zxw4000, zxw3000, dde)
new_esEs21(zxw4001, zxw3001, app(ty_[], cec)) → new_esEs13(zxw4001, zxw3001, cec)
new_ltEs21(zxw79002, zxw80002, ty_@0) → new_ltEs8(zxw79002, zxw80002)
new_primEqInt(Neg(Zero), Pos(Succ(zxw30000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(zxw30000))) → False
new_ltEs7(EQ, GT) → True
new_lt4(zxw79000, zxw80000, ty_Double) → new_lt15(zxw79000, zxw80000)
new_esEs21(zxw4001, zxw3001, ty_Integer) → new_esEs15(zxw4001, zxw3001)
new_primCompAux00(zxw276, EQ) → zxw276
new_esEs28(zxw4000, zxw3000, app(app(ty_Either, ddh), dea)) → new_esEs7(zxw4000, zxw3000, ddh, dea)
new_compare24(zxw79000, zxw80000, True) → EQ
new_compare6(Double(zxw79000, zxw79001), Double(zxw80000, zxw80001)) → new_compare16(new_sr(zxw79000, zxw80000), new_sr(zxw79001, zxw80001))
new_esEs8(zxw79000, zxw80000, ty_@0) → new_esEs10(zxw79000, zxw80000)
new_ltEs5(zxw79001, zxw80001, app(app(ty_Either, df), dg)) → new_ltEs14(zxw79001, zxw80001, df, dg)
new_lt13(zxw79000, zxw80000) → new_esEs9(new_compare32(zxw79000, zxw80000), LT)
new_esEs27(zxw4001, zxw3001, ty_Double) → new_esEs16(zxw4001, zxw3001)
new_esEs7(Left(zxw4000), Left(zxw3000), app(app(app(ty_@3, bcc), bcd), bce), bbd) → new_esEs4(zxw4000, zxw3000, bcc, bcd, bce)
new_esEs26(zxw4002, zxw3002, app(app(ty_@2, dbb), dbc)) → new_esEs5(zxw4002, zxw3002, dbb, dbc)
new_esEs21(zxw4001, zxw3001, app(app(ty_@2, cee), cef)) → new_esEs5(zxw4001, zxw3001, cee, cef)
new_lt19(zxw79000, zxw80000, app(ty_Maybe, bbb)) → new_lt18(zxw79000, zxw80000, bbb)
new_esEs12(Char(zxw4000), Char(zxw3000)) → new_primEqNat0(zxw4000, zxw3000)
new_ltEs20(zxw7900, zxw8000, app(app(app(ty_@3, hd), he), hf)) → new_ltEs6(zxw7900, zxw8000, hd, he, hf)
new_not(False) → True
new_lt20(zxw79001, zxw80001, ty_Char) → new_lt9(zxw79001, zxw80001)
new_esEs11(zxw400, zxw300) → new_primEqInt(zxw400, zxw300)
new_ltEs14(Right(zxw79000), Right(zxw80000), gh, app(ty_Maybe, cce)) → new_ltEs18(zxw79000, zxw80000, cce)
new_ltEs18(Just(zxw79000), Nothing, hc) → False
new_esEs8(zxw79000, zxw80000, app(ty_Maybe, cf)) → new_esEs6(zxw79000, zxw80000, cf)
new_esEs7(Left(zxw4000), Left(zxw3000), app(ty_Maybe, bbf), bbd) → new_esEs6(zxw4000, zxw3000, bbf)
new_compare210(zxw79000, zxw80000, True, baf, bag) → EQ
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Double, bbd) → new_esEs16(zxw4000, zxw3000)
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_esEs19(zxw79001, zxw80001, ty_Int) → new_esEs11(zxw79001, zxw80001)
new_compare12(zxw79000, zxw80000, False, ff, fg, fh) → GT
new_ltEs16(zxw7900, zxw8000) → new_fsEs(new_compare7(zxw7900, zxw8000))
new_esEs9(GT, GT) → True
new_esEs26(zxw4002, zxw3002, app(ty_Ratio, dag)) → new_esEs18(zxw4002, zxw3002, dag)
new_esEs25(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_lt20(zxw79001, zxw80001, app(ty_[], beg)) → new_lt10(zxw79001, zxw80001, beg)
new_lt4(zxw79000, zxw80000, app(app(ty_Either, cc), cd)) → new_lt14(zxw79000, zxw80000, cc, cd)
new_esEs26(zxw4002, zxw3002, ty_Bool) → new_esEs14(zxw4002, zxw3002)
new_compare19(zxw79000, zxw80000, baf, bag) → new_compare210(zxw79000, zxw80000, new_esEs5(zxw79000, zxw80000, baf, bag), baf, bag)
new_esEs8(zxw79000, zxw80000, ty_Bool) → new_esEs14(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Double) → new_ltEs15(zxw79000, zxw80000)
new_esEs28(zxw4000, zxw3000, app(app(ty_@2, ddf), ddg)) → new_esEs5(zxw4000, zxw3000, ddf, ddg)
new_ltEs19(zxw7900, zxw8000, app(app(app(ty_@3, gd), ge), gf)) → new_ltEs6(zxw7900, zxw8000, gd, ge, gf)
new_lt4(zxw79000, zxw80000, ty_Char) → new_lt9(zxw79000, zxw80000)
new_esEs22(zxw4000, zxw3000, app(app(app(ty_@3, cgc), cgd), cge)) → new_esEs4(zxw4000, zxw3000, cgc, cgd, cge)
new_esEs22(zxw4000, zxw3000, app(ty_[], cfe)) → new_esEs13(zxw4000, zxw3000, cfe)
new_ltEs14(Right(zxw79000), Right(zxw80000), gh, ty_@0) → new_ltEs8(zxw79000, zxw80000)
new_esEs23(zxw4000, zxw3000, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Float, bbd) → new_esEs17(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_esEs27(zxw4001, zxw3001, ty_Int) → new_esEs11(zxw4001, zxw3001)
new_esEs19(zxw79001, zxw80001, app(app(app(ty_@3, bed), bee), bef)) → new_esEs4(zxw79001, zxw80001, bed, bee, bef)
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_esEs7(Right(zxw4000), Right(zxw3000), bcf, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(app(app(ty_@3, cab), cac), cad), ha) → new_ltEs6(zxw79000, zxw80000, cab, cac, cad)
new_ltEs19(zxw7900, zxw8000, ty_Int) → new_ltEs9(zxw7900, zxw8000)
new_lt4(zxw79000, zxw80000, ty_@0) → new_lt7(zxw79000, zxw80000)
new_lt20(zxw79001, zxw80001, ty_Double) → new_lt15(zxw79001, zxw80001)
new_lt19(zxw79000, zxw80000, ty_Float) → new_lt16(zxw79000, zxw80000)
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_esEs26(zxw4002, zxw3002, ty_@0) → new_esEs10(zxw4002, zxw3002)
new_lt19(zxw79000, zxw80000, ty_Bool) → new_lt12(zxw79000, zxw80000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Char, bbd) → new_esEs12(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(ty_[], cda)) → new_ltEs11(zxw79000, zxw80000, cda)
new_lt4(zxw79000, zxw80000, ty_Float) → new_lt16(zxw79000, zxw80000)
new_primMulInt(Neg(zxw40000), Neg(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_ltEs5(zxw79001, zxw80001, app(app(app(ty_@3, cg), da), db)) → new_ltEs6(zxw79001, zxw80001, cg, da, db)
new_primCmpNat2(Zero, Zero) → EQ
new_esEs20(zxw79000, zxw80000, ty_Integer) → new_esEs15(zxw79000, zxw80000)
new_primEqNat0(Zero, Succ(zxw30000)) → False
new_primEqNat0(Succ(zxw40000), Zero) → False
new_esEs21(zxw4001, zxw3001, ty_@0) → new_esEs10(zxw4001, zxw3001)
new_esEs22(zxw4000, zxw3000, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_esEs20(zxw79000, zxw80000, ty_Bool) → new_esEs14(zxw79000, zxw80000)
new_ltEs5(zxw79001, zxw80001, app(ty_[], dc)) → new_ltEs11(zxw79001, zxw80001, dc)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs23(zxw4000, zxw3000, app(ty_Ratio, cgg)) → new_esEs18(zxw4000, zxw3000, cgg)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(app(ty_@2, cdb), cdc)) → new_ltEs4(zxw79000, zxw80000, cdb, cdc)
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_ltEs5(zxw79001, zxw80001, ty_Int) → new_ltEs9(zxw79001, zxw80001)
new_esEs27(zxw4001, zxw3001, app(app(ty_@2, dcd), dce)) → new_esEs5(zxw4001, zxw3001, dcd, dce)
new_primCmpNat0(zxw7900, Zero) → GT
new_compare26(Right(zxw7900), Left(zxw8000), False, gb, gc) → GT
new_esEs23(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_@0, ha) → new_ltEs8(zxw79000, zxw80000)
new_ltEs21(zxw79002, zxw80002, app(ty_Maybe, bgg)) → new_ltEs18(zxw79002, zxw80002, bgg)
new_esEs21(zxw4001, zxw3001, app(app(ty_Either, ceg), ceh)) → new_esEs7(zxw4001, zxw3001, ceg, ceh)
new_esEs22(zxw4000, zxw3000, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Bool) → new_ltEs12(zxw79000, zxw80000)
new_compare29(zxw79000, zxw80000, app(ty_Maybe, caa)) → new_compare27(zxw79000, zxw80000, caa)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_ltEs14(Left(zxw79000), Left(zxw80000), app(ty_Maybe, cbc), ha) → new_ltEs18(zxw79000, zxw80000, cbc)
new_lt20(zxw79001, zxw80001, ty_Float) → new_lt16(zxw79001, zxw80001)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Ordering) → new_ltEs7(zxw79000, zxw80000)
new_lt17(zxw79000, zxw80000, ga) → new_esEs9(new_compare8(zxw79000, zxw80000, ga), LT)
new_compare30(@0, @0) → EQ
new_lt19(zxw79000, zxw80000, app(ty_[], bea)) → new_lt10(zxw79000, zxw80000, bea)
new_esEs21(zxw4001, zxw3001, app(app(app(ty_@3, cfa), cfb), cfc)) → new_esEs4(zxw4001, zxw3001, cfa, cfb, cfc)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_esEs20(zxw79000, zxw80000, app(ty_Ratio, ga)) → new_esEs18(zxw79000, zxw80000, ga)
new_esEs6(Just(zxw4000), Just(zxw3000), app(app(app(ty_@3, fb), fc), fd)) → new_esEs4(zxw4000, zxw3000, fb, fc, fd)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(app(ty_Either, cdd), cde)) → new_ltEs14(zxw79000, zxw80000, cdd, cde)
new_esEs24(zxw4001, zxw3001, ty_Int) → new_esEs11(zxw4001, zxw3001)
new_esEs8(zxw79000, zxw80000, ty_Ordering) → new_esEs9(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), gh, ty_Ordering) → new_ltEs7(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, app(app(ty_Either, beb), bec)) → new_esEs7(zxw79000, zxw80000, beb, bec)
new_compare29(zxw79000, zxw80000, app(ty_Ratio, bhh)) → new_compare8(zxw79000, zxw80000, bhh)
new_lt4(zxw79000, zxw80000, app(app(ty_@2, ca), cb)) → new_lt11(zxw79000, zxw80000, ca, cb)
new_compare29(zxw79000, zxw80000, ty_Float) → new_compare7(zxw79000, zxw80000)
new_esEs19(zxw79001, zxw80001, app(app(ty_@2, beh), bfa)) → new_esEs5(zxw79001, zxw80001, beh, bfa)
new_esEs10(@0, @0) → True
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_compare29(zxw79000, zxw80000, ty_Double) → new_compare6(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, app(ty_Maybe, bbb)) → new_esEs6(zxw79000, zxw80000, bbb)
new_ltEs14(Left(zxw79000), Right(zxw80000), gh, ha) → True
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Float) → new_ltEs16(zxw79000, zxw80000)
new_esEs28(zxw4000, zxw3000, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_compare29(zxw79000, zxw80000, app(app(ty_Either, bhf), bhg)) → new_compare15(zxw79000, zxw80000, bhf, bhg)
new_esEs19(zxw79001, zxw80001, ty_Double) → new_esEs16(zxw79001, zxw80001)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_ltEs20(zxw7900, zxw8000, app(app(ty_Either, bab), bac)) → new_ltEs14(zxw7900, zxw8000, bab, bac)
new_asAs(False, zxw230) → False
new_ltEs13(zxw7900, zxw8000) → new_fsEs(new_compare32(zxw7900, zxw8000))
new_ltEs19(zxw7900, zxw8000, app(app(ty_Either, gh), ha)) → new_ltEs14(zxw7900, zxw8000, gh, ha)
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Pos(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_ltEs20(zxw7900, zxw8000, app(ty_[], hg)) → new_ltEs11(zxw7900, zxw8000, hg)
new_compare16(zxw79, zxw80) → new_primCmpInt(zxw79, zxw80)
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_esEs13(:(zxw4000, zxw4001), [], cgf) → False
new_esEs13([], :(zxw3000, zxw3001), cgf) → False
new_compare25(zxw79000, zxw80000, False, ff, fg, fh) → new_compare12(zxw79000, zxw80000, new_ltEs6(zxw79000, zxw80000, ff, fg, fh), ff, fg, fh)
new_esEs7(Right(zxw4000), Right(zxw3000), bcf, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(app(ty_@2, caf), cag), ha) → new_ltEs4(zxw79000, zxw80000, caf, cag)
new_esEs6(Just(zxw4000), Just(zxw3000), app(ty_Maybe, ee)) → new_esEs6(zxw4000, zxw3000, ee)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_@0) → new_esEs10(zxw4000, zxw3000)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(ty_[], cae), ha) → new_ltEs11(zxw79000, zxw80000, cae)
new_esEs7(Left(zxw4000), Left(zxw3000), app(ty_[], bbe), bbd) → new_esEs13(zxw4000, zxw3000, bbe)
new_esEs7(Right(zxw4000), Right(zxw3000), bcf, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_compare31(zxw79000, zxw80000) → new_compare23(zxw79000, zxw80000, new_esEs14(zxw79000, zxw80000))
new_ltEs18(Nothing, Just(zxw80000), hc) → True
new_esEs28(zxw4000, zxw3000, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_ltEs21(zxw79002, zxw80002, ty_Double) → new_ltEs15(zxw79002, zxw80002)
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_ltEs12(True, True) → True
new_esEs23(zxw4000, zxw3000, app(ty_Maybe, cha)) → new_esEs6(zxw4000, zxw3000, cha)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_ltEs14(Right(zxw79000), Right(zxw80000), gh, app(app(ty_Either, ccb), ccc)) → new_ltEs14(zxw79000, zxw80000, ccb, ccc)
new_esEs8(zxw79000, zxw80000, ty_Integer) → new_esEs15(zxw79000, zxw80000)
new_ltEs6(@3(zxw79000, zxw79001, zxw79002), @3(zxw80000, zxw80001, zxw80002), gd, ge, gf) → new_pePe(new_lt19(zxw79000, zxw80000, gd), new_asAs(new_esEs20(zxw79000, zxw80000, gd), new_pePe(new_lt20(zxw79001, zxw80001, ge), new_asAs(new_esEs19(zxw79001, zxw80001, ge), new_ltEs21(zxw79002, zxw80002, gf)))))
new_esEs28(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_lt16(zxw79000, zxw80000) → new_esEs9(new_compare7(zxw79000, zxw80000), LT)
new_esEs23(zxw4000, zxw3000, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Integer, ha) → new_ltEs13(zxw79000, zxw80000)
new_ltEs12(False, True) → True
new_esEs23(zxw4000, zxw3000, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs8(zxw79000, zxw80000, app(ty_Ratio, ce)) → new_esEs18(zxw79000, zxw80000, ce)
new_esEs23(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs14(True, True) → True
new_compare111(zxw79000, zxw80000, False, bbb) → GT
new_esEs27(zxw4001, zxw3001, ty_Bool) → new_esEs14(zxw4001, zxw3001)
new_esEs20(zxw79000, zxw80000, ty_Ordering) → new_esEs9(zxw79000, zxw80000)
new_ltEs19(zxw7900, zxw8000, ty_@0) → new_ltEs8(zxw7900, zxw8000)
new_ltEs14(Right(zxw79000), Right(zxw80000), gh, ty_Int) → new_ltEs9(zxw79000, zxw80000)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(app(ty_Either, cah), cba), ha) → new_ltEs14(zxw79000, zxw80000, cah, cba)
new_lt19(zxw79000, zxw80000, ty_Integer) → new_lt13(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, ty_Float) → new_esEs17(zxw79000, zxw80000)
new_esEs7(Right(zxw4000), Right(zxw3000), bcf, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Ordering, ha) → new_ltEs7(zxw79000, zxw80000)
new_compare11(zxw79000, zxw80000, False) → GT
new_esEs4(@3(zxw4000, zxw4001, zxw4002), @3(zxw3000, zxw3001, zxw3002), dad, dae, daf) → new_asAs(new_esEs28(zxw4000, zxw3000, dad), new_asAs(new_esEs27(zxw4001, zxw3001, dae), new_esEs26(zxw4002, zxw3002, daf)))
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Int) → new_ltEs9(zxw79000, zxw80000)
new_esEs6(Just(zxw4000), Just(zxw3000), app(ty_[], ed)) → new_esEs13(zxw4000, zxw3000, ed)
new_esEs9(EQ, LT) → False
new_esEs9(LT, EQ) → False
new_compare26(Right(zxw7900), Right(zxw8000), False, gb, gc) → new_compare14(zxw7900, zxw8000, new_ltEs20(zxw7900, zxw8000, gc), gb, gc)
new_compare11(zxw79000, zxw80000, True) → LT
new_ltEs5(zxw79001, zxw80001, ty_@0) → new_ltEs8(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, ty_Bool) → new_lt12(zxw79001, zxw80001)
new_compare14(zxw242, zxw243, True, dab, dac) → LT
new_esEs14(False, False) → True
new_esEs18(:%(zxw4000, zxw4001), :%(zxw3000, zxw3001), daa) → new_asAs(new_esEs25(zxw4000, zxw3000, daa), new_esEs24(zxw4001, zxw3001, daa))
new_compare26(Left(zxw7900), Left(zxw8000), False, gb, gc) → new_compare13(zxw7900, zxw8000, new_ltEs19(zxw7900, zxw8000, gb), gb, gc)
new_ltEs19(zxw7900, zxw8000, ty_Double) → new_ltEs15(zxw7900, zxw8000)
new_ltEs7(EQ, LT) → False
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Char) → new_esEs12(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_ltEs7(LT, LT) → True
new_lt20(zxw79001, zxw80001, app(app(app(ty_@3, bed), bee), bef)) → new_lt5(zxw79001, zxw80001, bed, bee, bef)
new_lt14(zxw790, zxw800, gb, gc) → new_esEs9(new_compare15(zxw790, zxw800, gb, gc), LT)
new_esEs22(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_ltEs9(zxw7900, zxw8000) → new_fsEs(new_compare16(zxw7900, zxw8000))
new_compare29(zxw79000, zxw80000, ty_Ordering) → new_compare18(zxw79000, zxw80000)
new_primPlusNat1(Zero, Zero) → Zero
new_esEs26(zxw4002, zxw3002, ty_Ordering) → new_esEs9(zxw4002, zxw3002)
new_esEs19(zxw79001, zxw80001, ty_Integer) → new_esEs15(zxw79001, zxw80001)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Char, ha) → new_ltEs10(zxw79000, zxw80000)
new_asAs(True, zxw230) → zxw230
new_esEs25(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_ltEs7(LT, GT) → True
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Float) → new_esEs17(zxw4000, zxw3000)
new_ltEs5(zxw79001, zxw80001, ty_Float) → new_ltEs16(zxw79001, zxw80001)
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_esEs7(Right(zxw4000), Right(zxw3000), bcf, app(ty_Ratio, bcg)) → new_esEs18(zxw4000, zxw3000, bcg)
new_esEs27(zxw4001, zxw3001, app(ty_[], dcb)) → new_esEs13(zxw4001, zxw3001, dcb)
new_esEs6(Just(zxw4000), Just(zxw3000), app(app(ty_Either, eh), fa)) → new_esEs7(zxw4000, zxw3000, eh, fa)
new_compare28(zxw79000, zxw80000, False, bbb) → new_compare111(zxw79000, zxw80000, new_ltEs18(zxw79000, zxw80000, bbb), bbb)
new_compare1(:(zxw79000, zxw79001), [], gg) → GT
new_esEs28(zxw4000, zxw3000, app(ty_Ratio, ddc)) → new_esEs18(zxw4000, zxw3000, ddc)
new_lt4(zxw79000, zxw80000, ty_Integer) → new_lt13(zxw79000, zxw80000)
new_esEs19(zxw79001, zxw80001, ty_@0) → new_esEs10(zxw79001, zxw80001)
new_compare29(zxw79000, zxw80000, ty_@0) → new_compare30(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), gh, app(ty_Ratio, ccd)) → new_ltEs17(zxw79000, zxw80000, ccd)
new_ltEs19(zxw7900, zxw8000, ty_Integer) → new_ltEs13(zxw7900, zxw8000)
new_ltEs14(Right(zxw79000), Right(zxw80000), gh, ty_Integer) → new_ltEs13(zxw79000, zxw80000)
new_ltEs19(zxw7900, zxw8000, ty_Ordering) → new_ltEs7(zxw7900, zxw8000)
new_compare28(zxw79000, zxw80000, True, bbb) → EQ
new_esEs26(zxw4002, zxw3002, ty_Double) → new_esEs16(zxw4002, zxw3002)
new_compare10(zxw79000, zxw80000, True) → LT
new_esEs19(zxw79001, zxw80001, app(ty_[], beg)) → new_esEs13(zxw79001, zxw80001, beg)
new_compare10(zxw79000, zxw80000, False) → GT
new_esEs9(LT, LT) → True
new_ltEs20(zxw7900, zxw8000, ty_Char) → new_ltEs10(zxw7900, zxw8000)
new_primCompAux00(zxw276, GT) → GT
new_ltEs20(zxw7900, zxw8000, ty_Ordering) → new_ltEs7(zxw7900, zxw8000)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_@0) → new_ltEs8(zxw79000, zxw80000)
new_compare18(zxw79000, zxw80000) → new_compare24(zxw79000, zxw80000, new_esEs9(zxw79000, zxw80000))
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs7(Right(zxw4000), Right(zxw3000), bcf, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_lt19(zxw79000, zxw80000, ty_Char) → new_lt9(zxw79000, zxw80000)
new_esEs28(zxw4000, zxw3000, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_ltEs19(zxw7900, zxw8000, app(ty_Maybe, hc)) → new_ltEs18(zxw7900, zxw8000, hc)
new_esEs27(zxw4001, zxw3001, ty_Integer) → new_esEs15(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, app(ty_Ratio, ceb)) → new_esEs18(zxw4001, zxw3001, ceb)
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_esEs19(zxw79001, zxw80001, ty_Char) → new_esEs12(zxw79001, zxw80001)
new_esEs23(zxw4000, zxw3000, app(ty_[], cgh)) → new_esEs13(zxw4000, zxw3000, cgh)
new_ltEs17(zxw7900, zxw8000, hb) → new_fsEs(new_compare8(zxw7900, zxw8000, hb))
new_not(True) → False
new_ltEs4(@2(zxw79000, zxw79001), @2(zxw80000, zxw80001), bc, bd) → new_pePe(new_lt4(zxw79000, zxw80000, bc), new_asAs(new_esEs8(zxw79000, zxw80000, bc), new_ltEs5(zxw79001, zxw80001, bd)))
new_compare1([], [], gg) → EQ
new_esEs6(Just(zxw4000), Just(zxw3000), app(ty_Ratio, ec)) → new_esEs18(zxw4000, zxw3000, ec)

The set Q consists of the following terms:

new_compare23(x0, x1, True)
new_lt6(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_lt19(x0, x1, ty_Integer)
new_ltEs18(Just(x0), Just(x1), ty_@0)
new_compare16(x0, x1)
new_ltEs18(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs13(:(x0, x1), :(x2, x3), x4)
new_esEs7(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs20(x0, x1, ty_Double)
new_esEs19(x0, x1, ty_Bool)
new_compare30(@0, @0)
new_primCompAux00(x0, GT)
new_lt5(x0, x1, x2, x3, x4)
new_lt19(x0, x1, ty_Char)
new_lt19(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_Int)
new_compare29(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, ty_Ordering)
new_compare17(Char(x0), Char(x1))
new_esEs28(x0, x1, ty_Int)
new_compare27(x0, x1, x2)
new_ltEs21(x0, x1, ty_Ordering)
new_compare12(x0, x1, True, x2, x3, x4)
new_ltEs15(x0, x1)
new_primPlusNat1(Zero, Succ(x0))
new_compare24(x0, x1, False)
new_esEs6(Just(x0), Just(x1), ty_Double)
new_lt20(x0, x1, ty_Char)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs5(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_Bool)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_sr0(Integer(x0), Integer(x1))
new_ltEs14(Right(x0), Right(x1), x2, ty_Double)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs13([], :(x0, x1), x2)
new_compare26(x0, x1, True, x2, x3)
new_ltEs7(EQ, EQ)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs19(x0, x1, ty_Integer)
new_compare14(x0, x1, True, x2, x3)
new_ltEs20(x0, x1, ty_Bool)
new_ltEs14(Right(x0), Right(x1), x2, ty_Ordering)
new_compare110(x0, x1, False, x2, x3)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_ltEs19(x0, x1, ty_Integer)
new_ltEs5(x0, x1, ty_Integer)
new_ltEs7(EQ, LT)
new_ltEs7(LT, EQ)
new_esEs20(x0, x1, ty_Ordering)
new_esEs17(Float(x0, x1), Float(x2, x3))
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_lt19(x0, x1, ty_Ordering)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs16(x0, x1)
new_ltEs18(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_sr(x0, x1)
new_ltEs19(x0, x1, ty_Double)
new_compare7(Float(x0, x1), Float(x2, x3))
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_ltEs14(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs9(x0, x1)
new_esEs6(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_lt7(x0, x1)
new_ltEs5(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Int)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat0(Zero, x0)
new_ltEs7(LT, LT)
new_esEs27(x0, x1, ty_Bool)
new_ltEs18(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_lt4(x0, x1, ty_Ordering)
new_ltEs14(Left(x0), Left(x1), ty_Int, x2)
new_primEqNat0(Zero, Succ(x0))
new_lt19(x0, x1, ty_Int)
new_esEs15(Integer(x0), Integer(x1))
new_esEs26(x0, x1, ty_Int)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Double)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs28(x0, x1, ty_@0)
new_primPlusNat1(Succ(x0), Zero)
new_esEs22(x0, x1, ty_Integer)
new_primMulInt(Neg(x0), Neg(x1))
new_lt4(x0, x1, app(ty_Maybe, x2))
new_esEs7(Left(x0), Left(x1), ty_Float, x2)
new_ltEs19(x0, x1, ty_Int)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_compare29(x0, x1, ty_Integer)
new_esEs14(True, True)
new_esEs21(x0, x1, ty_Char)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Int)
new_ltEs18(Just(x0), Just(x1), ty_Integer)
new_esEs7(Right(x0), Right(x1), x2, ty_Char)
new_esEs24(x0, x1, ty_Int)
new_compare14(x0, x1, False, x2, x3)
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_primEqNat0(Zero, Zero)
new_esEs16(Double(x0, x1), Double(x2, x3))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs12(Char(x0), Char(x1))
new_esEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_lt4(x0, x1, ty_Char)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_compare1(:(x0, x1), :(x2, x3), x4)
new_esEs20(x0, x1, ty_Bool)
new_esEs8(x0, x1, ty_Float)
new_ltEs14(Right(x0), Right(x1), x2, ty_Integer)
new_lt10(x0, x1, x2)
new_ltEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Integer)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_compare111(x0, x1, True, x2)
new_compare28(x0, x1, False, x2)
new_primCompAux00(x0, LT)
new_esEs27(x0, x1, ty_Integer)
new_ltEs14(Right(x0), Right(x1), x2, ty_Float)
new_ltEs5(x0, x1, ty_Double)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs7(Right(x0), Right(x1), x2, ty_Double)
new_ltEs18(Just(x0), Just(x1), ty_Char)
new_ltEs14(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_primMulNat0(Zero, Zero)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_compare1(:(x0, x1), [], x2)
new_lt9(x0, x1)
new_compare29(x0, x1, ty_Double)
new_ltEs5(x0, x1, ty_@0)
new_compare29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare29(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Right(x0), Right(x1), x2, ty_Bool)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs8(x0, x1, app(app(ty_@2, x2), x3))
new_lt4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_ltEs14(Right(x0), Right(x1), x2, ty_@0)
new_esEs8(x0, x1, ty_Ordering)
new_esEs6(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_compare10(x0, x1, True)
new_esEs22(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, ty_Ordering)
new_primEqNat0(Succ(x0), Succ(x1))
new_ltEs19(x0, x1, ty_Bool)
new_esEs28(x0, x1, ty_Double)
new_ltEs20(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_@0)
new_pePe(True, x0)
new_esEs19(x0, x1, ty_Float)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_primCmpNat2(Zero, Succ(x0))
new_compare25(x0, x1, False, x2, x3, x4)
new_primMulNat0(Zero, Succ(x0))
new_lt16(x0, x1)
new_compare29(x0, x1, ty_Bool)
new_lt4(x0, x1, app(app(ty_Either, x2), x3))
new_compare11(x0, x1, True)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1, ty_@0)
new_esEs6(Just(x0), Just(x1), ty_Ordering)
new_esEs23(x0, x1, ty_@0)
new_ltEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs5(x0, x1, ty_Char)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_ltEs21(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Float)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_compare29(x0, x1, ty_Ordering)
new_ltEs21(x0, x1, ty_@0)
new_esEs8(x0, x1, ty_Int)
new_ltEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs12(False, False)
new_esEs6(Just(x0), Just(x1), ty_Bool)
new_compare32(Integer(x0), Integer(x1))
new_esEs21(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_Int)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_primMulNat0(Succ(x0), Succ(x1))
new_ltEs21(x0, x1, ty_Integer)
new_compare29(x0, x1, ty_Float)
new_esEs7(Right(x0), Right(x1), x2, ty_Bool)
new_esEs6(Just(x0), Just(x1), ty_Float)
new_ltEs5(x0, x1, ty_Float)
new_ltEs5(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, app(ty_[], x2))
new_ltEs18(Just(x0), Just(x1), ty_Float)
new_esEs26(x0, x1, ty_Bool)
new_primCmpNat1(Zero, x0)
new_ltEs8(x0, x1)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primPlusNat1(Zero, Zero)
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Double)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_compare210(x0, x1, True, x2, x3)
new_primCmpNat2(Zero, Zero)
new_ltEs18(Just(x0), Just(x1), ty_Ordering)
new_esEs7(Left(x0), Left(x1), ty_Int, x2)
new_ltEs5(x0, x1, ty_Bool)
new_esEs13(:(x0, x1), [], x2)
new_ltEs14(Left(x0), Left(x1), ty_Char, x2)
new_asAs(False, x0)
new_ltEs20(x0, x1, ty_Char)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_compare26(Right(x0), Right(x1), False, x2, x3)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs8(x0, x1, ty_Integer)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs18(Just(x0), Just(x1), ty_Bool)
new_ltEs14(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_esEs19(x0, x1, app(ty_[], x2))
new_primCmpNat1(Succ(x0), x1)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, ty_Integer)
new_lt4(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_@0)
new_ltEs14(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_lt4(x0, x1, ty_Float)
new_esEs19(x0, x1, ty_Char)
new_ltEs14(Right(x0), Left(x1), x2, x3)
new_ltEs14(Left(x0), Right(x1), x2, x3)
new_lt4(x0, x1, ty_Double)
new_esEs19(x0, x1, ty_Ordering)
new_esEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs10(@0, @0)
new_esEs8(x0, x1, app(ty_Maybe, x2))
new_esEs11(x0, x1)
new_ltEs14(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs20(x0, x1, ty_Float)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs9(GT, GT)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs27(x0, x1, ty_Char)
new_compare11(x0, x1, False)
new_compare23(x0, x1, False)
new_compare13(x0, x1, False, x2, x3)
new_esEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt18(x0, x1, x2)
new_esEs28(x0, x1, ty_Bool)
new_compare24(x0, x1, True)
new_ltEs19(x0, x1, app(ty_[], x2))
new_primEqNat0(Succ(x0), Zero)
new_esEs23(x0, x1, ty_Ordering)
new_primPlusNat1(Succ(x0), Succ(x1))
new_ltEs14(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Int)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs7(Left(x0), Left(x1), ty_Char, x2)
new_esEs21(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Integer)
new_esEs23(x0, x1, ty_Int)
new_esEs13([], [], x0)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs14(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_lt4(x0, x1, ty_@0)
new_esEs23(x0, x1, ty_Char)
new_esEs28(x0, x1, ty_Ordering)
new_esEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs18(Just(x0), Just(x1), ty_Double)
new_ltEs20(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_@0)
new_esEs9(EQ, EQ)
new_pePe(False, x0)
new_esEs6(Nothing, Nothing, x0)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Just(x0), Just(x1), ty_Char)
new_esEs25(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Integer)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs6(Just(x0), Just(x1), app(ty_[], x2))
new_compare19(x0, x1, x2, x3)
new_primCompAux00(x0, EQ)
new_esEs19(x0, x1, ty_Int)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs14(True, False)
new_esEs14(False, True)
new_lt4(x0, x1, ty_Integer)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_fsEs(x0)
new_esEs7(Left(x0), Left(x1), ty_@0, x2)
new_esEs22(x0, x1, ty_Float)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs21(x0, x1, app(ty_[], x2))
new_lt4(x0, x1, ty_Bool)
new_primCmpNat2(Succ(x0), Succ(x1))
new_esEs7(Right(x0), Right(x1), x2, ty_Float)
new_asAs(True, x0)
new_ltEs14(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_compare9(x0, x1, x2, x3, x4)
new_esEs21(x0, x1, ty_Bool)
new_esEs6(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare13(x0, x1, True, x2, x3)
new_compare25(x0, x1, True, x2, x3, x4)
new_esEs7(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs21(x0, x1, app(ty_Maybe, x2))
new_esEs8(x0, x1, ty_Char)
new_lt19(x0, x1, ty_Float)
new_compare111(x0, x1, False, x2)
new_esEs22(x0, x1, ty_@0)
new_esEs8(x0, x1, app(ty_Ratio, x2))
new_esEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs20(x0, x1, ty_Char)
new_ltEs12(False, True)
new_ltEs12(True, False)
new_compare6(Double(x0, x1), Double(x2, x3))
new_ltEs20(x0, x1, ty_@0)
new_esEs22(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_@0)
new_ltEs11(x0, x1, x2)
new_lt19(x0, x1, ty_Double)
new_lt19(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_Char)
new_ltEs5(x0, x1, ty_Int)
new_compare12(x0, x1, False, x2, x3, x4)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, ty_Double)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs19(x0, x1, ty_@0)
new_ltEs21(x0, x1, ty_Bool)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs21(x0, x1, ty_Double)
new_compare110(x0, x1, True, x2, x3)
new_lt17(x0, x1, x2)
new_lt12(x0, x1)
new_esEs6(Just(x0), Nothing, x1)
new_ltEs18(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs8(x0, x1, ty_Bool)
new_ltEs21(x0, x1, ty_Char)
new_lt13(x0, x1)
new_lt4(x0, x1, app(ty_[], x2))
new_compare15(x0, x1, x2, x3)
new_ltEs14(Right(x0), Right(x1), x2, ty_Int)
new_esEs6(Nothing, Just(x0), x1)
new_esEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_compare10(x0, x1, False)
new_primMulNat0(Succ(x0), Zero)
new_ltEs19(x0, x1, ty_Float)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_Float)
new_compare29(x0, x1, ty_Int)
new_esEs22(x0, x1, ty_Int)
new_compare1([], :(x0, x1), x2)
new_compare1([], [], x0)
new_esEs20(x0, x1, ty_Int)
new_esEs8(x0, x1, app(ty_[], x2))
new_ltEs14(Left(x0), Left(x1), ty_Float, x2)
new_esEs21(x0, x1, ty_Float)
new_esEs6(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_compare31(x0, x1)
new_esEs6(Just(x0), Just(x1), ty_Int)
new_ltEs7(LT, GT)
new_ltEs7(GT, LT)
new_esEs21(x0, x1, ty_Integer)
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs18(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs18(Nothing, Nothing, x0)
new_esEs22(x0, x1, ty_Double)
new_esEs26(x0, x1, app(ty_[], x2))
new_primCompAux0(x0, x1, x2, x3)
new_ltEs13(x0, x1)
new_compare29(x0, x1, app(app(ty_@2, x2), x3))
new_lt4(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Float)
new_not(True)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs20(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Float)
new_ltEs17(x0, x1, x2)
new_compare28(x0, x1, True, x2)
new_esEs28(x0, x1, ty_Char)
new_esEs6(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Ordering)
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs7(Right(x0), Right(x1), x2, ty_@0)
new_esEs6(Just(x0), Just(x1), ty_Integer)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_not(False)
new_lt8(x0, x1)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt4(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs20(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, ty_Char)
new_esEs4(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Integer)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primMulInt(Pos(x0), Pos(x1))
new_esEs22(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(x0, x1, ty_@0)
new_ltEs18(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs20(x0, x1, app(ty_[], x2))
new_ltEs12(True, True)
new_lt15(x0, x1)
new_esEs27(x0, x1, ty_Float)
new_esEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_lt14(x0, x1, x2, x3)
new_esEs26(x0, x1, ty_Ordering)
new_esEs18(:%(x0, x1), :%(x2, x3), x4)
new_esEs27(x0, x1, ty_Double)
new_ltEs18(Just(x0), Nothing, x1)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_lt20(x0, x1, ty_Ordering)
new_compare29(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, ty_Char)
new_lt20(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Bool)
new_esEs7(Left(x0), Left(x1), ty_Double, x2)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_ltEs21(x0, x1, ty_Float)
new_compare29(x0, x1, app(ty_[], x2))
new_ltEs10(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs14(Left(x0), Left(x1), ty_Integer, x2)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs5(x0, x1, ty_Ordering)
new_compare26(Left(x0), Right(x1), False, x2, x3)
new_compare26(Right(x0), Left(x1), False, x2, x3)
new_ltEs14(Left(x0), Left(x1), ty_Bool, x2)
new_esEs8(x0, x1, ty_Double)
new_compare29(x0, x1, ty_Char)
new_ltEs18(Nothing, Just(x0), x1)
new_esEs6(Just(x0), Just(x1), ty_@0)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs7(Right(x0), Left(x1), x2, x3)
new_esEs7(Left(x0), Right(x1), x2, x3)
new_lt11(x0, x1, x2, x3)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs14(Left(x0), Left(x1), ty_@0, x2)
new_esEs8(x0, x1, app(app(ty_Either, x2), x3))
new_esEs19(x0, x1, ty_Double)
new_esEs14(False, False)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Zero), Pos(Zero))
new_compare210(x0, x1, False, x2, x3)
new_ltEs21(x0, x1, ty_Double)
new_primCmpNat2(Succ(x0), Zero)
new_esEs7(Right(x0), Right(x1), x2, ty_Int)
new_compare18(x0, x1)
new_esEs27(x0, x1, app(ty_[], x2))
new_compare26(Left(x0), Left(x1), False, x2, x3)
new_ltEs18(Just(x0), Just(x1), ty_Int)
new_ltEs21(x0, x1, app(ty_Ratio, x2))
new_primPlusNat0(Succ(x0), x1)
new_ltEs5(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, ty_Integer)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primCmpNat0(x0, Zero)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs7(GT, EQ)
new_ltEs7(EQ, GT)
new_ltEs7(GT, GT)
new_ltEs5(x0, x1, app(ty_Ratio, x2))
new_esEs9(LT, LT)
new_esEs8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare29(x0, x1, ty_@0)
new_ltEs14(Left(x0), Left(x1), ty_Double, x2)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(Right(x0), Right(x1), x2, ty_Char)
new_primCmpNat0(x0, Succ(x1))
new_esEs27(x0, x1, ty_Ordering)

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

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



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

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

new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_lt8(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), h, ba, bb)
new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), zxw193, h, ba, bb)
new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, zxw1074, Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb)
new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb) → new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_lt8(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), h, ba, bb)

The TRS R consists of the following rules:

new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Pos(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_compare16(zxw79, zxw80) → new_primCmpInt(zxw79, zxw80)
new_esEs9(GT, LT) → False
new_esEs9(LT, GT) → False
new_primMulInt(Neg(zxw40000), Neg(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primCmpNat2(Zero, Zero) → EQ
new_primPlusNat1(Zero, Zero) → Zero
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_sr(zxw4000, zxw3000) → new_primMulInt(zxw4000, zxw3000)
new_lt8(zxw790, zxw800) → new_esEs9(new_compare16(zxw790, zxw800), LT)
new_primCmpNat0(zxw7900, Zero) → GT
new_primMulNat0(Zero, Zero) → Zero
new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb) → new_sizeFM0(Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), h, ba, bb)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb) → new_sizeFM(zxw190, zxw191, zxw192, zxw193, zxw194, h, ba, bb)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_esEs9(GT, EQ) → False
new_esEs9(EQ, GT) → False
new_esEs9(EQ, EQ) → True
new_sizeFM0(EmptyFM, bc, bd, be) → Pos(Zero)
new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_esEs9(GT, GT) → True
new_esEs9(LT, LT) → True
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), bc, bd, be) → zxw542
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, bc, bd, be) → zxw52
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_esEs9(EQ, LT) → False
new_esEs9(LT, EQ) → False
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_compare16(x0, x1)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_sizeFM0(EmptyFM, x0, x1, x2)
new_sr(x0, x1)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_lt8(x0, x1)
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

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

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

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

new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_lt8(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), h, ba, bb)
new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), zxw193, h, ba, bb)
new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, zxw1074, Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb)
new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb) → new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_lt8(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), h, ba, bb)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb) → new_sizeFM0(Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), h, ba, bb)
new_sr(zxw4000, zxw3000) → new_primMulInt(zxw4000, zxw3000)
new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb) → new_sizeFM(zxw190, zxw191, zxw192, zxw193, zxw194, h, ba, bb)
new_lt8(zxw790, zxw800) → new_esEs9(new_compare16(zxw790, zxw800), LT)
new_compare16(zxw79, zxw80) → new_primCmpInt(zxw79, zxw80)
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, bc, bd, be) → zxw52
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Pos(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Neg(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), bc, bd, be) → zxw542

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_compare16(x0, x1)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_sizeFM0(EmptyFM, x0, x1, x2)
new_sr(x0, x1)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_lt8(x0, x1)
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_lt8(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), h, ba, bb) at position [12] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_compare16(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), LT), h, ba, bb)



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

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

new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), zxw193, h, ba, bb)
new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_compare16(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, zxw1074, Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb)
new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb) → new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_lt8(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), h, ba, bb)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb) → new_sizeFM0(Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), h, ba, bb)
new_sr(zxw4000, zxw3000) → new_primMulInt(zxw4000, zxw3000)
new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb) → new_sizeFM(zxw190, zxw191, zxw192, zxw193, zxw194, h, ba, bb)
new_lt8(zxw790, zxw800) → new_esEs9(new_compare16(zxw790, zxw800), LT)
new_compare16(zxw79, zxw80) → new_primCmpInt(zxw79, zxw80)
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, bc, bd, be) → zxw52
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Pos(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Neg(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), bc, bd, be) → zxw542

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_compare16(x0, x1)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_sizeFM0(EmptyFM, x0, x1, x2)
new_sr(x0, x1)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_lt8(x0, x1)
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb) → new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_lt8(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), h, ba, bb) at position [12] we obtained the following new rules:

new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb) → new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_compare16(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), LT), h, ba, bb)



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

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

new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), zxw193, h, ba, bb)
new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_compare16(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, zxw1074, Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb)
new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb) → new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_compare16(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb) → new_sizeFM0(Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), h, ba, bb)
new_sr(zxw4000, zxw3000) → new_primMulInt(zxw4000, zxw3000)
new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb) → new_sizeFM(zxw190, zxw191, zxw192, zxw193, zxw194, h, ba, bb)
new_lt8(zxw790, zxw800) → new_esEs9(new_compare16(zxw790, zxw800), LT)
new_compare16(zxw79, zxw80) → new_primCmpInt(zxw79, zxw80)
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, bc, bd, be) → zxw52
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Pos(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Neg(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), bc, bd, be) → zxw542

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_compare16(x0, x1)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_sizeFM0(EmptyFM, x0, x1, x2)
new_sr(x0, x1)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_lt8(x0, x1)
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

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

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

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

new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), zxw193, h, ba, bb)
new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_compare16(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, zxw1074, Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb)
new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb) → new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_compare16(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb) → new_sizeFM(zxw190, zxw191, zxw192, zxw193, zxw194, h, ba, bb)
new_sr(zxw4000, zxw3000) → new_primMulInt(zxw4000, zxw3000)
new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb) → new_sizeFM0(Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), h, ba, bb)
new_compare16(zxw79, zxw80) → new_primCmpInt(zxw79, zxw80)
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), bc, bd, be) → zxw542
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Pos(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Neg(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, bc, bd, be) → zxw52

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_compare16(x0, x1)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_sizeFM0(EmptyFM, x0, x1, x2)
new_sr(x0, x1)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_lt8(x0, x1)
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(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_lt8(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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ 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_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), zxw193, h, ba, bb)
new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_compare16(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, zxw1074, Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb)
new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb) → new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_compare16(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb) → new_sizeFM(zxw190, zxw191, zxw192, zxw193, zxw194, h, ba, bb)
new_sr(zxw4000, zxw3000) → new_primMulInt(zxw4000, zxw3000)
new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb) → new_sizeFM0(Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), h, ba, bb)
new_compare16(zxw79, zxw80) → new_primCmpInt(zxw79, zxw80)
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), bc, bd, be) → zxw542
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Pos(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Neg(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, bc, bd, be) → zxw52

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_compare16(x0, x1)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_sizeFM0(EmptyFM, x0, x1, x2)
new_sr(x0, x1)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_compare16(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), LT), h, ba, bb) at position [12,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), LT), h, ba, bb)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ 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_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), zxw193, h, ba, bb)
new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, zxw1074, Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb)
new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb) → new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_compare16(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb) → new_sizeFM(zxw190, zxw191, zxw192, zxw193, zxw194, h, ba, bb)
new_sr(zxw4000, zxw3000) → new_primMulInt(zxw4000, zxw3000)
new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb) → new_sizeFM0(Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), h, ba, bb)
new_compare16(zxw79, zxw80) → new_primCmpInt(zxw79, zxw80)
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), bc, bd, be) → zxw542
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Pos(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Neg(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, bc, bd, be) → zxw52

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_compare16(x0, x1)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_sizeFM0(EmptyFM, x0, x1, x2)
new_sr(x0, x1)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb) → new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_compare16(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), LT), h, ba, bb) at position [12,0] we obtained the following new rules:

new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb) → new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), LT), h, ba, bb)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ 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_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), zxw193, h, ba, bb)
new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, zxw1074, Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb)
new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb) → new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb) → new_sizeFM(zxw190, zxw191, zxw192, zxw193, zxw194, h, ba, bb)
new_sr(zxw4000, zxw3000) → new_primMulInt(zxw4000, zxw3000)
new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb) → new_sizeFM0(Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), h, ba, bb)
new_compare16(zxw79, zxw80) → new_primCmpInt(zxw79, zxw80)
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), bc, bd, be) → zxw542
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Pos(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Neg(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, bc, bd, be) → zxw52

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_compare16(x0, x1)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_sizeFM0(EmptyFM, x0, x1, x2)
new_sr(x0, x1)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

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

↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ 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_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), zxw193, h, ba, bb)
new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, zxw1074, Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb)
new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb) → new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb) → new_sizeFM(zxw190, zxw191, zxw192, zxw193, zxw194, h, ba, bb)
new_sr(zxw4000, zxw3000) → new_primMulInt(zxw4000, zxw3000)
new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb) → new_sizeFM0(Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), h, ba, bb)
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), bc, bd, be) → zxw542
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Pos(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Neg(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, bc, bd, be) → zxw52

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_compare16(x0, x1)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_sizeFM0(EmptyFM, x0, x1, x2)
new_sr(x0, x1)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ 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_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), zxw193, h, ba, bb)
new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, zxw1074, Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb)
new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb) → new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb) → new_sizeFM(zxw190, zxw191, zxw192, zxw193, zxw194, h, ba, bb)
new_sr(zxw4000, zxw3000) → new_primMulInt(zxw4000, zxw3000)
new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb) → new_sizeFM0(Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), h, ba, bb)
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), bc, bd, be) → zxw542
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Pos(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Neg(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, bc, bd, be) → zxw52

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_sizeFM0(EmptyFM, x0, x1, x2)
new_sr(x0, x1)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb) → new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), LT), h, ba, bb) at position [12,0,0] we obtained the following new rules:

new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb) → new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), LT), h, ba, bb)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ 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_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), zxw193, h, ba, bb)
new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, zxw1074, Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb)
new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb) → new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb) → new_sizeFM(zxw190, zxw191, zxw192, zxw193, zxw194, h, ba, bb)
new_sr(zxw4000, zxw3000) → new_primMulInt(zxw4000, zxw3000)
new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb) → new_sizeFM0(Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), h, ba, bb)
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), bc, bd, be) → zxw542
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Pos(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Neg(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, bc, bd, be) → zxw52

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_sizeFM0(EmptyFM, x0, x1, x2)
new_sr(x0, x1)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), LT), h, ba, bb) at position [12,0,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), LT), h, ba, bb)



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

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

new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), zxw193, h, ba, bb)
new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, zxw1074, Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb)
new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb) → new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb) → new_sizeFM(zxw190, zxw191, zxw192, zxw193, zxw194, h, ba, bb)
new_sr(zxw4000, zxw3000) → new_primMulInt(zxw4000, zxw3000)
new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb) → new_sizeFM0(Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), h, ba, bb)
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), bc, bd, be) → zxw542
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Pos(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Neg(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, bc, bd, be) → zxw52

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_sizeFM0(EmptyFM, x0, x1, x2)
new_sr(x0, x1)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

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

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

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

new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), zxw193, h, ba, bb)
new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, zxw1074, Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb)
new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb) → new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb) → new_sizeFM0(Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), h, ba, bb)
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Pos(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Neg(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb) → new_sizeFM(zxw190, zxw191, zxw192, zxw193, zxw194, h, ba, bb)
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, bc, bd, be) → zxw52
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), bc, bd, be) → zxw542

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_sizeFM0(EmptyFM, x0, x1, x2)
new_sr(x0, x1)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(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_sr(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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ UsableRulesProof
                                                  ↳ QDP
                                                    ↳ QReductionProof
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), zxw193, h, ba, bb)
new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, zxw1074, Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb)
new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb) → new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb) → new_sizeFM0(Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), h, ba, bb)
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Pos(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Neg(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb) → new_sizeFM(zxw190, zxw191, zxw192, zxw193, zxw194, h, ba, bb)
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, bc, bd, be) → zxw52
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), bc, bd, be) → zxw542

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_sizeFM0(EmptyFM, x0, x1, x2)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), LT), h, ba, bb) at position [12,0,0,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), LT), h, ba, bb)



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

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

new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), zxw193, h, ba, bb)
new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, zxw1074, Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb)
new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb) → new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb) → new_sizeFM0(Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), h, ba, bb)
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Pos(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Neg(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb) → new_sizeFM(zxw190, zxw191, zxw192, zxw193, zxw194, h, ba, bb)
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, bc, bd, be) → zxw52
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), bc, bd, be) → zxw542

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_sizeFM0(EmptyFM, x0, x1, x2)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb) → new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), LT), h, ba, bb) at position [12,0,0,0] we obtained the following new rules:

new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb) → new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), LT), h, ba, bb)



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

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

new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), zxw193, h, ba, bb)
new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, zxw1074, Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb)
new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb) → new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb) → new_sizeFM0(Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), h, ba, bb)
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Pos(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Neg(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb) → new_sizeFM(zxw190, zxw191, zxw192, zxw193, zxw194, h, ba, bb)
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, bc, bd, be) → zxw52
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), bc, bd, be) → zxw542

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_sizeFM0(EmptyFM, x0, x1, x2)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

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

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

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

new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), zxw193, h, ba, bb)
new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, zxw1074, Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb)
new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb) → new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb) → new_sizeFM0(Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), h, ba, bb)
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb) → new_sizeFM(zxw190, zxw191, zxw192, zxw193, zxw194, h, ba, bb)
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, bc, bd, be) → zxw52
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), bc, bd, be) → zxw542

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_sizeFM0(EmptyFM, x0, x1, x2)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sIZE_RATIO
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ UsableRulesProof
                                                  ↳ QDP
                                                    ↳ QReductionProof
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ UsableRulesProof
                                                                                                  ↳ QDP
                                                                                                    ↳ QReductionProof
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), zxw193, h, ba, bb)
new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, zxw1074, Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb)
new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb) → new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb) → new_sizeFM0(Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), h, ba, bb)
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb) → new_sizeFM(zxw190, zxw191, zxw192, zxw193, zxw194, h, ba, bb)
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, bc, bd, be) → zxw52
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), bc, bd, be) → zxw542

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_sizeFM0(EmptyFM, x0, x1, x2)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), LT), h, ba, bb) at position [12,0,0,1] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(zxw190, zxw191, zxw192, zxw193, zxw194, h, ba, bb)), new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), LT), h, ba, bb)



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

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

new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(zxw190, zxw191, zxw192, zxw193, zxw194, h, ba, bb)), new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), zxw193, h, ba, bb)
new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, zxw1074, Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb)
new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb) → new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb) → new_sizeFM0(Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), h, ba, bb)
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb) → new_sizeFM(zxw190, zxw191, zxw192, zxw193, zxw194, h, ba, bb)
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, bc, bd, be) → zxw52
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), bc, bd, be) → zxw542

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_sizeFM0(EmptyFM, x0, x1, x2)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb) → new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), LT), h, ba, bb) at position [12,0,0,1] we obtained the following new rules:

new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb) → new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM0(Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), h, ba, bb)), new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), LT), h, ba, bb)



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

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

new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb) → new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM0(Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), h, ba, bb)), new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(zxw190, zxw191, zxw192, zxw193, zxw194, h, ba, bb)), new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), zxw193, h, ba, bb)
new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, zxw1074, Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb)

The TRS R consists of the following rules:

new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb) → new_sizeFM0(Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), h, ba, bb)
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb) → new_sizeFM(zxw190, zxw191, zxw192, zxw193, zxw194, h, ba, bb)
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, bc, bd, be) → zxw52
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), bc, bd, be) → zxw542

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_sizeFM0(EmptyFM, x0, x1, x2)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(zxw190, zxw191, zxw192, zxw193, zxw194, h, ba, bb)), new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), LT), h, ba, bb) at position [12,0,0,1] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw192), new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), LT), h, ba, bb)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ UsableRulesProof
                                                  ↳ QDP
                                                    ↳ QReductionProof
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ 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_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb) → new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM0(Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), h, ba, bb)), new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), zxw193, h, ba, bb)
new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, zxw1074, Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb)
new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw192), new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb) → new_sizeFM0(Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), h, ba, bb)
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb) → new_sizeFM(zxw190, zxw191, zxw192, zxw193, zxw194, h, ba, bb)
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, bc, bd, be) → zxw52
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), bc, bd, be) → zxw542

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_sizeFM0(EmptyFM, x0, x1, x2)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb) → new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM0(Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), h, ba, bb)), new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), LT), h, ba, bb) at position [12,0,0,1] we obtained the following new rules:

new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb) → new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw1072), new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), LT), h, ba, bb)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ UsableRulesProof
                                                  ↳ QDP
                                                    ↳ QReductionProof
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ 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_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), zxw193, h, ba, bb)
new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, zxw1074, Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb)
new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw192), new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb) → new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw1072), new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb) → new_sizeFM0(Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), h, ba, bb)
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb) → new_sizeFM(zxw190, zxw191, zxw192, zxw193, zxw194, h, ba, bb)
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, bc, bd, be) → zxw52
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), bc, bd, be) → zxw542

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_sizeFM0(EmptyFM, x0, x1, x2)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw192), new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), LT), h, ba, bb) at position [12,0,1] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw192), new_sizeFM0(Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), h, ba, bb)), LT), h, ba, bb)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ UsableRulesProof
                                                  ↳ QDP
                                                    ↳ QReductionProof
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ UsableRulesProof
                                                                                                  ↳ QDP
                                                                                                    ↳ QReductionProof
                                                                                                      ↳ 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_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw192), new_sizeFM0(Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), zxw193, h, ba, bb)
new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, zxw1074, Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb)
new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb) → new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw1072), new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb) → new_sizeFM0(Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), h, ba, bb)
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb) → new_sizeFM(zxw190, zxw191, zxw192, zxw193, zxw194, h, ba, bb)
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, bc, bd, be) → zxw52
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), bc, bd, be) → zxw542

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_sizeFM0(EmptyFM, x0, x1, x2)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

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

↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ UsableRulesProof
                                                  ↳ QDP
                                                    ↳ QReductionProof
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ UsableRulesProof
                                                                                                  ↳ QDP
                                                                                                    ↳ QReductionProof
                                                                                                      ↳ 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_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw192), new_sizeFM0(Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), zxw193, h, ba, bb)
new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, zxw1074, Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb)
new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb) → new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw1072), new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb) → new_sizeFM(zxw190, zxw191, zxw192, zxw193, zxw194, h, ba, bb)
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, bc, bd, be) → zxw52
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), bc, bd, be) → zxw542

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_sizeFM0(EmptyFM, x0, x1, x2)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(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_l(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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ UsableRulesProof
                                                  ↳ QDP
                                                    ↳ QReductionProof
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ UsableRulesProof
                                                                                                  ↳ QDP
                                                                                                    ↳ QReductionProof
                                                                                                      ↳ 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_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), zxw193, h, ba, bb)
new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw192), new_sizeFM0(Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, zxw1074, Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb)
new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb) → new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw1072), new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb) → new_sizeFM(zxw190, zxw191, zxw192, zxw193, zxw194, h, ba, bb)
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, bc, bd, be) → zxw52
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), bc, bd, be) → zxw542

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_sizeFM0(EmptyFM, x0, x1, x2)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw192), new_sizeFM0(Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), h, ba, bb)), LT), h, ba, bb) at position [12,0,1] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw192), zxw1072), LT), h, ba, bb)



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

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

new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), zxw193, h, ba, bb)
new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, zxw1074, Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb)
new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw192), zxw1072), LT), h, ba, bb)
new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb) → new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw1072), new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb) → new_sizeFM(zxw190, zxw191, zxw192, zxw193, zxw194, h, ba, bb)
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, bc, bd, be) → zxw52
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), bc, bd, be) → zxw542

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_sizeFM0(EmptyFM, x0, x1, x2)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

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

↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ UsableRulesProof
                                                  ↳ QDP
                                                    ↳ QReductionProof
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ UsableRulesProof
                                                                                                  ↳ QDP
                                                                                                    ↳ QReductionProof
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ 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_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), zxw193, h, ba, bb)
new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, zxw1074, Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb)
new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw192), zxw1072), LT), h, ba, bb)
new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb) → new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw1072), new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb) → new_sizeFM(zxw190, zxw191, zxw192, zxw193, zxw194, h, ba, bb)
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, bc, bd, be) → zxw52
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_sizeFM0(EmptyFM, x0, x1, x2)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(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_sizeFM0(EmptyFM, x0, x1, x2)
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)



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

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

new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), zxw193, h, ba, bb)
new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, zxw1074, Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb)
new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw192), zxw1072), LT), h, ba, bb)
new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb) → new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw1072), new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb) → new_sizeFM(zxw190, zxw191, zxw192, zxw193, zxw194, h, ba, bb)
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, bc, bd, be) → zxw52
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb) → new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw1072), new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb)), LT), h, ba, bb) at position [12,0,1] we obtained the following new rules:

new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb) → new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw1072), new_sizeFM(zxw190, zxw191, zxw192, zxw193, zxw194, h, ba, bb)), LT), h, ba, bb)



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

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

new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), zxw193, h, ba, bb)
new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, zxw1074, Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb)
new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb) → new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw1072), new_sizeFM(zxw190, zxw191, zxw192, zxw193, zxw194, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw192), zxw1072), LT), h, ba, bb)

The TRS R consists of the following rules:

new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, h, ba, bb) → new_sizeFM(zxw190, zxw191, zxw192, zxw193, zxw194, h, ba, bb)
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, bc, bd, be) → zxw52
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

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

↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ UsableRulesProof
                                                  ↳ QDP
                                                    ↳ QReductionProof
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ UsableRulesProof
                                                                                                  ↳ QDP
                                                                                                    ↳ QReductionProof
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ UsableRulesProof
                                                                                                                              ↳ QDP
                                                                                                                                ↳ QReductionProof
                                                                                                                                  ↳ 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_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), zxw193, h, ba, bb)
new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, zxw1074, Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb)
new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb) → new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw1072), new_sizeFM(zxw190, zxw191, zxw192, zxw193, zxw194, h, ba, bb)), LT), h, ba, bb)
new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw192), zxw1072), LT), h, ba, bb)

The TRS R consists of the following rules:

new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, bc, bd, be) → zxw52

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(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, 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ UsableRulesProof
                                                  ↳ QDP
                                                    ↳ QReductionProof
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ UsableRulesProof
                                                                                                  ↳ QDP
                                                                                                    ↳ QReductionProof
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ UsableRulesProof
                                                                                                                              ↳ QDP
                                                                                                                                ↳ QReductionProof
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ UsableRulesProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ QReductionProof
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ UsableRulesProof
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ QReductionProof
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), zxw193, h, ba, bb)
new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, zxw1074, Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb)
new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw192), zxw1072), LT), h, ba, bb)
new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb) → new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw1072), new_sizeFM(zxw190, zxw191, zxw192, zxw193, zxw194, h, ba, bb)), LT), h, ba, bb)

The TRS R consists of the following rules:

new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, bc, bd, be) → zxw52

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb) → new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw1072), new_sizeFM(zxw190, zxw191, zxw192, zxw193, zxw194, h, ba, bb)), LT), h, ba, bb) at position [12,0,1] we obtained the following new rules:

new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb) → new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw1072), zxw192), LT), h, ba, bb)



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

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

new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), zxw193, h, ba, bb)
new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, zxw1074, Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb)
new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw192), zxw1072), LT), h, ba, bb)
new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb) → new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw1072), zxw192), LT), h, ba, bb)

The TRS R consists of the following rules:

new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, bc, bd, be) → zxw52

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

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

↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ UsableRulesProof
                                                  ↳ QDP
                                                    ↳ QReductionProof
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ UsableRulesProof
                                                                                                  ↳ QDP
                                                                                                    ↳ QReductionProof
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ UsableRulesProof
                                                                                                                              ↳ QDP
                                                                                                                                ↳ QReductionProof
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ UsableRulesProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ QReductionProof
                                                                                                                                              ↳ 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_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), zxw193, h, ba, bb)
new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, zxw1074, Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb)
new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw192), zxw1072), LT), h, ba, bb)
new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb) → new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw1072), zxw192), LT), h, ba, bb)

The TRS R consists of the following rules:

new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(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, x7)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ UsableRulesProof
                                                  ↳ QDP
                                                    ↳ QReductionProof
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ UsableRulesProof
                                                                                                  ↳ QDP
                                                                                                    ↳ QReductionProof
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ UsableRulesProof
                                                                                                                              ↳ QDP
                                                                                                                                ↳ QReductionProof
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ UsableRulesProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ QReductionProof
                                                                                                                                              ↳ 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_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), zxw193, h, ba, bb)
new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, zxw1074, Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb)
new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw192), zxw1072), LT), h, ba, bb)
new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb) → new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw1072), zxw192), LT), h, ba, bb)

The TRS R consists of the following rules:

new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)

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


The following pairs can be oriented strictly and are deleted.


new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb) → new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw1072), zxw192), LT), h, ba, bb)
The remaining pairs can at least be oriented weakly.

new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), zxw193, h, ba, bb)
new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, zxw1074, Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb)
new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw192), zxw1072), LT), h, ba, bb)
Used ordering: Polynomial interpretation [25]:

POL(Branch(x1, x2, x3, x4, x5)) = 1 + x1 + x2 + x4 + x5   
POL(EQ) = 0   
POL(False) = 0   
POL(GT) = 0   
POL(LT) = 0   
POL(Neg(x1)) = 0   
POL(Pos(x1)) = 0   
POL(Succ(x1)) = 0   
POL(True) = 0   
POL(Zero) = 0   
POL(new_esEs9(x1, x2)) = 0   
POL(new_mkVBalBranch0(x1, x2, x3, x4, x5, x6, x7)) = x3 + x4   
POL(new_mkVBalBranch3MkVBalBranch10(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16)) = 1 + x1 + x10 + x2 + x4 + x5   
POL(new_mkVBalBranch3MkVBalBranch20(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16)) = 1 + x1 + x10 + x2 + x4 + x5 + x6 + x7 + x9   
POL(new_primCmpInt(x1, x2)) = 0   
POL(new_primCmpNat0(x1, x2)) = 0   
POL(new_primCmpNat1(x1, x2)) = 0   
POL(new_primCmpNat2(x1, x2)) = 0   
POL(new_primMulInt(x1, x2)) = 0   
POL(new_primMulNat0(x1, x2)) = 0   
POL(new_primPlusNat0(x1, x2)) = 0   
POL(new_primPlusNat1(x1, x2)) = 0   

The following usable rules [17] were oriented: none



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ UsableRulesProof
                                                  ↳ QDP
                                                    ↳ QReductionProof
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ UsableRulesProof
                                                                                                  ↳ QDP
                                                                                                    ↳ QReductionProof
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ UsableRulesProof
                                                                                                                              ↳ QDP
                                                                                                                                ↳ QReductionProof
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ UsableRulesProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ QReductionProof
                                                                                                                                              ↳ 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_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), zxw193, h, ba, bb)
new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, h, ba, bb) → new_mkVBalBranch0(zxw15, zxw16, zxw1074, Branch(zxw190, zxw191, zxw192, zxw193, zxw194), h, ba, bb)
new_mkVBalBranch3MkVBalBranch20(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch10(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_esEs9(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw192), zxw1072), LT), h, ba, bb)

The TRS R consists of the following rules:

new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs9(GT, LT) → False
new_esEs9(LT, LT) → True
new_esEs9(EQ, LT) → False
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)

The set Q consists of the following terms:

new_esEs9(GT, GT)
new_primMulNat0(Succ(x0), Succ(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpNat1(Zero, x0)
new_esEs9(EQ, GT)
new_esEs9(GT, EQ)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primPlusNat0(Zero, x0)
new_primPlusNat1(Zero, Zero)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_esEs9(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpNat2(Succ(x0), Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat1(Succ(x0), x1)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_primPlusNat0(Succ(x0), x1)
new_primCmpNat0(x0, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs9(LT, LT)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpNat2(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat0(x0, Succ(x1))
new_primMulNat0(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 3 less nodes.

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

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

new_splitLT10(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, True, h, ba, bb) → new_splitLT(zxw34, zxw400, h, ba, bb)
new_splitLT3(Left(zxw300), zxw31, zxw32, zxw33, zxw34, Left(zxw400), h, ba, bb) → new_splitLT2(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs9(new_compare26(Left(zxw400), Left(zxw300), new_esEs29(zxw400, zxw300, h), h, ba), LT), h, ba, bb)
new_splitLT3(Right(zxw300), zxw31, zxw32, zxw33, zxw34, Left(zxw400), h, ba, bb) → new_splitLT20(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs9(new_compare26(Left(zxw400), Right(zxw300), False, h, ba), LT), h, ba, bb)
new_splitLT20(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, False, h, ba, bb) → new_splitLT10(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs9(new_compare34(zxw400, zxw300, h, ba), GT), h, ba, bb)
new_splitLT21(zxw300, zxw31, zxw32, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw34, zxw400, True, h, ba, bb) → new_splitLT3(zxw330, zxw331, zxw332, zxw333, zxw334, Right(zxw400), h, ba, bb)
new_splitLT0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw400, h, ba, bb) → new_splitLT3(zxw330, zxw331, zxw332, zxw333, zxw334, Right(zxw400), h, ba, bb)
new_splitLT1(zxw45, zxw46, zxw47, zxw48, zxw49, zxw50, True, bc, bd, be) → new_splitLT(zxw49, zxw50, bc, bd, be)
new_splitLT2(zxw45, zxw46, zxw47, zxw48, zxw49, zxw50, True, bc, bd, be) → new_splitLT(zxw48, zxw50, bc, bd, be)
new_splitLT(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw400, h, ba, bb) → new_splitLT3(zxw330, zxw331, zxw332, zxw333, zxw334, Left(zxw400), h, ba, bb)
new_splitLT22(zxw60, zxw61, zxw62, zxw63, zxw64, zxw65, True, bf, bg, bh) → new_splitLT0(zxw63, zxw65, bf, bg, bh)
new_splitLT11(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, True, h, ba, bb) → new_splitLT0(zxw34, zxw400, h, ba, bb)
new_splitLT21(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, False, h, ba, bb) → new_splitLT11(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs9(new_compare35(zxw400, zxw300, h, ba), GT), h, ba, bb)
new_splitLT3(Right(zxw300), zxw31, zxw32, zxw33, zxw34, Right(zxw400), h, ba, bb) → new_splitLT22(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs9(new_compare26(Right(zxw400), Right(zxw300), new_esEs30(zxw400, zxw300, ba), h, ba), LT), h, ba, bb)
new_splitLT20(zxw300, zxw31, zxw32, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw34, zxw400, True, h, ba, bb) → new_splitLT3(zxw330, zxw331, zxw332, zxw333, zxw334, Left(zxw400), h, ba, bb)
new_splitLT2(zxw45, zxw46, zxw47, zxw48, zxw49, zxw50, False, bc, bd, be) → new_splitLT1(zxw45, zxw46, zxw47, zxw48, zxw49, zxw50, new_esEs9(new_compare33(zxw50, zxw45, bc, bd), GT), bc, bd, be)
new_splitLT12(zxw60, zxw61, zxw62, zxw63, zxw64, zxw65, True, bf, bg, bh) → new_splitLT0(zxw64, zxw65, bf, bg, bh)
new_splitLT22(zxw60, zxw61, zxw62, zxw63, zxw64, zxw65, False, bf, bg, bh) → new_splitLT12(zxw60, zxw61, zxw62, zxw63, zxw64, zxw65, new_esEs9(new_compare36(zxw65, zxw60, bf, bg), GT), bf, bg, bh)
new_splitLT3(Left(zxw300), zxw31, zxw32, zxw33, zxw34, Right(zxw400), h, ba, bb) → new_splitLT21(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs9(new_compare26(Right(zxw400), Left(zxw300), False, h, ba), LT), h, ba, bb)

The TRS R consists of the following rules:

new_esEs30(zxw400, zxw300, app(ty_Maybe, dag)) → new_esEs6(zxw400, zxw300, dag)
new_ltEs15(zxw7900, zxw8000) → new_fsEs(new_compare6(zxw7900, zxw8000))
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Bool) → new_ltEs12(zxw79000, zxw80000)
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, app(ty_Maybe, bbc)) → new_ltEs18(zxw7900, zxw8000, bbc)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Char) → new_ltEs10(zxw79000, zxw80000)
new_esEs28(zxw4000, zxw3000, app(ty_[], ead)) → new_esEs13(zxw4000, zxw3000, ead)
new_esEs32(zxw20, zxw15, ty_Float) → new_esEs17(zxw20, zxw15)
new_esEs23(zxw4000, zxw3000, app(app(ty_Either, deh), dfa)) → new_esEs7(zxw4000, zxw3000, deh, dfa)
new_esEs6(Just(zxw4000), Just(zxw3000), app(app(ty_@2, fd), ff)) → new_esEs5(zxw4000, zxw3000, fd, ff)
new_lt4(zxw79000, zxw80000, app(app(app(ty_@3, cc), cd), ce)) → new_lt5(zxw79000, zxw80000, cc, cd, ce)
new_esEs31(zxw35, zxw30, ty_Ordering) → new_esEs9(zxw35, zxw30)
new_esEs7(Left(zxw4000), Left(zxw3000), app(app(ty_Either, bec), bed), bdf) → new_esEs7(zxw4000, zxw3000, bec, bed)
new_ltEs20(zxw7900, zxw8000, ty_Int) → new_ltEs9(zxw7900, zxw8000)
new_lt19(zxw79000, zxw80000, app(app(ty_Either, bgd), bge)) → new_lt14(zxw79000, zxw80000, bgd, bge)
new_esEs9(GT, LT) → False
new_esEs9(LT, GT) → False
new_esEs13([], [], cce) → True
new_lt4(zxw79000, zxw80000, app(ty_[], cf)) → new_lt10(zxw79000, zxw80000, cf)
new_compare110(zxw79000, zxw80000, True, bbd, bbe) → LT
new_esEs27(zxw4001, zxw3001, app(ty_Ratio, dha)) → new_esEs18(zxw4001, zxw3001, dha)
new_compare29(zxw79000, zxw80000, ty_Char) → new_compare17(zxw79000, zxw80000)
new_ltEs7(LT, EQ) → True
new_ltEs18(Just(zxw79000), Just(zxw80000), app(ty_Maybe, dad)) → new_ltEs18(zxw79000, zxw80000, dad)
new_esEs30(zxw400, zxw300, app(ty_[], daf)) → new_esEs13(zxw400, zxw300, daf)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Integer) → new_ltEs13(zxw79000, zxw80000)
new_ltEs20(zxw7900, zxw8000, ty_@0) → new_ltEs8(zxw7900, zxw8000)
new_lt20(zxw79001, zxw80001, app(app(ty_Either, bhd), bhe)) → new_lt14(zxw79001, zxw80001, bhd, bhe)
new_esEs23(zxw4000, zxw3000, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_compare35(zxw400, zxw300, h, ba) → new_compare26(Right(zxw400), Left(zxw300), False, h, ba)
new_ltEs8(zxw7900, zxw8000) → new_fsEs(new_compare30(zxw7900, zxw8000))
new_lt19(zxw79000, zxw80000, ty_Double) → new_lt15(zxw79000, zxw80000)
new_esEs22(zxw4000, zxw3000, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(ty_[], cgd)) → new_ltEs11(zxw79000, zxw80000, cgd)
new_ltEs21(zxw79002, zxw80002, ty_Char) → new_ltEs10(zxw79002, zxw80002)
new_esEs23(zxw4000, zxw3000, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Bool, hg) → new_ltEs12(zxw79000, zxw80000)
new_compare8(:%(zxw79000, zxw79001), :%(zxw80000, zxw80001), ty_Integer) → new_compare32(new_sr0(zxw79000, zxw80001), new_sr0(zxw80000, zxw79001))
new_esEs26(zxw4002, zxw3002, ty_Float) → new_esEs17(zxw4002, zxw3002)
new_esEs19(zxw79001, zxw80001, app(ty_Ratio, bhf)) → new_esEs18(zxw79001, zxw80001, bhf)
new_primMulNat0(Zero, Zero) → Zero
new_esEs20(zxw79000, zxw80000, app(ty_[], bgc)) → new_esEs13(zxw79000, zxw80000, bgc)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_lt20(zxw79001, zxw80001, ty_@0) → new_lt7(zxw79001, zxw80001)
new_esEs27(zxw4001, zxw3001, app(app(app(ty_@3, dhh), eaa), eab)) → new_esEs4(zxw4001, zxw3001, dhh, eaa, eab)
new_esEs19(zxw79001, zxw80001, ty_Ordering) → new_esEs9(zxw79001, zxw80001)
new_esEs31(zxw35, zxw30, ty_Char) → new_esEs12(zxw35, zxw30)
new_esEs32(zxw20, zxw15, ty_Integer) → new_esEs15(zxw20, zxw15)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(ty_Ratio, dac)) → new_ltEs17(zxw79000, zxw80000, dac)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Bool, bdf) → new_esEs14(zxw4000, zxw3000)
new_esEs24(zxw4001, zxw3001, ty_Integer) → new_esEs15(zxw4001, zxw3001)
new_lt19(zxw79000, zxw80000, ty_Ordering) → new_lt6(zxw79000, zxw80000)
new_lt20(zxw79001, zxw80001, app(app(ty_@2, bhb), bhc)) → new_lt11(zxw79001, zxw80001, bhb, bhc)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(ty_Ratio, cfg), hg) → new_ltEs17(zxw79000, zxw80000, cfg)
new_compare9(zxw79000, zxw80000, gd, ge, gf) → new_compare25(zxw79000, zxw80000, new_esEs4(zxw79000, zxw80000, gd, ge, gf), gd, ge, gf)
new_lt11(zxw79000, zxw80000, bbd, bbe) → new_esEs9(new_compare19(zxw79000, zxw80000, bbd, bbe), LT)
new_compare1([], :(zxw80000, zxw80001), he) → LT
new_esEs30(zxw400, zxw300, app(app(ty_Either, dbb), dbc)) → new_esEs7(zxw400, zxw300, dbb, dbc)
new_lt18(zxw79000, zxw80000, bbh) → new_esEs9(new_compare27(zxw79000, zxw80000, bbh), LT)
new_esEs8(zxw79000, zxw80000, ty_Int) → new_esEs11(zxw79000, zxw80000)
new_compare32(Integer(zxw79000), Integer(zxw80000)) → new_primCmpInt(zxw79000, zxw80000)
new_ltEs5(zxw79001, zxw80001, ty_Char) → new_ltEs10(zxw79001, zxw80001)
new_lt4(zxw79000, zxw80000, ty_Bool) → new_lt12(zxw79000, zxw80000)
new_compare27(zxw79000, zxw80000, bbh) → new_compare28(zxw79000, zxw80000, new_esEs6(zxw79000, zxw80000, bbh), bbh)
new_lt4(zxw79000, zxw80000, app(ty_Maybe, de)) → new_lt18(zxw79000, zxw80000, de)
new_compare29(zxw79000, zxw80000, ty_Bool) → new_compare31(zxw79000, zxw80000)
new_esEs31(zxw35, zxw30, ty_@0) → new_esEs10(zxw35, zxw30)
new_esEs8(zxw79000, zxw80000, ty_Double) → new_esEs16(zxw79000, zxw80000)
new_esEs22(zxw4000, zxw3000, app(app(ty_@2, ddd), dde)) → new_esEs5(zxw4000, zxw3000, ddd, dde)
new_lt4(zxw79000, zxw80000, ty_Ordering) → new_lt6(zxw79000, zxw80000)
new_esEs22(zxw4000, zxw3000, app(ty_Maybe, ddc)) → new_esEs6(zxw4000, zxw3000, ddc)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(app(app(ty_@3, cga), cgb), cgc)) → new_ltEs6(zxw79000, zxw80000, cga, cgb, cgc)
new_esEs27(zxw4001, zxw3001, app(ty_Maybe, dhc)) → new_esEs6(zxw4001, zxw3001, dhc)
new_esEs8(zxw79000, zxw80000, app(app(app(ty_@3, cc), cd), ce)) → new_esEs4(zxw79000, zxw80000, cc, cd, ce)
new_esEs15(Integer(zxw4000), Integer(zxw3000)) → new_primEqInt(zxw4000, zxw3000)
new_ltEs21(zxw79002, zxw80002, app(app(ty_@2, cad), cae)) → new_ltEs4(zxw79002, zxw80002, cad, cae)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Float, hg) → new_ltEs16(zxw79000, zxw80000)
new_lt5(zxw79000, zxw80000, gd, ge, gf) → new_esEs9(new_compare9(zxw79000, zxw80000, gd, ge, gf), LT)
new_esEs22(zxw4000, zxw3000, app(ty_Ratio, dda)) → new_esEs18(zxw4000, zxw3000, dda)
new_esEs29(zxw400, zxw300, ty_Integer) → new_esEs15(zxw400, zxw300)
new_esEs22(zxw4000, zxw3000, app(app(ty_Either, ddf), ddg)) → new_esEs7(zxw4000, zxw3000, ddf, ddg)
new_ltEs19(zxw7900, zxw8000, ty_Float) → new_ltEs16(zxw7900, zxw8000)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, app(ty_Maybe, bfc)) → new_esEs6(zxw4000, zxw3000, bfc)
new_pePe(False, zxw271) → zxw271
new_esEs29(zxw400, zxw300, ty_Double) → new_esEs16(zxw400, zxw300)
new_esEs7(Left(zxw4000), Right(zxw3000), beh, bdf) → False
new_esEs7(Right(zxw4000), Left(zxw3000), beh, bdf) → False
new_lt15(zxw79000, zxw80000) → new_esEs9(new_compare6(zxw79000, zxw80000), LT)
new_compare15(zxw790, zxw800, gh, ha) → new_compare26(zxw790, zxw800, new_esEs7(zxw790, zxw800, gh, ha), gh, ha)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Float) → new_ltEs16(zxw79000, zxw80000)
new_esEs31(zxw35, zxw30, app(app(app(ty_@3, bdb), bdc), bdd)) → new_esEs4(zxw35, zxw30, bdb, bdc, bdd)
new_ltEs12(True, False) → False
new_esEs20(zxw79000, zxw80000, ty_Double) → new_esEs16(zxw79000, zxw80000)
new_ltEs19(zxw7900, zxw8000, app(app(ty_@2, ca), cb)) → new_ltEs4(zxw7900, zxw8000, ca, cb)
new_esEs32(zxw20, zxw15, ty_@0) → new_esEs10(zxw20, zxw15)
new_compare23(zxw79000, zxw80000, True) → EQ
new_esEs31(zxw35, zxw30, ty_Float) → new_esEs17(zxw35, zxw30)
new_esEs27(zxw4001, zxw3001, app(app(ty_Either, dhf), dhg)) → new_esEs7(zxw4001, zxw3001, dhf, dhg)
new_esEs27(zxw4001, zxw3001, ty_Ordering) → new_esEs9(zxw4001, zxw3001)
new_esEs27(zxw4001, zxw3001, ty_Float) → new_esEs17(zxw4001, zxw3001)
new_esEs19(zxw79001, zxw80001, app(ty_Maybe, bhg)) → new_esEs6(zxw79001, zxw80001, bhg)
new_lt10(zxw79000, zxw80000, bgc) → new_esEs9(new_compare1(zxw79000, zxw80000, bgc), LT)
new_esEs26(zxw4002, zxw3002, ty_Char) → new_esEs12(zxw4002, zxw3002)
new_ltEs19(zxw7900, zxw8000, app(ty_[], he)) → new_ltEs11(zxw7900, zxw8000, he)
new_esEs26(zxw4002, zxw3002, ty_Int) → new_esEs11(zxw4002, zxw3002)
new_ltEs5(zxw79001, zxw80001, app(app(ty_@2, eb), ec)) → new_ltEs4(zxw79001, zxw80001, eb, ec)
new_lt19(zxw79000, zxw80000, app(ty_Ratio, gg)) → new_lt17(zxw79000, zxw80000, gg)
new_esEs22(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, app(app(app(ty_@3, ebb), ebc), ebd)) → new_esEs4(zxw4000, zxw3000, ebb, ebc, ebd)
new_esEs32(zxw20, zxw15, ty_Ordering) → new_esEs9(zxw20, zxw15)
new_compare29(zxw79000, zxw80000, app(app(ty_@2, cbf), cbg)) → new_compare19(zxw79000, zxw80000, cbf, cbg)
new_ltEs21(zxw79002, zxw80002, ty_Int) → new_ltEs9(zxw79002, zxw80002)
new_esEs20(zxw79000, zxw80000, ty_Char) → new_esEs12(zxw79000, zxw80000)
new_compare13(zxw235, zxw236, False, bbf, bbg) → GT
new_esEs9(GT, EQ) → False
new_esEs9(EQ, GT) → False
new_esEs19(zxw79001, zxw80001, app(app(ty_Either, bhd), bhe)) → new_esEs7(zxw79001, zxw80001, bhd, bhe)
new_esEs20(zxw79000, zxw80000, app(app(ty_@2, bbd), bbe)) → new_esEs5(zxw79000, zxw80000, bbd, bbe)
new_ltEs7(GT, GT) → True
new_compare36(zxw35, zxw30, bca, bcb) → new_compare26(Right(zxw35), Right(zxw30), new_esEs31(zxw35, zxw30, bcb), bca, bcb)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, app(app(ty_@2, bfd), bfe)) → new_esEs5(zxw4000, zxw3000, bfd, bfe)
new_ltEs20(zxw7900, zxw8000, app(app(ty_@2, baf), bag)) → new_ltEs4(zxw7900, zxw8000, baf, bag)
new_esEs21(zxw4001, zxw3001, ty_Bool) → new_esEs14(zxw4001, zxw3001)
new_esEs32(zxw20, zxw15, ty_Bool) → new_esEs14(zxw20, zxw15)
new_primCompAux0(zxw79000, zxw80000, zxw272, he) → new_primCompAux00(zxw272, new_compare29(zxw79000, zxw80000, he))
new_ltEs21(zxw79002, zxw80002, ty_Ordering) → new_ltEs7(zxw79002, zxw80002)
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_compare29(zxw79000, zxw80000, app(ty_[], cbe)) → new_compare1(zxw79000, zxw80000, cbe)
new_lt20(zxw79001, zxw80001, ty_Ordering) → new_lt6(zxw79001, zxw80001)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_esEs8(zxw79000, zxw80000, app(ty_[], cf)) → new_esEs13(zxw79000, zxw80000, cf)
new_esEs27(zxw4001, zxw3001, ty_@0) → new_esEs10(zxw4001, zxw3001)
new_compare25(zxw79000, zxw80000, True, gd, ge, gf) → EQ
new_esEs19(zxw79001, zxw80001, ty_Float) → new_esEs17(zxw79001, zxw80001)
new_ltEs5(zxw79001, zxw80001, ty_Ordering) → new_ltEs7(zxw79001, zxw80001)
new_lt4(zxw79000, zxw80000, app(ty_Ratio, dd)) → new_lt17(zxw79000, zxw80000, dd)
new_esEs28(zxw4000, zxw3000, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Int, bdf) → new_esEs11(zxw4000, zxw3000)
new_ltEs21(zxw79002, zxw80002, ty_Float) → new_ltEs16(zxw79002, zxw80002)
new_esEs28(zxw4000, zxw3000, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_compare29(zxw79000, zxw80000, app(app(app(ty_@3, cbb), cbc), cbd)) → new_compare9(zxw79000, zxw80000, cbb, cbc, cbd)
new_lt19(zxw79000, zxw80000, app(app(ty_@2, bbd), bbe)) → new_lt11(zxw79000, zxw80000, bbd, bbe)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(app(app(ty_@3, chc), chd), che)) → new_ltEs6(zxw79000, zxw80000, chc, chd, che)
new_pePe(True, zxw271) → True
new_primEqNat0(Zero, Zero) → True
new_compare14(zxw242, zxw243, False, dfe, dff) → GT
new_esEs20(zxw79000, zxw80000, ty_Int) → new_esEs11(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Double) → new_ltEs15(zxw79000, zxw80000)
new_ltEs21(zxw79002, zxw80002, ty_Bool) → new_ltEs12(zxw79002, zxw80002)
new_lt9(zxw79000, zxw80000) → new_esEs9(new_compare17(zxw79000, zxw80000), LT)
new_esEs29(zxw400, zxw300, app(ty_Maybe, eh)) → new_esEs6(zxw400, zxw300, eh)
new_ltEs12(False, False) → True
new_esEs7(Left(zxw4000), Left(zxw3000), app(app(ty_@2, bea), beb), bdf) → new_esEs5(zxw4000, zxw3000, bea, beb)
new_esEs26(zxw4002, zxw3002, app(ty_Maybe, dga)) → new_esEs6(zxw4002, zxw3002, dga)
new_compare8(:%(zxw79000, zxw79001), :%(zxw80000, zxw80001), ty_Int) → new_compare16(new_sr(zxw79000, zxw80001), new_sr(zxw80000, zxw79001))
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Ordering, bdf) → new_esEs9(zxw4000, zxw3000)
new_esEs29(zxw400, zxw300, app(ty_[], cce)) → new_esEs13(zxw400, zxw300, cce)
new_esEs27(zxw4001, zxw3001, ty_Char) → new_esEs12(zxw4001, zxw3001)
new_lt7(zxw79000, zxw80000) → new_esEs9(new_compare30(zxw79000, zxw80000), LT)
new_compare110(zxw79000, zxw80000, False, bbd, bbe) → GT
new_sr(zxw4000, zxw3000) → new_primMulInt(zxw4000, zxw3000)
new_compare12(zxw79000, zxw80000, True, gd, ge, gf) → LT
new_esEs30(zxw400, zxw300, ty_Char) → new_esEs12(zxw400, zxw300)
new_lt19(zxw79000, zxw80000, ty_Int) → new_lt8(zxw79000, zxw80000)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(app(ty_@2, cge), cgf)) → new_ltEs4(zxw79000, zxw80000, cge, cgf)
new_ltEs19(zxw7900, zxw8000, ty_Char) → new_ltEs10(zxw7900, zxw8000)
new_esEs30(zxw400, zxw300, app(app(app(ty_@3, dbd), dbe), dbf)) → new_esEs4(zxw400, zxw300, dbd, dbe, dbf)
new_esEs21(zxw4001, zxw3001, ty_Double) → new_esEs16(zxw4001, zxw3001)
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, app(app(ty_Either, bff), bfg)) → new_esEs7(zxw4000, zxw3000, bff, bfg)
new_esEs31(zxw35, zxw30, app(app(ty_Either, bch), bda)) → new_esEs7(zxw35, zxw30, bch, bda)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Double, hg) → new_ltEs15(zxw79000, zxw80000)
new_ltEs19(zxw7900, zxw8000, ty_Bool) → new_ltEs12(zxw7900, zxw8000)
new_esEs26(zxw4002, zxw3002, app(app(app(ty_@3, dgf), dgg), dgh)) → new_esEs4(zxw4002, zxw3002, dgf, dgg, dgh)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, app(ty_[], bfb)) → new_esEs13(zxw4000, zxw3000, bfb)
new_ltEs11(zxw7900, zxw8000, he) → new_fsEs(new_compare1(zxw7900, zxw8000, he))
new_ltEs20(zxw7900, zxw8000, ty_Float) → new_ltEs16(zxw7900, zxw8000)
new_esEs21(zxw4001, zxw3001, ty_Ordering) → new_esEs9(zxw4001, zxw3001)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_esEs9(EQ, EQ) → True
new_fsEs(zxw259) → new_not(new_esEs9(zxw259, GT))
new_esEs8(zxw79000, zxw80000, ty_Char) → new_esEs12(zxw79000, zxw80000)
new_primEqInt(Neg(Succ(zxw40000)), Neg(Succ(zxw30000))) → new_primEqNat0(zxw40000, zxw30000)
new_esEs8(zxw79000, zxw80000, app(app(ty_@2, cg), da)) → new_esEs5(zxw79000, zxw80000, cg, da)
new_compare13(zxw235, zxw236, True, bbf, bbg) → LT
new_compare26(Left(zxw7900), Right(zxw8000), False, gh, ha) → LT
new_esEs13(:(zxw4000, zxw4001), :(zxw3000, zxw3001), cce) → new_asAs(new_esEs23(zxw4000, zxw3000, cce), new_esEs13(zxw4001, zxw3001, cce))
new_esEs26(zxw4002, zxw3002, app(ty_[], dfh)) → new_esEs13(zxw4002, zxw3002, dfh)
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_ltEs19(zxw7900, zxw8000, app(ty_Ratio, hh)) → new_ltEs17(zxw7900, zxw8000, hh)
new_esEs30(zxw400, zxw300, ty_Float) → new_esEs17(zxw400, zxw300)
new_ltEs20(zxw7900, zxw8000, ty_Bool) → new_ltEs12(zxw7900, zxw8000)
new_esEs21(zxw4001, zxw3001, ty_Char) → new_esEs12(zxw4001, zxw3001)
new_compare23(zxw79000, zxw80000, False) → new_compare10(zxw79000, zxw80000, new_ltEs12(zxw79000, zxw80000))
new_ltEs14(Right(zxw79000), Left(zxw80000), hf, hg) → False
new_compare210(zxw79000, zxw80000, False, bbd, bbe) → new_compare110(zxw79000, zxw80000, new_ltEs4(zxw79000, zxw80000, bbd, bbe), bbd, bbe)
new_primCmpNat1(Zero, zxw7900) → LT
new_compare7(Float(zxw79000, zxw79001), Float(zxw80000, zxw80001)) → new_compare16(new_sr(zxw79000, zxw80000), new_sr(zxw79001, zxw80001))
new_ltEs21(zxw79002, zxw80002, ty_Integer) → new_ltEs13(zxw79002, zxw80002)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_lt20(zxw79001, zxw80001, app(ty_Maybe, bhg)) → new_lt18(zxw79001, zxw80001, bhg)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Integer, bdf) → new_esEs15(zxw4000, zxw3000)
new_ltEs5(zxw79001, zxw80001, ty_Bool) → new_ltEs12(zxw79001, zxw80001)
new_esEs19(zxw79001, zxw80001, ty_Bool) → new_esEs14(zxw79001, zxw80001)
new_ltEs7(EQ, EQ) → True
new_ltEs20(zxw7900, zxw8000, app(ty_Ratio, bbb)) → new_ltEs17(zxw7900, zxw8000, bbb)
new_primEqInt(Neg(Zero), Neg(Succ(zxw30000))) → False
new_primEqInt(Neg(Succ(zxw40000)), Neg(Zero)) → False
new_ltEs5(zxw79001, zxw80001, ty_Integer) → new_ltEs13(zxw79001, zxw80001)
new_compare26(zxw790, zxw800, True, gh, ha) → EQ
new_compare111(zxw79000, zxw80000, True, bbh) → LT
new_esEs20(zxw79000, zxw80000, ty_@0) → new_esEs10(zxw79000, zxw80000)
new_esEs31(zxw35, zxw30, app(ty_Ratio, bcc)) → new_esEs18(zxw35, zxw30, bcc)
new_ltEs21(zxw79002, zxw80002, app(app(ty_Either, caf), cag)) → new_ltEs14(zxw79002, zxw80002, caf, cag)
new_esEs8(zxw79000, zxw80000, ty_Float) → new_esEs17(zxw79000, zxw80000)
new_esEs23(zxw4000, zxw3000, app(app(app(ty_@3, dfb), dfc), dfd)) → new_esEs4(zxw4000, zxw3000, dfb, dfc, dfd)
new_ltEs21(zxw79002, zxw80002, app(ty_[], cac)) → new_ltEs11(zxw79002, zxw80002, cac)
new_esEs21(zxw4001, zxw3001, ty_Float) → new_esEs17(zxw4001, zxw3001)
new_compare24(zxw79000, zxw80000, False) → new_compare11(zxw79000, zxw80000, new_ltEs7(zxw79000, zxw80000))
new_ltEs5(zxw79001, zxw80001, app(ty_Ratio, ef)) → new_ltEs17(zxw79001, zxw80001, ef)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_esEs26(zxw4002, zxw3002, app(app(ty_Either, dgd), dge)) → new_esEs7(zxw4002, zxw3002, dgd, dge)
new_lt20(zxw79001, zxw80001, ty_Int) → new_lt8(zxw79001, zxw80001)
new_lt4(zxw79000, zxw80000, ty_Int) → new_lt8(zxw79000, zxw80000)
new_ltEs20(zxw7900, zxw8000, ty_Double) → new_ltEs15(zxw7900, zxw8000)
new_ltEs7(GT, LT) → False
new_lt12(zxw79000, zxw80000) → new_esEs9(new_compare31(zxw79000, zxw80000), LT)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Int, hg) → new_ltEs9(zxw79000, zxw80000)
new_lt20(zxw79001, zxw80001, ty_Integer) → new_lt13(zxw79001, zxw80001)
new_ltEs7(GT, EQ) → False
new_esEs6(Nothing, Nothing, eh) → True
new_primEqInt(Pos(Succ(zxw40000)), Pos(Succ(zxw30000))) → new_primEqNat0(zxw40000, zxw30000)
new_lt8(zxw790, zxw800) → new_esEs9(new_compare16(zxw790, zxw800), LT)
new_esEs21(zxw4001, zxw3001, app(ty_Maybe, dca)) → new_esEs6(zxw4001, zxw3001, dca)
new_lt6(zxw79000, zxw80000) → new_esEs9(new_compare18(zxw79000, zxw80000), LT)
new_esEs32(zxw20, zxw15, app(app(ty_Either, ceb), cec)) → new_esEs7(zxw20, zxw15, ceb, cec)
new_esEs14(False, True) → False
new_esEs14(True, False) → False
new_esEs32(zxw20, zxw15, app(ty_[], cdf)) → new_esEs13(zxw20, zxw15, cdf)
new_esEs26(zxw4002, zxw3002, ty_Integer) → new_esEs15(zxw4002, zxw3002)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, app(app(app(ty_@3, bfh), bga), bgb)) → new_esEs4(zxw4000, zxw3000, bfh, bga, bgb)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs6(Nothing, Just(zxw3000), eh) → False
new_esEs6(Just(zxw4000), Nothing, eh) → False
new_primEqNat0(Succ(zxw40000), Succ(zxw30000)) → new_primEqNat0(zxw40000, zxw30000)
new_esEs16(Double(zxw4000, zxw4001), Double(zxw3000, zxw3001)) → new_esEs11(new_sr(zxw4000, zxw3000), new_sr(zxw4001, zxw3001))
new_lt19(zxw79000, zxw80000, ty_@0) → new_lt7(zxw79000, zxw80000)
new_esEs30(zxw400, zxw300, app(ty_Ratio, dae)) → new_esEs18(zxw400, zxw300, dae)
new_ltEs5(zxw79001, zxw80001, app(ty_Maybe, eg)) → new_ltEs18(zxw79001, zxw80001, eg)
new_esEs17(Float(zxw4000, zxw4001), Float(zxw3000, zxw3001)) → new_esEs11(new_sr(zxw4000, zxw3000), new_sr(zxw4001, zxw3001))
new_primCompAux00(zxw276, LT) → LT
new_esEs28(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), app(ty_Ratio, bde), bdf) → new_esEs18(zxw4000, zxw3000, bde)
new_esEs21(zxw4001, zxw3001, ty_Int) → new_esEs11(zxw4001, zxw3001)
new_compare1(:(zxw79000, zxw79001), :(zxw80000, zxw80001), he) → new_primCompAux0(zxw79000, zxw80000, new_compare1(zxw79001, zxw80001, he), he)
new_primEqInt(Pos(Zero), Pos(Succ(zxw30000))) → False
new_primEqInt(Pos(Succ(zxw40000)), Pos(Zero)) → False
new_compare29(zxw79000, zxw80000, ty_Int) → new_compare16(zxw79000, zxw80000)
new_lt20(zxw79001, zxw80001, app(ty_Ratio, bhf)) → new_lt17(zxw79001, zxw80001, bhf)
new_ltEs20(zxw7900, zxw8000, ty_Integer) → new_ltEs13(zxw7900, zxw8000)
new_esEs31(zxw35, zxw30, app(app(ty_@2, bcf), bcg)) → new_esEs5(zxw35, zxw30, bcf, bcg)
new_esEs5(@2(zxw4000, zxw4001), @2(zxw3000, zxw3001), ccf, ccg) → new_asAs(new_esEs22(zxw4000, zxw3000, ccf), new_esEs21(zxw4001, zxw3001, ccg))
new_ltEs18(Nothing, Nothing, baa) → True
new_esEs32(zxw20, zxw15, app(ty_Maybe, cdg)) → new_esEs6(zxw20, zxw15, cdg)
new_ltEs21(zxw79002, zxw80002, app(ty_Ratio, cah)) → new_ltEs17(zxw79002, zxw80002, cah)
new_esEs23(zxw4000, zxw3000, app(app(ty_@2, def), deg)) → new_esEs5(zxw4000, zxw3000, def, deg)
new_esEs20(zxw79000, zxw80000, app(app(app(ty_@3, gd), ge), gf)) → new_esEs4(zxw79000, zxw80000, gd, ge, gf)
new_esEs29(zxw400, zxw300, app(app(app(ty_@3, cch), cda), cdb)) → new_esEs4(zxw400, zxw300, cch, cda, cdb)
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_ltEs21(zxw79002, zxw80002, app(app(app(ty_@3, bhh), caa), cab)) → new_ltEs6(zxw79002, zxw80002, bhh, caa, cab)
new_ltEs10(zxw7900, zxw8000) → new_fsEs(new_compare17(zxw7900, zxw8000))
new_compare17(Char(zxw79000), Char(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_sr0(Integer(zxw800000), Integer(zxw790010)) → Integer(new_primMulInt(zxw800000, zxw790010))
new_ltEs5(zxw79001, zxw80001, ty_Double) → new_ltEs15(zxw79001, zxw80001)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_esEs29(zxw400, zxw300, app(ty_Ratio, ccd)) → new_esEs18(zxw400, zxw300, ccd)
new_esEs8(zxw79000, zxw80000, app(app(ty_Either, db), dc)) → new_esEs7(zxw79000, zxw80000, db, dc)
new_primEqInt(Neg(Succ(zxw40000)), Pos(zxw3000)) → False
new_primEqInt(Pos(Succ(zxw40000)), Neg(zxw3000)) → False
new_compare29(zxw79000, zxw80000, ty_Integer) → new_compare32(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Char) → new_ltEs10(zxw79000, zxw80000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_@0, bdf) → new_esEs10(zxw4000, zxw3000)
new_lt19(zxw79000, zxw80000, app(app(app(ty_@3, gd), ge), gf)) → new_lt5(zxw79000, zxw80000, gd, ge, gf)
new_esEs29(zxw400, zxw300, app(app(ty_@2, ccf), ccg)) → new_esEs5(zxw400, zxw300, ccf, ccg)
new_esEs32(zxw20, zxw15, app(app(ty_@2, cdh), cea)) → new_esEs5(zxw20, zxw15, cdh, cea)
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_esEs28(zxw4000, zxw3000, app(ty_Maybe, eae)) → new_esEs6(zxw4000, zxw3000, eae)
new_ltEs21(zxw79002, zxw80002, ty_@0) → new_ltEs8(zxw79002, zxw80002)
new_esEs21(zxw4001, zxw3001, app(ty_[], dbh)) → new_esEs13(zxw4001, zxw3001, dbh)
new_primEqInt(Neg(Zero), Pos(Succ(zxw30000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(zxw30000))) → False
new_ltEs7(EQ, GT) → True
new_lt4(zxw79000, zxw80000, ty_Double) → new_lt15(zxw79000, zxw80000)
new_esEs21(zxw4001, zxw3001, ty_Integer) → new_esEs15(zxw4001, zxw3001)
new_esEs31(zxw35, zxw30, ty_Integer) → new_esEs15(zxw35, zxw30)
new_primCompAux00(zxw276, EQ) → zxw276
new_esEs28(zxw4000, zxw3000, app(app(ty_Either, eah), eba)) → new_esEs7(zxw4000, zxw3000, eah, eba)
new_compare24(zxw79000, zxw80000, True) → EQ
new_compare6(Double(zxw79000, zxw79001), Double(zxw80000, zxw80001)) → new_compare16(new_sr(zxw79000, zxw80000), new_sr(zxw79001, zxw80001))
new_esEs8(zxw79000, zxw80000, ty_@0) → new_esEs10(zxw79000, zxw80000)
new_ltEs5(zxw79001, zxw80001, app(app(ty_Either, ed), ee)) → new_ltEs14(zxw79001, zxw80001, ed, ee)
new_lt13(zxw79000, zxw80000) → new_esEs9(new_compare32(zxw79000, zxw80000), LT)
new_esEs27(zxw4001, zxw3001, ty_Double) → new_esEs16(zxw4001, zxw3001)
new_esEs7(Left(zxw4000), Left(zxw3000), app(app(app(ty_@3, bee), bef), beg), bdf) → new_esEs4(zxw4000, zxw3000, bee, bef, beg)
new_esEs26(zxw4002, zxw3002, app(app(ty_@2, dgb), dgc)) → new_esEs5(zxw4002, zxw3002, dgb, dgc)
new_esEs21(zxw4001, zxw3001, app(app(ty_@2, dcb), dcc)) → new_esEs5(zxw4001, zxw3001, dcb, dcc)
new_esEs30(zxw400, zxw300, ty_@0) → new_esEs10(zxw400, zxw300)
new_lt19(zxw79000, zxw80000, app(ty_Maybe, bbh)) → new_lt18(zxw79000, zxw80000, bbh)
new_esEs12(Char(zxw4000), Char(zxw3000)) → new_primEqNat0(zxw4000, zxw3000)
new_ltEs20(zxw7900, zxw8000, app(app(app(ty_@3, bab), bac), bad)) → new_ltEs6(zxw7900, zxw8000, bab, bac, bad)
new_not(False) → True
new_lt20(zxw79001, zxw80001, ty_Char) → new_lt9(zxw79001, zxw80001)
new_esEs11(zxw400, zxw300) → new_primEqInt(zxw400, zxw300)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(ty_Maybe, chb)) → new_ltEs18(zxw79000, zxw80000, chb)
new_ltEs18(Just(zxw79000), Nothing, baa) → False
new_esEs8(zxw79000, zxw80000, app(ty_Maybe, de)) → new_esEs6(zxw79000, zxw80000, de)
new_esEs7(Left(zxw4000), Left(zxw3000), app(ty_Maybe, bdh), bdf) → new_esEs6(zxw4000, zxw3000, bdh)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Double, bdf) → new_esEs16(zxw4000, zxw3000)
new_compare210(zxw79000, zxw80000, True, bbd, bbe) → EQ
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_esEs19(zxw79001, zxw80001, ty_Int) → new_esEs11(zxw79001, zxw80001)
new_compare12(zxw79000, zxw80000, False, gd, ge, gf) → GT
new_ltEs16(zxw7900, zxw8000) → new_fsEs(new_compare7(zxw7900, zxw8000))
new_esEs32(zxw20, zxw15, ty_Char) → new_esEs12(zxw20, zxw15)
new_esEs9(GT, GT) → True
new_esEs26(zxw4002, zxw3002, app(ty_Ratio, dfg)) → new_esEs18(zxw4002, zxw3002, dfg)
new_esEs25(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_lt20(zxw79001, zxw80001, app(ty_[], bha)) → new_lt10(zxw79001, zxw80001, bha)
new_lt4(zxw79000, zxw80000, app(app(ty_Either, db), dc)) → new_lt14(zxw79000, zxw80000, db, dc)
new_esEs26(zxw4002, zxw3002, ty_Bool) → new_esEs14(zxw4002, zxw3002)
new_compare19(zxw79000, zxw80000, bbd, bbe) → new_compare210(zxw79000, zxw80000, new_esEs5(zxw79000, zxw80000, bbd, bbe), bbd, bbe)
new_esEs8(zxw79000, zxw80000, ty_Bool) → new_esEs14(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Double) → new_ltEs15(zxw79000, zxw80000)
new_esEs28(zxw4000, zxw3000, app(app(ty_@2, eaf), eag)) → new_esEs5(zxw4000, zxw3000, eaf, eag)
new_ltEs19(zxw7900, zxw8000, app(app(app(ty_@3, hb), hc), hd)) → new_ltEs6(zxw7900, zxw8000, hb, hc, hd)
new_esEs32(zxw20, zxw15, app(app(app(ty_@3, ced), cee), cef)) → new_esEs4(zxw20, zxw15, ced, cee, cef)
new_lt4(zxw79000, zxw80000, ty_Char) → new_lt9(zxw79000, zxw80000)
new_esEs22(zxw4000, zxw3000, app(app(app(ty_@3, ddh), dea), deb)) → new_esEs4(zxw4000, zxw3000, ddh, dea, deb)
new_esEs22(zxw4000, zxw3000, app(ty_[], ddb)) → new_esEs13(zxw4000, zxw3000, ddb)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_@0) → new_ltEs8(zxw79000, zxw80000)
new_esEs23(zxw4000, zxw3000, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Float, bdf) → new_esEs17(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_esEs27(zxw4001, zxw3001, ty_Int) → new_esEs11(zxw4001, zxw3001)
new_esEs19(zxw79001, zxw80001, app(app(app(ty_@3, bgf), bgg), bgh)) → new_esEs4(zxw79001, zxw80001, bgf, bgg, bgh)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_ltEs14(Left(zxw79000), Left(zxw80000), app(app(app(ty_@3, ceg), ceh), cfa), hg) → new_ltEs6(zxw79000, zxw80000, ceg, ceh, cfa)
new_ltEs19(zxw7900, zxw8000, ty_Int) → new_ltEs9(zxw7900, zxw8000)
new_compare33(zxw20, zxw15, cdc, cdd) → new_compare26(Left(zxw20), Left(zxw15), new_esEs32(zxw20, zxw15, cdc), cdc, cdd)
new_lt4(zxw79000, zxw80000, ty_@0) → new_lt7(zxw79000, zxw80000)
new_lt20(zxw79001, zxw80001, ty_Double) → new_lt15(zxw79001, zxw80001)
new_lt19(zxw79000, zxw80000, ty_Float) → new_lt16(zxw79000, zxw80000)
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_esEs26(zxw4002, zxw3002, ty_@0) → new_esEs10(zxw4002, zxw3002)
new_esEs30(zxw400, zxw300, app(app(ty_@2, dah), dba)) → new_esEs5(zxw400, zxw300, dah, dba)
new_lt19(zxw79000, zxw80000, ty_Bool) → new_lt12(zxw79000, zxw80000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Char, bdf) → new_esEs12(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_lt4(zxw79000, zxw80000, ty_Float) → new_lt16(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(ty_[], chf)) → new_ltEs11(zxw79000, zxw80000, chf)
new_primMulInt(Neg(zxw40000), Neg(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_ltEs5(zxw79001, zxw80001, app(app(app(ty_@3, df), dg), dh)) → new_ltEs6(zxw79001, zxw80001, df, dg, dh)
new_primCmpNat2(Zero, Zero) → EQ
new_esEs20(zxw79000, zxw80000, ty_Integer) → new_esEs15(zxw79000, zxw80000)
new_primEqNat0(Zero, Succ(zxw30000)) → False
new_primEqNat0(Succ(zxw40000), Zero) → False
new_esEs21(zxw4001, zxw3001, ty_@0) → new_esEs10(zxw4001, zxw3001)
new_esEs22(zxw4000, zxw3000, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_esEs20(zxw79000, zxw80000, ty_Bool) → new_esEs14(zxw79000, zxw80000)
new_ltEs5(zxw79001, zxw80001, app(ty_[], ea)) → new_ltEs11(zxw79001, zxw80001, ea)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs23(zxw4000, zxw3000, app(ty_Ratio, dec)) → new_esEs18(zxw4000, zxw3000, dec)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(app(ty_@2, chg), chh)) → new_ltEs4(zxw79000, zxw80000, chg, chh)
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_ltEs5(zxw79001, zxw80001, ty_Int) → new_ltEs9(zxw79001, zxw80001)
new_esEs27(zxw4001, zxw3001, app(app(ty_@2, dhd), dhe)) → new_esEs5(zxw4001, zxw3001, dhd, dhe)
new_primCmpNat0(zxw7900, Zero) → GT
new_compare26(Right(zxw7900), Left(zxw8000), False, gh, ha) → GT
new_esEs23(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_@0, hg) → new_ltEs8(zxw79000, zxw80000)
new_ltEs21(zxw79002, zxw80002, app(ty_Maybe, cba)) → new_ltEs18(zxw79002, zxw80002, cba)
new_esEs21(zxw4001, zxw3001, app(app(ty_Either, dcd), dce)) → new_esEs7(zxw4001, zxw3001, dcd, dce)
new_esEs22(zxw4000, zxw3000, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Bool) → new_ltEs12(zxw79000, zxw80000)
new_compare29(zxw79000, zxw80000, app(ty_Maybe, ccc)) → new_compare27(zxw79000, zxw80000, ccc)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_ltEs14(Left(zxw79000), Left(zxw80000), app(ty_Maybe, cfh), hg) → new_ltEs18(zxw79000, zxw80000, cfh)
new_lt20(zxw79001, zxw80001, ty_Float) → new_lt16(zxw79001, zxw80001)
new_lt17(zxw79000, zxw80000, gg) → new_esEs9(new_compare8(zxw79000, zxw80000, gg), LT)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Ordering) → new_ltEs7(zxw79000, zxw80000)
new_esEs32(zxw20, zxw15, ty_Int) → new_esEs11(zxw20, zxw15)
new_compare30(@0, @0) → EQ
new_lt19(zxw79000, zxw80000, app(ty_[], bgc)) → new_lt10(zxw79000, zxw80000, bgc)
new_esEs21(zxw4001, zxw3001, app(app(app(ty_@3, dcf), dcg), dch)) → new_esEs4(zxw4001, zxw3001, dcf, dcg, dch)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_esEs20(zxw79000, zxw80000, app(ty_Ratio, gg)) → new_esEs18(zxw79000, zxw80000, gg)
new_esEs6(Just(zxw4000), Just(zxw3000), app(app(app(ty_@3, ga), gb), gc)) → new_esEs4(zxw4000, zxw3000, ga, gb, gc)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(app(ty_Either, daa), dab)) → new_ltEs14(zxw79000, zxw80000, daa, dab)
new_esEs24(zxw4001, zxw3001, ty_Int) → new_esEs11(zxw4001, zxw3001)
new_esEs8(zxw79000, zxw80000, ty_Ordering) → new_esEs9(zxw79000, zxw80000)
new_esEs30(zxw400, zxw300, ty_Ordering) → new_esEs9(zxw400, zxw300)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Ordering) → new_ltEs7(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, app(app(ty_Either, bgd), bge)) → new_esEs7(zxw79000, zxw80000, bgd, bge)
new_compare29(zxw79000, zxw80000, app(ty_Ratio, ccb)) → new_compare8(zxw79000, zxw80000, ccb)
new_lt4(zxw79000, zxw80000, app(app(ty_@2, cg), da)) → new_lt11(zxw79000, zxw80000, cg, da)
new_compare29(zxw79000, zxw80000, ty_Float) → new_compare7(zxw79000, zxw80000)
new_esEs19(zxw79001, zxw80001, app(app(ty_@2, bhb), bhc)) → new_esEs5(zxw79001, zxw80001, bhb, bhc)
new_esEs10(@0, @0) → True
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_compare29(zxw79000, zxw80000, ty_Double) → new_compare6(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, app(ty_Maybe, bbh)) → new_esEs6(zxw79000, zxw80000, bbh)
new_ltEs14(Left(zxw79000), Right(zxw80000), hf, hg) → True
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Float) → new_ltEs16(zxw79000, zxw80000)
new_esEs28(zxw4000, zxw3000, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_compare29(zxw79000, zxw80000, app(app(ty_Either, cbh), cca)) → new_compare15(zxw79000, zxw80000, cbh, cca)
new_esEs19(zxw79001, zxw80001, ty_Double) → new_esEs16(zxw79001, zxw80001)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs30(zxw400, zxw300, ty_Bool) → new_esEs14(zxw400, zxw300)
new_ltEs20(zxw7900, zxw8000, app(app(ty_Either, bah), bba)) → new_ltEs14(zxw7900, zxw8000, bah, bba)
new_asAs(False, zxw230) → False
new_ltEs13(zxw7900, zxw8000) → new_fsEs(new_compare32(zxw7900, zxw8000))
new_ltEs19(zxw7900, zxw8000, app(app(ty_Either, hf), hg)) → new_ltEs14(zxw7900, zxw8000, hf, hg)
new_compare34(zxw400, zxw300, h, ba) → new_compare26(Left(zxw400), Right(zxw300), False, h, ba)
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Pos(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_ltEs20(zxw7900, zxw8000, app(ty_[], bae)) → new_ltEs11(zxw7900, zxw8000, bae)
new_compare16(zxw79, zxw80) → new_primCmpInt(zxw79, zxw80)
new_esEs29(zxw400, zxw300, ty_Char) → new_esEs12(zxw400, zxw300)
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_esEs13(:(zxw4000, zxw4001), [], cce) → False
new_esEs13([], :(zxw3000, zxw3001), cce) → False
new_compare25(zxw79000, zxw80000, False, gd, ge, gf) → new_compare12(zxw79000, zxw80000, new_ltEs6(zxw79000, zxw80000, gd, ge, gf), gd, ge, gf)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(app(ty_@2, cfc), cfd), hg) → new_ltEs4(zxw79000, zxw80000, cfc, cfd)
new_esEs6(Just(zxw4000), Just(zxw3000), app(ty_Maybe, fc)) → new_esEs6(zxw4000, zxw3000, fc)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_@0) → new_esEs10(zxw4000, zxw3000)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(ty_[], cfb), hg) → new_ltEs11(zxw79000, zxw80000, cfb)
new_esEs7(Left(zxw4000), Left(zxw3000), app(ty_[], bdg), bdf) → new_esEs13(zxw4000, zxw3000, bdg)
new_esEs29(zxw400, zxw300, ty_Int) → new_esEs11(zxw400, zxw300)
new_esEs31(zxw35, zxw30, ty_Double) → new_esEs16(zxw35, zxw30)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_compare31(zxw79000, zxw80000) → new_compare23(zxw79000, zxw80000, new_esEs14(zxw79000, zxw80000))
new_ltEs18(Nothing, Just(zxw80000), baa) → True
new_esEs28(zxw4000, zxw3000, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_ltEs21(zxw79002, zxw80002, ty_Double) → new_ltEs15(zxw79002, zxw80002)
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_ltEs12(True, True) → True
new_esEs23(zxw4000, zxw3000, app(ty_Maybe, dee)) → new_esEs6(zxw4000, zxw3000, dee)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_esEs8(zxw79000, zxw80000, ty_Integer) → new_esEs15(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(app(ty_Either, cgg), cgh)) → new_ltEs14(zxw79000, zxw80000, cgg, cgh)
new_ltEs6(@3(zxw79000, zxw79001, zxw79002), @3(zxw80000, zxw80001, zxw80002), hb, hc, hd) → new_pePe(new_lt19(zxw79000, zxw80000, hb), new_asAs(new_esEs20(zxw79000, zxw80000, hb), new_pePe(new_lt20(zxw79001, zxw80001, hc), new_asAs(new_esEs19(zxw79001, zxw80001, hc), new_ltEs21(zxw79002, zxw80002, hd)))))
new_esEs28(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_lt16(zxw79000, zxw80000) → new_esEs9(new_compare7(zxw79000, zxw80000), LT)
new_esEs23(zxw4000, zxw3000, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Integer, hg) → new_ltEs13(zxw79000, zxw80000)
new_ltEs12(False, True) → True
new_esEs23(zxw4000, zxw3000, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs8(zxw79000, zxw80000, app(ty_Ratio, dd)) → new_esEs18(zxw79000, zxw80000, dd)
new_esEs23(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs14(True, True) → True
new_compare111(zxw79000, zxw80000, False, bbh) → GT
new_esEs31(zxw35, zxw30, app(ty_[], bcd)) → new_esEs13(zxw35, zxw30, bcd)
new_esEs27(zxw4001, zxw3001, ty_Bool) → new_esEs14(zxw4001, zxw3001)
new_esEs20(zxw79000, zxw80000, ty_Ordering) → new_esEs9(zxw79000, zxw80000)
new_ltEs19(zxw7900, zxw8000, ty_@0) → new_ltEs8(zxw7900, zxw8000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Int) → new_ltEs9(zxw79000, zxw80000)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(app(ty_Either, cfe), cff), hg) → new_ltEs14(zxw79000, zxw80000, cfe, cff)
new_lt19(zxw79000, zxw80000, ty_Integer) → new_lt13(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, ty_Float) → new_esEs17(zxw79000, zxw80000)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Ordering, hg) → new_ltEs7(zxw79000, zxw80000)
new_compare11(zxw79000, zxw80000, False) → GT
new_esEs4(@3(zxw4000, zxw4001, zxw4002), @3(zxw3000, zxw3001, zxw3002), cch, cda, cdb) → new_asAs(new_esEs28(zxw4000, zxw3000, cch), new_asAs(new_esEs27(zxw4001, zxw3001, cda), new_esEs26(zxw4002, zxw3002, cdb)))
new_esEs6(Just(zxw4000), Just(zxw3000), app(ty_[], fb)) → new_esEs13(zxw4000, zxw3000, fb)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Int) → new_ltEs9(zxw79000, zxw80000)
new_esEs9(EQ, LT) → False
new_esEs9(LT, EQ) → False
new_compare26(Right(zxw7900), Right(zxw8000), False, gh, ha) → new_compare14(zxw7900, zxw8000, new_ltEs20(zxw7900, zxw8000, ha), gh, ha)
new_compare11(zxw79000, zxw80000, True) → LT
new_ltEs5(zxw79001, zxw80001, ty_@0) → new_ltEs8(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, ty_Bool) → new_lt12(zxw79001, zxw80001)
new_esEs30(zxw400, zxw300, ty_Integer) → new_esEs15(zxw400, zxw300)
new_compare14(zxw242, zxw243, True, dfe, dff) → LT
new_esEs32(zxw20, zxw15, app(ty_Ratio, cde)) → new_esEs18(zxw20, zxw15, cde)
new_esEs29(zxw400, zxw300, app(app(ty_Either, beh), bdf)) → new_esEs7(zxw400, zxw300, beh, bdf)
new_esEs14(False, False) → True
new_esEs18(:%(zxw4000, zxw4001), :%(zxw3000, zxw3001), ccd) → new_asAs(new_esEs25(zxw4000, zxw3000, ccd), new_esEs24(zxw4001, zxw3001, ccd))
new_compare26(Left(zxw7900), Left(zxw8000), False, gh, ha) → new_compare13(zxw7900, zxw8000, new_ltEs19(zxw7900, zxw8000, gh), gh, ha)
new_ltEs19(zxw7900, zxw8000, ty_Double) → new_ltEs15(zxw7900, zxw8000)
new_ltEs7(EQ, LT) → False
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Char) → new_esEs12(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_ltEs7(LT, LT) → True
new_lt20(zxw79001, zxw80001, app(app(app(ty_@3, bgf), bgg), bgh)) → new_lt5(zxw79001, zxw80001, bgf, bgg, bgh)
new_esEs29(zxw400, zxw300, ty_@0) → new_esEs10(zxw400, zxw300)
new_lt14(zxw790, zxw800, gh, ha) → new_esEs9(new_compare15(zxw790, zxw800, gh, ha), LT)
new_esEs22(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_ltEs9(zxw7900, zxw8000) → new_fsEs(new_compare16(zxw7900, zxw8000))
new_compare29(zxw79000, zxw80000, ty_Ordering) → new_compare18(zxw79000, zxw80000)
new_primPlusNat1(Zero, Zero) → Zero
new_esEs26(zxw4002, zxw3002, ty_Ordering) → new_esEs9(zxw4002, zxw3002)
new_esEs19(zxw79001, zxw80001, ty_Integer) → new_esEs15(zxw79001, zxw80001)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Char, hg) → new_ltEs10(zxw79000, zxw80000)
new_asAs(True, zxw230) → zxw230
new_esEs25(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_ltEs7(LT, GT) → True
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Float) → new_esEs17(zxw4000, zxw3000)
new_ltEs5(zxw79001, zxw80001, ty_Float) → new_ltEs16(zxw79001, zxw80001)
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, app(ty_Ratio, bfa)) → new_esEs18(zxw4000, zxw3000, bfa)
new_esEs27(zxw4001, zxw3001, app(ty_[], dhb)) → new_esEs13(zxw4001, zxw3001, dhb)
new_esEs6(Just(zxw4000), Just(zxw3000), app(app(ty_Either, fg), fh)) → new_esEs7(zxw4000, zxw3000, fg, fh)
new_esEs32(zxw20, zxw15, ty_Double) → new_esEs16(zxw20, zxw15)
new_compare28(zxw79000, zxw80000, False, bbh) → new_compare111(zxw79000, zxw80000, new_ltEs18(zxw79000, zxw80000, bbh), bbh)
new_compare1(:(zxw79000, zxw79001), [], he) → GT
new_esEs28(zxw4000, zxw3000, app(ty_Ratio, eac)) → new_esEs18(zxw4000, zxw3000, eac)
new_lt4(zxw79000, zxw80000, ty_Integer) → new_lt13(zxw79000, zxw80000)
new_esEs30(zxw400, zxw300, ty_Int) → new_esEs11(zxw400, zxw300)
new_esEs19(zxw79001, zxw80001, ty_@0) → new_esEs10(zxw79001, zxw80001)
new_compare29(zxw79000, zxw80000, ty_@0) → new_compare30(zxw79000, zxw80000)
new_ltEs19(zxw7900, zxw8000, ty_Integer) → new_ltEs13(zxw7900, zxw8000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(ty_Ratio, cha)) → new_ltEs17(zxw79000, zxw80000, cha)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Integer) → new_ltEs13(zxw79000, zxw80000)
new_ltEs19(zxw7900, zxw8000, ty_Ordering) → new_ltEs7(zxw7900, zxw8000)
new_compare28(zxw79000, zxw80000, True, bbh) → EQ
new_esEs31(zxw35, zxw30, ty_Int) → new_esEs11(zxw35, zxw30)
new_esEs26(zxw4002, zxw3002, ty_Double) → new_esEs16(zxw4002, zxw3002)
new_esEs30(zxw400, zxw300, ty_Double) → new_esEs16(zxw400, zxw300)
new_esEs29(zxw400, zxw300, ty_Float) → new_esEs17(zxw400, zxw300)
new_compare10(zxw79000, zxw80000, True) → LT
new_esEs31(zxw35, zxw30, ty_Bool) → new_esEs14(zxw35, zxw30)
new_esEs19(zxw79001, zxw80001, app(ty_[], bha)) → new_esEs13(zxw79001, zxw80001, bha)
new_esEs29(zxw400, zxw300, ty_Bool) → new_esEs14(zxw400, zxw300)
new_compare10(zxw79000, zxw80000, False) → GT
new_esEs9(LT, LT) → True
new_ltEs20(zxw7900, zxw8000, ty_Char) → new_ltEs10(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, ty_Ordering) → new_ltEs7(zxw7900, zxw8000)
new_primCompAux00(zxw276, GT) → GT
new_esEs31(zxw35, zxw30, app(ty_Maybe, bce)) → new_esEs6(zxw35, zxw30, bce)
new_compare18(zxw79000, zxw80000) → new_compare24(zxw79000, zxw80000, new_esEs9(zxw79000, zxw80000))
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_@0) → new_ltEs8(zxw79000, zxw80000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs7(Right(zxw4000), Right(zxw3000), beh, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_esEs29(zxw400, zxw300, ty_Ordering) → new_esEs9(zxw400, zxw300)
new_lt19(zxw79000, zxw80000, ty_Char) → new_lt9(zxw79000, zxw80000)
new_esEs28(zxw4000, zxw3000, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_ltEs19(zxw7900, zxw8000, app(ty_Maybe, baa)) → new_ltEs18(zxw7900, zxw8000, baa)
new_esEs27(zxw4001, zxw3001, ty_Integer) → new_esEs15(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, app(ty_Ratio, dbg)) → new_esEs18(zxw4001, zxw3001, dbg)
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_esEs19(zxw79001, zxw80001, ty_Char) → new_esEs12(zxw79001, zxw80001)
new_esEs23(zxw4000, zxw3000, app(ty_[], ded)) → new_esEs13(zxw4000, zxw3000, ded)
new_ltEs17(zxw7900, zxw8000, hh) → new_fsEs(new_compare8(zxw7900, zxw8000, hh))
new_not(True) → False
new_ltEs4(@2(zxw79000, zxw79001), @2(zxw80000, zxw80001), ca, cb) → new_pePe(new_lt4(zxw79000, zxw80000, ca), new_asAs(new_esEs8(zxw79000, zxw80000, ca), new_ltEs5(zxw79001, zxw80001, cb)))
new_compare1([], [], he) → EQ
new_esEs6(Just(zxw4000), Just(zxw3000), app(ty_Ratio, fa)) → new_esEs18(zxw4000, zxw3000, fa)

The set Q consists of the following terms:

new_compare23(x0, x1, True)
new_lt6(x0, x1)
new_ltEs5(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, ty_Integer)
new_lt4(x0, x1, app(ty_[], x2))
new_ltEs18(Just(x0), Just(x1), ty_@0)
new_compare16(x0, x1)
new_lt4(x0, x1, app(app(ty_@2, x2), x3))
new_compare13(x0, x1, False, x2, x3)
new_ltEs18(Just(x0), Nothing, x1)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, ty_Double)
new_esEs19(x0, x1, ty_Bool)
new_esEs8(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(x0, x1, app(app(ty_Either, x2), x3))
new_compare30(@0, @0)
new_primCompAux00(x0, GT)
new_esEs30(x0, x1, ty_@0)
new_lt19(x0, x1, ty_Char)
new_esEs30(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_Ordering)
new_compare17(Char(x0), Char(x1))
new_esEs28(x0, x1, ty_Int)
new_ltEs20(x0, x1, app(ty_[], x2))
new_ltEs21(x0, x1, ty_Ordering)
new_ltEs15(x0, x1)
new_primPlusNat1(Zero, Succ(x0))
new_esEs6(Just(x0), Just(x1), ty_Double)
new_compare24(x0, x1, False)
new_lt20(x0, x1, ty_Char)
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, ty_Bool)
new_sr0(Integer(x0), Integer(x1))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare210(x0, x1, False, x2, x3)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs7(Right(x0), Right(x1), x2, ty_Float)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs18(Nothing, Nothing, x0)
new_ltEs7(EQ, EQ)
new_esEs7(Right(x0), Right(x1), x2, ty_Integer)
new_compare29(x0, x1, app(app(ty_@2, x2), x3))
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs19(x0, x1, ty_Integer)
new_ltEs20(x0, x1, ty_Bool)
new_ltEs14(Right(x0), Right(x1), x2, ty_Float)
new_esEs6(Just(x0), Just(x1), app(ty_[], x2))
new_esEs31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_compare25(x0, x1, False, x2, x3, x4)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_ltEs19(x0, x1, ty_Integer)
new_ltEs5(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(ty_[], x2))
new_lt10(x0, x1, x2)
new_ltEs7(EQ, LT)
new_ltEs7(LT, EQ)
new_esEs20(x0, x1, ty_Ordering)
new_esEs17(Float(x0, x1), Float(x2, x3))
new_compare25(x0, x1, True, x2, x3, x4)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_lt19(x0, x1, ty_Ordering)
new_esEs29(x0, x1, ty_@0)
new_esEs26(x0, x1, app(ty_[], x2))
new_ltEs16(x0, x1)
new_lt4(x0, x1, app(ty_Maybe, x2))
new_compare110(x0, x1, False, x2, x3)
new_ltEs14(Left(x0), Left(x1), ty_Char, x2)
new_sr(x0, x1)
new_ltEs19(x0, x1, ty_Double)
new_compare7(Float(x0, x1), Float(x2, x3))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs9(x0, x1)
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_lt7(x0, x1)
new_lt4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, ty_Int)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat0(Zero, x0)
new_esEs7(Right(x0), Right(x1), x2, ty_@0)
new_esEs32(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_ltEs7(LT, LT)
new_esEs7(Right(x0), Right(x1), x2, ty_Double)
new_esEs4(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_Bool)
new_lt5(x0, x1, x2, x3, x4)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt4(x0, x1, ty_Ordering)
new_primEqNat0(Zero, Succ(x0))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Int)
new_esEs15(Integer(x0), Integer(x1))
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Left(x0), Left(x1), ty_Char, x2)
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs26(x0, x1, ty_Double)
new_compare29(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_@0)
new_primPlusNat1(Succ(x0), Zero)
new_esEs22(x0, x1, ty_Integer)
new_ltEs14(Left(x0), Left(x1), ty_@0, x2)
new_primMulInt(Neg(x0), Neg(x1))
new_ltEs19(x0, x1, ty_Int)
new_ltEs21(x0, x1, app(ty_Maybe, x2))
new_compare29(x0, x1, ty_Integer)
new_esEs14(True, True)
new_esEs21(x0, x1, ty_Char)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Int)
new_ltEs18(Just(x0), Just(x1), ty_Integer)
new_esEs24(x0, x1, ty_Int)
new_primEqNat0(Zero, Zero)
new_esEs16(Double(x0, x1), Double(x2, x3))
new_esEs12(Char(x0), Char(x1))
new_lt4(x0, x1, ty_Char)
new_compare29(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, ty_Bool)
new_esEs8(x0, x1, ty_Float)
new_compare1([], :(x0, x1), x2)
new_esEs30(x0, x1, ty_Ordering)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, ty_Integer)
new_esEs29(x0, x1, ty_Bool)
new_esEs30(x0, x1, ty_Bool)
new_esEs30(x0, x1, ty_Float)
new_esEs32(x0, x1, ty_@0)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs14(Left(x0), Left(x1), ty_Int, x2)
new_primCompAux00(x0, LT)
new_esEs27(x0, x1, ty_Integer)
new_ltEs21(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs5(x0, x1, ty_Double)
new_ltEs18(Just(x0), Just(x1), ty_Char)
new_primMulNat0(Zero, Zero)
new_compare110(x0, x1, True, x2, x3)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_lt9(x0, x1)
new_compare29(x0, x1, ty_Double)
new_ltEs5(x0, x1, ty_@0)
new_lt17(x0, x1, x2)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_compare36(x0, x1, x2, x3)
new_ltEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs31(x0, x1, ty_Bool)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Left(x0), Left(x1), ty_Float, x2)
new_esEs32(x0, x1, ty_Float)
new_esEs13([], :(x0, x1), x2)
new_esEs8(x0, x1, ty_Ordering)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_compare10(x0, x1, True)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs7(Left(x0), Left(x1), ty_Float, x2)
new_primEqNat0(Succ(x0), Succ(x1))
new_ltEs19(x0, x1, ty_Bool)
new_esEs28(x0, x1, ty_Double)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, ty_Float)
new_esEs29(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_@0)
new_pePe(True, x0)
new_esEs19(x0, x1, ty_Float)
new_esEs8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_lt16(x0, x1)
new_compare29(x0, x1, ty_Bool)
new_esEs20(x0, x1, app(ty_[], x2))
new_compare11(x0, x1, True)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_compare14(x0, x1, True, x2, x3)
new_esEs6(Just(x0), Just(x1), app(ty_Maybe, x2))
new_lt19(x0, x1, ty_@0)
new_esEs6(Just(x0), Just(x1), ty_Ordering)
new_esEs23(x0, x1, ty_@0)
new_compare29(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Right(x0), Right(x1), x2, ty_Int)
new_ltEs5(x0, x1, ty_Char)
new_esEs30(x0, x1, ty_Double)
new_ltEs21(x0, x1, ty_Int)
new_compare29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Float)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_compare29(x0, x1, ty_Ordering)
new_ltEs21(x0, x1, ty_@0)
new_esEs8(x0, x1, ty_Int)
new_lt14(x0, x1, x2, x3)
new_ltEs12(False, False)
new_esEs6(Just(x0), Just(x1), ty_Bool)
new_compare32(Integer(x0), Integer(x1))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_Int)
new_primMulNat0(Succ(x0), Succ(x1))
new_compare29(x0, x1, ty_Float)
new_ltEs21(x0, x1, ty_Integer)
new_esEs6(Just(x0), Just(x1), ty_Float)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs5(x0, x1, ty_Float)
new_ltEs18(Just(x0), Just(x1), ty_Float)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Bool)
new_esEs31(x0, x1, ty_Double)
new_esEs31(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpNat1(Zero, x0)
new_ltEs8(x0, x1)
new_esEs29(x0, x1, ty_Integer)
new_ltEs21(x0, x1, app(ty_[], x2))
new_primPlusNat1(Zero, Zero)
new_esEs30(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(ty_[], x2))
new_ltEs14(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs23(x0, x1, ty_Double)
new_ltEs18(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs18(Just(x0), Just(x1), ty_Ordering)
new_primCmpNat2(Zero, Zero)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs5(x0, x1, ty_Bool)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_compare28(x0, x1, True, x2)
new_ltEs14(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs5(x0, x1, app(ty_[], x2))
new_asAs(False, x0)
new_esEs29(x0, x1, ty_Ordering)
new_esEs31(x0, x1, app(ty_[], x2))
new_esEs30(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, ty_Char)
new_esEs31(x0, x1, app(app(ty_@2, x2), x3))
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(x0, x1, ty_Integer)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs19(x0, x1, app(ty_[], x2))
new_ltEs18(Just(x0), Just(x1), ty_Bool)
new_lt11(x0, x1, x2, x3)
new_primCmpNat1(Succ(x0), x1)
new_esEs32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs24(x0, x1, ty_Integer)
new_ltEs14(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs27(x0, x1, ty_@0)
new_ltEs14(Right(x0), Right(x1), x2, ty_Double)
new_lt4(x0, x1, ty_Float)
new_compare19(x0, x1, x2, x3)
new_ltEs5(x0, x1, app(app(ty_Either, x2), x3))
new_esEs19(x0, x1, ty_Char)
new_lt4(x0, x1, ty_Double)
new_esEs19(x0, x1, ty_Ordering)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs10(@0, @0)
new_esEs31(x0, x1, ty_@0)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs11(x0, x1)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, ty_Float)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_Char)
new_esEs9(GT, GT)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs27(x0, x1, ty_Char)
new_compare11(x0, x1, False)
new_compare23(x0, x1, False)
new_compare12(x0, x1, True, x2, x3, x4)
new_esEs28(x0, x1, ty_Bool)
new_esEs7(Right(x0), Left(x1), x2, x3)
new_esEs7(Left(x0), Right(x1), x2, x3)
new_compare24(x0, x1, True)
new_compare15(x0, x1, x2, x3)
new_primEqNat0(Succ(x0), Zero)
new_esEs23(x0, x1, ty_Ordering)
new_esEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs7(Right(x0), Right(x1), x2, ty_Int)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_esEs32(x0, x1, app(app(ty_Either, x2), x3))
new_compare9(x0, x1, x2, x3, x4)
new_lt20(x0, x1, ty_Int)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Integer)
new_lt4(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Int)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs5(x0, x1, app(app(ty_@2, x2), x3))
new_lt4(x0, x1, ty_@0)
new_esEs23(x0, x1, ty_Char)
new_esEs28(x0, x1, ty_Ordering)
new_ltEs18(Just(x0), Just(x1), ty_Double)
new_esEs30(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_Integer)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_compare14(x0, x1, False, x2, x3)
new_lt20(x0, x1, ty_@0)
new_compare1([], [], x0)
new_esEs9(EQ, EQ)
new_pePe(False, x0)
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs5(x0, x1, app(ty_Ratio, x2))
new_ltEs18(Just(x0), Just(x1), app(ty_[], x2))
new_esEs6(Just(x0), Just(x1), ty_Char)
new_esEs25(x0, x1, ty_Integer)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs18(:%(x0, x1), :%(x2, x3), x4)
new_esEs26(x0, x1, ty_Integer)
new_compare12(x0, x1, False, x2, x3, x4)
new_esEs8(x0, x1, app(ty_Maybe, x2))
new_primCompAux00(x0, EQ)
new_esEs19(x0, x1, ty_Int)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs14(True, False)
new_esEs14(False, True)
new_lt4(x0, x1, ty_Integer)
new_esEs7(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs14(Right(x0), Right(x1), x2, ty_@0)
new_fsEs(x0)
new_esEs22(x0, x1, ty_Float)
new_lt4(x0, x1, ty_Bool)
new_primCmpNat2(Succ(x0), Succ(x1))
new_asAs(True, x0)
new_ltEs18(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, ty_Bool)
new_esEs6(Nothing, Just(x0), x1)
new_esEs6(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs6(Just(x0), Nothing, x1)
new_lt18(x0, x1, x2)
new_esEs8(x0, x1, app(ty_[], x2))
new_esEs31(x0, x1, ty_Integer)
new_compare111(x0, x1, False, x2)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs8(x0, x1, ty_Char)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, ty_Float)
new_ltEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs22(x0, x1, ty_@0)
new_esEs20(x0, x1, ty_Char)
new_esEs13(:(x0, x1), [], x2)
new_ltEs12(False, True)
new_ltEs12(True, False)
new_compare6(Double(x0, x1), Double(x2, x3))
new_ltEs20(x0, x1, ty_@0)
new_esEs22(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_@0)
new_ltEs18(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare35(x0, x1, x2, x3)
new_ltEs14(Right(x0), Right(x1), x2, ty_Integer)
new_lt19(x0, x1, ty_Double)
new_esEs32(x0, x1, app(ty_[], x2))
new_lt19(x0, x1, ty_Bool)
new_ltEs14(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs7(Right(x0), Right(x1), x2, ty_Char)
new_ltEs14(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs26(x0, x1, ty_Char)
new_ltEs14(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs5(x0, x1, ty_Int)
new_lt4(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_Double)
new_esEs32(x0, x1, app(ty_Ratio, x2))
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_esEs19(x0, x1, ty_@0)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs21(x0, x1, ty_Bool)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs14(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs21(x0, x1, ty_Double)
new_lt12(x0, x1)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs8(x0, x1, ty_Bool)
new_ltEs21(x0, x1, ty_Char)
new_lt13(x0, x1)
new_esEs13(:(x0, x1), :(x2, x3), x4)
new_esEs31(x0, x1, ty_Ordering)
new_ltEs14(Right(x0), Right(x1), x2, ty_Bool)
new_compare1(:(x0, x1), [], x2)
new_compare27(x0, x1, x2)
new_compare10(x0, x1, False)
new_esEs27(x0, x1, app(ty_[], x2))
new_primMulNat0(Succ(x0), Zero)
new_ltEs19(x0, x1, ty_Float)
new_ltEs14(Left(x0), Right(x1), x2, x3)
new_esEs23(x0, x1, ty_Float)
new_ltEs14(Right(x0), Left(x1), x2, x3)
new_compare29(x0, x1, ty_Int)
new_esEs22(x0, x1, ty_Int)
new_esEs31(x0, x1, app(ty_Maybe, x2))
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Float)
new_compare31(x0, x1)
new_esEs29(x0, x1, ty_Double)
new_esEs32(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Left(x0), Left(x1), ty_Double, x2)
new_esEs31(x0, x1, ty_Char)
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Just(x0), Just(x1), ty_Int)
new_compare33(x0, x1, x2, x3)
new_esEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs21(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs7(LT, GT)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs7(GT, LT)
new_ltEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Double)
new_compare29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare111(x0, x1, True, x2)
new_ltEs13(x0, x1)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs32(x0, x1, app(ty_Maybe, x2))
new_esEs31(x0, x1, ty_Int)
new_lt4(x0, x1, ty_Int)
new_ltEs11(x0, x1, x2)
new_lt20(x0, x1, ty_Float)
new_not(True)
new_esEs31(x0, x1, ty_Float)
new_esEs20(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Float)
new_esEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs6(Nothing, Nothing, x0)
new_esEs28(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Ordering)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(Left(x0), Left(x1), ty_Double, x2)
new_esEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs6(Just(x0), Just(x1), ty_Integer)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_not(False)
new_lt8(x0, x1)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_ltEs18(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare13(x0, x1, True, x2, x3)
new_esEs32(x0, x1, ty_Integer)
new_esEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs19(x0, x1, ty_Char)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_esEs6(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare8(:%(x0, x1), :%(x2, x3), ty_Integer)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_Integer)
new_esEs8(x0, x1, ty_@0)
new_compare26(Left(x0), Left(x1), False, x2, x3)
new_ltEs12(True, True)
new_esEs27(x0, x1, ty_Float)
new_lt15(x0, x1)
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, ty_Ordering)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, ty_Double)
new_esEs6(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_lt20(x0, x1, ty_Ordering)
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs22(x0, x1, ty_Char)
new_lt20(x0, x1, ty_Double)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Bool)
new_esEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_ltEs21(x0, x1, ty_Float)
new_ltEs10(x0, x1)
new_ltEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs14(Left(x0), Left(x1), ty_Bool, x2)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs14(Left(x0), Left(x1), ty_Integer, x2)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(x0, x1, ty_Ordering)
new_esEs8(x0, x1, ty_Double)
new_compare29(x0, x1, ty_Char)
new_esEs6(Just(x0), Just(x1), ty_@0)
new_compare1(:(x0, x1), :(x2, x3), x4)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_compare210(x0, x1, True, x2, x3)
new_esEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs6(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs29(x0, x1, ty_Float)
new_esEs19(x0, x1, ty_Double)
new_esEs14(False, False)
new_primEqInt(Pos(Zero), Pos(Zero))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs32(x0, x1, ty_Char)
new_lt19(x0, x1, app(ty_[], x2))
new_ltEs21(x0, x1, ty_Double)
new_esEs32(x0, x1, ty_Int)
new_primCmpNat2(Succ(x0), Zero)
new_compare34(x0, x1, x2, x3)
new_compare18(x0, x1)
new_esEs29(x0, x1, ty_Int)
new_esEs32(x0, x1, ty_Bool)
new_compare28(x0, x1, False, x2)
new_ltEs14(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs18(Just(x0), Just(x1), ty_Int)
new_compare26(Right(x0), Right(x1), False, x2, x3)
new_ltEs17(x0, x1, x2)
new_primPlusNat0(Succ(x0), x1)
new_esEs7(Left(x0), Left(x1), ty_Int, x2)
new_esEs20(x0, x1, ty_Integer)
new_primCmpNat0(x0, Zero)
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_esEs7(Left(x0), Left(x1), ty_@0, x2)
new_ltEs7(GT, EQ)
new_ltEs7(EQ, GT)
new_esEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs32(x0, x1, ty_Double)
new_ltEs7(GT, GT)
new_esEs31(x0, x1, app(ty_Ratio, x2))
new_esEs9(LT, LT)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs13([], [], x0)
new_primCompAux0(x0, x1, x2, x3)
new_compare29(x0, x1, ty_@0)
new_esEs7(Left(x0), Left(x1), ty_Bool, x2)
new_compare26(x0, x1, True, x2, x3)
new_compare26(Right(x0), Left(x1), False, x2, x3)
new_compare26(Left(x0), Right(x1), False, x2, x3)
new_ltEs18(Nothing, Just(x0), x1)
new_esEs27(x0, x1, ty_Ordering)
new_primCmpNat0(x0, Succ(x1))

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

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

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

new_splitLT22(zxw60, zxw61, zxw62, zxw63, zxw64, zxw65, True, bf, bg, bh) → new_splitLT0(zxw63, zxw65, bf, bg, bh)
new_splitLT11(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, True, h, ba, bb) → new_splitLT0(zxw34, zxw400, h, ba, bb)
new_splitLT21(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, False, h, ba, bb) → new_splitLT11(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs9(new_compare35(zxw400, zxw300, h, ba), GT), h, ba, bb)
new_splitLT21(zxw300, zxw31, zxw32, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw34, zxw400, True, h, ba, bb) → new_splitLT3(zxw330, zxw331, zxw332, zxw333, zxw334, Right(zxw400), h, ba, bb)
new_splitLT3(Right(zxw300), zxw31, zxw32, zxw33, zxw34, Right(zxw400), h, ba, bb) → new_splitLT22(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs9(new_compare26(Right(zxw400), Right(zxw300), new_esEs30(zxw400, zxw300, ba), h, ba), LT), h, ba, bb)
new_splitLT0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw400, h, ba, bb) → new_splitLT3(zxw330, zxw331, zxw332, zxw333, zxw334, Right(zxw400), h, ba, bb)
new_splitLT12(zxw60, zxw61, zxw62, zxw63, zxw64, zxw65, True, bf, bg, bh) → new_splitLT0(zxw64, zxw65, bf, bg, bh)
new_splitLT22(zxw60, zxw61, zxw62, zxw63, zxw64, zxw65, False, bf, bg, bh) → new_splitLT12(zxw60, zxw61, zxw62, zxw63, zxw64, zxw65, new_esEs9(new_compare36(zxw65, zxw60, bf, bg), GT), bf, bg, bh)
new_splitLT3(Left(zxw300), zxw31, zxw32, zxw33, zxw34, Right(zxw400), h, ba, bb) → new_splitLT21(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs9(new_compare26(Right(zxw400), Left(zxw300), False, h, ba), LT), h, ba, bb)

The TRS R consists of the following rules:

new_esEs30(zxw400, zxw300, app(ty_Maybe, dag)) → new_esEs6(zxw400, zxw300, dag)
new_ltEs15(zxw7900, zxw8000) → new_fsEs(new_compare6(zxw7900, zxw8000))
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Bool) → new_ltEs12(zxw79000, zxw80000)
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, app(ty_Maybe, bbc)) → new_ltEs18(zxw7900, zxw8000, bbc)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Char) → new_ltEs10(zxw79000, zxw80000)
new_esEs28(zxw4000, zxw3000, app(ty_[], ead)) → new_esEs13(zxw4000, zxw3000, ead)
new_esEs32(zxw20, zxw15, ty_Float) → new_esEs17(zxw20, zxw15)
new_esEs23(zxw4000, zxw3000, app(app(ty_Either, deh), dfa)) → new_esEs7(zxw4000, zxw3000, deh, dfa)
new_esEs6(Just(zxw4000), Just(zxw3000), app(app(ty_@2, fd), ff)) → new_esEs5(zxw4000, zxw3000, fd, ff)
new_lt4(zxw79000, zxw80000, app(app(app(ty_@3, cc), cd), ce)) → new_lt5(zxw79000, zxw80000, cc, cd, ce)
new_esEs31(zxw35, zxw30, ty_Ordering) → new_esEs9(zxw35, zxw30)
new_esEs7(Left(zxw4000), Left(zxw3000), app(app(ty_Either, bec), bed), bdf) → new_esEs7(zxw4000, zxw3000, bec, bed)
new_ltEs20(zxw7900, zxw8000, ty_Int) → new_ltEs9(zxw7900, zxw8000)
new_lt19(zxw79000, zxw80000, app(app(ty_Either, bgd), bge)) → new_lt14(zxw79000, zxw80000, bgd, bge)
new_esEs9(GT, LT) → False
new_esEs9(LT, GT) → False
new_esEs13([], [], cce) → True
new_lt4(zxw79000, zxw80000, app(ty_[], cf)) → new_lt10(zxw79000, zxw80000, cf)
new_compare110(zxw79000, zxw80000, True, bbd, bbe) → LT
new_esEs27(zxw4001, zxw3001, app(ty_Ratio, dha)) → new_esEs18(zxw4001, zxw3001, dha)
new_compare29(zxw79000, zxw80000, ty_Char) → new_compare17(zxw79000, zxw80000)
new_ltEs7(LT, EQ) → True
new_ltEs18(Just(zxw79000), Just(zxw80000), app(ty_Maybe, dad)) → new_ltEs18(zxw79000, zxw80000, dad)
new_esEs30(zxw400, zxw300, app(ty_[], daf)) → new_esEs13(zxw400, zxw300, daf)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Integer) → new_ltEs13(zxw79000, zxw80000)
new_ltEs20(zxw7900, zxw8000, ty_@0) → new_ltEs8(zxw7900, zxw8000)
new_lt20(zxw79001, zxw80001, app(app(ty_Either, bhd), bhe)) → new_lt14(zxw79001, zxw80001, bhd, bhe)
new_esEs23(zxw4000, zxw3000, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_compare35(zxw400, zxw300, h, ba) → new_compare26(Right(zxw400), Left(zxw300), False, h, ba)
new_ltEs8(zxw7900, zxw8000) → new_fsEs(new_compare30(zxw7900, zxw8000))
new_lt19(zxw79000, zxw80000, ty_Double) → new_lt15(zxw79000, zxw80000)
new_esEs22(zxw4000, zxw3000, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(ty_[], cgd)) → new_ltEs11(zxw79000, zxw80000, cgd)
new_ltEs21(zxw79002, zxw80002, ty_Char) → new_ltEs10(zxw79002, zxw80002)
new_esEs23(zxw4000, zxw3000, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Bool, hg) → new_ltEs12(zxw79000, zxw80000)
new_compare8(:%(zxw79000, zxw79001), :%(zxw80000, zxw80001), ty_Integer) → new_compare32(new_sr0(zxw79000, zxw80001), new_sr0(zxw80000, zxw79001))
new_esEs26(zxw4002, zxw3002, ty_Float) → new_esEs17(zxw4002, zxw3002)
new_esEs19(zxw79001, zxw80001, app(ty_Ratio, bhf)) → new_esEs18(zxw79001, zxw80001, bhf)
new_primMulNat0(Zero, Zero) → Zero
new_esEs20(zxw79000, zxw80000, app(ty_[], bgc)) → new_esEs13(zxw79000, zxw80000, bgc)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_lt20(zxw79001, zxw80001, ty_@0) → new_lt7(zxw79001, zxw80001)
new_esEs27(zxw4001, zxw3001, app(app(app(ty_@3, dhh), eaa), eab)) → new_esEs4(zxw4001, zxw3001, dhh, eaa, eab)
new_esEs19(zxw79001, zxw80001, ty_Ordering) → new_esEs9(zxw79001, zxw80001)
new_esEs31(zxw35, zxw30, ty_Char) → new_esEs12(zxw35, zxw30)
new_esEs32(zxw20, zxw15, ty_Integer) → new_esEs15(zxw20, zxw15)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(ty_Ratio, dac)) → new_ltEs17(zxw79000, zxw80000, dac)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Bool, bdf) → new_esEs14(zxw4000, zxw3000)
new_esEs24(zxw4001, zxw3001, ty_Integer) → new_esEs15(zxw4001, zxw3001)
new_lt19(zxw79000, zxw80000, ty_Ordering) → new_lt6(zxw79000, zxw80000)
new_lt20(zxw79001, zxw80001, app(app(ty_@2, bhb), bhc)) → new_lt11(zxw79001, zxw80001, bhb, bhc)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(ty_Ratio, cfg), hg) → new_ltEs17(zxw79000, zxw80000, cfg)
new_compare9(zxw79000, zxw80000, gd, ge, gf) → new_compare25(zxw79000, zxw80000, new_esEs4(zxw79000, zxw80000, gd, ge, gf), gd, ge, gf)
new_lt11(zxw79000, zxw80000, bbd, bbe) → new_esEs9(new_compare19(zxw79000, zxw80000, bbd, bbe), LT)
new_compare1([], :(zxw80000, zxw80001), he) → LT
new_esEs30(zxw400, zxw300, app(app(ty_Either, dbb), dbc)) → new_esEs7(zxw400, zxw300, dbb, dbc)
new_lt18(zxw79000, zxw80000, bbh) → new_esEs9(new_compare27(zxw79000, zxw80000, bbh), LT)
new_esEs8(zxw79000, zxw80000, ty_Int) → new_esEs11(zxw79000, zxw80000)
new_compare32(Integer(zxw79000), Integer(zxw80000)) → new_primCmpInt(zxw79000, zxw80000)
new_ltEs5(zxw79001, zxw80001, ty_Char) → new_ltEs10(zxw79001, zxw80001)
new_lt4(zxw79000, zxw80000, ty_Bool) → new_lt12(zxw79000, zxw80000)
new_compare27(zxw79000, zxw80000, bbh) → new_compare28(zxw79000, zxw80000, new_esEs6(zxw79000, zxw80000, bbh), bbh)
new_lt4(zxw79000, zxw80000, app(ty_Maybe, de)) → new_lt18(zxw79000, zxw80000, de)
new_compare29(zxw79000, zxw80000, ty_Bool) → new_compare31(zxw79000, zxw80000)
new_esEs31(zxw35, zxw30, ty_@0) → new_esEs10(zxw35, zxw30)
new_esEs8(zxw79000, zxw80000, ty_Double) → new_esEs16(zxw79000, zxw80000)
new_esEs22(zxw4000, zxw3000, app(app(ty_@2, ddd), dde)) → new_esEs5(zxw4000, zxw3000, ddd, dde)
new_lt4(zxw79000, zxw80000, ty_Ordering) → new_lt6(zxw79000, zxw80000)
new_esEs22(zxw4000, zxw3000, app(ty_Maybe, ddc)) → new_esEs6(zxw4000, zxw3000, ddc)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(app(app(ty_@3, cga), cgb), cgc)) → new_ltEs6(zxw79000, zxw80000, cga, cgb, cgc)
new_esEs27(zxw4001, zxw3001, app(ty_Maybe, dhc)) → new_esEs6(zxw4001, zxw3001, dhc)
new_esEs8(zxw79000, zxw80000, app(app(app(ty_@3, cc), cd), ce)) → new_esEs4(zxw79000, zxw80000, cc, cd, ce)
new_esEs15(Integer(zxw4000), Integer(zxw3000)) → new_primEqInt(zxw4000, zxw3000)
new_ltEs21(zxw79002, zxw80002, app(app(ty_@2, cad), cae)) → new_ltEs4(zxw79002, zxw80002, cad, cae)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Float, hg) → new_ltEs16(zxw79000, zxw80000)
new_lt5(zxw79000, zxw80000, gd, ge, gf) → new_esEs9(new_compare9(zxw79000, zxw80000, gd, ge, gf), LT)
new_esEs22(zxw4000, zxw3000, app(ty_Ratio, dda)) → new_esEs18(zxw4000, zxw3000, dda)
new_esEs29(zxw400, zxw300, ty_Integer) → new_esEs15(zxw400, zxw300)
new_esEs22(zxw4000, zxw3000, app(app(ty_Either, ddf), ddg)) → new_esEs7(zxw4000, zxw3000, ddf, ddg)
new_ltEs19(zxw7900, zxw8000, ty_Float) → new_ltEs16(zxw7900, zxw8000)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, app(ty_Maybe, bfc)) → new_esEs6(zxw4000, zxw3000, bfc)
new_pePe(False, zxw271) → zxw271
new_esEs29(zxw400, zxw300, ty_Double) → new_esEs16(zxw400, zxw300)
new_esEs7(Left(zxw4000), Right(zxw3000), beh, bdf) → False
new_esEs7(Right(zxw4000), Left(zxw3000), beh, bdf) → False
new_lt15(zxw79000, zxw80000) → new_esEs9(new_compare6(zxw79000, zxw80000), LT)
new_compare15(zxw790, zxw800, gh, ha) → new_compare26(zxw790, zxw800, new_esEs7(zxw790, zxw800, gh, ha), gh, ha)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Float) → new_ltEs16(zxw79000, zxw80000)
new_esEs31(zxw35, zxw30, app(app(app(ty_@3, bdb), bdc), bdd)) → new_esEs4(zxw35, zxw30, bdb, bdc, bdd)
new_ltEs12(True, False) → False
new_esEs20(zxw79000, zxw80000, ty_Double) → new_esEs16(zxw79000, zxw80000)
new_ltEs19(zxw7900, zxw8000, app(app(ty_@2, ca), cb)) → new_ltEs4(zxw7900, zxw8000, ca, cb)
new_esEs32(zxw20, zxw15, ty_@0) → new_esEs10(zxw20, zxw15)
new_compare23(zxw79000, zxw80000, True) → EQ
new_esEs31(zxw35, zxw30, ty_Float) → new_esEs17(zxw35, zxw30)
new_esEs27(zxw4001, zxw3001, app(app(ty_Either, dhf), dhg)) → new_esEs7(zxw4001, zxw3001, dhf, dhg)
new_esEs27(zxw4001, zxw3001, ty_Ordering) → new_esEs9(zxw4001, zxw3001)
new_esEs27(zxw4001, zxw3001, ty_Float) → new_esEs17(zxw4001, zxw3001)
new_esEs19(zxw79001, zxw80001, app(ty_Maybe, bhg)) → new_esEs6(zxw79001, zxw80001, bhg)
new_lt10(zxw79000, zxw80000, bgc) → new_esEs9(new_compare1(zxw79000, zxw80000, bgc), LT)
new_esEs26(zxw4002, zxw3002, ty_Char) → new_esEs12(zxw4002, zxw3002)
new_ltEs19(zxw7900, zxw8000, app(ty_[], he)) → new_ltEs11(zxw7900, zxw8000, he)
new_esEs26(zxw4002, zxw3002, ty_Int) → new_esEs11(zxw4002, zxw3002)
new_ltEs5(zxw79001, zxw80001, app(app(ty_@2, eb), ec)) → new_ltEs4(zxw79001, zxw80001, eb, ec)
new_lt19(zxw79000, zxw80000, app(ty_Ratio, gg)) → new_lt17(zxw79000, zxw80000, gg)
new_esEs22(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, app(app(app(ty_@3, ebb), ebc), ebd)) → new_esEs4(zxw4000, zxw3000, ebb, ebc, ebd)
new_esEs32(zxw20, zxw15, ty_Ordering) → new_esEs9(zxw20, zxw15)
new_compare29(zxw79000, zxw80000, app(app(ty_@2, cbf), cbg)) → new_compare19(zxw79000, zxw80000, cbf, cbg)
new_ltEs21(zxw79002, zxw80002, ty_Int) → new_ltEs9(zxw79002, zxw80002)
new_esEs20(zxw79000, zxw80000, ty_Char) → new_esEs12(zxw79000, zxw80000)
new_compare13(zxw235, zxw236, False, bbf, bbg) → GT
new_esEs9(GT, EQ) → False
new_esEs9(EQ, GT) → False
new_esEs19(zxw79001, zxw80001, app(app(ty_Either, bhd), bhe)) → new_esEs7(zxw79001, zxw80001, bhd, bhe)
new_esEs20(zxw79000, zxw80000, app(app(ty_@2, bbd), bbe)) → new_esEs5(zxw79000, zxw80000, bbd, bbe)
new_ltEs7(GT, GT) → True
new_compare36(zxw35, zxw30, bca, bcb) → new_compare26(Right(zxw35), Right(zxw30), new_esEs31(zxw35, zxw30, bcb), bca, bcb)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, app(app(ty_@2, bfd), bfe)) → new_esEs5(zxw4000, zxw3000, bfd, bfe)
new_ltEs20(zxw7900, zxw8000, app(app(ty_@2, baf), bag)) → new_ltEs4(zxw7900, zxw8000, baf, bag)
new_esEs21(zxw4001, zxw3001, ty_Bool) → new_esEs14(zxw4001, zxw3001)
new_esEs32(zxw20, zxw15, ty_Bool) → new_esEs14(zxw20, zxw15)
new_primCompAux0(zxw79000, zxw80000, zxw272, he) → new_primCompAux00(zxw272, new_compare29(zxw79000, zxw80000, he))
new_ltEs21(zxw79002, zxw80002, ty_Ordering) → new_ltEs7(zxw79002, zxw80002)
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_compare29(zxw79000, zxw80000, app(ty_[], cbe)) → new_compare1(zxw79000, zxw80000, cbe)
new_lt20(zxw79001, zxw80001, ty_Ordering) → new_lt6(zxw79001, zxw80001)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_esEs8(zxw79000, zxw80000, app(ty_[], cf)) → new_esEs13(zxw79000, zxw80000, cf)
new_esEs27(zxw4001, zxw3001, ty_@0) → new_esEs10(zxw4001, zxw3001)
new_compare25(zxw79000, zxw80000, True, gd, ge, gf) → EQ
new_esEs19(zxw79001, zxw80001, ty_Float) → new_esEs17(zxw79001, zxw80001)
new_ltEs5(zxw79001, zxw80001, ty_Ordering) → new_ltEs7(zxw79001, zxw80001)
new_lt4(zxw79000, zxw80000, app(ty_Ratio, dd)) → new_lt17(zxw79000, zxw80000, dd)
new_esEs28(zxw4000, zxw3000, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Int, bdf) → new_esEs11(zxw4000, zxw3000)
new_ltEs21(zxw79002, zxw80002, ty_Float) → new_ltEs16(zxw79002, zxw80002)
new_esEs28(zxw4000, zxw3000, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_compare29(zxw79000, zxw80000, app(app(app(ty_@3, cbb), cbc), cbd)) → new_compare9(zxw79000, zxw80000, cbb, cbc, cbd)
new_lt19(zxw79000, zxw80000, app(app(ty_@2, bbd), bbe)) → new_lt11(zxw79000, zxw80000, bbd, bbe)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(app(app(ty_@3, chc), chd), che)) → new_ltEs6(zxw79000, zxw80000, chc, chd, che)
new_pePe(True, zxw271) → True
new_primEqNat0(Zero, Zero) → True
new_compare14(zxw242, zxw243, False, dfe, dff) → GT
new_esEs20(zxw79000, zxw80000, ty_Int) → new_esEs11(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Double) → new_ltEs15(zxw79000, zxw80000)
new_ltEs21(zxw79002, zxw80002, ty_Bool) → new_ltEs12(zxw79002, zxw80002)
new_lt9(zxw79000, zxw80000) → new_esEs9(new_compare17(zxw79000, zxw80000), LT)
new_esEs29(zxw400, zxw300, app(ty_Maybe, eh)) → new_esEs6(zxw400, zxw300, eh)
new_ltEs12(False, False) → True
new_esEs7(Left(zxw4000), Left(zxw3000), app(app(ty_@2, bea), beb), bdf) → new_esEs5(zxw4000, zxw3000, bea, beb)
new_esEs26(zxw4002, zxw3002, app(ty_Maybe, dga)) → new_esEs6(zxw4002, zxw3002, dga)
new_compare8(:%(zxw79000, zxw79001), :%(zxw80000, zxw80001), ty_Int) → new_compare16(new_sr(zxw79000, zxw80001), new_sr(zxw80000, zxw79001))
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Ordering, bdf) → new_esEs9(zxw4000, zxw3000)
new_esEs29(zxw400, zxw300, app(ty_[], cce)) → new_esEs13(zxw400, zxw300, cce)
new_esEs27(zxw4001, zxw3001, ty_Char) → new_esEs12(zxw4001, zxw3001)
new_lt7(zxw79000, zxw80000) → new_esEs9(new_compare30(zxw79000, zxw80000), LT)
new_compare110(zxw79000, zxw80000, False, bbd, bbe) → GT
new_sr(zxw4000, zxw3000) → new_primMulInt(zxw4000, zxw3000)
new_compare12(zxw79000, zxw80000, True, gd, ge, gf) → LT
new_esEs30(zxw400, zxw300, ty_Char) → new_esEs12(zxw400, zxw300)
new_lt19(zxw79000, zxw80000, ty_Int) → new_lt8(zxw79000, zxw80000)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(app(ty_@2, cge), cgf)) → new_ltEs4(zxw79000, zxw80000, cge, cgf)
new_ltEs19(zxw7900, zxw8000, ty_Char) → new_ltEs10(zxw7900, zxw8000)
new_esEs30(zxw400, zxw300, app(app(app(ty_@3, dbd), dbe), dbf)) → new_esEs4(zxw400, zxw300, dbd, dbe, dbf)
new_esEs21(zxw4001, zxw3001, ty_Double) → new_esEs16(zxw4001, zxw3001)
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, app(app(ty_Either, bff), bfg)) → new_esEs7(zxw4000, zxw3000, bff, bfg)
new_esEs31(zxw35, zxw30, app(app(ty_Either, bch), bda)) → new_esEs7(zxw35, zxw30, bch, bda)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Double, hg) → new_ltEs15(zxw79000, zxw80000)
new_ltEs19(zxw7900, zxw8000, ty_Bool) → new_ltEs12(zxw7900, zxw8000)
new_esEs26(zxw4002, zxw3002, app(app(app(ty_@3, dgf), dgg), dgh)) → new_esEs4(zxw4002, zxw3002, dgf, dgg, dgh)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, app(ty_[], bfb)) → new_esEs13(zxw4000, zxw3000, bfb)
new_ltEs11(zxw7900, zxw8000, he) → new_fsEs(new_compare1(zxw7900, zxw8000, he))
new_ltEs20(zxw7900, zxw8000, ty_Float) → new_ltEs16(zxw7900, zxw8000)
new_esEs21(zxw4001, zxw3001, ty_Ordering) → new_esEs9(zxw4001, zxw3001)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_esEs9(EQ, EQ) → True
new_fsEs(zxw259) → new_not(new_esEs9(zxw259, GT))
new_esEs8(zxw79000, zxw80000, ty_Char) → new_esEs12(zxw79000, zxw80000)
new_primEqInt(Neg(Succ(zxw40000)), Neg(Succ(zxw30000))) → new_primEqNat0(zxw40000, zxw30000)
new_esEs8(zxw79000, zxw80000, app(app(ty_@2, cg), da)) → new_esEs5(zxw79000, zxw80000, cg, da)
new_compare13(zxw235, zxw236, True, bbf, bbg) → LT
new_compare26(Left(zxw7900), Right(zxw8000), False, gh, ha) → LT
new_esEs13(:(zxw4000, zxw4001), :(zxw3000, zxw3001), cce) → new_asAs(new_esEs23(zxw4000, zxw3000, cce), new_esEs13(zxw4001, zxw3001, cce))
new_esEs26(zxw4002, zxw3002, app(ty_[], dfh)) → new_esEs13(zxw4002, zxw3002, dfh)
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_ltEs19(zxw7900, zxw8000, app(ty_Ratio, hh)) → new_ltEs17(zxw7900, zxw8000, hh)
new_esEs30(zxw400, zxw300, ty_Float) → new_esEs17(zxw400, zxw300)
new_ltEs20(zxw7900, zxw8000, ty_Bool) → new_ltEs12(zxw7900, zxw8000)
new_esEs21(zxw4001, zxw3001, ty_Char) → new_esEs12(zxw4001, zxw3001)
new_compare23(zxw79000, zxw80000, False) → new_compare10(zxw79000, zxw80000, new_ltEs12(zxw79000, zxw80000))
new_ltEs14(Right(zxw79000), Left(zxw80000), hf, hg) → False
new_compare210(zxw79000, zxw80000, False, bbd, bbe) → new_compare110(zxw79000, zxw80000, new_ltEs4(zxw79000, zxw80000, bbd, bbe), bbd, bbe)
new_primCmpNat1(Zero, zxw7900) → LT
new_compare7(Float(zxw79000, zxw79001), Float(zxw80000, zxw80001)) → new_compare16(new_sr(zxw79000, zxw80000), new_sr(zxw79001, zxw80001))
new_ltEs21(zxw79002, zxw80002, ty_Integer) → new_ltEs13(zxw79002, zxw80002)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_lt20(zxw79001, zxw80001, app(ty_Maybe, bhg)) → new_lt18(zxw79001, zxw80001, bhg)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Integer, bdf) → new_esEs15(zxw4000, zxw3000)
new_ltEs5(zxw79001, zxw80001, ty_Bool) → new_ltEs12(zxw79001, zxw80001)
new_esEs19(zxw79001, zxw80001, ty_Bool) → new_esEs14(zxw79001, zxw80001)
new_ltEs7(EQ, EQ) → True
new_ltEs20(zxw7900, zxw8000, app(ty_Ratio, bbb)) → new_ltEs17(zxw7900, zxw8000, bbb)
new_primEqInt(Neg(Zero), Neg(Succ(zxw30000))) → False
new_primEqInt(Neg(Succ(zxw40000)), Neg(Zero)) → False
new_ltEs5(zxw79001, zxw80001, ty_Integer) → new_ltEs13(zxw79001, zxw80001)
new_compare26(zxw790, zxw800, True, gh, ha) → EQ
new_compare111(zxw79000, zxw80000, True, bbh) → LT
new_esEs20(zxw79000, zxw80000, ty_@0) → new_esEs10(zxw79000, zxw80000)
new_esEs31(zxw35, zxw30, app(ty_Ratio, bcc)) → new_esEs18(zxw35, zxw30, bcc)
new_ltEs21(zxw79002, zxw80002, app(app(ty_Either, caf), cag)) → new_ltEs14(zxw79002, zxw80002, caf, cag)
new_esEs8(zxw79000, zxw80000, ty_Float) → new_esEs17(zxw79000, zxw80000)
new_esEs23(zxw4000, zxw3000, app(app(app(ty_@3, dfb), dfc), dfd)) → new_esEs4(zxw4000, zxw3000, dfb, dfc, dfd)
new_ltEs21(zxw79002, zxw80002, app(ty_[], cac)) → new_ltEs11(zxw79002, zxw80002, cac)
new_esEs21(zxw4001, zxw3001, ty_Float) → new_esEs17(zxw4001, zxw3001)
new_compare24(zxw79000, zxw80000, False) → new_compare11(zxw79000, zxw80000, new_ltEs7(zxw79000, zxw80000))
new_ltEs5(zxw79001, zxw80001, app(ty_Ratio, ef)) → new_ltEs17(zxw79001, zxw80001, ef)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_esEs26(zxw4002, zxw3002, app(app(ty_Either, dgd), dge)) → new_esEs7(zxw4002, zxw3002, dgd, dge)
new_lt20(zxw79001, zxw80001, ty_Int) → new_lt8(zxw79001, zxw80001)
new_lt4(zxw79000, zxw80000, ty_Int) → new_lt8(zxw79000, zxw80000)
new_ltEs20(zxw7900, zxw8000, ty_Double) → new_ltEs15(zxw7900, zxw8000)
new_ltEs7(GT, LT) → False
new_lt12(zxw79000, zxw80000) → new_esEs9(new_compare31(zxw79000, zxw80000), LT)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Int, hg) → new_ltEs9(zxw79000, zxw80000)
new_lt20(zxw79001, zxw80001, ty_Integer) → new_lt13(zxw79001, zxw80001)
new_ltEs7(GT, EQ) → False
new_esEs6(Nothing, Nothing, eh) → True
new_primEqInt(Pos(Succ(zxw40000)), Pos(Succ(zxw30000))) → new_primEqNat0(zxw40000, zxw30000)
new_lt8(zxw790, zxw800) → new_esEs9(new_compare16(zxw790, zxw800), LT)
new_esEs21(zxw4001, zxw3001, app(ty_Maybe, dca)) → new_esEs6(zxw4001, zxw3001, dca)
new_lt6(zxw79000, zxw80000) → new_esEs9(new_compare18(zxw79000, zxw80000), LT)
new_esEs32(zxw20, zxw15, app(app(ty_Either, ceb), cec)) → new_esEs7(zxw20, zxw15, ceb, cec)
new_esEs14(False, True) → False
new_esEs14(True, False) → False
new_esEs32(zxw20, zxw15, app(ty_[], cdf)) → new_esEs13(zxw20, zxw15, cdf)
new_esEs26(zxw4002, zxw3002, ty_Integer) → new_esEs15(zxw4002, zxw3002)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, app(app(app(ty_@3, bfh), bga), bgb)) → new_esEs4(zxw4000, zxw3000, bfh, bga, bgb)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs6(Nothing, Just(zxw3000), eh) → False
new_esEs6(Just(zxw4000), Nothing, eh) → False
new_primEqNat0(Succ(zxw40000), Succ(zxw30000)) → new_primEqNat0(zxw40000, zxw30000)
new_esEs16(Double(zxw4000, zxw4001), Double(zxw3000, zxw3001)) → new_esEs11(new_sr(zxw4000, zxw3000), new_sr(zxw4001, zxw3001))
new_lt19(zxw79000, zxw80000, ty_@0) → new_lt7(zxw79000, zxw80000)
new_esEs30(zxw400, zxw300, app(ty_Ratio, dae)) → new_esEs18(zxw400, zxw300, dae)
new_ltEs5(zxw79001, zxw80001, app(ty_Maybe, eg)) → new_ltEs18(zxw79001, zxw80001, eg)
new_esEs17(Float(zxw4000, zxw4001), Float(zxw3000, zxw3001)) → new_esEs11(new_sr(zxw4000, zxw3000), new_sr(zxw4001, zxw3001))
new_primCompAux00(zxw276, LT) → LT
new_esEs28(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), app(ty_Ratio, bde), bdf) → new_esEs18(zxw4000, zxw3000, bde)
new_esEs21(zxw4001, zxw3001, ty_Int) → new_esEs11(zxw4001, zxw3001)
new_compare1(:(zxw79000, zxw79001), :(zxw80000, zxw80001), he) → new_primCompAux0(zxw79000, zxw80000, new_compare1(zxw79001, zxw80001, he), he)
new_primEqInt(Pos(Zero), Pos(Succ(zxw30000))) → False
new_primEqInt(Pos(Succ(zxw40000)), Pos(Zero)) → False
new_compare29(zxw79000, zxw80000, ty_Int) → new_compare16(zxw79000, zxw80000)
new_lt20(zxw79001, zxw80001, app(ty_Ratio, bhf)) → new_lt17(zxw79001, zxw80001, bhf)
new_ltEs20(zxw7900, zxw8000, ty_Integer) → new_ltEs13(zxw7900, zxw8000)
new_esEs31(zxw35, zxw30, app(app(ty_@2, bcf), bcg)) → new_esEs5(zxw35, zxw30, bcf, bcg)
new_esEs5(@2(zxw4000, zxw4001), @2(zxw3000, zxw3001), ccf, ccg) → new_asAs(new_esEs22(zxw4000, zxw3000, ccf), new_esEs21(zxw4001, zxw3001, ccg))
new_ltEs18(Nothing, Nothing, baa) → True
new_esEs32(zxw20, zxw15, app(ty_Maybe, cdg)) → new_esEs6(zxw20, zxw15, cdg)
new_ltEs21(zxw79002, zxw80002, app(ty_Ratio, cah)) → new_ltEs17(zxw79002, zxw80002, cah)
new_esEs23(zxw4000, zxw3000, app(app(ty_@2, def), deg)) → new_esEs5(zxw4000, zxw3000, def, deg)
new_esEs20(zxw79000, zxw80000, app(app(app(ty_@3, gd), ge), gf)) → new_esEs4(zxw79000, zxw80000, gd, ge, gf)
new_esEs29(zxw400, zxw300, app(app(app(ty_@3, cch), cda), cdb)) → new_esEs4(zxw400, zxw300, cch, cda, cdb)
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_ltEs21(zxw79002, zxw80002, app(app(app(ty_@3, bhh), caa), cab)) → new_ltEs6(zxw79002, zxw80002, bhh, caa, cab)
new_ltEs10(zxw7900, zxw8000) → new_fsEs(new_compare17(zxw7900, zxw8000))
new_compare17(Char(zxw79000), Char(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_sr0(Integer(zxw800000), Integer(zxw790010)) → Integer(new_primMulInt(zxw800000, zxw790010))
new_ltEs5(zxw79001, zxw80001, ty_Double) → new_ltEs15(zxw79001, zxw80001)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_esEs29(zxw400, zxw300, app(ty_Ratio, ccd)) → new_esEs18(zxw400, zxw300, ccd)
new_esEs8(zxw79000, zxw80000, app(app(ty_Either, db), dc)) → new_esEs7(zxw79000, zxw80000, db, dc)
new_primEqInt(Neg(Succ(zxw40000)), Pos(zxw3000)) → False
new_primEqInt(Pos(Succ(zxw40000)), Neg(zxw3000)) → False
new_compare29(zxw79000, zxw80000, ty_Integer) → new_compare32(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Char) → new_ltEs10(zxw79000, zxw80000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_@0, bdf) → new_esEs10(zxw4000, zxw3000)
new_lt19(zxw79000, zxw80000, app(app(app(ty_@3, gd), ge), gf)) → new_lt5(zxw79000, zxw80000, gd, ge, gf)
new_esEs29(zxw400, zxw300, app(app(ty_@2, ccf), ccg)) → new_esEs5(zxw400, zxw300, ccf, ccg)
new_esEs32(zxw20, zxw15, app(app(ty_@2, cdh), cea)) → new_esEs5(zxw20, zxw15, cdh, cea)
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_esEs28(zxw4000, zxw3000, app(ty_Maybe, eae)) → new_esEs6(zxw4000, zxw3000, eae)
new_ltEs21(zxw79002, zxw80002, ty_@0) → new_ltEs8(zxw79002, zxw80002)
new_esEs21(zxw4001, zxw3001, app(ty_[], dbh)) → new_esEs13(zxw4001, zxw3001, dbh)
new_primEqInt(Neg(Zero), Pos(Succ(zxw30000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(zxw30000))) → False
new_ltEs7(EQ, GT) → True
new_lt4(zxw79000, zxw80000, ty_Double) → new_lt15(zxw79000, zxw80000)
new_esEs21(zxw4001, zxw3001, ty_Integer) → new_esEs15(zxw4001, zxw3001)
new_esEs31(zxw35, zxw30, ty_Integer) → new_esEs15(zxw35, zxw30)
new_primCompAux00(zxw276, EQ) → zxw276
new_esEs28(zxw4000, zxw3000, app(app(ty_Either, eah), eba)) → new_esEs7(zxw4000, zxw3000, eah, eba)
new_compare24(zxw79000, zxw80000, True) → EQ
new_compare6(Double(zxw79000, zxw79001), Double(zxw80000, zxw80001)) → new_compare16(new_sr(zxw79000, zxw80000), new_sr(zxw79001, zxw80001))
new_esEs8(zxw79000, zxw80000, ty_@0) → new_esEs10(zxw79000, zxw80000)
new_ltEs5(zxw79001, zxw80001, app(app(ty_Either, ed), ee)) → new_ltEs14(zxw79001, zxw80001, ed, ee)
new_lt13(zxw79000, zxw80000) → new_esEs9(new_compare32(zxw79000, zxw80000), LT)
new_esEs27(zxw4001, zxw3001, ty_Double) → new_esEs16(zxw4001, zxw3001)
new_esEs7(Left(zxw4000), Left(zxw3000), app(app(app(ty_@3, bee), bef), beg), bdf) → new_esEs4(zxw4000, zxw3000, bee, bef, beg)
new_esEs26(zxw4002, zxw3002, app(app(ty_@2, dgb), dgc)) → new_esEs5(zxw4002, zxw3002, dgb, dgc)
new_esEs21(zxw4001, zxw3001, app(app(ty_@2, dcb), dcc)) → new_esEs5(zxw4001, zxw3001, dcb, dcc)
new_esEs30(zxw400, zxw300, ty_@0) → new_esEs10(zxw400, zxw300)
new_lt19(zxw79000, zxw80000, app(ty_Maybe, bbh)) → new_lt18(zxw79000, zxw80000, bbh)
new_esEs12(Char(zxw4000), Char(zxw3000)) → new_primEqNat0(zxw4000, zxw3000)
new_ltEs20(zxw7900, zxw8000, app(app(app(ty_@3, bab), bac), bad)) → new_ltEs6(zxw7900, zxw8000, bab, bac, bad)
new_not(False) → True
new_lt20(zxw79001, zxw80001, ty_Char) → new_lt9(zxw79001, zxw80001)
new_esEs11(zxw400, zxw300) → new_primEqInt(zxw400, zxw300)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(ty_Maybe, chb)) → new_ltEs18(zxw79000, zxw80000, chb)
new_ltEs18(Just(zxw79000), Nothing, baa) → False
new_esEs8(zxw79000, zxw80000, app(ty_Maybe, de)) → new_esEs6(zxw79000, zxw80000, de)
new_esEs7(Left(zxw4000), Left(zxw3000), app(ty_Maybe, bdh), bdf) → new_esEs6(zxw4000, zxw3000, bdh)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Double, bdf) → new_esEs16(zxw4000, zxw3000)
new_compare210(zxw79000, zxw80000, True, bbd, bbe) → EQ
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_esEs19(zxw79001, zxw80001, ty_Int) → new_esEs11(zxw79001, zxw80001)
new_compare12(zxw79000, zxw80000, False, gd, ge, gf) → GT
new_ltEs16(zxw7900, zxw8000) → new_fsEs(new_compare7(zxw7900, zxw8000))
new_esEs32(zxw20, zxw15, ty_Char) → new_esEs12(zxw20, zxw15)
new_esEs9(GT, GT) → True
new_esEs26(zxw4002, zxw3002, app(ty_Ratio, dfg)) → new_esEs18(zxw4002, zxw3002, dfg)
new_esEs25(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_lt20(zxw79001, zxw80001, app(ty_[], bha)) → new_lt10(zxw79001, zxw80001, bha)
new_lt4(zxw79000, zxw80000, app(app(ty_Either, db), dc)) → new_lt14(zxw79000, zxw80000, db, dc)
new_esEs26(zxw4002, zxw3002, ty_Bool) → new_esEs14(zxw4002, zxw3002)
new_compare19(zxw79000, zxw80000, bbd, bbe) → new_compare210(zxw79000, zxw80000, new_esEs5(zxw79000, zxw80000, bbd, bbe), bbd, bbe)
new_esEs8(zxw79000, zxw80000, ty_Bool) → new_esEs14(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Double) → new_ltEs15(zxw79000, zxw80000)
new_esEs28(zxw4000, zxw3000, app(app(ty_@2, eaf), eag)) → new_esEs5(zxw4000, zxw3000, eaf, eag)
new_ltEs19(zxw7900, zxw8000, app(app(app(ty_@3, hb), hc), hd)) → new_ltEs6(zxw7900, zxw8000, hb, hc, hd)
new_esEs32(zxw20, zxw15, app(app(app(ty_@3, ced), cee), cef)) → new_esEs4(zxw20, zxw15, ced, cee, cef)
new_lt4(zxw79000, zxw80000, ty_Char) → new_lt9(zxw79000, zxw80000)
new_esEs22(zxw4000, zxw3000, app(app(app(ty_@3, ddh), dea), deb)) → new_esEs4(zxw4000, zxw3000, ddh, dea, deb)
new_esEs22(zxw4000, zxw3000, app(ty_[], ddb)) → new_esEs13(zxw4000, zxw3000, ddb)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_@0) → new_ltEs8(zxw79000, zxw80000)
new_esEs23(zxw4000, zxw3000, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Float, bdf) → new_esEs17(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_esEs27(zxw4001, zxw3001, ty_Int) → new_esEs11(zxw4001, zxw3001)
new_esEs19(zxw79001, zxw80001, app(app(app(ty_@3, bgf), bgg), bgh)) → new_esEs4(zxw79001, zxw80001, bgf, bgg, bgh)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_ltEs14(Left(zxw79000), Left(zxw80000), app(app(app(ty_@3, ceg), ceh), cfa), hg) → new_ltEs6(zxw79000, zxw80000, ceg, ceh, cfa)
new_ltEs19(zxw7900, zxw8000, ty_Int) → new_ltEs9(zxw7900, zxw8000)
new_compare33(zxw20, zxw15, cdc, cdd) → new_compare26(Left(zxw20), Left(zxw15), new_esEs32(zxw20, zxw15, cdc), cdc, cdd)
new_lt4(zxw79000, zxw80000, ty_@0) → new_lt7(zxw79000, zxw80000)
new_lt20(zxw79001, zxw80001, ty_Double) → new_lt15(zxw79001, zxw80001)
new_lt19(zxw79000, zxw80000, ty_Float) → new_lt16(zxw79000, zxw80000)
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_esEs26(zxw4002, zxw3002, ty_@0) → new_esEs10(zxw4002, zxw3002)
new_esEs30(zxw400, zxw300, app(app(ty_@2, dah), dba)) → new_esEs5(zxw400, zxw300, dah, dba)
new_lt19(zxw79000, zxw80000, ty_Bool) → new_lt12(zxw79000, zxw80000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Char, bdf) → new_esEs12(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_lt4(zxw79000, zxw80000, ty_Float) → new_lt16(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(ty_[], chf)) → new_ltEs11(zxw79000, zxw80000, chf)
new_primMulInt(Neg(zxw40000), Neg(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_ltEs5(zxw79001, zxw80001, app(app(app(ty_@3, df), dg), dh)) → new_ltEs6(zxw79001, zxw80001, df, dg, dh)
new_primCmpNat2(Zero, Zero) → EQ
new_esEs20(zxw79000, zxw80000, ty_Integer) → new_esEs15(zxw79000, zxw80000)
new_primEqNat0(Zero, Succ(zxw30000)) → False
new_primEqNat0(Succ(zxw40000), Zero) → False
new_esEs21(zxw4001, zxw3001, ty_@0) → new_esEs10(zxw4001, zxw3001)
new_esEs22(zxw4000, zxw3000, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_esEs20(zxw79000, zxw80000, ty_Bool) → new_esEs14(zxw79000, zxw80000)
new_ltEs5(zxw79001, zxw80001, app(ty_[], ea)) → new_ltEs11(zxw79001, zxw80001, ea)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs23(zxw4000, zxw3000, app(ty_Ratio, dec)) → new_esEs18(zxw4000, zxw3000, dec)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(app(ty_@2, chg), chh)) → new_ltEs4(zxw79000, zxw80000, chg, chh)
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_ltEs5(zxw79001, zxw80001, ty_Int) → new_ltEs9(zxw79001, zxw80001)
new_esEs27(zxw4001, zxw3001, app(app(ty_@2, dhd), dhe)) → new_esEs5(zxw4001, zxw3001, dhd, dhe)
new_primCmpNat0(zxw7900, Zero) → GT
new_compare26(Right(zxw7900), Left(zxw8000), False, gh, ha) → GT
new_esEs23(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_@0, hg) → new_ltEs8(zxw79000, zxw80000)
new_ltEs21(zxw79002, zxw80002, app(ty_Maybe, cba)) → new_ltEs18(zxw79002, zxw80002, cba)
new_esEs21(zxw4001, zxw3001, app(app(ty_Either, dcd), dce)) → new_esEs7(zxw4001, zxw3001, dcd, dce)
new_esEs22(zxw4000, zxw3000, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Bool) → new_ltEs12(zxw79000, zxw80000)
new_compare29(zxw79000, zxw80000, app(ty_Maybe, ccc)) → new_compare27(zxw79000, zxw80000, ccc)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_ltEs14(Left(zxw79000), Left(zxw80000), app(ty_Maybe, cfh), hg) → new_ltEs18(zxw79000, zxw80000, cfh)
new_lt20(zxw79001, zxw80001, ty_Float) → new_lt16(zxw79001, zxw80001)
new_lt17(zxw79000, zxw80000, gg) → new_esEs9(new_compare8(zxw79000, zxw80000, gg), LT)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Ordering) → new_ltEs7(zxw79000, zxw80000)
new_esEs32(zxw20, zxw15, ty_Int) → new_esEs11(zxw20, zxw15)
new_compare30(@0, @0) → EQ
new_lt19(zxw79000, zxw80000, app(ty_[], bgc)) → new_lt10(zxw79000, zxw80000, bgc)
new_esEs21(zxw4001, zxw3001, app(app(app(ty_@3, dcf), dcg), dch)) → new_esEs4(zxw4001, zxw3001, dcf, dcg, dch)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_esEs20(zxw79000, zxw80000, app(ty_Ratio, gg)) → new_esEs18(zxw79000, zxw80000, gg)
new_esEs6(Just(zxw4000), Just(zxw3000), app(app(app(ty_@3, ga), gb), gc)) → new_esEs4(zxw4000, zxw3000, ga, gb, gc)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(app(ty_Either, daa), dab)) → new_ltEs14(zxw79000, zxw80000, daa, dab)
new_esEs24(zxw4001, zxw3001, ty_Int) → new_esEs11(zxw4001, zxw3001)
new_esEs8(zxw79000, zxw80000, ty_Ordering) → new_esEs9(zxw79000, zxw80000)
new_esEs30(zxw400, zxw300, ty_Ordering) → new_esEs9(zxw400, zxw300)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Ordering) → new_ltEs7(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, app(app(ty_Either, bgd), bge)) → new_esEs7(zxw79000, zxw80000, bgd, bge)
new_compare29(zxw79000, zxw80000, app(ty_Ratio, ccb)) → new_compare8(zxw79000, zxw80000, ccb)
new_lt4(zxw79000, zxw80000, app(app(ty_@2, cg), da)) → new_lt11(zxw79000, zxw80000, cg, da)
new_compare29(zxw79000, zxw80000, ty_Float) → new_compare7(zxw79000, zxw80000)
new_esEs19(zxw79001, zxw80001, app(app(ty_@2, bhb), bhc)) → new_esEs5(zxw79001, zxw80001, bhb, bhc)
new_esEs10(@0, @0) → True
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_compare29(zxw79000, zxw80000, ty_Double) → new_compare6(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, app(ty_Maybe, bbh)) → new_esEs6(zxw79000, zxw80000, bbh)
new_ltEs14(Left(zxw79000), Right(zxw80000), hf, hg) → True
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Float) → new_ltEs16(zxw79000, zxw80000)
new_esEs28(zxw4000, zxw3000, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_compare29(zxw79000, zxw80000, app(app(ty_Either, cbh), cca)) → new_compare15(zxw79000, zxw80000, cbh, cca)
new_esEs19(zxw79001, zxw80001, ty_Double) → new_esEs16(zxw79001, zxw80001)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs30(zxw400, zxw300, ty_Bool) → new_esEs14(zxw400, zxw300)
new_ltEs20(zxw7900, zxw8000, app(app(ty_Either, bah), bba)) → new_ltEs14(zxw7900, zxw8000, bah, bba)
new_asAs(False, zxw230) → False
new_ltEs13(zxw7900, zxw8000) → new_fsEs(new_compare32(zxw7900, zxw8000))
new_ltEs19(zxw7900, zxw8000, app(app(ty_Either, hf), hg)) → new_ltEs14(zxw7900, zxw8000, hf, hg)
new_compare34(zxw400, zxw300, h, ba) → new_compare26(Left(zxw400), Right(zxw300), False, h, ba)
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Pos(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_ltEs20(zxw7900, zxw8000, app(ty_[], bae)) → new_ltEs11(zxw7900, zxw8000, bae)
new_compare16(zxw79, zxw80) → new_primCmpInt(zxw79, zxw80)
new_esEs29(zxw400, zxw300, ty_Char) → new_esEs12(zxw400, zxw300)
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_esEs13(:(zxw4000, zxw4001), [], cce) → False
new_esEs13([], :(zxw3000, zxw3001), cce) → False
new_compare25(zxw79000, zxw80000, False, gd, ge, gf) → new_compare12(zxw79000, zxw80000, new_ltEs6(zxw79000, zxw80000, gd, ge, gf), gd, ge, gf)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(app(ty_@2, cfc), cfd), hg) → new_ltEs4(zxw79000, zxw80000, cfc, cfd)
new_esEs6(Just(zxw4000), Just(zxw3000), app(ty_Maybe, fc)) → new_esEs6(zxw4000, zxw3000, fc)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_@0) → new_esEs10(zxw4000, zxw3000)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(ty_[], cfb), hg) → new_ltEs11(zxw79000, zxw80000, cfb)
new_esEs7(Left(zxw4000), Left(zxw3000), app(ty_[], bdg), bdf) → new_esEs13(zxw4000, zxw3000, bdg)
new_esEs29(zxw400, zxw300, ty_Int) → new_esEs11(zxw400, zxw300)
new_esEs31(zxw35, zxw30, ty_Double) → new_esEs16(zxw35, zxw30)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_compare31(zxw79000, zxw80000) → new_compare23(zxw79000, zxw80000, new_esEs14(zxw79000, zxw80000))
new_ltEs18(Nothing, Just(zxw80000), baa) → True
new_esEs28(zxw4000, zxw3000, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_ltEs21(zxw79002, zxw80002, ty_Double) → new_ltEs15(zxw79002, zxw80002)
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_ltEs12(True, True) → True
new_esEs23(zxw4000, zxw3000, app(ty_Maybe, dee)) → new_esEs6(zxw4000, zxw3000, dee)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_esEs8(zxw79000, zxw80000, ty_Integer) → new_esEs15(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(app(ty_Either, cgg), cgh)) → new_ltEs14(zxw79000, zxw80000, cgg, cgh)
new_ltEs6(@3(zxw79000, zxw79001, zxw79002), @3(zxw80000, zxw80001, zxw80002), hb, hc, hd) → new_pePe(new_lt19(zxw79000, zxw80000, hb), new_asAs(new_esEs20(zxw79000, zxw80000, hb), new_pePe(new_lt20(zxw79001, zxw80001, hc), new_asAs(new_esEs19(zxw79001, zxw80001, hc), new_ltEs21(zxw79002, zxw80002, hd)))))
new_esEs28(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_lt16(zxw79000, zxw80000) → new_esEs9(new_compare7(zxw79000, zxw80000), LT)
new_esEs23(zxw4000, zxw3000, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Integer, hg) → new_ltEs13(zxw79000, zxw80000)
new_ltEs12(False, True) → True
new_esEs23(zxw4000, zxw3000, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs8(zxw79000, zxw80000, app(ty_Ratio, dd)) → new_esEs18(zxw79000, zxw80000, dd)
new_esEs23(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs14(True, True) → True
new_compare111(zxw79000, zxw80000, False, bbh) → GT
new_esEs31(zxw35, zxw30, app(ty_[], bcd)) → new_esEs13(zxw35, zxw30, bcd)
new_esEs27(zxw4001, zxw3001, ty_Bool) → new_esEs14(zxw4001, zxw3001)
new_esEs20(zxw79000, zxw80000, ty_Ordering) → new_esEs9(zxw79000, zxw80000)
new_ltEs19(zxw7900, zxw8000, ty_@0) → new_ltEs8(zxw7900, zxw8000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Int) → new_ltEs9(zxw79000, zxw80000)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(app(ty_Either, cfe), cff), hg) → new_ltEs14(zxw79000, zxw80000, cfe, cff)
new_lt19(zxw79000, zxw80000, ty_Integer) → new_lt13(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, ty_Float) → new_esEs17(zxw79000, zxw80000)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Ordering, hg) → new_ltEs7(zxw79000, zxw80000)
new_compare11(zxw79000, zxw80000, False) → GT
new_esEs4(@3(zxw4000, zxw4001, zxw4002), @3(zxw3000, zxw3001, zxw3002), cch, cda, cdb) → new_asAs(new_esEs28(zxw4000, zxw3000, cch), new_asAs(new_esEs27(zxw4001, zxw3001, cda), new_esEs26(zxw4002, zxw3002, cdb)))
new_esEs6(Just(zxw4000), Just(zxw3000), app(ty_[], fb)) → new_esEs13(zxw4000, zxw3000, fb)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Int) → new_ltEs9(zxw79000, zxw80000)
new_esEs9(EQ, LT) → False
new_esEs9(LT, EQ) → False
new_compare26(Right(zxw7900), Right(zxw8000), False, gh, ha) → new_compare14(zxw7900, zxw8000, new_ltEs20(zxw7900, zxw8000, ha), gh, ha)
new_compare11(zxw79000, zxw80000, True) → LT
new_ltEs5(zxw79001, zxw80001, ty_@0) → new_ltEs8(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, ty_Bool) → new_lt12(zxw79001, zxw80001)
new_esEs30(zxw400, zxw300, ty_Integer) → new_esEs15(zxw400, zxw300)
new_compare14(zxw242, zxw243, True, dfe, dff) → LT
new_esEs32(zxw20, zxw15, app(ty_Ratio, cde)) → new_esEs18(zxw20, zxw15, cde)
new_esEs29(zxw400, zxw300, app(app(ty_Either, beh), bdf)) → new_esEs7(zxw400, zxw300, beh, bdf)
new_esEs14(False, False) → True
new_esEs18(:%(zxw4000, zxw4001), :%(zxw3000, zxw3001), ccd) → new_asAs(new_esEs25(zxw4000, zxw3000, ccd), new_esEs24(zxw4001, zxw3001, ccd))
new_compare26(Left(zxw7900), Left(zxw8000), False, gh, ha) → new_compare13(zxw7900, zxw8000, new_ltEs19(zxw7900, zxw8000, gh), gh, ha)
new_ltEs19(zxw7900, zxw8000, ty_Double) → new_ltEs15(zxw7900, zxw8000)
new_ltEs7(EQ, LT) → False
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Char) → new_esEs12(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_ltEs7(LT, LT) → True
new_lt20(zxw79001, zxw80001, app(app(app(ty_@3, bgf), bgg), bgh)) → new_lt5(zxw79001, zxw80001, bgf, bgg, bgh)
new_esEs29(zxw400, zxw300, ty_@0) → new_esEs10(zxw400, zxw300)
new_lt14(zxw790, zxw800, gh, ha) → new_esEs9(new_compare15(zxw790, zxw800, gh, ha), LT)
new_esEs22(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_ltEs9(zxw7900, zxw8000) → new_fsEs(new_compare16(zxw7900, zxw8000))
new_compare29(zxw79000, zxw80000, ty_Ordering) → new_compare18(zxw79000, zxw80000)
new_primPlusNat1(Zero, Zero) → Zero
new_esEs26(zxw4002, zxw3002, ty_Ordering) → new_esEs9(zxw4002, zxw3002)
new_esEs19(zxw79001, zxw80001, ty_Integer) → new_esEs15(zxw79001, zxw80001)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Char, hg) → new_ltEs10(zxw79000, zxw80000)
new_asAs(True, zxw230) → zxw230
new_esEs25(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_ltEs7(LT, GT) → True
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Float) → new_esEs17(zxw4000, zxw3000)
new_ltEs5(zxw79001, zxw80001, ty_Float) → new_ltEs16(zxw79001, zxw80001)
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, app(ty_Ratio, bfa)) → new_esEs18(zxw4000, zxw3000, bfa)
new_esEs27(zxw4001, zxw3001, app(ty_[], dhb)) → new_esEs13(zxw4001, zxw3001, dhb)
new_esEs6(Just(zxw4000), Just(zxw3000), app(app(ty_Either, fg), fh)) → new_esEs7(zxw4000, zxw3000, fg, fh)
new_esEs32(zxw20, zxw15, ty_Double) → new_esEs16(zxw20, zxw15)
new_compare28(zxw79000, zxw80000, False, bbh) → new_compare111(zxw79000, zxw80000, new_ltEs18(zxw79000, zxw80000, bbh), bbh)
new_compare1(:(zxw79000, zxw79001), [], he) → GT
new_esEs28(zxw4000, zxw3000, app(ty_Ratio, eac)) → new_esEs18(zxw4000, zxw3000, eac)
new_lt4(zxw79000, zxw80000, ty_Integer) → new_lt13(zxw79000, zxw80000)
new_esEs30(zxw400, zxw300, ty_Int) → new_esEs11(zxw400, zxw300)
new_esEs19(zxw79001, zxw80001, ty_@0) → new_esEs10(zxw79001, zxw80001)
new_compare29(zxw79000, zxw80000, ty_@0) → new_compare30(zxw79000, zxw80000)
new_ltEs19(zxw7900, zxw8000, ty_Integer) → new_ltEs13(zxw7900, zxw8000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(ty_Ratio, cha)) → new_ltEs17(zxw79000, zxw80000, cha)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Integer) → new_ltEs13(zxw79000, zxw80000)
new_ltEs19(zxw7900, zxw8000, ty_Ordering) → new_ltEs7(zxw7900, zxw8000)
new_compare28(zxw79000, zxw80000, True, bbh) → EQ
new_esEs31(zxw35, zxw30, ty_Int) → new_esEs11(zxw35, zxw30)
new_esEs26(zxw4002, zxw3002, ty_Double) → new_esEs16(zxw4002, zxw3002)
new_esEs30(zxw400, zxw300, ty_Double) → new_esEs16(zxw400, zxw300)
new_esEs29(zxw400, zxw300, ty_Float) → new_esEs17(zxw400, zxw300)
new_compare10(zxw79000, zxw80000, True) → LT
new_esEs31(zxw35, zxw30, ty_Bool) → new_esEs14(zxw35, zxw30)
new_esEs19(zxw79001, zxw80001, app(ty_[], bha)) → new_esEs13(zxw79001, zxw80001, bha)
new_esEs29(zxw400, zxw300, ty_Bool) → new_esEs14(zxw400, zxw300)
new_compare10(zxw79000, zxw80000, False) → GT
new_esEs9(LT, LT) → True
new_ltEs20(zxw7900, zxw8000, ty_Char) → new_ltEs10(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, ty_Ordering) → new_ltEs7(zxw7900, zxw8000)
new_primCompAux00(zxw276, GT) → GT
new_esEs31(zxw35, zxw30, app(ty_Maybe, bce)) → new_esEs6(zxw35, zxw30, bce)
new_compare18(zxw79000, zxw80000) → new_compare24(zxw79000, zxw80000, new_esEs9(zxw79000, zxw80000))
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_@0) → new_ltEs8(zxw79000, zxw80000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs7(Right(zxw4000), Right(zxw3000), beh, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_esEs29(zxw400, zxw300, ty_Ordering) → new_esEs9(zxw400, zxw300)
new_lt19(zxw79000, zxw80000, ty_Char) → new_lt9(zxw79000, zxw80000)
new_esEs28(zxw4000, zxw3000, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_ltEs19(zxw7900, zxw8000, app(ty_Maybe, baa)) → new_ltEs18(zxw7900, zxw8000, baa)
new_esEs27(zxw4001, zxw3001, ty_Integer) → new_esEs15(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, app(ty_Ratio, dbg)) → new_esEs18(zxw4001, zxw3001, dbg)
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_esEs19(zxw79001, zxw80001, ty_Char) → new_esEs12(zxw79001, zxw80001)
new_esEs23(zxw4000, zxw3000, app(ty_[], ded)) → new_esEs13(zxw4000, zxw3000, ded)
new_ltEs17(zxw7900, zxw8000, hh) → new_fsEs(new_compare8(zxw7900, zxw8000, hh))
new_not(True) → False
new_ltEs4(@2(zxw79000, zxw79001), @2(zxw80000, zxw80001), ca, cb) → new_pePe(new_lt4(zxw79000, zxw80000, ca), new_asAs(new_esEs8(zxw79000, zxw80000, ca), new_ltEs5(zxw79001, zxw80001, cb)))
new_compare1([], [], he) → EQ
new_esEs6(Just(zxw4000), Just(zxw3000), app(ty_Ratio, fa)) → new_esEs18(zxw4000, zxw3000, fa)

The set Q consists of the following terms:

new_compare23(x0, x1, True)
new_lt6(x0, x1)
new_ltEs5(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, ty_Integer)
new_lt4(x0, x1, app(ty_[], x2))
new_ltEs18(Just(x0), Just(x1), ty_@0)
new_compare16(x0, x1)
new_lt4(x0, x1, app(app(ty_@2, x2), x3))
new_compare13(x0, x1, False, x2, x3)
new_ltEs18(Just(x0), Nothing, x1)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, ty_Double)
new_esEs19(x0, x1, ty_Bool)
new_esEs8(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(x0, x1, app(app(ty_Either, x2), x3))
new_compare30(@0, @0)
new_primCompAux00(x0, GT)
new_esEs30(x0, x1, ty_@0)
new_lt19(x0, x1, ty_Char)
new_esEs30(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_Ordering)
new_compare17(Char(x0), Char(x1))
new_esEs28(x0, x1, ty_Int)
new_ltEs20(x0, x1, app(ty_[], x2))
new_ltEs21(x0, x1, ty_Ordering)
new_ltEs15(x0, x1)
new_primPlusNat1(Zero, Succ(x0))
new_esEs6(Just(x0), Just(x1), ty_Double)
new_compare24(x0, x1, False)
new_lt20(x0, x1, ty_Char)
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, ty_Bool)
new_sr0(Integer(x0), Integer(x1))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare210(x0, x1, False, x2, x3)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs7(Right(x0), Right(x1), x2, ty_Float)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs18(Nothing, Nothing, x0)
new_ltEs7(EQ, EQ)
new_esEs7(Right(x0), Right(x1), x2, ty_Integer)
new_compare29(x0, x1, app(app(ty_@2, x2), x3))
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs19(x0, x1, ty_Integer)
new_ltEs20(x0, x1, ty_Bool)
new_ltEs14(Right(x0), Right(x1), x2, ty_Float)
new_esEs6(Just(x0), Just(x1), app(ty_[], x2))
new_esEs31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_compare25(x0, x1, False, x2, x3, x4)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_ltEs19(x0, x1, ty_Integer)
new_ltEs5(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(ty_[], x2))
new_lt10(x0, x1, x2)
new_ltEs7(EQ, LT)
new_ltEs7(LT, EQ)
new_esEs20(x0, x1, ty_Ordering)
new_esEs17(Float(x0, x1), Float(x2, x3))
new_compare25(x0, x1, True, x2, x3, x4)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_lt19(x0, x1, ty_Ordering)
new_esEs29(x0, x1, ty_@0)
new_esEs26(x0, x1, app(ty_[], x2))
new_ltEs16(x0, x1)
new_lt4(x0, x1, app(ty_Maybe, x2))
new_compare110(x0, x1, False, x2, x3)
new_ltEs14(Left(x0), Left(x1), ty_Char, x2)
new_sr(x0, x1)
new_ltEs19(x0, x1, ty_Double)
new_compare7(Float(x0, x1), Float(x2, x3))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs9(x0, x1)
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_lt7(x0, x1)
new_lt4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, ty_Int)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat0(Zero, x0)
new_esEs7(Right(x0), Right(x1), x2, ty_@0)
new_esEs32(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_ltEs7(LT, LT)
new_esEs7(Right(x0), Right(x1), x2, ty_Double)
new_esEs4(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_Bool)
new_lt5(x0, x1, x2, x3, x4)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt4(x0, x1, ty_Ordering)
new_primEqNat0(Zero, Succ(x0))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Int)
new_esEs15(Integer(x0), Integer(x1))
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Left(x0), Left(x1), ty_Char, x2)
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs26(x0, x1, ty_Double)
new_compare29(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_@0)
new_primPlusNat1(Succ(x0), Zero)
new_esEs22(x0, x1, ty_Integer)
new_ltEs14(Left(x0), Left(x1), ty_@0, x2)
new_primMulInt(Neg(x0), Neg(x1))
new_ltEs19(x0, x1, ty_Int)
new_ltEs21(x0, x1, app(ty_Maybe, x2))
new_compare29(x0, x1, ty_Integer)
new_esEs14(True, True)
new_esEs21(x0, x1, ty_Char)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Int)
new_ltEs18(Just(x0), Just(x1), ty_Integer)
new_esEs24(x0, x1, ty_Int)
new_primEqNat0(Zero, Zero)
new_esEs16(Double(x0, x1), Double(x2, x3))
new_esEs12(Char(x0), Char(x1))
new_lt4(x0, x1, ty_Char)
new_compare29(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, ty_Bool)
new_esEs8(x0, x1, ty_Float)
new_compare1([], :(x0, x1), x2)
new_esEs30(x0, x1, ty_Ordering)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, ty_Integer)
new_esEs29(x0, x1, ty_Bool)
new_esEs30(x0, x1, ty_Bool)
new_esEs30(x0, x1, ty_Float)
new_esEs32(x0, x1, ty_@0)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs14(Left(x0), Left(x1), ty_Int, x2)
new_primCompAux00(x0, LT)
new_esEs27(x0, x1, ty_Integer)
new_ltEs21(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs5(x0, x1, ty_Double)
new_ltEs18(Just(x0), Just(x1), ty_Char)
new_primMulNat0(Zero, Zero)
new_compare110(x0, x1, True, x2, x3)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_lt9(x0, x1)
new_compare29(x0, x1, ty_Double)
new_ltEs5(x0, x1, ty_@0)
new_lt17(x0, x1, x2)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_compare36(x0, x1, x2, x3)
new_ltEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs31(x0, x1, ty_Bool)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Left(x0), Left(x1), ty_Float, x2)
new_esEs32(x0, x1, ty_Float)
new_esEs13([], :(x0, x1), x2)
new_esEs8(x0, x1, ty_Ordering)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_compare10(x0, x1, True)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs7(Left(x0), Left(x1), ty_Float, x2)
new_primEqNat0(Succ(x0), Succ(x1))
new_ltEs19(x0, x1, ty_Bool)
new_esEs28(x0, x1, ty_Double)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, ty_Float)
new_esEs29(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_@0)
new_pePe(True, x0)
new_esEs19(x0, x1, ty_Float)
new_esEs8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_lt16(x0, x1)
new_compare29(x0, x1, ty_Bool)
new_esEs20(x0, x1, app(ty_[], x2))
new_compare11(x0, x1, True)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_compare14(x0, x1, True, x2, x3)
new_esEs6(Just(x0), Just(x1), app(ty_Maybe, x2))
new_lt19(x0, x1, ty_@0)
new_esEs6(Just(x0), Just(x1), ty_Ordering)
new_esEs23(x0, x1, ty_@0)
new_compare29(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Right(x0), Right(x1), x2, ty_Int)
new_ltEs5(x0, x1, ty_Char)
new_esEs30(x0, x1, ty_Double)
new_ltEs21(x0, x1, ty_Int)
new_compare29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Float)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_compare29(x0, x1, ty_Ordering)
new_ltEs21(x0, x1, ty_@0)
new_esEs8(x0, x1, ty_Int)
new_lt14(x0, x1, x2, x3)
new_ltEs12(False, False)
new_esEs6(Just(x0), Just(x1), ty_Bool)
new_compare32(Integer(x0), Integer(x1))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_Int)
new_primMulNat0(Succ(x0), Succ(x1))
new_compare29(x0, x1, ty_Float)
new_ltEs21(x0, x1, ty_Integer)
new_esEs6(Just(x0), Just(x1), ty_Float)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs5(x0, x1, ty_Float)
new_ltEs18(Just(x0), Just(x1), ty_Float)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Bool)
new_esEs31(x0, x1, ty_Double)
new_esEs31(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpNat1(Zero, x0)
new_ltEs8(x0, x1)
new_esEs29(x0, x1, ty_Integer)
new_ltEs21(x0, x1, app(ty_[], x2))
new_primPlusNat1(Zero, Zero)
new_esEs30(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(ty_[], x2))
new_ltEs14(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs23(x0, x1, ty_Double)
new_ltEs18(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs18(Just(x0), Just(x1), ty_Ordering)
new_primCmpNat2(Zero, Zero)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs5(x0, x1, ty_Bool)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_compare28(x0, x1, True, x2)
new_ltEs14(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs5(x0, x1, app(ty_[], x2))
new_asAs(False, x0)
new_esEs29(x0, x1, ty_Ordering)
new_esEs31(x0, x1, app(ty_[], x2))
new_esEs30(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, ty_Char)
new_esEs31(x0, x1, app(app(ty_@2, x2), x3))
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(x0, x1, ty_Integer)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs19(x0, x1, app(ty_[], x2))
new_ltEs18(Just(x0), Just(x1), ty_Bool)
new_lt11(x0, x1, x2, x3)
new_primCmpNat1(Succ(x0), x1)
new_esEs32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs24(x0, x1, ty_Integer)
new_ltEs14(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs27(x0, x1, ty_@0)
new_ltEs14(Right(x0), Right(x1), x2, ty_Double)
new_lt4(x0, x1, ty_Float)
new_compare19(x0, x1, x2, x3)
new_ltEs5(x0, x1, app(app(ty_Either, x2), x3))
new_esEs19(x0, x1, ty_Char)
new_lt4(x0, x1, ty_Double)
new_esEs19(x0, x1, ty_Ordering)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs10(@0, @0)
new_esEs31(x0, x1, ty_@0)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs11(x0, x1)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, ty_Float)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_Char)
new_esEs9(GT, GT)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs27(x0, x1, ty_Char)
new_compare11(x0, x1, False)
new_compare23(x0, x1, False)
new_compare12(x0, x1, True, x2, x3, x4)
new_esEs28(x0, x1, ty_Bool)
new_esEs7(Right(x0), Left(x1), x2, x3)
new_esEs7(Left(x0), Right(x1), x2, x3)
new_compare24(x0, x1, True)
new_compare15(x0, x1, x2, x3)
new_primEqNat0(Succ(x0), Zero)
new_esEs23(x0, x1, ty_Ordering)
new_esEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs7(Right(x0), Right(x1), x2, ty_Int)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_esEs32(x0, x1, app(app(ty_Either, x2), x3))
new_compare9(x0, x1, x2, x3, x4)
new_lt20(x0, x1, ty_Int)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Integer)
new_lt4(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Int)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs5(x0, x1, app(app(ty_@2, x2), x3))
new_lt4(x0, x1, ty_@0)
new_esEs23(x0, x1, ty_Char)
new_esEs28(x0, x1, ty_Ordering)
new_ltEs18(Just(x0), Just(x1), ty_Double)
new_esEs30(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_Integer)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_compare14(x0, x1, False, x2, x3)
new_lt20(x0, x1, ty_@0)
new_compare1([], [], x0)
new_esEs9(EQ, EQ)
new_pePe(False, x0)
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs5(x0, x1, app(ty_Ratio, x2))
new_ltEs18(Just(x0), Just(x1), app(ty_[], x2))
new_esEs6(Just(x0), Just(x1), ty_Char)
new_esEs25(x0, x1, ty_Integer)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs18(:%(x0, x1), :%(x2, x3), x4)
new_esEs26(x0, x1, ty_Integer)
new_compare12(x0, x1, False, x2, x3, x4)
new_esEs8(x0, x1, app(ty_Maybe, x2))
new_primCompAux00(x0, EQ)
new_esEs19(x0, x1, ty_Int)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs14(True, False)
new_esEs14(False, True)
new_lt4(x0, x1, ty_Integer)
new_esEs7(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs14(Right(x0), Right(x1), x2, ty_@0)
new_fsEs(x0)
new_esEs22(x0, x1, ty_Float)
new_lt4(x0, x1, ty_Bool)
new_primCmpNat2(Succ(x0), Succ(x1))
new_asAs(True, x0)
new_ltEs18(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, ty_Bool)
new_esEs6(Nothing, Just(x0), x1)
new_esEs6(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs6(Just(x0), Nothing, x1)
new_lt18(x0, x1, x2)
new_esEs8(x0, x1, app(ty_[], x2))
new_esEs31(x0, x1, ty_Integer)
new_compare111(x0, x1, False, x2)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs8(x0, x1, ty_Char)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, ty_Float)
new_ltEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs22(x0, x1, ty_@0)
new_esEs20(x0, x1, ty_Char)
new_esEs13(:(x0, x1), [], x2)
new_ltEs12(False, True)
new_ltEs12(True, False)
new_compare6(Double(x0, x1), Double(x2, x3))
new_ltEs20(x0, x1, ty_@0)
new_esEs22(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_@0)
new_ltEs18(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare35(x0, x1, x2, x3)
new_ltEs14(Right(x0), Right(x1), x2, ty_Integer)
new_lt19(x0, x1, ty_Double)
new_esEs32(x0, x1, app(ty_[], x2))
new_lt19(x0, x1, ty_Bool)
new_ltEs14(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs7(Right(x0), Right(x1), x2, ty_Char)
new_ltEs14(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs26(x0, x1, ty_Char)
new_ltEs14(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs5(x0, x1, ty_Int)
new_lt4(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_Double)
new_esEs32(x0, x1, app(ty_Ratio, x2))
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_esEs19(x0, x1, ty_@0)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs21(x0, x1, ty_Bool)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs14(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs21(x0, x1, ty_Double)
new_lt12(x0, x1)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs8(x0, x1, ty_Bool)
new_ltEs21(x0, x1, ty_Char)
new_lt13(x0, x1)
new_esEs13(:(x0, x1), :(x2, x3), x4)
new_esEs31(x0, x1, ty_Ordering)
new_ltEs14(Right(x0), Right(x1), x2, ty_Bool)
new_compare1(:(x0, x1), [], x2)
new_compare27(x0, x1, x2)
new_compare10(x0, x1, False)
new_esEs27(x0, x1, app(ty_[], x2))
new_primMulNat0(Succ(x0), Zero)
new_ltEs19(x0, x1, ty_Float)
new_ltEs14(Left(x0), Right(x1), x2, x3)
new_esEs23(x0, x1, ty_Float)
new_ltEs14(Right(x0), Left(x1), x2, x3)
new_compare29(x0, x1, ty_Int)
new_esEs22(x0, x1, ty_Int)
new_esEs31(x0, x1, app(ty_Maybe, x2))
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Float)
new_compare31(x0, x1)
new_esEs29(x0, x1, ty_Double)
new_esEs32(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Left(x0), Left(x1), ty_Double, x2)
new_esEs31(x0, x1, ty_Char)
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Just(x0), Just(x1), ty_Int)
new_compare33(x0, x1, x2, x3)
new_esEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs21(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs7(LT, GT)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs7(GT, LT)
new_ltEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Double)
new_compare29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare111(x0, x1, True, x2)
new_ltEs13(x0, x1)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs32(x0, x1, app(ty_Maybe, x2))
new_esEs31(x0, x1, ty_Int)
new_lt4(x0, x1, ty_Int)
new_ltEs11(x0, x1, x2)
new_lt20(x0, x1, ty_Float)
new_not(True)
new_esEs31(x0, x1, ty_Float)
new_esEs20(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Float)
new_esEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs6(Nothing, Nothing, x0)
new_esEs28(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Ordering)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(Left(x0), Left(x1), ty_Double, x2)
new_esEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs6(Just(x0), Just(x1), ty_Integer)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_not(False)
new_lt8(x0, x1)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_ltEs18(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare13(x0, x1, True, x2, x3)
new_esEs32(x0, x1, ty_Integer)
new_esEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs19(x0, x1, ty_Char)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_esEs6(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare8(:%(x0, x1), :%(x2, x3), ty_Integer)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_Integer)
new_esEs8(x0, x1, ty_@0)
new_compare26(Left(x0), Left(x1), False, x2, x3)
new_ltEs12(True, True)
new_esEs27(x0, x1, ty_Float)
new_lt15(x0, x1)
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, ty_Ordering)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, ty_Double)
new_esEs6(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_lt20(x0, x1, ty_Ordering)
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs22(x0, x1, ty_Char)
new_lt20(x0, x1, ty_Double)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Bool)
new_esEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_ltEs21(x0, x1, ty_Float)
new_ltEs10(x0, x1)
new_ltEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs14(Left(x0), Left(x1), ty_Bool, x2)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs14(Left(x0), Left(x1), ty_Integer, x2)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(x0, x1, ty_Ordering)
new_esEs8(x0, x1, ty_Double)
new_compare29(x0, x1, ty_Char)
new_esEs6(Just(x0), Just(x1), ty_@0)
new_compare1(:(x0, x1), :(x2, x3), x4)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_compare210(x0, x1, True, x2, x3)
new_esEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs6(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs29(x0, x1, ty_Float)
new_esEs19(x0, x1, ty_Double)
new_esEs14(False, False)
new_primEqInt(Pos(Zero), Pos(Zero))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs32(x0, x1, ty_Char)
new_lt19(x0, x1, app(ty_[], x2))
new_ltEs21(x0, x1, ty_Double)
new_esEs32(x0, x1, ty_Int)
new_primCmpNat2(Succ(x0), Zero)
new_compare34(x0, x1, x2, x3)
new_compare18(x0, x1)
new_esEs29(x0, x1, ty_Int)
new_esEs32(x0, x1, ty_Bool)
new_compare28(x0, x1, False, x2)
new_ltEs14(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs18(Just(x0), Just(x1), ty_Int)
new_compare26(Right(x0), Right(x1), False, x2, x3)
new_ltEs17(x0, x1, x2)
new_primPlusNat0(Succ(x0), x1)
new_esEs7(Left(x0), Left(x1), ty_Int, x2)
new_esEs20(x0, x1, ty_Integer)
new_primCmpNat0(x0, Zero)
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_esEs7(Left(x0), Left(x1), ty_@0, x2)
new_ltEs7(GT, EQ)
new_ltEs7(EQ, GT)
new_esEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs32(x0, x1, ty_Double)
new_ltEs7(GT, GT)
new_esEs31(x0, x1, app(ty_Ratio, x2))
new_esEs9(LT, LT)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs13([], [], x0)
new_primCompAux0(x0, x1, x2, x3)
new_compare29(x0, x1, ty_@0)
new_esEs7(Left(x0), Left(x1), ty_Bool, x2)
new_compare26(x0, x1, True, x2, x3)
new_compare26(Right(x0), Left(x1), False, x2, x3)
new_compare26(Left(x0), Right(x1), False, x2, x3)
new_ltEs18(Nothing, Just(x0), x1)
new_esEs27(x0, x1, ty_Ordering)
new_primCmpNat0(x0, Succ(x1))

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

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

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

new_splitLT22(zxw60, zxw61, zxw62, zxw63, zxw64, zxw65, True, bf, bg, bh) → new_splitLT0(zxw63, zxw65, bf, bg, bh)
new_splitLT11(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, True, h, ba, bb) → new_splitLT0(zxw34, zxw400, h, ba, bb)
new_splitLT21(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, False, h, ba, bb) → new_splitLT11(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs9(new_compare35(zxw400, zxw300, h, ba), GT), h, ba, bb)
new_splitLT21(zxw300, zxw31, zxw32, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw34, zxw400, True, h, ba, bb) → new_splitLT3(zxw330, zxw331, zxw332, zxw333, zxw334, Right(zxw400), h, ba, bb)
new_splitLT3(Right(zxw300), zxw31, zxw32, zxw33, zxw34, Right(zxw400), h, ba, bb) → new_splitLT22(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs9(new_compare26(Right(zxw400), Right(zxw300), new_esEs30(zxw400, zxw300, ba), h, ba), LT), h, ba, bb)
new_splitLT0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw400, h, ba, bb) → new_splitLT3(zxw330, zxw331, zxw332, zxw333, zxw334, Right(zxw400), h, ba, bb)
new_splitLT12(zxw60, zxw61, zxw62, zxw63, zxw64, zxw65, True, bf, bg, bh) → new_splitLT0(zxw64, zxw65, bf, bg, bh)
new_splitLT22(zxw60, zxw61, zxw62, zxw63, zxw64, zxw65, False, bf, bg, bh) → new_splitLT12(zxw60, zxw61, zxw62, zxw63, zxw64, zxw65, new_esEs9(new_compare36(zxw65, zxw60, bf, bg), GT), bf, bg, bh)
new_splitLT3(Left(zxw300), zxw31, zxw32, zxw33, zxw34, Right(zxw400), h, ba, bb) → new_splitLT21(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs9(new_compare26(Right(zxw400), Left(zxw300), False, h, ba), LT), h, ba, bb)

The TRS R consists of the following rules:

new_compare35(zxw400, zxw300, h, ba) → new_compare26(Right(zxw400), Left(zxw300), False, h, ba)
new_esEs9(LT, GT) → False
new_esEs9(EQ, GT) → False
new_esEs9(GT, GT) → True
new_compare26(Right(zxw7900), Left(zxw8000), False, gh, ha) → GT
new_compare36(zxw35, zxw30, bca, bcb) → new_compare26(Right(zxw35), Right(zxw30), new_esEs31(zxw35, zxw30, bcb), bca, bcb)
new_esEs31(zxw35, zxw30, ty_Ordering) → new_esEs9(zxw35, zxw30)
new_esEs31(zxw35, zxw30, ty_Char) → new_esEs12(zxw35, zxw30)
new_esEs31(zxw35, zxw30, ty_@0) → new_esEs10(zxw35, zxw30)
new_esEs31(zxw35, zxw30, app(app(app(ty_@3, bdb), bdc), bdd)) → new_esEs4(zxw35, zxw30, bdb, bdc, bdd)
new_esEs31(zxw35, zxw30, ty_Float) → new_esEs17(zxw35, zxw30)
new_esEs31(zxw35, zxw30, app(app(ty_Either, bch), bda)) → new_esEs7(zxw35, zxw30, bch, bda)
new_esEs31(zxw35, zxw30, app(ty_Ratio, bcc)) → new_esEs18(zxw35, zxw30, bcc)
new_esEs31(zxw35, zxw30, app(app(ty_@2, bcf), bcg)) → new_esEs5(zxw35, zxw30, bcf, bcg)
new_esEs31(zxw35, zxw30, ty_Integer) → new_esEs15(zxw35, zxw30)
new_esEs31(zxw35, zxw30, ty_Double) → new_esEs16(zxw35, zxw30)
new_esEs31(zxw35, zxw30, app(ty_[], bcd)) → new_esEs13(zxw35, zxw30, bcd)
new_esEs31(zxw35, zxw30, ty_Int) → new_esEs11(zxw35, zxw30)
new_esEs31(zxw35, zxw30, ty_Bool) → new_esEs14(zxw35, zxw30)
new_esEs31(zxw35, zxw30, app(ty_Maybe, bce)) → new_esEs6(zxw35, zxw30, bce)
new_compare26(zxw790, zxw800, True, gh, ha) → EQ
new_compare26(Right(zxw7900), Right(zxw8000), False, gh, ha) → new_compare14(zxw7900, zxw8000, new_ltEs20(zxw7900, zxw8000, ha), gh, ha)
new_ltEs20(zxw7900, zxw8000, app(ty_Maybe, bbc)) → new_ltEs18(zxw7900, zxw8000, bbc)
new_ltEs20(zxw7900, zxw8000, ty_Int) → new_ltEs9(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, ty_@0) → new_ltEs8(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, app(app(ty_@2, baf), bag)) → new_ltEs4(zxw7900, zxw8000, baf, bag)
new_ltEs20(zxw7900, zxw8000, ty_Float) → new_ltEs16(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, ty_Bool) → new_ltEs12(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, app(ty_Ratio, bbb)) → new_ltEs17(zxw7900, zxw8000, bbb)
new_ltEs20(zxw7900, zxw8000, ty_Double) → new_ltEs15(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, ty_Integer) → new_ltEs13(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, app(app(app(ty_@3, bab), bac), bad)) → new_ltEs6(zxw7900, zxw8000, bab, bac, bad)
new_ltEs20(zxw7900, zxw8000, app(app(ty_Either, bah), bba)) → new_ltEs14(zxw7900, zxw8000, bah, bba)
new_ltEs20(zxw7900, zxw8000, app(ty_[], bae)) → new_ltEs11(zxw7900, zxw8000, bae)
new_ltEs20(zxw7900, zxw8000, ty_Char) → new_ltEs10(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, ty_Ordering) → new_ltEs7(zxw7900, zxw8000)
new_compare14(zxw242, zxw243, False, dfe, dff) → GT
new_compare14(zxw242, zxw243, True, dfe, dff) → LT
new_ltEs7(LT, EQ) → True
new_ltEs7(GT, GT) → True
new_ltEs7(EQ, EQ) → True
new_ltEs7(GT, LT) → False
new_ltEs7(GT, EQ) → False
new_ltEs7(EQ, GT) → True
new_ltEs7(EQ, LT) → False
new_ltEs7(LT, LT) → True
new_ltEs7(LT, GT) → True
new_ltEs10(zxw7900, zxw8000) → new_fsEs(new_compare17(zxw7900, zxw8000))
new_compare17(Char(zxw79000), Char(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_fsEs(zxw259) → new_not(new_esEs9(zxw259, GT))
new_not(False) → True
new_not(True) → False
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_ltEs11(zxw7900, zxw8000, he) → new_fsEs(new_compare1(zxw7900, zxw8000, he))
new_compare1([], :(zxw80000, zxw80001), he) → LT
new_compare1(:(zxw79000, zxw79001), :(zxw80000, zxw80001), he) → new_primCompAux0(zxw79000, zxw80000, new_compare1(zxw79001, zxw80001, he), he)
new_compare1(:(zxw79000, zxw79001), [], he) → GT
new_compare1([], [], he) → EQ
new_primCompAux0(zxw79000, zxw80000, zxw272, he) → new_primCompAux00(zxw272, new_compare29(zxw79000, zxw80000, he))
new_compare29(zxw79000, zxw80000, ty_Char) → new_compare17(zxw79000, zxw80000)
new_compare29(zxw79000, zxw80000, ty_Bool) → new_compare31(zxw79000, zxw80000)
new_compare29(zxw79000, zxw80000, app(app(ty_@2, cbf), cbg)) → new_compare19(zxw79000, zxw80000, cbf, cbg)
new_compare29(zxw79000, zxw80000, app(ty_[], cbe)) → new_compare1(zxw79000, zxw80000, cbe)
new_compare29(zxw79000, zxw80000, app(app(app(ty_@3, cbb), cbc), cbd)) → new_compare9(zxw79000, zxw80000, cbb, cbc, cbd)
new_compare29(zxw79000, zxw80000, ty_Int) → new_compare16(zxw79000, zxw80000)
new_compare29(zxw79000, zxw80000, ty_Integer) → new_compare32(zxw79000, zxw80000)
new_compare29(zxw79000, zxw80000, app(ty_Maybe, ccc)) → new_compare27(zxw79000, zxw80000, ccc)
new_compare29(zxw79000, zxw80000, app(ty_Ratio, ccb)) → new_compare8(zxw79000, zxw80000, ccb)
new_compare29(zxw79000, zxw80000, ty_Float) → new_compare7(zxw79000, zxw80000)
new_compare29(zxw79000, zxw80000, ty_Double) → new_compare6(zxw79000, zxw80000)
new_compare29(zxw79000, zxw80000, app(app(ty_Either, cbh), cca)) → new_compare15(zxw79000, zxw80000, cbh, cca)
new_compare29(zxw79000, zxw80000, ty_Ordering) → new_compare18(zxw79000, zxw80000)
new_compare29(zxw79000, zxw80000, ty_@0) → new_compare30(zxw79000, zxw80000)
new_primCompAux00(zxw276, LT) → LT
new_primCompAux00(zxw276, EQ) → zxw276
new_primCompAux00(zxw276, GT) → GT
new_compare30(@0, @0) → EQ
new_compare18(zxw79000, zxw80000) → new_compare24(zxw79000, zxw80000, new_esEs9(zxw79000, zxw80000))
new_esEs9(GT, LT) → False
new_esEs9(GT, EQ) → False
new_esEs9(EQ, EQ) → True
new_esEs9(EQ, LT) → False
new_esEs9(LT, EQ) → False
new_esEs9(LT, LT) → True
new_compare24(zxw79000, zxw80000, False) → new_compare11(zxw79000, zxw80000, new_ltEs7(zxw79000, zxw80000))
new_compare24(zxw79000, zxw80000, True) → EQ
new_compare11(zxw79000, zxw80000, False) → GT
new_compare11(zxw79000, zxw80000, True) → LT
new_compare15(zxw790, zxw800, gh, ha) → new_compare26(zxw790, zxw800, new_esEs7(zxw790, zxw800, gh, ha), gh, ha)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Bool, bdf) → new_esEs14(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Right(zxw3000), beh, bdf) → False
new_esEs7(Right(zxw4000), Left(zxw3000), beh, bdf) → False
new_esEs7(Right(zxw4000), Right(zxw3000), beh, app(app(ty_@2, bfd), bfe)) → new_esEs5(zxw4000, zxw3000, bfd, bfe)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Int, bdf) → new_esEs11(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), app(app(ty_@2, bea), beb), bdf) → new_esEs5(zxw4000, zxw3000, bea, beb)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Ordering, bdf) → new_esEs9(zxw4000, zxw3000)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, app(ty_[], bfb)) → new_esEs13(zxw4000, zxw3000, bfb)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Integer, bdf) → new_esEs15(zxw4000, zxw3000)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, app(app(app(ty_@3, bfh), bga), bgb)) → new_esEs4(zxw4000, zxw3000, bfh, bga, bgb)
new_esEs7(Left(zxw4000), Left(zxw3000), app(ty_Ratio, bde), bdf) → new_esEs18(zxw4000, zxw3000, bde)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_@0, bdf) → new_esEs10(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), app(app(app(ty_@3, bee), bef), beg), bdf) → new_esEs4(zxw4000, zxw3000, bee, bef, beg)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Double, bdf) → new_esEs16(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Float, bdf) → new_esEs17(zxw4000, zxw3000)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Char, bdf) → new_esEs12(zxw4000, zxw3000)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), app(ty_[], bdg), bdf) → new_esEs13(zxw4000, zxw3000, bdg)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, app(ty_Ratio, bfa)) → new_esEs18(zxw4000, zxw3000, bfa)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_compare26(Left(zxw7900), Right(zxw8000), False, gh, ha) → LT
new_compare26(Left(zxw7900), Left(zxw8000), False, gh, ha) → new_compare13(zxw7900, zxw8000, new_ltEs19(zxw7900, zxw8000, gh), gh, ha)
new_esEs6(Just(zxw4000), Just(zxw3000), app(ty_Maybe, fc)) → new_esEs6(zxw4000, zxw3000, fc)
new_esEs7(Left(zxw4000), Left(zxw3000), app(app(ty_Either, bec), bed), bdf) → new_esEs7(zxw4000, zxw3000, bec, bed)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, app(ty_Maybe, bfc)) → new_esEs6(zxw4000, zxw3000, bfc)
new_esEs6(Just(zxw4000), Just(zxw3000), app(app(ty_Either, fg), fh)) → new_esEs7(zxw4000, zxw3000, fg, fh)
new_esEs7(Left(zxw4000), Left(zxw3000), app(ty_Maybe, bdh), bdf) → new_esEs6(zxw4000, zxw3000, bdh)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, app(app(ty_Either, bff), bfg)) → new_esEs7(zxw4000, zxw3000, bff, bfg)
new_esEs6(Just(zxw4000), Just(zxw3000), app(app(ty_@2, fd), ff)) → new_esEs5(zxw4000, zxw3000, fd, ff)
new_esEs6(Nothing, Nothing, eh) → True
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs6(Nothing, Just(zxw3000), eh) → False
new_esEs6(Just(zxw4000), Nothing, eh) → False
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), app(app(app(ty_@3, ga), gb), gc)) → new_esEs4(zxw4000, zxw3000, ga, gb, gc)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_@0) → new_esEs10(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), app(ty_[], fb)) → new_esEs13(zxw4000, zxw3000, fb)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Char) → new_esEs12(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Float) → new_esEs17(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), app(ty_Ratio, fa)) → new_esEs18(zxw4000, zxw3000, fa)
new_esEs18(:%(zxw4000, zxw4001), :%(zxw3000, zxw3001), ccd) → new_asAs(new_esEs25(zxw4000, zxw3000, ccd), new_esEs24(zxw4001, zxw3001, ccd))
new_esEs25(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs25(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs24(zxw4001, zxw3001, ty_Integer) → new_esEs15(zxw4001, zxw3001)
new_esEs24(zxw4001, zxw3001, ty_Int) → new_esEs11(zxw4001, zxw3001)
new_asAs(False, zxw230) → False
new_asAs(True, zxw230) → zxw230
new_esEs11(zxw400, zxw300) → new_primEqInt(zxw400, zxw300)
new_primEqInt(Neg(Succ(zxw40000)), Neg(Succ(zxw30000))) → new_primEqNat0(zxw40000, zxw30000)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Neg(Succ(zxw30000))) → False
new_primEqInt(Neg(Succ(zxw40000)), Neg(Zero)) → False
new_primEqInt(Pos(Succ(zxw40000)), Pos(Succ(zxw30000))) → new_primEqNat0(zxw40000, zxw30000)
new_primEqInt(Pos(Zero), Pos(Succ(zxw30000))) → False
new_primEqInt(Pos(Succ(zxw40000)), Pos(Zero)) → False
new_primEqInt(Neg(Succ(zxw40000)), Pos(zxw3000)) → False
new_primEqInt(Pos(Succ(zxw40000)), Neg(zxw3000)) → False
new_primEqInt(Neg(Zero), Pos(Succ(zxw30000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(zxw30000))) → False
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqNat0(Zero, Zero) → True
new_primEqNat0(Succ(zxw40000), Succ(zxw30000)) → new_primEqNat0(zxw40000, zxw30000)
new_primEqNat0(Zero, Succ(zxw30000)) → False
new_primEqNat0(Succ(zxw40000), Zero) → False
new_esEs15(Integer(zxw4000), Integer(zxw3000)) → new_primEqInt(zxw4000, zxw3000)
new_esEs17(Float(zxw4000, zxw4001), Float(zxw3000, zxw3001)) → new_esEs11(new_sr(zxw4000, zxw3000), new_sr(zxw4001, zxw3001))
new_sr(zxw4000, zxw3000) → new_primMulInt(zxw4000, zxw3000)
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Neg(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Pos(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulNat0(Zero, Zero) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_esEs12(Char(zxw4000), Char(zxw3000)) → new_primEqNat0(zxw4000, zxw3000)
new_esEs13([], [], cce) → True
new_esEs13(:(zxw4000, zxw4001), :(zxw3000, zxw3001), cce) → new_asAs(new_esEs23(zxw4000, zxw3000, cce), new_esEs13(zxw4001, zxw3001, cce))
new_esEs13(:(zxw4000, zxw4001), [], cce) → False
new_esEs13([], :(zxw3000, zxw3001), cce) → False
new_esEs23(zxw4000, zxw3000, app(app(ty_Either, deh), dfa)) → new_esEs7(zxw4000, zxw3000, deh, dfa)
new_esEs23(zxw4000, zxw3000, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, app(app(app(ty_@3, dfb), dfc), dfd)) → new_esEs4(zxw4000, zxw3000, dfb, dfc, dfd)
new_esEs23(zxw4000, zxw3000, app(app(ty_@2, def), deg)) → new_esEs5(zxw4000, zxw3000, def, deg)
new_esEs23(zxw4000, zxw3000, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, app(ty_Ratio, dec)) → new_esEs18(zxw4000, zxw3000, dec)
new_esEs23(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, app(ty_Maybe, dee)) → new_esEs6(zxw4000, zxw3000, dee)
new_esEs23(zxw4000, zxw3000, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, app(ty_[], ded)) → new_esEs13(zxw4000, zxw3000, ded)
new_esEs16(Double(zxw4000, zxw4001), Double(zxw3000, zxw3001)) → new_esEs11(new_sr(zxw4000, zxw3000), new_sr(zxw4001, zxw3001))
new_esEs10(@0, @0) → True
new_esEs5(@2(zxw4000, zxw4001), @2(zxw3000, zxw3001), ccf, ccg) → new_asAs(new_esEs22(zxw4000, zxw3000, ccf), new_esEs21(zxw4001, zxw3001, ccg))
new_esEs22(zxw4000, zxw3000, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, app(app(ty_@2, ddd), dde)) → new_esEs5(zxw4000, zxw3000, ddd, dde)
new_esEs22(zxw4000, zxw3000, app(ty_Maybe, ddc)) → new_esEs6(zxw4000, zxw3000, ddc)
new_esEs22(zxw4000, zxw3000, app(ty_Ratio, dda)) → new_esEs18(zxw4000, zxw3000, dda)
new_esEs22(zxw4000, zxw3000, app(app(ty_Either, ddf), ddg)) → new_esEs7(zxw4000, zxw3000, ddf, ddg)
new_esEs22(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, app(app(app(ty_@3, ddh), dea), deb)) → new_esEs4(zxw4000, zxw3000, ddh, dea, deb)
new_esEs22(zxw4000, zxw3000, app(ty_[], ddb)) → new_esEs13(zxw4000, zxw3000, ddb)
new_esEs22(zxw4000, zxw3000, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs21(zxw4001, zxw3001, ty_Bool) → new_esEs14(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, ty_Double) → new_esEs16(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, ty_Ordering) → new_esEs9(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, ty_Char) → new_esEs12(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, ty_Float) → new_esEs17(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, app(ty_Maybe, dca)) → new_esEs6(zxw4001, zxw3001, dca)
new_esEs21(zxw4001, zxw3001, ty_Int) → new_esEs11(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, app(ty_[], dbh)) → new_esEs13(zxw4001, zxw3001, dbh)
new_esEs21(zxw4001, zxw3001, ty_Integer) → new_esEs15(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, app(app(ty_@2, dcb), dcc)) → new_esEs5(zxw4001, zxw3001, dcb, dcc)
new_esEs21(zxw4001, zxw3001, ty_@0) → new_esEs10(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, app(app(ty_Either, dcd), dce)) → new_esEs7(zxw4001, zxw3001, dcd, dce)
new_esEs21(zxw4001, zxw3001, app(app(app(ty_@3, dcf), dcg), dch)) → new_esEs4(zxw4001, zxw3001, dcf, dcg, dch)
new_esEs21(zxw4001, zxw3001, app(ty_Ratio, dbg)) → new_esEs18(zxw4001, zxw3001, dbg)
new_esEs4(@3(zxw4000, zxw4001, zxw4002), @3(zxw3000, zxw3001, zxw3002), cch, cda, cdb) → new_asAs(new_esEs28(zxw4000, zxw3000, cch), new_asAs(new_esEs27(zxw4001, zxw3001, cda), new_esEs26(zxw4002, zxw3002, cdb)))
new_esEs28(zxw4000, zxw3000, app(ty_[], ead)) → new_esEs13(zxw4000, zxw3000, ead)
new_esEs28(zxw4000, zxw3000, app(app(app(ty_@3, ebb), ebc), ebd)) → new_esEs4(zxw4000, zxw3000, ebb, ebc, ebd)
new_esEs28(zxw4000, zxw3000, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, app(ty_Maybe, eae)) → new_esEs6(zxw4000, zxw3000, eae)
new_esEs28(zxw4000, zxw3000, app(app(ty_Either, eah), eba)) → new_esEs7(zxw4000, zxw3000, eah, eba)
new_esEs28(zxw4000, zxw3000, app(app(ty_@2, eaf), eag)) → new_esEs5(zxw4000, zxw3000, eaf, eag)
new_esEs28(zxw4000, zxw3000, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, app(ty_Ratio, eac)) → new_esEs18(zxw4000, zxw3000, eac)
new_esEs28(zxw4000, zxw3000, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_esEs27(zxw4001, zxw3001, app(ty_Ratio, dha)) → new_esEs18(zxw4001, zxw3001, dha)
new_esEs27(zxw4001, zxw3001, app(app(app(ty_@3, dhh), eaa), eab)) → new_esEs4(zxw4001, zxw3001, dhh, eaa, eab)
new_esEs27(zxw4001, zxw3001, app(ty_Maybe, dhc)) → new_esEs6(zxw4001, zxw3001, dhc)
new_esEs27(zxw4001, zxw3001, app(app(ty_Either, dhf), dhg)) → new_esEs7(zxw4001, zxw3001, dhf, dhg)
new_esEs27(zxw4001, zxw3001, ty_Ordering) → new_esEs9(zxw4001, zxw3001)
new_esEs27(zxw4001, zxw3001, ty_Float) → new_esEs17(zxw4001, zxw3001)
new_esEs27(zxw4001, zxw3001, ty_@0) → new_esEs10(zxw4001, zxw3001)
new_esEs27(zxw4001, zxw3001, ty_Char) → new_esEs12(zxw4001, zxw3001)
new_esEs27(zxw4001, zxw3001, ty_Double) → new_esEs16(zxw4001, zxw3001)
new_esEs27(zxw4001, zxw3001, ty_Int) → new_esEs11(zxw4001, zxw3001)
new_esEs27(zxw4001, zxw3001, app(app(ty_@2, dhd), dhe)) → new_esEs5(zxw4001, zxw3001, dhd, dhe)
new_esEs27(zxw4001, zxw3001, ty_Bool) → new_esEs14(zxw4001, zxw3001)
new_esEs27(zxw4001, zxw3001, app(ty_[], dhb)) → new_esEs13(zxw4001, zxw3001, dhb)
new_esEs27(zxw4001, zxw3001, ty_Integer) → new_esEs15(zxw4001, zxw3001)
new_esEs26(zxw4002, zxw3002, ty_Float) → new_esEs17(zxw4002, zxw3002)
new_esEs26(zxw4002, zxw3002, ty_Char) → new_esEs12(zxw4002, zxw3002)
new_esEs26(zxw4002, zxw3002, ty_Int) → new_esEs11(zxw4002, zxw3002)
new_esEs26(zxw4002, zxw3002, app(ty_Maybe, dga)) → new_esEs6(zxw4002, zxw3002, dga)
new_esEs26(zxw4002, zxw3002, app(app(app(ty_@3, dgf), dgg), dgh)) → new_esEs4(zxw4002, zxw3002, dgf, dgg, dgh)
new_esEs26(zxw4002, zxw3002, app(ty_[], dfh)) → new_esEs13(zxw4002, zxw3002, dfh)
new_esEs26(zxw4002, zxw3002, app(app(ty_Either, dgd), dge)) → new_esEs7(zxw4002, zxw3002, dgd, dge)
new_esEs26(zxw4002, zxw3002, ty_Integer) → new_esEs15(zxw4002, zxw3002)
new_esEs26(zxw4002, zxw3002, app(app(ty_@2, dgb), dgc)) → new_esEs5(zxw4002, zxw3002, dgb, dgc)
new_esEs26(zxw4002, zxw3002, app(ty_Ratio, dfg)) → new_esEs18(zxw4002, zxw3002, dfg)
new_esEs26(zxw4002, zxw3002, ty_Bool) → new_esEs14(zxw4002, zxw3002)
new_esEs26(zxw4002, zxw3002, ty_@0) → new_esEs10(zxw4002, zxw3002)
new_esEs26(zxw4002, zxw3002, ty_Ordering) → new_esEs9(zxw4002, zxw3002)
new_esEs26(zxw4002, zxw3002, ty_Double) → new_esEs16(zxw4002, zxw3002)
new_esEs14(False, True) → False
new_esEs14(True, False) → False
new_esEs14(True, True) → True
new_esEs14(False, False) → True
new_ltEs19(zxw7900, zxw8000, ty_Float) → new_ltEs16(zxw7900, zxw8000)
new_ltEs19(zxw7900, zxw8000, app(app(ty_@2, ca), cb)) → new_ltEs4(zxw7900, zxw8000, ca, cb)
new_ltEs19(zxw7900, zxw8000, app(ty_[], he)) → new_ltEs11(zxw7900, zxw8000, he)
new_ltEs19(zxw7900, zxw8000, ty_Char) → new_ltEs10(zxw7900, zxw8000)
new_ltEs19(zxw7900, zxw8000, ty_Bool) → new_ltEs12(zxw7900, zxw8000)
new_ltEs19(zxw7900, zxw8000, app(ty_Ratio, hh)) → new_ltEs17(zxw7900, zxw8000, hh)
new_ltEs19(zxw7900, zxw8000, app(app(app(ty_@3, hb), hc), hd)) → new_ltEs6(zxw7900, zxw8000, hb, hc, hd)
new_ltEs19(zxw7900, zxw8000, ty_Int) → new_ltEs9(zxw7900, zxw8000)
new_ltEs19(zxw7900, zxw8000, app(app(ty_Either, hf), hg)) → new_ltEs14(zxw7900, zxw8000, hf, hg)
new_ltEs19(zxw7900, zxw8000, ty_@0) → new_ltEs8(zxw7900, zxw8000)
new_ltEs19(zxw7900, zxw8000, ty_Double) → new_ltEs15(zxw7900, zxw8000)
new_ltEs19(zxw7900, zxw8000, ty_Integer) → new_ltEs13(zxw7900, zxw8000)
new_ltEs19(zxw7900, zxw8000, ty_Ordering) → new_ltEs7(zxw7900, zxw8000)
new_ltEs19(zxw7900, zxw8000, app(ty_Maybe, baa)) → new_ltEs18(zxw7900, zxw8000, baa)
new_compare13(zxw235, zxw236, False, bbf, bbg) → GT
new_compare13(zxw235, zxw236, True, bbf, bbg) → LT
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Char) → new_ltEs10(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Integer) → new_ltEs13(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(ty_Ratio, dac)) → new_ltEs17(zxw79000, zxw80000, dac)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(app(app(ty_@3, chc), chd), che)) → new_ltEs6(zxw79000, zxw80000, chc, chd, che)
new_ltEs18(Nothing, Nothing, baa) → True
new_ltEs18(Just(zxw79000), Nothing, baa) → False
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Double) → new_ltEs15(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(ty_[], chf)) → new_ltEs11(zxw79000, zxw80000, chf)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(app(ty_@2, chg), chh)) → new_ltEs4(zxw79000, zxw80000, chg, chh)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Bool) → new_ltEs12(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Ordering) → new_ltEs7(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Float) → new_ltEs16(zxw79000, zxw80000)
new_ltEs18(Nothing, Just(zxw80000), baa) → True
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Int) → new_ltEs9(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_@0) → new_ltEs8(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(ty_Maybe, dad)) → new_ltEs18(zxw79000, zxw80000, dad)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(ty_Maybe, chb)) → new_ltEs18(zxw79000, zxw80000, chb)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(app(ty_Either, daa), dab)) → new_ltEs14(zxw79000, zxw80000, daa, dab)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(app(ty_Either, cgg), cgh)) → new_ltEs14(zxw79000, zxw80000, cgg, cgh)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(app(ty_Either, cfe), cff), hg) → new_ltEs14(zxw79000, zxw80000, cfe, cff)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(ty_Maybe, cfh), hg) → new_ltEs18(zxw79000, zxw80000, cfh)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Bool) → new_ltEs12(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(ty_[], cgd)) → new_ltEs11(zxw79000, zxw80000, cgd)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Bool, hg) → new_ltEs12(zxw79000, zxw80000)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(ty_Ratio, cfg), hg) → new_ltEs17(zxw79000, zxw80000, cfg)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(app(app(ty_@3, cga), cgb), cgc)) → new_ltEs6(zxw79000, zxw80000, cga, cgb, cgc)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Float, hg) → new_ltEs16(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Float) → new_ltEs16(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Double) → new_ltEs15(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(app(ty_@2, cge), cgf)) → new_ltEs4(zxw79000, zxw80000, cge, cgf)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Double, hg) → new_ltEs15(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Left(zxw80000), hf, hg) → False
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Int, hg) → new_ltEs9(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Char) → new_ltEs10(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_@0) → new_ltEs8(zxw79000, zxw80000)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(app(app(ty_@3, ceg), ceh), cfa), hg) → new_ltEs6(zxw79000, zxw80000, ceg, ceh, cfa)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_@0, hg) → new_ltEs8(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Ordering) → new_ltEs7(zxw79000, zxw80000)
new_ltEs14(Left(zxw79000), Right(zxw80000), hf, hg) → True
new_ltEs14(Left(zxw79000), Left(zxw80000), app(app(ty_@2, cfc), cfd), hg) → new_ltEs4(zxw79000, zxw80000, cfc, cfd)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(ty_[], cfb), hg) → new_ltEs11(zxw79000, zxw80000, cfb)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Integer, hg) → new_ltEs13(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Int) → new_ltEs9(zxw79000, zxw80000)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Ordering, hg) → new_ltEs7(zxw79000, zxw80000)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Char, hg) → new_ltEs10(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(ty_Ratio, cha)) → new_ltEs17(zxw79000, zxw80000, cha)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Integer) → new_ltEs13(zxw79000, zxw80000)
new_ltEs13(zxw7900, zxw8000) → new_fsEs(new_compare32(zxw7900, zxw8000))
new_compare32(Integer(zxw79000), Integer(zxw80000)) → new_primCmpInt(zxw79000, zxw80000)
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_ltEs17(zxw7900, zxw8000, hh) → new_fsEs(new_compare8(zxw7900, zxw8000, hh))
new_compare8(:%(zxw79000, zxw79001), :%(zxw80000, zxw80001), ty_Integer) → new_compare32(new_sr0(zxw79000, zxw80001), new_sr0(zxw80000, zxw79001))
new_compare8(:%(zxw79000, zxw79001), :%(zxw80000, zxw80001), ty_Int) → new_compare16(new_sr(zxw79000, zxw80001), new_sr(zxw80000, zxw79001))
new_compare16(zxw79, zxw80) → new_primCmpInt(zxw79, zxw80)
new_sr0(Integer(zxw800000), Integer(zxw790010)) → Integer(new_primMulInt(zxw800000, zxw790010))
new_ltEs9(zxw7900, zxw8000) → new_fsEs(new_compare16(zxw7900, zxw8000))
new_ltEs4(@2(zxw79000, zxw79001), @2(zxw80000, zxw80001), ca, cb) → new_pePe(new_lt4(zxw79000, zxw80000, ca), new_asAs(new_esEs8(zxw79000, zxw80000, ca), new_ltEs5(zxw79001, zxw80001, cb)))
new_lt4(zxw79000, zxw80000, app(app(app(ty_@3, cc), cd), ce)) → new_lt5(zxw79000, zxw80000, cc, cd, ce)
new_lt4(zxw79000, zxw80000, app(ty_[], cf)) → new_lt10(zxw79000, zxw80000, cf)
new_lt4(zxw79000, zxw80000, ty_Bool) → new_lt12(zxw79000, zxw80000)
new_lt4(zxw79000, zxw80000, app(ty_Maybe, de)) → new_lt18(zxw79000, zxw80000, de)
new_lt4(zxw79000, zxw80000, ty_Ordering) → new_lt6(zxw79000, zxw80000)
new_lt4(zxw79000, zxw80000, app(ty_Ratio, dd)) → new_lt17(zxw79000, zxw80000, dd)
new_lt4(zxw79000, zxw80000, ty_Int) → new_lt8(zxw79000, zxw80000)
new_lt4(zxw79000, zxw80000, ty_Double) → new_lt15(zxw79000, zxw80000)
new_lt4(zxw79000, zxw80000, app(app(ty_Either, db), dc)) → new_lt14(zxw79000, zxw80000, db, dc)
new_lt4(zxw79000, zxw80000, ty_Char) → new_lt9(zxw79000, zxw80000)
new_lt4(zxw79000, zxw80000, ty_@0) → new_lt7(zxw79000, zxw80000)
new_lt4(zxw79000, zxw80000, ty_Float) → new_lt16(zxw79000, zxw80000)
new_lt4(zxw79000, zxw80000, app(app(ty_@2, cg), da)) → new_lt11(zxw79000, zxw80000, cg, da)
new_lt4(zxw79000, zxw80000, ty_Integer) → new_lt13(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, ty_Int) → new_esEs11(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, ty_Double) → new_esEs16(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, app(app(app(ty_@3, cc), cd), ce)) → new_esEs4(zxw79000, zxw80000, cc, cd, ce)
new_esEs8(zxw79000, zxw80000, app(ty_[], cf)) → new_esEs13(zxw79000, zxw80000, cf)
new_esEs8(zxw79000, zxw80000, ty_Char) → new_esEs12(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, app(app(ty_@2, cg), da)) → new_esEs5(zxw79000, zxw80000, cg, da)
new_esEs8(zxw79000, zxw80000, ty_Float) → new_esEs17(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, app(app(ty_Either, db), dc)) → new_esEs7(zxw79000, zxw80000, db, dc)
new_esEs8(zxw79000, zxw80000, ty_@0) → new_esEs10(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, app(ty_Maybe, de)) → new_esEs6(zxw79000, zxw80000, de)
new_esEs8(zxw79000, zxw80000, ty_Bool) → new_esEs14(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, ty_Ordering) → new_esEs9(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, ty_Integer) → new_esEs15(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, app(ty_Ratio, dd)) → new_esEs18(zxw79000, zxw80000, dd)
new_ltEs5(zxw79001, zxw80001, ty_Char) → new_ltEs10(zxw79001, zxw80001)
new_ltEs5(zxw79001, zxw80001, app(app(ty_@2, eb), ec)) → new_ltEs4(zxw79001, zxw80001, eb, ec)
new_ltEs5(zxw79001, zxw80001, ty_Ordering) → new_ltEs7(zxw79001, zxw80001)
new_ltEs5(zxw79001, zxw80001, ty_Bool) → new_ltEs12(zxw79001, zxw80001)
new_ltEs5(zxw79001, zxw80001, ty_Integer) → new_ltEs13(zxw79001, zxw80001)
new_ltEs5(zxw79001, zxw80001, app(ty_Ratio, ef)) → new_ltEs17(zxw79001, zxw80001, ef)
new_ltEs5(zxw79001, zxw80001, app(ty_Maybe, eg)) → new_ltEs18(zxw79001, zxw80001, eg)
new_ltEs5(zxw79001, zxw80001, ty_Double) → new_ltEs15(zxw79001, zxw80001)
new_ltEs5(zxw79001, zxw80001, app(app(ty_Either, ed), ee)) → new_ltEs14(zxw79001, zxw80001, ed, ee)
new_ltEs5(zxw79001, zxw80001, app(app(app(ty_@3, df), dg), dh)) → new_ltEs6(zxw79001, zxw80001, df, dg, dh)
new_ltEs5(zxw79001, zxw80001, app(ty_[], ea)) → new_ltEs11(zxw79001, zxw80001, ea)
new_ltEs5(zxw79001, zxw80001, ty_Int) → new_ltEs9(zxw79001, zxw80001)
new_ltEs5(zxw79001, zxw80001, ty_@0) → new_ltEs8(zxw79001, zxw80001)
new_ltEs5(zxw79001, zxw80001, ty_Float) → new_ltEs16(zxw79001, zxw80001)
new_pePe(False, zxw271) → zxw271
new_pePe(True, zxw271) → True
new_ltEs16(zxw7900, zxw8000) → new_fsEs(new_compare7(zxw7900, zxw8000))
new_compare7(Float(zxw79000, zxw79001), Float(zxw80000, zxw80001)) → new_compare16(new_sr(zxw79000, zxw80000), new_sr(zxw79001, zxw80001))
new_ltEs8(zxw7900, zxw8000) → new_fsEs(new_compare30(zxw7900, zxw8000))
new_ltEs6(@3(zxw79000, zxw79001, zxw79002), @3(zxw80000, zxw80001, zxw80002), hb, hc, hd) → new_pePe(new_lt19(zxw79000, zxw80000, hb), new_asAs(new_esEs20(zxw79000, zxw80000, hb), new_pePe(new_lt20(zxw79001, zxw80001, hc), new_asAs(new_esEs19(zxw79001, zxw80001, hc), new_ltEs21(zxw79002, zxw80002, hd)))))
new_lt19(zxw79000, zxw80000, app(app(ty_Either, bgd), bge)) → new_lt14(zxw79000, zxw80000, bgd, bge)
new_lt19(zxw79000, zxw80000, ty_Double) → new_lt15(zxw79000, zxw80000)
new_lt19(zxw79000, zxw80000, ty_Ordering) → new_lt6(zxw79000, zxw80000)
new_lt19(zxw79000, zxw80000, app(ty_Ratio, gg)) → new_lt17(zxw79000, zxw80000, gg)
new_lt19(zxw79000, zxw80000, app(app(ty_@2, bbd), bbe)) → new_lt11(zxw79000, zxw80000, bbd, bbe)
new_lt19(zxw79000, zxw80000, ty_Int) → new_lt8(zxw79000, zxw80000)
new_lt19(zxw79000, zxw80000, ty_@0) → new_lt7(zxw79000, zxw80000)
new_lt19(zxw79000, zxw80000, app(app(app(ty_@3, gd), ge), gf)) → new_lt5(zxw79000, zxw80000, gd, ge, gf)
new_lt19(zxw79000, zxw80000, app(ty_Maybe, bbh)) → new_lt18(zxw79000, zxw80000, bbh)
new_lt19(zxw79000, zxw80000, ty_Float) → new_lt16(zxw79000, zxw80000)
new_lt19(zxw79000, zxw80000, ty_Bool) → new_lt12(zxw79000, zxw80000)
new_lt19(zxw79000, zxw80000, app(ty_[], bgc)) → new_lt10(zxw79000, zxw80000, bgc)
new_lt19(zxw79000, zxw80000, ty_Integer) → new_lt13(zxw79000, zxw80000)
new_lt19(zxw79000, zxw80000, ty_Char) → new_lt9(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, app(ty_[], bgc)) → new_esEs13(zxw79000, zxw80000, bgc)
new_esEs20(zxw79000, zxw80000, ty_Double) → new_esEs16(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, ty_Char) → new_esEs12(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, app(app(ty_@2, bbd), bbe)) → new_esEs5(zxw79000, zxw80000, bbd, bbe)
new_esEs20(zxw79000, zxw80000, ty_Int) → new_esEs11(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, ty_@0) → new_esEs10(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, app(app(app(ty_@3, gd), ge), gf)) → new_esEs4(zxw79000, zxw80000, gd, ge, gf)
new_esEs20(zxw79000, zxw80000, ty_Integer) → new_esEs15(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, ty_Bool) → new_esEs14(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, app(ty_Ratio, gg)) → new_esEs18(zxw79000, zxw80000, gg)
new_esEs20(zxw79000, zxw80000, app(app(ty_Either, bgd), bge)) → new_esEs7(zxw79000, zxw80000, bgd, bge)
new_esEs20(zxw79000, zxw80000, app(ty_Maybe, bbh)) → new_esEs6(zxw79000, zxw80000, bbh)
new_esEs20(zxw79000, zxw80000, ty_Ordering) → new_esEs9(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, ty_Float) → new_esEs17(zxw79000, zxw80000)
new_lt20(zxw79001, zxw80001, app(app(ty_Either, bhd), bhe)) → new_lt14(zxw79001, zxw80001, bhd, bhe)
new_lt20(zxw79001, zxw80001, ty_@0) → new_lt7(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, app(app(ty_@2, bhb), bhc)) → new_lt11(zxw79001, zxw80001, bhb, bhc)
new_lt20(zxw79001, zxw80001, ty_Ordering) → new_lt6(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, app(ty_Maybe, bhg)) → new_lt18(zxw79001, zxw80001, bhg)
new_lt20(zxw79001, zxw80001, ty_Int) → new_lt8(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, ty_Integer) → new_lt13(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, app(ty_Ratio, bhf)) → new_lt17(zxw79001, zxw80001, bhf)
new_lt20(zxw79001, zxw80001, ty_Char) → new_lt9(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, app(ty_[], bha)) → new_lt10(zxw79001, zxw80001, bha)
new_lt20(zxw79001, zxw80001, ty_Double) → new_lt15(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, ty_Float) → new_lt16(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, ty_Bool) → new_lt12(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, app(app(app(ty_@3, bgf), bgg), bgh)) → new_lt5(zxw79001, zxw80001, bgf, bgg, bgh)
new_esEs19(zxw79001, zxw80001, app(ty_Ratio, bhf)) → new_esEs18(zxw79001, zxw80001, bhf)
new_esEs19(zxw79001, zxw80001, ty_Ordering) → new_esEs9(zxw79001, zxw80001)
new_esEs19(zxw79001, zxw80001, app(ty_Maybe, bhg)) → new_esEs6(zxw79001, zxw80001, bhg)
new_esEs19(zxw79001, zxw80001, app(app(ty_Either, bhd), bhe)) → new_esEs7(zxw79001, zxw80001, bhd, bhe)
new_esEs19(zxw79001, zxw80001, ty_Float) → new_esEs17(zxw79001, zxw80001)
new_esEs19(zxw79001, zxw80001, ty_Bool) → new_esEs14(zxw79001, zxw80001)
new_esEs19(zxw79001, zxw80001, ty_Int) → new_esEs11(zxw79001, zxw80001)
new_esEs19(zxw79001, zxw80001, app(app(app(ty_@3, bgf), bgg), bgh)) → new_esEs4(zxw79001, zxw80001, bgf, bgg, bgh)
new_esEs19(zxw79001, zxw80001, app(app(ty_@2, bhb), bhc)) → new_esEs5(zxw79001, zxw80001, bhb, bhc)
new_esEs19(zxw79001, zxw80001, ty_Double) → new_esEs16(zxw79001, zxw80001)
new_esEs19(zxw79001, zxw80001, ty_Integer) → new_esEs15(zxw79001, zxw80001)
new_esEs19(zxw79001, zxw80001, ty_@0) → new_esEs10(zxw79001, zxw80001)
new_esEs19(zxw79001, zxw80001, app(ty_[], bha)) → new_esEs13(zxw79001, zxw80001, bha)
new_esEs19(zxw79001, zxw80001, ty_Char) → new_esEs12(zxw79001, zxw80001)
new_ltEs21(zxw79002, zxw80002, ty_Char) → new_ltEs10(zxw79002, zxw80002)
new_ltEs21(zxw79002, zxw80002, app(app(ty_@2, cad), cae)) → new_ltEs4(zxw79002, zxw80002, cad, cae)
new_ltEs21(zxw79002, zxw80002, ty_Int) → new_ltEs9(zxw79002, zxw80002)
new_ltEs21(zxw79002, zxw80002, ty_Ordering) → new_ltEs7(zxw79002, zxw80002)
new_ltEs21(zxw79002, zxw80002, ty_Float) → new_ltEs16(zxw79002, zxw80002)
new_ltEs21(zxw79002, zxw80002, ty_Bool) → new_ltEs12(zxw79002, zxw80002)
new_ltEs21(zxw79002, zxw80002, ty_Integer) → new_ltEs13(zxw79002, zxw80002)
new_ltEs21(zxw79002, zxw80002, app(app(ty_Either, caf), cag)) → new_ltEs14(zxw79002, zxw80002, caf, cag)
new_ltEs21(zxw79002, zxw80002, app(ty_[], cac)) → new_ltEs11(zxw79002, zxw80002, cac)
new_ltEs21(zxw79002, zxw80002, app(ty_Ratio, cah)) → new_ltEs17(zxw79002, zxw80002, cah)
new_ltEs21(zxw79002, zxw80002, app(app(app(ty_@3, bhh), caa), cab)) → new_ltEs6(zxw79002, zxw80002, bhh, caa, cab)
new_ltEs21(zxw79002, zxw80002, ty_@0) → new_ltEs8(zxw79002, zxw80002)
new_ltEs21(zxw79002, zxw80002, app(ty_Maybe, cba)) → new_ltEs18(zxw79002, zxw80002, cba)
new_ltEs21(zxw79002, zxw80002, ty_Double) → new_ltEs15(zxw79002, zxw80002)
new_ltEs15(zxw7900, zxw8000) → new_fsEs(new_compare6(zxw7900, zxw8000))
new_compare6(Double(zxw79000, zxw79001), Double(zxw80000, zxw80001)) → new_compare16(new_sr(zxw79000, zxw80000), new_sr(zxw79001, zxw80001))
new_ltEs12(True, False) → False
new_ltEs12(False, False) → True
new_ltEs12(True, True) → True
new_ltEs12(False, True) → True
new_lt5(zxw79000, zxw80000, gd, ge, gf) → new_esEs9(new_compare9(zxw79000, zxw80000, gd, ge, gf), LT)
new_compare9(zxw79000, zxw80000, gd, ge, gf) → new_compare25(zxw79000, zxw80000, new_esEs4(zxw79000, zxw80000, gd, ge, gf), gd, ge, gf)
new_compare25(zxw79000, zxw80000, True, gd, ge, gf) → EQ
new_compare25(zxw79000, zxw80000, False, gd, ge, gf) → new_compare12(zxw79000, zxw80000, new_ltEs6(zxw79000, zxw80000, gd, ge, gf), gd, ge, gf)
new_compare12(zxw79000, zxw80000, True, gd, ge, gf) → LT
new_compare12(zxw79000, zxw80000, False, gd, ge, gf) → GT
new_lt12(zxw79000, zxw80000) → new_esEs9(new_compare31(zxw79000, zxw80000), LT)
new_compare31(zxw79000, zxw80000) → new_compare23(zxw79000, zxw80000, new_esEs14(zxw79000, zxw80000))
new_compare23(zxw79000, zxw80000, True) → EQ
new_compare23(zxw79000, zxw80000, False) → new_compare10(zxw79000, zxw80000, new_ltEs12(zxw79000, zxw80000))
new_compare10(zxw79000, zxw80000, True) → LT
new_compare10(zxw79000, zxw80000, False) → GT
new_lt16(zxw79000, zxw80000) → new_esEs9(new_compare7(zxw79000, zxw80000), LT)
new_lt15(zxw79000, zxw80000) → new_esEs9(new_compare6(zxw79000, zxw80000), LT)
new_lt10(zxw79000, zxw80000, bgc) → new_esEs9(new_compare1(zxw79000, zxw80000, bgc), LT)
new_lt9(zxw79000, zxw80000) → new_esEs9(new_compare17(zxw79000, zxw80000), LT)
new_lt17(zxw79000, zxw80000, gg) → new_esEs9(new_compare8(zxw79000, zxw80000, gg), LT)
new_lt13(zxw79000, zxw80000) → new_esEs9(new_compare32(zxw79000, zxw80000), LT)
new_lt8(zxw790, zxw800) → new_esEs9(new_compare16(zxw790, zxw800), LT)
new_lt18(zxw79000, zxw80000, bbh) → new_esEs9(new_compare27(zxw79000, zxw80000, bbh), LT)
new_compare27(zxw79000, zxw80000, bbh) → new_compare28(zxw79000, zxw80000, new_esEs6(zxw79000, zxw80000, bbh), bbh)
new_compare28(zxw79000, zxw80000, False, bbh) → new_compare111(zxw79000, zxw80000, new_ltEs18(zxw79000, zxw80000, bbh), bbh)
new_compare28(zxw79000, zxw80000, True, bbh) → EQ
new_compare111(zxw79000, zxw80000, True, bbh) → LT
new_compare111(zxw79000, zxw80000, False, bbh) → GT
new_lt6(zxw79000, zxw80000) → new_esEs9(new_compare18(zxw79000, zxw80000), LT)
new_lt11(zxw79000, zxw80000, bbd, bbe) → new_esEs9(new_compare19(zxw79000, zxw80000, bbd, bbe), LT)
new_compare19(zxw79000, zxw80000, bbd, bbe) → new_compare210(zxw79000, zxw80000, new_esEs5(zxw79000, zxw80000, bbd, bbe), bbd, bbe)
new_compare210(zxw79000, zxw80000, False, bbd, bbe) → new_compare110(zxw79000, zxw80000, new_ltEs4(zxw79000, zxw80000, bbd, bbe), bbd, bbe)
new_compare210(zxw79000, zxw80000, True, bbd, bbe) → EQ
new_compare110(zxw79000, zxw80000, True, bbd, bbe) → LT
new_compare110(zxw79000, zxw80000, False, bbd, bbe) → GT
new_lt7(zxw79000, zxw80000) → new_esEs9(new_compare30(zxw79000, zxw80000), LT)
new_lt14(zxw790, zxw800, gh, ha) → new_esEs9(new_compare15(zxw790, zxw800, gh, ha), LT)
new_esEs30(zxw400, zxw300, app(ty_Maybe, dag)) → new_esEs6(zxw400, zxw300, dag)
new_esEs30(zxw400, zxw300, app(ty_[], daf)) → new_esEs13(zxw400, zxw300, daf)
new_esEs30(zxw400, zxw300, app(app(ty_Either, dbb), dbc)) → new_esEs7(zxw400, zxw300, dbb, dbc)
new_esEs30(zxw400, zxw300, ty_Char) → new_esEs12(zxw400, zxw300)
new_esEs30(zxw400, zxw300, app(app(app(ty_@3, dbd), dbe), dbf)) → new_esEs4(zxw400, zxw300, dbd, dbe, dbf)
new_esEs30(zxw400, zxw300, ty_Float) → new_esEs17(zxw400, zxw300)
new_esEs30(zxw400, zxw300, app(ty_Ratio, dae)) → new_esEs18(zxw400, zxw300, dae)
new_esEs30(zxw400, zxw300, ty_@0) → new_esEs10(zxw400, zxw300)
new_esEs30(zxw400, zxw300, app(app(ty_@2, dah), dba)) → new_esEs5(zxw400, zxw300, dah, dba)
new_esEs30(zxw400, zxw300, ty_Ordering) → new_esEs9(zxw400, zxw300)
new_esEs30(zxw400, zxw300, ty_Bool) → new_esEs14(zxw400, zxw300)
new_esEs30(zxw400, zxw300, ty_Integer) → new_esEs15(zxw400, zxw300)
new_esEs30(zxw400, zxw300, ty_Int) → new_esEs11(zxw400, zxw300)
new_esEs30(zxw400, zxw300, ty_Double) → new_esEs16(zxw400, zxw300)

The set Q consists of the following terms:

new_compare23(x0, x1, True)
new_lt6(x0, x1)
new_ltEs5(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, ty_Integer)
new_lt4(x0, x1, app(ty_[], x2))
new_ltEs18(Just(x0), Just(x1), ty_@0)
new_compare16(x0, x1)
new_lt4(x0, x1, app(app(ty_@2, x2), x3))
new_compare13(x0, x1, False, x2, x3)
new_ltEs18(Just(x0), Nothing, x1)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, ty_Double)
new_esEs19(x0, x1, ty_Bool)
new_esEs8(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(x0, x1, app(app(ty_Either, x2), x3))
new_compare30(@0, @0)
new_primCompAux00(x0, GT)
new_esEs30(x0, x1, ty_@0)
new_lt19(x0, x1, ty_Char)
new_esEs30(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_Ordering)
new_compare17(Char(x0), Char(x1))
new_esEs28(x0, x1, ty_Int)
new_ltEs20(x0, x1, app(ty_[], x2))
new_ltEs21(x0, x1, ty_Ordering)
new_ltEs15(x0, x1)
new_primPlusNat1(Zero, Succ(x0))
new_esEs6(Just(x0), Just(x1), ty_Double)
new_compare24(x0, x1, False)
new_lt20(x0, x1, ty_Char)
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, ty_Bool)
new_sr0(Integer(x0), Integer(x1))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare210(x0, x1, False, x2, x3)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs7(Right(x0), Right(x1), x2, ty_Float)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs18(Nothing, Nothing, x0)
new_ltEs7(EQ, EQ)
new_esEs7(Right(x0), Right(x1), x2, ty_Integer)
new_compare29(x0, x1, app(app(ty_@2, x2), x3))
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs19(x0, x1, ty_Integer)
new_ltEs20(x0, x1, ty_Bool)
new_ltEs14(Right(x0), Right(x1), x2, ty_Float)
new_esEs6(Just(x0), Just(x1), app(ty_[], x2))
new_esEs31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_compare25(x0, x1, False, x2, x3, x4)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_ltEs19(x0, x1, ty_Integer)
new_ltEs5(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(ty_[], x2))
new_lt10(x0, x1, x2)
new_ltEs7(EQ, LT)
new_ltEs7(LT, EQ)
new_esEs20(x0, x1, ty_Ordering)
new_esEs17(Float(x0, x1), Float(x2, x3))
new_compare25(x0, x1, True, x2, x3, x4)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_lt19(x0, x1, ty_Ordering)
new_esEs29(x0, x1, ty_@0)
new_esEs26(x0, x1, app(ty_[], x2))
new_ltEs16(x0, x1)
new_lt4(x0, x1, app(ty_Maybe, x2))
new_compare110(x0, x1, False, x2, x3)
new_ltEs14(Left(x0), Left(x1), ty_Char, x2)
new_sr(x0, x1)
new_ltEs19(x0, x1, ty_Double)
new_compare7(Float(x0, x1), Float(x2, x3))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs9(x0, x1)
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_lt7(x0, x1)
new_lt4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, ty_Int)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat0(Zero, x0)
new_esEs7(Right(x0), Right(x1), x2, ty_@0)
new_esEs32(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_ltEs7(LT, LT)
new_esEs7(Right(x0), Right(x1), x2, ty_Double)
new_esEs4(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_Bool)
new_lt5(x0, x1, x2, x3, x4)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt4(x0, x1, ty_Ordering)
new_primEqNat0(Zero, Succ(x0))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Int)
new_esEs15(Integer(x0), Integer(x1))
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Left(x0), Left(x1), ty_Char, x2)
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs26(x0, x1, ty_Double)
new_compare29(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_@0)
new_primPlusNat1(Succ(x0), Zero)
new_esEs22(x0, x1, ty_Integer)
new_ltEs14(Left(x0), Left(x1), ty_@0, x2)
new_primMulInt(Neg(x0), Neg(x1))
new_ltEs19(x0, x1, ty_Int)
new_ltEs21(x0, x1, app(ty_Maybe, x2))
new_compare29(x0, x1, ty_Integer)
new_esEs14(True, True)
new_esEs21(x0, x1, ty_Char)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Int)
new_ltEs18(Just(x0), Just(x1), ty_Integer)
new_esEs24(x0, x1, ty_Int)
new_primEqNat0(Zero, Zero)
new_esEs16(Double(x0, x1), Double(x2, x3))
new_esEs12(Char(x0), Char(x1))
new_lt4(x0, x1, ty_Char)
new_compare29(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, ty_Bool)
new_esEs8(x0, x1, ty_Float)
new_compare1([], :(x0, x1), x2)
new_esEs30(x0, x1, ty_Ordering)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, ty_Integer)
new_esEs29(x0, x1, ty_Bool)
new_esEs30(x0, x1, ty_Bool)
new_esEs30(x0, x1, ty_Float)
new_esEs32(x0, x1, ty_@0)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs14(Left(x0), Left(x1), ty_Int, x2)
new_primCompAux00(x0, LT)
new_esEs27(x0, x1, ty_Integer)
new_ltEs21(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs5(x0, x1, ty_Double)
new_ltEs18(Just(x0), Just(x1), ty_Char)
new_primMulNat0(Zero, Zero)
new_compare110(x0, x1, True, x2, x3)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_lt9(x0, x1)
new_compare29(x0, x1, ty_Double)
new_ltEs5(x0, x1, ty_@0)
new_lt17(x0, x1, x2)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_compare36(x0, x1, x2, x3)
new_ltEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs31(x0, x1, ty_Bool)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Left(x0), Left(x1), ty_Float, x2)
new_esEs32(x0, x1, ty_Float)
new_esEs13([], :(x0, x1), x2)
new_esEs8(x0, x1, ty_Ordering)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_compare10(x0, x1, True)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs7(Left(x0), Left(x1), ty_Float, x2)
new_primEqNat0(Succ(x0), Succ(x1))
new_ltEs19(x0, x1, ty_Bool)
new_esEs28(x0, x1, ty_Double)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, ty_Float)
new_esEs29(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_@0)
new_pePe(True, x0)
new_esEs19(x0, x1, ty_Float)
new_esEs8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_lt16(x0, x1)
new_compare29(x0, x1, ty_Bool)
new_esEs20(x0, x1, app(ty_[], x2))
new_compare11(x0, x1, True)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_compare14(x0, x1, True, x2, x3)
new_esEs6(Just(x0), Just(x1), app(ty_Maybe, x2))
new_lt19(x0, x1, ty_@0)
new_esEs6(Just(x0), Just(x1), ty_Ordering)
new_esEs23(x0, x1, ty_@0)
new_compare29(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Right(x0), Right(x1), x2, ty_Int)
new_ltEs5(x0, x1, ty_Char)
new_esEs30(x0, x1, ty_Double)
new_ltEs21(x0, x1, ty_Int)
new_compare29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Float)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_compare29(x0, x1, ty_Ordering)
new_ltEs21(x0, x1, ty_@0)
new_esEs8(x0, x1, ty_Int)
new_lt14(x0, x1, x2, x3)
new_ltEs12(False, False)
new_esEs6(Just(x0), Just(x1), ty_Bool)
new_compare32(Integer(x0), Integer(x1))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_Int)
new_primMulNat0(Succ(x0), Succ(x1))
new_compare29(x0, x1, ty_Float)
new_ltEs21(x0, x1, ty_Integer)
new_esEs6(Just(x0), Just(x1), ty_Float)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs5(x0, x1, ty_Float)
new_ltEs18(Just(x0), Just(x1), ty_Float)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Bool)
new_esEs31(x0, x1, ty_Double)
new_esEs31(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpNat1(Zero, x0)
new_ltEs8(x0, x1)
new_esEs29(x0, x1, ty_Integer)
new_ltEs21(x0, x1, app(ty_[], x2))
new_primPlusNat1(Zero, Zero)
new_esEs30(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(ty_[], x2))
new_ltEs14(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs23(x0, x1, ty_Double)
new_ltEs18(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs18(Just(x0), Just(x1), ty_Ordering)
new_primCmpNat2(Zero, Zero)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs5(x0, x1, ty_Bool)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_compare28(x0, x1, True, x2)
new_ltEs14(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs5(x0, x1, app(ty_[], x2))
new_asAs(False, x0)
new_esEs29(x0, x1, ty_Ordering)
new_esEs31(x0, x1, app(ty_[], x2))
new_esEs30(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, ty_Char)
new_esEs31(x0, x1, app(app(ty_@2, x2), x3))
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(x0, x1, ty_Integer)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs19(x0, x1, app(ty_[], x2))
new_ltEs18(Just(x0), Just(x1), ty_Bool)
new_lt11(x0, x1, x2, x3)
new_primCmpNat1(Succ(x0), x1)
new_esEs32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs24(x0, x1, ty_Integer)
new_ltEs14(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs27(x0, x1, ty_@0)
new_ltEs14(Right(x0), Right(x1), x2, ty_Double)
new_lt4(x0, x1, ty_Float)
new_compare19(x0, x1, x2, x3)
new_ltEs5(x0, x1, app(app(ty_Either, x2), x3))
new_esEs19(x0, x1, ty_Char)
new_lt4(x0, x1, ty_Double)
new_esEs19(x0, x1, ty_Ordering)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs10(@0, @0)
new_esEs31(x0, x1, ty_@0)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs11(x0, x1)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, ty_Float)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_Char)
new_esEs9(GT, GT)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs27(x0, x1, ty_Char)
new_compare11(x0, x1, False)
new_compare23(x0, x1, False)
new_compare12(x0, x1, True, x2, x3, x4)
new_esEs28(x0, x1, ty_Bool)
new_esEs7(Right(x0), Left(x1), x2, x3)
new_esEs7(Left(x0), Right(x1), x2, x3)
new_compare24(x0, x1, True)
new_compare15(x0, x1, x2, x3)
new_primEqNat0(Succ(x0), Zero)
new_esEs23(x0, x1, ty_Ordering)
new_esEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs7(Right(x0), Right(x1), x2, ty_Int)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_esEs32(x0, x1, app(app(ty_Either, x2), x3))
new_compare9(x0, x1, x2, x3, x4)
new_lt20(x0, x1, ty_Int)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Integer)
new_lt4(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Int)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs5(x0, x1, app(app(ty_@2, x2), x3))
new_lt4(x0, x1, ty_@0)
new_esEs23(x0, x1, ty_Char)
new_esEs28(x0, x1, ty_Ordering)
new_ltEs18(Just(x0), Just(x1), ty_Double)
new_esEs30(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_Integer)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_compare14(x0, x1, False, x2, x3)
new_lt20(x0, x1, ty_@0)
new_compare1([], [], x0)
new_esEs9(EQ, EQ)
new_pePe(False, x0)
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs5(x0, x1, app(ty_Ratio, x2))
new_ltEs18(Just(x0), Just(x1), app(ty_[], x2))
new_esEs6(Just(x0), Just(x1), ty_Char)
new_esEs25(x0, x1, ty_Integer)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs18(:%(x0, x1), :%(x2, x3), x4)
new_esEs26(x0, x1, ty_Integer)
new_compare12(x0, x1, False, x2, x3, x4)
new_esEs8(x0, x1, app(ty_Maybe, x2))
new_primCompAux00(x0, EQ)
new_esEs19(x0, x1, ty_Int)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs14(True, False)
new_esEs14(False, True)
new_lt4(x0, x1, ty_Integer)
new_esEs7(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs14(Right(x0), Right(x1), x2, ty_@0)
new_fsEs(x0)
new_esEs22(x0, x1, ty_Float)
new_lt4(x0, x1, ty_Bool)
new_primCmpNat2(Succ(x0), Succ(x1))
new_asAs(True, x0)
new_ltEs18(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, ty_Bool)
new_esEs6(Nothing, Just(x0), x1)
new_esEs6(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs6(Just(x0), Nothing, x1)
new_lt18(x0, x1, x2)
new_esEs8(x0, x1, app(ty_[], x2))
new_esEs31(x0, x1, ty_Integer)
new_compare111(x0, x1, False, x2)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs8(x0, x1, ty_Char)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, ty_Float)
new_ltEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs22(x0, x1, ty_@0)
new_esEs20(x0, x1, ty_Char)
new_esEs13(:(x0, x1), [], x2)
new_ltEs12(False, True)
new_ltEs12(True, False)
new_compare6(Double(x0, x1), Double(x2, x3))
new_ltEs20(x0, x1, ty_@0)
new_esEs22(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_@0)
new_ltEs18(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare35(x0, x1, x2, x3)
new_ltEs14(Right(x0), Right(x1), x2, ty_Integer)
new_lt19(x0, x1, ty_Double)
new_esEs32(x0, x1, app(ty_[], x2))
new_lt19(x0, x1, ty_Bool)
new_ltEs14(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs7(Right(x0), Right(x1), x2, ty_Char)
new_ltEs14(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs26(x0, x1, ty_Char)
new_ltEs14(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs5(x0, x1, ty_Int)
new_lt4(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_Double)
new_esEs32(x0, x1, app(ty_Ratio, x2))
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_esEs19(x0, x1, ty_@0)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs21(x0, x1, ty_Bool)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs14(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs21(x0, x1, ty_Double)
new_lt12(x0, x1)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs8(x0, x1, ty_Bool)
new_ltEs21(x0, x1, ty_Char)
new_lt13(x0, x1)
new_esEs13(:(x0, x1), :(x2, x3), x4)
new_esEs31(x0, x1, ty_Ordering)
new_ltEs14(Right(x0), Right(x1), x2, ty_Bool)
new_compare1(:(x0, x1), [], x2)
new_compare27(x0, x1, x2)
new_compare10(x0, x1, False)
new_esEs27(x0, x1, app(ty_[], x2))
new_primMulNat0(Succ(x0), Zero)
new_ltEs19(x0, x1, ty_Float)
new_ltEs14(Left(x0), Right(x1), x2, x3)
new_esEs23(x0, x1, ty_Float)
new_ltEs14(Right(x0), Left(x1), x2, x3)
new_compare29(x0, x1, ty_Int)
new_esEs22(x0, x1, ty_Int)
new_esEs31(x0, x1, app(ty_Maybe, x2))
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Float)
new_compare31(x0, x1)
new_esEs29(x0, x1, ty_Double)
new_esEs32(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Left(x0), Left(x1), ty_Double, x2)
new_esEs31(x0, x1, ty_Char)
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Just(x0), Just(x1), ty_Int)
new_compare33(x0, x1, x2, x3)
new_esEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs21(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs7(LT, GT)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs7(GT, LT)
new_ltEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Double)
new_compare29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare111(x0, x1, True, x2)
new_ltEs13(x0, x1)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs32(x0, x1, app(ty_Maybe, x2))
new_esEs31(x0, x1, ty_Int)
new_lt4(x0, x1, ty_Int)
new_ltEs11(x0, x1, x2)
new_lt20(x0, x1, ty_Float)
new_not(True)
new_esEs31(x0, x1, ty_Float)
new_esEs20(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Float)
new_esEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs6(Nothing, Nothing, x0)
new_esEs28(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Ordering)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(Left(x0), Left(x1), ty_Double, x2)
new_esEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs6(Just(x0), Just(x1), ty_Integer)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_not(False)
new_lt8(x0, x1)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_ltEs18(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare13(x0, x1, True, x2, x3)
new_esEs32(x0, x1, ty_Integer)
new_esEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs19(x0, x1, ty_Char)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_esEs6(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare8(:%(x0, x1), :%(x2, x3), ty_Integer)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_Integer)
new_esEs8(x0, x1, ty_@0)
new_compare26(Left(x0), Left(x1), False, x2, x3)
new_ltEs12(True, True)
new_esEs27(x0, x1, ty_Float)
new_lt15(x0, x1)
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, ty_Ordering)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, ty_Double)
new_esEs6(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_lt20(x0, x1, ty_Ordering)
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs22(x0, x1, ty_Char)
new_lt20(x0, x1, ty_Double)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Bool)
new_esEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_ltEs21(x0, x1, ty_Float)
new_ltEs10(x0, x1)
new_ltEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs14(Left(x0), Left(x1), ty_Bool, x2)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs14(Left(x0), Left(x1), ty_Integer, x2)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(x0, x1, ty_Ordering)
new_esEs8(x0, x1, ty_Double)
new_compare29(x0, x1, ty_Char)
new_esEs6(Just(x0), Just(x1), ty_@0)
new_compare1(:(x0, x1), :(x2, x3), x4)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_compare210(x0, x1, True, x2, x3)
new_esEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs6(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs29(x0, x1, ty_Float)
new_esEs19(x0, x1, ty_Double)
new_esEs14(False, False)
new_primEqInt(Pos(Zero), Pos(Zero))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs32(x0, x1, ty_Char)
new_lt19(x0, x1, app(ty_[], x2))
new_ltEs21(x0, x1, ty_Double)
new_esEs32(x0, x1, ty_Int)
new_primCmpNat2(Succ(x0), Zero)
new_compare34(x0, x1, x2, x3)
new_compare18(x0, x1)
new_esEs29(x0, x1, ty_Int)
new_esEs32(x0, x1, ty_Bool)
new_compare28(x0, x1, False, x2)
new_ltEs14(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs18(Just(x0), Just(x1), ty_Int)
new_compare26(Right(x0), Right(x1), False, x2, x3)
new_ltEs17(x0, x1, x2)
new_primPlusNat0(Succ(x0), x1)
new_esEs7(Left(x0), Left(x1), ty_Int, x2)
new_esEs20(x0, x1, ty_Integer)
new_primCmpNat0(x0, Zero)
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_esEs7(Left(x0), Left(x1), ty_@0, x2)
new_ltEs7(GT, EQ)
new_ltEs7(EQ, GT)
new_esEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs32(x0, x1, ty_Double)
new_ltEs7(GT, GT)
new_esEs31(x0, x1, app(ty_Ratio, x2))
new_esEs9(LT, LT)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs13([], [], x0)
new_primCompAux0(x0, x1, x2, x3)
new_compare29(x0, x1, ty_@0)
new_esEs7(Left(x0), Left(x1), ty_Bool, x2)
new_compare26(x0, x1, True, x2, x3)
new_compare26(Right(x0), Left(x1), False, x2, x3)
new_compare26(Left(x0), Right(x1), False, x2, x3)
new_ltEs18(Nothing, Just(x0), x1)
new_esEs27(x0, x1, ty_Ordering)
new_primCmpNat0(x0, Succ(x1))

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

new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, ty_@0)
new_esEs32(x0, x1, ty_Ordering)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, ty_Bool)
new_esEs32(x0, x1, ty_@0)
new_esEs32(x0, x1, ty_Float)
new_esEs29(x0, x1, ty_Char)
new_esEs29(x0, x1, ty_Integer)
new_esEs29(x0, x1, ty_Ordering)
new_esEs32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs32(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_esEs32(x0, x1, app(ty_[], x2))
new_esEs32(x0, x1, app(ty_Ratio, x2))
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, ty_Double)
new_esEs32(x0, x1, app(app(ty_@2, x2), x3))
new_compare33(x0, x1, x2, x3)
new_esEs32(x0, x1, app(ty_Maybe, x2))
new_esEs32(x0, x1, ty_Integer)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_esEs29(x0, x1, ty_Float)
new_esEs32(x0, x1, ty_Char)
new_esEs32(x0, x1, ty_Int)
new_compare34(x0, x1, x2, x3)
new_esEs29(x0, x1, ty_Int)
new_esEs32(x0, x1, ty_Bool)
new_esEs32(x0, x1, ty_Double)



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

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

new_splitLT22(zxw60, zxw61, zxw62, zxw63, zxw64, zxw65, True, bf, bg, bh) → new_splitLT0(zxw63, zxw65, bf, bg, bh)
new_splitLT21(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, False, h, ba, bb) → new_splitLT11(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs9(new_compare35(zxw400, zxw300, h, ba), GT), h, ba, bb)
new_splitLT11(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, True, h, ba, bb) → new_splitLT0(zxw34, zxw400, h, ba, bb)
new_splitLT3(Right(zxw300), zxw31, zxw32, zxw33, zxw34, Right(zxw400), h, ba, bb) → new_splitLT22(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs9(new_compare26(Right(zxw400), Right(zxw300), new_esEs30(zxw400, zxw300, ba), h, ba), LT), h, ba, bb)
new_splitLT21(zxw300, zxw31, zxw32, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw34, zxw400, True, h, ba, bb) → new_splitLT3(zxw330, zxw331, zxw332, zxw333, zxw334, Right(zxw400), h, ba, bb)
new_splitLT0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw400, h, ba, bb) → new_splitLT3(zxw330, zxw331, zxw332, zxw333, zxw334, Right(zxw400), h, ba, bb)
new_splitLT12(zxw60, zxw61, zxw62, zxw63, zxw64, zxw65, True, bf, bg, bh) → new_splitLT0(zxw64, zxw65, bf, bg, bh)
new_splitLT22(zxw60, zxw61, zxw62, zxw63, zxw64, zxw65, False, bf, bg, bh) → new_splitLT12(zxw60, zxw61, zxw62, zxw63, zxw64, zxw65, new_esEs9(new_compare36(zxw65, zxw60, bf, bg), GT), bf, bg, bh)
new_splitLT3(Left(zxw300), zxw31, zxw32, zxw33, zxw34, Right(zxw400), h, ba, bb) → new_splitLT21(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs9(new_compare26(Right(zxw400), Left(zxw300), False, h, ba), LT), h, ba, bb)

The TRS R consists of the following rules:

new_compare35(zxw400, zxw300, h, ba) → new_compare26(Right(zxw400), Left(zxw300), False, h, ba)
new_esEs9(LT, GT) → False
new_esEs9(EQ, GT) → False
new_esEs9(GT, GT) → True
new_compare26(Right(zxw7900), Left(zxw8000), False, gh, ha) → GT
new_compare36(zxw35, zxw30, bca, bcb) → new_compare26(Right(zxw35), Right(zxw30), new_esEs31(zxw35, zxw30, bcb), bca, bcb)
new_esEs31(zxw35, zxw30, ty_Ordering) → new_esEs9(zxw35, zxw30)
new_esEs31(zxw35, zxw30, ty_Char) → new_esEs12(zxw35, zxw30)
new_esEs31(zxw35, zxw30, ty_@0) → new_esEs10(zxw35, zxw30)
new_esEs31(zxw35, zxw30, app(app(app(ty_@3, bdb), bdc), bdd)) → new_esEs4(zxw35, zxw30, bdb, bdc, bdd)
new_esEs31(zxw35, zxw30, ty_Float) → new_esEs17(zxw35, zxw30)
new_esEs31(zxw35, zxw30, app(app(ty_Either, bch), bda)) → new_esEs7(zxw35, zxw30, bch, bda)
new_esEs31(zxw35, zxw30, app(ty_Ratio, bcc)) → new_esEs18(zxw35, zxw30, bcc)
new_esEs31(zxw35, zxw30, app(app(ty_@2, bcf), bcg)) → new_esEs5(zxw35, zxw30, bcf, bcg)
new_esEs31(zxw35, zxw30, ty_Integer) → new_esEs15(zxw35, zxw30)
new_esEs31(zxw35, zxw30, ty_Double) → new_esEs16(zxw35, zxw30)
new_esEs31(zxw35, zxw30, app(ty_[], bcd)) → new_esEs13(zxw35, zxw30, bcd)
new_esEs31(zxw35, zxw30, ty_Int) → new_esEs11(zxw35, zxw30)
new_esEs31(zxw35, zxw30, ty_Bool) → new_esEs14(zxw35, zxw30)
new_esEs31(zxw35, zxw30, app(ty_Maybe, bce)) → new_esEs6(zxw35, zxw30, bce)
new_compare26(zxw790, zxw800, True, gh, ha) → EQ
new_compare26(Right(zxw7900), Right(zxw8000), False, gh, ha) → new_compare14(zxw7900, zxw8000, new_ltEs20(zxw7900, zxw8000, ha), gh, ha)
new_ltEs20(zxw7900, zxw8000, app(ty_Maybe, bbc)) → new_ltEs18(zxw7900, zxw8000, bbc)
new_ltEs20(zxw7900, zxw8000, ty_Int) → new_ltEs9(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, ty_@0) → new_ltEs8(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, app(app(ty_@2, baf), bag)) → new_ltEs4(zxw7900, zxw8000, baf, bag)
new_ltEs20(zxw7900, zxw8000, ty_Float) → new_ltEs16(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, ty_Bool) → new_ltEs12(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, app(ty_Ratio, bbb)) → new_ltEs17(zxw7900, zxw8000, bbb)
new_ltEs20(zxw7900, zxw8000, ty_Double) → new_ltEs15(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, ty_Integer) → new_ltEs13(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, app(app(app(ty_@3, bab), bac), bad)) → new_ltEs6(zxw7900, zxw8000, bab, bac, bad)
new_ltEs20(zxw7900, zxw8000, app(app(ty_Either, bah), bba)) → new_ltEs14(zxw7900, zxw8000, bah, bba)
new_ltEs20(zxw7900, zxw8000, app(ty_[], bae)) → new_ltEs11(zxw7900, zxw8000, bae)
new_ltEs20(zxw7900, zxw8000, ty_Char) → new_ltEs10(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, ty_Ordering) → new_ltEs7(zxw7900, zxw8000)
new_compare14(zxw242, zxw243, False, dfe, dff) → GT
new_compare14(zxw242, zxw243, True, dfe, dff) → LT
new_ltEs7(LT, EQ) → True
new_ltEs7(GT, GT) → True
new_ltEs7(EQ, EQ) → True
new_ltEs7(GT, LT) → False
new_ltEs7(GT, EQ) → False
new_ltEs7(EQ, GT) → True
new_ltEs7(EQ, LT) → False
new_ltEs7(LT, LT) → True
new_ltEs7(LT, GT) → True
new_ltEs10(zxw7900, zxw8000) → new_fsEs(new_compare17(zxw7900, zxw8000))
new_compare17(Char(zxw79000), Char(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_fsEs(zxw259) → new_not(new_esEs9(zxw259, GT))
new_not(False) → True
new_not(True) → False
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_ltEs11(zxw7900, zxw8000, he) → new_fsEs(new_compare1(zxw7900, zxw8000, he))
new_compare1([], :(zxw80000, zxw80001), he) → LT
new_compare1(:(zxw79000, zxw79001), :(zxw80000, zxw80001), he) → new_primCompAux0(zxw79000, zxw80000, new_compare1(zxw79001, zxw80001, he), he)
new_compare1(:(zxw79000, zxw79001), [], he) → GT
new_compare1([], [], he) → EQ
new_primCompAux0(zxw79000, zxw80000, zxw272, he) → new_primCompAux00(zxw272, new_compare29(zxw79000, zxw80000, he))
new_compare29(zxw79000, zxw80000, ty_Char) → new_compare17(zxw79000, zxw80000)
new_compare29(zxw79000, zxw80000, ty_Bool) → new_compare31(zxw79000, zxw80000)
new_compare29(zxw79000, zxw80000, app(app(ty_@2, cbf), cbg)) → new_compare19(zxw79000, zxw80000, cbf, cbg)
new_compare29(zxw79000, zxw80000, app(ty_[], cbe)) → new_compare1(zxw79000, zxw80000, cbe)
new_compare29(zxw79000, zxw80000, app(app(app(ty_@3, cbb), cbc), cbd)) → new_compare9(zxw79000, zxw80000, cbb, cbc, cbd)
new_compare29(zxw79000, zxw80000, ty_Int) → new_compare16(zxw79000, zxw80000)
new_compare29(zxw79000, zxw80000, ty_Integer) → new_compare32(zxw79000, zxw80000)
new_compare29(zxw79000, zxw80000, app(ty_Maybe, ccc)) → new_compare27(zxw79000, zxw80000, ccc)
new_compare29(zxw79000, zxw80000, app(ty_Ratio, ccb)) → new_compare8(zxw79000, zxw80000, ccb)
new_compare29(zxw79000, zxw80000, ty_Float) → new_compare7(zxw79000, zxw80000)
new_compare29(zxw79000, zxw80000, ty_Double) → new_compare6(zxw79000, zxw80000)
new_compare29(zxw79000, zxw80000, app(app(ty_Either, cbh), cca)) → new_compare15(zxw79000, zxw80000, cbh, cca)
new_compare29(zxw79000, zxw80000, ty_Ordering) → new_compare18(zxw79000, zxw80000)
new_compare29(zxw79000, zxw80000, ty_@0) → new_compare30(zxw79000, zxw80000)
new_primCompAux00(zxw276, LT) → LT
new_primCompAux00(zxw276, EQ) → zxw276
new_primCompAux00(zxw276, GT) → GT
new_compare30(@0, @0) → EQ
new_compare18(zxw79000, zxw80000) → new_compare24(zxw79000, zxw80000, new_esEs9(zxw79000, zxw80000))
new_esEs9(GT, LT) → False
new_esEs9(GT, EQ) → False
new_esEs9(EQ, EQ) → True
new_esEs9(EQ, LT) → False
new_esEs9(LT, EQ) → False
new_esEs9(LT, LT) → True
new_compare24(zxw79000, zxw80000, False) → new_compare11(zxw79000, zxw80000, new_ltEs7(zxw79000, zxw80000))
new_compare24(zxw79000, zxw80000, True) → EQ
new_compare11(zxw79000, zxw80000, False) → GT
new_compare11(zxw79000, zxw80000, True) → LT
new_compare15(zxw790, zxw800, gh, ha) → new_compare26(zxw790, zxw800, new_esEs7(zxw790, zxw800, gh, ha), gh, ha)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Bool, bdf) → new_esEs14(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Right(zxw3000), beh, bdf) → False
new_esEs7(Right(zxw4000), Left(zxw3000), beh, bdf) → False
new_esEs7(Right(zxw4000), Right(zxw3000), beh, app(app(ty_@2, bfd), bfe)) → new_esEs5(zxw4000, zxw3000, bfd, bfe)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Int, bdf) → new_esEs11(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), app(app(ty_@2, bea), beb), bdf) → new_esEs5(zxw4000, zxw3000, bea, beb)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Ordering, bdf) → new_esEs9(zxw4000, zxw3000)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, app(ty_[], bfb)) → new_esEs13(zxw4000, zxw3000, bfb)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Integer, bdf) → new_esEs15(zxw4000, zxw3000)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, app(app(app(ty_@3, bfh), bga), bgb)) → new_esEs4(zxw4000, zxw3000, bfh, bga, bgb)
new_esEs7(Left(zxw4000), Left(zxw3000), app(ty_Ratio, bde), bdf) → new_esEs18(zxw4000, zxw3000, bde)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_@0, bdf) → new_esEs10(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), app(app(app(ty_@3, bee), bef), beg), bdf) → new_esEs4(zxw4000, zxw3000, bee, bef, beg)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Double, bdf) → new_esEs16(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Float, bdf) → new_esEs17(zxw4000, zxw3000)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Char, bdf) → new_esEs12(zxw4000, zxw3000)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), app(ty_[], bdg), bdf) → new_esEs13(zxw4000, zxw3000, bdg)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, app(ty_Ratio, bfa)) → new_esEs18(zxw4000, zxw3000, bfa)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_compare26(Left(zxw7900), Right(zxw8000), False, gh, ha) → LT
new_compare26(Left(zxw7900), Left(zxw8000), False, gh, ha) → new_compare13(zxw7900, zxw8000, new_ltEs19(zxw7900, zxw8000, gh), gh, ha)
new_esEs6(Just(zxw4000), Just(zxw3000), app(ty_Maybe, fc)) → new_esEs6(zxw4000, zxw3000, fc)
new_esEs7(Left(zxw4000), Left(zxw3000), app(app(ty_Either, bec), bed), bdf) → new_esEs7(zxw4000, zxw3000, bec, bed)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, app(ty_Maybe, bfc)) → new_esEs6(zxw4000, zxw3000, bfc)
new_esEs6(Just(zxw4000), Just(zxw3000), app(app(ty_Either, fg), fh)) → new_esEs7(zxw4000, zxw3000, fg, fh)
new_esEs7(Left(zxw4000), Left(zxw3000), app(ty_Maybe, bdh), bdf) → new_esEs6(zxw4000, zxw3000, bdh)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, app(app(ty_Either, bff), bfg)) → new_esEs7(zxw4000, zxw3000, bff, bfg)
new_esEs6(Just(zxw4000), Just(zxw3000), app(app(ty_@2, fd), ff)) → new_esEs5(zxw4000, zxw3000, fd, ff)
new_esEs6(Nothing, Nothing, eh) → True
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs6(Nothing, Just(zxw3000), eh) → False
new_esEs6(Just(zxw4000), Nothing, eh) → False
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), app(app(app(ty_@3, ga), gb), gc)) → new_esEs4(zxw4000, zxw3000, ga, gb, gc)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_@0) → new_esEs10(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), app(ty_[], fb)) → new_esEs13(zxw4000, zxw3000, fb)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Char) → new_esEs12(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Float) → new_esEs17(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), app(ty_Ratio, fa)) → new_esEs18(zxw4000, zxw3000, fa)
new_esEs18(:%(zxw4000, zxw4001), :%(zxw3000, zxw3001), ccd) → new_asAs(new_esEs25(zxw4000, zxw3000, ccd), new_esEs24(zxw4001, zxw3001, ccd))
new_esEs25(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs25(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs24(zxw4001, zxw3001, ty_Integer) → new_esEs15(zxw4001, zxw3001)
new_esEs24(zxw4001, zxw3001, ty_Int) → new_esEs11(zxw4001, zxw3001)
new_asAs(False, zxw230) → False
new_asAs(True, zxw230) → zxw230
new_esEs11(zxw400, zxw300) → new_primEqInt(zxw400, zxw300)
new_primEqInt(Neg(Succ(zxw40000)), Neg(Succ(zxw30000))) → new_primEqNat0(zxw40000, zxw30000)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Neg(Succ(zxw30000))) → False
new_primEqInt(Neg(Succ(zxw40000)), Neg(Zero)) → False
new_primEqInt(Pos(Succ(zxw40000)), Pos(Succ(zxw30000))) → new_primEqNat0(zxw40000, zxw30000)
new_primEqInt(Pos(Zero), Pos(Succ(zxw30000))) → False
new_primEqInt(Pos(Succ(zxw40000)), Pos(Zero)) → False
new_primEqInt(Neg(Succ(zxw40000)), Pos(zxw3000)) → False
new_primEqInt(Pos(Succ(zxw40000)), Neg(zxw3000)) → False
new_primEqInt(Neg(Zero), Pos(Succ(zxw30000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(zxw30000))) → False
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqNat0(Zero, Zero) → True
new_primEqNat0(Succ(zxw40000), Succ(zxw30000)) → new_primEqNat0(zxw40000, zxw30000)
new_primEqNat0(Zero, Succ(zxw30000)) → False
new_primEqNat0(Succ(zxw40000), Zero) → False
new_esEs15(Integer(zxw4000), Integer(zxw3000)) → new_primEqInt(zxw4000, zxw3000)
new_esEs17(Float(zxw4000, zxw4001), Float(zxw3000, zxw3001)) → new_esEs11(new_sr(zxw4000, zxw3000), new_sr(zxw4001, zxw3001))
new_sr(zxw4000, zxw3000) → new_primMulInt(zxw4000, zxw3000)
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Neg(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Pos(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulNat0(Zero, Zero) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_esEs12(Char(zxw4000), Char(zxw3000)) → new_primEqNat0(zxw4000, zxw3000)
new_esEs13([], [], cce) → True
new_esEs13(:(zxw4000, zxw4001), :(zxw3000, zxw3001), cce) → new_asAs(new_esEs23(zxw4000, zxw3000, cce), new_esEs13(zxw4001, zxw3001, cce))
new_esEs13(:(zxw4000, zxw4001), [], cce) → False
new_esEs13([], :(zxw3000, zxw3001), cce) → False
new_esEs23(zxw4000, zxw3000, app(app(ty_Either, deh), dfa)) → new_esEs7(zxw4000, zxw3000, deh, dfa)
new_esEs23(zxw4000, zxw3000, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, app(app(app(ty_@3, dfb), dfc), dfd)) → new_esEs4(zxw4000, zxw3000, dfb, dfc, dfd)
new_esEs23(zxw4000, zxw3000, app(app(ty_@2, def), deg)) → new_esEs5(zxw4000, zxw3000, def, deg)
new_esEs23(zxw4000, zxw3000, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, app(ty_Ratio, dec)) → new_esEs18(zxw4000, zxw3000, dec)
new_esEs23(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, app(ty_Maybe, dee)) → new_esEs6(zxw4000, zxw3000, dee)
new_esEs23(zxw4000, zxw3000, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, app(ty_[], ded)) → new_esEs13(zxw4000, zxw3000, ded)
new_esEs16(Double(zxw4000, zxw4001), Double(zxw3000, zxw3001)) → new_esEs11(new_sr(zxw4000, zxw3000), new_sr(zxw4001, zxw3001))
new_esEs10(@0, @0) → True
new_esEs5(@2(zxw4000, zxw4001), @2(zxw3000, zxw3001), ccf, ccg) → new_asAs(new_esEs22(zxw4000, zxw3000, ccf), new_esEs21(zxw4001, zxw3001, ccg))
new_esEs22(zxw4000, zxw3000, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, app(app(ty_@2, ddd), dde)) → new_esEs5(zxw4000, zxw3000, ddd, dde)
new_esEs22(zxw4000, zxw3000, app(ty_Maybe, ddc)) → new_esEs6(zxw4000, zxw3000, ddc)
new_esEs22(zxw4000, zxw3000, app(ty_Ratio, dda)) → new_esEs18(zxw4000, zxw3000, dda)
new_esEs22(zxw4000, zxw3000, app(app(ty_Either, ddf), ddg)) → new_esEs7(zxw4000, zxw3000, ddf, ddg)
new_esEs22(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, app(app(app(ty_@3, ddh), dea), deb)) → new_esEs4(zxw4000, zxw3000, ddh, dea, deb)
new_esEs22(zxw4000, zxw3000, app(ty_[], ddb)) → new_esEs13(zxw4000, zxw3000, ddb)
new_esEs22(zxw4000, zxw3000, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs21(zxw4001, zxw3001, ty_Bool) → new_esEs14(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, ty_Double) → new_esEs16(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, ty_Ordering) → new_esEs9(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, ty_Char) → new_esEs12(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, ty_Float) → new_esEs17(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, app(ty_Maybe, dca)) → new_esEs6(zxw4001, zxw3001, dca)
new_esEs21(zxw4001, zxw3001, ty_Int) → new_esEs11(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, app(ty_[], dbh)) → new_esEs13(zxw4001, zxw3001, dbh)
new_esEs21(zxw4001, zxw3001, ty_Integer) → new_esEs15(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, app(app(ty_@2, dcb), dcc)) → new_esEs5(zxw4001, zxw3001, dcb, dcc)
new_esEs21(zxw4001, zxw3001, ty_@0) → new_esEs10(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, app(app(ty_Either, dcd), dce)) → new_esEs7(zxw4001, zxw3001, dcd, dce)
new_esEs21(zxw4001, zxw3001, app(app(app(ty_@3, dcf), dcg), dch)) → new_esEs4(zxw4001, zxw3001, dcf, dcg, dch)
new_esEs21(zxw4001, zxw3001, app(ty_Ratio, dbg)) → new_esEs18(zxw4001, zxw3001, dbg)
new_esEs4(@3(zxw4000, zxw4001, zxw4002), @3(zxw3000, zxw3001, zxw3002), cch, cda, cdb) → new_asAs(new_esEs28(zxw4000, zxw3000, cch), new_asAs(new_esEs27(zxw4001, zxw3001, cda), new_esEs26(zxw4002, zxw3002, cdb)))
new_esEs28(zxw4000, zxw3000, app(ty_[], ead)) → new_esEs13(zxw4000, zxw3000, ead)
new_esEs28(zxw4000, zxw3000, app(app(app(ty_@3, ebb), ebc), ebd)) → new_esEs4(zxw4000, zxw3000, ebb, ebc, ebd)
new_esEs28(zxw4000, zxw3000, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, app(ty_Maybe, eae)) → new_esEs6(zxw4000, zxw3000, eae)
new_esEs28(zxw4000, zxw3000, app(app(ty_Either, eah), eba)) → new_esEs7(zxw4000, zxw3000, eah, eba)
new_esEs28(zxw4000, zxw3000, app(app(ty_@2, eaf), eag)) → new_esEs5(zxw4000, zxw3000, eaf, eag)
new_esEs28(zxw4000, zxw3000, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, app(ty_Ratio, eac)) → new_esEs18(zxw4000, zxw3000, eac)
new_esEs28(zxw4000, zxw3000, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_esEs27(zxw4001, zxw3001, app(ty_Ratio, dha)) → new_esEs18(zxw4001, zxw3001, dha)
new_esEs27(zxw4001, zxw3001, app(app(app(ty_@3, dhh), eaa), eab)) → new_esEs4(zxw4001, zxw3001, dhh, eaa, eab)
new_esEs27(zxw4001, zxw3001, app(ty_Maybe, dhc)) → new_esEs6(zxw4001, zxw3001, dhc)
new_esEs27(zxw4001, zxw3001, app(app(ty_Either, dhf), dhg)) → new_esEs7(zxw4001, zxw3001, dhf, dhg)
new_esEs27(zxw4001, zxw3001, ty_Ordering) → new_esEs9(zxw4001, zxw3001)
new_esEs27(zxw4001, zxw3001, ty_Float) → new_esEs17(zxw4001, zxw3001)
new_esEs27(zxw4001, zxw3001, ty_@0) → new_esEs10(zxw4001, zxw3001)
new_esEs27(zxw4001, zxw3001, ty_Char) → new_esEs12(zxw4001, zxw3001)
new_esEs27(zxw4001, zxw3001, ty_Double) → new_esEs16(zxw4001, zxw3001)
new_esEs27(zxw4001, zxw3001, ty_Int) → new_esEs11(zxw4001, zxw3001)
new_esEs27(zxw4001, zxw3001, app(app(ty_@2, dhd), dhe)) → new_esEs5(zxw4001, zxw3001, dhd, dhe)
new_esEs27(zxw4001, zxw3001, ty_Bool) → new_esEs14(zxw4001, zxw3001)
new_esEs27(zxw4001, zxw3001, app(ty_[], dhb)) → new_esEs13(zxw4001, zxw3001, dhb)
new_esEs27(zxw4001, zxw3001, ty_Integer) → new_esEs15(zxw4001, zxw3001)
new_esEs26(zxw4002, zxw3002, ty_Float) → new_esEs17(zxw4002, zxw3002)
new_esEs26(zxw4002, zxw3002, ty_Char) → new_esEs12(zxw4002, zxw3002)
new_esEs26(zxw4002, zxw3002, ty_Int) → new_esEs11(zxw4002, zxw3002)
new_esEs26(zxw4002, zxw3002, app(ty_Maybe, dga)) → new_esEs6(zxw4002, zxw3002, dga)
new_esEs26(zxw4002, zxw3002, app(app(app(ty_@3, dgf), dgg), dgh)) → new_esEs4(zxw4002, zxw3002, dgf, dgg, dgh)
new_esEs26(zxw4002, zxw3002, app(ty_[], dfh)) → new_esEs13(zxw4002, zxw3002, dfh)
new_esEs26(zxw4002, zxw3002, app(app(ty_Either, dgd), dge)) → new_esEs7(zxw4002, zxw3002, dgd, dge)
new_esEs26(zxw4002, zxw3002, ty_Integer) → new_esEs15(zxw4002, zxw3002)
new_esEs26(zxw4002, zxw3002, app(app(ty_@2, dgb), dgc)) → new_esEs5(zxw4002, zxw3002, dgb, dgc)
new_esEs26(zxw4002, zxw3002, app(ty_Ratio, dfg)) → new_esEs18(zxw4002, zxw3002, dfg)
new_esEs26(zxw4002, zxw3002, ty_Bool) → new_esEs14(zxw4002, zxw3002)
new_esEs26(zxw4002, zxw3002, ty_@0) → new_esEs10(zxw4002, zxw3002)
new_esEs26(zxw4002, zxw3002, ty_Ordering) → new_esEs9(zxw4002, zxw3002)
new_esEs26(zxw4002, zxw3002, ty_Double) → new_esEs16(zxw4002, zxw3002)
new_esEs14(False, True) → False
new_esEs14(True, False) → False
new_esEs14(True, True) → True
new_esEs14(False, False) → True
new_ltEs19(zxw7900, zxw8000, ty_Float) → new_ltEs16(zxw7900, zxw8000)
new_ltEs19(zxw7900, zxw8000, app(app(ty_@2, ca), cb)) → new_ltEs4(zxw7900, zxw8000, ca, cb)
new_ltEs19(zxw7900, zxw8000, app(ty_[], he)) → new_ltEs11(zxw7900, zxw8000, he)
new_ltEs19(zxw7900, zxw8000, ty_Char) → new_ltEs10(zxw7900, zxw8000)
new_ltEs19(zxw7900, zxw8000, ty_Bool) → new_ltEs12(zxw7900, zxw8000)
new_ltEs19(zxw7900, zxw8000, app(ty_Ratio, hh)) → new_ltEs17(zxw7900, zxw8000, hh)
new_ltEs19(zxw7900, zxw8000, app(app(app(ty_@3, hb), hc), hd)) → new_ltEs6(zxw7900, zxw8000, hb, hc, hd)
new_ltEs19(zxw7900, zxw8000, ty_Int) → new_ltEs9(zxw7900, zxw8000)
new_ltEs19(zxw7900, zxw8000, app(app(ty_Either, hf), hg)) → new_ltEs14(zxw7900, zxw8000, hf, hg)
new_ltEs19(zxw7900, zxw8000, ty_@0) → new_ltEs8(zxw7900, zxw8000)
new_ltEs19(zxw7900, zxw8000, ty_Double) → new_ltEs15(zxw7900, zxw8000)
new_ltEs19(zxw7900, zxw8000, ty_Integer) → new_ltEs13(zxw7900, zxw8000)
new_ltEs19(zxw7900, zxw8000, ty_Ordering) → new_ltEs7(zxw7900, zxw8000)
new_ltEs19(zxw7900, zxw8000, app(ty_Maybe, baa)) → new_ltEs18(zxw7900, zxw8000, baa)
new_compare13(zxw235, zxw236, False, bbf, bbg) → GT
new_compare13(zxw235, zxw236, True, bbf, bbg) → LT
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Char) → new_ltEs10(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Integer) → new_ltEs13(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(ty_Ratio, dac)) → new_ltEs17(zxw79000, zxw80000, dac)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(app(app(ty_@3, chc), chd), che)) → new_ltEs6(zxw79000, zxw80000, chc, chd, che)
new_ltEs18(Nothing, Nothing, baa) → True
new_ltEs18(Just(zxw79000), Nothing, baa) → False
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Double) → new_ltEs15(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(ty_[], chf)) → new_ltEs11(zxw79000, zxw80000, chf)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(app(ty_@2, chg), chh)) → new_ltEs4(zxw79000, zxw80000, chg, chh)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Bool) → new_ltEs12(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Ordering) → new_ltEs7(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Float) → new_ltEs16(zxw79000, zxw80000)
new_ltEs18(Nothing, Just(zxw80000), baa) → True
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Int) → new_ltEs9(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_@0) → new_ltEs8(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(ty_Maybe, dad)) → new_ltEs18(zxw79000, zxw80000, dad)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(ty_Maybe, chb)) → new_ltEs18(zxw79000, zxw80000, chb)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(app(ty_Either, daa), dab)) → new_ltEs14(zxw79000, zxw80000, daa, dab)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(app(ty_Either, cgg), cgh)) → new_ltEs14(zxw79000, zxw80000, cgg, cgh)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(app(ty_Either, cfe), cff), hg) → new_ltEs14(zxw79000, zxw80000, cfe, cff)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(ty_Maybe, cfh), hg) → new_ltEs18(zxw79000, zxw80000, cfh)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Bool) → new_ltEs12(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(ty_[], cgd)) → new_ltEs11(zxw79000, zxw80000, cgd)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Bool, hg) → new_ltEs12(zxw79000, zxw80000)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(ty_Ratio, cfg), hg) → new_ltEs17(zxw79000, zxw80000, cfg)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(app(app(ty_@3, cga), cgb), cgc)) → new_ltEs6(zxw79000, zxw80000, cga, cgb, cgc)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Float, hg) → new_ltEs16(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Float) → new_ltEs16(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Double) → new_ltEs15(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(app(ty_@2, cge), cgf)) → new_ltEs4(zxw79000, zxw80000, cge, cgf)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Double, hg) → new_ltEs15(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Left(zxw80000), hf, hg) → False
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Int, hg) → new_ltEs9(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Char) → new_ltEs10(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_@0) → new_ltEs8(zxw79000, zxw80000)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(app(app(ty_@3, ceg), ceh), cfa), hg) → new_ltEs6(zxw79000, zxw80000, ceg, ceh, cfa)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_@0, hg) → new_ltEs8(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Ordering) → new_ltEs7(zxw79000, zxw80000)
new_ltEs14(Left(zxw79000), Right(zxw80000), hf, hg) → True
new_ltEs14(Left(zxw79000), Left(zxw80000), app(app(ty_@2, cfc), cfd), hg) → new_ltEs4(zxw79000, zxw80000, cfc, cfd)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(ty_[], cfb), hg) → new_ltEs11(zxw79000, zxw80000, cfb)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Integer, hg) → new_ltEs13(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Int) → new_ltEs9(zxw79000, zxw80000)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Ordering, hg) → new_ltEs7(zxw79000, zxw80000)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Char, hg) → new_ltEs10(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(ty_Ratio, cha)) → new_ltEs17(zxw79000, zxw80000, cha)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Integer) → new_ltEs13(zxw79000, zxw80000)
new_ltEs13(zxw7900, zxw8000) → new_fsEs(new_compare32(zxw7900, zxw8000))
new_compare32(Integer(zxw79000), Integer(zxw80000)) → new_primCmpInt(zxw79000, zxw80000)
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_ltEs17(zxw7900, zxw8000, hh) → new_fsEs(new_compare8(zxw7900, zxw8000, hh))
new_compare8(:%(zxw79000, zxw79001), :%(zxw80000, zxw80001), ty_Integer) → new_compare32(new_sr0(zxw79000, zxw80001), new_sr0(zxw80000, zxw79001))
new_compare8(:%(zxw79000, zxw79001), :%(zxw80000, zxw80001), ty_Int) → new_compare16(new_sr(zxw79000, zxw80001), new_sr(zxw80000, zxw79001))
new_compare16(zxw79, zxw80) → new_primCmpInt(zxw79, zxw80)
new_sr0(Integer(zxw800000), Integer(zxw790010)) → Integer(new_primMulInt(zxw800000, zxw790010))
new_ltEs9(zxw7900, zxw8000) → new_fsEs(new_compare16(zxw7900, zxw8000))
new_ltEs4(@2(zxw79000, zxw79001), @2(zxw80000, zxw80001), ca, cb) → new_pePe(new_lt4(zxw79000, zxw80000, ca), new_asAs(new_esEs8(zxw79000, zxw80000, ca), new_ltEs5(zxw79001, zxw80001, cb)))
new_lt4(zxw79000, zxw80000, app(app(app(ty_@3, cc), cd), ce)) → new_lt5(zxw79000, zxw80000, cc, cd, ce)
new_lt4(zxw79000, zxw80000, app(ty_[], cf)) → new_lt10(zxw79000, zxw80000, cf)
new_lt4(zxw79000, zxw80000, ty_Bool) → new_lt12(zxw79000, zxw80000)
new_lt4(zxw79000, zxw80000, app(ty_Maybe, de)) → new_lt18(zxw79000, zxw80000, de)
new_lt4(zxw79000, zxw80000, ty_Ordering) → new_lt6(zxw79000, zxw80000)
new_lt4(zxw79000, zxw80000, app(ty_Ratio, dd)) → new_lt17(zxw79000, zxw80000, dd)
new_lt4(zxw79000, zxw80000, ty_Int) → new_lt8(zxw79000, zxw80000)
new_lt4(zxw79000, zxw80000, ty_Double) → new_lt15(zxw79000, zxw80000)
new_lt4(zxw79000, zxw80000, app(app(ty_Either, db), dc)) → new_lt14(zxw79000, zxw80000, db, dc)
new_lt4(zxw79000, zxw80000, ty_Char) → new_lt9(zxw79000, zxw80000)
new_lt4(zxw79000, zxw80000, ty_@0) → new_lt7(zxw79000, zxw80000)
new_lt4(zxw79000, zxw80000, ty_Float) → new_lt16(zxw79000, zxw80000)
new_lt4(zxw79000, zxw80000, app(app(ty_@2, cg), da)) → new_lt11(zxw79000, zxw80000, cg, da)
new_lt4(zxw79000, zxw80000, ty_Integer) → new_lt13(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, ty_Int) → new_esEs11(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, ty_Double) → new_esEs16(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, app(app(app(ty_@3, cc), cd), ce)) → new_esEs4(zxw79000, zxw80000, cc, cd, ce)
new_esEs8(zxw79000, zxw80000, app(ty_[], cf)) → new_esEs13(zxw79000, zxw80000, cf)
new_esEs8(zxw79000, zxw80000, ty_Char) → new_esEs12(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, app(app(ty_@2, cg), da)) → new_esEs5(zxw79000, zxw80000, cg, da)
new_esEs8(zxw79000, zxw80000, ty_Float) → new_esEs17(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, app(app(ty_Either, db), dc)) → new_esEs7(zxw79000, zxw80000, db, dc)
new_esEs8(zxw79000, zxw80000, ty_@0) → new_esEs10(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, app(ty_Maybe, de)) → new_esEs6(zxw79000, zxw80000, de)
new_esEs8(zxw79000, zxw80000, ty_Bool) → new_esEs14(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, ty_Ordering) → new_esEs9(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, ty_Integer) → new_esEs15(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, app(ty_Ratio, dd)) → new_esEs18(zxw79000, zxw80000, dd)
new_ltEs5(zxw79001, zxw80001, ty_Char) → new_ltEs10(zxw79001, zxw80001)
new_ltEs5(zxw79001, zxw80001, app(app(ty_@2, eb), ec)) → new_ltEs4(zxw79001, zxw80001, eb, ec)
new_ltEs5(zxw79001, zxw80001, ty_Ordering) → new_ltEs7(zxw79001, zxw80001)
new_ltEs5(zxw79001, zxw80001, ty_Bool) → new_ltEs12(zxw79001, zxw80001)
new_ltEs5(zxw79001, zxw80001, ty_Integer) → new_ltEs13(zxw79001, zxw80001)
new_ltEs5(zxw79001, zxw80001, app(ty_Ratio, ef)) → new_ltEs17(zxw79001, zxw80001, ef)
new_ltEs5(zxw79001, zxw80001, app(ty_Maybe, eg)) → new_ltEs18(zxw79001, zxw80001, eg)
new_ltEs5(zxw79001, zxw80001, ty_Double) → new_ltEs15(zxw79001, zxw80001)
new_ltEs5(zxw79001, zxw80001, app(app(ty_Either, ed), ee)) → new_ltEs14(zxw79001, zxw80001, ed, ee)
new_ltEs5(zxw79001, zxw80001, app(app(app(ty_@3, df), dg), dh)) → new_ltEs6(zxw79001, zxw80001, df, dg, dh)
new_ltEs5(zxw79001, zxw80001, app(ty_[], ea)) → new_ltEs11(zxw79001, zxw80001, ea)
new_ltEs5(zxw79001, zxw80001, ty_Int) → new_ltEs9(zxw79001, zxw80001)
new_ltEs5(zxw79001, zxw80001, ty_@0) → new_ltEs8(zxw79001, zxw80001)
new_ltEs5(zxw79001, zxw80001, ty_Float) → new_ltEs16(zxw79001, zxw80001)
new_pePe(False, zxw271) → zxw271
new_pePe(True, zxw271) → True
new_ltEs16(zxw7900, zxw8000) → new_fsEs(new_compare7(zxw7900, zxw8000))
new_compare7(Float(zxw79000, zxw79001), Float(zxw80000, zxw80001)) → new_compare16(new_sr(zxw79000, zxw80000), new_sr(zxw79001, zxw80001))
new_ltEs8(zxw7900, zxw8000) → new_fsEs(new_compare30(zxw7900, zxw8000))
new_ltEs6(@3(zxw79000, zxw79001, zxw79002), @3(zxw80000, zxw80001, zxw80002), hb, hc, hd) → new_pePe(new_lt19(zxw79000, zxw80000, hb), new_asAs(new_esEs20(zxw79000, zxw80000, hb), new_pePe(new_lt20(zxw79001, zxw80001, hc), new_asAs(new_esEs19(zxw79001, zxw80001, hc), new_ltEs21(zxw79002, zxw80002, hd)))))
new_lt19(zxw79000, zxw80000, app(app(ty_Either, bgd), bge)) → new_lt14(zxw79000, zxw80000, bgd, bge)
new_lt19(zxw79000, zxw80000, ty_Double) → new_lt15(zxw79000, zxw80000)
new_lt19(zxw79000, zxw80000, ty_Ordering) → new_lt6(zxw79000, zxw80000)
new_lt19(zxw79000, zxw80000, app(ty_Ratio, gg)) → new_lt17(zxw79000, zxw80000, gg)
new_lt19(zxw79000, zxw80000, app(app(ty_@2, bbd), bbe)) → new_lt11(zxw79000, zxw80000, bbd, bbe)
new_lt19(zxw79000, zxw80000, ty_Int) → new_lt8(zxw79000, zxw80000)
new_lt19(zxw79000, zxw80000, ty_@0) → new_lt7(zxw79000, zxw80000)
new_lt19(zxw79000, zxw80000, app(app(app(ty_@3, gd), ge), gf)) → new_lt5(zxw79000, zxw80000, gd, ge, gf)
new_lt19(zxw79000, zxw80000, app(ty_Maybe, bbh)) → new_lt18(zxw79000, zxw80000, bbh)
new_lt19(zxw79000, zxw80000, ty_Float) → new_lt16(zxw79000, zxw80000)
new_lt19(zxw79000, zxw80000, ty_Bool) → new_lt12(zxw79000, zxw80000)
new_lt19(zxw79000, zxw80000, app(ty_[], bgc)) → new_lt10(zxw79000, zxw80000, bgc)
new_lt19(zxw79000, zxw80000, ty_Integer) → new_lt13(zxw79000, zxw80000)
new_lt19(zxw79000, zxw80000, ty_Char) → new_lt9(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, app(ty_[], bgc)) → new_esEs13(zxw79000, zxw80000, bgc)
new_esEs20(zxw79000, zxw80000, ty_Double) → new_esEs16(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, ty_Char) → new_esEs12(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, app(app(ty_@2, bbd), bbe)) → new_esEs5(zxw79000, zxw80000, bbd, bbe)
new_esEs20(zxw79000, zxw80000, ty_Int) → new_esEs11(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, ty_@0) → new_esEs10(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, app(app(app(ty_@3, gd), ge), gf)) → new_esEs4(zxw79000, zxw80000, gd, ge, gf)
new_esEs20(zxw79000, zxw80000, ty_Integer) → new_esEs15(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, ty_Bool) → new_esEs14(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, app(ty_Ratio, gg)) → new_esEs18(zxw79000, zxw80000, gg)
new_esEs20(zxw79000, zxw80000, app(app(ty_Either, bgd), bge)) → new_esEs7(zxw79000, zxw80000, bgd, bge)
new_esEs20(zxw79000, zxw80000, app(ty_Maybe, bbh)) → new_esEs6(zxw79000, zxw80000, bbh)
new_esEs20(zxw79000, zxw80000, ty_Ordering) → new_esEs9(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, ty_Float) → new_esEs17(zxw79000, zxw80000)
new_lt20(zxw79001, zxw80001, app(app(ty_Either, bhd), bhe)) → new_lt14(zxw79001, zxw80001, bhd, bhe)
new_lt20(zxw79001, zxw80001, ty_@0) → new_lt7(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, app(app(ty_@2, bhb), bhc)) → new_lt11(zxw79001, zxw80001, bhb, bhc)
new_lt20(zxw79001, zxw80001, ty_Ordering) → new_lt6(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, app(ty_Maybe, bhg)) → new_lt18(zxw79001, zxw80001, bhg)
new_lt20(zxw79001, zxw80001, ty_Int) → new_lt8(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, ty_Integer) → new_lt13(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, app(ty_Ratio, bhf)) → new_lt17(zxw79001, zxw80001, bhf)
new_lt20(zxw79001, zxw80001, ty_Char) → new_lt9(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, app(ty_[], bha)) → new_lt10(zxw79001, zxw80001, bha)
new_lt20(zxw79001, zxw80001, ty_Double) → new_lt15(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, ty_Float) → new_lt16(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, ty_Bool) → new_lt12(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, app(app(app(ty_@3, bgf), bgg), bgh)) → new_lt5(zxw79001, zxw80001, bgf, bgg, bgh)
new_esEs19(zxw79001, zxw80001, app(ty_Ratio, bhf)) → new_esEs18(zxw79001, zxw80001, bhf)
new_esEs19(zxw79001, zxw80001, ty_Ordering) → new_esEs9(zxw79001, zxw80001)
new_esEs19(zxw79001, zxw80001, app(ty_Maybe, bhg)) → new_esEs6(zxw79001, zxw80001, bhg)
new_esEs19(zxw79001, zxw80001, app(app(ty_Either, bhd), bhe)) → new_esEs7(zxw79001, zxw80001, bhd, bhe)
new_esEs19(zxw79001, zxw80001, ty_Float) → new_esEs17(zxw79001, zxw80001)
new_esEs19(zxw79001, zxw80001, ty_Bool) → new_esEs14(zxw79001, zxw80001)
new_esEs19(zxw79001, zxw80001, ty_Int) → new_esEs11(zxw79001, zxw80001)
new_esEs19(zxw79001, zxw80001, app(app(app(ty_@3, bgf), bgg), bgh)) → new_esEs4(zxw79001, zxw80001, bgf, bgg, bgh)
new_esEs19(zxw79001, zxw80001, app(app(ty_@2, bhb), bhc)) → new_esEs5(zxw79001, zxw80001, bhb, bhc)
new_esEs19(zxw79001, zxw80001, ty_Double) → new_esEs16(zxw79001, zxw80001)
new_esEs19(zxw79001, zxw80001, ty_Integer) → new_esEs15(zxw79001, zxw80001)
new_esEs19(zxw79001, zxw80001, ty_@0) → new_esEs10(zxw79001, zxw80001)
new_esEs19(zxw79001, zxw80001, app(ty_[], bha)) → new_esEs13(zxw79001, zxw80001, bha)
new_esEs19(zxw79001, zxw80001, ty_Char) → new_esEs12(zxw79001, zxw80001)
new_ltEs21(zxw79002, zxw80002, ty_Char) → new_ltEs10(zxw79002, zxw80002)
new_ltEs21(zxw79002, zxw80002, app(app(ty_@2, cad), cae)) → new_ltEs4(zxw79002, zxw80002, cad, cae)
new_ltEs21(zxw79002, zxw80002, ty_Int) → new_ltEs9(zxw79002, zxw80002)
new_ltEs21(zxw79002, zxw80002, ty_Ordering) → new_ltEs7(zxw79002, zxw80002)
new_ltEs21(zxw79002, zxw80002, ty_Float) → new_ltEs16(zxw79002, zxw80002)
new_ltEs21(zxw79002, zxw80002, ty_Bool) → new_ltEs12(zxw79002, zxw80002)
new_ltEs21(zxw79002, zxw80002, ty_Integer) → new_ltEs13(zxw79002, zxw80002)
new_ltEs21(zxw79002, zxw80002, app(app(ty_Either, caf), cag)) → new_ltEs14(zxw79002, zxw80002, caf, cag)
new_ltEs21(zxw79002, zxw80002, app(ty_[], cac)) → new_ltEs11(zxw79002, zxw80002, cac)
new_ltEs21(zxw79002, zxw80002, app(ty_Ratio, cah)) → new_ltEs17(zxw79002, zxw80002, cah)
new_ltEs21(zxw79002, zxw80002, app(app(app(ty_@3, bhh), caa), cab)) → new_ltEs6(zxw79002, zxw80002, bhh, caa, cab)
new_ltEs21(zxw79002, zxw80002, ty_@0) → new_ltEs8(zxw79002, zxw80002)
new_ltEs21(zxw79002, zxw80002, app(ty_Maybe, cba)) → new_ltEs18(zxw79002, zxw80002, cba)
new_ltEs21(zxw79002, zxw80002, ty_Double) → new_ltEs15(zxw79002, zxw80002)
new_ltEs15(zxw7900, zxw8000) → new_fsEs(new_compare6(zxw7900, zxw8000))
new_compare6(Double(zxw79000, zxw79001), Double(zxw80000, zxw80001)) → new_compare16(new_sr(zxw79000, zxw80000), new_sr(zxw79001, zxw80001))
new_ltEs12(True, False) → False
new_ltEs12(False, False) → True
new_ltEs12(True, True) → True
new_ltEs12(False, True) → True
new_lt5(zxw79000, zxw80000, gd, ge, gf) → new_esEs9(new_compare9(zxw79000, zxw80000, gd, ge, gf), LT)
new_compare9(zxw79000, zxw80000, gd, ge, gf) → new_compare25(zxw79000, zxw80000, new_esEs4(zxw79000, zxw80000, gd, ge, gf), gd, ge, gf)
new_compare25(zxw79000, zxw80000, True, gd, ge, gf) → EQ
new_compare25(zxw79000, zxw80000, False, gd, ge, gf) → new_compare12(zxw79000, zxw80000, new_ltEs6(zxw79000, zxw80000, gd, ge, gf), gd, ge, gf)
new_compare12(zxw79000, zxw80000, True, gd, ge, gf) → LT
new_compare12(zxw79000, zxw80000, False, gd, ge, gf) → GT
new_lt12(zxw79000, zxw80000) → new_esEs9(new_compare31(zxw79000, zxw80000), LT)
new_compare31(zxw79000, zxw80000) → new_compare23(zxw79000, zxw80000, new_esEs14(zxw79000, zxw80000))
new_compare23(zxw79000, zxw80000, True) → EQ
new_compare23(zxw79000, zxw80000, False) → new_compare10(zxw79000, zxw80000, new_ltEs12(zxw79000, zxw80000))
new_compare10(zxw79000, zxw80000, True) → LT
new_compare10(zxw79000, zxw80000, False) → GT
new_lt16(zxw79000, zxw80000) → new_esEs9(new_compare7(zxw79000, zxw80000), LT)
new_lt15(zxw79000, zxw80000) → new_esEs9(new_compare6(zxw79000, zxw80000), LT)
new_lt10(zxw79000, zxw80000, bgc) → new_esEs9(new_compare1(zxw79000, zxw80000, bgc), LT)
new_lt9(zxw79000, zxw80000) → new_esEs9(new_compare17(zxw79000, zxw80000), LT)
new_lt17(zxw79000, zxw80000, gg) → new_esEs9(new_compare8(zxw79000, zxw80000, gg), LT)
new_lt13(zxw79000, zxw80000) → new_esEs9(new_compare32(zxw79000, zxw80000), LT)
new_lt8(zxw790, zxw800) → new_esEs9(new_compare16(zxw790, zxw800), LT)
new_lt18(zxw79000, zxw80000, bbh) → new_esEs9(new_compare27(zxw79000, zxw80000, bbh), LT)
new_compare27(zxw79000, zxw80000, bbh) → new_compare28(zxw79000, zxw80000, new_esEs6(zxw79000, zxw80000, bbh), bbh)
new_compare28(zxw79000, zxw80000, False, bbh) → new_compare111(zxw79000, zxw80000, new_ltEs18(zxw79000, zxw80000, bbh), bbh)
new_compare28(zxw79000, zxw80000, True, bbh) → EQ
new_compare111(zxw79000, zxw80000, True, bbh) → LT
new_compare111(zxw79000, zxw80000, False, bbh) → GT
new_lt6(zxw79000, zxw80000) → new_esEs9(new_compare18(zxw79000, zxw80000), LT)
new_lt11(zxw79000, zxw80000, bbd, bbe) → new_esEs9(new_compare19(zxw79000, zxw80000, bbd, bbe), LT)
new_compare19(zxw79000, zxw80000, bbd, bbe) → new_compare210(zxw79000, zxw80000, new_esEs5(zxw79000, zxw80000, bbd, bbe), bbd, bbe)
new_compare210(zxw79000, zxw80000, False, bbd, bbe) → new_compare110(zxw79000, zxw80000, new_ltEs4(zxw79000, zxw80000, bbd, bbe), bbd, bbe)
new_compare210(zxw79000, zxw80000, True, bbd, bbe) → EQ
new_compare110(zxw79000, zxw80000, True, bbd, bbe) → LT
new_compare110(zxw79000, zxw80000, False, bbd, bbe) → GT
new_lt7(zxw79000, zxw80000) → new_esEs9(new_compare30(zxw79000, zxw80000), LT)
new_lt14(zxw790, zxw800, gh, ha) → new_esEs9(new_compare15(zxw790, zxw800, gh, ha), LT)
new_esEs30(zxw400, zxw300, app(ty_Maybe, dag)) → new_esEs6(zxw400, zxw300, dag)
new_esEs30(zxw400, zxw300, app(ty_[], daf)) → new_esEs13(zxw400, zxw300, daf)
new_esEs30(zxw400, zxw300, app(app(ty_Either, dbb), dbc)) → new_esEs7(zxw400, zxw300, dbb, dbc)
new_esEs30(zxw400, zxw300, ty_Char) → new_esEs12(zxw400, zxw300)
new_esEs30(zxw400, zxw300, app(app(app(ty_@3, dbd), dbe), dbf)) → new_esEs4(zxw400, zxw300, dbd, dbe, dbf)
new_esEs30(zxw400, zxw300, ty_Float) → new_esEs17(zxw400, zxw300)
new_esEs30(zxw400, zxw300, app(ty_Ratio, dae)) → new_esEs18(zxw400, zxw300, dae)
new_esEs30(zxw400, zxw300, ty_@0) → new_esEs10(zxw400, zxw300)
new_esEs30(zxw400, zxw300, app(app(ty_@2, dah), dba)) → new_esEs5(zxw400, zxw300, dah, dba)
new_esEs30(zxw400, zxw300, ty_Ordering) → new_esEs9(zxw400, zxw300)
new_esEs30(zxw400, zxw300, ty_Bool) → new_esEs14(zxw400, zxw300)
new_esEs30(zxw400, zxw300, ty_Integer) → new_esEs15(zxw400, zxw300)
new_esEs30(zxw400, zxw300, ty_Int) → new_esEs11(zxw400, zxw300)
new_esEs30(zxw400, zxw300, ty_Double) → new_esEs16(zxw400, zxw300)

The set Q consists of the following terms:

new_compare23(x0, x1, True)
new_lt6(x0, x1)
new_ltEs5(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, ty_Integer)
new_lt4(x0, x1, app(ty_[], x2))
new_ltEs18(Just(x0), Just(x1), ty_@0)
new_compare16(x0, x1)
new_lt4(x0, x1, app(app(ty_@2, x2), x3))
new_compare13(x0, x1, False, x2, x3)
new_ltEs18(Just(x0), Nothing, x1)
new_ltEs20(x0, x1, ty_Double)
new_esEs19(x0, x1, ty_Bool)
new_esEs8(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(x0, x1, app(app(ty_Either, x2), x3))
new_compare30(@0, @0)
new_primCompAux00(x0, GT)
new_esEs30(x0, x1, ty_@0)
new_lt19(x0, x1, ty_Char)
new_esEs30(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_Ordering)
new_compare17(Char(x0), Char(x1))
new_esEs28(x0, x1, ty_Int)
new_ltEs20(x0, x1, app(ty_[], x2))
new_ltEs21(x0, x1, ty_Ordering)
new_ltEs15(x0, x1)
new_primPlusNat1(Zero, Succ(x0))
new_esEs6(Just(x0), Just(x1), ty_Double)
new_compare24(x0, x1, False)
new_lt20(x0, x1, ty_Char)
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, ty_Bool)
new_sr0(Integer(x0), Integer(x1))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare210(x0, x1, False, x2, x3)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs7(Right(x0), Right(x1), x2, ty_Float)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs18(Nothing, Nothing, x0)
new_ltEs7(EQ, EQ)
new_esEs7(Right(x0), Right(x1), x2, ty_Integer)
new_compare29(x0, x1, app(app(ty_@2, x2), x3))
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs19(x0, x1, ty_Integer)
new_ltEs20(x0, x1, ty_Bool)
new_ltEs14(Right(x0), Right(x1), x2, ty_Float)
new_esEs6(Just(x0), Just(x1), app(ty_[], x2))
new_esEs31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_compare25(x0, x1, False, x2, x3, x4)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_ltEs19(x0, x1, ty_Integer)
new_ltEs5(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(ty_[], x2))
new_lt10(x0, x1, x2)
new_ltEs7(EQ, LT)
new_ltEs7(LT, EQ)
new_esEs20(x0, x1, ty_Ordering)
new_esEs17(Float(x0, x1), Float(x2, x3))
new_compare25(x0, x1, True, x2, x3, x4)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_lt19(x0, x1, ty_Ordering)
new_esEs26(x0, x1, app(ty_[], x2))
new_ltEs16(x0, x1)
new_lt4(x0, x1, app(ty_Maybe, x2))
new_compare110(x0, x1, False, x2, x3)
new_ltEs14(Left(x0), Left(x1), ty_Char, x2)
new_sr(x0, x1)
new_ltEs19(x0, x1, ty_Double)
new_compare7(Float(x0, x1), Float(x2, x3))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs9(x0, x1)
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_lt7(x0, x1)
new_lt4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, ty_Int)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat0(Zero, x0)
new_esEs7(Right(x0), Right(x1), x2, ty_@0)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_ltEs7(LT, LT)
new_esEs7(Right(x0), Right(x1), x2, ty_Double)
new_esEs4(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_Bool)
new_lt5(x0, x1, x2, x3, x4)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt4(x0, x1, ty_Ordering)
new_primEqNat0(Zero, Succ(x0))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Int)
new_esEs15(Integer(x0), Integer(x1))
new_esEs7(Left(x0), Left(x1), ty_Char, x2)
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs26(x0, x1, ty_Double)
new_compare29(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_@0)
new_primPlusNat1(Succ(x0), Zero)
new_esEs22(x0, x1, ty_Integer)
new_ltEs14(Left(x0), Left(x1), ty_@0, x2)
new_primMulInt(Neg(x0), Neg(x1))
new_ltEs19(x0, x1, ty_Int)
new_ltEs21(x0, x1, app(ty_Maybe, x2))
new_compare29(x0, x1, ty_Integer)
new_esEs14(True, True)
new_esEs21(x0, x1, ty_Char)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Int)
new_ltEs18(Just(x0), Just(x1), ty_Integer)
new_esEs24(x0, x1, ty_Int)
new_primEqNat0(Zero, Zero)
new_esEs16(Double(x0, x1), Double(x2, x3))
new_esEs12(Char(x0), Char(x1))
new_lt4(x0, x1, ty_Char)
new_compare29(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, ty_Bool)
new_esEs8(x0, x1, ty_Float)
new_compare1([], :(x0, x1), x2)
new_esEs30(x0, x1, ty_Ordering)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, ty_Integer)
new_esEs30(x0, x1, ty_Bool)
new_esEs30(x0, x1, ty_Float)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs14(Left(x0), Left(x1), ty_Int, x2)
new_primCompAux00(x0, LT)
new_esEs27(x0, x1, ty_Integer)
new_ltEs21(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs5(x0, x1, ty_Double)
new_ltEs18(Just(x0), Just(x1), ty_Char)
new_primMulNat0(Zero, Zero)
new_compare110(x0, x1, True, x2, x3)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_lt9(x0, x1)
new_compare29(x0, x1, ty_Double)
new_ltEs5(x0, x1, ty_@0)
new_lt17(x0, x1, x2)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_compare36(x0, x1, x2, x3)
new_ltEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs31(x0, x1, ty_Bool)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Left(x0), Left(x1), ty_Float, x2)
new_esEs13([], :(x0, x1), x2)
new_esEs8(x0, x1, ty_Ordering)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_compare10(x0, x1, True)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs7(Left(x0), Left(x1), ty_Float, x2)
new_primEqNat0(Succ(x0), Succ(x1))
new_ltEs19(x0, x1, ty_Bool)
new_esEs28(x0, x1, ty_Double)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_@0)
new_pePe(True, x0)
new_esEs19(x0, x1, ty_Float)
new_esEs8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_lt16(x0, x1)
new_compare29(x0, x1, ty_Bool)
new_esEs20(x0, x1, app(ty_[], x2))
new_compare11(x0, x1, True)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_compare14(x0, x1, True, x2, x3)
new_esEs6(Just(x0), Just(x1), app(ty_Maybe, x2))
new_lt19(x0, x1, ty_@0)
new_esEs6(Just(x0), Just(x1), ty_Ordering)
new_esEs23(x0, x1, ty_@0)
new_compare29(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Right(x0), Right(x1), x2, ty_Int)
new_ltEs5(x0, x1, ty_Char)
new_esEs30(x0, x1, ty_Double)
new_ltEs21(x0, x1, ty_Int)
new_compare29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Float)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_compare29(x0, x1, ty_Ordering)
new_ltEs21(x0, x1, ty_@0)
new_esEs8(x0, x1, ty_Int)
new_lt14(x0, x1, x2, x3)
new_ltEs12(False, False)
new_esEs6(Just(x0), Just(x1), ty_Bool)
new_compare32(Integer(x0), Integer(x1))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_Int)
new_primMulNat0(Succ(x0), Succ(x1))
new_compare29(x0, x1, ty_Float)
new_ltEs21(x0, x1, ty_Integer)
new_esEs6(Just(x0), Just(x1), ty_Float)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs5(x0, x1, ty_Float)
new_ltEs18(Just(x0), Just(x1), ty_Float)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Bool)
new_esEs31(x0, x1, ty_Double)
new_esEs31(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpNat1(Zero, x0)
new_ltEs8(x0, x1)
new_ltEs21(x0, x1, app(ty_[], x2))
new_primPlusNat1(Zero, Zero)
new_esEs30(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(ty_[], x2))
new_ltEs14(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs23(x0, x1, ty_Double)
new_ltEs18(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs18(Just(x0), Just(x1), ty_Ordering)
new_primCmpNat2(Zero, Zero)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs5(x0, x1, ty_Bool)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_compare28(x0, x1, True, x2)
new_ltEs14(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs5(x0, x1, app(ty_[], x2))
new_asAs(False, x0)
new_esEs31(x0, x1, app(ty_[], x2))
new_esEs30(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, ty_Char)
new_esEs31(x0, x1, app(app(ty_@2, x2), x3))
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(x0, x1, ty_Integer)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs19(x0, x1, app(ty_[], x2))
new_ltEs18(Just(x0), Just(x1), ty_Bool)
new_lt11(x0, x1, x2, x3)
new_primCmpNat1(Succ(x0), x1)
new_ltEs18(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs24(x0, x1, ty_Integer)
new_ltEs14(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs27(x0, x1, ty_@0)
new_ltEs14(Right(x0), Right(x1), x2, ty_Double)
new_lt4(x0, x1, ty_Float)
new_compare19(x0, x1, x2, x3)
new_ltEs5(x0, x1, app(app(ty_Either, x2), x3))
new_esEs19(x0, x1, ty_Char)
new_lt4(x0, x1, ty_Double)
new_esEs19(x0, x1, ty_Ordering)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs10(@0, @0)
new_esEs31(x0, x1, ty_@0)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs11(x0, x1)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, ty_Float)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_Char)
new_esEs9(GT, GT)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs27(x0, x1, ty_Char)
new_compare11(x0, x1, False)
new_compare23(x0, x1, False)
new_compare12(x0, x1, True, x2, x3, x4)
new_esEs28(x0, x1, ty_Bool)
new_esEs7(Right(x0), Left(x1), x2, x3)
new_esEs7(Left(x0), Right(x1), x2, x3)
new_compare24(x0, x1, True)
new_compare15(x0, x1, x2, x3)
new_primEqNat0(Succ(x0), Zero)
new_esEs23(x0, x1, ty_Ordering)
new_esEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs7(Right(x0), Right(x1), x2, ty_Int)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_compare9(x0, x1, x2, x3, x4)
new_lt20(x0, x1, ty_Int)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Integer)
new_lt4(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Int)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs5(x0, x1, app(app(ty_@2, x2), x3))
new_lt4(x0, x1, ty_@0)
new_esEs23(x0, x1, ty_Char)
new_esEs28(x0, x1, ty_Ordering)
new_ltEs18(Just(x0), Just(x1), ty_Double)
new_esEs30(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_compare14(x0, x1, False, x2, x3)
new_lt20(x0, x1, ty_@0)
new_compare1([], [], x0)
new_esEs9(EQ, EQ)
new_pePe(False, x0)
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs5(x0, x1, app(ty_Ratio, x2))
new_ltEs18(Just(x0), Just(x1), app(ty_[], x2))
new_esEs6(Just(x0), Just(x1), ty_Char)
new_esEs25(x0, x1, ty_Integer)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs18(:%(x0, x1), :%(x2, x3), x4)
new_esEs26(x0, x1, ty_Integer)
new_compare12(x0, x1, False, x2, x3, x4)
new_esEs8(x0, x1, app(ty_Maybe, x2))
new_primCompAux00(x0, EQ)
new_esEs19(x0, x1, ty_Int)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs14(True, False)
new_esEs14(False, True)
new_lt4(x0, x1, ty_Integer)
new_esEs7(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs14(Right(x0), Right(x1), x2, ty_@0)
new_fsEs(x0)
new_esEs22(x0, x1, ty_Float)
new_lt4(x0, x1, ty_Bool)
new_primCmpNat2(Succ(x0), Succ(x1))
new_asAs(True, x0)
new_ltEs18(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, ty_Bool)
new_esEs6(Nothing, Just(x0), x1)
new_esEs6(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs6(Just(x0), Nothing, x1)
new_lt18(x0, x1, x2)
new_esEs8(x0, x1, app(ty_[], x2))
new_esEs31(x0, x1, ty_Integer)
new_compare111(x0, x1, False, x2)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs8(x0, x1, ty_Char)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, ty_Float)
new_ltEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs22(x0, x1, ty_@0)
new_esEs20(x0, x1, ty_Char)
new_esEs13(:(x0, x1), [], x2)
new_ltEs12(False, True)
new_ltEs12(True, False)
new_compare6(Double(x0, x1), Double(x2, x3))
new_ltEs20(x0, x1, ty_@0)
new_esEs22(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_@0)
new_ltEs18(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare35(x0, x1, x2, x3)
new_ltEs14(Right(x0), Right(x1), x2, ty_Integer)
new_lt19(x0, x1, ty_Double)
new_lt19(x0, x1, ty_Bool)
new_ltEs14(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs7(Right(x0), Right(x1), x2, ty_Char)
new_ltEs14(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs26(x0, x1, ty_Char)
new_ltEs14(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs5(x0, x1, ty_Int)
new_lt4(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_Double)
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_esEs19(x0, x1, ty_@0)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs21(x0, x1, ty_Bool)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs14(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs21(x0, x1, ty_Double)
new_lt12(x0, x1)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs8(x0, x1, ty_Bool)
new_ltEs21(x0, x1, ty_Char)
new_lt13(x0, x1)
new_esEs13(:(x0, x1), :(x2, x3), x4)
new_esEs31(x0, x1, ty_Ordering)
new_ltEs14(Right(x0), Right(x1), x2, ty_Bool)
new_compare1(:(x0, x1), [], x2)
new_compare27(x0, x1, x2)
new_compare10(x0, x1, False)
new_esEs27(x0, x1, app(ty_[], x2))
new_primMulNat0(Succ(x0), Zero)
new_ltEs19(x0, x1, ty_Float)
new_ltEs14(Left(x0), Right(x1), x2, x3)
new_esEs23(x0, x1, ty_Float)
new_ltEs14(Right(x0), Left(x1), x2, x3)
new_compare29(x0, x1, ty_Int)
new_esEs22(x0, x1, ty_Int)
new_esEs31(x0, x1, app(ty_Maybe, x2))
new_esEs20(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Float)
new_compare31(x0, x1)
new_esEs7(Left(x0), Left(x1), ty_Double, x2)
new_esEs31(x0, x1, ty_Char)
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Just(x0), Just(x1), ty_Int)
new_esEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs21(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs7(LT, GT)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs7(GT, LT)
new_ltEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Double)
new_compare29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare111(x0, x1, True, x2)
new_ltEs13(x0, x1)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs31(x0, x1, ty_Int)
new_lt4(x0, x1, ty_Int)
new_ltEs11(x0, x1, x2)
new_lt20(x0, x1, ty_Float)
new_not(True)
new_esEs31(x0, x1, ty_Float)
new_esEs20(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Float)
new_esEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs6(Nothing, Nothing, x0)
new_esEs28(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Ordering)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(Left(x0), Left(x1), ty_Double, x2)
new_esEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs6(Just(x0), Just(x1), ty_Integer)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_not(False)
new_lt8(x0, x1)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_ltEs18(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare13(x0, x1, True, x2, x3)
new_esEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs19(x0, x1, ty_Char)
new_esEs6(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare8(:%(x0, x1), :%(x2, x3), ty_Integer)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_Integer)
new_esEs8(x0, x1, ty_@0)
new_compare26(Left(x0), Left(x1), False, x2, x3)
new_ltEs12(True, True)
new_esEs27(x0, x1, ty_Float)
new_lt15(x0, x1)
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, ty_Ordering)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, ty_Double)
new_esEs6(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_lt20(x0, x1, ty_Ordering)
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs22(x0, x1, ty_Char)
new_lt20(x0, x1, ty_Double)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Bool)
new_esEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_ltEs21(x0, x1, ty_Float)
new_ltEs10(x0, x1)
new_ltEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs14(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs14(Left(x0), Left(x1), ty_Integer, x2)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(x0, x1, ty_Ordering)
new_esEs8(x0, x1, ty_Double)
new_compare29(x0, x1, ty_Char)
new_esEs6(Just(x0), Just(x1), ty_@0)
new_compare1(:(x0, x1), :(x2, x3), x4)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_compare210(x0, x1, True, x2, x3)
new_esEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs6(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs19(x0, x1, ty_Double)
new_esEs14(False, False)
new_primEqInt(Pos(Zero), Pos(Zero))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1, app(ty_[], x2))
new_ltEs21(x0, x1, ty_Double)
new_primCmpNat2(Succ(x0), Zero)
new_compare18(x0, x1)
new_compare28(x0, x1, False, x2)
new_ltEs14(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs18(Just(x0), Just(x1), ty_Int)
new_compare26(Right(x0), Right(x1), False, x2, x3)
new_ltEs17(x0, x1, x2)
new_primPlusNat0(Succ(x0), x1)
new_esEs7(Left(x0), Left(x1), ty_Int, x2)
new_esEs20(x0, x1, ty_Integer)
new_primCmpNat0(x0, Zero)
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_esEs7(Left(x0), Left(x1), ty_@0, x2)
new_ltEs7(GT, EQ)
new_ltEs7(EQ, GT)
new_esEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs7(GT, GT)
new_esEs31(x0, x1, app(ty_Ratio, x2))
new_esEs9(LT, LT)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs13([], [], x0)
new_primCompAux0(x0, x1, x2, x3)
new_compare29(x0, x1, ty_@0)
new_esEs7(Left(x0), Left(x1), ty_Bool, x2)
new_compare26(x0, x1, True, x2, x3)
new_compare26(Right(x0), Left(x1), False, x2, x3)
new_compare26(Left(x0), Right(x1), False, x2, x3)
new_ltEs18(Nothing, Just(x0), x1)
new_esEs27(x0, x1, ty_Ordering)
new_primCmpNat0(x0, Succ(x1))

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

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



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

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

new_splitLT10(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, True, h, ba, bb) → new_splitLT(zxw34, zxw400, h, ba, bb)
new_splitLT3(Left(zxw300), zxw31, zxw32, zxw33, zxw34, Left(zxw400), h, ba, bb) → new_splitLT2(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs9(new_compare26(Left(zxw400), Left(zxw300), new_esEs29(zxw400, zxw300, h), h, ba), LT), h, ba, bb)
new_splitLT3(Right(zxw300), zxw31, zxw32, zxw33, zxw34, Left(zxw400), h, ba, bb) → new_splitLT20(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs9(new_compare26(Left(zxw400), Right(zxw300), False, h, ba), LT), h, ba, bb)
new_splitLT20(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, False, h, ba, bb) → new_splitLT10(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs9(new_compare34(zxw400, zxw300, h, ba), GT), h, ba, bb)
new_splitLT20(zxw300, zxw31, zxw32, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw34, zxw400, True, h, ba, bb) → new_splitLT3(zxw330, zxw331, zxw332, zxw333, zxw334, Left(zxw400), h, ba, bb)
new_splitLT1(zxw45, zxw46, zxw47, zxw48, zxw49, zxw50, True, bc, bd, be) → new_splitLT(zxw49, zxw50, bc, bd, be)
new_splitLT2(zxw45, zxw46, zxw47, zxw48, zxw49, zxw50, False, bc, bd, be) → new_splitLT1(zxw45, zxw46, zxw47, zxw48, zxw49, zxw50, new_esEs9(new_compare33(zxw50, zxw45, bc, bd), GT), bc, bd, be)
new_splitLT2(zxw45, zxw46, zxw47, zxw48, zxw49, zxw50, True, bc, bd, be) → new_splitLT(zxw48, zxw50, bc, bd, be)
new_splitLT(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw400, h, ba, bb) → new_splitLT3(zxw330, zxw331, zxw332, zxw333, zxw334, Left(zxw400), h, ba, bb)

The TRS R consists of the following rules:

new_esEs30(zxw400, zxw300, app(ty_Maybe, dag)) → new_esEs6(zxw400, zxw300, dag)
new_ltEs15(zxw7900, zxw8000) → new_fsEs(new_compare6(zxw7900, zxw8000))
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Bool) → new_ltEs12(zxw79000, zxw80000)
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, app(ty_Maybe, bbc)) → new_ltEs18(zxw7900, zxw8000, bbc)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Char) → new_ltEs10(zxw79000, zxw80000)
new_esEs28(zxw4000, zxw3000, app(ty_[], ead)) → new_esEs13(zxw4000, zxw3000, ead)
new_esEs32(zxw20, zxw15, ty_Float) → new_esEs17(zxw20, zxw15)
new_esEs23(zxw4000, zxw3000, app(app(ty_Either, deh), dfa)) → new_esEs7(zxw4000, zxw3000, deh, dfa)
new_esEs6(Just(zxw4000), Just(zxw3000), app(app(ty_@2, fd), ff)) → new_esEs5(zxw4000, zxw3000, fd, ff)
new_lt4(zxw79000, zxw80000, app(app(app(ty_@3, cc), cd), ce)) → new_lt5(zxw79000, zxw80000, cc, cd, ce)
new_esEs31(zxw35, zxw30, ty_Ordering) → new_esEs9(zxw35, zxw30)
new_esEs7(Left(zxw4000), Left(zxw3000), app(app(ty_Either, bec), bed), bdf) → new_esEs7(zxw4000, zxw3000, bec, bed)
new_ltEs20(zxw7900, zxw8000, ty_Int) → new_ltEs9(zxw7900, zxw8000)
new_lt19(zxw79000, zxw80000, app(app(ty_Either, bgd), bge)) → new_lt14(zxw79000, zxw80000, bgd, bge)
new_esEs9(GT, LT) → False
new_esEs9(LT, GT) → False
new_esEs13([], [], cce) → True
new_lt4(zxw79000, zxw80000, app(ty_[], cf)) → new_lt10(zxw79000, zxw80000, cf)
new_compare110(zxw79000, zxw80000, True, bbd, bbe) → LT
new_esEs27(zxw4001, zxw3001, app(ty_Ratio, dha)) → new_esEs18(zxw4001, zxw3001, dha)
new_compare29(zxw79000, zxw80000, ty_Char) → new_compare17(zxw79000, zxw80000)
new_ltEs7(LT, EQ) → True
new_ltEs18(Just(zxw79000), Just(zxw80000), app(ty_Maybe, dad)) → new_ltEs18(zxw79000, zxw80000, dad)
new_esEs30(zxw400, zxw300, app(ty_[], daf)) → new_esEs13(zxw400, zxw300, daf)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Integer) → new_ltEs13(zxw79000, zxw80000)
new_ltEs20(zxw7900, zxw8000, ty_@0) → new_ltEs8(zxw7900, zxw8000)
new_lt20(zxw79001, zxw80001, app(app(ty_Either, bhd), bhe)) → new_lt14(zxw79001, zxw80001, bhd, bhe)
new_esEs23(zxw4000, zxw3000, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_compare35(zxw400, zxw300, h, ba) → new_compare26(Right(zxw400), Left(zxw300), False, h, ba)
new_ltEs8(zxw7900, zxw8000) → new_fsEs(new_compare30(zxw7900, zxw8000))
new_lt19(zxw79000, zxw80000, ty_Double) → new_lt15(zxw79000, zxw80000)
new_esEs22(zxw4000, zxw3000, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(ty_[], cgd)) → new_ltEs11(zxw79000, zxw80000, cgd)
new_ltEs21(zxw79002, zxw80002, ty_Char) → new_ltEs10(zxw79002, zxw80002)
new_esEs23(zxw4000, zxw3000, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Bool, hg) → new_ltEs12(zxw79000, zxw80000)
new_compare8(:%(zxw79000, zxw79001), :%(zxw80000, zxw80001), ty_Integer) → new_compare32(new_sr0(zxw79000, zxw80001), new_sr0(zxw80000, zxw79001))
new_esEs26(zxw4002, zxw3002, ty_Float) → new_esEs17(zxw4002, zxw3002)
new_esEs19(zxw79001, zxw80001, app(ty_Ratio, bhf)) → new_esEs18(zxw79001, zxw80001, bhf)
new_primMulNat0(Zero, Zero) → Zero
new_esEs20(zxw79000, zxw80000, app(ty_[], bgc)) → new_esEs13(zxw79000, zxw80000, bgc)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_lt20(zxw79001, zxw80001, ty_@0) → new_lt7(zxw79001, zxw80001)
new_esEs27(zxw4001, zxw3001, app(app(app(ty_@3, dhh), eaa), eab)) → new_esEs4(zxw4001, zxw3001, dhh, eaa, eab)
new_esEs19(zxw79001, zxw80001, ty_Ordering) → new_esEs9(zxw79001, zxw80001)
new_esEs31(zxw35, zxw30, ty_Char) → new_esEs12(zxw35, zxw30)
new_esEs32(zxw20, zxw15, ty_Integer) → new_esEs15(zxw20, zxw15)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(ty_Ratio, dac)) → new_ltEs17(zxw79000, zxw80000, dac)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Bool, bdf) → new_esEs14(zxw4000, zxw3000)
new_esEs24(zxw4001, zxw3001, ty_Integer) → new_esEs15(zxw4001, zxw3001)
new_lt19(zxw79000, zxw80000, ty_Ordering) → new_lt6(zxw79000, zxw80000)
new_lt20(zxw79001, zxw80001, app(app(ty_@2, bhb), bhc)) → new_lt11(zxw79001, zxw80001, bhb, bhc)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(ty_Ratio, cfg), hg) → new_ltEs17(zxw79000, zxw80000, cfg)
new_compare9(zxw79000, zxw80000, gd, ge, gf) → new_compare25(zxw79000, zxw80000, new_esEs4(zxw79000, zxw80000, gd, ge, gf), gd, ge, gf)
new_lt11(zxw79000, zxw80000, bbd, bbe) → new_esEs9(new_compare19(zxw79000, zxw80000, bbd, bbe), LT)
new_compare1([], :(zxw80000, zxw80001), he) → LT
new_esEs30(zxw400, zxw300, app(app(ty_Either, dbb), dbc)) → new_esEs7(zxw400, zxw300, dbb, dbc)
new_lt18(zxw79000, zxw80000, bbh) → new_esEs9(new_compare27(zxw79000, zxw80000, bbh), LT)
new_esEs8(zxw79000, zxw80000, ty_Int) → new_esEs11(zxw79000, zxw80000)
new_compare32(Integer(zxw79000), Integer(zxw80000)) → new_primCmpInt(zxw79000, zxw80000)
new_ltEs5(zxw79001, zxw80001, ty_Char) → new_ltEs10(zxw79001, zxw80001)
new_lt4(zxw79000, zxw80000, ty_Bool) → new_lt12(zxw79000, zxw80000)
new_compare27(zxw79000, zxw80000, bbh) → new_compare28(zxw79000, zxw80000, new_esEs6(zxw79000, zxw80000, bbh), bbh)
new_lt4(zxw79000, zxw80000, app(ty_Maybe, de)) → new_lt18(zxw79000, zxw80000, de)
new_compare29(zxw79000, zxw80000, ty_Bool) → new_compare31(zxw79000, zxw80000)
new_esEs31(zxw35, zxw30, ty_@0) → new_esEs10(zxw35, zxw30)
new_esEs8(zxw79000, zxw80000, ty_Double) → new_esEs16(zxw79000, zxw80000)
new_esEs22(zxw4000, zxw3000, app(app(ty_@2, ddd), dde)) → new_esEs5(zxw4000, zxw3000, ddd, dde)
new_lt4(zxw79000, zxw80000, ty_Ordering) → new_lt6(zxw79000, zxw80000)
new_esEs22(zxw4000, zxw3000, app(ty_Maybe, ddc)) → new_esEs6(zxw4000, zxw3000, ddc)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(app(app(ty_@3, cga), cgb), cgc)) → new_ltEs6(zxw79000, zxw80000, cga, cgb, cgc)
new_esEs27(zxw4001, zxw3001, app(ty_Maybe, dhc)) → new_esEs6(zxw4001, zxw3001, dhc)
new_esEs8(zxw79000, zxw80000, app(app(app(ty_@3, cc), cd), ce)) → new_esEs4(zxw79000, zxw80000, cc, cd, ce)
new_esEs15(Integer(zxw4000), Integer(zxw3000)) → new_primEqInt(zxw4000, zxw3000)
new_ltEs21(zxw79002, zxw80002, app(app(ty_@2, cad), cae)) → new_ltEs4(zxw79002, zxw80002, cad, cae)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Float, hg) → new_ltEs16(zxw79000, zxw80000)
new_lt5(zxw79000, zxw80000, gd, ge, gf) → new_esEs9(new_compare9(zxw79000, zxw80000, gd, ge, gf), LT)
new_esEs22(zxw4000, zxw3000, app(ty_Ratio, dda)) → new_esEs18(zxw4000, zxw3000, dda)
new_esEs29(zxw400, zxw300, ty_Integer) → new_esEs15(zxw400, zxw300)
new_esEs22(zxw4000, zxw3000, app(app(ty_Either, ddf), ddg)) → new_esEs7(zxw4000, zxw3000, ddf, ddg)
new_ltEs19(zxw7900, zxw8000, ty_Float) → new_ltEs16(zxw7900, zxw8000)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, app(ty_Maybe, bfc)) → new_esEs6(zxw4000, zxw3000, bfc)
new_pePe(False, zxw271) → zxw271
new_esEs29(zxw400, zxw300, ty_Double) → new_esEs16(zxw400, zxw300)
new_esEs7(Left(zxw4000), Right(zxw3000), beh, bdf) → False
new_esEs7(Right(zxw4000), Left(zxw3000), beh, bdf) → False
new_lt15(zxw79000, zxw80000) → new_esEs9(new_compare6(zxw79000, zxw80000), LT)
new_compare15(zxw790, zxw800, gh, ha) → new_compare26(zxw790, zxw800, new_esEs7(zxw790, zxw800, gh, ha), gh, ha)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Float) → new_ltEs16(zxw79000, zxw80000)
new_esEs31(zxw35, zxw30, app(app(app(ty_@3, bdb), bdc), bdd)) → new_esEs4(zxw35, zxw30, bdb, bdc, bdd)
new_ltEs12(True, False) → False
new_esEs20(zxw79000, zxw80000, ty_Double) → new_esEs16(zxw79000, zxw80000)
new_ltEs19(zxw7900, zxw8000, app(app(ty_@2, ca), cb)) → new_ltEs4(zxw7900, zxw8000, ca, cb)
new_esEs32(zxw20, zxw15, ty_@0) → new_esEs10(zxw20, zxw15)
new_compare23(zxw79000, zxw80000, True) → EQ
new_esEs31(zxw35, zxw30, ty_Float) → new_esEs17(zxw35, zxw30)
new_esEs27(zxw4001, zxw3001, app(app(ty_Either, dhf), dhg)) → new_esEs7(zxw4001, zxw3001, dhf, dhg)
new_esEs27(zxw4001, zxw3001, ty_Ordering) → new_esEs9(zxw4001, zxw3001)
new_esEs27(zxw4001, zxw3001, ty_Float) → new_esEs17(zxw4001, zxw3001)
new_esEs19(zxw79001, zxw80001, app(ty_Maybe, bhg)) → new_esEs6(zxw79001, zxw80001, bhg)
new_lt10(zxw79000, zxw80000, bgc) → new_esEs9(new_compare1(zxw79000, zxw80000, bgc), LT)
new_esEs26(zxw4002, zxw3002, ty_Char) → new_esEs12(zxw4002, zxw3002)
new_ltEs19(zxw7900, zxw8000, app(ty_[], he)) → new_ltEs11(zxw7900, zxw8000, he)
new_esEs26(zxw4002, zxw3002, ty_Int) → new_esEs11(zxw4002, zxw3002)
new_ltEs5(zxw79001, zxw80001, app(app(ty_@2, eb), ec)) → new_ltEs4(zxw79001, zxw80001, eb, ec)
new_lt19(zxw79000, zxw80000, app(ty_Ratio, gg)) → new_lt17(zxw79000, zxw80000, gg)
new_esEs22(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, app(app(app(ty_@3, ebb), ebc), ebd)) → new_esEs4(zxw4000, zxw3000, ebb, ebc, ebd)
new_esEs32(zxw20, zxw15, ty_Ordering) → new_esEs9(zxw20, zxw15)
new_compare29(zxw79000, zxw80000, app(app(ty_@2, cbf), cbg)) → new_compare19(zxw79000, zxw80000, cbf, cbg)
new_ltEs21(zxw79002, zxw80002, ty_Int) → new_ltEs9(zxw79002, zxw80002)
new_esEs20(zxw79000, zxw80000, ty_Char) → new_esEs12(zxw79000, zxw80000)
new_compare13(zxw235, zxw236, False, bbf, bbg) → GT
new_esEs9(GT, EQ) → False
new_esEs9(EQ, GT) → False
new_esEs19(zxw79001, zxw80001, app(app(ty_Either, bhd), bhe)) → new_esEs7(zxw79001, zxw80001, bhd, bhe)
new_esEs20(zxw79000, zxw80000, app(app(ty_@2, bbd), bbe)) → new_esEs5(zxw79000, zxw80000, bbd, bbe)
new_ltEs7(GT, GT) → True
new_compare36(zxw35, zxw30, bca, bcb) → new_compare26(Right(zxw35), Right(zxw30), new_esEs31(zxw35, zxw30, bcb), bca, bcb)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, app(app(ty_@2, bfd), bfe)) → new_esEs5(zxw4000, zxw3000, bfd, bfe)
new_ltEs20(zxw7900, zxw8000, app(app(ty_@2, baf), bag)) → new_ltEs4(zxw7900, zxw8000, baf, bag)
new_esEs21(zxw4001, zxw3001, ty_Bool) → new_esEs14(zxw4001, zxw3001)
new_esEs32(zxw20, zxw15, ty_Bool) → new_esEs14(zxw20, zxw15)
new_primCompAux0(zxw79000, zxw80000, zxw272, he) → new_primCompAux00(zxw272, new_compare29(zxw79000, zxw80000, he))
new_ltEs21(zxw79002, zxw80002, ty_Ordering) → new_ltEs7(zxw79002, zxw80002)
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_compare29(zxw79000, zxw80000, app(ty_[], cbe)) → new_compare1(zxw79000, zxw80000, cbe)
new_lt20(zxw79001, zxw80001, ty_Ordering) → new_lt6(zxw79001, zxw80001)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_esEs8(zxw79000, zxw80000, app(ty_[], cf)) → new_esEs13(zxw79000, zxw80000, cf)
new_esEs27(zxw4001, zxw3001, ty_@0) → new_esEs10(zxw4001, zxw3001)
new_compare25(zxw79000, zxw80000, True, gd, ge, gf) → EQ
new_esEs19(zxw79001, zxw80001, ty_Float) → new_esEs17(zxw79001, zxw80001)
new_ltEs5(zxw79001, zxw80001, ty_Ordering) → new_ltEs7(zxw79001, zxw80001)
new_lt4(zxw79000, zxw80000, app(ty_Ratio, dd)) → new_lt17(zxw79000, zxw80000, dd)
new_esEs28(zxw4000, zxw3000, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Int, bdf) → new_esEs11(zxw4000, zxw3000)
new_ltEs21(zxw79002, zxw80002, ty_Float) → new_ltEs16(zxw79002, zxw80002)
new_esEs28(zxw4000, zxw3000, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_compare29(zxw79000, zxw80000, app(app(app(ty_@3, cbb), cbc), cbd)) → new_compare9(zxw79000, zxw80000, cbb, cbc, cbd)
new_lt19(zxw79000, zxw80000, app(app(ty_@2, bbd), bbe)) → new_lt11(zxw79000, zxw80000, bbd, bbe)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(app(app(ty_@3, chc), chd), che)) → new_ltEs6(zxw79000, zxw80000, chc, chd, che)
new_pePe(True, zxw271) → True
new_primEqNat0(Zero, Zero) → True
new_compare14(zxw242, zxw243, False, dfe, dff) → GT
new_esEs20(zxw79000, zxw80000, ty_Int) → new_esEs11(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Double) → new_ltEs15(zxw79000, zxw80000)
new_ltEs21(zxw79002, zxw80002, ty_Bool) → new_ltEs12(zxw79002, zxw80002)
new_lt9(zxw79000, zxw80000) → new_esEs9(new_compare17(zxw79000, zxw80000), LT)
new_esEs29(zxw400, zxw300, app(ty_Maybe, eh)) → new_esEs6(zxw400, zxw300, eh)
new_ltEs12(False, False) → True
new_esEs7(Left(zxw4000), Left(zxw3000), app(app(ty_@2, bea), beb), bdf) → new_esEs5(zxw4000, zxw3000, bea, beb)
new_esEs26(zxw4002, zxw3002, app(ty_Maybe, dga)) → new_esEs6(zxw4002, zxw3002, dga)
new_compare8(:%(zxw79000, zxw79001), :%(zxw80000, zxw80001), ty_Int) → new_compare16(new_sr(zxw79000, zxw80001), new_sr(zxw80000, zxw79001))
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Ordering, bdf) → new_esEs9(zxw4000, zxw3000)
new_esEs29(zxw400, zxw300, app(ty_[], cce)) → new_esEs13(zxw400, zxw300, cce)
new_esEs27(zxw4001, zxw3001, ty_Char) → new_esEs12(zxw4001, zxw3001)
new_lt7(zxw79000, zxw80000) → new_esEs9(new_compare30(zxw79000, zxw80000), LT)
new_compare110(zxw79000, zxw80000, False, bbd, bbe) → GT
new_sr(zxw4000, zxw3000) → new_primMulInt(zxw4000, zxw3000)
new_compare12(zxw79000, zxw80000, True, gd, ge, gf) → LT
new_esEs30(zxw400, zxw300, ty_Char) → new_esEs12(zxw400, zxw300)
new_lt19(zxw79000, zxw80000, ty_Int) → new_lt8(zxw79000, zxw80000)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(app(ty_@2, cge), cgf)) → new_ltEs4(zxw79000, zxw80000, cge, cgf)
new_ltEs19(zxw7900, zxw8000, ty_Char) → new_ltEs10(zxw7900, zxw8000)
new_esEs30(zxw400, zxw300, app(app(app(ty_@3, dbd), dbe), dbf)) → new_esEs4(zxw400, zxw300, dbd, dbe, dbf)
new_esEs21(zxw4001, zxw3001, ty_Double) → new_esEs16(zxw4001, zxw3001)
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, app(app(ty_Either, bff), bfg)) → new_esEs7(zxw4000, zxw3000, bff, bfg)
new_esEs31(zxw35, zxw30, app(app(ty_Either, bch), bda)) → new_esEs7(zxw35, zxw30, bch, bda)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Double, hg) → new_ltEs15(zxw79000, zxw80000)
new_ltEs19(zxw7900, zxw8000, ty_Bool) → new_ltEs12(zxw7900, zxw8000)
new_esEs26(zxw4002, zxw3002, app(app(app(ty_@3, dgf), dgg), dgh)) → new_esEs4(zxw4002, zxw3002, dgf, dgg, dgh)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, app(ty_[], bfb)) → new_esEs13(zxw4000, zxw3000, bfb)
new_ltEs11(zxw7900, zxw8000, he) → new_fsEs(new_compare1(zxw7900, zxw8000, he))
new_ltEs20(zxw7900, zxw8000, ty_Float) → new_ltEs16(zxw7900, zxw8000)
new_esEs21(zxw4001, zxw3001, ty_Ordering) → new_esEs9(zxw4001, zxw3001)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_esEs9(EQ, EQ) → True
new_fsEs(zxw259) → new_not(new_esEs9(zxw259, GT))
new_esEs8(zxw79000, zxw80000, ty_Char) → new_esEs12(zxw79000, zxw80000)
new_primEqInt(Neg(Succ(zxw40000)), Neg(Succ(zxw30000))) → new_primEqNat0(zxw40000, zxw30000)
new_esEs8(zxw79000, zxw80000, app(app(ty_@2, cg), da)) → new_esEs5(zxw79000, zxw80000, cg, da)
new_compare13(zxw235, zxw236, True, bbf, bbg) → LT
new_compare26(Left(zxw7900), Right(zxw8000), False, gh, ha) → LT
new_esEs13(:(zxw4000, zxw4001), :(zxw3000, zxw3001), cce) → new_asAs(new_esEs23(zxw4000, zxw3000, cce), new_esEs13(zxw4001, zxw3001, cce))
new_esEs26(zxw4002, zxw3002, app(ty_[], dfh)) → new_esEs13(zxw4002, zxw3002, dfh)
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_ltEs19(zxw7900, zxw8000, app(ty_Ratio, hh)) → new_ltEs17(zxw7900, zxw8000, hh)
new_esEs30(zxw400, zxw300, ty_Float) → new_esEs17(zxw400, zxw300)
new_ltEs20(zxw7900, zxw8000, ty_Bool) → new_ltEs12(zxw7900, zxw8000)
new_esEs21(zxw4001, zxw3001, ty_Char) → new_esEs12(zxw4001, zxw3001)
new_compare23(zxw79000, zxw80000, False) → new_compare10(zxw79000, zxw80000, new_ltEs12(zxw79000, zxw80000))
new_ltEs14(Right(zxw79000), Left(zxw80000), hf, hg) → False
new_compare210(zxw79000, zxw80000, False, bbd, bbe) → new_compare110(zxw79000, zxw80000, new_ltEs4(zxw79000, zxw80000, bbd, bbe), bbd, bbe)
new_primCmpNat1(Zero, zxw7900) → LT
new_compare7(Float(zxw79000, zxw79001), Float(zxw80000, zxw80001)) → new_compare16(new_sr(zxw79000, zxw80000), new_sr(zxw79001, zxw80001))
new_ltEs21(zxw79002, zxw80002, ty_Integer) → new_ltEs13(zxw79002, zxw80002)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_lt20(zxw79001, zxw80001, app(ty_Maybe, bhg)) → new_lt18(zxw79001, zxw80001, bhg)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Integer, bdf) → new_esEs15(zxw4000, zxw3000)
new_ltEs5(zxw79001, zxw80001, ty_Bool) → new_ltEs12(zxw79001, zxw80001)
new_esEs19(zxw79001, zxw80001, ty_Bool) → new_esEs14(zxw79001, zxw80001)
new_ltEs7(EQ, EQ) → True
new_ltEs20(zxw7900, zxw8000, app(ty_Ratio, bbb)) → new_ltEs17(zxw7900, zxw8000, bbb)
new_primEqInt(Neg(Zero), Neg(Succ(zxw30000))) → False
new_primEqInt(Neg(Succ(zxw40000)), Neg(Zero)) → False
new_ltEs5(zxw79001, zxw80001, ty_Integer) → new_ltEs13(zxw79001, zxw80001)
new_compare26(zxw790, zxw800, True, gh, ha) → EQ
new_compare111(zxw79000, zxw80000, True, bbh) → LT
new_esEs20(zxw79000, zxw80000, ty_@0) → new_esEs10(zxw79000, zxw80000)
new_esEs31(zxw35, zxw30, app(ty_Ratio, bcc)) → new_esEs18(zxw35, zxw30, bcc)
new_ltEs21(zxw79002, zxw80002, app(app(ty_Either, caf), cag)) → new_ltEs14(zxw79002, zxw80002, caf, cag)
new_esEs8(zxw79000, zxw80000, ty_Float) → new_esEs17(zxw79000, zxw80000)
new_esEs23(zxw4000, zxw3000, app(app(app(ty_@3, dfb), dfc), dfd)) → new_esEs4(zxw4000, zxw3000, dfb, dfc, dfd)
new_ltEs21(zxw79002, zxw80002, app(ty_[], cac)) → new_ltEs11(zxw79002, zxw80002, cac)
new_esEs21(zxw4001, zxw3001, ty_Float) → new_esEs17(zxw4001, zxw3001)
new_compare24(zxw79000, zxw80000, False) → new_compare11(zxw79000, zxw80000, new_ltEs7(zxw79000, zxw80000))
new_ltEs5(zxw79001, zxw80001, app(ty_Ratio, ef)) → new_ltEs17(zxw79001, zxw80001, ef)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_esEs26(zxw4002, zxw3002, app(app(ty_Either, dgd), dge)) → new_esEs7(zxw4002, zxw3002, dgd, dge)
new_lt20(zxw79001, zxw80001, ty_Int) → new_lt8(zxw79001, zxw80001)
new_lt4(zxw79000, zxw80000, ty_Int) → new_lt8(zxw79000, zxw80000)
new_ltEs20(zxw7900, zxw8000, ty_Double) → new_ltEs15(zxw7900, zxw8000)
new_ltEs7(GT, LT) → False
new_lt12(zxw79000, zxw80000) → new_esEs9(new_compare31(zxw79000, zxw80000), LT)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Int, hg) → new_ltEs9(zxw79000, zxw80000)
new_lt20(zxw79001, zxw80001, ty_Integer) → new_lt13(zxw79001, zxw80001)
new_ltEs7(GT, EQ) → False
new_esEs6(Nothing, Nothing, eh) → True
new_primEqInt(Pos(Succ(zxw40000)), Pos(Succ(zxw30000))) → new_primEqNat0(zxw40000, zxw30000)
new_lt8(zxw790, zxw800) → new_esEs9(new_compare16(zxw790, zxw800), LT)
new_esEs21(zxw4001, zxw3001, app(ty_Maybe, dca)) → new_esEs6(zxw4001, zxw3001, dca)
new_lt6(zxw79000, zxw80000) → new_esEs9(new_compare18(zxw79000, zxw80000), LT)
new_esEs32(zxw20, zxw15, app(app(ty_Either, ceb), cec)) → new_esEs7(zxw20, zxw15, ceb, cec)
new_esEs14(False, True) → False
new_esEs14(True, False) → False
new_esEs32(zxw20, zxw15, app(ty_[], cdf)) → new_esEs13(zxw20, zxw15, cdf)
new_esEs26(zxw4002, zxw3002, ty_Integer) → new_esEs15(zxw4002, zxw3002)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, app(app(app(ty_@3, bfh), bga), bgb)) → new_esEs4(zxw4000, zxw3000, bfh, bga, bgb)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs6(Nothing, Just(zxw3000), eh) → False
new_esEs6(Just(zxw4000), Nothing, eh) → False
new_primEqNat0(Succ(zxw40000), Succ(zxw30000)) → new_primEqNat0(zxw40000, zxw30000)
new_esEs16(Double(zxw4000, zxw4001), Double(zxw3000, zxw3001)) → new_esEs11(new_sr(zxw4000, zxw3000), new_sr(zxw4001, zxw3001))
new_lt19(zxw79000, zxw80000, ty_@0) → new_lt7(zxw79000, zxw80000)
new_esEs30(zxw400, zxw300, app(ty_Ratio, dae)) → new_esEs18(zxw400, zxw300, dae)
new_ltEs5(zxw79001, zxw80001, app(ty_Maybe, eg)) → new_ltEs18(zxw79001, zxw80001, eg)
new_esEs17(Float(zxw4000, zxw4001), Float(zxw3000, zxw3001)) → new_esEs11(new_sr(zxw4000, zxw3000), new_sr(zxw4001, zxw3001))
new_primCompAux00(zxw276, LT) → LT
new_esEs28(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), app(ty_Ratio, bde), bdf) → new_esEs18(zxw4000, zxw3000, bde)
new_esEs21(zxw4001, zxw3001, ty_Int) → new_esEs11(zxw4001, zxw3001)
new_compare1(:(zxw79000, zxw79001), :(zxw80000, zxw80001), he) → new_primCompAux0(zxw79000, zxw80000, new_compare1(zxw79001, zxw80001, he), he)
new_primEqInt(Pos(Zero), Pos(Succ(zxw30000))) → False
new_primEqInt(Pos(Succ(zxw40000)), Pos(Zero)) → False
new_compare29(zxw79000, zxw80000, ty_Int) → new_compare16(zxw79000, zxw80000)
new_lt20(zxw79001, zxw80001, app(ty_Ratio, bhf)) → new_lt17(zxw79001, zxw80001, bhf)
new_ltEs20(zxw7900, zxw8000, ty_Integer) → new_ltEs13(zxw7900, zxw8000)
new_esEs31(zxw35, zxw30, app(app(ty_@2, bcf), bcg)) → new_esEs5(zxw35, zxw30, bcf, bcg)
new_esEs5(@2(zxw4000, zxw4001), @2(zxw3000, zxw3001), ccf, ccg) → new_asAs(new_esEs22(zxw4000, zxw3000, ccf), new_esEs21(zxw4001, zxw3001, ccg))
new_ltEs18(Nothing, Nothing, baa) → True
new_esEs32(zxw20, zxw15, app(ty_Maybe, cdg)) → new_esEs6(zxw20, zxw15, cdg)
new_ltEs21(zxw79002, zxw80002, app(ty_Ratio, cah)) → new_ltEs17(zxw79002, zxw80002, cah)
new_esEs23(zxw4000, zxw3000, app(app(ty_@2, def), deg)) → new_esEs5(zxw4000, zxw3000, def, deg)
new_esEs20(zxw79000, zxw80000, app(app(app(ty_@3, gd), ge), gf)) → new_esEs4(zxw79000, zxw80000, gd, ge, gf)
new_esEs29(zxw400, zxw300, app(app(app(ty_@3, cch), cda), cdb)) → new_esEs4(zxw400, zxw300, cch, cda, cdb)
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_ltEs21(zxw79002, zxw80002, app(app(app(ty_@3, bhh), caa), cab)) → new_ltEs6(zxw79002, zxw80002, bhh, caa, cab)
new_ltEs10(zxw7900, zxw8000) → new_fsEs(new_compare17(zxw7900, zxw8000))
new_compare17(Char(zxw79000), Char(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_sr0(Integer(zxw800000), Integer(zxw790010)) → Integer(new_primMulInt(zxw800000, zxw790010))
new_ltEs5(zxw79001, zxw80001, ty_Double) → new_ltEs15(zxw79001, zxw80001)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_esEs29(zxw400, zxw300, app(ty_Ratio, ccd)) → new_esEs18(zxw400, zxw300, ccd)
new_esEs8(zxw79000, zxw80000, app(app(ty_Either, db), dc)) → new_esEs7(zxw79000, zxw80000, db, dc)
new_primEqInt(Neg(Succ(zxw40000)), Pos(zxw3000)) → False
new_primEqInt(Pos(Succ(zxw40000)), Neg(zxw3000)) → False
new_compare29(zxw79000, zxw80000, ty_Integer) → new_compare32(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Char) → new_ltEs10(zxw79000, zxw80000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_@0, bdf) → new_esEs10(zxw4000, zxw3000)
new_lt19(zxw79000, zxw80000, app(app(app(ty_@3, gd), ge), gf)) → new_lt5(zxw79000, zxw80000, gd, ge, gf)
new_esEs29(zxw400, zxw300, app(app(ty_@2, ccf), ccg)) → new_esEs5(zxw400, zxw300, ccf, ccg)
new_esEs32(zxw20, zxw15, app(app(ty_@2, cdh), cea)) → new_esEs5(zxw20, zxw15, cdh, cea)
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_esEs28(zxw4000, zxw3000, app(ty_Maybe, eae)) → new_esEs6(zxw4000, zxw3000, eae)
new_ltEs21(zxw79002, zxw80002, ty_@0) → new_ltEs8(zxw79002, zxw80002)
new_esEs21(zxw4001, zxw3001, app(ty_[], dbh)) → new_esEs13(zxw4001, zxw3001, dbh)
new_primEqInt(Neg(Zero), Pos(Succ(zxw30000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(zxw30000))) → False
new_ltEs7(EQ, GT) → True
new_lt4(zxw79000, zxw80000, ty_Double) → new_lt15(zxw79000, zxw80000)
new_esEs21(zxw4001, zxw3001, ty_Integer) → new_esEs15(zxw4001, zxw3001)
new_esEs31(zxw35, zxw30, ty_Integer) → new_esEs15(zxw35, zxw30)
new_primCompAux00(zxw276, EQ) → zxw276
new_esEs28(zxw4000, zxw3000, app(app(ty_Either, eah), eba)) → new_esEs7(zxw4000, zxw3000, eah, eba)
new_compare24(zxw79000, zxw80000, True) → EQ
new_compare6(Double(zxw79000, zxw79001), Double(zxw80000, zxw80001)) → new_compare16(new_sr(zxw79000, zxw80000), new_sr(zxw79001, zxw80001))
new_esEs8(zxw79000, zxw80000, ty_@0) → new_esEs10(zxw79000, zxw80000)
new_ltEs5(zxw79001, zxw80001, app(app(ty_Either, ed), ee)) → new_ltEs14(zxw79001, zxw80001, ed, ee)
new_lt13(zxw79000, zxw80000) → new_esEs9(new_compare32(zxw79000, zxw80000), LT)
new_esEs27(zxw4001, zxw3001, ty_Double) → new_esEs16(zxw4001, zxw3001)
new_esEs7(Left(zxw4000), Left(zxw3000), app(app(app(ty_@3, bee), bef), beg), bdf) → new_esEs4(zxw4000, zxw3000, bee, bef, beg)
new_esEs26(zxw4002, zxw3002, app(app(ty_@2, dgb), dgc)) → new_esEs5(zxw4002, zxw3002, dgb, dgc)
new_esEs21(zxw4001, zxw3001, app(app(ty_@2, dcb), dcc)) → new_esEs5(zxw4001, zxw3001, dcb, dcc)
new_esEs30(zxw400, zxw300, ty_@0) → new_esEs10(zxw400, zxw300)
new_lt19(zxw79000, zxw80000, app(ty_Maybe, bbh)) → new_lt18(zxw79000, zxw80000, bbh)
new_esEs12(Char(zxw4000), Char(zxw3000)) → new_primEqNat0(zxw4000, zxw3000)
new_ltEs20(zxw7900, zxw8000, app(app(app(ty_@3, bab), bac), bad)) → new_ltEs6(zxw7900, zxw8000, bab, bac, bad)
new_not(False) → True
new_lt20(zxw79001, zxw80001, ty_Char) → new_lt9(zxw79001, zxw80001)
new_esEs11(zxw400, zxw300) → new_primEqInt(zxw400, zxw300)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(ty_Maybe, chb)) → new_ltEs18(zxw79000, zxw80000, chb)
new_ltEs18(Just(zxw79000), Nothing, baa) → False
new_esEs8(zxw79000, zxw80000, app(ty_Maybe, de)) → new_esEs6(zxw79000, zxw80000, de)
new_esEs7(Left(zxw4000), Left(zxw3000), app(ty_Maybe, bdh), bdf) → new_esEs6(zxw4000, zxw3000, bdh)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Double, bdf) → new_esEs16(zxw4000, zxw3000)
new_compare210(zxw79000, zxw80000, True, bbd, bbe) → EQ
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_esEs19(zxw79001, zxw80001, ty_Int) → new_esEs11(zxw79001, zxw80001)
new_compare12(zxw79000, zxw80000, False, gd, ge, gf) → GT
new_ltEs16(zxw7900, zxw8000) → new_fsEs(new_compare7(zxw7900, zxw8000))
new_esEs32(zxw20, zxw15, ty_Char) → new_esEs12(zxw20, zxw15)
new_esEs9(GT, GT) → True
new_esEs26(zxw4002, zxw3002, app(ty_Ratio, dfg)) → new_esEs18(zxw4002, zxw3002, dfg)
new_esEs25(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_lt20(zxw79001, zxw80001, app(ty_[], bha)) → new_lt10(zxw79001, zxw80001, bha)
new_lt4(zxw79000, zxw80000, app(app(ty_Either, db), dc)) → new_lt14(zxw79000, zxw80000, db, dc)
new_esEs26(zxw4002, zxw3002, ty_Bool) → new_esEs14(zxw4002, zxw3002)
new_compare19(zxw79000, zxw80000, bbd, bbe) → new_compare210(zxw79000, zxw80000, new_esEs5(zxw79000, zxw80000, bbd, bbe), bbd, bbe)
new_esEs8(zxw79000, zxw80000, ty_Bool) → new_esEs14(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Double) → new_ltEs15(zxw79000, zxw80000)
new_esEs28(zxw4000, zxw3000, app(app(ty_@2, eaf), eag)) → new_esEs5(zxw4000, zxw3000, eaf, eag)
new_ltEs19(zxw7900, zxw8000, app(app(app(ty_@3, hb), hc), hd)) → new_ltEs6(zxw7900, zxw8000, hb, hc, hd)
new_esEs32(zxw20, zxw15, app(app(app(ty_@3, ced), cee), cef)) → new_esEs4(zxw20, zxw15, ced, cee, cef)
new_lt4(zxw79000, zxw80000, ty_Char) → new_lt9(zxw79000, zxw80000)
new_esEs22(zxw4000, zxw3000, app(app(app(ty_@3, ddh), dea), deb)) → new_esEs4(zxw4000, zxw3000, ddh, dea, deb)
new_esEs22(zxw4000, zxw3000, app(ty_[], ddb)) → new_esEs13(zxw4000, zxw3000, ddb)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_@0) → new_ltEs8(zxw79000, zxw80000)
new_esEs23(zxw4000, zxw3000, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Float, bdf) → new_esEs17(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_esEs27(zxw4001, zxw3001, ty_Int) → new_esEs11(zxw4001, zxw3001)
new_esEs19(zxw79001, zxw80001, app(app(app(ty_@3, bgf), bgg), bgh)) → new_esEs4(zxw79001, zxw80001, bgf, bgg, bgh)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_ltEs14(Left(zxw79000), Left(zxw80000), app(app(app(ty_@3, ceg), ceh), cfa), hg) → new_ltEs6(zxw79000, zxw80000, ceg, ceh, cfa)
new_ltEs19(zxw7900, zxw8000, ty_Int) → new_ltEs9(zxw7900, zxw8000)
new_compare33(zxw20, zxw15, cdc, cdd) → new_compare26(Left(zxw20), Left(zxw15), new_esEs32(zxw20, zxw15, cdc), cdc, cdd)
new_lt4(zxw79000, zxw80000, ty_@0) → new_lt7(zxw79000, zxw80000)
new_lt20(zxw79001, zxw80001, ty_Double) → new_lt15(zxw79001, zxw80001)
new_lt19(zxw79000, zxw80000, ty_Float) → new_lt16(zxw79000, zxw80000)
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_esEs26(zxw4002, zxw3002, ty_@0) → new_esEs10(zxw4002, zxw3002)
new_esEs30(zxw400, zxw300, app(app(ty_@2, dah), dba)) → new_esEs5(zxw400, zxw300, dah, dba)
new_lt19(zxw79000, zxw80000, ty_Bool) → new_lt12(zxw79000, zxw80000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Char, bdf) → new_esEs12(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_lt4(zxw79000, zxw80000, ty_Float) → new_lt16(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(ty_[], chf)) → new_ltEs11(zxw79000, zxw80000, chf)
new_primMulInt(Neg(zxw40000), Neg(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_ltEs5(zxw79001, zxw80001, app(app(app(ty_@3, df), dg), dh)) → new_ltEs6(zxw79001, zxw80001, df, dg, dh)
new_primCmpNat2(Zero, Zero) → EQ
new_esEs20(zxw79000, zxw80000, ty_Integer) → new_esEs15(zxw79000, zxw80000)
new_primEqNat0(Zero, Succ(zxw30000)) → False
new_primEqNat0(Succ(zxw40000), Zero) → False
new_esEs21(zxw4001, zxw3001, ty_@0) → new_esEs10(zxw4001, zxw3001)
new_esEs22(zxw4000, zxw3000, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_esEs20(zxw79000, zxw80000, ty_Bool) → new_esEs14(zxw79000, zxw80000)
new_ltEs5(zxw79001, zxw80001, app(ty_[], ea)) → new_ltEs11(zxw79001, zxw80001, ea)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs23(zxw4000, zxw3000, app(ty_Ratio, dec)) → new_esEs18(zxw4000, zxw3000, dec)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(app(ty_@2, chg), chh)) → new_ltEs4(zxw79000, zxw80000, chg, chh)
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_ltEs5(zxw79001, zxw80001, ty_Int) → new_ltEs9(zxw79001, zxw80001)
new_esEs27(zxw4001, zxw3001, app(app(ty_@2, dhd), dhe)) → new_esEs5(zxw4001, zxw3001, dhd, dhe)
new_primCmpNat0(zxw7900, Zero) → GT
new_compare26(Right(zxw7900), Left(zxw8000), False, gh, ha) → GT
new_esEs23(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_@0, hg) → new_ltEs8(zxw79000, zxw80000)
new_ltEs21(zxw79002, zxw80002, app(ty_Maybe, cba)) → new_ltEs18(zxw79002, zxw80002, cba)
new_esEs21(zxw4001, zxw3001, app(app(ty_Either, dcd), dce)) → new_esEs7(zxw4001, zxw3001, dcd, dce)
new_esEs22(zxw4000, zxw3000, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Bool) → new_ltEs12(zxw79000, zxw80000)
new_compare29(zxw79000, zxw80000, app(ty_Maybe, ccc)) → new_compare27(zxw79000, zxw80000, ccc)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_ltEs14(Left(zxw79000), Left(zxw80000), app(ty_Maybe, cfh), hg) → new_ltEs18(zxw79000, zxw80000, cfh)
new_lt20(zxw79001, zxw80001, ty_Float) → new_lt16(zxw79001, zxw80001)
new_lt17(zxw79000, zxw80000, gg) → new_esEs9(new_compare8(zxw79000, zxw80000, gg), LT)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Ordering) → new_ltEs7(zxw79000, zxw80000)
new_esEs32(zxw20, zxw15, ty_Int) → new_esEs11(zxw20, zxw15)
new_compare30(@0, @0) → EQ
new_lt19(zxw79000, zxw80000, app(ty_[], bgc)) → new_lt10(zxw79000, zxw80000, bgc)
new_esEs21(zxw4001, zxw3001, app(app(app(ty_@3, dcf), dcg), dch)) → new_esEs4(zxw4001, zxw3001, dcf, dcg, dch)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_esEs20(zxw79000, zxw80000, app(ty_Ratio, gg)) → new_esEs18(zxw79000, zxw80000, gg)
new_esEs6(Just(zxw4000), Just(zxw3000), app(app(app(ty_@3, ga), gb), gc)) → new_esEs4(zxw4000, zxw3000, ga, gb, gc)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(app(ty_Either, daa), dab)) → new_ltEs14(zxw79000, zxw80000, daa, dab)
new_esEs24(zxw4001, zxw3001, ty_Int) → new_esEs11(zxw4001, zxw3001)
new_esEs8(zxw79000, zxw80000, ty_Ordering) → new_esEs9(zxw79000, zxw80000)
new_esEs30(zxw400, zxw300, ty_Ordering) → new_esEs9(zxw400, zxw300)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Ordering) → new_ltEs7(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, app(app(ty_Either, bgd), bge)) → new_esEs7(zxw79000, zxw80000, bgd, bge)
new_compare29(zxw79000, zxw80000, app(ty_Ratio, ccb)) → new_compare8(zxw79000, zxw80000, ccb)
new_lt4(zxw79000, zxw80000, app(app(ty_@2, cg), da)) → new_lt11(zxw79000, zxw80000, cg, da)
new_compare29(zxw79000, zxw80000, ty_Float) → new_compare7(zxw79000, zxw80000)
new_esEs19(zxw79001, zxw80001, app(app(ty_@2, bhb), bhc)) → new_esEs5(zxw79001, zxw80001, bhb, bhc)
new_esEs10(@0, @0) → True
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_compare29(zxw79000, zxw80000, ty_Double) → new_compare6(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, app(ty_Maybe, bbh)) → new_esEs6(zxw79000, zxw80000, bbh)
new_ltEs14(Left(zxw79000), Right(zxw80000), hf, hg) → True
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Float) → new_ltEs16(zxw79000, zxw80000)
new_esEs28(zxw4000, zxw3000, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_compare29(zxw79000, zxw80000, app(app(ty_Either, cbh), cca)) → new_compare15(zxw79000, zxw80000, cbh, cca)
new_esEs19(zxw79001, zxw80001, ty_Double) → new_esEs16(zxw79001, zxw80001)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs30(zxw400, zxw300, ty_Bool) → new_esEs14(zxw400, zxw300)
new_ltEs20(zxw7900, zxw8000, app(app(ty_Either, bah), bba)) → new_ltEs14(zxw7900, zxw8000, bah, bba)
new_asAs(False, zxw230) → False
new_ltEs13(zxw7900, zxw8000) → new_fsEs(new_compare32(zxw7900, zxw8000))
new_ltEs19(zxw7900, zxw8000, app(app(ty_Either, hf), hg)) → new_ltEs14(zxw7900, zxw8000, hf, hg)
new_compare34(zxw400, zxw300, h, ba) → new_compare26(Left(zxw400), Right(zxw300), False, h, ba)
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Pos(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_ltEs20(zxw7900, zxw8000, app(ty_[], bae)) → new_ltEs11(zxw7900, zxw8000, bae)
new_compare16(zxw79, zxw80) → new_primCmpInt(zxw79, zxw80)
new_esEs29(zxw400, zxw300, ty_Char) → new_esEs12(zxw400, zxw300)
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_esEs13(:(zxw4000, zxw4001), [], cce) → False
new_esEs13([], :(zxw3000, zxw3001), cce) → False
new_compare25(zxw79000, zxw80000, False, gd, ge, gf) → new_compare12(zxw79000, zxw80000, new_ltEs6(zxw79000, zxw80000, gd, ge, gf), gd, ge, gf)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(app(ty_@2, cfc), cfd), hg) → new_ltEs4(zxw79000, zxw80000, cfc, cfd)
new_esEs6(Just(zxw4000), Just(zxw3000), app(ty_Maybe, fc)) → new_esEs6(zxw4000, zxw3000, fc)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_@0) → new_esEs10(zxw4000, zxw3000)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(ty_[], cfb), hg) → new_ltEs11(zxw79000, zxw80000, cfb)
new_esEs7(Left(zxw4000), Left(zxw3000), app(ty_[], bdg), bdf) → new_esEs13(zxw4000, zxw3000, bdg)
new_esEs29(zxw400, zxw300, ty_Int) → new_esEs11(zxw400, zxw300)
new_esEs31(zxw35, zxw30, ty_Double) → new_esEs16(zxw35, zxw30)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_compare31(zxw79000, zxw80000) → new_compare23(zxw79000, zxw80000, new_esEs14(zxw79000, zxw80000))
new_ltEs18(Nothing, Just(zxw80000), baa) → True
new_esEs28(zxw4000, zxw3000, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_ltEs21(zxw79002, zxw80002, ty_Double) → new_ltEs15(zxw79002, zxw80002)
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_ltEs12(True, True) → True
new_esEs23(zxw4000, zxw3000, app(ty_Maybe, dee)) → new_esEs6(zxw4000, zxw3000, dee)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_esEs8(zxw79000, zxw80000, ty_Integer) → new_esEs15(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(app(ty_Either, cgg), cgh)) → new_ltEs14(zxw79000, zxw80000, cgg, cgh)
new_ltEs6(@3(zxw79000, zxw79001, zxw79002), @3(zxw80000, zxw80001, zxw80002), hb, hc, hd) → new_pePe(new_lt19(zxw79000, zxw80000, hb), new_asAs(new_esEs20(zxw79000, zxw80000, hb), new_pePe(new_lt20(zxw79001, zxw80001, hc), new_asAs(new_esEs19(zxw79001, zxw80001, hc), new_ltEs21(zxw79002, zxw80002, hd)))))
new_esEs28(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_lt16(zxw79000, zxw80000) → new_esEs9(new_compare7(zxw79000, zxw80000), LT)
new_esEs23(zxw4000, zxw3000, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Integer, hg) → new_ltEs13(zxw79000, zxw80000)
new_ltEs12(False, True) → True
new_esEs23(zxw4000, zxw3000, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs8(zxw79000, zxw80000, app(ty_Ratio, dd)) → new_esEs18(zxw79000, zxw80000, dd)
new_esEs23(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs14(True, True) → True
new_compare111(zxw79000, zxw80000, False, bbh) → GT
new_esEs31(zxw35, zxw30, app(ty_[], bcd)) → new_esEs13(zxw35, zxw30, bcd)
new_esEs27(zxw4001, zxw3001, ty_Bool) → new_esEs14(zxw4001, zxw3001)
new_esEs20(zxw79000, zxw80000, ty_Ordering) → new_esEs9(zxw79000, zxw80000)
new_ltEs19(zxw7900, zxw8000, ty_@0) → new_ltEs8(zxw7900, zxw8000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Int) → new_ltEs9(zxw79000, zxw80000)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(app(ty_Either, cfe), cff), hg) → new_ltEs14(zxw79000, zxw80000, cfe, cff)
new_lt19(zxw79000, zxw80000, ty_Integer) → new_lt13(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, ty_Float) → new_esEs17(zxw79000, zxw80000)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Ordering, hg) → new_ltEs7(zxw79000, zxw80000)
new_compare11(zxw79000, zxw80000, False) → GT
new_esEs4(@3(zxw4000, zxw4001, zxw4002), @3(zxw3000, zxw3001, zxw3002), cch, cda, cdb) → new_asAs(new_esEs28(zxw4000, zxw3000, cch), new_asAs(new_esEs27(zxw4001, zxw3001, cda), new_esEs26(zxw4002, zxw3002, cdb)))
new_esEs6(Just(zxw4000), Just(zxw3000), app(ty_[], fb)) → new_esEs13(zxw4000, zxw3000, fb)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Int) → new_ltEs9(zxw79000, zxw80000)
new_esEs9(EQ, LT) → False
new_esEs9(LT, EQ) → False
new_compare26(Right(zxw7900), Right(zxw8000), False, gh, ha) → new_compare14(zxw7900, zxw8000, new_ltEs20(zxw7900, zxw8000, ha), gh, ha)
new_compare11(zxw79000, zxw80000, True) → LT
new_ltEs5(zxw79001, zxw80001, ty_@0) → new_ltEs8(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, ty_Bool) → new_lt12(zxw79001, zxw80001)
new_esEs30(zxw400, zxw300, ty_Integer) → new_esEs15(zxw400, zxw300)
new_compare14(zxw242, zxw243, True, dfe, dff) → LT
new_esEs32(zxw20, zxw15, app(ty_Ratio, cde)) → new_esEs18(zxw20, zxw15, cde)
new_esEs29(zxw400, zxw300, app(app(ty_Either, beh), bdf)) → new_esEs7(zxw400, zxw300, beh, bdf)
new_esEs14(False, False) → True
new_esEs18(:%(zxw4000, zxw4001), :%(zxw3000, zxw3001), ccd) → new_asAs(new_esEs25(zxw4000, zxw3000, ccd), new_esEs24(zxw4001, zxw3001, ccd))
new_compare26(Left(zxw7900), Left(zxw8000), False, gh, ha) → new_compare13(zxw7900, zxw8000, new_ltEs19(zxw7900, zxw8000, gh), gh, ha)
new_ltEs19(zxw7900, zxw8000, ty_Double) → new_ltEs15(zxw7900, zxw8000)
new_ltEs7(EQ, LT) → False
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Char) → new_esEs12(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_ltEs7(LT, LT) → True
new_lt20(zxw79001, zxw80001, app(app(app(ty_@3, bgf), bgg), bgh)) → new_lt5(zxw79001, zxw80001, bgf, bgg, bgh)
new_esEs29(zxw400, zxw300, ty_@0) → new_esEs10(zxw400, zxw300)
new_lt14(zxw790, zxw800, gh, ha) → new_esEs9(new_compare15(zxw790, zxw800, gh, ha), LT)
new_esEs22(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_ltEs9(zxw7900, zxw8000) → new_fsEs(new_compare16(zxw7900, zxw8000))
new_compare29(zxw79000, zxw80000, ty_Ordering) → new_compare18(zxw79000, zxw80000)
new_primPlusNat1(Zero, Zero) → Zero
new_esEs26(zxw4002, zxw3002, ty_Ordering) → new_esEs9(zxw4002, zxw3002)
new_esEs19(zxw79001, zxw80001, ty_Integer) → new_esEs15(zxw79001, zxw80001)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Char, hg) → new_ltEs10(zxw79000, zxw80000)
new_asAs(True, zxw230) → zxw230
new_esEs25(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_ltEs7(LT, GT) → True
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Float) → new_esEs17(zxw4000, zxw3000)
new_ltEs5(zxw79001, zxw80001, ty_Float) → new_ltEs16(zxw79001, zxw80001)
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, app(ty_Ratio, bfa)) → new_esEs18(zxw4000, zxw3000, bfa)
new_esEs27(zxw4001, zxw3001, app(ty_[], dhb)) → new_esEs13(zxw4001, zxw3001, dhb)
new_esEs6(Just(zxw4000), Just(zxw3000), app(app(ty_Either, fg), fh)) → new_esEs7(zxw4000, zxw3000, fg, fh)
new_esEs32(zxw20, zxw15, ty_Double) → new_esEs16(zxw20, zxw15)
new_compare28(zxw79000, zxw80000, False, bbh) → new_compare111(zxw79000, zxw80000, new_ltEs18(zxw79000, zxw80000, bbh), bbh)
new_compare1(:(zxw79000, zxw79001), [], he) → GT
new_esEs28(zxw4000, zxw3000, app(ty_Ratio, eac)) → new_esEs18(zxw4000, zxw3000, eac)
new_lt4(zxw79000, zxw80000, ty_Integer) → new_lt13(zxw79000, zxw80000)
new_esEs30(zxw400, zxw300, ty_Int) → new_esEs11(zxw400, zxw300)
new_esEs19(zxw79001, zxw80001, ty_@0) → new_esEs10(zxw79001, zxw80001)
new_compare29(zxw79000, zxw80000, ty_@0) → new_compare30(zxw79000, zxw80000)
new_ltEs19(zxw7900, zxw8000, ty_Integer) → new_ltEs13(zxw7900, zxw8000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(ty_Ratio, cha)) → new_ltEs17(zxw79000, zxw80000, cha)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Integer) → new_ltEs13(zxw79000, zxw80000)
new_ltEs19(zxw7900, zxw8000, ty_Ordering) → new_ltEs7(zxw7900, zxw8000)
new_compare28(zxw79000, zxw80000, True, bbh) → EQ
new_esEs31(zxw35, zxw30, ty_Int) → new_esEs11(zxw35, zxw30)
new_esEs26(zxw4002, zxw3002, ty_Double) → new_esEs16(zxw4002, zxw3002)
new_esEs30(zxw400, zxw300, ty_Double) → new_esEs16(zxw400, zxw300)
new_esEs29(zxw400, zxw300, ty_Float) → new_esEs17(zxw400, zxw300)
new_compare10(zxw79000, zxw80000, True) → LT
new_esEs31(zxw35, zxw30, ty_Bool) → new_esEs14(zxw35, zxw30)
new_esEs19(zxw79001, zxw80001, app(ty_[], bha)) → new_esEs13(zxw79001, zxw80001, bha)
new_esEs29(zxw400, zxw300, ty_Bool) → new_esEs14(zxw400, zxw300)
new_compare10(zxw79000, zxw80000, False) → GT
new_esEs9(LT, LT) → True
new_ltEs20(zxw7900, zxw8000, ty_Char) → new_ltEs10(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, ty_Ordering) → new_ltEs7(zxw7900, zxw8000)
new_primCompAux00(zxw276, GT) → GT
new_esEs31(zxw35, zxw30, app(ty_Maybe, bce)) → new_esEs6(zxw35, zxw30, bce)
new_compare18(zxw79000, zxw80000) → new_compare24(zxw79000, zxw80000, new_esEs9(zxw79000, zxw80000))
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_@0) → new_ltEs8(zxw79000, zxw80000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs7(Right(zxw4000), Right(zxw3000), beh, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_esEs29(zxw400, zxw300, ty_Ordering) → new_esEs9(zxw400, zxw300)
new_lt19(zxw79000, zxw80000, ty_Char) → new_lt9(zxw79000, zxw80000)
new_esEs28(zxw4000, zxw3000, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_ltEs19(zxw7900, zxw8000, app(ty_Maybe, baa)) → new_ltEs18(zxw7900, zxw8000, baa)
new_esEs27(zxw4001, zxw3001, ty_Integer) → new_esEs15(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, app(ty_Ratio, dbg)) → new_esEs18(zxw4001, zxw3001, dbg)
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_esEs19(zxw79001, zxw80001, ty_Char) → new_esEs12(zxw79001, zxw80001)
new_esEs23(zxw4000, zxw3000, app(ty_[], ded)) → new_esEs13(zxw4000, zxw3000, ded)
new_ltEs17(zxw7900, zxw8000, hh) → new_fsEs(new_compare8(zxw7900, zxw8000, hh))
new_not(True) → False
new_ltEs4(@2(zxw79000, zxw79001), @2(zxw80000, zxw80001), ca, cb) → new_pePe(new_lt4(zxw79000, zxw80000, ca), new_asAs(new_esEs8(zxw79000, zxw80000, ca), new_ltEs5(zxw79001, zxw80001, cb)))
new_compare1([], [], he) → EQ
new_esEs6(Just(zxw4000), Just(zxw3000), app(ty_Ratio, fa)) → new_esEs18(zxw4000, zxw3000, fa)

The set Q consists of the following terms:

new_compare23(x0, x1, True)
new_lt6(x0, x1)
new_ltEs5(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, ty_Integer)
new_lt4(x0, x1, app(ty_[], x2))
new_ltEs18(Just(x0), Just(x1), ty_@0)
new_compare16(x0, x1)
new_lt4(x0, x1, app(app(ty_@2, x2), x3))
new_compare13(x0, x1, False, x2, x3)
new_ltEs18(Just(x0), Nothing, x1)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, ty_Double)
new_esEs19(x0, x1, ty_Bool)
new_esEs8(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(x0, x1, app(app(ty_Either, x2), x3))
new_compare30(@0, @0)
new_primCompAux00(x0, GT)
new_esEs30(x0, x1, ty_@0)
new_lt19(x0, x1, ty_Char)
new_esEs30(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_Ordering)
new_compare17(Char(x0), Char(x1))
new_esEs28(x0, x1, ty_Int)
new_ltEs20(x0, x1, app(ty_[], x2))
new_ltEs21(x0, x1, ty_Ordering)
new_ltEs15(x0, x1)
new_primPlusNat1(Zero, Succ(x0))
new_esEs6(Just(x0), Just(x1), ty_Double)
new_compare24(x0, x1, False)
new_lt20(x0, x1, ty_Char)
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, ty_Bool)
new_sr0(Integer(x0), Integer(x1))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare210(x0, x1, False, x2, x3)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs7(Right(x0), Right(x1), x2, ty_Float)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs18(Nothing, Nothing, x0)
new_ltEs7(EQ, EQ)
new_esEs7(Right(x0), Right(x1), x2, ty_Integer)
new_compare29(x0, x1, app(app(ty_@2, x2), x3))
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs19(x0, x1, ty_Integer)
new_ltEs20(x0, x1, ty_Bool)
new_ltEs14(Right(x0), Right(x1), x2, ty_Float)
new_esEs6(Just(x0), Just(x1), app(ty_[], x2))
new_esEs31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_compare25(x0, x1, False, x2, x3, x4)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_ltEs19(x0, x1, ty_Integer)
new_ltEs5(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(ty_[], x2))
new_lt10(x0, x1, x2)
new_ltEs7(EQ, LT)
new_ltEs7(LT, EQ)
new_esEs20(x0, x1, ty_Ordering)
new_esEs17(Float(x0, x1), Float(x2, x3))
new_compare25(x0, x1, True, x2, x3, x4)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_lt19(x0, x1, ty_Ordering)
new_esEs29(x0, x1, ty_@0)
new_esEs26(x0, x1, app(ty_[], x2))
new_ltEs16(x0, x1)
new_lt4(x0, x1, app(ty_Maybe, x2))
new_compare110(x0, x1, False, x2, x3)
new_ltEs14(Left(x0), Left(x1), ty_Char, x2)
new_sr(x0, x1)
new_ltEs19(x0, x1, ty_Double)
new_compare7(Float(x0, x1), Float(x2, x3))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs9(x0, x1)
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_lt7(x0, x1)
new_lt4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, ty_Int)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat0(Zero, x0)
new_esEs7(Right(x0), Right(x1), x2, ty_@0)
new_esEs32(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_ltEs7(LT, LT)
new_esEs7(Right(x0), Right(x1), x2, ty_Double)
new_esEs4(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_Bool)
new_lt5(x0, x1, x2, x3, x4)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt4(x0, x1, ty_Ordering)
new_primEqNat0(Zero, Succ(x0))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Int)
new_esEs15(Integer(x0), Integer(x1))
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Left(x0), Left(x1), ty_Char, x2)
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs26(x0, x1, ty_Double)
new_compare29(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_@0)
new_primPlusNat1(Succ(x0), Zero)
new_esEs22(x0, x1, ty_Integer)
new_ltEs14(Left(x0), Left(x1), ty_@0, x2)
new_primMulInt(Neg(x0), Neg(x1))
new_ltEs19(x0, x1, ty_Int)
new_ltEs21(x0, x1, app(ty_Maybe, x2))
new_compare29(x0, x1, ty_Integer)
new_esEs14(True, True)
new_esEs21(x0, x1, ty_Char)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Int)
new_ltEs18(Just(x0), Just(x1), ty_Integer)
new_esEs24(x0, x1, ty_Int)
new_primEqNat0(Zero, Zero)
new_esEs16(Double(x0, x1), Double(x2, x3))
new_esEs12(Char(x0), Char(x1))
new_lt4(x0, x1, ty_Char)
new_compare29(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, ty_Bool)
new_esEs8(x0, x1, ty_Float)
new_compare1([], :(x0, x1), x2)
new_esEs30(x0, x1, ty_Ordering)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, ty_Integer)
new_esEs29(x0, x1, ty_Bool)
new_esEs30(x0, x1, ty_Bool)
new_esEs30(x0, x1, ty_Float)
new_esEs32(x0, x1, ty_@0)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs14(Left(x0), Left(x1), ty_Int, x2)
new_primCompAux00(x0, LT)
new_esEs27(x0, x1, ty_Integer)
new_ltEs21(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs5(x0, x1, ty_Double)
new_ltEs18(Just(x0), Just(x1), ty_Char)
new_primMulNat0(Zero, Zero)
new_compare110(x0, x1, True, x2, x3)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_lt9(x0, x1)
new_compare29(x0, x1, ty_Double)
new_ltEs5(x0, x1, ty_@0)
new_lt17(x0, x1, x2)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_compare36(x0, x1, x2, x3)
new_ltEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs31(x0, x1, ty_Bool)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Left(x0), Left(x1), ty_Float, x2)
new_esEs32(x0, x1, ty_Float)
new_esEs13([], :(x0, x1), x2)
new_esEs8(x0, x1, ty_Ordering)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_compare10(x0, x1, True)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs7(Left(x0), Left(x1), ty_Float, x2)
new_primEqNat0(Succ(x0), Succ(x1))
new_ltEs19(x0, x1, ty_Bool)
new_esEs28(x0, x1, ty_Double)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, ty_Float)
new_esEs29(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_@0)
new_pePe(True, x0)
new_esEs19(x0, x1, ty_Float)
new_esEs8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_lt16(x0, x1)
new_compare29(x0, x1, ty_Bool)
new_esEs20(x0, x1, app(ty_[], x2))
new_compare11(x0, x1, True)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_compare14(x0, x1, True, x2, x3)
new_esEs6(Just(x0), Just(x1), app(ty_Maybe, x2))
new_lt19(x0, x1, ty_@0)
new_esEs6(Just(x0), Just(x1), ty_Ordering)
new_esEs23(x0, x1, ty_@0)
new_compare29(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Right(x0), Right(x1), x2, ty_Int)
new_ltEs5(x0, x1, ty_Char)
new_esEs30(x0, x1, ty_Double)
new_ltEs21(x0, x1, ty_Int)
new_compare29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Float)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_compare29(x0, x1, ty_Ordering)
new_ltEs21(x0, x1, ty_@0)
new_esEs8(x0, x1, ty_Int)
new_lt14(x0, x1, x2, x3)
new_ltEs12(False, False)
new_esEs6(Just(x0), Just(x1), ty_Bool)
new_compare32(Integer(x0), Integer(x1))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_Int)
new_primMulNat0(Succ(x0), Succ(x1))
new_compare29(x0, x1, ty_Float)
new_ltEs21(x0, x1, ty_Integer)
new_esEs6(Just(x0), Just(x1), ty_Float)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs5(x0, x1, ty_Float)
new_ltEs18(Just(x0), Just(x1), ty_Float)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Bool)
new_esEs31(x0, x1, ty_Double)
new_esEs31(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpNat1(Zero, x0)
new_ltEs8(x0, x1)
new_esEs29(x0, x1, ty_Integer)
new_ltEs21(x0, x1, app(ty_[], x2))
new_primPlusNat1(Zero, Zero)
new_esEs30(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(ty_[], x2))
new_ltEs14(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs23(x0, x1, ty_Double)
new_ltEs18(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs18(Just(x0), Just(x1), ty_Ordering)
new_primCmpNat2(Zero, Zero)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs5(x0, x1, ty_Bool)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_compare28(x0, x1, True, x2)
new_ltEs14(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs5(x0, x1, app(ty_[], x2))
new_asAs(False, x0)
new_esEs29(x0, x1, ty_Ordering)
new_esEs31(x0, x1, app(ty_[], x2))
new_esEs30(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, ty_Char)
new_esEs31(x0, x1, app(app(ty_@2, x2), x3))
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(x0, x1, ty_Integer)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs19(x0, x1, app(ty_[], x2))
new_ltEs18(Just(x0), Just(x1), ty_Bool)
new_lt11(x0, x1, x2, x3)
new_primCmpNat1(Succ(x0), x1)
new_esEs32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs24(x0, x1, ty_Integer)
new_ltEs14(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs27(x0, x1, ty_@0)
new_ltEs14(Right(x0), Right(x1), x2, ty_Double)
new_lt4(x0, x1, ty_Float)
new_compare19(x0, x1, x2, x3)
new_ltEs5(x0, x1, app(app(ty_Either, x2), x3))
new_esEs19(x0, x1, ty_Char)
new_lt4(x0, x1, ty_Double)
new_esEs19(x0, x1, ty_Ordering)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs10(@0, @0)
new_esEs31(x0, x1, ty_@0)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs11(x0, x1)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, ty_Float)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_Char)
new_esEs9(GT, GT)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs27(x0, x1, ty_Char)
new_compare11(x0, x1, False)
new_compare23(x0, x1, False)
new_compare12(x0, x1, True, x2, x3, x4)
new_esEs28(x0, x1, ty_Bool)
new_esEs7(Right(x0), Left(x1), x2, x3)
new_esEs7(Left(x0), Right(x1), x2, x3)
new_compare24(x0, x1, True)
new_compare15(x0, x1, x2, x3)
new_primEqNat0(Succ(x0), Zero)
new_esEs23(x0, x1, ty_Ordering)
new_esEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs7(Right(x0), Right(x1), x2, ty_Int)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_esEs32(x0, x1, app(app(ty_Either, x2), x3))
new_compare9(x0, x1, x2, x3, x4)
new_lt20(x0, x1, ty_Int)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Integer)
new_lt4(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Int)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs5(x0, x1, app(app(ty_@2, x2), x3))
new_lt4(x0, x1, ty_@0)
new_esEs23(x0, x1, ty_Char)
new_esEs28(x0, x1, ty_Ordering)
new_ltEs18(Just(x0), Just(x1), ty_Double)
new_esEs30(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_Integer)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_compare14(x0, x1, False, x2, x3)
new_lt20(x0, x1, ty_@0)
new_compare1([], [], x0)
new_esEs9(EQ, EQ)
new_pePe(False, x0)
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs5(x0, x1, app(ty_Ratio, x2))
new_ltEs18(Just(x0), Just(x1), app(ty_[], x2))
new_esEs6(Just(x0), Just(x1), ty_Char)
new_esEs25(x0, x1, ty_Integer)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs18(:%(x0, x1), :%(x2, x3), x4)
new_esEs26(x0, x1, ty_Integer)
new_compare12(x0, x1, False, x2, x3, x4)
new_esEs8(x0, x1, app(ty_Maybe, x2))
new_primCompAux00(x0, EQ)
new_esEs19(x0, x1, ty_Int)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs14(True, False)
new_esEs14(False, True)
new_lt4(x0, x1, ty_Integer)
new_esEs7(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs14(Right(x0), Right(x1), x2, ty_@0)
new_fsEs(x0)
new_esEs22(x0, x1, ty_Float)
new_lt4(x0, x1, ty_Bool)
new_primCmpNat2(Succ(x0), Succ(x1))
new_asAs(True, x0)
new_ltEs18(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, ty_Bool)
new_esEs6(Nothing, Just(x0), x1)
new_esEs6(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs6(Just(x0), Nothing, x1)
new_lt18(x0, x1, x2)
new_esEs8(x0, x1, app(ty_[], x2))
new_esEs31(x0, x1, ty_Integer)
new_compare111(x0, x1, False, x2)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs8(x0, x1, ty_Char)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, ty_Float)
new_ltEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs22(x0, x1, ty_@0)
new_esEs20(x0, x1, ty_Char)
new_esEs13(:(x0, x1), [], x2)
new_ltEs12(False, True)
new_ltEs12(True, False)
new_compare6(Double(x0, x1), Double(x2, x3))
new_ltEs20(x0, x1, ty_@0)
new_esEs22(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_@0)
new_ltEs18(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare35(x0, x1, x2, x3)
new_ltEs14(Right(x0), Right(x1), x2, ty_Integer)
new_lt19(x0, x1, ty_Double)
new_esEs32(x0, x1, app(ty_[], x2))
new_lt19(x0, x1, ty_Bool)
new_ltEs14(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs7(Right(x0), Right(x1), x2, ty_Char)
new_ltEs14(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs26(x0, x1, ty_Char)
new_ltEs14(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs5(x0, x1, ty_Int)
new_lt4(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_Double)
new_esEs32(x0, x1, app(ty_Ratio, x2))
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_esEs19(x0, x1, ty_@0)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs21(x0, x1, ty_Bool)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs14(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs21(x0, x1, ty_Double)
new_lt12(x0, x1)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs8(x0, x1, ty_Bool)
new_ltEs21(x0, x1, ty_Char)
new_lt13(x0, x1)
new_esEs13(:(x0, x1), :(x2, x3), x4)
new_esEs31(x0, x1, ty_Ordering)
new_ltEs14(Right(x0), Right(x1), x2, ty_Bool)
new_compare1(:(x0, x1), [], x2)
new_compare27(x0, x1, x2)
new_compare10(x0, x1, False)
new_esEs27(x0, x1, app(ty_[], x2))
new_primMulNat0(Succ(x0), Zero)
new_ltEs19(x0, x1, ty_Float)
new_ltEs14(Left(x0), Right(x1), x2, x3)
new_esEs23(x0, x1, ty_Float)
new_ltEs14(Right(x0), Left(x1), x2, x3)
new_compare29(x0, x1, ty_Int)
new_esEs22(x0, x1, ty_Int)
new_esEs31(x0, x1, app(ty_Maybe, x2))
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Float)
new_compare31(x0, x1)
new_esEs29(x0, x1, ty_Double)
new_esEs32(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Left(x0), Left(x1), ty_Double, x2)
new_esEs31(x0, x1, ty_Char)
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Just(x0), Just(x1), ty_Int)
new_compare33(x0, x1, x2, x3)
new_esEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs21(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs7(LT, GT)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs7(GT, LT)
new_ltEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Double)
new_compare29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare111(x0, x1, True, x2)
new_ltEs13(x0, x1)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs32(x0, x1, app(ty_Maybe, x2))
new_esEs31(x0, x1, ty_Int)
new_lt4(x0, x1, ty_Int)
new_ltEs11(x0, x1, x2)
new_lt20(x0, x1, ty_Float)
new_not(True)
new_esEs31(x0, x1, ty_Float)
new_esEs20(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Float)
new_esEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs6(Nothing, Nothing, x0)
new_esEs28(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Ordering)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(Left(x0), Left(x1), ty_Double, x2)
new_esEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs6(Just(x0), Just(x1), ty_Integer)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_not(False)
new_lt8(x0, x1)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_ltEs18(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare13(x0, x1, True, x2, x3)
new_esEs32(x0, x1, ty_Integer)
new_esEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs19(x0, x1, ty_Char)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_esEs6(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare8(:%(x0, x1), :%(x2, x3), ty_Integer)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_Integer)
new_esEs8(x0, x1, ty_@0)
new_compare26(Left(x0), Left(x1), False, x2, x3)
new_ltEs12(True, True)
new_esEs27(x0, x1, ty_Float)
new_lt15(x0, x1)
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, ty_Ordering)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, ty_Double)
new_esEs6(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_lt20(x0, x1, ty_Ordering)
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs22(x0, x1, ty_Char)
new_lt20(x0, x1, ty_Double)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Bool)
new_esEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_ltEs21(x0, x1, ty_Float)
new_ltEs10(x0, x1)
new_ltEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs14(Left(x0), Left(x1), ty_Bool, x2)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs14(Left(x0), Left(x1), ty_Integer, x2)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(x0, x1, ty_Ordering)
new_esEs8(x0, x1, ty_Double)
new_compare29(x0, x1, ty_Char)
new_esEs6(Just(x0), Just(x1), ty_@0)
new_compare1(:(x0, x1), :(x2, x3), x4)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_compare210(x0, x1, True, x2, x3)
new_esEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs6(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs29(x0, x1, ty_Float)
new_esEs19(x0, x1, ty_Double)
new_esEs14(False, False)
new_primEqInt(Pos(Zero), Pos(Zero))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs32(x0, x1, ty_Char)
new_lt19(x0, x1, app(ty_[], x2))
new_ltEs21(x0, x1, ty_Double)
new_esEs32(x0, x1, ty_Int)
new_primCmpNat2(Succ(x0), Zero)
new_compare34(x0, x1, x2, x3)
new_compare18(x0, x1)
new_esEs29(x0, x1, ty_Int)
new_esEs32(x0, x1, ty_Bool)
new_compare28(x0, x1, False, x2)
new_ltEs14(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs18(Just(x0), Just(x1), ty_Int)
new_compare26(Right(x0), Right(x1), False, x2, x3)
new_ltEs17(x0, x1, x2)
new_primPlusNat0(Succ(x0), x1)
new_esEs7(Left(x0), Left(x1), ty_Int, x2)
new_esEs20(x0, x1, ty_Integer)
new_primCmpNat0(x0, Zero)
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_esEs7(Left(x0), Left(x1), ty_@0, x2)
new_ltEs7(GT, EQ)
new_ltEs7(EQ, GT)
new_esEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs32(x0, x1, ty_Double)
new_ltEs7(GT, GT)
new_esEs31(x0, x1, app(ty_Ratio, x2))
new_esEs9(LT, LT)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs13([], [], x0)
new_primCompAux0(x0, x1, x2, x3)
new_compare29(x0, x1, ty_@0)
new_esEs7(Left(x0), Left(x1), ty_Bool, x2)
new_compare26(x0, x1, True, x2, x3)
new_compare26(Right(x0), Left(x1), False, x2, x3)
new_compare26(Left(x0), Right(x1), False, x2, x3)
new_ltEs18(Nothing, Just(x0), x1)
new_esEs27(x0, x1, ty_Ordering)
new_primCmpNat0(x0, Succ(x1))

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

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

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

new_splitLT10(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, True, h, ba, bb) → new_splitLT(zxw34, zxw400, h, ba, bb)
new_splitLT3(Left(zxw300), zxw31, zxw32, zxw33, zxw34, Left(zxw400), h, ba, bb) → new_splitLT2(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs9(new_compare26(Left(zxw400), Left(zxw300), new_esEs29(zxw400, zxw300, h), h, ba), LT), h, ba, bb)
new_splitLT3(Right(zxw300), zxw31, zxw32, zxw33, zxw34, Left(zxw400), h, ba, bb) → new_splitLT20(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs9(new_compare26(Left(zxw400), Right(zxw300), False, h, ba), LT), h, ba, bb)
new_splitLT20(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, False, h, ba, bb) → new_splitLT10(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs9(new_compare34(zxw400, zxw300, h, ba), GT), h, ba, bb)
new_splitLT20(zxw300, zxw31, zxw32, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw34, zxw400, True, h, ba, bb) → new_splitLT3(zxw330, zxw331, zxw332, zxw333, zxw334, Left(zxw400), h, ba, bb)
new_splitLT1(zxw45, zxw46, zxw47, zxw48, zxw49, zxw50, True, bc, bd, be) → new_splitLT(zxw49, zxw50, bc, bd, be)
new_splitLT2(zxw45, zxw46, zxw47, zxw48, zxw49, zxw50, False, bc, bd, be) → new_splitLT1(zxw45, zxw46, zxw47, zxw48, zxw49, zxw50, new_esEs9(new_compare33(zxw50, zxw45, bc, bd), GT), bc, bd, be)
new_splitLT2(zxw45, zxw46, zxw47, zxw48, zxw49, zxw50, True, bc, bd, be) → new_splitLT(zxw48, zxw50, bc, bd, be)
new_splitLT(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw400, h, ba, bb) → new_splitLT3(zxw330, zxw331, zxw332, zxw333, zxw334, Left(zxw400), h, ba, bb)

The TRS R consists of the following rules:

new_compare33(zxw20, zxw15, cdc, cdd) → new_compare26(Left(zxw20), Left(zxw15), new_esEs32(zxw20, zxw15, cdc), cdc, cdd)
new_esEs9(LT, GT) → False
new_esEs9(EQ, GT) → False
new_esEs9(GT, GT) → True
new_esEs32(zxw20, zxw15, ty_Float) → new_esEs17(zxw20, zxw15)
new_esEs32(zxw20, zxw15, ty_Integer) → new_esEs15(zxw20, zxw15)
new_esEs32(zxw20, zxw15, ty_@0) → new_esEs10(zxw20, zxw15)
new_esEs32(zxw20, zxw15, ty_Ordering) → new_esEs9(zxw20, zxw15)
new_esEs32(zxw20, zxw15, ty_Bool) → new_esEs14(zxw20, zxw15)
new_esEs32(zxw20, zxw15, app(app(ty_Either, ceb), cec)) → new_esEs7(zxw20, zxw15, ceb, cec)
new_esEs32(zxw20, zxw15, app(ty_[], cdf)) → new_esEs13(zxw20, zxw15, cdf)
new_esEs32(zxw20, zxw15, app(ty_Maybe, cdg)) → new_esEs6(zxw20, zxw15, cdg)
new_esEs32(zxw20, zxw15, app(app(ty_@2, cdh), cea)) → new_esEs5(zxw20, zxw15, cdh, cea)
new_esEs32(zxw20, zxw15, ty_Char) → new_esEs12(zxw20, zxw15)
new_esEs32(zxw20, zxw15, app(app(app(ty_@3, ced), cee), cef)) → new_esEs4(zxw20, zxw15, ced, cee, cef)
new_esEs32(zxw20, zxw15, ty_Int) → new_esEs11(zxw20, zxw15)
new_esEs32(zxw20, zxw15, app(ty_Ratio, cde)) → new_esEs18(zxw20, zxw15, cde)
new_esEs32(zxw20, zxw15, ty_Double) → new_esEs16(zxw20, zxw15)
new_compare26(zxw790, zxw800, True, gh, ha) → EQ
new_compare26(Left(zxw7900), Left(zxw8000), False, gh, ha) → new_compare13(zxw7900, zxw8000, new_ltEs19(zxw7900, zxw8000, gh), gh, ha)
new_ltEs19(zxw7900, zxw8000, ty_Float) → new_ltEs16(zxw7900, zxw8000)
new_ltEs19(zxw7900, zxw8000, app(app(ty_@2, ca), cb)) → new_ltEs4(zxw7900, zxw8000, ca, cb)
new_ltEs19(zxw7900, zxw8000, app(ty_[], he)) → new_ltEs11(zxw7900, zxw8000, he)
new_ltEs19(zxw7900, zxw8000, ty_Char) → new_ltEs10(zxw7900, zxw8000)
new_ltEs19(zxw7900, zxw8000, ty_Bool) → new_ltEs12(zxw7900, zxw8000)
new_ltEs19(zxw7900, zxw8000, app(ty_Ratio, hh)) → new_ltEs17(zxw7900, zxw8000, hh)
new_ltEs19(zxw7900, zxw8000, app(app(app(ty_@3, hb), hc), hd)) → new_ltEs6(zxw7900, zxw8000, hb, hc, hd)
new_ltEs19(zxw7900, zxw8000, ty_Int) → new_ltEs9(zxw7900, zxw8000)
new_ltEs19(zxw7900, zxw8000, app(app(ty_Either, hf), hg)) → new_ltEs14(zxw7900, zxw8000, hf, hg)
new_ltEs19(zxw7900, zxw8000, ty_@0) → new_ltEs8(zxw7900, zxw8000)
new_ltEs19(zxw7900, zxw8000, ty_Double) → new_ltEs15(zxw7900, zxw8000)
new_ltEs19(zxw7900, zxw8000, ty_Integer) → new_ltEs13(zxw7900, zxw8000)
new_ltEs19(zxw7900, zxw8000, ty_Ordering) → new_ltEs7(zxw7900, zxw8000)
new_ltEs19(zxw7900, zxw8000, app(ty_Maybe, baa)) → new_ltEs18(zxw7900, zxw8000, baa)
new_compare13(zxw235, zxw236, False, bbf, bbg) → GT
new_compare13(zxw235, zxw236, True, bbf, bbg) → LT
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Char) → new_ltEs10(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Integer) → new_ltEs13(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(ty_Ratio, dac)) → new_ltEs17(zxw79000, zxw80000, dac)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(app(app(ty_@3, chc), chd), che)) → new_ltEs6(zxw79000, zxw80000, chc, chd, che)
new_ltEs18(Nothing, Nothing, baa) → True
new_ltEs18(Just(zxw79000), Nothing, baa) → False
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Double) → new_ltEs15(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(ty_[], chf)) → new_ltEs11(zxw79000, zxw80000, chf)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(app(ty_@2, chg), chh)) → new_ltEs4(zxw79000, zxw80000, chg, chh)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Bool) → new_ltEs12(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Ordering) → new_ltEs7(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Float) → new_ltEs16(zxw79000, zxw80000)
new_ltEs18(Nothing, Just(zxw80000), baa) → True
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Int) → new_ltEs9(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_@0) → new_ltEs8(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(ty_Maybe, dad)) → new_ltEs18(zxw79000, zxw80000, dad)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(ty_Maybe, chb)) → new_ltEs18(zxw79000, zxw80000, chb)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(app(ty_Either, daa), dab)) → new_ltEs14(zxw79000, zxw80000, daa, dab)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(app(ty_Either, cgg), cgh)) → new_ltEs14(zxw79000, zxw80000, cgg, cgh)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(app(ty_Either, cfe), cff), hg) → new_ltEs14(zxw79000, zxw80000, cfe, cff)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(ty_Maybe, cfh), hg) → new_ltEs18(zxw79000, zxw80000, cfh)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Bool) → new_ltEs12(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(ty_[], cgd)) → new_ltEs11(zxw79000, zxw80000, cgd)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Bool, hg) → new_ltEs12(zxw79000, zxw80000)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(ty_Ratio, cfg), hg) → new_ltEs17(zxw79000, zxw80000, cfg)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(app(app(ty_@3, cga), cgb), cgc)) → new_ltEs6(zxw79000, zxw80000, cga, cgb, cgc)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Float, hg) → new_ltEs16(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Float) → new_ltEs16(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Double) → new_ltEs15(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(app(ty_@2, cge), cgf)) → new_ltEs4(zxw79000, zxw80000, cge, cgf)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Double, hg) → new_ltEs15(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Left(zxw80000), hf, hg) → False
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Int, hg) → new_ltEs9(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Char) → new_ltEs10(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_@0) → new_ltEs8(zxw79000, zxw80000)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(app(app(ty_@3, ceg), ceh), cfa), hg) → new_ltEs6(zxw79000, zxw80000, ceg, ceh, cfa)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_@0, hg) → new_ltEs8(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Ordering) → new_ltEs7(zxw79000, zxw80000)
new_ltEs14(Left(zxw79000), Right(zxw80000), hf, hg) → True
new_ltEs14(Left(zxw79000), Left(zxw80000), app(app(ty_@2, cfc), cfd), hg) → new_ltEs4(zxw79000, zxw80000, cfc, cfd)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(ty_[], cfb), hg) → new_ltEs11(zxw79000, zxw80000, cfb)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Integer, hg) → new_ltEs13(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Int) → new_ltEs9(zxw79000, zxw80000)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Ordering, hg) → new_ltEs7(zxw79000, zxw80000)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Char, hg) → new_ltEs10(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(ty_Ratio, cha)) → new_ltEs17(zxw79000, zxw80000, cha)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Integer) → new_ltEs13(zxw79000, zxw80000)
new_ltEs13(zxw7900, zxw8000) → new_fsEs(new_compare32(zxw7900, zxw8000))
new_compare32(Integer(zxw79000), Integer(zxw80000)) → new_primCmpInt(zxw79000, zxw80000)
new_fsEs(zxw259) → new_not(new_esEs9(zxw259, GT))
new_not(False) → True
new_not(True) → False
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_ltEs17(zxw7900, zxw8000, hh) → new_fsEs(new_compare8(zxw7900, zxw8000, hh))
new_compare8(:%(zxw79000, zxw79001), :%(zxw80000, zxw80001), ty_Integer) → new_compare32(new_sr0(zxw79000, zxw80001), new_sr0(zxw80000, zxw79001))
new_compare8(:%(zxw79000, zxw79001), :%(zxw80000, zxw80001), ty_Int) → new_compare16(new_sr(zxw79000, zxw80001), new_sr(zxw80000, zxw79001))
new_sr(zxw4000, zxw3000) → new_primMulInt(zxw4000, zxw3000)
new_compare16(zxw79, zxw80) → new_primCmpInt(zxw79, zxw80)
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Neg(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Pos(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulNat0(Zero, Zero) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_sr0(Integer(zxw800000), Integer(zxw790010)) → Integer(new_primMulInt(zxw800000, zxw790010))
new_ltEs10(zxw7900, zxw8000) → new_fsEs(new_compare17(zxw7900, zxw8000))
new_compare17(Char(zxw79000), Char(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_ltEs7(LT, EQ) → True
new_ltEs7(GT, GT) → True
new_ltEs7(EQ, EQ) → True
new_ltEs7(GT, LT) → False
new_ltEs7(GT, EQ) → False
new_ltEs7(EQ, GT) → True
new_ltEs7(EQ, LT) → False
new_ltEs7(LT, LT) → True
new_ltEs7(LT, GT) → True
new_ltEs9(zxw7900, zxw8000) → new_fsEs(new_compare16(zxw7900, zxw8000))
new_ltEs11(zxw7900, zxw8000, he) → new_fsEs(new_compare1(zxw7900, zxw8000, he))
new_compare1([], :(zxw80000, zxw80001), he) → LT
new_compare1(:(zxw79000, zxw79001), :(zxw80000, zxw80001), he) → new_primCompAux0(zxw79000, zxw80000, new_compare1(zxw79001, zxw80001, he), he)
new_compare1(:(zxw79000, zxw79001), [], he) → GT
new_compare1([], [], he) → EQ
new_primCompAux0(zxw79000, zxw80000, zxw272, he) → new_primCompAux00(zxw272, new_compare29(zxw79000, zxw80000, he))
new_compare29(zxw79000, zxw80000, ty_Char) → new_compare17(zxw79000, zxw80000)
new_compare29(zxw79000, zxw80000, ty_Bool) → new_compare31(zxw79000, zxw80000)
new_compare29(zxw79000, zxw80000, app(app(ty_@2, cbf), cbg)) → new_compare19(zxw79000, zxw80000, cbf, cbg)
new_compare29(zxw79000, zxw80000, app(ty_[], cbe)) → new_compare1(zxw79000, zxw80000, cbe)
new_compare29(zxw79000, zxw80000, app(app(app(ty_@3, cbb), cbc), cbd)) → new_compare9(zxw79000, zxw80000, cbb, cbc, cbd)
new_compare29(zxw79000, zxw80000, ty_Int) → new_compare16(zxw79000, zxw80000)
new_compare29(zxw79000, zxw80000, ty_Integer) → new_compare32(zxw79000, zxw80000)
new_compare29(zxw79000, zxw80000, app(ty_Maybe, ccc)) → new_compare27(zxw79000, zxw80000, ccc)
new_compare29(zxw79000, zxw80000, app(ty_Ratio, ccb)) → new_compare8(zxw79000, zxw80000, ccb)
new_compare29(zxw79000, zxw80000, ty_Float) → new_compare7(zxw79000, zxw80000)
new_compare29(zxw79000, zxw80000, ty_Double) → new_compare6(zxw79000, zxw80000)
new_compare29(zxw79000, zxw80000, app(app(ty_Either, cbh), cca)) → new_compare15(zxw79000, zxw80000, cbh, cca)
new_compare29(zxw79000, zxw80000, ty_Ordering) → new_compare18(zxw79000, zxw80000)
new_compare29(zxw79000, zxw80000, ty_@0) → new_compare30(zxw79000, zxw80000)
new_primCompAux00(zxw276, LT) → LT
new_primCompAux00(zxw276, EQ) → zxw276
new_primCompAux00(zxw276, GT) → GT
new_compare30(@0, @0) → EQ
new_compare18(zxw79000, zxw80000) → new_compare24(zxw79000, zxw80000, new_esEs9(zxw79000, zxw80000))
new_esEs9(GT, LT) → False
new_esEs9(GT, EQ) → False
new_esEs9(EQ, EQ) → True
new_esEs9(EQ, LT) → False
new_esEs9(LT, EQ) → False
new_esEs9(LT, LT) → True
new_compare24(zxw79000, zxw80000, False) → new_compare11(zxw79000, zxw80000, new_ltEs7(zxw79000, zxw80000))
new_compare24(zxw79000, zxw80000, True) → EQ
new_compare11(zxw79000, zxw80000, False) → GT
new_compare11(zxw79000, zxw80000, True) → LT
new_compare15(zxw790, zxw800, gh, ha) → new_compare26(zxw790, zxw800, new_esEs7(zxw790, zxw800, gh, ha), gh, ha)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Bool, bdf) → new_esEs14(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Right(zxw3000), beh, bdf) → False
new_esEs7(Right(zxw4000), Left(zxw3000), beh, bdf) → False
new_esEs7(Right(zxw4000), Right(zxw3000), beh, app(app(ty_@2, bfd), bfe)) → new_esEs5(zxw4000, zxw3000, bfd, bfe)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Int, bdf) → new_esEs11(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), app(app(ty_@2, bea), beb), bdf) → new_esEs5(zxw4000, zxw3000, bea, beb)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Ordering, bdf) → new_esEs9(zxw4000, zxw3000)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, app(ty_[], bfb)) → new_esEs13(zxw4000, zxw3000, bfb)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Integer, bdf) → new_esEs15(zxw4000, zxw3000)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, app(app(app(ty_@3, bfh), bga), bgb)) → new_esEs4(zxw4000, zxw3000, bfh, bga, bgb)
new_esEs7(Left(zxw4000), Left(zxw3000), app(ty_Ratio, bde), bdf) → new_esEs18(zxw4000, zxw3000, bde)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_@0, bdf) → new_esEs10(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), app(app(app(ty_@3, bee), bef), beg), bdf) → new_esEs4(zxw4000, zxw3000, bee, bef, beg)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Double, bdf) → new_esEs16(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Float, bdf) → new_esEs17(zxw4000, zxw3000)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Char, bdf) → new_esEs12(zxw4000, zxw3000)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), app(ty_[], bdg), bdf) → new_esEs13(zxw4000, zxw3000, bdg)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, app(ty_Ratio, bfa)) → new_esEs18(zxw4000, zxw3000, bfa)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_compare26(Left(zxw7900), Right(zxw8000), False, gh, ha) → LT
new_compare26(Right(zxw7900), Left(zxw8000), False, gh, ha) → GT
new_compare26(Right(zxw7900), Right(zxw8000), False, gh, ha) → new_compare14(zxw7900, zxw8000, new_ltEs20(zxw7900, zxw8000, ha), gh, ha)
new_esEs6(Just(zxw4000), Just(zxw3000), app(ty_Maybe, fc)) → new_esEs6(zxw4000, zxw3000, fc)
new_esEs7(Left(zxw4000), Left(zxw3000), app(app(ty_Either, bec), bed), bdf) → new_esEs7(zxw4000, zxw3000, bec, bed)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, app(ty_Maybe, bfc)) → new_esEs6(zxw4000, zxw3000, bfc)
new_esEs6(Just(zxw4000), Just(zxw3000), app(app(ty_Either, fg), fh)) → new_esEs7(zxw4000, zxw3000, fg, fh)
new_esEs7(Left(zxw4000), Left(zxw3000), app(ty_Maybe, bdh), bdf) → new_esEs6(zxw4000, zxw3000, bdh)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, app(app(ty_Either, bff), bfg)) → new_esEs7(zxw4000, zxw3000, bff, bfg)
new_esEs6(Just(zxw4000), Just(zxw3000), app(app(ty_@2, fd), ff)) → new_esEs5(zxw4000, zxw3000, fd, ff)
new_esEs6(Nothing, Nothing, eh) → True
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs6(Nothing, Just(zxw3000), eh) → False
new_esEs6(Just(zxw4000), Nothing, eh) → False
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), app(app(app(ty_@3, ga), gb), gc)) → new_esEs4(zxw4000, zxw3000, ga, gb, gc)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_@0) → new_esEs10(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), app(ty_[], fb)) → new_esEs13(zxw4000, zxw3000, fb)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Char) → new_esEs12(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Float) → new_esEs17(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), app(ty_Ratio, fa)) → new_esEs18(zxw4000, zxw3000, fa)
new_esEs18(:%(zxw4000, zxw4001), :%(zxw3000, zxw3001), ccd) → new_asAs(new_esEs25(zxw4000, zxw3000, ccd), new_esEs24(zxw4001, zxw3001, ccd))
new_esEs25(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs25(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs24(zxw4001, zxw3001, ty_Integer) → new_esEs15(zxw4001, zxw3001)
new_esEs24(zxw4001, zxw3001, ty_Int) → new_esEs11(zxw4001, zxw3001)
new_asAs(False, zxw230) → False
new_asAs(True, zxw230) → zxw230
new_esEs11(zxw400, zxw300) → new_primEqInt(zxw400, zxw300)
new_primEqInt(Neg(Succ(zxw40000)), Neg(Succ(zxw30000))) → new_primEqNat0(zxw40000, zxw30000)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Neg(Succ(zxw30000))) → False
new_primEqInt(Neg(Succ(zxw40000)), Neg(Zero)) → False
new_primEqInt(Pos(Succ(zxw40000)), Pos(Succ(zxw30000))) → new_primEqNat0(zxw40000, zxw30000)
new_primEqInt(Pos(Zero), Pos(Succ(zxw30000))) → False
new_primEqInt(Pos(Succ(zxw40000)), Pos(Zero)) → False
new_primEqInt(Neg(Succ(zxw40000)), Pos(zxw3000)) → False
new_primEqInt(Pos(Succ(zxw40000)), Neg(zxw3000)) → False
new_primEqInt(Neg(Zero), Pos(Succ(zxw30000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(zxw30000))) → False
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqNat0(Zero, Zero) → True
new_primEqNat0(Succ(zxw40000), Succ(zxw30000)) → new_primEqNat0(zxw40000, zxw30000)
new_primEqNat0(Zero, Succ(zxw30000)) → False
new_primEqNat0(Succ(zxw40000), Zero) → False
new_esEs15(Integer(zxw4000), Integer(zxw3000)) → new_primEqInt(zxw4000, zxw3000)
new_esEs17(Float(zxw4000, zxw4001), Float(zxw3000, zxw3001)) → new_esEs11(new_sr(zxw4000, zxw3000), new_sr(zxw4001, zxw3001))
new_esEs12(Char(zxw4000), Char(zxw3000)) → new_primEqNat0(zxw4000, zxw3000)
new_esEs13([], [], cce) → True
new_esEs13(:(zxw4000, zxw4001), :(zxw3000, zxw3001), cce) → new_asAs(new_esEs23(zxw4000, zxw3000, cce), new_esEs13(zxw4001, zxw3001, cce))
new_esEs13(:(zxw4000, zxw4001), [], cce) → False
new_esEs13([], :(zxw3000, zxw3001), cce) → False
new_esEs23(zxw4000, zxw3000, app(app(ty_Either, deh), dfa)) → new_esEs7(zxw4000, zxw3000, deh, dfa)
new_esEs23(zxw4000, zxw3000, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, app(app(app(ty_@3, dfb), dfc), dfd)) → new_esEs4(zxw4000, zxw3000, dfb, dfc, dfd)
new_esEs23(zxw4000, zxw3000, app(app(ty_@2, def), deg)) → new_esEs5(zxw4000, zxw3000, def, deg)
new_esEs23(zxw4000, zxw3000, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, app(ty_Ratio, dec)) → new_esEs18(zxw4000, zxw3000, dec)
new_esEs23(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, app(ty_Maybe, dee)) → new_esEs6(zxw4000, zxw3000, dee)
new_esEs23(zxw4000, zxw3000, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, app(ty_[], ded)) → new_esEs13(zxw4000, zxw3000, ded)
new_esEs16(Double(zxw4000, zxw4001), Double(zxw3000, zxw3001)) → new_esEs11(new_sr(zxw4000, zxw3000), new_sr(zxw4001, zxw3001))
new_esEs10(@0, @0) → True
new_esEs5(@2(zxw4000, zxw4001), @2(zxw3000, zxw3001), ccf, ccg) → new_asAs(new_esEs22(zxw4000, zxw3000, ccf), new_esEs21(zxw4001, zxw3001, ccg))
new_esEs22(zxw4000, zxw3000, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, app(app(ty_@2, ddd), dde)) → new_esEs5(zxw4000, zxw3000, ddd, dde)
new_esEs22(zxw4000, zxw3000, app(ty_Maybe, ddc)) → new_esEs6(zxw4000, zxw3000, ddc)
new_esEs22(zxw4000, zxw3000, app(ty_Ratio, dda)) → new_esEs18(zxw4000, zxw3000, dda)
new_esEs22(zxw4000, zxw3000, app(app(ty_Either, ddf), ddg)) → new_esEs7(zxw4000, zxw3000, ddf, ddg)
new_esEs22(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, app(app(app(ty_@3, ddh), dea), deb)) → new_esEs4(zxw4000, zxw3000, ddh, dea, deb)
new_esEs22(zxw4000, zxw3000, app(ty_[], ddb)) → new_esEs13(zxw4000, zxw3000, ddb)
new_esEs22(zxw4000, zxw3000, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs21(zxw4001, zxw3001, ty_Bool) → new_esEs14(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, ty_Double) → new_esEs16(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, ty_Ordering) → new_esEs9(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, ty_Char) → new_esEs12(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, ty_Float) → new_esEs17(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, app(ty_Maybe, dca)) → new_esEs6(zxw4001, zxw3001, dca)
new_esEs21(zxw4001, zxw3001, ty_Int) → new_esEs11(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, app(ty_[], dbh)) → new_esEs13(zxw4001, zxw3001, dbh)
new_esEs21(zxw4001, zxw3001, ty_Integer) → new_esEs15(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, app(app(ty_@2, dcb), dcc)) → new_esEs5(zxw4001, zxw3001, dcb, dcc)
new_esEs21(zxw4001, zxw3001, ty_@0) → new_esEs10(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, app(app(ty_Either, dcd), dce)) → new_esEs7(zxw4001, zxw3001, dcd, dce)
new_esEs21(zxw4001, zxw3001, app(app(app(ty_@3, dcf), dcg), dch)) → new_esEs4(zxw4001, zxw3001, dcf, dcg, dch)
new_esEs21(zxw4001, zxw3001, app(ty_Ratio, dbg)) → new_esEs18(zxw4001, zxw3001, dbg)
new_esEs4(@3(zxw4000, zxw4001, zxw4002), @3(zxw3000, zxw3001, zxw3002), cch, cda, cdb) → new_asAs(new_esEs28(zxw4000, zxw3000, cch), new_asAs(new_esEs27(zxw4001, zxw3001, cda), new_esEs26(zxw4002, zxw3002, cdb)))
new_esEs28(zxw4000, zxw3000, app(ty_[], ead)) → new_esEs13(zxw4000, zxw3000, ead)
new_esEs28(zxw4000, zxw3000, app(app(app(ty_@3, ebb), ebc), ebd)) → new_esEs4(zxw4000, zxw3000, ebb, ebc, ebd)
new_esEs28(zxw4000, zxw3000, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, app(ty_Maybe, eae)) → new_esEs6(zxw4000, zxw3000, eae)
new_esEs28(zxw4000, zxw3000, app(app(ty_Either, eah), eba)) → new_esEs7(zxw4000, zxw3000, eah, eba)
new_esEs28(zxw4000, zxw3000, app(app(ty_@2, eaf), eag)) → new_esEs5(zxw4000, zxw3000, eaf, eag)
new_esEs28(zxw4000, zxw3000, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, app(ty_Ratio, eac)) → new_esEs18(zxw4000, zxw3000, eac)
new_esEs28(zxw4000, zxw3000, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_esEs27(zxw4001, zxw3001, app(ty_Ratio, dha)) → new_esEs18(zxw4001, zxw3001, dha)
new_esEs27(zxw4001, zxw3001, app(app(app(ty_@3, dhh), eaa), eab)) → new_esEs4(zxw4001, zxw3001, dhh, eaa, eab)
new_esEs27(zxw4001, zxw3001, app(ty_Maybe, dhc)) → new_esEs6(zxw4001, zxw3001, dhc)
new_esEs27(zxw4001, zxw3001, app(app(ty_Either, dhf), dhg)) → new_esEs7(zxw4001, zxw3001, dhf, dhg)
new_esEs27(zxw4001, zxw3001, ty_Ordering) → new_esEs9(zxw4001, zxw3001)
new_esEs27(zxw4001, zxw3001, ty_Float) → new_esEs17(zxw4001, zxw3001)
new_esEs27(zxw4001, zxw3001, ty_@0) → new_esEs10(zxw4001, zxw3001)
new_esEs27(zxw4001, zxw3001, ty_Char) → new_esEs12(zxw4001, zxw3001)
new_esEs27(zxw4001, zxw3001, ty_Double) → new_esEs16(zxw4001, zxw3001)
new_esEs27(zxw4001, zxw3001, ty_Int) → new_esEs11(zxw4001, zxw3001)
new_esEs27(zxw4001, zxw3001, app(app(ty_@2, dhd), dhe)) → new_esEs5(zxw4001, zxw3001, dhd, dhe)
new_esEs27(zxw4001, zxw3001, ty_Bool) → new_esEs14(zxw4001, zxw3001)
new_esEs27(zxw4001, zxw3001, app(ty_[], dhb)) → new_esEs13(zxw4001, zxw3001, dhb)
new_esEs27(zxw4001, zxw3001, ty_Integer) → new_esEs15(zxw4001, zxw3001)
new_esEs26(zxw4002, zxw3002, ty_Float) → new_esEs17(zxw4002, zxw3002)
new_esEs26(zxw4002, zxw3002, ty_Char) → new_esEs12(zxw4002, zxw3002)
new_esEs26(zxw4002, zxw3002, ty_Int) → new_esEs11(zxw4002, zxw3002)
new_esEs26(zxw4002, zxw3002, app(ty_Maybe, dga)) → new_esEs6(zxw4002, zxw3002, dga)
new_esEs26(zxw4002, zxw3002, app(app(app(ty_@3, dgf), dgg), dgh)) → new_esEs4(zxw4002, zxw3002, dgf, dgg, dgh)
new_esEs26(zxw4002, zxw3002, app(ty_[], dfh)) → new_esEs13(zxw4002, zxw3002, dfh)
new_esEs26(zxw4002, zxw3002, app(app(ty_Either, dgd), dge)) → new_esEs7(zxw4002, zxw3002, dgd, dge)
new_esEs26(zxw4002, zxw3002, ty_Integer) → new_esEs15(zxw4002, zxw3002)
new_esEs26(zxw4002, zxw3002, app(app(ty_@2, dgb), dgc)) → new_esEs5(zxw4002, zxw3002, dgb, dgc)
new_esEs26(zxw4002, zxw3002, app(ty_Ratio, dfg)) → new_esEs18(zxw4002, zxw3002, dfg)
new_esEs26(zxw4002, zxw3002, ty_Bool) → new_esEs14(zxw4002, zxw3002)
new_esEs26(zxw4002, zxw3002, ty_@0) → new_esEs10(zxw4002, zxw3002)
new_esEs26(zxw4002, zxw3002, ty_Ordering) → new_esEs9(zxw4002, zxw3002)
new_esEs26(zxw4002, zxw3002, ty_Double) → new_esEs16(zxw4002, zxw3002)
new_esEs14(False, True) → False
new_esEs14(True, False) → False
new_esEs14(True, True) → True
new_esEs14(False, False) → True
new_ltEs20(zxw7900, zxw8000, app(ty_Maybe, bbc)) → new_ltEs18(zxw7900, zxw8000, bbc)
new_ltEs20(zxw7900, zxw8000, ty_Int) → new_ltEs9(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, ty_@0) → new_ltEs8(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, app(app(ty_@2, baf), bag)) → new_ltEs4(zxw7900, zxw8000, baf, bag)
new_ltEs20(zxw7900, zxw8000, ty_Float) → new_ltEs16(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, ty_Bool) → new_ltEs12(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, app(ty_Ratio, bbb)) → new_ltEs17(zxw7900, zxw8000, bbb)
new_ltEs20(zxw7900, zxw8000, ty_Double) → new_ltEs15(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, ty_Integer) → new_ltEs13(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, app(app(app(ty_@3, bab), bac), bad)) → new_ltEs6(zxw7900, zxw8000, bab, bac, bad)
new_ltEs20(zxw7900, zxw8000, app(app(ty_Either, bah), bba)) → new_ltEs14(zxw7900, zxw8000, bah, bba)
new_ltEs20(zxw7900, zxw8000, app(ty_[], bae)) → new_ltEs11(zxw7900, zxw8000, bae)
new_ltEs20(zxw7900, zxw8000, ty_Char) → new_ltEs10(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, ty_Ordering) → new_ltEs7(zxw7900, zxw8000)
new_compare14(zxw242, zxw243, False, dfe, dff) → GT
new_compare14(zxw242, zxw243, True, dfe, dff) → LT
new_ltEs6(@3(zxw79000, zxw79001, zxw79002), @3(zxw80000, zxw80001, zxw80002), hb, hc, hd) → new_pePe(new_lt19(zxw79000, zxw80000, hb), new_asAs(new_esEs20(zxw79000, zxw80000, hb), new_pePe(new_lt20(zxw79001, zxw80001, hc), new_asAs(new_esEs19(zxw79001, zxw80001, hc), new_ltEs21(zxw79002, zxw80002, hd)))))
new_lt19(zxw79000, zxw80000, app(app(ty_Either, bgd), bge)) → new_lt14(zxw79000, zxw80000, bgd, bge)
new_lt19(zxw79000, zxw80000, ty_Double) → new_lt15(zxw79000, zxw80000)
new_lt19(zxw79000, zxw80000, ty_Ordering) → new_lt6(zxw79000, zxw80000)
new_lt19(zxw79000, zxw80000, app(ty_Ratio, gg)) → new_lt17(zxw79000, zxw80000, gg)
new_lt19(zxw79000, zxw80000, app(app(ty_@2, bbd), bbe)) → new_lt11(zxw79000, zxw80000, bbd, bbe)
new_lt19(zxw79000, zxw80000, ty_Int) → new_lt8(zxw79000, zxw80000)
new_lt19(zxw79000, zxw80000, ty_@0) → new_lt7(zxw79000, zxw80000)
new_lt19(zxw79000, zxw80000, app(app(app(ty_@3, gd), ge), gf)) → new_lt5(zxw79000, zxw80000, gd, ge, gf)
new_lt19(zxw79000, zxw80000, app(ty_Maybe, bbh)) → new_lt18(zxw79000, zxw80000, bbh)
new_lt19(zxw79000, zxw80000, ty_Float) → new_lt16(zxw79000, zxw80000)
new_lt19(zxw79000, zxw80000, ty_Bool) → new_lt12(zxw79000, zxw80000)
new_lt19(zxw79000, zxw80000, app(ty_[], bgc)) → new_lt10(zxw79000, zxw80000, bgc)
new_lt19(zxw79000, zxw80000, ty_Integer) → new_lt13(zxw79000, zxw80000)
new_lt19(zxw79000, zxw80000, ty_Char) → new_lt9(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, app(ty_[], bgc)) → new_esEs13(zxw79000, zxw80000, bgc)
new_esEs20(zxw79000, zxw80000, ty_Double) → new_esEs16(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, ty_Char) → new_esEs12(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, app(app(ty_@2, bbd), bbe)) → new_esEs5(zxw79000, zxw80000, bbd, bbe)
new_esEs20(zxw79000, zxw80000, ty_Int) → new_esEs11(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, ty_@0) → new_esEs10(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, app(app(app(ty_@3, gd), ge), gf)) → new_esEs4(zxw79000, zxw80000, gd, ge, gf)
new_esEs20(zxw79000, zxw80000, ty_Integer) → new_esEs15(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, ty_Bool) → new_esEs14(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, app(ty_Ratio, gg)) → new_esEs18(zxw79000, zxw80000, gg)
new_esEs20(zxw79000, zxw80000, app(app(ty_Either, bgd), bge)) → new_esEs7(zxw79000, zxw80000, bgd, bge)
new_esEs20(zxw79000, zxw80000, app(ty_Maybe, bbh)) → new_esEs6(zxw79000, zxw80000, bbh)
new_esEs20(zxw79000, zxw80000, ty_Ordering) → new_esEs9(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, ty_Float) → new_esEs17(zxw79000, zxw80000)
new_lt20(zxw79001, zxw80001, app(app(ty_Either, bhd), bhe)) → new_lt14(zxw79001, zxw80001, bhd, bhe)
new_lt20(zxw79001, zxw80001, ty_@0) → new_lt7(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, app(app(ty_@2, bhb), bhc)) → new_lt11(zxw79001, zxw80001, bhb, bhc)
new_lt20(zxw79001, zxw80001, ty_Ordering) → new_lt6(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, app(ty_Maybe, bhg)) → new_lt18(zxw79001, zxw80001, bhg)
new_lt20(zxw79001, zxw80001, ty_Int) → new_lt8(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, ty_Integer) → new_lt13(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, app(ty_Ratio, bhf)) → new_lt17(zxw79001, zxw80001, bhf)
new_lt20(zxw79001, zxw80001, ty_Char) → new_lt9(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, app(ty_[], bha)) → new_lt10(zxw79001, zxw80001, bha)
new_lt20(zxw79001, zxw80001, ty_Double) → new_lt15(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, ty_Float) → new_lt16(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, ty_Bool) → new_lt12(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, app(app(app(ty_@3, bgf), bgg), bgh)) → new_lt5(zxw79001, zxw80001, bgf, bgg, bgh)
new_esEs19(zxw79001, zxw80001, app(ty_Ratio, bhf)) → new_esEs18(zxw79001, zxw80001, bhf)
new_esEs19(zxw79001, zxw80001, ty_Ordering) → new_esEs9(zxw79001, zxw80001)
new_esEs19(zxw79001, zxw80001, app(ty_Maybe, bhg)) → new_esEs6(zxw79001, zxw80001, bhg)
new_esEs19(zxw79001, zxw80001, app(app(ty_Either, bhd), bhe)) → new_esEs7(zxw79001, zxw80001, bhd, bhe)
new_esEs19(zxw79001, zxw80001, ty_Float) → new_esEs17(zxw79001, zxw80001)
new_esEs19(zxw79001, zxw80001, ty_Bool) → new_esEs14(zxw79001, zxw80001)
new_esEs19(zxw79001, zxw80001, ty_Int) → new_esEs11(zxw79001, zxw80001)
new_esEs19(zxw79001, zxw80001, app(app(app(ty_@3, bgf), bgg), bgh)) → new_esEs4(zxw79001, zxw80001, bgf, bgg, bgh)
new_esEs19(zxw79001, zxw80001, app(app(ty_@2, bhb), bhc)) → new_esEs5(zxw79001, zxw80001, bhb, bhc)
new_esEs19(zxw79001, zxw80001, ty_Double) → new_esEs16(zxw79001, zxw80001)
new_esEs19(zxw79001, zxw80001, ty_Integer) → new_esEs15(zxw79001, zxw80001)
new_esEs19(zxw79001, zxw80001, ty_@0) → new_esEs10(zxw79001, zxw80001)
new_esEs19(zxw79001, zxw80001, app(ty_[], bha)) → new_esEs13(zxw79001, zxw80001, bha)
new_esEs19(zxw79001, zxw80001, ty_Char) → new_esEs12(zxw79001, zxw80001)
new_ltEs21(zxw79002, zxw80002, ty_Char) → new_ltEs10(zxw79002, zxw80002)
new_ltEs21(zxw79002, zxw80002, app(app(ty_@2, cad), cae)) → new_ltEs4(zxw79002, zxw80002, cad, cae)
new_ltEs21(zxw79002, zxw80002, ty_Int) → new_ltEs9(zxw79002, zxw80002)
new_ltEs21(zxw79002, zxw80002, ty_Ordering) → new_ltEs7(zxw79002, zxw80002)
new_ltEs21(zxw79002, zxw80002, ty_Float) → new_ltEs16(zxw79002, zxw80002)
new_ltEs21(zxw79002, zxw80002, ty_Bool) → new_ltEs12(zxw79002, zxw80002)
new_ltEs21(zxw79002, zxw80002, ty_Integer) → new_ltEs13(zxw79002, zxw80002)
new_ltEs21(zxw79002, zxw80002, app(app(ty_Either, caf), cag)) → new_ltEs14(zxw79002, zxw80002, caf, cag)
new_ltEs21(zxw79002, zxw80002, app(ty_[], cac)) → new_ltEs11(zxw79002, zxw80002, cac)
new_ltEs21(zxw79002, zxw80002, app(ty_Ratio, cah)) → new_ltEs17(zxw79002, zxw80002, cah)
new_ltEs21(zxw79002, zxw80002, app(app(app(ty_@3, bhh), caa), cab)) → new_ltEs6(zxw79002, zxw80002, bhh, caa, cab)
new_ltEs21(zxw79002, zxw80002, ty_@0) → new_ltEs8(zxw79002, zxw80002)
new_ltEs21(zxw79002, zxw80002, app(ty_Maybe, cba)) → new_ltEs18(zxw79002, zxw80002, cba)
new_ltEs21(zxw79002, zxw80002, ty_Double) → new_ltEs15(zxw79002, zxw80002)
new_pePe(False, zxw271) → zxw271
new_pePe(True, zxw271) → True
new_ltEs15(zxw7900, zxw8000) → new_fsEs(new_compare6(zxw7900, zxw8000))
new_compare6(Double(zxw79000, zxw79001), Double(zxw80000, zxw80001)) → new_compare16(new_sr(zxw79000, zxw80000), new_sr(zxw79001, zxw80001))
new_ltEs8(zxw7900, zxw8000) → new_fsEs(new_compare30(zxw7900, zxw8000))
new_ltEs12(True, False) → False
new_ltEs12(False, False) → True
new_ltEs12(True, True) → True
new_ltEs12(False, True) → True
new_ltEs16(zxw7900, zxw8000) → new_fsEs(new_compare7(zxw7900, zxw8000))
new_compare7(Float(zxw79000, zxw79001), Float(zxw80000, zxw80001)) → new_compare16(new_sr(zxw79000, zxw80000), new_sr(zxw79001, zxw80001))
new_ltEs4(@2(zxw79000, zxw79001), @2(zxw80000, zxw80001), ca, cb) → new_pePe(new_lt4(zxw79000, zxw80000, ca), new_asAs(new_esEs8(zxw79000, zxw80000, ca), new_ltEs5(zxw79001, zxw80001, cb)))
new_lt4(zxw79000, zxw80000, app(app(app(ty_@3, cc), cd), ce)) → new_lt5(zxw79000, zxw80000, cc, cd, ce)
new_lt4(zxw79000, zxw80000, app(ty_[], cf)) → new_lt10(zxw79000, zxw80000, cf)
new_lt4(zxw79000, zxw80000, ty_Bool) → new_lt12(zxw79000, zxw80000)
new_lt4(zxw79000, zxw80000, app(ty_Maybe, de)) → new_lt18(zxw79000, zxw80000, de)
new_lt4(zxw79000, zxw80000, ty_Ordering) → new_lt6(zxw79000, zxw80000)
new_lt4(zxw79000, zxw80000, app(ty_Ratio, dd)) → new_lt17(zxw79000, zxw80000, dd)
new_lt4(zxw79000, zxw80000, ty_Int) → new_lt8(zxw79000, zxw80000)
new_lt4(zxw79000, zxw80000, ty_Double) → new_lt15(zxw79000, zxw80000)
new_lt4(zxw79000, zxw80000, app(app(ty_Either, db), dc)) → new_lt14(zxw79000, zxw80000, db, dc)
new_lt4(zxw79000, zxw80000, ty_Char) → new_lt9(zxw79000, zxw80000)
new_lt4(zxw79000, zxw80000, ty_@0) → new_lt7(zxw79000, zxw80000)
new_lt4(zxw79000, zxw80000, ty_Float) → new_lt16(zxw79000, zxw80000)
new_lt4(zxw79000, zxw80000, app(app(ty_@2, cg), da)) → new_lt11(zxw79000, zxw80000, cg, da)
new_lt4(zxw79000, zxw80000, ty_Integer) → new_lt13(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, ty_Int) → new_esEs11(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, ty_Double) → new_esEs16(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, app(app(app(ty_@3, cc), cd), ce)) → new_esEs4(zxw79000, zxw80000, cc, cd, ce)
new_esEs8(zxw79000, zxw80000, app(ty_[], cf)) → new_esEs13(zxw79000, zxw80000, cf)
new_esEs8(zxw79000, zxw80000, ty_Char) → new_esEs12(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, app(app(ty_@2, cg), da)) → new_esEs5(zxw79000, zxw80000, cg, da)
new_esEs8(zxw79000, zxw80000, ty_Float) → new_esEs17(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, app(app(ty_Either, db), dc)) → new_esEs7(zxw79000, zxw80000, db, dc)
new_esEs8(zxw79000, zxw80000, ty_@0) → new_esEs10(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, app(ty_Maybe, de)) → new_esEs6(zxw79000, zxw80000, de)
new_esEs8(zxw79000, zxw80000, ty_Bool) → new_esEs14(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, ty_Ordering) → new_esEs9(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, ty_Integer) → new_esEs15(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, app(ty_Ratio, dd)) → new_esEs18(zxw79000, zxw80000, dd)
new_ltEs5(zxw79001, zxw80001, ty_Char) → new_ltEs10(zxw79001, zxw80001)
new_ltEs5(zxw79001, zxw80001, app(app(ty_@2, eb), ec)) → new_ltEs4(zxw79001, zxw80001, eb, ec)
new_ltEs5(zxw79001, zxw80001, ty_Ordering) → new_ltEs7(zxw79001, zxw80001)
new_ltEs5(zxw79001, zxw80001, ty_Bool) → new_ltEs12(zxw79001, zxw80001)
new_ltEs5(zxw79001, zxw80001, ty_Integer) → new_ltEs13(zxw79001, zxw80001)
new_ltEs5(zxw79001, zxw80001, app(ty_Ratio, ef)) → new_ltEs17(zxw79001, zxw80001, ef)
new_ltEs5(zxw79001, zxw80001, app(ty_Maybe, eg)) → new_ltEs18(zxw79001, zxw80001, eg)
new_ltEs5(zxw79001, zxw80001, ty_Double) → new_ltEs15(zxw79001, zxw80001)
new_ltEs5(zxw79001, zxw80001, app(app(ty_Either, ed), ee)) → new_ltEs14(zxw79001, zxw80001, ed, ee)
new_ltEs5(zxw79001, zxw80001, app(app(app(ty_@3, df), dg), dh)) → new_ltEs6(zxw79001, zxw80001, df, dg, dh)
new_ltEs5(zxw79001, zxw80001, app(ty_[], ea)) → new_ltEs11(zxw79001, zxw80001, ea)
new_ltEs5(zxw79001, zxw80001, ty_Int) → new_ltEs9(zxw79001, zxw80001)
new_ltEs5(zxw79001, zxw80001, ty_@0) → new_ltEs8(zxw79001, zxw80001)
new_ltEs5(zxw79001, zxw80001, ty_Float) → new_ltEs16(zxw79001, zxw80001)
new_lt13(zxw79000, zxw80000) → new_esEs9(new_compare32(zxw79000, zxw80000), LT)
new_lt11(zxw79000, zxw80000, bbd, bbe) → new_esEs9(new_compare19(zxw79000, zxw80000, bbd, bbe), LT)
new_compare19(zxw79000, zxw80000, bbd, bbe) → new_compare210(zxw79000, zxw80000, new_esEs5(zxw79000, zxw80000, bbd, bbe), bbd, bbe)
new_compare210(zxw79000, zxw80000, False, bbd, bbe) → new_compare110(zxw79000, zxw80000, new_ltEs4(zxw79000, zxw80000, bbd, bbe), bbd, bbe)
new_compare210(zxw79000, zxw80000, True, bbd, bbe) → EQ
new_compare110(zxw79000, zxw80000, True, bbd, bbe) → LT
new_compare110(zxw79000, zxw80000, False, bbd, bbe) → GT
new_lt16(zxw79000, zxw80000) → new_esEs9(new_compare7(zxw79000, zxw80000), LT)
new_lt7(zxw79000, zxw80000) → new_esEs9(new_compare30(zxw79000, zxw80000), LT)
new_lt9(zxw79000, zxw80000) → new_esEs9(new_compare17(zxw79000, zxw80000), LT)
new_lt14(zxw790, zxw800, gh, ha) → new_esEs9(new_compare15(zxw790, zxw800, gh, ha), LT)
new_lt15(zxw79000, zxw80000) → new_esEs9(new_compare6(zxw79000, zxw80000), LT)
new_lt8(zxw790, zxw800) → new_esEs9(new_compare16(zxw790, zxw800), LT)
new_lt17(zxw79000, zxw80000, gg) → new_esEs9(new_compare8(zxw79000, zxw80000, gg), LT)
new_lt6(zxw79000, zxw80000) → new_esEs9(new_compare18(zxw79000, zxw80000), LT)
new_lt18(zxw79000, zxw80000, bbh) → new_esEs9(new_compare27(zxw79000, zxw80000, bbh), LT)
new_compare27(zxw79000, zxw80000, bbh) → new_compare28(zxw79000, zxw80000, new_esEs6(zxw79000, zxw80000, bbh), bbh)
new_compare28(zxw79000, zxw80000, False, bbh) → new_compare111(zxw79000, zxw80000, new_ltEs18(zxw79000, zxw80000, bbh), bbh)
new_compare28(zxw79000, zxw80000, True, bbh) → EQ
new_compare111(zxw79000, zxw80000, True, bbh) → LT
new_compare111(zxw79000, zxw80000, False, bbh) → GT
new_lt12(zxw79000, zxw80000) → new_esEs9(new_compare31(zxw79000, zxw80000), LT)
new_compare31(zxw79000, zxw80000) → new_compare23(zxw79000, zxw80000, new_esEs14(zxw79000, zxw80000))
new_compare23(zxw79000, zxw80000, True) → EQ
new_compare23(zxw79000, zxw80000, False) → new_compare10(zxw79000, zxw80000, new_ltEs12(zxw79000, zxw80000))
new_compare10(zxw79000, zxw80000, True) → LT
new_compare10(zxw79000, zxw80000, False) → GT
new_lt10(zxw79000, zxw80000, bgc) → new_esEs9(new_compare1(zxw79000, zxw80000, bgc), LT)
new_lt5(zxw79000, zxw80000, gd, ge, gf) → new_esEs9(new_compare9(zxw79000, zxw80000, gd, ge, gf), LT)
new_compare9(zxw79000, zxw80000, gd, ge, gf) → new_compare25(zxw79000, zxw80000, new_esEs4(zxw79000, zxw80000, gd, ge, gf), gd, ge, gf)
new_compare25(zxw79000, zxw80000, True, gd, ge, gf) → EQ
new_compare25(zxw79000, zxw80000, False, gd, ge, gf) → new_compare12(zxw79000, zxw80000, new_ltEs6(zxw79000, zxw80000, gd, ge, gf), gd, ge, gf)
new_compare12(zxw79000, zxw80000, True, gd, ge, gf) → LT
new_compare12(zxw79000, zxw80000, False, gd, ge, gf) → GT
new_compare34(zxw400, zxw300, h, ba) → new_compare26(Left(zxw400), Right(zxw300), False, h, ba)
new_esEs29(zxw400, zxw300, ty_Integer) → new_esEs15(zxw400, zxw300)
new_esEs29(zxw400, zxw300, ty_Double) → new_esEs16(zxw400, zxw300)
new_esEs29(zxw400, zxw300, app(ty_Maybe, eh)) → new_esEs6(zxw400, zxw300, eh)
new_esEs29(zxw400, zxw300, app(ty_[], cce)) → new_esEs13(zxw400, zxw300, cce)
new_esEs29(zxw400, zxw300, app(app(app(ty_@3, cch), cda), cdb)) → new_esEs4(zxw400, zxw300, cch, cda, cdb)
new_esEs29(zxw400, zxw300, app(ty_Ratio, ccd)) → new_esEs18(zxw400, zxw300, ccd)
new_esEs29(zxw400, zxw300, app(app(ty_@2, ccf), ccg)) → new_esEs5(zxw400, zxw300, ccf, ccg)
new_esEs29(zxw400, zxw300, ty_Char) → new_esEs12(zxw400, zxw300)
new_esEs29(zxw400, zxw300, ty_Int) → new_esEs11(zxw400, zxw300)
new_esEs29(zxw400, zxw300, app(app(ty_Either, beh), bdf)) → new_esEs7(zxw400, zxw300, beh, bdf)
new_esEs29(zxw400, zxw300, ty_@0) → new_esEs10(zxw400, zxw300)
new_esEs29(zxw400, zxw300, ty_Float) → new_esEs17(zxw400, zxw300)
new_esEs29(zxw400, zxw300, ty_Bool) → new_esEs14(zxw400, zxw300)
new_esEs29(zxw400, zxw300, ty_Ordering) → new_esEs9(zxw400, zxw300)

The set Q consists of the following terms:

new_compare23(x0, x1, True)
new_lt6(x0, x1)
new_ltEs5(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, ty_Integer)
new_lt4(x0, x1, app(ty_[], x2))
new_ltEs18(Just(x0), Just(x1), ty_@0)
new_compare16(x0, x1)
new_lt4(x0, x1, app(app(ty_@2, x2), x3))
new_compare13(x0, x1, False, x2, x3)
new_ltEs18(Just(x0), Nothing, x1)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, ty_Double)
new_esEs19(x0, x1, ty_Bool)
new_esEs8(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(x0, x1, app(app(ty_Either, x2), x3))
new_compare30(@0, @0)
new_primCompAux00(x0, GT)
new_esEs30(x0, x1, ty_@0)
new_lt19(x0, x1, ty_Char)
new_esEs30(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_Ordering)
new_compare17(Char(x0), Char(x1))
new_esEs28(x0, x1, ty_Int)
new_ltEs20(x0, x1, app(ty_[], x2))
new_ltEs21(x0, x1, ty_Ordering)
new_ltEs15(x0, x1)
new_primPlusNat1(Zero, Succ(x0))
new_esEs6(Just(x0), Just(x1), ty_Double)
new_compare24(x0, x1, False)
new_lt20(x0, x1, ty_Char)
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, ty_Bool)
new_sr0(Integer(x0), Integer(x1))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare210(x0, x1, False, x2, x3)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs7(Right(x0), Right(x1), x2, ty_Float)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs18(Nothing, Nothing, x0)
new_ltEs7(EQ, EQ)
new_esEs7(Right(x0), Right(x1), x2, ty_Integer)
new_compare29(x0, x1, app(app(ty_@2, x2), x3))
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs19(x0, x1, ty_Integer)
new_ltEs20(x0, x1, ty_Bool)
new_ltEs14(Right(x0), Right(x1), x2, ty_Float)
new_esEs6(Just(x0), Just(x1), app(ty_[], x2))
new_esEs31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_compare25(x0, x1, False, x2, x3, x4)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_ltEs19(x0, x1, ty_Integer)
new_ltEs5(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(ty_[], x2))
new_lt10(x0, x1, x2)
new_ltEs7(EQ, LT)
new_ltEs7(LT, EQ)
new_esEs20(x0, x1, ty_Ordering)
new_esEs17(Float(x0, x1), Float(x2, x3))
new_compare25(x0, x1, True, x2, x3, x4)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_lt19(x0, x1, ty_Ordering)
new_esEs29(x0, x1, ty_@0)
new_esEs26(x0, x1, app(ty_[], x2))
new_ltEs16(x0, x1)
new_lt4(x0, x1, app(ty_Maybe, x2))
new_compare110(x0, x1, False, x2, x3)
new_ltEs14(Left(x0), Left(x1), ty_Char, x2)
new_sr(x0, x1)
new_ltEs19(x0, x1, ty_Double)
new_compare7(Float(x0, x1), Float(x2, x3))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs9(x0, x1)
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_lt7(x0, x1)
new_lt4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, ty_Int)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat0(Zero, x0)
new_esEs7(Right(x0), Right(x1), x2, ty_@0)
new_esEs32(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_ltEs7(LT, LT)
new_esEs7(Right(x0), Right(x1), x2, ty_Double)
new_esEs4(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_Bool)
new_lt5(x0, x1, x2, x3, x4)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt4(x0, x1, ty_Ordering)
new_primEqNat0(Zero, Succ(x0))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Int)
new_esEs15(Integer(x0), Integer(x1))
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Left(x0), Left(x1), ty_Char, x2)
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs26(x0, x1, ty_Double)
new_compare29(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_@0)
new_primPlusNat1(Succ(x0), Zero)
new_esEs22(x0, x1, ty_Integer)
new_ltEs14(Left(x0), Left(x1), ty_@0, x2)
new_primMulInt(Neg(x0), Neg(x1))
new_ltEs19(x0, x1, ty_Int)
new_ltEs21(x0, x1, app(ty_Maybe, x2))
new_compare29(x0, x1, ty_Integer)
new_esEs14(True, True)
new_esEs21(x0, x1, ty_Char)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Int)
new_ltEs18(Just(x0), Just(x1), ty_Integer)
new_esEs24(x0, x1, ty_Int)
new_primEqNat0(Zero, Zero)
new_esEs16(Double(x0, x1), Double(x2, x3))
new_esEs12(Char(x0), Char(x1))
new_lt4(x0, x1, ty_Char)
new_compare29(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, ty_Bool)
new_esEs8(x0, x1, ty_Float)
new_compare1([], :(x0, x1), x2)
new_esEs30(x0, x1, ty_Ordering)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, ty_Integer)
new_esEs29(x0, x1, ty_Bool)
new_esEs30(x0, x1, ty_Bool)
new_esEs30(x0, x1, ty_Float)
new_esEs32(x0, x1, ty_@0)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs14(Left(x0), Left(x1), ty_Int, x2)
new_primCompAux00(x0, LT)
new_esEs27(x0, x1, ty_Integer)
new_ltEs21(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs5(x0, x1, ty_Double)
new_ltEs18(Just(x0), Just(x1), ty_Char)
new_primMulNat0(Zero, Zero)
new_compare110(x0, x1, True, x2, x3)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_lt9(x0, x1)
new_compare29(x0, x1, ty_Double)
new_ltEs5(x0, x1, ty_@0)
new_lt17(x0, x1, x2)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_compare36(x0, x1, x2, x3)
new_ltEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs31(x0, x1, ty_Bool)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Left(x0), Left(x1), ty_Float, x2)
new_esEs32(x0, x1, ty_Float)
new_esEs13([], :(x0, x1), x2)
new_esEs8(x0, x1, ty_Ordering)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_compare10(x0, x1, True)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs7(Left(x0), Left(x1), ty_Float, x2)
new_primEqNat0(Succ(x0), Succ(x1))
new_ltEs19(x0, x1, ty_Bool)
new_esEs28(x0, x1, ty_Double)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, ty_Float)
new_esEs29(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_@0)
new_pePe(True, x0)
new_esEs19(x0, x1, ty_Float)
new_esEs8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_lt16(x0, x1)
new_compare29(x0, x1, ty_Bool)
new_esEs20(x0, x1, app(ty_[], x2))
new_compare11(x0, x1, True)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_compare14(x0, x1, True, x2, x3)
new_esEs6(Just(x0), Just(x1), app(ty_Maybe, x2))
new_lt19(x0, x1, ty_@0)
new_esEs6(Just(x0), Just(x1), ty_Ordering)
new_esEs23(x0, x1, ty_@0)
new_compare29(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Right(x0), Right(x1), x2, ty_Int)
new_ltEs5(x0, x1, ty_Char)
new_esEs30(x0, x1, ty_Double)
new_ltEs21(x0, x1, ty_Int)
new_compare29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Float)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_compare29(x0, x1, ty_Ordering)
new_ltEs21(x0, x1, ty_@0)
new_esEs8(x0, x1, ty_Int)
new_lt14(x0, x1, x2, x3)
new_ltEs12(False, False)
new_esEs6(Just(x0), Just(x1), ty_Bool)
new_compare32(Integer(x0), Integer(x1))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_Int)
new_primMulNat0(Succ(x0), Succ(x1))
new_compare29(x0, x1, ty_Float)
new_ltEs21(x0, x1, ty_Integer)
new_esEs6(Just(x0), Just(x1), ty_Float)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs5(x0, x1, ty_Float)
new_ltEs18(Just(x0), Just(x1), ty_Float)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Bool)
new_esEs31(x0, x1, ty_Double)
new_esEs31(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpNat1(Zero, x0)
new_ltEs8(x0, x1)
new_esEs29(x0, x1, ty_Integer)
new_ltEs21(x0, x1, app(ty_[], x2))
new_primPlusNat1(Zero, Zero)
new_esEs30(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(ty_[], x2))
new_ltEs14(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs23(x0, x1, ty_Double)
new_ltEs18(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs18(Just(x0), Just(x1), ty_Ordering)
new_primCmpNat2(Zero, Zero)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs5(x0, x1, ty_Bool)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_compare28(x0, x1, True, x2)
new_ltEs14(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs5(x0, x1, app(ty_[], x2))
new_asAs(False, x0)
new_esEs29(x0, x1, ty_Ordering)
new_esEs31(x0, x1, app(ty_[], x2))
new_esEs30(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, ty_Char)
new_esEs31(x0, x1, app(app(ty_@2, x2), x3))
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(x0, x1, ty_Integer)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs19(x0, x1, app(ty_[], x2))
new_ltEs18(Just(x0), Just(x1), ty_Bool)
new_lt11(x0, x1, x2, x3)
new_primCmpNat1(Succ(x0), x1)
new_esEs32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs24(x0, x1, ty_Integer)
new_ltEs14(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs27(x0, x1, ty_@0)
new_ltEs14(Right(x0), Right(x1), x2, ty_Double)
new_lt4(x0, x1, ty_Float)
new_compare19(x0, x1, x2, x3)
new_ltEs5(x0, x1, app(app(ty_Either, x2), x3))
new_esEs19(x0, x1, ty_Char)
new_lt4(x0, x1, ty_Double)
new_esEs19(x0, x1, ty_Ordering)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs10(@0, @0)
new_esEs31(x0, x1, ty_@0)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs11(x0, x1)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, ty_Float)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_Char)
new_esEs9(GT, GT)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs27(x0, x1, ty_Char)
new_compare11(x0, x1, False)
new_compare23(x0, x1, False)
new_compare12(x0, x1, True, x2, x3, x4)
new_esEs28(x0, x1, ty_Bool)
new_esEs7(Right(x0), Left(x1), x2, x3)
new_esEs7(Left(x0), Right(x1), x2, x3)
new_compare24(x0, x1, True)
new_compare15(x0, x1, x2, x3)
new_primEqNat0(Succ(x0), Zero)
new_esEs23(x0, x1, ty_Ordering)
new_esEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs7(Right(x0), Right(x1), x2, ty_Int)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_esEs32(x0, x1, app(app(ty_Either, x2), x3))
new_compare9(x0, x1, x2, x3, x4)
new_lt20(x0, x1, ty_Int)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Integer)
new_lt4(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Int)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs5(x0, x1, app(app(ty_@2, x2), x3))
new_lt4(x0, x1, ty_@0)
new_esEs23(x0, x1, ty_Char)
new_esEs28(x0, x1, ty_Ordering)
new_ltEs18(Just(x0), Just(x1), ty_Double)
new_esEs30(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_Integer)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_compare14(x0, x1, False, x2, x3)
new_lt20(x0, x1, ty_@0)
new_compare1([], [], x0)
new_esEs9(EQ, EQ)
new_pePe(False, x0)
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs5(x0, x1, app(ty_Ratio, x2))
new_ltEs18(Just(x0), Just(x1), app(ty_[], x2))
new_esEs6(Just(x0), Just(x1), ty_Char)
new_esEs25(x0, x1, ty_Integer)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs18(:%(x0, x1), :%(x2, x3), x4)
new_esEs26(x0, x1, ty_Integer)
new_compare12(x0, x1, False, x2, x3, x4)
new_esEs8(x0, x1, app(ty_Maybe, x2))
new_primCompAux00(x0, EQ)
new_esEs19(x0, x1, ty_Int)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs14(True, False)
new_esEs14(False, True)
new_lt4(x0, x1, ty_Integer)
new_esEs7(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs14(Right(x0), Right(x1), x2, ty_@0)
new_fsEs(x0)
new_esEs22(x0, x1, ty_Float)
new_lt4(x0, x1, ty_Bool)
new_primCmpNat2(Succ(x0), Succ(x1))
new_asAs(True, x0)
new_ltEs18(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, ty_Bool)
new_esEs6(Nothing, Just(x0), x1)
new_esEs6(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs6(Just(x0), Nothing, x1)
new_lt18(x0, x1, x2)
new_esEs8(x0, x1, app(ty_[], x2))
new_esEs31(x0, x1, ty_Integer)
new_compare111(x0, x1, False, x2)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs8(x0, x1, ty_Char)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, ty_Float)
new_ltEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs22(x0, x1, ty_@0)
new_esEs20(x0, x1, ty_Char)
new_esEs13(:(x0, x1), [], x2)
new_ltEs12(False, True)
new_ltEs12(True, False)
new_compare6(Double(x0, x1), Double(x2, x3))
new_ltEs20(x0, x1, ty_@0)
new_esEs22(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_@0)
new_ltEs18(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare35(x0, x1, x2, x3)
new_ltEs14(Right(x0), Right(x1), x2, ty_Integer)
new_lt19(x0, x1, ty_Double)
new_esEs32(x0, x1, app(ty_[], x2))
new_lt19(x0, x1, ty_Bool)
new_ltEs14(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs7(Right(x0), Right(x1), x2, ty_Char)
new_ltEs14(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs26(x0, x1, ty_Char)
new_ltEs14(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs5(x0, x1, ty_Int)
new_lt4(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_Double)
new_esEs32(x0, x1, app(ty_Ratio, x2))
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_esEs19(x0, x1, ty_@0)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs21(x0, x1, ty_Bool)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs14(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs21(x0, x1, ty_Double)
new_lt12(x0, x1)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs8(x0, x1, ty_Bool)
new_ltEs21(x0, x1, ty_Char)
new_lt13(x0, x1)
new_esEs13(:(x0, x1), :(x2, x3), x4)
new_esEs31(x0, x1, ty_Ordering)
new_ltEs14(Right(x0), Right(x1), x2, ty_Bool)
new_compare1(:(x0, x1), [], x2)
new_compare27(x0, x1, x2)
new_compare10(x0, x1, False)
new_esEs27(x0, x1, app(ty_[], x2))
new_primMulNat0(Succ(x0), Zero)
new_ltEs19(x0, x1, ty_Float)
new_ltEs14(Left(x0), Right(x1), x2, x3)
new_esEs23(x0, x1, ty_Float)
new_ltEs14(Right(x0), Left(x1), x2, x3)
new_compare29(x0, x1, ty_Int)
new_esEs22(x0, x1, ty_Int)
new_esEs31(x0, x1, app(ty_Maybe, x2))
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Float)
new_compare31(x0, x1)
new_esEs29(x0, x1, ty_Double)
new_esEs32(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Left(x0), Left(x1), ty_Double, x2)
new_esEs31(x0, x1, ty_Char)
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Just(x0), Just(x1), ty_Int)
new_compare33(x0, x1, x2, x3)
new_esEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs21(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs7(LT, GT)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs7(GT, LT)
new_ltEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Double)
new_compare29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare111(x0, x1, True, x2)
new_ltEs13(x0, x1)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs32(x0, x1, app(ty_Maybe, x2))
new_esEs31(x0, x1, ty_Int)
new_lt4(x0, x1, ty_Int)
new_ltEs11(x0, x1, x2)
new_lt20(x0, x1, ty_Float)
new_not(True)
new_esEs31(x0, x1, ty_Float)
new_esEs20(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Float)
new_esEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs6(Nothing, Nothing, x0)
new_esEs28(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Ordering)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(Left(x0), Left(x1), ty_Double, x2)
new_esEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs6(Just(x0), Just(x1), ty_Integer)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_not(False)
new_lt8(x0, x1)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_ltEs18(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare13(x0, x1, True, x2, x3)
new_esEs32(x0, x1, ty_Integer)
new_esEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs19(x0, x1, ty_Char)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_esEs6(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare8(:%(x0, x1), :%(x2, x3), ty_Integer)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_Integer)
new_esEs8(x0, x1, ty_@0)
new_compare26(Left(x0), Left(x1), False, x2, x3)
new_ltEs12(True, True)
new_esEs27(x0, x1, ty_Float)
new_lt15(x0, x1)
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, ty_Ordering)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, ty_Double)
new_esEs6(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_lt20(x0, x1, ty_Ordering)
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs22(x0, x1, ty_Char)
new_lt20(x0, x1, ty_Double)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Bool)
new_esEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_ltEs21(x0, x1, ty_Float)
new_ltEs10(x0, x1)
new_ltEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs14(Left(x0), Left(x1), ty_Bool, x2)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs14(Left(x0), Left(x1), ty_Integer, x2)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(x0, x1, ty_Ordering)
new_esEs8(x0, x1, ty_Double)
new_compare29(x0, x1, ty_Char)
new_esEs6(Just(x0), Just(x1), ty_@0)
new_compare1(:(x0, x1), :(x2, x3), x4)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_compare210(x0, x1, True, x2, x3)
new_esEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs6(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs29(x0, x1, ty_Float)
new_esEs19(x0, x1, ty_Double)
new_esEs14(False, False)
new_primEqInt(Pos(Zero), Pos(Zero))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs32(x0, x1, ty_Char)
new_lt19(x0, x1, app(ty_[], x2))
new_ltEs21(x0, x1, ty_Double)
new_esEs32(x0, x1, ty_Int)
new_primCmpNat2(Succ(x0), Zero)
new_compare34(x0, x1, x2, x3)
new_compare18(x0, x1)
new_esEs29(x0, x1, ty_Int)
new_esEs32(x0, x1, ty_Bool)
new_compare28(x0, x1, False, x2)
new_ltEs14(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs18(Just(x0), Just(x1), ty_Int)
new_compare26(Right(x0), Right(x1), False, x2, x3)
new_ltEs17(x0, x1, x2)
new_primPlusNat0(Succ(x0), x1)
new_esEs7(Left(x0), Left(x1), ty_Int, x2)
new_esEs20(x0, x1, ty_Integer)
new_primCmpNat0(x0, Zero)
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_esEs7(Left(x0), Left(x1), ty_@0, x2)
new_ltEs7(GT, EQ)
new_ltEs7(EQ, GT)
new_esEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs32(x0, x1, ty_Double)
new_ltEs7(GT, GT)
new_esEs31(x0, x1, app(ty_Ratio, x2))
new_esEs9(LT, LT)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs13([], [], x0)
new_primCompAux0(x0, x1, x2, x3)
new_compare29(x0, x1, ty_@0)
new_esEs7(Left(x0), Left(x1), ty_Bool, x2)
new_compare26(x0, x1, True, x2, x3)
new_compare26(Right(x0), Left(x1), False, x2, x3)
new_compare26(Left(x0), Right(x1), False, x2, x3)
new_ltEs18(Nothing, Just(x0), x1)
new_esEs27(x0, x1, ty_Ordering)
new_primCmpNat0(x0, Succ(x1))

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

new_esEs30(x0, x1, ty_@0)
new_esEs30(x0, x1, ty_Int)
new_esEs31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs30(x0, x1, ty_Ordering)
new_esEs30(x0, x1, ty_Bool)
new_esEs30(x0, x1, ty_Float)
new_compare36(x0, x1, x2, x3)
new_esEs31(x0, x1, ty_Bool)
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_esEs30(x0, x1, ty_Double)
new_esEs31(x0, x1, ty_Double)
new_esEs31(x0, x1, app(app(ty_Either, x2), x3))
new_esEs30(x0, x1, ty_Integer)
new_esEs31(x0, x1, app(ty_[], x2))
new_esEs30(x0, x1, app(ty_[], x2))
new_esEs31(x0, x1, app(app(ty_@2, x2), x3))
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs31(x0, x1, ty_@0)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs30(x0, x1, ty_Char)
new_esEs31(x0, x1, ty_Integer)
new_compare35(x0, x1, x2, x3)
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_esEs31(x0, x1, ty_Ordering)
new_esEs31(x0, x1, app(ty_Maybe, x2))
new_esEs31(x0, x1, ty_Char)
new_esEs31(x0, x1, ty_Int)
new_esEs31(x0, x1, ty_Float)
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs31(x0, x1, app(ty_Ratio, x2))



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

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

new_splitLT10(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, True, h, ba, bb) → new_splitLT(zxw34, zxw400, h, ba, bb)
new_splitLT3(Left(zxw300), zxw31, zxw32, zxw33, zxw34, Left(zxw400), h, ba, bb) → new_splitLT2(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs9(new_compare26(Left(zxw400), Left(zxw300), new_esEs29(zxw400, zxw300, h), h, ba), LT), h, ba, bb)
new_splitLT3(Right(zxw300), zxw31, zxw32, zxw33, zxw34, Left(zxw400), h, ba, bb) → new_splitLT20(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs9(new_compare26(Left(zxw400), Right(zxw300), False, h, ba), LT), h, ba, bb)
new_splitLT20(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, False, h, ba, bb) → new_splitLT10(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs9(new_compare34(zxw400, zxw300, h, ba), GT), h, ba, bb)
new_splitLT2(zxw45, zxw46, zxw47, zxw48, zxw49, zxw50, False, bc, bd, be) → new_splitLT1(zxw45, zxw46, zxw47, zxw48, zxw49, zxw50, new_esEs9(new_compare33(zxw50, zxw45, bc, bd), GT), bc, bd, be)
new_splitLT1(zxw45, zxw46, zxw47, zxw48, zxw49, zxw50, True, bc, bd, be) → new_splitLT(zxw49, zxw50, bc, bd, be)
new_splitLT20(zxw300, zxw31, zxw32, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw34, zxw400, True, h, ba, bb) → new_splitLT3(zxw330, zxw331, zxw332, zxw333, zxw334, Left(zxw400), h, ba, bb)
new_splitLT2(zxw45, zxw46, zxw47, zxw48, zxw49, zxw50, True, bc, bd, be) → new_splitLT(zxw48, zxw50, bc, bd, be)
new_splitLT(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw400, h, ba, bb) → new_splitLT3(zxw330, zxw331, zxw332, zxw333, zxw334, Left(zxw400), h, ba, bb)

The TRS R consists of the following rules:

new_compare33(zxw20, zxw15, cdc, cdd) → new_compare26(Left(zxw20), Left(zxw15), new_esEs32(zxw20, zxw15, cdc), cdc, cdd)
new_esEs9(LT, GT) → False
new_esEs9(EQ, GT) → False
new_esEs9(GT, GT) → True
new_esEs32(zxw20, zxw15, ty_Float) → new_esEs17(zxw20, zxw15)
new_esEs32(zxw20, zxw15, ty_Integer) → new_esEs15(zxw20, zxw15)
new_esEs32(zxw20, zxw15, ty_@0) → new_esEs10(zxw20, zxw15)
new_esEs32(zxw20, zxw15, ty_Ordering) → new_esEs9(zxw20, zxw15)
new_esEs32(zxw20, zxw15, ty_Bool) → new_esEs14(zxw20, zxw15)
new_esEs32(zxw20, zxw15, app(app(ty_Either, ceb), cec)) → new_esEs7(zxw20, zxw15, ceb, cec)
new_esEs32(zxw20, zxw15, app(ty_[], cdf)) → new_esEs13(zxw20, zxw15, cdf)
new_esEs32(zxw20, zxw15, app(ty_Maybe, cdg)) → new_esEs6(zxw20, zxw15, cdg)
new_esEs32(zxw20, zxw15, app(app(ty_@2, cdh), cea)) → new_esEs5(zxw20, zxw15, cdh, cea)
new_esEs32(zxw20, zxw15, ty_Char) → new_esEs12(zxw20, zxw15)
new_esEs32(zxw20, zxw15, app(app(app(ty_@3, ced), cee), cef)) → new_esEs4(zxw20, zxw15, ced, cee, cef)
new_esEs32(zxw20, zxw15, ty_Int) → new_esEs11(zxw20, zxw15)
new_esEs32(zxw20, zxw15, app(ty_Ratio, cde)) → new_esEs18(zxw20, zxw15, cde)
new_esEs32(zxw20, zxw15, ty_Double) → new_esEs16(zxw20, zxw15)
new_compare26(zxw790, zxw800, True, gh, ha) → EQ
new_compare26(Left(zxw7900), Left(zxw8000), False, gh, ha) → new_compare13(zxw7900, zxw8000, new_ltEs19(zxw7900, zxw8000, gh), gh, ha)
new_ltEs19(zxw7900, zxw8000, ty_Float) → new_ltEs16(zxw7900, zxw8000)
new_ltEs19(zxw7900, zxw8000, app(app(ty_@2, ca), cb)) → new_ltEs4(zxw7900, zxw8000, ca, cb)
new_ltEs19(zxw7900, zxw8000, app(ty_[], he)) → new_ltEs11(zxw7900, zxw8000, he)
new_ltEs19(zxw7900, zxw8000, ty_Char) → new_ltEs10(zxw7900, zxw8000)
new_ltEs19(zxw7900, zxw8000, ty_Bool) → new_ltEs12(zxw7900, zxw8000)
new_ltEs19(zxw7900, zxw8000, app(ty_Ratio, hh)) → new_ltEs17(zxw7900, zxw8000, hh)
new_ltEs19(zxw7900, zxw8000, app(app(app(ty_@3, hb), hc), hd)) → new_ltEs6(zxw7900, zxw8000, hb, hc, hd)
new_ltEs19(zxw7900, zxw8000, ty_Int) → new_ltEs9(zxw7900, zxw8000)
new_ltEs19(zxw7900, zxw8000, app(app(ty_Either, hf), hg)) → new_ltEs14(zxw7900, zxw8000, hf, hg)
new_ltEs19(zxw7900, zxw8000, ty_@0) → new_ltEs8(zxw7900, zxw8000)
new_ltEs19(zxw7900, zxw8000, ty_Double) → new_ltEs15(zxw7900, zxw8000)
new_ltEs19(zxw7900, zxw8000, ty_Integer) → new_ltEs13(zxw7900, zxw8000)
new_ltEs19(zxw7900, zxw8000, ty_Ordering) → new_ltEs7(zxw7900, zxw8000)
new_ltEs19(zxw7900, zxw8000, app(ty_Maybe, baa)) → new_ltEs18(zxw7900, zxw8000, baa)
new_compare13(zxw235, zxw236, False, bbf, bbg) → GT
new_compare13(zxw235, zxw236, True, bbf, bbg) → LT
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Char) → new_ltEs10(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Integer) → new_ltEs13(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(ty_Ratio, dac)) → new_ltEs17(zxw79000, zxw80000, dac)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(app(app(ty_@3, chc), chd), che)) → new_ltEs6(zxw79000, zxw80000, chc, chd, che)
new_ltEs18(Nothing, Nothing, baa) → True
new_ltEs18(Just(zxw79000), Nothing, baa) → False
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Double) → new_ltEs15(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(ty_[], chf)) → new_ltEs11(zxw79000, zxw80000, chf)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(app(ty_@2, chg), chh)) → new_ltEs4(zxw79000, zxw80000, chg, chh)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Bool) → new_ltEs12(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Ordering) → new_ltEs7(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Float) → new_ltEs16(zxw79000, zxw80000)
new_ltEs18(Nothing, Just(zxw80000), baa) → True
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Int) → new_ltEs9(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_@0) → new_ltEs8(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(ty_Maybe, dad)) → new_ltEs18(zxw79000, zxw80000, dad)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(ty_Maybe, chb)) → new_ltEs18(zxw79000, zxw80000, chb)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(app(ty_Either, daa), dab)) → new_ltEs14(zxw79000, zxw80000, daa, dab)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(app(ty_Either, cgg), cgh)) → new_ltEs14(zxw79000, zxw80000, cgg, cgh)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(app(ty_Either, cfe), cff), hg) → new_ltEs14(zxw79000, zxw80000, cfe, cff)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(ty_Maybe, cfh), hg) → new_ltEs18(zxw79000, zxw80000, cfh)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Bool) → new_ltEs12(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(ty_[], cgd)) → new_ltEs11(zxw79000, zxw80000, cgd)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Bool, hg) → new_ltEs12(zxw79000, zxw80000)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(ty_Ratio, cfg), hg) → new_ltEs17(zxw79000, zxw80000, cfg)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(app(app(ty_@3, cga), cgb), cgc)) → new_ltEs6(zxw79000, zxw80000, cga, cgb, cgc)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Float, hg) → new_ltEs16(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Float) → new_ltEs16(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Double) → new_ltEs15(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(app(ty_@2, cge), cgf)) → new_ltEs4(zxw79000, zxw80000, cge, cgf)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Double, hg) → new_ltEs15(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Left(zxw80000), hf, hg) → False
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Int, hg) → new_ltEs9(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Char) → new_ltEs10(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_@0) → new_ltEs8(zxw79000, zxw80000)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(app(app(ty_@3, ceg), ceh), cfa), hg) → new_ltEs6(zxw79000, zxw80000, ceg, ceh, cfa)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_@0, hg) → new_ltEs8(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Ordering) → new_ltEs7(zxw79000, zxw80000)
new_ltEs14(Left(zxw79000), Right(zxw80000), hf, hg) → True
new_ltEs14(Left(zxw79000), Left(zxw80000), app(app(ty_@2, cfc), cfd), hg) → new_ltEs4(zxw79000, zxw80000, cfc, cfd)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(ty_[], cfb), hg) → new_ltEs11(zxw79000, zxw80000, cfb)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Integer, hg) → new_ltEs13(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Int) → new_ltEs9(zxw79000, zxw80000)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Ordering, hg) → new_ltEs7(zxw79000, zxw80000)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Char, hg) → new_ltEs10(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(ty_Ratio, cha)) → new_ltEs17(zxw79000, zxw80000, cha)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Integer) → new_ltEs13(zxw79000, zxw80000)
new_ltEs13(zxw7900, zxw8000) → new_fsEs(new_compare32(zxw7900, zxw8000))
new_compare32(Integer(zxw79000), Integer(zxw80000)) → new_primCmpInt(zxw79000, zxw80000)
new_fsEs(zxw259) → new_not(new_esEs9(zxw259, GT))
new_not(False) → True
new_not(True) → False
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_ltEs17(zxw7900, zxw8000, hh) → new_fsEs(new_compare8(zxw7900, zxw8000, hh))
new_compare8(:%(zxw79000, zxw79001), :%(zxw80000, zxw80001), ty_Integer) → new_compare32(new_sr0(zxw79000, zxw80001), new_sr0(zxw80000, zxw79001))
new_compare8(:%(zxw79000, zxw79001), :%(zxw80000, zxw80001), ty_Int) → new_compare16(new_sr(zxw79000, zxw80001), new_sr(zxw80000, zxw79001))
new_sr(zxw4000, zxw3000) → new_primMulInt(zxw4000, zxw3000)
new_compare16(zxw79, zxw80) → new_primCmpInt(zxw79, zxw80)
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Neg(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Pos(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulNat0(Zero, Zero) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_sr0(Integer(zxw800000), Integer(zxw790010)) → Integer(new_primMulInt(zxw800000, zxw790010))
new_ltEs10(zxw7900, zxw8000) → new_fsEs(new_compare17(zxw7900, zxw8000))
new_compare17(Char(zxw79000), Char(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_ltEs7(LT, EQ) → True
new_ltEs7(GT, GT) → True
new_ltEs7(EQ, EQ) → True
new_ltEs7(GT, LT) → False
new_ltEs7(GT, EQ) → False
new_ltEs7(EQ, GT) → True
new_ltEs7(EQ, LT) → False
new_ltEs7(LT, LT) → True
new_ltEs7(LT, GT) → True
new_ltEs9(zxw7900, zxw8000) → new_fsEs(new_compare16(zxw7900, zxw8000))
new_ltEs11(zxw7900, zxw8000, he) → new_fsEs(new_compare1(zxw7900, zxw8000, he))
new_compare1([], :(zxw80000, zxw80001), he) → LT
new_compare1(:(zxw79000, zxw79001), :(zxw80000, zxw80001), he) → new_primCompAux0(zxw79000, zxw80000, new_compare1(zxw79001, zxw80001, he), he)
new_compare1(:(zxw79000, zxw79001), [], he) → GT
new_compare1([], [], he) → EQ
new_primCompAux0(zxw79000, zxw80000, zxw272, he) → new_primCompAux00(zxw272, new_compare29(zxw79000, zxw80000, he))
new_compare29(zxw79000, zxw80000, ty_Char) → new_compare17(zxw79000, zxw80000)
new_compare29(zxw79000, zxw80000, ty_Bool) → new_compare31(zxw79000, zxw80000)
new_compare29(zxw79000, zxw80000, app(app(ty_@2, cbf), cbg)) → new_compare19(zxw79000, zxw80000, cbf, cbg)
new_compare29(zxw79000, zxw80000, app(ty_[], cbe)) → new_compare1(zxw79000, zxw80000, cbe)
new_compare29(zxw79000, zxw80000, app(app(app(ty_@3, cbb), cbc), cbd)) → new_compare9(zxw79000, zxw80000, cbb, cbc, cbd)
new_compare29(zxw79000, zxw80000, ty_Int) → new_compare16(zxw79000, zxw80000)
new_compare29(zxw79000, zxw80000, ty_Integer) → new_compare32(zxw79000, zxw80000)
new_compare29(zxw79000, zxw80000, app(ty_Maybe, ccc)) → new_compare27(zxw79000, zxw80000, ccc)
new_compare29(zxw79000, zxw80000, app(ty_Ratio, ccb)) → new_compare8(zxw79000, zxw80000, ccb)
new_compare29(zxw79000, zxw80000, ty_Float) → new_compare7(zxw79000, zxw80000)
new_compare29(zxw79000, zxw80000, ty_Double) → new_compare6(zxw79000, zxw80000)
new_compare29(zxw79000, zxw80000, app(app(ty_Either, cbh), cca)) → new_compare15(zxw79000, zxw80000, cbh, cca)
new_compare29(zxw79000, zxw80000, ty_Ordering) → new_compare18(zxw79000, zxw80000)
new_compare29(zxw79000, zxw80000, ty_@0) → new_compare30(zxw79000, zxw80000)
new_primCompAux00(zxw276, LT) → LT
new_primCompAux00(zxw276, EQ) → zxw276
new_primCompAux00(zxw276, GT) → GT
new_compare30(@0, @0) → EQ
new_compare18(zxw79000, zxw80000) → new_compare24(zxw79000, zxw80000, new_esEs9(zxw79000, zxw80000))
new_esEs9(GT, LT) → False
new_esEs9(GT, EQ) → False
new_esEs9(EQ, EQ) → True
new_esEs9(EQ, LT) → False
new_esEs9(LT, EQ) → False
new_esEs9(LT, LT) → True
new_compare24(zxw79000, zxw80000, False) → new_compare11(zxw79000, zxw80000, new_ltEs7(zxw79000, zxw80000))
new_compare24(zxw79000, zxw80000, True) → EQ
new_compare11(zxw79000, zxw80000, False) → GT
new_compare11(zxw79000, zxw80000, True) → LT
new_compare15(zxw790, zxw800, gh, ha) → new_compare26(zxw790, zxw800, new_esEs7(zxw790, zxw800, gh, ha), gh, ha)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Bool, bdf) → new_esEs14(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Right(zxw3000), beh, bdf) → False
new_esEs7(Right(zxw4000), Left(zxw3000), beh, bdf) → False
new_esEs7(Right(zxw4000), Right(zxw3000), beh, app(app(ty_@2, bfd), bfe)) → new_esEs5(zxw4000, zxw3000, bfd, bfe)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Int, bdf) → new_esEs11(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), app(app(ty_@2, bea), beb), bdf) → new_esEs5(zxw4000, zxw3000, bea, beb)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Ordering, bdf) → new_esEs9(zxw4000, zxw3000)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, app(ty_[], bfb)) → new_esEs13(zxw4000, zxw3000, bfb)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Integer, bdf) → new_esEs15(zxw4000, zxw3000)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, app(app(app(ty_@3, bfh), bga), bgb)) → new_esEs4(zxw4000, zxw3000, bfh, bga, bgb)
new_esEs7(Left(zxw4000), Left(zxw3000), app(ty_Ratio, bde), bdf) → new_esEs18(zxw4000, zxw3000, bde)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_@0, bdf) → new_esEs10(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), app(app(app(ty_@3, bee), bef), beg), bdf) → new_esEs4(zxw4000, zxw3000, bee, bef, beg)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Double, bdf) → new_esEs16(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Float, bdf) → new_esEs17(zxw4000, zxw3000)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Char, bdf) → new_esEs12(zxw4000, zxw3000)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), app(ty_[], bdg), bdf) → new_esEs13(zxw4000, zxw3000, bdg)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, app(ty_Ratio, bfa)) → new_esEs18(zxw4000, zxw3000, bfa)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_compare26(Left(zxw7900), Right(zxw8000), False, gh, ha) → LT
new_compare26(Right(zxw7900), Left(zxw8000), False, gh, ha) → GT
new_compare26(Right(zxw7900), Right(zxw8000), False, gh, ha) → new_compare14(zxw7900, zxw8000, new_ltEs20(zxw7900, zxw8000, ha), gh, ha)
new_esEs6(Just(zxw4000), Just(zxw3000), app(ty_Maybe, fc)) → new_esEs6(zxw4000, zxw3000, fc)
new_esEs7(Left(zxw4000), Left(zxw3000), app(app(ty_Either, bec), bed), bdf) → new_esEs7(zxw4000, zxw3000, bec, bed)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, app(ty_Maybe, bfc)) → new_esEs6(zxw4000, zxw3000, bfc)
new_esEs6(Just(zxw4000), Just(zxw3000), app(app(ty_Either, fg), fh)) → new_esEs7(zxw4000, zxw3000, fg, fh)
new_esEs7(Left(zxw4000), Left(zxw3000), app(ty_Maybe, bdh), bdf) → new_esEs6(zxw4000, zxw3000, bdh)
new_esEs7(Right(zxw4000), Right(zxw3000), beh, app(app(ty_Either, bff), bfg)) → new_esEs7(zxw4000, zxw3000, bff, bfg)
new_esEs6(Just(zxw4000), Just(zxw3000), app(app(ty_@2, fd), ff)) → new_esEs5(zxw4000, zxw3000, fd, ff)
new_esEs6(Nothing, Nothing, eh) → True
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs6(Nothing, Just(zxw3000), eh) → False
new_esEs6(Just(zxw4000), Nothing, eh) → False
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), app(app(app(ty_@3, ga), gb), gc)) → new_esEs4(zxw4000, zxw3000, ga, gb, gc)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_@0) → new_esEs10(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), app(ty_[], fb)) → new_esEs13(zxw4000, zxw3000, fb)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Char) → new_esEs12(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Float) → new_esEs17(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), app(ty_Ratio, fa)) → new_esEs18(zxw4000, zxw3000, fa)
new_esEs18(:%(zxw4000, zxw4001), :%(zxw3000, zxw3001), ccd) → new_asAs(new_esEs25(zxw4000, zxw3000, ccd), new_esEs24(zxw4001, zxw3001, ccd))
new_esEs25(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs25(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs24(zxw4001, zxw3001, ty_Integer) → new_esEs15(zxw4001, zxw3001)
new_esEs24(zxw4001, zxw3001, ty_Int) → new_esEs11(zxw4001, zxw3001)
new_asAs(False, zxw230) → False
new_asAs(True, zxw230) → zxw230
new_esEs11(zxw400, zxw300) → new_primEqInt(zxw400, zxw300)
new_primEqInt(Neg(Succ(zxw40000)), Neg(Succ(zxw30000))) → new_primEqNat0(zxw40000, zxw30000)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Neg(Succ(zxw30000))) → False
new_primEqInt(Neg(Succ(zxw40000)), Neg(Zero)) → False
new_primEqInt(Pos(Succ(zxw40000)), Pos(Succ(zxw30000))) → new_primEqNat0(zxw40000, zxw30000)
new_primEqInt(Pos(Zero), Pos(Succ(zxw30000))) → False
new_primEqInt(Pos(Succ(zxw40000)), Pos(Zero)) → False
new_primEqInt(Neg(Succ(zxw40000)), Pos(zxw3000)) → False
new_primEqInt(Pos(Succ(zxw40000)), Neg(zxw3000)) → False
new_primEqInt(Neg(Zero), Pos(Succ(zxw30000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(zxw30000))) → False
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqNat0(Zero, Zero) → True
new_primEqNat0(Succ(zxw40000), Succ(zxw30000)) → new_primEqNat0(zxw40000, zxw30000)
new_primEqNat0(Zero, Succ(zxw30000)) → False
new_primEqNat0(Succ(zxw40000), Zero) → False
new_esEs15(Integer(zxw4000), Integer(zxw3000)) → new_primEqInt(zxw4000, zxw3000)
new_esEs17(Float(zxw4000, zxw4001), Float(zxw3000, zxw3001)) → new_esEs11(new_sr(zxw4000, zxw3000), new_sr(zxw4001, zxw3001))
new_esEs12(Char(zxw4000), Char(zxw3000)) → new_primEqNat0(zxw4000, zxw3000)
new_esEs13([], [], cce) → True
new_esEs13(:(zxw4000, zxw4001), :(zxw3000, zxw3001), cce) → new_asAs(new_esEs23(zxw4000, zxw3000, cce), new_esEs13(zxw4001, zxw3001, cce))
new_esEs13(:(zxw4000, zxw4001), [], cce) → False
new_esEs13([], :(zxw3000, zxw3001), cce) → False
new_esEs23(zxw4000, zxw3000, app(app(ty_Either, deh), dfa)) → new_esEs7(zxw4000, zxw3000, deh, dfa)
new_esEs23(zxw4000, zxw3000, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, app(app(app(ty_@3, dfb), dfc), dfd)) → new_esEs4(zxw4000, zxw3000, dfb, dfc, dfd)
new_esEs23(zxw4000, zxw3000, app(app(ty_@2, def), deg)) → new_esEs5(zxw4000, zxw3000, def, deg)
new_esEs23(zxw4000, zxw3000, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, app(ty_Ratio, dec)) → new_esEs18(zxw4000, zxw3000, dec)
new_esEs23(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, app(ty_Maybe, dee)) → new_esEs6(zxw4000, zxw3000, dee)
new_esEs23(zxw4000, zxw3000, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, app(ty_[], ded)) → new_esEs13(zxw4000, zxw3000, ded)
new_esEs16(Double(zxw4000, zxw4001), Double(zxw3000, zxw3001)) → new_esEs11(new_sr(zxw4000, zxw3000), new_sr(zxw4001, zxw3001))
new_esEs10(@0, @0) → True
new_esEs5(@2(zxw4000, zxw4001), @2(zxw3000, zxw3001), ccf, ccg) → new_asAs(new_esEs22(zxw4000, zxw3000, ccf), new_esEs21(zxw4001, zxw3001, ccg))
new_esEs22(zxw4000, zxw3000, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, app(app(ty_@2, ddd), dde)) → new_esEs5(zxw4000, zxw3000, ddd, dde)
new_esEs22(zxw4000, zxw3000, app(ty_Maybe, ddc)) → new_esEs6(zxw4000, zxw3000, ddc)
new_esEs22(zxw4000, zxw3000, app(ty_Ratio, dda)) → new_esEs18(zxw4000, zxw3000, dda)
new_esEs22(zxw4000, zxw3000, app(app(ty_Either, ddf), ddg)) → new_esEs7(zxw4000, zxw3000, ddf, ddg)
new_esEs22(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, app(app(app(ty_@3, ddh), dea), deb)) → new_esEs4(zxw4000, zxw3000, ddh, dea, deb)
new_esEs22(zxw4000, zxw3000, app(ty_[], ddb)) → new_esEs13(zxw4000, zxw3000, ddb)
new_esEs22(zxw4000, zxw3000, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs21(zxw4001, zxw3001, ty_Bool) → new_esEs14(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, ty_Double) → new_esEs16(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, ty_Ordering) → new_esEs9(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, ty_Char) → new_esEs12(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, ty_Float) → new_esEs17(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, app(ty_Maybe, dca)) → new_esEs6(zxw4001, zxw3001, dca)
new_esEs21(zxw4001, zxw3001, ty_Int) → new_esEs11(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, app(ty_[], dbh)) → new_esEs13(zxw4001, zxw3001, dbh)
new_esEs21(zxw4001, zxw3001, ty_Integer) → new_esEs15(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, app(app(ty_@2, dcb), dcc)) → new_esEs5(zxw4001, zxw3001, dcb, dcc)
new_esEs21(zxw4001, zxw3001, ty_@0) → new_esEs10(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, app(app(ty_Either, dcd), dce)) → new_esEs7(zxw4001, zxw3001, dcd, dce)
new_esEs21(zxw4001, zxw3001, app(app(app(ty_@3, dcf), dcg), dch)) → new_esEs4(zxw4001, zxw3001, dcf, dcg, dch)
new_esEs21(zxw4001, zxw3001, app(ty_Ratio, dbg)) → new_esEs18(zxw4001, zxw3001, dbg)
new_esEs4(@3(zxw4000, zxw4001, zxw4002), @3(zxw3000, zxw3001, zxw3002), cch, cda, cdb) → new_asAs(new_esEs28(zxw4000, zxw3000, cch), new_asAs(new_esEs27(zxw4001, zxw3001, cda), new_esEs26(zxw4002, zxw3002, cdb)))
new_esEs28(zxw4000, zxw3000, app(ty_[], ead)) → new_esEs13(zxw4000, zxw3000, ead)
new_esEs28(zxw4000, zxw3000, app(app(app(ty_@3, ebb), ebc), ebd)) → new_esEs4(zxw4000, zxw3000, ebb, ebc, ebd)
new_esEs28(zxw4000, zxw3000, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, app(ty_Maybe, eae)) → new_esEs6(zxw4000, zxw3000, eae)
new_esEs28(zxw4000, zxw3000, app(app(ty_Either, eah), eba)) → new_esEs7(zxw4000, zxw3000, eah, eba)
new_esEs28(zxw4000, zxw3000, app(app(ty_@2, eaf), eag)) → new_esEs5(zxw4000, zxw3000, eaf, eag)
new_esEs28(zxw4000, zxw3000, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, app(ty_Ratio, eac)) → new_esEs18(zxw4000, zxw3000, eac)
new_esEs28(zxw4000, zxw3000, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_esEs27(zxw4001, zxw3001, app(ty_Ratio, dha)) → new_esEs18(zxw4001, zxw3001, dha)
new_esEs27(zxw4001, zxw3001, app(app(app(ty_@3, dhh), eaa), eab)) → new_esEs4(zxw4001, zxw3001, dhh, eaa, eab)
new_esEs27(zxw4001, zxw3001, app(ty_Maybe, dhc)) → new_esEs6(zxw4001, zxw3001, dhc)
new_esEs27(zxw4001, zxw3001, app(app(ty_Either, dhf), dhg)) → new_esEs7(zxw4001, zxw3001, dhf, dhg)
new_esEs27(zxw4001, zxw3001, ty_Ordering) → new_esEs9(zxw4001, zxw3001)
new_esEs27(zxw4001, zxw3001, ty_Float) → new_esEs17(zxw4001, zxw3001)
new_esEs27(zxw4001, zxw3001, ty_@0) → new_esEs10(zxw4001, zxw3001)
new_esEs27(zxw4001, zxw3001, ty_Char) → new_esEs12(zxw4001, zxw3001)
new_esEs27(zxw4001, zxw3001, ty_Double) → new_esEs16(zxw4001, zxw3001)
new_esEs27(zxw4001, zxw3001, ty_Int) → new_esEs11(zxw4001, zxw3001)
new_esEs27(zxw4001, zxw3001, app(app(ty_@2, dhd), dhe)) → new_esEs5(zxw4001, zxw3001, dhd, dhe)
new_esEs27(zxw4001, zxw3001, ty_Bool) → new_esEs14(zxw4001, zxw3001)
new_esEs27(zxw4001, zxw3001, app(ty_[], dhb)) → new_esEs13(zxw4001, zxw3001, dhb)
new_esEs27(zxw4001, zxw3001, ty_Integer) → new_esEs15(zxw4001, zxw3001)
new_esEs26(zxw4002, zxw3002, ty_Float) → new_esEs17(zxw4002, zxw3002)
new_esEs26(zxw4002, zxw3002, ty_Char) → new_esEs12(zxw4002, zxw3002)
new_esEs26(zxw4002, zxw3002, ty_Int) → new_esEs11(zxw4002, zxw3002)
new_esEs26(zxw4002, zxw3002, app(ty_Maybe, dga)) → new_esEs6(zxw4002, zxw3002, dga)
new_esEs26(zxw4002, zxw3002, app(app(app(ty_@3, dgf), dgg), dgh)) → new_esEs4(zxw4002, zxw3002, dgf, dgg, dgh)
new_esEs26(zxw4002, zxw3002, app(ty_[], dfh)) → new_esEs13(zxw4002, zxw3002, dfh)
new_esEs26(zxw4002, zxw3002, app(app(ty_Either, dgd), dge)) → new_esEs7(zxw4002, zxw3002, dgd, dge)
new_esEs26(zxw4002, zxw3002, ty_Integer) → new_esEs15(zxw4002, zxw3002)
new_esEs26(zxw4002, zxw3002, app(app(ty_@2, dgb), dgc)) → new_esEs5(zxw4002, zxw3002, dgb, dgc)
new_esEs26(zxw4002, zxw3002, app(ty_Ratio, dfg)) → new_esEs18(zxw4002, zxw3002, dfg)
new_esEs26(zxw4002, zxw3002, ty_Bool) → new_esEs14(zxw4002, zxw3002)
new_esEs26(zxw4002, zxw3002, ty_@0) → new_esEs10(zxw4002, zxw3002)
new_esEs26(zxw4002, zxw3002, ty_Ordering) → new_esEs9(zxw4002, zxw3002)
new_esEs26(zxw4002, zxw3002, ty_Double) → new_esEs16(zxw4002, zxw3002)
new_esEs14(False, True) → False
new_esEs14(True, False) → False
new_esEs14(True, True) → True
new_esEs14(False, False) → True
new_ltEs20(zxw7900, zxw8000, app(ty_Maybe, bbc)) → new_ltEs18(zxw7900, zxw8000, bbc)
new_ltEs20(zxw7900, zxw8000, ty_Int) → new_ltEs9(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, ty_@0) → new_ltEs8(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, app(app(ty_@2, baf), bag)) → new_ltEs4(zxw7900, zxw8000, baf, bag)
new_ltEs20(zxw7900, zxw8000, ty_Float) → new_ltEs16(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, ty_Bool) → new_ltEs12(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, app(ty_Ratio, bbb)) → new_ltEs17(zxw7900, zxw8000, bbb)
new_ltEs20(zxw7900, zxw8000, ty_Double) → new_ltEs15(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, ty_Integer) → new_ltEs13(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, app(app(app(ty_@3, bab), bac), bad)) → new_ltEs6(zxw7900, zxw8000, bab, bac, bad)
new_ltEs20(zxw7900, zxw8000, app(app(ty_Either, bah), bba)) → new_ltEs14(zxw7900, zxw8000, bah, bba)
new_ltEs20(zxw7900, zxw8000, app(ty_[], bae)) → new_ltEs11(zxw7900, zxw8000, bae)
new_ltEs20(zxw7900, zxw8000, ty_Char) → new_ltEs10(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, ty_Ordering) → new_ltEs7(zxw7900, zxw8000)
new_compare14(zxw242, zxw243, False, dfe, dff) → GT
new_compare14(zxw242, zxw243, True, dfe, dff) → LT
new_ltEs6(@3(zxw79000, zxw79001, zxw79002), @3(zxw80000, zxw80001, zxw80002), hb, hc, hd) → new_pePe(new_lt19(zxw79000, zxw80000, hb), new_asAs(new_esEs20(zxw79000, zxw80000, hb), new_pePe(new_lt20(zxw79001, zxw80001, hc), new_asAs(new_esEs19(zxw79001, zxw80001, hc), new_ltEs21(zxw79002, zxw80002, hd)))))
new_lt19(zxw79000, zxw80000, app(app(ty_Either, bgd), bge)) → new_lt14(zxw79000, zxw80000, bgd, bge)
new_lt19(zxw79000, zxw80000, ty_Double) → new_lt15(zxw79000, zxw80000)
new_lt19(zxw79000, zxw80000, ty_Ordering) → new_lt6(zxw79000, zxw80000)
new_lt19(zxw79000, zxw80000, app(ty_Ratio, gg)) → new_lt17(zxw79000, zxw80000, gg)
new_lt19(zxw79000, zxw80000, app(app(ty_@2, bbd), bbe)) → new_lt11(zxw79000, zxw80000, bbd, bbe)
new_lt19(zxw79000, zxw80000, ty_Int) → new_lt8(zxw79000, zxw80000)
new_lt19(zxw79000, zxw80000, ty_@0) → new_lt7(zxw79000, zxw80000)
new_lt19(zxw79000, zxw80000, app(app(app(ty_@3, gd), ge), gf)) → new_lt5(zxw79000, zxw80000, gd, ge, gf)
new_lt19(zxw79000, zxw80000, app(ty_Maybe, bbh)) → new_lt18(zxw79000, zxw80000, bbh)
new_lt19(zxw79000, zxw80000, ty_Float) → new_lt16(zxw79000, zxw80000)
new_lt19(zxw79000, zxw80000, ty_Bool) → new_lt12(zxw79000, zxw80000)
new_lt19(zxw79000, zxw80000, app(ty_[], bgc)) → new_lt10(zxw79000, zxw80000, bgc)
new_lt19(zxw79000, zxw80000, ty_Integer) → new_lt13(zxw79000, zxw80000)
new_lt19(zxw79000, zxw80000, ty_Char) → new_lt9(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, app(ty_[], bgc)) → new_esEs13(zxw79000, zxw80000, bgc)
new_esEs20(zxw79000, zxw80000, ty_Double) → new_esEs16(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, ty_Char) → new_esEs12(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, app(app(ty_@2, bbd), bbe)) → new_esEs5(zxw79000, zxw80000, bbd, bbe)
new_esEs20(zxw79000, zxw80000, ty_Int) → new_esEs11(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, ty_@0) → new_esEs10(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, app(app(app(ty_@3, gd), ge), gf)) → new_esEs4(zxw79000, zxw80000, gd, ge, gf)
new_esEs20(zxw79000, zxw80000, ty_Integer) → new_esEs15(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, ty_Bool) → new_esEs14(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, app(ty_Ratio, gg)) → new_esEs18(zxw79000, zxw80000, gg)
new_esEs20(zxw79000, zxw80000, app(app(ty_Either, bgd), bge)) → new_esEs7(zxw79000, zxw80000, bgd, bge)
new_esEs20(zxw79000, zxw80000, app(ty_Maybe, bbh)) → new_esEs6(zxw79000, zxw80000, bbh)
new_esEs20(zxw79000, zxw80000, ty_Ordering) → new_esEs9(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, ty_Float) → new_esEs17(zxw79000, zxw80000)
new_lt20(zxw79001, zxw80001, app(app(ty_Either, bhd), bhe)) → new_lt14(zxw79001, zxw80001, bhd, bhe)
new_lt20(zxw79001, zxw80001, ty_@0) → new_lt7(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, app(app(ty_@2, bhb), bhc)) → new_lt11(zxw79001, zxw80001, bhb, bhc)
new_lt20(zxw79001, zxw80001, ty_Ordering) → new_lt6(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, app(ty_Maybe, bhg)) → new_lt18(zxw79001, zxw80001, bhg)
new_lt20(zxw79001, zxw80001, ty_Int) → new_lt8(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, ty_Integer) → new_lt13(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, app(ty_Ratio, bhf)) → new_lt17(zxw79001, zxw80001, bhf)
new_lt20(zxw79001, zxw80001, ty_Char) → new_lt9(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, app(ty_[], bha)) → new_lt10(zxw79001, zxw80001, bha)
new_lt20(zxw79001, zxw80001, ty_Double) → new_lt15(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, ty_Float) → new_lt16(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, ty_Bool) → new_lt12(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, app(app(app(ty_@3, bgf), bgg), bgh)) → new_lt5(zxw79001, zxw80001, bgf, bgg, bgh)
new_esEs19(zxw79001, zxw80001, app(ty_Ratio, bhf)) → new_esEs18(zxw79001, zxw80001, bhf)
new_esEs19(zxw79001, zxw80001, ty_Ordering) → new_esEs9(zxw79001, zxw80001)
new_esEs19(zxw79001, zxw80001, app(ty_Maybe, bhg)) → new_esEs6(zxw79001, zxw80001, bhg)
new_esEs19(zxw79001, zxw80001, app(app(ty_Either, bhd), bhe)) → new_esEs7(zxw79001, zxw80001, bhd, bhe)
new_esEs19(zxw79001, zxw80001, ty_Float) → new_esEs17(zxw79001, zxw80001)
new_esEs19(zxw79001, zxw80001, ty_Bool) → new_esEs14(zxw79001, zxw80001)
new_esEs19(zxw79001, zxw80001, ty_Int) → new_esEs11(zxw79001, zxw80001)
new_esEs19(zxw79001, zxw80001, app(app(app(ty_@3, bgf), bgg), bgh)) → new_esEs4(zxw79001, zxw80001, bgf, bgg, bgh)
new_esEs19(zxw79001, zxw80001, app(app(ty_@2, bhb), bhc)) → new_esEs5(zxw79001, zxw80001, bhb, bhc)
new_esEs19(zxw79001, zxw80001, ty_Double) → new_esEs16(zxw79001, zxw80001)
new_esEs19(zxw79001, zxw80001, ty_Integer) → new_esEs15(zxw79001, zxw80001)
new_esEs19(zxw79001, zxw80001, ty_@0) → new_esEs10(zxw79001, zxw80001)
new_esEs19(zxw79001, zxw80001, app(ty_[], bha)) → new_esEs13(zxw79001, zxw80001, bha)
new_esEs19(zxw79001, zxw80001, ty_Char) → new_esEs12(zxw79001, zxw80001)
new_ltEs21(zxw79002, zxw80002, ty_Char) → new_ltEs10(zxw79002, zxw80002)
new_ltEs21(zxw79002, zxw80002, app(app(ty_@2, cad), cae)) → new_ltEs4(zxw79002, zxw80002, cad, cae)
new_ltEs21(zxw79002, zxw80002, ty_Int) → new_ltEs9(zxw79002, zxw80002)
new_ltEs21(zxw79002, zxw80002, ty_Ordering) → new_ltEs7(zxw79002, zxw80002)
new_ltEs21(zxw79002, zxw80002, ty_Float) → new_ltEs16(zxw79002, zxw80002)
new_ltEs21(zxw79002, zxw80002, ty_Bool) → new_ltEs12(zxw79002, zxw80002)
new_ltEs21(zxw79002, zxw80002, ty_Integer) → new_ltEs13(zxw79002, zxw80002)
new_ltEs21(zxw79002, zxw80002, app(app(ty_Either, caf), cag)) → new_ltEs14(zxw79002, zxw80002, caf, cag)
new_ltEs21(zxw79002, zxw80002, app(ty_[], cac)) → new_ltEs11(zxw79002, zxw80002, cac)
new_ltEs21(zxw79002, zxw80002, app(ty_Ratio, cah)) → new_ltEs17(zxw79002, zxw80002, cah)
new_ltEs21(zxw79002, zxw80002, app(app(app(ty_@3, bhh), caa), cab)) → new_ltEs6(zxw79002, zxw80002, bhh, caa, cab)
new_ltEs21(zxw79002, zxw80002, ty_@0) → new_ltEs8(zxw79002, zxw80002)
new_ltEs21(zxw79002, zxw80002, app(ty_Maybe, cba)) → new_ltEs18(zxw79002, zxw80002, cba)
new_ltEs21(zxw79002, zxw80002, ty_Double) → new_ltEs15(zxw79002, zxw80002)
new_pePe(False, zxw271) → zxw271
new_pePe(True, zxw271) → True
new_ltEs15(zxw7900, zxw8000) → new_fsEs(new_compare6(zxw7900, zxw8000))
new_compare6(Double(zxw79000, zxw79001), Double(zxw80000, zxw80001)) → new_compare16(new_sr(zxw79000, zxw80000), new_sr(zxw79001, zxw80001))
new_ltEs8(zxw7900, zxw8000) → new_fsEs(new_compare30(zxw7900, zxw8000))
new_ltEs12(True, False) → False
new_ltEs12(False, False) → True
new_ltEs12(True, True) → True
new_ltEs12(False, True) → True
new_ltEs16(zxw7900, zxw8000) → new_fsEs(new_compare7(zxw7900, zxw8000))
new_compare7(Float(zxw79000, zxw79001), Float(zxw80000, zxw80001)) → new_compare16(new_sr(zxw79000, zxw80000), new_sr(zxw79001, zxw80001))
new_ltEs4(@2(zxw79000, zxw79001), @2(zxw80000, zxw80001), ca, cb) → new_pePe(new_lt4(zxw79000, zxw80000, ca), new_asAs(new_esEs8(zxw79000, zxw80000, ca), new_ltEs5(zxw79001, zxw80001, cb)))
new_lt4(zxw79000, zxw80000, app(app(app(ty_@3, cc), cd), ce)) → new_lt5(zxw79000, zxw80000, cc, cd, ce)
new_lt4(zxw79000, zxw80000, app(ty_[], cf)) → new_lt10(zxw79000, zxw80000, cf)
new_lt4(zxw79000, zxw80000, ty_Bool) → new_lt12(zxw79000, zxw80000)
new_lt4(zxw79000, zxw80000, app(ty_Maybe, de)) → new_lt18(zxw79000, zxw80000, de)
new_lt4(zxw79000, zxw80000, ty_Ordering) → new_lt6(zxw79000, zxw80000)
new_lt4(zxw79000, zxw80000, app(ty_Ratio, dd)) → new_lt17(zxw79000, zxw80000, dd)
new_lt4(zxw79000, zxw80000, ty_Int) → new_lt8(zxw79000, zxw80000)
new_lt4(zxw79000, zxw80000, ty_Double) → new_lt15(zxw79000, zxw80000)
new_lt4(zxw79000, zxw80000, app(app(ty_Either, db), dc)) → new_lt14(zxw79000, zxw80000, db, dc)
new_lt4(zxw79000, zxw80000, ty_Char) → new_lt9(zxw79000, zxw80000)
new_lt4(zxw79000, zxw80000, ty_@0) → new_lt7(zxw79000, zxw80000)
new_lt4(zxw79000, zxw80000, ty_Float) → new_lt16(zxw79000, zxw80000)
new_lt4(zxw79000, zxw80000, app(app(ty_@2, cg), da)) → new_lt11(zxw79000, zxw80000, cg, da)
new_lt4(zxw79000, zxw80000, ty_Integer) → new_lt13(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, ty_Int) → new_esEs11(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, ty_Double) → new_esEs16(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, app(app(app(ty_@3, cc), cd), ce)) → new_esEs4(zxw79000, zxw80000, cc, cd, ce)
new_esEs8(zxw79000, zxw80000, app(ty_[], cf)) → new_esEs13(zxw79000, zxw80000, cf)
new_esEs8(zxw79000, zxw80000, ty_Char) → new_esEs12(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, app(app(ty_@2, cg), da)) → new_esEs5(zxw79000, zxw80000, cg, da)
new_esEs8(zxw79000, zxw80000, ty_Float) → new_esEs17(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, app(app(ty_Either, db), dc)) → new_esEs7(zxw79000, zxw80000, db, dc)
new_esEs8(zxw79000, zxw80000, ty_@0) → new_esEs10(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, app(ty_Maybe, de)) → new_esEs6(zxw79000, zxw80000, de)
new_esEs8(zxw79000, zxw80000, ty_Bool) → new_esEs14(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, ty_Ordering) → new_esEs9(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, ty_Integer) → new_esEs15(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, app(ty_Ratio, dd)) → new_esEs18(zxw79000, zxw80000, dd)
new_ltEs5(zxw79001, zxw80001, ty_Char) → new_ltEs10(zxw79001, zxw80001)
new_ltEs5(zxw79001, zxw80001, app(app(ty_@2, eb), ec)) → new_ltEs4(zxw79001, zxw80001, eb, ec)
new_ltEs5(zxw79001, zxw80001, ty_Ordering) → new_ltEs7(zxw79001, zxw80001)
new_ltEs5(zxw79001, zxw80001, ty_Bool) → new_ltEs12(zxw79001, zxw80001)
new_ltEs5(zxw79001, zxw80001, ty_Integer) → new_ltEs13(zxw79001, zxw80001)
new_ltEs5(zxw79001, zxw80001, app(ty_Ratio, ef)) → new_ltEs17(zxw79001, zxw80001, ef)
new_ltEs5(zxw79001, zxw80001, app(ty_Maybe, eg)) → new_ltEs18(zxw79001, zxw80001, eg)
new_ltEs5(zxw79001, zxw80001, ty_Double) → new_ltEs15(zxw79001, zxw80001)
new_ltEs5(zxw79001, zxw80001, app(app(ty_Either, ed), ee)) → new_ltEs14(zxw79001, zxw80001, ed, ee)
new_ltEs5(zxw79001, zxw80001, app(app(app(ty_@3, df), dg), dh)) → new_ltEs6(zxw79001, zxw80001, df, dg, dh)
new_ltEs5(zxw79001, zxw80001, app(ty_[], ea)) → new_ltEs11(zxw79001, zxw80001, ea)
new_ltEs5(zxw79001, zxw80001, ty_Int) → new_ltEs9(zxw79001, zxw80001)
new_ltEs5(zxw79001, zxw80001, ty_@0) → new_ltEs8(zxw79001, zxw80001)
new_ltEs5(zxw79001, zxw80001, ty_Float) → new_ltEs16(zxw79001, zxw80001)
new_lt13(zxw79000, zxw80000) → new_esEs9(new_compare32(zxw79000, zxw80000), LT)
new_lt11(zxw79000, zxw80000, bbd, bbe) → new_esEs9(new_compare19(zxw79000, zxw80000, bbd, bbe), LT)
new_compare19(zxw79000, zxw80000, bbd, bbe) → new_compare210(zxw79000, zxw80000, new_esEs5(zxw79000, zxw80000, bbd, bbe), bbd, bbe)
new_compare210(zxw79000, zxw80000, False, bbd, bbe) → new_compare110(zxw79000, zxw80000, new_ltEs4(zxw79000, zxw80000, bbd, bbe), bbd, bbe)
new_compare210(zxw79000, zxw80000, True, bbd, bbe) → EQ
new_compare110(zxw79000, zxw80000, True, bbd, bbe) → LT
new_compare110(zxw79000, zxw80000, False, bbd, bbe) → GT
new_lt16(zxw79000, zxw80000) → new_esEs9(new_compare7(zxw79000, zxw80000), LT)
new_lt7(zxw79000, zxw80000) → new_esEs9(new_compare30(zxw79000, zxw80000), LT)
new_lt9(zxw79000, zxw80000) → new_esEs9(new_compare17(zxw79000, zxw80000), LT)
new_lt14(zxw790, zxw800, gh, ha) → new_esEs9(new_compare15(zxw790, zxw800, gh, ha), LT)
new_lt15(zxw79000, zxw80000) → new_esEs9(new_compare6(zxw79000, zxw80000), LT)
new_lt8(zxw790, zxw800) → new_esEs9(new_compare16(zxw790, zxw800), LT)
new_lt17(zxw79000, zxw80000, gg) → new_esEs9(new_compare8(zxw79000, zxw80000, gg), LT)
new_lt6(zxw79000, zxw80000) → new_esEs9(new_compare18(zxw79000, zxw80000), LT)
new_lt18(zxw79000, zxw80000, bbh) → new_esEs9(new_compare27(zxw79000, zxw80000, bbh), LT)
new_compare27(zxw79000, zxw80000, bbh) → new_compare28(zxw79000, zxw80000, new_esEs6(zxw79000, zxw80000, bbh), bbh)
new_compare28(zxw79000, zxw80000, False, bbh) → new_compare111(zxw79000, zxw80000, new_ltEs18(zxw79000, zxw80000, bbh), bbh)
new_compare28(zxw79000, zxw80000, True, bbh) → EQ
new_compare111(zxw79000, zxw80000, True, bbh) → LT
new_compare111(zxw79000, zxw80000, False, bbh) → GT
new_lt12(zxw79000, zxw80000) → new_esEs9(new_compare31(zxw79000, zxw80000), LT)
new_compare31(zxw79000, zxw80000) → new_compare23(zxw79000, zxw80000, new_esEs14(zxw79000, zxw80000))
new_compare23(zxw79000, zxw80000, True) → EQ
new_compare23(zxw79000, zxw80000, False) → new_compare10(zxw79000, zxw80000, new_ltEs12(zxw79000, zxw80000))
new_compare10(zxw79000, zxw80000, True) → LT
new_compare10(zxw79000, zxw80000, False) → GT
new_lt10(zxw79000, zxw80000, bgc) → new_esEs9(new_compare1(zxw79000, zxw80000, bgc), LT)
new_lt5(zxw79000, zxw80000, gd, ge, gf) → new_esEs9(new_compare9(zxw79000, zxw80000, gd, ge, gf), LT)
new_compare9(zxw79000, zxw80000, gd, ge, gf) → new_compare25(zxw79000, zxw80000, new_esEs4(zxw79000, zxw80000, gd, ge, gf), gd, ge, gf)
new_compare25(zxw79000, zxw80000, True, gd, ge, gf) → EQ
new_compare25(zxw79000, zxw80000, False, gd, ge, gf) → new_compare12(zxw79000, zxw80000, new_ltEs6(zxw79000, zxw80000, gd, ge, gf), gd, ge, gf)
new_compare12(zxw79000, zxw80000, True, gd, ge, gf) → LT
new_compare12(zxw79000, zxw80000, False, gd, ge, gf) → GT
new_compare34(zxw400, zxw300, h, ba) → new_compare26(Left(zxw400), Right(zxw300), False, h, ba)
new_esEs29(zxw400, zxw300, ty_Integer) → new_esEs15(zxw400, zxw300)
new_esEs29(zxw400, zxw300, ty_Double) → new_esEs16(zxw400, zxw300)
new_esEs29(zxw400, zxw300, app(ty_Maybe, eh)) → new_esEs6(zxw400, zxw300, eh)
new_esEs29(zxw400, zxw300, app(ty_[], cce)) → new_esEs13(zxw400, zxw300, cce)
new_esEs29(zxw400, zxw300, app(app(app(ty_@3, cch), cda), cdb)) → new_esEs4(zxw400, zxw300, cch, cda, cdb)
new_esEs29(zxw400, zxw300, app(ty_Ratio, ccd)) → new_esEs18(zxw400, zxw300, ccd)
new_esEs29(zxw400, zxw300, app(app(ty_@2, ccf), ccg)) → new_esEs5(zxw400, zxw300, ccf, ccg)
new_esEs29(zxw400, zxw300, ty_Char) → new_esEs12(zxw400, zxw300)
new_esEs29(zxw400, zxw300, ty_Int) → new_esEs11(zxw400, zxw300)
new_esEs29(zxw400, zxw300, app(app(ty_Either, beh), bdf)) → new_esEs7(zxw400, zxw300, beh, bdf)
new_esEs29(zxw400, zxw300, ty_@0) → new_esEs10(zxw400, zxw300)
new_esEs29(zxw400, zxw300, ty_Float) → new_esEs17(zxw400, zxw300)
new_esEs29(zxw400, zxw300, ty_Bool) → new_esEs14(zxw400, zxw300)
new_esEs29(zxw400, zxw300, ty_Ordering) → new_esEs9(zxw400, zxw300)

The set Q consists of the following terms:

new_compare23(x0, x1, True)
new_lt6(x0, x1)
new_ltEs5(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, ty_Integer)
new_lt4(x0, x1, app(ty_[], x2))
new_ltEs18(Just(x0), Just(x1), ty_@0)
new_compare16(x0, x1)
new_lt4(x0, x1, app(app(ty_@2, x2), x3))
new_compare13(x0, x1, False, x2, x3)
new_ltEs18(Just(x0), Nothing, x1)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, ty_Double)
new_esEs19(x0, x1, ty_Bool)
new_esEs8(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(x0, x1, app(app(ty_Either, x2), x3))
new_compare30(@0, @0)
new_primCompAux00(x0, GT)
new_lt19(x0, x1, ty_Char)
new_esEs27(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_Ordering)
new_compare17(Char(x0), Char(x1))
new_esEs28(x0, x1, ty_Int)
new_ltEs20(x0, x1, app(ty_[], x2))
new_ltEs21(x0, x1, ty_Ordering)
new_ltEs15(x0, x1)
new_primPlusNat1(Zero, Succ(x0))
new_esEs6(Just(x0), Just(x1), ty_Double)
new_compare24(x0, x1, False)
new_lt20(x0, x1, ty_Char)
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, ty_Bool)
new_sr0(Integer(x0), Integer(x1))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare210(x0, x1, False, x2, x3)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs7(Right(x0), Right(x1), x2, ty_Float)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs18(Nothing, Nothing, x0)
new_ltEs7(EQ, EQ)
new_esEs7(Right(x0), Right(x1), x2, ty_Integer)
new_compare29(x0, x1, app(app(ty_@2, x2), x3))
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs19(x0, x1, ty_Integer)
new_ltEs20(x0, x1, ty_Bool)
new_ltEs14(Right(x0), Right(x1), x2, ty_Float)
new_esEs6(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_compare25(x0, x1, False, x2, x3, x4)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_ltEs19(x0, x1, ty_Integer)
new_ltEs5(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(ty_[], x2))
new_lt10(x0, x1, x2)
new_ltEs7(EQ, LT)
new_ltEs7(LT, EQ)
new_esEs20(x0, x1, ty_Ordering)
new_esEs17(Float(x0, x1), Float(x2, x3))
new_compare25(x0, x1, True, x2, x3, x4)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_lt19(x0, x1, ty_Ordering)
new_esEs29(x0, x1, ty_@0)
new_esEs26(x0, x1, app(ty_[], x2))
new_ltEs16(x0, x1)
new_lt4(x0, x1, app(ty_Maybe, x2))
new_compare110(x0, x1, False, x2, x3)
new_ltEs14(Left(x0), Left(x1), ty_Char, x2)
new_sr(x0, x1)
new_ltEs19(x0, x1, ty_Double)
new_compare7(Float(x0, x1), Float(x2, x3))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs9(x0, x1)
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_lt7(x0, x1)
new_lt4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, ty_Int)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat0(Zero, x0)
new_esEs7(Right(x0), Right(x1), x2, ty_@0)
new_esEs32(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_ltEs7(LT, LT)
new_esEs7(Right(x0), Right(x1), x2, ty_Double)
new_esEs4(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_Bool)
new_lt5(x0, x1, x2, x3, x4)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt4(x0, x1, ty_Ordering)
new_primEqNat0(Zero, Succ(x0))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Int)
new_esEs15(Integer(x0), Integer(x1))
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Left(x0), Left(x1), ty_Char, x2)
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs26(x0, x1, ty_Double)
new_compare29(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_@0)
new_primPlusNat1(Succ(x0), Zero)
new_esEs22(x0, x1, ty_Integer)
new_ltEs14(Left(x0), Left(x1), ty_@0, x2)
new_primMulInt(Neg(x0), Neg(x1))
new_ltEs19(x0, x1, ty_Int)
new_ltEs21(x0, x1, app(ty_Maybe, x2))
new_compare29(x0, x1, ty_Integer)
new_esEs14(True, True)
new_esEs21(x0, x1, ty_Char)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Int)
new_ltEs18(Just(x0), Just(x1), ty_Integer)
new_esEs24(x0, x1, ty_Int)
new_primEqNat0(Zero, Zero)
new_esEs16(Double(x0, x1), Double(x2, x3))
new_esEs12(Char(x0), Char(x1))
new_lt4(x0, x1, ty_Char)
new_compare29(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, ty_Bool)
new_esEs8(x0, x1, ty_Float)
new_compare1([], :(x0, x1), x2)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, ty_Integer)
new_esEs29(x0, x1, ty_Bool)
new_esEs32(x0, x1, ty_@0)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs14(Left(x0), Left(x1), ty_Int, x2)
new_primCompAux00(x0, LT)
new_esEs27(x0, x1, ty_Integer)
new_ltEs21(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs5(x0, x1, ty_Double)
new_ltEs18(Just(x0), Just(x1), ty_Char)
new_primMulNat0(Zero, Zero)
new_compare110(x0, x1, True, x2, x3)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_lt9(x0, x1)
new_compare29(x0, x1, ty_Double)
new_ltEs5(x0, x1, ty_@0)
new_lt17(x0, x1, x2)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Left(x0), Left(x1), ty_Float, x2)
new_esEs32(x0, x1, ty_Float)
new_esEs13([], :(x0, x1), x2)
new_esEs8(x0, x1, ty_Ordering)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare10(x0, x1, True)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs7(Left(x0), Left(x1), ty_Float, x2)
new_primEqNat0(Succ(x0), Succ(x1))
new_ltEs19(x0, x1, ty_Bool)
new_esEs28(x0, x1, ty_Double)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, ty_Float)
new_esEs29(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_@0)
new_pePe(True, x0)
new_esEs19(x0, x1, ty_Float)
new_esEs8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_lt16(x0, x1)
new_compare29(x0, x1, ty_Bool)
new_esEs20(x0, x1, app(ty_[], x2))
new_compare11(x0, x1, True)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_compare14(x0, x1, True, x2, x3)
new_esEs6(Just(x0), Just(x1), app(ty_Maybe, x2))
new_lt19(x0, x1, ty_@0)
new_esEs6(Just(x0), Just(x1), ty_Ordering)
new_esEs23(x0, x1, ty_@0)
new_compare29(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Right(x0), Right(x1), x2, ty_Int)
new_ltEs5(x0, x1, ty_Char)
new_ltEs21(x0, x1, ty_Int)
new_compare29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Float)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_compare29(x0, x1, ty_Ordering)
new_ltEs21(x0, x1, ty_@0)
new_esEs8(x0, x1, ty_Int)
new_lt14(x0, x1, x2, x3)
new_ltEs12(False, False)
new_esEs6(Just(x0), Just(x1), ty_Bool)
new_compare32(Integer(x0), Integer(x1))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_Int)
new_primMulNat0(Succ(x0), Succ(x1))
new_compare29(x0, x1, ty_Float)
new_ltEs21(x0, x1, ty_Integer)
new_esEs6(Just(x0), Just(x1), ty_Float)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs5(x0, x1, ty_Float)
new_ltEs18(Just(x0), Just(x1), ty_Float)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Bool)
new_primCmpNat1(Zero, x0)
new_ltEs8(x0, x1)
new_esEs29(x0, x1, ty_Integer)
new_ltEs21(x0, x1, app(ty_[], x2))
new_primPlusNat1(Zero, Zero)
new_esEs23(x0, x1, app(ty_[], x2))
new_ltEs14(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs23(x0, x1, ty_Double)
new_ltEs18(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs18(Just(x0), Just(x1), ty_Ordering)
new_primCmpNat2(Zero, Zero)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs5(x0, x1, ty_Bool)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_compare28(x0, x1, True, x2)
new_ltEs14(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs5(x0, x1, app(ty_[], x2))
new_asAs(False, x0)
new_esEs29(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, ty_Char)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(x0, x1, ty_Integer)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs19(x0, x1, app(ty_[], x2))
new_ltEs18(Just(x0), Just(x1), ty_Bool)
new_lt11(x0, x1, x2, x3)
new_primCmpNat1(Succ(x0), x1)
new_esEs32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs24(x0, x1, ty_Integer)
new_ltEs14(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs27(x0, x1, ty_@0)
new_ltEs14(Right(x0), Right(x1), x2, ty_Double)
new_lt4(x0, x1, ty_Float)
new_compare19(x0, x1, x2, x3)
new_ltEs5(x0, x1, app(app(ty_Either, x2), x3))
new_esEs19(x0, x1, ty_Char)
new_lt4(x0, x1, ty_Double)
new_esEs19(x0, x1, ty_Ordering)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs8(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs10(@0, @0)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs11(x0, x1)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, ty_Float)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_Char)
new_esEs9(GT, GT)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs27(x0, x1, ty_Char)
new_compare11(x0, x1, False)
new_compare23(x0, x1, False)
new_compare12(x0, x1, True, x2, x3, x4)
new_esEs28(x0, x1, ty_Bool)
new_esEs7(Right(x0), Left(x1), x2, x3)
new_esEs7(Left(x0), Right(x1), x2, x3)
new_compare24(x0, x1, True)
new_compare15(x0, x1, x2, x3)
new_primEqNat0(Succ(x0), Zero)
new_esEs23(x0, x1, ty_Ordering)
new_esEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs7(Right(x0), Right(x1), x2, ty_Int)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_esEs32(x0, x1, app(app(ty_Either, x2), x3))
new_compare9(x0, x1, x2, x3, x4)
new_lt20(x0, x1, ty_Int)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Integer)
new_lt4(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Int)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs5(x0, x1, app(app(ty_@2, x2), x3))
new_lt4(x0, x1, ty_@0)
new_esEs23(x0, x1, ty_Char)
new_esEs28(x0, x1, ty_Ordering)
new_ltEs18(Just(x0), Just(x1), ty_Double)
new_ltEs20(x0, x1, ty_Integer)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_compare14(x0, x1, False, x2, x3)
new_lt20(x0, x1, ty_@0)
new_compare1([], [], x0)
new_esEs9(EQ, EQ)
new_pePe(False, x0)
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs5(x0, x1, app(ty_Ratio, x2))
new_ltEs18(Just(x0), Just(x1), app(ty_[], x2))
new_esEs6(Just(x0), Just(x1), ty_Char)
new_esEs25(x0, x1, ty_Integer)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs18(:%(x0, x1), :%(x2, x3), x4)
new_esEs26(x0, x1, ty_Integer)
new_compare12(x0, x1, False, x2, x3, x4)
new_esEs8(x0, x1, app(ty_Maybe, x2))
new_primCompAux00(x0, EQ)
new_esEs19(x0, x1, ty_Int)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs14(True, False)
new_esEs14(False, True)
new_lt4(x0, x1, ty_Integer)
new_esEs7(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs14(Right(x0), Right(x1), x2, ty_@0)
new_fsEs(x0)
new_esEs22(x0, x1, ty_Float)
new_lt4(x0, x1, ty_Bool)
new_primCmpNat2(Succ(x0), Succ(x1))
new_asAs(True, x0)
new_ltEs18(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, ty_Bool)
new_esEs6(Nothing, Just(x0), x1)
new_esEs6(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs6(Just(x0), Nothing, x1)
new_lt18(x0, x1, x2)
new_esEs8(x0, x1, app(ty_[], x2))
new_compare111(x0, x1, False, x2)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs8(x0, x1, ty_Char)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, ty_Float)
new_ltEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs22(x0, x1, ty_@0)
new_esEs20(x0, x1, ty_Char)
new_esEs13(:(x0, x1), [], x2)
new_ltEs12(False, True)
new_ltEs12(True, False)
new_compare6(Double(x0, x1), Double(x2, x3))
new_ltEs20(x0, x1, ty_@0)
new_esEs22(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_@0)
new_ltEs18(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs14(Right(x0), Right(x1), x2, ty_Integer)
new_lt19(x0, x1, ty_Double)
new_esEs32(x0, x1, app(ty_[], x2))
new_lt19(x0, x1, ty_Bool)
new_ltEs14(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs7(Right(x0), Right(x1), x2, ty_Char)
new_ltEs14(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs26(x0, x1, ty_Char)
new_ltEs14(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs5(x0, x1, ty_Int)
new_lt4(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_Double)
new_esEs32(x0, x1, app(ty_Ratio, x2))
new_esEs19(x0, x1, ty_@0)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs21(x0, x1, ty_Bool)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs14(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs21(x0, x1, ty_Double)
new_lt12(x0, x1)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs8(x0, x1, ty_Bool)
new_ltEs21(x0, x1, ty_Char)
new_lt13(x0, x1)
new_esEs13(:(x0, x1), :(x2, x3), x4)
new_ltEs14(Right(x0), Right(x1), x2, ty_Bool)
new_compare1(:(x0, x1), [], x2)
new_compare27(x0, x1, x2)
new_compare10(x0, x1, False)
new_esEs27(x0, x1, app(ty_[], x2))
new_primMulNat0(Succ(x0), Zero)
new_ltEs19(x0, x1, ty_Float)
new_ltEs14(Left(x0), Right(x1), x2, x3)
new_esEs23(x0, x1, ty_Float)
new_ltEs14(Right(x0), Left(x1), x2, x3)
new_compare29(x0, x1, ty_Int)
new_esEs22(x0, x1, ty_Int)
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Float)
new_compare31(x0, x1)
new_esEs29(x0, x1, ty_Double)
new_esEs32(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Left(x0), Left(x1), ty_Double, x2)
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Just(x0), Just(x1), ty_Int)
new_compare33(x0, x1, x2, x3)
new_esEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs21(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs7(LT, GT)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs7(GT, LT)
new_ltEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Double)
new_compare29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare111(x0, x1, True, x2)
new_ltEs13(x0, x1)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs32(x0, x1, app(ty_Maybe, x2))
new_lt4(x0, x1, ty_Int)
new_ltEs11(x0, x1, x2)
new_lt20(x0, x1, ty_Float)
new_not(True)
new_esEs20(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Float)
new_esEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs6(Nothing, Nothing, x0)
new_esEs28(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Ordering)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(Left(x0), Left(x1), ty_Double, x2)
new_esEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs6(Just(x0), Just(x1), ty_Integer)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_not(False)
new_lt8(x0, x1)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_ltEs18(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare13(x0, x1, True, x2, x3)
new_esEs32(x0, x1, ty_Integer)
new_esEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs19(x0, x1, ty_Char)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_esEs6(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare8(:%(x0, x1), :%(x2, x3), ty_Integer)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_Integer)
new_esEs8(x0, x1, ty_@0)
new_compare26(Left(x0), Left(x1), False, x2, x3)
new_ltEs12(True, True)
new_esEs27(x0, x1, ty_Float)
new_lt15(x0, x1)
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, ty_Ordering)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, ty_Double)
new_esEs6(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_lt20(x0, x1, ty_Ordering)
new_ltEs14(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs22(x0, x1, ty_Char)
new_lt20(x0, x1, ty_Double)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Bool)
new_esEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_ltEs21(x0, x1, ty_Float)
new_ltEs10(x0, x1)
new_ltEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs14(Left(x0), Left(x1), ty_Bool, x2)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs14(Left(x0), Left(x1), ty_Integer, x2)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(x0, x1, ty_Ordering)
new_esEs8(x0, x1, ty_Double)
new_compare29(x0, x1, ty_Char)
new_esEs6(Just(x0), Just(x1), ty_@0)
new_compare1(:(x0, x1), :(x2, x3), x4)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_compare210(x0, x1, True, x2, x3)
new_esEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs6(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs29(x0, x1, ty_Float)
new_esEs19(x0, x1, ty_Double)
new_esEs14(False, False)
new_primEqInt(Pos(Zero), Pos(Zero))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs32(x0, x1, ty_Char)
new_lt19(x0, x1, app(ty_[], x2))
new_ltEs21(x0, x1, ty_Double)
new_esEs32(x0, x1, ty_Int)
new_primCmpNat2(Succ(x0), Zero)
new_compare34(x0, x1, x2, x3)
new_compare18(x0, x1)
new_esEs29(x0, x1, ty_Int)
new_esEs32(x0, x1, ty_Bool)
new_compare28(x0, x1, False, x2)
new_ltEs14(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs18(Just(x0), Just(x1), ty_Int)
new_compare26(Right(x0), Right(x1), False, x2, x3)
new_ltEs17(x0, x1, x2)
new_primPlusNat0(Succ(x0), x1)
new_esEs7(Left(x0), Left(x1), ty_Int, x2)
new_esEs20(x0, x1, ty_Integer)
new_primCmpNat0(x0, Zero)
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_esEs7(Left(x0), Left(x1), ty_@0, x2)
new_ltEs7(GT, EQ)
new_ltEs7(EQ, GT)
new_esEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs32(x0, x1, ty_Double)
new_ltEs7(GT, GT)
new_esEs9(LT, LT)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs13([], [], x0)
new_primCompAux0(x0, x1, x2, x3)
new_compare29(x0, x1, ty_@0)
new_esEs7(Left(x0), Left(x1), ty_Bool, x2)
new_compare26(x0, x1, True, x2, x3)
new_compare26(Right(x0), Left(x1), False, x2, x3)
new_compare26(Left(x0), Right(x1), False, x2, x3)
new_ltEs18(Nothing, Just(x0), x1)
new_esEs27(x0, x1, ty_Ordering)
new_primCmpNat0(x0, Succ(x1))

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

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



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

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

new_splitGT2(zxw15, zxw16, zxw17, zxw18, zxw19, zxw20, True, bc, bd, be) → new_splitGT(zxw19, zxw20, bc, bd, be)
new_splitGT3(Left(zxw300), zxw31, zxw32, zxw33, zxw34, Left(zxw400), h, ba, bb) → new_splitGT2(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs9(new_compare26(Left(zxw400), Left(zxw300), new_esEs33(zxw400, zxw300, h), h, ba), GT), h, ba, bb)
new_splitGT3(Right(zxw300), zxw31, zxw32, zxw33, zxw34, Right(zxw400), h, ba, bb) → new_splitGT22(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs9(new_compare26(Right(zxw400), Right(zxw300), new_esEs34(zxw400, zxw300, ba), h, ba), GT), h, ba, bb)
new_splitGT3(Left(zxw300), zxw31, zxw32, zxw33, zxw34, Right(zxw400), h, ba, bb) → new_splitGT21(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs9(new_compare26(Right(zxw400), Left(zxw300), False, h, ba), GT), h, ba, bb)
new_splitGT10(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, True, h, ba, bb) → new_splitGT(zxw33, zxw400, h, ba, bb)
new_splitGT22(zxw30, zxw31, zxw32, zxw33, zxw34, zxw35, False, bf, bg, bh) → new_splitGT12(zxw30, zxw31, zxw32, zxw33, zxw34, zxw35, new_esEs9(new_compare36(zxw35, zxw30, bf, bg), LT), bf, bg, bh)
new_splitGT11(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, True, h, ba, bb) → new_splitGT0(zxw33, zxw400, h, ba, bb)
new_splitGT3(Right(zxw300), zxw31, zxw32, zxw33, zxw34, Left(zxw400), h, ba, bb) → new_splitGT20(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs9(new_compare26(Left(zxw400), Right(zxw300), False, h, ba), GT), h, ba, bb)
new_splitGT2(zxw15, zxw16, zxw17, zxw18, zxw19, zxw20, False, bc, bd, be) → new_splitGT1(zxw15, zxw16, zxw17, zxw18, zxw19, zxw20, new_esEs9(new_compare33(zxw20, zxw15, bc, bd), LT), bc, bd, be)
new_splitGT(Branch(zxw340, zxw341, zxw342, zxw343, zxw344), zxw400, h, ba, bb) → new_splitGT3(zxw340, zxw341, zxw342, zxw343, zxw344, Left(zxw400), h, ba, bb)
new_splitGT21(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, False, h, ba, bb) → new_splitGT11(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs9(new_compare35(zxw400, zxw300, h, ba), LT), h, ba, bb)
new_splitGT20(zxw300, zxw31, zxw32, zxw33, Branch(zxw340, zxw341, zxw342, zxw343, zxw344), zxw400, True, h, ba, bb) → new_splitGT3(zxw340, zxw341, zxw342, zxw343, zxw344, Left(zxw400), h, ba, bb)
new_splitGT21(zxw300, zxw31, zxw32, zxw33, Branch(zxw340, zxw341, zxw342, zxw343, zxw344), zxw400, True, h, ba, bb) → new_splitGT3(zxw340, zxw341, zxw342, zxw343, zxw344, Right(zxw400), h, ba, bb)
new_splitGT12(zxw30, zxw31, zxw32, zxw33, zxw34, zxw35, True, bf, bg, bh) → new_splitGT0(zxw33, zxw35, bf, bg, bh)
new_splitGT20(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, False, h, ba, bb) → new_splitGT10(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs9(new_compare34(zxw400, zxw300, h, ba), LT), h, ba, bb)
new_splitGT22(zxw30, zxw31, zxw32, zxw33, zxw34, zxw35, True, bf, bg, bh) → new_splitGT0(zxw34, zxw35, bf, bg, bh)
new_splitGT1(zxw15, zxw16, zxw17, zxw18, zxw19, zxw20, True, bc, bd, be) → new_splitGT(zxw18, zxw20, bc, bd, be)
new_splitGT0(Branch(zxw340, zxw341, zxw342, zxw343, zxw344), zxw400, h, ba, bb) → new_splitGT3(zxw340, zxw341, zxw342, zxw343, zxw344, Right(zxw400), h, ba, bb)

The TRS R consists of the following rules:

new_ltEs15(zxw7900, zxw8000) → new_fsEs(new_compare6(zxw7900, zxw8000))
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Bool) → new_ltEs12(zxw79000, zxw80000)
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, app(ty_Maybe, bbc)) → new_ltEs18(zxw7900, zxw8000, bbc)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Char) → new_ltEs10(zxw79000, zxw80000)
new_esEs28(zxw4000, zxw3000, app(ty_[], dhh)) → new_esEs13(zxw4000, zxw3000, dhh)
new_esEs32(zxw20, zxw15, ty_Float) → new_esEs17(zxw20, zxw15)
new_esEs23(zxw4000, zxw3000, app(app(ty_Either, ddh), dea)) → new_esEs7(zxw4000, zxw3000, ddh, dea)
new_esEs6(Just(zxw4000), Just(zxw3000), app(app(ty_@2, fd), ff)) → new_esEs5(zxw4000, zxw3000, fd, ff)
new_lt4(zxw79000, zxw80000, app(app(app(ty_@3, cc), cd), ce)) → new_lt5(zxw79000, zxw80000, cc, cd, ce)
new_esEs7(Left(zxw4000), Left(zxw3000), app(app(ty_Either, bfc), bfd), bef) → new_esEs7(zxw4000, zxw3000, bfc, bfd)
new_esEs31(zxw35, zxw30, ty_Ordering) → new_esEs9(zxw35, zxw30)
new_ltEs20(zxw7900, zxw8000, ty_Int) → new_ltEs9(zxw7900, zxw8000)
new_esEs33(zxw400, zxw300, app(app(ty_Either, bfh), bef)) → new_esEs7(zxw400, zxw300, bfh, bef)
new_lt19(zxw79000, zxw80000, app(app(ty_Either, bhd), bhe)) → new_lt14(zxw79000, zxw80000, bhd, bhe)
new_esEs33(zxw400, zxw300, app(ty_[], ddb)) → new_esEs13(zxw400, zxw300, ddb)
new_esEs9(GT, LT) → False
new_esEs9(LT, GT) → False
new_esEs33(zxw400, zxw300, ty_Char) → new_esEs12(zxw400, zxw300)
new_esEs13([], [], ddb) → True
new_lt4(zxw79000, zxw80000, app(ty_[], cf)) → new_lt10(zxw79000, zxw80000, cf)
new_compare110(zxw79000, zxw80000, True, bcf, bcg) → LT
new_esEs27(zxw4001, zxw3001, app(ty_Ratio, dge)) → new_esEs18(zxw4001, zxw3001, dge)
new_compare29(zxw79000, zxw80000, ty_Char) → new_compare17(zxw79000, zxw80000)
new_ltEs7(LT, EQ) → True
new_ltEs18(Just(zxw79000), Just(zxw80000), app(ty_Maybe, dac)) → new_ltEs18(zxw79000, zxw80000, dac)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Integer) → new_ltEs13(zxw79000, zxw80000)
new_ltEs20(zxw7900, zxw8000, ty_@0) → new_ltEs8(zxw7900, zxw8000)
new_lt20(zxw79001, zxw80001, app(app(ty_Either, cad), cae)) → new_lt14(zxw79001, zxw80001, cad, cae)
new_esEs23(zxw4000, zxw3000, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_compare35(zxw400, zxw300, h, ba) → new_compare26(Right(zxw400), Left(zxw300), False, h, ba)
new_ltEs8(zxw7900, zxw8000) → new_fsEs(new_compare30(zxw7900, zxw8000))
new_lt19(zxw79000, zxw80000, ty_Double) → new_lt15(zxw79000, zxw80000)
new_esEs22(zxw4000, zxw3000, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(ty_[], cgc)) → new_ltEs11(zxw79000, zxw80000, cgc)
new_ltEs21(zxw79002, zxw80002, ty_Char) → new_ltEs10(zxw79002, zxw80002)
new_esEs23(zxw4000, zxw3000, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Bool, hg) → new_ltEs12(zxw79000, zxw80000)
new_compare8(:%(zxw79000, zxw79001), :%(zxw80000, zxw80001), ty_Integer) → new_compare32(new_sr0(zxw79000, zxw80001), new_sr0(zxw80000, zxw79001))
new_esEs26(zxw4002, zxw3002, ty_Float) → new_esEs17(zxw4002, zxw3002)
new_esEs19(zxw79001, zxw80001, app(ty_Ratio, caf)) → new_esEs18(zxw79001, zxw80001, caf)
new_primMulNat0(Zero, Zero) → Zero
new_esEs20(zxw79000, zxw80000, app(ty_[], bhc)) → new_esEs13(zxw79000, zxw80000, bhc)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs34(zxw400, zxw300, ty_Char) → new_esEs12(zxw400, zxw300)
new_lt20(zxw79001, zxw80001, ty_@0) → new_lt7(zxw79001, zxw80001)
new_esEs27(zxw4001, zxw3001, app(app(app(ty_@3, dhd), dhe), dhf)) → new_esEs4(zxw4001, zxw3001, dhd, dhe, dhf)
new_esEs19(zxw79001, zxw80001, ty_Ordering) → new_esEs9(zxw79001, zxw80001)
new_esEs31(zxw35, zxw30, ty_Char) → new_esEs12(zxw35, zxw30)
new_esEs33(zxw400, zxw300, ty_Ordering) → new_esEs9(zxw400, zxw300)
new_esEs32(zxw20, zxw15, ty_Integer) → new_esEs15(zxw20, zxw15)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(ty_Ratio, dab)) → new_ltEs17(zxw79000, zxw80000, dab)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Bool, bef) → new_esEs14(zxw4000, zxw3000)
new_esEs24(zxw4001, zxw3001, ty_Integer) → new_esEs15(zxw4001, zxw3001)
new_lt19(zxw79000, zxw80000, ty_Ordering) → new_lt6(zxw79000, zxw80000)
new_lt20(zxw79001, zxw80001, app(app(ty_@2, cab), cac)) → new_lt11(zxw79001, zxw80001, cab, cac)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(ty_Ratio, cff), hg) → new_ltEs17(zxw79000, zxw80000, cff)
new_compare9(zxw79000, zxw80000, gd, ge, gf) → new_compare25(zxw79000, zxw80000, new_esEs4(zxw79000, zxw80000, gd, ge, gf), gd, ge, gf)
new_lt11(zxw79000, zxw80000, bcf, bcg) → new_esEs9(new_compare19(zxw79000, zxw80000, bcf, bcg), LT)
new_compare1([], :(zxw80000, zxw80001), he) → LT
new_esEs33(zxw400, zxw300, ty_@0) → new_esEs10(zxw400, zxw300)
new_lt18(zxw79000, zxw80000, bdb) → new_esEs9(new_compare27(zxw79000, zxw80000, bdb), LT)
new_esEs33(zxw400, zxw300, ty_Integer) → new_esEs15(zxw400, zxw300)
new_esEs8(zxw79000, zxw80000, ty_Int) → new_esEs11(zxw79000, zxw80000)
new_compare32(Integer(zxw79000), Integer(zxw80000)) → new_primCmpInt(zxw79000, zxw80000)
new_ltEs5(zxw79001, zxw80001, ty_Char) → new_ltEs10(zxw79001, zxw80001)
new_lt4(zxw79000, zxw80000, ty_Bool) → new_lt12(zxw79000, zxw80000)
new_compare27(zxw79000, zxw80000, bdb) → new_compare28(zxw79000, zxw80000, new_esEs6(zxw79000, zxw80000, bdb), bdb)
new_lt4(zxw79000, zxw80000, app(ty_Maybe, de)) → new_lt18(zxw79000, zxw80000, de)
new_compare29(zxw79000, zxw80000, ty_Bool) → new_compare31(zxw79000, zxw80000)
new_esEs31(zxw35, zxw30, ty_@0) → new_esEs10(zxw35, zxw30)
new_esEs8(zxw79000, zxw80000, ty_Double) → new_esEs16(zxw79000, zxw80000)
new_esEs22(zxw4000, zxw3000, app(app(ty_@2, dcc), dcd)) → new_esEs5(zxw4000, zxw3000, dcc, dcd)
new_lt4(zxw79000, zxw80000, ty_Ordering) → new_lt6(zxw79000, zxw80000)
new_esEs22(zxw4000, zxw3000, app(ty_Maybe, dcb)) → new_esEs6(zxw4000, zxw3000, dcb)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(app(app(ty_@3, cfh), cga), cgb)) → new_ltEs6(zxw79000, zxw80000, cfh, cga, cgb)
new_esEs34(zxw400, zxw300, app(app(ty_Either, bca), bcb)) → new_esEs7(zxw400, zxw300, bca, bcb)
new_esEs27(zxw4001, zxw3001, app(ty_Maybe, dgg)) → new_esEs6(zxw4001, zxw3001, dgg)
new_esEs8(zxw79000, zxw80000, app(app(app(ty_@3, cc), cd), ce)) → new_esEs4(zxw79000, zxw80000, cc, cd, ce)
new_esEs15(Integer(zxw4000), Integer(zxw3000)) → new_primEqInt(zxw4000, zxw3000)
new_ltEs21(zxw79002, zxw80002, app(app(ty_@2, cbd), cbe)) → new_ltEs4(zxw79002, zxw80002, cbd, cbe)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Float, hg) → new_ltEs16(zxw79000, zxw80000)
new_lt5(zxw79000, zxw80000, gd, ge, gf) → new_esEs9(new_compare9(zxw79000, zxw80000, gd, ge, gf), LT)
new_esEs22(zxw4000, zxw3000, app(ty_Ratio, dbh)) → new_esEs18(zxw4000, zxw3000, dbh)
new_esEs22(zxw4000, zxw3000, app(app(ty_Either, dce), dcf)) → new_esEs7(zxw4000, zxw3000, dce, dcf)
new_ltEs19(zxw7900, zxw8000, ty_Float) → new_ltEs16(zxw7900, zxw8000)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, app(ty_Maybe, bgc)) → new_esEs6(zxw4000, zxw3000, bgc)
new_pePe(False, zxw271) → zxw271
new_esEs7(Right(zxw4000), Left(zxw3000), bfh, bef) → False
new_esEs7(Left(zxw4000), Right(zxw3000), bfh, bef) → False
new_lt15(zxw79000, zxw80000) → new_esEs9(new_compare6(zxw79000, zxw80000), LT)
new_compare15(zxw790, zxw800, gh, ha) → new_compare26(zxw790, zxw800, new_esEs7(zxw790, zxw800, gh, ha), gh, ha)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Float) → new_ltEs16(zxw79000, zxw80000)
new_esEs31(zxw35, zxw30, app(app(app(ty_@3, beb), bec), bed)) → new_esEs4(zxw35, zxw30, beb, bec, bed)
new_ltEs12(True, False) → False
new_esEs34(zxw400, zxw300, app(ty_[], bbe)) → new_esEs13(zxw400, zxw300, bbe)
new_esEs20(zxw79000, zxw80000, ty_Double) → new_esEs16(zxw79000, zxw80000)
new_ltEs19(zxw7900, zxw8000, app(app(ty_@2, ca), cb)) → new_ltEs4(zxw7900, zxw8000, ca, cb)
new_esEs32(zxw20, zxw15, ty_@0) → new_esEs10(zxw20, zxw15)
new_compare23(zxw79000, zxw80000, True) → EQ
new_esEs31(zxw35, zxw30, ty_Float) → new_esEs17(zxw35, zxw30)
new_esEs27(zxw4001, zxw3001, app(app(ty_Either, dhb), dhc)) → new_esEs7(zxw4001, zxw3001, dhb, dhc)
new_esEs27(zxw4001, zxw3001, ty_Ordering) → new_esEs9(zxw4001, zxw3001)
new_esEs27(zxw4001, zxw3001, ty_Float) → new_esEs17(zxw4001, zxw3001)
new_esEs19(zxw79001, zxw80001, app(ty_Maybe, cag)) → new_esEs6(zxw79001, zxw80001, cag)
new_lt10(zxw79000, zxw80000, bhc) → new_esEs9(new_compare1(zxw79000, zxw80000, bhc), LT)
new_esEs26(zxw4002, zxw3002, ty_Char) → new_esEs12(zxw4002, zxw3002)
new_ltEs19(zxw7900, zxw8000, app(ty_[], he)) → new_ltEs11(zxw7900, zxw8000, he)
new_esEs26(zxw4002, zxw3002, ty_Int) → new_esEs11(zxw4002, zxw3002)
new_ltEs5(zxw79001, zxw80001, app(app(ty_@2, eb), ec)) → new_ltEs4(zxw79001, zxw80001, eb, ec)
new_lt19(zxw79000, zxw80000, app(ty_Ratio, gg)) → new_lt17(zxw79000, zxw80000, gg)
new_esEs22(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, app(app(app(ty_@3, eaf), eag), eah)) → new_esEs4(zxw4000, zxw3000, eaf, eag, eah)
new_esEs32(zxw20, zxw15, ty_Ordering) → new_esEs9(zxw20, zxw15)
new_compare29(zxw79000, zxw80000, app(app(ty_@2, ccf), ccg)) → new_compare19(zxw79000, zxw80000, ccf, ccg)
new_ltEs21(zxw79002, zxw80002, ty_Int) → new_ltEs9(zxw79002, zxw80002)
new_esEs20(zxw79000, zxw80000, ty_Char) → new_esEs12(zxw79000, zxw80000)
new_compare13(zxw235, zxw236, False, bch, bda) → GT
new_esEs9(GT, EQ) → False
new_esEs9(EQ, GT) → False
new_esEs19(zxw79001, zxw80001, app(app(ty_Either, cad), cae)) → new_esEs7(zxw79001, zxw80001, cad, cae)
new_esEs20(zxw79000, zxw80000, app(app(ty_@2, bcf), bcg)) → new_esEs5(zxw79000, zxw80000, bcf, bcg)
new_ltEs7(GT, GT) → True
new_compare36(zxw35, zxw30, bf, bg) → new_compare26(Right(zxw35), Right(zxw30), new_esEs31(zxw35, zxw30, bg), bf, bg)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, app(app(ty_@2, bgd), bge)) → new_esEs5(zxw4000, zxw3000, bgd, bge)
new_ltEs20(zxw7900, zxw8000, app(app(ty_@2, baf), bag)) → new_ltEs4(zxw7900, zxw8000, baf, bag)
new_esEs21(zxw4001, zxw3001, ty_Bool) → new_esEs14(zxw4001, zxw3001)
new_esEs32(zxw20, zxw15, ty_Bool) → new_esEs14(zxw20, zxw15)
new_primCompAux0(zxw79000, zxw80000, zxw272, he) → new_primCompAux00(zxw272, new_compare29(zxw79000, zxw80000, he))
new_ltEs21(zxw79002, zxw80002, ty_Ordering) → new_ltEs7(zxw79002, zxw80002)
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_compare29(zxw79000, zxw80000, app(ty_[], cce)) → new_compare1(zxw79000, zxw80000, cce)
new_lt20(zxw79001, zxw80001, ty_Ordering) → new_lt6(zxw79001, zxw80001)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_esEs8(zxw79000, zxw80000, app(ty_[], cf)) → new_esEs13(zxw79000, zxw80000, cf)
new_esEs33(zxw400, zxw300, app(app(app(ty_@3, deh), dfa), dfb)) → new_esEs4(zxw400, zxw300, deh, dfa, dfb)
new_esEs27(zxw4001, zxw3001, ty_@0) → new_esEs10(zxw4001, zxw3001)
new_compare25(zxw79000, zxw80000, True, gd, ge, gf) → EQ
new_esEs19(zxw79001, zxw80001, ty_Float) → new_esEs17(zxw79001, zxw80001)
new_ltEs5(zxw79001, zxw80001, ty_Ordering) → new_ltEs7(zxw79001, zxw80001)
new_lt4(zxw79000, zxw80000, app(ty_Ratio, dd)) → new_lt17(zxw79000, zxw80000, dd)
new_esEs28(zxw4000, zxw3000, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Int, bef) → new_esEs11(zxw4000, zxw3000)
new_ltEs21(zxw79002, zxw80002, ty_Float) → new_ltEs16(zxw79002, zxw80002)
new_esEs28(zxw4000, zxw3000, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_compare29(zxw79000, zxw80000, app(app(app(ty_@3, ccb), ccc), ccd)) → new_compare9(zxw79000, zxw80000, ccb, ccc, ccd)
new_lt19(zxw79000, zxw80000, app(app(ty_@2, bcf), bcg)) → new_lt11(zxw79000, zxw80000, bcf, bcg)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(app(app(ty_@3, chb), chc), chd)) → new_ltEs6(zxw79000, zxw80000, chb, chc, chd)
new_pePe(True, zxw271) → True
new_primEqNat0(Zero, Zero) → True
new_compare14(zxw242, zxw243, False, def, deg) → GT
new_esEs20(zxw79000, zxw80000, ty_Int) → new_esEs11(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Double) → new_ltEs15(zxw79000, zxw80000)
new_ltEs21(zxw79002, zxw80002, ty_Bool) → new_ltEs12(zxw79002, zxw80002)
new_esEs33(zxw400, zxw300, app(app(ty_@2, dad), dae)) → new_esEs5(zxw400, zxw300, dad, dae)
new_lt9(zxw79000, zxw80000) → new_esEs9(new_compare17(zxw79000, zxw80000), LT)
new_ltEs12(False, False) → True
new_esEs7(Left(zxw4000), Left(zxw3000), app(app(ty_@2, bfa), bfb), bef) → new_esEs5(zxw4000, zxw3000, bfa, bfb)
new_esEs26(zxw4002, zxw3002, app(ty_Maybe, dfe)) → new_esEs6(zxw4002, zxw3002, dfe)
new_compare8(:%(zxw79000, zxw79001), :%(zxw80000, zxw80001), ty_Int) → new_compare16(new_sr(zxw79000, zxw80001), new_sr(zxw80000, zxw79001))
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Ordering, bef) → new_esEs9(zxw4000, zxw3000)
new_esEs27(zxw4001, zxw3001, ty_Char) → new_esEs12(zxw4001, zxw3001)
new_esEs34(zxw400, zxw300, ty_Float) → new_esEs17(zxw400, zxw300)
new_lt7(zxw79000, zxw80000) → new_esEs9(new_compare30(zxw79000, zxw80000), LT)
new_compare110(zxw79000, zxw80000, False, bcf, bcg) → GT
new_sr(zxw4000, zxw3000) → new_primMulInt(zxw4000, zxw3000)
new_compare12(zxw79000, zxw80000, True, gd, ge, gf) → LT
new_lt19(zxw79000, zxw80000, ty_Int) → new_lt8(zxw79000, zxw80000)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(app(ty_@2, cgd), cge)) → new_ltEs4(zxw79000, zxw80000, cgd, cge)
new_ltEs19(zxw7900, zxw8000, ty_Char) → new_ltEs10(zxw7900, zxw8000)
new_esEs21(zxw4001, zxw3001, ty_Double) → new_esEs16(zxw4001, zxw3001)
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, app(app(ty_Either, bgf), bgg)) → new_esEs7(zxw4000, zxw3000, bgf, bgg)
new_esEs31(zxw35, zxw30, app(app(ty_Either, bdh), bea)) → new_esEs7(zxw35, zxw30, bdh, bea)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Double, hg) → new_ltEs15(zxw79000, zxw80000)
new_ltEs19(zxw7900, zxw8000, ty_Bool) → new_ltEs12(zxw7900, zxw8000)
new_esEs26(zxw4002, zxw3002, app(app(app(ty_@3, dgb), dgc), dgd)) → new_esEs4(zxw4002, zxw3002, dgb, dgc, dgd)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, app(ty_[], bgb)) → new_esEs13(zxw4000, zxw3000, bgb)
new_ltEs11(zxw7900, zxw8000, he) → new_fsEs(new_compare1(zxw7900, zxw8000, he))
new_ltEs20(zxw7900, zxw8000, ty_Float) → new_ltEs16(zxw7900, zxw8000)
new_esEs21(zxw4001, zxw3001, ty_Ordering) → new_esEs9(zxw4001, zxw3001)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_esEs9(EQ, EQ) → True
new_fsEs(zxw259) → new_not(new_esEs9(zxw259, GT))
new_esEs8(zxw79000, zxw80000, ty_Char) → new_esEs12(zxw79000, zxw80000)
new_primEqInt(Neg(Succ(zxw40000)), Neg(Succ(zxw30000))) → new_primEqNat0(zxw40000, zxw30000)
new_esEs8(zxw79000, zxw80000, app(app(ty_@2, cg), da)) → new_esEs5(zxw79000, zxw80000, cg, da)
new_compare13(zxw235, zxw236, True, bch, bda) → LT
new_compare26(Left(zxw7900), Right(zxw8000), False, gh, ha) → LT
new_esEs13(:(zxw4000, zxw4001), :(zxw3000, zxw3001), ddb) → new_asAs(new_esEs23(zxw4000, zxw3000, ddb), new_esEs13(zxw4001, zxw3001, ddb))
new_esEs26(zxw4002, zxw3002, app(ty_[], dfd)) → new_esEs13(zxw4002, zxw3002, dfd)
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_ltEs19(zxw7900, zxw8000, app(ty_Ratio, hh)) → new_ltEs17(zxw7900, zxw8000, hh)
new_ltEs20(zxw7900, zxw8000, ty_Bool) → new_ltEs12(zxw7900, zxw8000)
new_esEs21(zxw4001, zxw3001, ty_Char) → new_esEs12(zxw4001, zxw3001)
new_compare23(zxw79000, zxw80000, False) → new_compare10(zxw79000, zxw80000, new_ltEs12(zxw79000, zxw80000))
new_ltEs14(Right(zxw79000), Left(zxw80000), hf, hg) → False
new_compare210(zxw79000, zxw80000, False, bcf, bcg) → new_compare110(zxw79000, zxw80000, new_ltEs4(zxw79000, zxw80000, bcf, bcg), bcf, bcg)
new_primCmpNat1(Zero, zxw7900) → LT
new_compare7(Float(zxw79000, zxw79001), Float(zxw80000, zxw80001)) → new_compare16(new_sr(zxw79000, zxw80000), new_sr(zxw79001, zxw80001))
new_ltEs21(zxw79002, zxw80002, ty_Integer) → new_ltEs13(zxw79002, zxw80002)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_lt20(zxw79001, zxw80001, app(ty_Maybe, cag)) → new_lt18(zxw79001, zxw80001, cag)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Integer, bef) → new_esEs15(zxw4000, zxw3000)
new_ltEs5(zxw79001, zxw80001, ty_Bool) → new_ltEs12(zxw79001, zxw80001)
new_esEs19(zxw79001, zxw80001, ty_Bool) → new_esEs14(zxw79001, zxw80001)
new_ltEs7(EQ, EQ) → True
new_ltEs20(zxw7900, zxw8000, app(ty_Ratio, bbb)) → new_ltEs17(zxw7900, zxw8000, bbb)
new_primEqInt(Neg(Zero), Neg(Succ(zxw30000))) → False
new_primEqInt(Neg(Succ(zxw40000)), Neg(Zero)) → False
new_ltEs5(zxw79001, zxw80001, ty_Integer) → new_ltEs13(zxw79001, zxw80001)
new_compare26(zxw790, zxw800, True, gh, ha) → EQ
new_compare111(zxw79000, zxw80000, True, bdb) → LT
new_esEs20(zxw79000, zxw80000, ty_@0) → new_esEs10(zxw79000, zxw80000)
new_esEs31(zxw35, zxw30, app(ty_Ratio, bdc)) → new_esEs18(zxw35, zxw30, bdc)
new_ltEs21(zxw79002, zxw80002, app(app(ty_Either, cbf), cbg)) → new_ltEs14(zxw79002, zxw80002, cbf, cbg)
new_esEs8(zxw79000, zxw80000, ty_Float) → new_esEs17(zxw79000, zxw80000)
new_esEs34(zxw400, zxw300, app(app(ty_@2, bbg), bbh)) → new_esEs5(zxw400, zxw300, bbg, bbh)
new_esEs23(zxw4000, zxw3000, app(app(app(ty_@3, deb), dec), ded)) → new_esEs4(zxw4000, zxw3000, deb, dec, ded)
new_ltEs21(zxw79002, zxw80002, app(ty_[], cbc)) → new_ltEs11(zxw79002, zxw80002, cbc)
new_esEs21(zxw4001, zxw3001, ty_Float) → new_esEs17(zxw4001, zxw3001)
new_compare24(zxw79000, zxw80000, False) → new_compare11(zxw79000, zxw80000, new_ltEs7(zxw79000, zxw80000))
new_ltEs5(zxw79001, zxw80001, app(ty_Ratio, ef)) → new_ltEs17(zxw79001, zxw80001, ef)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_esEs26(zxw4002, zxw3002, app(app(ty_Either, dfh), dga)) → new_esEs7(zxw4002, zxw3002, dfh, dga)
new_lt20(zxw79001, zxw80001, ty_Int) → new_lt8(zxw79001, zxw80001)
new_lt4(zxw79000, zxw80000, ty_Int) → new_lt8(zxw79000, zxw80000)
new_ltEs20(zxw7900, zxw8000, ty_Double) → new_ltEs15(zxw7900, zxw8000)
new_esEs34(zxw400, zxw300, app(app(app(ty_@3, bcc), bcd), bce)) → new_esEs4(zxw400, zxw300, bcc, bcd, bce)
new_ltEs7(GT, LT) → False
new_lt12(zxw79000, zxw80000) → new_esEs9(new_compare31(zxw79000, zxw80000), LT)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Int, hg) → new_ltEs9(zxw79000, zxw80000)
new_lt20(zxw79001, zxw80001, ty_Integer) → new_lt13(zxw79001, zxw80001)
new_ltEs7(GT, EQ) → False
new_esEs6(Nothing, Nothing, eh) → True
new_primEqInt(Pos(Succ(zxw40000)), Pos(Succ(zxw30000))) → new_primEqNat0(zxw40000, zxw30000)
new_lt8(zxw790, zxw800) → new_esEs9(new_compare16(zxw790, zxw800), LT)
new_esEs21(zxw4001, zxw3001, app(ty_Maybe, dah)) → new_esEs6(zxw4001, zxw3001, dah)
new_lt6(zxw79000, zxw80000) → new_esEs9(new_compare18(zxw79000, zxw80000), LT)
new_esEs32(zxw20, zxw15, app(app(ty_Either, cea), ceb)) → new_esEs7(zxw20, zxw15, cea, ceb)
new_esEs14(False, True) → False
new_esEs14(True, False) → False
new_esEs32(zxw20, zxw15, app(ty_[], cde)) → new_esEs13(zxw20, zxw15, cde)
new_esEs26(zxw4002, zxw3002, ty_Integer) → new_esEs15(zxw4002, zxw3002)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, app(app(app(ty_@3, bgh), bha), bhb)) → new_esEs4(zxw4000, zxw3000, bgh, bha, bhb)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs6(Nothing, Just(zxw3000), eh) → False
new_esEs6(Just(zxw4000), Nothing, eh) → False
new_primEqNat0(Succ(zxw40000), Succ(zxw30000)) → new_primEqNat0(zxw40000, zxw30000)
new_esEs33(zxw400, zxw300, app(ty_Ratio, dee)) → new_esEs18(zxw400, zxw300, dee)
new_esEs16(Double(zxw4000, zxw4001), Double(zxw3000, zxw3001)) → new_esEs11(new_sr(zxw4000, zxw3000), new_sr(zxw4001, zxw3001))
new_lt19(zxw79000, zxw80000, ty_@0) → new_lt7(zxw79000, zxw80000)
new_ltEs5(zxw79001, zxw80001, app(ty_Maybe, eg)) → new_ltEs18(zxw79001, zxw80001, eg)
new_esEs17(Float(zxw4000, zxw4001), Float(zxw3000, zxw3001)) → new_esEs11(new_sr(zxw4000, zxw3000), new_sr(zxw4001, zxw3001))
new_primCompAux00(zxw276, LT) → LT
new_esEs28(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), app(ty_Ratio, bee), bef) → new_esEs18(zxw4000, zxw3000, bee)
new_esEs21(zxw4001, zxw3001, ty_Int) → new_esEs11(zxw4001, zxw3001)
new_compare1(:(zxw79000, zxw79001), :(zxw80000, zxw80001), he) → new_primCompAux0(zxw79000, zxw80000, new_compare1(zxw79001, zxw80001, he), he)
new_primEqInt(Pos(Zero), Pos(Succ(zxw30000))) → False
new_primEqInt(Pos(Succ(zxw40000)), Pos(Zero)) → False
new_compare29(zxw79000, zxw80000, ty_Int) → new_compare16(zxw79000, zxw80000)
new_lt20(zxw79001, zxw80001, app(ty_Ratio, caf)) → new_lt17(zxw79001, zxw80001, caf)
new_esEs34(zxw400, zxw300, ty_Double) → new_esEs16(zxw400, zxw300)
new_ltEs20(zxw7900, zxw8000, ty_Integer) → new_ltEs13(zxw7900, zxw8000)
new_esEs31(zxw35, zxw30, app(app(ty_@2, bdf), bdg)) → new_esEs5(zxw35, zxw30, bdf, bdg)
new_esEs5(@2(zxw4000, zxw4001), @2(zxw3000, zxw3001), dad, dae) → new_asAs(new_esEs22(zxw4000, zxw3000, dad), new_esEs21(zxw4001, zxw3001, dae))
new_ltEs18(Nothing, Nothing, baa) → True
new_esEs32(zxw20, zxw15, app(ty_Maybe, cdf)) → new_esEs6(zxw20, zxw15, cdf)
new_ltEs21(zxw79002, zxw80002, app(ty_Ratio, cbh)) → new_ltEs17(zxw79002, zxw80002, cbh)
new_esEs23(zxw4000, zxw3000, app(app(ty_@2, ddf), ddg)) → new_esEs5(zxw4000, zxw3000, ddf, ddg)
new_esEs33(zxw400, zxw300, ty_Bool) → new_esEs14(zxw400, zxw300)
new_esEs20(zxw79000, zxw80000, app(app(app(ty_@3, gd), ge), gf)) → new_esEs4(zxw79000, zxw80000, gd, ge, gf)
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_ltEs21(zxw79002, zxw80002, app(app(app(ty_@3, cah), cba), cbb)) → new_ltEs6(zxw79002, zxw80002, cah, cba, cbb)
new_ltEs10(zxw7900, zxw8000) → new_fsEs(new_compare17(zxw7900, zxw8000))
new_compare17(Char(zxw79000), Char(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_sr0(Integer(zxw800000), Integer(zxw790010)) → Integer(new_primMulInt(zxw800000, zxw790010))
new_ltEs5(zxw79001, zxw80001, ty_Double) → new_ltEs15(zxw79001, zxw80001)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_esEs8(zxw79000, zxw80000, app(app(ty_Either, db), dc)) → new_esEs7(zxw79000, zxw80000, db, dc)
new_primEqInt(Neg(Succ(zxw40000)), Pos(zxw3000)) → False
new_primEqInt(Pos(Succ(zxw40000)), Neg(zxw3000)) → False
new_compare29(zxw79000, zxw80000, ty_Integer) → new_compare32(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Char) → new_ltEs10(zxw79000, zxw80000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_@0, bef) → new_esEs10(zxw4000, zxw3000)
new_lt19(zxw79000, zxw80000, app(app(app(ty_@3, gd), ge), gf)) → new_lt5(zxw79000, zxw80000, gd, ge, gf)
new_esEs32(zxw20, zxw15, app(app(ty_@2, cdg), cdh)) → new_esEs5(zxw20, zxw15, cdg, cdh)
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_esEs28(zxw4000, zxw3000, app(ty_Maybe, eaa)) → new_esEs6(zxw4000, zxw3000, eaa)
new_ltEs21(zxw79002, zxw80002, ty_@0) → new_ltEs8(zxw79002, zxw80002)
new_esEs21(zxw4001, zxw3001, app(ty_[], dag)) → new_esEs13(zxw4001, zxw3001, dag)
new_primEqInt(Neg(Zero), Pos(Succ(zxw30000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(zxw30000))) → False
new_ltEs7(EQ, GT) → True
new_lt4(zxw79000, zxw80000, ty_Double) → new_lt15(zxw79000, zxw80000)
new_esEs34(zxw400, zxw300, ty_Ordering) → new_esEs9(zxw400, zxw300)
new_esEs21(zxw4001, zxw3001, ty_Integer) → new_esEs15(zxw4001, zxw3001)
new_esEs31(zxw35, zxw30, ty_Integer) → new_esEs15(zxw35, zxw30)
new_primCompAux00(zxw276, EQ) → zxw276
new_esEs28(zxw4000, zxw3000, app(app(ty_Either, ead), eae)) → new_esEs7(zxw4000, zxw3000, ead, eae)
new_compare24(zxw79000, zxw80000, True) → EQ
new_compare6(Double(zxw79000, zxw79001), Double(zxw80000, zxw80001)) → new_compare16(new_sr(zxw79000, zxw80000), new_sr(zxw79001, zxw80001))
new_esEs8(zxw79000, zxw80000, ty_@0) → new_esEs10(zxw79000, zxw80000)
new_ltEs5(zxw79001, zxw80001, app(app(ty_Either, ed), ee)) → new_ltEs14(zxw79001, zxw80001, ed, ee)
new_lt13(zxw79000, zxw80000) → new_esEs9(new_compare32(zxw79000, zxw80000), LT)
new_esEs27(zxw4001, zxw3001, ty_Double) → new_esEs16(zxw4001, zxw3001)
new_esEs7(Left(zxw4000), Left(zxw3000), app(app(app(ty_@3, bfe), bff), bfg), bef) → new_esEs4(zxw4000, zxw3000, bfe, bff, bfg)
new_esEs26(zxw4002, zxw3002, app(app(ty_@2, dff), dfg)) → new_esEs5(zxw4002, zxw3002, dff, dfg)
new_esEs21(zxw4001, zxw3001, app(app(ty_@2, dba), dbb)) → new_esEs5(zxw4001, zxw3001, dba, dbb)
new_lt19(zxw79000, zxw80000, app(ty_Maybe, bdb)) → new_lt18(zxw79000, zxw80000, bdb)
new_esEs12(Char(zxw4000), Char(zxw3000)) → new_primEqNat0(zxw4000, zxw3000)
new_ltEs20(zxw7900, zxw8000, app(app(app(ty_@3, bab), bac), bad)) → new_ltEs6(zxw7900, zxw8000, bab, bac, bad)
new_not(False) → True
new_lt20(zxw79001, zxw80001, ty_Char) → new_lt9(zxw79001, zxw80001)
new_esEs11(zxw400, zxw300) → new_primEqInt(zxw400, zxw300)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(ty_Maybe, cha)) → new_ltEs18(zxw79000, zxw80000, cha)
new_ltEs18(Just(zxw79000), Nothing, baa) → False
new_esEs7(Left(zxw4000), Left(zxw3000), app(ty_Maybe, beh), bef) → new_esEs6(zxw4000, zxw3000, beh)
new_esEs8(zxw79000, zxw80000, app(ty_Maybe, de)) → new_esEs6(zxw79000, zxw80000, de)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Double, bef) → new_esEs16(zxw4000, zxw3000)
new_compare210(zxw79000, zxw80000, True, bcf, bcg) → EQ
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_esEs19(zxw79001, zxw80001, ty_Int) → new_esEs11(zxw79001, zxw80001)
new_compare12(zxw79000, zxw80000, False, gd, ge, gf) → GT
new_ltEs16(zxw7900, zxw8000) → new_fsEs(new_compare7(zxw7900, zxw8000))
new_esEs32(zxw20, zxw15, ty_Char) → new_esEs12(zxw20, zxw15)
new_esEs9(GT, GT) → True
new_esEs26(zxw4002, zxw3002, app(ty_Ratio, dfc)) → new_esEs18(zxw4002, zxw3002, dfc)
new_esEs25(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_lt20(zxw79001, zxw80001, app(ty_[], caa)) → new_lt10(zxw79001, zxw80001, caa)
new_lt4(zxw79000, zxw80000, app(app(ty_Either, db), dc)) → new_lt14(zxw79000, zxw80000, db, dc)
new_esEs26(zxw4002, zxw3002, ty_Bool) → new_esEs14(zxw4002, zxw3002)
new_compare19(zxw79000, zxw80000, bcf, bcg) → new_compare210(zxw79000, zxw80000, new_esEs5(zxw79000, zxw80000, bcf, bcg), bcf, bcg)
new_esEs8(zxw79000, zxw80000, ty_Bool) → new_esEs14(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Double) → new_ltEs15(zxw79000, zxw80000)
new_esEs28(zxw4000, zxw3000, app(app(ty_@2, eab), eac)) → new_esEs5(zxw4000, zxw3000, eab, eac)
new_esEs34(zxw400, zxw300, ty_Int) → new_esEs11(zxw400, zxw300)
new_ltEs19(zxw7900, zxw8000, app(app(app(ty_@3, hb), hc), hd)) → new_ltEs6(zxw7900, zxw8000, hb, hc, hd)
new_esEs32(zxw20, zxw15, app(app(app(ty_@3, cec), ced), cee)) → new_esEs4(zxw20, zxw15, cec, ced, cee)
new_lt4(zxw79000, zxw80000, ty_Char) → new_lt9(zxw79000, zxw80000)
new_esEs22(zxw4000, zxw3000, app(app(app(ty_@3, dcg), dch), dda)) → new_esEs4(zxw4000, zxw3000, dcg, dch, dda)
new_esEs22(zxw4000, zxw3000, app(ty_[], dca)) → new_esEs13(zxw4000, zxw3000, dca)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_@0) → new_ltEs8(zxw79000, zxw80000)
new_esEs23(zxw4000, zxw3000, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Float, bef) → new_esEs17(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_esEs27(zxw4001, zxw3001, ty_Int) → new_esEs11(zxw4001, zxw3001)
new_esEs19(zxw79001, zxw80001, app(app(app(ty_@3, bhf), bhg), bhh)) → new_esEs4(zxw79001, zxw80001, bhf, bhg, bhh)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_ltEs14(Left(zxw79000), Left(zxw80000), app(app(app(ty_@3, cef), ceg), ceh), hg) → new_ltEs6(zxw79000, zxw80000, cef, ceg, ceh)
new_ltEs19(zxw7900, zxw8000, ty_Int) → new_ltEs9(zxw7900, zxw8000)
new_compare33(zxw20, zxw15, bc, bd) → new_compare26(Left(zxw20), Left(zxw15), new_esEs32(zxw20, zxw15, bc), bc, bd)
new_lt4(zxw79000, zxw80000, ty_@0) → new_lt7(zxw79000, zxw80000)
new_lt20(zxw79001, zxw80001, ty_Double) → new_lt15(zxw79001, zxw80001)
new_lt19(zxw79000, zxw80000, ty_Float) → new_lt16(zxw79000, zxw80000)
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_esEs26(zxw4002, zxw3002, ty_@0) → new_esEs10(zxw4002, zxw3002)
new_lt19(zxw79000, zxw80000, ty_Bool) → new_lt12(zxw79000, zxw80000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Char, bef) → new_esEs12(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_lt4(zxw79000, zxw80000, ty_Float) → new_lt16(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(ty_[], che)) → new_ltEs11(zxw79000, zxw80000, che)
new_primMulInt(Neg(zxw40000), Neg(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_ltEs5(zxw79001, zxw80001, app(app(app(ty_@3, df), dg), dh)) → new_ltEs6(zxw79001, zxw80001, df, dg, dh)
new_primCmpNat2(Zero, Zero) → EQ
new_esEs20(zxw79000, zxw80000, ty_Integer) → new_esEs15(zxw79000, zxw80000)
new_primEqNat0(Zero, Succ(zxw30000)) → False
new_primEqNat0(Succ(zxw40000), Zero) → False
new_esEs21(zxw4001, zxw3001, ty_@0) → new_esEs10(zxw4001, zxw3001)
new_esEs22(zxw4000, zxw3000, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_esEs20(zxw79000, zxw80000, ty_Bool) → new_esEs14(zxw79000, zxw80000)
new_ltEs5(zxw79001, zxw80001, app(ty_[], ea)) → new_ltEs11(zxw79001, zxw80001, ea)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs23(zxw4000, zxw3000, app(ty_Ratio, ddc)) → new_esEs18(zxw4000, zxw3000, ddc)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(app(ty_@2, chf), chg)) → new_ltEs4(zxw79000, zxw80000, chf, chg)
new_esEs33(zxw400, zxw300, app(ty_Maybe, eh)) → new_esEs6(zxw400, zxw300, eh)
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_esEs34(zxw400, zxw300, ty_Bool) → new_esEs14(zxw400, zxw300)
new_ltEs5(zxw79001, zxw80001, ty_Int) → new_ltEs9(zxw79001, zxw80001)
new_esEs27(zxw4001, zxw3001, app(app(ty_@2, dgh), dha)) → new_esEs5(zxw4001, zxw3001, dgh, dha)
new_primCmpNat0(zxw7900, Zero) → GT
new_compare26(Right(zxw7900), Left(zxw8000), False, gh, ha) → GT
new_esEs33(zxw400, zxw300, ty_Double) → new_esEs16(zxw400, zxw300)
new_esEs23(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_@0, hg) → new_ltEs8(zxw79000, zxw80000)
new_ltEs21(zxw79002, zxw80002, app(ty_Maybe, cca)) → new_ltEs18(zxw79002, zxw80002, cca)
new_esEs21(zxw4001, zxw3001, app(app(ty_Either, dbc), dbd)) → new_esEs7(zxw4001, zxw3001, dbc, dbd)
new_esEs22(zxw4000, zxw3000, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Bool) → new_ltEs12(zxw79000, zxw80000)
new_compare29(zxw79000, zxw80000, app(ty_Maybe, cdc)) → new_compare27(zxw79000, zxw80000, cdc)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_ltEs14(Left(zxw79000), Left(zxw80000), app(ty_Maybe, cfg), hg) → new_ltEs18(zxw79000, zxw80000, cfg)
new_lt20(zxw79001, zxw80001, ty_Float) → new_lt16(zxw79001, zxw80001)
new_lt17(zxw79000, zxw80000, gg) → new_esEs9(new_compare8(zxw79000, zxw80000, gg), LT)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Ordering) → new_ltEs7(zxw79000, zxw80000)
new_esEs32(zxw20, zxw15, ty_Int) → new_esEs11(zxw20, zxw15)
new_compare30(@0, @0) → EQ
new_lt19(zxw79000, zxw80000, app(ty_[], bhc)) → new_lt10(zxw79000, zxw80000, bhc)
new_esEs21(zxw4001, zxw3001, app(app(app(ty_@3, dbe), dbf), dbg)) → new_esEs4(zxw4001, zxw3001, dbe, dbf, dbg)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_esEs20(zxw79000, zxw80000, app(ty_Ratio, gg)) → new_esEs18(zxw79000, zxw80000, gg)
new_esEs6(Just(zxw4000), Just(zxw3000), app(app(app(ty_@3, ga), gb), gc)) → new_esEs4(zxw4000, zxw3000, ga, gb, gc)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(app(ty_Either, chh), daa)) → new_ltEs14(zxw79000, zxw80000, chh, daa)
new_esEs24(zxw4001, zxw3001, ty_Int) → new_esEs11(zxw4001, zxw3001)
new_esEs8(zxw79000, zxw80000, ty_Ordering) → new_esEs9(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Ordering) → new_ltEs7(zxw79000, zxw80000)
new_esEs34(zxw400, zxw300, ty_Integer) → new_esEs15(zxw400, zxw300)
new_esEs20(zxw79000, zxw80000, app(app(ty_Either, bhd), bhe)) → new_esEs7(zxw79000, zxw80000, bhd, bhe)
new_compare29(zxw79000, zxw80000, app(ty_Ratio, cdb)) → new_compare8(zxw79000, zxw80000, cdb)
new_lt4(zxw79000, zxw80000, app(app(ty_@2, cg), da)) → new_lt11(zxw79000, zxw80000, cg, da)
new_compare29(zxw79000, zxw80000, ty_Float) → new_compare7(zxw79000, zxw80000)
new_esEs19(zxw79001, zxw80001, app(app(ty_@2, cab), cac)) → new_esEs5(zxw79001, zxw80001, cab, cac)
new_esEs10(@0, @0) → True
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_compare29(zxw79000, zxw80000, ty_Double) → new_compare6(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, app(ty_Maybe, bdb)) → new_esEs6(zxw79000, zxw80000, bdb)
new_ltEs14(Left(zxw79000), Right(zxw80000), hf, hg) → True
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Float) → new_ltEs16(zxw79000, zxw80000)
new_esEs28(zxw4000, zxw3000, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_compare29(zxw79000, zxw80000, app(app(ty_Either, cch), cda)) → new_compare15(zxw79000, zxw80000, cch, cda)
new_esEs19(zxw79001, zxw80001, ty_Double) → new_esEs16(zxw79001, zxw80001)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_ltEs20(zxw7900, zxw8000, app(app(ty_Either, bah), bba)) → new_ltEs14(zxw7900, zxw8000, bah, bba)
new_asAs(False, zxw230) → False
new_ltEs13(zxw7900, zxw8000) → new_fsEs(new_compare32(zxw7900, zxw8000))
new_ltEs19(zxw7900, zxw8000, app(app(ty_Either, hf), hg)) → new_ltEs14(zxw7900, zxw8000, hf, hg)
new_compare34(zxw400, zxw300, h, ba) → new_compare26(Left(zxw400), Right(zxw300), False, h, ba)
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Pos(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_ltEs20(zxw7900, zxw8000, app(ty_[], bae)) → new_ltEs11(zxw7900, zxw8000, bae)
new_compare16(zxw79, zxw80) → new_primCmpInt(zxw79, zxw80)
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_esEs13(:(zxw4000, zxw4001), [], ddb) → False
new_esEs13([], :(zxw3000, zxw3001), ddb) → False
new_compare25(zxw79000, zxw80000, False, gd, ge, gf) → new_compare12(zxw79000, zxw80000, new_ltEs6(zxw79000, zxw80000, gd, ge, gf), gd, ge, gf)
new_esEs34(zxw400, zxw300, ty_@0) → new_esEs10(zxw400, zxw300)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(app(ty_@2, cfb), cfc), hg) → new_ltEs4(zxw79000, zxw80000, cfb, cfc)
new_esEs6(Just(zxw4000), Just(zxw3000), app(ty_Maybe, fc)) → new_esEs6(zxw4000, zxw3000, fc)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_@0) → new_esEs10(zxw4000, zxw3000)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(ty_[], cfa), hg) → new_ltEs11(zxw79000, zxw80000, cfa)
new_esEs7(Left(zxw4000), Left(zxw3000), app(ty_[], beg), bef) → new_esEs13(zxw4000, zxw3000, beg)
new_esEs31(zxw35, zxw30, ty_Double) → new_esEs16(zxw35, zxw30)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_compare31(zxw79000, zxw80000) → new_compare23(zxw79000, zxw80000, new_esEs14(zxw79000, zxw80000))
new_ltEs18(Nothing, Just(zxw80000), baa) → True
new_esEs28(zxw4000, zxw3000, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_ltEs21(zxw79002, zxw80002, ty_Double) → new_ltEs15(zxw79002, zxw80002)
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_ltEs12(True, True) → True
new_esEs23(zxw4000, zxw3000, app(ty_Maybe, dde)) → new_esEs6(zxw4000, zxw3000, dde)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_esEs8(zxw79000, zxw80000, ty_Integer) → new_esEs15(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(app(ty_Either, cgf), cgg)) → new_ltEs14(zxw79000, zxw80000, cgf, cgg)
new_ltEs6(@3(zxw79000, zxw79001, zxw79002), @3(zxw80000, zxw80001, zxw80002), hb, hc, hd) → new_pePe(new_lt19(zxw79000, zxw80000, hb), new_asAs(new_esEs20(zxw79000, zxw80000, hb), new_pePe(new_lt20(zxw79001, zxw80001, hc), new_asAs(new_esEs19(zxw79001, zxw80001, hc), new_ltEs21(zxw79002, zxw80002, hd)))))
new_esEs28(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_lt16(zxw79000, zxw80000) → new_esEs9(new_compare7(zxw79000, zxw80000), LT)
new_esEs23(zxw4000, zxw3000, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Integer, hg) → new_ltEs13(zxw79000, zxw80000)
new_esEs34(zxw400, zxw300, app(ty_Ratio, bbd)) → new_esEs18(zxw400, zxw300, bbd)
new_ltEs12(False, True) → True
new_esEs23(zxw4000, zxw3000, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs8(zxw79000, zxw80000, app(ty_Ratio, dd)) → new_esEs18(zxw79000, zxw80000, dd)
new_esEs23(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs14(True, True) → True
new_compare111(zxw79000, zxw80000, False, bdb) → GT
new_esEs31(zxw35, zxw30, app(ty_[], bdd)) → new_esEs13(zxw35, zxw30, bdd)
new_esEs27(zxw4001, zxw3001, ty_Bool) → new_esEs14(zxw4001, zxw3001)
new_esEs20(zxw79000, zxw80000, ty_Ordering) → new_esEs9(zxw79000, zxw80000)
new_ltEs19(zxw7900, zxw8000, ty_@0) → new_ltEs8(zxw7900, zxw8000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Int) → new_ltEs9(zxw79000, zxw80000)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(app(ty_Either, cfd), cfe), hg) → new_ltEs14(zxw79000, zxw80000, cfd, cfe)
new_lt19(zxw79000, zxw80000, ty_Integer) → new_lt13(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, ty_Float) → new_esEs17(zxw79000, zxw80000)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs34(zxw400, zxw300, app(ty_Maybe, bbf)) → new_esEs6(zxw400, zxw300, bbf)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Ordering, hg) → new_ltEs7(zxw79000, zxw80000)
new_compare11(zxw79000, zxw80000, False) → GT
new_esEs4(@3(zxw4000, zxw4001, zxw4002), @3(zxw3000, zxw3001, zxw3002), deh, dfa, dfb) → new_asAs(new_esEs28(zxw4000, zxw3000, deh), new_asAs(new_esEs27(zxw4001, zxw3001, dfa), new_esEs26(zxw4002, zxw3002, dfb)))
new_esEs6(Just(zxw4000), Just(zxw3000), app(ty_[], fb)) → new_esEs13(zxw4000, zxw3000, fb)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Int) → new_ltEs9(zxw79000, zxw80000)
new_esEs9(EQ, LT) → False
new_esEs9(LT, EQ) → False
new_compare26(Right(zxw7900), Right(zxw8000), False, gh, ha) → new_compare14(zxw7900, zxw8000, new_ltEs20(zxw7900, zxw8000, ha), gh, ha)
new_compare11(zxw79000, zxw80000, True) → LT
new_ltEs5(zxw79001, zxw80001, ty_@0) → new_ltEs8(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, ty_Bool) → new_lt12(zxw79001, zxw80001)
new_compare14(zxw242, zxw243, True, def, deg) → LT
new_esEs32(zxw20, zxw15, app(ty_Ratio, cdd)) → new_esEs18(zxw20, zxw15, cdd)
new_esEs14(False, False) → True
new_esEs18(:%(zxw4000, zxw4001), :%(zxw3000, zxw3001), dee) → new_asAs(new_esEs25(zxw4000, zxw3000, dee), new_esEs24(zxw4001, zxw3001, dee))
new_compare26(Left(zxw7900), Left(zxw8000), False, gh, ha) → new_compare13(zxw7900, zxw8000, new_ltEs19(zxw7900, zxw8000, gh), gh, ha)
new_esEs33(zxw400, zxw300, ty_Float) → new_esEs17(zxw400, zxw300)
new_ltEs19(zxw7900, zxw8000, ty_Double) → new_ltEs15(zxw7900, zxw8000)
new_ltEs7(EQ, LT) → False
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Char) → new_esEs12(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_ltEs7(LT, LT) → True
new_lt20(zxw79001, zxw80001, app(app(app(ty_@3, bhf), bhg), bhh)) → new_lt5(zxw79001, zxw80001, bhf, bhg, bhh)
new_lt14(zxw790, zxw800, gh, ha) → new_esEs9(new_compare15(zxw790, zxw800, gh, ha), LT)
new_esEs22(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_ltEs9(zxw7900, zxw8000) → new_fsEs(new_compare16(zxw7900, zxw8000))
new_compare29(zxw79000, zxw80000, ty_Ordering) → new_compare18(zxw79000, zxw80000)
new_primPlusNat1(Zero, Zero) → Zero
new_esEs26(zxw4002, zxw3002, ty_Ordering) → new_esEs9(zxw4002, zxw3002)
new_esEs19(zxw79001, zxw80001, ty_Integer) → new_esEs15(zxw79001, zxw80001)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Char, hg) → new_ltEs10(zxw79000, zxw80000)
new_asAs(True, zxw230) → zxw230
new_esEs25(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_ltEs7(LT, GT) → True
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Float) → new_esEs17(zxw4000, zxw3000)
new_ltEs5(zxw79001, zxw80001, ty_Float) → new_ltEs16(zxw79001, zxw80001)
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, app(ty_Ratio, bga)) → new_esEs18(zxw4000, zxw3000, bga)
new_esEs27(zxw4001, zxw3001, app(ty_[], dgf)) → new_esEs13(zxw4001, zxw3001, dgf)
new_esEs6(Just(zxw4000), Just(zxw3000), app(app(ty_Either, fg), fh)) → new_esEs7(zxw4000, zxw3000, fg, fh)
new_esEs32(zxw20, zxw15, ty_Double) → new_esEs16(zxw20, zxw15)
new_compare28(zxw79000, zxw80000, False, bdb) → new_compare111(zxw79000, zxw80000, new_ltEs18(zxw79000, zxw80000, bdb), bdb)
new_compare1(:(zxw79000, zxw79001), [], he) → GT
new_esEs28(zxw4000, zxw3000, app(ty_Ratio, dhg)) → new_esEs18(zxw4000, zxw3000, dhg)
new_lt4(zxw79000, zxw80000, ty_Integer) → new_lt13(zxw79000, zxw80000)
new_esEs19(zxw79001, zxw80001, ty_@0) → new_esEs10(zxw79001, zxw80001)
new_compare29(zxw79000, zxw80000, ty_@0) → new_compare30(zxw79000, zxw80000)
new_ltEs19(zxw7900, zxw8000, ty_Integer) → new_ltEs13(zxw7900, zxw8000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(ty_Ratio, cgh)) → new_ltEs17(zxw79000, zxw80000, cgh)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Integer) → new_ltEs13(zxw79000, zxw80000)
new_ltEs19(zxw7900, zxw8000, ty_Ordering) → new_ltEs7(zxw7900, zxw8000)
new_compare28(zxw79000, zxw80000, True, bdb) → EQ
new_esEs31(zxw35, zxw30, ty_Int) → new_esEs11(zxw35, zxw30)
new_esEs26(zxw4002, zxw3002, ty_Double) → new_esEs16(zxw4002, zxw3002)
new_esEs33(zxw400, zxw300, ty_Int) → new_esEs11(zxw400, zxw300)
new_compare10(zxw79000, zxw80000, True) → LT
new_esEs31(zxw35, zxw30, ty_Bool) → new_esEs14(zxw35, zxw30)
new_esEs19(zxw79001, zxw80001, app(ty_[], caa)) → new_esEs13(zxw79001, zxw80001, caa)
new_compare10(zxw79000, zxw80000, False) → GT
new_esEs9(LT, LT) → True
new_ltEs20(zxw7900, zxw8000, ty_Char) → new_ltEs10(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, ty_Ordering) → new_ltEs7(zxw7900, zxw8000)
new_primCompAux00(zxw276, GT) → GT
new_esEs31(zxw35, zxw30, app(ty_Maybe, bde)) → new_esEs6(zxw35, zxw30, bde)
new_compare18(zxw79000, zxw80000) → new_compare24(zxw79000, zxw80000, new_esEs9(zxw79000, zxw80000))
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_@0) → new_ltEs8(zxw79000, zxw80000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_lt19(zxw79000, zxw80000, ty_Char) → new_lt9(zxw79000, zxw80000)
new_esEs28(zxw4000, zxw3000, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_ltEs19(zxw7900, zxw8000, app(ty_Maybe, baa)) → new_ltEs18(zxw7900, zxw8000, baa)
new_esEs27(zxw4001, zxw3001, ty_Integer) → new_esEs15(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, app(ty_Ratio, daf)) → new_esEs18(zxw4001, zxw3001, daf)
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_esEs19(zxw79001, zxw80001, ty_Char) → new_esEs12(zxw79001, zxw80001)
new_esEs23(zxw4000, zxw3000, app(ty_[], ddd)) → new_esEs13(zxw4000, zxw3000, ddd)
new_ltEs17(zxw7900, zxw8000, hh) → new_fsEs(new_compare8(zxw7900, zxw8000, hh))
new_not(True) → False
new_ltEs4(@2(zxw79000, zxw79001), @2(zxw80000, zxw80001), ca, cb) → new_pePe(new_lt4(zxw79000, zxw80000, ca), new_asAs(new_esEs8(zxw79000, zxw80000, ca), new_ltEs5(zxw79001, zxw80001, cb)))
new_compare1([], [], he) → EQ
new_esEs6(Just(zxw4000), Just(zxw3000), app(ty_Ratio, fa)) → new_esEs18(zxw4000, zxw3000, fa)

The set Q consists of the following terms:

new_compare23(x0, x1, True)
new_lt6(x0, x1)
new_ltEs5(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, ty_Integer)
new_esEs33(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt4(x0, x1, app(ty_[], x2))
new_ltEs18(Just(x0), Just(x1), ty_@0)
new_compare16(x0, x1)
new_lt4(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(Just(x0), Nothing, x1)
new_ltEs20(x0, x1, ty_Double)
new_esEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs19(x0, x1, ty_Bool)
new_esEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs8(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(x0, x1, app(app(ty_Either, x2), x3))
new_compare30(@0, @0)
new_esEs32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCompAux00(x0, GT)
new_lt19(x0, x1, ty_Char)
new_esEs27(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_Ordering)
new_compare17(Char(x0), Char(x1))
new_esEs28(x0, x1, ty_Int)
new_ltEs20(x0, x1, app(ty_[], x2))
new_ltEs21(x0, x1, ty_Ordering)
new_compare111(x0, x1, True, x2)
new_ltEs15(x0, x1)
new_primPlusNat1(Zero, Succ(x0))
new_esEs6(Just(x0), Just(x1), ty_Double)
new_compare24(x0, x1, False)
new_compare210(x0, x1, False, x2, x3)
new_lt20(x0, x1, ty_Char)
new_esEs33(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, ty_Bool)
new_sr0(Integer(x0), Integer(x1))
new_esEs32(x0, x1, app(ty_[], x2))
new_esEs33(x0, x1, ty_Float)
new_compare28(x0, x1, True, x2)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(Nothing, Nothing, x0)
new_ltEs18(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs34(x0, x1, ty_Integer)
new_esEs34(x0, x1, app(ty_Maybe, x2))
new_ltEs7(EQ, EQ)
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs19(x0, x1, ty_Integer)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_ltEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Bool)
new_ltEs14(Right(x0), Right(x1), x2, ty_Float)
new_compare27(x0, x1, x2)
new_esEs31(x0, x1, app(ty_Ratio, x2))
new_esEs6(Just(x0), Just(x1), app(ty_[], x2))
new_compare14(x0, x1, True, x2, x3)
new_ltEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs13([], :(x0, x1), x2)
new_compare25(x0, x1, False, x2, x3, x4)
new_esEs7(Left(x0), Left(x1), ty_Integer, x2)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs7(Right(x0), Right(x1), x2, ty_@0)
new_esEs31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Integer)
new_ltEs5(x0, x1, ty_Integer)
new_ltEs21(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs7(EQ, LT)
new_ltEs7(LT, EQ)
new_esEs20(x0, x1, ty_Ordering)
new_esEs17(Float(x0, x1), Float(x2, x3))
new_compare25(x0, x1, True, x2, x3, x4)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_lt19(x0, x1, ty_Ordering)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs16(x0, x1)
new_lt4(x0, x1, app(ty_Maybe, x2))
new_esEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs14(Left(x0), Left(x1), ty_Char, x2)
new_sr(x0, x1)
new_ltEs19(x0, x1, ty_Double)
new_compare7(Float(x0, x1), Float(x2, x3))
new_ltEs9(x0, x1)
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_compare19(x0, x1, x2, x3)
new_lt7(x0, x1)
new_lt4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, ty_Int)
new_esEs26(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat0(Zero, x0)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs32(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_ltEs7(LT, LT)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs27(x0, x1, ty_Bool)
new_lt5(x0, x1, x2, x3, x4)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare29(x0, x1, app(app(ty_@2, x2), x3))
new_lt4(x0, x1, ty_Ordering)
new_esEs34(x0, x1, app(ty_Ratio, x2))
new_primEqNat0(Zero, Succ(x0))
new_lt19(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Int)
new_esEs15(Integer(x0), Integer(x1))
new_esEs26(x0, x1, ty_Double)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs28(x0, x1, ty_@0)
new_primPlusNat1(Succ(x0), Zero)
new_esEs22(x0, x1, ty_Integer)
new_ltEs14(Left(x0), Left(x1), ty_@0, x2)
new_primMulInt(Neg(x0), Neg(x1))
new_ltEs19(x0, x1, ty_Int)
new_esEs7(Left(x0), Left(x1), ty_Double, x2)
new_compare29(x0, x1, ty_Integer)
new_esEs14(True, True)
new_esEs21(x0, x1, ty_Char)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(Just(x0), Just(x1), ty_Integer)
new_compare29(x0, x1, app(ty_[], x2))
new_ltEs18(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, ty_Int)
new_esEs7(Right(x0), Right(x1), x2, ty_Int)
new_primEqNat0(Zero, Zero)
new_esEs16(Double(x0, x1), Double(x2, x3))
new_esEs12(Char(x0), Char(x1))
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_lt4(x0, x1, ty_Char)
new_esEs20(x0, x1, ty_Bool)
new_esEs8(x0, x1, ty_Float)
new_compare1([], :(x0, x1), x2)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_Integer)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs32(x0, x1, ty_@0)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(Left(x0), Left(x1), ty_Int, x2)
new_primCompAux00(x0, LT)
new_esEs27(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(ty_[], x2))
new_ltEs5(x0, x1, ty_Double)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs18(Just(x0), Just(x1), ty_Char)
new_primMulNat0(Zero, Zero)
new_lt9(x0, x1)
new_compare29(x0, x1, ty_Double)
new_esEs34(x0, x1, app(ty_[], x2))
new_ltEs5(x0, x1, ty_@0)
new_lt17(x0, x1, x2)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_ltEs21(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs31(x0, x1, ty_Bool)
new_ltEs14(Left(x0), Left(x1), ty_Float, x2)
new_esEs32(x0, x1, ty_Float)
new_esEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs8(x0, x1, ty_Ordering)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_compare10(x0, x1, True)
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Ordering)
new_primEqNat0(Succ(x0), Succ(x1))
new_ltEs19(x0, x1, ty_Bool)
new_esEs28(x0, x1, ty_Double)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_@0)
new_pePe(True, x0)
new_esEs19(x0, x1, ty_Float)
new_lt19(x0, x1, app(ty_[], x2))
new_esEs8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_lt16(x0, x1)
new_compare29(x0, x1, ty_Bool)
new_lt10(x0, x1, x2)
new_esEs7(Right(x0), Right(x1), x2, ty_Integer)
new_esEs32(x0, x1, app(app(ty_Either, x2), x3))
new_compare11(x0, x1, True)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs32(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs33(x0, x1, app(ty_[], x2))
new_esEs34(x0, x1, ty_Char)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1, ty_@0)
new_esEs6(Just(x0), Just(x1), ty_Ordering)
new_esEs23(x0, x1, ty_@0)
new_ltEs14(Right(x0), Right(x1), x2, ty_Int)
new_ltEs5(x0, x1, ty_Char)
new_ltEs21(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Float)
new_lt18(x0, x1, x2)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_compare29(x0, x1, ty_Ordering)
new_ltEs21(x0, x1, ty_@0)
new_esEs8(x0, x1, ty_Int)
new_lt14(x0, x1, x2, x3)
new_ltEs12(False, False)
new_compare210(x0, x1, True, x2, x3)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Just(x0), Just(x1), ty_Bool)
new_compare32(Integer(x0), Integer(x1))
new_lt19(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_Int)
new_primMulNat0(Succ(x0), Succ(x1))
new_compare29(x0, x1, ty_Float)
new_ltEs21(x0, x1, ty_Integer)
new_esEs6(Just(x0), Just(x1), ty_Float)
new_ltEs5(x0, x1, ty_Float)
new_ltEs18(Just(x0), Just(x1), ty_Float)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_Bool)
new_esEs31(x0, x1, ty_Double)
new_primCmpNat1(Zero, x0)
new_ltEs14(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs8(x0, x1)
new_ltEs18(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs14(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs33(x0, x1, app(ty_Ratio, x2))
new_compare13(x0, x1, False, x2, x3)
new_esEs34(x0, x1, ty_Float)
new_primPlusNat1(Zero, Zero)
new_esEs23(x0, x1, ty_Double)
new_ltEs18(Just(x0), Just(x1), ty_Ordering)
new_primCmpNat2(Zero, Zero)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(x0, x1, ty_Bool)
new_esEs34(x0, x1, ty_Ordering)
new_ltEs18(Just(x0), Just(x1), app(ty_[], x2))
new_esEs33(x0, x1, app(ty_Maybe, x2))
new_ltEs5(x0, x1, app(ty_[], x2))
new_asAs(False, x0)
new_ltEs20(x0, x1, ty_Char)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs31(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs8(x0, x1, ty_Integer)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs33(x0, x1, ty_Ordering)
new_ltEs18(Just(x0), Just(x1), ty_Bool)
new_compare14(x0, x1, False, x2, x3)
new_primCmpNat1(Succ(x0), x1)
new_esEs34(x0, x1, ty_Bool)
new_esEs33(x0, x1, ty_Double)
new_esEs24(x0, x1, ty_Integer)
new_esEs27(x0, x1, ty_@0)
new_esEs7(Left(x0), Left(x1), ty_Int, x2)
new_ltEs14(Right(x0), Right(x1), x2, ty_Double)
new_lt4(x0, x1, ty_Float)
new_ltEs5(x0, x1, app(app(ty_Either, x2), x3))
new_esEs19(x0, x1, ty_Char)
new_lt4(x0, x1, ty_Double)
new_esEs19(x0, x1, ty_Ordering)
new_esEs8(x0, x1, app(ty_Ratio, x2))
new_esEs33(x0, x1, ty_Int)
new_esEs10(@0, @0)
new_esEs31(x0, x1, ty_@0)
new_esEs33(x0, x1, ty_@0)
new_esEs11(x0, x1)
new_esEs20(x0, x1, ty_Float)
new_ltEs14(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs7(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs14(Right(x0), Right(x1), x2, ty_Char)
new_esEs9(GT, GT)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs27(x0, x1, ty_Char)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_compare11(x0, x1, False)
new_compare23(x0, x1, False)
new_compare12(x0, x1, True, x2, x3, x4)
new_esEs7(Right(x0), Right(x1), x2, ty_Double)
new_esEs28(x0, x1, ty_Bool)
new_esEs33(x0, x1, app(app(ty_Either, x2), x3))
new_compare24(x0, x1, True)
new_compare36(x0, x1, x2, x3)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_compare15(x0, x1, x2, x3)
new_primEqNat0(Succ(x0), Zero)
new_esEs13([], [], x0)
new_esEs23(x0, x1, ty_Ordering)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs7(Left(x0), Right(x1), x2, x3)
new_esEs7(Right(x0), Left(x1), x2, x3)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_esEs34(x0, x1, ty_Int)
new_compare9(x0, x1, x2, x3, x4)
new_lt20(x0, x1, ty_Int)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs21(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Integer)
new_esEs33(x0, x1, ty_Bool)
new_lt4(x0, x1, app(app(ty_Either, x2), x3))
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs23(x0, x1, ty_Int)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs5(x0, x1, app(app(ty_@2, x2), x3))
new_esEs33(x0, x1, ty_Char)
new_lt4(x0, x1, ty_@0)
new_esEs23(x0, x1, ty_Char)
new_esEs28(x0, x1, ty_Ordering)
new_ltEs18(Just(x0), Just(x1), ty_Double)
new_ltEs20(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_lt20(x0, x1, ty_@0)
new_compare1([], [], x0)
new_esEs9(EQ, EQ)
new_pePe(False, x0)
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs5(x0, x1, app(ty_Ratio, x2))
new_ltEs14(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs6(Just(x0), Just(x1), ty_Char)
new_esEs25(x0, x1, ty_Integer)
new_esEs31(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_Integer)
new_compare12(x0, x1, False, x2, x3, x4)
new_esEs8(x0, x1, app(ty_Maybe, x2))
new_primCompAux00(x0, EQ)
new_esEs19(x0, x1, ty_Int)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs14(True, False)
new_esEs14(False, True)
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_lt4(x0, x1, ty_Integer)
new_esEs7(Left(x0), Left(x1), ty_@0, x2)
new_ltEs14(Right(x0), Right(x1), x2, ty_@0)
new_fsEs(x0)
new_esEs22(x0, x1, ty_Float)
new_ltEs14(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs32(x0, x1, app(ty_Ratio, x2))
new_esEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_primCmpNat2(Succ(x0), Succ(x1))
new_compare110(x0, x1, False, x2, x3)
new_lt4(x0, x1, ty_Bool)
new_asAs(True, x0)
new_esEs21(x0, x1, ty_Bool)
new_esEs4(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs6(Nothing, Just(x0), x1)
new_esEs6(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs21(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Just(x0), Nothing, x1)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_compare29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs8(x0, x1, app(ty_[], x2))
new_esEs31(x0, x1, ty_Integer)
new_esEs13(:(x0, x1), [], x2)
new_ltEs14(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs8(x0, x1, ty_Char)
new_lt19(x0, x1, ty_Float)
new_compare33(x0, x1, x2, x3)
new_ltEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs22(x0, x1, ty_@0)
new_esEs34(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_Char)
new_ltEs12(False, True)
new_ltEs12(True, False)
new_compare6(Double(x0, x1), Double(x2, x3))
new_ltEs20(x0, x1, ty_@0)
new_esEs22(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_@0)
new_compare35(x0, x1, x2, x3)
new_ltEs14(Right(x0), Right(x1), x2, ty_Integer)
new_lt19(x0, x1, ty_Double)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1, ty_Bool)
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs7(Left(x0), Left(x1), ty_Char, x2)
new_esEs7(Right(x0), Right(x1), x2, ty_Float)
new_ltEs14(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs26(x0, x1, ty_Char)
new_ltEs5(x0, x1, ty_Int)
new_lt4(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_Double)
new_esEs19(x0, x1, ty_@0)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_compare13(x0, x1, True, x2, x3)
new_esEs34(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs21(x0, x1, ty_Bool)
new_ltEs14(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs21(x0, x1, ty_Double)
new_lt12(x0, x1)
new_esEs8(x0, x1, ty_Bool)
new_ltEs21(x0, x1, ty_Char)
new_lt13(x0, x1)
new_esEs31(x0, x1, ty_Ordering)
new_ltEs14(Right(x0), Right(x1), x2, ty_Bool)
new_compare1(:(x0, x1), [], x2)
new_compare10(x0, x1, False)
new_primMulNat0(Succ(x0), Zero)
new_ltEs19(x0, x1, ty_Float)
new_ltEs14(Left(x0), Right(x1), x2, x3)
new_esEs23(x0, x1, ty_Float)
new_ltEs14(Right(x0), Left(x1), x2, x3)
new_compare29(x0, x1, ty_Int)
new_esEs20(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, ty_Int)
new_esEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs20(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Float)
new_compare31(x0, x1)
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs31(x0, x1, ty_Char)
new_esEs6(Just(x0), Just(x1), ty_Int)
new_ltEs7(LT, GT)
new_ltEs7(GT, LT)
new_esEs21(x0, x1, ty_Integer)
new_esEs22(x0, x1, app(ty_[], x2))
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs22(x0, x1, ty_Double)
new_compare110(x0, x1, True, x2, x3)
new_lt20(x0, x1, app(ty_[], x2))
new_ltEs13(x0, x1)
new_ltEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs34(x0, x1, ty_@0)
new_esEs31(x0, x1, ty_Int)
new_lt4(x0, x1, ty_Int)
new_ltEs11(x0, x1, x2)
new_lt20(x0, x1, ty_Float)
new_not(True)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs31(x0, x1, ty_Float)
new_esEs20(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Float)
new_esEs19(x0, x1, app(ty_[], x2))
new_esEs18(:%(x0, x1), :%(x2, x3), x4)
new_esEs6(Nothing, Nothing, x0)
new_esEs28(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Ordering)
new_ltEs14(Left(x0), Left(x1), ty_Double, x2)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Just(x0), Just(x1), ty_Integer)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_not(False)
new_compare29(x0, x1, app(ty_Ratio, x2))
new_lt8(x0, x1)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_compare28(x0, x1, False, x2)
new_esEs32(x0, x1, ty_Integer)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, ty_Char)
new_esEs6(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare8(:%(x0, x1), :%(x2, x3), ty_Integer)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs22(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_Integer)
new_esEs8(x0, x1, ty_@0)
new_compare26(Left(x0), Left(x1), False, x2, x3)
new_esEs32(x0, x1, app(ty_Maybe, x2))
new_ltEs12(True, True)
new_esEs27(x0, x1, ty_Float)
new_lt15(x0, x1)
new_lt11(x0, x1, x2, x3)
new_esEs26(x0, x1, ty_Ordering)
new_esEs7(Left(x0), Left(x1), ty_Float, x2)
new_esEs27(x0, x1, ty_Double)
new_esEs6(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs34(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs33(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Ordering)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs13(:(x0, x1), :(x2, x3), x4)
new_esEs22(x0, x1, ty_Char)
new_lt20(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Bool)
new_esEs34(x0, x1, ty_Double)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_ltEs21(x0, x1, ty_Float)
new_ltEs10(x0, x1)
new_ltEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_compare29(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs14(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs5(x0, x1, ty_Ordering)
new_esEs8(x0, x1, ty_Double)
new_compare29(x0, x1, ty_Char)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs6(Just(x0), Just(x1), ty_@0)
new_esEs31(x0, x1, app(app(ty_Either, x2), x3))
new_compare1(:(x0, x1), :(x2, x3), x4)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs31(x0, x1, app(ty_[], x2))
new_esEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs6(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs19(x0, x1, ty_Double)
new_esEs14(False, False)
new_ltEs21(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs32(x0, x1, ty_Char)
new_ltEs21(x0, x1, ty_Double)
new_esEs32(x0, x1, ty_Int)
new_ltEs14(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpNat2(Succ(x0), Zero)
new_esEs7(Right(x0), Right(x1), x2, ty_Char)
new_esEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_compare34(x0, x1, x2, x3)
new_compare18(x0, x1)
new_esEs32(x0, x1, ty_Bool)
new_esEs7(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs18(Just(x0), Just(x1), ty_Int)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare26(Right(x0), Right(x1), False, x2, x3)
new_esEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs17(x0, x1, x2)
new_primPlusNat0(Succ(x0), x1)
new_esEs20(x0, x1, ty_Integer)
new_primCmpNat0(x0, Zero)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_ltEs7(GT, EQ)
new_ltEs7(EQ, GT)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs32(x0, x1, ty_Double)
new_ltEs7(GT, GT)
new_esEs9(LT, LT)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_primCompAux0(x0, x1, x2, x3)
new_compare29(x0, x1, ty_@0)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_compare26(x0, x1, True, x2, x3)
new_compare26(Right(x0), Left(x1), False, x2, x3)
new_compare26(Left(x0), Right(x1), False, x2, x3)
new_ltEs18(Nothing, Just(x0), x1)
new_compare111(x0, x1, False, x2)
new_compare29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Ordering)
new_primCmpNat0(x0, Succ(x1))

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

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

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

new_splitGT3(Right(zxw300), zxw31, zxw32, zxw33, zxw34, Right(zxw400), h, ba, bb) → new_splitGT22(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs9(new_compare26(Right(zxw400), Right(zxw300), new_esEs34(zxw400, zxw300, ba), h, ba), GT), h, ba, bb)
new_splitGT21(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, False, h, ba, bb) → new_splitGT11(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs9(new_compare35(zxw400, zxw300, h, ba), LT), h, ba, bb)
new_splitGT3(Left(zxw300), zxw31, zxw32, zxw33, zxw34, Right(zxw400), h, ba, bb) → new_splitGT21(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs9(new_compare26(Right(zxw400), Left(zxw300), False, h, ba), GT), h, ba, bb)
new_splitGT21(zxw300, zxw31, zxw32, zxw33, Branch(zxw340, zxw341, zxw342, zxw343, zxw344), zxw400, True, h, ba, bb) → new_splitGT3(zxw340, zxw341, zxw342, zxw343, zxw344, Right(zxw400), h, ba, bb)
new_splitGT12(zxw30, zxw31, zxw32, zxw33, zxw34, zxw35, True, bf, bg, bh) → new_splitGT0(zxw33, zxw35, bf, bg, bh)
new_splitGT22(zxw30, zxw31, zxw32, zxw33, zxw34, zxw35, True, bf, bg, bh) → new_splitGT0(zxw34, zxw35, bf, bg, bh)
new_splitGT22(zxw30, zxw31, zxw32, zxw33, zxw34, zxw35, False, bf, bg, bh) → new_splitGT12(zxw30, zxw31, zxw32, zxw33, zxw34, zxw35, new_esEs9(new_compare36(zxw35, zxw30, bf, bg), LT), bf, bg, bh)
new_splitGT11(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, True, h, ba, bb) → new_splitGT0(zxw33, zxw400, h, ba, bb)
new_splitGT0(Branch(zxw340, zxw341, zxw342, zxw343, zxw344), zxw400, h, ba, bb) → new_splitGT3(zxw340, zxw341, zxw342, zxw343, zxw344, Right(zxw400), h, ba, bb)

The TRS R consists of the following rules:

new_ltEs15(zxw7900, zxw8000) → new_fsEs(new_compare6(zxw7900, zxw8000))
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Bool) → new_ltEs12(zxw79000, zxw80000)
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, app(ty_Maybe, bbc)) → new_ltEs18(zxw7900, zxw8000, bbc)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Char) → new_ltEs10(zxw79000, zxw80000)
new_esEs28(zxw4000, zxw3000, app(ty_[], dhh)) → new_esEs13(zxw4000, zxw3000, dhh)
new_esEs32(zxw20, zxw15, ty_Float) → new_esEs17(zxw20, zxw15)
new_esEs23(zxw4000, zxw3000, app(app(ty_Either, ddh), dea)) → new_esEs7(zxw4000, zxw3000, ddh, dea)
new_esEs6(Just(zxw4000), Just(zxw3000), app(app(ty_@2, fd), ff)) → new_esEs5(zxw4000, zxw3000, fd, ff)
new_lt4(zxw79000, zxw80000, app(app(app(ty_@3, cc), cd), ce)) → new_lt5(zxw79000, zxw80000, cc, cd, ce)
new_esEs7(Left(zxw4000), Left(zxw3000), app(app(ty_Either, bfc), bfd), bef) → new_esEs7(zxw4000, zxw3000, bfc, bfd)
new_esEs31(zxw35, zxw30, ty_Ordering) → new_esEs9(zxw35, zxw30)
new_ltEs20(zxw7900, zxw8000, ty_Int) → new_ltEs9(zxw7900, zxw8000)
new_esEs33(zxw400, zxw300, app(app(ty_Either, bfh), bef)) → new_esEs7(zxw400, zxw300, bfh, bef)
new_lt19(zxw79000, zxw80000, app(app(ty_Either, bhd), bhe)) → new_lt14(zxw79000, zxw80000, bhd, bhe)
new_esEs33(zxw400, zxw300, app(ty_[], ddb)) → new_esEs13(zxw400, zxw300, ddb)
new_esEs9(GT, LT) → False
new_esEs9(LT, GT) → False
new_esEs33(zxw400, zxw300, ty_Char) → new_esEs12(zxw400, zxw300)
new_esEs13([], [], ddb) → True
new_lt4(zxw79000, zxw80000, app(ty_[], cf)) → new_lt10(zxw79000, zxw80000, cf)
new_compare110(zxw79000, zxw80000, True, bcf, bcg) → LT
new_esEs27(zxw4001, zxw3001, app(ty_Ratio, dge)) → new_esEs18(zxw4001, zxw3001, dge)
new_compare29(zxw79000, zxw80000, ty_Char) → new_compare17(zxw79000, zxw80000)
new_ltEs7(LT, EQ) → True
new_ltEs18(Just(zxw79000), Just(zxw80000), app(ty_Maybe, dac)) → new_ltEs18(zxw79000, zxw80000, dac)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Integer) → new_ltEs13(zxw79000, zxw80000)
new_ltEs20(zxw7900, zxw8000, ty_@0) → new_ltEs8(zxw7900, zxw8000)
new_lt20(zxw79001, zxw80001, app(app(ty_Either, cad), cae)) → new_lt14(zxw79001, zxw80001, cad, cae)
new_esEs23(zxw4000, zxw3000, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_compare35(zxw400, zxw300, h, ba) → new_compare26(Right(zxw400), Left(zxw300), False, h, ba)
new_ltEs8(zxw7900, zxw8000) → new_fsEs(new_compare30(zxw7900, zxw8000))
new_lt19(zxw79000, zxw80000, ty_Double) → new_lt15(zxw79000, zxw80000)
new_esEs22(zxw4000, zxw3000, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(ty_[], cgc)) → new_ltEs11(zxw79000, zxw80000, cgc)
new_ltEs21(zxw79002, zxw80002, ty_Char) → new_ltEs10(zxw79002, zxw80002)
new_esEs23(zxw4000, zxw3000, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Bool, hg) → new_ltEs12(zxw79000, zxw80000)
new_compare8(:%(zxw79000, zxw79001), :%(zxw80000, zxw80001), ty_Integer) → new_compare32(new_sr0(zxw79000, zxw80001), new_sr0(zxw80000, zxw79001))
new_esEs26(zxw4002, zxw3002, ty_Float) → new_esEs17(zxw4002, zxw3002)
new_esEs19(zxw79001, zxw80001, app(ty_Ratio, caf)) → new_esEs18(zxw79001, zxw80001, caf)
new_primMulNat0(Zero, Zero) → Zero
new_esEs20(zxw79000, zxw80000, app(ty_[], bhc)) → new_esEs13(zxw79000, zxw80000, bhc)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs34(zxw400, zxw300, ty_Char) → new_esEs12(zxw400, zxw300)
new_lt20(zxw79001, zxw80001, ty_@0) → new_lt7(zxw79001, zxw80001)
new_esEs27(zxw4001, zxw3001, app(app(app(ty_@3, dhd), dhe), dhf)) → new_esEs4(zxw4001, zxw3001, dhd, dhe, dhf)
new_esEs19(zxw79001, zxw80001, ty_Ordering) → new_esEs9(zxw79001, zxw80001)
new_esEs31(zxw35, zxw30, ty_Char) → new_esEs12(zxw35, zxw30)
new_esEs33(zxw400, zxw300, ty_Ordering) → new_esEs9(zxw400, zxw300)
new_esEs32(zxw20, zxw15, ty_Integer) → new_esEs15(zxw20, zxw15)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(ty_Ratio, dab)) → new_ltEs17(zxw79000, zxw80000, dab)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Bool, bef) → new_esEs14(zxw4000, zxw3000)
new_esEs24(zxw4001, zxw3001, ty_Integer) → new_esEs15(zxw4001, zxw3001)
new_lt19(zxw79000, zxw80000, ty_Ordering) → new_lt6(zxw79000, zxw80000)
new_lt20(zxw79001, zxw80001, app(app(ty_@2, cab), cac)) → new_lt11(zxw79001, zxw80001, cab, cac)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(ty_Ratio, cff), hg) → new_ltEs17(zxw79000, zxw80000, cff)
new_compare9(zxw79000, zxw80000, gd, ge, gf) → new_compare25(zxw79000, zxw80000, new_esEs4(zxw79000, zxw80000, gd, ge, gf), gd, ge, gf)
new_lt11(zxw79000, zxw80000, bcf, bcg) → new_esEs9(new_compare19(zxw79000, zxw80000, bcf, bcg), LT)
new_compare1([], :(zxw80000, zxw80001), he) → LT
new_esEs33(zxw400, zxw300, ty_@0) → new_esEs10(zxw400, zxw300)
new_lt18(zxw79000, zxw80000, bdb) → new_esEs9(new_compare27(zxw79000, zxw80000, bdb), LT)
new_esEs33(zxw400, zxw300, ty_Integer) → new_esEs15(zxw400, zxw300)
new_esEs8(zxw79000, zxw80000, ty_Int) → new_esEs11(zxw79000, zxw80000)
new_compare32(Integer(zxw79000), Integer(zxw80000)) → new_primCmpInt(zxw79000, zxw80000)
new_ltEs5(zxw79001, zxw80001, ty_Char) → new_ltEs10(zxw79001, zxw80001)
new_lt4(zxw79000, zxw80000, ty_Bool) → new_lt12(zxw79000, zxw80000)
new_compare27(zxw79000, zxw80000, bdb) → new_compare28(zxw79000, zxw80000, new_esEs6(zxw79000, zxw80000, bdb), bdb)
new_lt4(zxw79000, zxw80000, app(ty_Maybe, de)) → new_lt18(zxw79000, zxw80000, de)
new_compare29(zxw79000, zxw80000, ty_Bool) → new_compare31(zxw79000, zxw80000)
new_esEs31(zxw35, zxw30, ty_@0) → new_esEs10(zxw35, zxw30)
new_esEs8(zxw79000, zxw80000, ty_Double) → new_esEs16(zxw79000, zxw80000)
new_esEs22(zxw4000, zxw3000, app(app(ty_@2, dcc), dcd)) → new_esEs5(zxw4000, zxw3000, dcc, dcd)
new_lt4(zxw79000, zxw80000, ty_Ordering) → new_lt6(zxw79000, zxw80000)
new_esEs22(zxw4000, zxw3000, app(ty_Maybe, dcb)) → new_esEs6(zxw4000, zxw3000, dcb)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(app(app(ty_@3, cfh), cga), cgb)) → new_ltEs6(zxw79000, zxw80000, cfh, cga, cgb)
new_esEs34(zxw400, zxw300, app(app(ty_Either, bca), bcb)) → new_esEs7(zxw400, zxw300, bca, bcb)
new_esEs27(zxw4001, zxw3001, app(ty_Maybe, dgg)) → new_esEs6(zxw4001, zxw3001, dgg)
new_esEs8(zxw79000, zxw80000, app(app(app(ty_@3, cc), cd), ce)) → new_esEs4(zxw79000, zxw80000, cc, cd, ce)
new_esEs15(Integer(zxw4000), Integer(zxw3000)) → new_primEqInt(zxw4000, zxw3000)
new_ltEs21(zxw79002, zxw80002, app(app(ty_@2, cbd), cbe)) → new_ltEs4(zxw79002, zxw80002, cbd, cbe)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Float, hg) → new_ltEs16(zxw79000, zxw80000)
new_lt5(zxw79000, zxw80000, gd, ge, gf) → new_esEs9(new_compare9(zxw79000, zxw80000, gd, ge, gf), LT)
new_esEs22(zxw4000, zxw3000, app(ty_Ratio, dbh)) → new_esEs18(zxw4000, zxw3000, dbh)
new_esEs22(zxw4000, zxw3000, app(app(ty_Either, dce), dcf)) → new_esEs7(zxw4000, zxw3000, dce, dcf)
new_ltEs19(zxw7900, zxw8000, ty_Float) → new_ltEs16(zxw7900, zxw8000)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, app(ty_Maybe, bgc)) → new_esEs6(zxw4000, zxw3000, bgc)
new_pePe(False, zxw271) → zxw271
new_esEs7(Right(zxw4000), Left(zxw3000), bfh, bef) → False
new_esEs7(Left(zxw4000), Right(zxw3000), bfh, bef) → False
new_lt15(zxw79000, zxw80000) → new_esEs9(new_compare6(zxw79000, zxw80000), LT)
new_compare15(zxw790, zxw800, gh, ha) → new_compare26(zxw790, zxw800, new_esEs7(zxw790, zxw800, gh, ha), gh, ha)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Float) → new_ltEs16(zxw79000, zxw80000)
new_esEs31(zxw35, zxw30, app(app(app(ty_@3, beb), bec), bed)) → new_esEs4(zxw35, zxw30, beb, bec, bed)
new_ltEs12(True, False) → False
new_esEs34(zxw400, zxw300, app(ty_[], bbe)) → new_esEs13(zxw400, zxw300, bbe)
new_esEs20(zxw79000, zxw80000, ty_Double) → new_esEs16(zxw79000, zxw80000)
new_ltEs19(zxw7900, zxw8000, app(app(ty_@2, ca), cb)) → new_ltEs4(zxw7900, zxw8000, ca, cb)
new_esEs32(zxw20, zxw15, ty_@0) → new_esEs10(zxw20, zxw15)
new_compare23(zxw79000, zxw80000, True) → EQ
new_esEs31(zxw35, zxw30, ty_Float) → new_esEs17(zxw35, zxw30)
new_esEs27(zxw4001, zxw3001, app(app(ty_Either, dhb), dhc)) → new_esEs7(zxw4001, zxw3001, dhb, dhc)
new_esEs27(zxw4001, zxw3001, ty_Ordering) → new_esEs9(zxw4001, zxw3001)
new_esEs27(zxw4001, zxw3001, ty_Float) → new_esEs17(zxw4001, zxw3001)
new_esEs19(zxw79001, zxw80001, app(ty_Maybe, cag)) → new_esEs6(zxw79001, zxw80001, cag)
new_lt10(zxw79000, zxw80000, bhc) → new_esEs9(new_compare1(zxw79000, zxw80000, bhc), LT)
new_esEs26(zxw4002, zxw3002, ty_Char) → new_esEs12(zxw4002, zxw3002)
new_ltEs19(zxw7900, zxw8000, app(ty_[], he)) → new_ltEs11(zxw7900, zxw8000, he)
new_esEs26(zxw4002, zxw3002, ty_Int) → new_esEs11(zxw4002, zxw3002)
new_ltEs5(zxw79001, zxw80001, app(app(ty_@2, eb), ec)) → new_ltEs4(zxw79001, zxw80001, eb, ec)
new_lt19(zxw79000, zxw80000, app(ty_Ratio, gg)) → new_lt17(zxw79000, zxw80000, gg)
new_esEs22(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, app(app(app(ty_@3, eaf), eag), eah)) → new_esEs4(zxw4000, zxw3000, eaf, eag, eah)
new_esEs32(zxw20, zxw15, ty_Ordering) → new_esEs9(zxw20, zxw15)
new_compare29(zxw79000, zxw80000, app(app(ty_@2, ccf), ccg)) → new_compare19(zxw79000, zxw80000, ccf, ccg)
new_ltEs21(zxw79002, zxw80002, ty_Int) → new_ltEs9(zxw79002, zxw80002)
new_esEs20(zxw79000, zxw80000, ty_Char) → new_esEs12(zxw79000, zxw80000)
new_compare13(zxw235, zxw236, False, bch, bda) → GT
new_esEs9(GT, EQ) → False
new_esEs9(EQ, GT) → False
new_esEs19(zxw79001, zxw80001, app(app(ty_Either, cad), cae)) → new_esEs7(zxw79001, zxw80001, cad, cae)
new_esEs20(zxw79000, zxw80000, app(app(ty_@2, bcf), bcg)) → new_esEs5(zxw79000, zxw80000, bcf, bcg)
new_ltEs7(GT, GT) → True
new_compare36(zxw35, zxw30, bf, bg) → new_compare26(Right(zxw35), Right(zxw30), new_esEs31(zxw35, zxw30, bg), bf, bg)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, app(app(ty_@2, bgd), bge)) → new_esEs5(zxw4000, zxw3000, bgd, bge)
new_ltEs20(zxw7900, zxw8000, app(app(ty_@2, baf), bag)) → new_ltEs4(zxw7900, zxw8000, baf, bag)
new_esEs21(zxw4001, zxw3001, ty_Bool) → new_esEs14(zxw4001, zxw3001)
new_esEs32(zxw20, zxw15, ty_Bool) → new_esEs14(zxw20, zxw15)
new_primCompAux0(zxw79000, zxw80000, zxw272, he) → new_primCompAux00(zxw272, new_compare29(zxw79000, zxw80000, he))
new_ltEs21(zxw79002, zxw80002, ty_Ordering) → new_ltEs7(zxw79002, zxw80002)
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_compare29(zxw79000, zxw80000, app(ty_[], cce)) → new_compare1(zxw79000, zxw80000, cce)
new_lt20(zxw79001, zxw80001, ty_Ordering) → new_lt6(zxw79001, zxw80001)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_esEs8(zxw79000, zxw80000, app(ty_[], cf)) → new_esEs13(zxw79000, zxw80000, cf)
new_esEs33(zxw400, zxw300, app(app(app(ty_@3, deh), dfa), dfb)) → new_esEs4(zxw400, zxw300, deh, dfa, dfb)
new_esEs27(zxw4001, zxw3001, ty_@0) → new_esEs10(zxw4001, zxw3001)
new_compare25(zxw79000, zxw80000, True, gd, ge, gf) → EQ
new_esEs19(zxw79001, zxw80001, ty_Float) → new_esEs17(zxw79001, zxw80001)
new_ltEs5(zxw79001, zxw80001, ty_Ordering) → new_ltEs7(zxw79001, zxw80001)
new_lt4(zxw79000, zxw80000, app(ty_Ratio, dd)) → new_lt17(zxw79000, zxw80000, dd)
new_esEs28(zxw4000, zxw3000, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Int, bef) → new_esEs11(zxw4000, zxw3000)
new_ltEs21(zxw79002, zxw80002, ty_Float) → new_ltEs16(zxw79002, zxw80002)
new_esEs28(zxw4000, zxw3000, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_compare29(zxw79000, zxw80000, app(app(app(ty_@3, ccb), ccc), ccd)) → new_compare9(zxw79000, zxw80000, ccb, ccc, ccd)
new_lt19(zxw79000, zxw80000, app(app(ty_@2, bcf), bcg)) → new_lt11(zxw79000, zxw80000, bcf, bcg)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(app(app(ty_@3, chb), chc), chd)) → new_ltEs6(zxw79000, zxw80000, chb, chc, chd)
new_pePe(True, zxw271) → True
new_primEqNat0(Zero, Zero) → True
new_compare14(zxw242, zxw243, False, def, deg) → GT
new_esEs20(zxw79000, zxw80000, ty_Int) → new_esEs11(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Double) → new_ltEs15(zxw79000, zxw80000)
new_ltEs21(zxw79002, zxw80002, ty_Bool) → new_ltEs12(zxw79002, zxw80002)
new_esEs33(zxw400, zxw300, app(app(ty_@2, dad), dae)) → new_esEs5(zxw400, zxw300, dad, dae)
new_lt9(zxw79000, zxw80000) → new_esEs9(new_compare17(zxw79000, zxw80000), LT)
new_ltEs12(False, False) → True
new_esEs7(Left(zxw4000), Left(zxw3000), app(app(ty_@2, bfa), bfb), bef) → new_esEs5(zxw4000, zxw3000, bfa, bfb)
new_esEs26(zxw4002, zxw3002, app(ty_Maybe, dfe)) → new_esEs6(zxw4002, zxw3002, dfe)
new_compare8(:%(zxw79000, zxw79001), :%(zxw80000, zxw80001), ty_Int) → new_compare16(new_sr(zxw79000, zxw80001), new_sr(zxw80000, zxw79001))
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Ordering, bef) → new_esEs9(zxw4000, zxw3000)
new_esEs27(zxw4001, zxw3001, ty_Char) → new_esEs12(zxw4001, zxw3001)
new_esEs34(zxw400, zxw300, ty_Float) → new_esEs17(zxw400, zxw300)
new_lt7(zxw79000, zxw80000) → new_esEs9(new_compare30(zxw79000, zxw80000), LT)
new_compare110(zxw79000, zxw80000, False, bcf, bcg) → GT
new_sr(zxw4000, zxw3000) → new_primMulInt(zxw4000, zxw3000)
new_compare12(zxw79000, zxw80000, True, gd, ge, gf) → LT
new_lt19(zxw79000, zxw80000, ty_Int) → new_lt8(zxw79000, zxw80000)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(app(ty_@2, cgd), cge)) → new_ltEs4(zxw79000, zxw80000, cgd, cge)
new_ltEs19(zxw7900, zxw8000, ty_Char) → new_ltEs10(zxw7900, zxw8000)
new_esEs21(zxw4001, zxw3001, ty_Double) → new_esEs16(zxw4001, zxw3001)
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, app(app(ty_Either, bgf), bgg)) → new_esEs7(zxw4000, zxw3000, bgf, bgg)
new_esEs31(zxw35, zxw30, app(app(ty_Either, bdh), bea)) → new_esEs7(zxw35, zxw30, bdh, bea)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Double, hg) → new_ltEs15(zxw79000, zxw80000)
new_ltEs19(zxw7900, zxw8000, ty_Bool) → new_ltEs12(zxw7900, zxw8000)
new_esEs26(zxw4002, zxw3002, app(app(app(ty_@3, dgb), dgc), dgd)) → new_esEs4(zxw4002, zxw3002, dgb, dgc, dgd)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, app(ty_[], bgb)) → new_esEs13(zxw4000, zxw3000, bgb)
new_ltEs11(zxw7900, zxw8000, he) → new_fsEs(new_compare1(zxw7900, zxw8000, he))
new_ltEs20(zxw7900, zxw8000, ty_Float) → new_ltEs16(zxw7900, zxw8000)
new_esEs21(zxw4001, zxw3001, ty_Ordering) → new_esEs9(zxw4001, zxw3001)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_esEs9(EQ, EQ) → True
new_fsEs(zxw259) → new_not(new_esEs9(zxw259, GT))
new_esEs8(zxw79000, zxw80000, ty_Char) → new_esEs12(zxw79000, zxw80000)
new_primEqInt(Neg(Succ(zxw40000)), Neg(Succ(zxw30000))) → new_primEqNat0(zxw40000, zxw30000)
new_esEs8(zxw79000, zxw80000, app(app(ty_@2, cg), da)) → new_esEs5(zxw79000, zxw80000, cg, da)
new_compare13(zxw235, zxw236, True, bch, bda) → LT
new_compare26(Left(zxw7900), Right(zxw8000), False, gh, ha) → LT
new_esEs13(:(zxw4000, zxw4001), :(zxw3000, zxw3001), ddb) → new_asAs(new_esEs23(zxw4000, zxw3000, ddb), new_esEs13(zxw4001, zxw3001, ddb))
new_esEs26(zxw4002, zxw3002, app(ty_[], dfd)) → new_esEs13(zxw4002, zxw3002, dfd)
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_ltEs19(zxw7900, zxw8000, app(ty_Ratio, hh)) → new_ltEs17(zxw7900, zxw8000, hh)
new_ltEs20(zxw7900, zxw8000, ty_Bool) → new_ltEs12(zxw7900, zxw8000)
new_esEs21(zxw4001, zxw3001, ty_Char) → new_esEs12(zxw4001, zxw3001)
new_compare23(zxw79000, zxw80000, False) → new_compare10(zxw79000, zxw80000, new_ltEs12(zxw79000, zxw80000))
new_ltEs14(Right(zxw79000), Left(zxw80000), hf, hg) → False
new_compare210(zxw79000, zxw80000, False, bcf, bcg) → new_compare110(zxw79000, zxw80000, new_ltEs4(zxw79000, zxw80000, bcf, bcg), bcf, bcg)
new_primCmpNat1(Zero, zxw7900) → LT
new_compare7(Float(zxw79000, zxw79001), Float(zxw80000, zxw80001)) → new_compare16(new_sr(zxw79000, zxw80000), new_sr(zxw79001, zxw80001))
new_ltEs21(zxw79002, zxw80002, ty_Integer) → new_ltEs13(zxw79002, zxw80002)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_lt20(zxw79001, zxw80001, app(ty_Maybe, cag)) → new_lt18(zxw79001, zxw80001, cag)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Integer, bef) → new_esEs15(zxw4000, zxw3000)
new_ltEs5(zxw79001, zxw80001, ty_Bool) → new_ltEs12(zxw79001, zxw80001)
new_esEs19(zxw79001, zxw80001, ty_Bool) → new_esEs14(zxw79001, zxw80001)
new_ltEs7(EQ, EQ) → True
new_ltEs20(zxw7900, zxw8000, app(ty_Ratio, bbb)) → new_ltEs17(zxw7900, zxw8000, bbb)
new_primEqInt(Neg(Zero), Neg(Succ(zxw30000))) → False
new_primEqInt(Neg(Succ(zxw40000)), Neg(Zero)) → False
new_ltEs5(zxw79001, zxw80001, ty_Integer) → new_ltEs13(zxw79001, zxw80001)
new_compare26(zxw790, zxw800, True, gh, ha) → EQ
new_compare111(zxw79000, zxw80000, True, bdb) → LT
new_esEs20(zxw79000, zxw80000, ty_@0) → new_esEs10(zxw79000, zxw80000)
new_esEs31(zxw35, zxw30, app(ty_Ratio, bdc)) → new_esEs18(zxw35, zxw30, bdc)
new_ltEs21(zxw79002, zxw80002, app(app(ty_Either, cbf), cbg)) → new_ltEs14(zxw79002, zxw80002, cbf, cbg)
new_esEs8(zxw79000, zxw80000, ty_Float) → new_esEs17(zxw79000, zxw80000)
new_esEs34(zxw400, zxw300, app(app(ty_@2, bbg), bbh)) → new_esEs5(zxw400, zxw300, bbg, bbh)
new_esEs23(zxw4000, zxw3000, app(app(app(ty_@3, deb), dec), ded)) → new_esEs4(zxw4000, zxw3000, deb, dec, ded)
new_ltEs21(zxw79002, zxw80002, app(ty_[], cbc)) → new_ltEs11(zxw79002, zxw80002, cbc)
new_esEs21(zxw4001, zxw3001, ty_Float) → new_esEs17(zxw4001, zxw3001)
new_compare24(zxw79000, zxw80000, False) → new_compare11(zxw79000, zxw80000, new_ltEs7(zxw79000, zxw80000))
new_ltEs5(zxw79001, zxw80001, app(ty_Ratio, ef)) → new_ltEs17(zxw79001, zxw80001, ef)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_esEs26(zxw4002, zxw3002, app(app(ty_Either, dfh), dga)) → new_esEs7(zxw4002, zxw3002, dfh, dga)
new_lt20(zxw79001, zxw80001, ty_Int) → new_lt8(zxw79001, zxw80001)
new_lt4(zxw79000, zxw80000, ty_Int) → new_lt8(zxw79000, zxw80000)
new_ltEs20(zxw7900, zxw8000, ty_Double) → new_ltEs15(zxw7900, zxw8000)
new_esEs34(zxw400, zxw300, app(app(app(ty_@3, bcc), bcd), bce)) → new_esEs4(zxw400, zxw300, bcc, bcd, bce)
new_ltEs7(GT, LT) → False
new_lt12(zxw79000, zxw80000) → new_esEs9(new_compare31(zxw79000, zxw80000), LT)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Int, hg) → new_ltEs9(zxw79000, zxw80000)
new_lt20(zxw79001, zxw80001, ty_Integer) → new_lt13(zxw79001, zxw80001)
new_ltEs7(GT, EQ) → False
new_esEs6(Nothing, Nothing, eh) → True
new_primEqInt(Pos(Succ(zxw40000)), Pos(Succ(zxw30000))) → new_primEqNat0(zxw40000, zxw30000)
new_lt8(zxw790, zxw800) → new_esEs9(new_compare16(zxw790, zxw800), LT)
new_esEs21(zxw4001, zxw3001, app(ty_Maybe, dah)) → new_esEs6(zxw4001, zxw3001, dah)
new_lt6(zxw79000, zxw80000) → new_esEs9(new_compare18(zxw79000, zxw80000), LT)
new_esEs32(zxw20, zxw15, app(app(ty_Either, cea), ceb)) → new_esEs7(zxw20, zxw15, cea, ceb)
new_esEs14(False, True) → False
new_esEs14(True, False) → False
new_esEs32(zxw20, zxw15, app(ty_[], cde)) → new_esEs13(zxw20, zxw15, cde)
new_esEs26(zxw4002, zxw3002, ty_Integer) → new_esEs15(zxw4002, zxw3002)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, app(app(app(ty_@3, bgh), bha), bhb)) → new_esEs4(zxw4000, zxw3000, bgh, bha, bhb)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs6(Nothing, Just(zxw3000), eh) → False
new_esEs6(Just(zxw4000), Nothing, eh) → False
new_primEqNat0(Succ(zxw40000), Succ(zxw30000)) → new_primEqNat0(zxw40000, zxw30000)
new_esEs33(zxw400, zxw300, app(ty_Ratio, dee)) → new_esEs18(zxw400, zxw300, dee)
new_esEs16(Double(zxw4000, zxw4001), Double(zxw3000, zxw3001)) → new_esEs11(new_sr(zxw4000, zxw3000), new_sr(zxw4001, zxw3001))
new_lt19(zxw79000, zxw80000, ty_@0) → new_lt7(zxw79000, zxw80000)
new_ltEs5(zxw79001, zxw80001, app(ty_Maybe, eg)) → new_ltEs18(zxw79001, zxw80001, eg)
new_esEs17(Float(zxw4000, zxw4001), Float(zxw3000, zxw3001)) → new_esEs11(new_sr(zxw4000, zxw3000), new_sr(zxw4001, zxw3001))
new_primCompAux00(zxw276, LT) → LT
new_esEs28(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), app(ty_Ratio, bee), bef) → new_esEs18(zxw4000, zxw3000, bee)
new_esEs21(zxw4001, zxw3001, ty_Int) → new_esEs11(zxw4001, zxw3001)
new_compare1(:(zxw79000, zxw79001), :(zxw80000, zxw80001), he) → new_primCompAux0(zxw79000, zxw80000, new_compare1(zxw79001, zxw80001, he), he)
new_primEqInt(Pos(Zero), Pos(Succ(zxw30000))) → False
new_primEqInt(Pos(Succ(zxw40000)), Pos(Zero)) → False
new_compare29(zxw79000, zxw80000, ty_Int) → new_compare16(zxw79000, zxw80000)
new_lt20(zxw79001, zxw80001, app(ty_Ratio, caf)) → new_lt17(zxw79001, zxw80001, caf)
new_esEs34(zxw400, zxw300, ty_Double) → new_esEs16(zxw400, zxw300)
new_ltEs20(zxw7900, zxw8000, ty_Integer) → new_ltEs13(zxw7900, zxw8000)
new_esEs31(zxw35, zxw30, app(app(ty_@2, bdf), bdg)) → new_esEs5(zxw35, zxw30, bdf, bdg)
new_esEs5(@2(zxw4000, zxw4001), @2(zxw3000, zxw3001), dad, dae) → new_asAs(new_esEs22(zxw4000, zxw3000, dad), new_esEs21(zxw4001, zxw3001, dae))
new_ltEs18(Nothing, Nothing, baa) → True
new_esEs32(zxw20, zxw15, app(ty_Maybe, cdf)) → new_esEs6(zxw20, zxw15, cdf)
new_ltEs21(zxw79002, zxw80002, app(ty_Ratio, cbh)) → new_ltEs17(zxw79002, zxw80002, cbh)
new_esEs23(zxw4000, zxw3000, app(app(ty_@2, ddf), ddg)) → new_esEs5(zxw4000, zxw3000, ddf, ddg)
new_esEs33(zxw400, zxw300, ty_Bool) → new_esEs14(zxw400, zxw300)
new_esEs20(zxw79000, zxw80000, app(app(app(ty_@3, gd), ge), gf)) → new_esEs4(zxw79000, zxw80000, gd, ge, gf)
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_ltEs21(zxw79002, zxw80002, app(app(app(ty_@3, cah), cba), cbb)) → new_ltEs6(zxw79002, zxw80002, cah, cba, cbb)
new_ltEs10(zxw7900, zxw8000) → new_fsEs(new_compare17(zxw7900, zxw8000))
new_compare17(Char(zxw79000), Char(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_sr0(Integer(zxw800000), Integer(zxw790010)) → Integer(new_primMulInt(zxw800000, zxw790010))
new_ltEs5(zxw79001, zxw80001, ty_Double) → new_ltEs15(zxw79001, zxw80001)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_esEs8(zxw79000, zxw80000, app(app(ty_Either, db), dc)) → new_esEs7(zxw79000, zxw80000, db, dc)
new_primEqInt(Neg(Succ(zxw40000)), Pos(zxw3000)) → False
new_primEqInt(Pos(Succ(zxw40000)), Neg(zxw3000)) → False
new_compare29(zxw79000, zxw80000, ty_Integer) → new_compare32(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Char) → new_ltEs10(zxw79000, zxw80000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_@0, bef) → new_esEs10(zxw4000, zxw3000)
new_lt19(zxw79000, zxw80000, app(app(app(ty_@3, gd), ge), gf)) → new_lt5(zxw79000, zxw80000, gd, ge, gf)
new_esEs32(zxw20, zxw15, app(app(ty_@2, cdg), cdh)) → new_esEs5(zxw20, zxw15, cdg, cdh)
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_esEs28(zxw4000, zxw3000, app(ty_Maybe, eaa)) → new_esEs6(zxw4000, zxw3000, eaa)
new_ltEs21(zxw79002, zxw80002, ty_@0) → new_ltEs8(zxw79002, zxw80002)
new_esEs21(zxw4001, zxw3001, app(ty_[], dag)) → new_esEs13(zxw4001, zxw3001, dag)
new_primEqInt(Neg(Zero), Pos(Succ(zxw30000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(zxw30000))) → False
new_ltEs7(EQ, GT) → True
new_lt4(zxw79000, zxw80000, ty_Double) → new_lt15(zxw79000, zxw80000)
new_esEs34(zxw400, zxw300, ty_Ordering) → new_esEs9(zxw400, zxw300)
new_esEs21(zxw4001, zxw3001, ty_Integer) → new_esEs15(zxw4001, zxw3001)
new_esEs31(zxw35, zxw30, ty_Integer) → new_esEs15(zxw35, zxw30)
new_primCompAux00(zxw276, EQ) → zxw276
new_esEs28(zxw4000, zxw3000, app(app(ty_Either, ead), eae)) → new_esEs7(zxw4000, zxw3000, ead, eae)
new_compare24(zxw79000, zxw80000, True) → EQ
new_compare6(Double(zxw79000, zxw79001), Double(zxw80000, zxw80001)) → new_compare16(new_sr(zxw79000, zxw80000), new_sr(zxw79001, zxw80001))
new_esEs8(zxw79000, zxw80000, ty_@0) → new_esEs10(zxw79000, zxw80000)
new_ltEs5(zxw79001, zxw80001, app(app(ty_Either, ed), ee)) → new_ltEs14(zxw79001, zxw80001, ed, ee)
new_lt13(zxw79000, zxw80000) → new_esEs9(new_compare32(zxw79000, zxw80000), LT)
new_esEs27(zxw4001, zxw3001, ty_Double) → new_esEs16(zxw4001, zxw3001)
new_esEs7(Left(zxw4000), Left(zxw3000), app(app(app(ty_@3, bfe), bff), bfg), bef) → new_esEs4(zxw4000, zxw3000, bfe, bff, bfg)
new_esEs26(zxw4002, zxw3002, app(app(ty_@2, dff), dfg)) → new_esEs5(zxw4002, zxw3002, dff, dfg)
new_esEs21(zxw4001, zxw3001, app(app(ty_@2, dba), dbb)) → new_esEs5(zxw4001, zxw3001, dba, dbb)
new_lt19(zxw79000, zxw80000, app(ty_Maybe, bdb)) → new_lt18(zxw79000, zxw80000, bdb)
new_esEs12(Char(zxw4000), Char(zxw3000)) → new_primEqNat0(zxw4000, zxw3000)
new_ltEs20(zxw7900, zxw8000, app(app(app(ty_@3, bab), bac), bad)) → new_ltEs6(zxw7900, zxw8000, bab, bac, bad)
new_not(False) → True
new_lt20(zxw79001, zxw80001, ty_Char) → new_lt9(zxw79001, zxw80001)
new_esEs11(zxw400, zxw300) → new_primEqInt(zxw400, zxw300)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(ty_Maybe, cha)) → new_ltEs18(zxw79000, zxw80000, cha)
new_ltEs18(Just(zxw79000), Nothing, baa) → False
new_esEs7(Left(zxw4000), Left(zxw3000), app(ty_Maybe, beh), bef) → new_esEs6(zxw4000, zxw3000, beh)
new_esEs8(zxw79000, zxw80000, app(ty_Maybe, de)) → new_esEs6(zxw79000, zxw80000, de)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Double, bef) → new_esEs16(zxw4000, zxw3000)
new_compare210(zxw79000, zxw80000, True, bcf, bcg) → EQ
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_esEs19(zxw79001, zxw80001, ty_Int) → new_esEs11(zxw79001, zxw80001)
new_compare12(zxw79000, zxw80000, False, gd, ge, gf) → GT
new_ltEs16(zxw7900, zxw8000) → new_fsEs(new_compare7(zxw7900, zxw8000))
new_esEs32(zxw20, zxw15, ty_Char) → new_esEs12(zxw20, zxw15)
new_esEs9(GT, GT) → True
new_esEs26(zxw4002, zxw3002, app(ty_Ratio, dfc)) → new_esEs18(zxw4002, zxw3002, dfc)
new_esEs25(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_lt20(zxw79001, zxw80001, app(ty_[], caa)) → new_lt10(zxw79001, zxw80001, caa)
new_lt4(zxw79000, zxw80000, app(app(ty_Either, db), dc)) → new_lt14(zxw79000, zxw80000, db, dc)
new_esEs26(zxw4002, zxw3002, ty_Bool) → new_esEs14(zxw4002, zxw3002)
new_compare19(zxw79000, zxw80000, bcf, bcg) → new_compare210(zxw79000, zxw80000, new_esEs5(zxw79000, zxw80000, bcf, bcg), bcf, bcg)
new_esEs8(zxw79000, zxw80000, ty_Bool) → new_esEs14(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Double) → new_ltEs15(zxw79000, zxw80000)
new_esEs28(zxw4000, zxw3000, app(app(ty_@2, eab), eac)) → new_esEs5(zxw4000, zxw3000, eab, eac)
new_esEs34(zxw400, zxw300, ty_Int) → new_esEs11(zxw400, zxw300)
new_ltEs19(zxw7900, zxw8000, app(app(app(ty_@3, hb), hc), hd)) → new_ltEs6(zxw7900, zxw8000, hb, hc, hd)
new_esEs32(zxw20, zxw15, app(app(app(ty_@3, cec), ced), cee)) → new_esEs4(zxw20, zxw15, cec, ced, cee)
new_lt4(zxw79000, zxw80000, ty_Char) → new_lt9(zxw79000, zxw80000)
new_esEs22(zxw4000, zxw3000, app(app(app(ty_@3, dcg), dch), dda)) → new_esEs4(zxw4000, zxw3000, dcg, dch, dda)
new_esEs22(zxw4000, zxw3000, app(ty_[], dca)) → new_esEs13(zxw4000, zxw3000, dca)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_@0) → new_ltEs8(zxw79000, zxw80000)
new_esEs23(zxw4000, zxw3000, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Float, bef) → new_esEs17(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_esEs27(zxw4001, zxw3001, ty_Int) → new_esEs11(zxw4001, zxw3001)
new_esEs19(zxw79001, zxw80001, app(app(app(ty_@3, bhf), bhg), bhh)) → new_esEs4(zxw79001, zxw80001, bhf, bhg, bhh)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_ltEs14(Left(zxw79000), Left(zxw80000), app(app(app(ty_@3, cef), ceg), ceh), hg) → new_ltEs6(zxw79000, zxw80000, cef, ceg, ceh)
new_ltEs19(zxw7900, zxw8000, ty_Int) → new_ltEs9(zxw7900, zxw8000)
new_compare33(zxw20, zxw15, bc, bd) → new_compare26(Left(zxw20), Left(zxw15), new_esEs32(zxw20, zxw15, bc), bc, bd)
new_lt4(zxw79000, zxw80000, ty_@0) → new_lt7(zxw79000, zxw80000)
new_lt20(zxw79001, zxw80001, ty_Double) → new_lt15(zxw79001, zxw80001)
new_lt19(zxw79000, zxw80000, ty_Float) → new_lt16(zxw79000, zxw80000)
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_esEs26(zxw4002, zxw3002, ty_@0) → new_esEs10(zxw4002, zxw3002)
new_lt19(zxw79000, zxw80000, ty_Bool) → new_lt12(zxw79000, zxw80000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Char, bef) → new_esEs12(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_lt4(zxw79000, zxw80000, ty_Float) → new_lt16(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(ty_[], che)) → new_ltEs11(zxw79000, zxw80000, che)
new_primMulInt(Neg(zxw40000), Neg(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_ltEs5(zxw79001, zxw80001, app(app(app(ty_@3, df), dg), dh)) → new_ltEs6(zxw79001, zxw80001, df, dg, dh)
new_primCmpNat2(Zero, Zero) → EQ
new_esEs20(zxw79000, zxw80000, ty_Integer) → new_esEs15(zxw79000, zxw80000)
new_primEqNat0(Zero, Succ(zxw30000)) → False
new_primEqNat0(Succ(zxw40000), Zero) → False
new_esEs21(zxw4001, zxw3001, ty_@0) → new_esEs10(zxw4001, zxw3001)
new_esEs22(zxw4000, zxw3000, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_esEs20(zxw79000, zxw80000, ty_Bool) → new_esEs14(zxw79000, zxw80000)
new_ltEs5(zxw79001, zxw80001, app(ty_[], ea)) → new_ltEs11(zxw79001, zxw80001, ea)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs23(zxw4000, zxw3000, app(ty_Ratio, ddc)) → new_esEs18(zxw4000, zxw3000, ddc)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(app(ty_@2, chf), chg)) → new_ltEs4(zxw79000, zxw80000, chf, chg)
new_esEs33(zxw400, zxw300, app(ty_Maybe, eh)) → new_esEs6(zxw400, zxw300, eh)
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_esEs34(zxw400, zxw300, ty_Bool) → new_esEs14(zxw400, zxw300)
new_ltEs5(zxw79001, zxw80001, ty_Int) → new_ltEs9(zxw79001, zxw80001)
new_esEs27(zxw4001, zxw3001, app(app(ty_@2, dgh), dha)) → new_esEs5(zxw4001, zxw3001, dgh, dha)
new_primCmpNat0(zxw7900, Zero) → GT
new_compare26(Right(zxw7900), Left(zxw8000), False, gh, ha) → GT
new_esEs33(zxw400, zxw300, ty_Double) → new_esEs16(zxw400, zxw300)
new_esEs23(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_@0, hg) → new_ltEs8(zxw79000, zxw80000)
new_ltEs21(zxw79002, zxw80002, app(ty_Maybe, cca)) → new_ltEs18(zxw79002, zxw80002, cca)
new_esEs21(zxw4001, zxw3001, app(app(ty_Either, dbc), dbd)) → new_esEs7(zxw4001, zxw3001, dbc, dbd)
new_esEs22(zxw4000, zxw3000, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Bool) → new_ltEs12(zxw79000, zxw80000)
new_compare29(zxw79000, zxw80000, app(ty_Maybe, cdc)) → new_compare27(zxw79000, zxw80000, cdc)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_ltEs14(Left(zxw79000), Left(zxw80000), app(ty_Maybe, cfg), hg) → new_ltEs18(zxw79000, zxw80000, cfg)
new_lt20(zxw79001, zxw80001, ty_Float) → new_lt16(zxw79001, zxw80001)
new_lt17(zxw79000, zxw80000, gg) → new_esEs9(new_compare8(zxw79000, zxw80000, gg), LT)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Ordering) → new_ltEs7(zxw79000, zxw80000)
new_esEs32(zxw20, zxw15, ty_Int) → new_esEs11(zxw20, zxw15)
new_compare30(@0, @0) → EQ
new_lt19(zxw79000, zxw80000, app(ty_[], bhc)) → new_lt10(zxw79000, zxw80000, bhc)
new_esEs21(zxw4001, zxw3001, app(app(app(ty_@3, dbe), dbf), dbg)) → new_esEs4(zxw4001, zxw3001, dbe, dbf, dbg)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_esEs20(zxw79000, zxw80000, app(ty_Ratio, gg)) → new_esEs18(zxw79000, zxw80000, gg)
new_esEs6(Just(zxw4000), Just(zxw3000), app(app(app(ty_@3, ga), gb), gc)) → new_esEs4(zxw4000, zxw3000, ga, gb, gc)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(app(ty_Either, chh), daa)) → new_ltEs14(zxw79000, zxw80000, chh, daa)
new_esEs24(zxw4001, zxw3001, ty_Int) → new_esEs11(zxw4001, zxw3001)
new_esEs8(zxw79000, zxw80000, ty_Ordering) → new_esEs9(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Ordering) → new_ltEs7(zxw79000, zxw80000)
new_esEs34(zxw400, zxw300, ty_Integer) → new_esEs15(zxw400, zxw300)
new_esEs20(zxw79000, zxw80000, app(app(ty_Either, bhd), bhe)) → new_esEs7(zxw79000, zxw80000, bhd, bhe)
new_compare29(zxw79000, zxw80000, app(ty_Ratio, cdb)) → new_compare8(zxw79000, zxw80000, cdb)
new_lt4(zxw79000, zxw80000, app(app(ty_@2, cg), da)) → new_lt11(zxw79000, zxw80000, cg, da)
new_compare29(zxw79000, zxw80000, ty_Float) → new_compare7(zxw79000, zxw80000)
new_esEs19(zxw79001, zxw80001, app(app(ty_@2, cab), cac)) → new_esEs5(zxw79001, zxw80001, cab, cac)
new_esEs10(@0, @0) → True
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_compare29(zxw79000, zxw80000, ty_Double) → new_compare6(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, app(ty_Maybe, bdb)) → new_esEs6(zxw79000, zxw80000, bdb)
new_ltEs14(Left(zxw79000), Right(zxw80000), hf, hg) → True
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Float) → new_ltEs16(zxw79000, zxw80000)
new_esEs28(zxw4000, zxw3000, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_compare29(zxw79000, zxw80000, app(app(ty_Either, cch), cda)) → new_compare15(zxw79000, zxw80000, cch, cda)
new_esEs19(zxw79001, zxw80001, ty_Double) → new_esEs16(zxw79001, zxw80001)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_ltEs20(zxw7900, zxw8000, app(app(ty_Either, bah), bba)) → new_ltEs14(zxw7900, zxw8000, bah, bba)
new_asAs(False, zxw230) → False
new_ltEs13(zxw7900, zxw8000) → new_fsEs(new_compare32(zxw7900, zxw8000))
new_ltEs19(zxw7900, zxw8000, app(app(ty_Either, hf), hg)) → new_ltEs14(zxw7900, zxw8000, hf, hg)
new_compare34(zxw400, zxw300, h, ba) → new_compare26(Left(zxw400), Right(zxw300), False, h, ba)
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Pos(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_ltEs20(zxw7900, zxw8000, app(ty_[], bae)) → new_ltEs11(zxw7900, zxw8000, bae)
new_compare16(zxw79, zxw80) → new_primCmpInt(zxw79, zxw80)
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_esEs13(:(zxw4000, zxw4001), [], ddb) → False
new_esEs13([], :(zxw3000, zxw3001), ddb) → False
new_compare25(zxw79000, zxw80000, False, gd, ge, gf) → new_compare12(zxw79000, zxw80000, new_ltEs6(zxw79000, zxw80000, gd, ge, gf), gd, ge, gf)
new_esEs34(zxw400, zxw300, ty_@0) → new_esEs10(zxw400, zxw300)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(app(ty_@2, cfb), cfc), hg) → new_ltEs4(zxw79000, zxw80000, cfb, cfc)
new_esEs6(Just(zxw4000), Just(zxw3000), app(ty_Maybe, fc)) → new_esEs6(zxw4000, zxw3000, fc)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_@0) → new_esEs10(zxw4000, zxw3000)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(ty_[], cfa), hg) → new_ltEs11(zxw79000, zxw80000, cfa)
new_esEs7(Left(zxw4000), Left(zxw3000), app(ty_[], beg), bef) → new_esEs13(zxw4000, zxw3000, beg)
new_esEs31(zxw35, zxw30, ty_Double) → new_esEs16(zxw35, zxw30)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_compare31(zxw79000, zxw80000) → new_compare23(zxw79000, zxw80000, new_esEs14(zxw79000, zxw80000))
new_ltEs18(Nothing, Just(zxw80000), baa) → True
new_esEs28(zxw4000, zxw3000, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_ltEs21(zxw79002, zxw80002, ty_Double) → new_ltEs15(zxw79002, zxw80002)
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_ltEs12(True, True) → True
new_esEs23(zxw4000, zxw3000, app(ty_Maybe, dde)) → new_esEs6(zxw4000, zxw3000, dde)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_esEs8(zxw79000, zxw80000, ty_Integer) → new_esEs15(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(app(ty_Either, cgf), cgg)) → new_ltEs14(zxw79000, zxw80000, cgf, cgg)
new_ltEs6(@3(zxw79000, zxw79001, zxw79002), @3(zxw80000, zxw80001, zxw80002), hb, hc, hd) → new_pePe(new_lt19(zxw79000, zxw80000, hb), new_asAs(new_esEs20(zxw79000, zxw80000, hb), new_pePe(new_lt20(zxw79001, zxw80001, hc), new_asAs(new_esEs19(zxw79001, zxw80001, hc), new_ltEs21(zxw79002, zxw80002, hd)))))
new_esEs28(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_lt16(zxw79000, zxw80000) → new_esEs9(new_compare7(zxw79000, zxw80000), LT)
new_esEs23(zxw4000, zxw3000, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Integer, hg) → new_ltEs13(zxw79000, zxw80000)
new_esEs34(zxw400, zxw300, app(ty_Ratio, bbd)) → new_esEs18(zxw400, zxw300, bbd)
new_ltEs12(False, True) → True
new_esEs23(zxw4000, zxw3000, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs8(zxw79000, zxw80000, app(ty_Ratio, dd)) → new_esEs18(zxw79000, zxw80000, dd)
new_esEs23(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs14(True, True) → True
new_compare111(zxw79000, zxw80000, False, bdb) → GT
new_esEs31(zxw35, zxw30, app(ty_[], bdd)) → new_esEs13(zxw35, zxw30, bdd)
new_esEs27(zxw4001, zxw3001, ty_Bool) → new_esEs14(zxw4001, zxw3001)
new_esEs20(zxw79000, zxw80000, ty_Ordering) → new_esEs9(zxw79000, zxw80000)
new_ltEs19(zxw7900, zxw8000, ty_@0) → new_ltEs8(zxw7900, zxw8000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Int) → new_ltEs9(zxw79000, zxw80000)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(app(ty_Either, cfd), cfe), hg) → new_ltEs14(zxw79000, zxw80000, cfd, cfe)
new_lt19(zxw79000, zxw80000, ty_Integer) → new_lt13(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, ty_Float) → new_esEs17(zxw79000, zxw80000)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs34(zxw400, zxw300, app(ty_Maybe, bbf)) → new_esEs6(zxw400, zxw300, bbf)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Ordering, hg) → new_ltEs7(zxw79000, zxw80000)
new_compare11(zxw79000, zxw80000, False) → GT
new_esEs4(@3(zxw4000, zxw4001, zxw4002), @3(zxw3000, zxw3001, zxw3002), deh, dfa, dfb) → new_asAs(new_esEs28(zxw4000, zxw3000, deh), new_asAs(new_esEs27(zxw4001, zxw3001, dfa), new_esEs26(zxw4002, zxw3002, dfb)))
new_esEs6(Just(zxw4000), Just(zxw3000), app(ty_[], fb)) → new_esEs13(zxw4000, zxw3000, fb)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Int) → new_ltEs9(zxw79000, zxw80000)
new_esEs9(EQ, LT) → False
new_esEs9(LT, EQ) → False
new_compare26(Right(zxw7900), Right(zxw8000), False, gh, ha) → new_compare14(zxw7900, zxw8000, new_ltEs20(zxw7900, zxw8000, ha), gh, ha)
new_compare11(zxw79000, zxw80000, True) → LT
new_ltEs5(zxw79001, zxw80001, ty_@0) → new_ltEs8(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, ty_Bool) → new_lt12(zxw79001, zxw80001)
new_compare14(zxw242, zxw243, True, def, deg) → LT
new_esEs32(zxw20, zxw15, app(ty_Ratio, cdd)) → new_esEs18(zxw20, zxw15, cdd)
new_esEs14(False, False) → True
new_esEs18(:%(zxw4000, zxw4001), :%(zxw3000, zxw3001), dee) → new_asAs(new_esEs25(zxw4000, zxw3000, dee), new_esEs24(zxw4001, zxw3001, dee))
new_compare26(Left(zxw7900), Left(zxw8000), False, gh, ha) → new_compare13(zxw7900, zxw8000, new_ltEs19(zxw7900, zxw8000, gh), gh, ha)
new_esEs33(zxw400, zxw300, ty_Float) → new_esEs17(zxw400, zxw300)
new_ltEs19(zxw7900, zxw8000, ty_Double) → new_ltEs15(zxw7900, zxw8000)
new_ltEs7(EQ, LT) → False
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Char) → new_esEs12(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_ltEs7(LT, LT) → True
new_lt20(zxw79001, zxw80001, app(app(app(ty_@3, bhf), bhg), bhh)) → new_lt5(zxw79001, zxw80001, bhf, bhg, bhh)
new_lt14(zxw790, zxw800, gh, ha) → new_esEs9(new_compare15(zxw790, zxw800, gh, ha), LT)
new_esEs22(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_ltEs9(zxw7900, zxw8000) → new_fsEs(new_compare16(zxw7900, zxw8000))
new_compare29(zxw79000, zxw80000, ty_Ordering) → new_compare18(zxw79000, zxw80000)
new_primPlusNat1(Zero, Zero) → Zero
new_esEs26(zxw4002, zxw3002, ty_Ordering) → new_esEs9(zxw4002, zxw3002)
new_esEs19(zxw79001, zxw80001, ty_Integer) → new_esEs15(zxw79001, zxw80001)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Char, hg) → new_ltEs10(zxw79000, zxw80000)
new_asAs(True, zxw230) → zxw230
new_esEs25(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_ltEs7(LT, GT) → True
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Float) → new_esEs17(zxw4000, zxw3000)
new_ltEs5(zxw79001, zxw80001, ty_Float) → new_ltEs16(zxw79001, zxw80001)
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, app(ty_Ratio, bga)) → new_esEs18(zxw4000, zxw3000, bga)
new_esEs27(zxw4001, zxw3001, app(ty_[], dgf)) → new_esEs13(zxw4001, zxw3001, dgf)
new_esEs6(Just(zxw4000), Just(zxw3000), app(app(ty_Either, fg), fh)) → new_esEs7(zxw4000, zxw3000, fg, fh)
new_esEs32(zxw20, zxw15, ty_Double) → new_esEs16(zxw20, zxw15)
new_compare28(zxw79000, zxw80000, False, bdb) → new_compare111(zxw79000, zxw80000, new_ltEs18(zxw79000, zxw80000, bdb), bdb)
new_compare1(:(zxw79000, zxw79001), [], he) → GT
new_esEs28(zxw4000, zxw3000, app(ty_Ratio, dhg)) → new_esEs18(zxw4000, zxw3000, dhg)
new_lt4(zxw79000, zxw80000, ty_Integer) → new_lt13(zxw79000, zxw80000)
new_esEs19(zxw79001, zxw80001, ty_@0) → new_esEs10(zxw79001, zxw80001)
new_compare29(zxw79000, zxw80000, ty_@0) → new_compare30(zxw79000, zxw80000)
new_ltEs19(zxw7900, zxw8000, ty_Integer) → new_ltEs13(zxw7900, zxw8000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(ty_Ratio, cgh)) → new_ltEs17(zxw79000, zxw80000, cgh)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Integer) → new_ltEs13(zxw79000, zxw80000)
new_ltEs19(zxw7900, zxw8000, ty_Ordering) → new_ltEs7(zxw7900, zxw8000)
new_compare28(zxw79000, zxw80000, True, bdb) → EQ
new_esEs31(zxw35, zxw30, ty_Int) → new_esEs11(zxw35, zxw30)
new_esEs26(zxw4002, zxw3002, ty_Double) → new_esEs16(zxw4002, zxw3002)
new_esEs33(zxw400, zxw300, ty_Int) → new_esEs11(zxw400, zxw300)
new_compare10(zxw79000, zxw80000, True) → LT
new_esEs31(zxw35, zxw30, ty_Bool) → new_esEs14(zxw35, zxw30)
new_esEs19(zxw79001, zxw80001, app(ty_[], caa)) → new_esEs13(zxw79001, zxw80001, caa)
new_compare10(zxw79000, zxw80000, False) → GT
new_esEs9(LT, LT) → True
new_ltEs20(zxw7900, zxw8000, ty_Char) → new_ltEs10(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, ty_Ordering) → new_ltEs7(zxw7900, zxw8000)
new_primCompAux00(zxw276, GT) → GT
new_esEs31(zxw35, zxw30, app(ty_Maybe, bde)) → new_esEs6(zxw35, zxw30, bde)
new_compare18(zxw79000, zxw80000) → new_compare24(zxw79000, zxw80000, new_esEs9(zxw79000, zxw80000))
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_@0) → new_ltEs8(zxw79000, zxw80000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_lt19(zxw79000, zxw80000, ty_Char) → new_lt9(zxw79000, zxw80000)
new_esEs28(zxw4000, zxw3000, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_ltEs19(zxw7900, zxw8000, app(ty_Maybe, baa)) → new_ltEs18(zxw7900, zxw8000, baa)
new_esEs27(zxw4001, zxw3001, ty_Integer) → new_esEs15(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, app(ty_Ratio, daf)) → new_esEs18(zxw4001, zxw3001, daf)
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_esEs19(zxw79001, zxw80001, ty_Char) → new_esEs12(zxw79001, zxw80001)
new_esEs23(zxw4000, zxw3000, app(ty_[], ddd)) → new_esEs13(zxw4000, zxw3000, ddd)
new_ltEs17(zxw7900, zxw8000, hh) → new_fsEs(new_compare8(zxw7900, zxw8000, hh))
new_not(True) → False
new_ltEs4(@2(zxw79000, zxw79001), @2(zxw80000, zxw80001), ca, cb) → new_pePe(new_lt4(zxw79000, zxw80000, ca), new_asAs(new_esEs8(zxw79000, zxw80000, ca), new_ltEs5(zxw79001, zxw80001, cb)))
new_compare1([], [], he) → EQ
new_esEs6(Just(zxw4000), Just(zxw3000), app(ty_Ratio, fa)) → new_esEs18(zxw4000, zxw3000, fa)

The set Q consists of the following terms:

new_compare23(x0, x1, True)
new_lt6(x0, x1)
new_ltEs5(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, ty_Integer)
new_esEs33(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt4(x0, x1, app(ty_[], x2))
new_ltEs18(Just(x0), Just(x1), ty_@0)
new_compare16(x0, x1)
new_lt4(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(Just(x0), Nothing, x1)
new_ltEs20(x0, x1, ty_Double)
new_esEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs19(x0, x1, ty_Bool)
new_esEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs8(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(x0, x1, app(app(ty_Either, x2), x3))
new_compare30(@0, @0)
new_esEs32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCompAux00(x0, GT)
new_lt19(x0, x1, ty_Char)
new_esEs27(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_Ordering)
new_compare17(Char(x0), Char(x1))
new_esEs28(x0, x1, ty_Int)
new_ltEs20(x0, x1, app(ty_[], x2))
new_ltEs21(x0, x1, ty_Ordering)
new_compare111(x0, x1, True, x2)
new_ltEs15(x0, x1)
new_primPlusNat1(Zero, Succ(x0))
new_esEs6(Just(x0), Just(x1), ty_Double)
new_compare24(x0, x1, False)
new_compare210(x0, x1, False, x2, x3)
new_lt20(x0, x1, ty_Char)
new_esEs33(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, ty_Bool)
new_sr0(Integer(x0), Integer(x1))
new_esEs32(x0, x1, app(ty_[], x2))
new_esEs33(x0, x1, ty_Float)
new_compare28(x0, x1, True, x2)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(Nothing, Nothing, x0)
new_ltEs18(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs34(x0, x1, ty_Integer)
new_esEs34(x0, x1, app(ty_Maybe, x2))
new_ltEs7(EQ, EQ)
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs19(x0, x1, ty_Integer)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_ltEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Bool)
new_ltEs14(Right(x0), Right(x1), x2, ty_Float)
new_compare27(x0, x1, x2)
new_esEs31(x0, x1, app(ty_Ratio, x2))
new_esEs6(Just(x0), Just(x1), app(ty_[], x2))
new_compare14(x0, x1, True, x2, x3)
new_ltEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs13([], :(x0, x1), x2)
new_compare25(x0, x1, False, x2, x3, x4)
new_esEs7(Left(x0), Left(x1), ty_Integer, x2)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs7(Right(x0), Right(x1), x2, ty_@0)
new_esEs31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Integer)
new_ltEs5(x0, x1, ty_Integer)
new_ltEs21(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs7(EQ, LT)
new_ltEs7(LT, EQ)
new_esEs20(x0, x1, ty_Ordering)
new_esEs17(Float(x0, x1), Float(x2, x3))
new_compare25(x0, x1, True, x2, x3, x4)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_lt19(x0, x1, ty_Ordering)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs16(x0, x1)
new_lt4(x0, x1, app(ty_Maybe, x2))
new_esEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs14(Left(x0), Left(x1), ty_Char, x2)
new_sr(x0, x1)
new_ltEs19(x0, x1, ty_Double)
new_compare7(Float(x0, x1), Float(x2, x3))
new_ltEs9(x0, x1)
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_compare19(x0, x1, x2, x3)
new_lt7(x0, x1)
new_lt4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, ty_Int)
new_esEs26(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat0(Zero, x0)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs32(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_ltEs7(LT, LT)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs27(x0, x1, ty_Bool)
new_lt5(x0, x1, x2, x3, x4)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare29(x0, x1, app(app(ty_@2, x2), x3))
new_lt4(x0, x1, ty_Ordering)
new_esEs34(x0, x1, app(ty_Ratio, x2))
new_primEqNat0(Zero, Succ(x0))
new_lt19(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Int)
new_esEs15(Integer(x0), Integer(x1))
new_esEs26(x0, x1, ty_Double)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs28(x0, x1, ty_@0)
new_primPlusNat1(Succ(x0), Zero)
new_esEs22(x0, x1, ty_Integer)
new_ltEs14(Left(x0), Left(x1), ty_@0, x2)
new_primMulInt(Neg(x0), Neg(x1))
new_ltEs19(x0, x1, ty_Int)
new_esEs7(Left(x0), Left(x1), ty_Double, x2)
new_compare29(x0, x1, ty_Integer)
new_esEs14(True, True)
new_esEs21(x0, x1, ty_Char)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(Just(x0), Just(x1), ty_Integer)
new_compare29(x0, x1, app(ty_[], x2))
new_ltEs18(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, ty_Int)
new_esEs7(Right(x0), Right(x1), x2, ty_Int)
new_primEqNat0(Zero, Zero)
new_esEs16(Double(x0, x1), Double(x2, x3))
new_esEs12(Char(x0), Char(x1))
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_lt4(x0, x1, ty_Char)
new_esEs20(x0, x1, ty_Bool)
new_esEs8(x0, x1, ty_Float)
new_compare1([], :(x0, x1), x2)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_Integer)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs32(x0, x1, ty_@0)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(Left(x0), Left(x1), ty_Int, x2)
new_primCompAux00(x0, LT)
new_esEs27(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(ty_[], x2))
new_ltEs5(x0, x1, ty_Double)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs18(Just(x0), Just(x1), ty_Char)
new_primMulNat0(Zero, Zero)
new_lt9(x0, x1)
new_compare29(x0, x1, ty_Double)
new_esEs34(x0, x1, app(ty_[], x2))
new_ltEs5(x0, x1, ty_@0)
new_lt17(x0, x1, x2)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_ltEs21(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs31(x0, x1, ty_Bool)
new_ltEs14(Left(x0), Left(x1), ty_Float, x2)
new_esEs32(x0, x1, ty_Float)
new_esEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs8(x0, x1, ty_Ordering)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_compare10(x0, x1, True)
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Ordering)
new_primEqNat0(Succ(x0), Succ(x1))
new_ltEs19(x0, x1, ty_Bool)
new_esEs28(x0, x1, ty_Double)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_@0)
new_pePe(True, x0)
new_esEs19(x0, x1, ty_Float)
new_lt19(x0, x1, app(ty_[], x2))
new_esEs8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_lt16(x0, x1)
new_compare29(x0, x1, ty_Bool)
new_lt10(x0, x1, x2)
new_esEs7(Right(x0), Right(x1), x2, ty_Integer)
new_esEs32(x0, x1, app(app(ty_Either, x2), x3))
new_compare11(x0, x1, True)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs32(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs33(x0, x1, app(ty_[], x2))
new_esEs34(x0, x1, ty_Char)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1, ty_@0)
new_esEs6(Just(x0), Just(x1), ty_Ordering)
new_esEs23(x0, x1, ty_@0)
new_ltEs14(Right(x0), Right(x1), x2, ty_Int)
new_ltEs5(x0, x1, ty_Char)
new_ltEs21(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Float)
new_lt18(x0, x1, x2)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_compare29(x0, x1, ty_Ordering)
new_ltEs21(x0, x1, ty_@0)
new_esEs8(x0, x1, ty_Int)
new_lt14(x0, x1, x2, x3)
new_ltEs12(False, False)
new_compare210(x0, x1, True, x2, x3)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Just(x0), Just(x1), ty_Bool)
new_compare32(Integer(x0), Integer(x1))
new_lt19(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_Int)
new_primMulNat0(Succ(x0), Succ(x1))
new_compare29(x0, x1, ty_Float)
new_ltEs21(x0, x1, ty_Integer)
new_esEs6(Just(x0), Just(x1), ty_Float)
new_ltEs5(x0, x1, ty_Float)
new_ltEs18(Just(x0), Just(x1), ty_Float)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_Bool)
new_esEs31(x0, x1, ty_Double)
new_primCmpNat1(Zero, x0)
new_ltEs14(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs8(x0, x1)
new_ltEs18(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs14(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs33(x0, x1, app(ty_Ratio, x2))
new_compare13(x0, x1, False, x2, x3)
new_esEs34(x0, x1, ty_Float)
new_primPlusNat1(Zero, Zero)
new_esEs23(x0, x1, ty_Double)
new_ltEs18(Just(x0), Just(x1), ty_Ordering)
new_primCmpNat2(Zero, Zero)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(x0, x1, ty_Bool)
new_esEs34(x0, x1, ty_Ordering)
new_ltEs18(Just(x0), Just(x1), app(ty_[], x2))
new_esEs33(x0, x1, app(ty_Maybe, x2))
new_ltEs5(x0, x1, app(ty_[], x2))
new_asAs(False, x0)
new_ltEs20(x0, x1, ty_Char)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs31(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs8(x0, x1, ty_Integer)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs33(x0, x1, ty_Ordering)
new_ltEs18(Just(x0), Just(x1), ty_Bool)
new_compare14(x0, x1, False, x2, x3)
new_primCmpNat1(Succ(x0), x1)
new_esEs34(x0, x1, ty_Bool)
new_esEs33(x0, x1, ty_Double)
new_esEs24(x0, x1, ty_Integer)
new_esEs27(x0, x1, ty_@0)
new_esEs7(Left(x0), Left(x1), ty_Int, x2)
new_ltEs14(Right(x0), Right(x1), x2, ty_Double)
new_lt4(x0, x1, ty_Float)
new_ltEs5(x0, x1, app(app(ty_Either, x2), x3))
new_esEs19(x0, x1, ty_Char)
new_lt4(x0, x1, ty_Double)
new_esEs19(x0, x1, ty_Ordering)
new_esEs8(x0, x1, app(ty_Ratio, x2))
new_esEs33(x0, x1, ty_Int)
new_esEs10(@0, @0)
new_esEs31(x0, x1, ty_@0)
new_esEs33(x0, x1, ty_@0)
new_esEs11(x0, x1)
new_esEs20(x0, x1, ty_Float)
new_ltEs14(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs7(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs14(Right(x0), Right(x1), x2, ty_Char)
new_esEs9(GT, GT)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs27(x0, x1, ty_Char)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_compare11(x0, x1, False)
new_compare23(x0, x1, False)
new_compare12(x0, x1, True, x2, x3, x4)
new_esEs7(Right(x0), Right(x1), x2, ty_Double)
new_esEs28(x0, x1, ty_Bool)
new_esEs33(x0, x1, app(app(ty_Either, x2), x3))
new_compare24(x0, x1, True)
new_compare36(x0, x1, x2, x3)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_compare15(x0, x1, x2, x3)
new_primEqNat0(Succ(x0), Zero)
new_esEs13([], [], x0)
new_esEs23(x0, x1, ty_Ordering)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs7(Left(x0), Right(x1), x2, x3)
new_esEs7(Right(x0), Left(x1), x2, x3)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_esEs34(x0, x1, ty_Int)
new_compare9(x0, x1, x2, x3, x4)
new_lt20(x0, x1, ty_Int)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs21(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Integer)
new_esEs33(x0, x1, ty_Bool)
new_lt4(x0, x1, app(app(ty_Either, x2), x3))
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs23(x0, x1, ty_Int)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs5(x0, x1, app(app(ty_@2, x2), x3))
new_esEs33(x0, x1, ty_Char)
new_lt4(x0, x1, ty_@0)
new_esEs23(x0, x1, ty_Char)
new_esEs28(x0, x1, ty_Ordering)
new_ltEs18(Just(x0), Just(x1), ty_Double)
new_ltEs20(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_lt20(x0, x1, ty_@0)
new_compare1([], [], x0)
new_esEs9(EQ, EQ)
new_pePe(False, x0)
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs5(x0, x1, app(ty_Ratio, x2))
new_ltEs14(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs6(Just(x0), Just(x1), ty_Char)
new_esEs25(x0, x1, ty_Integer)
new_esEs31(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_Integer)
new_compare12(x0, x1, False, x2, x3, x4)
new_esEs8(x0, x1, app(ty_Maybe, x2))
new_primCompAux00(x0, EQ)
new_esEs19(x0, x1, ty_Int)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs14(True, False)
new_esEs14(False, True)
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_lt4(x0, x1, ty_Integer)
new_esEs7(Left(x0), Left(x1), ty_@0, x2)
new_ltEs14(Right(x0), Right(x1), x2, ty_@0)
new_fsEs(x0)
new_esEs22(x0, x1, ty_Float)
new_ltEs14(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs32(x0, x1, app(ty_Ratio, x2))
new_esEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_primCmpNat2(Succ(x0), Succ(x1))
new_compare110(x0, x1, False, x2, x3)
new_lt4(x0, x1, ty_Bool)
new_asAs(True, x0)
new_esEs21(x0, x1, ty_Bool)
new_esEs4(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs6(Nothing, Just(x0), x1)
new_esEs6(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs21(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Just(x0), Nothing, x1)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_compare29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs8(x0, x1, app(ty_[], x2))
new_esEs31(x0, x1, ty_Integer)
new_esEs13(:(x0, x1), [], x2)
new_ltEs14(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs8(x0, x1, ty_Char)
new_lt19(x0, x1, ty_Float)
new_compare33(x0, x1, x2, x3)
new_ltEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs22(x0, x1, ty_@0)
new_esEs34(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_Char)
new_ltEs12(False, True)
new_ltEs12(True, False)
new_compare6(Double(x0, x1), Double(x2, x3))
new_ltEs20(x0, x1, ty_@0)
new_esEs22(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_@0)
new_compare35(x0, x1, x2, x3)
new_ltEs14(Right(x0), Right(x1), x2, ty_Integer)
new_lt19(x0, x1, ty_Double)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1, ty_Bool)
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs7(Left(x0), Left(x1), ty_Char, x2)
new_esEs7(Right(x0), Right(x1), x2, ty_Float)
new_ltEs14(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs26(x0, x1, ty_Char)
new_ltEs5(x0, x1, ty_Int)
new_lt4(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_Double)
new_esEs19(x0, x1, ty_@0)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_compare13(x0, x1, True, x2, x3)
new_esEs34(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs21(x0, x1, ty_Bool)
new_ltEs14(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs21(x0, x1, ty_Double)
new_lt12(x0, x1)
new_esEs8(x0, x1, ty_Bool)
new_ltEs21(x0, x1, ty_Char)
new_lt13(x0, x1)
new_esEs31(x0, x1, ty_Ordering)
new_ltEs14(Right(x0), Right(x1), x2, ty_Bool)
new_compare1(:(x0, x1), [], x2)
new_compare10(x0, x1, False)
new_primMulNat0(Succ(x0), Zero)
new_ltEs19(x0, x1, ty_Float)
new_ltEs14(Left(x0), Right(x1), x2, x3)
new_esEs23(x0, x1, ty_Float)
new_ltEs14(Right(x0), Left(x1), x2, x3)
new_compare29(x0, x1, ty_Int)
new_esEs20(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, ty_Int)
new_esEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs20(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Float)
new_compare31(x0, x1)
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs31(x0, x1, ty_Char)
new_esEs6(Just(x0), Just(x1), ty_Int)
new_ltEs7(LT, GT)
new_ltEs7(GT, LT)
new_esEs21(x0, x1, ty_Integer)
new_esEs22(x0, x1, app(ty_[], x2))
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs22(x0, x1, ty_Double)
new_compare110(x0, x1, True, x2, x3)
new_lt20(x0, x1, app(ty_[], x2))
new_ltEs13(x0, x1)
new_ltEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs34(x0, x1, ty_@0)
new_esEs31(x0, x1, ty_Int)
new_lt4(x0, x1, ty_Int)
new_ltEs11(x0, x1, x2)
new_lt20(x0, x1, ty_Float)
new_not(True)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs31(x0, x1, ty_Float)
new_esEs20(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Float)
new_esEs19(x0, x1, app(ty_[], x2))
new_esEs18(:%(x0, x1), :%(x2, x3), x4)
new_esEs6(Nothing, Nothing, x0)
new_esEs28(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Ordering)
new_ltEs14(Left(x0), Left(x1), ty_Double, x2)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Just(x0), Just(x1), ty_Integer)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_not(False)
new_compare29(x0, x1, app(ty_Ratio, x2))
new_lt8(x0, x1)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_compare28(x0, x1, False, x2)
new_esEs32(x0, x1, ty_Integer)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, ty_Char)
new_esEs6(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare8(:%(x0, x1), :%(x2, x3), ty_Integer)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs22(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_Integer)
new_esEs8(x0, x1, ty_@0)
new_compare26(Left(x0), Left(x1), False, x2, x3)
new_esEs32(x0, x1, app(ty_Maybe, x2))
new_ltEs12(True, True)
new_esEs27(x0, x1, ty_Float)
new_lt15(x0, x1)
new_lt11(x0, x1, x2, x3)
new_esEs26(x0, x1, ty_Ordering)
new_esEs7(Left(x0), Left(x1), ty_Float, x2)
new_esEs27(x0, x1, ty_Double)
new_esEs6(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs34(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs33(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Ordering)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs13(:(x0, x1), :(x2, x3), x4)
new_esEs22(x0, x1, ty_Char)
new_lt20(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Bool)
new_esEs34(x0, x1, ty_Double)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_ltEs21(x0, x1, ty_Float)
new_ltEs10(x0, x1)
new_ltEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_compare29(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs14(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs5(x0, x1, ty_Ordering)
new_esEs8(x0, x1, ty_Double)
new_compare29(x0, x1, ty_Char)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs6(Just(x0), Just(x1), ty_@0)
new_esEs31(x0, x1, app(app(ty_Either, x2), x3))
new_compare1(:(x0, x1), :(x2, x3), x4)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs31(x0, x1, app(ty_[], x2))
new_esEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs6(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs19(x0, x1, ty_Double)
new_esEs14(False, False)
new_ltEs21(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs32(x0, x1, ty_Char)
new_ltEs21(x0, x1, ty_Double)
new_esEs32(x0, x1, ty_Int)
new_ltEs14(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpNat2(Succ(x0), Zero)
new_esEs7(Right(x0), Right(x1), x2, ty_Char)
new_esEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_compare34(x0, x1, x2, x3)
new_compare18(x0, x1)
new_esEs32(x0, x1, ty_Bool)
new_esEs7(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs18(Just(x0), Just(x1), ty_Int)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare26(Right(x0), Right(x1), False, x2, x3)
new_esEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs17(x0, x1, x2)
new_primPlusNat0(Succ(x0), x1)
new_esEs20(x0, x1, ty_Integer)
new_primCmpNat0(x0, Zero)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_ltEs7(GT, EQ)
new_ltEs7(EQ, GT)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs32(x0, x1, ty_Double)
new_ltEs7(GT, GT)
new_esEs9(LT, LT)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_primCompAux0(x0, x1, x2, x3)
new_compare29(x0, x1, ty_@0)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_compare26(x0, x1, True, x2, x3)
new_compare26(Right(x0), Left(x1), False, x2, x3)
new_compare26(Left(x0), Right(x1), False, x2, x3)
new_ltEs18(Nothing, Just(x0), x1)
new_compare111(x0, x1, False, x2)
new_compare29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Ordering)
new_primCmpNat0(x0, Succ(x1))

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

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

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

new_splitGT3(Right(zxw300), zxw31, zxw32, zxw33, zxw34, Right(zxw400), h, ba, bb) → new_splitGT22(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs9(new_compare26(Right(zxw400), Right(zxw300), new_esEs34(zxw400, zxw300, ba), h, ba), GT), h, ba, bb)
new_splitGT21(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, False, h, ba, bb) → new_splitGT11(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs9(new_compare35(zxw400, zxw300, h, ba), LT), h, ba, bb)
new_splitGT3(Left(zxw300), zxw31, zxw32, zxw33, zxw34, Right(zxw400), h, ba, bb) → new_splitGT21(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs9(new_compare26(Right(zxw400), Left(zxw300), False, h, ba), GT), h, ba, bb)
new_splitGT21(zxw300, zxw31, zxw32, zxw33, Branch(zxw340, zxw341, zxw342, zxw343, zxw344), zxw400, True, h, ba, bb) → new_splitGT3(zxw340, zxw341, zxw342, zxw343, zxw344, Right(zxw400), h, ba, bb)
new_splitGT12(zxw30, zxw31, zxw32, zxw33, zxw34, zxw35, True, bf, bg, bh) → new_splitGT0(zxw33, zxw35, bf, bg, bh)
new_splitGT22(zxw30, zxw31, zxw32, zxw33, zxw34, zxw35, True, bf, bg, bh) → new_splitGT0(zxw34, zxw35, bf, bg, bh)
new_splitGT22(zxw30, zxw31, zxw32, zxw33, zxw34, zxw35, False, bf, bg, bh) → new_splitGT12(zxw30, zxw31, zxw32, zxw33, zxw34, zxw35, new_esEs9(new_compare36(zxw35, zxw30, bf, bg), LT), bf, bg, bh)
new_splitGT11(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, True, h, ba, bb) → new_splitGT0(zxw33, zxw400, h, ba, bb)
new_splitGT0(Branch(zxw340, zxw341, zxw342, zxw343, zxw344), zxw400, h, ba, bb) → new_splitGT3(zxw340, zxw341, zxw342, zxw343, zxw344, Right(zxw400), h, ba, bb)

The TRS R consists of the following rules:

new_compare36(zxw35, zxw30, bf, bg) → new_compare26(Right(zxw35), Right(zxw30), new_esEs31(zxw35, zxw30, bg), bf, bg)
new_esEs9(GT, LT) → False
new_esEs9(EQ, LT) → False
new_esEs9(LT, LT) → True
new_esEs31(zxw35, zxw30, ty_Ordering) → new_esEs9(zxw35, zxw30)
new_esEs31(zxw35, zxw30, ty_Char) → new_esEs12(zxw35, zxw30)
new_esEs31(zxw35, zxw30, ty_@0) → new_esEs10(zxw35, zxw30)
new_esEs31(zxw35, zxw30, app(app(app(ty_@3, beb), bec), bed)) → new_esEs4(zxw35, zxw30, beb, bec, bed)
new_esEs31(zxw35, zxw30, ty_Float) → new_esEs17(zxw35, zxw30)
new_esEs31(zxw35, zxw30, app(app(ty_Either, bdh), bea)) → new_esEs7(zxw35, zxw30, bdh, bea)
new_esEs31(zxw35, zxw30, app(ty_Ratio, bdc)) → new_esEs18(zxw35, zxw30, bdc)
new_esEs31(zxw35, zxw30, app(app(ty_@2, bdf), bdg)) → new_esEs5(zxw35, zxw30, bdf, bdg)
new_esEs31(zxw35, zxw30, ty_Integer) → new_esEs15(zxw35, zxw30)
new_esEs31(zxw35, zxw30, ty_Double) → new_esEs16(zxw35, zxw30)
new_esEs31(zxw35, zxw30, app(ty_[], bdd)) → new_esEs13(zxw35, zxw30, bdd)
new_esEs31(zxw35, zxw30, ty_Int) → new_esEs11(zxw35, zxw30)
new_esEs31(zxw35, zxw30, ty_Bool) → new_esEs14(zxw35, zxw30)
new_esEs31(zxw35, zxw30, app(ty_Maybe, bde)) → new_esEs6(zxw35, zxw30, bde)
new_compare26(zxw790, zxw800, True, gh, ha) → EQ
new_compare26(Right(zxw7900), Right(zxw8000), False, gh, ha) → new_compare14(zxw7900, zxw8000, new_ltEs20(zxw7900, zxw8000, ha), gh, ha)
new_ltEs20(zxw7900, zxw8000, app(ty_Maybe, bbc)) → new_ltEs18(zxw7900, zxw8000, bbc)
new_ltEs20(zxw7900, zxw8000, ty_Int) → new_ltEs9(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, ty_@0) → new_ltEs8(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, app(app(ty_@2, baf), bag)) → new_ltEs4(zxw7900, zxw8000, baf, bag)
new_ltEs20(zxw7900, zxw8000, ty_Float) → new_ltEs16(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, ty_Bool) → new_ltEs12(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, app(ty_Ratio, bbb)) → new_ltEs17(zxw7900, zxw8000, bbb)
new_ltEs20(zxw7900, zxw8000, ty_Double) → new_ltEs15(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, ty_Integer) → new_ltEs13(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, app(app(app(ty_@3, bab), bac), bad)) → new_ltEs6(zxw7900, zxw8000, bab, bac, bad)
new_ltEs20(zxw7900, zxw8000, app(app(ty_Either, bah), bba)) → new_ltEs14(zxw7900, zxw8000, bah, bba)
new_ltEs20(zxw7900, zxw8000, app(ty_[], bae)) → new_ltEs11(zxw7900, zxw8000, bae)
new_ltEs20(zxw7900, zxw8000, ty_Char) → new_ltEs10(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, ty_Ordering) → new_ltEs7(zxw7900, zxw8000)
new_compare14(zxw242, zxw243, False, def, deg) → GT
new_compare14(zxw242, zxw243, True, def, deg) → LT
new_ltEs7(LT, EQ) → True
new_ltEs7(GT, GT) → True
new_ltEs7(EQ, EQ) → True
new_ltEs7(GT, LT) → False
new_ltEs7(GT, EQ) → False
new_ltEs7(EQ, GT) → True
new_ltEs7(EQ, LT) → False
new_ltEs7(LT, LT) → True
new_ltEs7(LT, GT) → True
new_ltEs10(zxw7900, zxw8000) → new_fsEs(new_compare17(zxw7900, zxw8000))
new_compare17(Char(zxw79000), Char(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_fsEs(zxw259) → new_not(new_esEs9(zxw259, GT))
new_esEs9(LT, GT) → False
new_esEs9(EQ, GT) → False
new_esEs9(GT, GT) → True
new_not(False) → True
new_not(True) → False
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_ltEs11(zxw7900, zxw8000, he) → new_fsEs(new_compare1(zxw7900, zxw8000, he))
new_compare1([], :(zxw80000, zxw80001), he) → LT
new_compare1(:(zxw79000, zxw79001), :(zxw80000, zxw80001), he) → new_primCompAux0(zxw79000, zxw80000, new_compare1(zxw79001, zxw80001, he), he)
new_compare1(:(zxw79000, zxw79001), [], he) → GT
new_compare1([], [], he) → EQ
new_primCompAux0(zxw79000, zxw80000, zxw272, he) → new_primCompAux00(zxw272, new_compare29(zxw79000, zxw80000, he))
new_compare29(zxw79000, zxw80000, ty_Char) → new_compare17(zxw79000, zxw80000)
new_compare29(zxw79000, zxw80000, ty_Bool) → new_compare31(zxw79000, zxw80000)
new_compare29(zxw79000, zxw80000, app(app(ty_@2, ccf), ccg)) → new_compare19(zxw79000, zxw80000, ccf, ccg)
new_compare29(zxw79000, zxw80000, app(ty_[], cce)) → new_compare1(zxw79000, zxw80000, cce)
new_compare29(zxw79000, zxw80000, app(app(app(ty_@3, ccb), ccc), ccd)) → new_compare9(zxw79000, zxw80000, ccb, ccc, ccd)
new_compare29(zxw79000, zxw80000, ty_Int) → new_compare16(zxw79000, zxw80000)
new_compare29(zxw79000, zxw80000, ty_Integer) → new_compare32(zxw79000, zxw80000)
new_compare29(zxw79000, zxw80000, app(ty_Maybe, cdc)) → new_compare27(zxw79000, zxw80000, cdc)
new_compare29(zxw79000, zxw80000, app(ty_Ratio, cdb)) → new_compare8(zxw79000, zxw80000, cdb)
new_compare29(zxw79000, zxw80000, ty_Float) → new_compare7(zxw79000, zxw80000)
new_compare29(zxw79000, zxw80000, ty_Double) → new_compare6(zxw79000, zxw80000)
new_compare29(zxw79000, zxw80000, app(app(ty_Either, cch), cda)) → new_compare15(zxw79000, zxw80000, cch, cda)
new_compare29(zxw79000, zxw80000, ty_Ordering) → new_compare18(zxw79000, zxw80000)
new_compare29(zxw79000, zxw80000, ty_@0) → new_compare30(zxw79000, zxw80000)
new_primCompAux00(zxw276, LT) → LT
new_primCompAux00(zxw276, EQ) → zxw276
new_primCompAux00(zxw276, GT) → GT
new_compare30(@0, @0) → EQ
new_compare18(zxw79000, zxw80000) → new_compare24(zxw79000, zxw80000, new_esEs9(zxw79000, zxw80000))
new_esEs9(GT, EQ) → False
new_esEs9(EQ, EQ) → True
new_esEs9(LT, EQ) → False
new_compare24(zxw79000, zxw80000, False) → new_compare11(zxw79000, zxw80000, new_ltEs7(zxw79000, zxw80000))
new_compare24(zxw79000, zxw80000, True) → EQ
new_compare11(zxw79000, zxw80000, False) → GT
new_compare11(zxw79000, zxw80000, True) → LT
new_compare15(zxw790, zxw800, gh, ha) → new_compare26(zxw790, zxw800, new_esEs7(zxw790, zxw800, gh, ha), gh, ha)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Bool, bef) → new_esEs14(zxw4000, zxw3000)
new_esEs7(Right(zxw4000), Left(zxw3000), bfh, bef) → False
new_esEs7(Left(zxw4000), Right(zxw3000), bfh, bef) → False
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, app(app(ty_@2, bgd), bge)) → new_esEs5(zxw4000, zxw3000, bgd, bge)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Int, bef) → new_esEs11(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), app(app(ty_@2, bfa), bfb), bef) → new_esEs5(zxw4000, zxw3000, bfa, bfb)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Ordering, bef) → new_esEs9(zxw4000, zxw3000)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, app(ty_[], bgb)) → new_esEs13(zxw4000, zxw3000, bgb)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Integer, bef) → new_esEs15(zxw4000, zxw3000)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, app(app(app(ty_@3, bgh), bha), bhb)) → new_esEs4(zxw4000, zxw3000, bgh, bha, bhb)
new_esEs7(Left(zxw4000), Left(zxw3000), app(ty_Ratio, bee), bef) → new_esEs18(zxw4000, zxw3000, bee)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_@0, bef) → new_esEs10(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), app(app(app(ty_@3, bfe), bff), bfg), bef) → new_esEs4(zxw4000, zxw3000, bfe, bff, bfg)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Double, bef) → new_esEs16(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Float, bef) → new_esEs17(zxw4000, zxw3000)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Char, bef) → new_esEs12(zxw4000, zxw3000)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), app(ty_[], beg), bef) → new_esEs13(zxw4000, zxw3000, beg)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, app(ty_Ratio, bga)) → new_esEs18(zxw4000, zxw3000, bga)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_compare26(Left(zxw7900), Right(zxw8000), False, gh, ha) → LT
new_compare26(Right(zxw7900), Left(zxw8000), False, gh, ha) → GT
new_compare26(Left(zxw7900), Left(zxw8000), False, gh, ha) → new_compare13(zxw7900, zxw8000, new_ltEs19(zxw7900, zxw8000, gh), gh, ha)
new_esEs6(Just(zxw4000), Just(zxw3000), app(ty_Maybe, fc)) → new_esEs6(zxw4000, zxw3000, fc)
new_esEs7(Left(zxw4000), Left(zxw3000), app(app(ty_Either, bfc), bfd), bef) → new_esEs7(zxw4000, zxw3000, bfc, bfd)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, app(ty_Maybe, bgc)) → new_esEs6(zxw4000, zxw3000, bgc)
new_esEs6(Just(zxw4000), Just(zxw3000), app(app(ty_Either, fg), fh)) → new_esEs7(zxw4000, zxw3000, fg, fh)
new_esEs7(Left(zxw4000), Left(zxw3000), app(ty_Maybe, beh), bef) → new_esEs6(zxw4000, zxw3000, beh)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, app(app(ty_Either, bgf), bgg)) → new_esEs7(zxw4000, zxw3000, bgf, bgg)
new_esEs6(Just(zxw4000), Just(zxw3000), app(app(ty_@2, fd), ff)) → new_esEs5(zxw4000, zxw3000, fd, ff)
new_esEs6(Nothing, Nothing, eh) → True
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs6(Nothing, Just(zxw3000), eh) → False
new_esEs6(Just(zxw4000), Nothing, eh) → False
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), app(app(app(ty_@3, ga), gb), gc)) → new_esEs4(zxw4000, zxw3000, ga, gb, gc)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_@0) → new_esEs10(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), app(ty_[], fb)) → new_esEs13(zxw4000, zxw3000, fb)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Char) → new_esEs12(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Float) → new_esEs17(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), app(ty_Ratio, fa)) → new_esEs18(zxw4000, zxw3000, fa)
new_esEs18(:%(zxw4000, zxw4001), :%(zxw3000, zxw3001), dee) → new_asAs(new_esEs25(zxw4000, zxw3000, dee), new_esEs24(zxw4001, zxw3001, dee))
new_esEs25(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs25(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs24(zxw4001, zxw3001, ty_Integer) → new_esEs15(zxw4001, zxw3001)
new_esEs24(zxw4001, zxw3001, ty_Int) → new_esEs11(zxw4001, zxw3001)
new_asAs(False, zxw230) → False
new_asAs(True, zxw230) → zxw230
new_esEs11(zxw400, zxw300) → new_primEqInt(zxw400, zxw300)
new_primEqInt(Neg(Succ(zxw40000)), Neg(Succ(zxw30000))) → new_primEqNat0(zxw40000, zxw30000)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Neg(Succ(zxw30000))) → False
new_primEqInt(Neg(Succ(zxw40000)), Neg(Zero)) → False
new_primEqInt(Pos(Succ(zxw40000)), Pos(Succ(zxw30000))) → new_primEqNat0(zxw40000, zxw30000)
new_primEqInt(Pos(Zero), Pos(Succ(zxw30000))) → False
new_primEqInt(Pos(Succ(zxw40000)), Pos(Zero)) → False
new_primEqInt(Neg(Succ(zxw40000)), Pos(zxw3000)) → False
new_primEqInt(Pos(Succ(zxw40000)), Neg(zxw3000)) → False
new_primEqInt(Neg(Zero), Pos(Succ(zxw30000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(zxw30000))) → False
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqNat0(Zero, Zero) → True
new_primEqNat0(Succ(zxw40000), Succ(zxw30000)) → new_primEqNat0(zxw40000, zxw30000)
new_primEqNat0(Zero, Succ(zxw30000)) → False
new_primEqNat0(Succ(zxw40000), Zero) → False
new_esEs15(Integer(zxw4000), Integer(zxw3000)) → new_primEqInt(zxw4000, zxw3000)
new_esEs17(Float(zxw4000, zxw4001), Float(zxw3000, zxw3001)) → new_esEs11(new_sr(zxw4000, zxw3000), new_sr(zxw4001, zxw3001))
new_sr(zxw4000, zxw3000) → new_primMulInt(zxw4000, zxw3000)
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Neg(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Pos(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulNat0(Zero, Zero) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_esEs12(Char(zxw4000), Char(zxw3000)) → new_primEqNat0(zxw4000, zxw3000)
new_esEs13([], [], ddb) → True
new_esEs13(:(zxw4000, zxw4001), :(zxw3000, zxw3001), ddb) → new_asAs(new_esEs23(zxw4000, zxw3000, ddb), new_esEs13(zxw4001, zxw3001, ddb))
new_esEs13(:(zxw4000, zxw4001), [], ddb) → False
new_esEs13([], :(zxw3000, zxw3001), ddb) → False
new_esEs23(zxw4000, zxw3000, app(app(ty_Either, ddh), dea)) → new_esEs7(zxw4000, zxw3000, ddh, dea)
new_esEs23(zxw4000, zxw3000, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, app(app(app(ty_@3, deb), dec), ded)) → new_esEs4(zxw4000, zxw3000, deb, dec, ded)
new_esEs23(zxw4000, zxw3000, app(app(ty_@2, ddf), ddg)) → new_esEs5(zxw4000, zxw3000, ddf, ddg)
new_esEs23(zxw4000, zxw3000, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, app(ty_Ratio, ddc)) → new_esEs18(zxw4000, zxw3000, ddc)
new_esEs23(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, app(ty_Maybe, dde)) → new_esEs6(zxw4000, zxw3000, dde)
new_esEs23(zxw4000, zxw3000, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, app(ty_[], ddd)) → new_esEs13(zxw4000, zxw3000, ddd)
new_esEs16(Double(zxw4000, zxw4001), Double(zxw3000, zxw3001)) → new_esEs11(new_sr(zxw4000, zxw3000), new_sr(zxw4001, zxw3001))
new_esEs10(@0, @0) → True
new_esEs5(@2(zxw4000, zxw4001), @2(zxw3000, zxw3001), dad, dae) → new_asAs(new_esEs22(zxw4000, zxw3000, dad), new_esEs21(zxw4001, zxw3001, dae))
new_esEs22(zxw4000, zxw3000, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, app(app(ty_@2, dcc), dcd)) → new_esEs5(zxw4000, zxw3000, dcc, dcd)
new_esEs22(zxw4000, zxw3000, app(ty_Maybe, dcb)) → new_esEs6(zxw4000, zxw3000, dcb)
new_esEs22(zxw4000, zxw3000, app(ty_Ratio, dbh)) → new_esEs18(zxw4000, zxw3000, dbh)
new_esEs22(zxw4000, zxw3000, app(app(ty_Either, dce), dcf)) → new_esEs7(zxw4000, zxw3000, dce, dcf)
new_esEs22(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, app(app(app(ty_@3, dcg), dch), dda)) → new_esEs4(zxw4000, zxw3000, dcg, dch, dda)
new_esEs22(zxw4000, zxw3000, app(ty_[], dca)) → new_esEs13(zxw4000, zxw3000, dca)
new_esEs22(zxw4000, zxw3000, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs21(zxw4001, zxw3001, ty_Bool) → new_esEs14(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, ty_Double) → new_esEs16(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, ty_Ordering) → new_esEs9(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, ty_Char) → new_esEs12(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, ty_Float) → new_esEs17(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, app(ty_Maybe, dah)) → new_esEs6(zxw4001, zxw3001, dah)
new_esEs21(zxw4001, zxw3001, ty_Int) → new_esEs11(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, app(ty_[], dag)) → new_esEs13(zxw4001, zxw3001, dag)
new_esEs21(zxw4001, zxw3001, ty_Integer) → new_esEs15(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, app(app(ty_@2, dba), dbb)) → new_esEs5(zxw4001, zxw3001, dba, dbb)
new_esEs21(zxw4001, zxw3001, ty_@0) → new_esEs10(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, app(app(ty_Either, dbc), dbd)) → new_esEs7(zxw4001, zxw3001, dbc, dbd)
new_esEs21(zxw4001, zxw3001, app(app(app(ty_@3, dbe), dbf), dbg)) → new_esEs4(zxw4001, zxw3001, dbe, dbf, dbg)
new_esEs21(zxw4001, zxw3001, app(ty_Ratio, daf)) → new_esEs18(zxw4001, zxw3001, daf)
new_esEs4(@3(zxw4000, zxw4001, zxw4002), @3(zxw3000, zxw3001, zxw3002), deh, dfa, dfb) → new_asAs(new_esEs28(zxw4000, zxw3000, deh), new_asAs(new_esEs27(zxw4001, zxw3001, dfa), new_esEs26(zxw4002, zxw3002, dfb)))
new_esEs28(zxw4000, zxw3000, app(ty_[], dhh)) → new_esEs13(zxw4000, zxw3000, dhh)
new_esEs28(zxw4000, zxw3000, app(app(app(ty_@3, eaf), eag), eah)) → new_esEs4(zxw4000, zxw3000, eaf, eag, eah)
new_esEs28(zxw4000, zxw3000, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, app(ty_Maybe, eaa)) → new_esEs6(zxw4000, zxw3000, eaa)
new_esEs28(zxw4000, zxw3000, app(app(ty_Either, ead), eae)) → new_esEs7(zxw4000, zxw3000, ead, eae)
new_esEs28(zxw4000, zxw3000, app(app(ty_@2, eab), eac)) → new_esEs5(zxw4000, zxw3000, eab, eac)
new_esEs28(zxw4000, zxw3000, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, app(ty_Ratio, dhg)) → new_esEs18(zxw4000, zxw3000, dhg)
new_esEs28(zxw4000, zxw3000, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_esEs27(zxw4001, zxw3001, app(ty_Ratio, dge)) → new_esEs18(zxw4001, zxw3001, dge)
new_esEs27(zxw4001, zxw3001, app(app(app(ty_@3, dhd), dhe), dhf)) → new_esEs4(zxw4001, zxw3001, dhd, dhe, dhf)
new_esEs27(zxw4001, zxw3001, app(ty_Maybe, dgg)) → new_esEs6(zxw4001, zxw3001, dgg)
new_esEs27(zxw4001, zxw3001, app(app(ty_Either, dhb), dhc)) → new_esEs7(zxw4001, zxw3001, dhb, dhc)
new_esEs27(zxw4001, zxw3001, ty_Ordering) → new_esEs9(zxw4001, zxw3001)
new_esEs27(zxw4001, zxw3001, ty_Float) → new_esEs17(zxw4001, zxw3001)
new_esEs27(zxw4001, zxw3001, ty_@0) → new_esEs10(zxw4001, zxw3001)
new_esEs27(zxw4001, zxw3001, ty_Char) → new_esEs12(zxw4001, zxw3001)
new_esEs27(zxw4001, zxw3001, ty_Double) → new_esEs16(zxw4001, zxw3001)
new_esEs27(zxw4001, zxw3001, ty_Int) → new_esEs11(zxw4001, zxw3001)
new_esEs27(zxw4001, zxw3001, app(app(ty_@2, dgh), dha)) → new_esEs5(zxw4001, zxw3001, dgh, dha)
new_esEs27(zxw4001, zxw3001, ty_Bool) → new_esEs14(zxw4001, zxw3001)
new_esEs27(zxw4001, zxw3001, app(ty_[], dgf)) → new_esEs13(zxw4001, zxw3001, dgf)
new_esEs27(zxw4001, zxw3001, ty_Integer) → new_esEs15(zxw4001, zxw3001)
new_esEs26(zxw4002, zxw3002, ty_Float) → new_esEs17(zxw4002, zxw3002)
new_esEs26(zxw4002, zxw3002, ty_Char) → new_esEs12(zxw4002, zxw3002)
new_esEs26(zxw4002, zxw3002, ty_Int) → new_esEs11(zxw4002, zxw3002)
new_esEs26(zxw4002, zxw3002, app(ty_Maybe, dfe)) → new_esEs6(zxw4002, zxw3002, dfe)
new_esEs26(zxw4002, zxw3002, app(app(app(ty_@3, dgb), dgc), dgd)) → new_esEs4(zxw4002, zxw3002, dgb, dgc, dgd)
new_esEs26(zxw4002, zxw3002, app(ty_[], dfd)) → new_esEs13(zxw4002, zxw3002, dfd)
new_esEs26(zxw4002, zxw3002, app(app(ty_Either, dfh), dga)) → new_esEs7(zxw4002, zxw3002, dfh, dga)
new_esEs26(zxw4002, zxw3002, ty_Integer) → new_esEs15(zxw4002, zxw3002)
new_esEs26(zxw4002, zxw3002, app(app(ty_@2, dff), dfg)) → new_esEs5(zxw4002, zxw3002, dff, dfg)
new_esEs26(zxw4002, zxw3002, app(ty_Ratio, dfc)) → new_esEs18(zxw4002, zxw3002, dfc)
new_esEs26(zxw4002, zxw3002, ty_Bool) → new_esEs14(zxw4002, zxw3002)
new_esEs26(zxw4002, zxw3002, ty_@0) → new_esEs10(zxw4002, zxw3002)
new_esEs26(zxw4002, zxw3002, ty_Ordering) → new_esEs9(zxw4002, zxw3002)
new_esEs26(zxw4002, zxw3002, ty_Double) → new_esEs16(zxw4002, zxw3002)
new_esEs14(False, True) → False
new_esEs14(True, False) → False
new_esEs14(True, True) → True
new_esEs14(False, False) → True
new_ltEs19(zxw7900, zxw8000, ty_Float) → new_ltEs16(zxw7900, zxw8000)
new_ltEs19(zxw7900, zxw8000, app(app(ty_@2, ca), cb)) → new_ltEs4(zxw7900, zxw8000, ca, cb)
new_ltEs19(zxw7900, zxw8000, app(ty_[], he)) → new_ltEs11(zxw7900, zxw8000, he)
new_ltEs19(zxw7900, zxw8000, ty_Char) → new_ltEs10(zxw7900, zxw8000)
new_ltEs19(zxw7900, zxw8000, ty_Bool) → new_ltEs12(zxw7900, zxw8000)
new_ltEs19(zxw7900, zxw8000, app(ty_Ratio, hh)) → new_ltEs17(zxw7900, zxw8000, hh)
new_ltEs19(zxw7900, zxw8000, app(app(app(ty_@3, hb), hc), hd)) → new_ltEs6(zxw7900, zxw8000, hb, hc, hd)
new_ltEs19(zxw7900, zxw8000, ty_Int) → new_ltEs9(zxw7900, zxw8000)
new_ltEs19(zxw7900, zxw8000, app(app(ty_Either, hf), hg)) → new_ltEs14(zxw7900, zxw8000, hf, hg)
new_ltEs19(zxw7900, zxw8000, ty_@0) → new_ltEs8(zxw7900, zxw8000)
new_ltEs19(zxw7900, zxw8000, ty_Double) → new_ltEs15(zxw7900, zxw8000)
new_ltEs19(zxw7900, zxw8000, ty_Integer) → new_ltEs13(zxw7900, zxw8000)
new_ltEs19(zxw7900, zxw8000, ty_Ordering) → new_ltEs7(zxw7900, zxw8000)
new_ltEs19(zxw7900, zxw8000, app(ty_Maybe, baa)) → new_ltEs18(zxw7900, zxw8000, baa)
new_compare13(zxw235, zxw236, False, bch, bda) → GT
new_compare13(zxw235, zxw236, True, bch, bda) → LT
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Char) → new_ltEs10(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Integer) → new_ltEs13(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(ty_Ratio, dab)) → new_ltEs17(zxw79000, zxw80000, dab)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(app(app(ty_@3, chb), chc), chd)) → new_ltEs6(zxw79000, zxw80000, chb, chc, chd)
new_ltEs18(Nothing, Nothing, baa) → True
new_ltEs18(Just(zxw79000), Nothing, baa) → False
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Double) → new_ltEs15(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(ty_[], che)) → new_ltEs11(zxw79000, zxw80000, che)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(app(ty_@2, chf), chg)) → new_ltEs4(zxw79000, zxw80000, chf, chg)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Bool) → new_ltEs12(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Ordering) → new_ltEs7(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Float) → new_ltEs16(zxw79000, zxw80000)
new_ltEs18(Nothing, Just(zxw80000), baa) → True
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Int) → new_ltEs9(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_@0) → new_ltEs8(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(ty_Maybe, dac)) → new_ltEs18(zxw79000, zxw80000, dac)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(ty_Maybe, cha)) → new_ltEs18(zxw79000, zxw80000, cha)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(app(ty_Either, chh), daa)) → new_ltEs14(zxw79000, zxw80000, chh, daa)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(app(ty_Either, cgf), cgg)) → new_ltEs14(zxw79000, zxw80000, cgf, cgg)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(app(ty_Either, cfd), cfe), hg) → new_ltEs14(zxw79000, zxw80000, cfd, cfe)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(ty_Maybe, cfg), hg) → new_ltEs18(zxw79000, zxw80000, cfg)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Bool) → new_ltEs12(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(ty_[], cgc)) → new_ltEs11(zxw79000, zxw80000, cgc)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Bool, hg) → new_ltEs12(zxw79000, zxw80000)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(ty_Ratio, cff), hg) → new_ltEs17(zxw79000, zxw80000, cff)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(app(app(ty_@3, cfh), cga), cgb)) → new_ltEs6(zxw79000, zxw80000, cfh, cga, cgb)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Float, hg) → new_ltEs16(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Float) → new_ltEs16(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Double) → new_ltEs15(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(app(ty_@2, cgd), cge)) → new_ltEs4(zxw79000, zxw80000, cgd, cge)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Double, hg) → new_ltEs15(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Left(zxw80000), hf, hg) → False
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Int, hg) → new_ltEs9(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Char) → new_ltEs10(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_@0) → new_ltEs8(zxw79000, zxw80000)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(app(app(ty_@3, cef), ceg), ceh), hg) → new_ltEs6(zxw79000, zxw80000, cef, ceg, ceh)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_@0, hg) → new_ltEs8(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Ordering) → new_ltEs7(zxw79000, zxw80000)
new_ltEs14(Left(zxw79000), Right(zxw80000), hf, hg) → True
new_ltEs14(Left(zxw79000), Left(zxw80000), app(app(ty_@2, cfb), cfc), hg) → new_ltEs4(zxw79000, zxw80000, cfb, cfc)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(ty_[], cfa), hg) → new_ltEs11(zxw79000, zxw80000, cfa)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Integer, hg) → new_ltEs13(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Int) → new_ltEs9(zxw79000, zxw80000)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Ordering, hg) → new_ltEs7(zxw79000, zxw80000)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Char, hg) → new_ltEs10(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(ty_Ratio, cgh)) → new_ltEs17(zxw79000, zxw80000, cgh)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Integer) → new_ltEs13(zxw79000, zxw80000)
new_ltEs13(zxw7900, zxw8000) → new_fsEs(new_compare32(zxw7900, zxw8000))
new_compare32(Integer(zxw79000), Integer(zxw80000)) → new_primCmpInt(zxw79000, zxw80000)
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_ltEs17(zxw7900, zxw8000, hh) → new_fsEs(new_compare8(zxw7900, zxw8000, hh))
new_compare8(:%(zxw79000, zxw79001), :%(zxw80000, zxw80001), ty_Integer) → new_compare32(new_sr0(zxw79000, zxw80001), new_sr0(zxw80000, zxw79001))
new_compare8(:%(zxw79000, zxw79001), :%(zxw80000, zxw80001), ty_Int) → new_compare16(new_sr(zxw79000, zxw80001), new_sr(zxw80000, zxw79001))
new_compare16(zxw79, zxw80) → new_primCmpInt(zxw79, zxw80)
new_sr0(Integer(zxw800000), Integer(zxw790010)) → Integer(new_primMulInt(zxw800000, zxw790010))
new_ltEs9(zxw7900, zxw8000) → new_fsEs(new_compare16(zxw7900, zxw8000))
new_ltEs4(@2(zxw79000, zxw79001), @2(zxw80000, zxw80001), ca, cb) → new_pePe(new_lt4(zxw79000, zxw80000, ca), new_asAs(new_esEs8(zxw79000, zxw80000, ca), new_ltEs5(zxw79001, zxw80001, cb)))
new_lt4(zxw79000, zxw80000, app(app(app(ty_@3, cc), cd), ce)) → new_lt5(zxw79000, zxw80000, cc, cd, ce)
new_lt4(zxw79000, zxw80000, app(ty_[], cf)) → new_lt10(zxw79000, zxw80000, cf)
new_lt4(zxw79000, zxw80000, ty_Bool) → new_lt12(zxw79000, zxw80000)
new_lt4(zxw79000, zxw80000, app(ty_Maybe, de)) → new_lt18(zxw79000, zxw80000, de)
new_lt4(zxw79000, zxw80000, ty_Ordering) → new_lt6(zxw79000, zxw80000)
new_lt4(zxw79000, zxw80000, app(ty_Ratio, dd)) → new_lt17(zxw79000, zxw80000, dd)
new_lt4(zxw79000, zxw80000, ty_Int) → new_lt8(zxw79000, zxw80000)
new_lt4(zxw79000, zxw80000, ty_Double) → new_lt15(zxw79000, zxw80000)
new_lt4(zxw79000, zxw80000, app(app(ty_Either, db), dc)) → new_lt14(zxw79000, zxw80000, db, dc)
new_lt4(zxw79000, zxw80000, ty_Char) → new_lt9(zxw79000, zxw80000)
new_lt4(zxw79000, zxw80000, ty_@0) → new_lt7(zxw79000, zxw80000)
new_lt4(zxw79000, zxw80000, ty_Float) → new_lt16(zxw79000, zxw80000)
new_lt4(zxw79000, zxw80000, app(app(ty_@2, cg), da)) → new_lt11(zxw79000, zxw80000, cg, da)
new_lt4(zxw79000, zxw80000, ty_Integer) → new_lt13(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, ty_Int) → new_esEs11(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, ty_Double) → new_esEs16(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, app(app(app(ty_@3, cc), cd), ce)) → new_esEs4(zxw79000, zxw80000, cc, cd, ce)
new_esEs8(zxw79000, zxw80000, app(ty_[], cf)) → new_esEs13(zxw79000, zxw80000, cf)
new_esEs8(zxw79000, zxw80000, ty_Char) → new_esEs12(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, app(app(ty_@2, cg), da)) → new_esEs5(zxw79000, zxw80000, cg, da)
new_esEs8(zxw79000, zxw80000, ty_Float) → new_esEs17(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, app(app(ty_Either, db), dc)) → new_esEs7(zxw79000, zxw80000, db, dc)
new_esEs8(zxw79000, zxw80000, ty_@0) → new_esEs10(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, app(ty_Maybe, de)) → new_esEs6(zxw79000, zxw80000, de)
new_esEs8(zxw79000, zxw80000, ty_Bool) → new_esEs14(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, ty_Ordering) → new_esEs9(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, ty_Integer) → new_esEs15(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, app(ty_Ratio, dd)) → new_esEs18(zxw79000, zxw80000, dd)
new_ltEs5(zxw79001, zxw80001, ty_Char) → new_ltEs10(zxw79001, zxw80001)
new_ltEs5(zxw79001, zxw80001, app(app(ty_@2, eb), ec)) → new_ltEs4(zxw79001, zxw80001, eb, ec)
new_ltEs5(zxw79001, zxw80001, ty_Ordering) → new_ltEs7(zxw79001, zxw80001)
new_ltEs5(zxw79001, zxw80001, ty_Bool) → new_ltEs12(zxw79001, zxw80001)
new_ltEs5(zxw79001, zxw80001, ty_Integer) → new_ltEs13(zxw79001, zxw80001)
new_ltEs5(zxw79001, zxw80001, app(ty_Ratio, ef)) → new_ltEs17(zxw79001, zxw80001, ef)
new_ltEs5(zxw79001, zxw80001, app(ty_Maybe, eg)) → new_ltEs18(zxw79001, zxw80001, eg)
new_ltEs5(zxw79001, zxw80001, ty_Double) → new_ltEs15(zxw79001, zxw80001)
new_ltEs5(zxw79001, zxw80001, app(app(ty_Either, ed), ee)) → new_ltEs14(zxw79001, zxw80001, ed, ee)
new_ltEs5(zxw79001, zxw80001, app(app(app(ty_@3, df), dg), dh)) → new_ltEs6(zxw79001, zxw80001, df, dg, dh)
new_ltEs5(zxw79001, zxw80001, app(ty_[], ea)) → new_ltEs11(zxw79001, zxw80001, ea)
new_ltEs5(zxw79001, zxw80001, ty_Int) → new_ltEs9(zxw79001, zxw80001)
new_ltEs5(zxw79001, zxw80001, ty_@0) → new_ltEs8(zxw79001, zxw80001)
new_ltEs5(zxw79001, zxw80001, ty_Float) → new_ltEs16(zxw79001, zxw80001)
new_pePe(False, zxw271) → zxw271
new_pePe(True, zxw271) → True
new_ltEs16(zxw7900, zxw8000) → new_fsEs(new_compare7(zxw7900, zxw8000))
new_compare7(Float(zxw79000, zxw79001), Float(zxw80000, zxw80001)) → new_compare16(new_sr(zxw79000, zxw80000), new_sr(zxw79001, zxw80001))
new_ltEs8(zxw7900, zxw8000) → new_fsEs(new_compare30(zxw7900, zxw8000))
new_ltEs6(@3(zxw79000, zxw79001, zxw79002), @3(zxw80000, zxw80001, zxw80002), hb, hc, hd) → new_pePe(new_lt19(zxw79000, zxw80000, hb), new_asAs(new_esEs20(zxw79000, zxw80000, hb), new_pePe(new_lt20(zxw79001, zxw80001, hc), new_asAs(new_esEs19(zxw79001, zxw80001, hc), new_ltEs21(zxw79002, zxw80002, hd)))))
new_lt19(zxw79000, zxw80000, app(app(ty_Either, bhd), bhe)) → new_lt14(zxw79000, zxw80000, bhd, bhe)
new_lt19(zxw79000, zxw80000, ty_Double) → new_lt15(zxw79000, zxw80000)
new_lt19(zxw79000, zxw80000, ty_Ordering) → new_lt6(zxw79000, zxw80000)
new_lt19(zxw79000, zxw80000, app(ty_Ratio, gg)) → new_lt17(zxw79000, zxw80000, gg)
new_lt19(zxw79000, zxw80000, app(app(ty_@2, bcf), bcg)) → new_lt11(zxw79000, zxw80000, bcf, bcg)
new_lt19(zxw79000, zxw80000, ty_Int) → new_lt8(zxw79000, zxw80000)
new_lt19(zxw79000, zxw80000, ty_@0) → new_lt7(zxw79000, zxw80000)
new_lt19(zxw79000, zxw80000, app(app(app(ty_@3, gd), ge), gf)) → new_lt5(zxw79000, zxw80000, gd, ge, gf)
new_lt19(zxw79000, zxw80000, app(ty_Maybe, bdb)) → new_lt18(zxw79000, zxw80000, bdb)
new_lt19(zxw79000, zxw80000, ty_Float) → new_lt16(zxw79000, zxw80000)
new_lt19(zxw79000, zxw80000, ty_Bool) → new_lt12(zxw79000, zxw80000)
new_lt19(zxw79000, zxw80000, app(ty_[], bhc)) → new_lt10(zxw79000, zxw80000, bhc)
new_lt19(zxw79000, zxw80000, ty_Integer) → new_lt13(zxw79000, zxw80000)
new_lt19(zxw79000, zxw80000, ty_Char) → new_lt9(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, app(ty_[], bhc)) → new_esEs13(zxw79000, zxw80000, bhc)
new_esEs20(zxw79000, zxw80000, ty_Double) → new_esEs16(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, ty_Char) → new_esEs12(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, app(app(ty_@2, bcf), bcg)) → new_esEs5(zxw79000, zxw80000, bcf, bcg)
new_esEs20(zxw79000, zxw80000, ty_Int) → new_esEs11(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, ty_@0) → new_esEs10(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, app(app(app(ty_@3, gd), ge), gf)) → new_esEs4(zxw79000, zxw80000, gd, ge, gf)
new_esEs20(zxw79000, zxw80000, ty_Integer) → new_esEs15(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, ty_Bool) → new_esEs14(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, app(ty_Ratio, gg)) → new_esEs18(zxw79000, zxw80000, gg)
new_esEs20(zxw79000, zxw80000, app(app(ty_Either, bhd), bhe)) → new_esEs7(zxw79000, zxw80000, bhd, bhe)
new_esEs20(zxw79000, zxw80000, app(ty_Maybe, bdb)) → new_esEs6(zxw79000, zxw80000, bdb)
new_esEs20(zxw79000, zxw80000, ty_Ordering) → new_esEs9(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, ty_Float) → new_esEs17(zxw79000, zxw80000)
new_lt20(zxw79001, zxw80001, app(app(ty_Either, cad), cae)) → new_lt14(zxw79001, zxw80001, cad, cae)
new_lt20(zxw79001, zxw80001, ty_@0) → new_lt7(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, app(app(ty_@2, cab), cac)) → new_lt11(zxw79001, zxw80001, cab, cac)
new_lt20(zxw79001, zxw80001, ty_Ordering) → new_lt6(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, app(ty_Maybe, cag)) → new_lt18(zxw79001, zxw80001, cag)
new_lt20(zxw79001, zxw80001, ty_Int) → new_lt8(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, ty_Integer) → new_lt13(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, app(ty_Ratio, caf)) → new_lt17(zxw79001, zxw80001, caf)
new_lt20(zxw79001, zxw80001, ty_Char) → new_lt9(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, app(ty_[], caa)) → new_lt10(zxw79001, zxw80001, caa)
new_lt20(zxw79001, zxw80001, ty_Double) → new_lt15(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, ty_Float) → new_lt16(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, ty_Bool) → new_lt12(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, app(app(app(ty_@3, bhf), bhg), bhh)) → new_lt5(zxw79001, zxw80001, bhf, bhg, bhh)
new_esEs19(zxw79001, zxw80001, app(ty_Ratio, caf)) → new_esEs18(zxw79001, zxw80001, caf)
new_esEs19(zxw79001, zxw80001, ty_Ordering) → new_esEs9(zxw79001, zxw80001)
new_esEs19(zxw79001, zxw80001, app(ty_Maybe, cag)) → new_esEs6(zxw79001, zxw80001, cag)
new_esEs19(zxw79001, zxw80001, app(app(ty_Either, cad), cae)) → new_esEs7(zxw79001, zxw80001, cad, cae)
new_esEs19(zxw79001, zxw80001, ty_Float) → new_esEs17(zxw79001, zxw80001)
new_esEs19(zxw79001, zxw80001, ty_Bool) → new_esEs14(zxw79001, zxw80001)
new_esEs19(zxw79001, zxw80001, ty_Int) → new_esEs11(zxw79001, zxw80001)
new_esEs19(zxw79001, zxw80001, app(app(app(ty_@3, bhf), bhg), bhh)) → new_esEs4(zxw79001, zxw80001, bhf, bhg, bhh)
new_esEs19(zxw79001, zxw80001, app(app(ty_@2, cab), cac)) → new_esEs5(zxw79001, zxw80001, cab, cac)
new_esEs19(zxw79001, zxw80001, ty_Double) → new_esEs16(zxw79001, zxw80001)
new_esEs19(zxw79001, zxw80001, ty_Integer) → new_esEs15(zxw79001, zxw80001)
new_esEs19(zxw79001, zxw80001, ty_@0) → new_esEs10(zxw79001, zxw80001)
new_esEs19(zxw79001, zxw80001, app(ty_[], caa)) → new_esEs13(zxw79001, zxw80001, caa)
new_esEs19(zxw79001, zxw80001, ty_Char) → new_esEs12(zxw79001, zxw80001)
new_ltEs21(zxw79002, zxw80002, ty_Char) → new_ltEs10(zxw79002, zxw80002)
new_ltEs21(zxw79002, zxw80002, app(app(ty_@2, cbd), cbe)) → new_ltEs4(zxw79002, zxw80002, cbd, cbe)
new_ltEs21(zxw79002, zxw80002, ty_Int) → new_ltEs9(zxw79002, zxw80002)
new_ltEs21(zxw79002, zxw80002, ty_Ordering) → new_ltEs7(zxw79002, zxw80002)
new_ltEs21(zxw79002, zxw80002, ty_Float) → new_ltEs16(zxw79002, zxw80002)
new_ltEs21(zxw79002, zxw80002, ty_Bool) → new_ltEs12(zxw79002, zxw80002)
new_ltEs21(zxw79002, zxw80002, ty_Integer) → new_ltEs13(zxw79002, zxw80002)
new_ltEs21(zxw79002, zxw80002, app(app(ty_Either, cbf), cbg)) → new_ltEs14(zxw79002, zxw80002, cbf, cbg)
new_ltEs21(zxw79002, zxw80002, app(ty_[], cbc)) → new_ltEs11(zxw79002, zxw80002, cbc)
new_ltEs21(zxw79002, zxw80002, app(ty_Ratio, cbh)) → new_ltEs17(zxw79002, zxw80002, cbh)
new_ltEs21(zxw79002, zxw80002, app(app(app(ty_@3, cah), cba), cbb)) → new_ltEs6(zxw79002, zxw80002, cah, cba, cbb)
new_ltEs21(zxw79002, zxw80002, ty_@0) → new_ltEs8(zxw79002, zxw80002)
new_ltEs21(zxw79002, zxw80002, app(ty_Maybe, cca)) → new_ltEs18(zxw79002, zxw80002, cca)
new_ltEs21(zxw79002, zxw80002, ty_Double) → new_ltEs15(zxw79002, zxw80002)
new_ltEs15(zxw7900, zxw8000) → new_fsEs(new_compare6(zxw7900, zxw8000))
new_compare6(Double(zxw79000, zxw79001), Double(zxw80000, zxw80001)) → new_compare16(new_sr(zxw79000, zxw80000), new_sr(zxw79001, zxw80001))
new_ltEs12(True, False) → False
new_ltEs12(False, False) → True
new_ltEs12(True, True) → True
new_ltEs12(False, True) → True
new_lt5(zxw79000, zxw80000, gd, ge, gf) → new_esEs9(new_compare9(zxw79000, zxw80000, gd, ge, gf), LT)
new_compare9(zxw79000, zxw80000, gd, ge, gf) → new_compare25(zxw79000, zxw80000, new_esEs4(zxw79000, zxw80000, gd, ge, gf), gd, ge, gf)
new_compare25(zxw79000, zxw80000, True, gd, ge, gf) → EQ
new_compare25(zxw79000, zxw80000, False, gd, ge, gf) → new_compare12(zxw79000, zxw80000, new_ltEs6(zxw79000, zxw80000, gd, ge, gf), gd, ge, gf)
new_compare12(zxw79000, zxw80000, True, gd, ge, gf) → LT
new_compare12(zxw79000, zxw80000, False, gd, ge, gf) → GT
new_lt12(zxw79000, zxw80000) → new_esEs9(new_compare31(zxw79000, zxw80000), LT)
new_compare31(zxw79000, zxw80000) → new_compare23(zxw79000, zxw80000, new_esEs14(zxw79000, zxw80000))
new_compare23(zxw79000, zxw80000, True) → EQ
new_compare23(zxw79000, zxw80000, False) → new_compare10(zxw79000, zxw80000, new_ltEs12(zxw79000, zxw80000))
new_compare10(zxw79000, zxw80000, True) → LT
new_compare10(zxw79000, zxw80000, False) → GT
new_lt16(zxw79000, zxw80000) → new_esEs9(new_compare7(zxw79000, zxw80000), LT)
new_lt15(zxw79000, zxw80000) → new_esEs9(new_compare6(zxw79000, zxw80000), LT)
new_lt10(zxw79000, zxw80000, bhc) → new_esEs9(new_compare1(zxw79000, zxw80000, bhc), LT)
new_lt9(zxw79000, zxw80000) → new_esEs9(new_compare17(zxw79000, zxw80000), LT)
new_lt17(zxw79000, zxw80000, gg) → new_esEs9(new_compare8(zxw79000, zxw80000, gg), LT)
new_lt13(zxw79000, zxw80000) → new_esEs9(new_compare32(zxw79000, zxw80000), LT)
new_lt8(zxw790, zxw800) → new_esEs9(new_compare16(zxw790, zxw800), LT)
new_lt18(zxw79000, zxw80000, bdb) → new_esEs9(new_compare27(zxw79000, zxw80000, bdb), LT)
new_compare27(zxw79000, zxw80000, bdb) → new_compare28(zxw79000, zxw80000, new_esEs6(zxw79000, zxw80000, bdb), bdb)
new_compare28(zxw79000, zxw80000, False, bdb) → new_compare111(zxw79000, zxw80000, new_ltEs18(zxw79000, zxw80000, bdb), bdb)
new_compare28(zxw79000, zxw80000, True, bdb) → EQ
new_compare111(zxw79000, zxw80000, True, bdb) → LT
new_compare111(zxw79000, zxw80000, False, bdb) → GT
new_lt6(zxw79000, zxw80000) → new_esEs9(new_compare18(zxw79000, zxw80000), LT)
new_lt11(zxw79000, zxw80000, bcf, bcg) → new_esEs9(new_compare19(zxw79000, zxw80000, bcf, bcg), LT)
new_compare19(zxw79000, zxw80000, bcf, bcg) → new_compare210(zxw79000, zxw80000, new_esEs5(zxw79000, zxw80000, bcf, bcg), bcf, bcg)
new_compare210(zxw79000, zxw80000, False, bcf, bcg) → new_compare110(zxw79000, zxw80000, new_ltEs4(zxw79000, zxw80000, bcf, bcg), bcf, bcg)
new_compare210(zxw79000, zxw80000, True, bcf, bcg) → EQ
new_compare110(zxw79000, zxw80000, True, bcf, bcg) → LT
new_compare110(zxw79000, zxw80000, False, bcf, bcg) → GT
new_lt7(zxw79000, zxw80000) → new_esEs9(new_compare30(zxw79000, zxw80000), LT)
new_lt14(zxw790, zxw800, gh, ha) → new_esEs9(new_compare15(zxw790, zxw800, gh, ha), LT)
new_compare35(zxw400, zxw300, h, ba) → new_compare26(Right(zxw400), Left(zxw300), False, h, ba)
new_esEs34(zxw400, zxw300, ty_Char) → new_esEs12(zxw400, zxw300)
new_esEs34(zxw400, zxw300, app(app(ty_Either, bca), bcb)) → new_esEs7(zxw400, zxw300, bca, bcb)
new_esEs34(zxw400, zxw300, app(ty_[], bbe)) → new_esEs13(zxw400, zxw300, bbe)
new_esEs34(zxw400, zxw300, ty_Float) → new_esEs17(zxw400, zxw300)
new_esEs34(zxw400, zxw300, app(app(ty_@2, bbg), bbh)) → new_esEs5(zxw400, zxw300, bbg, bbh)
new_esEs34(zxw400, zxw300, app(app(app(ty_@3, bcc), bcd), bce)) → new_esEs4(zxw400, zxw300, bcc, bcd, bce)
new_esEs34(zxw400, zxw300, ty_Double) → new_esEs16(zxw400, zxw300)
new_esEs34(zxw400, zxw300, ty_Ordering) → new_esEs9(zxw400, zxw300)
new_esEs34(zxw400, zxw300, ty_Int) → new_esEs11(zxw400, zxw300)
new_esEs34(zxw400, zxw300, ty_Bool) → new_esEs14(zxw400, zxw300)
new_esEs34(zxw400, zxw300, ty_Integer) → new_esEs15(zxw400, zxw300)
new_esEs34(zxw400, zxw300, ty_@0) → new_esEs10(zxw400, zxw300)
new_esEs34(zxw400, zxw300, app(ty_Ratio, bbd)) → new_esEs18(zxw400, zxw300, bbd)
new_esEs34(zxw400, zxw300, app(ty_Maybe, bbf)) → new_esEs6(zxw400, zxw300, bbf)

The set Q consists of the following terms:

new_compare23(x0, x1, True)
new_lt6(x0, x1)
new_ltEs5(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, ty_Integer)
new_esEs33(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt4(x0, x1, app(ty_[], x2))
new_ltEs18(Just(x0), Just(x1), ty_@0)
new_compare16(x0, x1)
new_lt4(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(Just(x0), Nothing, x1)
new_ltEs20(x0, x1, ty_Double)
new_esEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs19(x0, x1, ty_Bool)
new_esEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs8(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(x0, x1, app(app(ty_Either, x2), x3))
new_compare30(@0, @0)
new_esEs32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCompAux00(x0, GT)
new_lt19(x0, x1, ty_Char)
new_esEs27(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_Ordering)
new_compare17(Char(x0), Char(x1))
new_esEs28(x0, x1, ty_Int)
new_ltEs20(x0, x1, app(ty_[], x2))
new_ltEs21(x0, x1, ty_Ordering)
new_compare111(x0, x1, True, x2)
new_ltEs15(x0, x1)
new_primPlusNat1(Zero, Succ(x0))
new_esEs6(Just(x0), Just(x1), ty_Double)
new_compare24(x0, x1, False)
new_compare210(x0, x1, False, x2, x3)
new_lt20(x0, x1, ty_Char)
new_esEs33(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, ty_Bool)
new_sr0(Integer(x0), Integer(x1))
new_esEs32(x0, x1, app(ty_[], x2))
new_esEs33(x0, x1, ty_Float)
new_compare28(x0, x1, True, x2)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(Nothing, Nothing, x0)
new_ltEs18(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs34(x0, x1, ty_Integer)
new_esEs34(x0, x1, app(ty_Maybe, x2))
new_ltEs7(EQ, EQ)
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs19(x0, x1, ty_Integer)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_ltEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Bool)
new_ltEs14(Right(x0), Right(x1), x2, ty_Float)
new_compare27(x0, x1, x2)
new_esEs31(x0, x1, app(ty_Ratio, x2))
new_esEs6(Just(x0), Just(x1), app(ty_[], x2))
new_compare14(x0, x1, True, x2, x3)
new_ltEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs13([], :(x0, x1), x2)
new_compare25(x0, x1, False, x2, x3, x4)
new_esEs7(Left(x0), Left(x1), ty_Integer, x2)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs7(Right(x0), Right(x1), x2, ty_@0)
new_esEs31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Integer)
new_ltEs5(x0, x1, ty_Integer)
new_ltEs21(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs7(EQ, LT)
new_ltEs7(LT, EQ)
new_esEs20(x0, x1, ty_Ordering)
new_esEs17(Float(x0, x1), Float(x2, x3))
new_compare25(x0, x1, True, x2, x3, x4)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_lt19(x0, x1, ty_Ordering)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs16(x0, x1)
new_lt4(x0, x1, app(ty_Maybe, x2))
new_esEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs14(Left(x0), Left(x1), ty_Char, x2)
new_sr(x0, x1)
new_ltEs19(x0, x1, ty_Double)
new_compare7(Float(x0, x1), Float(x2, x3))
new_ltEs9(x0, x1)
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_compare19(x0, x1, x2, x3)
new_lt7(x0, x1)
new_lt4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, ty_Int)
new_esEs26(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat0(Zero, x0)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs32(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_ltEs7(LT, LT)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs27(x0, x1, ty_Bool)
new_lt5(x0, x1, x2, x3, x4)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare29(x0, x1, app(app(ty_@2, x2), x3))
new_lt4(x0, x1, ty_Ordering)
new_esEs34(x0, x1, app(ty_Ratio, x2))
new_primEqNat0(Zero, Succ(x0))
new_lt19(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Int)
new_esEs15(Integer(x0), Integer(x1))
new_esEs26(x0, x1, ty_Double)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs28(x0, x1, ty_@0)
new_primPlusNat1(Succ(x0), Zero)
new_esEs22(x0, x1, ty_Integer)
new_ltEs14(Left(x0), Left(x1), ty_@0, x2)
new_primMulInt(Neg(x0), Neg(x1))
new_ltEs19(x0, x1, ty_Int)
new_esEs7(Left(x0), Left(x1), ty_Double, x2)
new_compare29(x0, x1, ty_Integer)
new_esEs14(True, True)
new_esEs21(x0, x1, ty_Char)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(Just(x0), Just(x1), ty_Integer)
new_compare29(x0, x1, app(ty_[], x2))
new_ltEs18(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, ty_Int)
new_esEs7(Right(x0), Right(x1), x2, ty_Int)
new_primEqNat0(Zero, Zero)
new_esEs16(Double(x0, x1), Double(x2, x3))
new_esEs12(Char(x0), Char(x1))
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_lt4(x0, x1, ty_Char)
new_esEs20(x0, x1, ty_Bool)
new_esEs8(x0, x1, ty_Float)
new_compare1([], :(x0, x1), x2)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_Integer)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs32(x0, x1, ty_@0)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(Left(x0), Left(x1), ty_Int, x2)
new_primCompAux00(x0, LT)
new_esEs27(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(ty_[], x2))
new_ltEs5(x0, x1, ty_Double)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs18(Just(x0), Just(x1), ty_Char)
new_primMulNat0(Zero, Zero)
new_lt9(x0, x1)
new_compare29(x0, x1, ty_Double)
new_esEs34(x0, x1, app(ty_[], x2))
new_ltEs5(x0, x1, ty_@0)
new_lt17(x0, x1, x2)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_ltEs21(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs31(x0, x1, ty_Bool)
new_ltEs14(Left(x0), Left(x1), ty_Float, x2)
new_esEs32(x0, x1, ty_Float)
new_esEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs8(x0, x1, ty_Ordering)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_compare10(x0, x1, True)
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Ordering)
new_primEqNat0(Succ(x0), Succ(x1))
new_ltEs19(x0, x1, ty_Bool)
new_esEs28(x0, x1, ty_Double)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_@0)
new_pePe(True, x0)
new_esEs19(x0, x1, ty_Float)
new_lt19(x0, x1, app(ty_[], x2))
new_esEs8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_lt16(x0, x1)
new_compare29(x0, x1, ty_Bool)
new_lt10(x0, x1, x2)
new_esEs7(Right(x0), Right(x1), x2, ty_Integer)
new_esEs32(x0, x1, app(app(ty_Either, x2), x3))
new_compare11(x0, x1, True)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs32(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs33(x0, x1, app(ty_[], x2))
new_esEs34(x0, x1, ty_Char)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1, ty_@0)
new_esEs6(Just(x0), Just(x1), ty_Ordering)
new_esEs23(x0, x1, ty_@0)
new_ltEs14(Right(x0), Right(x1), x2, ty_Int)
new_ltEs5(x0, x1, ty_Char)
new_ltEs21(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Float)
new_lt18(x0, x1, x2)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_compare29(x0, x1, ty_Ordering)
new_ltEs21(x0, x1, ty_@0)
new_esEs8(x0, x1, ty_Int)
new_lt14(x0, x1, x2, x3)
new_ltEs12(False, False)
new_compare210(x0, x1, True, x2, x3)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Just(x0), Just(x1), ty_Bool)
new_compare32(Integer(x0), Integer(x1))
new_lt19(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_Int)
new_primMulNat0(Succ(x0), Succ(x1))
new_compare29(x0, x1, ty_Float)
new_ltEs21(x0, x1, ty_Integer)
new_esEs6(Just(x0), Just(x1), ty_Float)
new_ltEs5(x0, x1, ty_Float)
new_ltEs18(Just(x0), Just(x1), ty_Float)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_Bool)
new_esEs31(x0, x1, ty_Double)
new_primCmpNat1(Zero, x0)
new_ltEs14(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs8(x0, x1)
new_ltEs18(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs14(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs33(x0, x1, app(ty_Ratio, x2))
new_compare13(x0, x1, False, x2, x3)
new_esEs34(x0, x1, ty_Float)
new_primPlusNat1(Zero, Zero)
new_esEs23(x0, x1, ty_Double)
new_ltEs18(Just(x0), Just(x1), ty_Ordering)
new_primCmpNat2(Zero, Zero)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(x0, x1, ty_Bool)
new_esEs34(x0, x1, ty_Ordering)
new_ltEs18(Just(x0), Just(x1), app(ty_[], x2))
new_esEs33(x0, x1, app(ty_Maybe, x2))
new_ltEs5(x0, x1, app(ty_[], x2))
new_asAs(False, x0)
new_ltEs20(x0, x1, ty_Char)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs31(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs8(x0, x1, ty_Integer)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs33(x0, x1, ty_Ordering)
new_ltEs18(Just(x0), Just(x1), ty_Bool)
new_compare14(x0, x1, False, x2, x3)
new_primCmpNat1(Succ(x0), x1)
new_esEs34(x0, x1, ty_Bool)
new_esEs33(x0, x1, ty_Double)
new_esEs24(x0, x1, ty_Integer)
new_esEs27(x0, x1, ty_@0)
new_esEs7(Left(x0), Left(x1), ty_Int, x2)
new_ltEs14(Right(x0), Right(x1), x2, ty_Double)
new_lt4(x0, x1, ty_Float)
new_ltEs5(x0, x1, app(app(ty_Either, x2), x3))
new_esEs19(x0, x1, ty_Char)
new_lt4(x0, x1, ty_Double)
new_esEs19(x0, x1, ty_Ordering)
new_esEs8(x0, x1, app(ty_Ratio, x2))
new_esEs33(x0, x1, ty_Int)
new_esEs10(@0, @0)
new_esEs31(x0, x1, ty_@0)
new_esEs33(x0, x1, ty_@0)
new_esEs11(x0, x1)
new_esEs20(x0, x1, ty_Float)
new_ltEs14(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs7(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs14(Right(x0), Right(x1), x2, ty_Char)
new_esEs9(GT, GT)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs27(x0, x1, ty_Char)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_compare11(x0, x1, False)
new_compare23(x0, x1, False)
new_compare12(x0, x1, True, x2, x3, x4)
new_esEs7(Right(x0), Right(x1), x2, ty_Double)
new_esEs28(x0, x1, ty_Bool)
new_esEs33(x0, x1, app(app(ty_Either, x2), x3))
new_compare24(x0, x1, True)
new_compare36(x0, x1, x2, x3)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_compare15(x0, x1, x2, x3)
new_primEqNat0(Succ(x0), Zero)
new_esEs13([], [], x0)
new_esEs23(x0, x1, ty_Ordering)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs7(Left(x0), Right(x1), x2, x3)
new_esEs7(Right(x0), Left(x1), x2, x3)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_esEs34(x0, x1, ty_Int)
new_compare9(x0, x1, x2, x3, x4)
new_lt20(x0, x1, ty_Int)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs21(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Integer)
new_esEs33(x0, x1, ty_Bool)
new_lt4(x0, x1, app(app(ty_Either, x2), x3))
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs23(x0, x1, ty_Int)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs5(x0, x1, app(app(ty_@2, x2), x3))
new_esEs33(x0, x1, ty_Char)
new_lt4(x0, x1, ty_@0)
new_esEs23(x0, x1, ty_Char)
new_esEs28(x0, x1, ty_Ordering)
new_ltEs18(Just(x0), Just(x1), ty_Double)
new_ltEs20(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_lt20(x0, x1, ty_@0)
new_compare1([], [], x0)
new_esEs9(EQ, EQ)
new_pePe(False, x0)
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs5(x0, x1, app(ty_Ratio, x2))
new_ltEs14(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs6(Just(x0), Just(x1), ty_Char)
new_esEs25(x0, x1, ty_Integer)
new_esEs31(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_Integer)
new_compare12(x0, x1, False, x2, x3, x4)
new_esEs8(x0, x1, app(ty_Maybe, x2))
new_primCompAux00(x0, EQ)
new_esEs19(x0, x1, ty_Int)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs14(True, False)
new_esEs14(False, True)
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_lt4(x0, x1, ty_Integer)
new_esEs7(Left(x0), Left(x1), ty_@0, x2)
new_ltEs14(Right(x0), Right(x1), x2, ty_@0)
new_fsEs(x0)
new_esEs22(x0, x1, ty_Float)
new_ltEs14(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs32(x0, x1, app(ty_Ratio, x2))
new_esEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_primCmpNat2(Succ(x0), Succ(x1))
new_compare110(x0, x1, False, x2, x3)
new_lt4(x0, x1, ty_Bool)
new_asAs(True, x0)
new_esEs21(x0, x1, ty_Bool)
new_esEs4(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs6(Nothing, Just(x0), x1)
new_esEs6(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs21(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Just(x0), Nothing, x1)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_compare29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs8(x0, x1, app(ty_[], x2))
new_esEs31(x0, x1, ty_Integer)
new_esEs13(:(x0, x1), [], x2)
new_ltEs14(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs8(x0, x1, ty_Char)
new_lt19(x0, x1, ty_Float)
new_compare33(x0, x1, x2, x3)
new_ltEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs22(x0, x1, ty_@0)
new_esEs34(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_Char)
new_ltEs12(False, True)
new_ltEs12(True, False)
new_compare6(Double(x0, x1), Double(x2, x3))
new_ltEs20(x0, x1, ty_@0)
new_esEs22(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_@0)
new_compare35(x0, x1, x2, x3)
new_ltEs14(Right(x0), Right(x1), x2, ty_Integer)
new_lt19(x0, x1, ty_Double)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1, ty_Bool)
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs7(Left(x0), Left(x1), ty_Char, x2)
new_esEs7(Right(x0), Right(x1), x2, ty_Float)
new_ltEs14(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs26(x0, x1, ty_Char)
new_ltEs5(x0, x1, ty_Int)
new_lt4(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_Double)
new_esEs19(x0, x1, ty_@0)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_compare13(x0, x1, True, x2, x3)
new_esEs34(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs21(x0, x1, ty_Bool)
new_ltEs14(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs21(x0, x1, ty_Double)
new_lt12(x0, x1)
new_esEs8(x0, x1, ty_Bool)
new_ltEs21(x0, x1, ty_Char)
new_lt13(x0, x1)
new_esEs31(x0, x1, ty_Ordering)
new_ltEs14(Right(x0), Right(x1), x2, ty_Bool)
new_compare1(:(x0, x1), [], x2)
new_compare10(x0, x1, False)
new_primMulNat0(Succ(x0), Zero)
new_ltEs19(x0, x1, ty_Float)
new_ltEs14(Left(x0), Right(x1), x2, x3)
new_esEs23(x0, x1, ty_Float)
new_ltEs14(Right(x0), Left(x1), x2, x3)
new_compare29(x0, x1, ty_Int)
new_esEs20(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, ty_Int)
new_esEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs20(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Float)
new_compare31(x0, x1)
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs31(x0, x1, ty_Char)
new_esEs6(Just(x0), Just(x1), ty_Int)
new_ltEs7(LT, GT)
new_ltEs7(GT, LT)
new_esEs21(x0, x1, ty_Integer)
new_esEs22(x0, x1, app(ty_[], x2))
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs22(x0, x1, ty_Double)
new_compare110(x0, x1, True, x2, x3)
new_lt20(x0, x1, app(ty_[], x2))
new_ltEs13(x0, x1)
new_ltEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs34(x0, x1, ty_@0)
new_esEs31(x0, x1, ty_Int)
new_lt4(x0, x1, ty_Int)
new_ltEs11(x0, x1, x2)
new_lt20(x0, x1, ty_Float)
new_not(True)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs31(x0, x1, ty_Float)
new_esEs20(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Float)
new_esEs19(x0, x1, app(ty_[], x2))
new_esEs18(:%(x0, x1), :%(x2, x3), x4)
new_esEs6(Nothing, Nothing, x0)
new_esEs28(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Ordering)
new_ltEs14(Left(x0), Left(x1), ty_Double, x2)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Just(x0), Just(x1), ty_Integer)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_not(False)
new_compare29(x0, x1, app(ty_Ratio, x2))
new_lt8(x0, x1)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_compare28(x0, x1, False, x2)
new_esEs32(x0, x1, ty_Integer)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, ty_Char)
new_esEs6(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare8(:%(x0, x1), :%(x2, x3), ty_Integer)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs22(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_Integer)
new_esEs8(x0, x1, ty_@0)
new_compare26(Left(x0), Left(x1), False, x2, x3)
new_esEs32(x0, x1, app(ty_Maybe, x2))
new_ltEs12(True, True)
new_esEs27(x0, x1, ty_Float)
new_lt15(x0, x1)
new_lt11(x0, x1, x2, x3)
new_esEs26(x0, x1, ty_Ordering)
new_esEs7(Left(x0), Left(x1), ty_Float, x2)
new_esEs27(x0, x1, ty_Double)
new_esEs6(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs34(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs33(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Ordering)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs13(:(x0, x1), :(x2, x3), x4)
new_esEs22(x0, x1, ty_Char)
new_lt20(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Bool)
new_esEs34(x0, x1, ty_Double)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_ltEs21(x0, x1, ty_Float)
new_ltEs10(x0, x1)
new_ltEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_compare29(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs14(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs5(x0, x1, ty_Ordering)
new_esEs8(x0, x1, ty_Double)
new_compare29(x0, x1, ty_Char)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs6(Just(x0), Just(x1), ty_@0)
new_esEs31(x0, x1, app(app(ty_Either, x2), x3))
new_compare1(:(x0, x1), :(x2, x3), x4)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs31(x0, x1, app(ty_[], x2))
new_esEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs6(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs19(x0, x1, ty_Double)
new_esEs14(False, False)
new_ltEs21(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs32(x0, x1, ty_Char)
new_ltEs21(x0, x1, ty_Double)
new_esEs32(x0, x1, ty_Int)
new_ltEs14(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpNat2(Succ(x0), Zero)
new_esEs7(Right(x0), Right(x1), x2, ty_Char)
new_esEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_compare34(x0, x1, x2, x3)
new_compare18(x0, x1)
new_esEs32(x0, x1, ty_Bool)
new_esEs7(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs18(Just(x0), Just(x1), ty_Int)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare26(Right(x0), Right(x1), False, x2, x3)
new_esEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs17(x0, x1, x2)
new_primPlusNat0(Succ(x0), x1)
new_esEs20(x0, x1, ty_Integer)
new_primCmpNat0(x0, Zero)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_ltEs7(GT, EQ)
new_ltEs7(EQ, GT)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs32(x0, x1, ty_Double)
new_ltEs7(GT, GT)
new_esEs9(LT, LT)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_primCompAux0(x0, x1, x2, x3)
new_compare29(x0, x1, ty_@0)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_compare26(x0, x1, True, x2, x3)
new_compare26(Right(x0), Left(x1), False, x2, x3)
new_compare26(Left(x0), Right(x1), False, x2, x3)
new_ltEs18(Nothing, Just(x0), x1)
new_compare111(x0, x1, False, x2)
new_compare29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Ordering)
new_primCmpNat0(x0, Succ(x1))

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

new_esEs33(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs33(x0, x1, app(app(ty_@2, x2), x3))
new_esEs32(x0, x1, app(ty_[], x2))
new_esEs33(x0, x1, ty_Float)
new_esEs32(x0, x1, ty_Ordering)
new_esEs32(x0, x1, ty_@0)
new_esEs32(x0, x1, ty_Float)
new_esEs32(x0, x1, app(app(ty_Either, x2), x3))
new_esEs32(x0, x1, app(app(ty_@2, x2), x3))
new_esEs33(x0, x1, app(ty_[], x2))
new_esEs33(x0, x1, app(ty_Ratio, x2))
new_esEs33(x0, x1, app(ty_Maybe, x2))
new_esEs33(x0, x1, ty_Ordering)
new_esEs33(x0, x1, ty_Double)
new_esEs33(x0, x1, ty_Int)
new_esEs33(x0, x1, ty_@0)
new_esEs33(x0, x1, app(app(ty_Either, x2), x3))
new_esEs33(x0, x1, ty_Bool)
new_esEs33(x0, x1, ty_Char)
new_esEs32(x0, x1, app(ty_Ratio, x2))
new_compare33(x0, x1, x2, x3)
new_esEs32(x0, x1, ty_Integer)
new_esEs32(x0, x1, app(ty_Maybe, x2))
new_esEs33(x0, x1, ty_Integer)
new_esEs32(x0, x1, ty_Char)
new_esEs32(x0, x1, ty_Int)
new_compare34(x0, x1, x2, x3)
new_esEs32(x0, x1, ty_Bool)
new_esEs32(x0, x1, ty_Double)



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

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

new_splitGT3(Right(zxw300), zxw31, zxw32, zxw33, zxw34, Right(zxw400), h, ba, bb) → new_splitGT22(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs9(new_compare26(Right(zxw400), Right(zxw300), new_esEs34(zxw400, zxw300, ba), h, ba), GT), h, ba, bb)
new_splitGT3(Left(zxw300), zxw31, zxw32, zxw33, zxw34, Right(zxw400), h, ba, bb) → new_splitGT21(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs9(new_compare26(Right(zxw400), Left(zxw300), False, h, ba), GT), h, ba, bb)
new_splitGT21(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, False, h, ba, bb) → new_splitGT11(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs9(new_compare35(zxw400, zxw300, h, ba), LT), h, ba, bb)
new_splitGT21(zxw300, zxw31, zxw32, zxw33, Branch(zxw340, zxw341, zxw342, zxw343, zxw344), zxw400, True, h, ba, bb) → new_splitGT3(zxw340, zxw341, zxw342, zxw343, zxw344, Right(zxw400), h, ba, bb)
new_splitGT12(zxw30, zxw31, zxw32, zxw33, zxw34, zxw35, True, bf, bg, bh) → new_splitGT0(zxw33, zxw35, bf, bg, bh)
new_splitGT22(zxw30, zxw31, zxw32, zxw33, zxw34, zxw35, True, bf, bg, bh) → new_splitGT0(zxw34, zxw35, bf, bg, bh)
new_splitGT22(zxw30, zxw31, zxw32, zxw33, zxw34, zxw35, False, bf, bg, bh) → new_splitGT12(zxw30, zxw31, zxw32, zxw33, zxw34, zxw35, new_esEs9(new_compare36(zxw35, zxw30, bf, bg), LT), bf, bg, bh)
new_splitGT0(Branch(zxw340, zxw341, zxw342, zxw343, zxw344), zxw400, h, ba, bb) → new_splitGT3(zxw340, zxw341, zxw342, zxw343, zxw344, Right(zxw400), h, ba, bb)
new_splitGT11(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, True, h, ba, bb) → new_splitGT0(zxw33, zxw400, h, ba, bb)

The TRS R consists of the following rules:

new_compare36(zxw35, zxw30, bf, bg) → new_compare26(Right(zxw35), Right(zxw30), new_esEs31(zxw35, zxw30, bg), bf, bg)
new_esEs9(GT, LT) → False
new_esEs9(EQ, LT) → False
new_esEs9(LT, LT) → True
new_esEs31(zxw35, zxw30, ty_Ordering) → new_esEs9(zxw35, zxw30)
new_esEs31(zxw35, zxw30, ty_Char) → new_esEs12(zxw35, zxw30)
new_esEs31(zxw35, zxw30, ty_@0) → new_esEs10(zxw35, zxw30)
new_esEs31(zxw35, zxw30, app(app(app(ty_@3, beb), bec), bed)) → new_esEs4(zxw35, zxw30, beb, bec, bed)
new_esEs31(zxw35, zxw30, ty_Float) → new_esEs17(zxw35, zxw30)
new_esEs31(zxw35, zxw30, app(app(ty_Either, bdh), bea)) → new_esEs7(zxw35, zxw30, bdh, bea)
new_esEs31(zxw35, zxw30, app(ty_Ratio, bdc)) → new_esEs18(zxw35, zxw30, bdc)
new_esEs31(zxw35, zxw30, app(app(ty_@2, bdf), bdg)) → new_esEs5(zxw35, zxw30, bdf, bdg)
new_esEs31(zxw35, zxw30, ty_Integer) → new_esEs15(zxw35, zxw30)
new_esEs31(zxw35, zxw30, ty_Double) → new_esEs16(zxw35, zxw30)
new_esEs31(zxw35, zxw30, app(ty_[], bdd)) → new_esEs13(zxw35, zxw30, bdd)
new_esEs31(zxw35, zxw30, ty_Int) → new_esEs11(zxw35, zxw30)
new_esEs31(zxw35, zxw30, ty_Bool) → new_esEs14(zxw35, zxw30)
new_esEs31(zxw35, zxw30, app(ty_Maybe, bde)) → new_esEs6(zxw35, zxw30, bde)
new_compare26(zxw790, zxw800, True, gh, ha) → EQ
new_compare26(Right(zxw7900), Right(zxw8000), False, gh, ha) → new_compare14(zxw7900, zxw8000, new_ltEs20(zxw7900, zxw8000, ha), gh, ha)
new_ltEs20(zxw7900, zxw8000, app(ty_Maybe, bbc)) → new_ltEs18(zxw7900, zxw8000, bbc)
new_ltEs20(zxw7900, zxw8000, ty_Int) → new_ltEs9(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, ty_@0) → new_ltEs8(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, app(app(ty_@2, baf), bag)) → new_ltEs4(zxw7900, zxw8000, baf, bag)
new_ltEs20(zxw7900, zxw8000, ty_Float) → new_ltEs16(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, ty_Bool) → new_ltEs12(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, app(ty_Ratio, bbb)) → new_ltEs17(zxw7900, zxw8000, bbb)
new_ltEs20(zxw7900, zxw8000, ty_Double) → new_ltEs15(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, ty_Integer) → new_ltEs13(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, app(app(app(ty_@3, bab), bac), bad)) → new_ltEs6(zxw7900, zxw8000, bab, bac, bad)
new_ltEs20(zxw7900, zxw8000, app(app(ty_Either, bah), bba)) → new_ltEs14(zxw7900, zxw8000, bah, bba)
new_ltEs20(zxw7900, zxw8000, app(ty_[], bae)) → new_ltEs11(zxw7900, zxw8000, bae)
new_ltEs20(zxw7900, zxw8000, ty_Char) → new_ltEs10(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, ty_Ordering) → new_ltEs7(zxw7900, zxw8000)
new_compare14(zxw242, zxw243, False, def, deg) → GT
new_compare14(zxw242, zxw243, True, def, deg) → LT
new_ltEs7(LT, EQ) → True
new_ltEs7(GT, GT) → True
new_ltEs7(EQ, EQ) → True
new_ltEs7(GT, LT) → False
new_ltEs7(GT, EQ) → False
new_ltEs7(EQ, GT) → True
new_ltEs7(EQ, LT) → False
new_ltEs7(LT, LT) → True
new_ltEs7(LT, GT) → True
new_ltEs10(zxw7900, zxw8000) → new_fsEs(new_compare17(zxw7900, zxw8000))
new_compare17(Char(zxw79000), Char(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_fsEs(zxw259) → new_not(new_esEs9(zxw259, GT))
new_esEs9(LT, GT) → False
new_esEs9(EQ, GT) → False
new_esEs9(GT, GT) → True
new_not(False) → True
new_not(True) → False
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_ltEs11(zxw7900, zxw8000, he) → new_fsEs(new_compare1(zxw7900, zxw8000, he))
new_compare1([], :(zxw80000, zxw80001), he) → LT
new_compare1(:(zxw79000, zxw79001), :(zxw80000, zxw80001), he) → new_primCompAux0(zxw79000, zxw80000, new_compare1(zxw79001, zxw80001, he), he)
new_compare1(:(zxw79000, zxw79001), [], he) → GT
new_compare1([], [], he) → EQ
new_primCompAux0(zxw79000, zxw80000, zxw272, he) → new_primCompAux00(zxw272, new_compare29(zxw79000, zxw80000, he))
new_compare29(zxw79000, zxw80000, ty_Char) → new_compare17(zxw79000, zxw80000)
new_compare29(zxw79000, zxw80000, ty_Bool) → new_compare31(zxw79000, zxw80000)
new_compare29(zxw79000, zxw80000, app(app(ty_@2, ccf), ccg)) → new_compare19(zxw79000, zxw80000, ccf, ccg)
new_compare29(zxw79000, zxw80000, app(ty_[], cce)) → new_compare1(zxw79000, zxw80000, cce)
new_compare29(zxw79000, zxw80000, app(app(app(ty_@3, ccb), ccc), ccd)) → new_compare9(zxw79000, zxw80000, ccb, ccc, ccd)
new_compare29(zxw79000, zxw80000, ty_Int) → new_compare16(zxw79000, zxw80000)
new_compare29(zxw79000, zxw80000, ty_Integer) → new_compare32(zxw79000, zxw80000)
new_compare29(zxw79000, zxw80000, app(ty_Maybe, cdc)) → new_compare27(zxw79000, zxw80000, cdc)
new_compare29(zxw79000, zxw80000, app(ty_Ratio, cdb)) → new_compare8(zxw79000, zxw80000, cdb)
new_compare29(zxw79000, zxw80000, ty_Float) → new_compare7(zxw79000, zxw80000)
new_compare29(zxw79000, zxw80000, ty_Double) → new_compare6(zxw79000, zxw80000)
new_compare29(zxw79000, zxw80000, app(app(ty_Either, cch), cda)) → new_compare15(zxw79000, zxw80000, cch, cda)
new_compare29(zxw79000, zxw80000, ty_Ordering) → new_compare18(zxw79000, zxw80000)
new_compare29(zxw79000, zxw80000, ty_@0) → new_compare30(zxw79000, zxw80000)
new_primCompAux00(zxw276, LT) → LT
new_primCompAux00(zxw276, EQ) → zxw276
new_primCompAux00(zxw276, GT) → GT
new_compare30(@0, @0) → EQ
new_compare18(zxw79000, zxw80000) → new_compare24(zxw79000, zxw80000, new_esEs9(zxw79000, zxw80000))
new_esEs9(GT, EQ) → False
new_esEs9(EQ, EQ) → True
new_esEs9(LT, EQ) → False
new_compare24(zxw79000, zxw80000, False) → new_compare11(zxw79000, zxw80000, new_ltEs7(zxw79000, zxw80000))
new_compare24(zxw79000, zxw80000, True) → EQ
new_compare11(zxw79000, zxw80000, False) → GT
new_compare11(zxw79000, zxw80000, True) → LT
new_compare15(zxw790, zxw800, gh, ha) → new_compare26(zxw790, zxw800, new_esEs7(zxw790, zxw800, gh, ha), gh, ha)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Bool, bef) → new_esEs14(zxw4000, zxw3000)
new_esEs7(Right(zxw4000), Left(zxw3000), bfh, bef) → False
new_esEs7(Left(zxw4000), Right(zxw3000), bfh, bef) → False
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, app(app(ty_@2, bgd), bge)) → new_esEs5(zxw4000, zxw3000, bgd, bge)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Int, bef) → new_esEs11(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), app(app(ty_@2, bfa), bfb), bef) → new_esEs5(zxw4000, zxw3000, bfa, bfb)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Ordering, bef) → new_esEs9(zxw4000, zxw3000)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, app(ty_[], bgb)) → new_esEs13(zxw4000, zxw3000, bgb)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Integer, bef) → new_esEs15(zxw4000, zxw3000)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, app(app(app(ty_@3, bgh), bha), bhb)) → new_esEs4(zxw4000, zxw3000, bgh, bha, bhb)
new_esEs7(Left(zxw4000), Left(zxw3000), app(ty_Ratio, bee), bef) → new_esEs18(zxw4000, zxw3000, bee)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_@0, bef) → new_esEs10(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), app(app(app(ty_@3, bfe), bff), bfg), bef) → new_esEs4(zxw4000, zxw3000, bfe, bff, bfg)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Double, bef) → new_esEs16(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Float, bef) → new_esEs17(zxw4000, zxw3000)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Char, bef) → new_esEs12(zxw4000, zxw3000)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), app(ty_[], beg), bef) → new_esEs13(zxw4000, zxw3000, beg)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, app(ty_Ratio, bga)) → new_esEs18(zxw4000, zxw3000, bga)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_compare26(Left(zxw7900), Right(zxw8000), False, gh, ha) → LT
new_compare26(Right(zxw7900), Left(zxw8000), False, gh, ha) → GT
new_compare26(Left(zxw7900), Left(zxw8000), False, gh, ha) → new_compare13(zxw7900, zxw8000, new_ltEs19(zxw7900, zxw8000, gh), gh, ha)
new_esEs6(Just(zxw4000), Just(zxw3000), app(ty_Maybe, fc)) → new_esEs6(zxw4000, zxw3000, fc)
new_esEs7(Left(zxw4000), Left(zxw3000), app(app(ty_Either, bfc), bfd), bef) → new_esEs7(zxw4000, zxw3000, bfc, bfd)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, app(ty_Maybe, bgc)) → new_esEs6(zxw4000, zxw3000, bgc)
new_esEs6(Just(zxw4000), Just(zxw3000), app(app(ty_Either, fg), fh)) → new_esEs7(zxw4000, zxw3000, fg, fh)
new_esEs7(Left(zxw4000), Left(zxw3000), app(ty_Maybe, beh), bef) → new_esEs6(zxw4000, zxw3000, beh)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, app(app(ty_Either, bgf), bgg)) → new_esEs7(zxw4000, zxw3000, bgf, bgg)
new_esEs6(Just(zxw4000), Just(zxw3000), app(app(ty_@2, fd), ff)) → new_esEs5(zxw4000, zxw3000, fd, ff)
new_esEs6(Nothing, Nothing, eh) → True
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs6(Nothing, Just(zxw3000), eh) → False
new_esEs6(Just(zxw4000), Nothing, eh) → False
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), app(app(app(ty_@3, ga), gb), gc)) → new_esEs4(zxw4000, zxw3000, ga, gb, gc)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_@0) → new_esEs10(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), app(ty_[], fb)) → new_esEs13(zxw4000, zxw3000, fb)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Char) → new_esEs12(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Float) → new_esEs17(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), app(ty_Ratio, fa)) → new_esEs18(zxw4000, zxw3000, fa)
new_esEs18(:%(zxw4000, zxw4001), :%(zxw3000, zxw3001), dee) → new_asAs(new_esEs25(zxw4000, zxw3000, dee), new_esEs24(zxw4001, zxw3001, dee))
new_esEs25(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs25(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs24(zxw4001, zxw3001, ty_Integer) → new_esEs15(zxw4001, zxw3001)
new_esEs24(zxw4001, zxw3001, ty_Int) → new_esEs11(zxw4001, zxw3001)
new_asAs(False, zxw230) → False
new_asAs(True, zxw230) → zxw230
new_esEs11(zxw400, zxw300) → new_primEqInt(zxw400, zxw300)
new_primEqInt(Neg(Succ(zxw40000)), Neg(Succ(zxw30000))) → new_primEqNat0(zxw40000, zxw30000)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Neg(Succ(zxw30000))) → False
new_primEqInt(Neg(Succ(zxw40000)), Neg(Zero)) → False
new_primEqInt(Pos(Succ(zxw40000)), Pos(Succ(zxw30000))) → new_primEqNat0(zxw40000, zxw30000)
new_primEqInt(Pos(Zero), Pos(Succ(zxw30000))) → False
new_primEqInt(Pos(Succ(zxw40000)), Pos(Zero)) → False
new_primEqInt(Neg(Succ(zxw40000)), Pos(zxw3000)) → False
new_primEqInt(Pos(Succ(zxw40000)), Neg(zxw3000)) → False
new_primEqInt(Neg(Zero), Pos(Succ(zxw30000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(zxw30000))) → False
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqNat0(Zero, Zero) → True
new_primEqNat0(Succ(zxw40000), Succ(zxw30000)) → new_primEqNat0(zxw40000, zxw30000)
new_primEqNat0(Zero, Succ(zxw30000)) → False
new_primEqNat0(Succ(zxw40000), Zero) → False
new_esEs15(Integer(zxw4000), Integer(zxw3000)) → new_primEqInt(zxw4000, zxw3000)
new_esEs17(Float(zxw4000, zxw4001), Float(zxw3000, zxw3001)) → new_esEs11(new_sr(zxw4000, zxw3000), new_sr(zxw4001, zxw3001))
new_sr(zxw4000, zxw3000) → new_primMulInt(zxw4000, zxw3000)
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Neg(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Pos(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulNat0(Zero, Zero) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_esEs12(Char(zxw4000), Char(zxw3000)) → new_primEqNat0(zxw4000, zxw3000)
new_esEs13([], [], ddb) → True
new_esEs13(:(zxw4000, zxw4001), :(zxw3000, zxw3001), ddb) → new_asAs(new_esEs23(zxw4000, zxw3000, ddb), new_esEs13(zxw4001, zxw3001, ddb))
new_esEs13(:(zxw4000, zxw4001), [], ddb) → False
new_esEs13([], :(zxw3000, zxw3001), ddb) → False
new_esEs23(zxw4000, zxw3000, app(app(ty_Either, ddh), dea)) → new_esEs7(zxw4000, zxw3000, ddh, dea)
new_esEs23(zxw4000, zxw3000, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, app(app(app(ty_@3, deb), dec), ded)) → new_esEs4(zxw4000, zxw3000, deb, dec, ded)
new_esEs23(zxw4000, zxw3000, app(app(ty_@2, ddf), ddg)) → new_esEs5(zxw4000, zxw3000, ddf, ddg)
new_esEs23(zxw4000, zxw3000, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, app(ty_Ratio, ddc)) → new_esEs18(zxw4000, zxw3000, ddc)
new_esEs23(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, app(ty_Maybe, dde)) → new_esEs6(zxw4000, zxw3000, dde)
new_esEs23(zxw4000, zxw3000, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, app(ty_[], ddd)) → new_esEs13(zxw4000, zxw3000, ddd)
new_esEs16(Double(zxw4000, zxw4001), Double(zxw3000, zxw3001)) → new_esEs11(new_sr(zxw4000, zxw3000), new_sr(zxw4001, zxw3001))
new_esEs10(@0, @0) → True
new_esEs5(@2(zxw4000, zxw4001), @2(zxw3000, zxw3001), dad, dae) → new_asAs(new_esEs22(zxw4000, zxw3000, dad), new_esEs21(zxw4001, zxw3001, dae))
new_esEs22(zxw4000, zxw3000, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, app(app(ty_@2, dcc), dcd)) → new_esEs5(zxw4000, zxw3000, dcc, dcd)
new_esEs22(zxw4000, zxw3000, app(ty_Maybe, dcb)) → new_esEs6(zxw4000, zxw3000, dcb)
new_esEs22(zxw4000, zxw3000, app(ty_Ratio, dbh)) → new_esEs18(zxw4000, zxw3000, dbh)
new_esEs22(zxw4000, zxw3000, app(app(ty_Either, dce), dcf)) → new_esEs7(zxw4000, zxw3000, dce, dcf)
new_esEs22(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, app(app(app(ty_@3, dcg), dch), dda)) → new_esEs4(zxw4000, zxw3000, dcg, dch, dda)
new_esEs22(zxw4000, zxw3000, app(ty_[], dca)) → new_esEs13(zxw4000, zxw3000, dca)
new_esEs22(zxw4000, zxw3000, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs21(zxw4001, zxw3001, ty_Bool) → new_esEs14(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, ty_Double) → new_esEs16(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, ty_Ordering) → new_esEs9(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, ty_Char) → new_esEs12(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, ty_Float) → new_esEs17(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, app(ty_Maybe, dah)) → new_esEs6(zxw4001, zxw3001, dah)
new_esEs21(zxw4001, zxw3001, ty_Int) → new_esEs11(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, app(ty_[], dag)) → new_esEs13(zxw4001, zxw3001, dag)
new_esEs21(zxw4001, zxw3001, ty_Integer) → new_esEs15(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, app(app(ty_@2, dba), dbb)) → new_esEs5(zxw4001, zxw3001, dba, dbb)
new_esEs21(zxw4001, zxw3001, ty_@0) → new_esEs10(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, app(app(ty_Either, dbc), dbd)) → new_esEs7(zxw4001, zxw3001, dbc, dbd)
new_esEs21(zxw4001, zxw3001, app(app(app(ty_@3, dbe), dbf), dbg)) → new_esEs4(zxw4001, zxw3001, dbe, dbf, dbg)
new_esEs21(zxw4001, zxw3001, app(ty_Ratio, daf)) → new_esEs18(zxw4001, zxw3001, daf)
new_esEs4(@3(zxw4000, zxw4001, zxw4002), @3(zxw3000, zxw3001, zxw3002), deh, dfa, dfb) → new_asAs(new_esEs28(zxw4000, zxw3000, deh), new_asAs(new_esEs27(zxw4001, zxw3001, dfa), new_esEs26(zxw4002, zxw3002, dfb)))
new_esEs28(zxw4000, zxw3000, app(ty_[], dhh)) → new_esEs13(zxw4000, zxw3000, dhh)
new_esEs28(zxw4000, zxw3000, app(app(app(ty_@3, eaf), eag), eah)) → new_esEs4(zxw4000, zxw3000, eaf, eag, eah)
new_esEs28(zxw4000, zxw3000, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, app(ty_Maybe, eaa)) → new_esEs6(zxw4000, zxw3000, eaa)
new_esEs28(zxw4000, zxw3000, app(app(ty_Either, ead), eae)) → new_esEs7(zxw4000, zxw3000, ead, eae)
new_esEs28(zxw4000, zxw3000, app(app(ty_@2, eab), eac)) → new_esEs5(zxw4000, zxw3000, eab, eac)
new_esEs28(zxw4000, zxw3000, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, app(ty_Ratio, dhg)) → new_esEs18(zxw4000, zxw3000, dhg)
new_esEs28(zxw4000, zxw3000, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_esEs27(zxw4001, zxw3001, app(ty_Ratio, dge)) → new_esEs18(zxw4001, zxw3001, dge)
new_esEs27(zxw4001, zxw3001, app(app(app(ty_@3, dhd), dhe), dhf)) → new_esEs4(zxw4001, zxw3001, dhd, dhe, dhf)
new_esEs27(zxw4001, zxw3001, app(ty_Maybe, dgg)) → new_esEs6(zxw4001, zxw3001, dgg)
new_esEs27(zxw4001, zxw3001, app(app(ty_Either, dhb), dhc)) → new_esEs7(zxw4001, zxw3001, dhb, dhc)
new_esEs27(zxw4001, zxw3001, ty_Ordering) → new_esEs9(zxw4001, zxw3001)
new_esEs27(zxw4001, zxw3001, ty_Float) → new_esEs17(zxw4001, zxw3001)
new_esEs27(zxw4001, zxw3001, ty_@0) → new_esEs10(zxw4001, zxw3001)
new_esEs27(zxw4001, zxw3001, ty_Char) → new_esEs12(zxw4001, zxw3001)
new_esEs27(zxw4001, zxw3001, ty_Double) → new_esEs16(zxw4001, zxw3001)
new_esEs27(zxw4001, zxw3001, ty_Int) → new_esEs11(zxw4001, zxw3001)
new_esEs27(zxw4001, zxw3001, app(app(ty_@2, dgh), dha)) → new_esEs5(zxw4001, zxw3001, dgh, dha)
new_esEs27(zxw4001, zxw3001, ty_Bool) → new_esEs14(zxw4001, zxw3001)
new_esEs27(zxw4001, zxw3001, app(ty_[], dgf)) → new_esEs13(zxw4001, zxw3001, dgf)
new_esEs27(zxw4001, zxw3001, ty_Integer) → new_esEs15(zxw4001, zxw3001)
new_esEs26(zxw4002, zxw3002, ty_Float) → new_esEs17(zxw4002, zxw3002)
new_esEs26(zxw4002, zxw3002, ty_Char) → new_esEs12(zxw4002, zxw3002)
new_esEs26(zxw4002, zxw3002, ty_Int) → new_esEs11(zxw4002, zxw3002)
new_esEs26(zxw4002, zxw3002, app(ty_Maybe, dfe)) → new_esEs6(zxw4002, zxw3002, dfe)
new_esEs26(zxw4002, zxw3002, app(app(app(ty_@3, dgb), dgc), dgd)) → new_esEs4(zxw4002, zxw3002, dgb, dgc, dgd)
new_esEs26(zxw4002, zxw3002, app(ty_[], dfd)) → new_esEs13(zxw4002, zxw3002, dfd)
new_esEs26(zxw4002, zxw3002, app(app(ty_Either, dfh), dga)) → new_esEs7(zxw4002, zxw3002, dfh, dga)
new_esEs26(zxw4002, zxw3002, ty_Integer) → new_esEs15(zxw4002, zxw3002)
new_esEs26(zxw4002, zxw3002, app(app(ty_@2, dff), dfg)) → new_esEs5(zxw4002, zxw3002, dff, dfg)
new_esEs26(zxw4002, zxw3002, app(ty_Ratio, dfc)) → new_esEs18(zxw4002, zxw3002, dfc)
new_esEs26(zxw4002, zxw3002, ty_Bool) → new_esEs14(zxw4002, zxw3002)
new_esEs26(zxw4002, zxw3002, ty_@0) → new_esEs10(zxw4002, zxw3002)
new_esEs26(zxw4002, zxw3002, ty_Ordering) → new_esEs9(zxw4002, zxw3002)
new_esEs26(zxw4002, zxw3002, ty_Double) → new_esEs16(zxw4002, zxw3002)
new_esEs14(False, True) → False
new_esEs14(True, False) → False
new_esEs14(True, True) → True
new_esEs14(False, False) → True
new_ltEs19(zxw7900, zxw8000, ty_Float) → new_ltEs16(zxw7900, zxw8000)
new_ltEs19(zxw7900, zxw8000, app(app(ty_@2, ca), cb)) → new_ltEs4(zxw7900, zxw8000, ca, cb)
new_ltEs19(zxw7900, zxw8000, app(ty_[], he)) → new_ltEs11(zxw7900, zxw8000, he)
new_ltEs19(zxw7900, zxw8000, ty_Char) → new_ltEs10(zxw7900, zxw8000)
new_ltEs19(zxw7900, zxw8000, ty_Bool) → new_ltEs12(zxw7900, zxw8000)
new_ltEs19(zxw7900, zxw8000, app(ty_Ratio, hh)) → new_ltEs17(zxw7900, zxw8000, hh)
new_ltEs19(zxw7900, zxw8000, app(app(app(ty_@3, hb), hc), hd)) → new_ltEs6(zxw7900, zxw8000, hb, hc, hd)
new_ltEs19(zxw7900, zxw8000, ty_Int) → new_ltEs9(zxw7900, zxw8000)
new_ltEs19(zxw7900, zxw8000, app(app(ty_Either, hf), hg)) → new_ltEs14(zxw7900, zxw8000, hf, hg)
new_ltEs19(zxw7900, zxw8000, ty_@0) → new_ltEs8(zxw7900, zxw8000)
new_ltEs19(zxw7900, zxw8000, ty_Double) → new_ltEs15(zxw7900, zxw8000)
new_ltEs19(zxw7900, zxw8000, ty_Integer) → new_ltEs13(zxw7900, zxw8000)
new_ltEs19(zxw7900, zxw8000, ty_Ordering) → new_ltEs7(zxw7900, zxw8000)
new_ltEs19(zxw7900, zxw8000, app(ty_Maybe, baa)) → new_ltEs18(zxw7900, zxw8000, baa)
new_compare13(zxw235, zxw236, False, bch, bda) → GT
new_compare13(zxw235, zxw236, True, bch, bda) → LT
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Char) → new_ltEs10(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Integer) → new_ltEs13(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(ty_Ratio, dab)) → new_ltEs17(zxw79000, zxw80000, dab)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(app(app(ty_@3, chb), chc), chd)) → new_ltEs6(zxw79000, zxw80000, chb, chc, chd)
new_ltEs18(Nothing, Nothing, baa) → True
new_ltEs18(Just(zxw79000), Nothing, baa) → False
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Double) → new_ltEs15(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(ty_[], che)) → new_ltEs11(zxw79000, zxw80000, che)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(app(ty_@2, chf), chg)) → new_ltEs4(zxw79000, zxw80000, chf, chg)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Bool) → new_ltEs12(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Ordering) → new_ltEs7(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Float) → new_ltEs16(zxw79000, zxw80000)
new_ltEs18(Nothing, Just(zxw80000), baa) → True
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Int) → new_ltEs9(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_@0) → new_ltEs8(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(ty_Maybe, dac)) → new_ltEs18(zxw79000, zxw80000, dac)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(ty_Maybe, cha)) → new_ltEs18(zxw79000, zxw80000, cha)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(app(ty_Either, chh), daa)) → new_ltEs14(zxw79000, zxw80000, chh, daa)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(app(ty_Either, cgf), cgg)) → new_ltEs14(zxw79000, zxw80000, cgf, cgg)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(app(ty_Either, cfd), cfe), hg) → new_ltEs14(zxw79000, zxw80000, cfd, cfe)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(ty_Maybe, cfg), hg) → new_ltEs18(zxw79000, zxw80000, cfg)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Bool) → new_ltEs12(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(ty_[], cgc)) → new_ltEs11(zxw79000, zxw80000, cgc)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Bool, hg) → new_ltEs12(zxw79000, zxw80000)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(ty_Ratio, cff), hg) → new_ltEs17(zxw79000, zxw80000, cff)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(app(app(ty_@3, cfh), cga), cgb)) → new_ltEs6(zxw79000, zxw80000, cfh, cga, cgb)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Float, hg) → new_ltEs16(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Float) → new_ltEs16(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Double) → new_ltEs15(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(app(ty_@2, cgd), cge)) → new_ltEs4(zxw79000, zxw80000, cgd, cge)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Double, hg) → new_ltEs15(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Left(zxw80000), hf, hg) → False
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Int, hg) → new_ltEs9(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Char) → new_ltEs10(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_@0) → new_ltEs8(zxw79000, zxw80000)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(app(app(ty_@3, cef), ceg), ceh), hg) → new_ltEs6(zxw79000, zxw80000, cef, ceg, ceh)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_@0, hg) → new_ltEs8(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Ordering) → new_ltEs7(zxw79000, zxw80000)
new_ltEs14(Left(zxw79000), Right(zxw80000), hf, hg) → True
new_ltEs14(Left(zxw79000), Left(zxw80000), app(app(ty_@2, cfb), cfc), hg) → new_ltEs4(zxw79000, zxw80000, cfb, cfc)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(ty_[], cfa), hg) → new_ltEs11(zxw79000, zxw80000, cfa)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Integer, hg) → new_ltEs13(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Int) → new_ltEs9(zxw79000, zxw80000)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Ordering, hg) → new_ltEs7(zxw79000, zxw80000)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Char, hg) → new_ltEs10(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(ty_Ratio, cgh)) → new_ltEs17(zxw79000, zxw80000, cgh)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Integer) → new_ltEs13(zxw79000, zxw80000)
new_ltEs13(zxw7900, zxw8000) → new_fsEs(new_compare32(zxw7900, zxw8000))
new_compare32(Integer(zxw79000), Integer(zxw80000)) → new_primCmpInt(zxw79000, zxw80000)
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_ltEs17(zxw7900, zxw8000, hh) → new_fsEs(new_compare8(zxw7900, zxw8000, hh))
new_compare8(:%(zxw79000, zxw79001), :%(zxw80000, zxw80001), ty_Integer) → new_compare32(new_sr0(zxw79000, zxw80001), new_sr0(zxw80000, zxw79001))
new_compare8(:%(zxw79000, zxw79001), :%(zxw80000, zxw80001), ty_Int) → new_compare16(new_sr(zxw79000, zxw80001), new_sr(zxw80000, zxw79001))
new_compare16(zxw79, zxw80) → new_primCmpInt(zxw79, zxw80)
new_sr0(Integer(zxw800000), Integer(zxw790010)) → Integer(new_primMulInt(zxw800000, zxw790010))
new_ltEs9(zxw7900, zxw8000) → new_fsEs(new_compare16(zxw7900, zxw8000))
new_ltEs4(@2(zxw79000, zxw79001), @2(zxw80000, zxw80001), ca, cb) → new_pePe(new_lt4(zxw79000, zxw80000, ca), new_asAs(new_esEs8(zxw79000, zxw80000, ca), new_ltEs5(zxw79001, zxw80001, cb)))
new_lt4(zxw79000, zxw80000, app(app(app(ty_@3, cc), cd), ce)) → new_lt5(zxw79000, zxw80000, cc, cd, ce)
new_lt4(zxw79000, zxw80000, app(ty_[], cf)) → new_lt10(zxw79000, zxw80000, cf)
new_lt4(zxw79000, zxw80000, ty_Bool) → new_lt12(zxw79000, zxw80000)
new_lt4(zxw79000, zxw80000, app(ty_Maybe, de)) → new_lt18(zxw79000, zxw80000, de)
new_lt4(zxw79000, zxw80000, ty_Ordering) → new_lt6(zxw79000, zxw80000)
new_lt4(zxw79000, zxw80000, app(ty_Ratio, dd)) → new_lt17(zxw79000, zxw80000, dd)
new_lt4(zxw79000, zxw80000, ty_Int) → new_lt8(zxw79000, zxw80000)
new_lt4(zxw79000, zxw80000, ty_Double) → new_lt15(zxw79000, zxw80000)
new_lt4(zxw79000, zxw80000, app(app(ty_Either, db), dc)) → new_lt14(zxw79000, zxw80000, db, dc)
new_lt4(zxw79000, zxw80000, ty_Char) → new_lt9(zxw79000, zxw80000)
new_lt4(zxw79000, zxw80000, ty_@0) → new_lt7(zxw79000, zxw80000)
new_lt4(zxw79000, zxw80000, ty_Float) → new_lt16(zxw79000, zxw80000)
new_lt4(zxw79000, zxw80000, app(app(ty_@2, cg), da)) → new_lt11(zxw79000, zxw80000, cg, da)
new_lt4(zxw79000, zxw80000, ty_Integer) → new_lt13(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, ty_Int) → new_esEs11(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, ty_Double) → new_esEs16(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, app(app(app(ty_@3, cc), cd), ce)) → new_esEs4(zxw79000, zxw80000, cc, cd, ce)
new_esEs8(zxw79000, zxw80000, app(ty_[], cf)) → new_esEs13(zxw79000, zxw80000, cf)
new_esEs8(zxw79000, zxw80000, ty_Char) → new_esEs12(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, app(app(ty_@2, cg), da)) → new_esEs5(zxw79000, zxw80000, cg, da)
new_esEs8(zxw79000, zxw80000, ty_Float) → new_esEs17(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, app(app(ty_Either, db), dc)) → new_esEs7(zxw79000, zxw80000, db, dc)
new_esEs8(zxw79000, zxw80000, ty_@0) → new_esEs10(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, app(ty_Maybe, de)) → new_esEs6(zxw79000, zxw80000, de)
new_esEs8(zxw79000, zxw80000, ty_Bool) → new_esEs14(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, ty_Ordering) → new_esEs9(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, ty_Integer) → new_esEs15(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, app(ty_Ratio, dd)) → new_esEs18(zxw79000, zxw80000, dd)
new_ltEs5(zxw79001, zxw80001, ty_Char) → new_ltEs10(zxw79001, zxw80001)
new_ltEs5(zxw79001, zxw80001, app(app(ty_@2, eb), ec)) → new_ltEs4(zxw79001, zxw80001, eb, ec)
new_ltEs5(zxw79001, zxw80001, ty_Ordering) → new_ltEs7(zxw79001, zxw80001)
new_ltEs5(zxw79001, zxw80001, ty_Bool) → new_ltEs12(zxw79001, zxw80001)
new_ltEs5(zxw79001, zxw80001, ty_Integer) → new_ltEs13(zxw79001, zxw80001)
new_ltEs5(zxw79001, zxw80001, app(ty_Ratio, ef)) → new_ltEs17(zxw79001, zxw80001, ef)
new_ltEs5(zxw79001, zxw80001, app(ty_Maybe, eg)) → new_ltEs18(zxw79001, zxw80001, eg)
new_ltEs5(zxw79001, zxw80001, ty_Double) → new_ltEs15(zxw79001, zxw80001)
new_ltEs5(zxw79001, zxw80001, app(app(ty_Either, ed), ee)) → new_ltEs14(zxw79001, zxw80001, ed, ee)
new_ltEs5(zxw79001, zxw80001, app(app(app(ty_@3, df), dg), dh)) → new_ltEs6(zxw79001, zxw80001, df, dg, dh)
new_ltEs5(zxw79001, zxw80001, app(ty_[], ea)) → new_ltEs11(zxw79001, zxw80001, ea)
new_ltEs5(zxw79001, zxw80001, ty_Int) → new_ltEs9(zxw79001, zxw80001)
new_ltEs5(zxw79001, zxw80001, ty_@0) → new_ltEs8(zxw79001, zxw80001)
new_ltEs5(zxw79001, zxw80001, ty_Float) → new_ltEs16(zxw79001, zxw80001)
new_pePe(False, zxw271) → zxw271
new_pePe(True, zxw271) → True
new_ltEs16(zxw7900, zxw8000) → new_fsEs(new_compare7(zxw7900, zxw8000))
new_compare7(Float(zxw79000, zxw79001), Float(zxw80000, zxw80001)) → new_compare16(new_sr(zxw79000, zxw80000), new_sr(zxw79001, zxw80001))
new_ltEs8(zxw7900, zxw8000) → new_fsEs(new_compare30(zxw7900, zxw8000))
new_ltEs6(@3(zxw79000, zxw79001, zxw79002), @3(zxw80000, zxw80001, zxw80002), hb, hc, hd) → new_pePe(new_lt19(zxw79000, zxw80000, hb), new_asAs(new_esEs20(zxw79000, zxw80000, hb), new_pePe(new_lt20(zxw79001, zxw80001, hc), new_asAs(new_esEs19(zxw79001, zxw80001, hc), new_ltEs21(zxw79002, zxw80002, hd)))))
new_lt19(zxw79000, zxw80000, app(app(ty_Either, bhd), bhe)) → new_lt14(zxw79000, zxw80000, bhd, bhe)
new_lt19(zxw79000, zxw80000, ty_Double) → new_lt15(zxw79000, zxw80000)
new_lt19(zxw79000, zxw80000, ty_Ordering) → new_lt6(zxw79000, zxw80000)
new_lt19(zxw79000, zxw80000, app(ty_Ratio, gg)) → new_lt17(zxw79000, zxw80000, gg)
new_lt19(zxw79000, zxw80000, app(app(ty_@2, bcf), bcg)) → new_lt11(zxw79000, zxw80000, bcf, bcg)
new_lt19(zxw79000, zxw80000, ty_Int) → new_lt8(zxw79000, zxw80000)
new_lt19(zxw79000, zxw80000, ty_@0) → new_lt7(zxw79000, zxw80000)
new_lt19(zxw79000, zxw80000, app(app(app(ty_@3, gd), ge), gf)) → new_lt5(zxw79000, zxw80000, gd, ge, gf)
new_lt19(zxw79000, zxw80000, app(ty_Maybe, bdb)) → new_lt18(zxw79000, zxw80000, bdb)
new_lt19(zxw79000, zxw80000, ty_Float) → new_lt16(zxw79000, zxw80000)
new_lt19(zxw79000, zxw80000, ty_Bool) → new_lt12(zxw79000, zxw80000)
new_lt19(zxw79000, zxw80000, app(ty_[], bhc)) → new_lt10(zxw79000, zxw80000, bhc)
new_lt19(zxw79000, zxw80000, ty_Integer) → new_lt13(zxw79000, zxw80000)
new_lt19(zxw79000, zxw80000, ty_Char) → new_lt9(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, app(ty_[], bhc)) → new_esEs13(zxw79000, zxw80000, bhc)
new_esEs20(zxw79000, zxw80000, ty_Double) → new_esEs16(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, ty_Char) → new_esEs12(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, app(app(ty_@2, bcf), bcg)) → new_esEs5(zxw79000, zxw80000, bcf, bcg)
new_esEs20(zxw79000, zxw80000, ty_Int) → new_esEs11(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, ty_@0) → new_esEs10(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, app(app(app(ty_@3, gd), ge), gf)) → new_esEs4(zxw79000, zxw80000, gd, ge, gf)
new_esEs20(zxw79000, zxw80000, ty_Integer) → new_esEs15(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, ty_Bool) → new_esEs14(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, app(ty_Ratio, gg)) → new_esEs18(zxw79000, zxw80000, gg)
new_esEs20(zxw79000, zxw80000, app(app(ty_Either, bhd), bhe)) → new_esEs7(zxw79000, zxw80000, bhd, bhe)
new_esEs20(zxw79000, zxw80000, app(ty_Maybe, bdb)) → new_esEs6(zxw79000, zxw80000, bdb)
new_esEs20(zxw79000, zxw80000, ty_Ordering) → new_esEs9(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, ty_Float) → new_esEs17(zxw79000, zxw80000)
new_lt20(zxw79001, zxw80001, app(app(ty_Either, cad), cae)) → new_lt14(zxw79001, zxw80001, cad, cae)
new_lt20(zxw79001, zxw80001, ty_@0) → new_lt7(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, app(app(ty_@2, cab), cac)) → new_lt11(zxw79001, zxw80001, cab, cac)
new_lt20(zxw79001, zxw80001, ty_Ordering) → new_lt6(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, app(ty_Maybe, cag)) → new_lt18(zxw79001, zxw80001, cag)
new_lt20(zxw79001, zxw80001, ty_Int) → new_lt8(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, ty_Integer) → new_lt13(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, app(ty_Ratio, caf)) → new_lt17(zxw79001, zxw80001, caf)
new_lt20(zxw79001, zxw80001, ty_Char) → new_lt9(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, app(ty_[], caa)) → new_lt10(zxw79001, zxw80001, caa)
new_lt20(zxw79001, zxw80001, ty_Double) → new_lt15(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, ty_Float) → new_lt16(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, ty_Bool) → new_lt12(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, app(app(app(ty_@3, bhf), bhg), bhh)) → new_lt5(zxw79001, zxw80001, bhf, bhg, bhh)
new_esEs19(zxw79001, zxw80001, app(ty_Ratio, caf)) → new_esEs18(zxw79001, zxw80001, caf)
new_esEs19(zxw79001, zxw80001, ty_Ordering) → new_esEs9(zxw79001, zxw80001)
new_esEs19(zxw79001, zxw80001, app(ty_Maybe, cag)) → new_esEs6(zxw79001, zxw80001, cag)
new_esEs19(zxw79001, zxw80001, app(app(ty_Either, cad), cae)) → new_esEs7(zxw79001, zxw80001, cad, cae)
new_esEs19(zxw79001, zxw80001, ty_Float) → new_esEs17(zxw79001, zxw80001)
new_esEs19(zxw79001, zxw80001, ty_Bool) → new_esEs14(zxw79001, zxw80001)
new_esEs19(zxw79001, zxw80001, ty_Int) → new_esEs11(zxw79001, zxw80001)
new_esEs19(zxw79001, zxw80001, app(app(app(ty_@3, bhf), bhg), bhh)) → new_esEs4(zxw79001, zxw80001, bhf, bhg, bhh)
new_esEs19(zxw79001, zxw80001, app(app(ty_@2, cab), cac)) → new_esEs5(zxw79001, zxw80001, cab, cac)
new_esEs19(zxw79001, zxw80001, ty_Double) → new_esEs16(zxw79001, zxw80001)
new_esEs19(zxw79001, zxw80001, ty_Integer) → new_esEs15(zxw79001, zxw80001)
new_esEs19(zxw79001, zxw80001, ty_@0) → new_esEs10(zxw79001, zxw80001)
new_esEs19(zxw79001, zxw80001, app(ty_[], caa)) → new_esEs13(zxw79001, zxw80001, caa)
new_esEs19(zxw79001, zxw80001, ty_Char) → new_esEs12(zxw79001, zxw80001)
new_ltEs21(zxw79002, zxw80002, ty_Char) → new_ltEs10(zxw79002, zxw80002)
new_ltEs21(zxw79002, zxw80002, app(app(ty_@2, cbd), cbe)) → new_ltEs4(zxw79002, zxw80002, cbd, cbe)
new_ltEs21(zxw79002, zxw80002, ty_Int) → new_ltEs9(zxw79002, zxw80002)
new_ltEs21(zxw79002, zxw80002, ty_Ordering) → new_ltEs7(zxw79002, zxw80002)
new_ltEs21(zxw79002, zxw80002, ty_Float) → new_ltEs16(zxw79002, zxw80002)
new_ltEs21(zxw79002, zxw80002, ty_Bool) → new_ltEs12(zxw79002, zxw80002)
new_ltEs21(zxw79002, zxw80002, ty_Integer) → new_ltEs13(zxw79002, zxw80002)
new_ltEs21(zxw79002, zxw80002, app(app(ty_Either, cbf), cbg)) → new_ltEs14(zxw79002, zxw80002, cbf, cbg)
new_ltEs21(zxw79002, zxw80002, app(ty_[], cbc)) → new_ltEs11(zxw79002, zxw80002, cbc)
new_ltEs21(zxw79002, zxw80002, app(ty_Ratio, cbh)) → new_ltEs17(zxw79002, zxw80002, cbh)
new_ltEs21(zxw79002, zxw80002, app(app(app(ty_@3, cah), cba), cbb)) → new_ltEs6(zxw79002, zxw80002, cah, cba, cbb)
new_ltEs21(zxw79002, zxw80002, ty_@0) → new_ltEs8(zxw79002, zxw80002)
new_ltEs21(zxw79002, zxw80002, app(ty_Maybe, cca)) → new_ltEs18(zxw79002, zxw80002, cca)
new_ltEs21(zxw79002, zxw80002, ty_Double) → new_ltEs15(zxw79002, zxw80002)
new_ltEs15(zxw7900, zxw8000) → new_fsEs(new_compare6(zxw7900, zxw8000))
new_compare6(Double(zxw79000, zxw79001), Double(zxw80000, zxw80001)) → new_compare16(new_sr(zxw79000, zxw80000), new_sr(zxw79001, zxw80001))
new_ltEs12(True, False) → False
new_ltEs12(False, False) → True
new_ltEs12(True, True) → True
new_ltEs12(False, True) → True
new_lt5(zxw79000, zxw80000, gd, ge, gf) → new_esEs9(new_compare9(zxw79000, zxw80000, gd, ge, gf), LT)
new_compare9(zxw79000, zxw80000, gd, ge, gf) → new_compare25(zxw79000, zxw80000, new_esEs4(zxw79000, zxw80000, gd, ge, gf), gd, ge, gf)
new_compare25(zxw79000, zxw80000, True, gd, ge, gf) → EQ
new_compare25(zxw79000, zxw80000, False, gd, ge, gf) → new_compare12(zxw79000, zxw80000, new_ltEs6(zxw79000, zxw80000, gd, ge, gf), gd, ge, gf)
new_compare12(zxw79000, zxw80000, True, gd, ge, gf) → LT
new_compare12(zxw79000, zxw80000, False, gd, ge, gf) → GT
new_lt12(zxw79000, zxw80000) → new_esEs9(new_compare31(zxw79000, zxw80000), LT)
new_compare31(zxw79000, zxw80000) → new_compare23(zxw79000, zxw80000, new_esEs14(zxw79000, zxw80000))
new_compare23(zxw79000, zxw80000, True) → EQ
new_compare23(zxw79000, zxw80000, False) → new_compare10(zxw79000, zxw80000, new_ltEs12(zxw79000, zxw80000))
new_compare10(zxw79000, zxw80000, True) → LT
new_compare10(zxw79000, zxw80000, False) → GT
new_lt16(zxw79000, zxw80000) → new_esEs9(new_compare7(zxw79000, zxw80000), LT)
new_lt15(zxw79000, zxw80000) → new_esEs9(new_compare6(zxw79000, zxw80000), LT)
new_lt10(zxw79000, zxw80000, bhc) → new_esEs9(new_compare1(zxw79000, zxw80000, bhc), LT)
new_lt9(zxw79000, zxw80000) → new_esEs9(new_compare17(zxw79000, zxw80000), LT)
new_lt17(zxw79000, zxw80000, gg) → new_esEs9(new_compare8(zxw79000, zxw80000, gg), LT)
new_lt13(zxw79000, zxw80000) → new_esEs9(new_compare32(zxw79000, zxw80000), LT)
new_lt8(zxw790, zxw800) → new_esEs9(new_compare16(zxw790, zxw800), LT)
new_lt18(zxw79000, zxw80000, bdb) → new_esEs9(new_compare27(zxw79000, zxw80000, bdb), LT)
new_compare27(zxw79000, zxw80000, bdb) → new_compare28(zxw79000, zxw80000, new_esEs6(zxw79000, zxw80000, bdb), bdb)
new_compare28(zxw79000, zxw80000, False, bdb) → new_compare111(zxw79000, zxw80000, new_ltEs18(zxw79000, zxw80000, bdb), bdb)
new_compare28(zxw79000, zxw80000, True, bdb) → EQ
new_compare111(zxw79000, zxw80000, True, bdb) → LT
new_compare111(zxw79000, zxw80000, False, bdb) → GT
new_lt6(zxw79000, zxw80000) → new_esEs9(new_compare18(zxw79000, zxw80000), LT)
new_lt11(zxw79000, zxw80000, bcf, bcg) → new_esEs9(new_compare19(zxw79000, zxw80000, bcf, bcg), LT)
new_compare19(zxw79000, zxw80000, bcf, bcg) → new_compare210(zxw79000, zxw80000, new_esEs5(zxw79000, zxw80000, bcf, bcg), bcf, bcg)
new_compare210(zxw79000, zxw80000, False, bcf, bcg) → new_compare110(zxw79000, zxw80000, new_ltEs4(zxw79000, zxw80000, bcf, bcg), bcf, bcg)
new_compare210(zxw79000, zxw80000, True, bcf, bcg) → EQ
new_compare110(zxw79000, zxw80000, True, bcf, bcg) → LT
new_compare110(zxw79000, zxw80000, False, bcf, bcg) → GT
new_lt7(zxw79000, zxw80000) → new_esEs9(new_compare30(zxw79000, zxw80000), LT)
new_lt14(zxw790, zxw800, gh, ha) → new_esEs9(new_compare15(zxw790, zxw800, gh, ha), LT)
new_compare35(zxw400, zxw300, h, ba) → new_compare26(Right(zxw400), Left(zxw300), False, h, ba)
new_esEs34(zxw400, zxw300, ty_Char) → new_esEs12(zxw400, zxw300)
new_esEs34(zxw400, zxw300, app(app(ty_Either, bca), bcb)) → new_esEs7(zxw400, zxw300, bca, bcb)
new_esEs34(zxw400, zxw300, app(ty_[], bbe)) → new_esEs13(zxw400, zxw300, bbe)
new_esEs34(zxw400, zxw300, ty_Float) → new_esEs17(zxw400, zxw300)
new_esEs34(zxw400, zxw300, app(app(ty_@2, bbg), bbh)) → new_esEs5(zxw400, zxw300, bbg, bbh)
new_esEs34(zxw400, zxw300, app(app(app(ty_@3, bcc), bcd), bce)) → new_esEs4(zxw400, zxw300, bcc, bcd, bce)
new_esEs34(zxw400, zxw300, ty_Double) → new_esEs16(zxw400, zxw300)
new_esEs34(zxw400, zxw300, ty_Ordering) → new_esEs9(zxw400, zxw300)
new_esEs34(zxw400, zxw300, ty_Int) → new_esEs11(zxw400, zxw300)
new_esEs34(zxw400, zxw300, ty_Bool) → new_esEs14(zxw400, zxw300)
new_esEs34(zxw400, zxw300, ty_Integer) → new_esEs15(zxw400, zxw300)
new_esEs34(zxw400, zxw300, ty_@0) → new_esEs10(zxw400, zxw300)
new_esEs34(zxw400, zxw300, app(ty_Ratio, bbd)) → new_esEs18(zxw400, zxw300, bbd)
new_esEs34(zxw400, zxw300, app(ty_Maybe, bbf)) → new_esEs6(zxw400, zxw300, bbf)

The set Q consists of the following terms:

new_compare23(x0, x1, True)
new_lt6(x0, x1)
new_ltEs5(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, ty_Integer)
new_lt4(x0, x1, app(ty_[], x2))
new_ltEs18(Just(x0), Just(x1), ty_@0)
new_compare16(x0, x1)
new_lt4(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(Just(x0), Nothing, x1)
new_ltEs20(x0, x1, ty_Double)
new_esEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs19(x0, x1, ty_Bool)
new_esEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs8(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(x0, x1, app(app(ty_Either, x2), x3))
new_compare30(@0, @0)
new_primCompAux00(x0, GT)
new_lt19(x0, x1, ty_Char)
new_esEs27(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_Ordering)
new_compare17(Char(x0), Char(x1))
new_esEs28(x0, x1, ty_Int)
new_ltEs20(x0, x1, app(ty_[], x2))
new_ltEs21(x0, x1, ty_Ordering)
new_compare111(x0, x1, True, x2)
new_ltEs15(x0, x1)
new_primPlusNat1(Zero, Succ(x0))
new_esEs6(Just(x0), Just(x1), ty_Double)
new_compare24(x0, x1, False)
new_compare210(x0, x1, False, x2, x3)
new_lt20(x0, x1, ty_Char)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, ty_Bool)
new_sr0(Integer(x0), Integer(x1))
new_compare28(x0, x1, True, x2)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(Nothing, Nothing, x0)
new_ltEs18(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs34(x0, x1, ty_Integer)
new_esEs34(x0, x1, app(ty_Maybe, x2))
new_ltEs7(EQ, EQ)
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs19(x0, x1, ty_Integer)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_ltEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Bool)
new_ltEs14(Right(x0), Right(x1), x2, ty_Float)
new_compare27(x0, x1, x2)
new_esEs31(x0, x1, app(ty_Ratio, x2))
new_esEs6(Just(x0), Just(x1), app(ty_[], x2))
new_compare14(x0, x1, True, x2, x3)
new_ltEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs13([], :(x0, x1), x2)
new_compare25(x0, x1, False, x2, x3, x4)
new_esEs7(Left(x0), Left(x1), ty_Integer, x2)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs7(Right(x0), Right(x1), x2, ty_@0)
new_esEs31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Integer)
new_ltEs5(x0, x1, ty_Integer)
new_ltEs21(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs7(EQ, LT)
new_ltEs7(LT, EQ)
new_esEs20(x0, x1, ty_Ordering)
new_esEs17(Float(x0, x1), Float(x2, x3))
new_compare25(x0, x1, True, x2, x3, x4)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_lt19(x0, x1, ty_Ordering)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs16(x0, x1)
new_lt4(x0, x1, app(ty_Maybe, x2))
new_esEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs14(Left(x0), Left(x1), ty_Char, x2)
new_sr(x0, x1)
new_ltEs19(x0, x1, ty_Double)
new_compare7(Float(x0, x1), Float(x2, x3))
new_ltEs9(x0, x1)
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_compare19(x0, x1, x2, x3)
new_lt7(x0, x1)
new_lt4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, ty_Int)
new_esEs26(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat0(Zero, x0)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_ltEs7(LT, LT)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs27(x0, x1, ty_Bool)
new_lt5(x0, x1, x2, x3, x4)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare29(x0, x1, app(app(ty_@2, x2), x3))
new_lt4(x0, x1, ty_Ordering)
new_esEs34(x0, x1, app(ty_Ratio, x2))
new_primEqNat0(Zero, Succ(x0))
new_lt19(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Int)
new_esEs15(Integer(x0), Integer(x1))
new_esEs26(x0, x1, ty_Double)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs28(x0, x1, ty_@0)
new_primPlusNat1(Succ(x0), Zero)
new_esEs22(x0, x1, ty_Integer)
new_ltEs14(Left(x0), Left(x1), ty_@0, x2)
new_primMulInt(Neg(x0), Neg(x1))
new_ltEs19(x0, x1, ty_Int)
new_esEs7(Left(x0), Left(x1), ty_Double, x2)
new_compare29(x0, x1, ty_Integer)
new_esEs14(True, True)
new_esEs21(x0, x1, ty_Char)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(Just(x0), Just(x1), ty_Integer)
new_compare29(x0, x1, app(ty_[], x2))
new_ltEs18(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, ty_Int)
new_esEs7(Right(x0), Right(x1), x2, ty_Int)
new_primEqNat0(Zero, Zero)
new_esEs16(Double(x0, x1), Double(x2, x3))
new_esEs12(Char(x0), Char(x1))
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_lt4(x0, x1, ty_Char)
new_esEs20(x0, x1, ty_Bool)
new_esEs8(x0, x1, ty_Float)
new_compare1([], :(x0, x1), x2)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_Integer)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(Left(x0), Left(x1), ty_Int, x2)
new_primCompAux00(x0, LT)
new_esEs27(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(ty_[], x2))
new_ltEs5(x0, x1, ty_Double)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs18(Just(x0), Just(x1), ty_Char)
new_primMulNat0(Zero, Zero)
new_lt9(x0, x1)
new_compare29(x0, x1, ty_Double)
new_esEs34(x0, x1, app(ty_[], x2))
new_ltEs5(x0, x1, ty_@0)
new_lt17(x0, x1, x2)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_ltEs21(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs31(x0, x1, ty_Bool)
new_ltEs14(Left(x0), Left(x1), ty_Float, x2)
new_esEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs8(x0, x1, ty_Ordering)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_compare10(x0, x1, True)
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Ordering)
new_primEqNat0(Succ(x0), Succ(x1))
new_ltEs19(x0, x1, ty_Bool)
new_esEs28(x0, x1, ty_Double)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_@0)
new_pePe(True, x0)
new_esEs19(x0, x1, ty_Float)
new_lt19(x0, x1, app(ty_[], x2))
new_esEs8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_lt16(x0, x1)
new_compare29(x0, x1, ty_Bool)
new_lt10(x0, x1, x2)
new_esEs7(Right(x0), Right(x1), x2, ty_Integer)
new_compare11(x0, x1, True)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs34(x0, x1, ty_Char)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1, ty_@0)
new_esEs6(Just(x0), Just(x1), ty_Ordering)
new_esEs23(x0, x1, ty_@0)
new_ltEs14(Right(x0), Right(x1), x2, ty_Int)
new_ltEs5(x0, x1, ty_Char)
new_ltEs21(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Float)
new_lt18(x0, x1, x2)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_compare29(x0, x1, ty_Ordering)
new_ltEs21(x0, x1, ty_@0)
new_esEs8(x0, x1, ty_Int)
new_lt14(x0, x1, x2, x3)
new_ltEs12(False, False)
new_compare210(x0, x1, True, x2, x3)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Just(x0), Just(x1), ty_Bool)
new_compare32(Integer(x0), Integer(x1))
new_lt19(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_Int)
new_primMulNat0(Succ(x0), Succ(x1))
new_compare29(x0, x1, ty_Float)
new_ltEs21(x0, x1, ty_Integer)
new_esEs6(Just(x0), Just(x1), ty_Float)
new_ltEs5(x0, x1, ty_Float)
new_ltEs18(Just(x0), Just(x1), ty_Float)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_Bool)
new_esEs31(x0, x1, ty_Double)
new_primCmpNat1(Zero, x0)
new_ltEs14(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs8(x0, x1)
new_ltEs18(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs14(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_compare13(x0, x1, False, x2, x3)
new_esEs34(x0, x1, ty_Float)
new_primPlusNat1(Zero, Zero)
new_esEs23(x0, x1, ty_Double)
new_ltEs18(Just(x0), Just(x1), ty_Ordering)
new_primCmpNat2(Zero, Zero)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(x0, x1, ty_Bool)
new_esEs34(x0, x1, ty_Ordering)
new_ltEs18(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs5(x0, x1, app(ty_[], x2))
new_asAs(False, x0)
new_ltEs20(x0, x1, ty_Char)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs31(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs8(x0, x1, ty_Integer)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(Just(x0), Just(x1), ty_Bool)
new_compare14(x0, x1, False, x2, x3)
new_primCmpNat1(Succ(x0), x1)
new_esEs34(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_Integer)
new_esEs27(x0, x1, ty_@0)
new_esEs7(Left(x0), Left(x1), ty_Int, x2)
new_ltEs14(Right(x0), Right(x1), x2, ty_Double)
new_lt4(x0, x1, ty_Float)
new_ltEs5(x0, x1, app(app(ty_Either, x2), x3))
new_esEs19(x0, x1, ty_Char)
new_lt4(x0, x1, ty_Double)
new_esEs19(x0, x1, ty_Ordering)
new_esEs8(x0, x1, app(ty_Ratio, x2))
new_esEs10(@0, @0)
new_esEs31(x0, x1, ty_@0)
new_esEs11(x0, x1)
new_esEs20(x0, x1, ty_Float)
new_ltEs14(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs7(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs14(Right(x0), Right(x1), x2, ty_Char)
new_esEs9(GT, GT)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs27(x0, x1, ty_Char)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_compare11(x0, x1, False)
new_compare23(x0, x1, False)
new_compare12(x0, x1, True, x2, x3, x4)
new_esEs7(Right(x0), Right(x1), x2, ty_Double)
new_esEs28(x0, x1, ty_Bool)
new_compare24(x0, x1, True)
new_compare36(x0, x1, x2, x3)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_compare15(x0, x1, x2, x3)
new_primEqNat0(Succ(x0), Zero)
new_esEs13([], [], x0)
new_esEs23(x0, x1, ty_Ordering)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs7(Left(x0), Right(x1), x2, x3)
new_esEs7(Right(x0), Left(x1), x2, x3)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_esEs34(x0, x1, ty_Int)
new_compare9(x0, x1, x2, x3, x4)
new_lt20(x0, x1, ty_Int)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs21(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Integer)
new_lt4(x0, x1, app(app(ty_Either, x2), x3))
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs23(x0, x1, ty_Int)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs5(x0, x1, app(app(ty_@2, x2), x3))
new_lt4(x0, x1, ty_@0)
new_esEs23(x0, x1, ty_Char)
new_esEs28(x0, x1, ty_Ordering)
new_ltEs18(Just(x0), Just(x1), ty_Double)
new_ltEs20(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_lt20(x0, x1, ty_@0)
new_compare1([], [], x0)
new_esEs9(EQ, EQ)
new_pePe(False, x0)
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs5(x0, x1, app(ty_Ratio, x2))
new_ltEs14(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs6(Just(x0), Just(x1), ty_Char)
new_esEs25(x0, x1, ty_Integer)
new_esEs31(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_Integer)
new_compare12(x0, x1, False, x2, x3, x4)
new_esEs8(x0, x1, app(ty_Maybe, x2))
new_primCompAux00(x0, EQ)
new_esEs19(x0, x1, ty_Int)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs14(True, False)
new_esEs14(False, True)
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_lt4(x0, x1, ty_Integer)
new_esEs7(Left(x0), Left(x1), ty_@0, x2)
new_ltEs14(Right(x0), Right(x1), x2, ty_@0)
new_fsEs(x0)
new_esEs22(x0, x1, ty_Float)
new_ltEs14(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_primCmpNat2(Succ(x0), Succ(x1))
new_compare110(x0, x1, False, x2, x3)
new_lt4(x0, x1, ty_Bool)
new_asAs(True, x0)
new_esEs21(x0, x1, ty_Bool)
new_esEs4(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs6(Nothing, Just(x0), x1)
new_esEs6(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs21(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Just(x0), Nothing, x1)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_compare29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs8(x0, x1, app(ty_[], x2))
new_esEs31(x0, x1, ty_Integer)
new_esEs13(:(x0, x1), [], x2)
new_ltEs14(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs8(x0, x1, ty_Char)
new_lt19(x0, x1, ty_Float)
new_ltEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs22(x0, x1, ty_@0)
new_esEs34(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_Char)
new_ltEs12(False, True)
new_ltEs12(True, False)
new_compare6(Double(x0, x1), Double(x2, x3))
new_ltEs20(x0, x1, ty_@0)
new_esEs22(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_@0)
new_compare35(x0, x1, x2, x3)
new_ltEs14(Right(x0), Right(x1), x2, ty_Integer)
new_lt19(x0, x1, ty_Double)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1, ty_Bool)
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs7(Left(x0), Left(x1), ty_Char, x2)
new_esEs7(Right(x0), Right(x1), x2, ty_Float)
new_ltEs14(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs26(x0, x1, ty_Char)
new_ltEs5(x0, x1, ty_Int)
new_lt4(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_Double)
new_esEs19(x0, x1, ty_@0)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_compare13(x0, x1, True, x2, x3)
new_esEs34(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs21(x0, x1, ty_Bool)
new_ltEs14(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs21(x0, x1, ty_Double)
new_lt12(x0, x1)
new_esEs8(x0, x1, ty_Bool)
new_ltEs21(x0, x1, ty_Char)
new_lt13(x0, x1)
new_esEs31(x0, x1, ty_Ordering)
new_ltEs14(Right(x0), Right(x1), x2, ty_Bool)
new_compare1(:(x0, x1), [], x2)
new_compare10(x0, x1, False)
new_primMulNat0(Succ(x0), Zero)
new_ltEs19(x0, x1, ty_Float)
new_ltEs14(Left(x0), Right(x1), x2, x3)
new_esEs23(x0, x1, ty_Float)
new_ltEs14(Right(x0), Left(x1), x2, x3)
new_compare29(x0, x1, ty_Int)
new_esEs20(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, ty_Int)
new_esEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs20(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Float)
new_compare31(x0, x1)
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs31(x0, x1, ty_Char)
new_esEs6(Just(x0), Just(x1), ty_Int)
new_ltEs7(LT, GT)
new_ltEs7(GT, LT)
new_esEs21(x0, x1, ty_Integer)
new_esEs22(x0, x1, app(ty_[], x2))
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs22(x0, x1, ty_Double)
new_compare110(x0, x1, True, x2, x3)
new_lt20(x0, x1, app(ty_[], x2))
new_ltEs13(x0, x1)
new_ltEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs34(x0, x1, ty_@0)
new_esEs31(x0, x1, ty_Int)
new_lt4(x0, x1, ty_Int)
new_ltEs11(x0, x1, x2)
new_lt20(x0, x1, ty_Float)
new_not(True)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs31(x0, x1, ty_Float)
new_esEs20(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Float)
new_esEs19(x0, x1, app(ty_[], x2))
new_esEs18(:%(x0, x1), :%(x2, x3), x4)
new_esEs6(Nothing, Nothing, x0)
new_esEs28(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Ordering)
new_ltEs14(Left(x0), Left(x1), ty_Double, x2)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Just(x0), Just(x1), ty_Integer)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_not(False)
new_compare29(x0, x1, app(ty_Ratio, x2))
new_lt8(x0, x1)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_compare28(x0, x1, False, x2)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, ty_Char)
new_esEs6(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare8(:%(x0, x1), :%(x2, x3), ty_Integer)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs22(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_Integer)
new_esEs8(x0, x1, ty_@0)
new_compare26(Left(x0), Left(x1), False, x2, x3)
new_ltEs12(True, True)
new_esEs27(x0, x1, ty_Float)
new_lt15(x0, x1)
new_lt11(x0, x1, x2, x3)
new_esEs26(x0, x1, ty_Ordering)
new_esEs7(Left(x0), Left(x1), ty_Float, x2)
new_esEs27(x0, x1, ty_Double)
new_esEs6(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs34(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Ordering)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs13(:(x0, x1), :(x2, x3), x4)
new_esEs22(x0, x1, ty_Char)
new_lt20(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Bool)
new_esEs34(x0, x1, ty_Double)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_ltEs21(x0, x1, ty_Float)
new_ltEs10(x0, x1)
new_ltEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_compare29(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs14(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs5(x0, x1, ty_Ordering)
new_esEs8(x0, x1, ty_Double)
new_compare29(x0, x1, ty_Char)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs6(Just(x0), Just(x1), ty_@0)
new_esEs31(x0, x1, app(app(ty_Either, x2), x3))
new_compare1(:(x0, x1), :(x2, x3), x4)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs31(x0, x1, app(ty_[], x2))
new_esEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs6(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs19(x0, x1, ty_Double)
new_esEs14(False, False)
new_ltEs21(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Zero), Pos(Zero))
new_ltEs21(x0, x1, ty_Double)
new_ltEs14(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpNat2(Succ(x0), Zero)
new_esEs7(Right(x0), Right(x1), x2, ty_Char)
new_esEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_compare18(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs18(Just(x0), Just(x1), ty_Int)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare26(Right(x0), Right(x1), False, x2, x3)
new_esEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs17(x0, x1, x2)
new_primPlusNat0(Succ(x0), x1)
new_esEs20(x0, x1, ty_Integer)
new_primCmpNat0(x0, Zero)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_ltEs7(GT, EQ)
new_ltEs7(EQ, GT)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs7(GT, GT)
new_esEs9(LT, LT)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_primCompAux0(x0, x1, x2, x3)
new_compare29(x0, x1, ty_@0)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_compare26(x0, x1, True, x2, x3)
new_compare26(Right(x0), Left(x1), False, x2, x3)
new_compare26(Left(x0), Right(x1), False, x2, x3)
new_ltEs18(Nothing, Just(x0), x1)
new_compare111(x0, x1, False, x2)
new_compare29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Ordering)
new_primCmpNat0(x0, Succ(x1))

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

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



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

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

new_splitGT2(zxw15, zxw16, zxw17, zxw18, zxw19, zxw20, False, bc, bd, be) → new_splitGT1(zxw15, zxw16, zxw17, zxw18, zxw19, zxw20, new_esEs9(new_compare33(zxw20, zxw15, bc, bd), LT), bc, bd, be)
new_splitGT2(zxw15, zxw16, zxw17, zxw18, zxw19, zxw20, True, bc, bd, be) → new_splitGT(zxw19, zxw20, bc, bd, be)
new_splitGT3(Left(zxw300), zxw31, zxw32, zxw33, zxw34, Left(zxw400), h, ba, bb) → new_splitGT2(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs9(new_compare26(Left(zxw400), Left(zxw300), new_esEs33(zxw400, zxw300, h), h, ba), GT), h, ba, bb)
new_splitGT(Branch(zxw340, zxw341, zxw342, zxw343, zxw344), zxw400, h, ba, bb) → new_splitGT3(zxw340, zxw341, zxw342, zxw343, zxw344, Left(zxw400), h, ba, bb)
new_splitGT20(zxw300, zxw31, zxw32, zxw33, Branch(zxw340, zxw341, zxw342, zxw343, zxw344), zxw400, True, h, ba, bb) → new_splitGT3(zxw340, zxw341, zxw342, zxw343, zxw344, Left(zxw400), h, ba, bb)
new_splitGT10(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, True, h, ba, bb) → new_splitGT(zxw33, zxw400, h, ba, bb)
new_splitGT20(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, False, h, ba, bb) → new_splitGT10(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs9(new_compare34(zxw400, zxw300, h, ba), LT), h, ba, bb)
new_splitGT1(zxw15, zxw16, zxw17, zxw18, zxw19, zxw20, True, bc, bd, be) → new_splitGT(zxw18, zxw20, bc, bd, be)
new_splitGT3(Right(zxw300), zxw31, zxw32, zxw33, zxw34, Left(zxw400), h, ba, bb) → new_splitGT20(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs9(new_compare26(Left(zxw400), Right(zxw300), False, h, ba), GT), h, ba, bb)

The TRS R consists of the following rules:

new_ltEs15(zxw7900, zxw8000) → new_fsEs(new_compare6(zxw7900, zxw8000))
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Bool) → new_ltEs12(zxw79000, zxw80000)
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, app(ty_Maybe, bbc)) → new_ltEs18(zxw7900, zxw8000, bbc)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Char) → new_ltEs10(zxw79000, zxw80000)
new_esEs28(zxw4000, zxw3000, app(ty_[], dhh)) → new_esEs13(zxw4000, zxw3000, dhh)
new_esEs32(zxw20, zxw15, ty_Float) → new_esEs17(zxw20, zxw15)
new_esEs23(zxw4000, zxw3000, app(app(ty_Either, ddh), dea)) → new_esEs7(zxw4000, zxw3000, ddh, dea)
new_esEs6(Just(zxw4000), Just(zxw3000), app(app(ty_@2, fd), ff)) → new_esEs5(zxw4000, zxw3000, fd, ff)
new_lt4(zxw79000, zxw80000, app(app(app(ty_@3, cc), cd), ce)) → new_lt5(zxw79000, zxw80000, cc, cd, ce)
new_esEs7(Left(zxw4000), Left(zxw3000), app(app(ty_Either, bfc), bfd), bef) → new_esEs7(zxw4000, zxw3000, bfc, bfd)
new_esEs31(zxw35, zxw30, ty_Ordering) → new_esEs9(zxw35, zxw30)
new_ltEs20(zxw7900, zxw8000, ty_Int) → new_ltEs9(zxw7900, zxw8000)
new_esEs33(zxw400, zxw300, app(app(ty_Either, bfh), bef)) → new_esEs7(zxw400, zxw300, bfh, bef)
new_lt19(zxw79000, zxw80000, app(app(ty_Either, bhd), bhe)) → new_lt14(zxw79000, zxw80000, bhd, bhe)
new_esEs33(zxw400, zxw300, app(ty_[], ddb)) → new_esEs13(zxw400, zxw300, ddb)
new_esEs9(GT, LT) → False
new_esEs9(LT, GT) → False
new_esEs33(zxw400, zxw300, ty_Char) → new_esEs12(zxw400, zxw300)
new_esEs13([], [], ddb) → True
new_lt4(zxw79000, zxw80000, app(ty_[], cf)) → new_lt10(zxw79000, zxw80000, cf)
new_compare110(zxw79000, zxw80000, True, bcf, bcg) → LT
new_esEs27(zxw4001, zxw3001, app(ty_Ratio, dge)) → new_esEs18(zxw4001, zxw3001, dge)
new_compare29(zxw79000, zxw80000, ty_Char) → new_compare17(zxw79000, zxw80000)
new_ltEs7(LT, EQ) → True
new_ltEs18(Just(zxw79000), Just(zxw80000), app(ty_Maybe, dac)) → new_ltEs18(zxw79000, zxw80000, dac)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Integer) → new_ltEs13(zxw79000, zxw80000)
new_ltEs20(zxw7900, zxw8000, ty_@0) → new_ltEs8(zxw7900, zxw8000)
new_lt20(zxw79001, zxw80001, app(app(ty_Either, cad), cae)) → new_lt14(zxw79001, zxw80001, cad, cae)
new_esEs23(zxw4000, zxw3000, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_compare35(zxw400, zxw300, h, ba) → new_compare26(Right(zxw400), Left(zxw300), False, h, ba)
new_ltEs8(zxw7900, zxw8000) → new_fsEs(new_compare30(zxw7900, zxw8000))
new_lt19(zxw79000, zxw80000, ty_Double) → new_lt15(zxw79000, zxw80000)
new_esEs22(zxw4000, zxw3000, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(ty_[], cgc)) → new_ltEs11(zxw79000, zxw80000, cgc)
new_ltEs21(zxw79002, zxw80002, ty_Char) → new_ltEs10(zxw79002, zxw80002)
new_esEs23(zxw4000, zxw3000, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Bool, hg) → new_ltEs12(zxw79000, zxw80000)
new_compare8(:%(zxw79000, zxw79001), :%(zxw80000, zxw80001), ty_Integer) → new_compare32(new_sr0(zxw79000, zxw80001), new_sr0(zxw80000, zxw79001))
new_esEs26(zxw4002, zxw3002, ty_Float) → new_esEs17(zxw4002, zxw3002)
new_esEs19(zxw79001, zxw80001, app(ty_Ratio, caf)) → new_esEs18(zxw79001, zxw80001, caf)
new_primMulNat0(Zero, Zero) → Zero
new_esEs20(zxw79000, zxw80000, app(ty_[], bhc)) → new_esEs13(zxw79000, zxw80000, bhc)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs34(zxw400, zxw300, ty_Char) → new_esEs12(zxw400, zxw300)
new_lt20(zxw79001, zxw80001, ty_@0) → new_lt7(zxw79001, zxw80001)
new_esEs27(zxw4001, zxw3001, app(app(app(ty_@3, dhd), dhe), dhf)) → new_esEs4(zxw4001, zxw3001, dhd, dhe, dhf)
new_esEs19(zxw79001, zxw80001, ty_Ordering) → new_esEs9(zxw79001, zxw80001)
new_esEs31(zxw35, zxw30, ty_Char) → new_esEs12(zxw35, zxw30)
new_esEs33(zxw400, zxw300, ty_Ordering) → new_esEs9(zxw400, zxw300)
new_esEs32(zxw20, zxw15, ty_Integer) → new_esEs15(zxw20, zxw15)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(ty_Ratio, dab)) → new_ltEs17(zxw79000, zxw80000, dab)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Bool, bef) → new_esEs14(zxw4000, zxw3000)
new_esEs24(zxw4001, zxw3001, ty_Integer) → new_esEs15(zxw4001, zxw3001)
new_lt19(zxw79000, zxw80000, ty_Ordering) → new_lt6(zxw79000, zxw80000)
new_lt20(zxw79001, zxw80001, app(app(ty_@2, cab), cac)) → new_lt11(zxw79001, zxw80001, cab, cac)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(ty_Ratio, cff), hg) → new_ltEs17(zxw79000, zxw80000, cff)
new_compare9(zxw79000, zxw80000, gd, ge, gf) → new_compare25(zxw79000, zxw80000, new_esEs4(zxw79000, zxw80000, gd, ge, gf), gd, ge, gf)
new_lt11(zxw79000, zxw80000, bcf, bcg) → new_esEs9(new_compare19(zxw79000, zxw80000, bcf, bcg), LT)
new_compare1([], :(zxw80000, zxw80001), he) → LT
new_esEs33(zxw400, zxw300, ty_@0) → new_esEs10(zxw400, zxw300)
new_lt18(zxw79000, zxw80000, bdb) → new_esEs9(new_compare27(zxw79000, zxw80000, bdb), LT)
new_esEs33(zxw400, zxw300, ty_Integer) → new_esEs15(zxw400, zxw300)
new_esEs8(zxw79000, zxw80000, ty_Int) → new_esEs11(zxw79000, zxw80000)
new_compare32(Integer(zxw79000), Integer(zxw80000)) → new_primCmpInt(zxw79000, zxw80000)
new_ltEs5(zxw79001, zxw80001, ty_Char) → new_ltEs10(zxw79001, zxw80001)
new_lt4(zxw79000, zxw80000, ty_Bool) → new_lt12(zxw79000, zxw80000)
new_compare27(zxw79000, zxw80000, bdb) → new_compare28(zxw79000, zxw80000, new_esEs6(zxw79000, zxw80000, bdb), bdb)
new_lt4(zxw79000, zxw80000, app(ty_Maybe, de)) → new_lt18(zxw79000, zxw80000, de)
new_compare29(zxw79000, zxw80000, ty_Bool) → new_compare31(zxw79000, zxw80000)
new_esEs31(zxw35, zxw30, ty_@0) → new_esEs10(zxw35, zxw30)
new_esEs8(zxw79000, zxw80000, ty_Double) → new_esEs16(zxw79000, zxw80000)
new_esEs22(zxw4000, zxw3000, app(app(ty_@2, dcc), dcd)) → new_esEs5(zxw4000, zxw3000, dcc, dcd)
new_lt4(zxw79000, zxw80000, ty_Ordering) → new_lt6(zxw79000, zxw80000)
new_esEs22(zxw4000, zxw3000, app(ty_Maybe, dcb)) → new_esEs6(zxw4000, zxw3000, dcb)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(app(app(ty_@3, cfh), cga), cgb)) → new_ltEs6(zxw79000, zxw80000, cfh, cga, cgb)
new_esEs34(zxw400, zxw300, app(app(ty_Either, bca), bcb)) → new_esEs7(zxw400, zxw300, bca, bcb)
new_esEs27(zxw4001, zxw3001, app(ty_Maybe, dgg)) → new_esEs6(zxw4001, zxw3001, dgg)
new_esEs8(zxw79000, zxw80000, app(app(app(ty_@3, cc), cd), ce)) → new_esEs4(zxw79000, zxw80000, cc, cd, ce)
new_esEs15(Integer(zxw4000), Integer(zxw3000)) → new_primEqInt(zxw4000, zxw3000)
new_ltEs21(zxw79002, zxw80002, app(app(ty_@2, cbd), cbe)) → new_ltEs4(zxw79002, zxw80002, cbd, cbe)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Float, hg) → new_ltEs16(zxw79000, zxw80000)
new_lt5(zxw79000, zxw80000, gd, ge, gf) → new_esEs9(new_compare9(zxw79000, zxw80000, gd, ge, gf), LT)
new_esEs22(zxw4000, zxw3000, app(ty_Ratio, dbh)) → new_esEs18(zxw4000, zxw3000, dbh)
new_esEs22(zxw4000, zxw3000, app(app(ty_Either, dce), dcf)) → new_esEs7(zxw4000, zxw3000, dce, dcf)
new_ltEs19(zxw7900, zxw8000, ty_Float) → new_ltEs16(zxw7900, zxw8000)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, app(ty_Maybe, bgc)) → new_esEs6(zxw4000, zxw3000, bgc)
new_pePe(False, zxw271) → zxw271
new_esEs7(Right(zxw4000), Left(zxw3000), bfh, bef) → False
new_esEs7(Left(zxw4000), Right(zxw3000), bfh, bef) → False
new_lt15(zxw79000, zxw80000) → new_esEs9(new_compare6(zxw79000, zxw80000), LT)
new_compare15(zxw790, zxw800, gh, ha) → new_compare26(zxw790, zxw800, new_esEs7(zxw790, zxw800, gh, ha), gh, ha)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Float) → new_ltEs16(zxw79000, zxw80000)
new_esEs31(zxw35, zxw30, app(app(app(ty_@3, beb), bec), bed)) → new_esEs4(zxw35, zxw30, beb, bec, bed)
new_ltEs12(True, False) → False
new_esEs34(zxw400, zxw300, app(ty_[], bbe)) → new_esEs13(zxw400, zxw300, bbe)
new_esEs20(zxw79000, zxw80000, ty_Double) → new_esEs16(zxw79000, zxw80000)
new_ltEs19(zxw7900, zxw8000, app(app(ty_@2, ca), cb)) → new_ltEs4(zxw7900, zxw8000, ca, cb)
new_esEs32(zxw20, zxw15, ty_@0) → new_esEs10(zxw20, zxw15)
new_compare23(zxw79000, zxw80000, True) → EQ
new_esEs31(zxw35, zxw30, ty_Float) → new_esEs17(zxw35, zxw30)
new_esEs27(zxw4001, zxw3001, app(app(ty_Either, dhb), dhc)) → new_esEs7(zxw4001, zxw3001, dhb, dhc)
new_esEs27(zxw4001, zxw3001, ty_Ordering) → new_esEs9(zxw4001, zxw3001)
new_esEs27(zxw4001, zxw3001, ty_Float) → new_esEs17(zxw4001, zxw3001)
new_esEs19(zxw79001, zxw80001, app(ty_Maybe, cag)) → new_esEs6(zxw79001, zxw80001, cag)
new_lt10(zxw79000, zxw80000, bhc) → new_esEs9(new_compare1(zxw79000, zxw80000, bhc), LT)
new_esEs26(zxw4002, zxw3002, ty_Char) → new_esEs12(zxw4002, zxw3002)
new_ltEs19(zxw7900, zxw8000, app(ty_[], he)) → new_ltEs11(zxw7900, zxw8000, he)
new_esEs26(zxw4002, zxw3002, ty_Int) → new_esEs11(zxw4002, zxw3002)
new_ltEs5(zxw79001, zxw80001, app(app(ty_@2, eb), ec)) → new_ltEs4(zxw79001, zxw80001, eb, ec)
new_lt19(zxw79000, zxw80000, app(ty_Ratio, gg)) → new_lt17(zxw79000, zxw80000, gg)
new_esEs22(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, app(app(app(ty_@3, eaf), eag), eah)) → new_esEs4(zxw4000, zxw3000, eaf, eag, eah)
new_esEs32(zxw20, zxw15, ty_Ordering) → new_esEs9(zxw20, zxw15)
new_compare29(zxw79000, zxw80000, app(app(ty_@2, ccf), ccg)) → new_compare19(zxw79000, zxw80000, ccf, ccg)
new_ltEs21(zxw79002, zxw80002, ty_Int) → new_ltEs9(zxw79002, zxw80002)
new_esEs20(zxw79000, zxw80000, ty_Char) → new_esEs12(zxw79000, zxw80000)
new_compare13(zxw235, zxw236, False, bch, bda) → GT
new_esEs9(GT, EQ) → False
new_esEs9(EQ, GT) → False
new_esEs19(zxw79001, zxw80001, app(app(ty_Either, cad), cae)) → new_esEs7(zxw79001, zxw80001, cad, cae)
new_esEs20(zxw79000, zxw80000, app(app(ty_@2, bcf), bcg)) → new_esEs5(zxw79000, zxw80000, bcf, bcg)
new_ltEs7(GT, GT) → True
new_compare36(zxw35, zxw30, bf, bg) → new_compare26(Right(zxw35), Right(zxw30), new_esEs31(zxw35, zxw30, bg), bf, bg)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, app(app(ty_@2, bgd), bge)) → new_esEs5(zxw4000, zxw3000, bgd, bge)
new_ltEs20(zxw7900, zxw8000, app(app(ty_@2, baf), bag)) → new_ltEs4(zxw7900, zxw8000, baf, bag)
new_esEs21(zxw4001, zxw3001, ty_Bool) → new_esEs14(zxw4001, zxw3001)
new_esEs32(zxw20, zxw15, ty_Bool) → new_esEs14(zxw20, zxw15)
new_primCompAux0(zxw79000, zxw80000, zxw272, he) → new_primCompAux00(zxw272, new_compare29(zxw79000, zxw80000, he))
new_ltEs21(zxw79002, zxw80002, ty_Ordering) → new_ltEs7(zxw79002, zxw80002)
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_compare29(zxw79000, zxw80000, app(ty_[], cce)) → new_compare1(zxw79000, zxw80000, cce)
new_lt20(zxw79001, zxw80001, ty_Ordering) → new_lt6(zxw79001, zxw80001)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_esEs8(zxw79000, zxw80000, app(ty_[], cf)) → new_esEs13(zxw79000, zxw80000, cf)
new_esEs33(zxw400, zxw300, app(app(app(ty_@3, deh), dfa), dfb)) → new_esEs4(zxw400, zxw300, deh, dfa, dfb)
new_esEs27(zxw4001, zxw3001, ty_@0) → new_esEs10(zxw4001, zxw3001)
new_compare25(zxw79000, zxw80000, True, gd, ge, gf) → EQ
new_esEs19(zxw79001, zxw80001, ty_Float) → new_esEs17(zxw79001, zxw80001)
new_ltEs5(zxw79001, zxw80001, ty_Ordering) → new_ltEs7(zxw79001, zxw80001)
new_lt4(zxw79000, zxw80000, app(ty_Ratio, dd)) → new_lt17(zxw79000, zxw80000, dd)
new_esEs28(zxw4000, zxw3000, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Int, bef) → new_esEs11(zxw4000, zxw3000)
new_ltEs21(zxw79002, zxw80002, ty_Float) → new_ltEs16(zxw79002, zxw80002)
new_esEs28(zxw4000, zxw3000, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_compare29(zxw79000, zxw80000, app(app(app(ty_@3, ccb), ccc), ccd)) → new_compare9(zxw79000, zxw80000, ccb, ccc, ccd)
new_lt19(zxw79000, zxw80000, app(app(ty_@2, bcf), bcg)) → new_lt11(zxw79000, zxw80000, bcf, bcg)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(app(app(ty_@3, chb), chc), chd)) → new_ltEs6(zxw79000, zxw80000, chb, chc, chd)
new_pePe(True, zxw271) → True
new_primEqNat0(Zero, Zero) → True
new_compare14(zxw242, zxw243, False, def, deg) → GT
new_esEs20(zxw79000, zxw80000, ty_Int) → new_esEs11(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Double) → new_ltEs15(zxw79000, zxw80000)
new_ltEs21(zxw79002, zxw80002, ty_Bool) → new_ltEs12(zxw79002, zxw80002)
new_esEs33(zxw400, zxw300, app(app(ty_@2, dad), dae)) → new_esEs5(zxw400, zxw300, dad, dae)
new_lt9(zxw79000, zxw80000) → new_esEs9(new_compare17(zxw79000, zxw80000), LT)
new_ltEs12(False, False) → True
new_esEs7(Left(zxw4000), Left(zxw3000), app(app(ty_@2, bfa), bfb), bef) → new_esEs5(zxw4000, zxw3000, bfa, bfb)
new_esEs26(zxw4002, zxw3002, app(ty_Maybe, dfe)) → new_esEs6(zxw4002, zxw3002, dfe)
new_compare8(:%(zxw79000, zxw79001), :%(zxw80000, zxw80001), ty_Int) → new_compare16(new_sr(zxw79000, zxw80001), new_sr(zxw80000, zxw79001))
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Ordering, bef) → new_esEs9(zxw4000, zxw3000)
new_esEs27(zxw4001, zxw3001, ty_Char) → new_esEs12(zxw4001, zxw3001)
new_esEs34(zxw400, zxw300, ty_Float) → new_esEs17(zxw400, zxw300)
new_lt7(zxw79000, zxw80000) → new_esEs9(new_compare30(zxw79000, zxw80000), LT)
new_compare110(zxw79000, zxw80000, False, bcf, bcg) → GT
new_sr(zxw4000, zxw3000) → new_primMulInt(zxw4000, zxw3000)
new_compare12(zxw79000, zxw80000, True, gd, ge, gf) → LT
new_lt19(zxw79000, zxw80000, ty_Int) → new_lt8(zxw79000, zxw80000)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(app(ty_@2, cgd), cge)) → new_ltEs4(zxw79000, zxw80000, cgd, cge)
new_ltEs19(zxw7900, zxw8000, ty_Char) → new_ltEs10(zxw7900, zxw8000)
new_esEs21(zxw4001, zxw3001, ty_Double) → new_esEs16(zxw4001, zxw3001)
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, app(app(ty_Either, bgf), bgg)) → new_esEs7(zxw4000, zxw3000, bgf, bgg)
new_esEs31(zxw35, zxw30, app(app(ty_Either, bdh), bea)) → new_esEs7(zxw35, zxw30, bdh, bea)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Double, hg) → new_ltEs15(zxw79000, zxw80000)
new_ltEs19(zxw7900, zxw8000, ty_Bool) → new_ltEs12(zxw7900, zxw8000)
new_esEs26(zxw4002, zxw3002, app(app(app(ty_@3, dgb), dgc), dgd)) → new_esEs4(zxw4002, zxw3002, dgb, dgc, dgd)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, app(ty_[], bgb)) → new_esEs13(zxw4000, zxw3000, bgb)
new_ltEs11(zxw7900, zxw8000, he) → new_fsEs(new_compare1(zxw7900, zxw8000, he))
new_ltEs20(zxw7900, zxw8000, ty_Float) → new_ltEs16(zxw7900, zxw8000)
new_esEs21(zxw4001, zxw3001, ty_Ordering) → new_esEs9(zxw4001, zxw3001)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_esEs9(EQ, EQ) → True
new_fsEs(zxw259) → new_not(new_esEs9(zxw259, GT))
new_esEs8(zxw79000, zxw80000, ty_Char) → new_esEs12(zxw79000, zxw80000)
new_primEqInt(Neg(Succ(zxw40000)), Neg(Succ(zxw30000))) → new_primEqNat0(zxw40000, zxw30000)
new_esEs8(zxw79000, zxw80000, app(app(ty_@2, cg), da)) → new_esEs5(zxw79000, zxw80000, cg, da)
new_compare13(zxw235, zxw236, True, bch, bda) → LT
new_compare26(Left(zxw7900), Right(zxw8000), False, gh, ha) → LT
new_esEs13(:(zxw4000, zxw4001), :(zxw3000, zxw3001), ddb) → new_asAs(new_esEs23(zxw4000, zxw3000, ddb), new_esEs13(zxw4001, zxw3001, ddb))
new_esEs26(zxw4002, zxw3002, app(ty_[], dfd)) → new_esEs13(zxw4002, zxw3002, dfd)
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_ltEs19(zxw7900, zxw8000, app(ty_Ratio, hh)) → new_ltEs17(zxw7900, zxw8000, hh)
new_ltEs20(zxw7900, zxw8000, ty_Bool) → new_ltEs12(zxw7900, zxw8000)
new_esEs21(zxw4001, zxw3001, ty_Char) → new_esEs12(zxw4001, zxw3001)
new_compare23(zxw79000, zxw80000, False) → new_compare10(zxw79000, zxw80000, new_ltEs12(zxw79000, zxw80000))
new_ltEs14(Right(zxw79000), Left(zxw80000), hf, hg) → False
new_compare210(zxw79000, zxw80000, False, bcf, bcg) → new_compare110(zxw79000, zxw80000, new_ltEs4(zxw79000, zxw80000, bcf, bcg), bcf, bcg)
new_primCmpNat1(Zero, zxw7900) → LT
new_compare7(Float(zxw79000, zxw79001), Float(zxw80000, zxw80001)) → new_compare16(new_sr(zxw79000, zxw80000), new_sr(zxw79001, zxw80001))
new_ltEs21(zxw79002, zxw80002, ty_Integer) → new_ltEs13(zxw79002, zxw80002)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_lt20(zxw79001, zxw80001, app(ty_Maybe, cag)) → new_lt18(zxw79001, zxw80001, cag)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Integer, bef) → new_esEs15(zxw4000, zxw3000)
new_ltEs5(zxw79001, zxw80001, ty_Bool) → new_ltEs12(zxw79001, zxw80001)
new_esEs19(zxw79001, zxw80001, ty_Bool) → new_esEs14(zxw79001, zxw80001)
new_ltEs7(EQ, EQ) → True
new_ltEs20(zxw7900, zxw8000, app(ty_Ratio, bbb)) → new_ltEs17(zxw7900, zxw8000, bbb)
new_primEqInt(Neg(Zero), Neg(Succ(zxw30000))) → False
new_primEqInt(Neg(Succ(zxw40000)), Neg(Zero)) → False
new_ltEs5(zxw79001, zxw80001, ty_Integer) → new_ltEs13(zxw79001, zxw80001)
new_compare26(zxw790, zxw800, True, gh, ha) → EQ
new_compare111(zxw79000, zxw80000, True, bdb) → LT
new_esEs20(zxw79000, zxw80000, ty_@0) → new_esEs10(zxw79000, zxw80000)
new_esEs31(zxw35, zxw30, app(ty_Ratio, bdc)) → new_esEs18(zxw35, zxw30, bdc)
new_ltEs21(zxw79002, zxw80002, app(app(ty_Either, cbf), cbg)) → new_ltEs14(zxw79002, zxw80002, cbf, cbg)
new_esEs8(zxw79000, zxw80000, ty_Float) → new_esEs17(zxw79000, zxw80000)
new_esEs34(zxw400, zxw300, app(app(ty_@2, bbg), bbh)) → new_esEs5(zxw400, zxw300, bbg, bbh)
new_esEs23(zxw4000, zxw3000, app(app(app(ty_@3, deb), dec), ded)) → new_esEs4(zxw4000, zxw3000, deb, dec, ded)
new_ltEs21(zxw79002, zxw80002, app(ty_[], cbc)) → new_ltEs11(zxw79002, zxw80002, cbc)
new_esEs21(zxw4001, zxw3001, ty_Float) → new_esEs17(zxw4001, zxw3001)
new_compare24(zxw79000, zxw80000, False) → new_compare11(zxw79000, zxw80000, new_ltEs7(zxw79000, zxw80000))
new_ltEs5(zxw79001, zxw80001, app(ty_Ratio, ef)) → new_ltEs17(zxw79001, zxw80001, ef)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_esEs26(zxw4002, zxw3002, app(app(ty_Either, dfh), dga)) → new_esEs7(zxw4002, zxw3002, dfh, dga)
new_lt20(zxw79001, zxw80001, ty_Int) → new_lt8(zxw79001, zxw80001)
new_lt4(zxw79000, zxw80000, ty_Int) → new_lt8(zxw79000, zxw80000)
new_ltEs20(zxw7900, zxw8000, ty_Double) → new_ltEs15(zxw7900, zxw8000)
new_esEs34(zxw400, zxw300, app(app(app(ty_@3, bcc), bcd), bce)) → new_esEs4(zxw400, zxw300, bcc, bcd, bce)
new_ltEs7(GT, LT) → False
new_lt12(zxw79000, zxw80000) → new_esEs9(new_compare31(zxw79000, zxw80000), LT)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Int, hg) → new_ltEs9(zxw79000, zxw80000)
new_lt20(zxw79001, zxw80001, ty_Integer) → new_lt13(zxw79001, zxw80001)
new_ltEs7(GT, EQ) → False
new_esEs6(Nothing, Nothing, eh) → True
new_primEqInt(Pos(Succ(zxw40000)), Pos(Succ(zxw30000))) → new_primEqNat0(zxw40000, zxw30000)
new_lt8(zxw790, zxw800) → new_esEs9(new_compare16(zxw790, zxw800), LT)
new_esEs21(zxw4001, zxw3001, app(ty_Maybe, dah)) → new_esEs6(zxw4001, zxw3001, dah)
new_lt6(zxw79000, zxw80000) → new_esEs9(new_compare18(zxw79000, zxw80000), LT)
new_esEs32(zxw20, zxw15, app(app(ty_Either, cea), ceb)) → new_esEs7(zxw20, zxw15, cea, ceb)
new_esEs14(False, True) → False
new_esEs14(True, False) → False
new_esEs32(zxw20, zxw15, app(ty_[], cde)) → new_esEs13(zxw20, zxw15, cde)
new_esEs26(zxw4002, zxw3002, ty_Integer) → new_esEs15(zxw4002, zxw3002)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, app(app(app(ty_@3, bgh), bha), bhb)) → new_esEs4(zxw4000, zxw3000, bgh, bha, bhb)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs6(Nothing, Just(zxw3000), eh) → False
new_esEs6(Just(zxw4000), Nothing, eh) → False
new_primEqNat0(Succ(zxw40000), Succ(zxw30000)) → new_primEqNat0(zxw40000, zxw30000)
new_esEs33(zxw400, zxw300, app(ty_Ratio, dee)) → new_esEs18(zxw400, zxw300, dee)
new_esEs16(Double(zxw4000, zxw4001), Double(zxw3000, zxw3001)) → new_esEs11(new_sr(zxw4000, zxw3000), new_sr(zxw4001, zxw3001))
new_lt19(zxw79000, zxw80000, ty_@0) → new_lt7(zxw79000, zxw80000)
new_ltEs5(zxw79001, zxw80001, app(ty_Maybe, eg)) → new_ltEs18(zxw79001, zxw80001, eg)
new_esEs17(Float(zxw4000, zxw4001), Float(zxw3000, zxw3001)) → new_esEs11(new_sr(zxw4000, zxw3000), new_sr(zxw4001, zxw3001))
new_primCompAux00(zxw276, LT) → LT
new_esEs28(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), app(ty_Ratio, bee), bef) → new_esEs18(zxw4000, zxw3000, bee)
new_esEs21(zxw4001, zxw3001, ty_Int) → new_esEs11(zxw4001, zxw3001)
new_compare1(:(zxw79000, zxw79001), :(zxw80000, zxw80001), he) → new_primCompAux0(zxw79000, zxw80000, new_compare1(zxw79001, zxw80001, he), he)
new_primEqInt(Pos(Zero), Pos(Succ(zxw30000))) → False
new_primEqInt(Pos(Succ(zxw40000)), Pos(Zero)) → False
new_compare29(zxw79000, zxw80000, ty_Int) → new_compare16(zxw79000, zxw80000)
new_lt20(zxw79001, zxw80001, app(ty_Ratio, caf)) → new_lt17(zxw79001, zxw80001, caf)
new_esEs34(zxw400, zxw300, ty_Double) → new_esEs16(zxw400, zxw300)
new_ltEs20(zxw7900, zxw8000, ty_Integer) → new_ltEs13(zxw7900, zxw8000)
new_esEs31(zxw35, zxw30, app(app(ty_@2, bdf), bdg)) → new_esEs5(zxw35, zxw30, bdf, bdg)
new_esEs5(@2(zxw4000, zxw4001), @2(zxw3000, zxw3001), dad, dae) → new_asAs(new_esEs22(zxw4000, zxw3000, dad), new_esEs21(zxw4001, zxw3001, dae))
new_ltEs18(Nothing, Nothing, baa) → True
new_esEs32(zxw20, zxw15, app(ty_Maybe, cdf)) → new_esEs6(zxw20, zxw15, cdf)
new_ltEs21(zxw79002, zxw80002, app(ty_Ratio, cbh)) → new_ltEs17(zxw79002, zxw80002, cbh)
new_esEs23(zxw4000, zxw3000, app(app(ty_@2, ddf), ddg)) → new_esEs5(zxw4000, zxw3000, ddf, ddg)
new_esEs33(zxw400, zxw300, ty_Bool) → new_esEs14(zxw400, zxw300)
new_esEs20(zxw79000, zxw80000, app(app(app(ty_@3, gd), ge), gf)) → new_esEs4(zxw79000, zxw80000, gd, ge, gf)
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_ltEs21(zxw79002, zxw80002, app(app(app(ty_@3, cah), cba), cbb)) → new_ltEs6(zxw79002, zxw80002, cah, cba, cbb)
new_ltEs10(zxw7900, zxw8000) → new_fsEs(new_compare17(zxw7900, zxw8000))
new_compare17(Char(zxw79000), Char(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_sr0(Integer(zxw800000), Integer(zxw790010)) → Integer(new_primMulInt(zxw800000, zxw790010))
new_ltEs5(zxw79001, zxw80001, ty_Double) → new_ltEs15(zxw79001, zxw80001)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_esEs8(zxw79000, zxw80000, app(app(ty_Either, db), dc)) → new_esEs7(zxw79000, zxw80000, db, dc)
new_primEqInt(Neg(Succ(zxw40000)), Pos(zxw3000)) → False
new_primEqInt(Pos(Succ(zxw40000)), Neg(zxw3000)) → False
new_compare29(zxw79000, zxw80000, ty_Integer) → new_compare32(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Char) → new_ltEs10(zxw79000, zxw80000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_@0, bef) → new_esEs10(zxw4000, zxw3000)
new_lt19(zxw79000, zxw80000, app(app(app(ty_@3, gd), ge), gf)) → new_lt5(zxw79000, zxw80000, gd, ge, gf)
new_esEs32(zxw20, zxw15, app(app(ty_@2, cdg), cdh)) → new_esEs5(zxw20, zxw15, cdg, cdh)
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_esEs28(zxw4000, zxw3000, app(ty_Maybe, eaa)) → new_esEs6(zxw4000, zxw3000, eaa)
new_ltEs21(zxw79002, zxw80002, ty_@0) → new_ltEs8(zxw79002, zxw80002)
new_esEs21(zxw4001, zxw3001, app(ty_[], dag)) → new_esEs13(zxw4001, zxw3001, dag)
new_primEqInt(Neg(Zero), Pos(Succ(zxw30000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(zxw30000))) → False
new_ltEs7(EQ, GT) → True
new_lt4(zxw79000, zxw80000, ty_Double) → new_lt15(zxw79000, zxw80000)
new_esEs34(zxw400, zxw300, ty_Ordering) → new_esEs9(zxw400, zxw300)
new_esEs21(zxw4001, zxw3001, ty_Integer) → new_esEs15(zxw4001, zxw3001)
new_esEs31(zxw35, zxw30, ty_Integer) → new_esEs15(zxw35, zxw30)
new_primCompAux00(zxw276, EQ) → zxw276
new_esEs28(zxw4000, zxw3000, app(app(ty_Either, ead), eae)) → new_esEs7(zxw4000, zxw3000, ead, eae)
new_compare24(zxw79000, zxw80000, True) → EQ
new_compare6(Double(zxw79000, zxw79001), Double(zxw80000, zxw80001)) → new_compare16(new_sr(zxw79000, zxw80000), new_sr(zxw79001, zxw80001))
new_esEs8(zxw79000, zxw80000, ty_@0) → new_esEs10(zxw79000, zxw80000)
new_ltEs5(zxw79001, zxw80001, app(app(ty_Either, ed), ee)) → new_ltEs14(zxw79001, zxw80001, ed, ee)
new_lt13(zxw79000, zxw80000) → new_esEs9(new_compare32(zxw79000, zxw80000), LT)
new_esEs27(zxw4001, zxw3001, ty_Double) → new_esEs16(zxw4001, zxw3001)
new_esEs7(Left(zxw4000), Left(zxw3000), app(app(app(ty_@3, bfe), bff), bfg), bef) → new_esEs4(zxw4000, zxw3000, bfe, bff, bfg)
new_esEs26(zxw4002, zxw3002, app(app(ty_@2, dff), dfg)) → new_esEs5(zxw4002, zxw3002, dff, dfg)
new_esEs21(zxw4001, zxw3001, app(app(ty_@2, dba), dbb)) → new_esEs5(zxw4001, zxw3001, dba, dbb)
new_lt19(zxw79000, zxw80000, app(ty_Maybe, bdb)) → new_lt18(zxw79000, zxw80000, bdb)
new_esEs12(Char(zxw4000), Char(zxw3000)) → new_primEqNat0(zxw4000, zxw3000)
new_ltEs20(zxw7900, zxw8000, app(app(app(ty_@3, bab), bac), bad)) → new_ltEs6(zxw7900, zxw8000, bab, bac, bad)
new_not(False) → True
new_lt20(zxw79001, zxw80001, ty_Char) → new_lt9(zxw79001, zxw80001)
new_esEs11(zxw400, zxw300) → new_primEqInt(zxw400, zxw300)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(ty_Maybe, cha)) → new_ltEs18(zxw79000, zxw80000, cha)
new_ltEs18(Just(zxw79000), Nothing, baa) → False
new_esEs7(Left(zxw4000), Left(zxw3000), app(ty_Maybe, beh), bef) → new_esEs6(zxw4000, zxw3000, beh)
new_esEs8(zxw79000, zxw80000, app(ty_Maybe, de)) → new_esEs6(zxw79000, zxw80000, de)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Double, bef) → new_esEs16(zxw4000, zxw3000)
new_compare210(zxw79000, zxw80000, True, bcf, bcg) → EQ
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_esEs19(zxw79001, zxw80001, ty_Int) → new_esEs11(zxw79001, zxw80001)
new_compare12(zxw79000, zxw80000, False, gd, ge, gf) → GT
new_ltEs16(zxw7900, zxw8000) → new_fsEs(new_compare7(zxw7900, zxw8000))
new_esEs32(zxw20, zxw15, ty_Char) → new_esEs12(zxw20, zxw15)
new_esEs9(GT, GT) → True
new_esEs26(zxw4002, zxw3002, app(ty_Ratio, dfc)) → new_esEs18(zxw4002, zxw3002, dfc)
new_esEs25(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_lt20(zxw79001, zxw80001, app(ty_[], caa)) → new_lt10(zxw79001, zxw80001, caa)
new_lt4(zxw79000, zxw80000, app(app(ty_Either, db), dc)) → new_lt14(zxw79000, zxw80000, db, dc)
new_esEs26(zxw4002, zxw3002, ty_Bool) → new_esEs14(zxw4002, zxw3002)
new_compare19(zxw79000, zxw80000, bcf, bcg) → new_compare210(zxw79000, zxw80000, new_esEs5(zxw79000, zxw80000, bcf, bcg), bcf, bcg)
new_esEs8(zxw79000, zxw80000, ty_Bool) → new_esEs14(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Double) → new_ltEs15(zxw79000, zxw80000)
new_esEs28(zxw4000, zxw3000, app(app(ty_@2, eab), eac)) → new_esEs5(zxw4000, zxw3000, eab, eac)
new_esEs34(zxw400, zxw300, ty_Int) → new_esEs11(zxw400, zxw300)
new_ltEs19(zxw7900, zxw8000, app(app(app(ty_@3, hb), hc), hd)) → new_ltEs6(zxw7900, zxw8000, hb, hc, hd)
new_esEs32(zxw20, zxw15, app(app(app(ty_@3, cec), ced), cee)) → new_esEs4(zxw20, zxw15, cec, ced, cee)
new_lt4(zxw79000, zxw80000, ty_Char) → new_lt9(zxw79000, zxw80000)
new_esEs22(zxw4000, zxw3000, app(app(app(ty_@3, dcg), dch), dda)) → new_esEs4(zxw4000, zxw3000, dcg, dch, dda)
new_esEs22(zxw4000, zxw3000, app(ty_[], dca)) → new_esEs13(zxw4000, zxw3000, dca)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_@0) → new_ltEs8(zxw79000, zxw80000)
new_esEs23(zxw4000, zxw3000, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Float, bef) → new_esEs17(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_esEs27(zxw4001, zxw3001, ty_Int) → new_esEs11(zxw4001, zxw3001)
new_esEs19(zxw79001, zxw80001, app(app(app(ty_@3, bhf), bhg), bhh)) → new_esEs4(zxw79001, zxw80001, bhf, bhg, bhh)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_ltEs14(Left(zxw79000), Left(zxw80000), app(app(app(ty_@3, cef), ceg), ceh), hg) → new_ltEs6(zxw79000, zxw80000, cef, ceg, ceh)
new_ltEs19(zxw7900, zxw8000, ty_Int) → new_ltEs9(zxw7900, zxw8000)
new_compare33(zxw20, zxw15, bc, bd) → new_compare26(Left(zxw20), Left(zxw15), new_esEs32(zxw20, zxw15, bc), bc, bd)
new_lt4(zxw79000, zxw80000, ty_@0) → new_lt7(zxw79000, zxw80000)
new_lt20(zxw79001, zxw80001, ty_Double) → new_lt15(zxw79001, zxw80001)
new_lt19(zxw79000, zxw80000, ty_Float) → new_lt16(zxw79000, zxw80000)
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_esEs26(zxw4002, zxw3002, ty_@0) → new_esEs10(zxw4002, zxw3002)
new_lt19(zxw79000, zxw80000, ty_Bool) → new_lt12(zxw79000, zxw80000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Char, bef) → new_esEs12(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_lt4(zxw79000, zxw80000, ty_Float) → new_lt16(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(ty_[], che)) → new_ltEs11(zxw79000, zxw80000, che)
new_primMulInt(Neg(zxw40000), Neg(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_ltEs5(zxw79001, zxw80001, app(app(app(ty_@3, df), dg), dh)) → new_ltEs6(zxw79001, zxw80001, df, dg, dh)
new_primCmpNat2(Zero, Zero) → EQ
new_esEs20(zxw79000, zxw80000, ty_Integer) → new_esEs15(zxw79000, zxw80000)
new_primEqNat0(Zero, Succ(zxw30000)) → False
new_primEqNat0(Succ(zxw40000), Zero) → False
new_esEs21(zxw4001, zxw3001, ty_@0) → new_esEs10(zxw4001, zxw3001)
new_esEs22(zxw4000, zxw3000, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_esEs20(zxw79000, zxw80000, ty_Bool) → new_esEs14(zxw79000, zxw80000)
new_ltEs5(zxw79001, zxw80001, app(ty_[], ea)) → new_ltEs11(zxw79001, zxw80001, ea)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs23(zxw4000, zxw3000, app(ty_Ratio, ddc)) → new_esEs18(zxw4000, zxw3000, ddc)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(app(ty_@2, chf), chg)) → new_ltEs4(zxw79000, zxw80000, chf, chg)
new_esEs33(zxw400, zxw300, app(ty_Maybe, eh)) → new_esEs6(zxw400, zxw300, eh)
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_esEs34(zxw400, zxw300, ty_Bool) → new_esEs14(zxw400, zxw300)
new_ltEs5(zxw79001, zxw80001, ty_Int) → new_ltEs9(zxw79001, zxw80001)
new_esEs27(zxw4001, zxw3001, app(app(ty_@2, dgh), dha)) → new_esEs5(zxw4001, zxw3001, dgh, dha)
new_primCmpNat0(zxw7900, Zero) → GT
new_compare26(Right(zxw7900), Left(zxw8000), False, gh, ha) → GT
new_esEs33(zxw400, zxw300, ty_Double) → new_esEs16(zxw400, zxw300)
new_esEs23(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_@0, hg) → new_ltEs8(zxw79000, zxw80000)
new_ltEs21(zxw79002, zxw80002, app(ty_Maybe, cca)) → new_ltEs18(zxw79002, zxw80002, cca)
new_esEs21(zxw4001, zxw3001, app(app(ty_Either, dbc), dbd)) → new_esEs7(zxw4001, zxw3001, dbc, dbd)
new_esEs22(zxw4000, zxw3000, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Bool) → new_ltEs12(zxw79000, zxw80000)
new_compare29(zxw79000, zxw80000, app(ty_Maybe, cdc)) → new_compare27(zxw79000, zxw80000, cdc)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_ltEs14(Left(zxw79000), Left(zxw80000), app(ty_Maybe, cfg), hg) → new_ltEs18(zxw79000, zxw80000, cfg)
new_lt20(zxw79001, zxw80001, ty_Float) → new_lt16(zxw79001, zxw80001)
new_lt17(zxw79000, zxw80000, gg) → new_esEs9(new_compare8(zxw79000, zxw80000, gg), LT)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Ordering) → new_ltEs7(zxw79000, zxw80000)
new_esEs32(zxw20, zxw15, ty_Int) → new_esEs11(zxw20, zxw15)
new_compare30(@0, @0) → EQ
new_lt19(zxw79000, zxw80000, app(ty_[], bhc)) → new_lt10(zxw79000, zxw80000, bhc)
new_esEs21(zxw4001, zxw3001, app(app(app(ty_@3, dbe), dbf), dbg)) → new_esEs4(zxw4001, zxw3001, dbe, dbf, dbg)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_esEs20(zxw79000, zxw80000, app(ty_Ratio, gg)) → new_esEs18(zxw79000, zxw80000, gg)
new_esEs6(Just(zxw4000), Just(zxw3000), app(app(app(ty_@3, ga), gb), gc)) → new_esEs4(zxw4000, zxw3000, ga, gb, gc)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(app(ty_Either, chh), daa)) → new_ltEs14(zxw79000, zxw80000, chh, daa)
new_esEs24(zxw4001, zxw3001, ty_Int) → new_esEs11(zxw4001, zxw3001)
new_esEs8(zxw79000, zxw80000, ty_Ordering) → new_esEs9(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Ordering) → new_ltEs7(zxw79000, zxw80000)
new_esEs34(zxw400, zxw300, ty_Integer) → new_esEs15(zxw400, zxw300)
new_esEs20(zxw79000, zxw80000, app(app(ty_Either, bhd), bhe)) → new_esEs7(zxw79000, zxw80000, bhd, bhe)
new_compare29(zxw79000, zxw80000, app(ty_Ratio, cdb)) → new_compare8(zxw79000, zxw80000, cdb)
new_lt4(zxw79000, zxw80000, app(app(ty_@2, cg), da)) → new_lt11(zxw79000, zxw80000, cg, da)
new_compare29(zxw79000, zxw80000, ty_Float) → new_compare7(zxw79000, zxw80000)
new_esEs19(zxw79001, zxw80001, app(app(ty_@2, cab), cac)) → new_esEs5(zxw79001, zxw80001, cab, cac)
new_esEs10(@0, @0) → True
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_compare29(zxw79000, zxw80000, ty_Double) → new_compare6(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, app(ty_Maybe, bdb)) → new_esEs6(zxw79000, zxw80000, bdb)
new_ltEs14(Left(zxw79000), Right(zxw80000), hf, hg) → True
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Float) → new_ltEs16(zxw79000, zxw80000)
new_esEs28(zxw4000, zxw3000, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_compare29(zxw79000, zxw80000, app(app(ty_Either, cch), cda)) → new_compare15(zxw79000, zxw80000, cch, cda)
new_esEs19(zxw79001, zxw80001, ty_Double) → new_esEs16(zxw79001, zxw80001)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_ltEs20(zxw7900, zxw8000, app(app(ty_Either, bah), bba)) → new_ltEs14(zxw7900, zxw8000, bah, bba)
new_asAs(False, zxw230) → False
new_ltEs13(zxw7900, zxw8000) → new_fsEs(new_compare32(zxw7900, zxw8000))
new_ltEs19(zxw7900, zxw8000, app(app(ty_Either, hf), hg)) → new_ltEs14(zxw7900, zxw8000, hf, hg)
new_compare34(zxw400, zxw300, h, ba) → new_compare26(Left(zxw400), Right(zxw300), False, h, ba)
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Pos(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_ltEs20(zxw7900, zxw8000, app(ty_[], bae)) → new_ltEs11(zxw7900, zxw8000, bae)
new_compare16(zxw79, zxw80) → new_primCmpInt(zxw79, zxw80)
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_esEs13(:(zxw4000, zxw4001), [], ddb) → False
new_esEs13([], :(zxw3000, zxw3001), ddb) → False
new_compare25(zxw79000, zxw80000, False, gd, ge, gf) → new_compare12(zxw79000, zxw80000, new_ltEs6(zxw79000, zxw80000, gd, ge, gf), gd, ge, gf)
new_esEs34(zxw400, zxw300, ty_@0) → new_esEs10(zxw400, zxw300)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(app(ty_@2, cfb), cfc), hg) → new_ltEs4(zxw79000, zxw80000, cfb, cfc)
new_esEs6(Just(zxw4000), Just(zxw3000), app(ty_Maybe, fc)) → new_esEs6(zxw4000, zxw3000, fc)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_@0) → new_esEs10(zxw4000, zxw3000)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(ty_[], cfa), hg) → new_ltEs11(zxw79000, zxw80000, cfa)
new_esEs7(Left(zxw4000), Left(zxw3000), app(ty_[], beg), bef) → new_esEs13(zxw4000, zxw3000, beg)
new_esEs31(zxw35, zxw30, ty_Double) → new_esEs16(zxw35, zxw30)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_compare31(zxw79000, zxw80000) → new_compare23(zxw79000, zxw80000, new_esEs14(zxw79000, zxw80000))
new_ltEs18(Nothing, Just(zxw80000), baa) → True
new_esEs28(zxw4000, zxw3000, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_ltEs21(zxw79002, zxw80002, ty_Double) → new_ltEs15(zxw79002, zxw80002)
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_ltEs12(True, True) → True
new_esEs23(zxw4000, zxw3000, app(ty_Maybe, dde)) → new_esEs6(zxw4000, zxw3000, dde)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_esEs8(zxw79000, zxw80000, ty_Integer) → new_esEs15(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(app(ty_Either, cgf), cgg)) → new_ltEs14(zxw79000, zxw80000, cgf, cgg)
new_ltEs6(@3(zxw79000, zxw79001, zxw79002), @3(zxw80000, zxw80001, zxw80002), hb, hc, hd) → new_pePe(new_lt19(zxw79000, zxw80000, hb), new_asAs(new_esEs20(zxw79000, zxw80000, hb), new_pePe(new_lt20(zxw79001, zxw80001, hc), new_asAs(new_esEs19(zxw79001, zxw80001, hc), new_ltEs21(zxw79002, zxw80002, hd)))))
new_esEs28(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_lt16(zxw79000, zxw80000) → new_esEs9(new_compare7(zxw79000, zxw80000), LT)
new_esEs23(zxw4000, zxw3000, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Integer, hg) → new_ltEs13(zxw79000, zxw80000)
new_esEs34(zxw400, zxw300, app(ty_Ratio, bbd)) → new_esEs18(zxw400, zxw300, bbd)
new_ltEs12(False, True) → True
new_esEs23(zxw4000, zxw3000, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs8(zxw79000, zxw80000, app(ty_Ratio, dd)) → new_esEs18(zxw79000, zxw80000, dd)
new_esEs23(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs14(True, True) → True
new_compare111(zxw79000, zxw80000, False, bdb) → GT
new_esEs31(zxw35, zxw30, app(ty_[], bdd)) → new_esEs13(zxw35, zxw30, bdd)
new_esEs27(zxw4001, zxw3001, ty_Bool) → new_esEs14(zxw4001, zxw3001)
new_esEs20(zxw79000, zxw80000, ty_Ordering) → new_esEs9(zxw79000, zxw80000)
new_ltEs19(zxw7900, zxw8000, ty_@0) → new_ltEs8(zxw7900, zxw8000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Int) → new_ltEs9(zxw79000, zxw80000)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(app(ty_Either, cfd), cfe), hg) → new_ltEs14(zxw79000, zxw80000, cfd, cfe)
new_lt19(zxw79000, zxw80000, ty_Integer) → new_lt13(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, ty_Float) → new_esEs17(zxw79000, zxw80000)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs34(zxw400, zxw300, app(ty_Maybe, bbf)) → new_esEs6(zxw400, zxw300, bbf)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Ordering, hg) → new_ltEs7(zxw79000, zxw80000)
new_compare11(zxw79000, zxw80000, False) → GT
new_esEs4(@3(zxw4000, zxw4001, zxw4002), @3(zxw3000, zxw3001, zxw3002), deh, dfa, dfb) → new_asAs(new_esEs28(zxw4000, zxw3000, deh), new_asAs(new_esEs27(zxw4001, zxw3001, dfa), new_esEs26(zxw4002, zxw3002, dfb)))
new_esEs6(Just(zxw4000), Just(zxw3000), app(ty_[], fb)) → new_esEs13(zxw4000, zxw3000, fb)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Int) → new_ltEs9(zxw79000, zxw80000)
new_esEs9(EQ, LT) → False
new_esEs9(LT, EQ) → False
new_compare26(Right(zxw7900), Right(zxw8000), False, gh, ha) → new_compare14(zxw7900, zxw8000, new_ltEs20(zxw7900, zxw8000, ha), gh, ha)
new_compare11(zxw79000, zxw80000, True) → LT
new_ltEs5(zxw79001, zxw80001, ty_@0) → new_ltEs8(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, ty_Bool) → new_lt12(zxw79001, zxw80001)
new_compare14(zxw242, zxw243, True, def, deg) → LT
new_esEs32(zxw20, zxw15, app(ty_Ratio, cdd)) → new_esEs18(zxw20, zxw15, cdd)
new_esEs14(False, False) → True
new_esEs18(:%(zxw4000, zxw4001), :%(zxw3000, zxw3001), dee) → new_asAs(new_esEs25(zxw4000, zxw3000, dee), new_esEs24(zxw4001, zxw3001, dee))
new_compare26(Left(zxw7900), Left(zxw8000), False, gh, ha) → new_compare13(zxw7900, zxw8000, new_ltEs19(zxw7900, zxw8000, gh), gh, ha)
new_esEs33(zxw400, zxw300, ty_Float) → new_esEs17(zxw400, zxw300)
new_ltEs19(zxw7900, zxw8000, ty_Double) → new_ltEs15(zxw7900, zxw8000)
new_ltEs7(EQ, LT) → False
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Char) → new_esEs12(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_ltEs7(LT, LT) → True
new_lt20(zxw79001, zxw80001, app(app(app(ty_@3, bhf), bhg), bhh)) → new_lt5(zxw79001, zxw80001, bhf, bhg, bhh)
new_lt14(zxw790, zxw800, gh, ha) → new_esEs9(new_compare15(zxw790, zxw800, gh, ha), LT)
new_esEs22(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_ltEs9(zxw7900, zxw8000) → new_fsEs(new_compare16(zxw7900, zxw8000))
new_compare29(zxw79000, zxw80000, ty_Ordering) → new_compare18(zxw79000, zxw80000)
new_primPlusNat1(Zero, Zero) → Zero
new_esEs26(zxw4002, zxw3002, ty_Ordering) → new_esEs9(zxw4002, zxw3002)
new_esEs19(zxw79001, zxw80001, ty_Integer) → new_esEs15(zxw79001, zxw80001)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Char, hg) → new_ltEs10(zxw79000, zxw80000)
new_asAs(True, zxw230) → zxw230
new_esEs25(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_ltEs7(LT, GT) → True
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Float) → new_esEs17(zxw4000, zxw3000)
new_ltEs5(zxw79001, zxw80001, ty_Float) → new_ltEs16(zxw79001, zxw80001)
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, app(ty_Ratio, bga)) → new_esEs18(zxw4000, zxw3000, bga)
new_esEs27(zxw4001, zxw3001, app(ty_[], dgf)) → new_esEs13(zxw4001, zxw3001, dgf)
new_esEs6(Just(zxw4000), Just(zxw3000), app(app(ty_Either, fg), fh)) → new_esEs7(zxw4000, zxw3000, fg, fh)
new_esEs32(zxw20, zxw15, ty_Double) → new_esEs16(zxw20, zxw15)
new_compare28(zxw79000, zxw80000, False, bdb) → new_compare111(zxw79000, zxw80000, new_ltEs18(zxw79000, zxw80000, bdb), bdb)
new_compare1(:(zxw79000, zxw79001), [], he) → GT
new_esEs28(zxw4000, zxw3000, app(ty_Ratio, dhg)) → new_esEs18(zxw4000, zxw3000, dhg)
new_lt4(zxw79000, zxw80000, ty_Integer) → new_lt13(zxw79000, zxw80000)
new_esEs19(zxw79001, zxw80001, ty_@0) → new_esEs10(zxw79001, zxw80001)
new_compare29(zxw79000, zxw80000, ty_@0) → new_compare30(zxw79000, zxw80000)
new_ltEs19(zxw7900, zxw8000, ty_Integer) → new_ltEs13(zxw7900, zxw8000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(ty_Ratio, cgh)) → new_ltEs17(zxw79000, zxw80000, cgh)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Integer) → new_ltEs13(zxw79000, zxw80000)
new_ltEs19(zxw7900, zxw8000, ty_Ordering) → new_ltEs7(zxw7900, zxw8000)
new_compare28(zxw79000, zxw80000, True, bdb) → EQ
new_esEs31(zxw35, zxw30, ty_Int) → new_esEs11(zxw35, zxw30)
new_esEs26(zxw4002, zxw3002, ty_Double) → new_esEs16(zxw4002, zxw3002)
new_esEs33(zxw400, zxw300, ty_Int) → new_esEs11(zxw400, zxw300)
new_compare10(zxw79000, zxw80000, True) → LT
new_esEs31(zxw35, zxw30, ty_Bool) → new_esEs14(zxw35, zxw30)
new_esEs19(zxw79001, zxw80001, app(ty_[], caa)) → new_esEs13(zxw79001, zxw80001, caa)
new_compare10(zxw79000, zxw80000, False) → GT
new_esEs9(LT, LT) → True
new_ltEs20(zxw7900, zxw8000, ty_Char) → new_ltEs10(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, ty_Ordering) → new_ltEs7(zxw7900, zxw8000)
new_primCompAux00(zxw276, GT) → GT
new_esEs31(zxw35, zxw30, app(ty_Maybe, bde)) → new_esEs6(zxw35, zxw30, bde)
new_compare18(zxw79000, zxw80000) → new_compare24(zxw79000, zxw80000, new_esEs9(zxw79000, zxw80000))
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_@0) → new_ltEs8(zxw79000, zxw80000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_lt19(zxw79000, zxw80000, ty_Char) → new_lt9(zxw79000, zxw80000)
new_esEs28(zxw4000, zxw3000, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_ltEs19(zxw7900, zxw8000, app(ty_Maybe, baa)) → new_ltEs18(zxw7900, zxw8000, baa)
new_esEs27(zxw4001, zxw3001, ty_Integer) → new_esEs15(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, app(ty_Ratio, daf)) → new_esEs18(zxw4001, zxw3001, daf)
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_esEs19(zxw79001, zxw80001, ty_Char) → new_esEs12(zxw79001, zxw80001)
new_esEs23(zxw4000, zxw3000, app(ty_[], ddd)) → new_esEs13(zxw4000, zxw3000, ddd)
new_ltEs17(zxw7900, zxw8000, hh) → new_fsEs(new_compare8(zxw7900, zxw8000, hh))
new_not(True) → False
new_ltEs4(@2(zxw79000, zxw79001), @2(zxw80000, zxw80001), ca, cb) → new_pePe(new_lt4(zxw79000, zxw80000, ca), new_asAs(new_esEs8(zxw79000, zxw80000, ca), new_ltEs5(zxw79001, zxw80001, cb)))
new_compare1([], [], he) → EQ
new_esEs6(Just(zxw4000), Just(zxw3000), app(ty_Ratio, fa)) → new_esEs18(zxw4000, zxw3000, fa)

The set Q consists of the following terms:

new_compare23(x0, x1, True)
new_lt6(x0, x1)
new_ltEs5(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, ty_Integer)
new_esEs33(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt4(x0, x1, app(ty_[], x2))
new_ltEs18(Just(x0), Just(x1), ty_@0)
new_compare16(x0, x1)
new_lt4(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(Just(x0), Nothing, x1)
new_ltEs20(x0, x1, ty_Double)
new_esEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs19(x0, x1, ty_Bool)
new_esEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs8(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(x0, x1, app(app(ty_Either, x2), x3))
new_compare30(@0, @0)
new_esEs32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCompAux00(x0, GT)
new_lt19(x0, x1, ty_Char)
new_esEs27(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_Ordering)
new_compare17(Char(x0), Char(x1))
new_esEs28(x0, x1, ty_Int)
new_ltEs20(x0, x1, app(ty_[], x2))
new_ltEs21(x0, x1, ty_Ordering)
new_compare111(x0, x1, True, x2)
new_ltEs15(x0, x1)
new_primPlusNat1(Zero, Succ(x0))
new_esEs6(Just(x0), Just(x1), ty_Double)
new_compare24(x0, x1, False)
new_compare210(x0, x1, False, x2, x3)
new_lt20(x0, x1, ty_Char)
new_esEs33(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, ty_Bool)
new_sr0(Integer(x0), Integer(x1))
new_esEs32(x0, x1, app(ty_[], x2))
new_esEs33(x0, x1, ty_Float)
new_compare28(x0, x1, True, x2)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(Nothing, Nothing, x0)
new_ltEs18(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs34(x0, x1, ty_Integer)
new_esEs34(x0, x1, app(ty_Maybe, x2))
new_ltEs7(EQ, EQ)
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs19(x0, x1, ty_Integer)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_ltEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Bool)
new_ltEs14(Right(x0), Right(x1), x2, ty_Float)
new_compare27(x0, x1, x2)
new_esEs31(x0, x1, app(ty_Ratio, x2))
new_esEs6(Just(x0), Just(x1), app(ty_[], x2))
new_compare14(x0, x1, True, x2, x3)
new_ltEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs13([], :(x0, x1), x2)
new_compare25(x0, x1, False, x2, x3, x4)
new_esEs7(Left(x0), Left(x1), ty_Integer, x2)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs7(Right(x0), Right(x1), x2, ty_@0)
new_esEs31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Integer)
new_ltEs5(x0, x1, ty_Integer)
new_ltEs21(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs7(EQ, LT)
new_ltEs7(LT, EQ)
new_esEs20(x0, x1, ty_Ordering)
new_esEs17(Float(x0, x1), Float(x2, x3))
new_compare25(x0, x1, True, x2, x3, x4)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_lt19(x0, x1, ty_Ordering)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs16(x0, x1)
new_lt4(x0, x1, app(ty_Maybe, x2))
new_esEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs14(Left(x0), Left(x1), ty_Char, x2)
new_sr(x0, x1)
new_ltEs19(x0, x1, ty_Double)
new_compare7(Float(x0, x1), Float(x2, x3))
new_ltEs9(x0, x1)
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_compare19(x0, x1, x2, x3)
new_lt7(x0, x1)
new_lt4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, ty_Int)
new_esEs26(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat0(Zero, x0)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs32(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_ltEs7(LT, LT)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs27(x0, x1, ty_Bool)
new_lt5(x0, x1, x2, x3, x4)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare29(x0, x1, app(app(ty_@2, x2), x3))
new_lt4(x0, x1, ty_Ordering)
new_esEs34(x0, x1, app(ty_Ratio, x2))
new_primEqNat0(Zero, Succ(x0))
new_lt19(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Int)
new_esEs15(Integer(x0), Integer(x1))
new_esEs26(x0, x1, ty_Double)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs28(x0, x1, ty_@0)
new_primPlusNat1(Succ(x0), Zero)
new_esEs22(x0, x1, ty_Integer)
new_ltEs14(Left(x0), Left(x1), ty_@0, x2)
new_primMulInt(Neg(x0), Neg(x1))
new_ltEs19(x0, x1, ty_Int)
new_esEs7(Left(x0), Left(x1), ty_Double, x2)
new_compare29(x0, x1, ty_Integer)
new_esEs14(True, True)
new_esEs21(x0, x1, ty_Char)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(Just(x0), Just(x1), ty_Integer)
new_compare29(x0, x1, app(ty_[], x2))
new_ltEs18(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, ty_Int)
new_esEs7(Right(x0), Right(x1), x2, ty_Int)
new_primEqNat0(Zero, Zero)
new_esEs16(Double(x0, x1), Double(x2, x3))
new_esEs12(Char(x0), Char(x1))
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_lt4(x0, x1, ty_Char)
new_esEs20(x0, x1, ty_Bool)
new_esEs8(x0, x1, ty_Float)
new_compare1([], :(x0, x1), x2)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_Integer)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs32(x0, x1, ty_@0)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(Left(x0), Left(x1), ty_Int, x2)
new_primCompAux00(x0, LT)
new_esEs27(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(ty_[], x2))
new_ltEs5(x0, x1, ty_Double)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs18(Just(x0), Just(x1), ty_Char)
new_primMulNat0(Zero, Zero)
new_lt9(x0, x1)
new_compare29(x0, x1, ty_Double)
new_esEs34(x0, x1, app(ty_[], x2))
new_ltEs5(x0, x1, ty_@0)
new_lt17(x0, x1, x2)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_ltEs21(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs31(x0, x1, ty_Bool)
new_ltEs14(Left(x0), Left(x1), ty_Float, x2)
new_esEs32(x0, x1, ty_Float)
new_esEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs8(x0, x1, ty_Ordering)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_compare10(x0, x1, True)
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Ordering)
new_primEqNat0(Succ(x0), Succ(x1))
new_ltEs19(x0, x1, ty_Bool)
new_esEs28(x0, x1, ty_Double)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_@0)
new_pePe(True, x0)
new_esEs19(x0, x1, ty_Float)
new_lt19(x0, x1, app(ty_[], x2))
new_esEs8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_lt16(x0, x1)
new_compare29(x0, x1, ty_Bool)
new_lt10(x0, x1, x2)
new_esEs7(Right(x0), Right(x1), x2, ty_Integer)
new_esEs32(x0, x1, app(app(ty_Either, x2), x3))
new_compare11(x0, x1, True)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs32(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs33(x0, x1, app(ty_[], x2))
new_esEs34(x0, x1, ty_Char)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1, ty_@0)
new_esEs6(Just(x0), Just(x1), ty_Ordering)
new_esEs23(x0, x1, ty_@0)
new_ltEs14(Right(x0), Right(x1), x2, ty_Int)
new_ltEs5(x0, x1, ty_Char)
new_ltEs21(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Float)
new_lt18(x0, x1, x2)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_compare29(x0, x1, ty_Ordering)
new_ltEs21(x0, x1, ty_@0)
new_esEs8(x0, x1, ty_Int)
new_lt14(x0, x1, x2, x3)
new_ltEs12(False, False)
new_compare210(x0, x1, True, x2, x3)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Just(x0), Just(x1), ty_Bool)
new_compare32(Integer(x0), Integer(x1))
new_lt19(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_Int)
new_primMulNat0(Succ(x0), Succ(x1))
new_compare29(x0, x1, ty_Float)
new_ltEs21(x0, x1, ty_Integer)
new_esEs6(Just(x0), Just(x1), ty_Float)
new_ltEs5(x0, x1, ty_Float)
new_ltEs18(Just(x0), Just(x1), ty_Float)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_Bool)
new_esEs31(x0, x1, ty_Double)
new_primCmpNat1(Zero, x0)
new_ltEs14(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs8(x0, x1)
new_ltEs18(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs14(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs33(x0, x1, app(ty_Ratio, x2))
new_compare13(x0, x1, False, x2, x3)
new_esEs34(x0, x1, ty_Float)
new_primPlusNat1(Zero, Zero)
new_esEs23(x0, x1, ty_Double)
new_ltEs18(Just(x0), Just(x1), ty_Ordering)
new_primCmpNat2(Zero, Zero)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(x0, x1, ty_Bool)
new_esEs34(x0, x1, ty_Ordering)
new_ltEs18(Just(x0), Just(x1), app(ty_[], x2))
new_esEs33(x0, x1, app(ty_Maybe, x2))
new_ltEs5(x0, x1, app(ty_[], x2))
new_asAs(False, x0)
new_ltEs20(x0, x1, ty_Char)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs31(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs8(x0, x1, ty_Integer)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs33(x0, x1, ty_Ordering)
new_ltEs18(Just(x0), Just(x1), ty_Bool)
new_compare14(x0, x1, False, x2, x3)
new_primCmpNat1(Succ(x0), x1)
new_esEs34(x0, x1, ty_Bool)
new_esEs33(x0, x1, ty_Double)
new_esEs24(x0, x1, ty_Integer)
new_esEs27(x0, x1, ty_@0)
new_esEs7(Left(x0), Left(x1), ty_Int, x2)
new_ltEs14(Right(x0), Right(x1), x2, ty_Double)
new_lt4(x0, x1, ty_Float)
new_ltEs5(x0, x1, app(app(ty_Either, x2), x3))
new_esEs19(x0, x1, ty_Char)
new_lt4(x0, x1, ty_Double)
new_esEs19(x0, x1, ty_Ordering)
new_esEs8(x0, x1, app(ty_Ratio, x2))
new_esEs33(x0, x1, ty_Int)
new_esEs10(@0, @0)
new_esEs31(x0, x1, ty_@0)
new_esEs33(x0, x1, ty_@0)
new_esEs11(x0, x1)
new_esEs20(x0, x1, ty_Float)
new_ltEs14(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs7(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs14(Right(x0), Right(x1), x2, ty_Char)
new_esEs9(GT, GT)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs27(x0, x1, ty_Char)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_compare11(x0, x1, False)
new_compare23(x0, x1, False)
new_compare12(x0, x1, True, x2, x3, x4)
new_esEs7(Right(x0), Right(x1), x2, ty_Double)
new_esEs28(x0, x1, ty_Bool)
new_esEs33(x0, x1, app(app(ty_Either, x2), x3))
new_compare24(x0, x1, True)
new_compare36(x0, x1, x2, x3)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_compare15(x0, x1, x2, x3)
new_primEqNat0(Succ(x0), Zero)
new_esEs13([], [], x0)
new_esEs23(x0, x1, ty_Ordering)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs7(Left(x0), Right(x1), x2, x3)
new_esEs7(Right(x0), Left(x1), x2, x3)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_esEs34(x0, x1, ty_Int)
new_compare9(x0, x1, x2, x3, x4)
new_lt20(x0, x1, ty_Int)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs21(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Integer)
new_esEs33(x0, x1, ty_Bool)
new_lt4(x0, x1, app(app(ty_Either, x2), x3))
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs23(x0, x1, ty_Int)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs5(x0, x1, app(app(ty_@2, x2), x3))
new_esEs33(x0, x1, ty_Char)
new_lt4(x0, x1, ty_@0)
new_esEs23(x0, x1, ty_Char)
new_esEs28(x0, x1, ty_Ordering)
new_ltEs18(Just(x0), Just(x1), ty_Double)
new_ltEs20(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_lt20(x0, x1, ty_@0)
new_compare1([], [], x0)
new_esEs9(EQ, EQ)
new_pePe(False, x0)
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs5(x0, x1, app(ty_Ratio, x2))
new_ltEs14(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs6(Just(x0), Just(x1), ty_Char)
new_esEs25(x0, x1, ty_Integer)
new_esEs31(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_Integer)
new_compare12(x0, x1, False, x2, x3, x4)
new_esEs8(x0, x1, app(ty_Maybe, x2))
new_primCompAux00(x0, EQ)
new_esEs19(x0, x1, ty_Int)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs14(True, False)
new_esEs14(False, True)
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_lt4(x0, x1, ty_Integer)
new_esEs7(Left(x0), Left(x1), ty_@0, x2)
new_ltEs14(Right(x0), Right(x1), x2, ty_@0)
new_fsEs(x0)
new_esEs22(x0, x1, ty_Float)
new_ltEs14(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs32(x0, x1, app(ty_Ratio, x2))
new_esEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_primCmpNat2(Succ(x0), Succ(x1))
new_compare110(x0, x1, False, x2, x3)
new_lt4(x0, x1, ty_Bool)
new_asAs(True, x0)
new_esEs21(x0, x1, ty_Bool)
new_esEs4(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs6(Nothing, Just(x0), x1)
new_esEs6(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs21(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Just(x0), Nothing, x1)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_compare29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs8(x0, x1, app(ty_[], x2))
new_esEs31(x0, x1, ty_Integer)
new_esEs13(:(x0, x1), [], x2)
new_ltEs14(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs8(x0, x1, ty_Char)
new_lt19(x0, x1, ty_Float)
new_compare33(x0, x1, x2, x3)
new_ltEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs22(x0, x1, ty_@0)
new_esEs34(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_Char)
new_ltEs12(False, True)
new_ltEs12(True, False)
new_compare6(Double(x0, x1), Double(x2, x3))
new_ltEs20(x0, x1, ty_@0)
new_esEs22(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_@0)
new_compare35(x0, x1, x2, x3)
new_ltEs14(Right(x0), Right(x1), x2, ty_Integer)
new_lt19(x0, x1, ty_Double)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1, ty_Bool)
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs7(Left(x0), Left(x1), ty_Char, x2)
new_esEs7(Right(x0), Right(x1), x2, ty_Float)
new_ltEs14(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs26(x0, x1, ty_Char)
new_ltEs5(x0, x1, ty_Int)
new_lt4(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_Double)
new_esEs19(x0, x1, ty_@0)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_compare13(x0, x1, True, x2, x3)
new_esEs34(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs21(x0, x1, ty_Bool)
new_ltEs14(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs21(x0, x1, ty_Double)
new_lt12(x0, x1)
new_esEs8(x0, x1, ty_Bool)
new_ltEs21(x0, x1, ty_Char)
new_lt13(x0, x1)
new_esEs31(x0, x1, ty_Ordering)
new_ltEs14(Right(x0), Right(x1), x2, ty_Bool)
new_compare1(:(x0, x1), [], x2)
new_compare10(x0, x1, False)
new_primMulNat0(Succ(x0), Zero)
new_ltEs19(x0, x1, ty_Float)
new_ltEs14(Left(x0), Right(x1), x2, x3)
new_esEs23(x0, x1, ty_Float)
new_ltEs14(Right(x0), Left(x1), x2, x3)
new_compare29(x0, x1, ty_Int)
new_esEs20(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, ty_Int)
new_esEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs20(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Float)
new_compare31(x0, x1)
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs31(x0, x1, ty_Char)
new_esEs6(Just(x0), Just(x1), ty_Int)
new_ltEs7(LT, GT)
new_ltEs7(GT, LT)
new_esEs21(x0, x1, ty_Integer)
new_esEs22(x0, x1, app(ty_[], x2))
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs22(x0, x1, ty_Double)
new_compare110(x0, x1, True, x2, x3)
new_lt20(x0, x1, app(ty_[], x2))
new_ltEs13(x0, x1)
new_ltEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs34(x0, x1, ty_@0)
new_esEs31(x0, x1, ty_Int)
new_lt4(x0, x1, ty_Int)
new_ltEs11(x0, x1, x2)
new_lt20(x0, x1, ty_Float)
new_not(True)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs31(x0, x1, ty_Float)
new_esEs20(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Float)
new_esEs19(x0, x1, app(ty_[], x2))
new_esEs18(:%(x0, x1), :%(x2, x3), x4)
new_esEs6(Nothing, Nothing, x0)
new_esEs28(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Ordering)
new_ltEs14(Left(x0), Left(x1), ty_Double, x2)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Just(x0), Just(x1), ty_Integer)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_not(False)
new_compare29(x0, x1, app(ty_Ratio, x2))
new_lt8(x0, x1)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_compare28(x0, x1, False, x2)
new_esEs32(x0, x1, ty_Integer)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, ty_Char)
new_esEs6(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare8(:%(x0, x1), :%(x2, x3), ty_Integer)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs22(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_Integer)
new_esEs8(x0, x1, ty_@0)
new_compare26(Left(x0), Left(x1), False, x2, x3)
new_esEs32(x0, x1, app(ty_Maybe, x2))
new_ltEs12(True, True)
new_esEs27(x0, x1, ty_Float)
new_lt15(x0, x1)
new_lt11(x0, x1, x2, x3)
new_esEs26(x0, x1, ty_Ordering)
new_esEs7(Left(x0), Left(x1), ty_Float, x2)
new_esEs27(x0, x1, ty_Double)
new_esEs6(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs34(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs33(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Ordering)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs13(:(x0, x1), :(x2, x3), x4)
new_esEs22(x0, x1, ty_Char)
new_lt20(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Bool)
new_esEs34(x0, x1, ty_Double)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_ltEs21(x0, x1, ty_Float)
new_ltEs10(x0, x1)
new_ltEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_compare29(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs14(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs5(x0, x1, ty_Ordering)
new_esEs8(x0, x1, ty_Double)
new_compare29(x0, x1, ty_Char)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs6(Just(x0), Just(x1), ty_@0)
new_esEs31(x0, x1, app(app(ty_Either, x2), x3))
new_compare1(:(x0, x1), :(x2, x3), x4)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs31(x0, x1, app(ty_[], x2))
new_esEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs6(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs19(x0, x1, ty_Double)
new_esEs14(False, False)
new_ltEs21(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs32(x0, x1, ty_Char)
new_ltEs21(x0, x1, ty_Double)
new_esEs32(x0, x1, ty_Int)
new_ltEs14(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpNat2(Succ(x0), Zero)
new_esEs7(Right(x0), Right(x1), x2, ty_Char)
new_esEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_compare34(x0, x1, x2, x3)
new_compare18(x0, x1)
new_esEs32(x0, x1, ty_Bool)
new_esEs7(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs18(Just(x0), Just(x1), ty_Int)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare26(Right(x0), Right(x1), False, x2, x3)
new_esEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs17(x0, x1, x2)
new_primPlusNat0(Succ(x0), x1)
new_esEs20(x0, x1, ty_Integer)
new_primCmpNat0(x0, Zero)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_ltEs7(GT, EQ)
new_ltEs7(EQ, GT)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs32(x0, x1, ty_Double)
new_ltEs7(GT, GT)
new_esEs9(LT, LT)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_primCompAux0(x0, x1, x2, x3)
new_compare29(x0, x1, ty_@0)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_compare26(x0, x1, True, x2, x3)
new_compare26(Right(x0), Left(x1), False, x2, x3)
new_compare26(Left(x0), Right(x1), False, x2, x3)
new_ltEs18(Nothing, Just(x0), x1)
new_compare111(x0, x1, False, x2)
new_compare29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Ordering)
new_primCmpNat0(x0, Succ(x1))

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

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

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

new_splitGT2(zxw15, zxw16, zxw17, zxw18, zxw19, zxw20, False, bc, bd, be) → new_splitGT1(zxw15, zxw16, zxw17, zxw18, zxw19, zxw20, new_esEs9(new_compare33(zxw20, zxw15, bc, bd), LT), bc, bd, be)
new_splitGT2(zxw15, zxw16, zxw17, zxw18, zxw19, zxw20, True, bc, bd, be) → new_splitGT(zxw19, zxw20, bc, bd, be)
new_splitGT3(Left(zxw300), zxw31, zxw32, zxw33, zxw34, Left(zxw400), h, ba, bb) → new_splitGT2(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs9(new_compare26(Left(zxw400), Left(zxw300), new_esEs33(zxw400, zxw300, h), h, ba), GT), h, ba, bb)
new_splitGT(Branch(zxw340, zxw341, zxw342, zxw343, zxw344), zxw400, h, ba, bb) → new_splitGT3(zxw340, zxw341, zxw342, zxw343, zxw344, Left(zxw400), h, ba, bb)
new_splitGT20(zxw300, zxw31, zxw32, zxw33, Branch(zxw340, zxw341, zxw342, zxw343, zxw344), zxw400, True, h, ba, bb) → new_splitGT3(zxw340, zxw341, zxw342, zxw343, zxw344, Left(zxw400), h, ba, bb)
new_splitGT10(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, True, h, ba, bb) → new_splitGT(zxw33, zxw400, h, ba, bb)
new_splitGT20(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, False, h, ba, bb) → new_splitGT10(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs9(new_compare34(zxw400, zxw300, h, ba), LT), h, ba, bb)
new_splitGT1(zxw15, zxw16, zxw17, zxw18, zxw19, zxw20, True, bc, bd, be) → new_splitGT(zxw18, zxw20, bc, bd, be)
new_splitGT3(Right(zxw300), zxw31, zxw32, zxw33, zxw34, Left(zxw400), h, ba, bb) → new_splitGT20(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs9(new_compare26(Left(zxw400), Right(zxw300), False, h, ba), GT), h, ba, bb)

The TRS R consists of the following rules:

new_compare26(Left(zxw7900), Right(zxw8000), False, gh, ha) → LT
new_esEs9(LT, GT) → False
new_esEs9(EQ, GT) → False
new_esEs9(GT, GT) → True
new_esEs33(zxw400, zxw300, app(app(ty_Either, bfh), bef)) → new_esEs7(zxw400, zxw300, bfh, bef)
new_esEs33(zxw400, zxw300, app(ty_[], ddb)) → new_esEs13(zxw400, zxw300, ddb)
new_esEs33(zxw400, zxw300, ty_Char) → new_esEs12(zxw400, zxw300)
new_esEs33(zxw400, zxw300, ty_Ordering) → new_esEs9(zxw400, zxw300)
new_esEs33(zxw400, zxw300, ty_@0) → new_esEs10(zxw400, zxw300)
new_esEs33(zxw400, zxw300, ty_Integer) → new_esEs15(zxw400, zxw300)
new_esEs33(zxw400, zxw300, app(app(app(ty_@3, deh), dfa), dfb)) → new_esEs4(zxw400, zxw300, deh, dfa, dfb)
new_esEs33(zxw400, zxw300, app(app(ty_@2, dad), dae)) → new_esEs5(zxw400, zxw300, dad, dae)
new_esEs33(zxw400, zxw300, app(ty_Ratio, dee)) → new_esEs18(zxw400, zxw300, dee)
new_esEs33(zxw400, zxw300, ty_Bool) → new_esEs14(zxw400, zxw300)
new_esEs33(zxw400, zxw300, app(ty_Maybe, eh)) → new_esEs6(zxw400, zxw300, eh)
new_esEs33(zxw400, zxw300, ty_Double) → new_esEs16(zxw400, zxw300)
new_esEs33(zxw400, zxw300, ty_Float) → new_esEs17(zxw400, zxw300)
new_esEs33(zxw400, zxw300, ty_Int) → new_esEs11(zxw400, zxw300)
new_compare26(zxw790, zxw800, True, gh, ha) → EQ
new_compare26(Left(zxw7900), Left(zxw8000), False, gh, ha) → new_compare13(zxw7900, zxw8000, new_ltEs19(zxw7900, zxw8000, gh), gh, ha)
new_ltEs19(zxw7900, zxw8000, ty_Float) → new_ltEs16(zxw7900, zxw8000)
new_ltEs19(zxw7900, zxw8000, app(app(ty_@2, ca), cb)) → new_ltEs4(zxw7900, zxw8000, ca, cb)
new_ltEs19(zxw7900, zxw8000, app(ty_[], he)) → new_ltEs11(zxw7900, zxw8000, he)
new_ltEs19(zxw7900, zxw8000, ty_Char) → new_ltEs10(zxw7900, zxw8000)
new_ltEs19(zxw7900, zxw8000, ty_Bool) → new_ltEs12(zxw7900, zxw8000)
new_ltEs19(zxw7900, zxw8000, app(ty_Ratio, hh)) → new_ltEs17(zxw7900, zxw8000, hh)
new_ltEs19(zxw7900, zxw8000, app(app(app(ty_@3, hb), hc), hd)) → new_ltEs6(zxw7900, zxw8000, hb, hc, hd)
new_ltEs19(zxw7900, zxw8000, ty_Int) → new_ltEs9(zxw7900, zxw8000)
new_ltEs19(zxw7900, zxw8000, app(app(ty_Either, hf), hg)) → new_ltEs14(zxw7900, zxw8000, hf, hg)
new_ltEs19(zxw7900, zxw8000, ty_@0) → new_ltEs8(zxw7900, zxw8000)
new_ltEs19(zxw7900, zxw8000, ty_Double) → new_ltEs15(zxw7900, zxw8000)
new_ltEs19(zxw7900, zxw8000, ty_Integer) → new_ltEs13(zxw7900, zxw8000)
new_ltEs19(zxw7900, zxw8000, ty_Ordering) → new_ltEs7(zxw7900, zxw8000)
new_ltEs19(zxw7900, zxw8000, app(ty_Maybe, baa)) → new_ltEs18(zxw7900, zxw8000, baa)
new_compare13(zxw235, zxw236, False, bch, bda) → GT
new_compare13(zxw235, zxw236, True, bch, bda) → LT
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Char) → new_ltEs10(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Integer) → new_ltEs13(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(ty_Ratio, dab)) → new_ltEs17(zxw79000, zxw80000, dab)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(app(app(ty_@3, chb), chc), chd)) → new_ltEs6(zxw79000, zxw80000, chb, chc, chd)
new_ltEs18(Nothing, Nothing, baa) → True
new_ltEs18(Just(zxw79000), Nothing, baa) → False
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Double) → new_ltEs15(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(ty_[], che)) → new_ltEs11(zxw79000, zxw80000, che)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(app(ty_@2, chf), chg)) → new_ltEs4(zxw79000, zxw80000, chf, chg)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Bool) → new_ltEs12(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Ordering) → new_ltEs7(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Float) → new_ltEs16(zxw79000, zxw80000)
new_ltEs18(Nothing, Just(zxw80000), baa) → True
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Int) → new_ltEs9(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_@0) → new_ltEs8(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(ty_Maybe, dac)) → new_ltEs18(zxw79000, zxw80000, dac)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(ty_Maybe, cha)) → new_ltEs18(zxw79000, zxw80000, cha)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(app(ty_Either, chh), daa)) → new_ltEs14(zxw79000, zxw80000, chh, daa)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(app(ty_Either, cgf), cgg)) → new_ltEs14(zxw79000, zxw80000, cgf, cgg)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(app(ty_Either, cfd), cfe), hg) → new_ltEs14(zxw79000, zxw80000, cfd, cfe)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(ty_Maybe, cfg), hg) → new_ltEs18(zxw79000, zxw80000, cfg)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Bool) → new_ltEs12(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(ty_[], cgc)) → new_ltEs11(zxw79000, zxw80000, cgc)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Bool, hg) → new_ltEs12(zxw79000, zxw80000)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(ty_Ratio, cff), hg) → new_ltEs17(zxw79000, zxw80000, cff)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(app(app(ty_@3, cfh), cga), cgb)) → new_ltEs6(zxw79000, zxw80000, cfh, cga, cgb)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Float, hg) → new_ltEs16(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Float) → new_ltEs16(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Double) → new_ltEs15(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(app(ty_@2, cgd), cge)) → new_ltEs4(zxw79000, zxw80000, cgd, cge)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Double, hg) → new_ltEs15(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Left(zxw80000), hf, hg) → False
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Int, hg) → new_ltEs9(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Char) → new_ltEs10(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_@0) → new_ltEs8(zxw79000, zxw80000)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(app(app(ty_@3, cef), ceg), ceh), hg) → new_ltEs6(zxw79000, zxw80000, cef, ceg, ceh)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_@0, hg) → new_ltEs8(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Ordering) → new_ltEs7(zxw79000, zxw80000)
new_ltEs14(Left(zxw79000), Right(zxw80000), hf, hg) → True
new_ltEs14(Left(zxw79000), Left(zxw80000), app(app(ty_@2, cfb), cfc), hg) → new_ltEs4(zxw79000, zxw80000, cfb, cfc)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(ty_[], cfa), hg) → new_ltEs11(zxw79000, zxw80000, cfa)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Integer, hg) → new_ltEs13(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Int) → new_ltEs9(zxw79000, zxw80000)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Ordering, hg) → new_ltEs7(zxw79000, zxw80000)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Char, hg) → new_ltEs10(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(ty_Ratio, cgh)) → new_ltEs17(zxw79000, zxw80000, cgh)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Integer) → new_ltEs13(zxw79000, zxw80000)
new_ltEs13(zxw7900, zxw8000) → new_fsEs(new_compare32(zxw7900, zxw8000))
new_compare32(Integer(zxw79000), Integer(zxw80000)) → new_primCmpInt(zxw79000, zxw80000)
new_fsEs(zxw259) → new_not(new_esEs9(zxw259, GT))
new_not(False) → True
new_not(True) → False
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_ltEs17(zxw7900, zxw8000, hh) → new_fsEs(new_compare8(zxw7900, zxw8000, hh))
new_compare8(:%(zxw79000, zxw79001), :%(zxw80000, zxw80001), ty_Integer) → new_compare32(new_sr0(zxw79000, zxw80001), new_sr0(zxw80000, zxw79001))
new_compare8(:%(zxw79000, zxw79001), :%(zxw80000, zxw80001), ty_Int) → new_compare16(new_sr(zxw79000, zxw80001), new_sr(zxw80000, zxw79001))
new_sr(zxw4000, zxw3000) → new_primMulInt(zxw4000, zxw3000)
new_compare16(zxw79, zxw80) → new_primCmpInt(zxw79, zxw80)
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Neg(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Pos(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulNat0(Zero, Zero) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_sr0(Integer(zxw800000), Integer(zxw790010)) → Integer(new_primMulInt(zxw800000, zxw790010))
new_ltEs10(zxw7900, zxw8000) → new_fsEs(new_compare17(zxw7900, zxw8000))
new_compare17(Char(zxw79000), Char(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_ltEs7(LT, EQ) → True
new_ltEs7(GT, GT) → True
new_ltEs7(EQ, EQ) → True
new_ltEs7(GT, LT) → False
new_ltEs7(GT, EQ) → False
new_ltEs7(EQ, GT) → True
new_ltEs7(EQ, LT) → False
new_ltEs7(LT, LT) → True
new_ltEs7(LT, GT) → True
new_ltEs9(zxw7900, zxw8000) → new_fsEs(new_compare16(zxw7900, zxw8000))
new_ltEs11(zxw7900, zxw8000, he) → new_fsEs(new_compare1(zxw7900, zxw8000, he))
new_compare1([], :(zxw80000, zxw80001), he) → LT
new_compare1(:(zxw79000, zxw79001), :(zxw80000, zxw80001), he) → new_primCompAux0(zxw79000, zxw80000, new_compare1(zxw79001, zxw80001, he), he)
new_compare1(:(zxw79000, zxw79001), [], he) → GT
new_compare1([], [], he) → EQ
new_primCompAux0(zxw79000, zxw80000, zxw272, he) → new_primCompAux00(zxw272, new_compare29(zxw79000, zxw80000, he))
new_compare29(zxw79000, zxw80000, ty_Char) → new_compare17(zxw79000, zxw80000)
new_compare29(zxw79000, zxw80000, ty_Bool) → new_compare31(zxw79000, zxw80000)
new_compare29(zxw79000, zxw80000, app(app(ty_@2, ccf), ccg)) → new_compare19(zxw79000, zxw80000, ccf, ccg)
new_compare29(zxw79000, zxw80000, app(ty_[], cce)) → new_compare1(zxw79000, zxw80000, cce)
new_compare29(zxw79000, zxw80000, app(app(app(ty_@3, ccb), ccc), ccd)) → new_compare9(zxw79000, zxw80000, ccb, ccc, ccd)
new_compare29(zxw79000, zxw80000, ty_Int) → new_compare16(zxw79000, zxw80000)
new_compare29(zxw79000, zxw80000, ty_Integer) → new_compare32(zxw79000, zxw80000)
new_compare29(zxw79000, zxw80000, app(ty_Maybe, cdc)) → new_compare27(zxw79000, zxw80000, cdc)
new_compare29(zxw79000, zxw80000, app(ty_Ratio, cdb)) → new_compare8(zxw79000, zxw80000, cdb)
new_compare29(zxw79000, zxw80000, ty_Float) → new_compare7(zxw79000, zxw80000)
new_compare29(zxw79000, zxw80000, ty_Double) → new_compare6(zxw79000, zxw80000)
new_compare29(zxw79000, zxw80000, app(app(ty_Either, cch), cda)) → new_compare15(zxw79000, zxw80000, cch, cda)
new_compare29(zxw79000, zxw80000, ty_Ordering) → new_compare18(zxw79000, zxw80000)
new_compare29(zxw79000, zxw80000, ty_@0) → new_compare30(zxw79000, zxw80000)
new_primCompAux00(zxw276, LT) → LT
new_primCompAux00(zxw276, EQ) → zxw276
new_primCompAux00(zxw276, GT) → GT
new_compare30(@0, @0) → EQ
new_compare18(zxw79000, zxw80000) → new_compare24(zxw79000, zxw80000, new_esEs9(zxw79000, zxw80000))
new_esEs9(GT, LT) → False
new_esEs9(GT, EQ) → False
new_esEs9(EQ, EQ) → True
new_esEs9(EQ, LT) → False
new_esEs9(LT, EQ) → False
new_esEs9(LT, LT) → True
new_compare24(zxw79000, zxw80000, False) → new_compare11(zxw79000, zxw80000, new_ltEs7(zxw79000, zxw80000))
new_compare24(zxw79000, zxw80000, True) → EQ
new_compare11(zxw79000, zxw80000, False) → GT
new_compare11(zxw79000, zxw80000, True) → LT
new_compare15(zxw790, zxw800, gh, ha) → new_compare26(zxw790, zxw800, new_esEs7(zxw790, zxw800, gh, ha), gh, ha)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Bool, bef) → new_esEs14(zxw4000, zxw3000)
new_esEs7(Right(zxw4000), Left(zxw3000), bfh, bef) → False
new_esEs7(Left(zxw4000), Right(zxw3000), bfh, bef) → False
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, app(app(ty_@2, bgd), bge)) → new_esEs5(zxw4000, zxw3000, bgd, bge)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Int, bef) → new_esEs11(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), app(app(ty_@2, bfa), bfb), bef) → new_esEs5(zxw4000, zxw3000, bfa, bfb)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Ordering, bef) → new_esEs9(zxw4000, zxw3000)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, app(ty_[], bgb)) → new_esEs13(zxw4000, zxw3000, bgb)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Integer, bef) → new_esEs15(zxw4000, zxw3000)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, app(app(app(ty_@3, bgh), bha), bhb)) → new_esEs4(zxw4000, zxw3000, bgh, bha, bhb)
new_esEs7(Left(zxw4000), Left(zxw3000), app(ty_Ratio, bee), bef) → new_esEs18(zxw4000, zxw3000, bee)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_@0, bef) → new_esEs10(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), app(app(app(ty_@3, bfe), bff), bfg), bef) → new_esEs4(zxw4000, zxw3000, bfe, bff, bfg)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Double, bef) → new_esEs16(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Float, bef) → new_esEs17(zxw4000, zxw3000)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Char, bef) → new_esEs12(zxw4000, zxw3000)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), app(ty_[], beg), bef) → new_esEs13(zxw4000, zxw3000, beg)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, app(ty_Ratio, bga)) → new_esEs18(zxw4000, zxw3000, bga)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_compare26(Right(zxw7900), Left(zxw8000), False, gh, ha) → GT
new_compare26(Right(zxw7900), Right(zxw8000), False, gh, ha) → new_compare14(zxw7900, zxw8000, new_ltEs20(zxw7900, zxw8000, ha), gh, ha)
new_esEs6(Just(zxw4000), Just(zxw3000), app(ty_Maybe, fc)) → new_esEs6(zxw4000, zxw3000, fc)
new_esEs7(Left(zxw4000), Left(zxw3000), app(app(ty_Either, bfc), bfd), bef) → new_esEs7(zxw4000, zxw3000, bfc, bfd)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, app(ty_Maybe, bgc)) → new_esEs6(zxw4000, zxw3000, bgc)
new_esEs6(Just(zxw4000), Just(zxw3000), app(app(ty_Either, fg), fh)) → new_esEs7(zxw4000, zxw3000, fg, fh)
new_esEs7(Left(zxw4000), Left(zxw3000), app(ty_Maybe, beh), bef) → new_esEs6(zxw4000, zxw3000, beh)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, app(app(ty_Either, bgf), bgg)) → new_esEs7(zxw4000, zxw3000, bgf, bgg)
new_esEs6(Just(zxw4000), Just(zxw3000), app(app(ty_@2, fd), ff)) → new_esEs5(zxw4000, zxw3000, fd, ff)
new_esEs6(Nothing, Nothing, eh) → True
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs6(Nothing, Just(zxw3000), eh) → False
new_esEs6(Just(zxw4000), Nothing, eh) → False
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), app(app(app(ty_@3, ga), gb), gc)) → new_esEs4(zxw4000, zxw3000, ga, gb, gc)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_@0) → new_esEs10(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), app(ty_[], fb)) → new_esEs13(zxw4000, zxw3000, fb)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Char) → new_esEs12(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Float) → new_esEs17(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), app(ty_Ratio, fa)) → new_esEs18(zxw4000, zxw3000, fa)
new_esEs18(:%(zxw4000, zxw4001), :%(zxw3000, zxw3001), dee) → new_asAs(new_esEs25(zxw4000, zxw3000, dee), new_esEs24(zxw4001, zxw3001, dee))
new_esEs25(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs25(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs24(zxw4001, zxw3001, ty_Integer) → new_esEs15(zxw4001, zxw3001)
new_esEs24(zxw4001, zxw3001, ty_Int) → new_esEs11(zxw4001, zxw3001)
new_asAs(False, zxw230) → False
new_asAs(True, zxw230) → zxw230
new_esEs11(zxw400, zxw300) → new_primEqInt(zxw400, zxw300)
new_primEqInt(Neg(Succ(zxw40000)), Neg(Succ(zxw30000))) → new_primEqNat0(zxw40000, zxw30000)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Neg(Succ(zxw30000))) → False
new_primEqInt(Neg(Succ(zxw40000)), Neg(Zero)) → False
new_primEqInt(Pos(Succ(zxw40000)), Pos(Succ(zxw30000))) → new_primEqNat0(zxw40000, zxw30000)
new_primEqInt(Pos(Zero), Pos(Succ(zxw30000))) → False
new_primEqInt(Pos(Succ(zxw40000)), Pos(Zero)) → False
new_primEqInt(Neg(Succ(zxw40000)), Pos(zxw3000)) → False
new_primEqInt(Pos(Succ(zxw40000)), Neg(zxw3000)) → False
new_primEqInt(Neg(Zero), Pos(Succ(zxw30000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(zxw30000))) → False
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqNat0(Zero, Zero) → True
new_primEqNat0(Succ(zxw40000), Succ(zxw30000)) → new_primEqNat0(zxw40000, zxw30000)
new_primEqNat0(Zero, Succ(zxw30000)) → False
new_primEqNat0(Succ(zxw40000), Zero) → False
new_esEs15(Integer(zxw4000), Integer(zxw3000)) → new_primEqInt(zxw4000, zxw3000)
new_esEs17(Float(zxw4000, zxw4001), Float(zxw3000, zxw3001)) → new_esEs11(new_sr(zxw4000, zxw3000), new_sr(zxw4001, zxw3001))
new_esEs12(Char(zxw4000), Char(zxw3000)) → new_primEqNat0(zxw4000, zxw3000)
new_esEs13([], [], ddb) → True
new_esEs13(:(zxw4000, zxw4001), :(zxw3000, zxw3001), ddb) → new_asAs(new_esEs23(zxw4000, zxw3000, ddb), new_esEs13(zxw4001, zxw3001, ddb))
new_esEs13(:(zxw4000, zxw4001), [], ddb) → False
new_esEs13([], :(zxw3000, zxw3001), ddb) → False
new_esEs23(zxw4000, zxw3000, app(app(ty_Either, ddh), dea)) → new_esEs7(zxw4000, zxw3000, ddh, dea)
new_esEs23(zxw4000, zxw3000, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, app(app(app(ty_@3, deb), dec), ded)) → new_esEs4(zxw4000, zxw3000, deb, dec, ded)
new_esEs23(zxw4000, zxw3000, app(app(ty_@2, ddf), ddg)) → new_esEs5(zxw4000, zxw3000, ddf, ddg)
new_esEs23(zxw4000, zxw3000, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, app(ty_Ratio, ddc)) → new_esEs18(zxw4000, zxw3000, ddc)
new_esEs23(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, app(ty_Maybe, dde)) → new_esEs6(zxw4000, zxw3000, dde)
new_esEs23(zxw4000, zxw3000, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, app(ty_[], ddd)) → new_esEs13(zxw4000, zxw3000, ddd)
new_esEs16(Double(zxw4000, zxw4001), Double(zxw3000, zxw3001)) → new_esEs11(new_sr(zxw4000, zxw3000), new_sr(zxw4001, zxw3001))
new_esEs10(@0, @0) → True
new_esEs5(@2(zxw4000, zxw4001), @2(zxw3000, zxw3001), dad, dae) → new_asAs(new_esEs22(zxw4000, zxw3000, dad), new_esEs21(zxw4001, zxw3001, dae))
new_esEs22(zxw4000, zxw3000, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, app(app(ty_@2, dcc), dcd)) → new_esEs5(zxw4000, zxw3000, dcc, dcd)
new_esEs22(zxw4000, zxw3000, app(ty_Maybe, dcb)) → new_esEs6(zxw4000, zxw3000, dcb)
new_esEs22(zxw4000, zxw3000, app(ty_Ratio, dbh)) → new_esEs18(zxw4000, zxw3000, dbh)
new_esEs22(zxw4000, zxw3000, app(app(ty_Either, dce), dcf)) → new_esEs7(zxw4000, zxw3000, dce, dcf)
new_esEs22(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, app(app(app(ty_@3, dcg), dch), dda)) → new_esEs4(zxw4000, zxw3000, dcg, dch, dda)
new_esEs22(zxw4000, zxw3000, app(ty_[], dca)) → new_esEs13(zxw4000, zxw3000, dca)
new_esEs22(zxw4000, zxw3000, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs21(zxw4001, zxw3001, ty_Bool) → new_esEs14(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, ty_Double) → new_esEs16(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, ty_Ordering) → new_esEs9(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, ty_Char) → new_esEs12(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, ty_Float) → new_esEs17(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, app(ty_Maybe, dah)) → new_esEs6(zxw4001, zxw3001, dah)
new_esEs21(zxw4001, zxw3001, ty_Int) → new_esEs11(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, app(ty_[], dag)) → new_esEs13(zxw4001, zxw3001, dag)
new_esEs21(zxw4001, zxw3001, ty_Integer) → new_esEs15(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, app(app(ty_@2, dba), dbb)) → new_esEs5(zxw4001, zxw3001, dba, dbb)
new_esEs21(zxw4001, zxw3001, ty_@0) → new_esEs10(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, app(app(ty_Either, dbc), dbd)) → new_esEs7(zxw4001, zxw3001, dbc, dbd)
new_esEs21(zxw4001, zxw3001, app(app(app(ty_@3, dbe), dbf), dbg)) → new_esEs4(zxw4001, zxw3001, dbe, dbf, dbg)
new_esEs21(zxw4001, zxw3001, app(ty_Ratio, daf)) → new_esEs18(zxw4001, zxw3001, daf)
new_esEs4(@3(zxw4000, zxw4001, zxw4002), @3(zxw3000, zxw3001, zxw3002), deh, dfa, dfb) → new_asAs(new_esEs28(zxw4000, zxw3000, deh), new_asAs(new_esEs27(zxw4001, zxw3001, dfa), new_esEs26(zxw4002, zxw3002, dfb)))
new_esEs28(zxw4000, zxw3000, app(ty_[], dhh)) → new_esEs13(zxw4000, zxw3000, dhh)
new_esEs28(zxw4000, zxw3000, app(app(app(ty_@3, eaf), eag), eah)) → new_esEs4(zxw4000, zxw3000, eaf, eag, eah)
new_esEs28(zxw4000, zxw3000, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, app(ty_Maybe, eaa)) → new_esEs6(zxw4000, zxw3000, eaa)
new_esEs28(zxw4000, zxw3000, app(app(ty_Either, ead), eae)) → new_esEs7(zxw4000, zxw3000, ead, eae)
new_esEs28(zxw4000, zxw3000, app(app(ty_@2, eab), eac)) → new_esEs5(zxw4000, zxw3000, eab, eac)
new_esEs28(zxw4000, zxw3000, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, app(ty_Ratio, dhg)) → new_esEs18(zxw4000, zxw3000, dhg)
new_esEs28(zxw4000, zxw3000, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_esEs27(zxw4001, zxw3001, app(ty_Ratio, dge)) → new_esEs18(zxw4001, zxw3001, dge)
new_esEs27(zxw4001, zxw3001, app(app(app(ty_@3, dhd), dhe), dhf)) → new_esEs4(zxw4001, zxw3001, dhd, dhe, dhf)
new_esEs27(zxw4001, zxw3001, app(ty_Maybe, dgg)) → new_esEs6(zxw4001, zxw3001, dgg)
new_esEs27(zxw4001, zxw3001, app(app(ty_Either, dhb), dhc)) → new_esEs7(zxw4001, zxw3001, dhb, dhc)
new_esEs27(zxw4001, zxw3001, ty_Ordering) → new_esEs9(zxw4001, zxw3001)
new_esEs27(zxw4001, zxw3001, ty_Float) → new_esEs17(zxw4001, zxw3001)
new_esEs27(zxw4001, zxw3001, ty_@0) → new_esEs10(zxw4001, zxw3001)
new_esEs27(zxw4001, zxw3001, ty_Char) → new_esEs12(zxw4001, zxw3001)
new_esEs27(zxw4001, zxw3001, ty_Double) → new_esEs16(zxw4001, zxw3001)
new_esEs27(zxw4001, zxw3001, ty_Int) → new_esEs11(zxw4001, zxw3001)
new_esEs27(zxw4001, zxw3001, app(app(ty_@2, dgh), dha)) → new_esEs5(zxw4001, zxw3001, dgh, dha)
new_esEs27(zxw4001, zxw3001, ty_Bool) → new_esEs14(zxw4001, zxw3001)
new_esEs27(zxw4001, zxw3001, app(ty_[], dgf)) → new_esEs13(zxw4001, zxw3001, dgf)
new_esEs27(zxw4001, zxw3001, ty_Integer) → new_esEs15(zxw4001, zxw3001)
new_esEs26(zxw4002, zxw3002, ty_Float) → new_esEs17(zxw4002, zxw3002)
new_esEs26(zxw4002, zxw3002, ty_Char) → new_esEs12(zxw4002, zxw3002)
new_esEs26(zxw4002, zxw3002, ty_Int) → new_esEs11(zxw4002, zxw3002)
new_esEs26(zxw4002, zxw3002, app(ty_Maybe, dfe)) → new_esEs6(zxw4002, zxw3002, dfe)
new_esEs26(zxw4002, zxw3002, app(app(app(ty_@3, dgb), dgc), dgd)) → new_esEs4(zxw4002, zxw3002, dgb, dgc, dgd)
new_esEs26(zxw4002, zxw3002, app(ty_[], dfd)) → new_esEs13(zxw4002, zxw3002, dfd)
new_esEs26(zxw4002, zxw3002, app(app(ty_Either, dfh), dga)) → new_esEs7(zxw4002, zxw3002, dfh, dga)
new_esEs26(zxw4002, zxw3002, ty_Integer) → new_esEs15(zxw4002, zxw3002)
new_esEs26(zxw4002, zxw3002, app(app(ty_@2, dff), dfg)) → new_esEs5(zxw4002, zxw3002, dff, dfg)
new_esEs26(zxw4002, zxw3002, app(ty_Ratio, dfc)) → new_esEs18(zxw4002, zxw3002, dfc)
new_esEs26(zxw4002, zxw3002, ty_Bool) → new_esEs14(zxw4002, zxw3002)
new_esEs26(zxw4002, zxw3002, ty_@0) → new_esEs10(zxw4002, zxw3002)
new_esEs26(zxw4002, zxw3002, ty_Ordering) → new_esEs9(zxw4002, zxw3002)
new_esEs26(zxw4002, zxw3002, ty_Double) → new_esEs16(zxw4002, zxw3002)
new_esEs14(False, True) → False
new_esEs14(True, False) → False
new_esEs14(True, True) → True
new_esEs14(False, False) → True
new_ltEs20(zxw7900, zxw8000, app(ty_Maybe, bbc)) → new_ltEs18(zxw7900, zxw8000, bbc)
new_ltEs20(zxw7900, zxw8000, ty_Int) → new_ltEs9(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, ty_@0) → new_ltEs8(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, app(app(ty_@2, baf), bag)) → new_ltEs4(zxw7900, zxw8000, baf, bag)
new_ltEs20(zxw7900, zxw8000, ty_Float) → new_ltEs16(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, ty_Bool) → new_ltEs12(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, app(ty_Ratio, bbb)) → new_ltEs17(zxw7900, zxw8000, bbb)
new_ltEs20(zxw7900, zxw8000, ty_Double) → new_ltEs15(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, ty_Integer) → new_ltEs13(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, app(app(app(ty_@3, bab), bac), bad)) → new_ltEs6(zxw7900, zxw8000, bab, bac, bad)
new_ltEs20(zxw7900, zxw8000, app(app(ty_Either, bah), bba)) → new_ltEs14(zxw7900, zxw8000, bah, bba)
new_ltEs20(zxw7900, zxw8000, app(ty_[], bae)) → new_ltEs11(zxw7900, zxw8000, bae)
new_ltEs20(zxw7900, zxw8000, ty_Char) → new_ltEs10(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, ty_Ordering) → new_ltEs7(zxw7900, zxw8000)
new_compare14(zxw242, zxw243, False, def, deg) → GT
new_compare14(zxw242, zxw243, True, def, deg) → LT
new_ltEs6(@3(zxw79000, zxw79001, zxw79002), @3(zxw80000, zxw80001, zxw80002), hb, hc, hd) → new_pePe(new_lt19(zxw79000, zxw80000, hb), new_asAs(new_esEs20(zxw79000, zxw80000, hb), new_pePe(new_lt20(zxw79001, zxw80001, hc), new_asAs(new_esEs19(zxw79001, zxw80001, hc), new_ltEs21(zxw79002, zxw80002, hd)))))
new_lt19(zxw79000, zxw80000, app(app(ty_Either, bhd), bhe)) → new_lt14(zxw79000, zxw80000, bhd, bhe)
new_lt19(zxw79000, zxw80000, ty_Double) → new_lt15(zxw79000, zxw80000)
new_lt19(zxw79000, zxw80000, ty_Ordering) → new_lt6(zxw79000, zxw80000)
new_lt19(zxw79000, zxw80000, app(ty_Ratio, gg)) → new_lt17(zxw79000, zxw80000, gg)
new_lt19(zxw79000, zxw80000, app(app(ty_@2, bcf), bcg)) → new_lt11(zxw79000, zxw80000, bcf, bcg)
new_lt19(zxw79000, zxw80000, ty_Int) → new_lt8(zxw79000, zxw80000)
new_lt19(zxw79000, zxw80000, ty_@0) → new_lt7(zxw79000, zxw80000)
new_lt19(zxw79000, zxw80000, app(app(app(ty_@3, gd), ge), gf)) → new_lt5(zxw79000, zxw80000, gd, ge, gf)
new_lt19(zxw79000, zxw80000, app(ty_Maybe, bdb)) → new_lt18(zxw79000, zxw80000, bdb)
new_lt19(zxw79000, zxw80000, ty_Float) → new_lt16(zxw79000, zxw80000)
new_lt19(zxw79000, zxw80000, ty_Bool) → new_lt12(zxw79000, zxw80000)
new_lt19(zxw79000, zxw80000, app(ty_[], bhc)) → new_lt10(zxw79000, zxw80000, bhc)
new_lt19(zxw79000, zxw80000, ty_Integer) → new_lt13(zxw79000, zxw80000)
new_lt19(zxw79000, zxw80000, ty_Char) → new_lt9(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, app(ty_[], bhc)) → new_esEs13(zxw79000, zxw80000, bhc)
new_esEs20(zxw79000, zxw80000, ty_Double) → new_esEs16(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, ty_Char) → new_esEs12(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, app(app(ty_@2, bcf), bcg)) → new_esEs5(zxw79000, zxw80000, bcf, bcg)
new_esEs20(zxw79000, zxw80000, ty_Int) → new_esEs11(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, ty_@0) → new_esEs10(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, app(app(app(ty_@3, gd), ge), gf)) → new_esEs4(zxw79000, zxw80000, gd, ge, gf)
new_esEs20(zxw79000, zxw80000, ty_Integer) → new_esEs15(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, ty_Bool) → new_esEs14(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, app(ty_Ratio, gg)) → new_esEs18(zxw79000, zxw80000, gg)
new_esEs20(zxw79000, zxw80000, app(app(ty_Either, bhd), bhe)) → new_esEs7(zxw79000, zxw80000, bhd, bhe)
new_esEs20(zxw79000, zxw80000, app(ty_Maybe, bdb)) → new_esEs6(zxw79000, zxw80000, bdb)
new_esEs20(zxw79000, zxw80000, ty_Ordering) → new_esEs9(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, ty_Float) → new_esEs17(zxw79000, zxw80000)
new_lt20(zxw79001, zxw80001, app(app(ty_Either, cad), cae)) → new_lt14(zxw79001, zxw80001, cad, cae)
new_lt20(zxw79001, zxw80001, ty_@0) → new_lt7(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, app(app(ty_@2, cab), cac)) → new_lt11(zxw79001, zxw80001, cab, cac)
new_lt20(zxw79001, zxw80001, ty_Ordering) → new_lt6(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, app(ty_Maybe, cag)) → new_lt18(zxw79001, zxw80001, cag)
new_lt20(zxw79001, zxw80001, ty_Int) → new_lt8(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, ty_Integer) → new_lt13(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, app(ty_Ratio, caf)) → new_lt17(zxw79001, zxw80001, caf)
new_lt20(zxw79001, zxw80001, ty_Char) → new_lt9(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, app(ty_[], caa)) → new_lt10(zxw79001, zxw80001, caa)
new_lt20(zxw79001, zxw80001, ty_Double) → new_lt15(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, ty_Float) → new_lt16(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, ty_Bool) → new_lt12(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, app(app(app(ty_@3, bhf), bhg), bhh)) → new_lt5(zxw79001, zxw80001, bhf, bhg, bhh)
new_esEs19(zxw79001, zxw80001, app(ty_Ratio, caf)) → new_esEs18(zxw79001, zxw80001, caf)
new_esEs19(zxw79001, zxw80001, ty_Ordering) → new_esEs9(zxw79001, zxw80001)
new_esEs19(zxw79001, zxw80001, app(ty_Maybe, cag)) → new_esEs6(zxw79001, zxw80001, cag)
new_esEs19(zxw79001, zxw80001, app(app(ty_Either, cad), cae)) → new_esEs7(zxw79001, zxw80001, cad, cae)
new_esEs19(zxw79001, zxw80001, ty_Float) → new_esEs17(zxw79001, zxw80001)
new_esEs19(zxw79001, zxw80001, ty_Bool) → new_esEs14(zxw79001, zxw80001)
new_esEs19(zxw79001, zxw80001, ty_Int) → new_esEs11(zxw79001, zxw80001)
new_esEs19(zxw79001, zxw80001, app(app(app(ty_@3, bhf), bhg), bhh)) → new_esEs4(zxw79001, zxw80001, bhf, bhg, bhh)
new_esEs19(zxw79001, zxw80001, app(app(ty_@2, cab), cac)) → new_esEs5(zxw79001, zxw80001, cab, cac)
new_esEs19(zxw79001, zxw80001, ty_Double) → new_esEs16(zxw79001, zxw80001)
new_esEs19(zxw79001, zxw80001, ty_Integer) → new_esEs15(zxw79001, zxw80001)
new_esEs19(zxw79001, zxw80001, ty_@0) → new_esEs10(zxw79001, zxw80001)
new_esEs19(zxw79001, zxw80001, app(ty_[], caa)) → new_esEs13(zxw79001, zxw80001, caa)
new_esEs19(zxw79001, zxw80001, ty_Char) → new_esEs12(zxw79001, zxw80001)
new_ltEs21(zxw79002, zxw80002, ty_Char) → new_ltEs10(zxw79002, zxw80002)
new_ltEs21(zxw79002, zxw80002, app(app(ty_@2, cbd), cbe)) → new_ltEs4(zxw79002, zxw80002, cbd, cbe)
new_ltEs21(zxw79002, zxw80002, ty_Int) → new_ltEs9(zxw79002, zxw80002)
new_ltEs21(zxw79002, zxw80002, ty_Ordering) → new_ltEs7(zxw79002, zxw80002)
new_ltEs21(zxw79002, zxw80002, ty_Float) → new_ltEs16(zxw79002, zxw80002)
new_ltEs21(zxw79002, zxw80002, ty_Bool) → new_ltEs12(zxw79002, zxw80002)
new_ltEs21(zxw79002, zxw80002, ty_Integer) → new_ltEs13(zxw79002, zxw80002)
new_ltEs21(zxw79002, zxw80002, app(app(ty_Either, cbf), cbg)) → new_ltEs14(zxw79002, zxw80002, cbf, cbg)
new_ltEs21(zxw79002, zxw80002, app(ty_[], cbc)) → new_ltEs11(zxw79002, zxw80002, cbc)
new_ltEs21(zxw79002, zxw80002, app(ty_Ratio, cbh)) → new_ltEs17(zxw79002, zxw80002, cbh)
new_ltEs21(zxw79002, zxw80002, app(app(app(ty_@3, cah), cba), cbb)) → new_ltEs6(zxw79002, zxw80002, cah, cba, cbb)
new_ltEs21(zxw79002, zxw80002, ty_@0) → new_ltEs8(zxw79002, zxw80002)
new_ltEs21(zxw79002, zxw80002, app(ty_Maybe, cca)) → new_ltEs18(zxw79002, zxw80002, cca)
new_ltEs21(zxw79002, zxw80002, ty_Double) → new_ltEs15(zxw79002, zxw80002)
new_pePe(False, zxw271) → zxw271
new_pePe(True, zxw271) → True
new_ltEs15(zxw7900, zxw8000) → new_fsEs(new_compare6(zxw7900, zxw8000))
new_compare6(Double(zxw79000, zxw79001), Double(zxw80000, zxw80001)) → new_compare16(new_sr(zxw79000, zxw80000), new_sr(zxw79001, zxw80001))
new_ltEs8(zxw7900, zxw8000) → new_fsEs(new_compare30(zxw7900, zxw8000))
new_ltEs12(True, False) → False
new_ltEs12(False, False) → True
new_ltEs12(True, True) → True
new_ltEs12(False, True) → True
new_ltEs16(zxw7900, zxw8000) → new_fsEs(new_compare7(zxw7900, zxw8000))
new_compare7(Float(zxw79000, zxw79001), Float(zxw80000, zxw80001)) → new_compare16(new_sr(zxw79000, zxw80000), new_sr(zxw79001, zxw80001))
new_ltEs4(@2(zxw79000, zxw79001), @2(zxw80000, zxw80001), ca, cb) → new_pePe(new_lt4(zxw79000, zxw80000, ca), new_asAs(new_esEs8(zxw79000, zxw80000, ca), new_ltEs5(zxw79001, zxw80001, cb)))
new_lt4(zxw79000, zxw80000, app(app(app(ty_@3, cc), cd), ce)) → new_lt5(zxw79000, zxw80000, cc, cd, ce)
new_lt4(zxw79000, zxw80000, app(ty_[], cf)) → new_lt10(zxw79000, zxw80000, cf)
new_lt4(zxw79000, zxw80000, ty_Bool) → new_lt12(zxw79000, zxw80000)
new_lt4(zxw79000, zxw80000, app(ty_Maybe, de)) → new_lt18(zxw79000, zxw80000, de)
new_lt4(zxw79000, zxw80000, ty_Ordering) → new_lt6(zxw79000, zxw80000)
new_lt4(zxw79000, zxw80000, app(ty_Ratio, dd)) → new_lt17(zxw79000, zxw80000, dd)
new_lt4(zxw79000, zxw80000, ty_Int) → new_lt8(zxw79000, zxw80000)
new_lt4(zxw79000, zxw80000, ty_Double) → new_lt15(zxw79000, zxw80000)
new_lt4(zxw79000, zxw80000, app(app(ty_Either, db), dc)) → new_lt14(zxw79000, zxw80000, db, dc)
new_lt4(zxw79000, zxw80000, ty_Char) → new_lt9(zxw79000, zxw80000)
new_lt4(zxw79000, zxw80000, ty_@0) → new_lt7(zxw79000, zxw80000)
new_lt4(zxw79000, zxw80000, ty_Float) → new_lt16(zxw79000, zxw80000)
new_lt4(zxw79000, zxw80000, app(app(ty_@2, cg), da)) → new_lt11(zxw79000, zxw80000, cg, da)
new_lt4(zxw79000, zxw80000, ty_Integer) → new_lt13(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, ty_Int) → new_esEs11(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, ty_Double) → new_esEs16(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, app(app(app(ty_@3, cc), cd), ce)) → new_esEs4(zxw79000, zxw80000, cc, cd, ce)
new_esEs8(zxw79000, zxw80000, app(ty_[], cf)) → new_esEs13(zxw79000, zxw80000, cf)
new_esEs8(zxw79000, zxw80000, ty_Char) → new_esEs12(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, app(app(ty_@2, cg), da)) → new_esEs5(zxw79000, zxw80000, cg, da)
new_esEs8(zxw79000, zxw80000, ty_Float) → new_esEs17(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, app(app(ty_Either, db), dc)) → new_esEs7(zxw79000, zxw80000, db, dc)
new_esEs8(zxw79000, zxw80000, ty_@0) → new_esEs10(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, app(ty_Maybe, de)) → new_esEs6(zxw79000, zxw80000, de)
new_esEs8(zxw79000, zxw80000, ty_Bool) → new_esEs14(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, ty_Ordering) → new_esEs9(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, ty_Integer) → new_esEs15(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, app(ty_Ratio, dd)) → new_esEs18(zxw79000, zxw80000, dd)
new_ltEs5(zxw79001, zxw80001, ty_Char) → new_ltEs10(zxw79001, zxw80001)
new_ltEs5(zxw79001, zxw80001, app(app(ty_@2, eb), ec)) → new_ltEs4(zxw79001, zxw80001, eb, ec)
new_ltEs5(zxw79001, zxw80001, ty_Ordering) → new_ltEs7(zxw79001, zxw80001)
new_ltEs5(zxw79001, zxw80001, ty_Bool) → new_ltEs12(zxw79001, zxw80001)
new_ltEs5(zxw79001, zxw80001, ty_Integer) → new_ltEs13(zxw79001, zxw80001)
new_ltEs5(zxw79001, zxw80001, app(ty_Ratio, ef)) → new_ltEs17(zxw79001, zxw80001, ef)
new_ltEs5(zxw79001, zxw80001, app(ty_Maybe, eg)) → new_ltEs18(zxw79001, zxw80001, eg)
new_ltEs5(zxw79001, zxw80001, ty_Double) → new_ltEs15(zxw79001, zxw80001)
new_ltEs5(zxw79001, zxw80001, app(app(ty_Either, ed), ee)) → new_ltEs14(zxw79001, zxw80001, ed, ee)
new_ltEs5(zxw79001, zxw80001, app(app(app(ty_@3, df), dg), dh)) → new_ltEs6(zxw79001, zxw80001, df, dg, dh)
new_ltEs5(zxw79001, zxw80001, app(ty_[], ea)) → new_ltEs11(zxw79001, zxw80001, ea)
new_ltEs5(zxw79001, zxw80001, ty_Int) → new_ltEs9(zxw79001, zxw80001)
new_ltEs5(zxw79001, zxw80001, ty_@0) → new_ltEs8(zxw79001, zxw80001)
new_ltEs5(zxw79001, zxw80001, ty_Float) → new_ltEs16(zxw79001, zxw80001)
new_lt13(zxw79000, zxw80000) → new_esEs9(new_compare32(zxw79000, zxw80000), LT)
new_lt11(zxw79000, zxw80000, bcf, bcg) → new_esEs9(new_compare19(zxw79000, zxw80000, bcf, bcg), LT)
new_compare19(zxw79000, zxw80000, bcf, bcg) → new_compare210(zxw79000, zxw80000, new_esEs5(zxw79000, zxw80000, bcf, bcg), bcf, bcg)
new_compare210(zxw79000, zxw80000, False, bcf, bcg) → new_compare110(zxw79000, zxw80000, new_ltEs4(zxw79000, zxw80000, bcf, bcg), bcf, bcg)
new_compare210(zxw79000, zxw80000, True, bcf, bcg) → EQ
new_compare110(zxw79000, zxw80000, True, bcf, bcg) → LT
new_compare110(zxw79000, zxw80000, False, bcf, bcg) → GT
new_lt16(zxw79000, zxw80000) → new_esEs9(new_compare7(zxw79000, zxw80000), LT)
new_lt7(zxw79000, zxw80000) → new_esEs9(new_compare30(zxw79000, zxw80000), LT)
new_lt9(zxw79000, zxw80000) → new_esEs9(new_compare17(zxw79000, zxw80000), LT)
new_lt14(zxw790, zxw800, gh, ha) → new_esEs9(new_compare15(zxw790, zxw800, gh, ha), LT)
new_lt15(zxw79000, zxw80000) → new_esEs9(new_compare6(zxw79000, zxw80000), LT)
new_lt8(zxw790, zxw800) → new_esEs9(new_compare16(zxw790, zxw800), LT)
new_lt17(zxw79000, zxw80000, gg) → new_esEs9(new_compare8(zxw79000, zxw80000, gg), LT)
new_lt6(zxw79000, zxw80000) → new_esEs9(new_compare18(zxw79000, zxw80000), LT)
new_lt18(zxw79000, zxw80000, bdb) → new_esEs9(new_compare27(zxw79000, zxw80000, bdb), LT)
new_compare27(zxw79000, zxw80000, bdb) → new_compare28(zxw79000, zxw80000, new_esEs6(zxw79000, zxw80000, bdb), bdb)
new_compare28(zxw79000, zxw80000, False, bdb) → new_compare111(zxw79000, zxw80000, new_ltEs18(zxw79000, zxw80000, bdb), bdb)
new_compare28(zxw79000, zxw80000, True, bdb) → EQ
new_compare111(zxw79000, zxw80000, True, bdb) → LT
new_compare111(zxw79000, zxw80000, False, bdb) → GT
new_lt12(zxw79000, zxw80000) → new_esEs9(new_compare31(zxw79000, zxw80000), LT)
new_compare31(zxw79000, zxw80000) → new_compare23(zxw79000, zxw80000, new_esEs14(zxw79000, zxw80000))
new_compare23(zxw79000, zxw80000, True) → EQ
new_compare23(zxw79000, zxw80000, False) → new_compare10(zxw79000, zxw80000, new_ltEs12(zxw79000, zxw80000))
new_compare10(zxw79000, zxw80000, True) → LT
new_compare10(zxw79000, zxw80000, False) → GT
new_lt10(zxw79000, zxw80000, bhc) → new_esEs9(new_compare1(zxw79000, zxw80000, bhc), LT)
new_lt5(zxw79000, zxw80000, gd, ge, gf) → new_esEs9(new_compare9(zxw79000, zxw80000, gd, ge, gf), LT)
new_compare9(zxw79000, zxw80000, gd, ge, gf) → new_compare25(zxw79000, zxw80000, new_esEs4(zxw79000, zxw80000, gd, ge, gf), gd, ge, gf)
new_compare25(zxw79000, zxw80000, True, gd, ge, gf) → EQ
new_compare25(zxw79000, zxw80000, False, gd, ge, gf) → new_compare12(zxw79000, zxw80000, new_ltEs6(zxw79000, zxw80000, gd, ge, gf), gd, ge, gf)
new_compare12(zxw79000, zxw80000, True, gd, ge, gf) → LT
new_compare12(zxw79000, zxw80000, False, gd, ge, gf) → GT
new_compare34(zxw400, zxw300, h, ba) → new_compare26(Left(zxw400), Right(zxw300), False, h, ba)
new_compare33(zxw20, zxw15, bc, bd) → new_compare26(Left(zxw20), Left(zxw15), new_esEs32(zxw20, zxw15, bc), bc, bd)
new_esEs32(zxw20, zxw15, ty_Float) → new_esEs17(zxw20, zxw15)
new_esEs32(zxw20, zxw15, ty_Integer) → new_esEs15(zxw20, zxw15)
new_esEs32(zxw20, zxw15, ty_@0) → new_esEs10(zxw20, zxw15)
new_esEs32(zxw20, zxw15, ty_Ordering) → new_esEs9(zxw20, zxw15)
new_esEs32(zxw20, zxw15, ty_Bool) → new_esEs14(zxw20, zxw15)
new_esEs32(zxw20, zxw15, app(app(ty_Either, cea), ceb)) → new_esEs7(zxw20, zxw15, cea, ceb)
new_esEs32(zxw20, zxw15, app(ty_[], cde)) → new_esEs13(zxw20, zxw15, cde)
new_esEs32(zxw20, zxw15, app(ty_Maybe, cdf)) → new_esEs6(zxw20, zxw15, cdf)
new_esEs32(zxw20, zxw15, app(app(ty_@2, cdg), cdh)) → new_esEs5(zxw20, zxw15, cdg, cdh)
new_esEs32(zxw20, zxw15, ty_Char) → new_esEs12(zxw20, zxw15)
new_esEs32(zxw20, zxw15, app(app(app(ty_@3, cec), ced), cee)) → new_esEs4(zxw20, zxw15, cec, ced, cee)
new_esEs32(zxw20, zxw15, ty_Int) → new_esEs11(zxw20, zxw15)
new_esEs32(zxw20, zxw15, app(ty_Ratio, cdd)) → new_esEs18(zxw20, zxw15, cdd)
new_esEs32(zxw20, zxw15, ty_Double) → new_esEs16(zxw20, zxw15)

The set Q consists of the following terms:

new_compare23(x0, x1, True)
new_lt6(x0, x1)
new_ltEs5(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, ty_Integer)
new_esEs33(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt4(x0, x1, app(ty_[], x2))
new_ltEs18(Just(x0), Just(x1), ty_@0)
new_compare16(x0, x1)
new_lt4(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(Just(x0), Nothing, x1)
new_ltEs20(x0, x1, ty_Double)
new_esEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs19(x0, x1, ty_Bool)
new_esEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs8(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(x0, x1, app(app(ty_Either, x2), x3))
new_compare30(@0, @0)
new_esEs32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCompAux00(x0, GT)
new_lt19(x0, x1, ty_Char)
new_esEs27(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_Ordering)
new_compare17(Char(x0), Char(x1))
new_esEs28(x0, x1, ty_Int)
new_ltEs20(x0, x1, app(ty_[], x2))
new_ltEs21(x0, x1, ty_Ordering)
new_compare111(x0, x1, True, x2)
new_ltEs15(x0, x1)
new_primPlusNat1(Zero, Succ(x0))
new_esEs6(Just(x0), Just(x1), ty_Double)
new_compare24(x0, x1, False)
new_compare210(x0, x1, False, x2, x3)
new_lt20(x0, x1, ty_Char)
new_esEs33(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, ty_Bool)
new_sr0(Integer(x0), Integer(x1))
new_esEs32(x0, x1, app(ty_[], x2))
new_esEs33(x0, x1, ty_Float)
new_compare28(x0, x1, True, x2)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(Nothing, Nothing, x0)
new_ltEs18(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs34(x0, x1, ty_Integer)
new_esEs34(x0, x1, app(ty_Maybe, x2))
new_ltEs7(EQ, EQ)
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs19(x0, x1, ty_Integer)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_ltEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Bool)
new_ltEs14(Right(x0), Right(x1), x2, ty_Float)
new_compare27(x0, x1, x2)
new_esEs31(x0, x1, app(ty_Ratio, x2))
new_esEs6(Just(x0), Just(x1), app(ty_[], x2))
new_compare14(x0, x1, True, x2, x3)
new_ltEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs13([], :(x0, x1), x2)
new_compare25(x0, x1, False, x2, x3, x4)
new_esEs7(Left(x0), Left(x1), ty_Integer, x2)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs7(Right(x0), Right(x1), x2, ty_@0)
new_esEs31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Integer)
new_ltEs5(x0, x1, ty_Integer)
new_ltEs21(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs7(EQ, LT)
new_ltEs7(LT, EQ)
new_esEs20(x0, x1, ty_Ordering)
new_esEs17(Float(x0, x1), Float(x2, x3))
new_compare25(x0, x1, True, x2, x3, x4)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_lt19(x0, x1, ty_Ordering)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs16(x0, x1)
new_lt4(x0, x1, app(ty_Maybe, x2))
new_esEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs14(Left(x0), Left(x1), ty_Char, x2)
new_sr(x0, x1)
new_ltEs19(x0, x1, ty_Double)
new_compare7(Float(x0, x1), Float(x2, x3))
new_ltEs9(x0, x1)
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_compare19(x0, x1, x2, x3)
new_lt7(x0, x1)
new_lt4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, ty_Int)
new_esEs26(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat0(Zero, x0)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs32(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_ltEs7(LT, LT)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs27(x0, x1, ty_Bool)
new_lt5(x0, x1, x2, x3, x4)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare29(x0, x1, app(app(ty_@2, x2), x3))
new_lt4(x0, x1, ty_Ordering)
new_esEs34(x0, x1, app(ty_Ratio, x2))
new_primEqNat0(Zero, Succ(x0))
new_lt19(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Int)
new_esEs15(Integer(x0), Integer(x1))
new_esEs26(x0, x1, ty_Double)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs28(x0, x1, ty_@0)
new_primPlusNat1(Succ(x0), Zero)
new_esEs22(x0, x1, ty_Integer)
new_ltEs14(Left(x0), Left(x1), ty_@0, x2)
new_primMulInt(Neg(x0), Neg(x1))
new_ltEs19(x0, x1, ty_Int)
new_esEs7(Left(x0), Left(x1), ty_Double, x2)
new_compare29(x0, x1, ty_Integer)
new_esEs14(True, True)
new_esEs21(x0, x1, ty_Char)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(Just(x0), Just(x1), ty_Integer)
new_compare29(x0, x1, app(ty_[], x2))
new_ltEs18(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, ty_Int)
new_esEs7(Right(x0), Right(x1), x2, ty_Int)
new_primEqNat0(Zero, Zero)
new_esEs16(Double(x0, x1), Double(x2, x3))
new_esEs12(Char(x0), Char(x1))
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_lt4(x0, x1, ty_Char)
new_esEs20(x0, x1, ty_Bool)
new_esEs8(x0, x1, ty_Float)
new_compare1([], :(x0, x1), x2)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_Integer)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs32(x0, x1, ty_@0)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(Left(x0), Left(x1), ty_Int, x2)
new_primCompAux00(x0, LT)
new_esEs27(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(ty_[], x2))
new_ltEs5(x0, x1, ty_Double)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs18(Just(x0), Just(x1), ty_Char)
new_primMulNat0(Zero, Zero)
new_lt9(x0, x1)
new_compare29(x0, x1, ty_Double)
new_esEs34(x0, x1, app(ty_[], x2))
new_ltEs5(x0, x1, ty_@0)
new_lt17(x0, x1, x2)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_ltEs21(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs31(x0, x1, ty_Bool)
new_ltEs14(Left(x0), Left(x1), ty_Float, x2)
new_esEs32(x0, x1, ty_Float)
new_esEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs8(x0, x1, ty_Ordering)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_compare10(x0, x1, True)
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Ordering)
new_primEqNat0(Succ(x0), Succ(x1))
new_ltEs19(x0, x1, ty_Bool)
new_esEs28(x0, x1, ty_Double)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_@0)
new_pePe(True, x0)
new_esEs19(x0, x1, ty_Float)
new_lt19(x0, x1, app(ty_[], x2))
new_esEs8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_lt16(x0, x1)
new_compare29(x0, x1, ty_Bool)
new_lt10(x0, x1, x2)
new_esEs7(Right(x0), Right(x1), x2, ty_Integer)
new_esEs32(x0, x1, app(app(ty_Either, x2), x3))
new_compare11(x0, x1, True)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs32(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs33(x0, x1, app(ty_[], x2))
new_esEs34(x0, x1, ty_Char)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1, ty_@0)
new_esEs6(Just(x0), Just(x1), ty_Ordering)
new_esEs23(x0, x1, ty_@0)
new_ltEs14(Right(x0), Right(x1), x2, ty_Int)
new_ltEs5(x0, x1, ty_Char)
new_ltEs21(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Float)
new_lt18(x0, x1, x2)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_compare29(x0, x1, ty_Ordering)
new_ltEs21(x0, x1, ty_@0)
new_esEs8(x0, x1, ty_Int)
new_lt14(x0, x1, x2, x3)
new_ltEs12(False, False)
new_compare210(x0, x1, True, x2, x3)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Just(x0), Just(x1), ty_Bool)
new_compare32(Integer(x0), Integer(x1))
new_lt19(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_Int)
new_primMulNat0(Succ(x0), Succ(x1))
new_compare29(x0, x1, ty_Float)
new_ltEs21(x0, x1, ty_Integer)
new_esEs6(Just(x0), Just(x1), ty_Float)
new_ltEs5(x0, x1, ty_Float)
new_ltEs18(Just(x0), Just(x1), ty_Float)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_Bool)
new_esEs31(x0, x1, ty_Double)
new_primCmpNat1(Zero, x0)
new_ltEs14(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs8(x0, x1)
new_ltEs18(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs14(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs33(x0, x1, app(ty_Ratio, x2))
new_compare13(x0, x1, False, x2, x3)
new_esEs34(x0, x1, ty_Float)
new_primPlusNat1(Zero, Zero)
new_esEs23(x0, x1, ty_Double)
new_ltEs18(Just(x0), Just(x1), ty_Ordering)
new_primCmpNat2(Zero, Zero)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(x0, x1, ty_Bool)
new_esEs34(x0, x1, ty_Ordering)
new_ltEs18(Just(x0), Just(x1), app(ty_[], x2))
new_esEs33(x0, x1, app(ty_Maybe, x2))
new_ltEs5(x0, x1, app(ty_[], x2))
new_asAs(False, x0)
new_ltEs20(x0, x1, ty_Char)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs31(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs8(x0, x1, ty_Integer)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs33(x0, x1, ty_Ordering)
new_ltEs18(Just(x0), Just(x1), ty_Bool)
new_compare14(x0, x1, False, x2, x3)
new_primCmpNat1(Succ(x0), x1)
new_esEs34(x0, x1, ty_Bool)
new_esEs33(x0, x1, ty_Double)
new_esEs24(x0, x1, ty_Integer)
new_esEs27(x0, x1, ty_@0)
new_esEs7(Left(x0), Left(x1), ty_Int, x2)
new_ltEs14(Right(x0), Right(x1), x2, ty_Double)
new_lt4(x0, x1, ty_Float)
new_ltEs5(x0, x1, app(app(ty_Either, x2), x3))
new_esEs19(x0, x1, ty_Char)
new_lt4(x0, x1, ty_Double)
new_esEs19(x0, x1, ty_Ordering)
new_esEs8(x0, x1, app(ty_Ratio, x2))
new_esEs33(x0, x1, ty_Int)
new_esEs10(@0, @0)
new_esEs31(x0, x1, ty_@0)
new_esEs33(x0, x1, ty_@0)
new_esEs11(x0, x1)
new_esEs20(x0, x1, ty_Float)
new_ltEs14(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs7(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs14(Right(x0), Right(x1), x2, ty_Char)
new_esEs9(GT, GT)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs27(x0, x1, ty_Char)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_compare11(x0, x1, False)
new_compare23(x0, x1, False)
new_compare12(x0, x1, True, x2, x3, x4)
new_esEs7(Right(x0), Right(x1), x2, ty_Double)
new_esEs28(x0, x1, ty_Bool)
new_esEs33(x0, x1, app(app(ty_Either, x2), x3))
new_compare24(x0, x1, True)
new_compare36(x0, x1, x2, x3)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_compare15(x0, x1, x2, x3)
new_primEqNat0(Succ(x0), Zero)
new_esEs13([], [], x0)
new_esEs23(x0, x1, ty_Ordering)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs7(Left(x0), Right(x1), x2, x3)
new_esEs7(Right(x0), Left(x1), x2, x3)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_esEs34(x0, x1, ty_Int)
new_compare9(x0, x1, x2, x3, x4)
new_lt20(x0, x1, ty_Int)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs21(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Integer)
new_esEs33(x0, x1, ty_Bool)
new_lt4(x0, x1, app(app(ty_Either, x2), x3))
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs23(x0, x1, ty_Int)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs5(x0, x1, app(app(ty_@2, x2), x3))
new_esEs33(x0, x1, ty_Char)
new_lt4(x0, x1, ty_@0)
new_esEs23(x0, x1, ty_Char)
new_esEs28(x0, x1, ty_Ordering)
new_ltEs18(Just(x0), Just(x1), ty_Double)
new_ltEs20(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_lt20(x0, x1, ty_@0)
new_compare1([], [], x0)
new_esEs9(EQ, EQ)
new_pePe(False, x0)
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs5(x0, x1, app(ty_Ratio, x2))
new_ltEs14(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs6(Just(x0), Just(x1), ty_Char)
new_esEs25(x0, x1, ty_Integer)
new_esEs31(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_Integer)
new_compare12(x0, x1, False, x2, x3, x4)
new_esEs8(x0, x1, app(ty_Maybe, x2))
new_primCompAux00(x0, EQ)
new_esEs19(x0, x1, ty_Int)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs14(True, False)
new_esEs14(False, True)
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_lt4(x0, x1, ty_Integer)
new_esEs7(Left(x0), Left(x1), ty_@0, x2)
new_ltEs14(Right(x0), Right(x1), x2, ty_@0)
new_fsEs(x0)
new_esEs22(x0, x1, ty_Float)
new_ltEs14(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs32(x0, x1, app(ty_Ratio, x2))
new_esEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_primCmpNat2(Succ(x0), Succ(x1))
new_compare110(x0, x1, False, x2, x3)
new_lt4(x0, x1, ty_Bool)
new_asAs(True, x0)
new_esEs21(x0, x1, ty_Bool)
new_esEs4(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs6(Nothing, Just(x0), x1)
new_esEs6(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs21(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Just(x0), Nothing, x1)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_compare29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs8(x0, x1, app(ty_[], x2))
new_esEs31(x0, x1, ty_Integer)
new_esEs13(:(x0, x1), [], x2)
new_ltEs14(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs8(x0, x1, ty_Char)
new_lt19(x0, x1, ty_Float)
new_compare33(x0, x1, x2, x3)
new_ltEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs22(x0, x1, ty_@0)
new_esEs34(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_Char)
new_ltEs12(False, True)
new_ltEs12(True, False)
new_compare6(Double(x0, x1), Double(x2, x3))
new_ltEs20(x0, x1, ty_@0)
new_esEs22(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_@0)
new_compare35(x0, x1, x2, x3)
new_ltEs14(Right(x0), Right(x1), x2, ty_Integer)
new_lt19(x0, x1, ty_Double)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1, ty_Bool)
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs7(Left(x0), Left(x1), ty_Char, x2)
new_esEs7(Right(x0), Right(x1), x2, ty_Float)
new_ltEs14(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs26(x0, x1, ty_Char)
new_ltEs5(x0, x1, ty_Int)
new_lt4(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_Double)
new_esEs19(x0, x1, ty_@0)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_compare13(x0, x1, True, x2, x3)
new_esEs34(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs21(x0, x1, ty_Bool)
new_ltEs14(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs21(x0, x1, ty_Double)
new_lt12(x0, x1)
new_esEs8(x0, x1, ty_Bool)
new_ltEs21(x0, x1, ty_Char)
new_lt13(x0, x1)
new_esEs31(x0, x1, ty_Ordering)
new_ltEs14(Right(x0), Right(x1), x2, ty_Bool)
new_compare1(:(x0, x1), [], x2)
new_compare10(x0, x1, False)
new_primMulNat0(Succ(x0), Zero)
new_ltEs19(x0, x1, ty_Float)
new_ltEs14(Left(x0), Right(x1), x2, x3)
new_esEs23(x0, x1, ty_Float)
new_ltEs14(Right(x0), Left(x1), x2, x3)
new_compare29(x0, x1, ty_Int)
new_esEs20(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, ty_Int)
new_esEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs20(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Float)
new_compare31(x0, x1)
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs31(x0, x1, ty_Char)
new_esEs6(Just(x0), Just(x1), ty_Int)
new_ltEs7(LT, GT)
new_ltEs7(GT, LT)
new_esEs21(x0, x1, ty_Integer)
new_esEs22(x0, x1, app(ty_[], x2))
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs22(x0, x1, ty_Double)
new_compare110(x0, x1, True, x2, x3)
new_lt20(x0, x1, app(ty_[], x2))
new_ltEs13(x0, x1)
new_ltEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs34(x0, x1, ty_@0)
new_esEs31(x0, x1, ty_Int)
new_lt4(x0, x1, ty_Int)
new_ltEs11(x0, x1, x2)
new_lt20(x0, x1, ty_Float)
new_not(True)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs31(x0, x1, ty_Float)
new_esEs20(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Float)
new_esEs19(x0, x1, app(ty_[], x2))
new_esEs18(:%(x0, x1), :%(x2, x3), x4)
new_esEs6(Nothing, Nothing, x0)
new_esEs28(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Ordering)
new_ltEs14(Left(x0), Left(x1), ty_Double, x2)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Just(x0), Just(x1), ty_Integer)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_not(False)
new_compare29(x0, x1, app(ty_Ratio, x2))
new_lt8(x0, x1)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_compare28(x0, x1, False, x2)
new_esEs32(x0, x1, ty_Integer)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, ty_Char)
new_esEs6(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare8(:%(x0, x1), :%(x2, x3), ty_Integer)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs22(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_Integer)
new_esEs8(x0, x1, ty_@0)
new_compare26(Left(x0), Left(x1), False, x2, x3)
new_esEs32(x0, x1, app(ty_Maybe, x2))
new_ltEs12(True, True)
new_esEs27(x0, x1, ty_Float)
new_lt15(x0, x1)
new_lt11(x0, x1, x2, x3)
new_esEs26(x0, x1, ty_Ordering)
new_esEs7(Left(x0), Left(x1), ty_Float, x2)
new_esEs27(x0, x1, ty_Double)
new_esEs6(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs34(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs33(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Ordering)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs13(:(x0, x1), :(x2, x3), x4)
new_esEs22(x0, x1, ty_Char)
new_lt20(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Bool)
new_esEs34(x0, x1, ty_Double)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_ltEs21(x0, x1, ty_Float)
new_ltEs10(x0, x1)
new_ltEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_compare29(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs14(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs5(x0, x1, ty_Ordering)
new_esEs8(x0, x1, ty_Double)
new_compare29(x0, x1, ty_Char)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs6(Just(x0), Just(x1), ty_@0)
new_esEs31(x0, x1, app(app(ty_Either, x2), x3))
new_compare1(:(x0, x1), :(x2, x3), x4)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs31(x0, x1, app(ty_[], x2))
new_esEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs6(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs19(x0, x1, ty_Double)
new_esEs14(False, False)
new_ltEs21(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs32(x0, x1, ty_Char)
new_ltEs21(x0, x1, ty_Double)
new_esEs32(x0, x1, ty_Int)
new_ltEs14(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpNat2(Succ(x0), Zero)
new_esEs7(Right(x0), Right(x1), x2, ty_Char)
new_esEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_compare34(x0, x1, x2, x3)
new_compare18(x0, x1)
new_esEs32(x0, x1, ty_Bool)
new_esEs7(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs18(Just(x0), Just(x1), ty_Int)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare26(Right(x0), Right(x1), False, x2, x3)
new_esEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs17(x0, x1, x2)
new_primPlusNat0(Succ(x0), x1)
new_esEs20(x0, x1, ty_Integer)
new_primCmpNat0(x0, Zero)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_ltEs7(GT, EQ)
new_ltEs7(EQ, GT)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs32(x0, x1, ty_Double)
new_ltEs7(GT, GT)
new_esEs9(LT, LT)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_primCompAux0(x0, x1, x2, x3)
new_compare29(x0, x1, ty_@0)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_compare26(x0, x1, True, x2, x3)
new_compare26(Right(x0), Left(x1), False, x2, x3)
new_compare26(Left(x0), Right(x1), False, x2, x3)
new_ltEs18(Nothing, Just(x0), x1)
new_compare111(x0, x1, False, x2)
new_compare29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Ordering)
new_primCmpNat0(x0, Succ(x1))

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

new_esEs34(x0, x1, ty_Integer)
new_esEs34(x0, x1, app(ty_Maybe, x2))
new_esEs31(x0, x1, app(ty_Ratio, x2))
new_esEs31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs34(x0, x1, app(ty_Ratio, x2))
new_esEs34(x0, x1, app(ty_[], x2))
new_esEs31(x0, x1, ty_Bool)
new_esEs34(x0, x1, ty_Char)
new_esEs31(x0, x1, ty_Double)
new_esEs34(x0, x1, ty_Float)
new_esEs34(x0, x1, ty_Ordering)
new_esEs31(x0, x1, app(app(ty_@2, x2), x3))
new_esEs34(x0, x1, ty_Bool)
new_esEs31(x0, x1, ty_@0)
new_compare36(x0, x1, x2, x3)
new_esEs34(x0, x1, ty_Int)
new_esEs31(x0, x1, app(ty_Maybe, x2))
new_esEs31(x0, x1, ty_Integer)
new_esEs34(x0, x1, app(app(ty_Either, x2), x3))
new_compare35(x0, x1, x2, x3)
new_esEs34(x0, x1, app(app(ty_@2, x2), x3))
new_esEs31(x0, x1, ty_Ordering)
new_esEs31(x0, x1, ty_Char)
new_esEs34(x0, x1, ty_@0)
new_esEs31(x0, x1, ty_Int)
new_esEs31(x0, x1, ty_Float)
new_esEs34(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs34(x0, x1, ty_Double)
new_esEs31(x0, x1, app(app(ty_Either, x2), x3))
new_esEs31(x0, x1, app(ty_[], x2))



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

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

new_splitGT2(zxw15, zxw16, zxw17, zxw18, zxw19, zxw20, True, bc, bd, be) → new_splitGT(zxw19, zxw20, bc, bd, be)
new_splitGT2(zxw15, zxw16, zxw17, zxw18, zxw19, zxw20, False, bc, bd, be) → new_splitGT1(zxw15, zxw16, zxw17, zxw18, zxw19, zxw20, new_esEs9(new_compare33(zxw20, zxw15, bc, bd), LT), bc, bd, be)
new_splitGT3(Left(zxw300), zxw31, zxw32, zxw33, zxw34, Left(zxw400), h, ba, bb) → new_splitGT2(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs9(new_compare26(Left(zxw400), Left(zxw300), new_esEs33(zxw400, zxw300, h), h, ba), GT), h, ba, bb)
new_splitGT(Branch(zxw340, zxw341, zxw342, zxw343, zxw344), zxw400, h, ba, bb) → new_splitGT3(zxw340, zxw341, zxw342, zxw343, zxw344, Left(zxw400), h, ba, bb)
new_splitGT20(zxw300, zxw31, zxw32, zxw33, Branch(zxw340, zxw341, zxw342, zxw343, zxw344), zxw400, True, h, ba, bb) → new_splitGT3(zxw340, zxw341, zxw342, zxw343, zxw344, Left(zxw400), h, ba, bb)
new_splitGT10(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, True, h, ba, bb) → new_splitGT(zxw33, zxw400, h, ba, bb)
new_splitGT20(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, False, h, ba, bb) → new_splitGT10(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs9(new_compare34(zxw400, zxw300, h, ba), LT), h, ba, bb)
new_splitGT1(zxw15, zxw16, zxw17, zxw18, zxw19, zxw20, True, bc, bd, be) → new_splitGT(zxw18, zxw20, bc, bd, be)
new_splitGT3(Right(zxw300), zxw31, zxw32, zxw33, zxw34, Left(zxw400), h, ba, bb) → new_splitGT20(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs9(new_compare26(Left(zxw400), Right(zxw300), False, h, ba), GT), h, ba, bb)

The TRS R consists of the following rules:

new_compare26(Left(zxw7900), Right(zxw8000), False, gh, ha) → LT
new_esEs9(LT, GT) → False
new_esEs9(EQ, GT) → False
new_esEs9(GT, GT) → True
new_esEs33(zxw400, zxw300, app(app(ty_Either, bfh), bef)) → new_esEs7(zxw400, zxw300, bfh, bef)
new_esEs33(zxw400, zxw300, app(ty_[], ddb)) → new_esEs13(zxw400, zxw300, ddb)
new_esEs33(zxw400, zxw300, ty_Char) → new_esEs12(zxw400, zxw300)
new_esEs33(zxw400, zxw300, ty_Ordering) → new_esEs9(zxw400, zxw300)
new_esEs33(zxw400, zxw300, ty_@0) → new_esEs10(zxw400, zxw300)
new_esEs33(zxw400, zxw300, ty_Integer) → new_esEs15(zxw400, zxw300)
new_esEs33(zxw400, zxw300, app(app(app(ty_@3, deh), dfa), dfb)) → new_esEs4(zxw400, zxw300, deh, dfa, dfb)
new_esEs33(zxw400, zxw300, app(app(ty_@2, dad), dae)) → new_esEs5(zxw400, zxw300, dad, dae)
new_esEs33(zxw400, zxw300, app(ty_Ratio, dee)) → new_esEs18(zxw400, zxw300, dee)
new_esEs33(zxw400, zxw300, ty_Bool) → new_esEs14(zxw400, zxw300)
new_esEs33(zxw400, zxw300, app(ty_Maybe, eh)) → new_esEs6(zxw400, zxw300, eh)
new_esEs33(zxw400, zxw300, ty_Double) → new_esEs16(zxw400, zxw300)
new_esEs33(zxw400, zxw300, ty_Float) → new_esEs17(zxw400, zxw300)
new_esEs33(zxw400, zxw300, ty_Int) → new_esEs11(zxw400, zxw300)
new_compare26(zxw790, zxw800, True, gh, ha) → EQ
new_compare26(Left(zxw7900), Left(zxw8000), False, gh, ha) → new_compare13(zxw7900, zxw8000, new_ltEs19(zxw7900, zxw8000, gh), gh, ha)
new_ltEs19(zxw7900, zxw8000, ty_Float) → new_ltEs16(zxw7900, zxw8000)
new_ltEs19(zxw7900, zxw8000, app(app(ty_@2, ca), cb)) → new_ltEs4(zxw7900, zxw8000, ca, cb)
new_ltEs19(zxw7900, zxw8000, app(ty_[], he)) → new_ltEs11(zxw7900, zxw8000, he)
new_ltEs19(zxw7900, zxw8000, ty_Char) → new_ltEs10(zxw7900, zxw8000)
new_ltEs19(zxw7900, zxw8000, ty_Bool) → new_ltEs12(zxw7900, zxw8000)
new_ltEs19(zxw7900, zxw8000, app(ty_Ratio, hh)) → new_ltEs17(zxw7900, zxw8000, hh)
new_ltEs19(zxw7900, zxw8000, app(app(app(ty_@3, hb), hc), hd)) → new_ltEs6(zxw7900, zxw8000, hb, hc, hd)
new_ltEs19(zxw7900, zxw8000, ty_Int) → new_ltEs9(zxw7900, zxw8000)
new_ltEs19(zxw7900, zxw8000, app(app(ty_Either, hf), hg)) → new_ltEs14(zxw7900, zxw8000, hf, hg)
new_ltEs19(zxw7900, zxw8000, ty_@0) → new_ltEs8(zxw7900, zxw8000)
new_ltEs19(zxw7900, zxw8000, ty_Double) → new_ltEs15(zxw7900, zxw8000)
new_ltEs19(zxw7900, zxw8000, ty_Integer) → new_ltEs13(zxw7900, zxw8000)
new_ltEs19(zxw7900, zxw8000, ty_Ordering) → new_ltEs7(zxw7900, zxw8000)
new_ltEs19(zxw7900, zxw8000, app(ty_Maybe, baa)) → new_ltEs18(zxw7900, zxw8000, baa)
new_compare13(zxw235, zxw236, False, bch, bda) → GT
new_compare13(zxw235, zxw236, True, bch, bda) → LT
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Char) → new_ltEs10(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Integer) → new_ltEs13(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(ty_Ratio, dab)) → new_ltEs17(zxw79000, zxw80000, dab)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(app(app(ty_@3, chb), chc), chd)) → new_ltEs6(zxw79000, zxw80000, chb, chc, chd)
new_ltEs18(Nothing, Nothing, baa) → True
new_ltEs18(Just(zxw79000), Nothing, baa) → False
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Double) → new_ltEs15(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(ty_[], che)) → new_ltEs11(zxw79000, zxw80000, che)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(app(ty_@2, chf), chg)) → new_ltEs4(zxw79000, zxw80000, chf, chg)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Bool) → new_ltEs12(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Ordering) → new_ltEs7(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Float) → new_ltEs16(zxw79000, zxw80000)
new_ltEs18(Nothing, Just(zxw80000), baa) → True
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Int) → new_ltEs9(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_@0) → new_ltEs8(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(ty_Maybe, dac)) → new_ltEs18(zxw79000, zxw80000, dac)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(ty_Maybe, cha)) → new_ltEs18(zxw79000, zxw80000, cha)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(app(ty_Either, chh), daa)) → new_ltEs14(zxw79000, zxw80000, chh, daa)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(app(ty_Either, cgf), cgg)) → new_ltEs14(zxw79000, zxw80000, cgf, cgg)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(app(ty_Either, cfd), cfe), hg) → new_ltEs14(zxw79000, zxw80000, cfd, cfe)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(ty_Maybe, cfg), hg) → new_ltEs18(zxw79000, zxw80000, cfg)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Bool) → new_ltEs12(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(ty_[], cgc)) → new_ltEs11(zxw79000, zxw80000, cgc)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Bool, hg) → new_ltEs12(zxw79000, zxw80000)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(ty_Ratio, cff), hg) → new_ltEs17(zxw79000, zxw80000, cff)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(app(app(ty_@3, cfh), cga), cgb)) → new_ltEs6(zxw79000, zxw80000, cfh, cga, cgb)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Float, hg) → new_ltEs16(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Float) → new_ltEs16(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Double) → new_ltEs15(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(app(ty_@2, cgd), cge)) → new_ltEs4(zxw79000, zxw80000, cgd, cge)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Double, hg) → new_ltEs15(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Left(zxw80000), hf, hg) → False
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Int, hg) → new_ltEs9(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Char) → new_ltEs10(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_@0) → new_ltEs8(zxw79000, zxw80000)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(app(app(ty_@3, cef), ceg), ceh), hg) → new_ltEs6(zxw79000, zxw80000, cef, ceg, ceh)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_@0, hg) → new_ltEs8(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Ordering) → new_ltEs7(zxw79000, zxw80000)
new_ltEs14(Left(zxw79000), Right(zxw80000), hf, hg) → True
new_ltEs14(Left(zxw79000), Left(zxw80000), app(app(ty_@2, cfb), cfc), hg) → new_ltEs4(zxw79000, zxw80000, cfb, cfc)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(ty_[], cfa), hg) → new_ltEs11(zxw79000, zxw80000, cfa)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Integer, hg) → new_ltEs13(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Int) → new_ltEs9(zxw79000, zxw80000)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Ordering, hg) → new_ltEs7(zxw79000, zxw80000)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Char, hg) → new_ltEs10(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, app(ty_Ratio, cgh)) → new_ltEs17(zxw79000, zxw80000, cgh)
new_ltEs14(Right(zxw79000), Right(zxw80000), hf, ty_Integer) → new_ltEs13(zxw79000, zxw80000)
new_ltEs13(zxw7900, zxw8000) → new_fsEs(new_compare32(zxw7900, zxw8000))
new_compare32(Integer(zxw79000), Integer(zxw80000)) → new_primCmpInt(zxw79000, zxw80000)
new_fsEs(zxw259) → new_not(new_esEs9(zxw259, GT))
new_not(False) → True
new_not(True) → False
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_primCmpNat0(zxw7900, Zero) → GT
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_primCmpNat2(Zero, Zero) → EQ
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_primCmpNat1(Zero, zxw7900) → LT
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_ltEs17(zxw7900, zxw8000, hh) → new_fsEs(new_compare8(zxw7900, zxw8000, hh))
new_compare8(:%(zxw79000, zxw79001), :%(zxw80000, zxw80001), ty_Integer) → new_compare32(new_sr0(zxw79000, zxw80001), new_sr0(zxw80000, zxw79001))
new_compare8(:%(zxw79000, zxw79001), :%(zxw80000, zxw80001), ty_Int) → new_compare16(new_sr(zxw79000, zxw80001), new_sr(zxw80000, zxw79001))
new_sr(zxw4000, zxw3000) → new_primMulInt(zxw4000, zxw3000)
new_compare16(zxw79, zxw80) → new_primCmpInt(zxw79, zxw80)
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Neg(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Neg(zxw40000), Pos(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulNat0(Zero, Zero) → Zero
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_sr0(Integer(zxw800000), Integer(zxw790010)) → Integer(new_primMulInt(zxw800000, zxw790010))
new_ltEs10(zxw7900, zxw8000) → new_fsEs(new_compare17(zxw7900, zxw8000))
new_compare17(Char(zxw79000), Char(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_ltEs7(LT, EQ) → True
new_ltEs7(GT, GT) → True
new_ltEs7(EQ, EQ) → True
new_ltEs7(GT, LT) → False
new_ltEs7(GT, EQ) → False
new_ltEs7(EQ, GT) → True
new_ltEs7(EQ, LT) → False
new_ltEs7(LT, LT) → True
new_ltEs7(LT, GT) → True
new_ltEs9(zxw7900, zxw8000) → new_fsEs(new_compare16(zxw7900, zxw8000))
new_ltEs11(zxw7900, zxw8000, he) → new_fsEs(new_compare1(zxw7900, zxw8000, he))
new_compare1([], :(zxw80000, zxw80001), he) → LT
new_compare1(:(zxw79000, zxw79001), :(zxw80000, zxw80001), he) → new_primCompAux0(zxw79000, zxw80000, new_compare1(zxw79001, zxw80001, he), he)
new_compare1(:(zxw79000, zxw79001), [], he) → GT
new_compare1([], [], he) → EQ
new_primCompAux0(zxw79000, zxw80000, zxw272, he) → new_primCompAux00(zxw272, new_compare29(zxw79000, zxw80000, he))
new_compare29(zxw79000, zxw80000, ty_Char) → new_compare17(zxw79000, zxw80000)
new_compare29(zxw79000, zxw80000, ty_Bool) → new_compare31(zxw79000, zxw80000)
new_compare29(zxw79000, zxw80000, app(app(ty_@2, ccf), ccg)) → new_compare19(zxw79000, zxw80000, ccf, ccg)
new_compare29(zxw79000, zxw80000, app(ty_[], cce)) → new_compare1(zxw79000, zxw80000, cce)
new_compare29(zxw79000, zxw80000, app(app(app(ty_@3, ccb), ccc), ccd)) → new_compare9(zxw79000, zxw80000, ccb, ccc, ccd)
new_compare29(zxw79000, zxw80000, ty_Int) → new_compare16(zxw79000, zxw80000)
new_compare29(zxw79000, zxw80000, ty_Integer) → new_compare32(zxw79000, zxw80000)
new_compare29(zxw79000, zxw80000, app(ty_Maybe, cdc)) → new_compare27(zxw79000, zxw80000, cdc)
new_compare29(zxw79000, zxw80000, app(ty_Ratio, cdb)) → new_compare8(zxw79000, zxw80000, cdb)
new_compare29(zxw79000, zxw80000, ty_Float) → new_compare7(zxw79000, zxw80000)
new_compare29(zxw79000, zxw80000, ty_Double) → new_compare6(zxw79000, zxw80000)
new_compare29(zxw79000, zxw80000, app(app(ty_Either, cch), cda)) → new_compare15(zxw79000, zxw80000, cch, cda)
new_compare29(zxw79000, zxw80000, ty_Ordering) → new_compare18(zxw79000, zxw80000)
new_compare29(zxw79000, zxw80000, ty_@0) → new_compare30(zxw79000, zxw80000)
new_primCompAux00(zxw276, LT) → LT
new_primCompAux00(zxw276, EQ) → zxw276
new_primCompAux00(zxw276, GT) → GT
new_compare30(@0, @0) → EQ
new_compare18(zxw79000, zxw80000) → new_compare24(zxw79000, zxw80000, new_esEs9(zxw79000, zxw80000))
new_esEs9(GT, LT) → False
new_esEs9(GT, EQ) → False
new_esEs9(EQ, EQ) → True
new_esEs9(EQ, LT) → False
new_esEs9(LT, EQ) → False
new_esEs9(LT, LT) → True
new_compare24(zxw79000, zxw80000, False) → new_compare11(zxw79000, zxw80000, new_ltEs7(zxw79000, zxw80000))
new_compare24(zxw79000, zxw80000, True) → EQ
new_compare11(zxw79000, zxw80000, False) → GT
new_compare11(zxw79000, zxw80000, True) → LT
new_compare15(zxw790, zxw800, gh, ha) → new_compare26(zxw790, zxw800, new_esEs7(zxw790, zxw800, gh, ha), gh, ha)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Bool, bef) → new_esEs14(zxw4000, zxw3000)
new_esEs7(Right(zxw4000), Left(zxw3000), bfh, bef) → False
new_esEs7(Left(zxw4000), Right(zxw3000), bfh, bef) → False
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, app(app(ty_@2, bgd), bge)) → new_esEs5(zxw4000, zxw3000, bgd, bge)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Int, bef) → new_esEs11(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), app(app(ty_@2, bfa), bfb), bef) → new_esEs5(zxw4000, zxw3000, bfa, bfb)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Ordering, bef) → new_esEs9(zxw4000, zxw3000)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, app(ty_[], bgb)) → new_esEs13(zxw4000, zxw3000, bgb)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Integer, bef) → new_esEs15(zxw4000, zxw3000)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, app(app(app(ty_@3, bgh), bha), bhb)) → new_esEs4(zxw4000, zxw3000, bgh, bha, bhb)
new_esEs7(Left(zxw4000), Left(zxw3000), app(ty_Ratio, bee), bef) → new_esEs18(zxw4000, zxw3000, bee)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_@0, bef) → new_esEs10(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), app(app(app(ty_@3, bfe), bff), bfg), bef) → new_esEs4(zxw4000, zxw3000, bfe, bff, bfg)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Double, bef) → new_esEs16(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Float, bef) → new_esEs17(zxw4000, zxw3000)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Char, bef) → new_esEs12(zxw4000, zxw3000)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), app(ty_[], beg), bef) → new_esEs13(zxw4000, zxw3000, beg)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, app(ty_Ratio, bga)) → new_esEs18(zxw4000, zxw3000, bga)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_compare26(Right(zxw7900), Left(zxw8000), False, gh, ha) → GT
new_compare26(Right(zxw7900), Right(zxw8000), False, gh, ha) → new_compare14(zxw7900, zxw8000, new_ltEs20(zxw7900, zxw8000, ha), gh, ha)
new_esEs6(Just(zxw4000), Just(zxw3000), app(ty_Maybe, fc)) → new_esEs6(zxw4000, zxw3000, fc)
new_esEs7(Left(zxw4000), Left(zxw3000), app(app(ty_Either, bfc), bfd), bef) → new_esEs7(zxw4000, zxw3000, bfc, bfd)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, app(ty_Maybe, bgc)) → new_esEs6(zxw4000, zxw3000, bgc)
new_esEs6(Just(zxw4000), Just(zxw3000), app(app(ty_Either, fg), fh)) → new_esEs7(zxw4000, zxw3000, fg, fh)
new_esEs7(Left(zxw4000), Left(zxw3000), app(ty_Maybe, beh), bef) → new_esEs6(zxw4000, zxw3000, beh)
new_esEs7(Right(zxw4000), Right(zxw3000), bfh, app(app(ty_Either, bgf), bgg)) → new_esEs7(zxw4000, zxw3000, bgf, bgg)
new_esEs6(Just(zxw4000), Just(zxw3000), app(app(ty_@2, fd), ff)) → new_esEs5(zxw4000, zxw3000, fd, ff)
new_esEs6(Nothing, Nothing, eh) → True
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs6(Nothing, Just(zxw3000), eh) → False
new_esEs6(Just(zxw4000), Nothing, eh) → False
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), app(app(app(ty_@3, ga), gb), gc)) → new_esEs4(zxw4000, zxw3000, ga, gb, gc)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_@0) → new_esEs10(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), app(ty_[], fb)) → new_esEs13(zxw4000, zxw3000, fb)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Char) → new_esEs12(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Float) → new_esEs17(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), app(ty_Ratio, fa)) → new_esEs18(zxw4000, zxw3000, fa)
new_esEs18(:%(zxw4000, zxw4001), :%(zxw3000, zxw3001), dee) → new_asAs(new_esEs25(zxw4000, zxw3000, dee), new_esEs24(zxw4001, zxw3001, dee))
new_esEs25(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs25(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs24(zxw4001, zxw3001, ty_Integer) → new_esEs15(zxw4001, zxw3001)
new_esEs24(zxw4001, zxw3001, ty_Int) → new_esEs11(zxw4001, zxw3001)
new_asAs(False, zxw230) → False
new_asAs(True, zxw230) → zxw230
new_esEs11(zxw400, zxw300) → new_primEqInt(zxw400, zxw300)
new_primEqInt(Neg(Succ(zxw40000)), Neg(Succ(zxw30000))) → new_primEqNat0(zxw40000, zxw30000)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Neg(Succ(zxw30000))) → False
new_primEqInt(Neg(Succ(zxw40000)), Neg(Zero)) → False
new_primEqInt(Pos(Succ(zxw40000)), Pos(Succ(zxw30000))) → new_primEqNat0(zxw40000, zxw30000)
new_primEqInt(Pos(Zero), Pos(Succ(zxw30000))) → False
new_primEqInt(Pos(Succ(zxw40000)), Pos(Zero)) → False
new_primEqInt(Neg(Succ(zxw40000)), Pos(zxw3000)) → False
new_primEqInt(Pos(Succ(zxw40000)), Neg(zxw3000)) → False
new_primEqInt(Neg(Zero), Pos(Succ(zxw30000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(zxw30000))) → False
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqNat0(Zero, Zero) → True
new_primEqNat0(Succ(zxw40000), Succ(zxw30000)) → new_primEqNat0(zxw40000, zxw30000)
new_primEqNat0(Zero, Succ(zxw30000)) → False
new_primEqNat0(Succ(zxw40000), Zero) → False
new_esEs15(Integer(zxw4000), Integer(zxw3000)) → new_primEqInt(zxw4000, zxw3000)
new_esEs17(Float(zxw4000, zxw4001), Float(zxw3000, zxw3001)) → new_esEs11(new_sr(zxw4000, zxw3000), new_sr(zxw4001, zxw3001))
new_esEs12(Char(zxw4000), Char(zxw3000)) → new_primEqNat0(zxw4000, zxw3000)
new_esEs13([], [], ddb) → True
new_esEs13(:(zxw4000, zxw4001), :(zxw3000, zxw3001), ddb) → new_asAs(new_esEs23(zxw4000, zxw3000, ddb), new_esEs13(zxw4001, zxw3001, ddb))
new_esEs13(:(zxw4000, zxw4001), [], ddb) → False
new_esEs13([], :(zxw3000, zxw3001), ddb) → False
new_esEs23(zxw4000, zxw3000, app(app(ty_Either, ddh), dea)) → new_esEs7(zxw4000, zxw3000, ddh, dea)
new_esEs23(zxw4000, zxw3000, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, app(app(app(ty_@3, deb), dec), ded)) → new_esEs4(zxw4000, zxw3000, deb, dec, ded)
new_esEs23(zxw4000, zxw3000, app(app(ty_@2, ddf), ddg)) → new_esEs5(zxw4000, zxw3000, ddf, ddg)
new_esEs23(zxw4000, zxw3000, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, app(ty_Ratio, ddc)) → new_esEs18(zxw4000, zxw3000, ddc)
new_esEs23(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, app(ty_Maybe, dde)) → new_esEs6(zxw4000, zxw3000, dde)
new_esEs23(zxw4000, zxw3000, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, app(ty_[], ddd)) → new_esEs13(zxw4000, zxw3000, ddd)
new_esEs16(Double(zxw4000, zxw4001), Double(zxw3000, zxw3001)) → new_esEs11(new_sr(zxw4000, zxw3000), new_sr(zxw4001, zxw3001))
new_esEs10(@0, @0) → True
new_esEs5(@2(zxw4000, zxw4001), @2(zxw3000, zxw3001), dad, dae) → new_asAs(new_esEs22(zxw4000, zxw3000, dad), new_esEs21(zxw4001, zxw3001, dae))
new_esEs22(zxw4000, zxw3000, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, app(app(ty_@2, dcc), dcd)) → new_esEs5(zxw4000, zxw3000, dcc, dcd)
new_esEs22(zxw4000, zxw3000, app(ty_Maybe, dcb)) → new_esEs6(zxw4000, zxw3000, dcb)
new_esEs22(zxw4000, zxw3000, app(ty_Ratio, dbh)) → new_esEs18(zxw4000, zxw3000, dbh)
new_esEs22(zxw4000, zxw3000, app(app(ty_Either, dce), dcf)) → new_esEs7(zxw4000, zxw3000, dce, dcf)
new_esEs22(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, app(app(app(ty_@3, dcg), dch), dda)) → new_esEs4(zxw4000, zxw3000, dcg, dch, dda)
new_esEs22(zxw4000, zxw3000, app(ty_[], dca)) → new_esEs13(zxw4000, zxw3000, dca)
new_esEs22(zxw4000, zxw3000, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs21(zxw4001, zxw3001, ty_Bool) → new_esEs14(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, ty_Double) → new_esEs16(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, ty_Ordering) → new_esEs9(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, ty_Char) → new_esEs12(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, ty_Float) → new_esEs17(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, app(ty_Maybe, dah)) → new_esEs6(zxw4001, zxw3001, dah)
new_esEs21(zxw4001, zxw3001, ty_Int) → new_esEs11(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, app(ty_[], dag)) → new_esEs13(zxw4001, zxw3001, dag)
new_esEs21(zxw4001, zxw3001, ty_Integer) → new_esEs15(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, app(app(ty_@2, dba), dbb)) → new_esEs5(zxw4001, zxw3001, dba, dbb)
new_esEs21(zxw4001, zxw3001, ty_@0) → new_esEs10(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, app(app(ty_Either, dbc), dbd)) → new_esEs7(zxw4001, zxw3001, dbc, dbd)
new_esEs21(zxw4001, zxw3001, app(app(app(ty_@3, dbe), dbf), dbg)) → new_esEs4(zxw4001, zxw3001, dbe, dbf, dbg)
new_esEs21(zxw4001, zxw3001, app(ty_Ratio, daf)) → new_esEs18(zxw4001, zxw3001, daf)
new_esEs4(@3(zxw4000, zxw4001, zxw4002), @3(zxw3000, zxw3001, zxw3002), deh, dfa, dfb) → new_asAs(new_esEs28(zxw4000, zxw3000, deh), new_asAs(new_esEs27(zxw4001, zxw3001, dfa), new_esEs26(zxw4002, zxw3002, dfb)))
new_esEs28(zxw4000, zxw3000, app(ty_[], dhh)) → new_esEs13(zxw4000, zxw3000, dhh)
new_esEs28(zxw4000, zxw3000, app(app(app(ty_@3, eaf), eag), eah)) → new_esEs4(zxw4000, zxw3000, eaf, eag, eah)
new_esEs28(zxw4000, zxw3000, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, app(ty_Maybe, eaa)) → new_esEs6(zxw4000, zxw3000, eaa)
new_esEs28(zxw4000, zxw3000, app(app(ty_Either, ead), eae)) → new_esEs7(zxw4000, zxw3000, ead, eae)
new_esEs28(zxw4000, zxw3000, app(app(ty_@2, eab), eac)) → new_esEs5(zxw4000, zxw3000, eab, eac)
new_esEs28(zxw4000, zxw3000, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, app(ty_Ratio, dhg)) → new_esEs18(zxw4000, zxw3000, dhg)
new_esEs28(zxw4000, zxw3000, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_esEs27(zxw4001, zxw3001, app(ty_Ratio, dge)) → new_esEs18(zxw4001, zxw3001, dge)
new_esEs27(zxw4001, zxw3001, app(app(app(ty_@3, dhd), dhe), dhf)) → new_esEs4(zxw4001, zxw3001, dhd, dhe, dhf)
new_esEs27(zxw4001, zxw3001, app(ty_Maybe, dgg)) → new_esEs6(zxw4001, zxw3001, dgg)
new_esEs27(zxw4001, zxw3001, app(app(ty_Either, dhb), dhc)) → new_esEs7(zxw4001, zxw3001, dhb, dhc)
new_esEs27(zxw4001, zxw3001, ty_Ordering) → new_esEs9(zxw4001, zxw3001)
new_esEs27(zxw4001, zxw3001, ty_Float) → new_esEs17(zxw4001, zxw3001)
new_esEs27(zxw4001, zxw3001, ty_@0) → new_esEs10(zxw4001, zxw3001)
new_esEs27(zxw4001, zxw3001, ty_Char) → new_esEs12(zxw4001, zxw3001)
new_esEs27(zxw4001, zxw3001, ty_Double) → new_esEs16(zxw4001, zxw3001)
new_esEs27(zxw4001, zxw3001, ty_Int) → new_esEs11(zxw4001, zxw3001)
new_esEs27(zxw4001, zxw3001, app(app(ty_@2, dgh), dha)) → new_esEs5(zxw4001, zxw3001, dgh, dha)
new_esEs27(zxw4001, zxw3001, ty_Bool) → new_esEs14(zxw4001, zxw3001)
new_esEs27(zxw4001, zxw3001, app(ty_[], dgf)) → new_esEs13(zxw4001, zxw3001, dgf)
new_esEs27(zxw4001, zxw3001, ty_Integer) → new_esEs15(zxw4001, zxw3001)
new_esEs26(zxw4002, zxw3002, ty_Float) → new_esEs17(zxw4002, zxw3002)
new_esEs26(zxw4002, zxw3002, ty_Char) → new_esEs12(zxw4002, zxw3002)
new_esEs26(zxw4002, zxw3002, ty_Int) → new_esEs11(zxw4002, zxw3002)
new_esEs26(zxw4002, zxw3002, app(ty_Maybe, dfe)) → new_esEs6(zxw4002, zxw3002, dfe)
new_esEs26(zxw4002, zxw3002, app(app(app(ty_@3, dgb), dgc), dgd)) → new_esEs4(zxw4002, zxw3002, dgb, dgc, dgd)
new_esEs26(zxw4002, zxw3002, app(ty_[], dfd)) → new_esEs13(zxw4002, zxw3002, dfd)
new_esEs26(zxw4002, zxw3002, app(app(ty_Either, dfh), dga)) → new_esEs7(zxw4002, zxw3002, dfh, dga)
new_esEs26(zxw4002, zxw3002, ty_Integer) → new_esEs15(zxw4002, zxw3002)
new_esEs26(zxw4002, zxw3002, app(app(ty_@2, dff), dfg)) → new_esEs5(zxw4002, zxw3002, dff, dfg)
new_esEs26(zxw4002, zxw3002, app(ty_Ratio, dfc)) → new_esEs18(zxw4002, zxw3002, dfc)
new_esEs26(zxw4002, zxw3002, ty_Bool) → new_esEs14(zxw4002, zxw3002)
new_esEs26(zxw4002, zxw3002, ty_@0) → new_esEs10(zxw4002, zxw3002)
new_esEs26(zxw4002, zxw3002, ty_Ordering) → new_esEs9(zxw4002, zxw3002)
new_esEs26(zxw4002, zxw3002, ty_Double) → new_esEs16(zxw4002, zxw3002)
new_esEs14(False, True) → False
new_esEs14(True, False) → False
new_esEs14(True, True) → True
new_esEs14(False, False) → True
new_ltEs20(zxw7900, zxw8000, app(ty_Maybe, bbc)) → new_ltEs18(zxw7900, zxw8000, bbc)
new_ltEs20(zxw7900, zxw8000, ty_Int) → new_ltEs9(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, ty_@0) → new_ltEs8(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, app(app(ty_@2, baf), bag)) → new_ltEs4(zxw7900, zxw8000, baf, bag)
new_ltEs20(zxw7900, zxw8000, ty_Float) → new_ltEs16(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, ty_Bool) → new_ltEs12(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, app(ty_Ratio, bbb)) → new_ltEs17(zxw7900, zxw8000, bbb)
new_ltEs20(zxw7900, zxw8000, ty_Double) → new_ltEs15(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, ty_Integer) → new_ltEs13(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, app(app(app(ty_@3, bab), bac), bad)) → new_ltEs6(zxw7900, zxw8000, bab, bac, bad)
new_ltEs20(zxw7900, zxw8000, app(app(ty_Either, bah), bba)) → new_ltEs14(zxw7900, zxw8000, bah, bba)
new_ltEs20(zxw7900, zxw8000, app(ty_[], bae)) → new_ltEs11(zxw7900, zxw8000, bae)
new_ltEs20(zxw7900, zxw8000, ty_Char) → new_ltEs10(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, ty_Ordering) → new_ltEs7(zxw7900, zxw8000)
new_compare14(zxw242, zxw243, False, def, deg) → GT
new_compare14(zxw242, zxw243, True, def, deg) → LT
new_ltEs6(@3(zxw79000, zxw79001, zxw79002), @3(zxw80000, zxw80001, zxw80002), hb, hc, hd) → new_pePe(new_lt19(zxw79000, zxw80000, hb), new_asAs(new_esEs20(zxw79000, zxw80000, hb), new_pePe(new_lt20(zxw79001, zxw80001, hc), new_asAs(new_esEs19(zxw79001, zxw80001, hc), new_ltEs21(zxw79002, zxw80002, hd)))))
new_lt19(zxw79000, zxw80000, app(app(ty_Either, bhd), bhe)) → new_lt14(zxw79000, zxw80000, bhd, bhe)
new_lt19(zxw79000, zxw80000, ty_Double) → new_lt15(zxw79000, zxw80000)
new_lt19(zxw79000, zxw80000, ty_Ordering) → new_lt6(zxw79000, zxw80000)
new_lt19(zxw79000, zxw80000, app(ty_Ratio, gg)) → new_lt17(zxw79000, zxw80000, gg)
new_lt19(zxw79000, zxw80000, app(app(ty_@2, bcf), bcg)) → new_lt11(zxw79000, zxw80000, bcf, bcg)
new_lt19(zxw79000, zxw80000, ty_Int) → new_lt8(zxw79000, zxw80000)
new_lt19(zxw79000, zxw80000, ty_@0) → new_lt7(zxw79000, zxw80000)
new_lt19(zxw79000, zxw80000, app(app(app(ty_@3, gd), ge), gf)) → new_lt5(zxw79000, zxw80000, gd, ge, gf)
new_lt19(zxw79000, zxw80000, app(ty_Maybe, bdb)) → new_lt18(zxw79000, zxw80000, bdb)
new_lt19(zxw79000, zxw80000, ty_Float) → new_lt16(zxw79000, zxw80000)
new_lt19(zxw79000, zxw80000, ty_Bool) → new_lt12(zxw79000, zxw80000)
new_lt19(zxw79000, zxw80000, app(ty_[], bhc)) → new_lt10(zxw79000, zxw80000, bhc)
new_lt19(zxw79000, zxw80000, ty_Integer) → new_lt13(zxw79000, zxw80000)
new_lt19(zxw79000, zxw80000, ty_Char) → new_lt9(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, app(ty_[], bhc)) → new_esEs13(zxw79000, zxw80000, bhc)
new_esEs20(zxw79000, zxw80000, ty_Double) → new_esEs16(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, ty_Char) → new_esEs12(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, app(app(ty_@2, bcf), bcg)) → new_esEs5(zxw79000, zxw80000, bcf, bcg)
new_esEs20(zxw79000, zxw80000, ty_Int) → new_esEs11(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, ty_@0) → new_esEs10(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, app(app(app(ty_@3, gd), ge), gf)) → new_esEs4(zxw79000, zxw80000, gd, ge, gf)
new_esEs20(zxw79000, zxw80000, ty_Integer) → new_esEs15(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, ty_Bool) → new_esEs14(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, app(ty_Ratio, gg)) → new_esEs18(zxw79000, zxw80000, gg)
new_esEs20(zxw79000, zxw80000, app(app(ty_Either, bhd), bhe)) → new_esEs7(zxw79000, zxw80000, bhd, bhe)
new_esEs20(zxw79000, zxw80000, app(ty_Maybe, bdb)) → new_esEs6(zxw79000, zxw80000, bdb)
new_esEs20(zxw79000, zxw80000, ty_Ordering) → new_esEs9(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, ty_Float) → new_esEs17(zxw79000, zxw80000)
new_lt20(zxw79001, zxw80001, app(app(ty_Either, cad), cae)) → new_lt14(zxw79001, zxw80001, cad, cae)
new_lt20(zxw79001, zxw80001, ty_@0) → new_lt7(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, app(app(ty_@2, cab), cac)) → new_lt11(zxw79001, zxw80001, cab, cac)
new_lt20(zxw79001, zxw80001, ty_Ordering) → new_lt6(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, app(ty_Maybe, cag)) → new_lt18(zxw79001, zxw80001, cag)
new_lt20(zxw79001, zxw80001, ty_Int) → new_lt8(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, ty_Integer) → new_lt13(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, app(ty_Ratio, caf)) → new_lt17(zxw79001, zxw80001, caf)
new_lt20(zxw79001, zxw80001, ty_Char) → new_lt9(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, app(ty_[], caa)) → new_lt10(zxw79001, zxw80001, caa)
new_lt20(zxw79001, zxw80001, ty_Double) → new_lt15(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, ty_Float) → new_lt16(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, ty_Bool) → new_lt12(zxw79001, zxw80001)
new_lt20(zxw79001, zxw80001, app(app(app(ty_@3, bhf), bhg), bhh)) → new_lt5(zxw79001, zxw80001, bhf, bhg, bhh)
new_esEs19(zxw79001, zxw80001, app(ty_Ratio, caf)) → new_esEs18(zxw79001, zxw80001, caf)
new_esEs19(zxw79001, zxw80001, ty_Ordering) → new_esEs9(zxw79001, zxw80001)
new_esEs19(zxw79001, zxw80001, app(ty_Maybe, cag)) → new_esEs6(zxw79001, zxw80001, cag)
new_esEs19(zxw79001, zxw80001, app(app(ty_Either, cad), cae)) → new_esEs7(zxw79001, zxw80001, cad, cae)
new_esEs19(zxw79001, zxw80001, ty_Float) → new_esEs17(zxw79001, zxw80001)
new_esEs19(zxw79001, zxw80001, ty_Bool) → new_esEs14(zxw79001, zxw80001)
new_esEs19(zxw79001, zxw80001, ty_Int) → new_esEs11(zxw79001, zxw80001)
new_esEs19(zxw79001, zxw80001, app(app(app(ty_@3, bhf), bhg), bhh)) → new_esEs4(zxw79001, zxw80001, bhf, bhg, bhh)
new_esEs19(zxw79001, zxw80001, app(app(ty_@2, cab), cac)) → new_esEs5(zxw79001, zxw80001, cab, cac)
new_esEs19(zxw79001, zxw80001, ty_Double) → new_esEs16(zxw79001, zxw80001)
new_esEs19(zxw79001, zxw80001, ty_Integer) → new_esEs15(zxw79001, zxw80001)
new_esEs19(zxw79001, zxw80001, ty_@0) → new_esEs10(zxw79001, zxw80001)
new_esEs19(zxw79001, zxw80001, app(ty_[], caa)) → new_esEs13(zxw79001, zxw80001, caa)
new_esEs19(zxw79001, zxw80001, ty_Char) → new_esEs12(zxw79001, zxw80001)
new_ltEs21(zxw79002, zxw80002, ty_Char) → new_ltEs10(zxw79002, zxw80002)
new_ltEs21(zxw79002, zxw80002, app(app(ty_@2, cbd), cbe)) → new_ltEs4(zxw79002, zxw80002, cbd, cbe)
new_ltEs21(zxw79002, zxw80002, ty_Int) → new_ltEs9(zxw79002, zxw80002)
new_ltEs21(zxw79002, zxw80002, ty_Ordering) → new_ltEs7(zxw79002, zxw80002)
new_ltEs21(zxw79002, zxw80002, ty_Float) → new_ltEs16(zxw79002, zxw80002)
new_ltEs21(zxw79002, zxw80002, ty_Bool) → new_ltEs12(zxw79002, zxw80002)
new_ltEs21(zxw79002, zxw80002, ty_Integer) → new_ltEs13(zxw79002, zxw80002)
new_ltEs21(zxw79002, zxw80002, app(app(ty_Either, cbf), cbg)) → new_ltEs14(zxw79002, zxw80002, cbf, cbg)
new_ltEs21(zxw79002, zxw80002, app(ty_[], cbc)) → new_ltEs11(zxw79002, zxw80002, cbc)
new_ltEs21(zxw79002, zxw80002, app(ty_Ratio, cbh)) → new_ltEs17(zxw79002, zxw80002, cbh)
new_ltEs21(zxw79002, zxw80002, app(app(app(ty_@3, cah), cba), cbb)) → new_ltEs6(zxw79002, zxw80002, cah, cba, cbb)
new_ltEs21(zxw79002, zxw80002, ty_@0) → new_ltEs8(zxw79002, zxw80002)
new_ltEs21(zxw79002, zxw80002, app(ty_Maybe, cca)) → new_ltEs18(zxw79002, zxw80002, cca)
new_ltEs21(zxw79002, zxw80002, ty_Double) → new_ltEs15(zxw79002, zxw80002)
new_pePe(False, zxw271) → zxw271
new_pePe(True, zxw271) → True
new_ltEs15(zxw7900, zxw8000) → new_fsEs(new_compare6(zxw7900, zxw8000))
new_compare6(Double(zxw79000, zxw79001), Double(zxw80000, zxw80001)) → new_compare16(new_sr(zxw79000, zxw80000), new_sr(zxw79001, zxw80001))
new_ltEs8(zxw7900, zxw8000) → new_fsEs(new_compare30(zxw7900, zxw8000))
new_ltEs12(True, False) → False
new_ltEs12(False, False) → True
new_ltEs12(True, True) → True
new_ltEs12(False, True) → True
new_ltEs16(zxw7900, zxw8000) → new_fsEs(new_compare7(zxw7900, zxw8000))
new_compare7(Float(zxw79000, zxw79001), Float(zxw80000, zxw80001)) → new_compare16(new_sr(zxw79000, zxw80000), new_sr(zxw79001, zxw80001))
new_ltEs4(@2(zxw79000, zxw79001), @2(zxw80000, zxw80001), ca, cb) → new_pePe(new_lt4(zxw79000, zxw80000, ca), new_asAs(new_esEs8(zxw79000, zxw80000, ca), new_ltEs5(zxw79001, zxw80001, cb)))
new_lt4(zxw79000, zxw80000, app(app(app(ty_@3, cc), cd), ce)) → new_lt5(zxw79000, zxw80000, cc, cd, ce)
new_lt4(zxw79000, zxw80000, app(ty_[], cf)) → new_lt10(zxw79000, zxw80000, cf)
new_lt4(zxw79000, zxw80000, ty_Bool) → new_lt12(zxw79000, zxw80000)
new_lt4(zxw79000, zxw80000, app(ty_Maybe, de)) → new_lt18(zxw79000, zxw80000, de)
new_lt4(zxw79000, zxw80000, ty_Ordering) → new_lt6(zxw79000, zxw80000)
new_lt4(zxw79000, zxw80000, app(ty_Ratio, dd)) → new_lt17(zxw79000, zxw80000, dd)
new_lt4(zxw79000, zxw80000, ty_Int) → new_lt8(zxw79000, zxw80000)
new_lt4(zxw79000, zxw80000, ty_Double) → new_lt15(zxw79000, zxw80000)
new_lt4(zxw79000, zxw80000, app(app(ty_Either, db), dc)) → new_lt14(zxw79000, zxw80000, db, dc)
new_lt4(zxw79000, zxw80000, ty_Char) → new_lt9(zxw79000, zxw80000)
new_lt4(zxw79000, zxw80000, ty_@0) → new_lt7(zxw79000, zxw80000)
new_lt4(zxw79000, zxw80000, ty_Float) → new_lt16(zxw79000, zxw80000)
new_lt4(zxw79000, zxw80000, app(app(ty_@2, cg), da)) → new_lt11(zxw79000, zxw80000, cg, da)
new_lt4(zxw79000, zxw80000, ty_Integer) → new_lt13(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, ty_Int) → new_esEs11(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, ty_Double) → new_esEs16(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, app(app(app(ty_@3, cc), cd), ce)) → new_esEs4(zxw79000, zxw80000, cc, cd, ce)
new_esEs8(zxw79000, zxw80000, app(ty_[], cf)) → new_esEs13(zxw79000, zxw80000, cf)
new_esEs8(zxw79000, zxw80000, ty_Char) → new_esEs12(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, app(app(ty_@2, cg), da)) → new_esEs5(zxw79000, zxw80000, cg, da)
new_esEs8(zxw79000, zxw80000, ty_Float) → new_esEs17(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, app(app(ty_Either, db), dc)) → new_esEs7(zxw79000, zxw80000, db, dc)
new_esEs8(zxw79000, zxw80000, ty_@0) → new_esEs10(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, app(ty_Maybe, de)) → new_esEs6(zxw79000, zxw80000, de)
new_esEs8(zxw79000, zxw80000, ty_Bool) → new_esEs14(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, ty_Ordering) → new_esEs9(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, ty_Integer) → new_esEs15(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, app(ty_Ratio, dd)) → new_esEs18(zxw79000, zxw80000, dd)
new_ltEs5(zxw79001, zxw80001, ty_Char) → new_ltEs10(zxw79001, zxw80001)
new_ltEs5(zxw79001, zxw80001, app(app(ty_@2, eb), ec)) → new_ltEs4(zxw79001, zxw80001, eb, ec)
new_ltEs5(zxw79001, zxw80001, ty_Ordering) → new_ltEs7(zxw79001, zxw80001)
new_ltEs5(zxw79001, zxw80001, ty_Bool) → new_ltEs12(zxw79001, zxw80001)
new_ltEs5(zxw79001, zxw80001, ty_Integer) → new_ltEs13(zxw79001, zxw80001)
new_ltEs5(zxw79001, zxw80001, app(ty_Ratio, ef)) → new_ltEs17(zxw79001, zxw80001, ef)
new_ltEs5(zxw79001, zxw80001, app(ty_Maybe, eg)) → new_ltEs18(zxw79001, zxw80001, eg)
new_ltEs5(zxw79001, zxw80001, ty_Double) → new_ltEs15(zxw79001, zxw80001)
new_ltEs5(zxw79001, zxw80001, app(app(ty_Either, ed), ee)) → new_ltEs14(zxw79001, zxw80001, ed, ee)
new_ltEs5(zxw79001, zxw80001, app(app(app(ty_@3, df), dg), dh)) → new_ltEs6(zxw79001, zxw80001, df, dg, dh)
new_ltEs5(zxw79001, zxw80001, app(ty_[], ea)) → new_ltEs11(zxw79001, zxw80001, ea)
new_ltEs5(zxw79001, zxw80001, ty_Int) → new_ltEs9(zxw79001, zxw80001)
new_ltEs5(zxw79001, zxw80001, ty_@0) → new_ltEs8(zxw79001, zxw80001)
new_ltEs5(zxw79001, zxw80001, ty_Float) → new_ltEs16(zxw79001, zxw80001)
new_lt13(zxw79000, zxw80000) → new_esEs9(new_compare32(zxw79000, zxw80000), LT)
new_lt11(zxw79000, zxw80000, bcf, bcg) → new_esEs9(new_compare19(zxw79000, zxw80000, bcf, bcg), LT)
new_compare19(zxw79000, zxw80000, bcf, bcg) → new_compare210(zxw79000, zxw80000, new_esEs5(zxw79000, zxw80000, bcf, bcg), bcf, bcg)
new_compare210(zxw79000, zxw80000, False, bcf, bcg) → new_compare110(zxw79000, zxw80000, new_ltEs4(zxw79000, zxw80000, bcf, bcg), bcf, bcg)
new_compare210(zxw79000, zxw80000, True, bcf, bcg) → EQ
new_compare110(zxw79000, zxw80000, True, bcf, bcg) → LT
new_compare110(zxw79000, zxw80000, False, bcf, bcg) → GT
new_lt16(zxw79000, zxw80000) → new_esEs9(new_compare7(zxw79000, zxw80000), LT)
new_lt7(zxw79000, zxw80000) → new_esEs9(new_compare30(zxw79000, zxw80000), LT)
new_lt9(zxw79000, zxw80000) → new_esEs9(new_compare17(zxw79000, zxw80000), LT)
new_lt14(zxw790, zxw800, gh, ha) → new_esEs9(new_compare15(zxw790, zxw800, gh, ha), LT)
new_lt15(zxw79000, zxw80000) → new_esEs9(new_compare6(zxw79000, zxw80000), LT)
new_lt8(zxw790, zxw800) → new_esEs9(new_compare16(zxw790, zxw800), LT)
new_lt17(zxw79000, zxw80000, gg) → new_esEs9(new_compare8(zxw79000, zxw80000, gg), LT)
new_lt6(zxw79000, zxw80000) → new_esEs9(new_compare18(zxw79000, zxw80000), LT)
new_lt18(zxw79000, zxw80000, bdb) → new_esEs9(new_compare27(zxw79000, zxw80000, bdb), LT)
new_compare27(zxw79000, zxw80000, bdb) → new_compare28(zxw79000, zxw80000, new_esEs6(zxw79000, zxw80000, bdb), bdb)
new_compare28(zxw79000, zxw80000, False, bdb) → new_compare111(zxw79000, zxw80000, new_ltEs18(zxw79000, zxw80000, bdb), bdb)
new_compare28(zxw79000, zxw80000, True, bdb) → EQ
new_compare111(zxw79000, zxw80000, True, bdb) → LT
new_compare111(zxw79000, zxw80000, False, bdb) → GT
new_lt12(zxw79000, zxw80000) → new_esEs9(new_compare31(zxw79000, zxw80000), LT)
new_compare31(zxw79000, zxw80000) → new_compare23(zxw79000, zxw80000, new_esEs14(zxw79000, zxw80000))
new_compare23(zxw79000, zxw80000, True) → EQ
new_compare23(zxw79000, zxw80000, False) → new_compare10(zxw79000, zxw80000, new_ltEs12(zxw79000, zxw80000))
new_compare10(zxw79000, zxw80000, True) → LT
new_compare10(zxw79000, zxw80000, False) → GT
new_lt10(zxw79000, zxw80000, bhc) → new_esEs9(new_compare1(zxw79000, zxw80000, bhc), LT)
new_lt5(zxw79000, zxw80000, gd, ge, gf) → new_esEs9(new_compare9(zxw79000, zxw80000, gd, ge, gf), LT)
new_compare9(zxw79000, zxw80000, gd, ge, gf) → new_compare25(zxw79000, zxw80000, new_esEs4(zxw79000, zxw80000, gd, ge, gf), gd, ge, gf)
new_compare25(zxw79000, zxw80000, True, gd, ge, gf) → EQ
new_compare25(zxw79000, zxw80000, False, gd, ge, gf) → new_compare12(zxw79000, zxw80000, new_ltEs6(zxw79000, zxw80000, gd, ge, gf), gd, ge, gf)
new_compare12(zxw79000, zxw80000, True, gd, ge, gf) → LT
new_compare12(zxw79000, zxw80000, False, gd, ge, gf) → GT
new_compare34(zxw400, zxw300, h, ba) → new_compare26(Left(zxw400), Right(zxw300), False, h, ba)
new_compare33(zxw20, zxw15, bc, bd) → new_compare26(Left(zxw20), Left(zxw15), new_esEs32(zxw20, zxw15, bc), bc, bd)
new_esEs32(zxw20, zxw15, ty_Float) → new_esEs17(zxw20, zxw15)
new_esEs32(zxw20, zxw15, ty_Integer) → new_esEs15(zxw20, zxw15)
new_esEs32(zxw20, zxw15, ty_@0) → new_esEs10(zxw20, zxw15)
new_esEs32(zxw20, zxw15, ty_Ordering) → new_esEs9(zxw20, zxw15)
new_esEs32(zxw20, zxw15, ty_Bool) → new_esEs14(zxw20, zxw15)
new_esEs32(zxw20, zxw15, app(app(ty_Either, cea), ceb)) → new_esEs7(zxw20, zxw15, cea, ceb)
new_esEs32(zxw20, zxw15, app(ty_[], cde)) → new_esEs13(zxw20, zxw15, cde)
new_esEs32(zxw20, zxw15, app(ty_Maybe, cdf)) → new_esEs6(zxw20, zxw15, cdf)
new_esEs32(zxw20, zxw15, app(app(ty_@2, cdg), cdh)) → new_esEs5(zxw20, zxw15, cdg, cdh)
new_esEs32(zxw20, zxw15, ty_Char) → new_esEs12(zxw20, zxw15)
new_esEs32(zxw20, zxw15, app(app(app(ty_@3, cec), ced), cee)) → new_esEs4(zxw20, zxw15, cec, ced, cee)
new_esEs32(zxw20, zxw15, ty_Int) → new_esEs11(zxw20, zxw15)
new_esEs32(zxw20, zxw15, app(ty_Ratio, cdd)) → new_esEs18(zxw20, zxw15, cdd)
new_esEs32(zxw20, zxw15, ty_Double) → new_esEs16(zxw20, zxw15)

The set Q consists of the following terms:

new_compare23(x0, x1, True)
new_lt6(x0, x1)
new_ltEs5(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, ty_Integer)
new_esEs33(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt4(x0, x1, app(ty_[], x2))
new_ltEs18(Just(x0), Just(x1), ty_@0)
new_compare16(x0, x1)
new_lt4(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(Just(x0), Nothing, x1)
new_ltEs20(x0, x1, ty_Double)
new_esEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs19(x0, x1, ty_Bool)
new_esEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs8(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(x0, x1, app(app(ty_Either, x2), x3))
new_compare30(@0, @0)
new_esEs32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCompAux00(x0, GT)
new_lt19(x0, x1, ty_Char)
new_esEs27(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_Ordering)
new_compare17(Char(x0), Char(x1))
new_esEs28(x0, x1, ty_Int)
new_ltEs20(x0, x1, app(ty_[], x2))
new_ltEs21(x0, x1, ty_Ordering)
new_compare111(x0, x1, True, x2)
new_ltEs15(x0, x1)
new_primPlusNat1(Zero, Succ(x0))
new_esEs6(Just(x0), Just(x1), ty_Double)
new_compare24(x0, x1, False)
new_compare210(x0, x1, False, x2, x3)
new_lt20(x0, x1, ty_Char)
new_esEs33(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, ty_Bool)
new_sr0(Integer(x0), Integer(x1))
new_esEs32(x0, x1, app(ty_[], x2))
new_esEs33(x0, x1, ty_Float)
new_compare28(x0, x1, True, x2)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(Nothing, Nothing, x0)
new_ltEs18(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs7(EQ, EQ)
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs19(x0, x1, ty_Integer)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_ltEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Bool)
new_ltEs14(Right(x0), Right(x1), x2, ty_Float)
new_compare27(x0, x1, x2)
new_esEs6(Just(x0), Just(x1), app(ty_[], x2))
new_compare14(x0, x1, True, x2, x3)
new_ltEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs13([], :(x0, x1), x2)
new_compare25(x0, x1, False, x2, x3, x4)
new_esEs7(Left(x0), Left(x1), ty_Integer, x2)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs7(Right(x0), Right(x1), x2, ty_@0)
new_ltEs19(x0, x1, ty_Integer)
new_ltEs5(x0, x1, ty_Integer)
new_ltEs21(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs7(EQ, LT)
new_ltEs7(LT, EQ)
new_esEs20(x0, x1, ty_Ordering)
new_esEs17(Float(x0, x1), Float(x2, x3))
new_compare25(x0, x1, True, x2, x3, x4)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_lt19(x0, x1, ty_Ordering)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs16(x0, x1)
new_lt4(x0, x1, app(ty_Maybe, x2))
new_esEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs14(Left(x0), Left(x1), ty_Char, x2)
new_sr(x0, x1)
new_ltEs19(x0, x1, ty_Double)
new_compare7(Float(x0, x1), Float(x2, x3))
new_ltEs9(x0, x1)
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_compare19(x0, x1, x2, x3)
new_lt7(x0, x1)
new_lt4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, ty_Int)
new_esEs26(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat0(Zero, x0)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs32(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_ltEs7(LT, LT)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs27(x0, x1, ty_Bool)
new_lt5(x0, x1, x2, x3, x4)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare29(x0, x1, app(app(ty_@2, x2), x3))
new_lt4(x0, x1, ty_Ordering)
new_primEqNat0(Zero, Succ(x0))
new_lt19(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Int)
new_esEs15(Integer(x0), Integer(x1))
new_esEs26(x0, x1, ty_Double)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs28(x0, x1, ty_@0)
new_primPlusNat1(Succ(x0), Zero)
new_esEs22(x0, x1, ty_Integer)
new_ltEs14(Left(x0), Left(x1), ty_@0, x2)
new_primMulInt(Neg(x0), Neg(x1))
new_ltEs19(x0, x1, ty_Int)
new_esEs7(Left(x0), Left(x1), ty_Double, x2)
new_compare29(x0, x1, ty_Integer)
new_esEs14(True, True)
new_esEs21(x0, x1, ty_Char)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(Just(x0), Just(x1), ty_Integer)
new_compare29(x0, x1, app(ty_[], x2))
new_ltEs18(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, ty_Int)
new_esEs7(Right(x0), Right(x1), x2, ty_Int)
new_primEqNat0(Zero, Zero)
new_esEs16(Double(x0, x1), Double(x2, x3))
new_esEs12(Char(x0), Char(x1))
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_lt4(x0, x1, ty_Char)
new_esEs20(x0, x1, ty_Bool)
new_esEs8(x0, x1, ty_Float)
new_compare1([], :(x0, x1), x2)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_Integer)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs32(x0, x1, ty_@0)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(Left(x0), Left(x1), ty_Int, x2)
new_primCompAux00(x0, LT)
new_esEs27(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(ty_[], x2))
new_ltEs5(x0, x1, ty_Double)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs18(Just(x0), Just(x1), ty_Char)
new_primMulNat0(Zero, Zero)
new_lt9(x0, x1)
new_compare29(x0, x1, ty_Double)
new_ltEs5(x0, x1, ty_@0)
new_lt17(x0, x1, x2)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_ltEs21(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_ltEs14(Left(x0), Left(x1), ty_Float, x2)
new_esEs32(x0, x1, ty_Float)
new_esEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs8(x0, x1, ty_Ordering)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_compare10(x0, x1, True)
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Ordering)
new_primEqNat0(Succ(x0), Succ(x1))
new_ltEs19(x0, x1, ty_Bool)
new_esEs28(x0, x1, ty_Double)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, ty_Float)
new_ltEs19(x0, x1, ty_@0)
new_pePe(True, x0)
new_esEs19(x0, x1, ty_Float)
new_lt19(x0, x1, app(ty_[], x2))
new_esEs8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_lt16(x0, x1)
new_compare29(x0, x1, ty_Bool)
new_lt10(x0, x1, x2)
new_esEs7(Right(x0), Right(x1), x2, ty_Integer)
new_esEs32(x0, x1, app(app(ty_Either, x2), x3))
new_compare11(x0, x1, True)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs32(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs33(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1, ty_@0)
new_esEs6(Just(x0), Just(x1), ty_Ordering)
new_esEs23(x0, x1, ty_@0)
new_ltEs14(Right(x0), Right(x1), x2, ty_Int)
new_ltEs5(x0, x1, ty_Char)
new_ltEs21(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Float)
new_lt18(x0, x1, x2)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_compare29(x0, x1, ty_Ordering)
new_ltEs21(x0, x1, ty_@0)
new_esEs8(x0, x1, ty_Int)
new_lt14(x0, x1, x2, x3)
new_ltEs12(False, False)
new_compare210(x0, x1, True, x2, x3)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Just(x0), Just(x1), ty_Bool)
new_compare32(Integer(x0), Integer(x1))
new_lt19(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_Int)
new_primMulNat0(Succ(x0), Succ(x1))
new_compare29(x0, x1, ty_Float)
new_ltEs21(x0, x1, ty_Integer)
new_esEs6(Just(x0), Just(x1), ty_Float)
new_ltEs5(x0, x1, ty_Float)
new_ltEs18(Just(x0), Just(x1), ty_Float)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_Bool)
new_primCmpNat1(Zero, x0)
new_ltEs14(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs8(x0, x1)
new_ltEs18(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs14(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs33(x0, x1, app(ty_Ratio, x2))
new_compare13(x0, x1, False, x2, x3)
new_primPlusNat1(Zero, Zero)
new_esEs23(x0, x1, ty_Double)
new_ltEs18(Just(x0), Just(x1), ty_Ordering)
new_primCmpNat2(Zero, Zero)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(x0, x1, ty_Bool)
new_ltEs18(Just(x0), Just(x1), app(ty_[], x2))
new_esEs33(x0, x1, app(ty_Maybe, x2))
new_ltEs5(x0, x1, app(ty_[], x2))
new_asAs(False, x0)
new_ltEs20(x0, x1, ty_Char)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs8(x0, x1, ty_Integer)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs33(x0, x1, ty_Ordering)
new_ltEs18(Just(x0), Just(x1), ty_Bool)
new_compare14(x0, x1, False, x2, x3)
new_primCmpNat1(Succ(x0), x1)
new_esEs33(x0, x1, ty_Double)
new_esEs24(x0, x1, ty_Integer)
new_esEs27(x0, x1, ty_@0)
new_esEs7(Left(x0), Left(x1), ty_Int, x2)
new_ltEs14(Right(x0), Right(x1), x2, ty_Double)
new_lt4(x0, x1, ty_Float)
new_ltEs5(x0, x1, app(app(ty_Either, x2), x3))
new_esEs19(x0, x1, ty_Char)
new_lt4(x0, x1, ty_Double)
new_esEs19(x0, x1, ty_Ordering)
new_esEs8(x0, x1, app(ty_Ratio, x2))
new_esEs33(x0, x1, ty_Int)
new_esEs10(@0, @0)
new_esEs33(x0, x1, ty_@0)
new_esEs11(x0, x1)
new_esEs20(x0, x1, ty_Float)
new_ltEs14(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs7(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs14(Right(x0), Right(x1), x2, ty_Char)
new_esEs9(GT, GT)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs27(x0, x1, ty_Char)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_compare11(x0, x1, False)
new_compare23(x0, x1, False)
new_compare12(x0, x1, True, x2, x3, x4)
new_esEs7(Right(x0), Right(x1), x2, ty_Double)
new_esEs28(x0, x1, ty_Bool)
new_esEs33(x0, x1, app(app(ty_Either, x2), x3))
new_compare24(x0, x1, True)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_compare15(x0, x1, x2, x3)
new_primEqNat0(Succ(x0), Zero)
new_esEs13([], [], x0)
new_esEs23(x0, x1, ty_Ordering)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs7(Left(x0), Right(x1), x2, x3)
new_esEs7(Right(x0), Left(x1), x2, x3)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_compare9(x0, x1, x2, x3, x4)
new_lt20(x0, x1, ty_Int)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs21(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Integer)
new_esEs33(x0, x1, ty_Bool)
new_lt4(x0, x1, app(app(ty_Either, x2), x3))
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs23(x0, x1, ty_Int)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs5(x0, x1, app(app(ty_@2, x2), x3))
new_esEs33(x0, x1, ty_Char)
new_lt4(x0, x1, ty_@0)
new_esEs23(x0, x1, ty_Char)
new_esEs28(x0, x1, ty_Ordering)
new_ltEs18(Just(x0), Just(x1), ty_Double)
new_ltEs20(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_lt20(x0, x1, ty_@0)
new_compare1([], [], x0)
new_esEs9(EQ, EQ)
new_pePe(False, x0)
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs5(x0, x1, app(ty_Ratio, x2))
new_ltEs14(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs6(Just(x0), Just(x1), ty_Char)
new_esEs25(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Integer)
new_compare12(x0, x1, False, x2, x3, x4)
new_esEs8(x0, x1, app(ty_Maybe, x2))
new_primCompAux00(x0, EQ)
new_esEs19(x0, x1, ty_Int)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs14(True, False)
new_esEs14(False, True)
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_lt4(x0, x1, ty_Integer)
new_esEs7(Left(x0), Left(x1), ty_@0, x2)
new_ltEs14(Right(x0), Right(x1), x2, ty_@0)
new_fsEs(x0)
new_esEs22(x0, x1, ty_Float)
new_ltEs14(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs32(x0, x1, app(ty_Ratio, x2))
new_esEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_primCmpNat2(Succ(x0), Succ(x1))
new_compare110(x0, x1, False, x2, x3)
new_lt4(x0, x1, ty_Bool)
new_asAs(True, x0)
new_esEs21(x0, x1, ty_Bool)
new_esEs4(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs6(Nothing, Just(x0), x1)
new_esEs6(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs21(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Just(x0), Nothing, x1)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_compare29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs8(x0, x1, app(ty_[], x2))
new_esEs13(:(x0, x1), [], x2)
new_ltEs14(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs8(x0, x1, ty_Char)
new_lt19(x0, x1, ty_Float)
new_compare33(x0, x1, x2, x3)
new_ltEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs22(x0, x1, ty_@0)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_Char)
new_ltEs12(False, True)
new_ltEs12(True, False)
new_compare6(Double(x0, x1), Double(x2, x3))
new_ltEs20(x0, x1, ty_@0)
new_esEs22(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_@0)
new_ltEs14(Right(x0), Right(x1), x2, ty_Integer)
new_lt19(x0, x1, ty_Double)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1, ty_Bool)
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs7(Left(x0), Left(x1), ty_Char, x2)
new_esEs7(Right(x0), Right(x1), x2, ty_Float)
new_ltEs14(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs26(x0, x1, ty_Char)
new_ltEs5(x0, x1, ty_Int)
new_lt4(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_Double)
new_esEs19(x0, x1, ty_@0)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_compare13(x0, x1, True, x2, x3)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs21(x0, x1, ty_Bool)
new_ltEs14(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs21(x0, x1, ty_Double)
new_lt12(x0, x1)
new_esEs8(x0, x1, ty_Bool)
new_ltEs21(x0, x1, ty_Char)
new_lt13(x0, x1)
new_ltEs14(Right(x0), Right(x1), x2, ty_Bool)
new_compare1(:(x0, x1), [], x2)
new_compare10(x0, x1, False)
new_primMulNat0(Succ(x0), Zero)
new_ltEs19(x0, x1, ty_Float)
new_ltEs14(Left(x0), Right(x1), x2, x3)
new_esEs23(x0, x1, ty_Float)
new_ltEs14(Right(x0), Left(x1), x2, x3)
new_compare29(x0, x1, ty_Int)
new_esEs20(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, ty_Int)
new_esEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs20(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Float)
new_compare31(x0, x1)
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs6(Just(x0), Just(x1), ty_Int)
new_ltEs7(LT, GT)
new_ltEs7(GT, LT)
new_esEs21(x0, x1, ty_Integer)
new_esEs22(x0, x1, app(ty_[], x2))
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs22(x0, x1, ty_Double)
new_compare110(x0, x1, True, x2, x3)
new_lt20(x0, x1, app(ty_[], x2))
new_ltEs13(x0, x1)
new_ltEs21(x0, x1, app(app(ty_Either, x2), x3))
new_lt4(x0, x1, ty_Int)
new_ltEs11(x0, x1, x2)
new_lt20(x0, x1, ty_Float)
new_not(True)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs20(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Float)
new_esEs19(x0, x1, app(ty_[], x2))
new_esEs18(:%(x0, x1), :%(x2, x3), x4)
new_esEs6(Nothing, Nothing, x0)
new_esEs28(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Ordering)
new_ltEs14(Left(x0), Left(x1), ty_Double, x2)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Just(x0), Just(x1), ty_Integer)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_not(False)
new_compare29(x0, x1, app(ty_Ratio, x2))
new_lt8(x0, x1)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_compare28(x0, x1, False, x2)
new_esEs32(x0, x1, ty_Integer)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, ty_Char)
new_esEs6(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare8(:%(x0, x1), :%(x2, x3), ty_Integer)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs22(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_Integer)
new_esEs8(x0, x1, ty_@0)
new_compare26(Left(x0), Left(x1), False, x2, x3)
new_esEs32(x0, x1, app(ty_Maybe, x2))
new_ltEs12(True, True)
new_esEs27(x0, x1, ty_Float)
new_lt15(x0, x1)
new_lt11(x0, x1, x2, x3)
new_esEs26(x0, x1, ty_Ordering)
new_esEs7(Left(x0), Left(x1), ty_Float, x2)
new_esEs27(x0, x1, ty_Double)
new_esEs6(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs33(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Ordering)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs13(:(x0, x1), :(x2, x3), x4)
new_esEs22(x0, x1, ty_Char)
new_lt20(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Bool)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_ltEs21(x0, x1, ty_Float)
new_ltEs10(x0, x1)
new_ltEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_compare29(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs14(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs5(x0, x1, ty_Ordering)
new_esEs8(x0, x1, ty_Double)
new_compare29(x0, x1, ty_Char)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs6(Just(x0), Just(x1), ty_@0)
new_compare1(:(x0, x1), :(x2, x3), x4)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs6(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs19(x0, x1, ty_Double)
new_esEs14(False, False)
new_ltEs21(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs32(x0, x1, ty_Char)
new_ltEs21(x0, x1, ty_Double)
new_esEs32(x0, x1, ty_Int)
new_ltEs14(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpNat2(Succ(x0), Zero)
new_esEs7(Right(x0), Right(x1), x2, ty_Char)
new_esEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_compare34(x0, x1, x2, x3)
new_compare18(x0, x1)
new_esEs32(x0, x1, ty_Bool)
new_esEs7(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs18(Just(x0), Just(x1), ty_Int)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare26(Right(x0), Right(x1), False, x2, x3)
new_esEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs17(x0, x1, x2)
new_primPlusNat0(Succ(x0), x1)
new_esEs20(x0, x1, ty_Integer)
new_primCmpNat0(x0, Zero)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_ltEs7(GT, EQ)
new_ltEs7(EQ, GT)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs32(x0, x1, ty_Double)
new_ltEs7(GT, GT)
new_esEs9(LT, LT)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_primCompAux0(x0, x1, x2, x3)
new_compare29(x0, x1, ty_@0)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_compare26(x0, x1, True, x2, x3)
new_compare26(Right(x0), Left(x1), False, x2, x3)
new_compare26(Left(x0), Right(x1), False, x2, x3)
new_ltEs18(Nothing, Just(x0), x1)
new_compare111(x0, x1, False, x2)
new_compare29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Ordering)
new_primCmpNat0(x0, Succ(x1))

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

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



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

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

new_minusFM(Branch(zxw30, zxw31, zxw32, zxw33, zxw34), Branch(zxw40, zxw41, zxw42, zxw43, zxw44), h, ba, bb, bc) → new_minusFM(new_splitGT30(zxw30, zxw31, zxw32, zxw33, zxw34, zxw40, h, ba, bb), zxw44, h, ba, bb, bc)
new_minusFM(Branch(zxw30, zxw31, zxw32, zxw33, zxw34), Branch(zxw40, zxw41, zxw42, zxw43, zxw44), h, ba, bb, bc) → new_minusFM(new_splitLT30(zxw30, zxw31, zxw32, zxw33, zxw34, zxw40, h, ba, bb), zxw43, h, ba, bb, bc)

The TRS R consists of the following rules:

new_esEs30(zxw400, zxw300, app(ty_Maybe, he)) → new_esEs6(zxw400, zxw300, he)
new_ltEs15(zxw7900, zxw8000) → new_fsEs(new_compare6(zxw7900, zxw8000))
new_esEs28(zxw4000, zxw3000, app(ty_[], ceb)) → new_esEs13(zxw4000, zxw3000, ceb)
new_ltEs20(zxw7900, zxw8000, app(ty_Maybe, fa)) → new_ltEs18(zxw7900, zxw8000, fa)
new_primCmpNat0(zxw7900, Succ(zxw8000)) → new_primCmpNat2(zxw7900, zxw8000)
new_ltEs14(Right(zxw79000), Right(zxw80000), dd, ty_Bool) → new_ltEs12(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Char) → new_ltEs10(zxw79000, zxw80000)
new_esEs23(zxw4000, zxw3000, app(app(ty_Either, cac), cad)) → new_esEs7(zxw4000, zxw3000, cac, cad)
new_esEs32(zxw20, zxw15, ty_Float) → new_esEs17(zxw20, zxw15)
new_esEs6(Just(zxw4000), Just(zxw3000), app(app(ty_@2, dab), dac)) → new_esEs5(zxw4000, zxw3000, dab, dac)
new_lt4(zxw79000, zxw80000, app(app(app(ty_@3, cfc), cfd), cfe)) → new_lt5(zxw79000, zxw80000, cfc, cfd, cfe)
new_addToFM_C11(zxw340, zxw341, zxw342, zxw343, zxw344, zxw300, zxw31, False, h, ba, bb) → Branch(Right(zxw300), new_addToFM0(zxw341, zxw31, bb), zxw342, zxw343, zxw344)
new_esEs31(zxw35, zxw30, ty_Ordering) → new_esEs9(zxw35, zxw30)
new_esEs7(Left(zxw4000), Left(zxw3000), app(app(ty_Either, ddb), ddc), gg) → new_esEs7(zxw4000, zxw3000, ddb, ddc)
new_ltEs20(zxw7900, zxw8000, ty_Int) → new_ltEs9(zxw7900, zxw8000)
new_esEs33(zxw400, zxw300, app(app(ty_Either, gf), gg)) → new_esEs7(zxw400, zxw300, gf, gg)
new_lt19(zxw79000, zxw80000, app(app(ty_Either, bbb), bbc)) → new_lt14(zxw79000, zxw80000, bbb, bbc)
new_esEs33(zxw400, zxw300, app(ty_[], gb)) → new_esEs13(zxw400, zxw300, gb)
new_addToFM_C3(Branch(zxw340, zxw341, zxw342, zxw343, zxw344), zxw300, zxw31, h, ba, bb) → new_addToFM_C22(zxw340, zxw341, zxw342, zxw343, zxw344, zxw300, zxw31, new_lt14(Right(zxw300), zxw340, h, ba), h, ba, bb)
new_esEs9(GT, LT) → False
new_esEs9(LT, GT) → False
new_esEs33(zxw400, zxw300, ty_Char) → new_esEs12(zxw400, zxw300)
new_esEs13([], [], gb) → True
new_compare110(zxw79000, zxw80000, True, fb, fc) → LT
new_lt4(zxw79000, zxw80000, app(ty_[], cff)) → new_lt10(zxw79000, zxw80000, cff)
new_esEs27(zxw4001, zxw3001, app(ty_Ratio, ccg)) → new_esEs18(zxw4001, zxw3001, ccg)
new_splitGT24(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, False, h, ba, bb) → new_splitGT13(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs9(new_compare35(zxw400, zxw300, h, ba), LT), h, ba, bb)
new_compare29(zxw79000, zxw80000, ty_Char) → new_compare17(zxw79000, zxw80000)
new_ltEs7(LT, EQ) → True
new_esEs30(zxw400, zxw300, app(ty_[], hd)) → new_esEs13(zxw400, zxw300, hd)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(ty_Maybe, ebh)) → new_ltEs18(zxw79000, zxw80000, ebh)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Integer) → new_ltEs13(zxw79000, zxw80000)
new_ltEs20(zxw7900, zxw8000, ty_@0) → new_ltEs8(zxw7900, zxw8000)
new_splitGT14(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, False, h, ba, bb) → zxw34
new_mkVBalBranch3MkVBalBranch11(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, False, h, ba, bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Right(zxw300), zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), Branch(zxw340, zxw341, zxw342, zxw343, zxw344), app(app(ty_Either, h), ba), bb)
new_esEs23(zxw4000, zxw3000, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_lt20(zxw79001, zxw80001, app(app(ty_Either, bcb), bcc)) → new_lt14(zxw79001, zxw80001, bcb, bcc)
new_compare35(zxw400, zxw300, h, ba) → new_compare26(Right(zxw400), Left(zxw300), False, h, ba)
new_ltEs8(zxw7900, zxw8000) → new_fsEs(new_compare30(zxw7900, zxw8000))
new_esEs22(zxw4000, zxw3000, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_lt19(zxw79000, zxw80000, ty_Double) → new_lt15(zxw79000, zxw80000)
new_mkVBalBranch2(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), Branch(zxw190, zxw191, zxw192, zxw193, zxw194), bg, bh, ca) → new_mkVBalBranch3MkVBalBranch21(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_lt8(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, bg, bh, ca)), new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, bg, bh, ca)), bg, bh, ca)
new_esEs22(zxw4000, zxw3000, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_ltEs21(zxw79002, zxw80002, ty_Char) → new_ltEs10(zxw79002, zxw80002)
new_ltEs14(Right(zxw79000), Right(zxw80000), dd, app(ty_[], dhh)) → new_ltEs11(zxw79000, zxw80000, dhh)
new_esEs23(zxw4000, zxw3000, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Bool, de) → new_ltEs12(zxw79000, zxw80000)
new_compare8(:%(zxw79000, zxw79001), :%(zxw80000, zxw80001), ty_Integer) → new_compare32(new_sr0(zxw79000, zxw80001), new_sr0(zxw80000, zxw79001))
new_esEs26(zxw4002, zxw3002, ty_Float) → new_esEs17(zxw4002, zxw3002)
new_splitLT13(zxw60, zxw61, zxw62, zxw63, zxw64, zxw65, False, bd, be, bf) → zxw63
new_addToFM1(zxw34, zxw300, zxw31, h, ba, bb) → new_addToFM_C3(zxw34, zxw300, zxw31, h, ba, bb)
new_esEs19(zxw79001, zxw80001, app(ty_Ratio, bcd)) → new_esEs18(zxw79001, zxw80001, bcd)
new_primMulNat0(Zero, Zero) → Zero
new_esEs20(zxw79000, zxw80000, app(ty_[], bba)) → new_esEs13(zxw79000, zxw80000, bba)
new_esEs7(Right(zxw4000), Right(zxw3000), gf, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs34(zxw400, zxw300, ty_Char) → new_esEs12(zxw400, zxw300)
new_splitGT16(zxw30, zxw31, zxw32, zxw33, zxw34, zxw35, True, dba, dbb, eca) → new_mkVBalBranch1(zxw30, zxw31, new_splitGT4(zxw33, zxw35, dba, dbb, eca), zxw34, dba, dbb, eca)
new_lt20(zxw79001, zxw80001, ty_@0) → new_lt7(zxw79001, zxw80001)
new_esEs27(zxw4001, zxw3001, app(app(app(ty_@3, cdf), cdg), cdh)) → new_esEs4(zxw4001, zxw3001, cdf, cdg, cdh)
new_splitGT25(zxw15, zxw16, zxw17, zxw18, zxw19, zxw20, False, bg, bh, ca) → new_splitGT15(zxw15, zxw16, zxw17, zxw18, zxw19, zxw20, new_esEs9(new_compare33(zxw20, zxw15, bg, bh), LT), bg, bh, ca)
new_mkVBalBranch3MkVBalBranch22(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkBalBranch(zxw340, zxw341, new_mkVBalBranch1(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), zxw343, h, ba, bb), zxw344, h, ba, bb)
new_splitGT30(Left(zxw300), zxw31, zxw32, zxw33, zxw34, Right(zxw400), h, ba, bb) → new_splitGT24(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs9(new_compare26(Right(zxw400), Left(zxw300), False, h, ba), GT), h, ba, bb)
new_esEs19(zxw79001, zxw80001, ty_Ordering) → new_esEs9(zxw79001, zxw80001)
new_esEs33(zxw400, zxw300, ty_Ordering) → new_esEs9(zxw400, zxw300)
new_esEs31(zxw35, zxw30, ty_Char) → new_esEs12(zxw35, zxw30)
new_esEs32(zxw20, zxw15, ty_Integer) → new_esEs15(zxw20, zxw15)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(ty_Ratio, ebg)) → new_ltEs17(zxw79000, zxw80000, ebg)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Bool, gg) → new_esEs14(zxw4000, zxw3000)
new_splitLT16(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, False, h, ba, bb) → zxw33
new_mkVBalBranch1(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb) → new_mkVBalBranch3MkVBalBranch22(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_lt8(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), new_mkVBalBranch3Size_r(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), h, ba, bb)
new_splitGT15(zxw15, zxw16, zxw17, zxw18, zxw19, zxw20, False, bg, bh, ca) → zxw19
new_mkVBalBranch3MkVBalBranch12(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, bg, bh, ca) → new_mkBalBranch(zxw1070, zxw1071, zxw1073, new_mkVBalBranch2(zxw15, zxw16, zxw1074, Branch(zxw190, zxw191, zxw192, zxw193, zxw194), bg, bh, ca), bg, bh, ca)
new_esEs24(zxw4001, zxw3001, ty_Integer) → new_esEs15(zxw4001, zxw3001)
new_splitLT23(zxw45, zxw46, zxw47, zxw48, zxw49, zxw50, False, cbb, cbc, cbd) → new_splitLT15(zxw45, zxw46, zxw47, zxw48, zxw49, zxw50, new_esEs9(new_compare33(zxw50, zxw45, cbb, cbc), GT), cbb, cbc, cbd)
new_lt19(zxw79000, zxw80000, ty_Ordering) → new_lt6(zxw79000, zxw80000)
new_lt20(zxw79001, zxw80001, app(app(ty_@2, bbh), bca)) → new_lt11(zxw79001, zxw80001, bbh, bca)
new_lt11(zxw79000, zxw80000, fb, fc) → new_esEs9(new_compare19(zxw79000, zxw80000, fb, fc), LT)
new_compare9(zxw79000, zxw80000, baf, bag, bah) → new_compare25(zxw79000, zxw80000, new_esEs4(zxw79000, zxw80000, baf, bag, bah), baf, bag, bah)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(ty_Ratio, dhc), de) → new_ltEs17(zxw79000, zxw80000, dhc)
new_compare1([], :(zxw80000, zxw80001), da) → LT
new_esEs33(zxw400, zxw300, ty_@0) → new_esEs10(zxw400, zxw300)
new_lt18(zxw79000, zxw80000, bae) → new_esEs9(new_compare27(zxw79000, zxw80000, bae), LT)
new_esEs30(zxw400, zxw300, app(app(ty_Either, hh), baa)) → new_esEs7(zxw400, zxw300, hh, baa)
new_esEs33(zxw400, zxw300, ty_Integer) → new_esEs15(zxw400, zxw300)
new_compare32(Integer(zxw79000), Integer(zxw80000)) → new_primCmpInt(zxw79000, zxw80000)
new_esEs8(zxw79000, zxw80000, ty_Int) → new_esEs11(zxw79000, zxw80000)
new_mkBalBranch6Size_r(zxw50, zxw51, zxw99, zxw54, h, ba, bb) → new_sizeFM0(zxw54, h, ba, bb)
new_lt4(zxw79000, zxw80000, ty_Bool) → new_lt12(zxw79000, zxw80000)
new_ltEs5(zxw79001, zxw80001, ty_Char) → new_ltEs10(zxw79001, zxw80001)
new_compare27(zxw79000, zxw80000, bae) → new_compare28(zxw79000, zxw80000, new_esEs6(zxw79000, zxw80000, bae), bae)
new_mkVBalBranch3MkVBalBranch12(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, False, bg, bh, ca) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Left(zxw15), zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), Branch(zxw190, zxw191, zxw192, zxw193, zxw194), app(app(ty_Either, bg), bh), ca)
new_lt4(zxw79000, zxw80000, app(ty_Maybe, cgd)) → new_lt18(zxw79000, zxw80000, cgd)
new_compare29(zxw79000, zxw80000, ty_Bool) → new_compare31(zxw79000, zxw80000)
new_esEs31(zxw35, zxw30, ty_@0) → new_esEs10(zxw35, zxw30)
new_mkBalBranch6MkBalBranch01(zxw50, zxw51, zxw99, zxw540, zxw541, zxw542, Branch(zxw5430, zxw5431, zxw5432, zxw5433, zxw5434), zxw544, False, h, ba, bb) → new_mkBranch(Succ(Succ(Succ(Succ(Zero)))), zxw5430, zxw5431, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Zero))))), zxw50, zxw51, zxw99, zxw5433, app(app(ty_Either, h), ba), bb), new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw540, zxw541, zxw5434, zxw544, app(app(ty_Either, h), ba), bb), app(app(ty_Either, h), ba), bb)
new_esEs8(zxw79000, zxw80000, ty_Double) → new_esEs16(zxw79000, zxw80000)
new_esEs22(zxw4000, zxw3000, app(app(ty_@2, bgg), bgh)) → new_esEs5(zxw4000, zxw3000, bgg, bgh)
new_lt4(zxw79000, zxw80000, ty_Ordering) → new_lt6(zxw79000, zxw80000)
new_esEs22(zxw4000, zxw3000, app(ty_Maybe, bgf)) → new_esEs6(zxw4000, zxw3000, bgf)
new_ltEs14(Right(zxw79000), Right(zxw80000), dd, app(app(app(ty_@3, dhe), dhf), dhg)) → new_ltEs6(zxw79000, zxw80000, dhe, dhf, dhg)
new_esEs34(zxw400, zxw300, app(app(ty_Either, hh), baa)) → new_esEs7(zxw400, zxw300, hh, baa)
new_esEs27(zxw4001, zxw3001, app(ty_Maybe, cda)) → new_esEs6(zxw4001, zxw3001, cda)
new_esEs8(zxw79000, zxw80000, app(app(app(ty_@3, cfc), cfd), cfe)) → new_esEs4(zxw79000, zxw80000, cfc, cfd, cfe)
new_esEs15(Integer(zxw4000), Integer(zxw3000)) → new_primEqInt(zxw4000, zxw3000)
new_ltEs21(zxw79002, zxw80002, app(app(ty_@2, bdb), bdc)) → new_ltEs4(zxw79002, zxw80002, bdb, bdc)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Float, de) → new_ltEs16(zxw79000, zxw80000)
new_lt5(zxw79000, zxw80000, baf, bag, bah) → new_esEs9(new_compare9(zxw79000, zxw80000, baf, bag, bah), LT)
new_esEs22(zxw4000, zxw3000, app(ty_Ratio, bgd)) → new_esEs18(zxw4000, zxw3000, bgd)
new_splitGT26(zxw30, zxw31, zxw32, zxw33, zxw34, zxw35, False, dba, dbb, eca) → new_splitGT16(zxw30, zxw31, zxw32, zxw33, zxw34, zxw35, new_esEs9(new_compare36(zxw35, zxw30, dba, dbb), LT), dba, dbb, eca)
new_esEs22(zxw4000, zxw3000, app(app(ty_Either, bha), bhb)) → new_esEs7(zxw4000, zxw3000, bha, bhb)
new_esEs29(zxw400, zxw300, ty_Integer) → new_esEs15(zxw400, zxw300)
new_mkBalBranch6MkBalBranch4(zxw50, zxw51, zxw99, Branch(zxw540, zxw541, zxw542, zxw543, zxw544), True, h, ba, bb) → new_mkBalBranch6MkBalBranch01(zxw50, zxw51, zxw99, zxw540, zxw541, zxw542, zxw543, zxw544, new_lt8(new_sizeFM0(zxw543, h, ba, bb), new_sr(Pos(Succ(Succ(Zero))), new_sizeFM0(zxw544, h, ba, bb))), h, ba, bb)
new_mkVBalBranch3MkVBalBranch21(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, True, bg, bh, ca) → new_mkBalBranch(zxw190, zxw191, new_mkVBalBranch2(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), zxw193, bg, bh, ca), zxw194, bg, bh, ca)
new_ltEs19(zxw7900, zxw8000, ty_Float) → new_ltEs16(zxw7900, zxw8000)
new_splitLT4(EmptyFM, zxw400, h, ba, bb) → new_emptyFM(h, ba, bb)
new_esEs7(Right(zxw4000), Right(zxw3000), gf, app(ty_Maybe, dea)) → new_esEs6(zxw4000, zxw3000, dea)
new_pePe(False, zxw271) → zxw271
new_esEs29(zxw400, zxw300, ty_Double) → new_esEs16(zxw400, zxw300)
new_splitGT15(zxw15, zxw16, zxw17, zxw18, zxw19, zxw20, True, bg, bh, ca) → new_mkVBalBranch2(zxw15, zxw16, new_splitGT5(zxw18, zxw20, bg, bh, ca), zxw19, bg, bh, ca)
new_esEs7(Left(zxw4000), Right(zxw3000), gf, gg) → False
new_esEs7(Right(zxw4000), Left(zxw3000), gf, gg) → False
new_lt15(zxw79000, zxw80000) → new_esEs9(new_compare6(zxw79000, zxw80000), LT)
new_compare15(zxw790, zxw800, cc, cd) → new_compare26(zxw790, zxw800, new_esEs7(zxw790, zxw800, cc, cd), cc, cd)
new_ltEs14(Right(zxw79000), Right(zxw80000), dd, ty_Float) → new_ltEs16(zxw79000, zxw80000)
new_esEs31(zxw35, zxw30, app(app(app(ty_@3, dcb), dcc), dcd)) → new_esEs4(zxw35, zxw30, dcb, dcc, dcd)
new_ltEs12(True, False) → False
new_esEs34(zxw400, zxw300, app(ty_[], hd)) → new_esEs13(zxw400, zxw300, hd)
new_esEs20(zxw79000, zxw80000, ty_Double) → new_esEs16(zxw79000, zxw80000)
new_ltEs19(zxw7900, zxw8000, app(app(ty_@2, db), dc)) → new_ltEs4(zxw7900, zxw8000, db, dc)
new_compare23(zxw79000, zxw80000, True) → EQ
new_esEs32(zxw20, zxw15, ty_@0) → new_esEs10(zxw20, zxw15)
new_esEs27(zxw4001, zxw3001, app(app(ty_Either, cdd), cde)) → new_esEs7(zxw4001, zxw3001, cdd, cde)
new_esEs31(zxw35, zxw30, ty_Float) → new_esEs17(zxw35, zxw30)
new_esEs27(zxw4001, zxw3001, ty_Float) → new_esEs17(zxw4001, zxw3001)
new_esEs27(zxw4001, zxw3001, ty_Ordering) → new_esEs9(zxw4001, zxw3001)
new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, bg, bh, ca) → new_sizeFM0(Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), bg, bh, ca)
new_esEs19(zxw79001, zxw80001, app(ty_Maybe, bce)) → new_esEs6(zxw79001, zxw80001, bce)
new_esEs26(zxw4002, zxw3002, ty_Char) → new_esEs12(zxw4002, zxw3002)
new_lt10(zxw79000, zxw80000, bba) → new_esEs9(new_compare1(zxw79000, zxw80000, bba), LT)
new_ltEs19(zxw7900, zxw8000, app(ty_[], da)) → new_ltEs11(zxw7900, zxw8000, da)
new_esEs26(zxw4002, zxw3002, ty_Int) → new_esEs11(zxw4002, zxw3002)
new_ltEs5(zxw79001, zxw80001, app(app(ty_@2, cha), chb)) → new_ltEs4(zxw79001, zxw80001, cha, chb)
new_lt19(zxw79000, zxw80000, app(ty_Ratio, cb)) → new_lt17(zxw79000, zxw80000, cb)
new_esEs22(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, app(app(app(ty_@3, ceh), cfa), cfb)) → new_esEs4(zxw4000, zxw3000, ceh, cfa, cfb)
new_esEs32(zxw20, zxw15, ty_Ordering) → new_esEs9(zxw20, zxw15)
new_compare29(zxw79000, zxw80000, app(app(ty_@2, bed), bee)) → new_compare19(zxw79000, zxw80000, bed, bee)
new_ltEs21(zxw79002, zxw80002, ty_Int) → new_ltEs9(zxw79002, zxw80002)
new_esEs20(zxw79000, zxw80000, ty_Char) → new_esEs12(zxw79000, zxw80000)
new_compare13(zxw235, zxw236, False, fg, fh) → GT
new_esEs9(GT, EQ) → False
new_esEs9(EQ, GT) → False
new_esEs19(zxw79001, zxw80001, app(app(ty_Either, bcb), bcc)) → new_esEs7(zxw79001, zxw80001, bcb, bcc)
new_splitGT23(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, False, h, ba, bb) → new_splitGT14(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs9(new_compare34(zxw400, zxw300, h, ba), LT), h, ba, bb)
new_esEs20(zxw79000, zxw80000, app(app(ty_@2, fb), fc)) → new_esEs5(zxw79000, zxw80000, fb, fc)
new_ltEs7(GT, GT) → True
new_mkBalBranch6MkBalBranch01(zxw50, zxw51, zxw99, zxw540, zxw541, zxw542, zxw543, zxw544, True, h, ba, bb) → new_mkBranch(Succ(Succ(Zero)), zxw540, zxw541, new_mkBranch(Succ(Succ(Succ(Zero))), zxw50, zxw51, zxw99, zxw543, app(app(ty_Either, h), ba), bb), zxw544, app(app(ty_Either, h), ba), bb)
new_compare36(zxw35, zxw30, dba, dbb) → new_compare26(Right(zxw35), Right(zxw30), new_esEs31(zxw35, zxw30, dbb), dba, dbb)
new_ltEs20(zxw7900, zxw8000, app(app(ty_@2, ed), ee)) → new_ltEs4(zxw7900, zxw8000, ed, ee)
new_esEs7(Right(zxw4000), Right(zxw3000), gf, app(app(ty_@2, deb), dec)) → new_esEs5(zxw4000, zxw3000, deb, dec)
new_esEs21(zxw4001, zxw3001, ty_Bool) → new_esEs14(zxw4001, zxw3001)
new_primCompAux0(zxw79000, zxw80000, zxw272, da) → new_primCompAux00(zxw272, new_compare29(zxw79000, zxw80000, da))
new_primCmpInt(Neg(Succ(zxw7900)), Neg(zxw800)) → new_primCmpNat1(zxw800, zxw7900)
new_ltEs21(zxw79002, zxw80002, ty_Ordering) → new_ltEs7(zxw79002, zxw80002)
new_esEs32(zxw20, zxw15, ty_Bool) → new_esEs14(zxw20, zxw15)
new_compare29(zxw79000, zxw80000, app(ty_[], bec)) → new_compare1(zxw79000, zxw80000, bec)
new_splitGT5(EmptyFM, zxw400, h, ba, bb) → new_emptyFM(h, ba, bb)
new_lt20(zxw79001, zxw80001, ty_Ordering) → new_lt6(zxw79001, zxw80001)
new_esEs8(zxw79000, zxw80000, app(ty_[], cff)) → new_esEs13(zxw79000, zxw80000, cff)
new_esEs7(Right(zxw4000), Right(zxw3000), gf, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_esEs27(zxw4001, zxw3001, ty_@0) → new_esEs10(zxw4001, zxw3001)
new_esEs33(zxw400, zxw300, app(app(app(ty_@3, gh), ha), hb)) → new_esEs4(zxw400, zxw300, gh, ha, hb)
new_compare25(zxw79000, zxw80000, True, baf, bag, bah) → EQ
new_esEs19(zxw79001, zxw80001, ty_Float) → new_esEs17(zxw79001, zxw80001)
new_ltEs5(zxw79001, zxw80001, ty_Ordering) → new_ltEs7(zxw79001, zxw80001)
new_esEs28(zxw4000, zxw3000, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_lt4(zxw79000, zxw80000, app(ty_Ratio, cgc)) → new_lt17(zxw79000, zxw80000, cgc)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Int, gg) → new_esEs11(zxw4000, zxw3000)
new_ltEs21(zxw79002, zxw80002, ty_Float) → new_ltEs16(zxw79002, zxw80002)
new_mkVBalBranch3MkVBalBranch22(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, False, h, ba, bb) → new_mkVBalBranch3MkVBalBranch11(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, new_lt8(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), new_mkVBalBranch3Size_l(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, h, ba, bb)), h, ba, bb)
new_esEs28(zxw4000, zxw3000, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_compare29(zxw79000, zxw80000, app(app(app(ty_@3, bdh), bea), beb)) → new_compare9(zxw79000, zxw80000, bdh, bea, beb)
new_lt19(zxw79000, zxw80000, app(app(ty_@2, fb), fc)) → new_lt11(zxw79000, zxw80000, fb, fc)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(app(app(ty_@3, eag), eah), eba)) → new_ltEs6(zxw79000, zxw80000, eag, eah, eba)
new_pePe(True, zxw271) → True
new_compare14(zxw242, zxw243, False, cah, cba) → GT
new_primEqNat0(Zero, Zero) → True
new_esEs20(zxw79000, zxw80000, ty_Int) → new_esEs11(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), dd, ty_Double) → new_ltEs15(zxw79000, zxw80000)
new_ltEs21(zxw79002, zxw80002, ty_Bool) → new_ltEs12(zxw79002, zxw80002)
new_esEs33(zxw400, zxw300, app(app(ty_@2, gd), ge)) → new_esEs5(zxw400, zxw300, gd, ge)
new_lt9(zxw79000, zxw80000) → new_esEs9(new_compare17(zxw79000, zxw80000), LT)
new_esEs29(zxw400, zxw300, app(ty_Maybe, gc)) → new_esEs6(zxw400, zxw300, gc)
new_ltEs12(False, False) → True
new_esEs7(Left(zxw4000), Left(zxw3000), app(app(ty_@2, dch), dda), gg) → new_esEs5(zxw4000, zxw3000, dch, dda)
new_esEs26(zxw4002, zxw3002, app(ty_Maybe, cbg)) → new_esEs6(zxw4002, zxw3002, cbg)
new_compare8(:%(zxw79000, zxw79001), :%(zxw80000, zxw80001), ty_Int) → new_compare16(new_sr(zxw79000, zxw80001), new_sr(zxw80000, zxw79001))
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Ordering, gg) → new_esEs9(zxw4000, zxw3000)
new_esEs29(zxw400, zxw300, app(ty_[], gb)) → new_esEs13(zxw400, zxw300, gb)
new_esEs27(zxw4001, zxw3001, ty_Char) → new_esEs12(zxw4001, zxw3001)
new_esEs34(zxw400, zxw300, ty_Float) → new_esEs17(zxw400, zxw300)
new_lt7(zxw79000, zxw80000) → new_esEs9(new_compare30(zxw79000, zxw80000), LT)
new_splitLT30(Left(zxw300), zxw31, zxw32, zxw33, zxw34, Right(zxw400), h, ba, bb) → new_splitLT25(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs9(new_compare26(Right(zxw400), Left(zxw300), False, h, ba), LT), h, ba, bb)
new_compare110(zxw79000, zxw80000, False, fb, fc) → GT
new_sr(zxw4000, zxw3000) → new_primMulInt(zxw4000, zxw3000)
new_compare12(zxw79000, zxw80000, True, baf, bag, bah) → LT
new_esEs30(zxw400, zxw300, ty_Char) → new_esEs12(zxw400, zxw300)
new_lt19(zxw79000, zxw80000, ty_Int) → new_lt8(zxw79000, zxw80000)
new_primPlusInt(Neg(zxw1890), Neg(zxw1800)) → Neg(new_primPlusNat1(zxw1890, zxw1800))
new_primCmpInt(Neg(Zero), Neg(Succ(zxw8000))) → new_primCmpNat0(zxw8000, Zero)
new_ltEs19(zxw7900, zxw8000, ty_Char) → new_ltEs10(zxw7900, zxw8000)
new_ltEs14(Right(zxw79000), Right(zxw80000), dd, app(app(ty_@2, eaa), eab)) → new_ltEs4(zxw79000, zxw80000, eaa, eab)
new_esEs30(zxw400, zxw300, app(app(app(ty_@3, bab), bac), bad)) → new_esEs4(zxw400, zxw300, bab, bac, bad)
new_esEs21(zxw4001, zxw3001, ty_Double) → new_esEs16(zxw4001, zxw3001)
new_primPlusNat0(Succ(zxw1900), zxw300000) → Succ(Succ(new_primPlusNat1(zxw1900, zxw300000)))
new_primCmpInt(Pos(Zero), Pos(Succ(zxw8000))) → new_primCmpNat1(Zero, zxw8000)
new_esEs31(zxw35, zxw30, app(app(ty_Either, dbh), dca)) → new_esEs7(zxw35, zxw30, dbh, dca)
new_esEs7(Right(zxw4000), Right(zxw3000), gf, app(app(ty_Either, ded), dee)) → new_esEs7(zxw4000, zxw3000, ded, dee)
new_splitLT4(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw400, h, ba, bb) → new_splitLT30(zxw330, zxw331, zxw332, zxw333, zxw334, Right(zxw400), h, ba, bb)
new_esEs26(zxw4002, zxw3002, app(app(app(ty_@3, ccd), cce), ccf)) → new_esEs4(zxw4002, zxw3002, ccd, cce, ccf)
new_ltEs19(zxw7900, zxw8000, ty_Bool) → new_ltEs12(zxw7900, zxw8000)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Double, de) → new_ltEs15(zxw79000, zxw80000)
new_esEs7(Right(zxw4000), Right(zxw3000), gf, app(ty_[], ddh)) → new_esEs13(zxw4000, zxw3000, ddh)
new_ltEs11(zxw7900, zxw8000, da) → new_fsEs(new_compare1(zxw7900, zxw8000, da))
new_ltEs20(zxw7900, zxw8000, ty_Float) → new_ltEs16(zxw7900, zxw8000)
new_esEs21(zxw4001, zxw3001, ty_Ordering) → new_esEs9(zxw4001, zxw3001)
new_mkVBalBranch1(zxw300, zxw31, EmptyFM, zxw34, h, ba, bb) → new_addToFM1(zxw34, zxw300, zxw31, h, ba, bb)
new_esEs7(Right(zxw4000), Right(zxw3000), gf, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_esEs9(EQ, EQ) → True
new_fsEs(zxw259) → new_not(new_esEs9(zxw259, GT))
new_esEs8(zxw79000, zxw80000, ty_Char) → new_esEs12(zxw79000, zxw80000)
new_primEqInt(Neg(Succ(zxw40000)), Neg(Succ(zxw30000))) → new_primEqNat0(zxw40000, zxw30000)
new_esEs8(zxw79000, zxw80000, app(app(ty_@2, cfg), cfh)) → new_esEs5(zxw79000, zxw80000, cfg, cfh)
new_mkBalBranch6MkBalBranch4(zxw50, zxw51, zxw99, zxw54, False, h, ba, bb) → new_mkBalBranch6MkBalBranch3(zxw50, zxw51, zxw99, zxw54, new_gt(new_mkBalBranch6Size_l(zxw50, zxw51, zxw99, zxw54, h, ba, bb), new_sr(new_sIZE_RATIO, new_mkBalBranch6Size_r(zxw50, zxw51, zxw99, zxw54, h, ba, bb))), h, ba, bb)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba, bb) → zxw542
new_compare13(zxw235, zxw236, True, fg, fh) → LT
new_compare26(Left(zxw7900), Right(zxw8000), False, cc, cd) → LT
new_esEs26(zxw4002, zxw3002, app(ty_[], cbf)) → new_esEs13(zxw4002, zxw3002, cbf)
new_esEs13(:(zxw4000, zxw4001), :(zxw3000, zxw3001), gb) → new_asAs(new_esEs23(zxw4000, zxw3000, gb), new_esEs13(zxw4001, zxw3001, gb))
new_splitLT30(Right(zxw300), zxw31, zxw32, zxw33, zxw34, Left(zxw400), h, ba, bb) → new_splitLT24(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs9(new_compare26(Left(zxw400), Right(zxw300), False, h, ba), LT), h, ba, bb)
new_mkBalBranch6MkBalBranch11(zxw50, zxw51, zxw990, zxw991, zxw992, zxw993, zxw994, zxw54, True, h, ba, bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), zxw990, zxw991, zxw993, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), zxw50, zxw51, zxw994, zxw54, app(app(ty_Either, h), ba), bb), app(app(ty_Either, h), ba), bb)
new_sizeFM1(Branch(zxw3560, zxw3561, zxw3562, zxw3563, zxw3564), fd, ff) → zxw3562
new_splitGT16(zxw30, zxw31, zxw32, zxw33, zxw34, zxw35, False, dba, dbb, eca) → zxw34
new_primPlusNat1(Succ(zxw19000), Zero) → Succ(zxw19000)
new_primPlusNat1(Zero, Succ(zxw3000000)) → Succ(zxw3000000)
new_addToFM0(zxw191, zxw16, ca) → zxw16
new_ltEs19(zxw7900, zxw8000, app(ty_Ratio, df)) → new_ltEs17(zxw7900, zxw8000, df)
new_esEs30(zxw400, zxw300, ty_Float) → new_esEs17(zxw400, zxw300)
new_ltEs20(zxw7900, zxw8000, ty_Bool) → new_ltEs12(zxw7900, zxw8000)
new_esEs21(zxw4001, zxw3001, ty_Char) → new_esEs12(zxw4001, zxw3001)
new_compare23(zxw79000, zxw80000, False) → new_compare10(zxw79000, zxw80000, new_ltEs12(zxw79000, zxw80000))
new_ltEs14(Right(zxw79000), Left(zxw80000), dd, de) → False
new_compare210(zxw79000, zxw80000, False, fb, fc) → new_compare110(zxw79000, zxw80000, new_ltEs4(zxw79000, zxw80000, fb, fc), fb, fc)
new_primCmpNat1(Zero, zxw7900) → LT
new_compare7(Float(zxw79000, zxw79001), Float(zxw80000, zxw80001)) → new_compare16(new_sr(zxw79000, zxw80000), new_sr(zxw79001, zxw80001))
new_ltEs21(zxw79002, zxw80002, ty_Integer) → new_ltEs13(zxw79002, zxw80002)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_lt20(zxw79001, zxw80001, app(ty_Maybe, bce)) → new_lt18(zxw79001, zxw80001, bce)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Integer, gg) → new_esEs15(zxw4000, zxw3000)
new_ltEs5(zxw79001, zxw80001, ty_Bool) → new_ltEs12(zxw79001, zxw80001)
new_esEs19(zxw79001, zxw80001, ty_Bool) → new_esEs14(zxw79001, zxw80001)
new_ltEs7(EQ, EQ) → True
new_ltEs20(zxw7900, zxw8000, app(ty_Ratio, eh)) → new_ltEs17(zxw7900, zxw8000, eh)
new_primEqInt(Neg(Zero), Neg(Succ(zxw30000))) → False
new_primEqInt(Neg(Succ(zxw40000)), Neg(Zero)) → False
new_splitGT25(zxw15, zxw16, zxw17, zxw18, zxw19, zxw20, True, bg, bh, ca) → new_splitGT5(zxw19, zxw20, bg, bh, ca)
new_ltEs5(zxw79001, zxw80001, ty_Integer) → new_ltEs13(zxw79001, zxw80001)
new_compare26(zxw790, zxw800, True, cc, cd) → EQ
new_compare111(zxw79000, zxw80000, True, bae) → LT
new_esEs20(zxw79000, zxw80000, ty_@0) → new_esEs10(zxw79000, zxw80000)
new_esEs31(zxw35, zxw30, app(ty_Ratio, dbc)) → new_esEs18(zxw35, zxw30, dbc)
new_ltEs21(zxw79002, zxw80002, app(app(ty_Either, bdd), bde)) → new_ltEs14(zxw79002, zxw80002, bdd, bde)
new_esEs8(zxw79000, zxw80000, ty_Float) → new_esEs17(zxw79000, zxw80000)
new_esEs34(zxw400, zxw300, app(app(ty_@2, hf), hg)) → new_esEs5(zxw400, zxw300, hf, hg)
new_esEs23(zxw4000, zxw3000, app(app(app(ty_@3, cae), caf), cag)) → new_esEs4(zxw4000, zxw3000, cae, caf, cag)
new_ltEs21(zxw79002, zxw80002, app(ty_[], bda)) → new_ltEs11(zxw79002, zxw80002, bda)
new_esEs21(zxw4001, zxw3001, ty_Float) → new_esEs17(zxw4001, zxw3001)
new_compare24(zxw79000, zxw80000, False) → new_compare11(zxw79000, zxw80000, new_ltEs7(zxw79000, zxw80000))
new_esEs26(zxw4002, zxw3002, app(app(ty_Either, ccb), ccc)) → new_esEs7(zxw4002, zxw3002, ccb, ccc)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_ltEs5(zxw79001, zxw80001, app(ty_Ratio, che)) → new_ltEs17(zxw79001, zxw80001, che)
new_mkVBalBranch3MkVBalBranch11(zxw340, zxw341, zxw342, zxw343, zxw344, zxw1080, zxw1081, zxw1082, zxw1083, zxw1084, zxw300, zxw31, True, h, ba, bb) → new_mkBalBranch(zxw1080, zxw1081, zxw1083, new_mkVBalBranch1(zxw300, zxw31, zxw1084, Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba, bb), h, ba, bb)
new_lt20(zxw79001, zxw80001, ty_Int) → new_lt8(zxw79001, zxw80001)
new_ltEs20(zxw7900, zxw8000, ty_Double) → new_ltEs15(zxw7900, zxw8000)
new_lt4(zxw79000, zxw80000, ty_Int) → new_lt8(zxw79000, zxw80000)
new_esEs34(zxw400, zxw300, app(app(app(ty_@3, bab), bac), bad)) → new_esEs4(zxw400, zxw300, bab, bac, bad)
new_lt12(zxw79000, zxw80000) → new_esEs9(new_compare31(zxw79000, zxw80000), LT)
new_ltEs7(GT, LT) → False
new_splitGT23(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, True, h, ba, bb) → new_splitGT5(zxw34, zxw400, h, ba, bb)
new_mkVBalBranch1(zxw300, zxw31, Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), EmptyFM, h, ba, bb) → new_addToFM1(Branch(zxw1080, zxw1081, zxw1082, zxw1083, zxw1084), zxw300, zxw31, h, ba, bb)
new_primMinusNat0(Succ(zxw18900), Zero) → Pos(Succ(zxw18900))
new_lt20(zxw79001, zxw80001, ty_Integer) → new_lt13(zxw79001, zxw80001)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Int, de) → new_ltEs9(zxw79000, zxw80000)
new_ltEs7(GT, EQ) → False
new_esEs6(Nothing, Nothing, gc) → True
new_primEqInt(Pos(Succ(zxw40000)), Pos(Succ(zxw30000))) → new_primEqNat0(zxw40000, zxw30000)
new_lt8(zxw790, zxw800) → new_esEs9(new_compare16(zxw790, zxw800), LT)
new_esEs21(zxw4001, zxw3001, app(ty_Maybe, bfd)) → new_esEs6(zxw4001, zxw3001, bfd)
new_lt6(zxw79000, zxw80000) → new_esEs9(new_compare18(zxw79000, zxw80000), LT)
new_mkBalBranch6MkBalBranch01(zxw50, zxw51, zxw99, zxw540, zxw541, zxw542, EmptyFM, zxw544, False, h, ba, bb) → error([])
new_esEs32(zxw20, zxw15, app(app(ty_Either, dff), dfg)) → new_esEs7(zxw20, zxw15, dff, dfg)
new_esEs14(True, False) → False
new_esEs14(False, True) → False
new_esEs26(zxw4002, zxw3002, ty_Integer) → new_esEs15(zxw4002, zxw3002)
new_esEs32(zxw20, zxw15, app(ty_[], dfb)) → new_esEs13(zxw20, zxw15, dfb)
new_splitLT16(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, True, h, ba, bb) → new_mkVBalBranch1(zxw300, zxw31, zxw33, new_splitLT5(zxw34, zxw400, h, ba, bb), h, ba, bb)
new_esEs7(Right(zxw4000), Right(zxw3000), gf, app(app(app(ty_@3, def), deg), deh)) → new_esEs4(zxw4000, zxw3000, def, deg, deh)
new_esEs6(Nothing, Just(zxw3000), gc) → False
new_esEs6(Just(zxw4000), Nothing, gc) → False
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Int) → new_esEs11(zxw4000, zxw3000)
new_primEqNat0(Succ(zxw40000), Succ(zxw30000)) → new_primEqNat0(zxw40000, zxw30000)
new_esEs16(Double(zxw4000, zxw4001), Double(zxw3000, zxw3001)) → new_esEs11(new_sr(zxw4000, zxw3000), new_sr(zxw4001, zxw3001))
new_esEs33(zxw400, zxw300, app(ty_Ratio, ga)) → new_esEs18(zxw400, zxw300, ga)
new_lt19(zxw79000, zxw80000, ty_@0) → new_lt7(zxw79000, zxw80000)
new_sizeFM0(EmptyFM, h, ba, bb) → Pos(Zero)
new_esEs30(zxw400, zxw300, app(ty_Ratio, hc)) → new_esEs18(zxw400, zxw300, hc)
new_ltEs5(zxw79001, zxw80001, app(ty_Maybe, chf)) → new_ltEs18(zxw79001, zxw80001, chf)
new_splitGT14(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, True, h, ba, bb) → new_mkVBalBranch1(zxw300, zxw31, new_splitGT5(zxw33, zxw400, h, ba, bb), zxw34, h, ba, bb)
new_esEs17(Float(zxw4000, zxw4001), Float(zxw3000, zxw3001)) → new_esEs11(new_sr(zxw4000, zxw3000), new_sr(zxw4001, zxw3001))
new_primCompAux00(zxw276, LT) → LT
new_esEs28(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_mkBalBranch6MkBalBranch11(zxw50, zxw51, zxw990, zxw991, zxw992, zxw993, EmptyFM, zxw54, False, h, ba, bb) → error([])
new_mkBalBranch6MkBalBranch5(zxw50, zxw51, zxw99, zxw54, False, h, ba, bb) → new_mkBalBranch6MkBalBranch4(zxw50, zxw51, zxw99, zxw54, new_gt(new_mkBalBranch6Size_r(zxw50, zxw51, zxw99, zxw54, h, ba, bb), new_sr(new_sIZE_RATIO, new_mkBalBranch6Size_l(zxw50, zxw51, zxw99, zxw54, h, ba, bb))), h, ba, bb)
new_esEs7(Left(zxw4000), Left(zxw3000), app(ty_Ratio, dce), gg) → new_esEs18(zxw4000, zxw3000, dce)
new_esEs21(zxw4001, zxw3001, ty_Int) → new_esEs11(zxw4001, zxw3001)
new_splitGT26(zxw30, zxw31, zxw32, zxw33, zxw34, zxw35, True, dba, dbb, eca) → new_splitGT4(zxw34, zxw35, dba, dbb, eca)
new_compare1(:(zxw79000, zxw79001), :(zxw80000, zxw80001), da) → new_primCompAux0(zxw79000, zxw80000, new_compare1(zxw79001, zxw80001, da), da)
new_primEqInt(Pos(Zero), Pos(Succ(zxw30000))) → False
new_primEqInt(Pos(Succ(zxw40000)), Pos(Zero)) → False
new_compare29(zxw79000, zxw80000, ty_Int) → new_compare16(zxw79000, zxw80000)
new_lt20(zxw79001, zxw80001, app(ty_Ratio, bcd)) → new_lt17(zxw79001, zxw80001, bcd)
new_esEs34(zxw400, zxw300, ty_Double) → new_esEs16(zxw400, zxw300)
new_ltEs20(zxw7900, zxw8000, ty_Integer) → new_ltEs13(zxw7900, zxw8000)
new_esEs31(zxw35, zxw30, app(app(ty_@2, dbf), dbg)) → new_esEs5(zxw35, zxw30, dbf, dbg)
new_esEs5(@2(zxw4000, zxw4001), @2(zxw3000, zxw3001), gd, ge) → new_asAs(new_esEs22(zxw4000, zxw3000, gd), new_esEs21(zxw4001, zxw3001, ge))
new_ltEs18(Nothing, Nothing, dg) → True
new_esEs23(zxw4000, zxw3000, app(app(ty_@2, caa), cab)) → new_esEs5(zxw4000, zxw3000, caa, cab)
new_ltEs21(zxw79002, zxw80002, app(ty_Ratio, bdf)) → new_ltEs17(zxw79002, zxw80002, bdf)
new_esEs33(zxw400, zxw300, ty_Bool) → new_esEs14(zxw400, zxw300)
new_esEs32(zxw20, zxw15, app(ty_Maybe, dfc)) → new_esEs6(zxw20, zxw15, dfc)
new_esEs20(zxw79000, zxw80000, app(app(app(ty_@3, baf), bag), bah)) → new_esEs4(zxw79000, zxw80000, baf, bag, bah)
new_esEs29(zxw400, zxw300, app(app(app(ty_@3, gh), ha), hb)) → new_esEs4(zxw400, zxw300, gh, ha, hb)
new_primCmpInt(Neg(Zero), Pos(Succ(zxw8000))) → LT
new_ltEs21(zxw79002, zxw80002, app(app(app(ty_@3, bcf), bcg), bch)) → new_ltEs6(zxw79002, zxw80002, bcf, bcg, bch)
new_ltEs10(zxw7900, zxw8000) → new_fsEs(new_compare17(zxw7900, zxw8000))
new_splitLT24(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, True, h, ba, bb) → new_splitLT5(zxw33, zxw400, h, ba, bb)
new_compare17(Char(zxw79000), Char(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_sr0(Integer(zxw800000), Integer(zxw790010)) → Integer(new_primMulInt(zxw800000, zxw790010))
new_ltEs5(zxw79001, zxw80001, ty_Double) → new_ltEs15(zxw79001, zxw80001)
new_primPlusNat1(Succ(zxw19000), Succ(zxw3000000)) → Succ(Succ(new_primPlusNat1(zxw19000, zxw3000000)))
new_esEs29(zxw400, zxw300, app(ty_Ratio, ga)) → new_esEs18(zxw400, zxw300, ga)
new_esEs8(zxw79000, zxw80000, app(app(ty_Either, cga), cgb)) → new_esEs7(zxw79000, zxw80000, cga, cgb)
new_primEqInt(Neg(Succ(zxw40000)), Pos(zxw3000)) → False
new_primEqInt(Pos(Succ(zxw40000)), Neg(zxw3000)) → False
new_compare29(zxw79000, zxw80000, ty_Integer) → new_compare32(zxw79000, zxw80000)
new_splitGT4(EmptyFM, zxw400, h, ba, bb) → new_emptyFM(h, ba, bb)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_@0, gg) → new_esEs10(zxw4000, zxw3000)
new_ltEs14(Right(zxw79000), Right(zxw80000), dd, ty_Char) → new_ltEs10(zxw79000, zxw80000)
new_primPlusInt(Pos(zxw1890), Neg(zxw1800)) → new_primMinusNat0(zxw1890, zxw1800)
new_primPlusInt(Neg(zxw1890), Pos(zxw1800)) → new_primMinusNat0(zxw1800, zxw1890)
new_lt19(zxw79000, zxw80000, app(app(app(ty_@3, baf), bag), bah)) → new_lt5(zxw79000, zxw80000, baf, bag, bah)
new_esEs29(zxw400, zxw300, app(app(ty_@2, gd), ge)) → new_esEs5(zxw400, zxw300, gd, ge)
new_addToFM(zxw19, zxw15, zxw16, bg, bh, ca) → new_addToFM_C4(zxw19, zxw15, zxw16, bg, bh, ca)
new_esEs32(zxw20, zxw15, app(app(ty_@2, dfd), dfe)) → new_esEs5(zxw20, zxw15, dfd, dfe)
new_primCmpNat2(Zero, Succ(zxw80000)) → LT
new_esEs28(zxw4000, zxw3000, app(ty_Maybe, cec)) → new_esEs6(zxw4000, zxw3000, cec)
new_esEs21(zxw4001, zxw3001, app(ty_[], bfc)) → new_esEs13(zxw4001, zxw3001, bfc)
new_ltEs21(zxw79002, zxw80002, ty_@0) → new_ltEs8(zxw79002, zxw80002)
new_primEqInt(Neg(Zero), Pos(Succ(zxw30000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(zxw30000))) → False
new_ltEs7(EQ, GT) → True
new_lt4(zxw79000, zxw80000, ty_Double) → new_lt15(zxw79000, zxw80000)
new_esEs21(zxw4001, zxw3001, ty_Integer) → new_esEs15(zxw4001, zxw3001)
new_esEs34(zxw400, zxw300, ty_Ordering) → new_esEs9(zxw400, zxw300)
new_esEs31(zxw35, zxw30, ty_Integer) → new_esEs15(zxw35, zxw30)
new_primCompAux00(zxw276, EQ) → zxw276
new_esEs28(zxw4000, zxw3000, app(app(ty_Either, cef), ceg)) → new_esEs7(zxw4000, zxw3000, cef, ceg)
new_splitLT15(zxw45, zxw46, zxw47, zxw48, zxw49, zxw50, True, cbb, cbc, cbd) → new_mkVBalBranch2(zxw45, zxw46, zxw48, new_splitLT5(zxw49, zxw50, cbb, cbc, cbd), cbb, cbc, cbd)
new_compare24(zxw79000, zxw80000, True) → EQ
new_compare6(Double(zxw79000, zxw79001), Double(zxw80000, zxw80001)) → new_compare16(new_sr(zxw79000, zxw80000), new_sr(zxw79001, zxw80001))
new_esEs8(zxw79000, zxw80000, ty_@0) → new_esEs10(zxw79000, zxw80000)
new_splitGT13(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, False, h, ba, bb) → zxw34
new_splitGT30(Right(zxw300), zxw31, zxw32, zxw33, zxw34, Left(zxw400), h, ba, bb) → new_splitGT23(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs9(new_compare26(Left(zxw400), Right(zxw300), False, h, ba), GT), h, ba, bb)
new_ltEs5(zxw79001, zxw80001, app(app(ty_Either, chc), chd)) → new_ltEs14(zxw79001, zxw80001, chc, chd)
new_lt13(zxw79000, zxw80000) → new_esEs9(new_compare32(zxw79000, zxw80000), LT)
new_esEs27(zxw4001, zxw3001, ty_Double) → new_esEs16(zxw4001, zxw3001)
new_esEs26(zxw4002, zxw3002, app(app(ty_@2, cbh), cca)) → new_esEs5(zxw4002, zxw3002, cbh, cca)
new_esEs7(Left(zxw4000), Left(zxw3000), app(app(app(ty_@3, ddd), dde), ddf), gg) → new_esEs4(zxw4000, zxw3000, ddd, dde, ddf)
new_addToFM_C21(zxw190, zxw191, zxw192, zxw193, zxw194, zxw15, zxw16, False, bg, bh, ca) → new_addToFM_C12(zxw190, zxw191, zxw192, zxw193, zxw194, zxw15, zxw16, new_esEs9(new_compare15(Left(zxw15), zxw190, bg, bh), GT), bg, bh, ca)
new_esEs21(zxw4001, zxw3001, app(app(ty_@2, bfe), bff)) → new_esEs5(zxw4001, zxw3001, bfe, bff)
new_addToFM_C4(Branch(zxw190, zxw191, zxw192, zxw193, zxw194), zxw15, zxw16, bg, bh, ca) → new_addToFM_C21(zxw190, zxw191, zxw192, zxw193, zxw194, zxw15, zxw16, new_lt14(Left(zxw15), zxw190, bg, bh), bg, bh, ca)
new_esEs30(zxw400, zxw300, ty_@0) → new_esEs10(zxw400, zxw300)
new_esEs12(Char(zxw4000), Char(zxw3000)) → new_primEqNat0(zxw4000, zxw3000)
new_lt19(zxw79000, zxw80000, app(ty_Maybe, bae)) → new_lt18(zxw79000, zxw80000, bae)
new_ltEs20(zxw7900, zxw8000, app(app(app(ty_@3, dh), ea), eb)) → new_ltEs6(zxw7900, zxw8000, dh, ea, eb)
new_esEs11(zxw400, zxw300) → new_primEqInt(zxw400, zxw300)
new_lt20(zxw79001, zxw80001, ty_Char) → new_lt9(zxw79001, zxw80001)
new_not(False) → True
new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, bg, bh, ca) → new_sizeFM(zxw190, zxw191, zxw192, zxw193, zxw194, bg, bh, ca)
new_ltEs14(Right(zxw79000), Right(zxw80000), dd, app(ty_Maybe, eaf)) → new_ltEs18(zxw79000, zxw80000, eaf)
new_ltEs18(Just(zxw79000), Nothing, dg) → False
new_esEs8(zxw79000, zxw80000, app(ty_Maybe, cgd)) → new_esEs6(zxw79000, zxw80000, cgd)
new_esEs7(Left(zxw4000), Left(zxw3000), app(ty_Maybe, dcg), gg) → new_esEs6(zxw4000, zxw3000, dcg)
new_splitLT25(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, True, h, ba, bb) → new_splitLT4(zxw33, zxw400, h, ba, bb)
new_primPlusNat0(Zero, zxw300000) → Succ(zxw300000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Double, gg) → new_esEs16(zxw4000, zxw3000)
new_compare210(zxw79000, zxw80000, True, fb, fc) → EQ
new_esEs19(zxw79001, zxw80001, ty_Int) → new_esEs11(zxw79001, zxw80001)
new_compare12(zxw79000, zxw80000, False, baf, bag, bah) → GT
new_ltEs16(zxw7900, zxw8000) → new_fsEs(new_compare7(zxw7900, zxw8000))
new_esEs32(zxw20, zxw15, ty_Char) → new_esEs12(zxw20, zxw15)
new_esEs26(zxw4002, zxw3002, app(ty_Ratio, cbe)) → new_esEs18(zxw4002, zxw3002, cbe)
new_esEs9(GT, GT) → True
new_esEs25(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_lt20(zxw79001, zxw80001, app(ty_[], bbg)) → new_lt10(zxw79001, zxw80001, bbg)
new_lt4(zxw79000, zxw80000, app(app(ty_Either, cga), cgb)) → new_lt14(zxw79000, zxw80000, cga, cgb)
new_esEs26(zxw4002, zxw3002, ty_Bool) → new_esEs14(zxw4002, zxw3002)
new_compare19(zxw79000, zxw80000, fb, fc) → new_compare210(zxw79000, zxw80000, new_esEs5(zxw79000, zxw80000, fb, fc), fb, fc)
new_esEs8(zxw79000, zxw80000, ty_Bool) → new_esEs14(zxw79000, zxw80000)
new_addToFM_C3(EmptyFM, zxw300, zxw31, h, ba, bb) → Branch(Right(zxw300), zxw31, Pos(Succ(Zero)), new_emptyFM(h, ba, bb), new_emptyFM(h, ba, bb))
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Double) → new_ltEs15(zxw79000, zxw80000)
new_esEs28(zxw4000, zxw3000, app(app(ty_@2, ced), cee)) → new_esEs5(zxw4000, zxw3000, ced, cee)
new_splitLT5(EmptyFM, zxw400, h, ba, bb) → new_emptyFM(h, ba, bb)
new_esEs34(zxw400, zxw300, ty_Int) → new_esEs11(zxw400, zxw300)
new_ltEs19(zxw7900, zxw8000, app(app(app(ty_@3, ce), cf), cg)) → new_ltEs6(zxw7900, zxw8000, ce, cf, cg)
new_lt4(zxw79000, zxw80000, ty_Char) → new_lt9(zxw79000, zxw80000)
new_esEs32(zxw20, zxw15, app(app(app(ty_@3, dfh), dga), dgb)) → new_esEs4(zxw20, zxw15, dfh, dga, dgb)
new_esEs22(zxw4000, zxw3000, app(app(app(ty_@3, bhc), bhd), bhe)) → new_esEs4(zxw4000, zxw3000, bhc, bhd, bhe)
new_esEs22(zxw4000, zxw3000, app(ty_[], bge)) → new_esEs13(zxw4000, zxw3000, bge)
new_esEs23(zxw4000, zxw3000, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_ltEs14(Right(zxw79000), Right(zxw80000), dd, ty_@0) → new_ltEs8(zxw79000, zxw80000)
new_esEs28(zxw4000, zxw3000, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Float, gg) → new_esEs17(zxw4000, zxw3000)
new_esEs27(zxw4001, zxw3001, ty_Int) → new_esEs11(zxw4001, zxw3001)
new_esEs19(zxw79001, zxw80001, app(app(app(ty_@3, bbd), bbe), bbf)) → new_esEs4(zxw79001, zxw80001, bbd, bbe, bbf)
new_primCmpInt(Pos(Succ(zxw7900)), Neg(zxw800)) → GT
new_esEs7(Right(zxw4000), Right(zxw3000), gf, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_ltEs19(zxw7900, zxw8000, ty_Int) → new_ltEs9(zxw7900, zxw8000)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(app(app(ty_@3, dgc), dgd), dge), de) → new_ltEs6(zxw79000, zxw80000, dgc, dgd, dge)
new_compare33(zxw20, zxw15, bg, bh) → new_compare26(Left(zxw20), Left(zxw15), new_esEs32(zxw20, zxw15, bg), bg, bh)
new_splitGT30(Right(zxw300), zxw31, zxw32, zxw33, zxw34, Right(zxw400), h, ba, bb) → new_splitGT26(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs9(new_compare26(Right(zxw400), Right(zxw300), new_esEs34(zxw400, zxw300, ba), h, ba), GT), h, ba, bb)
new_lt4(zxw79000, zxw80000, ty_@0) → new_lt7(zxw79000, zxw80000)
new_addToFM_C22(zxw340, zxw341, zxw342, zxw343, zxw344, zxw300, zxw31, True, h, ba, bb) → new_mkBalBranch(zxw340, zxw341, new_addToFM_C3(zxw343, zxw300, zxw31, h, ba, bb), zxw344, h, ba, bb)
new_lt20(zxw79001, zxw80001, ty_Double) → new_lt15(zxw79001, zxw80001)
new_esEs26(zxw4002, zxw3002, ty_@0) → new_esEs10(zxw4002, zxw3002)
new_primMulInt(Pos(zxw40000), Pos(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_lt19(zxw79000, zxw80000, ty_Float) → new_lt16(zxw79000, zxw80000)
new_esEs30(zxw400, zxw300, app(app(ty_@2, hf), hg)) → new_esEs5(zxw400, zxw300, hf, hg)
new_lt19(zxw79000, zxw80000, ty_Bool) → new_lt12(zxw79000, zxw80000)
new_esEs7(Left(zxw4000), Left(zxw3000), ty_Char, gg) → new_esEs12(zxw4000, zxw3000)
new_esEs23(zxw4000, zxw3000, ty_Ordering) → new_esEs9(zxw4000, zxw3000)
new_primMulInt(Neg(zxw40000), Neg(zxw30000)) → Pos(new_primMulNat0(zxw40000, zxw30000))
new_lt4(zxw79000, zxw80000, ty_Float) → new_lt16(zxw79000, zxw80000)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(ty_[], ebb)) → new_ltEs11(zxw79000, zxw80000, ebb)
new_ltEs5(zxw79001, zxw80001, app(app(app(ty_@3, cge), cgf), cgg)) → new_ltEs6(zxw79001, zxw80001, cge, cgf, cgg)
new_primCmpNat2(Zero, Zero) → EQ
new_esEs20(zxw79000, zxw80000, ty_Integer) → new_esEs15(zxw79000, zxw80000)
new_mkBalBranch6Size_l(zxw50, zxw51, zxw99, zxw54, h, ba, bb) → new_sizeFM0(zxw99, h, ba, bb)
new_mkBalBranch6MkBalBranch4(zxw50, zxw51, zxw99, EmptyFM, True, h, ba, bb) → error([])
new_primEqNat0(Succ(zxw40000), Zero) → False
new_primEqNat0(Zero, Succ(zxw30000)) → False
new_esEs22(zxw4000, zxw3000, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_esEs21(zxw4001, zxw3001, ty_@0) → new_esEs10(zxw4001, zxw3001)
new_esEs20(zxw79000, zxw80000, ty_Bool) → new_esEs14(zxw79000, zxw80000)
new_ltEs5(zxw79001, zxw80001, app(ty_[], cgh)) → new_ltEs11(zxw79001, zxw80001, cgh)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs23(zxw4000, zxw3000, app(ty_Ratio, bhf)) → new_esEs18(zxw4000, zxw3000, bhf)
new_esEs33(zxw400, zxw300, app(ty_Maybe, gc)) → new_esEs6(zxw400, zxw300, gc)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(app(ty_@2, ebc), ebd)) → new_ltEs4(zxw79000, zxw80000, ebc, ebd)
new_splitLT26(zxw60, zxw61, zxw62, zxw63, zxw64, zxw65, False, bd, be, bf) → new_splitLT13(zxw60, zxw61, zxw62, zxw63, zxw64, zxw65, new_esEs9(new_compare36(zxw65, zxw60, bd, be), GT), bd, be, bf)
new_addToFM_C12(zxw190, zxw191, zxw192, zxw193, zxw194, zxw15, zxw16, False, bg, bh, ca) → Branch(Left(zxw15), new_addToFM0(zxw191, zxw16, ca), zxw192, zxw193, zxw194)
new_primCmpInt(Pos(Succ(zxw7900)), Pos(zxw800)) → new_primCmpNat0(zxw7900, zxw800)
new_primCmpNat2(Succ(zxw79000), Succ(zxw80000)) → new_primCmpNat2(zxw79000, zxw80000)
new_esEs34(zxw400, zxw300, ty_Bool) → new_esEs14(zxw400, zxw300)
new_ltEs5(zxw79001, zxw80001, ty_Int) → new_ltEs9(zxw79001, zxw80001)
new_esEs27(zxw4001, zxw3001, app(app(ty_@2, cdb), cdc)) → new_esEs5(zxw4001, zxw3001, cdb, cdc)
new_compare26(Right(zxw7900), Left(zxw8000), False, cc, cd) → GT
new_primCmpNat0(zxw7900, Zero) → GT
new_esEs33(zxw400, zxw300, ty_Double) → new_esEs16(zxw400, zxw300)
new_esEs23(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_@0, de) → new_ltEs8(zxw79000, zxw80000)
new_esEs21(zxw4001, zxw3001, app(app(ty_Either, bfg), bfh)) → new_esEs7(zxw4001, zxw3001, bfg, bfh)
new_ltEs21(zxw79002, zxw80002, app(ty_Maybe, bdg)) → new_ltEs18(zxw79002, zxw80002, bdg)
new_mkBalBranch6MkBalBranch3(zxw50, zxw51, EmptyFM, zxw54, True, h, ba, bb) → error([])
new_esEs22(zxw4000, zxw3000, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_splitGT4(Branch(zxw340, zxw341, zxw342, zxw343, zxw344), zxw400, h, ba, bb) → new_splitGT30(zxw340, zxw341, zxw342, zxw343, zxw344, Right(zxw400), h, ba, bb)
new_splitLT26(zxw60, zxw61, zxw62, zxw63, zxw64, zxw65, True, bd, be, bf) → new_splitLT4(zxw63, zxw65, bd, be, bf)
new_primMinusNat0(Zero, Zero) → Pos(Zero)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Bool) → new_ltEs12(zxw79000, zxw80000)
new_splitLT24(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, False, h, ba, bb) → new_splitLT16(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs9(new_compare34(zxw400, zxw300, h, ba), GT), h, ba, bb)
new_compare29(zxw79000, zxw80000, app(ty_Maybe, bfa)) → new_compare27(zxw79000, zxw80000, bfa)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw8000))) → GT
new_lt20(zxw79001, zxw80001, ty_Float) → new_lt16(zxw79001, zxw80001)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(ty_Maybe, dhd), de) → new_ltEs18(zxw79000, zxw80000, dhd)
new_lt17(zxw79000, zxw80000, cb) → new_esEs9(new_compare8(zxw79000, zxw80000, cb), LT)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Ordering) → new_ltEs7(zxw79000, zxw80000)
new_compare30(@0, @0) → EQ
new_lt19(zxw79000, zxw80000, app(ty_[], bba)) → new_lt10(zxw79000, zxw80000, bba)
new_esEs32(zxw20, zxw15, ty_Int) → new_esEs11(zxw20, zxw15)
new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_esEs21(zxw4001, zxw3001, app(app(app(ty_@3, bga), bgb), bgc)) → new_esEs4(zxw4001, zxw3001, bga, bgb, bgc)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs20(zxw79000, zxw80000, app(ty_Ratio, cb)) → new_esEs18(zxw79000, zxw80000, cb)
new_esEs6(Just(zxw4000), Just(zxw3000), app(app(app(ty_@3, daf), dag), dah)) → new_esEs4(zxw4000, zxw3000, daf, dag, dah)
new_ltEs18(Just(zxw79000), Just(zxw80000), app(app(ty_Either, ebe), ebf)) → new_ltEs14(zxw79000, zxw80000, ebe, ebf)
new_emptyFM(h, ba, bb) → EmptyFM
new_esEs24(zxw4001, zxw3001, ty_Int) → new_esEs11(zxw4001, zxw3001)
new_mkVBalBranch3MkVBalBranch21(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, False, bg, bh, ca) → new_mkVBalBranch3MkVBalBranch12(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, zxw15, zxw16, new_lt8(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, bg, bh, ca)), new_mkVBalBranch3Size_l(zxw190, zxw191, zxw192, zxw193, zxw194, zxw1070, zxw1071, zxw1072, zxw1073, zxw1074, bg, bh, ca)), bg, bh, ca)
new_splitGT13(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, True, h, ba, bb) → new_mkVBalBranch2(zxw300, zxw31, new_splitGT4(zxw33, zxw400, h, ba, bb), zxw34, h, ba, bb)
new_esEs30(zxw400, zxw300, ty_Ordering) → new_esEs9(zxw400, zxw300)
new_esEs8(zxw79000, zxw80000, ty_Ordering) → new_esEs9(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), dd, ty_Ordering) → new_ltEs7(zxw79000, zxw80000)
new_esEs34(zxw400, zxw300, ty_Integer) → new_esEs15(zxw400, zxw300)
new_esEs20(zxw79000, zxw80000, app(app(ty_Either, bbb), bbc)) → new_esEs7(zxw79000, zxw80000, bbb, bbc)
new_splitGT5(Branch(zxw340, zxw341, zxw342, zxw343, zxw344), zxw400, h, ba, bb) → new_splitGT30(zxw340, zxw341, zxw342, zxw343, zxw344, Left(zxw400), h, ba, bb)
new_compare29(zxw79000, zxw80000, app(ty_Ratio, beh)) → new_compare8(zxw79000, zxw80000, beh)
new_mkBalBranch6MkBalBranch3(zxw50, zxw51, zxw99, zxw54, False, h, ba, bb) → new_mkBranch(Succ(Zero), zxw50, zxw51, zxw99, zxw54, app(app(ty_Either, h), ba), bb)
new_lt4(zxw79000, zxw80000, app(app(ty_@2, cfg), cfh)) → new_lt11(zxw79000, zxw80000, cfg, cfh)
new_compare29(zxw79000, zxw80000, ty_Float) → new_compare7(zxw79000, zxw80000)
new_primPlusInt(Pos(zxw1890), Pos(zxw1800)) → Pos(new_primPlusNat1(zxw1890, zxw1800))
new_esEs19(zxw79001, zxw80001, app(app(ty_@2, bbh), bca)) → new_esEs5(zxw79001, zxw80001, bbh, bca)
new_esEs10(@0, @0) → True
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_splitLT5(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw400, h, ba, bb) → new_splitLT30(zxw330, zxw331, zxw332, zxw333, zxw334, Left(zxw400), h, ba, bb)
new_compare29(zxw79000, zxw80000, ty_Double) → new_compare6(zxw79000, zxw80000)
new_splitLT30(Right(zxw300), zxw31, zxw32, zxw33, zxw34, Right(zxw400), h, ba, bb) → new_splitLT26(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs9(new_compare26(Right(zxw400), Right(zxw300), new_esEs30(zxw400, zxw300, ba), h, ba), LT), h, ba, bb)
new_esEs20(zxw79000, zxw80000, app(ty_Maybe, bae)) → new_esEs6(zxw79000, zxw80000, bae)
new_ltEs14(Left(zxw79000), Right(zxw80000), dd, de) → True
new_addToFM_C21(zxw190, zxw191, zxw192, zxw193, zxw194, zxw15, zxw16, True, bg, bh, ca) → new_mkBalBranch(zxw190, zxw191, new_addToFM_C4(zxw193, zxw15, zxw16, bg, bh, ca), zxw194, bg, bh, ca)
new_esEs28(zxw4000, zxw3000, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Float) → new_ltEs16(zxw79000, zxw80000)
new_compare29(zxw79000, zxw80000, app(app(ty_Either, bef), beg)) → new_compare15(zxw79000, zxw80000, bef, beg)
new_esEs19(zxw79001, zxw80001, ty_Double) → new_esEs16(zxw79001, zxw80001)
new_esEs30(zxw400, zxw300, ty_Bool) → new_esEs14(zxw400, zxw300)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_ltEs20(zxw7900, zxw8000, app(app(ty_Either, ef), eg)) → new_ltEs14(zxw7900, zxw8000, ef, eg)
new_asAs(False, zxw230) → False
new_ltEs13(zxw7900, zxw8000) → new_fsEs(new_compare32(zxw7900, zxw8000))
new_primMulInt(Neg(zxw40000), Pos(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_primMulInt(Pos(zxw40000), Neg(zxw30000)) → Neg(new_primMulNat0(zxw40000, zxw30000))
new_compare34(zxw400, zxw300, h, ba) → new_compare26(Left(zxw400), Right(zxw300), False, h, ba)
new_ltEs19(zxw7900, zxw8000, app(app(ty_Either, dd), de)) → new_ltEs14(zxw7900, zxw8000, dd, de)
new_sizeFM1(EmptyFM, fd, ff) → Pos(Zero)
new_ltEs20(zxw7900, zxw8000, app(ty_[], ec)) → new_ltEs11(zxw7900, zxw8000, ec)
new_esEs13([], :(zxw3000, zxw3001), gb) → False
new_esEs13(:(zxw4000, zxw4001), [], gb) → False
new_esEs29(zxw400, zxw300, ty_Char) → new_esEs12(zxw400, zxw300)
new_primMulNat0(Succ(zxw400000), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300000)) → Zero
new_compare16(zxw79, zxw80) → new_primCmpInt(zxw79, zxw80)
new_compare25(zxw79000, zxw80000, False, baf, bag, bah) → new_compare12(zxw79000, zxw80000, new_ltEs6(zxw79000, zxw80000, baf, bag, bah), baf, bag, bah)
new_esEs34(zxw400, zxw300, ty_@0) → new_esEs10(zxw400, zxw300)
new_esEs7(Right(zxw4000), Right(zxw3000), gf, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), app(ty_Maybe, daa)) → new_esEs6(zxw4000, zxw3000, daa)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(app(ty_@2, dgg), dgh), de) → new_ltEs4(zxw79000, zxw80000, dgg, dgh)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_@0) → new_esEs10(zxw4000, zxw3000)
new_splitLT15(zxw45, zxw46, zxw47, zxw48, zxw49, zxw50, False, cbb, cbc, cbd) → zxw48
new_esEs7(Left(zxw4000), Left(zxw3000), app(ty_[], dcf), gg) → new_esEs13(zxw4000, zxw3000, dcf)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(ty_[], dgf), de) → new_ltEs11(zxw79000, zxw80000, dgf)
new_splitGT24(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, True, h, ba, bb) → new_splitGT4(zxw34, zxw400, h, ba, bb)
new_esEs29(zxw400, zxw300, ty_Int) → new_esEs11(zxw400, zxw300)
new_esEs31(zxw35, zxw30, ty_Double) → new_esEs16(zxw35, zxw30)
new_esEs7(Right(zxw4000), Right(zxw3000), gf, ty_Float) → new_esEs17(zxw4000, zxw3000)
new_compare31(zxw79000, zxw80000) → new_compare23(zxw79000, zxw80000, new_esEs14(zxw79000, zxw80000))
new_ltEs18(Nothing, Just(zxw80000), dg) → True
new_esEs28(zxw4000, zxw3000, ty_Bool) → new_esEs14(zxw4000, zxw3000)
new_ltEs21(zxw79002, zxw80002, ty_Double) → new_ltEs15(zxw79002, zxw80002)
new_primCmpNat1(Succ(zxw8000), zxw7900) → new_primCmpNat2(zxw8000, zxw7900)
new_ltEs12(True, True) → True
new_esEs23(zxw4000, zxw3000, app(ty_Maybe, bhh)) → new_esEs6(zxw4000, zxw3000, bhh)
new_primCmpNat2(Succ(zxw79000), Zero) → GT
new_esEs8(zxw79000, zxw80000, ty_Integer) → new_esEs15(zxw79000, zxw80000)
new_ltEs14(Right(zxw79000), Right(zxw80000), dd, app(app(ty_Either, eac), ead)) → new_ltEs14(zxw79000, zxw80000, eac, ead)
new_esEs28(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_ltEs6(@3(zxw79000, zxw79001, zxw79002), @3(zxw80000, zxw80001, zxw80002), ce, cf, cg) → new_pePe(new_lt19(zxw79000, zxw80000, ce), new_asAs(new_esEs20(zxw79000, zxw80000, ce), new_pePe(new_lt20(zxw79001, zxw80001, cf), new_asAs(new_esEs19(zxw79001, zxw80001, cf), new_ltEs21(zxw79002, zxw80002, cg)))))
new_lt16(zxw79000, zxw80000) → new_esEs9(new_compare7(zxw79000, zxw80000), LT)
new_esEs23(zxw4000, zxw3000, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Integer, de) → new_ltEs13(zxw79000, zxw80000)
new_mkVBalBranch2(zxw15, zxw16, Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), EmptyFM, bg, bh, ca) → new_addToFM(Branch(zxw1070, zxw1071, zxw1072, zxw1073, zxw1074), zxw15, zxw16, bg, bh, ca)
new_addToFM_C4(EmptyFM, zxw15, zxw16, bg, bh, ca) → Branch(Left(zxw15), zxw16, Pos(Succ(Zero)), new_emptyFM(bg, bh, ca), new_emptyFM(bg, bh, ca))
new_esEs34(zxw400, zxw300, app(ty_Ratio, hc)) → new_esEs18(zxw400, zxw300, hc)
new_ltEs12(False, True) → True
new_addToFM_C11(zxw340, zxw341, zxw342, zxw343, zxw344, zxw300, zxw31, True, h, ba, bb) → new_mkBalBranch(zxw340, zxw341, zxw343, new_addToFM_C3(zxw344, zxw300, zxw31, h, ba, bb), h, ba, bb)
new_esEs23(zxw4000, zxw3000, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs8(zxw79000, zxw80000, app(ty_Ratio, cgc)) → new_esEs18(zxw79000, zxw80000, cgc)
new_esEs23(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_gt(zxw179, zxw178) → new_esEs9(new_compare16(zxw179, zxw178), GT)
new_esEs14(True, True) → True
new_compare111(zxw79000, zxw80000, False, bae) → GT
new_esEs27(zxw4001, zxw3001, ty_Bool) → new_esEs14(zxw4001, zxw3001)
new_esEs31(zxw35, zxw30, app(ty_[], dbd)) → new_esEs13(zxw35, zxw30, dbd)
new_mkVBalBranch2(zxw15, zxw16, EmptyFM, zxw19, bg, bh, ca) → new_addToFM(zxw19, zxw15, zxw16, bg, bh, ca)
new_addToFM_C22(zxw340, zxw341, zxw342, zxw343, zxw344, zxw300, zxw31, False, h, ba, bb) → new_addToFM_C11(zxw340, zxw341, zxw342, zxw343, zxw344, zxw300, zxw31, new_esEs9(new_compare15(Right(zxw300), zxw340, h, ba), GT), h, ba, bb)
new_esEs20(zxw79000, zxw80000, ty_Ordering) → new_esEs9(zxw79000, zxw80000)
new_ltEs19(zxw7900, zxw8000, ty_@0) → new_ltEs8(zxw7900, zxw8000)
new_primMinusNat0(Zero, Succ(zxw18000)) → Neg(Succ(zxw18000))
new_ltEs14(Right(zxw79000), Right(zxw80000), dd, ty_Int) → new_ltEs9(zxw79000, zxw80000)
new_ltEs14(Left(zxw79000), Left(zxw80000), app(app(ty_Either, dha), dhb), de) → new_ltEs14(zxw79000, zxw80000, dha, dhb)
new_splitLT23(zxw45, zxw46, zxw47, zxw48, zxw49, zxw50, True, cbb, cbc, cbd) → new_splitLT5(zxw48, zxw50, cbb, cbc, cbd)
new_splitLT13(zxw60, zxw61, zxw62, zxw63, zxw64, zxw65, True, bd, be, bf) → new_mkVBalBranch1(zxw60, zxw61, zxw63, new_splitLT4(zxw64, zxw65, bd, be, bf), bd, be, bf)
new_lt19(zxw79000, zxw80000, ty_Integer) → new_lt13(zxw79000, zxw80000)
new_esEs20(zxw79000, zxw80000, ty_Float) → new_esEs17(zxw79000, zxw80000)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba, bb) → zxw52
new_esEs7(Right(zxw4000), Right(zxw3000), gf, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_splitLT25(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, False, h, ba, bb) → new_splitLT14(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs9(new_compare35(zxw400, zxw300, h, ba), GT), h, ba, bb)
new_esEs34(zxw400, zxw300, app(ty_Maybe, he)) → new_esEs6(zxw400, zxw300, he)
new_compare11(zxw79000, zxw80000, False) → GT
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Ordering, de) → new_ltEs7(zxw79000, zxw80000)
new_esEs4(@3(zxw4000, zxw4001, zxw4002), @3(zxw3000, zxw3001, zxw3002), gh, ha, hb) → new_asAs(new_esEs28(zxw4000, zxw3000, gh), new_asAs(new_esEs27(zxw4001, zxw3001, ha), new_esEs26(zxw4002, zxw3002, hb)))
new_esEs6(Just(zxw4000), Just(zxw3000), app(ty_[], chh)) → new_esEs13(zxw4000, zxw3000, chh)
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_Int) → new_ltEs9(zxw79000, zxw80000)
new_mkBalBranch6MkBalBranch3(zxw50, zxw51, Branch(zxw990, zxw991, zxw992, zxw993, zxw994), zxw54, True, h, ba, bb) → new_mkBalBranch6MkBalBranch11(zxw50, zxw51, zxw990, zxw991, zxw992, zxw993, zxw994, zxw54, new_lt8(new_sizeFM0(zxw994, h, ba, bb), new_sr(Pos(Succ(Succ(Zero))), new_sizeFM0(zxw993, h, ba, bb))), h, ba, bb)
new_addToFM_C12(zxw190, zxw191, zxw192, zxw193, zxw194, zxw15, zxw16, True, bg, bh, ca) → new_mkBalBranch(zxw190, zxw191, zxw193, new_addToFM_C4(zxw194, zxw15, zxw16, bg, bh, ca), bg, bh, ca)
new_esEs9(EQ, LT) → False
new_esEs9(LT, EQ) → False
new_compare26(Right(zxw7900), Right(zxw8000), False, cc, cd) → new_compare14(zxw7900, zxw8000, new_ltEs20(zxw7900, zxw8000, cd), cc, cd)
new_compare11(zxw79000, zxw80000, True) → LT
new_ltEs5(zxw79001, zxw80001, ty_@0) → new_ltEs8(zxw79001, zxw80001)
new_splitLT14(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, False, h, ba, bb) → zxw33
new_lt20(zxw79001, zxw80001, ty_Bool) → new_lt12(zxw79001, zxw80001)
new_esEs30(zxw400, zxw300, ty_Integer) → new_esEs15(zxw400, zxw300)
new_compare14(zxw242, zxw243, True, cah, cba) → LT
new_esEs29(zxw400, zxw300, app(app(ty_Either, gf), gg)) → new_esEs7(zxw400, zxw300, gf, gg)
new_esEs32(zxw20, zxw15, app(ty_Ratio, dfa)) → new_esEs18(zxw20, zxw15, dfa)
new_esEs14(False, False) → True
new_esEs18(:%(zxw4000, zxw4001), :%(zxw3000, zxw3001), ga) → new_asAs(new_esEs25(zxw4000, zxw3000, ga), new_esEs24(zxw4001, zxw3001, ga))
new_compare26(Left(zxw7900), Left(zxw8000), False, cc, cd) → new_compare13(zxw7900, zxw8000, new_ltEs19(zxw7900, zxw8000, cc), cc, cd)
new_esEs33(zxw400, zxw300, ty_Float) → new_esEs17(zxw400, zxw300)
new_splitLT14(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, True, h, ba, bb) → new_mkVBalBranch2(zxw300, zxw31, zxw33, new_splitLT4(zxw34, zxw400, h, ba, bb), h, ba, bb)
new_ltEs19(zxw7900, zxw8000, ty_Double) → new_ltEs15(zxw7900, zxw8000)
new_ltEs7(EQ, LT) → False
new_esEs22(zxw4000, zxw3000, ty_Double) → new_esEs16(zxw4000, zxw3000)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Char) → new_esEs12(zxw4000, zxw3000)
new_ltEs7(LT, LT) → True
new_lt20(zxw79001, zxw80001, app(app(app(ty_@3, bbd), bbe), bbf)) → new_lt5(zxw79001, zxw80001, bbd, bbe, bbf)
new_esEs29(zxw400, zxw300, ty_@0) → new_esEs10(zxw400, zxw300)
new_lt14(zxw790, zxw800, cc, cd) → new_esEs9(new_compare15(zxw790, zxw800, cc, cd), LT)
new_ltEs9(zxw7900, zxw8000) → new_fsEs(new_compare16(zxw7900, zxw8000))
new_esEs22(zxw4000, zxw3000, ty_Integer) → new_esEs15(zxw4000, zxw3000)
new_compare29(zxw79000, zxw80000, ty_Ordering) → new_compare18(zxw79000, zxw80000)
new_primPlusNat1(Zero, Zero) → Zero
new_esEs26(zxw4002, zxw3002, ty_Ordering) → new_esEs9(zxw4002, zxw3002)
new_esEs19(zxw79001, zxw80001, ty_Integer) → new_esEs15(zxw79001, zxw80001)
new_asAs(True, zxw230) → zxw230
new_ltEs14(Left(zxw79000), Left(zxw80000), ty_Char, de) → new_ltEs10(zxw79000, zxw80000)
new_esEs25(zxw4000, zxw3000, ty_Int) → new_esEs11(zxw4000, zxw3000)
new_ltEs7(LT, GT) → True
new_ltEs5(zxw79001, zxw80001, ty_Float) → new_ltEs16(zxw79001, zxw80001)
new_esEs6(Just(zxw4000), Just(zxw3000), ty_Float) → new_esEs17(zxw4000, zxw3000)
new_primMulNat0(Succ(zxw400000), Succ(zxw300000)) → new_primPlusNat0(new_primMulNat0(zxw400000, Succ(zxw300000)), zxw300000)
new_esEs27(zxw4001, zxw3001, app(ty_[], cch)) → new_esEs13(zxw4001, zxw3001, cch)
new_esEs7(Right(zxw4000), Right(zxw3000), gf, app(ty_Ratio, ddg)) → new_esEs18(zxw4000, zxw3000, ddg)
new_splitLT30(Left(zxw300), zxw31, zxw32, zxw33, zxw34, Left(zxw400), h, ba, bb) → new_splitLT23(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs9(new_compare26(Left(zxw400), Left(zxw300), new_esEs29(zxw400, zxw300, h), h, ba), LT), h, ba, bb)
new_esEs6(Just(zxw4000), Just(zxw3000), app(app(ty_Either, dad), dae)) → new_esEs7(zxw4000, zxw3000, dad, dae)
new_esEs32(zxw20, zxw15, ty_Double) → new_esEs16(zxw20, zxw15)
new_compare28(zxw79000, zxw80000, False, bae) → new_compare111(zxw79000, zxw80000, new_ltEs18(zxw79000, zxw80000, bae), bae)
new_esEs28(zxw4000, zxw3000, app(ty_Ratio, cea)) → new_esEs18(zxw4000, zxw3000, cea)
new_compare1(:(zxw79000, zxw79001), [], da) → GT
new_lt4(zxw79000, zxw80000, ty_Integer) → new_lt13(zxw79000, zxw80000)
new_esEs30(zxw400, zxw300, ty_Int) → new_esEs11(zxw400, zxw300)
new_mkBalBranch6MkBalBranch5(zxw50, zxw51, zxw99, zxw54, True, h, ba, bb) → new_mkBranch(Zero, zxw50, zxw51, zxw99, zxw54, app(app(ty_Either, h), ba), bb)
new_esEs19(zxw79001, zxw80001, ty_@0) → new_esEs10(zxw79001, zxw80001)
new_compare29(zxw79000, zxw80000, ty_@0) → new_compare30(zxw79000, zxw80000)
new_ltEs19(zxw7900, zxw8000, ty_Integer) → new_ltEs13(zxw7900, zxw8000)
new_ltEs14(Right(zxw79000), Right(zxw80000), dd, app(ty_Ratio, eae)) → new_ltEs17(zxw79000, zxw80000, eae)
new_mkBranch(zxw352, zxw353, zxw354, zxw355, zxw356, fd, ff) → Branch(zxw353, zxw354, new_primPlusInt(new_primPlusInt(Pos(Succ(Zero)), new_sizeFM1(zxw355, fd, ff)), new_sizeFM1(zxw356, fd, ff)), zxw355, zxw356)
new_ltEs14(Right(zxw79000), Right(zxw80000), dd, ty_Integer) → new_ltEs13(zxw79000, zxw80000)
new_ltEs19(zxw7900, zxw8000, ty_Ordering) → new_ltEs7(zxw7900, zxw8000)
new_compare28(zxw79000, zxw80000, True, bae) → EQ
new_esEs31(zxw35, zxw30, ty_Int) → new_esEs11(zxw35, zxw30)
new_esEs26(zxw4002, zxw3002, ty_Double) → new_esEs16(zxw4002, zxw3002)
new_esEs30(zxw400, zxw300, ty_Double) → new_esEs16(zxw400, zxw300)
new_esEs29(zxw400, zxw300, ty_Float) → new_esEs17(zxw400, zxw300)
new_esEs33(zxw400, zxw300, ty_Int) → new_esEs11(zxw400, zxw300)
new_compare10(zxw79000, zxw80000, True) → LT
new_esEs31(zxw35, zxw30, ty_Bool) → new_esEs14(zxw35, zxw30)
new_esEs19(zxw79001, zxw80001, app(ty_[], bbg)) → new_esEs13(zxw79001, zxw80001, bbg)
new_esEs29(zxw400, zxw300, ty_Bool) → new_esEs14(zxw400, zxw300)
new_compare10(zxw79000, zxw80000, False) → GT
new_esEs9(LT, LT) → True
new_ltEs20(zxw7900, zxw8000, ty_Char) → new_ltEs10(zxw7900, zxw8000)
new_ltEs20(zxw7900, zxw8000, ty_Ordering) → new_ltEs7(zxw7900, zxw8000)
new_primCompAux00(zxw276, GT) → GT
new_esEs31(zxw35, zxw30, app(ty_Maybe, dbe)) → new_esEs6(zxw35, zxw30, dbe)
new_splitGT30(Left(zxw300), zxw31, zxw32, zxw33, zxw34, Left(zxw400), h, ba, bb) → new_splitGT25(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs9(new_compare26(Left(zxw400), Left(zxw300), new_esEs33(zxw400, zxw300, h), h, ba), GT), h, ba, bb)
new_compare18(zxw79000, zxw80000) → new_compare24(zxw79000, zxw80000, new_esEs9(zxw79000, zxw80000))
new_ltEs18(Just(zxw79000), Just(zxw80000), ty_@0) → new_ltEs8(zxw79000, zxw80000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs7(Right(zxw4000), Right(zxw3000), gf, ty_@0) → new_esEs10(zxw4000, zxw3000)
new_esEs29(zxw400, zxw300, ty_Ordering) → new_esEs9(zxw400, zxw300)
new_lt19(zxw79000, zxw80000, ty_Char) → new_lt9(zxw79000, zxw80000)
new_mkBalBranch6MkBalBranch11(zxw50, zxw51, zxw990, zxw991, zxw992, zxw993, Branch(zxw9940, zxw9941, zxw9942, zxw9943, zxw9944), zxw54, False, h, ba, bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))), zxw9940, zxw9941, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), zxw990, zxw991, zxw993, zxw9943, app(app(ty_Either, h), ba), bb), new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), zxw50, zxw51, zxw9944, zxw54, app(app(ty_Either, h), ba), bb), app(app(ty_Either, h), ba), bb)
new_esEs28(zxw4000, zxw3000, ty_Char) → new_esEs12(zxw4000, zxw3000)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_ltEs19(zxw7900, zxw8000, app(ty_Maybe, dg)) → new_ltEs18(zxw7900, zxw8000, dg)
new_esEs27(zxw4001, zxw3001, ty_Integer) → new_esEs15(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, app(ty_Ratio, bfb)) → new_esEs18(zxw4001, zxw3001, bfb)
new_primCmpInt(Neg(Succ(zxw7900)), Pos(zxw800)) → LT
new_esEs23(zxw4000, zxw3000, app(ty_[], bhg)) → new_esEs13(zxw4000, zxw3000, bhg)
new_esEs19(zxw79001, zxw80001, ty_Char) → new_esEs12(zxw79001, zxw80001)
new_mkBalBranch(zxw50, zxw51, zxw99, zxw54, h, ba, bb) → new_mkBalBranch6MkBalBranch5(zxw50, zxw51, zxw99, zxw54, new_esEs9(new_primCmpInt(new_primPlusInt(new_mkBalBranch6Size_l(zxw50, zxw51, zxw99, zxw54, h, ba, bb), new_mkBalBranch6Size_r(zxw50, zxw51, zxw99, zxw54, h, ba, bb)), Pos(Succ(Succ(Zero)))), LT), h, ba, bb)
new_ltEs17(zxw7900, zxw8000, df) → new_fsEs(new_compare8(zxw7900, zxw8000, df))
new_not(True) → False
new_primMinusNat0(Succ(zxw18900), Succ(zxw18000)) → new_primMinusNat0(zxw18900, zxw18000)
new_ltEs4(@2(zxw79000, zxw79001), @2(zxw80000, zxw80001), db, dc) → new_pePe(new_lt4(zxw79000, zxw80000, db), new_asAs(new_esEs8(zxw79000, zxw80000, db), new_ltEs5(zxw79001, zxw80001, dc)))
new_compare1([], [], da) → EQ
new_esEs6(Just(zxw4000), Just(zxw3000), app(ty_Ratio, chg)) → new_esEs18(zxw4000, zxw3000, chg)

The set Q consists of the following terms:

new_compare23(x0, x1, True)
new_lt6(x0, x1)
new_compare28(x0, x1, False, x2)
new_splitLT14(x0, x1, x2, x3, x4, x5, False, x6, x7, x8)
new_compare25(x0, x1, False, x2, x3, x4)
new_addToFM_C21(x0, x1, x2, x3, x4, x5, x6, True, x7, x8, x9)
new_esEs18(:%(x0, x1), :%(x2, x3), x4)
new_lt19(x0, x1, ty_Integer)
new_ltEs18(Just(x0), Just(x1), ty_@0)
new_compare111(x0, x1, False, x2)
new_compare29(x0, x1, app(app(ty_@2, x2), x3))
new_compare16(x0, x1)
new_ltEs20(x0, x1, ty_Double)
new_esEs21(x0, x1, app(ty_[], x2))
new_primPlusInt(Pos(x0), Pos(x1))
new_esEs7(Left(x0), Left(x1), ty_Int, x2)
new_esEs19(x0, x1, ty_Bool)
new_esEs7(Left(x0), Left(x1), ty_@0, x2)
new_compare30(@0, @0)
new_compare1([], [], x0)
new_primCompAux00(x0, GT)
new_primMinusNat0(Zero, Zero)
new_esEs30(x0, x1, ty_@0)
new_lt19(x0, x1, ty_Char)
new_ltEs14(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs30(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Int)
new_esEs32(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Ordering)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_compare17(Char(x0), Char(x1))
new_esEs28(x0, x1, ty_Int)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_primMinusNat0(Succ(x0), Zero)
new_ltEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs21(x0, x1, ty_Ordering)
new_ltEs15(x0, x1)
new_primPlusNat1(Zero, Succ(x0))
new_esEs6(Just(x0), Just(x1), ty_Double)
new_compare24(x0, x1, False)
new_lt20(x0, x1, ty_Char)
new_sizeFM0(EmptyFM, x0, x1, x2)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_compare29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, ty_@0)
new_ltEs14(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_lt4(x0, x1, app(ty_Ratio, x2))
new_splitGT16(x0, x1, x2, x3, x4, x5, True, x6, x7, x8)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs23(x0, x1, ty_Bool)
new_splitGT25(x0, x1, x2, x3, x4, x5, True, x6, x7, x8)
new_sr0(Integer(x0), Integer(x1))
new_esEs33(x0, x1, ty_Float)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs32(x0, x1, app(ty_Maybe, x2))
new_esEs34(x0, x1, ty_Integer)
new_ltEs7(EQ, EQ)
new_splitGT15(x0, x1, x2, x3, x4, x5, False, x6, x7, x8)
new_esEs7(Left(x0), Left(x1), ty_Float, x2)
new_esEs19(x0, x1, ty_Integer)
new_compare110(x0, x1, True, x2, x3)
new_ltEs20(x0, x1, ty_Bool)
new_addToFM_C3(EmptyFM, x0, x1, x2, x3, x4)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs6(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_compare110(x0, x1, False, x2, x3)
new_esEs7(Right(x0), Right(x1), x2, ty_Int)
new_mkBalBranch6MkBalBranch3(x0, x1, Branch(x2, x3, x4, x5, x6), x7, True, x8, x9, x10)
new_compare111(x0, x1, True, x2)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_splitGT4(Branch(x0, x1, x2, x3, x4), x5, x6, x7, x8)
new_ltEs19(x0, x1, ty_Integer)
new_mkBalBranch6MkBalBranch5(x0, x1, x2, x3, True, x4, x5, x6)
new_ltEs5(x0, x1, ty_Integer)
new_addToFM_C12(x0, x1, x2, x3, x4, x5, x6, False, x7, x8, x9)
new_compare29(x0, x1, app(ty_[], x2))
new_ltEs7(EQ, LT)
new_ltEs7(LT, EQ)
new_esEs20(x0, x1, ty_Ordering)
new_esEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs17(Float(x0, x1), Float(x2, x3))
new_splitLT4(EmptyFM, x0, x1, x2, x3)
new_esEs9(LT, GT)
new_esEs9(GT, LT)
new_esEs6(Nothing, Nothing, x0)
new_lt19(x0, x1, ty_Ordering)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs13(:(x0, x1), :(x2, x3), x4)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs29(x0, x1, ty_@0)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs16(x0, x1)
new_sr(x0, x1)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, ty_Double)
new_compare7(Float(x0, x1), Float(x2, x3))
new_ltEs9(x0, x1)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_mkBalBranch6Size_r(x0, x1, x2, x3, x4, x5, x6)
new_esEs9(GT, EQ)
new_esEs9(EQ, GT)
new_esEs34(x0, x1, app(ty_Ratio, x2))
new_lt7(x0, x1)
new_esEs25(x0, x1, ty_Int)
new_primPlusNat0(Zero, x0)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs32(x0, x1, ty_Ordering)
new_splitGT30(Left(x0), x1, x2, x3, x4, Left(x5), x6, x7, x8)
new_ltEs7(LT, LT)
new_esEs7(Left(x0), Left(x1), ty_Char, x2)
new_addToFM_C4(Branch(x0, x1, x2, x3, x4), x5, x6, x7, x8, x9)
new_compare9(x0, x1, x2, x3, x4)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs7(Left(x0), Left(x1), ty_Integer, x2)
new_esEs27(x0, x1, ty_Bool)
new_esEs30(x0, x1, app(ty_[], x2))
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_lt4(x0, x1, ty_Ordering)
new_primEqNat0(Zero, Succ(x0))
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs6(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, ty_Int)
new_esEs15(Integer(x0), Integer(x1))
new_lt19(x0, x1, ty_Int)
new_esEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs26(x0, x1, ty_Double)
new_mkVBalBranch3MkVBalBranch22(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, False, x12, x13, x14)
new_compare1([], :(x0, x1), x2)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6, x7)
new_esEs28(x0, x1, ty_@0)
new_primPlusNat1(Succ(x0), Zero)
new_mkBranch(x0, x1, x2, x3, x4, x5, x6)
new_esEs22(x0, x1, ty_Integer)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs4(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs19(x0, x1, ty_Int)
new_esEs22(x0, x1, app(ty_[], x2))
new_compare29(x0, x1, ty_Integer)
new_primMinusNat0(Zero, Succ(x0))
new_esEs14(True, True)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_splitLT23(x0, x1, x2, x3, x4, x5, True, x6, x7, x8)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Char)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs18(Just(x0), Just(x1), ty_Integer)
new_splitLT25(x0, x1, x2, x3, x4, x5, False, x6, x7, x8)
new_mkBalBranch6MkBalBranch01(x0, x1, x2, x3, x4, x5, x6, x7, True, x8, x9, x10)
new_esEs24(x0, x1, ty_Int)
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_mkVBalBranch3MkVBalBranch11(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, False, x12, x13, x14)
new_primEqNat0(Zero, Zero)
new_esEs16(Double(x0, x1), Double(x2, x3))
new_esEs12(Char(x0), Char(x1))
new_lt4(x0, x1, ty_Char)
new_esEs32(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, ty_Bool)
new_esEs8(x0, x1, ty_Float)
new_lt18(x0, x1, x2)
new_esEs30(x0, x1, ty_Ordering)
new_lt4(x0, x1, app(app(ty_Either, x2), x3))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs23(x0, x1, ty_Integer)
new_esEs29(x0, x1, ty_Bool)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs30(x0, x1, ty_Bool)
new_esEs30(x0, x1, ty_Float)
new_esEs32(x0, x1, ty_@0)
new_mkBalBranch6MkBalBranch01(x0, x1, x2, x3, x4, x5, Branch(x6, x7, x8, x9, x10), x11, False, x12, x13, x14)
new_primCompAux00(x0, LT)
new_esEs27(x0, x1, ty_Integer)
new_esEs20(x0, x1, app(ty_[], x2))
new_esEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_Int)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_ltEs5(x0, x1, ty_Double)
new_esEs8(x0, x1, app(ty_[], x2))
new_ltEs14(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs18(Nothing, Nothing, x0)
new_ltEs18(Just(x0), Just(x1), ty_Char)
new_primMulNat0(Zero, Zero)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt9(x0, x1)
new_splitGT4(EmptyFM, x0, x1, x2, x3)
new_compare29(x0, x1, ty_Double)
new_mkBalBranch6MkBalBranch4(x0, x1, x2, EmptyFM, True, x3, x4, x5)
new_ltEs5(x0, x1, ty_@0)
new_ltEs5(x0, x1, app(ty_Ratio, x2))
new_ltEs14(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_mkVBalBranch3MkVBalBranch12(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, True, x12, x13, x14)
new_esEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_mkVBalBranch3MkVBalBranch21(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, False, x12, x13, x14)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs31(x0, x1, ty_Bool)
new_esEs32(x0, x1, ty_Float)
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_esEs8(x0, x1, ty_Ordering)
new_lt14(x0, x1, x2, x3)
new_compare10(x0, x1, True)
new_splitLT24(x0, x1, x2, x3, x4, x5, False, x6, x7, x8)
new_ltEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs19(x0, x1, ty_Ordering)
new_sIZE_RATIO
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, ty_Double)
new_ltEs19(x0, x1, ty_Bool)
new_ltEs20(x0, x1, ty_Float)
new_esEs29(x0, x1, ty_Char)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, ty_@0)
new_pePe(True, x0)
new_esEs8(x0, x1, app(app(ty_Either, x2), x3))
new_esEs19(x0, x1, ty_Float)
new_primCmpNat2(Zero, Succ(x0))
new_primMulNat0(Zero, Succ(x0))
new_lt16(x0, x1)
new_compare29(x0, x1, ty_Bool)
new_lt5(x0, x1, x2, x3, x4)
new_compare11(x0, x1, True)
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_lt19(x0, x1, app(ty_Maybe, x2))
new_esEs9(EQ, LT)
new_esEs9(LT, EQ)
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs34(x0, x1, ty_Char)
new_ltEs14(Right(x0), Right(x1), x2, ty_Bool)
new_lt19(x0, x1, ty_@0)
new_compare29(x0, x1, app(ty_Ratio, x2))
new_esEs6(Just(x0), Just(x1), ty_Ordering)
new_esEs23(x0, x1, ty_@0)
new_ltEs21(x0, x1, app(ty_Maybe, x2))
new_ltEs5(x0, x1, ty_Char)
new_esEs30(x0, x1, ty_Double)
new_ltEs21(x0, x1, ty_Int)
new_ltEs14(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs26(x0, x1, ty_Float)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_compare29(x0, x1, ty_Ordering)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs21(x0, x1, ty_@0)
new_esEs8(x0, x1, ty_Int)
new_ltEs12(False, False)
new_esEs6(Just(x0), Just(x1), ty_Bool)
new_compare32(Integer(x0), Integer(x1))
new_esEs21(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_Int)
new_primMulNat0(Succ(x0), Succ(x1))
new_compare29(x0, x1, ty_Float)
new_mkBalBranch6MkBalBranch11(x0, x1, x2, x3, x4, x5, x6, x7, True, x8, x9, x10)
new_ltEs21(x0, x1, ty_Integer)
new_esEs6(Just(x0), Just(x1), ty_Float)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs5(x0, x1, ty_Float)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_addToFM_C4(EmptyFM, x0, x1, x2, x3, x4)
new_esEs6(Just(x0), Nothing, x1)
new_ltEs18(Just(x0), Just(x1), ty_Float)
new_esEs32(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Bool)
new_esEs31(x0, x1, ty_Double)
new_primCmpNat1(Zero, x0)
new_ltEs8(x0, x1)
new_esEs29(x0, x1, ty_Integer)
new_ltEs5(x0, x1, app(app(ty_Either, x2), x3))
new_esEs34(x0, x1, ty_Float)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_primPlusNat1(Zero, Zero)
new_esEs30(x0, x1, ty_Integer)
new_esEs8(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_Double)
new_ltEs18(Just(x0), Just(x1), ty_Ordering)
new_primCmpNat2(Zero, Zero)
new_mkVBalBranch1(x0, x1, Branch(x2, x3, x4, x5, x6), Branch(x7, x8, x9, x10, x11), x12, x13, x14)
new_esEs23(x0, x1, app(ty_[], x2))
new_ltEs5(x0, x1, ty_Bool)
new_esEs34(x0, x1, app(app(ty_Either, x2), x3))
new_splitLT24(x0, x1, x2, x3, x4, x5, True, x6, x7, x8)
new_esEs34(x0, x1, ty_Ordering)
new_ltEs18(Nothing, Just(x0), x1)
new_ltEs18(Just(x0), Just(x1), app(ty_[], x2))
new_asAs(False, x0)
new_esEs29(x0, x1, ty_Ordering)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, ty_Char)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs8(x0, x1, app(ty_Ratio, x2))
new_ltEs14(Left(x0), Left(x1), ty_@0, x2)
new_esEs34(x0, x1, app(ty_Maybe, x2))
new_esEs8(x0, x1, ty_Integer)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs33(x0, x1, ty_Ordering)
new_ltEs18(Just(x0), Just(x1), ty_Bool)
new_splitLT25(x0, x1, x2, x3, x4, x5, True, x6, x7, x8)
new_primCmpNat1(Succ(x0), x1)
new_esEs34(x0, x1, ty_Bool)
new_mkBalBranch6MkBalBranch3(x0, x1, EmptyFM, x2, True, x3, x4, x5)
new_splitLT13(x0, x1, x2, x3, x4, x5, True, x6, x7, x8)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs33(x0, x1, ty_Double)
new_addToFM_C21(x0, x1, x2, x3, x4, x5, x6, False, x7, x8, x9)
new_esEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs14(Right(x0), Right(x1), x2, ty_Char)
new_compare15(x0, x1, x2, x3)
new_esEs24(x0, x1, ty_Integer)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs27(x0, x1, ty_@0)
new_gt(x0, x1)
new_esEs31(x0, x1, app(ty_[], x2))
new_esEs33(x0, x1, app(ty_Ratio, x2))
new_splitGT5(Branch(x0, x1, x2, x3, x4), x5, x6, x7, x8)
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs13([], :(x0, x1), x2)
new_lt4(x0, x1, ty_Float)
new_esEs19(x0, x1, ty_Char)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_splitLT5(EmptyFM, x0, x1, x2, x3)
new_lt4(x0, x1, ty_Double)
new_esEs19(x0, x1, ty_Ordering)
new_esEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_mkVBalBranch2(x0, x1, Branch(x2, x3, x4, x5, x6), EmptyFM, x7, x8, x9)
new_esEs33(x0, x1, ty_Int)
new_esEs10(@0, @0)
new_esEs31(x0, x1, ty_@0)
new_esEs33(x0, x1, ty_@0)
new_esEs11(x0, x1)
new_esEs20(x0, x1, ty_Float)
new_primCompAux0(x0, x1, x2, x3)
new_esEs9(GT, GT)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs27(x0, x1, ty_Char)
new_compare11(x0, x1, False)
new_compare23(x0, x1, False)
new_esEs28(x0, x1, ty_Bool)
new_compare24(x0, x1, True)
new_splitLT26(x0, x1, x2, x3, x4, x5, True, x6, x7, x8)
new_primEqNat0(Succ(x0), Zero)
new_esEs23(x0, x1, ty_Ordering)
new_compare1(:(x0, x1), [], x2)
new_primPlusNat1(Succ(x0), Succ(x1))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_esEs34(x0, x1, ty_Int)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_lt20(x0, x1, ty_Int)
new_ltEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_ltEs21(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_Float)
new_addToFM0(x0, x1, x2)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Integer)
new_esEs33(x0, x1, ty_Bool)
new_compare210(x0, x1, False, x2, x3)
new_esEs23(x0, x1, ty_Int)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs33(x0, x1, app(ty_Maybe, x2))
new_compare29(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_lt4(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, ty_Char)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs6(Just(x0), Just(x1), app(ty_[], x2))
new_lt4(x0, x1, ty_@0)
new_esEs23(x0, x1, ty_Char)
new_esEs28(x0, x1, ty_Ordering)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(Left(x0), Left(x1), ty_Int, x2)
new_ltEs18(Just(x0), Just(x1), ty_Double)
new_esEs30(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_Integer)
new_splitLT13(x0, x1, x2, x3, x4, x5, False, x6, x7, x8)
new_compare26(x0, x1, True, x2, x3)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_splitGT23(x0, x1, x2, x3, x4, x5, True, x6, x7, x8)
new_lt20(x0, x1, ty_@0)
new_splitLT4(Branch(x0, x1, x2, x3, x4), x5, x6, x7, x8)
new_esEs26(x0, x1, app(ty_[], x2))
new_pePe(False, x0)
new_esEs9(EQ, EQ)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_addToFM_C12(x0, x1, x2, x3, x4, x5, x6, True, x7, x8, x9)
new_ltEs5(x0, x1, app(ty_[], x2))
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs34(x0, x1, app(ty_[], x2))
new_emptyFM(x0, x1, x2)
new_compare26(Left(x0), Left(x1), False, x2, x3)
new_esEs6(Just(x0), Just(x1), ty_Char)
new_esEs25(x0, x1, ty_Integer)
new_ltEs18(Just(x0), Nothing, x1)
new_ltEs17(x0, x1, x2)
new_splitGT13(x0, x1, x2, x3, x4, x5, True, x6, x7, x8)
new_mkVBalBranch1(x0, x1, EmptyFM, x2, x3, x4, x5)
new_primPlusInt(Neg(x0), Neg(x1))
new_esEs26(x0, x1, ty_Integer)
new_primCompAux00(x0, EQ)
new_esEs19(x0, x1, ty_Int)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs14(False, True)
new_esEs14(True, False)
new_lt4(x0, x1, ty_Integer)
new_ltEs14(Right(x0), Right(x1), x2, ty_Double)
new_esEs22(x0, x1, ty_Float)
new_fsEs(x0)
new_esEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs7(Right(x0), Right(x1), x2, ty_Integer)
new_esEs13([], [], x0)
new_esEs33(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, app(ty_[], x2))
new_primCmpNat2(Succ(x0), Succ(x1))
new_lt4(x0, x1, ty_Bool)
new_esEs13(:(x0, x1), [], x2)
new_esEs7(Right(x0), Right(x1), x2, ty_Char)
new_asAs(True, x0)
new_splitGT13(x0, x1, x2, x3, x4, x5, False, x6, x7, x8)
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_compare33(x0, x1, x2, x3)
new_splitLT16(x0, x1, x2, x3, x4, x5, True, x6, x7, x8)
new_esEs21(x0, x1, ty_Bool)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, app(ty_[], x2))
new_ltEs5(x0, x1, app(ty_Maybe, x2))
new_splitGT14(x0, x1, x2, x3, x4, x5, True, x6, x7, x8)
new_compare36(x0, x1, x2, x3)
new_ltEs14(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs11(x0, x1, x2)
new_compare29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primMinusNat0(Succ(x0), Succ(x1))
new_esEs31(x0, x1, ty_Integer)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_splitLT15(x0, x1, x2, x3, x4, x5, True, x6, x7, x8)
new_mkBalBranch6MkBalBranch4(x0, x1, x2, Branch(x3, x4, x5, x6, x7), True, x8, x9, x10)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs21(x0, x1, app(ty_[], x2))
new_lt10(x0, x1, x2)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs8(x0, x1, ty_Char)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_splitLT30(Right(x0), x1, x2, x3, x4, Right(x5), x6, x7, x8)
new_esEs31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare26(Right(x0), Left(x1), False, x2, x3)
new_lt19(x0, x1, ty_Float)
new_compare26(Left(x0), Right(x1), False, x2, x3)
new_mkVBalBranch1(x0, x1, Branch(x2, x3, x4, x5, x6), EmptyFM, x7, x8, x9)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, ty_@0)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_splitGT30(Left(x0), x1, x2, x3, x4, Right(x5), x6, x7, x8)
new_compare1(:(x0, x1), :(x2, x3), x4)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_splitGT30(Right(x0), x1, x2, x3, x4, Left(x5), x6, x7, x8)
new_esEs20(x0, x1, ty_Char)
new_ltEs12(False, True)
new_ltEs12(True, False)
new_esEs7(Right(x0), Right(x1), x2, ty_Double)
new_compare6(Double(x0, x1), Double(x2, x3))
new_esEs26(x0, x1, ty_@0)
new_ltEs20(x0, x1, ty_@0)
new_esEs22(x0, x1, ty_Bool)
new_esEs6(Just(x0), Just(x1), app(ty_Maybe, x2))
new_splitGT16(x0, x1, x2, x3, x4, x5, False, x6, x7, x8)
new_compare35(x0, x1, x2, x3)
new_lt19(x0, x1, ty_Double)
new_compare28(x0, x1, True, x2)
new_lt19(x0, x1, ty_Bool)
new_addToFM_C11(x0, x1, x2, x3, x4, x5, x6, True, x7, x8, x9)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(x0, x1, app(app(ty_@2, x2), x3))
new_compare25(x0, x1, True, x2, x3, x4)
new_ltEs14(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs26(x0, x1, ty_Char)
new_ltEs5(x0, x1, ty_Int)
new_esEs34(x0, x1, app(app(ty_@2, x2), x3))
new_mkBalBranch6Size_l(x0, x1, x2, x3, x4, x5, x6)
new_esEs8(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs20(x0, x1, ty_Double)
new_ltEs14(Left(x0), Left(x1), ty_Double, x2)
new_esEs19(x0, x1, ty_@0)
new_mkBalBranch6MkBalBranch5(x0, x1, x2, x3, False, x4, x5, x6)
new_ltEs14(Right(x0), Right(x1), x2, ty_@0)
new_splitGT23(x0, x1, x2, x3, x4, x5, False, x6, x7, x8)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_compare12(x0, x1, True, x2, x3, x4)
new_ltEs21(x0, x1, ty_Bool)
new_sizeFM1(EmptyFM, x0, x1)
new_esEs31(x0, x1, app(app(ty_Either, x2), x3))
new_compare14(x0, x1, True, x2, x3)
new_esEs21(x0, x1, ty_Double)
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_lt12(x0, x1)
new_ltEs18(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs8(x0, x1, ty_Bool)
new_mkVBalBranch3MkVBalBranch12(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, False, x12, x13, x14)
new_splitLT26(x0, x1, x2, x3, x4, x5, False, x6, x7, x8)
new_lt13(x0, x1)
new_ltEs21(x0, x1, ty_Char)
new_ltEs14(Left(x0), Left(x1), ty_Bool, x2)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs31(x0, x1, ty_Ordering)
new_addToFM_C11(x0, x1, x2, x3, x4, x5, x6, False, x7, x8, x9)
new_esEs6(Nothing, Just(x0), x1)
new_compare10(x0, x1, False)
new_primMulNat0(Succ(x0), Zero)
new_ltEs14(Left(x0), Right(x1), x2, x3)
new_splitGT30(Right(x0), x1, x2, x3, x4, Right(x5), x6, x7, x8)
new_ltEs19(x0, x1, ty_Float)
new_ltEs14(Right(x0), Left(x1), x2, x3)
new_esEs23(x0, x1, ty_Float)
new_compare29(x0, x1, ty_Int)
new_splitLT30(Left(x0), x1, x2, x3, x4, Right(x5), x6, x7, x8)
new_splitLT30(Right(x0), x1, x2, x3, x4, Left(x5), x6, x7, x8)
new_esEs22(x0, x1, ty_Int)
new_primPlusInt(Neg(x0), Pos(x1))
new_primPlusInt(Pos(x0), Neg(x1))
new_esEs20(x0, x1, ty_Int)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Float)
new_compare31(x0, x1)
new_esEs29(x0, x1, ty_Double)
new_esEs31(x0, x1, ty_Char)
new_compare14(x0, x1, False, x2, x3)
new_esEs6(Just(x0), Just(x1), ty_Int)
new_splitGT24(x0, x1, x2, x3, x4, x5, True, x6, x7, x8)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs7(LT, GT)
new_ltEs7(GT, LT)
new_esEs33(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Integer)
new_splitLT16(x0, x1, x2, x3, x4, x5, False, x6, x7, x8)
new_esEs22(x0, x1, ty_Double)
new_splitGT24(x0, x1, x2, x3, x4, x5, False, x6, x7, x8)
new_compare13(x0, x1, True, x2, x3)
new_esEs31(x0, x1, app(ty_Ratio, x2))
new_mkVBalBranch3MkVBalBranch11(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, True, x12, x13, x14)
new_splitLT15(x0, x1, x2, x3, x4, x5, False, x6, x7, x8)
new_addToFM_C22(x0, x1, x2, x3, x4, x5, x6, False, x7, x8, x9)
new_ltEs13(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, ty_Bool)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_lt4(x0, x1, app(ty_[], x2))
new_splitGT15(x0, x1, x2, x3, x4, x5, True, x6, x7, x8)
new_ltEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs34(x0, x1, ty_@0)
new_esEs31(x0, x1, ty_Int)
new_compare13(x0, x1, False, x2, x3)
new_lt4(x0, x1, ty_Int)
new_esEs8(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt20(x0, x1, ty_Float)
new_mkVBalBranch3MkVBalBranch21(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, True, x12, x13, x14)
new_not(True)
new_esEs31(x0, x1, ty_Float)
new_esEs20(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Float)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_ltEs18(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Ordering)
new_mkBalBranch6MkBalBranch11(x0, x1, x2, x3, x4, x5, Branch(x6, x7, x8, x9, x10), x11, False, x12, x13, x14)
new_esEs7(Left(x0), Left(x1), ty_Double, x2)
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_lt11(x0, x1, x2, x3)
new_esEs6(Just(x0), Just(x1), ty_Integer)
new_mkBalBranch6MkBalBranch4(x0, x1, x2, x3, False, x4, x5, x6)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_not(False)
new_mkVBalBranch3MkVBalBranch22(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, True, x12, x13, x14)
new_lt8(x0, x1)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs32(x0, x1, ty_Integer)
new_splitGT25(x0, x1, x2, x3, x4, x5, False, x6, x7, x8)
new_ltEs19(x0, x1, ty_Char)
new_mkBalBranch6MkBalBranch3(x0, x1, x2, x3, False, x4, x5, x6)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_primMulInt(Pos(x0), Pos(x1))
new_compare8(:%(x0, x1), :%(x2, x3), ty_Integer)
new_ltEs18(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs6(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Ordering)
new_ltEs18(Just(x0), Just(x1), app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Integer)
new_esEs8(x0, x1, ty_@0)
new_mkBalBranch6MkBalBranch11(x0, x1, x2, x3, x4, x5, EmptyFM, x6, False, x7, x8, x9)
new_ltEs12(True, True)
new_esEs6(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, ty_Float)
new_lt15(x0, x1)
new_esEs26(x0, x1, ty_Ordering)
new_addToFM_C22(x0, x1, x2, x3, x4, x5, x6, True, x7, x8, x9)
new_compare210(x0, x1, True, x2, x3)
new_splitGT26(x0, x1, x2, x3, x4, x5, True, x6, x7, x8)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, ty_Double)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs33(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_compare26(Right(x0), Right(x1), False, x2, x3)
new_lt20(x0, x1, ty_Ordering)
new_splitGT5(EmptyFM, x0, x1, x2, x3)
new_ltEs21(x0, x1, app(ty_Ratio, x2))
new_mkVBalBranch2(x0, x1, EmptyFM, x2, x3, x4, x5)
new_esEs7(Right(x0), Right(x1), x2, ty_Float)
new_compare19(x0, x1, x2, x3)
new_esEs34(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt17(x0, x1, x2)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs32(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, ty_Char)
new_lt20(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Bool)
new_splitLT5(Branch(x0, x1, x2, x3, x4), x5, x6, x7, x8)
new_esEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs34(x0, x1, ty_Double)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_ltEs21(x0, x1, ty_Float)
new_ltEs10(x0, x1)
new_esEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs14(Left(x0), Left(x1), ty_Char, x2)
new_compare27(x0, x1, x2)
new_esEs33(x0, x1, app(ty_[], x2))
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_lt4(x0, x1, app(ty_Maybe, x2))
new_ltEs5(x0, x1, ty_Ordering)
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_splitLT30(Left(x0), x1, x2, x3, x4, Left(x5), x6, x7, x8)
new_sizeFM1(Branch(x0, x1, x2, x3, x4), x5, x6)
new_splitLT23(x0, x1, x2, x3, x4, x5, False, x6, x7, x8)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs8(x0, x1, ty_Double)
new_ltEs14(Left(x0), Left(x1), ty_Float, x2)
new_compare29(x0, x1, ty_Char)
new_esEs6(Just(x0), Just(x1), ty_@0)
new_esEs31(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_mkBalBranch(x0, x1, x2, x3, x4, x5, x6)
new_esEs29(x0, x1, ty_Float)
new_esEs19(x0, x1, ty_Double)
new_splitGT14(x0, x1, x2, x3, x4, x5, False, x6, x7, x8)
new_esEs14(False, False)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs31(x0, x1, app(app(ty_@2, x2), x3))
new_addToFM_C3(Branch(x0, x1, x2, x3, x4), x5, x6, x7, x8, x9)
new_esEs32(x0, x1, ty_Char)
new_mkVBalBranch2(x0, x1, Branch(x2, x3, x4, x5, x6), Branch(x7, x8, x9, x10, x11), x12, x13, x14)
new_esEs19(x0, x1, app(ty_[], x2))
new_ltEs21(x0, x1, ty_Double)
new_esEs32(x0, x1, ty_Int)
new_splitLT14(x0, x1, x2, x3, x4, x5, True, x6, x7, x8)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpNat2(Succ(x0), Zero)
new_compare34(x0, x1, x2, x3)
new_compare18(x0, x1)
new_esEs29(x0, x1, ty_Int)
new_esEs33(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, app(ty_[], x2))
new_esEs32(x0, x1, ty_Bool)
new_ltEs18(Just(x0), Just(x1), ty_Int)
new_lt4(x0, x1, app(app(ty_@2, x2), x3))
new_splitGT26(x0, x1, x2, x3, x4, x5, False, x6, x7, x8)
new_primPlusNat0(Succ(x0), x1)
new_esEs20(x0, x1, ty_Integer)
new_primCmpNat0(x0, Zero)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_compare12(x0, x1, False, x2, x3, x4)
new_ltEs7(GT, EQ)
new_mkBalBranch6MkBalBranch01(x0, x1, x2, x3, x4, x5, EmptyFM, x6, False, x7, x8, x9)
new_ltEs7(EQ, GT)
new_esEs32(x0, x1, ty_Double)
new_ltEs7(GT, GT)
new_esEs9(LT, LT)
new_esEs7(Left(x0), Right(x1), x2, x3)
new_esEs7(Right(x0), Left(x1), x2, x3)
new_compare29(x0, x1, ty_@0)
new_addToFM1(x0, x1, x2, x3, x4, x5)
new_ltEs14(Right(x0), Right(x1), x2, ty_Integer)
new_esEs7(Left(x0), Left(x1), ty_Bool, x2)
new_addToFM(x0, x1, x2, x3, x4, x5)
new_esEs27(x0, x1, ty_Ordering)
new_primCmpNat0(x0, Succ(x1))

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

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