YES 30.395 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 a => FiniteMap (Maybe a) b  ->  FiniteMap (Maybe a) c  ->  FiniteMap (Maybe a) b) :: Ord a => FiniteMap (Maybe a) b  ->  FiniteMap (Maybe a) c  ->  FiniteMap (Maybe a) b)

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

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

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

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

  deleteMin :: Ord 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 (\key elt rest ->(key,elt) : rest) [] fm

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

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

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

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

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

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

  sIZE_RATIO :: Int
sIZE_RATIO = 5

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

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

  splitLT :: Ord 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 c => FiniteMap (Maybe c) b  ->  FiniteMap (Maybe c) a  ->  FiniteMap (Maybe c) b) :: Ord c => FiniteMap (Maybe c) b  ->  FiniteMap (Maybe c) a  ->  FiniteMap (Maybe c) b)

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

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

  
addToFM0 old new = new

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

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

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

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

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

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

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

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

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

  sIZE_RATIO :: Int
sIZE_RATIO = 5

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

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

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


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

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

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

  emptyFM :: FiniteMap a b
emptyFM = EmptyFM

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

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

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

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

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

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

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

  mkVBalBranch :: Ord 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 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


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 a => FiniteMap (Maybe a) c  ->  FiniteMap (Maybe a) b  ->  FiniteMap (Maybe a) c) :: Ord a => FiniteMap (Maybe a) c  ->  FiniteMap (Maybe a) b  ->  FiniteMap (Maybe a) c)

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

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

  
addToFM0 old new = new

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

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

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

  emptyFM :: FiniteMap b a
emptyFM = EmptyFM

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

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

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

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

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

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

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

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

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

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

  sIZE_RATIO :: Int
sIZE_RATIO = 5

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

  splitGT :: Ord 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


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 => FiniteMap (Maybe b) a  ->  FiniteMap (Maybe b) c  ->  FiniteMap (Maybe b) a) :: Ord b => FiniteMap (Maybe b) a  ->  FiniteMap (Maybe b) c  ->  FiniteMap (Maybe 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 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 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 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 :: (a  ->  c  ->  b  ->  b)  ->  b  ->  FiniteMap a c  ->  b
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 b => FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a
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 a => a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b
mkBalBranch key elt fm_L fm_R 
 | size_l + size_r < 2 = 
mkBranch 1 key elt fm_L fm_R
 | size_r > sIZE_RATIO * size_l = 
mkBalBranch0 fm_L fm_R fm_R
 | size_l > sIZE_RATIO * size_r = 
mkBalBranch1 fm_L fm_R fm_L
 | otherwise = 
mkBranch 2 key elt fm_L fm_R where 
double_L fm_l (Branch key_r elt_r 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 a => a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b
mkVBalBranch key elt EmptyFM fm_r = addToFM fm_r key elt
mkVBalBranch key elt fm_l EmptyFM = addToFM fm_l key elt
mkVBalBranch key elt (Branch 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 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 = 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 :: a  ->  b  ->  FiniteMap a b
unitFM key elt = Branch key elt 1 emptyFM emptyFM


module Maybe where
  import qualified FiniteMap
import qualified Prelude


Cond Reductions:
The following Function with conditions
splitLT EmptyFM split_key = emptyFM
splitLT (Branch key elt xx fm_l fm_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)

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

splitLT0 key elt xx fm_l fm_r split_key True = fm_l

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

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

splitGT0 key elt xy fm_l fm_r split_key True = fm_r

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

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

splitGT4 EmptyFM split_key = emptyFM
splitGT4 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_C0 combiner key elt size fm_l fm_r new_key new_elt True = Branch new_key (combiner elt new_elt) size fm_l fm_r

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

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

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

addToFM_C4 combiner EmptyFM key elt = unitFM key elt
addToFM_C4 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

compare0 x y True = GT

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

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

compare3 x y = compare2 x y (x == y)

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

is transformed to
gcd' x 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 a => FiniteMap (Maybe a) c  ->  FiniteMap (Maybe a) b  ->  FiniteMap (Maybe a) c) :: Ord a => FiniteMap (Maybe a) c  ->  FiniteMap (Maybe a) b  ->  FiniteMap (Maybe a) c)

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

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

  
addToFM0 old new = new

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

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

  
glueBal2 fm1 fm2 = 
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 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) = 
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 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) = 
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 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 :: 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
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)

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

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)

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)

mkBalBranch6Size_r ywz yxu yxv yxw = sizeFM yxv

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

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

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)

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

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)

mkBalBranch6Size_l 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)

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

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

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

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)

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
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_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)

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
minusFMGts yzv yzw = splitGT yzv yzw

minusFMLts yzv yzw = splitLT 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
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

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

mkBranchLeft_size yzx yzy yzz = sizeFM yzx

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

mkBranchUnbox yzx yzy yzz x = x

mkBranchRight_size yzx yzy yzz = sizeFM 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)) zuw zux

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_elt20 zuy zuz (vzy,mid_elt2) = mid_elt2

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_elt2 zuy zuz = glueBal2Mid_elt20 zuy zuz (glueBal2Vv3 zuy zuz)

glueBal2Mid_key20 zuy zuz (mid_key2,wuu) = mid_key2

glueBal2Vv2 zuy zuz = findMax zuy

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

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

glueBal2Vv3 zuy zuz = findMin zuz

glueBal2Mid_elt10 zuy zuz (vzx,mid_elt1) = mid_elt1

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

glueBal2Mid_key10 zuy zuz (mid_key1,vzz) = mid_key1

glueBal2Mid_key1 zuy zuz = glueBal2Mid_key10 zuy zuz (glueBal2Vv2 zuy 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
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

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

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)

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
reduce2D zxu zxv = gcd zxu zxv

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

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'0 x y = gcd0Gcd' y (x `rem` y)

gcd0Gcd' x yuv = gcd0Gcd'2 x yuv
gcd0Gcd' x y = gcd0Gcd'0 x y

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

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



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

mainModule FiniteMap
  ((minusFM :: Ord b => FiniteMap (Maybe b) c  ->  FiniteMap (Maybe b) a  ->  FiniteMap (Maybe b) c) :: Ord b => FiniteMap (Maybe b) c  ->  FiniteMap (Maybe b) a  ->  FiniteMap (Maybe b) 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 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 a b
emptyFM = EmptyFM

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

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

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

  
mkBalBranch6Double_L 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 yxw

  
mkBalBranch6Size_r ywz yxu yxv yxw = sizeFM yxv

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

  
mkBranchBalance_ok yzx yzy yzz = True

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

  
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 yzx

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

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

  
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 yzz

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

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

  
splitGT0 key elt xy fm_l fm_r split_key True = fm_r

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

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

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

  
splitGT4 EmptyFM split_key = emptyFM
splitGT4 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 => FiniteMap (Maybe a) b  ->  FiniteMap (Maybe a) c  ->  FiniteMap (Maybe a) b)

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

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

  
addToFM0 old new = new

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

  deleteMin :: Ord b => FiniteMap b a  ->  FiniteMap b a
deleteMin (Branch key elt 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  ->  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 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 c => FiniteMap c b  ->  FiniteMap c a  ->  FiniteMap c b
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_R fm_L key elt fm_L fm_R (mkBalBranch6Size_l key elt fm_R fm_L + mkBalBranch6Size_r key elt fm_R fm_L < Pos (Succ (Succ Zero)))

  
mkBalBranch6Double_L 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 yxw

  
mkBalBranch6Size_r ywz yxu yxv yxw = sizeFM yxv

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

  
mkBranchBalance_ok yzx yzy yzz = True

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

  
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 yzx

  
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)) zuw zux

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

  
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 yzz

  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 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 (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(zxw316, zxw317, zxw318, zxw319, zxw320, zxw321, zxw322, zxw323, zxw324, zxw325, zxw326, zxw327, zxw328, Branch(zxw3290, zxw3291, zxw3292, zxw3293, zxw3294), zxw330, h, ba) → new_glueBal2Mid_key20(zxw316, zxw317, zxw318, zxw319, zxw320, zxw321, zxw322, zxw323, zxw324, zxw325, zxw3290, zxw3291, zxw3292, zxw3293, zxw3294, 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(zxw300, zxw301, zxw302, zxw303, zxw304, zxw305, zxw306, zxw307, zxw308, zxw309, zxw310, zxw311, zxw312, Branch(zxw3130, zxw3131, zxw3132, zxw3133, zxw3134), zxw314, h, ba) → new_glueBal2Mid_elt20(zxw300, zxw301, zxw302, zxw303, zxw304, zxw305, zxw306, zxw307, zxw308, zxw309, zxw3130, zxw3131, zxw3132, zxw3133, zxw3134, 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(zxw380, zxw381, zxw382, zxw383, zxw384, zxw385, zxw386, zxw387, zxw388, zxw389, zxw390, zxw391, zxw392, zxw393, Branch(zxw3940, zxw3941, zxw3942, zxw3943, zxw3944), h, ba) → new_glueBal2Mid_key10(zxw380, zxw381, zxw382, zxw383, zxw384, zxw385, zxw386, zxw387, zxw388, zxw389, zxw3940, zxw3941, zxw3942, zxw3943, zxw3944, 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(zxw364, zxw365, zxw366, zxw367, zxw368, zxw369, zxw370, zxw371, zxw372, zxw373, zxw374, zxw375, zxw376, zxw377, Branch(zxw3780, zxw3781, zxw3782, zxw3783, zxw3784), h, ba) → new_glueBal2Mid_elt10(zxw364, zxw365, zxw366, zxw367, zxw368, zxw369, zxw370, zxw371, zxw372, zxw373, zxw3780, zxw3781, zxw3782, zxw3783, zxw3784, 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(zxw278, zxw279, zxw280, zxw281, zxw282, zxw283, zxw284, zxw285, zxw286, zxw287, zxw288, zxw289, zxw290, Branch(zxw2910, zxw2911, zxw2912, zxw2913, zxw2914), zxw292, h, ba) → new_glueBal2Mid_key200(zxw278, zxw279, zxw280, zxw281, zxw282, zxw283, zxw284, zxw285, zxw286, zxw287, zxw2910, zxw2911, zxw2912, zxw2913, zxw2914, 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(zxw262, zxw263, zxw264, zxw265, zxw266, zxw267, zxw268, zxw269, zxw270, zxw271, zxw272, zxw273, zxw274, Branch(zxw2750, zxw2751, zxw2752, zxw2753, zxw2754), zxw276, h, ba) → new_glueBal2Mid_elt200(zxw262, zxw263, zxw264, zxw265, zxw266, zxw267, zxw268, zxw269, zxw270, zxw271, zxw2750, zxw2751, zxw2752, zxw2753, zxw2754, 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(zxw348, zxw349, zxw350, zxw351, zxw352, zxw353, zxw354, zxw355, zxw356, zxw357, zxw358, zxw359, zxw360, zxw361, Branch(zxw3620, zxw3621, zxw3622, zxw3623, zxw3624), h, ba) → new_glueBal2Mid_key100(zxw348, zxw349, zxw350, zxw351, zxw352, zxw353, zxw354, zxw355, zxw356, zxw357, zxw3620, zxw3621, zxw3622, zxw3623, zxw3624, 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(zxw332, zxw333, zxw334, zxw335, zxw336, zxw337, zxw338, zxw339, zxw340, zxw341, zxw342, zxw343, zxw344, zxw345, Branch(zxw3460, zxw3461, zxw3462, zxw3463, zxw3464), h, ba) → new_glueBal2Mid_elt100(zxw332, zxw333, zxw334, zxw335, zxw336, zxw337, zxw338, zxw339, zxw340, zxw341, zxw3460, zxw3461, zxw3462, zxw3463, zxw3464, 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(zxw49000), Succ(zxw50000)) → new_primCmpNat(zxw49000, zxw50000)

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(zxw14300), Succ(zxw13400)) → new_primMinusNat(zxw14300, zxw13400)

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(zxw14400), Succ(zxw3001000)) → new_primPlusNat(zxw14400, zxw3001000)

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(zxw400100), Succ(zxw300100)) → new_primMulNat(zxw400100, Succ(zxw300100))

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_esEs1(@3(zxw4000, zxw4001, zxw4002), @3(zxw3000, zxw3001, zxw3002), dd, app(app(ty_@2, fh), ga), eh) → new_esEs3(zxw4001, zxw3001, fh, ga)
new_esEs0(:(zxw4000, zxw4001), :(zxw3000, zxw3001), app(app(ty_@2, db), dc)) → new_esEs3(zxw4000, zxw3000, db, dc)
new_esEs1(@3(zxw4000, zxw4001, zxw4002), @3(zxw3000, zxw3001, zxw3002), dd, app(ty_Maybe, eg), eh) → new_esEs(zxw4001, zxw3001, eg)
new_esEs1(@3(zxw4000, zxw4001, zxw4002), @3(zxw3000, zxw3001, zxw3002), dd, app(app(app(ty_@3, fb), fc), fd), eh) → new_esEs1(zxw4001, zxw3001, fb, fc, fd)
new_esEs2(Left(zxw4000), Left(zxw3000), app(app(ty_@2, bac), bad), hd) → new_esEs3(zxw4000, zxw3000, bac, bad)
new_esEs1(@3(zxw4000, zxw4001, zxw4002), @3(zxw3000, zxw3001, zxw3002), dd, de, app(app(ty_Either, ec), ed)) → new_esEs2(zxw4002, zxw3002, ec, ed)
new_esEs1(@3(zxw4000, zxw4001, zxw4002), @3(zxw3000, zxw3001, zxw3002), app(app(ty_Either, gg), gh), de, eh) → new_esEs2(zxw4000, zxw3000, gg, gh)
new_esEs1(@3(zxw4000, zxw4001, zxw4002), @3(zxw3000, zxw3001, zxw3002), app(ty_[], gc), de, eh) → new_esEs0(zxw4000, zxw3000, gc)
new_esEs(Just(zxw4000), Just(zxw3000), app(app(ty_Either, be), bf)) → new_esEs2(zxw4000, zxw3000, be, bf)
new_esEs1(@3(zxw4000, zxw4001, zxw4002), @3(zxw3000, zxw3001, zxw3002), dd, de, app(app(app(ty_@3, dh), ea), eb)) → new_esEs1(zxw4002, zxw3002, dh, ea, eb)
new_esEs(Just(zxw4000), Just(zxw3000), app(ty_Maybe, h)) → new_esEs(zxw4000, zxw3000, h)
new_esEs2(Left(zxw4000), Left(zxw3000), app(app(ty_Either, baa), bab), hd) → new_esEs2(zxw4000, zxw3000, baa, bab)
new_esEs2(Right(zxw4000), Right(zxw3000), bae, app(app(ty_@2, bbe), bbf)) → new_esEs3(zxw4000, zxw3000, bbe, bbf)
new_esEs0(:(zxw4000, zxw4001), :(zxw3000, zxw3001), app(ty_Maybe, cb)) → new_esEs(zxw4000, zxw3000, cb)
new_esEs1(@3(zxw4000, zxw4001, zxw4002), @3(zxw3000, zxw3001, zxw3002), dd, app(app(ty_Either, ff), fg), eh) → new_esEs2(zxw4001, zxw3001, ff, fg)
new_esEs3(@2(zxw4000, zxw4001), @2(zxw3000, zxw3001), app(app(app(ty_@3, bdd), bde), bdf), bdb) → new_esEs1(zxw4000, zxw3000, bdd, bde, bdf)
new_esEs(Just(zxw4000), Just(zxw3000), app(ty_[], ba)) → new_esEs0(zxw4000, zxw3000, ba)
new_esEs2(Right(zxw4000), Right(zxw3000), bae, app(app(app(ty_@3, bah), bba), bbb)) → new_esEs1(zxw4000, zxw3000, bah, bba, bbb)
new_esEs1(@3(zxw4000, zxw4001, zxw4002), @3(zxw3000, zxw3001, zxw3002), app(ty_Maybe, gb), de, eh) → new_esEs(zxw4000, zxw3000, gb)
new_esEs3(@2(zxw4000, zxw4001), @2(zxw3000, zxw3001), bbg, app(app(ty_@2, bcg), bch)) → new_esEs3(zxw4001, zxw3001, bcg, bch)
new_esEs(Just(zxw4000), Just(zxw3000), app(app(ty_@2, bg), bh)) → new_esEs3(zxw4000, zxw3000, bg, bh)
new_esEs2(Left(zxw4000), Left(zxw3000), app(ty_Maybe, hc), hd) → new_esEs(zxw4000, zxw3000, hc)
new_esEs1(@3(zxw4000, zxw4001, zxw4002), @3(zxw3000, zxw3001, zxw3002), dd, de, app(ty_[], dg)) → new_esEs0(zxw4002, zxw3002, dg)
new_esEs1(@3(zxw4000, zxw4001, zxw4002), @3(zxw3000, zxw3001, zxw3002), app(app(app(ty_@3, gd), ge), gf), de, eh) → new_esEs1(zxw4000, zxw3000, gd, ge, gf)
new_esEs2(Left(zxw4000), Left(zxw3000), app(app(app(ty_@3, hf), hg), hh), hd) → new_esEs1(zxw4000, zxw3000, hf, hg, hh)
new_esEs1(@3(zxw4000, zxw4001, zxw4002), @3(zxw3000, zxw3001, zxw3002), app(app(ty_@2, ha), hb), de, eh) → new_esEs3(zxw4000, zxw3000, ha, hb)
new_esEs0(:(zxw4000, zxw4001), :(zxw3000, zxw3001), app(app(app(ty_@3, cd), ce), cf)) → new_esEs1(zxw4000, zxw3000, cd, ce, cf)
new_esEs0(:(zxw4000, zxw4001), :(zxw3000, zxw3001), app(app(ty_Either, cg), da)) → new_esEs2(zxw4000, zxw3000, cg, da)
new_esEs1(@3(zxw4000, zxw4001, zxw4002), @3(zxw3000, zxw3001, zxw3002), dd, app(ty_[], fa), eh) → new_esEs0(zxw4001, zxw3001, fa)
new_esEs2(Right(zxw4000), Right(zxw3000), bae, app(ty_Maybe, baf)) → new_esEs(zxw4000, zxw3000, baf)
new_esEs2(Right(zxw4000), Right(zxw3000), bae, app(ty_[], bag)) → new_esEs0(zxw4000, zxw3000, bag)
new_esEs2(Right(zxw4000), Right(zxw3000), bae, app(app(ty_Either, bbc), bbd)) → new_esEs2(zxw4000, zxw3000, bbc, bbd)
new_esEs3(@2(zxw4000, zxw4001), @2(zxw3000, zxw3001), app(app(ty_@2, bea), beb), bdb) → new_esEs3(zxw4000, zxw3000, bea, beb)
new_esEs3(@2(zxw4000, zxw4001), @2(zxw3000, zxw3001), bbg, app(ty_Maybe, bbh)) → new_esEs(zxw4001, zxw3001, bbh)
new_esEs3(@2(zxw4000, zxw4001), @2(zxw3000, zxw3001), bbg, app(ty_[], bca)) → new_esEs0(zxw4001, zxw3001, bca)
new_esEs3(@2(zxw4000, zxw4001), @2(zxw3000, zxw3001), bbg, app(app(app(ty_@3, bcb), bcc), bcd)) → new_esEs1(zxw4001, zxw3001, bcb, bcc, bcd)
new_esEs1(@3(zxw4000, zxw4001, zxw4002), @3(zxw3000, zxw3001, zxw3002), dd, de, app(app(ty_@2, ee), ef)) → new_esEs3(zxw4002, zxw3002, ee, ef)
new_esEs0(:(zxw4000, zxw4001), :(zxw3000, zxw3001), app(ty_[], cc)) → new_esEs0(zxw4000, zxw3000, cc)
new_esEs2(Left(zxw4000), Left(zxw3000), app(ty_[], he), hd) → new_esEs0(zxw4000, zxw3000, he)
new_esEs3(@2(zxw4000, zxw4001), @2(zxw3000, zxw3001), bbg, app(app(ty_Either, bce), bcf)) → new_esEs2(zxw4001, zxw3001, bce, bcf)
new_esEs3(@2(zxw4000, zxw4001), @2(zxw3000, zxw3001), app(app(ty_Either, bdg), bdh), bdb) → new_esEs2(zxw4000, zxw3000, bdg, bdh)
new_esEs3(@2(zxw4000, zxw4001), @2(zxw3000, zxw3001), app(ty_[], bdc), bdb) → new_esEs0(zxw4000, zxw3000, bdc)
new_esEs(Just(zxw4000), Just(zxw3000), app(app(app(ty_@3, bb), bc), bd)) → new_esEs1(zxw4000, zxw3000, bb, bc, bd)
new_esEs0(:(zxw4000, zxw4001), :(zxw3000, zxw3001), ca) → new_esEs0(zxw4001, zxw3001, ca)
new_esEs3(@2(zxw4000, zxw4001), @2(zxw3000, zxw3001), app(ty_Maybe, bda), bdb) → new_esEs(zxw4000, zxw3000, bda)
new_esEs1(@3(zxw4000, zxw4001, zxw4002), @3(zxw3000, zxw3001, zxw3002), dd, de, app(ty_Maybe, df)) → new_esEs(zxw4002, zxw3002, df)

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_ltEs1(:(zxw49000, zxw49001), :(zxw50000, zxw50001), ef) → new_compare(zxw49001, zxw50001, ef)
new_ltEs3(Left(zxw49000), Left(zxw50000), app(app(ty_Either, bch), bda), bcb) → new_ltEs3(zxw49000, zxw50000, bch, bda)
new_ltEs(@2(zxw49000, zxw49001), @2(zxw50000, zxw50001), app(app(app(ty_@3, cg), da), db), cd) → new_compare20(zxw49000, zxw50000, new_esEs5(zxw49000, zxw50000, cg, da, db), cg, da, db)
new_compare22(Just(@3(zxw49000, zxw49001, zxw49002)), Just(@3(zxw50000, zxw50001, zxw50002)), False, app(app(app(ty_@3, app(app(app(ty_@3, bbc), bbd), bbe)), gc), hg)) → new_lt2(zxw49000, zxw50000, bbc, bbd, bbe)
new_compare22(Just(Left(zxw49000)), Just(Left(zxw50000)), False, app(app(ty_Either, app(app(ty_@2, bbh), bca)), bcb)) → new_ltEs(zxw49000, zxw50000, bbh, bca)
new_ltEs2(@3(zxw49000, zxw49001, zxw49002), @3(zxw50000, zxw50001, zxw50002), gb, gc, app(app(ty_Either, hc), hd)) → new_ltEs3(zxw49002, zxw50002, hc, hd)
new_ltEs(@2(zxw49000, zxw49001), @2(zxw50000, zxw50001), app(ty_Maybe, ce), cd) → new_lt(zxw49000, zxw50000, ce)
new_compare22(Just(@2(zxw49000, zxw49001)), Just(@2(zxw50000, zxw50001)), False, app(app(ty_@2, h), app(app(app(ty_@3, be), bf), bg))) → new_ltEs2(zxw49001, zxw50001, be, bf, bg)
new_ltEs2(@3(zxw49000, zxw49001, zxw49002), @3(zxw50000, zxw50001, zxw50002), gb, app(app(app(ty_@3, bab), bac), bad), hg) → new_lt2(zxw49001, zxw50001, bab, bac, bad)
new_compare22(Just(@3(zxw49000, zxw49001, zxw49002)), Just(@3(zxw50000, zxw50001, zxw50002)), False, app(app(app(ty_@3, gb), app(app(app(ty_@3, bab), bac), bad)), hg)) → new_lt2(zxw49001, zxw50001, bab, bac, bad)
new_compare20(zxw49000, zxw50000, False, cg, da, db) → new_ltEs2(zxw49000, zxw50000, cg, da, db)
new_compare22(Just(Right(zxw49000)), Just(Right(zxw50000)), False, app(app(ty_Either, bdb), app(ty_Maybe, bde))) → new_ltEs0(zxw49000, zxw50000, bde)
new_ltEs0(Just(zxw49000), Just(zxw50000), app(ty_Maybe, dg)) → new_ltEs0(zxw49000, zxw50000, dg)
new_compare21(zxw49000, zxw50000, False, dc, dd) → new_ltEs3(zxw49000, zxw50000, dc, dd)
new_compare22(Just(@2(zxw49000, zxw49001)), Just(@2(zxw50000, zxw50001)), False, app(app(ty_@2, h), app(ty_[], bd))) → new_ltEs1(zxw49001, zxw50001, bd)
new_compare22(Just(Right(zxw49000)), Just(Right(zxw50000)), False, app(app(ty_Either, bdb), app(app(app(ty_@3, bdg), bdh), bea))) → new_ltEs2(zxw49000, zxw50000, bdg, bdh, bea)
new_compare22(Just(@3(zxw49000, zxw49001, zxw49002)), Just(@3(zxw50000, zxw50001, zxw50002)), False, app(app(app(ty_@3, app(ty_[], bbb)), gc), hg)) → new_lt1(zxw49000, zxw50000, bbb)
new_primCompAux(zxw49000, zxw50000, zxw214, app(ty_[], fb)) → new_compare(zxw49000, zxw50000, fb)
new_ltEs3(Left(zxw49000), Left(zxw50000), app(ty_Maybe, bcc), bcb) → new_ltEs0(zxw49000, zxw50000, bcc)
new_compare22(Just(@3(zxw49000, zxw49001, zxw49002)), Just(@3(zxw50000, zxw50001, zxw50002)), False, app(app(app(ty_@3, gb), gc), app(app(ty_Either, hc), hd))) → new_ltEs3(zxw49002, zxw50002, hc, hd)
new_compare22(Just(Just(zxw49000)), Just(Just(zxw50000)), False, app(ty_Maybe, app(ty_Maybe, dg))) → new_ltEs0(zxw49000, zxw50000, dg)
new_compare22(Just(:(zxw49000, zxw49001)), Just(:(zxw50000, zxw50001)), False, app(ty_[], ef)) → new_primCompAux(zxw49000, zxw50000, new_compare0(zxw49001, zxw50001, ef), ef)
new_primCompAux(zxw49000, zxw50000, zxw214, app(app(ty_Either, fg), fh)) → new_compare5(zxw49000, zxw50000, fg, fh)
new_ltEs2(@3(zxw49000, zxw49001, zxw49002), @3(zxw50000, zxw50001, zxw50002), app(ty_[], bbb), gc, hg) → new_lt1(zxw49000, zxw50000, bbb)
new_ltEs2(@3(zxw49000, zxw49001, zxw49002), @3(zxw50000, zxw50001, zxw50002), gb, app(app(ty_@2, he), hf), hg) → new_lt0(zxw49001, zxw50001, he, hf)
new_lt(zxw490, zxw500, ga) → new_compare22(zxw490, zxw500, new_esEs7(zxw490, zxw500, ga), ga)
new_lt0(zxw49000, zxw50000, cb, cc) → new_compare2(zxw49000, zxw50000, new_esEs4(zxw49000, zxw50000, cb, cc), cb, cc)
new_ltEs3(Right(zxw49000), Right(zxw50000), bdb, app(app(ty_Either, beb), bec)) → new_ltEs3(zxw49000, zxw50000, beb, bec)
new_ltEs2(@3(zxw49000, zxw49001, zxw49002), @3(zxw50000, zxw50001, zxw50002), gb, gc, app(ty_[], gg)) → new_ltEs1(zxw49002, zxw50002, gg)
new_compare22(Just(:(zxw49000, zxw49001)), Just(:(zxw50000, zxw50001)), False, app(ty_[], ef)) → new_compare(zxw49001, zxw50001, ef)
new_compare22(Just(@3(zxw49000, zxw49001, zxw49002)), Just(@3(zxw50000, zxw50001, zxw50002)), False, app(app(app(ty_@3, app(app(ty_@2, bag), bah)), gc), hg)) → new_lt0(zxw49000, zxw50000, bag, bah)
new_compare22(Just(@3(zxw49000, zxw49001, zxw49002)), Just(@3(zxw50000, zxw50001, zxw50002)), False, app(app(app(ty_@3, gb), gc), app(ty_[], gg))) → new_ltEs1(zxw49002, zxw50002, gg)
new_compare22(Just(Left(zxw49000)), Just(Left(zxw50000)), False, app(app(ty_Either, app(ty_[], bcd)), bcb)) → new_ltEs1(zxw49000, zxw50000, bcd)
new_ltEs(@2(zxw49000, zxw49001), @2(zxw50000, zxw50001), h, app(app(ty_Either, bh), ca)) → new_ltEs3(zxw49001, zxw50001, bh, ca)
new_ltEs2(@3(zxw49000, zxw49001, zxw49002), @3(zxw50000, zxw50001, zxw50002), gb, app(ty_Maybe, hh), hg) → new_lt(zxw49001, zxw50001, hh)
new_ltEs(@2(zxw49000, zxw49001), @2(zxw50000, zxw50001), h, app(app(ty_@2, ba), bb)) → new_ltEs(zxw49001, zxw50001, ba, bb)
new_ltEs(@2(zxw49000, zxw49001), @2(zxw50000, zxw50001), app(app(ty_Either, dc), dd), cd) → new_compare21(zxw49000, zxw50000, new_esEs6(zxw49000, zxw50000, dc, dd), dc, dd)
new_ltEs3(Left(zxw49000), Left(zxw50000), app(ty_[], bcd), bcb) → new_ltEs1(zxw49000, zxw50000, bcd)
new_compare5(zxw49000, zxw50000, dc, dd) → new_compare21(zxw49000, zxw50000, new_esEs6(zxw49000, zxw50000, dc, dd), dc, dd)
new_ltEs3(Left(zxw49000), Left(zxw50000), app(app(app(ty_@3, bce), bcf), bcg), bcb) → new_ltEs2(zxw49000, zxw50000, bce, bcf, bcg)
new_ltEs(@2(zxw49000, zxw49001), @2(zxw50000, zxw50001), h, app(ty_Maybe, bc)) → new_ltEs0(zxw49001, zxw50001, bc)
new_ltEs(@2(zxw49000, zxw49001), @2(zxw50000, zxw50001), app(app(ty_@2, cb), cc), cd) → new_compare2(zxw49000, zxw50000, new_esEs4(zxw49000, zxw50000, cb, cc), cb, cc)
new_compare22(Just(Left(zxw49000)), Just(Left(zxw50000)), False, app(app(ty_Either, app(app(app(ty_@3, bce), bcf), bcg)), bcb)) → new_ltEs2(zxw49000, zxw50000, bce, bcf, bcg)
new_primCompAux(zxw49000, zxw50000, zxw214, app(app(ty_@2, eg), eh)) → new_compare1(zxw49000, zxw50000, eg, eh)
new_ltEs2(@3(zxw49000, zxw49001, zxw49002), @3(zxw50000, zxw50001, zxw50002), app(app(ty_@2, bag), bah), gc, hg) → new_lt0(zxw49000, zxw50000, bag, bah)
new_ltEs2(@3(zxw49000, zxw49001, zxw49002), @3(zxw50000, zxw50001, zxw50002), gb, app(ty_[], baa), hg) → new_lt1(zxw49001, zxw50001, baa)
new_compare22(Just(@3(zxw49000, zxw49001, zxw49002)), Just(@3(zxw50000, zxw50001, zxw50002)), False, app(app(app(ty_@3, app(ty_Maybe, bba)), gc), hg)) → new_lt(zxw49000, zxw50000, bba)
new_compare22(Just(@3(zxw49000, zxw49001, zxw49002)), Just(@3(zxw50000, zxw50001, zxw50002)), False, app(app(app(ty_@3, gb), gc), app(app(app(ty_@3, gh), ha), hb))) → new_ltEs2(zxw49002, zxw50002, gh, ha, hb)
new_compare22(Just(Just(zxw49000)), Just(Just(zxw50000)), False, app(ty_Maybe, app(app(ty_@2, de), df))) → new_ltEs(zxw49000, zxw50000, de, df)
new_compare4(zxw49000, zxw50000, cg, da, db) → new_compare20(zxw49000, zxw50000, new_esEs5(zxw49000, zxw50000, cg, da, db), cg, da, db)
new_ltEs3(Right(zxw49000), Right(zxw50000), bdb, app(app(app(ty_@3, bdg), bdh), bea)) → new_ltEs2(zxw49000, zxw50000, bdg, bdh, bea)
new_compare22(Just(@2(zxw49000, zxw49001)), Just(@2(zxw50000, zxw50001)), False, app(app(ty_@2, h), app(app(ty_@2, ba), bb))) → new_ltEs(zxw49001, zxw50001, ba, bb)
new_compare2(zxw49000, zxw50000, False, cb, cc) → new_ltEs(zxw49000, zxw50000, cb, cc)
new_compare22(Just(Just(zxw49000)), Just(Just(zxw50000)), False, app(ty_Maybe, app(app(ty_Either, ed), ee))) → new_ltEs3(zxw49000, zxw50000, ed, ee)
new_ltEs2(@3(zxw49000, zxw49001, zxw49002), @3(zxw50000, zxw50001, zxw50002), gb, gc, app(app(app(ty_@3, gh), ha), hb)) → new_ltEs2(zxw49002, zxw50002, gh, ha, hb)
new_ltEs(@2(zxw49000, zxw49001), @2(zxw50000, zxw50001), h, app(ty_[], bd)) → new_ltEs1(zxw49001, zxw50001, bd)
new_compare22(Just(@3(zxw49000, zxw49001, zxw49002)), Just(@3(zxw50000, zxw50001, zxw50002)), False, app(app(app(ty_@3, gb), app(ty_[], baa)), hg)) → new_lt1(zxw49001, zxw50001, baa)
new_compare22(Just(@2(zxw49000, zxw49001)), Just(@2(zxw50000, zxw50001)), False, app(app(ty_@2, app(ty_[], cf)), cd)) → new_compare(zxw49000, zxw50000, cf)
new_compare22(Just(@3(zxw49000, zxw49001, zxw49002)), Just(@3(zxw50000, zxw50001, zxw50002)), False, app(app(app(ty_@3, gb), gc), app(app(ty_@2, gd), ge))) → new_ltEs(zxw49002, zxw50002, gd, ge)
new_ltEs2(@3(zxw49000, zxw49001, zxw49002), @3(zxw50000, zxw50001, zxw50002), app(app(ty_Either, bbf), bbg), gc, hg) → new_lt3(zxw49000, zxw50000, bbf, bbg)
new_ltEs0(Just(zxw49000), Just(zxw50000), app(app(app(ty_@3, ea), eb), ec)) → new_ltEs2(zxw49000, zxw50000, ea, eb, ec)
new_ltEs(@2(zxw49000, zxw49001), @2(zxw50000, zxw50001), app(ty_[], cf), cd) → new_compare(zxw49000, zxw50000, cf)
new_ltEs0(Just(zxw49000), Just(zxw50000), app(app(ty_Either, ed), ee)) → new_ltEs3(zxw49000, zxw50000, ed, ee)
new_ltEs(@2(zxw49000, zxw49001), @2(zxw50000, zxw50001), h, app(app(app(ty_@3, be), bf), bg)) → new_ltEs2(zxw49001, zxw50001, be, bf, bg)
new_compare22(Just(@2(zxw49000, zxw49001)), Just(@2(zxw50000, zxw50001)), False, app(app(ty_@2, h), app(ty_Maybe, bc))) → new_ltEs0(zxw49001, zxw50001, bc)
new_compare22(Just(Just(zxw49000)), Just(Just(zxw50000)), False, app(ty_Maybe, app(app(app(ty_@3, ea), eb), ec))) → new_ltEs2(zxw49000, zxw50000, ea, eb, ec)
new_compare3(zxw490, zxw500, ga) → new_compare22(zxw490, zxw500, new_esEs7(zxw490, zxw500, ga), ga)
new_compare22(Just(@3(zxw49000, zxw49001, zxw49002)), Just(@3(zxw50000, zxw50001, zxw50002)), False, app(app(app(ty_@3, gb), gc), app(ty_Maybe, gf))) → new_ltEs0(zxw49002, zxw50002, gf)
new_lt3(zxw49000, zxw50000, dc, dd) → new_compare21(zxw49000, zxw50000, new_esEs6(zxw49000, zxw50000, dc, dd), dc, dd)
new_compare22(Just(@2(zxw49000, zxw49001)), Just(@2(zxw50000, zxw50001)), False, app(app(ty_@2, app(ty_Maybe, ce)), cd)) → new_lt(zxw49000, zxw50000, ce)
new_ltEs3(Left(zxw49000), Left(zxw50000), app(app(ty_@2, bbh), bca), bcb) → new_ltEs(zxw49000, zxw50000, bbh, bca)
new_ltEs2(@3(zxw49000, zxw49001, zxw49002), @3(zxw50000, zxw50001, zxw50002), gb, gc, app(app(ty_@2, gd), ge)) → new_ltEs(zxw49002, zxw50002, gd, ge)
new_ltEs3(Right(zxw49000), Right(zxw50000), bdb, app(ty_[], bdf)) → new_ltEs1(zxw49000, zxw50000, bdf)
new_ltEs2(@3(zxw49000, zxw49001, zxw49002), @3(zxw50000, zxw50001, zxw50002), gb, gc, app(ty_Maybe, gf)) → new_ltEs0(zxw49002, zxw50002, gf)
new_lt2(zxw49000, zxw50000, cg, da, db) → new_compare20(zxw49000, zxw50000, new_esEs5(zxw49000, zxw50000, cg, da, db), cg, da, db)
new_lt1(zxw49000, zxw50000, cf) → new_compare(zxw49000, zxw50000, cf)
new_compare22(Just(@2(zxw49000, zxw49001)), Just(@2(zxw50000, zxw50001)), False, app(app(ty_@2, app(app(ty_@2, cb), cc)), cd)) → new_compare2(zxw49000, zxw50000, new_esEs4(zxw49000, zxw50000, cb, cc), cb, cc)
new_compare22(Just(Right(zxw49000)), Just(Right(zxw50000)), False, app(app(ty_Either, bdb), app(app(ty_@2, bdc), bdd))) → new_ltEs(zxw49000, zxw50000, bdc, bdd)
new_compare22(Just(Right(zxw49000)), Just(Right(zxw50000)), False, app(app(ty_Either, bdb), app(ty_[], bdf))) → new_ltEs1(zxw49000, zxw50000, bdf)
new_compare(:(zxw49000, zxw49001), :(zxw50000, zxw50001), ef) → new_compare(zxw49001, zxw50001, ef)
new_ltEs0(Just(zxw49000), Just(zxw50000), app(app(ty_@2, de), df)) → new_ltEs(zxw49000, zxw50000, de, df)
new_ltEs2(@3(zxw49000, zxw49001, zxw49002), @3(zxw50000, zxw50001, zxw50002), app(ty_Maybe, bba), gc, hg) → new_lt(zxw49000, zxw50000, bba)
new_compare(:(zxw49000, zxw49001), :(zxw50000, zxw50001), ef) → new_primCompAux(zxw49000, zxw50000, new_compare0(zxw49001, zxw50001, ef), ef)
new_compare22(Just(@3(zxw49000, zxw49001, zxw49002)), Just(@3(zxw50000, zxw50001, zxw50002)), False, app(app(app(ty_@3, gb), app(app(ty_@2, he), hf)), hg)) → new_lt0(zxw49001, zxw50001, he, hf)
new_compare22(Just(Right(zxw49000)), Just(Right(zxw50000)), False, app(app(ty_Either, bdb), app(app(ty_Either, beb), bec))) → new_ltEs3(zxw49000, zxw50000, beb, bec)
new_compare22(Just(Just(zxw49000)), Just(Just(zxw50000)), False, app(ty_Maybe, app(ty_[], dh))) → new_ltEs1(zxw49000, zxw50000, dh)
new_compare22(Just(Left(zxw49000)), Just(Left(zxw50000)), False, app(app(ty_Either, app(ty_Maybe, bcc)), bcb)) → new_ltEs0(zxw49000, zxw50000, bcc)
new_ltEs3(Right(zxw49000), Right(zxw50000), bdb, app(app(ty_@2, bdc), bdd)) → new_ltEs(zxw49000, zxw50000, bdc, bdd)
new_ltEs2(@3(zxw49000, zxw49001, zxw49002), @3(zxw50000, zxw50001, zxw50002), app(app(app(ty_@3, bbc), bbd), bbe), gc, hg) → new_lt2(zxw49000, zxw50000, bbc, bbd, bbe)
new_ltEs0(Just(zxw49000), Just(zxw50000), app(ty_[], dh)) → new_ltEs1(zxw49000, zxw50000, dh)
new_compare22(Just(@2(zxw49000, zxw49001)), Just(@2(zxw50000, zxw50001)), False, app(app(ty_@2, app(app(ty_Either, dc), dd)), cd)) → new_compare21(zxw49000, zxw50000, new_esEs6(zxw49000, zxw50000, dc, dd), dc, dd)
new_ltEs2(@3(zxw49000, zxw49001, zxw49002), @3(zxw50000, zxw50001, zxw50002), gb, app(app(ty_Either, bae), baf), hg) → new_lt3(zxw49001, zxw50001, bae, baf)
new_compare22(Just(@2(zxw49000, zxw49001)), Just(@2(zxw50000, zxw50001)), False, app(app(ty_@2, app(app(app(ty_@3, cg), da), db)), cd)) → new_compare20(zxw49000, zxw50000, new_esEs5(zxw49000, zxw50000, cg, da, db), cg, da, db)
new_ltEs1(:(zxw49000, zxw49001), :(zxw50000, zxw50001), ef) → new_primCompAux(zxw49000, zxw50000, new_compare0(zxw49001, zxw50001, ef), ef)
new_compare22(Just(@3(zxw49000, zxw49001, zxw49002)), Just(@3(zxw50000, zxw50001, zxw50002)), False, app(app(app(ty_@3, gb), app(ty_Maybe, hh)), hg)) → new_lt(zxw49001, zxw50001, hh)
new_compare22(Just(@2(zxw49000, zxw49001)), Just(@2(zxw50000, zxw50001)), False, app(app(ty_@2, h), app(app(ty_Either, bh), ca))) → new_ltEs3(zxw49001, zxw50001, bh, ca)
new_ltEs3(Right(zxw49000), Right(zxw50000), bdb, app(ty_Maybe, bde)) → new_ltEs0(zxw49000, zxw50000, bde)
new_compare22(Just(Left(zxw49000)), Just(Left(zxw50000)), False, app(app(ty_Either, app(app(ty_Either, bch), bda)), bcb)) → new_ltEs3(zxw49000, zxw50000, bch, bda)
new_compare22(Just(@3(zxw49000, zxw49001, zxw49002)), Just(@3(zxw50000, zxw50001, zxw50002)), False, app(app(app(ty_@3, gb), app(app(ty_Either, bae), baf)), hg)) → new_lt3(zxw49001, zxw50001, bae, baf)
new_compare22(Just(@3(zxw49000, zxw49001, zxw49002)), Just(@3(zxw50000, zxw50001, zxw50002)), False, app(app(app(ty_@3, app(app(ty_Either, bbf), bbg)), gc), hg)) → new_lt3(zxw49000, zxw50000, bbf, bbg)
new_primCompAux(zxw49000, zxw50000, zxw214, app(ty_Maybe, fa)) → new_compare3(zxw49000, zxw50000, fa)
new_primCompAux(zxw49000, zxw50000, zxw214, app(app(app(ty_@3, fc), fd), ff)) → new_compare4(zxw49000, zxw50000, fc, fd, ff)
new_compare1(zxw49000, zxw50000, cb, cc) → new_compare2(zxw49000, zxw50000, new_esEs4(zxw49000, zxw50000, cb, cc), cb, cc)

The TRS R consists of the following rules:

new_esEs6(Right(zxw4000), Right(zxw3000), cha, ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_esEs7(Just(zxw4000), Just(zxw3000), app(ty_Maybe, ceb)) → new_esEs7(zxw4000, zxw3000, ceb)
new_ltEs19(zxw4900, zxw5000, ty_Integer) → new_ltEs16(zxw4900, zxw5000)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_@0, bcb) → new_ltEs14(zxw49000, zxw50000)
new_esEs27(zxw49000, zxw50000, app(ty_[], bbb)) → new_esEs16(zxw49000, zxw50000, bbb)
new_ltEs4(EQ, GT) → True
new_esEs22(zxw4000, zxw3000, ty_@0) → new_esEs20(zxw4000, zxw3000)
new_compare15(zxw49000, zxw50000, True, dc, dd) → LT
new_esEs6(Right(zxw4000), Right(zxw3000), cha, ty_Float) → new_esEs19(zxw4000, zxw3000)
new_ltEs9(@2(zxw49000, zxw49001), @2(zxw50000, zxw50001), h, cd) → new_pePe(new_lt10(zxw49000, zxw50000, h), new_asAs(new_esEs23(zxw49000, zxw50000, h), new_ltEs18(zxw49001, zxw50001, cd)))
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Integer, cfg) → new_esEs17(zxw4000, zxw3000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_esEs23(zxw49000, zxw50000, app(app(ty_@2, cb), cc)) → new_esEs4(zxw49000, zxw50000, cb, cc)
new_compare29(zxw49000, zxw50000, ty_Char) → new_compare12(zxw49000, zxw50000)
new_esEs22(zxw4000, zxw3000, ty_Float) → new_esEs19(zxw4000, zxw3000)
new_esEs6(Right(zxw4000), Right(zxw3000), cha, ty_Int) → new_esEs13(zxw4000, zxw3000)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Bool) → new_ltEs5(zxw49000, zxw50000)
new_lt19(zxw49001, zxw50001, ty_Integer) → new_lt5(zxw49001, zxw50001)
new_esEs12(zxw4000, zxw3000, ty_Bool) → new_esEs9(zxw4000, zxw3000)
new_esEs27(zxw49000, zxw50000, app(ty_Maybe, bba)) → new_esEs7(zxw49000, zxw50000, bba)
new_esEs12(zxw4000, zxw3000, ty_Char) → new_esEs15(zxw4000, zxw3000)
new_esEs11(zxw4001, zxw3001, app(ty_[], bgd)) → new_esEs16(zxw4001, zxw3001, bgd)
new_compare12(Char(zxw49000), Char(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_ltEs19(zxw4900, zxw5000, ty_Double) → new_ltEs11(zxw4900, zxw5000)
new_ltEs20(zxw49002, zxw50002, ty_Bool) → new_ltEs5(zxw49002, zxw50002)
new_compare29(zxw49000, zxw50000, ty_Double) → new_compare16(zxw49000, zxw50000)
new_esEs23(zxw49000, zxw50000, ty_Float) → new_esEs19(zxw49000, zxw50000)
new_lt19(zxw49001, zxw50001, ty_Ordering) → new_lt14(zxw49001, zxw50001)
new_lt19(zxw49001, zxw50001, ty_Int) → new_lt4(zxw49001, zxw50001)
new_esEs7(Just(zxw4000), Just(zxw3000), app(app(ty_Either, ceh), cfa)) → new_esEs6(zxw4000, zxw3000, ceh, cfa)
new_primMulNat0(Zero, Zero) → Zero
new_ltEs7(Left(zxw49000), Right(zxw50000), bdb, bcb) → True
new_compare26(Just(zxw4900), Nothing, False, ga) → GT
new_esEs26(zxw49001, zxw50001, app(ty_[], baa)) → new_esEs16(zxw49001, zxw50001, baa)
new_esEs27(zxw49000, zxw50000, ty_Bool) → new_esEs9(zxw49000, zxw50000)
new_ltEs18(zxw49001, zxw50001, ty_Integer) → new_ltEs16(zxw49001, zxw50001)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_ltEs18(zxw49001, zxw50001, app(ty_[], bd)) → new_ltEs13(zxw49001, zxw50001, bd)
new_ltEs20(zxw49002, zxw50002, app(ty_Maybe, gf)) → new_ltEs8(zxw49002, zxw50002, gf)
new_esEs11(zxw4001, zxw3001, ty_Char) → new_esEs15(zxw4001, zxw3001)
new_esEs11(zxw4001, zxw3001, ty_Float) → new_esEs19(zxw4001, zxw3001)
new_lt8(zxw49000, zxw50000) → new_esEs8(new_compare16(zxw49000, zxw50000), LT)
new_esEs26(zxw49001, zxw50001, ty_Char) → new_esEs15(zxw49001, zxw50001)
new_lt20(zxw49000, zxw50000, app(app(ty_@2, bag), bah)) → new_lt11(zxw49000, zxw50000, bag, bah)
new_esEs23(zxw49000, zxw50000, ty_Char) → new_esEs15(zxw49000, zxw50000)
new_esEs23(zxw49000, zxw50000, ty_Bool) → new_esEs9(zxw49000, zxw50000)
new_esEs27(zxw49000, zxw50000, ty_Char) → new_esEs15(zxw49000, zxw50000)
new_compare26(Nothing, Just(zxw5000), False, ga) → LT
new_lt10(zxw49000, zxw50000, ty_Float) → new_lt7(zxw49000, zxw50000)
new_esEs21(zxw4001, zxw3001, ty_Double) → new_esEs18(zxw4001, zxw3001)
new_ltEs19(zxw4900, zxw5000, ty_Int) → new_ltEs10(zxw4900, zxw5000)
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_lt9(zxw49000, zxw50000, cf) → new_esEs8(new_compare0(zxw49000, zxw50000, cf), LT)
new_compare210(zxw49000, zxw50000, False, cg, da, db) → new_compare110(zxw49000, zxw50000, new_ltEs15(zxw49000, zxw50000, cg, da, db), cg, da, db)
new_esEs22(zxw4000, zxw3000, app(ty_Ratio, ccf)) → new_esEs14(zxw4000, zxw3000, ccf)
new_esEs21(zxw4001, zxw3001, app(ty_Ratio, cbd)) → new_esEs14(zxw4001, zxw3001, cbd)
new_esEs7(Just(zxw4000), Just(zxw3000), app(app(ty_@2, cfb), cfc)) → new_esEs4(zxw4000, zxw3000, cfb, cfc)
new_esEs25(zxw4000, zxw3000, ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Bool) → new_esEs9(zxw4000, zxw3000)
new_ltEs20(zxw49002, zxw50002, ty_Integer) → new_ltEs16(zxw49002, zxw50002)
new_esEs21(zxw4001, zxw3001, app(app(ty_Either, cca), ccb)) → new_esEs6(zxw4001, zxw3001, cca, ccb)
new_ltEs7(Left(zxw49000), Left(zxw50000), app(app(app(ty_@3, bce), bcf), bcg), bcb) → new_ltEs15(zxw49000, zxw50000, bce, bcf, bcg)
new_ltEs14(zxw4900, zxw5000) → new_fsEs(new_compare31(zxw4900, zxw5000))
new_compare24(zxw49000, zxw50000, False) → new_compare13(zxw49000, zxw50000, new_ltEs5(zxw49000, zxw50000))
new_esEs7(Just(zxw4000), Just(zxw3000), app(ty_Ratio, cec)) → new_esEs14(zxw4000, zxw3000, cec)
new_ltEs7(Right(zxw49000), Right(zxw50000), bdb, app(app(ty_@2, bdc), bdd)) → new_ltEs9(zxw49000, zxw50000, bdc, bdd)
new_lt4(zxw490, zxw500) → new_esEs8(new_compare7(zxw490, zxw500), LT)
new_esEs28(zxw4000, zxw3000, app(app(app(ty_@3, dbe), dbf), dbg)) → new_esEs5(zxw4000, zxw3000, dbe, dbf, dbg)
new_esEs28(zxw4000, zxw3000, ty_Bool) → new_esEs9(zxw4000, zxw3000)
new_compare19(zxw490, zxw500, ga) → new_compare26(zxw490, zxw500, new_esEs7(zxw490, zxw500, ga), ga)
new_esEs17(Integer(zxw4000), Integer(zxw3000)) → new_primEqInt(zxw4000, zxw3000)
new_pePe(False, zxw213) → zxw213
new_lt12(zxw490, zxw500, ga) → new_esEs8(new_compare19(zxw490, zxw500, ga), LT)
new_esEs20(@0, @0) → True
new_esEs6(Right(zxw4000), Right(zxw3000), cha, app(ty_Ratio, chc)) → new_esEs14(zxw4000, zxw3000, chc)
new_esEs6(Left(zxw4000), Left(zxw3000), app(app(ty_@2, cgg), cgh), cfg) → new_esEs4(zxw4000, zxw3000, cgg, cgh)
new_compare23(zxw49000, zxw50000, True) → EQ
new_esEs11(zxw4001, zxw3001, ty_Int) → new_esEs13(zxw4001, zxw3001)
new_lt19(zxw49001, zxw50001, app(ty_[], baa)) → new_lt9(zxw49001, zxw50001, baa)
new_compare29(zxw49000, zxw50000, ty_@0) → new_compare31(zxw49000, zxw50000)
new_compare26(Nothing, Nothing, False, ga) → LT
new_esEs10(zxw4002, zxw3002, app(ty_Maybe, beh)) → new_esEs7(zxw4002, zxw3002, beh)
new_ltEs16(zxw4900, zxw5000) → new_fsEs(new_compare9(zxw4900, zxw5000))
new_esEs22(zxw4000, zxw3000, app(app(ty_@2, cde), cdf)) → new_esEs4(zxw4000, zxw3000, cde, cdf)
new_esEs23(zxw49000, zxw50000, app(ty_Maybe, ce)) → new_esEs7(zxw49000, zxw50000, ce)
new_ltEs7(Right(zxw49000), Right(zxw50000), bdb, app(ty_Ratio, dah)) → new_ltEs17(zxw49000, zxw50000, dah)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Char, bcb) → new_ltEs12(zxw49000, zxw50000)
new_esEs28(zxw4000, zxw3000, ty_@0) → new_esEs20(zxw4000, zxw3000)
new_ltEs20(zxw49002, zxw50002, app(ty_[], gg)) → new_ltEs13(zxw49002, zxw50002, gg)
new_esEs10(zxw4002, zxw3002, app(app(app(ty_@3, bfc), bfd), bfe)) → new_esEs5(zxw4002, zxw3002, bfc, bfd, bfe)
new_esEs27(zxw49000, zxw50000, ty_Float) → new_esEs19(zxw49000, zxw50000)
new_ltEs20(zxw49002, zxw50002, app(app(app(ty_@3, gh), ha), hb)) → new_ltEs15(zxw49002, zxw50002, gh, ha, hb)
new_esEs22(zxw4000, zxw3000, ty_Ordering) → new_esEs8(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Bool) → new_esEs9(zxw4000, zxw3000)
new_compare6(zxw49000, zxw50000) → new_compare23(zxw49000, zxw50000, new_esEs8(zxw49000, zxw50000))
new_esEs12(zxw4000, zxw3000, app(ty_[], bhf)) → new_esEs16(zxw4000, zxw3000, bhf)
new_compare32(zxw49000, zxw50000, dc, dd) → new_compare25(zxw49000, zxw50000, new_esEs6(zxw49000, zxw50000, dc, dd), dc, dd)
new_compare29(zxw49000, zxw50000, ty_Int) → new_compare7(zxw49000, zxw50000)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Bool, cfg) → new_esEs9(zxw4000, zxw3000)
new_ltEs8(Nothing, Just(zxw50000), caf) → True
new_ltEs7(Left(zxw49000), Left(zxw50000), app(app(ty_@2, bbh), bca), bcb) → new_ltEs9(zxw49000, zxw50000, bbh, bca)
new_esEs6(Right(zxw4000), Left(zxw3000), cha, cfg) → False
new_esEs6(Left(zxw4000), Right(zxw3000), cha, cfg) → False
new_esEs8(LT, LT) → True
new_lt20(zxw49000, zxw50000, ty_@0) → new_lt15(zxw49000, zxw50000)
new_esEs10(zxw4002, zxw3002, ty_Integer) → new_esEs17(zxw4002, zxw3002)
new_esEs28(zxw4000, zxw3000, ty_Float) → new_esEs19(zxw4000, zxw3000)
new_compare29(zxw49000, zxw50000, app(app(app(ty_@3, fc), fd), ff)) → new_compare28(zxw49000, zxw50000, fc, fd, ff)
new_lt19(zxw49001, zxw50001, ty_@0) → new_lt15(zxw49001, zxw50001)
new_ltEs7(Right(zxw49000), Right(zxw50000), bdb, ty_Bool) → new_ltEs5(zxw49000, zxw50000)
new_ltEs5(True, False) → False
new_lt19(zxw49001, zxw50001, app(app(ty_@2, he), hf)) → new_lt11(zxw49001, zxw50001, he, hf)
new_compare0([], [], ef) → EQ
new_pePe(True, zxw213) → True
new_primEqNat0(Zero, Zero) → True
new_esEs14(:%(zxw4000, zxw4001), :%(zxw3000, zxw3001), cfe) → new_asAs(new_esEs25(zxw4000, zxw3000, cfe), new_esEs24(zxw4001, zxw3001, cfe))
new_lt10(zxw49000, zxw50000, ty_Double) → new_lt8(zxw49000, zxw50000)
new_ltEs20(zxw49002, zxw50002, ty_Ordering) → new_ltEs4(zxw49002, zxw50002)
new_compare27(zxw49000, zxw50000, False, cb, cc) → new_compare17(zxw49000, zxw50000, new_ltEs9(zxw49000, zxw50000, cb, cc), cb, cc)
new_compare11(zxw180, zxw181, True, bed) → LT
new_esEs23(zxw49000, zxw50000, app(app(ty_Either, dc), dd)) → new_esEs6(zxw49000, zxw50000, dc, dd)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_@0, cfg) → new_esEs20(zxw4000, zxw3000)
new_esEs6(Right(zxw4000), Right(zxw3000), cha, ty_Bool) → new_esEs9(zxw4000, zxw3000)
new_esEs12(zxw4000, zxw3000, ty_Int) → new_esEs13(zxw4000, zxw3000)
new_lt20(zxw49000, zxw50000, app(ty_[], bbb)) → new_lt9(zxw49000, zxw50000, bbb)
new_esEs6(Right(zxw4000), Right(zxw3000), cha, app(app(ty_Either, chh), daa)) → new_esEs6(zxw4000, zxw3000, chh, daa)
new_compare26(Just(zxw4900), Just(zxw5000), False, ga) → new_compare11(zxw4900, zxw5000, new_ltEs19(zxw4900, zxw5000, ga), ga)
new_ltEs5(True, True) → True
new_ltEs7(Left(zxw49000), Left(zxw50000), app(ty_Maybe, bcc), bcb) → new_ltEs8(zxw49000, zxw50000, bcc)
new_ltEs20(zxw49002, zxw50002, app(app(ty_@2, gd), ge)) → new_ltEs9(zxw49002, zxw50002, gd, ge)
new_esEs15(Char(zxw4000), Char(zxw3000)) → new_primEqNat0(zxw4000, zxw3000)
new_sr(zxw4001, zxw3001) → new_primMulInt(zxw4001, zxw3001)
new_ltEs18(zxw49001, zxw50001, ty_Int) → new_ltEs10(zxw49001, zxw50001)
new_esEs25(zxw4000, zxw3000, ty_Int) → new_esEs13(zxw4000, zxw3000)
new_compare7(zxw49, zxw50) → new_primCmpInt(zxw49, zxw50)
new_primCmpNat1(Zero, Zero) → EQ
new_esEs7(Just(zxw4000), Just(zxw3000), app(ty_[], ced)) → new_esEs16(zxw4000, zxw3000, ced)
new_lt10(zxw49000, zxw50000, ty_Int) → new_lt4(zxw49000, zxw50000)
new_esEs28(zxw4000, zxw3000, app(app(ty_Either, dbh), dca)) → new_esEs6(zxw4000, zxw3000, dbh, dca)
new_ltEs7(Right(zxw49000), Right(zxw50000), bdb, app(ty_Maybe, bde)) → new_ltEs8(zxw49000, zxw50000, bde)
new_ltEs7(Right(zxw49000), Right(zxw50000), bdb, ty_Integer) → new_ltEs16(zxw49000, zxw50000)
new_ltEs7(Right(zxw49000), Right(zxw50000), bdb, app(app(app(ty_@3, bdg), bdh), bea)) → new_ltEs15(zxw49000, zxw50000, bdg, bdh, bea)
new_esEs26(zxw49001, zxw50001, ty_Ordering) → new_esEs8(zxw49001, zxw50001)
new_esEs8(GT, GT) → True
new_esEs27(zxw49000, zxw50000, ty_@0) → new_esEs20(zxw49000, zxw50000)
new_esEs13(zxw400, zxw300) → new_primEqInt(zxw400, zxw300)
new_lt13(zxw49000, zxw50000) → new_esEs8(new_compare18(zxw49000, zxw50000), LT)
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_lt20(zxw49000, zxw50000, ty_Ordering) → new_lt14(zxw49000, zxw50000)
new_esEs11(zxw4001, zxw3001, ty_Ordering) → new_esEs8(zxw4001, zxw3001)
new_esEs11(zxw4001, zxw3001, app(app(ty_@2, bhb), bhc)) → new_esEs4(zxw4001, zxw3001, bhb, bhc)
new_compare23(zxw49000, zxw50000, False) → new_compare10(zxw49000, zxw50000, new_ltEs4(zxw49000, zxw50000))
new_lt10(zxw49000, zxw50000, app(app(ty_@2, cb), cc)) → new_lt11(zxw49000, zxw50000, cb, cc)
new_esEs8(LT, GT) → False
new_esEs8(GT, LT) → False
new_ltEs19(zxw4900, zxw5000, app(app(app(ty_@3, gb), gc), hg)) → new_ltEs15(zxw4900, zxw5000, gb, gc, hg)
new_lt20(zxw49000, zxw50000, app(app(ty_Either, bbf), bbg)) → new_lt17(zxw49000, zxw50000, bbf, bbg)
new_esEs26(zxw49001, zxw50001, ty_Bool) → new_esEs9(zxw49001, zxw50001)
new_ltEs11(zxw4900, zxw5000) → new_fsEs(new_compare16(zxw4900, zxw5000))
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_compare17(zxw49000, zxw50000, True, cb, cc) → LT
new_primEqInt(Neg(Succ(zxw40000)), Neg(Succ(zxw30000))) → new_primEqNat0(zxw40000, zxw30000)
new_ltEs5(False, False) → True
new_esEs23(zxw49000, zxw50000, ty_Ordering) → new_esEs8(zxw49000, zxw50000)
new_ltEs18(zxw49001, zxw50001, app(app(ty_Either, bh), ca)) → new_ltEs7(zxw49001, zxw50001, bh, ca)
new_esEs28(zxw4000, zxw3000, ty_Char) → new_esEs15(zxw4000, zxw3000)
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)
new_ltEs19(zxw4900, zxw5000, app(ty_Ratio, cah)) → new_ltEs17(zxw4900, zxw5000, cah)
new_esEs10(zxw4002, zxw3002, ty_Bool) → new_esEs9(zxw4002, zxw3002)
new_lt20(zxw49000, zxw50000, ty_Char) → new_lt6(zxw49000, zxw50000)
new_compare13(zxw49000, zxw50000, False) → GT
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Bool, bcb) → new_ltEs5(zxw49000, zxw50000)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Int, bcb) → new_ltEs10(zxw49000, zxw50000)
new_lt11(zxw49000, zxw50000, cb, cc) → new_esEs8(new_compare30(zxw49000, zxw50000, cb, cc), LT)
new_esEs21(zxw4001, zxw3001, ty_Char) → new_esEs15(zxw4001, zxw3001)
new_lt20(zxw49000, zxw50000, ty_Int) → new_lt4(zxw49000, zxw50000)
new_primCompAux1(zxw49000, zxw50000, zxw214, ef) → new_primCompAux0(zxw214, new_compare29(zxw49000, zxw50000, ef))
new_esEs7(Just(zxw4000), Just(zxw3000), ty_@0) → new_esEs20(zxw4000, zxw3000)
new_lt16(zxw49000, zxw50000, cg, da, db) → new_esEs8(new_compare28(zxw49000, zxw50000, cg, da, db), LT)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_ltEs7(Right(zxw49000), Left(zxw50000), bdb, bcb) → False
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Ordering) → new_esEs8(zxw4000, zxw3000)
new_ltEs7(Left(zxw49000), Left(zxw50000), app(ty_[], bcd), bcb) → new_ltEs13(zxw49000, zxw50000, bcd)
new_ltEs19(zxw4900, zxw5000, ty_Ordering) → new_ltEs4(zxw4900, zxw5000)
new_ltEs20(zxw49002, zxw50002, ty_Char) → new_ltEs12(zxw49002, zxw50002)
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_ltEs20(zxw49002, zxw50002, app(ty_Ratio, dad)) → new_ltEs17(zxw49002, zxw50002, dad)
new_esEs11(zxw4001, zxw3001, app(app(app(ty_@3, bge), bgf), bgg)) → new_esEs5(zxw4001, zxw3001, bge, bgf, bgg)
new_ltEs18(zxw49001, zxw50001, ty_@0) → new_ltEs14(zxw49001, zxw50001)
new_primEqInt(Neg(Succ(zxw40000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(zxw30000))) → False
new_ltEs19(zxw4900, zxw5000, ty_Char) → new_ltEs12(zxw4900, zxw5000)
new_esEs12(zxw4000, zxw3000, ty_Double) → new_esEs18(zxw4000, zxw3000)
new_primCompAux0(zxw218, GT) → GT
new_esEs8(EQ, EQ) → True
new_esEs6(Left(zxw4000), Left(zxw3000), app(ty_Ratio, cfh), cfg) → new_esEs14(zxw4000, zxw3000, cfh)
new_ltEs8(Just(zxw49000), Just(zxw50000), app(app(ty_Either, ed), ee)) → new_ltEs7(zxw49000, zxw50000, ed, ee)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Integer, bcb) → new_ltEs16(zxw49000, zxw50000)
new_esEs6(Right(zxw4000), Right(zxw3000), cha, app(ty_[], chd)) → new_esEs16(zxw4000, zxw3000, chd)
new_esEs23(zxw49000, zxw50000, ty_Integer) → new_esEs17(zxw49000, zxw50000)
new_esEs28(zxw4000, zxw3000, ty_Int) → new_esEs13(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, app(app(app(ty_@3, cch), cda), cdb)) → new_esEs5(zxw4000, zxw3000, cch, cda, cdb)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_ltEs18(zxw49001, zxw50001, ty_Ordering) → new_ltEs4(zxw49001, zxw50001)
new_ltEs4(EQ, LT) → False
new_esEs12(zxw4000, zxw3000, app(ty_Maybe, bhd)) → new_esEs7(zxw4000, zxw3000, bhd)
new_lt20(zxw49000, zxw50000, ty_Double) → new_lt8(zxw49000, zxw50000)
new_esEs10(zxw4002, zxw3002, ty_Float) → new_esEs19(zxw4002, zxw3002)
new_esEs11(zxw4001, zxw3001, ty_Bool) → new_esEs9(zxw4001, zxw3001)
new_compare11(zxw180, zxw181, False, bed) → GT
new_esEs26(zxw49001, zxw50001, ty_Integer) → new_esEs17(zxw49001, zxw50001)
new_lt10(zxw49000, zxw50000, ty_Ordering) → new_lt14(zxw49000, zxw50000)
new_ltEs18(zxw49001, zxw50001, ty_Bool) → new_ltEs5(zxw49001, zxw50001)
new_esEs12(zxw4000, zxw3000, app(app(app(ty_@3, bhg), bhh), caa)) → new_esEs5(zxw4000, zxw3000, bhg, bhh, caa)
new_primEqInt(Pos(Succ(zxw40000)), Pos(Succ(zxw30000))) → new_primEqNat0(zxw40000, zxw30000)
new_compare27(zxw49000, zxw50000, True, cb, cc) → EQ
new_esEs6(Left(zxw4000), Left(zxw3000), app(app(app(ty_@3, cgb), cgc), cgd), cfg) → new_esEs5(zxw4000, zxw3000, cgb, cgc, cgd)
new_lt18(zxw49000, zxw50000, cdh) → new_esEs8(new_compare8(zxw49000, zxw50000, cdh), LT)
new_ltEs18(zxw49001, zxw50001, app(app(app(ty_@3, be), bf), bg)) → new_ltEs15(zxw49001, zxw50001, be, bf, bg)
new_lt10(zxw49000, zxw50000, app(ty_Maybe, ce)) → new_lt12(zxw49000, zxw50000, ce)
new_esEs26(zxw49001, zxw50001, ty_Int) → new_esEs13(zxw49001, zxw50001)
new_ltEs8(Just(zxw49000), Just(zxw50000), app(app(ty_@2, de), df)) → new_ltEs9(zxw49000, zxw50000, de, df)
new_primEqNat0(Succ(zxw40000), Succ(zxw30000)) → new_primEqNat0(zxw40000, zxw30000)
new_compare29(zxw49000, zxw50000, app(ty_[], fb)) → new_compare0(zxw49000, zxw50000, fb)
new_esEs27(zxw49000, zxw50000, ty_Ordering) → new_esEs8(zxw49000, zxw50000)
new_esEs27(zxw49000, zxw50000, ty_Integer) → new_esEs17(zxw49000, zxw50000)
new_esEs23(zxw49000, zxw50000, app(ty_Ratio, cdh)) → new_esEs14(zxw49000, zxw50000, cdh)
new_ltEs18(zxw49001, zxw50001, ty_Float) → new_ltEs6(zxw49001, zxw50001)
new_esEs22(zxw4000, zxw3000, ty_Int) → new_esEs13(zxw4000, zxw3000)
new_ltEs7(Right(zxw49000), Right(zxw50000), bdb, app(ty_[], bdf)) → new_ltEs13(zxw49000, zxw50000, bdf)
new_ltEs4(GT, EQ) → False
new_lt7(zxw49000, zxw50000) → new_esEs8(new_compare14(zxw49000, zxw50000), LT)
new_lt10(zxw49000, zxw50000, app(app(app(ty_@3, cg), da), db)) → new_lt16(zxw49000, zxw50000, cg, da, db)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Int) → new_esEs13(zxw4000, zxw3000)
new_ltEs19(zxw4900, zxw5000, app(app(ty_Either, bdb), bcb)) → new_ltEs7(zxw4900, zxw5000, bdb, bcb)
new_ltEs8(Just(zxw49000), Nothing, caf) → False
new_esEs21(zxw4001, zxw3001, ty_Float) → new_esEs19(zxw4001, zxw3001)
new_esEs26(zxw49001, zxw50001, app(app(ty_@2, he), hf)) → new_esEs4(zxw49001, zxw50001, he, hf)
new_esEs27(zxw49000, zxw50000, app(app(app(ty_@3, bbc), bbd), bbe)) → new_esEs5(zxw49000, zxw50000, bbc, bbd, bbe)
new_ltEs13(zxw4900, zxw5000, ef) → new_fsEs(new_compare0(zxw4900, zxw5000, ef))
new_esEs22(zxw4000, zxw3000, ty_Char) → new_esEs15(zxw4000, zxw3000)
new_ltEs18(zxw49001, zxw50001, ty_Double) → new_ltEs11(zxw49001, zxw50001)
new_esEs7(Nothing, Nothing, cea) → True
new_esEs28(zxw4000, zxw3000, ty_Ordering) → new_esEs8(zxw4000, zxw3000)
new_lt10(zxw49000, zxw50000, app(app(ty_Either, dc), dd)) → new_lt17(zxw49000, zxw50000, dc, dd)
new_esEs8(EQ, LT) → False
new_esEs8(LT, EQ) → False
new_esEs10(zxw4002, zxw3002, ty_Char) → new_esEs15(zxw4002, zxw3002)
new_primEqInt(Pos(Succ(zxw40000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(zxw30000))) → False
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Double, bcb) → new_ltEs11(zxw49000, zxw50000)
new_ltEs4(EQ, EQ) → True
new_esEs6(Right(zxw4000), Right(zxw3000), cha, app(ty_Maybe, chb)) → new_esEs7(zxw4000, zxw3000, chb)
new_ltEs7(Right(zxw49000), Right(zxw50000), bdb, ty_Ordering) → new_ltEs4(zxw49000, zxw50000)
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_ltEs20(zxw49002, zxw50002, ty_@0) → new_ltEs14(zxw49002, zxw50002)
new_esEs23(zxw49000, zxw50000, ty_@0) → new_esEs20(zxw49000, zxw50000)
new_esEs6(Right(zxw4000), Right(zxw3000), cha, ty_@0) → new_esEs20(zxw4000, zxw3000)
new_compare210(zxw49000, zxw50000, True, cg, da, db) → EQ
new_ltEs4(GT, LT) → False
new_sr0(Integer(zxw500000), Integer(zxw490010)) → Integer(new_primMulInt(zxw500000, zxw490010))
new_compare13(zxw49000, zxw50000, True) → LT
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_compare14(Float(zxw49000, zxw49001), Float(zxw50000, zxw50001)) → new_compare7(new_sr(zxw49000, zxw50000), new_sr(zxw49001, zxw50001))
new_primEqInt(Pos(Succ(zxw40000)), Neg(zxw3000)) → False
new_primEqInt(Neg(Succ(zxw40000)), Pos(zxw3000)) → False
new_esEs7(Just(zxw4000), Nothing, cea) → False
new_esEs7(Nothing, Just(zxw3000), cea) → False
new_esEs18(Double(zxw4000, zxw4001), Double(zxw3000, zxw3001)) → new_esEs13(new_sr(zxw4000, zxw3000), new_sr(zxw4001, zxw3001))
new_ltEs5(False, True) → True
new_esEs26(zxw49001, zxw50001, ty_Double) → new_esEs18(zxw49001, zxw50001)
new_compare28(zxw49000, zxw50000, cg, da, db) → new_compare210(zxw49000, zxw50000, new_esEs5(zxw49000, zxw50000, cg, da, db), cg, da, db)
new_esEs11(zxw4001, zxw3001, ty_Double) → new_esEs18(zxw4001, zxw3001)
new_ltEs6(zxw4900, zxw5000) → new_fsEs(new_compare14(zxw4900, zxw5000))
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Ordering, bcb) → new_ltEs4(zxw49000, zxw50000)
new_primEqInt(Pos(Zero), Neg(Succ(zxw30000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(zxw30000))) → False
new_ltEs19(zxw4900, zxw5000, app(app(ty_@2, h), cd)) → new_ltEs9(zxw4900, zxw5000, h, cd)
new_ltEs20(zxw49002, zxw50002, ty_Float) → new_ltEs6(zxw49002, zxw50002)
new_compare29(zxw49000, zxw50000, app(app(ty_@2, eg), eh)) → new_compare30(zxw49000, zxw50000, eg, eh)
new_compare24(zxw49000, zxw50000, True) → EQ
new_esEs27(zxw49000, zxw50000, ty_Int) → new_esEs13(zxw49000, zxw50000)
new_ltEs18(zxw49001, zxw50001, app(app(ty_@2, ba), bb)) → new_ltEs9(zxw49001, zxw50001, ba, bb)
new_esEs6(Right(zxw4000), Right(zxw3000), cha, ty_Double) → new_esEs18(zxw4000, zxw3000)
new_lt20(zxw49000, zxw50000, ty_Bool) → new_lt13(zxw49000, zxw50000)
new_primCmpNat0(Zero, zxw4900) → LT
new_ltEs7(Right(zxw49000), Right(zxw50000), bdb, ty_Char) → new_ltEs12(zxw49000, zxw50000)
new_esEs8(EQ, GT) → False
new_esEs8(GT, EQ) → False
new_esEs10(zxw4002, zxw3002, app(ty_[], bfb)) → new_esEs16(zxw4002, zxw3002, bfb)
new_lt15(zxw49000, zxw50000) → new_esEs8(new_compare31(zxw49000, zxw50000), LT)
new_compare17(zxw49000, zxw50000, False, cb, cc) → GT
new_compare29(zxw49000, zxw50000, ty_Float) → new_compare14(zxw49000, zxw50000)
new_esEs28(zxw4000, zxw3000, app(ty_Ratio, dbc)) → new_esEs14(zxw4000, zxw3000, dbc)
new_compare26(zxw490, zxw500, True, ga) → EQ
new_primCompAux0(zxw218, LT) → LT
new_esEs11(zxw4001, zxw3001, ty_@0) → new_esEs20(zxw4001, zxw3001)
new_esEs12(zxw4000, zxw3000, ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_not(False) → True
new_esEs6(Left(zxw4000), Left(zxw3000), app(app(ty_Either, cge), cgf), cfg) → new_esEs6(zxw4000, zxw3000, cge, cgf)
new_esEs28(zxw4000, zxw3000, app(ty_[], dbd)) → new_esEs16(zxw4000, zxw3000, dbd)
new_esEs24(zxw4001, zxw3001, ty_Int) → new_esEs13(zxw4001, zxw3001)
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_esEs26(zxw49001, zxw50001, app(ty_Ratio, dae)) → new_esEs14(zxw49001, zxw50001, dae)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Double) → new_ltEs11(zxw49000, zxw50000)
new_esEs11(zxw4001, zxw3001, app(app(ty_Either, bgh), bha)) → new_esEs6(zxw4001, zxw3001, bgh, bha)
new_esEs21(zxw4001, zxw3001, ty_@0) → new_esEs20(zxw4001, zxw3001)
new_lt19(zxw49001, zxw50001, ty_Float) → new_lt7(zxw49001, zxw50001)
new_ltEs7(Right(zxw49000), Right(zxw50000), bdb, ty_Int) → new_ltEs10(zxw49000, zxw50000)
new_compare0(:(zxw49000, zxw49001), [], ef) → GT
new_esEs12(zxw4000, zxw3000, ty_Float) → new_esEs19(zxw4000, zxw3000)
new_ltEs8(Just(zxw49000), Just(zxw50000), app(ty_[], dh)) → new_ltEs13(zxw49000, zxw50000, dh)
new_lt14(zxw49000, zxw50000) → new_esEs8(new_compare6(zxw49000, zxw50000), LT)
new_ltEs19(zxw4900, zxw5000, ty_Float) → new_ltEs6(zxw4900, zxw5000)
new_esEs27(zxw49000, zxw50000, app(app(ty_Either, bbf), bbg)) → new_esEs6(zxw49000, zxw50000, bbf, bbg)
new_lt19(zxw49001, zxw50001, app(ty_Ratio, dae)) → new_lt18(zxw49001, zxw50001, dae)
new_esEs9(True, True) → True
new_lt19(zxw49001, zxw50001, app(app(app(ty_@3, bab), bac), bad)) → new_lt16(zxw49001, zxw50001, bab, bac, bad)
new_lt19(zxw49001, zxw50001, ty_Char) → new_lt6(zxw49001, zxw50001)
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Double, cfg) → new_esEs18(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, app(ty_Maybe, dbb)) → new_esEs7(zxw4000, zxw3000, dbb)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_esEs21(zxw4001, zxw3001, app(app(app(ty_@3, cbf), cbg), cbh)) → new_esEs5(zxw4001, zxw3001, cbf, cbg, cbh)
new_esEs22(zxw4000, zxw3000, app(ty_[], ccg)) → new_esEs16(zxw4000, zxw3000, ccg)
new_esEs21(zxw4001, zxw3001, app(ty_Maybe, cbc)) → new_esEs7(zxw4001, zxw3001, cbc)
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_esEs22(zxw4000, zxw3000, ty_Double) → new_esEs18(zxw4000, zxw3000)
new_esEs21(zxw4001, zxw3001, app(app(ty_@2, ccc), ccd)) → new_esEs4(zxw4001, zxw3001, ccc, ccd)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_@0) → new_ltEs14(zxw49000, zxw50000)
new_esEs19(Float(zxw4000, zxw4001), Float(zxw3000, zxw3001)) → new_esEs13(new_sr(zxw4000, zxw3000), new_sr(zxw4001, zxw3001))
new_ltEs19(zxw4900, zxw5000, app(ty_Maybe, caf)) → new_ltEs8(zxw4900, zxw5000, caf)
new_primMulInt(Neg(zxw40010), Neg(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primEqNat0(Zero, Succ(zxw30000)) → False
new_primEqNat0(Succ(zxw40000), Zero) → False
new_compare25(zxw49000, zxw50000, True, dc, dd) → EQ
new_ltEs7(Left(zxw49000), Left(zxw50000), app(app(ty_Either, bch), bda), bcb) → new_ltEs7(zxw49000, zxw50000, bch, bda)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_lt10(zxw49000, zxw50000, app(ty_Ratio, cdh)) → new_lt18(zxw49000, zxw50000, cdh)
new_esEs12(zxw4000, zxw3000, ty_@0) → new_esEs20(zxw4000, zxw3000)
new_esEs21(zxw4001, zxw3001, ty_Bool) → new_esEs9(zxw4001, zxw3001)
new_esEs5(@3(zxw4000, zxw4001, zxw4002), @3(zxw3000, zxw3001, zxw3002), bee, bef, beg) → new_asAs(new_esEs12(zxw4000, zxw3000, bee), new_asAs(new_esEs11(zxw4001, zxw3001, bef), new_esEs10(zxw4002, zxw3002, beg)))
new_esEs16(:(zxw4000, zxw4001), [], dba) → False
new_esEs16([], :(zxw3000, zxw3001), dba) → False
new_lt10(zxw49000, zxw50000, ty_Integer) → new_lt5(zxw49000, zxw50000)
new_lt6(zxw49000, zxw50000) → new_esEs8(new_compare12(zxw49000, zxw50000), LT)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_ltEs4(LT, GT) → True
new_esEs23(zxw49000, zxw50000, ty_Double) → new_esEs18(zxw49000, zxw50000)
new_compare25(zxw49000, zxw50000, False, dc, dd) → new_compare15(zxw49000, zxw50000, new_ltEs7(zxw49000, zxw50000, dc, dd), dc, dd)
new_lt19(zxw49001, zxw50001, app(app(ty_Either, bae), baf)) → new_lt17(zxw49001, zxw50001, bae, baf)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_esEs6(Left(zxw4000), Left(zxw3000), app(ty_Maybe, cff), cfg) → new_esEs7(zxw4000, zxw3000, cff)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Ordering, cfg) → new_esEs8(zxw4000, zxw3000)
new_esEs16(:(zxw4000, zxw4001), :(zxw3000, zxw3001), dba) → new_asAs(new_esEs28(zxw4000, zxw3000, dba), new_esEs16(zxw4001, zxw3001, dba))
new_ltEs8(Just(zxw49000), Just(zxw50000), app(ty_Ratio, cag)) → new_ltEs17(zxw49000, zxw50000, cag)
new_compare0(:(zxw49000, zxw49001), :(zxw50000, zxw50001), ef) → new_primCompAux1(zxw49000, zxw50000, new_compare0(zxw49001, zxw50001, ef), ef)
new_esEs11(zxw4001, zxw3001, app(ty_Maybe, bgb)) → new_esEs7(zxw4001, zxw3001, bgb)
new_esEs6(Right(zxw4000), Right(zxw3000), cha, app(app(ty_@2, dab), dac)) → new_esEs4(zxw4000, zxw3000, dab, dac)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Float) → new_ltEs6(zxw49000, zxw50000)
new_compare15(zxw49000, zxw50000, False, dc, dd) → GT
new_compare29(zxw49000, zxw50000, app(app(ty_Either, fg), fh)) → new_compare32(zxw49000, zxw50000, fg, fh)
new_lt20(zxw49000, zxw50000, ty_Float) → new_lt7(zxw49000, zxw50000)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Char) → new_esEs15(zxw4000, zxw3000)
new_esEs23(zxw49000, zxw50000, ty_Int) → new_esEs13(zxw49000, zxw50000)
new_esEs7(Just(zxw4000), Just(zxw3000), app(app(app(ty_@3, cee), cef), ceg)) → new_esEs5(zxw4000, zxw3000, cee, cef, ceg)
new_esEs9(True, False) → False
new_esEs9(False, True) → False
new_compare29(zxw49000, zxw50000, app(ty_Ratio, cfd)) → new_compare8(zxw49000, zxw50000, cfd)
new_esEs10(zxw4002, zxw3002, app(app(ty_@2, bfh), bga)) → new_esEs4(zxw4002, zxw3002, bfh, bga)
new_esEs11(zxw4001, zxw3001, app(ty_Ratio, bgc)) → new_esEs14(zxw4001, zxw3001, bgc)
new_compare29(zxw49000, zxw50000, ty_Ordering) → new_compare6(zxw49000, zxw50000)
new_esEs21(zxw4001, zxw3001, ty_Integer) → new_esEs17(zxw4001, zxw3001)
new_esEs27(zxw49000, zxw50000, ty_Double) → new_esEs18(zxw49000, zxw50000)
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs27(zxw49000, zxw50000, app(ty_Ratio, daf)) → new_esEs14(zxw49000, zxw50000, daf)
new_ltEs4(LT, EQ) → True
new_esEs6(Right(zxw4000), Right(zxw3000), cha, ty_Char) → new_esEs15(zxw4000, zxw3000)
new_esEs10(zxw4002, zxw3002, ty_Double) → new_esEs18(zxw4002, zxw3002)
new_compare31(@0, @0) → EQ
new_esEs12(zxw4000, zxw3000, app(app(ty_Either, cab), cac)) → new_esEs6(zxw4000, zxw3000, cab, cac)
new_ltEs8(Just(zxw49000), Just(zxw50000), app(ty_Maybe, dg)) → new_ltEs8(zxw49000, zxw50000, dg)
new_lt19(zxw49001, zxw50001, ty_Bool) → new_lt13(zxw49001, zxw50001)
new_ltEs7(Right(zxw49000), Right(zxw50000), bdb, app(app(ty_Either, beb), bec)) → new_ltEs7(zxw49000, zxw50000, beb, bec)
new_esEs28(zxw4000, zxw3000, app(app(ty_@2, dcb), dcc)) → new_esEs4(zxw4000, zxw3000, dcb, dcc)
new_compare9(Integer(zxw49000), Integer(zxw50000)) → new_primCmpInt(zxw49000, zxw50000)
new_asAs(False, zxw187) → False
new_primMulInt(Neg(zxw40010), Pos(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Double) → new_esEs18(zxw4000, zxw3000)
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Ordering) → new_ltEs4(zxw49000, zxw50000)
new_esEs21(zxw4001, zxw3001, ty_Ordering) → new_esEs8(zxw4001, zxw3001)
new_primCmpNat2(zxw4900, Zero) → GT
new_ltEs20(zxw49002, zxw50002, ty_Double) → new_ltEs11(zxw49002, zxw50002)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Char, cfg) → new_esEs15(zxw4000, zxw3000)
new_esEs26(zxw49001, zxw50001, app(ty_Maybe, hh)) → new_esEs7(zxw49001, zxw50001, hh)
new_esEs10(zxw4002, zxw3002, ty_@0) → new_esEs20(zxw4002, zxw3002)
new_lt19(zxw49001, zxw50001, ty_Double) → new_lt8(zxw49001, zxw50001)
new_esEs28(zxw4000, zxw3000, ty_Double) → new_esEs18(zxw4000, zxw3000)
new_compare110(zxw49000, zxw50000, True, cg, da, db) → LT
new_esEs24(zxw4001, zxw3001, ty_Integer) → new_esEs17(zxw4001, zxw3001)
new_lt19(zxw49001, zxw50001, app(ty_Maybe, hh)) → new_lt12(zxw49001, zxw50001, hh)
new_ltEs18(zxw49001, zxw50001, app(ty_Ratio, cdg)) → new_ltEs17(zxw49001, zxw50001, cdg)
new_ltEs18(zxw49001, zxw50001, ty_Char) → new_ltEs12(zxw49001, zxw50001)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Float, cfg) → new_esEs19(zxw4000, zxw3000)
new_esEs21(zxw4001, zxw3001, ty_Int) → new_esEs13(zxw4001, zxw3001)
new_lt20(zxw49000, zxw50000, app(ty_Ratio, daf)) → new_lt18(zxw49000, zxw50000, daf)
new_ltEs19(zxw4900, zxw5000, ty_@0) → new_ltEs14(zxw4900, zxw5000)
new_ltEs7(Right(zxw49000), Right(zxw50000), bdb, ty_Double) → new_ltEs11(zxw49000, zxw50000)
new_lt17(zxw49000, zxw50000, dc, dd) → new_esEs8(new_compare32(zxw49000, zxw50000, dc, dd), LT)
new_esEs9(False, False) → True
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Int) → new_ltEs10(zxw49000, zxw50000)
new_ltEs19(zxw4900, zxw5000, ty_Bool) → new_ltEs5(zxw4900, zxw5000)
new_compare29(zxw49000, zxw50000, ty_Integer) → new_compare9(zxw49000, zxw50000)
new_lt20(zxw49000, zxw50000, app(app(app(ty_@3, bbc), bbd), bbe)) → new_lt16(zxw49000, zxw50000, bbc, bbd, bbe)
new_ltEs20(zxw49002, zxw50002, app(app(ty_Either, hc), hd)) → new_ltEs7(zxw49002, zxw50002, hc, hd)
new_esEs4(@2(zxw4000, zxw4001), @2(zxw3000, zxw3001), cba, cbb) → new_asAs(new_esEs22(zxw4000, zxw3000, cba), new_esEs21(zxw4001, zxw3001, cbb))
new_esEs27(zxw49000, zxw50000, app(app(ty_@2, bag), bah)) → new_esEs4(zxw49000, zxw50000, bag, bah)
new_lt20(zxw49000, zxw50000, ty_Integer) → new_lt5(zxw49000, zxw50000)
new_ltEs18(zxw49001, zxw50001, app(ty_Maybe, bc)) → new_ltEs8(zxw49001, zxw50001, bc)
new_compare8(:%(zxw49000, zxw49001), :%(zxw50000, zxw50001), ty_Integer) → new_compare9(new_sr0(zxw49000, zxw50001), new_sr0(zxw50000, zxw49001))
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Float, bcb) → new_ltEs6(zxw49000, zxw50000)
new_ltEs4(LT, LT) → True
new_esEs16([], [], dba) → True
new_ltEs20(zxw49002, zxw50002, ty_Int) → new_ltEs10(zxw49002, zxw50002)
new_ltEs8(Nothing, Nothing, caf) → True
new_lt10(zxw49000, zxw50000, ty_Char) → new_lt6(zxw49000, zxw50000)
new_lt10(zxw49000, zxw50000, ty_Bool) → new_lt13(zxw49000, zxw50000)
new_esEs22(zxw4000, zxw3000, app(app(ty_Either, cdc), cdd)) → new_esEs6(zxw4000, zxw3000, cdc, cdd)
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_lt5(zxw49000, zxw50000) → new_esEs8(new_compare9(zxw49000, zxw50000), LT)
new_esEs26(zxw49001, zxw50001, ty_Float) → new_esEs19(zxw49001, zxw50001)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Int, cfg) → new_esEs13(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_esEs10(zxw4002, zxw3002, ty_Int) → new_esEs13(zxw4002, zxw3002)
new_ltEs15(@3(zxw49000, zxw49001, zxw49002), @3(zxw50000, zxw50001, zxw50002), gb, gc, hg) → new_pePe(new_lt20(zxw49000, zxw50000, gb), new_asAs(new_esEs27(zxw49000, zxw50000, gb), new_pePe(new_lt19(zxw49001, zxw50001, gc), new_asAs(new_esEs26(zxw49001, zxw50001, gc), new_ltEs20(zxw49002, zxw50002, hg)))))
new_lt10(zxw49000, zxw50000, app(ty_[], cf)) → new_lt9(zxw49000, zxw50000, cf)
new_esEs12(zxw4000, zxw3000, app(ty_Ratio, bhe)) → new_esEs14(zxw4000, zxw3000, bhe)
new_ltEs10(zxw4900, zxw5000) → new_fsEs(new_compare7(zxw4900, zxw5000))
new_esEs10(zxw4002, zxw3002, app(ty_Ratio, bfa)) → new_esEs14(zxw4002, zxw3002, bfa)
new_ltEs12(zxw4900, zxw5000) → new_fsEs(new_compare12(zxw4900, zxw5000))
new_esEs10(zxw4002, zxw3002, ty_Ordering) → new_esEs8(zxw4002, zxw3002)
new_ltEs7(Right(zxw49000), Right(zxw50000), bdb, ty_Float) → new_ltEs6(zxw49000, zxw50000)
new_esEs23(zxw49000, zxw50000, app(ty_[], cf)) → new_esEs16(zxw49000, zxw50000, cf)
new_esEs11(zxw4001, zxw3001, ty_Integer) → new_esEs17(zxw4001, zxw3001)
new_esEs26(zxw49001, zxw50001, app(app(ty_Either, bae), baf)) → new_esEs6(zxw49001, zxw50001, bae, baf)
new_compare16(Double(zxw49000, zxw49001), Double(zxw50000, zxw50001)) → new_compare7(new_sr(zxw49000, zxw50000), new_sr(zxw49001, zxw50001))
new_compare0([], :(zxw50000, zxw50001), ef) → LT
new_primPlusNat1(Zero, Zero) → Zero
new_esEs12(zxw4000, zxw3000, ty_Ordering) → new_esEs8(zxw4000, zxw3000)
new_lt10(zxw49000, zxw50000, ty_@0) → new_lt15(zxw49000, zxw50000)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Char) → new_ltEs12(zxw49000, zxw50000)
new_asAs(True, zxw187) → zxw187
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_esEs26(zxw49001, zxw50001, app(app(app(ty_@3, bab), bac), bad)) → new_esEs5(zxw49001, zxw50001, bab, bac, bad)
new_esEs10(zxw4002, zxw3002, app(app(ty_Either, bff), bfg)) → new_esEs6(zxw4002, zxw3002, bff, bfg)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Integer) → new_ltEs16(zxw49000, zxw50000)
new_compare30(zxw49000, zxw50000, cb, cc) → new_compare27(zxw49000, zxw50000, new_esEs4(zxw49000, zxw50000, cb, cc), cb, cc)
new_compare29(zxw49000, zxw50000, ty_Bool) → new_compare18(zxw49000, zxw50000)
new_fsEs(zxw202) → new_not(new_esEs8(zxw202, GT))
new_esEs23(zxw49000, zxw50000, app(app(app(ty_@3, cg), da), db)) → new_esEs5(zxw49000, zxw50000, cg, da, db)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Float) → new_esEs19(zxw4000, zxw3000)
new_compare10(zxw49000, zxw50000, True) → LT
new_compare29(zxw49000, zxw50000, app(ty_Maybe, fa)) → new_compare19(zxw49000, zxw50000, fa)
new_ltEs4(GT, GT) → True
new_esEs26(zxw49001, zxw50001, ty_@0) → new_esEs20(zxw49001, zxw50001)
new_compare110(zxw49000, zxw50000, False, cg, da, db) → GT
new_ltEs7(Left(zxw49000), Left(zxw50000), app(ty_Ratio, dag), bcb) → new_ltEs17(zxw49000, zxw50000, dag)
new_compare10(zxw49000, zxw50000, False) → GT
new_ltEs8(Just(zxw49000), Just(zxw50000), app(app(app(ty_@3, ea), eb), ec)) → new_ltEs15(zxw49000, zxw50000, ea, eb, ec)
new_esEs21(zxw4001, zxw3001, app(ty_[], cbe)) → new_esEs16(zxw4001, zxw3001, cbe)
new_compare18(zxw49000, zxw50000) → new_compare24(zxw49000, zxw50000, new_esEs9(zxw49000, zxw50000))
new_esEs6(Right(zxw4000), Right(zxw3000), cha, ty_Ordering) → new_esEs8(zxw4000, zxw3000)
new_esEs6(Left(zxw4000), Left(zxw3000), app(ty_[], cga), cfg) → new_esEs16(zxw4000, zxw3000, cga)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs6(Right(zxw4000), Right(zxw3000), cha, app(app(app(ty_@3, che), chf), chg)) → new_esEs5(zxw4000, zxw3000, che, chf, chg)
new_primCompAux0(zxw218, EQ) → zxw218
new_lt20(zxw49000, zxw50000, app(ty_Maybe, bba)) → new_lt12(zxw49000, zxw50000, bba)
new_esEs12(zxw4000, zxw3000, app(app(ty_@2, cad), cae)) → new_esEs4(zxw4000, zxw3000, cad, cae)
new_ltEs19(zxw4900, zxw5000, app(ty_[], ef)) → new_ltEs13(zxw4900, zxw5000, ef)
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_esEs22(zxw4000, zxw3000, app(ty_Maybe, cce)) → new_esEs7(zxw4000, zxw3000, cce)
new_ltEs7(Right(zxw49000), Right(zxw50000), bdb, ty_@0) → new_ltEs14(zxw49000, zxw50000)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_compare8(:%(zxw49000, zxw49001), :%(zxw50000, zxw50001), ty_Int) → new_compare7(new_sr(zxw49000, zxw50001), new_sr(zxw50000, zxw49001))
new_ltEs17(zxw4900, zxw5000, cah) → new_fsEs(new_compare8(zxw4900, zxw5000, cah))
new_not(True) → False

The set Q consists of the following terms:

new_esEs17(Integer(x0), Integer(x1))
new_compare8(:%(x0, x1), :%(x2, x3), ty_Integer)
new_lt10(x0, x1, ty_Double)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_compare18(x0, x1)
new_compare29(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Double)
new_lt18(x0, x1, x2)
new_esEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_pePe(False, x0)
new_compare26(Nothing, Nothing, False, x0)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_compare0([], :(x0, x1), x2)
new_compare7(x0, x1)
new_primMulNat0(Succ(x0), Zero)
new_esEs7(Just(x0), Just(x1), ty_Double)
new_esEs27(x0, x1, app(ty_[], x2))
new_ltEs8(Just(x0), Just(x1), ty_Integer)
new_esEs10(x0, x1, ty_Int)
new_ltEs10(x0, x1)
new_esEs28(x0, x1, ty_Int)
new_esEs23(x0, x1, app(ty_[], x2))
new_lt17(x0, x1, x2, x3)
new_esEs27(x0, x1, ty_Ordering)
new_ltEs7(Left(x0), Left(x1), ty_@0, x2)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs6(Right(x0), Right(x1), x2, ty_Float)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs12(x0, x1, ty_Char)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_esEs6(Left(x0), Left(x1), ty_@0, x2)
new_primMulNat0(Succ(x0), Succ(x1))
new_ltEs15(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs8(Just(x0), Nothing, x1)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_compare8(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_compare27(x0, x1, False, x2, x3)
new_ltEs16(x0, x1)
new_ltEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare13(x0, x1, True)
new_esEs10(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, ty_Float)
new_esEs11(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_Int)
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Ordering)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs8(GT, GT)
new_ltEs8(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt10(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs16(:(x0, x1), [], x2)
new_esEs11(x0, x1, app(ty_Maybe, x2))
new_lt10(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(LT, LT)
new_compare29(x0, x1, ty_Double)
new_esEs18(Double(x0, x1), Double(x2, x3))
new_primCmpNat0(Zero, x0)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_ltEs8(Just(x0), Just(x1), ty_Bool)
new_compare28(x0, x1, x2, x3, x4)
new_esEs11(x0, x1, ty_@0)
new_primCmpNat1(Zero, Succ(x0))
new_esEs16([], :(x0, x1), x2)
new_esEs25(x0, x1, ty_Int)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_sr(x0, x1)
new_ltEs5(False, False)
new_ltEs13(x0, x1, x2)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_compare6(x0, x1)
new_lt10(x0, x1, ty_Ordering)
new_compare110(x0, x1, True, x2, x3, x4)
new_esEs6(Left(x0), Left(x1), ty_Integer, x2)
new_compare29(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Integer)
new_primEqNat0(Zero, Succ(x0))
new_primCmpNat1(Zero, Zero)
new_compare0(:(x0, x1), [], x2)
new_esEs12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare16(Double(x0, x1), Double(x2, x3))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_lt7(x0, x1)
new_lt9(x0, x1, x2)
new_esEs28(x0, x1, ty_@0)
new_ltEs20(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Integer)
new_ltEs7(Left(x0), Left(x1), ty_Double, x2)
new_esEs23(x0, x1, ty_Integer)
new_ltEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_lt20(x0, x1, ty_Double)
new_compare110(x0, x1, False, x2, x3, x4)
new_ltEs19(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_Char)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, ty_Int)
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_primEqNat0(Zero, Zero)
new_esEs6(Right(x0), Right(x1), x2, ty_Integer)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs8(Just(x0), Just(x1), ty_Double)
new_ltEs8(Just(x0), Just(x1), ty_Ordering)
new_ltEs7(Right(x0), Left(x1), x2, x3)
new_ltEs7(Left(x0), Right(x1), x2, x3)
new_compare29(x0, x1, app(ty_[], x2))
new_ltEs17(x0, x1, x2)
new_ltEs19(x0, x1, ty_@0)
new_compare24(x0, x1, False)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_esEs9(True, True)
new_ltEs7(Left(x0), Left(x1), ty_Int, x2)
new_esEs10(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs7(Right(x0), Right(x1), x2, ty_@0)
new_ltEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_lt4(x0, x1)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_primMulNat0(Zero, Zero)
new_esEs7(Just(x0), Nothing, x1)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_Char)
new_esEs10(x0, x1, ty_@0)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Left(x0), Left(x1), ty_Double, x2)
new_lt10(x0, x1, ty_Char)
new_ltEs7(Left(x0), Left(x1), ty_Integer, x2)
new_esEs12(x0, x1, app(ty_Maybe, x2))
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs18(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_Integer)
new_ltEs8(Just(x0), Just(x1), app(ty_Maybe, x2))
new_fsEs(x0)
new_ltEs4(GT, GT)
new_esEs6(Right(x0), Right(x1), x2, ty_Double)
new_lt8(x0, x1)
new_ltEs7(Right(x0), Right(x1), x2, ty_Char)
new_ltEs8(Just(x0), Just(x1), app(ty_[], x2))
new_esEs10(x0, x1, ty_Float)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs28(x0, x1, ty_Double)
new_esEs14(:%(x0, x1), :%(x2, x3), x4)
new_esEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_primCompAux1(x0, x1, x2, x3)
new_lt10(x0, x1, ty_Int)
new_esEs10(x0, x1, ty_Bool)
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs6(Right(x0), Left(x1), x2, x3)
new_esEs6(Left(x0), Right(x1), x2, x3)
new_esEs11(x0, x1, app(app(ty_@2, x2), x3))
new_lt16(x0, x1, x2, x3, x4)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, ty_Ordering)
new_esEs7(Just(x0), Just(x1), ty_Int)
new_esEs10(x0, x1, ty_Char)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs10(x0, x1, app(ty_[], x2))
new_pePe(True, x0)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_primPlusNat0(Zero, x0)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, ty_Int)
new_lt6(x0, x1)
new_esEs26(x0, x1, ty_Bool)
new_compare24(x0, x1, True)
new_compare29(x0, x1, app(ty_Maybe, x2))
new_ltEs18(x0, x1, ty_Integer)
new_esEs12(x0, x1, app(app(ty_@2, x2), x3))
new_compare210(x0, x1, False, x2, x3, x4)
new_lt10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare14(Float(x0, x1), Float(x2, x3))
new_compare26(Just(x0), Nothing, False, x1)
new_compare210(x0, x1, True, x2, x3, x4)
new_compare29(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(x0, x1)
new_compare25(x0, x1, False, x2, x3)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_primPlusNat1(Zero, Zero)
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_primCompAux0(x0, GT)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_compare23(x0, x1, True)
new_esEs7(Nothing, Nothing, x0)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_lt15(x0, x1)
new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs11(x0, x1, app(ty_[], x2))
new_compare11(x0, x1, True, x2)
new_compare13(x0, x1, False)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_lt20(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_@0)
new_primPlusNat0(Succ(x0), x1)
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs4(EQ, EQ)
new_esEs6(Right(x0), Right(x1), x2, ty_Int)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, ty_Char)
new_lt11(x0, x1, x2, x3)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs11(x0, x1)
new_esEs12(x0, x1, ty_@0)
new_esEs24(x0, x1, ty_Integer)
new_ltEs20(x0, x1, ty_Char)
new_esEs7(Nothing, Just(x0), x1)
new_esEs12(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Just(x0), Just(x1), ty_Char)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs12(x0, x1, ty_Float)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_compare31(@0, @0)
new_esEs7(Just(x0), Just(x1), ty_Float)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_primCmpNat2(x0, Zero)
new_lt19(x0, x1, app(ty_[], x2))
new_ltEs4(EQ, LT)
new_ltEs4(LT, EQ)
new_esEs12(x0, x1, ty_Int)
new_lt19(x0, x1, ty_Double)
new_esEs10(x0, x1, app(ty_Maybe, x2))
new_primMulInt(Pos(x0), Pos(x1))
new_compare25(x0, x1, True, x2, x3)
new_esEs6(Left(x0), Left(x1), ty_Float, x2)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Bool)
new_lt10(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs26(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_@0)
new_asAs(True, x0)
new_primEqNat0(Succ(x0), Zero)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_esEs13(x0, x1)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs16([], [], x0)
new_esEs21(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Integer)
new_lt20(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Bool)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Char)
new_compare19(x0, x1, x2)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_Ordering)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_ltEs20(x0, x1, ty_Bool)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs27(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_Double)
new_esEs25(x0, x1, ty_Integer)
new_compare26(x0, x1, True, x2)
new_primMulInt(Neg(x0), Neg(x1))
new_ltEs7(Left(x0), Left(x1), ty_Bool, x2)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Left(x0), Left(x1), ty_Char, x2)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare0(:(x0, x1), :(x2, x3), x4)
new_lt10(x0, x1, ty_Bool)
new_compare26(Just(x0), Just(x1), False, x2)
new_primPlusNat1(Succ(x0), Zero)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, ty_Float)
new_ltEs4(LT, LT)
new_esEs10(x0, x1, ty_Integer)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Integer)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_compare23(x0, x1, False)
new_esEs6(Right(x0), Right(x1), x2, ty_Bool)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs12(x0, x1, app(ty_[], x2))
new_esEs11(x0, x1, ty_Bool)
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_compare0([], [], x0)
new_esEs23(x0, x1, ty_Double)
new_esEs21(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_Ordering)
new_ltEs7(Right(x0), Right(x1), x2, ty_Double)
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_primPlusNat1(Zero, Succ(x0))
new_ltEs12(x0, x1)
new_compare10(x0, x1, False)
new_esEs11(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpNat0(Succ(x0), x1)
new_esEs22(x0, x1, ty_@0)
new_ltEs7(Left(x0), Left(x1), ty_Char, x2)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs8(GT, EQ)
new_esEs8(EQ, GT)
new_compare17(x0, x1, True, x2, x3)
new_esEs22(x0, x1, ty_Bool)
new_lt19(x0, x1, ty_Float)
new_lt19(x0, x1, ty_Integer)
new_ltEs8(Just(x0), Just(x1), ty_Char)
new_compare27(x0, x1, True, x2, x3)
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs8(Just(x0), Just(x1), ty_Float)
new_lt5(x0, x1)
new_ltEs18(x0, x1, ty_Bool)
new_compare29(x0, x1, ty_Ordering)
new_esEs11(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_@0)
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs11(x0, x1, ty_Int)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs11(x0, x1, app(ty_Ratio, x2))
new_esEs11(x0, x1, ty_Char)
new_esEs27(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Float)
new_lt19(x0, x1, ty_Ordering)
new_ltEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_compare29(x0, x1, ty_Integer)
new_ltEs18(x0, x1, ty_Float)
new_esEs9(False, False)
new_esEs21(x0, x1, ty_Double)
new_esEs12(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_primCmpNat1(Succ(x0), Succ(x1))
new_lt10(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_@0)
new_ltEs7(Left(x0), Left(x1), ty_Float, x2)
new_ltEs6(x0, x1)
new_lt10(x0, x1, ty_Float)
new_esEs16(:(x0, x1), :(x2, x3), x4)
new_esEs22(x0, x1, ty_Int)
new_ltEs8(Nothing, Nothing, x0)
new_lt12(x0, x1, x2)
new_esEs21(x0, x1, ty_Float)
new_primCompAux0(x0, EQ)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs6(Right(x0), Right(x1), x2, ty_@0)
new_esEs21(x0, x1, ty_Integer)
new_esEs10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpNat1(Succ(x0), Zero)
new_esEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs18(x0, x1, ty_@0)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, ty_Double)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_compare29(x0, x1, app(app(ty_Either, x2), x3))
new_lt13(x0, x1)
new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs23(x0, x1, ty_Bool)
new_esEs6(Right(x0), Right(x1), x2, ty_Char)
new_ltEs5(True, True)
new_lt19(x0, x1, ty_Int)
new_lt19(x0, x1, ty_Char)
new_ltEs4(EQ, GT)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(GT, EQ)
new_not(True)
new_esEs11(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Float)
new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_compare26(Nothing, Just(x0), False, x1)
new_esEs28(x0, x1, ty_Char)
new_lt19(x0, x1, ty_@0)
new_ltEs18(x0, x1, app(ty_[], x2))
new_compare15(x0, x1, False, x2, x3)
new_esEs21(x0, x1, ty_Ordering)
new_esEs26(x0, x1, ty_Char)
new_ltEs18(x0, x1, ty_Int)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_ltEs20(x0, x1, ty_Ordering)
new_not(False)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_lt14(x0, x1)
new_compare12(Char(x0), Char(x1))
new_esEs15(Char(x0), Char(x1))
new_ltEs8(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare29(x0, x1, app(ty_Ratio, x2))
new_esEs10(x0, x1, app(app(ty_@2, x2), x3))
new_compare10(x0, x1, True)
new_compare15(x0, x1, True, x2, x3)
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt10(x0, x1, ty_@0)
new_asAs(False, x0)
new_esEs22(x0, x1, ty_Ordering)
new_ltEs18(x0, x1, ty_Char)
new_compare29(x0, x1, ty_Float)
new_esEs27(x0, x1, ty_Char)
new_lt19(x0, x1, ty_Bool)
new_lt10(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_ltEs8(Just(x0), Just(x1), ty_@0)
new_esEs20(@0, @0)
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_ltEs7(Right(x0), Right(x1), x2, ty_Int)
new_compare11(x0, x1, False, x2)
new_esEs26(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_Int)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_ltEs19(x0, x1, ty_Double)
new_esEs6(Left(x0), Left(x1), ty_Int, x2)
new_esEs22(x0, x1, ty_Char)
new_esEs9(False, True)
new_esEs9(True, False)
new_esEs12(x0, x1, app(ty_Ratio, x2))
new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_compare29(x0, x1, ty_Bool)
new_compare32(x0, x1, x2, x3)
new_ltEs8(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, ty_Integer)
new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs11(x0, x1, ty_Double)
new_ltEs20(x0, x1, ty_Float)
new_primCompAux0(x0, LT)
new_primCmpNat2(x0, Succ(x1))
new_esEs12(x0, x1, ty_Integer)
new_esEs10(x0, x1, ty_Double)
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare17(x0, x1, False, x2, x3)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_sr0(Integer(x0), Integer(x1))
new_primEqInt(Pos(Zero), Pos(Zero))
new_compare30(x0, x1, x2, x3)
new_ltEs18(x0, x1, ty_Double)
new_esEs12(x0, x1, ty_Double)
new_ltEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs12(x0, x1, ty_Bool)
new_esEs10(x0, x1, app(ty_Ratio, x2))
new_compare9(Integer(x0), Integer(x1))
new_lt10(x0, x1, ty_Integer)
new_ltEs9(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs19(Float(x0, x1), Float(x2, x3))
new_primMulNat0(Zero, Succ(x0))
new_esEs7(Just(x0), Just(x1), ty_@0)
new_ltEs4(GT, LT)
new_ltEs4(LT, GT)
new_ltEs7(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs5(True, False)
new_ltEs5(False, True)
new_ltEs7(Right(x0), Right(x1), x2, ty_Bool)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_ltEs8(Just(x0), Just(x1), ty_Int)
new_esEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs8(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, app(ty_[], x2))
new_compare29(x0, x1, ty_@0)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_Float)
new_esEs23(x0, x1, ty_Float)
new_ltEs8(Nothing, Just(x0), x1)
new_ltEs7(Right(x0), Right(x1), x2, ty_Float)

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) → new_deleteMin(zxw530, zxw531, zxw532, zxw533, zxw534, h, ba)

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

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



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

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) → new_deleteMax(zxw6440, zxw6441, zxw6442, zxw6443, zxw6444, h, ba)

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

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



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ 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) → new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), zxw53, h, ba)
new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba) → new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt3(new_sr(new_sIZE_RATIO, new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba), LT), h, ba)
new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba) → new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt2(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba), LT), h, ba)
new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba) → new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt0(new_sr(new_sIZE_RATIO, new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba), LT), h, ba)
new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba) → new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), zxw53, h, ba)
new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba) → new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt1(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba), LT), h, ba)

The TRS R consists of the following rules:

new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_esEs8(EQ, EQ) → True
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primMulInt(Neg(zxw40010), Pos(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primCmpInt1(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → new_primCmpInt4(zxw6200, new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba))
new_primMulInt(Neg(zxw40010), Neg(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpInt0(Neg(Succ(zxw8900)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Succ(zxw8900)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primPlusNat1(Zero, Zero) → Zero
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt2(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primCmpInt4(zxw6200, zxw104) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw104)
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → GT
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpInt3(Pos(Succ(zxw9100)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Succ(zxw9100)), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba))
new_sr(zxw4001, zxw3001) → new_primMulInt(zxw4001, zxw3001)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba)
new_primCmpNat1(Zero, Zero) → EQ
new_esEs8(GT, EQ) → False
new_esEs8(EQ, GT) → False
new_sizeFM0(EmptyFM, h, ba) → Pos(Zero)
new_primMulNat0(Zero, Zero) → Zero
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_esEs8(GT, GT) → True
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → GT
new_esEs8(GT, LT) → False
new_esEs8(LT, GT) → False
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → LT
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpInt3(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Zero), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba))
new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_primCmpInt5(zxw6200, zxw107) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw107)
new_primCmpInt0(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba) → zxw52
new_esEs8(EQ, LT) → False
new_esEs8(LT, EQ) → False
new_primCmpInt0(Pos(Succ(zxw8900)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Succ(zxw8900)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primCmpInt2(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → new_primCmpInt5(zxw6200, new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba))
new_primCmpInt0(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_esEs8(LT, LT) → True
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt3(Neg(Succ(zxw9100)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Succ(zxw9100)), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba))
new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba)
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt2(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → LT
new_primCmpInt3(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Zero), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba))
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)

The set Q consists of the following terms:

new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primMulNat0(Zero, Zero)
new_glueVBal3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt4(x0, x1)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_sr(x0, x1)
new_primCmpInt2(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt3(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt2(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpInt0(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sIZE_RATIO
new_sizeFM0(EmptyFM, x0, x1)
new_primCmpInt3(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt0(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt0(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt2(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpInt3(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpInt2(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat1(Succ(x0), Succ(x1))
new_primCmpInt3(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt2(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpNat2(x0, Zero)
new_primCmpInt0(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt5(x0, x1)
new_primPlusNat0(Zero, x0)

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

↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ 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_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba) → new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), zxw53, h, ba)
new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba) → new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt3(new_sr(new_sIZE_RATIO, new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba), LT), h, ba)
new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba) → new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt2(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba), LT), h, ba)
new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba) → new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt0(new_sr(new_sIZE_RATIO, new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba), LT), h, ba)
new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba) → new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), zxw53, h, ba)
new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba) → new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt1(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba), LT), h, ba)

The TRS R consists of the following rules:

new_primCmpInt2(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → GT
new_primCmpInt2(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → new_primCmpInt5(zxw6200, new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba))
new_primCmpInt2(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → LT
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba)
new_primCmpInt5(zxw6200, zxw107) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw107)
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba) → zxw52
new_primCmpInt1(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → new_primCmpInt4(zxw6200, new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba))
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → GT
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → LT
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba)
new_primCmpInt4(zxw6200, zxw104) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw104)
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_sr(zxw4001, zxw3001) → new_primMulInt(zxw4001, zxw3001)
new_primCmpInt3(Pos(Succ(zxw9100)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Succ(zxw9100)), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba))
new_primCmpInt3(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Zero), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba))
new_primCmpInt3(Neg(Succ(zxw9100)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Succ(zxw9100)), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba))
new_primCmpInt3(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Zero), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba))
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Pos(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Neg(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primCmpInt0(Neg(Succ(zxw8900)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Succ(zxw8900)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primCmpInt0(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primCmpInt0(Pos(Succ(zxw8900)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Succ(zxw8900)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primCmpInt0(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))

The set Q consists of the following terms:

new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primMulNat0(Zero, Zero)
new_glueVBal3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt4(x0, x1)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_sr(x0, x1)
new_primCmpInt2(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt3(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt2(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpInt0(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sIZE_RATIO
new_sizeFM0(EmptyFM, x0, x1)
new_primCmpInt3(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt0(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt0(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt2(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpInt3(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpInt2(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat1(Succ(x0), Succ(x1))
new_primCmpInt3(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt2(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpNat2(x0, Zero)
new_primCmpInt0(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt5(x0, x1)
new_primPlusNat0(Zero, x0)

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) → new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt3(new_sr(new_sIZE_RATIO, new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba), LT), h, ba) 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) → new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt3(new_primMulInt(new_sIZE_RATIO, new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba), LT), h, ba)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ 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) → new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), zxw53, h, ba)
new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba) → new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt3(new_primMulInt(new_sIZE_RATIO, new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba), LT), h, ba)
new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba) → new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt2(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba), LT), h, ba)
new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba) → new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt0(new_sr(new_sIZE_RATIO, new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba), LT), h, ba)
new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba)
new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba) → new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt1(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba), LT), h, ba)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba) → new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), zxw53, h, ba)

The TRS R consists of the following rules:

new_primCmpInt2(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → GT
new_primCmpInt2(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → new_primCmpInt5(zxw6200, new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba))
new_primCmpInt2(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → LT
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba)
new_primCmpInt5(zxw6200, zxw107) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw107)
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba) → zxw52
new_primCmpInt1(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → new_primCmpInt4(zxw6200, new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba))
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → GT
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → LT
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba)
new_primCmpInt4(zxw6200, zxw104) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw104)
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_sr(zxw4001, zxw3001) → new_primMulInt(zxw4001, zxw3001)
new_primCmpInt3(Pos(Succ(zxw9100)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Succ(zxw9100)), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba))
new_primCmpInt3(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Zero), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba))
new_primCmpInt3(Neg(Succ(zxw9100)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Succ(zxw9100)), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba))
new_primCmpInt3(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Zero), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba))
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Pos(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Neg(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primCmpInt0(Neg(Succ(zxw8900)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Succ(zxw8900)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primCmpInt0(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primCmpInt0(Pos(Succ(zxw8900)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Succ(zxw8900)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primCmpInt0(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))

The set Q consists of the following terms:

new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primMulNat0(Zero, Zero)
new_glueVBal3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt4(x0, x1)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_sr(x0, x1)
new_primCmpInt2(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt3(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt2(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpInt0(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sIZE_RATIO
new_sizeFM0(EmptyFM, x0, x1)
new_primCmpInt3(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt0(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt0(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt2(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpInt3(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpInt2(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat1(Succ(x0), Succ(x1))
new_primCmpInt3(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt2(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpNat2(x0, Zero)
new_primCmpInt0(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt5(x0, x1)
new_primPlusNat0(Zero, x0)

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) → new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt0(new_sr(new_sIZE_RATIO, new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba), LT), h, ba) 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) → new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt0(new_primMulInt(new_sIZE_RATIO, new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba), LT), h, ba)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ 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_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba) → new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), zxw53, h, ba)
new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba) → new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt3(new_primMulInt(new_sIZE_RATIO, new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba), LT), h, ba)
new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba) → new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt2(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba), LT), h, ba)
new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba) → new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt0(new_primMulInt(new_sIZE_RATIO, new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba), LT), h, ba)
new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba) → new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), zxw53, h, ba)
new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba) → new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt1(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba), LT), h, ba)

The TRS R consists of the following rules:

new_primCmpInt2(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → GT
new_primCmpInt2(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → new_primCmpInt5(zxw6200, new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba))
new_primCmpInt2(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → LT
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba)
new_primCmpInt5(zxw6200, zxw107) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw107)
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba) → zxw52
new_primCmpInt1(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → new_primCmpInt4(zxw6200, new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba))
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → GT
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → LT
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba)
new_primCmpInt4(zxw6200, zxw104) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw104)
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_sr(zxw4001, zxw3001) → new_primMulInt(zxw4001, zxw3001)
new_primCmpInt3(Pos(Succ(zxw9100)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Succ(zxw9100)), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba))
new_primCmpInt3(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Zero), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba))
new_primCmpInt3(Neg(Succ(zxw9100)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Succ(zxw9100)), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba))
new_primCmpInt3(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Zero), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba))
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Pos(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Neg(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primCmpInt0(Neg(Succ(zxw8900)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Succ(zxw8900)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primCmpInt0(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primCmpInt0(Pos(Succ(zxw8900)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Succ(zxw8900)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primCmpInt0(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))

The set Q consists of the following terms:

new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primMulNat0(Zero, Zero)
new_glueVBal3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt4(x0, x1)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_sr(x0, x1)
new_primCmpInt2(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt3(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt2(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpInt0(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sIZE_RATIO
new_sizeFM0(EmptyFM, x0, x1)
new_primCmpInt3(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt0(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt0(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt2(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpInt3(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpInt2(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat1(Succ(x0), Succ(x1))
new_primCmpInt3(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt2(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpNat2(x0, Zero)
new_primCmpInt0(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt5(x0, x1)
new_primPlusNat0(Zero, x0)

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

↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ 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_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba) → new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), zxw53, h, ba)
new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba) → new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt3(new_primMulInt(new_sIZE_RATIO, new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba), LT), h, ba)
new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba) → new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt2(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba), LT), h, ba)
new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba) → new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt0(new_primMulInt(new_sIZE_RATIO, new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba), LT), h, ba)
new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba) → new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), zxw53, h, ba)
new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba) → new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt1(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba), LT), h, ba)

The TRS R consists of the following rules:

new_primCmpInt2(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → GT
new_primCmpInt2(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → new_primCmpInt5(zxw6200, new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba))
new_primCmpInt2(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → LT
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba)
new_primCmpInt5(zxw6200, zxw107) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw107)
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba) → zxw52
new_primCmpInt1(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → new_primCmpInt4(zxw6200, new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba))
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → GT
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → LT
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba)
new_primCmpInt4(zxw6200, zxw104) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw104)
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Pos(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Neg(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primCmpInt3(Pos(Succ(zxw9100)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Succ(zxw9100)), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba))
new_primCmpInt3(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Zero), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba))
new_primCmpInt3(Neg(Succ(zxw9100)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Succ(zxw9100)), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba))
new_primCmpInt3(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Zero), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba))
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primCmpInt0(Neg(Succ(zxw8900)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Succ(zxw8900)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primCmpInt0(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primCmpInt0(Pos(Succ(zxw8900)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Succ(zxw8900)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primCmpInt0(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))

The set Q consists of the following terms:

new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primMulNat0(Zero, Zero)
new_glueVBal3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt4(x0, x1)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_sr(x0, x1)
new_primCmpInt2(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt3(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt2(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpInt0(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sIZE_RATIO
new_sizeFM0(EmptyFM, x0, x1)
new_primCmpInt3(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt0(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt0(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt2(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpInt3(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpInt2(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat1(Succ(x0), Succ(x1))
new_primCmpInt3(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt2(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpNat2(x0, Zero)
new_primCmpInt0(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt5(x0, x1)
new_primPlusNat0(Zero, x0)

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

new_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) → new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), zxw53, h, ba)
new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba) → new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt3(new_primMulInt(new_sIZE_RATIO, new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba), LT), h, ba)
new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba) → new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt2(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba), LT), h, ba)
new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba) → new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt0(new_primMulInt(new_sIZE_RATIO, new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba), LT), h, ba)
new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba)
new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba) → new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt1(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba), LT), h, ba)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba) → new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), zxw53, h, ba)

The TRS R consists of the following rules:

new_primCmpInt2(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → GT
new_primCmpInt2(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → new_primCmpInt5(zxw6200, new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba))
new_primCmpInt2(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → LT
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba)
new_primCmpInt5(zxw6200, zxw107) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw107)
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba) → zxw52
new_primCmpInt1(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → new_primCmpInt4(zxw6200, new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba))
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → GT
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → LT
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba)
new_primCmpInt4(zxw6200, zxw104) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw104)
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Pos(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Neg(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primCmpInt3(Pos(Succ(zxw9100)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Succ(zxw9100)), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba))
new_primCmpInt3(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Zero), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba))
new_primCmpInt3(Neg(Succ(zxw9100)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Succ(zxw9100)), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba))
new_primCmpInt3(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Zero), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba))
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primCmpInt0(Neg(Succ(zxw8900)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Succ(zxw8900)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primCmpInt0(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primCmpInt0(Pos(Succ(zxw8900)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Succ(zxw8900)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primCmpInt0(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))

The set Q consists of the following terms:

new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primMulNat0(Zero, Zero)
new_glueVBal3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt4(x0, x1)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpInt2(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt3(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt2(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpInt0(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sIZE_RATIO
new_sizeFM0(EmptyFM, x0, x1)
new_primCmpInt3(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt0(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt0(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt2(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpInt3(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpInt2(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat1(Succ(x0), Succ(x1))
new_primCmpInt3(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt2(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpNat2(x0, Zero)
new_primCmpInt0(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt5(x0, x1)
new_primPlusNat0(Zero, x0)

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) → new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt3(new_primMulInt(new_sIZE_RATIO, new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba), LT), h, ba) 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) → new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(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)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba), LT), h, ba)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ 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_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba) → new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), zxw53, h, ba)
new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba) → new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt2(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba), LT), h, ba)
new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba) → new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt0(new_primMulInt(new_sIZE_RATIO, new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba), LT), h, ba)
new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba)
new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba) → new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(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)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba), LT), h, ba)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba) → new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), zxw53, h, ba)
new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba) → new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt1(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba), LT), h, ba)

The TRS R consists of the following rules:

new_primCmpInt2(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → GT
new_primCmpInt2(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → new_primCmpInt5(zxw6200, new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba))
new_primCmpInt2(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → LT
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba)
new_primCmpInt5(zxw6200, zxw107) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw107)
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba) → zxw52
new_primCmpInt1(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → new_primCmpInt4(zxw6200, new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba))
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → GT
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → LT
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba)
new_primCmpInt4(zxw6200, zxw104) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw104)
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Pos(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Neg(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primCmpInt3(Pos(Succ(zxw9100)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Succ(zxw9100)), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba))
new_primCmpInt3(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Zero), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba))
new_primCmpInt3(Neg(Succ(zxw9100)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Succ(zxw9100)), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba))
new_primCmpInt3(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Zero), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba))
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primCmpInt0(Neg(Succ(zxw8900)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Succ(zxw8900)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primCmpInt0(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primCmpInt0(Pos(Succ(zxw8900)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Succ(zxw8900)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primCmpInt0(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))

The set Q consists of the following terms:

new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primMulNat0(Zero, Zero)
new_glueVBal3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt4(x0, x1)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpInt2(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt3(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt2(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpInt0(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sIZE_RATIO
new_sizeFM0(EmptyFM, x0, x1)
new_primCmpInt3(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt0(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt0(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt2(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpInt3(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpInt2(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat1(Succ(x0), Succ(x1))
new_primCmpInt3(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt2(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpNat2(x0, Zero)
new_primCmpInt0(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt5(x0, x1)
new_primPlusNat0(Zero, x0)

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) → new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt0(new_primMulInt(new_sIZE_RATIO, new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba), LT), h, ba) 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) → new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(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)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba), LT), h, ba)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ 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) → new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), zxw53, h, ba)
new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba) → new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt2(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba), LT), h, ba)
new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba)
new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba) → new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(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)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba), LT), h, ba)
new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba) → new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt1(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba), LT), h, ba)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba) → new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), zxw53, h, ba)
new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba) → new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(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)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba), LT), h, ba)

The TRS R consists of the following rules:

new_primCmpInt2(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → GT
new_primCmpInt2(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → new_primCmpInt5(zxw6200, new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba))
new_primCmpInt2(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → LT
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba)
new_primCmpInt5(zxw6200, zxw107) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw107)
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba) → zxw52
new_primCmpInt1(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → new_primCmpInt4(zxw6200, new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba))
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → GT
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → LT
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba)
new_primCmpInt4(zxw6200, zxw104) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw104)
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Pos(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Neg(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primCmpInt3(Pos(Succ(zxw9100)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Succ(zxw9100)), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba))
new_primCmpInt3(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Zero), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba))
new_primCmpInt3(Neg(Succ(zxw9100)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Succ(zxw9100)), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba))
new_primCmpInt3(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Zero), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba))
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primCmpInt0(Neg(Succ(zxw8900)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Succ(zxw8900)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primCmpInt0(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primCmpInt0(Pos(Succ(zxw8900)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Succ(zxw8900)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primCmpInt0(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))

The set Q consists of the following terms:

new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primMulNat0(Zero, Zero)
new_glueVBal3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt4(x0, x1)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpInt2(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt3(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt2(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpInt0(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sIZE_RATIO
new_sizeFM0(EmptyFM, x0, x1)
new_primCmpInt3(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt0(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt0(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt2(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpInt3(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpInt2(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat1(Succ(x0), Succ(x1))
new_primCmpInt3(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt2(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpNat2(x0, Zero)
new_primCmpInt0(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt5(x0, x1)
new_primPlusNat0(Zero, x0)

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

↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ 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) → new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), zxw53, h, ba)
new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba) → new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt2(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba), LT), h, ba)
new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba)
new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba) → new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(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)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba), LT), h, ba)
new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba) → new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(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)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba), LT), h, ba)
new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba) → new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt1(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba), LT), h, ba)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba) → new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), zxw53, h, ba)

The TRS R consists of the following rules:

new_primCmpInt1(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → new_primCmpInt4(zxw6200, new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba))
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → GT
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → LT
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba)
new_primCmpInt4(zxw6200, zxw104) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw104)
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat0(Zero, zxw4900) → LT
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba) → zxw52
new_primCmpInt2(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → GT
new_primCmpInt2(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → new_primCmpInt5(zxw6200, new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba))
new_primCmpInt2(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → LT
new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba)
new_primCmpInt5(zxw6200, zxw107) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw107)
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primCmpInt0(Neg(Succ(zxw8900)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Succ(zxw8900)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primCmpInt0(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primCmpInt0(Pos(Succ(zxw8900)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Succ(zxw8900)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primCmpInt0(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primCmpInt3(Pos(Succ(zxw9100)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Succ(zxw9100)), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba))
new_primCmpInt3(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Zero), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba))
new_primCmpInt3(Neg(Succ(zxw9100)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Succ(zxw9100)), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba))
new_primCmpInt3(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Zero), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba))
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542

The set Q consists of the following terms:

new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primMulNat0(Zero, Zero)
new_glueVBal3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt4(x0, x1)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpInt2(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt3(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt2(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpInt0(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sIZE_RATIO
new_sizeFM0(EmptyFM, x0, x1)
new_primCmpInt3(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt0(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt0(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt2(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpInt3(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpInt2(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat1(Succ(x0), Succ(x1))
new_primCmpInt3(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt2(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpNat2(x0, Zero)
new_primCmpInt0(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt5(x0, x1)
new_primPlusNat0(Zero, x0)

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

new_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_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba) → new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), zxw53, h, ba)
new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba) → new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt2(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba), LT), h, ba)
new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba)
new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba) → new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), zxw53, h, ba)
new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba) → new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt1(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba), LT), h, ba)
new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba) → new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(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)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba), LT), h, ba)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba) → new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(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)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba), LT), h, ba)

The TRS R consists of the following rules:

new_primCmpInt1(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → new_primCmpInt4(zxw6200, new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba))
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → GT
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → LT
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba)
new_primCmpInt4(zxw6200, zxw104) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw104)
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat0(Zero, zxw4900) → LT
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba) → zxw52
new_primCmpInt2(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → GT
new_primCmpInt2(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → new_primCmpInt5(zxw6200, new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba))
new_primCmpInt2(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → LT
new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba)
new_primCmpInt5(zxw6200, zxw107) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw107)
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primCmpInt0(Neg(Succ(zxw8900)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Succ(zxw8900)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primCmpInt0(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primCmpInt0(Pos(Succ(zxw8900)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Succ(zxw8900)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primCmpInt0(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primCmpInt3(Pos(Succ(zxw9100)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Succ(zxw9100)), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba))
new_primCmpInt3(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Zero), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba))
new_primCmpInt3(Neg(Succ(zxw9100)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Succ(zxw9100)), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba))
new_primCmpInt3(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Zero), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba))
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542

The set Q consists of the following terms:

new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primMulNat0(Zero, Zero)
new_glueVBal3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt4(x0, x1)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpInt2(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt3(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt2(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpInt0(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sizeFM0(EmptyFM, x0, x1)
new_primCmpInt3(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt0(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt0(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt2(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpInt3(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpInt2(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat1(Succ(x0), Succ(x1))
new_primCmpInt3(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt2(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpNat2(x0, Zero)
new_primCmpInt0(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt5(x0, x1)
new_primPlusNat0(Zero, x0)

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) → new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(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)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba), LT), h, ba) 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) → new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt0(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba), LT), h, ba)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ 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) → new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), zxw53, h, ba)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba) → new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt0(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba), LT), h, ba)
new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba) → new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt2(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba), LT), h, ba)
new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba)
new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba)
new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba) → new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(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)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba), LT), h, ba)
new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba) → new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt1(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba), LT), h, ba)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba) → new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), zxw53, h, ba)

The TRS R consists of the following rules:

new_primCmpInt1(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → new_primCmpInt4(zxw6200, new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba))
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → GT
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → LT
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba)
new_primCmpInt4(zxw6200, zxw104) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw104)
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat0(Zero, zxw4900) → LT
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba) → zxw52
new_primCmpInt2(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → GT
new_primCmpInt2(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → new_primCmpInt5(zxw6200, new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba))
new_primCmpInt2(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → LT
new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba)
new_primCmpInt5(zxw6200, zxw107) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw107)
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primCmpInt0(Neg(Succ(zxw8900)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Succ(zxw8900)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primCmpInt0(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primCmpInt0(Pos(Succ(zxw8900)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Succ(zxw8900)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primCmpInt0(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primCmpInt3(Pos(Succ(zxw9100)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Succ(zxw9100)), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba))
new_primCmpInt3(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Zero), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba))
new_primCmpInt3(Neg(Succ(zxw9100)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Succ(zxw9100)), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba))
new_primCmpInt3(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Zero), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba))
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542

The set Q consists of the following terms:

new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primMulNat0(Zero, Zero)
new_glueVBal3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt4(x0, x1)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpInt2(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt3(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt2(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpInt0(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sizeFM0(EmptyFM, x0, x1)
new_primCmpInt3(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt0(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt0(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt2(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpInt3(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpInt2(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat1(Succ(x0), Succ(x1))
new_primCmpInt3(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt2(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpNat2(x0, Zero)
new_primCmpInt0(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt5(x0, x1)
new_primPlusNat0(Zero, x0)

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) → new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(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)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba), LT), h, ba) 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) → new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt3(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba), LT), h, ba)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ 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_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba) → new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), zxw53, h, ba)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba) → new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt0(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba), LT), h, ba)
new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba) → new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt2(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba), LT), h, ba)
new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba) → new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt3(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba), LT), h, ba)
new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba)
new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba) → new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), zxw53, h, ba)
new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba) → new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt1(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba), LT), h, ba)

The TRS R consists of the following rules:

new_primCmpInt1(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → new_primCmpInt4(zxw6200, new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba))
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → GT
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → LT
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba)
new_primCmpInt4(zxw6200, zxw104) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw104)
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat0(Zero, zxw4900) → LT
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba) → zxw52
new_primCmpInt2(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → GT
new_primCmpInt2(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → new_primCmpInt5(zxw6200, new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba))
new_primCmpInt2(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → LT
new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba)
new_primCmpInt5(zxw6200, zxw107) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw107)
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primCmpInt0(Neg(Succ(zxw8900)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Succ(zxw8900)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primCmpInt0(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primCmpInt0(Pos(Succ(zxw8900)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Succ(zxw8900)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primCmpInt0(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primCmpInt3(Pos(Succ(zxw9100)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Succ(zxw9100)), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba))
new_primCmpInt3(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Zero), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba))
new_primCmpInt3(Neg(Succ(zxw9100)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Succ(zxw9100)), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba))
new_primCmpInt3(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Zero), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba))
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542

The set Q consists of the following terms:

new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primMulNat0(Zero, Zero)
new_glueVBal3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt4(x0, x1)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpInt2(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt3(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt2(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpInt0(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sizeFM0(EmptyFM, x0, x1)
new_primCmpInt3(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt0(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt0(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt2(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpInt3(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpInt2(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat1(Succ(x0), Succ(x1))
new_primCmpInt3(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt2(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpNat2(x0, Zero)
new_primCmpInt0(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt5(x0, x1)
new_primPlusNat0(Zero, x0)

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) → new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt0(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba), LT), h, ba) 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) → new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt0(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw52), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba), LT), h, ba)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ 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) → new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), zxw53, h, ba)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba) → new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt0(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw52), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba), LT), h, ba)
new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba) → new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt2(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba), LT), h, ba)
new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba)
new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba) → new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt3(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba), LT), h, ba)
new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba)
new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba) → new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt1(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba), LT), h, ba)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba) → new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), zxw53, h, ba)

The TRS R consists of the following rules:

new_primCmpInt1(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → new_primCmpInt4(zxw6200, new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba))
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → GT
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → LT
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba)
new_primCmpInt4(zxw6200, zxw104) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw104)
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat0(Zero, zxw4900) → LT
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba) → zxw52
new_primCmpInt2(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → GT
new_primCmpInt2(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → new_primCmpInt5(zxw6200, new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba))
new_primCmpInt2(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → LT
new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba)
new_primCmpInt5(zxw6200, zxw107) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw107)
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primCmpInt0(Neg(Succ(zxw8900)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Succ(zxw8900)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primCmpInt0(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primCmpInt0(Pos(Succ(zxw8900)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Succ(zxw8900)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primCmpInt0(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primCmpInt3(Pos(Succ(zxw9100)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Succ(zxw9100)), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba))
new_primCmpInt3(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Zero), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba))
new_primCmpInt3(Neg(Succ(zxw9100)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Succ(zxw9100)), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba))
new_primCmpInt3(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Zero), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba))
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542

The set Q consists of the following terms:

new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primMulNat0(Zero, Zero)
new_glueVBal3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt4(x0, x1)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpInt2(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt3(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt2(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpInt0(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sizeFM0(EmptyFM, x0, x1)
new_primCmpInt3(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt0(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt0(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt2(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpInt3(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpInt2(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat1(Succ(x0), Succ(x1))
new_primCmpInt3(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt2(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpNat2(x0, Zero)
new_primCmpInt0(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt5(x0, x1)
new_primPlusNat0(Zero, x0)

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) → new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt3(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba), LT), h, ba) 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) → new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt3(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw52), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba), LT), h, ba)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ 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_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba) → new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), zxw53, h, ba)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba) → new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt0(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw52), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba), LT), h, ba)
new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba) → new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt2(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba), LT), h, ba)
new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba)
new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba) → new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt3(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw52), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba), LT), h, ba)
new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba) → new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), zxw53, h, ba)
new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba) → new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt1(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba), LT), h, ba)

The TRS R consists of the following rules:

new_primCmpInt1(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → new_primCmpInt4(zxw6200, new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba))
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → GT
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → LT
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba)
new_primCmpInt4(zxw6200, zxw104) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw104)
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat0(Zero, zxw4900) → LT
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba) → zxw52
new_primCmpInt2(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → GT
new_primCmpInt2(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → new_primCmpInt5(zxw6200, new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba))
new_primCmpInt2(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → LT
new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba)
new_primCmpInt5(zxw6200, zxw107) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw107)
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primCmpInt0(Neg(Succ(zxw8900)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Succ(zxw8900)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primCmpInt0(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primCmpInt0(Pos(Succ(zxw8900)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Succ(zxw8900)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primCmpInt0(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primCmpInt3(Pos(Succ(zxw9100)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Succ(zxw9100)), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba))
new_primCmpInt3(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Zero), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba))
new_primCmpInt3(Neg(Succ(zxw9100)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Succ(zxw9100)), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba))
new_primCmpInt3(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Zero), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba))
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542

The set Q consists of the following terms:

new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primMulNat0(Zero, Zero)
new_glueVBal3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt4(x0, x1)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpInt2(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt3(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt2(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpInt0(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sizeFM0(EmptyFM, x0, x1)
new_primCmpInt3(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt0(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt0(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt2(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpInt3(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpInt2(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat1(Succ(x0), Succ(x1))
new_primCmpInt3(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt2(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpNat2(x0, Zero)
new_primCmpInt0(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt5(x0, x1)
new_primPlusNat0(Zero, x0)

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) → new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt3(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw52), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba), LT), h, ba)
The remaining pairs can at least be oriented weakly.

new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba) → new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), zxw53, h, ba)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba) → new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt0(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw52), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba), LT), h, ba)
new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba) → new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt2(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba), LT), h, ba)
new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba)
new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba) → new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), zxw53, h, ba)
new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba) → new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt1(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba), LT), h, ba)
Used ordering: Polynomial interpretation [25]:

POL(Branch(x1, x2, x3, x4, x5)) = x1 + x3 + x5   
POL(EQ) = 0   
POL(False) = 0   
POL(GT) = 0   
POL(LT) = 0   
POL(Neg(x1)) = 1 + x1   
POL(Pos(x1)) = 0   
POL(Succ(x1)) = 0   
POL(True) = 0   
POL(Zero) = 0   
POL(new_esEs8(x1, x2)) = 0   
POL(new_glueVBal(x1, x2, x3, x4)) = x1   
POL(new_glueVBal3GlueVBal1(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = x10   
POL(new_glueVBal3GlueVBal10(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = x10   
POL(new_glueVBal3GlueVBal2(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = x10 + x6   
POL(new_glueVBal3GlueVBal20(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = 1 + x10 + x6 + x8   
POL(new_glueVBal3Size_r(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)) = x1 + x11 + x12 + x2 + x4 + x5   
POL(new_glueVBal3Size_r0(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)) = 1 + x1 + x11 + x12 + x2 + x4 + x5   
POL(new_primCmpInt(x1, x2)) = 0   
POL(new_primCmpInt0(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = 0   
POL(new_primCmpInt1(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)) = 0   
POL(new_primCmpInt2(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)) = 1 + x10 + x3 + x8   
POL(new_primCmpInt3(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = 1 + x10 + x8 + x9   
POL(new_primCmpInt4(x1, x2)) = 0   
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)) = 0   
POL(new_primMulNat0(x1, x2)) = 0   
POL(new_primPlusNat0(x1, x2)) = 0   
POL(new_primPlusNat1(x1, x2)) = 0   
POL(new_sizeFM(x1, x2, x3, x4, x5, x6, x7)) = 0   
POL(new_sizeFM0(x1, x2, x3)) = 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
                                    ↳ 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) → new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), zxw53, h, ba)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba) → new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt0(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw52), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba), LT), h, ba)
new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba) → new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt2(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba), LT), h, ba)
new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba)
new_glueVBal3GlueVBal10(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba)
new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba) → new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt1(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba), LT), h, ba)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba) → new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), zxw53, h, ba)

The TRS R consists of the following rules:

new_primCmpInt1(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → new_primCmpInt4(zxw6200, new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba))
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → GT
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → LT
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba)
new_primCmpInt4(zxw6200, zxw104) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw104)
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat0(Zero, zxw4900) → LT
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba) → zxw52
new_primCmpInt2(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → GT
new_primCmpInt2(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → new_primCmpInt5(zxw6200, new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba))
new_primCmpInt2(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → LT
new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba)
new_primCmpInt5(zxw6200, zxw107) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw107)
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primCmpInt0(Neg(Succ(zxw8900)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Succ(zxw8900)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primCmpInt0(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primCmpInt0(Pos(Succ(zxw8900)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Succ(zxw8900)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primCmpInt0(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primCmpInt3(Pos(Succ(zxw9100)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Succ(zxw9100)), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba))
new_primCmpInt3(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Zero), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba))
new_primCmpInt3(Neg(Succ(zxw9100)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Succ(zxw9100)), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba))
new_primCmpInt3(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Zero), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba))
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542

The set Q consists of the following terms:

new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primMulNat0(Zero, Zero)
new_glueVBal3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt4(x0, x1)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpInt2(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt3(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt2(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpInt0(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sizeFM0(EmptyFM, x0, x1)
new_primCmpInt3(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt0(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt0(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt2(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpInt3(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpInt2(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat1(Succ(x0), Succ(x1))
new_primCmpInt3(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt2(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpNat2(x0, Zero)
new_primCmpInt0(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt5(x0, x1)
new_primPlusNat0(Zero, x0)

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) → new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), zxw53, h, ba)
new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba) → new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt2(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba), LT), h, ba)

The TRS R consists of the following rules:

new_primCmpInt1(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → new_primCmpInt4(zxw6200, new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba))
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → GT
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → LT
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba)
new_primCmpInt4(zxw6200, zxw104) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw104)
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat0(Zero, zxw4900) → LT
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba) → zxw52
new_primCmpInt2(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → GT
new_primCmpInt2(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → new_primCmpInt5(zxw6200, new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba))
new_primCmpInt2(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → LT
new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba)
new_primCmpInt5(zxw6200, zxw107) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw107)
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primCmpInt0(Neg(Succ(zxw8900)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Succ(zxw8900)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primCmpInt0(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primCmpInt0(Pos(Succ(zxw8900)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Succ(zxw8900)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primCmpInt0(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primCmpInt3(Pos(Succ(zxw9100)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Succ(zxw9100)), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba))
new_primCmpInt3(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Zero), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba))
new_primCmpInt3(Neg(Succ(zxw9100)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Succ(zxw9100)), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba))
new_primCmpInt3(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Zero), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba))
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542

The set Q consists of the following terms:

new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primMulNat0(Zero, Zero)
new_glueVBal3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt4(x0, x1)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpInt2(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt3(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt2(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpInt0(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sizeFM0(EmptyFM, x0, x1)
new_primCmpInt3(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt0(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt0(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt2(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpInt3(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpInt2(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat1(Succ(x0), Succ(x1))
new_primCmpInt3(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt2(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpNat2(x0, Zero)
new_primCmpInt0(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt5(x0, x1)
new_primPlusNat0(Zero, x0)

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

↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ 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) → new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), zxw53, h, ba)
new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba) → new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt2(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba), LT), h, ba)

The TRS R consists of the following rules:

new_primCmpInt2(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → GT
new_primCmpInt2(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → new_primCmpInt5(zxw6200, new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba))
new_primCmpInt2(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → LT
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba)
new_primCmpInt5(zxw6200, zxw107) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw107)
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba) → zxw52

The set Q consists of the following terms:

new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primMulNat0(Zero, Zero)
new_glueVBal3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt4(x0, x1)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpInt2(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt3(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt2(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpInt0(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sizeFM0(EmptyFM, x0, x1)
new_primCmpInt3(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt0(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt0(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt2(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpInt3(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpInt2(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat1(Succ(x0), Succ(x1))
new_primCmpInt3(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt2(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpNat2(x0, Zero)
new_primCmpInt0(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt5(x0, x1)
new_primPlusNat0(Zero, x0)

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

new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primMulNat0(Zero, Zero)
new_primCmpInt4(x0, x1)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt1(Zero, x0, x1, Neg(Succ(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)
new_primCmpInt0(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_sizeFM0(EmptyFM, x0, x1)
new_primCmpInt3(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt0(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt0(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt3(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpInt3(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt0(Neg(Succ(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
                                                                                                  ↳ 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) → new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), zxw53, h, ba)
new_glueVBal(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba) → new_glueVBal3GlueVBal20(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt2(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba), LT), h, ba)

The TRS R consists of the following rules:

new_primCmpInt2(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → GT
new_primCmpInt2(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → new_primCmpInt5(zxw6200, new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba))
new_primCmpInt2(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → LT
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba)
new_primCmpInt5(zxw6200, zxw107) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw107)
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba) → zxw52

The set Q consists of the following terms:

new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_glueVBal3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt2(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt2(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primCmpNat1(Zero, Zero)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt2(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpInt2(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat1(Succ(x0), Succ(x1))
new_primCmpInt2(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt5(x0, x1)
new_primPlusNat0(Zero, x0)

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

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



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ 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_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba) → new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt0(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw52), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba), LT), h, ba)
new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba) → new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), zxw53, h, ba)
new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba) → new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt1(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba), LT), h, ba)

The TRS R consists of the following rules:

new_primCmpInt1(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → new_primCmpInt4(zxw6200, new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba))
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → GT
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → LT
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba)
new_primCmpInt4(zxw6200, zxw104) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw104)
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat0(Zero, zxw4900) → LT
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba) → zxw52
new_primCmpInt2(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_primCmpInt2(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → GT
new_primCmpInt2(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → new_primCmpInt5(zxw6200, new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba))
new_primCmpInt2(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → LT
new_glueVBal3Size_r0(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba)
new_primCmpInt5(zxw6200, zxw107) → new_primCmpInt(Neg(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw107)
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primCmpInt0(Neg(Succ(zxw8900)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Succ(zxw8900)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primCmpInt0(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primCmpInt0(Pos(Succ(zxw8900)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Succ(zxw8900)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primCmpInt0(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primCmpInt3(Pos(Succ(zxw9100)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Succ(zxw9100)), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba))
new_primCmpInt3(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Zero), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba))
new_primCmpInt3(Neg(Succ(zxw9100)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Succ(zxw9100)), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba))
new_primCmpInt3(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Zero), new_sizeFM0(Branch(zxw60, zxw61, Neg(zxw620), zxw63, zxw64), h, ba))
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542

The set Q consists of the following terms:

new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primMulNat0(Zero, Zero)
new_glueVBal3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt4(x0, x1)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpInt2(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt3(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt2(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpInt0(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sizeFM0(EmptyFM, x0, x1)
new_primCmpInt3(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt0(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt0(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt2(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpInt3(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpInt2(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat1(Succ(x0), Succ(x1))
new_primCmpInt3(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt2(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpNat2(x0, Zero)
new_primCmpInt0(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt5(x0, x1)
new_primPlusNat0(Zero, x0)

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

↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ 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_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba) → new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt0(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw52), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba), LT), h, ba)
new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba) → new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), zxw53, h, ba)
new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba) → new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt1(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba), LT), h, ba)

The TRS R consists of the following rules:

new_primCmpInt1(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → new_primCmpInt4(zxw6200, new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba))
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → GT
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → LT
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba)
new_primCmpInt4(zxw6200, zxw104) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw104)
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat0(Zero, zxw4900) → LT
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba) → zxw52
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primCmpInt0(Neg(Succ(zxw8900)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Succ(zxw8900)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primCmpInt0(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primCmpInt0(Pos(Succ(zxw8900)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Succ(zxw8900)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primCmpInt0(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero

The set Q consists of the following terms:

new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primMulNat0(Zero, Zero)
new_glueVBal3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt4(x0, x1)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpInt2(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt3(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt2(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpInt0(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sizeFM0(EmptyFM, x0, x1)
new_primCmpInt3(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt0(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt0(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt2(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpInt3(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpInt2(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat1(Succ(x0), Succ(x1))
new_primCmpInt3(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt2(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpNat2(x0, Zero)
new_primCmpInt0(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt5(x0, x1)
new_primPlusNat0(Zero, x0)

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

new_glueVBal3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt2(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt3(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt2(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_sizeFM0(EmptyFM, x0, x1)
new_primCmpInt3(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt2(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpInt3(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpInt2(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt3(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt2(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpInt5(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
                                                            ↳ 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_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, False, h, ba) → new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt0(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw52), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba), LT), h, ba)
new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba)
new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba) → new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt1(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba), LT), h, ba)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba) → new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), zxw53, h, ba)

The TRS R consists of the following rules:

new_primCmpInt1(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → new_primCmpInt4(zxw6200, new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba))
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → GT
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → LT
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba)
new_primCmpInt4(zxw6200, zxw104) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw104)
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat0(Zero, zxw4900) → LT
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba) → zxw52
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primCmpInt0(Neg(Succ(zxw8900)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Succ(zxw8900)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primCmpInt0(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primCmpInt0(Pos(Succ(zxw8900)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Succ(zxw8900)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primCmpInt0(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero

The set Q consists of the following terms:

new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primMulNat0(Zero, Zero)
new_primCmpInt4(x0, x1)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt0(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt0(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt0(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primPlusNat0(Succ(x0), x1)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpNat1(Succ(x0), Succ(x1))
new_primCmpNat2(x0, Zero)
new_primCmpInt0(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

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) → new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt0(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw52), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba), LT), h, ba)
The remaining pairs can at least be oriented weakly.

new_glueVBal3GlueVBal1(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba)
new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba) → new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt1(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba), LT), h, ba)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba) → new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), zxw53, h, ba)
Used ordering: Polynomial interpretation [25]:

POL(Branch(x1, x2, x3, x4, x5)) = x2 + x3 + x5   
POL(EQ) = 0   
POL(False) = 0   
POL(GT) = 0   
POL(LT) = 0   
POL(Neg(x1)) = 0   
POL(Pos(x1)) = 1   
POL(Succ(x1)) = 0   
POL(True) = 0   
POL(Zero) = 0   
POL(new_esEs8(x1, x2)) = 0   
POL(new_glueVBal(x1, x2, x3, x4)) = x1   
POL(new_glueVBal3GlueVBal1(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = x10   
POL(new_glueVBal3GlueVBal2(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = 1 + x10 + x7   
POL(new_glueVBal3Size_r(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)) = x1 + x11 + x12 + x2 + x3 + x4 + x5   
POL(new_primCmpInt(x1, x2)) = 0   
POL(new_primCmpInt0(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = 0   
POL(new_primCmpInt1(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)) = 0   
POL(new_primCmpInt4(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)) = x2   
POL(new_primPlusNat1(x1, x2)) = 0   
POL(new_sizeFM(x1, x2, x3, x4, x5, x6, x7)) = 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
                                    ↳ 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) → new_glueVBal(zxw64, Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba) → new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), zxw53, h, ba)
new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba) → new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt1(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba), LT), h, ba)

The TRS R consists of the following rules:

new_primCmpInt1(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → new_primCmpInt4(zxw6200, new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba))
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → GT
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → LT
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba)
new_primCmpInt4(zxw6200, zxw104) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw104)
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat0(Zero, zxw4900) → LT
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba) → zxw52
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primCmpInt0(Neg(Succ(zxw8900)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Succ(zxw8900)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primCmpInt0(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primCmpInt0(Pos(Succ(zxw8900)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Succ(zxw8900)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primCmpInt0(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero

The set Q consists of the following terms:

new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primMulNat0(Zero, Zero)
new_primCmpInt4(x0, x1)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt0(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt0(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt0(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primPlusNat0(Succ(x0), x1)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpNat1(Succ(x0), Succ(x1))
new_primCmpNat2(x0, Zero)
new_primCmpInt0(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

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_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba) → new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt1(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba), LT), h, ba)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba) → new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), zxw53, h, ba)

The TRS R consists of the following rules:

new_primCmpInt1(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → new_primCmpInt4(zxw6200, new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba))
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → GT
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → LT
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba)
new_primCmpInt4(zxw6200, zxw104) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw104)
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat0(Zero, zxw4900) → LT
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba) → zxw52
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primCmpInt0(Neg(Succ(zxw8900)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Succ(zxw8900)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primCmpInt0(Pos(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primCmpInt0(Pos(Succ(zxw8900)), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Pos(Succ(zxw8900)), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primCmpInt0(Neg(Zero), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_primCmpInt(Neg(Zero), new_sizeFM(zxw60, zxw61, Pos(zxw620), zxw63, zxw64, h, ba))
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero

The set Q consists of the following terms:

new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primMulNat0(Zero, Zero)
new_primCmpInt4(x0, x1)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt0(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt0(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt0(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primPlusNat0(Succ(x0), x1)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpNat1(Succ(x0), Succ(x1))
new_primCmpNat2(x0, Zero)
new_primCmpInt0(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

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

↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ 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_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba) → new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt1(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba), LT), h, ba)
new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, True, h, ba) → new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), zxw53, h, ba)

The TRS R consists of the following rules:

new_primCmpInt1(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → new_primCmpInt4(zxw6200, new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba))
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → GT
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → LT
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba)
new_primCmpInt4(zxw6200, zxw104) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw104)
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat0(Zero, zxw4900) → LT
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba) → zxw52

The set Q consists of the following terms:

new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primMulNat0(Zero, Zero)
new_primCmpInt4(x0, x1)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt0(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt0(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt0(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primPlusNat0(Succ(x0), x1)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpNat1(Succ(x0), Succ(x1))
new_primCmpNat2(x0, Zero)
new_primCmpInt0(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

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

new_primMulInt(Pos(x0), Pos(x1))
new_primMulNat0(Zero, Zero)
new_primMulNat0(Succ(x0), Zero)
new_primCmpInt0(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt0(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt0(Pos(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt0(Neg(Succ(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
                                                                                                              ↳ 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) → new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), zxw53, h, ba)
new_glueVBal(Branch(zxw60, zxw61, Pos(zxw620), zxw63, zxw64), Branch(zxw50, zxw51, zxw52, zxw53, zxw54), h, ba) → new_glueVBal3GlueVBal2(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, new_esEs8(new_primCmpInt1(zxw620, zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba), LT), h, ba)

The TRS R consists of the following rules:

new_primCmpInt1(Succ(zxw6200), zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → new_primCmpInt4(zxw6200, new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, Succ(zxw6200), zxw63, zxw64, h, ba))
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → GT
new_primCmpInt1(Zero, zxw50, zxw51, Neg(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Succ(zxw5200)), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → LT
new_primCmpInt1(Zero, zxw50, zxw51, Pos(Zero), zxw53, zxw54, zxw60, zxw61, zxw63, zxw64, h, ba) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_glueVBal3Size_r(zxw50, zxw51, zxw52, zxw53, zxw54, zxw60, zxw61, zxw620, zxw63, zxw64, h, ba) → new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba)
new_primCmpInt4(zxw6200, zxw104) → new_primCmpInt(Pos(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(zxw6200), zxw6200), zxw6200), zxw6200), zxw6200)), zxw104)
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat0(Zero, zxw4900) → LT
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)
new_sizeFM(zxw50, zxw51, zxw52, zxw53, zxw54, h, ba) → zxw52

The set Q consists of the following terms:

new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primCmpInt1(Zero, x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpInt4(x0, x1)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primCmpInt1(Zero, x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt1(Zero, x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primCmpNat1(Zero, Zero)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpInt1(Succ(x0), x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primPlusNat0(Succ(x0), x1)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpInt1(Zero, x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9)
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpNat1(Succ(x0), Succ(x1))
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

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

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



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ 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_C2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw300, zxw31, False, h, ba) → new_addToFM_C1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw300, zxw31, new_esEs8(new_compare19(Just(zxw300), zxw620, h), GT), h, ba)
new_addToFM_C1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw300, zxw31, True, h, ba) → new_addToFM_C(zxw624, zxw300, zxw31, h, ba)
new_addToFM_C2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw300, zxw31, True, h, ba) → new_addToFM_C(zxw623, zxw300, zxw31, h, ba)
new_addToFM_C(Branch(zxw620, zxw621, zxw622, zxw623, zxw624), zxw300, zxw31, h, ba) → new_addToFM_C2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw300, zxw31, new_lt12(Just(zxw300), zxw620, h), h, ba)

The TRS R consists of the following rules:

new_esEs6(Right(zxw4000), Right(zxw3000), cbf, ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_esEs7(Just(zxw4000), Just(zxw3000), app(ty_Maybe, beh)) → new_esEs7(zxw4000, zxw3000, beh)
new_ltEs19(zxw4900, zxw5000, ty_Integer) → new_ltEs16(zxw4900, zxw5000)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_@0, cab) → new_ltEs14(zxw49000, zxw50000)
new_esEs27(zxw49000, zxw50000, app(ty_[], cfh)) → new_esEs16(zxw49000, zxw50000, cfh)
new_ltEs4(EQ, GT) → True
new_esEs22(zxw4000, zxw3000, ty_@0) → new_esEs20(zxw4000, zxw3000)
new_compare15(zxw49000, zxw50000, True, bc, bd) → LT
new_esEs6(Right(zxw4000), Right(zxw3000), cbf, ty_Float) → new_esEs19(zxw4000, zxw3000)
new_ltEs9(@2(zxw49000, zxw49001), @2(zxw50000, zxw50001), bcf, bcg) → new_pePe(new_lt10(zxw49000, zxw50000, bcf), new_asAs(new_esEs23(zxw49000, zxw50000, bcf), new_ltEs18(zxw49001, zxw50001, bcg)))
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Integer, cad) → new_esEs17(zxw4000, zxw3000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_esEs23(zxw49000, zxw50000, app(app(ty_@2, ga), gb)) → new_esEs4(zxw49000, zxw50000, ga, gb)
new_compare29(zxw49000, zxw50000, ty_Char) → new_compare12(zxw49000, zxw50000)
new_esEs22(zxw4000, zxw3000, ty_Float) → new_esEs19(zxw4000, zxw3000)
new_esEs6(Right(zxw4000), Right(zxw3000), cbf, ty_Int) → new_esEs13(zxw4000, zxw3000)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Bool) → new_ltEs5(zxw49000, zxw50000)
new_lt19(zxw49001, zxw50001, ty_Integer) → new_lt5(zxw49001, zxw50001)
new_esEs12(zxw4000, zxw3000, ty_Bool) → new_esEs9(zxw4000, zxw3000)
new_esEs27(zxw49000, zxw50000, app(ty_Maybe, cfg)) → new_esEs7(zxw49000, zxw50000, cfg)
new_esEs12(zxw4000, zxw3000, ty_Char) → new_esEs15(zxw4000, zxw3000)
new_esEs11(zxw4001, zxw3001, app(ty_[], df)) → new_esEs16(zxw4001, zxw3001, df)
new_compare12(Char(zxw49000), Char(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_ltEs19(zxw4900, zxw5000, ty_Double) → new_ltEs11(zxw4900, zxw5000)
new_ltEs20(zxw49002, zxw50002, ty_Bool) → new_ltEs5(zxw49002, zxw50002)
new_compare29(zxw49000, zxw50000, ty_Double) → new_compare16(zxw49000, zxw50000)
new_esEs23(zxw49000, zxw50000, ty_Float) → new_esEs19(zxw49000, zxw50000)
new_lt19(zxw49001, zxw50001, ty_Ordering) → new_lt14(zxw49001, zxw50001)
new_lt19(zxw49001, zxw50001, ty_Int) → new_lt4(zxw49001, zxw50001)
new_esEs7(Just(zxw4000), Just(zxw3000), app(app(ty_Either, bff), bfg)) → new_esEs6(zxw4000, zxw3000, bff, bfg)
new_primMulNat0(Zero, Zero) → Zero
new_ltEs7(Left(zxw49000), Right(zxw50000), caa, cab) → True
new_compare26(Just(zxw4900), Nothing, False, bce) → GT
new_esEs26(zxw49001, zxw50001, app(ty_[], cef)) → new_esEs16(zxw49001, zxw50001, cef)
new_esEs27(zxw49000, zxw50000, ty_Bool) → new_esEs9(zxw49000, zxw50000)
new_ltEs18(zxw49001, zxw50001, ty_Integer) → new_ltEs16(zxw49001, zxw50001)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_ltEs18(zxw49001, zxw50001, app(ty_[], bdc)) → new_ltEs13(zxw49001, zxw50001, bdc)
new_ltEs20(zxw49002, zxw50002, app(ty_Maybe, cdc)) → new_ltEs8(zxw49002, zxw50002, cdc)
new_esEs11(zxw4001, zxw3001, ty_Char) → new_esEs15(zxw4001, zxw3001)
new_esEs11(zxw4001, zxw3001, ty_Float) → new_esEs19(zxw4001, zxw3001)
new_lt8(zxw49000, zxw50000) → new_esEs8(new_compare16(zxw49000, zxw50000), LT)
new_esEs26(zxw49001, zxw50001, ty_Char) → new_esEs15(zxw49001, zxw50001)
new_lt20(zxw49000, zxw50000, app(app(ty_@2, cfe), cff)) → new_lt11(zxw49000, zxw50000, cfe, cff)
new_esEs23(zxw49000, zxw50000, ty_Char) → new_esEs15(zxw49000, zxw50000)
new_esEs23(zxw49000, zxw50000, ty_Bool) → new_esEs9(zxw49000, zxw50000)
new_esEs27(zxw49000, zxw50000, ty_Char) → new_esEs15(zxw49000, zxw50000)
new_compare26(Nothing, Just(zxw5000), False, bce) → LT
new_lt10(zxw49000, zxw50000, ty_Float) → new_lt7(zxw49000, zxw50000)
new_esEs21(zxw4001, zxw3001, ty_Double) → new_esEs18(zxw4001, zxw3001)
new_ltEs19(zxw4900, zxw5000, ty_Int) → new_ltEs10(zxw4900, zxw5000)
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_lt9(zxw49000, zxw50000, be) → new_esEs8(new_compare0(zxw49000, zxw50000, be), LT)
new_compare210(zxw49000, zxw50000, False, bec, bed, bee) → new_compare110(zxw49000, zxw50000, new_ltEs15(zxw49000, zxw50000, bec, bed, bee), bec, bed, bee)
new_esEs22(zxw4000, zxw3000, app(ty_Ratio, bbd)) → new_esEs14(zxw4000, zxw3000, bbd)
new_esEs21(zxw4001, zxw3001, app(ty_Ratio, bab)) → new_esEs14(zxw4001, zxw3001, bab)
new_esEs7(Just(zxw4000), Just(zxw3000), app(app(ty_@2, bfh), bga)) → new_esEs4(zxw4000, zxw3000, bfh, bga)
new_esEs25(zxw4000, zxw3000, ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Bool) → new_esEs9(zxw4000, zxw3000)
new_ltEs20(zxw49002, zxw50002, ty_Integer) → new_ltEs16(zxw49002, zxw50002)
new_esEs21(zxw4001, zxw3001, app(app(ty_Either, bag), bah)) → new_esEs6(zxw4001, zxw3001, bag, bah)
new_ltEs7(Left(zxw49000), Left(zxw50000), app(app(app(ty_@3, chc), chd), che), cab) → new_ltEs15(zxw49000, zxw50000, chc, chd, che)
new_ltEs14(zxw4900, zxw5000) → new_fsEs(new_compare31(zxw4900, zxw5000))
new_compare24(zxw49000, zxw50000, False) → new_compare13(zxw49000, zxw50000, new_ltEs5(zxw49000, zxw50000))
new_esEs7(Just(zxw4000), Just(zxw3000), app(ty_Ratio, bfa)) → new_esEs14(zxw4000, zxw3000, bfa)
new_ltEs7(Right(zxw49000), Right(zxw50000), caa, app(app(ty_@2, daa), dab)) → new_ltEs9(zxw49000, zxw50000, daa, dab)
new_lt4(zxw490, zxw500) → new_esEs8(new_compare7(zxw490, zxw500), LT)
new_esEs28(zxw4000, zxw3000, app(app(app(ty_@3, dbg), dbh), dca)) → new_esEs5(zxw4000, zxw3000, dbg, dbh, dca)
new_esEs28(zxw4000, zxw3000, ty_Bool) → new_esEs9(zxw4000, zxw3000)
new_compare19(zxw490, zxw500, bce) → new_compare26(zxw490, zxw500, new_esEs7(zxw490, zxw500, bce), bce)
new_esEs17(Integer(zxw4000), Integer(zxw3000)) → new_primEqInt(zxw4000, zxw3000)
new_pePe(False, zxw213) → zxw213
new_lt12(zxw490, zxw500, bce) → new_esEs8(new_compare19(zxw490, zxw500, bce), LT)
new_esEs20(@0, @0) → True
new_esEs6(Right(zxw4000), Right(zxw3000), cbf, app(ty_Ratio, cbh)) → new_esEs14(zxw4000, zxw3000, cbh)
new_esEs6(Left(zxw4000), Left(zxw3000), app(app(ty_@2, cbd), cbe), cad) → new_esEs4(zxw4000, zxw3000, cbd, cbe)
new_compare23(zxw49000, zxw50000, True) → EQ
new_esEs11(zxw4001, zxw3001, ty_Int) → new_esEs13(zxw4001, zxw3001)
new_lt19(zxw49001, zxw50001, app(ty_[], cef)) → new_lt9(zxw49001, zxw50001, cef)
new_compare29(zxw49000, zxw50000, ty_@0) → new_compare31(zxw49000, zxw50000)
new_compare26(Nothing, Nothing, False, bce) → LT
new_esEs10(zxw4002, zxw3002, app(ty_Maybe, ca)) → new_esEs7(zxw4002, zxw3002, ca)
new_ltEs16(zxw4900, zxw5000) → new_fsEs(new_compare9(zxw4900, zxw5000))
new_esEs22(zxw4000, zxw3000, app(app(ty_@2, bcc), bcd)) → new_esEs4(zxw4000, zxw3000, bcc, bcd)
new_esEs23(zxw49000, zxw50000, app(ty_Maybe, beb)) → new_esEs7(zxw49000, zxw50000, beb)
new_ltEs7(Right(zxw49000), Right(zxw50000), caa, app(ty_Ratio, dbb)) → new_ltEs17(zxw49000, zxw50000, dbb)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Char, cab) → new_ltEs12(zxw49000, zxw50000)
new_esEs28(zxw4000, zxw3000, ty_@0) → new_esEs20(zxw4000, zxw3000)
new_ltEs20(zxw49002, zxw50002, app(ty_[], cdd)) → new_ltEs13(zxw49002, zxw50002, cdd)
new_esEs10(zxw4002, zxw3002, app(app(app(ty_@3, cd), ce), cf)) → new_esEs5(zxw4002, zxw3002, cd, ce, cf)
new_esEs27(zxw49000, zxw50000, ty_Float) → new_esEs19(zxw49000, zxw50000)
new_ltEs20(zxw49002, zxw50002, app(app(app(ty_@3, cde), cdf), cdg)) → new_ltEs15(zxw49002, zxw50002, cde, cdf, cdg)
new_esEs22(zxw4000, zxw3000, ty_Ordering) → new_esEs8(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Bool) → new_esEs9(zxw4000, zxw3000)
new_compare6(zxw49000, zxw50000) → new_compare23(zxw49000, zxw50000, new_esEs8(zxw49000, zxw50000))
new_esEs12(zxw4000, zxw3000, app(ty_[], eh)) → new_esEs16(zxw4000, zxw3000, eh)
new_compare32(zxw49000, zxw50000, bc, bd) → new_compare25(zxw49000, zxw50000, new_esEs6(zxw49000, zxw50000, bc, bd), bc, bd)
new_compare29(zxw49000, zxw50000, ty_Int) → new_compare7(zxw49000, zxw50000)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Bool, cad) → new_esEs9(zxw4000, zxw3000)
new_ltEs8(Nothing, Just(zxw50000), gc) → True
new_ltEs7(Left(zxw49000), Left(zxw50000), app(app(ty_@2, cgg), cgh), cab) → new_ltEs9(zxw49000, zxw50000, cgg, cgh)
new_esEs6(Right(zxw4000), Left(zxw3000), cbf, cad) → False
new_esEs6(Left(zxw4000), Right(zxw3000), cbf, cad) → False
new_esEs8(LT, LT) → True
new_lt20(zxw49000, zxw50000, ty_@0) → new_lt15(zxw49000, zxw50000)
new_esEs10(zxw4002, zxw3002, ty_Integer) → new_esEs17(zxw4002, zxw3002)
new_esEs28(zxw4000, zxw3000, ty_Float) → new_esEs19(zxw4000, zxw3000)
new_compare29(zxw49000, zxw50000, app(app(app(ty_@3, bgg), bgh), bha)) → new_compare28(zxw49000, zxw50000, bgg, bgh, bha)
new_lt19(zxw49001, zxw50001, ty_@0) → new_lt15(zxw49001, zxw50001)
new_ltEs7(Right(zxw49000), Right(zxw50000), caa, ty_Bool) → new_ltEs5(zxw49000, zxw50000)
new_ltEs5(True, False) → False
new_lt19(zxw49001, zxw50001, app(app(ty_@2, cec), ced)) → new_lt11(zxw49001, zxw50001, cec, ced)
new_compare0([], [], bgb) → EQ
new_pePe(True, zxw213) → True
new_primEqNat0(Zero, Zero) → True
new_esEs14(:%(zxw4000, zxw4001), :%(zxw3000, zxw3001), bhe) → new_asAs(new_esEs25(zxw4000, zxw3000, bhe), new_esEs24(zxw4001, zxw3001, bhe))
new_lt10(zxw49000, zxw50000, ty_Double) → new_lt8(zxw49000, zxw50000)
new_ltEs20(zxw49002, zxw50002, ty_Ordering) → new_ltEs4(zxw49002, zxw50002)
new_compare27(zxw49000, zxw50000, False, ga, gb) → new_compare17(zxw49000, zxw50000, new_ltEs9(zxw49000, zxw50000, ga, gb), ga, gb)
new_compare11(zxw180, zxw181, True, bb) → LT
new_esEs23(zxw49000, zxw50000, app(app(ty_Either, bc), bd)) → new_esEs6(zxw49000, zxw50000, bc, bd)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_@0, cad) → new_esEs20(zxw4000, zxw3000)
new_esEs6(Right(zxw4000), Right(zxw3000), cbf, ty_Bool) → new_esEs9(zxw4000, zxw3000)
new_esEs12(zxw4000, zxw3000, ty_Int) → new_esEs13(zxw4000, zxw3000)
new_lt20(zxw49000, zxw50000, app(ty_[], cfh)) → new_lt9(zxw49000, zxw50000, cfh)
new_esEs6(Right(zxw4000), Right(zxw3000), cbf, app(app(ty_Either, cce), ccf)) → new_esEs6(zxw4000, zxw3000, cce, ccf)
new_compare26(Just(zxw4900), Just(zxw5000), False, bce) → new_compare11(zxw4900, zxw5000, new_ltEs19(zxw4900, zxw5000, bce), bce)
new_ltEs5(True, True) → True
new_ltEs7(Left(zxw49000), Left(zxw50000), app(ty_Maybe, cha), cab) → new_ltEs8(zxw49000, zxw50000, cha)
new_ltEs20(zxw49002, zxw50002, app(app(ty_@2, cda), cdb)) → new_ltEs9(zxw49002, zxw50002, cda, cdb)
new_esEs15(Char(zxw4000), Char(zxw3000)) → new_primEqNat0(zxw4000, zxw3000)
new_sr(zxw4001, zxw3001) → new_primMulInt(zxw4001, zxw3001)
new_ltEs18(zxw49001, zxw50001, ty_Int) → new_ltEs10(zxw49001, zxw50001)
new_esEs25(zxw4000, zxw3000, ty_Int) → new_esEs13(zxw4000, zxw3000)
new_compare7(zxw49, zxw50) → new_primCmpInt(zxw49, zxw50)
new_primCmpNat1(Zero, Zero) → EQ
new_esEs7(Just(zxw4000), Just(zxw3000), app(ty_[], bfb)) → new_esEs16(zxw4000, zxw3000, bfb)
new_lt10(zxw49000, zxw50000, ty_Int) → new_lt4(zxw49000, zxw50000)
new_esEs28(zxw4000, zxw3000, app(app(ty_Either, dcb), dcc)) → new_esEs6(zxw4000, zxw3000, dcb, dcc)
new_ltEs7(Right(zxw49000), Right(zxw50000), caa, app(ty_Maybe, dac)) → new_ltEs8(zxw49000, zxw50000, dac)
new_ltEs7(Right(zxw49000), Right(zxw50000), caa, ty_Integer) → new_ltEs16(zxw49000, zxw50000)
new_ltEs7(Right(zxw49000), Right(zxw50000), caa, app(app(app(ty_@3, dae), daf), dag)) → new_ltEs15(zxw49000, zxw50000, dae, daf, dag)
new_esEs26(zxw49001, zxw50001, ty_Ordering) → new_esEs8(zxw49001, zxw50001)
new_esEs8(GT, GT) → True
new_esEs27(zxw49000, zxw50000, ty_@0) → new_esEs20(zxw49000, zxw50000)
new_esEs13(zxw400, zxw300) → new_primEqInt(zxw400, zxw300)
new_lt13(zxw49000, zxw50000) → new_esEs8(new_compare18(zxw49000, zxw50000), LT)
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_lt20(zxw49000, zxw50000, ty_Ordering) → new_lt14(zxw49000, zxw50000)
new_esEs11(zxw4001, zxw3001, ty_Ordering) → new_esEs8(zxw4001, zxw3001)
new_esEs11(zxw4001, zxw3001, app(app(ty_@2, ed), ee)) → new_esEs4(zxw4001, zxw3001, ed, ee)
new_compare23(zxw49000, zxw50000, False) → new_compare10(zxw49000, zxw50000, new_ltEs4(zxw49000, zxw50000))
new_lt10(zxw49000, zxw50000, app(app(ty_@2, ga), gb)) → new_lt11(zxw49000, zxw50000, ga, gb)
new_esEs8(LT, GT) → False
new_esEs8(GT, LT) → False
new_ltEs19(zxw4900, zxw5000, app(app(app(ty_@3, bhf), bhg), bhh)) → new_ltEs15(zxw4900, zxw5000, bhf, bhg, bhh)
new_lt20(zxw49000, zxw50000, app(app(ty_Either, cgd), cge)) → new_lt17(zxw49000, zxw50000, cgd, cge)
new_esEs26(zxw49001, zxw50001, ty_Bool) → new_esEs9(zxw49001, zxw50001)
new_ltEs11(zxw4900, zxw5000) → new_fsEs(new_compare16(zxw4900, zxw5000))
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_compare17(zxw49000, zxw50000, True, ga, gb) → LT
new_primEqInt(Neg(Succ(zxw40000)), Neg(Succ(zxw30000))) → new_primEqNat0(zxw40000, zxw30000)
new_ltEs5(False, False) → True
new_esEs23(zxw49000, zxw50000, ty_Ordering) → new_esEs8(zxw49000, zxw50000)
new_ltEs18(zxw49001, zxw50001, app(app(ty_Either, bdg), bdh)) → new_ltEs7(zxw49001, zxw50001, bdg, bdh)
new_esEs28(zxw4000, zxw3000, ty_Char) → new_esEs15(zxw4000, zxw3000)
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)
new_ltEs19(zxw4900, zxw5000, app(ty_Ratio, hf)) → new_ltEs17(zxw4900, zxw5000, hf)
new_esEs10(zxw4002, zxw3002, ty_Bool) → new_esEs9(zxw4002, zxw3002)
new_lt20(zxw49000, zxw50000, ty_Char) → new_lt6(zxw49000, zxw50000)
new_compare13(zxw49000, zxw50000, False) → GT
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Bool, cab) → new_ltEs5(zxw49000, zxw50000)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Int, cab) → new_ltEs10(zxw49000, zxw50000)
new_lt11(zxw49000, zxw50000, ga, gb) → new_esEs8(new_compare30(zxw49000, zxw50000, ga, gb), LT)
new_esEs21(zxw4001, zxw3001, ty_Char) → new_esEs15(zxw4001, zxw3001)
new_lt20(zxw49000, zxw50000, ty_Int) → new_lt4(zxw49000, zxw50000)
new_primCompAux1(zxw49000, zxw50000, zxw214, bgb) → new_primCompAux0(zxw214, new_compare29(zxw49000, zxw50000, bgb))
new_esEs7(Just(zxw4000), Just(zxw3000), ty_@0) → new_esEs20(zxw4000, zxw3000)
new_lt16(zxw49000, zxw50000, bec, bed, bee) → new_esEs8(new_compare28(zxw49000, zxw50000, bec, bed, bee), LT)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_ltEs7(Right(zxw49000), Left(zxw50000), caa, cab) → False
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Ordering) → new_esEs8(zxw4000, zxw3000)
new_ltEs7(Left(zxw49000), Left(zxw50000), app(ty_[], chb), cab) → new_ltEs13(zxw49000, zxw50000, chb)
new_ltEs19(zxw4900, zxw5000, ty_Ordering) → new_ltEs4(zxw4900, zxw5000)
new_ltEs20(zxw49002, zxw50002, ty_Char) → new_ltEs12(zxw49002, zxw50002)
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_ltEs20(zxw49002, zxw50002, app(ty_Ratio, ceb)) → new_ltEs17(zxw49002, zxw50002, ceb)
new_esEs11(zxw4001, zxw3001, app(app(app(ty_@3, dg), dh), ea)) → new_esEs5(zxw4001, zxw3001, dg, dh, ea)
new_ltEs18(zxw49001, zxw50001, ty_@0) → new_ltEs14(zxw49001, zxw50001)
new_primEqInt(Neg(Succ(zxw40000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(zxw30000))) → False
new_ltEs19(zxw4900, zxw5000, ty_Char) → new_ltEs12(zxw4900, zxw5000)
new_esEs12(zxw4000, zxw3000, ty_Double) → new_esEs18(zxw4000, zxw3000)
new_primCompAux0(zxw218, GT) → GT
new_esEs8(EQ, EQ) → True
new_esEs6(Left(zxw4000), Left(zxw3000), app(ty_Ratio, cae), cad) → new_esEs14(zxw4000, zxw3000, cae)
new_ltEs8(Just(zxw49000), Just(zxw50000), app(app(ty_Either, hc), hd)) → new_ltEs7(zxw49000, zxw50000, hc, hd)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Integer, cab) → new_ltEs16(zxw49000, zxw50000)
new_esEs6(Right(zxw4000), Right(zxw3000), cbf, app(ty_[], cca)) → new_esEs16(zxw4000, zxw3000, cca)
new_esEs23(zxw49000, zxw50000, ty_Integer) → new_esEs17(zxw49000, zxw50000)
new_esEs28(zxw4000, zxw3000, ty_Int) → new_esEs13(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, app(app(app(ty_@3, bbf), bbg), bbh)) → new_esEs5(zxw4000, zxw3000, bbf, bbg, bbh)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_ltEs18(zxw49001, zxw50001, ty_Ordering) → new_ltEs4(zxw49001, zxw50001)
new_ltEs4(EQ, LT) → False
new_esEs12(zxw4000, zxw3000, app(ty_Maybe, ef)) → new_esEs7(zxw4000, zxw3000, ef)
new_lt20(zxw49000, zxw50000, ty_Double) → new_lt8(zxw49000, zxw50000)
new_esEs10(zxw4002, zxw3002, ty_Float) → new_esEs19(zxw4002, zxw3002)
new_esEs11(zxw4001, zxw3001, ty_Bool) → new_esEs9(zxw4001, zxw3001)
new_compare11(zxw180, zxw181, False, bb) → GT
new_esEs26(zxw49001, zxw50001, ty_Integer) → new_esEs17(zxw49001, zxw50001)
new_lt10(zxw49000, zxw50000, ty_Ordering) → new_lt14(zxw49000, zxw50000)
new_ltEs18(zxw49001, zxw50001, ty_Bool) → new_ltEs5(zxw49001, zxw50001)
new_esEs12(zxw4000, zxw3000, app(app(app(ty_@3, fa), fb), fc)) → new_esEs5(zxw4000, zxw3000, fa, fb, fc)
new_primEqInt(Pos(Succ(zxw40000)), Pos(Succ(zxw30000))) → new_primEqNat0(zxw40000, zxw30000)
new_compare27(zxw49000, zxw50000, True, ga, gb) → EQ
new_esEs6(Left(zxw4000), Left(zxw3000), app(app(app(ty_@3, cag), cah), cba), cad) → new_esEs5(zxw4000, zxw3000, cag, cah, cba)
new_lt18(zxw49000, zxw50000, bef) → new_esEs8(new_compare8(zxw49000, zxw50000, bef), LT)
new_ltEs18(zxw49001, zxw50001, app(app(app(ty_@3, bdd), bde), bdf)) → new_ltEs15(zxw49001, zxw50001, bdd, bde, bdf)
new_lt10(zxw49000, zxw50000, app(ty_Maybe, beb)) → new_lt12(zxw49000, zxw50000, beb)
new_esEs26(zxw49001, zxw50001, ty_Int) → new_esEs13(zxw49001, zxw50001)
new_ltEs8(Just(zxw49000), Just(zxw50000), app(app(ty_@2, gd), ge)) → new_ltEs9(zxw49000, zxw50000, gd, ge)
new_primEqNat0(Succ(zxw40000), Succ(zxw30000)) → new_primEqNat0(zxw40000, zxw30000)
new_compare29(zxw49000, zxw50000, app(ty_[], bgf)) → new_compare0(zxw49000, zxw50000, bgf)
new_esEs27(zxw49000, zxw50000, ty_Ordering) → new_esEs8(zxw49000, zxw50000)
new_esEs27(zxw49000, zxw50000, ty_Integer) → new_esEs17(zxw49000, zxw50000)
new_esEs23(zxw49000, zxw50000, app(ty_Ratio, bef)) → new_esEs14(zxw49000, zxw50000, bef)
new_ltEs18(zxw49001, zxw50001, ty_Float) → new_ltEs6(zxw49001, zxw50001)
new_esEs22(zxw4000, zxw3000, ty_Int) → new_esEs13(zxw4000, zxw3000)
new_ltEs7(Right(zxw49000), Right(zxw50000), caa, app(ty_[], dad)) → new_ltEs13(zxw49000, zxw50000, dad)
new_ltEs4(GT, EQ) → False
new_lt7(zxw49000, zxw50000) → new_esEs8(new_compare14(zxw49000, zxw50000), LT)
new_lt10(zxw49000, zxw50000, app(app(app(ty_@3, bec), bed), bee)) → new_lt16(zxw49000, zxw50000, bec, bed, bee)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Int) → new_esEs13(zxw4000, zxw3000)
new_ltEs19(zxw4900, zxw5000, app(app(ty_Either, caa), cab)) → new_ltEs7(zxw4900, zxw5000, caa, cab)
new_ltEs8(Just(zxw49000), Nothing, gc) → False
new_esEs21(zxw4001, zxw3001, ty_Float) → new_esEs19(zxw4001, zxw3001)
new_esEs26(zxw49001, zxw50001, app(app(ty_@2, cec), ced)) → new_esEs4(zxw49001, zxw50001, cec, ced)
new_esEs27(zxw49000, zxw50000, app(app(app(ty_@3, cga), cgb), cgc)) → new_esEs5(zxw49000, zxw50000, cga, cgb, cgc)
new_ltEs13(zxw4900, zxw5000, bgb) → new_fsEs(new_compare0(zxw4900, zxw5000, bgb))
new_esEs22(zxw4000, zxw3000, ty_Char) → new_esEs15(zxw4000, zxw3000)
new_ltEs18(zxw49001, zxw50001, ty_Double) → new_ltEs11(zxw49001, zxw50001)
new_esEs7(Nothing, Nothing, beg) → True
new_esEs28(zxw4000, zxw3000, ty_Ordering) → new_esEs8(zxw4000, zxw3000)
new_lt10(zxw49000, zxw50000, app(app(ty_Either, bc), bd)) → new_lt17(zxw49000, zxw50000, bc, bd)
new_esEs8(EQ, LT) → False
new_esEs8(LT, EQ) → False
new_esEs10(zxw4002, zxw3002, ty_Char) → new_esEs15(zxw4002, zxw3002)
new_primEqInt(Pos(Succ(zxw40000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(zxw30000))) → False
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Double, cab) → new_ltEs11(zxw49000, zxw50000)
new_ltEs4(EQ, EQ) → True
new_esEs6(Right(zxw4000), Right(zxw3000), cbf, app(ty_Maybe, cbg)) → new_esEs7(zxw4000, zxw3000, cbg)
new_ltEs7(Right(zxw49000), Right(zxw50000), caa, ty_Ordering) → new_ltEs4(zxw49000, zxw50000)
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_ltEs20(zxw49002, zxw50002, ty_@0) → new_ltEs14(zxw49002, zxw50002)
new_esEs23(zxw49000, zxw50000, ty_@0) → new_esEs20(zxw49000, zxw50000)
new_esEs6(Right(zxw4000), Right(zxw3000), cbf, ty_@0) → new_esEs20(zxw4000, zxw3000)
new_compare210(zxw49000, zxw50000, True, bec, bed, bee) → EQ
new_ltEs4(GT, LT) → False
new_sr0(Integer(zxw500000), Integer(zxw490010)) → Integer(new_primMulInt(zxw500000, zxw490010))
new_compare13(zxw49000, zxw50000, True) → LT
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_compare14(Float(zxw49000, zxw49001), Float(zxw50000, zxw50001)) → new_compare7(new_sr(zxw49000, zxw50000), new_sr(zxw49001, zxw50001))
new_primEqInt(Pos(Succ(zxw40000)), Neg(zxw3000)) → False
new_primEqInt(Neg(Succ(zxw40000)), Pos(zxw3000)) → False
new_esEs7(Just(zxw4000), Nothing, beg) → False
new_esEs7(Nothing, Just(zxw3000), beg) → False
new_esEs18(Double(zxw4000, zxw4001), Double(zxw3000, zxw3001)) → new_esEs13(new_sr(zxw4000, zxw3000), new_sr(zxw4001, zxw3001))
new_ltEs5(False, True) → True
new_esEs26(zxw49001, zxw50001, ty_Double) → new_esEs18(zxw49001, zxw50001)
new_compare28(zxw49000, zxw50000, bec, bed, bee) → new_compare210(zxw49000, zxw50000, new_esEs5(zxw49000, zxw50000, bec, bed, bee), bec, bed, bee)
new_esEs11(zxw4001, zxw3001, ty_Double) → new_esEs18(zxw4001, zxw3001)
new_ltEs6(zxw4900, zxw5000) → new_fsEs(new_compare14(zxw4900, zxw5000))
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Ordering, cab) → new_ltEs4(zxw49000, zxw50000)
new_primEqInt(Pos(Zero), Neg(Succ(zxw30000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(zxw30000))) → False
new_ltEs19(zxw4900, zxw5000, app(app(ty_@2, bcf), bcg)) → new_ltEs9(zxw4900, zxw5000, bcf, bcg)
new_ltEs20(zxw49002, zxw50002, ty_Float) → new_ltEs6(zxw49002, zxw50002)
new_compare29(zxw49000, zxw50000, app(app(ty_@2, bgc), bgd)) → new_compare30(zxw49000, zxw50000, bgc, bgd)
new_compare24(zxw49000, zxw50000, True) → EQ
new_esEs27(zxw49000, zxw50000, ty_Int) → new_esEs13(zxw49000, zxw50000)
new_ltEs18(zxw49001, zxw50001, app(app(ty_@2, bch), bda)) → new_ltEs9(zxw49001, zxw50001, bch, bda)
new_esEs6(Right(zxw4000), Right(zxw3000), cbf, ty_Double) → new_esEs18(zxw4000, zxw3000)
new_lt20(zxw49000, zxw50000, ty_Bool) → new_lt13(zxw49000, zxw50000)
new_primCmpNat0(Zero, zxw4900) → LT
new_ltEs7(Right(zxw49000), Right(zxw50000), caa, ty_Char) → new_ltEs12(zxw49000, zxw50000)
new_esEs8(EQ, GT) → False
new_esEs8(GT, EQ) → False
new_esEs10(zxw4002, zxw3002, app(ty_[], cc)) → new_esEs16(zxw4002, zxw3002, cc)
new_lt15(zxw49000, zxw50000) → new_esEs8(new_compare31(zxw49000, zxw50000), LT)
new_compare17(zxw49000, zxw50000, False, ga, gb) → GT
new_compare29(zxw49000, zxw50000, ty_Float) → new_compare14(zxw49000, zxw50000)
new_esEs28(zxw4000, zxw3000, app(ty_Ratio, dbe)) → new_esEs14(zxw4000, zxw3000, dbe)
new_compare26(zxw490, zxw500, True, bce) → EQ
new_primCompAux0(zxw218, LT) → LT
new_esEs11(zxw4001, zxw3001, ty_@0) → new_esEs20(zxw4001, zxw3001)
new_esEs12(zxw4000, zxw3000, ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_not(False) → True
new_esEs6(Left(zxw4000), Left(zxw3000), app(app(ty_Either, cbb), cbc), cad) → new_esEs6(zxw4000, zxw3000, cbb, cbc)
new_esEs28(zxw4000, zxw3000, app(ty_[], dbf)) → new_esEs16(zxw4000, zxw3000, dbf)
new_esEs24(zxw4001, zxw3001, ty_Int) → new_esEs13(zxw4001, zxw3001)
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_esEs26(zxw49001, zxw50001, app(ty_Ratio, cfd)) → new_esEs14(zxw49001, zxw50001, cfd)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Double) → new_ltEs11(zxw49000, zxw50000)
new_esEs11(zxw4001, zxw3001, app(app(ty_Either, eb), ec)) → new_esEs6(zxw4001, zxw3001, eb, ec)
new_esEs21(zxw4001, zxw3001, ty_@0) → new_esEs20(zxw4001, zxw3001)
new_lt19(zxw49001, zxw50001, ty_Float) → new_lt7(zxw49001, zxw50001)
new_ltEs7(Right(zxw49000), Right(zxw50000), caa, ty_Int) → new_ltEs10(zxw49000, zxw50000)
new_compare0(:(zxw49000, zxw49001), [], bgb) → GT
new_esEs12(zxw4000, zxw3000, ty_Float) → new_esEs19(zxw4000, zxw3000)
new_ltEs8(Just(zxw49000), Just(zxw50000), app(ty_[], gg)) → new_ltEs13(zxw49000, zxw50000, gg)
new_lt14(zxw49000, zxw50000) → new_esEs8(new_compare6(zxw49000, zxw50000), LT)
new_ltEs19(zxw4900, zxw5000, ty_Float) → new_ltEs6(zxw4900, zxw5000)
new_esEs27(zxw49000, zxw50000, app(app(ty_Either, cgd), cge)) → new_esEs6(zxw49000, zxw50000, cgd, cge)
new_lt19(zxw49001, zxw50001, app(ty_Ratio, cfd)) → new_lt18(zxw49001, zxw50001, cfd)
new_esEs9(True, True) → True
new_lt19(zxw49001, zxw50001, app(app(app(ty_@3, ceg), ceh), cfa)) → new_lt16(zxw49001, zxw50001, ceg, ceh, cfa)
new_lt19(zxw49001, zxw50001, ty_Char) → new_lt6(zxw49001, zxw50001)
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Double, cad) → new_esEs18(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, app(ty_Maybe, dbd)) → new_esEs7(zxw4000, zxw3000, dbd)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_esEs21(zxw4001, zxw3001, app(app(app(ty_@3, bad), bae), baf)) → new_esEs5(zxw4001, zxw3001, bad, bae, baf)
new_esEs22(zxw4000, zxw3000, app(ty_[], bbe)) → new_esEs16(zxw4000, zxw3000, bbe)
new_esEs21(zxw4001, zxw3001, app(ty_Maybe, baa)) → new_esEs7(zxw4001, zxw3001, baa)
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_esEs22(zxw4000, zxw3000, ty_Double) → new_esEs18(zxw4000, zxw3000)
new_esEs21(zxw4001, zxw3001, app(app(ty_@2, bba), bbb)) → new_esEs4(zxw4001, zxw3001, bba, bbb)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_@0) → new_ltEs14(zxw49000, zxw50000)
new_esEs19(Float(zxw4000, zxw4001), Float(zxw3000, zxw3001)) → new_esEs13(new_sr(zxw4000, zxw3000), new_sr(zxw4001, zxw3001))
new_ltEs19(zxw4900, zxw5000, app(ty_Maybe, gc)) → new_ltEs8(zxw4900, zxw5000, gc)
new_primMulInt(Neg(zxw40010), Neg(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primEqNat0(Zero, Succ(zxw30000)) → False
new_primEqNat0(Succ(zxw40000), Zero) → False
new_compare25(zxw49000, zxw50000, True, bc, bd) → EQ
new_ltEs7(Left(zxw49000), Left(zxw50000), app(app(ty_Either, chf), chg), cab) → new_ltEs7(zxw49000, zxw50000, chf, chg)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_lt10(zxw49000, zxw50000, app(ty_Ratio, bef)) → new_lt18(zxw49000, zxw50000, bef)
new_esEs12(zxw4000, zxw3000, ty_@0) → new_esEs20(zxw4000, zxw3000)
new_esEs21(zxw4001, zxw3001, ty_Bool) → new_esEs9(zxw4001, zxw3001)
new_esEs5(@3(zxw4000, zxw4001, zxw4002), @3(zxw3000, zxw3001, zxw3002), bf, bg, bh) → new_asAs(new_esEs12(zxw4000, zxw3000, bf), new_asAs(new_esEs11(zxw4001, zxw3001, bg), new_esEs10(zxw4002, zxw3002, bh)))
new_esEs16(:(zxw4000, zxw4001), [], dbc) → False
new_esEs16([], :(zxw3000, zxw3001), dbc) → False
new_lt10(zxw49000, zxw50000, ty_Integer) → new_lt5(zxw49000, zxw50000)
new_lt6(zxw49000, zxw50000) → new_esEs8(new_compare12(zxw49000, zxw50000), LT)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_ltEs4(LT, GT) → True
new_esEs23(zxw49000, zxw50000, ty_Double) → new_esEs18(zxw49000, zxw50000)
new_compare25(zxw49000, zxw50000, False, bc, bd) → new_compare15(zxw49000, zxw50000, new_ltEs7(zxw49000, zxw50000, bc, bd), bc, bd)
new_lt19(zxw49001, zxw50001, app(app(ty_Either, cfb), cfc)) → new_lt17(zxw49001, zxw50001, cfb, cfc)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_esEs6(Left(zxw4000), Left(zxw3000), app(ty_Maybe, cac), cad) → new_esEs7(zxw4000, zxw3000, cac)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Ordering, cad) → new_esEs8(zxw4000, zxw3000)
new_esEs16(:(zxw4000, zxw4001), :(zxw3000, zxw3001), dbc) → new_asAs(new_esEs28(zxw4000, zxw3000, dbc), new_esEs16(zxw4001, zxw3001, dbc))
new_ltEs8(Just(zxw49000), Just(zxw50000), app(ty_Ratio, he)) → new_ltEs17(zxw49000, zxw50000, he)
new_compare0(:(zxw49000, zxw49001), :(zxw50000, zxw50001), bgb) → new_primCompAux1(zxw49000, zxw50000, new_compare0(zxw49001, zxw50001, bgb), bgb)
new_esEs11(zxw4001, zxw3001, app(ty_Maybe, dd)) → new_esEs7(zxw4001, zxw3001, dd)
new_esEs6(Right(zxw4000), Right(zxw3000), cbf, app(app(ty_@2, ccg), cch)) → new_esEs4(zxw4000, zxw3000, ccg, cch)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Float) → new_ltEs6(zxw49000, zxw50000)
new_compare15(zxw49000, zxw50000, False, bc, bd) → GT
new_compare29(zxw49000, zxw50000, app(app(ty_Either, bhb), bhc)) → new_compare32(zxw49000, zxw50000, bhb, bhc)
new_lt20(zxw49000, zxw50000, ty_Float) → new_lt7(zxw49000, zxw50000)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Char) → new_esEs15(zxw4000, zxw3000)
new_esEs23(zxw49000, zxw50000, ty_Int) → new_esEs13(zxw49000, zxw50000)
new_esEs7(Just(zxw4000), Just(zxw3000), app(app(app(ty_@3, bfc), bfd), bfe)) → new_esEs5(zxw4000, zxw3000, bfc, bfd, bfe)
new_esEs9(True, False) → False
new_esEs9(False, True) → False
new_compare29(zxw49000, zxw50000, app(ty_Ratio, bhd)) → new_compare8(zxw49000, zxw50000, bhd)
new_esEs10(zxw4002, zxw3002, app(app(ty_@2, db), dc)) → new_esEs4(zxw4002, zxw3002, db, dc)
new_esEs11(zxw4001, zxw3001, app(ty_Ratio, de)) → new_esEs14(zxw4001, zxw3001, de)
new_compare29(zxw49000, zxw50000, ty_Ordering) → new_compare6(zxw49000, zxw50000)
new_esEs21(zxw4001, zxw3001, ty_Integer) → new_esEs17(zxw4001, zxw3001)
new_esEs27(zxw49000, zxw50000, ty_Double) → new_esEs18(zxw49000, zxw50000)
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs27(zxw49000, zxw50000, app(ty_Ratio, cgf)) → new_esEs14(zxw49000, zxw50000, cgf)
new_ltEs4(LT, EQ) → True
new_esEs6(Right(zxw4000), Right(zxw3000), cbf, ty_Char) → new_esEs15(zxw4000, zxw3000)
new_esEs10(zxw4002, zxw3002, ty_Double) → new_esEs18(zxw4002, zxw3002)
new_compare31(@0, @0) → EQ
new_esEs12(zxw4000, zxw3000, app(app(ty_Either, fd), ff)) → new_esEs6(zxw4000, zxw3000, fd, ff)
new_ltEs8(Just(zxw49000), Just(zxw50000), app(ty_Maybe, gf)) → new_ltEs8(zxw49000, zxw50000, gf)
new_lt19(zxw49001, zxw50001, ty_Bool) → new_lt13(zxw49001, zxw50001)
new_ltEs7(Right(zxw49000), Right(zxw50000), caa, app(app(ty_Either, dah), dba)) → new_ltEs7(zxw49000, zxw50000, dah, dba)
new_esEs28(zxw4000, zxw3000, app(app(ty_@2, dcd), dce)) → new_esEs4(zxw4000, zxw3000, dcd, dce)
new_compare9(Integer(zxw49000), Integer(zxw50000)) → new_primCmpInt(zxw49000, zxw50000)
new_asAs(False, zxw187) → False
new_primMulInt(Neg(zxw40010), Pos(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Double) → new_esEs18(zxw4000, zxw3000)
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Ordering) → new_ltEs4(zxw49000, zxw50000)
new_esEs21(zxw4001, zxw3001, ty_Ordering) → new_esEs8(zxw4001, zxw3001)
new_primCmpNat2(zxw4900, Zero) → GT
new_ltEs20(zxw49002, zxw50002, ty_Double) → new_ltEs11(zxw49002, zxw50002)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Char, cad) → new_esEs15(zxw4000, zxw3000)
new_esEs26(zxw49001, zxw50001, app(ty_Maybe, cee)) → new_esEs7(zxw49001, zxw50001, cee)
new_esEs10(zxw4002, zxw3002, ty_@0) → new_esEs20(zxw4002, zxw3002)
new_lt19(zxw49001, zxw50001, ty_Double) → new_lt8(zxw49001, zxw50001)
new_esEs28(zxw4000, zxw3000, ty_Double) → new_esEs18(zxw4000, zxw3000)
new_compare110(zxw49000, zxw50000, True, bec, bed, bee) → LT
new_esEs24(zxw4001, zxw3001, ty_Integer) → new_esEs17(zxw4001, zxw3001)
new_lt19(zxw49001, zxw50001, app(ty_Maybe, cee)) → new_lt12(zxw49001, zxw50001, cee)
new_ltEs18(zxw49001, zxw50001, app(ty_Ratio, bea)) → new_ltEs17(zxw49001, zxw50001, bea)
new_ltEs18(zxw49001, zxw50001, ty_Char) → new_ltEs12(zxw49001, zxw50001)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Float, cad) → new_esEs19(zxw4000, zxw3000)
new_esEs21(zxw4001, zxw3001, ty_Int) → new_esEs13(zxw4001, zxw3001)
new_lt20(zxw49000, zxw50000, app(ty_Ratio, cgf)) → new_lt18(zxw49000, zxw50000, cgf)
new_ltEs19(zxw4900, zxw5000, ty_@0) → new_ltEs14(zxw4900, zxw5000)
new_ltEs7(Right(zxw49000), Right(zxw50000), caa, ty_Double) → new_ltEs11(zxw49000, zxw50000)
new_lt17(zxw49000, zxw50000, bc, bd) → new_esEs8(new_compare32(zxw49000, zxw50000, bc, bd), LT)
new_esEs9(False, False) → True
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Int) → new_ltEs10(zxw49000, zxw50000)
new_ltEs19(zxw4900, zxw5000, ty_Bool) → new_ltEs5(zxw4900, zxw5000)
new_compare29(zxw49000, zxw50000, ty_Integer) → new_compare9(zxw49000, zxw50000)
new_lt20(zxw49000, zxw50000, app(app(app(ty_@3, cga), cgb), cgc)) → new_lt16(zxw49000, zxw50000, cga, cgb, cgc)
new_ltEs20(zxw49002, zxw50002, app(app(ty_Either, cdh), cea)) → new_ltEs7(zxw49002, zxw50002, cdh, cea)
new_esEs4(@2(zxw4000, zxw4001), @2(zxw3000, zxw3001), hg, hh) → new_asAs(new_esEs22(zxw4000, zxw3000, hg), new_esEs21(zxw4001, zxw3001, hh))
new_esEs27(zxw49000, zxw50000, app(app(ty_@2, cfe), cff)) → new_esEs4(zxw49000, zxw50000, cfe, cff)
new_lt20(zxw49000, zxw50000, ty_Integer) → new_lt5(zxw49000, zxw50000)
new_ltEs18(zxw49001, zxw50001, app(ty_Maybe, bdb)) → new_ltEs8(zxw49001, zxw50001, bdb)
new_compare8(:%(zxw49000, zxw49001), :%(zxw50000, zxw50001), ty_Integer) → new_compare9(new_sr0(zxw49000, zxw50001), new_sr0(zxw50000, zxw49001))
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Float, cab) → new_ltEs6(zxw49000, zxw50000)
new_ltEs4(LT, LT) → True
new_esEs16([], [], dbc) → True
new_ltEs20(zxw49002, zxw50002, ty_Int) → new_ltEs10(zxw49002, zxw50002)
new_ltEs8(Nothing, Nothing, gc) → True
new_lt10(zxw49000, zxw50000, ty_Char) → new_lt6(zxw49000, zxw50000)
new_lt10(zxw49000, zxw50000, ty_Bool) → new_lt13(zxw49000, zxw50000)
new_esEs22(zxw4000, zxw3000, app(app(ty_Either, bca), bcb)) → new_esEs6(zxw4000, zxw3000, bca, bcb)
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_lt5(zxw49000, zxw50000) → new_esEs8(new_compare9(zxw49000, zxw50000), LT)
new_esEs26(zxw49001, zxw50001, ty_Float) → new_esEs19(zxw49001, zxw50001)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Int, cad) → new_esEs13(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_esEs10(zxw4002, zxw3002, ty_Int) → new_esEs13(zxw4002, zxw3002)
new_ltEs15(@3(zxw49000, zxw49001, zxw49002), @3(zxw50000, zxw50001, zxw50002), bhf, bhg, bhh) → new_pePe(new_lt20(zxw49000, zxw50000, bhf), new_asAs(new_esEs27(zxw49000, zxw50000, bhf), new_pePe(new_lt19(zxw49001, zxw50001, bhg), new_asAs(new_esEs26(zxw49001, zxw50001, bhg), new_ltEs20(zxw49002, zxw50002, bhh)))))
new_lt10(zxw49000, zxw50000, app(ty_[], be)) → new_lt9(zxw49000, zxw50000, be)
new_esEs12(zxw4000, zxw3000, app(ty_Ratio, eg)) → new_esEs14(zxw4000, zxw3000, eg)
new_ltEs10(zxw4900, zxw5000) → new_fsEs(new_compare7(zxw4900, zxw5000))
new_esEs10(zxw4002, zxw3002, app(ty_Ratio, cb)) → new_esEs14(zxw4002, zxw3002, cb)
new_ltEs12(zxw4900, zxw5000) → new_fsEs(new_compare12(zxw4900, zxw5000))
new_esEs10(zxw4002, zxw3002, ty_Ordering) → new_esEs8(zxw4002, zxw3002)
new_ltEs7(Right(zxw49000), Right(zxw50000), caa, ty_Float) → new_ltEs6(zxw49000, zxw50000)
new_esEs23(zxw49000, zxw50000, app(ty_[], be)) → new_esEs16(zxw49000, zxw50000, be)
new_esEs11(zxw4001, zxw3001, ty_Integer) → new_esEs17(zxw4001, zxw3001)
new_esEs26(zxw49001, zxw50001, app(app(ty_Either, cfb), cfc)) → new_esEs6(zxw49001, zxw50001, cfb, cfc)
new_compare16(Double(zxw49000, zxw49001), Double(zxw50000, zxw50001)) → new_compare7(new_sr(zxw49000, zxw50000), new_sr(zxw49001, zxw50001))
new_compare0([], :(zxw50000, zxw50001), bgb) → LT
new_primPlusNat1(Zero, Zero) → Zero
new_esEs12(zxw4000, zxw3000, ty_Ordering) → new_esEs8(zxw4000, zxw3000)
new_lt10(zxw49000, zxw50000, ty_@0) → new_lt15(zxw49000, zxw50000)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Char) → new_ltEs12(zxw49000, zxw50000)
new_asAs(True, zxw187) → zxw187
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_esEs26(zxw49001, zxw50001, app(app(app(ty_@3, ceg), ceh), cfa)) → new_esEs5(zxw49001, zxw50001, ceg, ceh, cfa)
new_esEs10(zxw4002, zxw3002, app(app(ty_Either, cg), da)) → new_esEs6(zxw4002, zxw3002, cg, da)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Integer) → new_ltEs16(zxw49000, zxw50000)
new_compare30(zxw49000, zxw50000, ga, gb) → new_compare27(zxw49000, zxw50000, new_esEs4(zxw49000, zxw50000, ga, gb), ga, gb)
new_compare29(zxw49000, zxw50000, ty_Bool) → new_compare18(zxw49000, zxw50000)
new_fsEs(zxw202) → new_not(new_esEs8(zxw202, GT))
new_esEs23(zxw49000, zxw50000, app(app(app(ty_@3, bec), bed), bee)) → new_esEs5(zxw49000, zxw50000, bec, bed, bee)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Float) → new_esEs19(zxw4000, zxw3000)
new_compare10(zxw49000, zxw50000, True) → LT
new_compare29(zxw49000, zxw50000, app(ty_Maybe, bge)) → new_compare19(zxw49000, zxw50000, bge)
new_ltEs4(GT, GT) → True
new_esEs26(zxw49001, zxw50001, ty_@0) → new_esEs20(zxw49001, zxw50001)
new_compare110(zxw49000, zxw50000, False, bec, bed, bee) → GT
new_ltEs7(Left(zxw49000), Left(zxw50000), app(ty_Ratio, chh), cab) → new_ltEs17(zxw49000, zxw50000, chh)
new_compare10(zxw49000, zxw50000, False) → GT
new_ltEs8(Just(zxw49000), Just(zxw50000), app(app(app(ty_@3, gh), ha), hb)) → new_ltEs15(zxw49000, zxw50000, gh, ha, hb)
new_esEs21(zxw4001, zxw3001, app(ty_[], bac)) → new_esEs16(zxw4001, zxw3001, bac)
new_compare18(zxw49000, zxw50000) → new_compare24(zxw49000, zxw50000, new_esEs9(zxw49000, zxw50000))
new_esEs6(Right(zxw4000), Right(zxw3000), cbf, ty_Ordering) → new_esEs8(zxw4000, zxw3000)
new_esEs6(Left(zxw4000), Left(zxw3000), app(ty_[], caf), cad) → new_esEs16(zxw4000, zxw3000, caf)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs6(Right(zxw4000), Right(zxw3000), cbf, app(app(app(ty_@3, ccb), ccc), ccd)) → new_esEs5(zxw4000, zxw3000, ccb, ccc, ccd)
new_primCompAux0(zxw218, EQ) → zxw218
new_lt20(zxw49000, zxw50000, app(ty_Maybe, cfg)) → new_lt12(zxw49000, zxw50000, cfg)
new_esEs12(zxw4000, zxw3000, app(app(ty_@2, fg), fh)) → new_esEs4(zxw4000, zxw3000, fg, fh)
new_ltEs19(zxw4900, zxw5000, app(ty_[], bgb)) → new_ltEs13(zxw4900, zxw5000, bgb)
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_esEs22(zxw4000, zxw3000, app(ty_Maybe, bbc)) → new_esEs7(zxw4000, zxw3000, bbc)
new_ltEs7(Right(zxw49000), Right(zxw50000), caa, ty_@0) → new_ltEs14(zxw49000, zxw50000)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_compare8(:%(zxw49000, zxw49001), :%(zxw50000, zxw50001), ty_Int) → new_compare7(new_sr(zxw49000, zxw50001), new_sr(zxw50000, zxw49001))
new_ltEs17(zxw4900, zxw5000, hf) → new_fsEs(new_compare8(zxw4900, zxw5000, hf))
new_not(True) → False

The set Q consists of the following terms:

new_esEs17(Integer(x0), Integer(x1))
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare8(:%(x0, x1), :%(x2, x3), ty_Integer)
new_lt10(x0, x1, ty_Double)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_compare18(x0, x1)
new_compare29(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Double)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_pePe(False, x0)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_esEs22(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare7(x0, x1)
new_lt11(x0, x1, x2, x3)
new_primMulNat0(Succ(x0), Zero)
new_esEs7(Just(x0), Just(x1), ty_Double)
new_ltEs8(Just(x0), Just(x1), ty_Integer)
new_esEs10(x0, x1, ty_Int)
new_ltEs10(x0, x1)
new_esEs12(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Ordering)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs12(x0, x1, ty_Char)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_esEs6(Right(x0), Right(x1), x2, ty_Int)
new_lt10(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs13(x0, x1, x2)
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs8(Just(x0), Just(x1), app(ty_[], x2))
new_compare8(:%(x0, x1), :%(x2, x3), ty_Int)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs16(x0, x1)
new_compare13(x0, x1, True)
new_esEs10(x0, x1, ty_Ordering)
new_compare32(x0, x1, x2, x3)
new_ltEs19(x0, x1, ty_Float)
new_esEs11(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_Int)
new_lt18(x0, x1, x2)
new_ltEs19(x0, x1, ty_Ordering)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_lt10(x0, x1, app(ty_Ratio, x2))
new_esEs8(GT, GT)
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_compare17(x0, x1, False, x2, x3)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs7(Just(x0), Nothing, x1)
new_esEs8(LT, LT)
new_esEs14(:%(x0, x1), :%(x2, x3), x4)
new_compare29(x0, x1, ty_Double)
new_compare29(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs18(Double(x0, x1), Double(x2, x3))
new_primCmpNat0(Zero, x0)
new_ltEs7(Left(x0), Left(x1), ty_Double, x2)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_ltEs8(Just(x0), Just(x1), ty_Bool)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, ty_@0)
new_primCmpNat1(Zero, Succ(x0))
new_ltEs7(Left(x0), Left(x1), ty_Bool, x2)
new_esEs25(x0, x1, ty_Int)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_sr(x0, x1)
new_ltEs5(False, False)
new_compare19(x0, x1, x2)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Right(x0), Left(x1), x2, x3)
new_esEs6(Left(x0), Right(x1), x2, x3)
new_ltEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_compare6(x0, x1)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt10(x0, x1, ty_Ordering)
new_compare29(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Integer)
new_primEqNat0(Zero, Succ(x0))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpNat1(Zero, Zero)
new_ltEs17(x0, x1, x2)
new_compare16(Double(x0, x1), Double(x2, x3))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_lt7(x0, x1)
new_esEs28(x0, x1, ty_@0)
new_ltEs20(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Integer)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_compare26(Just(x0), Just(x1), False, x2)
new_esEs23(x0, x1, ty_Integer)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_compare27(x0, x1, False, x2, x3)
new_esEs12(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Double)
new_ltEs19(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_Char)
new_esEs11(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, ty_Int)
new_esEs7(Nothing, Nothing, x0)
new_primEqNat0(Zero, Zero)
new_compare26(Just(x0), Nothing, False, x1)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_ltEs7(Left(x0), Left(x1), ty_Int, x2)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs9(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs8(Just(x0), Just(x1), ty_Double)
new_esEs10(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, app(ty_[], x2))
new_ltEs8(Just(x0), Just(x1), ty_Ordering)
new_ltEs19(x0, x1, ty_@0)
new_esEs6(Right(x0), Right(x1), x2, ty_Integer)
new_compare24(x0, x1, False)
new_esEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs9(True, True)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs10(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs12(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs16(:(x0, x1), :(x2, x3), x4)
new_compare29(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs7(Right(x0), Right(x1), x2, ty_Char)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_lt19(x0, x1, app(ty_Maybe, x2))
new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_lt4(x0, x1)
new_primMulNat0(Zero, Zero)
new_esEs23(x0, x1, ty_Char)
new_esEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_lt17(x0, x1, x2, x3)
new_esEs10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs10(x0, x1, ty_@0)
new_lt10(x0, x1, ty_Char)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Left(x0), Left(x1), ty_@0, x2)
new_ltEs18(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_Integer)
new_fsEs(x0)
new_ltEs4(GT, GT)
new_lt8(x0, x1)
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs15(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs10(x0, x1, ty_Float)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs28(x0, x1, ty_Double)
new_ltEs8(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, ty_@0)
new_lt10(x0, x1, ty_Int)
new_esEs10(x0, x1, ty_Bool)
new_ltEs8(Nothing, Nothing, x0)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs23(x0, x1, ty_Ordering)
new_esEs7(Just(x0), Just(x1), ty_Int)
new_esEs10(x0, x1, ty_Char)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, app(ty_[], x2))
new_ltEs7(Right(x0), Right(x1), x2, ty_Double)
new_esEs11(x0, x1, app(ty_[], x2))
new_esEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_compare110(x0, x1, False, x2, x3, x4)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_lt12(x0, x1, x2)
new_esEs12(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs7(Right(x0), Right(x1), x2, ty_Bool)
new_pePe(True, x0)
new_lt19(x0, x1, app(ty_[], x2))
new_lt10(x0, x1, app(ty_Maybe, x2))
new_esEs16(:(x0, x1), [], x2)
new_compare0([], :(x0, x1), x2)
new_primPlusNat0(Zero, x0)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_compare17(x0, x1, True, x2, x3)
new_ltEs7(Right(x0), Right(x1), x2, ty_Int)
new_esEs21(x0, x1, ty_Int)
new_lt6(x0, x1)
new_esEs26(x0, x1, ty_Bool)
new_compare24(x0, x1, True)
new_compare29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, ty_Integer)
new_esEs6(Left(x0), Left(x1), ty_Float, x2)
new_esEs26(x0, x1, app(ty_[], x2))
new_ltEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_compare25(x0, x1, True, x2, x3)
new_compare14(Float(x0, x1), Float(x2, x3))
new_esEs6(Left(x0), Left(x1), ty_Bool, x2)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_ltEs14(x0, x1)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_primPlusNat1(Zero, Zero)
new_primCompAux0(x0, GT)
new_compare23(x0, x1, True)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_ltEs8(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt15(x0, x1)
new_compare13(x0, x1, False)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_lt20(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_@0)
new_primCompAux1(x0, x1, x2, x3)
new_primPlusNat0(Succ(x0), x1)
new_ltEs4(EQ, EQ)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs7(Right(x0), Right(x1), x2, ty_@0)
new_ltEs19(x0, x1, ty_Char)
new_esEs12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, app(ty_Ratio, x2))
new_ltEs11(x0, x1)
new_esEs12(x0, x1, ty_@0)
new_esEs24(x0, x1, ty_Integer)
new_esEs11(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, ty_Char)
new_compare15(x0, x1, False, x2, x3)
new_esEs7(Just(x0), Just(x1), ty_Char)
new_esEs12(x0, x1, ty_Float)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs8(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare0(:(x0, x1), [], x2)
new_compare31(@0, @0)
new_ltEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs7(Just(x0), Just(x1), ty_Float)
new_primCmpNat2(x0, Zero)
new_ltEs7(Left(x0), Left(x1), ty_@0, x2)
new_ltEs4(EQ, LT)
new_ltEs4(LT, EQ)
new_esEs12(x0, x1, ty_Int)
new_lt19(x0, x1, ty_Double)
new_esEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs7(Right(x0), Right(x1), x2, ty_Integer)
new_compare11(x0, x1, False, x2)
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_primMulInt(Pos(x0), Pos(x1))
new_lt10(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Bool)
new_lt16(x0, x1, x2, x3, x4)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_@0)
new_asAs(True, x0)
new_primEqNat0(Succ(x0), Zero)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_esEs13(x0, x1)
new_compare210(x0, x1, True, x2, x3, x4)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Integer)
new_lt20(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Bool)
new_lt20(x0, x1, ty_Char)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs16([], :(x0, x1), x2)
new_compare29(x0, x1, app(ty_Ratio, x2))
new_ltEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs28(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_Ordering)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_ltEs20(x0, x1, ty_Bool)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs27(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_Double)
new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs25(x0, x1, ty_Integer)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_primMulInt(Neg(x0), Neg(x1))
new_lt10(x0, x1, ty_Bool)
new_compare15(x0, x1, True, x2, x3)
new_primPlusNat1(Succ(x0), Zero)
new_esEs10(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, ty_Bool)
new_esEs22(x0, x1, ty_Float)
new_ltEs4(LT, LT)
new_esEs10(x0, x1, ty_Integer)
new_esEs12(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Integer)
new_compare23(x0, x1, False)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs11(x0, x1, ty_Bool)
new_esEs11(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_Double)
new_esEs21(x0, x1, ty_Bool)
new_compare210(x0, x1, False, x2, x3, x4)
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, ty_Ordering)
new_compare30(x0, x1, x2, x3)
new_esEs28(x0, x1, app(ty_[], x2))
new_primPlusNat1(Zero, Succ(x0))
new_ltEs12(x0, x1)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_compare10(x0, x1, False)
new_compare27(x0, x1, True, x2, x3)
new_ltEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpNat0(Succ(x0), x1)
new_esEs22(x0, x1, ty_@0)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs8(GT, EQ)
new_esEs8(EQ, GT)
new_esEs22(x0, x1, ty_Bool)
new_lt19(x0, x1, ty_Float)
new_esEs10(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs8(Just(x0), Just(x1), app(ty_Ratio, x2))
new_lt19(x0, x1, ty_Integer)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs8(Just(x0), Just(x1), ty_Char)
new_ltEs8(Just(x0), Just(x1), ty_Float)
new_lt5(x0, x1)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_ltEs18(x0, x1, ty_Bool)
new_compare29(x0, x1, ty_Ordering)
new_ltEs7(Right(x0), Right(x1), x2, ty_Float)
new_esEs11(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_@0)
new_ltEs7(Left(x0), Left(x1), ty_Float, x2)
new_esEs11(x0, x1, ty_Int)
new_esEs11(x0, x1, ty_Char)
new_esEs6(Right(x0), Right(x1), x2, ty_Char)
new_esEs27(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Float)
new_lt19(x0, x1, ty_Ordering)
new_compare29(x0, x1, ty_Integer)
new_ltEs18(x0, x1, ty_Float)
new_esEs9(False, False)
new_esEs6(Left(x0), Left(x1), ty_Char, x2)
new_esEs21(x0, x1, ty_Double)
new_compare29(x0, x1, app(ty_[], x2))
new_esEs6(Left(x0), Left(x1), ty_Double, x2)
new_esEs12(x0, x1, ty_Ordering)
new_compare29(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_ltEs8(Nothing, Just(x0), x1)
new_ltEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_primCmpNat1(Succ(x0), Succ(x1))
new_esEs26(x0, x1, ty_@0)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_ltEs6(x0, x1)
new_lt10(x0, x1, ty_Float)
new_esEs22(x0, x1, ty_Int)
new_esEs16([], [], x0)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs21(x0, x1, ty_Float)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCompAux0(x0, EQ)
new_compare11(x0, x1, True, x2)
new_esEs21(x0, x1, ty_Integer)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_primCmpNat1(Succ(x0), Zero)
new_esEs6(Left(x0), Left(x1), ty_Int, x2)
new_ltEs18(x0, x1, ty_@0)
new_esEs22(x0, x1, ty_Double)
new_compare25(x0, x1, False, x2, x3)
new_lt13(x0, x1)
new_esEs23(x0, x1, ty_Bool)
new_ltEs5(True, True)
new_lt19(x0, x1, ty_Int)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_ltEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_lt19(x0, x1, ty_Char)
new_ltEs4(EQ, GT)
new_ltEs4(GT, EQ)
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_not(True)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs7(Left(x0), Left(x1), ty_Char, x2)
new_esEs11(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Float)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, ty_Char)
new_lt19(x0, x1, ty_@0)
new_esEs21(x0, x1, ty_Ordering)
new_compare0([], [], x0)
new_esEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs26(x0, x1, ty_Char)
new_ltEs18(x0, x1, ty_Int)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_ltEs20(x0, x1, ty_Ordering)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_not(False)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_lt14(x0, x1)
new_compare12(Char(x0), Char(x1))
new_esEs15(Char(x0), Char(x1))
new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs20(x0, x1, app(ty_[], x2))
new_compare10(x0, x1, True)
new_lt10(x0, x1, ty_@0)
new_asAs(False, x0)
new_esEs22(x0, x1, ty_Ordering)
new_compare26(x0, x1, True, x2)
new_ltEs18(x0, x1, ty_Char)
new_lt10(x0, x1, app(ty_[], x2))
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare29(x0, x1, ty_Float)
new_esEs27(x0, x1, ty_Char)
new_lt19(x0, x1, ty_Bool)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_ltEs8(Just(x0), Just(x1), ty_@0)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs20(@0, @0)
new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_ltEs18(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_Int)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_ltEs19(x0, x1, ty_Double)
new_esEs22(x0, x1, ty_Char)
new_esEs9(False, True)
new_esEs9(True, False)
new_compare29(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_Integer)
new_ltEs8(Just(x0), Nothing, x1)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs11(x0, x1, ty_Double)
new_ltEs20(x0, x1, ty_Float)
new_primCompAux0(x0, LT)
new_compare26(Nothing, Just(x0), False, x1)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs7(Left(x0), Left(x1), ty_Integer, x2)
new_primCmpNat2(x0, Succ(x1))
new_compare28(x0, x1, x2, x3, x4)
new_lt10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Nothing, Just(x0), x1)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs12(x0, x1, ty_Integer)
new_esEs10(x0, x1, ty_Double)
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_sr0(Integer(x0), Integer(x1))
new_compare110(x0, x1, True, x2, x3, x4)
new_compare26(Nothing, Nothing, False, x0)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs10(x0, x1, app(ty_[], x2))
new_ltEs18(x0, x1, ty_Double)
new_ltEs7(Right(x0), Left(x1), x2, x3)
new_ltEs7(Left(x0), Right(x1), x2, x3)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs12(x0, x1, ty_Double)
new_esEs12(x0, x1, ty_Bool)
new_compare9(Integer(x0), Integer(x1))
new_lt10(x0, x1, ty_Integer)
new_ltEs8(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs19(Float(x0, x1), Float(x2, x3))
new_primMulNat0(Zero, Succ(x0))
new_esEs7(Just(x0), Just(x1), ty_@0)
new_lt9(x0, x1, x2)
new_ltEs4(GT, LT)
new_ltEs4(LT, GT)
new_ltEs5(True, False)
new_ltEs5(False, True)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs8(Just(x0), Just(x1), ty_Int)
new_compare29(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Float)
new_esEs6(Right(x0), Right(x1), x2, ty_Double)
new_ltEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs23(x0, x1, ty_Float)
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs6(Right(x0), Right(x1), x2, ty_Float)

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(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw623, h, ba)
new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_lt4(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), h, ba)
new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba) → new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_lt21(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, zxw334, Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba)

The TRS R consists of the following rules:

new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_esEs8(EQ, EQ) → True
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Pos(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_lt21(zxw112, zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_esEs8(new_compare7(zxw112, new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT)
new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_lt4(zxw490, zxw500) → new_esEs8(new_compare7(zxw490, zxw500), LT)
new_primMulInt(Neg(zxw40010), Neg(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primCmpNat2(zxw4900, Zero) → GT
new_primPlusNat1(Zero, Zero) → Zero
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primCmpNat0(Zero, zxw4900) → LT
new_sr(zxw4001, zxw3001) → new_primMulInt(zxw4001, zxw3001)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_compare7(zxw49, zxw50) → new_primCmpInt(zxw49, zxw50)
new_primCmpNat1(Zero, Zero) → EQ
new_esEs8(GT, EQ) → False
new_esEs8(EQ, GT) → False
new_sizeFM0(EmptyFM, h, ba) → Pos(Zero)
new_primMulNat0(Zero, Zero) → Zero
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_esEs8(GT, GT) → True
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_esEs8(GT, LT) → False
new_esEs8(LT, GT) → False
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)
new_esEs8(EQ, LT) → False
new_esEs8(LT, EQ) → False
new_esEs8(LT, LT) → True
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_lt4(x0, x1)
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_compare7(x0, x1)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_sr(x0, x1)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sIZE_RATIO
new_sizeFM0(EmptyFM, x0, x1)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_lt21(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

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

↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ 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(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw623, h, ba)
new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_lt4(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), h, ba)
new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba) → new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_lt21(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, zxw334, Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)
new_sr(zxw4001, zxw3001) → new_primMulInt(zxw4001, zxw3001)
new_lt21(zxw112, zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_esEs8(new_compare7(zxw112, new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT)
new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_compare7(zxw49, zxw50) → new_primCmpInt(zxw49, zxw50)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Pos(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Neg(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)
new_lt4(zxw490, zxw500) → new_esEs8(new_compare7(zxw490, zxw500), LT)

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_lt4(x0, x1)
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_compare7(x0, x1)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_sr(x0, x1)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sIZE_RATIO
new_sizeFM0(EmptyFM, x0, x1)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_lt21(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_lt4(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), h, ba) at position [12] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_compare7(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw623, h, ba)
new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba) → new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_lt21(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_compare7(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, zxw334, Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)
new_sr(zxw4001, zxw3001) → new_primMulInt(zxw4001, zxw3001)
new_lt21(zxw112, zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_esEs8(new_compare7(zxw112, new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT)
new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_compare7(zxw49, zxw50) → new_primCmpInt(zxw49, zxw50)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Pos(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Neg(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)
new_lt4(zxw490, zxw500) → new_esEs8(new_compare7(zxw490, zxw500), LT)

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_lt4(x0, x1)
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_compare7(x0, x1)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_sr(x0, x1)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sIZE_RATIO
new_sizeFM0(EmptyFM, x0, x1)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_lt21(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

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

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

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

new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw623, h, ba)
new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba) → new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_lt21(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_compare7(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, zxw334, Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_sr(zxw4001, zxw3001) → new_primMulInt(zxw4001, zxw3001)
new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)
new_compare7(zxw49, zxw50) → new_primCmpInt(zxw49, zxw50)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Pos(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Neg(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)
new_lt21(zxw112, zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_esEs8(new_compare7(zxw112, new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT)

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_lt4(x0, x1)
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_compare7(x0, x1)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_sr(x0, x1)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sIZE_RATIO
new_sizeFM0(EmptyFM, x0, x1)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_lt21(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

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

new_lt4(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
                                            ↳ UsableRulesProof
                                              ↳ QDP
                                                ↳ QReductionProof
                                                  ↳ QDP
                                                    ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw623, h, ba)
new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba) → new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_lt21(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_compare7(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, zxw334, Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_sr(zxw4001, zxw3001) → new_primMulInt(zxw4001, zxw3001)
new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)
new_compare7(zxw49, zxw50) → new_primCmpInt(zxw49, zxw50)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Pos(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Neg(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)
new_lt21(zxw112, zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_esEs8(new_compare7(zxw112, new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT)

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_compare7(x0, x1)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_sr(x0, x1)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sIZE_RATIO
new_sizeFM0(EmptyFM, x0, x1)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_lt21(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba) → new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_lt21(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba), h, ba) at position [12] we obtained the following new rules:

new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba) → new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_compare7(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_r(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ 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(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw623, h, ba)
new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba) → new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_compare7(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_r(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_compare7(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, zxw334, Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_sr(zxw4001, zxw3001) → new_primMulInt(zxw4001, zxw3001)
new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)
new_compare7(zxw49, zxw50) → new_primCmpInt(zxw49, zxw50)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Pos(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Neg(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)
new_lt21(zxw112, zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_esEs8(new_compare7(zxw112, new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT)

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_compare7(x0, x1)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_sr(x0, x1)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sIZE_RATIO
new_sizeFM0(EmptyFM, x0, x1)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_lt21(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

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

↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ 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
                                            ↳ 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(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw623, h, ba)
new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba) → new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_compare7(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_r(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_compare7(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, zxw334, Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_sr(zxw4001, zxw3001) → new_primMulInt(zxw4001, zxw3001)
new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)
new_compare7(zxw49, zxw50) → new_primCmpInt(zxw49, zxw50)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Pos(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Neg(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_compare7(x0, x1)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_sr(x0, x1)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sIZE_RATIO
new_sizeFM0(EmptyFM, x0, x1)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_lt21(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

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

new_lt21(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
                                            ↳ 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(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw623, h, ba)
new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba) → new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_compare7(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_r(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_compare7(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, zxw334, Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_sr(zxw4001, zxw3001) → new_primMulInt(zxw4001, zxw3001)
new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)
new_compare7(zxw49, zxw50) → new_primCmpInt(zxw49, zxw50)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Pos(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Neg(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_compare7(x0, x1)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_sr(x0, x1)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sIZE_RATIO
new_sizeFM0(EmptyFM, x0, x1)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba) → new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_compare7(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_r(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba) at position [12,0] we obtained the following new rules:

new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba) → new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_r(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ UsableRulesProof
                                              ↳ QDP
                                                ↳ QReductionProof
                                                  ↳ 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(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw623, h, ba)
new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba) → new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_r(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_compare7(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, zxw334, Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_sr(zxw4001, zxw3001) → new_primMulInt(zxw4001, zxw3001)
new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)
new_compare7(zxw49, zxw50) → new_primCmpInt(zxw49, zxw50)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Pos(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Neg(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_compare7(x0, x1)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_sr(x0, x1)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sIZE_RATIO
new_sizeFM0(EmptyFM, x0, x1)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_compare7(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba) at position [12,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ UsableRulesProof
                                              ↳ QDP
                                                ↳ QReductionProof
                                                  ↳ 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(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw623, h, ba)
new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)
new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba) → new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_r(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, zxw334, Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_sr(zxw4001, zxw3001) → new_primMulInt(zxw4001, zxw3001)
new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)
new_compare7(zxw49, zxw50) → new_primCmpInt(zxw49, zxw50)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Pos(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Neg(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_compare7(x0, x1)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_sr(x0, x1)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sIZE_RATIO
new_sizeFM0(EmptyFM, x0, x1)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

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

↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ 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
                                            ↳ UsableRulesProof
                                              ↳ QDP
                                                ↳ QReductionProof
                                                  ↳ 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(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw623, h, ba)
new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)
new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba) → new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_r(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, zxw334, Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)
new_sr(zxw4001, zxw3001) → new_primMulInt(zxw4001, zxw3001)
new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Pos(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Neg(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_compare7(x0, x1)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_sr(x0, x1)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sIZE_RATIO
new_sizeFM0(EmptyFM, x0, x1)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

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

new_compare7(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
                                            ↳ UsableRulesProof
                                              ↳ QDP
                                                ↳ QReductionProof
                                                  ↳ 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(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw623, h, ba)
new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)
new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba) → new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_r(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, zxw334, Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)
new_sr(zxw4001, zxw3001) → new_primMulInt(zxw4001, zxw3001)
new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Pos(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Neg(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_sr(x0, x1)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sIZE_RATIO
new_sizeFM0(EmptyFM, x0, x1)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba) at position [12,0,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ UsableRulesProof
                                              ↳ QDP
                                                ↳ QReductionProof
                                                  ↳ 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(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw623, h, ba)
new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba) → new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_r(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, zxw334, Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba)
new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)
new_sr(zxw4001, zxw3001) → new_primMulInt(zxw4001, zxw3001)
new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Pos(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Neg(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_sr(x0, x1)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sIZE_RATIO
new_sizeFM0(EmptyFM, x0, x1)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba) → new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_r(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba) at position [12,0,0] we obtained the following new rules:

new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba) → new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_r(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ UsableRulesProof
                                              ↳ QDP
                                                ↳ QReductionProof
                                                  ↳ 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(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw623, h, ba)
new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba) → new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_r(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, zxw334, Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba)
new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)
new_sr(zxw4001, zxw3001) → new_primMulInt(zxw4001, zxw3001)
new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Pos(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Neg(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_sr(x0, x1)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sIZE_RATIO
new_sizeFM0(EmptyFM, x0, x1)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

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

↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ 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
                                            ↳ UsableRulesProof
                                              ↳ QDP
                                                ↳ QReductionProof
                                                  ↳ 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_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw623, h, ba)
new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba) → new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_r(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, zxw334, Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba)
new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Pos(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Neg(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_sr(x0, x1)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sIZE_RATIO
new_sizeFM0(EmptyFM, x0, x1)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

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

new_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
                                            ↳ UsableRulesProof
                                              ↳ QDP
                                                ↳ QReductionProof
                                                  ↳ 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(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw623, h, ba)
new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba) → new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_r(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, zxw334, Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba)
new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Pos(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Neg(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sIZE_RATIO
new_sizeFM0(EmptyFM, x0, x1)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba) → new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_r(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba) at position [12,0,0,0] we obtained the following new rules:

new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba) → new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_r(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ UsableRulesProof
                                              ↳ QDP
                                                ↳ QReductionProof
                                                  ↳ 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(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba) → new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_r(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw623, h, ba)
new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, zxw334, Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba)
new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Pos(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Neg(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sIZE_RATIO
new_sizeFM0(EmptyFM, x0, x1)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba) at position [12,0,0,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ UsableRulesProof
                                              ↳ QDP
                                                ↳ QReductionProof
                                                  ↳ 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_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba) → new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_r(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw623, h, ba)
new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, zxw334, Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba)
new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Pos(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Neg(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sIZE_RATIO
new_sizeFM0(EmptyFM, x0, x1)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

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

↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ 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
                                            ↳ UsableRulesProof
                                              ↳ QDP
                                                ↳ QReductionProof
                                                  ↳ 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(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba) → new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_r(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw623, h, ba)
new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, zxw334, Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba)
new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sIZE_RATIO
new_sizeFM0(EmptyFM, x0, x1)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

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

new_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
                                            ↳ UsableRulesProof
                                              ↳ QDP
                                                ↳ QReductionProof
                                                  ↳ 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_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba) → new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_r(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw623, h, ba)
new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, zxw334, Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba)
new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sizeFM0(EmptyFM, x0, x1)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba) → new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_r(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba) at position [12,0,0,1] we obtained the following new rules:

new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba) → new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)), new_mkVBalBranch3Size_r(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ UsableRulesProof
                                              ↳ QDP
                                                ↳ QReductionProof
                                                  ↳ 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(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw623, h, ba)
new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba) → new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)), new_mkVBalBranch3Size_r(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, zxw334, Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba)
new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sizeFM0(EmptyFM, x0, x1)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba) at position [12,0,0,1] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM0(Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba)), new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ UsableRulesProof
                                              ↳ QDP
                                                ↳ QReductionProof
                                                  ↳ 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(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw623, h, ba)
new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM0(Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba)), new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)
new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba) → new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)), new_mkVBalBranch3Size_r(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, zxw334, Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba)

The TRS R consists of the following rules:

new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sizeFM0(EmptyFM, x0, x1)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba) → new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)), new_mkVBalBranch3Size_r(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba) at position [12,0,0,1] we obtained the following new rules:

new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba) → new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw332), new_mkVBalBranch3Size_r(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ UsableRulesProof
                                              ↳ QDP
                                                ↳ QReductionProof
                                                  ↳ 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(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw623, h, ba)
new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM0(Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba)), new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)
new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba) → new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw332), new_mkVBalBranch3Size_r(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, zxw334, Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba)

The TRS R consists of the following rules:

new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sizeFM0(EmptyFM, x0, x1)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM0(Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba)), new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba) at position [12,0,0,1] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw622), new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ UsableRulesProof
                                              ↳ QDP
                                                ↳ QReductionProof
                                                  ↳ 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(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw622), new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw623, h, ba)
new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba) → new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw332), new_mkVBalBranch3Size_r(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, zxw334, Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba)

The TRS R consists of the following rules:

new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sizeFM0(EmptyFM, x0, x1)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba) → new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw332), new_mkVBalBranch3Size_r(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba) at position [12,0,1] we obtained the following new rules:

new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba) → new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw332), new_sizeFM0(Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba)), LT), h, ba)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ UsableRulesProof
                                              ↳ QDP
                                                ↳ QReductionProof
                                                  ↳ 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(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw622), new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw623, h, ba)
new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, zxw334, Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba)
new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba) → new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw332), new_sizeFM0(Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sizeFM0(EmptyFM, x0, x1)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

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

↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ 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
                                            ↳ UsableRulesProof
                                              ↳ QDP
                                                ↳ QReductionProof
                                                  ↳ 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(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw622), new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw623, h, ba)
new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, zxw334, Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba)
new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba) → new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw332), new_sizeFM0(Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)
new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sizeFM0(EmptyFM, x0, x1)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

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

new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ UsableRulesProof
                                              ↳ QDP
                                                ↳ QReductionProof
                                                  ↳ 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(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw622), new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw623, h, ba)
new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, zxw334, Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba)
new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba) → new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw332), new_sizeFM0(Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)
new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sizeFM0(EmptyFM, x0, x1)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw622), new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba) at position [12,0,1] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw622), new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)), LT), h, ba)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ UsableRulesProof
                                              ↳ QDP
                                                ↳ QReductionProof
                                                  ↳ 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(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw623, h, ba)
new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, zxw334, Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba)
new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba) → new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw332), new_sizeFM0(Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw622), new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)
new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sizeFM0(EmptyFM, x0, x1)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

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

↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ 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
                                            ↳ UsableRulesProof
                                              ↳ QDP
                                                ↳ QReductionProof
                                                  ↳ 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(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw623, h, ba)
new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, zxw334, Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba)
new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba) → new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw332), new_sizeFM0(Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw622), new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sizeFM0(EmptyFM, x0, x1)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

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

new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ UsableRulesProof
                                              ↳ QDP
                                                ↳ QReductionProof
                                                  ↳ 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(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw623, h, ba)
new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, zxw334, Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba)
new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba) → new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw332), new_sizeFM0(Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw622), new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sizeFM0(EmptyFM, x0, x1)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpNat1(Succ(x0), Succ(x1))
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba) → new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw332), new_sizeFM0(Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba)), LT), h, ba) at position [12,0,1] we obtained the following new rules:

new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba) → new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw332), zxw622), LT), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw623, h, ba)
new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, zxw334, Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba)
new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba) → new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw332), zxw622), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw622), new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sizeFM0(EmptyFM, x0, x1)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpNat1(Succ(x0), Succ(x1))
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw622), new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)), LT), h, ba) at position [12,0,1] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw622), zxw332), LT), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw623, h, ba)
new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw622), zxw332), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, zxw334, Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba)
new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba) → new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw332), zxw622), LT), h, ba)

The TRS R consists of the following rules:

new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sizeFM0(EmptyFM, x0, x1)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpNat1(Succ(x0), Succ(x1))
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

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

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

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

new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw623, h, ba)
new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw622), zxw332), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, zxw334, Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba)
new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba) → new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw332), zxw622), LT), h, ba)

The TRS R consists of the following rules:

new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sizeFM0(EmptyFM, x0, x1)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpNat1(Succ(x0), Succ(x1))
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

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

new_sizeFM0(EmptyFM, x0, x1)
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ UsableRulesProof
                                              ↳ QDP
                                                ↳ QReductionProof
                                                  ↳ 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
                                                                                                                                                            ↳ 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(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw623, h, ba)
new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw622), zxw332), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, zxw334, Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba)
new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba) → new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw332), zxw622), LT), h, ba)

The TRS R consists of the following rules:

new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpNat1(Succ(x0), Succ(x1))
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

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_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, zxw334, Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba)
The remaining pairs can at least be oriented weakly.

new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw623, h, ba)
new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw622), zxw332), LT), h, ba)
new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba) → new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw332), zxw622), LT), h, ba)
Used ordering: Polynomial interpretation [25]:

POL(Branch(x1, x2, x3, x4, x5)) = x1 + x3 + x4 + x5   
POL(EQ) = 0   
POL(False) = 0   
POL(GT) = 0   
POL(LT) = 1   
POL(Neg(x1)) = 1 + x1   
POL(Pos(x1)) = 1   
POL(Succ(x1)) = 0   
POL(True) = 1   
POL(Zero) = 0   
POL(new_esEs8(x1, x2)) = x1   
POL(new_mkVBalBranch(x1, x2, x3, x4, x5, x6)) = x3   
POL(new_mkVBalBranch3MkVBalBranch1(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15)) = x10 + x13   
POL(new_mkVBalBranch3MkVBalBranch2(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15)) = x10 + x6 + x8 + x9   
POL(new_primCmpInt(x1, x2)) = x2   
POL(new_primCmpNat0(x1, x2)) = 1 + x1   
POL(new_primCmpNat1(x1, x2)) = 1   
POL(new_primCmpNat2(x1, x2)) = 1   
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:

new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_esEs8(EQ, LT) → False
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(LT, LT) → True
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_esEs8(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
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ UsableRulesProof
                                              ↳ QDP
                                                ↳ QReductionProof
                                                  ↳ 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
                                                                                                                                                            ↳ 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(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw623, h, ba)
new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw622), zxw332), LT), h, ba)
new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba) → new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw332), zxw622), LT), h, ba)

The TRS R consists of the following rules:

new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpNat1(Succ(x0), Succ(x1))
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

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
                                            ↳ UsableRulesProof
                                              ↳ QDP
                                                ↳ QReductionProof
                                                  ↳ 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
                                                                                                                                                            ↳ 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(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw623, h, ba)
new_mkVBalBranch(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba) → new_mkVBalBranch3MkVBalBranch2(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw332), zxw622), LT), h, ba)

The TRS R consists of the following rules:

new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpNat1(Succ(x0), Succ(x1))
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

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

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



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ 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_C0(Branch(zxw610, zxw611, zxw612, zxw613, zxw614), zxw31, h, ba) → new_addToFM_C20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw31, new_lt12(Nothing, zxw610, h), h, ba)
new_addToFM_C10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw31, True, h, ba) → new_addToFM_C0(zxw614, zxw31, h, ba)
new_addToFM_C20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw31, True, h, ba) → new_addToFM_C0(zxw613, zxw31, h, ba)
new_addToFM_C20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw31, False, h, ba) → new_addToFM_C10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw31, new_esEs8(new_compare19(Nothing, zxw610, h), GT), h, ba)

The TRS R consists of the following rules:

new_esEs6(Right(zxw4000), Right(zxw3000), cbf, ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_esEs7(Just(zxw4000), Just(zxw3000), app(ty_Maybe, beh)) → new_esEs7(zxw4000, zxw3000, beh)
new_ltEs19(zxw4900, zxw5000, ty_Integer) → new_ltEs16(zxw4900, zxw5000)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_@0, cab) → new_ltEs14(zxw49000, zxw50000)
new_esEs27(zxw49000, zxw50000, app(ty_[], cfh)) → new_esEs16(zxw49000, zxw50000, cfh)
new_ltEs4(EQ, GT) → True
new_esEs22(zxw4000, zxw3000, ty_@0) → new_esEs20(zxw4000, zxw3000)
new_compare15(zxw49000, zxw50000, True, bc, bd) → LT
new_esEs6(Right(zxw4000), Right(zxw3000), cbf, ty_Float) → new_esEs19(zxw4000, zxw3000)
new_ltEs9(@2(zxw49000, zxw49001), @2(zxw50000, zxw50001), bcf, bcg) → new_pePe(new_lt10(zxw49000, zxw50000, bcf), new_asAs(new_esEs23(zxw49000, zxw50000, bcf), new_ltEs18(zxw49001, zxw50001, bcg)))
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Integer, cad) → new_esEs17(zxw4000, zxw3000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_esEs23(zxw49000, zxw50000, app(app(ty_@2, ga), gb)) → new_esEs4(zxw49000, zxw50000, ga, gb)
new_compare29(zxw49000, zxw50000, ty_Char) → new_compare12(zxw49000, zxw50000)
new_esEs22(zxw4000, zxw3000, ty_Float) → new_esEs19(zxw4000, zxw3000)
new_esEs6(Right(zxw4000), Right(zxw3000), cbf, ty_Int) → new_esEs13(zxw4000, zxw3000)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Bool) → new_ltEs5(zxw49000, zxw50000)
new_lt19(zxw49001, zxw50001, ty_Integer) → new_lt5(zxw49001, zxw50001)
new_esEs12(zxw4000, zxw3000, ty_Bool) → new_esEs9(zxw4000, zxw3000)
new_esEs27(zxw49000, zxw50000, app(ty_Maybe, cfg)) → new_esEs7(zxw49000, zxw50000, cfg)
new_esEs12(zxw4000, zxw3000, ty_Char) → new_esEs15(zxw4000, zxw3000)
new_esEs11(zxw4001, zxw3001, app(ty_[], df)) → new_esEs16(zxw4001, zxw3001, df)
new_compare12(Char(zxw49000), Char(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_ltEs19(zxw4900, zxw5000, ty_Double) → new_ltEs11(zxw4900, zxw5000)
new_ltEs20(zxw49002, zxw50002, ty_Bool) → new_ltEs5(zxw49002, zxw50002)
new_compare29(zxw49000, zxw50000, ty_Double) → new_compare16(zxw49000, zxw50000)
new_esEs23(zxw49000, zxw50000, ty_Float) → new_esEs19(zxw49000, zxw50000)
new_lt19(zxw49001, zxw50001, ty_Ordering) → new_lt14(zxw49001, zxw50001)
new_lt19(zxw49001, zxw50001, ty_Int) → new_lt4(zxw49001, zxw50001)
new_esEs7(Just(zxw4000), Just(zxw3000), app(app(ty_Either, bff), bfg)) → new_esEs6(zxw4000, zxw3000, bff, bfg)
new_primMulNat0(Zero, Zero) → Zero
new_ltEs7(Left(zxw49000), Right(zxw50000), caa, cab) → True
new_compare26(Just(zxw4900), Nothing, False, bce) → GT
new_esEs26(zxw49001, zxw50001, app(ty_[], cef)) → new_esEs16(zxw49001, zxw50001, cef)
new_esEs27(zxw49000, zxw50000, ty_Bool) → new_esEs9(zxw49000, zxw50000)
new_ltEs18(zxw49001, zxw50001, ty_Integer) → new_ltEs16(zxw49001, zxw50001)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_ltEs18(zxw49001, zxw50001, app(ty_[], bdc)) → new_ltEs13(zxw49001, zxw50001, bdc)
new_ltEs20(zxw49002, zxw50002, app(ty_Maybe, cdc)) → new_ltEs8(zxw49002, zxw50002, cdc)
new_esEs11(zxw4001, zxw3001, ty_Char) → new_esEs15(zxw4001, zxw3001)
new_esEs11(zxw4001, zxw3001, ty_Float) → new_esEs19(zxw4001, zxw3001)
new_lt8(zxw49000, zxw50000) → new_esEs8(new_compare16(zxw49000, zxw50000), LT)
new_esEs26(zxw49001, zxw50001, ty_Char) → new_esEs15(zxw49001, zxw50001)
new_lt20(zxw49000, zxw50000, app(app(ty_@2, cfe), cff)) → new_lt11(zxw49000, zxw50000, cfe, cff)
new_esEs23(zxw49000, zxw50000, ty_Char) → new_esEs15(zxw49000, zxw50000)
new_esEs23(zxw49000, zxw50000, ty_Bool) → new_esEs9(zxw49000, zxw50000)
new_esEs27(zxw49000, zxw50000, ty_Char) → new_esEs15(zxw49000, zxw50000)
new_compare26(Nothing, Just(zxw5000), False, bce) → LT
new_lt10(zxw49000, zxw50000, ty_Float) → new_lt7(zxw49000, zxw50000)
new_esEs21(zxw4001, zxw3001, ty_Double) → new_esEs18(zxw4001, zxw3001)
new_ltEs19(zxw4900, zxw5000, ty_Int) → new_ltEs10(zxw4900, zxw5000)
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_lt9(zxw49000, zxw50000, be) → new_esEs8(new_compare0(zxw49000, zxw50000, be), LT)
new_compare210(zxw49000, zxw50000, False, bec, bed, bee) → new_compare110(zxw49000, zxw50000, new_ltEs15(zxw49000, zxw50000, bec, bed, bee), bec, bed, bee)
new_esEs22(zxw4000, zxw3000, app(ty_Ratio, bbd)) → new_esEs14(zxw4000, zxw3000, bbd)
new_esEs21(zxw4001, zxw3001, app(ty_Ratio, bab)) → new_esEs14(zxw4001, zxw3001, bab)
new_esEs7(Just(zxw4000), Just(zxw3000), app(app(ty_@2, bfh), bga)) → new_esEs4(zxw4000, zxw3000, bfh, bga)
new_esEs25(zxw4000, zxw3000, ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Bool) → new_esEs9(zxw4000, zxw3000)
new_ltEs20(zxw49002, zxw50002, ty_Integer) → new_ltEs16(zxw49002, zxw50002)
new_esEs21(zxw4001, zxw3001, app(app(ty_Either, bag), bah)) → new_esEs6(zxw4001, zxw3001, bag, bah)
new_ltEs7(Left(zxw49000), Left(zxw50000), app(app(app(ty_@3, chc), chd), che), cab) → new_ltEs15(zxw49000, zxw50000, chc, chd, che)
new_ltEs14(zxw4900, zxw5000) → new_fsEs(new_compare31(zxw4900, zxw5000))
new_compare24(zxw49000, zxw50000, False) → new_compare13(zxw49000, zxw50000, new_ltEs5(zxw49000, zxw50000))
new_esEs7(Just(zxw4000), Just(zxw3000), app(ty_Ratio, bfa)) → new_esEs14(zxw4000, zxw3000, bfa)
new_ltEs7(Right(zxw49000), Right(zxw50000), caa, app(app(ty_@2, daa), dab)) → new_ltEs9(zxw49000, zxw50000, daa, dab)
new_lt4(zxw490, zxw500) → new_esEs8(new_compare7(zxw490, zxw500), LT)
new_esEs28(zxw4000, zxw3000, app(app(app(ty_@3, dbg), dbh), dca)) → new_esEs5(zxw4000, zxw3000, dbg, dbh, dca)
new_esEs28(zxw4000, zxw3000, ty_Bool) → new_esEs9(zxw4000, zxw3000)
new_compare19(zxw490, zxw500, bce) → new_compare26(zxw490, zxw500, new_esEs7(zxw490, zxw500, bce), bce)
new_esEs17(Integer(zxw4000), Integer(zxw3000)) → new_primEqInt(zxw4000, zxw3000)
new_pePe(False, zxw213) → zxw213
new_lt12(zxw490, zxw500, bce) → new_esEs8(new_compare19(zxw490, zxw500, bce), LT)
new_esEs20(@0, @0) → True
new_esEs6(Right(zxw4000), Right(zxw3000), cbf, app(ty_Ratio, cbh)) → new_esEs14(zxw4000, zxw3000, cbh)
new_esEs6(Left(zxw4000), Left(zxw3000), app(app(ty_@2, cbd), cbe), cad) → new_esEs4(zxw4000, zxw3000, cbd, cbe)
new_compare23(zxw49000, zxw50000, True) → EQ
new_esEs11(zxw4001, zxw3001, ty_Int) → new_esEs13(zxw4001, zxw3001)
new_lt19(zxw49001, zxw50001, app(ty_[], cef)) → new_lt9(zxw49001, zxw50001, cef)
new_compare29(zxw49000, zxw50000, ty_@0) → new_compare31(zxw49000, zxw50000)
new_compare26(Nothing, Nothing, False, bce) → LT
new_esEs10(zxw4002, zxw3002, app(ty_Maybe, ca)) → new_esEs7(zxw4002, zxw3002, ca)
new_ltEs16(zxw4900, zxw5000) → new_fsEs(new_compare9(zxw4900, zxw5000))
new_esEs22(zxw4000, zxw3000, app(app(ty_@2, bcc), bcd)) → new_esEs4(zxw4000, zxw3000, bcc, bcd)
new_esEs23(zxw49000, zxw50000, app(ty_Maybe, beb)) → new_esEs7(zxw49000, zxw50000, beb)
new_ltEs7(Right(zxw49000), Right(zxw50000), caa, app(ty_Ratio, dbb)) → new_ltEs17(zxw49000, zxw50000, dbb)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Char, cab) → new_ltEs12(zxw49000, zxw50000)
new_esEs28(zxw4000, zxw3000, ty_@0) → new_esEs20(zxw4000, zxw3000)
new_ltEs20(zxw49002, zxw50002, app(ty_[], cdd)) → new_ltEs13(zxw49002, zxw50002, cdd)
new_esEs10(zxw4002, zxw3002, app(app(app(ty_@3, cd), ce), cf)) → new_esEs5(zxw4002, zxw3002, cd, ce, cf)
new_esEs27(zxw49000, zxw50000, ty_Float) → new_esEs19(zxw49000, zxw50000)
new_ltEs20(zxw49002, zxw50002, app(app(app(ty_@3, cde), cdf), cdg)) → new_ltEs15(zxw49002, zxw50002, cde, cdf, cdg)
new_esEs22(zxw4000, zxw3000, ty_Ordering) → new_esEs8(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Bool) → new_esEs9(zxw4000, zxw3000)
new_compare6(zxw49000, zxw50000) → new_compare23(zxw49000, zxw50000, new_esEs8(zxw49000, zxw50000))
new_esEs12(zxw4000, zxw3000, app(ty_[], eh)) → new_esEs16(zxw4000, zxw3000, eh)
new_compare32(zxw49000, zxw50000, bc, bd) → new_compare25(zxw49000, zxw50000, new_esEs6(zxw49000, zxw50000, bc, bd), bc, bd)
new_compare29(zxw49000, zxw50000, ty_Int) → new_compare7(zxw49000, zxw50000)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Bool, cad) → new_esEs9(zxw4000, zxw3000)
new_ltEs8(Nothing, Just(zxw50000), gc) → True
new_ltEs7(Left(zxw49000), Left(zxw50000), app(app(ty_@2, cgg), cgh), cab) → new_ltEs9(zxw49000, zxw50000, cgg, cgh)
new_esEs6(Right(zxw4000), Left(zxw3000), cbf, cad) → False
new_esEs6(Left(zxw4000), Right(zxw3000), cbf, cad) → False
new_esEs8(LT, LT) → True
new_lt20(zxw49000, zxw50000, ty_@0) → new_lt15(zxw49000, zxw50000)
new_esEs10(zxw4002, zxw3002, ty_Integer) → new_esEs17(zxw4002, zxw3002)
new_esEs28(zxw4000, zxw3000, ty_Float) → new_esEs19(zxw4000, zxw3000)
new_compare29(zxw49000, zxw50000, app(app(app(ty_@3, bgg), bgh), bha)) → new_compare28(zxw49000, zxw50000, bgg, bgh, bha)
new_lt19(zxw49001, zxw50001, ty_@0) → new_lt15(zxw49001, zxw50001)
new_ltEs7(Right(zxw49000), Right(zxw50000), caa, ty_Bool) → new_ltEs5(zxw49000, zxw50000)
new_ltEs5(True, False) → False
new_lt19(zxw49001, zxw50001, app(app(ty_@2, cec), ced)) → new_lt11(zxw49001, zxw50001, cec, ced)
new_compare0([], [], bgb) → EQ
new_pePe(True, zxw213) → True
new_primEqNat0(Zero, Zero) → True
new_esEs14(:%(zxw4000, zxw4001), :%(zxw3000, zxw3001), bhe) → new_asAs(new_esEs25(zxw4000, zxw3000, bhe), new_esEs24(zxw4001, zxw3001, bhe))
new_lt10(zxw49000, zxw50000, ty_Double) → new_lt8(zxw49000, zxw50000)
new_ltEs20(zxw49002, zxw50002, ty_Ordering) → new_ltEs4(zxw49002, zxw50002)
new_compare27(zxw49000, zxw50000, False, ga, gb) → new_compare17(zxw49000, zxw50000, new_ltEs9(zxw49000, zxw50000, ga, gb), ga, gb)
new_compare11(zxw180, zxw181, True, bb) → LT
new_esEs23(zxw49000, zxw50000, app(app(ty_Either, bc), bd)) → new_esEs6(zxw49000, zxw50000, bc, bd)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_@0, cad) → new_esEs20(zxw4000, zxw3000)
new_esEs6(Right(zxw4000), Right(zxw3000), cbf, ty_Bool) → new_esEs9(zxw4000, zxw3000)
new_esEs12(zxw4000, zxw3000, ty_Int) → new_esEs13(zxw4000, zxw3000)
new_lt20(zxw49000, zxw50000, app(ty_[], cfh)) → new_lt9(zxw49000, zxw50000, cfh)
new_esEs6(Right(zxw4000), Right(zxw3000), cbf, app(app(ty_Either, cce), ccf)) → new_esEs6(zxw4000, zxw3000, cce, ccf)
new_compare26(Just(zxw4900), Just(zxw5000), False, bce) → new_compare11(zxw4900, zxw5000, new_ltEs19(zxw4900, zxw5000, bce), bce)
new_ltEs5(True, True) → True
new_ltEs7(Left(zxw49000), Left(zxw50000), app(ty_Maybe, cha), cab) → new_ltEs8(zxw49000, zxw50000, cha)
new_ltEs20(zxw49002, zxw50002, app(app(ty_@2, cda), cdb)) → new_ltEs9(zxw49002, zxw50002, cda, cdb)
new_esEs15(Char(zxw4000), Char(zxw3000)) → new_primEqNat0(zxw4000, zxw3000)
new_sr(zxw4001, zxw3001) → new_primMulInt(zxw4001, zxw3001)
new_ltEs18(zxw49001, zxw50001, ty_Int) → new_ltEs10(zxw49001, zxw50001)
new_esEs25(zxw4000, zxw3000, ty_Int) → new_esEs13(zxw4000, zxw3000)
new_compare7(zxw49, zxw50) → new_primCmpInt(zxw49, zxw50)
new_primCmpNat1(Zero, Zero) → EQ
new_esEs7(Just(zxw4000), Just(zxw3000), app(ty_[], bfb)) → new_esEs16(zxw4000, zxw3000, bfb)
new_lt10(zxw49000, zxw50000, ty_Int) → new_lt4(zxw49000, zxw50000)
new_esEs28(zxw4000, zxw3000, app(app(ty_Either, dcb), dcc)) → new_esEs6(zxw4000, zxw3000, dcb, dcc)
new_ltEs7(Right(zxw49000), Right(zxw50000), caa, app(ty_Maybe, dac)) → new_ltEs8(zxw49000, zxw50000, dac)
new_ltEs7(Right(zxw49000), Right(zxw50000), caa, ty_Integer) → new_ltEs16(zxw49000, zxw50000)
new_ltEs7(Right(zxw49000), Right(zxw50000), caa, app(app(app(ty_@3, dae), daf), dag)) → new_ltEs15(zxw49000, zxw50000, dae, daf, dag)
new_esEs26(zxw49001, zxw50001, ty_Ordering) → new_esEs8(zxw49001, zxw50001)
new_esEs8(GT, GT) → True
new_esEs27(zxw49000, zxw50000, ty_@0) → new_esEs20(zxw49000, zxw50000)
new_esEs13(zxw400, zxw300) → new_primEqInt(zxw400, zxw300)
new_lt13(zxw49000, zxw50000) → new_esEs8(new_compare18(zxw49000, zxw50000), LT)
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_lt20(zxw49000, zxw50000, ty_Ordering) → new_lt14(zxw49000, zxw50000)
new_esEs11(zxw4001, zxw3001, ty_Ordering) → new_esEs8(zxw4001, zxw3001)
new_esEs11(zxw4001, zxw3001, app(app(ty_@2, ed), ee)) → new_esEs4(zxw4001, zxw3001, ed, ee)
new_compare23(zxw49000, zxw50000, False) → new_compare10(zxw49000, zxw50000, new_ltEs4(zxw49000, zxw50000))
new_lt10(zxw49000, zxw50000, app(app(ty_@2, ga), gb)) → new_lt11(zxw49000, zxw50000, ga, gb)
new_esEs8(LT, GT) → False
new_esEs8(GT, LT) → False
new_ltEs19(zxw4900, zxw5000, app(app(app(ty_@3, bhf), bhg), bhh)) → new_ltEs15(zxw4900, zxw5000, bhf, bhg, bhh)
new_lt20(zxw49000, zxw50000, app(app(ty_Either, cgd), cge)) → new_lt17(zxw49000, zxw50000, cgd, cge)
new_esEs26(zxw49001, zxw50001, ty_Bool) → new_esEs9(zxw49001, zxw50001)
new_ltEs11(zxw4900, zxw5000) → new_fsEs(new_compare16(zxw4900, zxw5000))
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_compare17(zxw49000, zxw50000, True, ga, gb) → LT
new_primEqInt(Neg(Succ(zxw40000)), Neg(Succ(zxw30000))) → new_primEqNat0(zxw40000, zxw30000)
new_ltEs5(False, False) → True
new_esEs23(zxw49000, zxw50000, ty_Ordering) → new_esEs8(zxw49000, zxw50000)
new_ltEs18(zxw49001, zxw50001, app(app(ty_Either, bdg), bdh)) → new_ltEs7(zxw49001, zxw50001, bdg, bdh)
new_esEs28(zxw4000, zxw3000, ty_Char) → new_esEs15(zxw4000, zxw3000)
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)
new_ltEs19(zxw4900, zxw5000, app(ty_Ratio, hf)) → new_ltEs17(zxw4900, zxw5000, hf)
new_esEs10(zxw4002, zxw3002, ty_Bool) → new_esEs9(zxw4002, zxw3002)
new_lt20(zxw49000, zxw50000, ty_Char) → new_lt6(zxw49000, zxw50000)
new_compare13(zxw49000, zxw50000, False) → GT
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Bool, cab) → new_ltEs5(zxw49000, zxw50000)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Int, cab) → new_ltEs10(zxw49000, zxw50000)
new_lt11(zxw49000, zxw50000, ga, gb) → new_esEs8(new_compare30(zxw49000, zxw50000, ga, gb), LT)
new_esEs21(zxw4001, zxw3001, ty_Char) → new_esEs15(zxw4001, zxw3001)
new_lt20(zxw49000, zxw50000, ty_Int) → new_lt4(zxw49000, zxw50000)
new_primCompAux1(zxw49000, zxw50000, zxw214, bgb) → new_primCompAux0(zxw214, new_compare29(zxw49000, zxw50000, bgb))
new_esEs7(Just(zxw4000), Just(zxw3000), ty_@0) → new_esEs20(zxw4000, zxw3000)
new_lt16(zxw49000, zxw50000, bec, bed, bee) → new_esEs8(new_compare28(zxw49000, zxw50000, bec, bed, bee), LT)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_ltEs7(Right(zxw49000), Left(zxw50000), caa, cab) → False
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Ordering) → new_esEs8(zxw4000, zxw3000)
new_ltEs7(Left(zxw49000), Left(zxw50000), app(ty_[], chb), cab) → new_ltEs13(zxw49000, zxw50000, chb)
new_ltEs19(zxw4900, zxw5000, ty_Ordering) → new_ltEs4(zxw4900, zxw5000)
new_ltEs20(zxw49002, zxw50002, ty_Char) → new_ltEs12(zxw49002, zxw50002)
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_ltEs20(zxw49002, zxw50002, app(ty_Ratio, ceb)) → new_ltEs17(zxw49002, zxw50002, ceb)
new_esEs11(zxw4001, zxw3001, app(app(app(ty_@3, dg), dh), ea)) → new_esEs5(zxw4001, zxw3001, dg, dh, ea)
new_ltEs18(zxw49001, zxw50001, ty_@0) → new_ltEs14(zxw49001, zxw50001)
new_primEqInt(Neg(Succ(zxw40000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(zxw30000))) → False
new_ltEs19(zxw4900, zxw5000, ty_Char) → new_ltEs12(zxw4900, zxw5000)
new_esEs12(zxw4000, zxw3000, ty_Double) → new_esEs18(zxw4000, zxw3000)
new_primCompAux0(zxw218, GT) → GT
new_esEs8(EQ, EQ) → True
new_esEs6(Left(zxw4000), Left(zxw3000), app(ty_Ratio, cae), cad) → new_esEs14(zxw4000, zxw3000, cae)
new_ltEs8(Just(zxw49000), Just(zxw50000), app(app(ty_Either, hc), hd)) → new_ltEs7(zxw49000, zxw50000, hc, hd)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Integer, cab) → new_ltEs16(zxw49000, zxw50000)
new_esEs6(Right(zxw4000), Right(zxw3000), cbf, app(ty_[], cca)) → new_esEs16(zxw4000, zxw3000, cca)
new_esEs23(zxw49000, zxw50000, ty_Integer) → new_esEs17(zxw49000, zxw50000)
new_esEs28(zxw4000, zxw3000, ty_Int) → new_esEs13(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, app(app(app(ty_@3, bbf), bbg), bbh)) → new_esEs5(zxw4000, zxw3000, bbf, bbg, bbh)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_ltEs18(zxw49001, zxw50001, ty_Ordering) → new_ltEs4(zxw49001, zxw50001)
new_ltEs4(EQ, LT) → False
new_esEs12(zxw4000, zxw3000, app(ty_Maybe, ef)) → new_esEs7(zxw4000, zxw3000, ef)
new_lt20(zxw49000, zxw50000, ty_Double) → new_lt8(zxw49000, zxw50000)
new_esEs10(zxw4002, zxw3002, ty_Float) → new_esEs19(zxw4002, zxw3002)
new_esEs11(zxw4001, zxw3001, ty_Bool) → new_esEs9(zxw4001, zxw3001)
new_compare11(zxw180, zxw181, False, bb) → GT
new_esEs26(zxw49001, zxw50001, ty_Integer) → new_esEs17(zxw49001, zxw50001)
new_lt10(zxw49000, zxw50000, ty_Ordering) → new_lt14(zxw49000, zxw50000)
new_ltEs18(zxw49001, zxw50001, ty_Bool) → new_ltEs5(zxw49001, zxw50001)
new_esEs12(zxw4000, zxw3000, app(app(app(ty_@3, fa), fb), fc)) → new_esEs5(zxw4000, zxw3000, fa, fb, fc)
new_primEqInt(Pos(Succ(zxw40000)), Pos(Succ(zxw30000))) → new_primEqNat0(zxw40000, zxw30000)
new_compare27(zxw49000, zxw50000, True, ga, gb) → EQ
new_esEs6(Left(zxw4000), Left(zxw3000), app(app(app(ty_@3, cag), cah), cba), cad) → new_esEs5(zxw4000, zxw3000, cag, cah, cba)
new_lt18(zxw49000, zxw50000, bef) → new_esEs8(new_compare8(zxw49000, zxw50000, bef), LT)
new_ltEs18(zxw49001, zxw50001, app(app(app(ty_@3, bdd), bde), bdf)) → new_ltEs15(zxw49001, zxw50001, bdd, bde, bdf)
new_lt10(zxw49000, zxw50000, app(ty_Maybe, beb)) → new_lt12(zxw49000, zxw50000, beb)
new_esEs26(zxw49001, zxw50001, ty_Int) → new_esEs13(zxw49001, zxw50001)
new_ltEs8(Just(zxw49000), Just(zxw50000), app(app(ty_@2, gd), ge)) → new_ltEs9(zxw49000, zxw50000, gd, ge)
new_primEqNat0(Succ(zxw40000), Succ(zxw30000)) → new_primEqNat0(zxw40000, zxw30000)
new_compare29(zxw49000, zxw50000, app(ty_[], bgf)) → new_compare0(zxw49000, zxw50000, bgf)
new_esEs27(zxw49000, zxw50000, ty_Ordering) → new_esEs8(zxw49000, zxw50000)
new_esEs27(zxw49000, zxw50000, ty_Integer) → new_esEs17(zxw49000, zxw50000)
new_esEs23(zxw49000, zxw50000, app(ty_Ratio, bef)) → new_esEs14(zxw49000, zxw50000, bef)
new_ltEs18(zxw49001, zxw50001, ty_Float) → new_ltEs6(zxw49001, zxw50001)
new_esEs22(zxw4000, zxw3000, ty_Int) → new_esEs13(zxw4000, zxw3000)
new_ltEs7(Right(zxw49000), Right(zxw50000), caa, app(ty_[], dad)) → new_ltEs13(zxw49000, zxw50000, dad)
new_ltEs4(GT, EQ) → False
new_lt7(zxw49000, zxw50000) → new_esEs8(new_compare14(zxw49000, zxw50000), LT)
new_lt10(zxw49000, zxw50000, app(app(app(ty_@3, bec), bed), bee)) → new_lt16(zxw49000, zxw50000, bec, bed, bee)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Int) → new_esEs13(zxw4000, zxw3000)
new_ltEs19(zxw4900, zxw5000, app(app(ty_Either, caa), cab)) → new_ltEs7(zxw4900, zxw5000, caa, cab)
new_ltEs8(Just(zxw49000), Nothing, gc) → False
new_esEs21(zxw4001, zxw3001, ty_Float) → new_esEs19(zxw4001, zxw3001)
new_esEs26(zxw49001, zxw50001, app(app(ty_@2, cec), ced)) → new_esEs4(zxw49001, zxw50001, cec, ced)
new_esEs27(zxw49000, zxw50000, app(app(app(ty_@3, cga), cgb), cgc)) → new_esEs5(zxw49000, zxw50000, cga, cgb, cgc)
new_ltEs13(zxw4900, zxw5000, bgb) → new_fsEs(new_compare0(zxw4900, zxw5000, bgb))
new_esEs22(zxw4000, zxw3000, ty_Char) → new_esEs15(zxw4000, zxw3000)
new_ltEs18(zxw49001, zxw50001, ty_Double) → new_ltEs11(zxw49001, zxw50001)
new_esEs7(Nothing, Nothing, beg) → True
new_esEs28(zxw4000, zxw3000, ty_Ordering) → new_esEs8(zxw4000, zxw3000)
new_lt10(zxw49000, zxw50000, app(app(ty_Either, bc), bd)) → new_lt17(zxw49000, zxw50000, bc, bd)
new_esEs8(EQ, LT) → False
new_esEs8(LT, EQ) → False
new_esEs10(zxw4002, zxw3002, ty_Char) → new_esEs15(zxw4002, zxw3002)
new_primEqInt(Pos(Succ(zxw40000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(zxw30000))) → False
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Double, cab) → new_ltEs11(zxw49000, zxw50000)
new_ltEs4(EQ, EQ) → True
new_esEs6(Right(zxw4000), Right(zxw3000), cbf, app(ty_Maybe, cbg)) → new_esEs7(zxw4000, zxw3000, cbg)
new_ltEs7(Right(zxw49000), Right(zxw50000), caa, ty_Ordering) → new_ltEs4(zxw49000, zxw50000)
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_ltEs20(zxw49002, zxw50002, ty_@0) → new_ltEs14(zxw49002, zxw50002)
new_esEs23(zxw49000, zxw50000, ty_@0) → new_esEs20(zxw49000, zxw50000)
new_esEs6(Right(zxw4000), Right(zxw3000), cbf, ty_@0) → new_esEs20(zxw4000, zxw3000)
new_compare210(zxw49000, zxw50000, True, bec, bed, bee) → EQ
new_ltEs4(GT, LT) → False
new_sr0(Integer(zxw500000), Integer(zxw490010)) → Integer(new_primMulInt(zxw500000, zxw490010))
new_compare13(zxw49000, zxw50000, True) → LT
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_compare14(Float(zxw49000, zxw49001), Float(zxw50000, zxw50001)) → new_compare7(new_sr(zxw49000, zxw50000), new_sr(zxw49001, zxw50001))
new_primEqInt(Pos(Succ(zxw40000)), Neg(zxw3000)) → False
new_primEqInt(Neg(Succ(zxw40000)), Pos(zxw3000)) → False
new_esEs7(Just(zxw4000), Nothing, beg) → False
new_esEs7(Nothing, Just(zxw3000), beg) → False
new_esEs18(Double(zxw4000, zxw4001), Double(zxw3000, zxw3001)) → new_esEs13(new_sr(zxw4000, zxw3000), new_sr(zxw4001, zxw3001))
new_ltEs5(False, True) → True
new_esEs26(zxw49001, zxw50001, ty_Double) → new_esEs18(zxw49001, zxw50001)
new_compare28(zxw49000, zxw50000, bec, bed, bee) → new_compare210(zxw49000, zxw50000, new_esEs5(zxw49000, zxw50000, bec, bed, bee), bec, bed, bee)
new_esEs11(zxw4001, zxw3001, ty_Double) → new_esEs18(zxw4001, zxw3001)
new_ltEs6(zxw4900, zxw5000) → new_fsEs(new_compare14(zxw4900, zxw5000))
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Ordering, cab) → new_ltEs4(zxw49000, zxw50000)
new_primEqInt(Pos(Zero), Neg(Succ(zxw30000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(zxw30000))) → False
new_ltEs19(zxw4900, zxw5000, app(app(ty_@2, bcf), bcg)) → new_ltEs9(zxw4900, zxw5000, bcf, bcg)
new_ltEs20(zxw49002, zxw50002, ty_Float) → new_ltEs6(zxw49002, zxw50002)
new_compare29(zxw49000, zxw50000, app(app(ty_@2, bgc), bgd)) → new_compare30(zxw49000, zxw50000, bgc, bgd)
new_compare24(zxw49000, zxw50000, True) → EQ
new_esEs27(zxw49000, zxw50000, ty_Int) → new_esEs13(zxw49000, zxw50000)
new_ltEs18(zxw49001, zxw50001, app(app(ty_@2, bch), bda)) → new_ltEs9(zxw49001, zxw50001, bch, bda)
new_esEs6(Right(zxw4000), Right(zxw3000), cbf, ty_Double) → new_esEs18(zxw4000, zxw3000)
new_lt20(zxw49000, zxw50000, ty_Bool) → new_lt13(zxw49000, zxw50000)
new_primCmpNat0(Zero, zxw4900) → LT
new_ltEs7(Right(zxw49000), Right(zxw50000), caa, ty_Char) → new_ltEs12(zxw49000, zxw50000)
new_esEs8(EQ, GT) → False
new_esEs8(GT, EQ) → False
new_esEs10(zxw4002, zxw3002, app(ty_[], cc)) → new_esEs16(zxw4002, zxw3002, cc)
new_lt15(zxw49000, zxw50000) → new_esEs8(new_compare31(zxw49000, zxw50000), LT)
new_compare17(zxw49000, zxw50000, False, ga, gb) → GT
new_compare29(zxw49000, zxw50000, ty_Float) → new_compare14(zxw49000, zxw50000)
new_esEs28(zxw4000, zxw3000, app(ty_Ratio, dbe)) → new_esEs14(zxw4000, zxw3000, dbe)
new_compare26(zxw490, zxw500, True, bce) → EQ
new_primCompAux0(zxw218, LT) → LT
new_esEs11(zxw4001, zxw3001, ty_@0) → new_esEs20(zxw4001, zxw3001)
new_esEs12(zxw4000, zxw3000, ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_not(False) → True
new_esEs6(Left(zxw4000), Left(zxw3000), app(app(ty_Either, cbb), cbc), cad) → new_esEs6(zxw4000, zxw3000, cbb, cbc)
new_esEs28(zxw4000, zxw3000, app(ty_[], dbf)) → new_esEs16(zxw4000, zxw3000, dbf)
new_esEs24(zxw4001, zxw3001, ty_Int) → new_esEs13(zxw4001, zxw3001)
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_esEs26(zxw49001, zxw50001, app(ty_Ratio, cfd)) → new_esEs14(zxw49001, zxw50001, cfd)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Double) → new_ltEs11(zxw49000, zxw50000)
new_esEs11(zxw4001, zxw3001, app(app(ty_Either, eb), ec)) → new_esEs6(zxw4001, zxw3001, eb, ec)
new_esEs21(zxw4001, zxw3001, ty_@0) → new_esEs20(zxw4001, zxw3001)
new_lt19(zxw49001, zxw50001, ty_Float) → new_lt7(zxw49001, zxw50001)
new_ltEs7(Right(zxw49000), Right(zxw50000), caa, ty_Int) → new_ltEs10(zxw49000, zxw50000)
new_compare0(:(zxw49000, zxw49001), [], bgb) → GT
new_esEs12(zxw4000, zxw3000, ty_Float) → new_esEs19(zxw4000, zxw3000)
new_ltEs8(Just(zxw49000), Just(zxw50000), app(ty_[], gg)) → new_ltEs13(zxw49000, zxw50000, gg)
new_lt14(zxw49000, zxw50000) → new_esEs8(new_compare6(zxw49000, zxw50000), LT)
new_ltEs19(zxw4900, zxw5000, ty_Float) → new_ltEs6(zxw4900, zxw5000)
new_esEs27(zxw49000, zxw50000, app(app(ty_Either, cgd), cge)) → new_esEs6(zxw49000, zxw50000, cgd, cge)
new_lt19(zxw49001, zxw50001, app(ty_Ratio, cfd)) → new_lt18(zxw49001, zxw50001, cfd)
new_esEs9(True, True) → True
new_lt19(zxw49001, zxw50001, app(app(app(ty_@3, ceg), ceh), cfa)) → new_lt16(zxw49001, zxw50001, ceg, ceh, cfa)
new_lt19(zxw49001, zxw50001, ty_Char) → new_lt6(zxw49001, zxw50001)
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Double, cad) → new_esEs18(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, app(ty_Maybe, dbd)) → new_esEs7(zxw4000, zxw3000, dbd)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_esEs21(zxw4001, zxw3001, app(app(app(ty_@3, bad), bae), baf)) → new_esEs5(zxw4001, zxw3001, bad, bae, baf)
new_esEs22(zxw4000, zxw3000, app(ty_[], bbe)) → new_esEs16(zxw4000, zxw3000, bbe)
new_esEs21(zxw4001, zxw3001, app(ty_Maybe, baa)) → new_esEs7(zxw4001, zxw3001, baa)
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_esEs22(zxw4000, zxw3000, ty_Double) → new_esEs18(zxw4000, zxw3000)
new_esEs21(zxw4001, zxw3001, app(app(ty_@2, bba), bbb)) → new_esEs4(zxw4001, zxw3001, bba, bbb)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_@0) → new_ltEs14(zxw49000, zxw50000)
new_esEs19(Float(zxw4000, zxw4001), Float(zxw3000, zxw3001)) → new_esEs13(new_sr(zxw4000, zxw3000), new_sr(zxw4001, zxw3001))
new_ltEs19(zxw4900, zxw5000, app(ty_Maybe, gc)) → new_ltEs8(zxw4900, zxw5000, gc)
new_primMulInt(Neg(zxw40010), Neg(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primEqNat0(Zero, Succ(zxw30000)) → False
new_primEqNat0(Succ(zxw40000), Zero) → False
new_compare25(zxw49000, zxw50000, True, bc, bd) → EQ
new_ltEs7(Left(zxw49000), Left(zxw50000), app(app(ty_Either, chf), chg), cab) → new_ltEs7(zxw49000, zxw50000, chf, chg)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_lt10(zxw49000, zxw50000, app(ty_Ratio, bef)) → new_lt18(zxw49000, zxw50000, bef)
new_esEs12(zxw4000, zxw3000, ty_@0) → new_esEs20(zxw4000, zxw3000)
new_esEs21(zxw4001, zxw3001, ty_Bool) → new_esEs9(zxw4001, zxw3001)
new_esEs5(@3(zxw4000, zxw4001, zxw4002), @3(zxw3000, zxw3001, zxw3002), bf, bg, bh) → new_asAs(new_esEs12(zxw4000, zxw3000, bf), new_asAs(new_esEs11(zxw4001, zxw3001, bg), new_esEs10(zxw4002, zxw3002, bh)))
new_esEs16(:(zxw4000, zxw4001), [], dbc) → False
new_esEs16([], :(zxw3000, zxw3001), dbc) → False
new_lt10(zxw49000, zxw50000, ty_Integer) → new_lt5(zxw49000, zxw50000)
new_lt6(zxw49000, zxw50000) → new_esEs8(new_compare12(zxw49000, zxw50000), LT)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_ltEs4(LT, GT) → True
new_esEs23(zxw49000, zxw50000, ty_Double) → new_esEs18(zxw49000, zxw50000)
new_compare25(zxw49000, zxw50000, False, bc, bd) → new_compare15(zxw49000, zxw50000, new_ltEs7(zxw49000, zxw50000, bc, bd), bc, bd)
new_lt19(zxw49001, zxw50001, app(app(ty_Either, cfb), cfc)) → new_lt17(zxw49001, zxw50001, cfb, cfc)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_esEs6(Left(zxw4000), Left(zxw3000), app(ty_Maybe, cac), cad) → new_esEs7(zxw4000, zxw3000, cac)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Ordering, cad) → new_esEs8(zxw4000, zxw3000)
new_esEs16(:(zxw4000, zxw4001), :(zxw3000, zxw3001), dbc) → new_asAs(new_esEs28(zxw4000, zxw3000, dbc), new_esEs16(zxw4001, zxw3001, dbc))
new_ltEs8(Just(zxw49000), Just(zxw50000), app(ty_Ratio, he)) → new_ltEs17(zxw49000, zxw50000, he)
new_compare0(:(zxw49000, zxw49001), :(zxw50000, zxw50001), bgb) → new_primCompAux1(zxw49000, zxw50000, new_compare0(zxw49001, zxw50001, bgb), bgb)
new_esEs11(zxw4001, zxw3001, app(ty_Maybe, dd)) → new_esEs7(zxw4001, zxw3001, dd)
new_esEs6(Right(zxw4000), Right(zxw3000), cbf, app(app(ty_@2, ccg), cch)) → new_esEs4(zxw4000, zxw3000, ccg, cch)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Float) → new_ltEs6(zxw49000, zxw50000)
new_compare15(zxw49000, zxw50000, False, bc, bd) → GT
new_compare29(zxw49000, zxw50000, app(app(ty_Either, bhb), bhc)) → new_compare32(zxw49000, zxw50000, bhb, bhc)
new_lt20(zxw49000, zxw50000, ty_Float) → new_lt7(zxw49000, zxw50000)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Char) → new_esEs15(zxw4000, zxw3000)
new_esEs23(zxw49000, zxw50000, ty_Int) → new_esEs13(zxw49000, zxw50000)
new_esEs7(Just(zxw4000), Just(zxw3000), app(app(app(ty_@3, bfc), bfd), bfe)) → new_esEs5(zxw4000, zxw3000, bfc, bfd, bfe)
new_esEs9(True, False) → False
new_esEs9(False, True) → False
new_compare29(zxw49000, zxw50000, app(ty_Ratio, bhd)) → new_compare8(zxw49000, zxw50000, bhd)
new_esEs10(zxw4002, zxw3002, app(app(ty_@2, db), dc)) → new_esEs4(zxw4002, zxw3002, db, dc)
new_esEs11(zxw4001, zxw3001, app(ty_Ratio, de)) → new_esEs14(zxw4001, zxw3001, de)
new_compare29(zxw49000, zxw50000, ty_Ordering) → new_compare6(zxw49000, zxw50000)
new_esEs21(zxw4001, zxw3001, ty_Integer) → new_esEs17(zxw4001, zxw3001)
new_esEs27(zxw49000, zxw50000, ty_Double) → new_esEs18(zxw49000, zxw50000)
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs27(zxw49000, zxw50000, app(ty_Ratio, cgf)) → new_esEs14(zxw49000, zxw50000, cgf)
new_ltEs4(LT, EQ) → True
new_esEs6(Right(zxw4000), Right(zxw3000), cbf, ty_Char) → new_esEs15(zxw4000, zxw3000)
new_esEs10(zxw4002, zxw3002, ty_Double) → new_esEs18(zxw4002, zxw3002)
new_compare31(@0, @0) → EQ
new_esEs12(zxw4000, zxw3000, app(app(ty_Either, fd), ff)) → new_esEs6(zxw4000, zxw3000, fd, ff)
new_ltEs8(Just(zxw49000), Just(zxw50000), app(ty_Maybe, gf)) → new_ltEs8(zxw49000, zxw50000, gf)
new_lt19(zxw49001, zxw50001, ty_Bool) → new_lt13(zxw49001, zxw50001)
new_ltEs7(Right(zxw49000), Right(zxw50000), caa, app(app(ty_Either, dah), dba)) → new_ltEs7(zxw49000, zxw50000, dah, dba)
new_esEs28(zxw4000, zxw3000, app(app(ty_@2, dcd), dce)) → new_esEs4(zxw4000, zxw3000, dcd, dce)
new_compare9(Integer(zxw49000), Integer(zxw50000)) → new_primCmpInt(zxw49000, zxw50000)
new_asAs(False, zxw187) → False
new_primMulInt(Neg(zxw40010), Pos(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Double) → new_esEs18(zxw4000, zxw3000)
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Ordering) → new_ltEs4(zxw49000, zxw50000)
new_esEs21(zxw4001, zxw3001, ty_Ordering) → new_esEs8(zxw4001, zxw3001)
new_primCmpNat2(zxw4900, Zero) → GT
new_ltEs20(zxw49002, zxw50002, ty_Double) → new_ltEs11(zxw49002, zxw50002)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Char, cad) → new_esEs15(zxw4000, zxw3000)
new_esEs26(zxw49001, zxw50001, app(ty_Maybe, cee)) → new_esEs7(zxw49001, zxw50001, cee)
new_esEs10(zxw4002, zxw3002, ty_@0) → new_esEs20(zxw4002, zxw3002)
new_lt19(zxw49001, zxw50001, ty_Double) → new_lt8(zxw49001, zxw50001)
new_esEs28(zxw4000, zxw3000, ty_Double) → new_esEs18(zxw4000, zxw3000)
new_compare110(zxw49000, zxw50000, True, bec, bed, bee) → LT
new_esEs24(zxw4001, zxw3001, ty_Integer) → new_esEs17(zxw4001, zxw3001)
new_lt19(zxw49001, zxw50001, app(ty_Maybe, cee)) → new_lt12(zxw49001, zxw50001, cee)
new_ltEs18(zxw49001, zxw50001, app(ty_Ratio, bea)) → new_ltEs17(zxw49001, zxw50001, bea)
new_ltEs18(zxw49001, zxw50001, ty_Char) → new_ltEs12(zxw49001, zxw50001)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Float, cad) → new_esEs19(zxw4000, zxw3000)
new_esEs21(zxw4001, zxw3001, ty_Int) → new_esEs13(zxw4001, zxw3001)
new_lt20(zxw49000, zxw50000, app(ty_Ratio, cgf)) → new_lt18(zxw49000, zxw50000, cgf)
new_ltEs19(zxw4900, zxw5000, ty_@0) → new_ltEs14(zxw4900, zxw5000)
new_ltEs7(Right(zxw49000), Right(zxw50000), caa, ty_Double) → new_ltEs11(zxw49000, zxw50000)
new_lt17(zxw49000, zxw50000, bc, bd) → new_esEs8(new_compare32(zxw49000, zxw50000, bc, bd), LT)
new_esEs9(False, False) → True
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Int) → new_ltEs10(zxw49000, zxw50000)
new_ltEs19(zxw4900, zxw5000, ty_Bool) → new_ltEs5(zxw4900, zxw5000)
new_compare29(zxw49000, zxw50000, ty_Integer) → new_compare9(zxw49000, zxw50000)
new_lt20(zxw49000, zxw50000, app(app(app(ty_@3, cga), cgb), cgc)) → new_lt16(zxw49000, zxw50000, cga, cgb, cgc)
new_ltEs20(zxw49002, zxw50002, app(app(ty_Either, cdh), cea)) → new_ltEs7(zxw49002, zxw50002, cdh, cea)
new_esEs4(@2(zxw4000, zxw4001), @2(zxw3000, zxw3001), hg, hh) → new_asAs(new_esEs22(zxw4000, zxw3000, hg), new_esEs21(zxw4001, zxw3001, hh))
new_esEs27(zxw49000, zxw50000, app(app(ty_@2, cfe), cff)) → new_esEs4(zxw49000, zxw50000, cfe, cff)
new_lt20(zxw49000, zxw50000, ty_Integer) → new_lt5(zxw49000, zxw50000)
new_ltEs18(zxw49001, zxw50001, app(ty_Maybe, bdb)) → new_ltEs8(zxw49001, zxw50001, bdb)
new_compare8(:%(zxw49000, zxw49001), :%(zxw50000, zxw50001), ty_Integer) → new_compare9(new_sr0(zxw49000, zxw50001), new_sr0(zxw50000, zxw49001))
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Float, cab) → new_ltEs6(zxw49000, zxw50000)
new_ltEs4(LT, LT) → True
new_esEs16([], [], dbc) → True
new_ltEs20(zxw49002, zxw50002, ty_Int) → new_ltEs10(zxw49002, zxw50002)
new_ltEs8(Nothing, Nothing, gc) → True
new_lt10(zxw49000, zxw50000, ty_Char) → new_lt6(zxw49000, zxw50000)
new_lt10(zxw49000, zxw50000, ty_Bool) → new_lt13(zxw49000, zxw50000)
new_esEs22(zxw4000, zxw3000, app(app(ty_Either, bca), bcb)) → new_esEs6(zxw4000, zxw3000, bca, bcb)
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_lt5(zxw49000, zxw50000) → new_esEs8(new_compare9(zxw49000, zxw50000), LT)
new_esEs26(zxw49001, zxw50001, ty_Float) → new_esEs19(zxw49001, zxw50001)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Int, cad) → new_esEs13(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_esEs10(zxw4002, zxw3002, ty_Int) → new_esEs13(zxw4002, zxw3002)
new_ltEs15(@3(zxw49000, zxw49001, zxw49002), @3(zxw50000, zxw50001, zxw50002), bhf, bhg, bhh) → new_pePe(new_lt20(zxw49000, zxw50000, bhf), new_asAs(new_esEs27(zxw49000, zxw50000, bhf), new_pePe(new_lt19(zxw49001, zxw50001, bhg), new_asAs(new_esEs26(zxw49001, zxw50001, bhg), new_ltEs20(zxw49002, zxw50002, bhh)))))
new_lt10(zxw49000, zxw50000, app(ty_[], be)) → new_lt9(zxw49000, zxw50000, be)
new_esEs12(zxw4000, zxw3000, app(ty_Ratio, eg)) → new_esEs14(zxw4000, zxw3000, eg)
new_ltEs10(zxw4900, zxw5000) → new_fsEs(new_compare7(zxw4900, zxw5000))
new_esEs10(zxw4002, zxw3002, app(ty_Ratio, cb)) → new_esEs14(zxw4002, zxw3002, cb)
new_ltEs12(zxw4900, zxw5000) → new_fsEs(new_compare12(zxw4900, zxw5000))
new_esEs10(zxw4002, zxw3002, ty_Ordering) → new_esEs8(zxw4002, zxw3002)
new_ltEs7(Right(zxw49000), Right(zxw50000), caa, ty_Float) → new_ltEs6(zxw49000, zxw50000)
new_esEs23(zxw49000, zxw50000, app(ty_[], be)) → new_esEs16(zxw49000, zxw50000, be)
new_esEs11(zxw4001, zxw3001, ty_Integer) → new_esEs17(zxw4001, zxw3001)
new_esEs26(zxw49001, zxw50001, app(app(ty_Either, cfb), cfc)) → new_esEs6(zxw49001, zxw50001, cfb, cfc)
new_compare16(Double(zxw49000, zxw49001), Double(zxw50000, zxw50001)) → new_compare7(new_sr(zxw49000, zxw50000), new_sr(zxw49001, zxw50001))
new_compare0([], :(zxw50000, zxw50001), bgb) → LT
new_primPlusNat1(Zero, Zero) → Zero
new_esEs12(zxw4000, zxw3000, ty_Ordering) → new_esEs8(zxw4000, zxw3000)
new_lt10(zxw49000, zxw50000, ty_@0) → new_lt15(zxw49000, zxw50000)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Char) → new_ltEs12(zxw49000, zxw50000)
new_asAs(True, zxw187) → zxw187
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_esEs26(zxw49001, zxw50001, app(app(app(ty_@3, ceg), ceh), cfa)) → new_esEs5(zxw49001, zxw50001, ceg, ceh, cfa)
new_esEs10(zxw4002, zxw3002, app(app(ty_Either, cg), da)) → new_esEs6(zxw4002, zxw3002, cg, da)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Integer) → new_ltEs16(zxw49000, zxw50000)
new_compare30(zxw49000, zxw50000, ga, gb) → new_compare27(zxw49000, zxw50000, new_esEs4(zxw49000, zxw50000, ga, gb), ga, gb)
new_compare29(zxw49000, zxw50000, ty_Bool) → new_compare18(zxw49000, zxw50000)
new_fsEs(zxw202) → new_not(new_esEs8(zxw202, GT))
new_esEs23(zxw49000, zxw50000, app(app(app(ty_@3, bec), bed), bee)) → new_esEs5(zxw49000, zxw50000, bec, bed, bee)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Float) → new_esEs19(zxw4000, zxw3000)
new_compare10(zxw49000, zxw50000, True) → LT
new_compare29(zxw49000, zxw50000, app(ty_Maybe, bge)) → new_compare19(zxw49000, zxw50000, bge)
new_ltEs4(GT, GT) → True
new_esEs26(zxw49001, zxw50001, ty_@0) → new_esEs20(zxw49001, zxw50001)
new_compare110(zxw49000, zxw50000, False, bec, bed, bee) → GT
new_ltEs7(Left(zxw49000), Left(zxw50000), app(ty_Ratio, chh), cab) → new_ltEs17(zxw49000, zxw50000, chh)
new_compare10(zxw49000, zxw50000, False) → GT
new_ltEs8(Just(zxw49000), Just(zxw50000), app(app(app(ty_@3, gh), ha), hb)) → new_ltEs15(zxw49000, zxw50000, gh, ha, hb)
new_esEs21(zxw4001, zxw3001, app(ty_[], bac)) → new_esEs16(zxw4001, zxw3001, bac)
new_compare18(zxw49000, zxw50000) → new_compare24(zxw49000, zxw50000, new_esEs9(zxw49000, zxw50000))
new_esEs6(Right(zxw4000), Right(zxw3000), cbf, ty_Ordering) → new_esEs8(zxw4000, zxw3000)
new_esEs6(Left(zxw4000), Left(zxw3000), app(ty_[], caf), cad) → new_esEs16(zxw4000, zxw3000, caf)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs6(Right(zxw4000), Right(zxw3000), cbf, app(app(app(ty_@3, ccb), ccc), ccd)) → new_esEs5(zxw4000, zxw3000, ccb, ccc, ccd)
new_primCompAux0(zxw218, EQ) → zxw218
new_lt20(zxw49000, zxw50000, app(ty_Maybe, cfg)) → new_lt12(zxw49000, zxw50000, cfg)
new_esEs12(zxw4000, zxw3000, app(app(ty_@2, fg), fh)) → new_esEs4(zxw4000, zxw3000, fg, fh)
new_ltEs19(zxw4900, zxw5000, app(ty_[], bgb)) → new_ltEs13(zxw4900, zxw5000, bgb)
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_esEs22(zxw4000, zxw3000, app(ty_Maybe, bbc)) → new_esEs7(zxw4000, zxw3000, bbc)
new_ltEs7(Right(zxw49000), Right(zxw50000), caa, ty_@0) → new_ltEs14(zxw49000, zxw50000)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_compare8(:%(zxw49000, zxw49001), :%(zxw50000, zxw50001), ty_Int) → new_compare7(new_sr(zxw49000, zxw50001), new_sr(zxw50000, zxw49001))
new_ltEs17(zxw4900, zxw5000, hf) → new_fsEs(new_compare8(zxw4900, zxw5000, hf))
new_not(True) → False

The set Q consists of the following terms:

new_esEs17(Integer(x0), Integer(x1))
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare8(:%(x0, x1), :%(x2, x3), ty_Integer)
new_lt10(x0, x1, ty_Double)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_compare18(x0, x1)
new_compare29(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Double)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_pePe(False, x0)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_esEs22(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare7(x0, x1)
new_lt11(x0, x1, x2, x3)
new_primMulNat0(Succ(x0), Zero)
new_esEs7(Just(x0), Just(x1), ty_Double)
new_ltEs8(Just(x0), Just(x1), ty_Integer)
new_esEs10(x0, x1, ty_Int)
new_ltEs10(x0, x1)
new_esEs12(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Ordering)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs12(x0, x1, ty_Char)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_esEs6(Right(x0), Right(x1), x2, ty_Int)
new_lt10(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs13(x0, x1, x2)
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs8(Just(x0), Just(x1), app(ty_[], x2))
new_compare8(:%(x0, x1), :%(x2, x3), ty_Int)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs16(x0, x1)
new_compare13(x0, x1, True)
new_esEs10(x0, x1, ty_Ordering)
new_compare32(x0, x1, x2, x3)
new_ltEs19(x0, x1, ty_Float)
new_esEs11(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_Int)
new_lt18(x0, x1, x2)
new_ltEs19(x0, x1, ty_Ordering)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_lt10(x0, x1, app(ty_Ratio, x2))
new_esEs8(GT, GT)
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_compare17(x0, x1, False, x2, x3)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs7(Just(x0), Nothing, x1)
new_esEs8(LT, LT)
new_esEs14(:%(x0, x1), :%(x2, x3), x4)
new_compare29(x0, x1, ty_Double)
new_compare29(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs18(Double(x0, x1), Double(x2, x3))
new_primCmpNat0(Zero, x0)
new_ltEs7(Left(x0), Left(x1), ty_Double, x2)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_ltEs8(Just(x0), Just(x1), ty_Bool)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, ty_@0)
new_primCmpNat1(Zero, Succ(x0))
new_ltEs7(Left(x0), Left(x1), ty_Bool, x2)
new_esEs25(x0, x1, ty_Int)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_sr(x0, x1)
new_ltEs5(False, False)
new_compare19(x0, x1, x2)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Right(x0), Left(x1), x2, x3)
new_esEs6(Left(x0), Right(x1), x2, x3)
new_ltEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_compare6(x0, x1)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt10(x0, x1, ty_Ordering)
new_compare29(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Integer)
new_primEqNat0(Zero, Succ(x0))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpNat1(Zero, Zero)
new_ltEs17(x0, x1, x2)
new_compare16(Double(x0, x1), Double(x2, x3))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_lt7(x0, x1)
new_esEs28(x0, x1, ty_@0)
new_ltEs20(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Integer)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_compare26(Just(x0), Just(x1), False, x2)
new_esEs23(x0, x1, ty_Integer)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_compare27(x0, x1, False, x2, x3)
new_esEs12(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Double)
new_ltEs19(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_Char)
new_esEs11(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, ty_Int)
new_esEs7(Nothing, Nothing, x0)
new_primEqNat0(Zero, Zero)
new_compare26(Just(x0), Nothing, False, x1)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_ltEs7(Left(x0), Left(x1), ty_Int, x2)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs9(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs8(Just(x0), Just(x1), ty_Double)
new_esEs10(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, app(ty_[], x2))
new_ltEs8(Just(x0), Just(x1), ty_Ordering)
new_ltEs19(x0, x1, ty_@0)
new_esEs6(Right(x0), Right(x1), x2, ty_Integer)
new_compare24(x0, x1, False)
new_esEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs9(True, True)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs10(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs12(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs16(:(x0, x1), :(x2, x3), x4)
new_compare29(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs7(Right(x0), Right(x1), x2, ty_Char)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_lt19(x0, x1, app(ty_Maybe, x2))
new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_lt4(x0, x1)
new_primMulNat0(Zero, Zero)
new_esEs23(x0, x1, ty_Char)
new_esEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_lt17(x0, x1, x2, x3)
new_esEs10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs10(x0, x1, ty_@0)
new_lt10(x0, x1, ty_Char)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Left(x0), Left(x1), ty_@0, x2)
new_ltEs18(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_Integer)
new_fsEs(x0)
new_ltEs4(GT, GT)
new_lt8(x0, x1)
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs15(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs10(x0, x1, ty_Float)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs28(x0, x1, ty_Double)
new_ltEs8(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, ty_@0)
new_lt10(x0, x1, ty_Int)
new_esEs10(x0, x1, ty_Bool)
new_ltEs8(Nothing, Nothing, x0)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs23(x0, x1, ty_Ordering)
new_esEs7(Just(x0), Just(x1), ty_Int)
new_esEs10(x0, x1, ty_Char)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, app(ty_[], x2))
new_ltEs7(Right(x0), Right(x1), x2, ty_Double)
new_esEs11(x0, x1, app(ty_[], x2))
new_esEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_compare110(x0, x1, False, x2, x3, x4)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_lt12(x0, x1, x2)
new_esEs12(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs7(Right(x0), Right(x1), x2, ty_Bool)
new_pePe(True, x0)
new_lt19(x0, x1, app(ty_[], x2))
new_lt10(x0, x1, app(ty_Maybe, x2))
new_esEs16(:(x0, x1), [], x2)
new_compare0([], :(x0, x1), x2)
new_primPlusNat0(Zero, x0)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_compare17(x0, x1, True, x2, x3)
new_ltEs7(Right(x0), Right(x1), x2, ty_Int)
new_esEs21(x0, x1, ty_Int)
new_lt6(x0, x1)
new_esEs26(x0, x1, ty_Bool)
new_compare24(x0, x1, True)
new_compare29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, ty_Integer)
new_esEs6(Left(x0), Left(x1), ty_Float, x2)
new_esEs26(x0, x1, app(ty_[], x2))
new_ltEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_compare25(x0, x1, True, x2, x3)
new_compare14(Float(x0, x1), Float(x2, x3))
new_esEs6(Left(x0), Left(x1), ty_Bool, x2)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_ltEs14(x0, x1)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_primPlusNat1(Zero, Zero)
new_primCompAux0(x0, GT)
new_compare23(x0, x1, True)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_ltEs8(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt15(x0, x1)
new_compare13(x0, x1, False)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_lt20(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_@0)
new_primCompAux1(x0, x1, x2, x3)
new_primPlusNat0(Succ(x0), x1)
new_ltEs4(EQ, EQ)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs7(Right(x0), Right(x1), x2, ty_@0)
new_ltEs19(x0, x1, ty_Char)
new_esEs12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, app(ty_Ratio, x2))
new_ltEs11(x0, x1)
new_esEs12(x0, x1, ty_@0)
new_esEs24(x0, x1, ty_Integer)
new_esEs11(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, ty_Char)
new_compare15(x0, x1, False, x2, x3)
new_esEs7(Just(x0), Just(x1), ty_Char)
new_esEs12(x0, x1, ty_Float)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs8(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare0(:(x0, x1), [], x2)
new_compare31(@0, @0)
new_ltEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs7(Just(x0), Just(x1), ty_Float)
new_primCmpNat2(x0, Zero)
new_ltEs7(Left(x0), Left(x1), ty_@0, x2)
new_ltEs4(EQ, LT)
new_ltEs4(LT, EQ)
new_esEs12(x0, x1, ty_Int)
new_lt19(x0, x1, ty_Double)
new_esEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs7(Right(x0), Right(x1), x2, ty_Integer)
new_compare11(x0, x1, False, x2)
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_primMulInt(Pos(x0), Pos(x1))
new_lt10(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Bool)
new_lt16(x0, x1, x2, x3, x4)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_@0)
new_asAs(True, x0)
new_primEqNat0(Succ(x0), Zero)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_esEs13(x0, x1)
new_compare210(x0, x1, True, x2, x3, x4)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Integer)
new_lt20(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Bool)
new_lt20(x0, x1, ty_Char)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs16([], :(x0, x1), x2)
new_compare29(x0, x1, app(ty_Ratio, x2))
new_ltEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs28(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_Ordering)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_ltEs20(x0, x1, ty_Bool)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs27(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_Double)
new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs25(x0, x1, ty_Integer)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_primMulInt(Neg(x0), Neg(x1))
new_lt10(x0, x1, ty_Bool)
new_compare15(x0, x1, True, x2, x3)
new_primPlusNat1(Succ(x0), Zero)
new_esEs10(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, ty_Bool)
new_esEs22(x0, x1, ty_Float)
new_ltEs4(LT, LT)
new_esEs10(x0, x1, ty_Integer)
new_esEs12(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Integer)
new_compare23(x0, x1, False)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs11(x0, x1, ty_Bool)
new_esEs11(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_Double)
new_esEs21(x0, x1, ty_Bool)
new_compare210(x0, x1, False, x2, x3, x4)
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, ty_Ordering)
new_compare30(x0, x1, x2, x3)
new_esEs28(x0, x1, app(ty_[], x2))
new_primPlusNat1(Zero, Succ(x0))
new_ltEs12(x0, x1)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_compare10(x0, x1, False)
new_compare27(x0, x1, True, x2, x3)
new_ltEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpNat0(Succ(x0), x1)
new_esEs22(x0, x1, ty_@0)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs8(GT, EQ)
new_esEs8(EQ, GT)
new_esEs22(x0, x1, ty_Bool)
new_lt19(x0, x1, ty_Float)
new_esEs10(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs8(Just(x0), Just(x1), app(ty_Ratio, x2))
new_lt19(x0, x1, ty_Integer)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs8(Just(x0), Just(x1), ty_Char)
new_ltEs8(Just(x0), Just(x1), ty_Float)
new_lt5(x0, x1)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_ltEs18(x0, x1, ty_Bool)
new_compare29(x0, x1, ty_Ordering)
new_ltEs7(Right(x0), Right(x1), x2, ty_Float)
new_esEs11(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_@0)
new_ltEs7(Left(x0), Left(x1), ty_Float, x2)
new_esEs11(x0, x1, ty_Int)
new_esEs11(x0, x1, ty_Char)
new_esEs6(Right(x0), Right(x1), x2, ty_Char)
new_esEs27(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Float)
new_lt19(x0, x1, ty_Ordering)
new_compare29(x0, x1, ty_Integer)
new_ltEs18(x0, x1, ty_Float)
new_esEs9(False, False)
new_esEs6(Left(x0), Left(x1), ty_Char, x2)
new_esEs21(x0, x1, ty_Double)
new_compare29(x0, x1, app(ty_[], x2))
new_esEs6(Left(x0), Left(x1), ty_Double, x2)
new_esEs12(x0, x1, ty_Ordering)
new_compare29(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_ltEs8(Nothing, Just(x0), x1)
new_ltEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_primCmpNat1(Succ(x0), Succ(x1))
new_esEs26(x0, x1, ty_@0)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_ltEs6(x0, x1)
new_lt10(x0, x1, ty_Float)
new_esEs22(x0, x1, ty_Int)
new_esEs16([], [], x0)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs21(x0, x1, ty_Float)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCompAux0(x0, EQ)
new_compare11(x0, x1, True, x2)
new_esEs21(x0, x1, ty_Integer)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_primCmpNat1(Succ(x0), Zero)
new_esEs6(Left(x0), Left(x1), ty_Int, x2)
new_ltEs18(x0, x1, ty_@0)
new_esEs22(x0, x1, ty_Double)
new_compare25(x0, x1, False, x2, x3)
new_lt13(x0, x1)
new_esEs23(x0, x1, ty_Bool)
new_ltEs5(True, True)
new_lt19(x0, x1, ty_Int)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_ltEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_lt19(x0, x1, ty_Char)
new_ltEs4(EQ, GT)
new_ltEs4(GT, EQ)
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_not(True)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs7(Left(x0), Left(x1), ty_Char, x2)
new_esEs11(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Float)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, ty_Char)
new_lt19(x0, x1, ty_@0)
new_esEs21(x0, x1, ty_Ordering)
new_compare0([], [], x0)
new_esEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs26(x0, x1, ty_Char)
new_ltEs18(x0, x1, ty_Int)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_ltEs20(x0, x1, ty_Ordering)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_not(False)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_lt14(x0, x1)
new_compare12(Char(x0), Char(x1))
new_esEs15(Char(x0), Char(x1))
new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs20(x0, x1, app(ty_[], x2))
new_compare10(x0, x1, True)
new_lt10(x0, x1, ty_@0)
new_asAs(False, x0)
new_esEs22(x0, x1, ty_Ordering)
new_compare26(x0, x1, True, x2)
new_ltEs18(x0, x1, ty_Char)
new_lt10(x0, x1, app(ty_[], x2))
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare29(x0, x1, ty_Float)
new_esEs27(x0, x1, ty_Char)
new_lt19(x0, x1, ty_Bool)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_ltEs8(Just(x0), Just(x1), ty_@0)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs20(@0, @0)
new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_ltEs18(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_Int)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_ltEs19(x0, x1, ty_Double)
new_esEs22(x0, x1, ty_Char)
new_esEs9(False, True)
new_esEs9(True, False)
new_compare29(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_Integer)
new_ltEs8(Just(x0), Nothing, x1)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs11(x0, x1, ty_Double)
new_ltEs20(x0, x1, ty_Float)
new_primCompAux0(x0, LT)
new_compare26(Nothing, Just(x0), False, x1)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs7(Left(x0), Left(x1), ty_Integer, x2)
new_primCmpNat2(x0, Succ(x1))
new_compare28(x0, x1, x2, x3, x4)
new_lt10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Nothing, Just(x0), x1)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs12(x0, x1, ty_Integer)
new_esEs10(x0, x1, ty_Double)
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_sr0(Integer(x0), Integer(x1))
new_compare110(x0, x1, True, x2, x3, x4)
new_compare26(Nothing, Nothing, False, x0)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs10(x0, x1, app(ty_[], x2))
new_ltEs18(x0, x1, ty_Double)
new_ltEs7(Right(x0), Left(x1), x2, x3)
new_ltEs7(Left(x0), Right(x1), x2, x3)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs12(x0, x1, ty_Double)
new_esEs12(x0, x1, ty_Bool)
new_compare9(Integer(x0), Integer(x1))
new_lt10(x0, x1, ty_Integer)
new_ltEs8(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs19(Float(x0, x1), Float(x2, x3))
new_primMulNat0(Zero, Succ(x0))
new_esEs7(Just(x0), Just(x1), ty_@0)
new_lt9(x0, x1, x2)
new_ltEs4(GT, LT)
new_ltEs4(LT, GT)
new_ltEs5(True, False)
new_ltEs5(False, True)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs8(Just(x0), Just(x1), ty_Int)
new_compare29(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Float)
new_esEs6(Right(x0), Right(x1), x2, ty_Double)
new_ltEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs23(x0, x1, ty_Float)
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs6(Right(x0), Right(x1), x2, ty_Float)

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(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw613, h, ba)
new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba) → new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_lt21(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, zxw334, Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_lt4(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), h, ba)

The TRS R consists of the following rules:

new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_esEs8(EQ, EQ) → True
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Pos(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_lt21(zxw112, zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_esEs8(new_compare7(zxw112, new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT)
new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_lt4(zxw490, zxw500) → new_esEs8(new_compare7(zxw490, zxw500), LT)
new_primMulInt(Neg(zxw40010), Neg(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primCmpNat2(zxw4900, Zero) → GT
new_primPlusNat1(Zero, Zero) → Zero
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primCmpNat0(Zero, zxw4900) → LT
new_sr(zxw4001, zxw3001) → new_primMulInt(zxw4001, zxw3001)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_compare7(zxw49, zxw50) → new_primCmpInt(zxw49, zxw50)
new_primCmpNat1(Zero, Zero) → EQ
new_esEs8(GT, EQ) → False
new_esEs8(EQ, GT) → False
new_sizeFM0(EmptyFM, h, ba) → Pos(Zero)
new_primMulNat0(Zero, Zero) → Zero
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_esEs8(GT, GT) → True
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_esEs8(GT, LT) → False
new_esEs8(LT, GT) → False
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)
new_esEs8(EQ, LT) → False
new_esEs8(LT, EQ) → False
new_esEs8(LT, LT) → True
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_lt4(x0, x1)
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_compare7(x0, x1)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_sr(x0, x1)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sIZE_RATIO
new_sizeFM0(EmptyFM, x0, x1)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_lt21(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

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

↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ 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(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw613, h, ba)
new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba) → new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_lt21(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba), h, ba)
new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, zxw334, Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_lt4(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_sr(zxw4001, zxw3001) → new_primMulInt(zxw4001, zxw3001)
new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)
new_lt4(zxw490, zxw500) → new_esEs8(new_compare7(zxw490, zxw500), LT)
new_compare7(zxw49, zxw50) → new_primCmpInt(zxw49, zxw50)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Pos(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Neg(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)
new_lt21(zxw112, zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_esEs8(new_compare7(zxw112, new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT)

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_lt4(x0, x1)
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_compare7(x0, x1)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_sr(x0, x1)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sIZE_RATIO
new_sizeFM0(EmptyFM, x0, x1)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_lt21(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba) → new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_lt21(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba), h, ba) at position [11] we obtained the following new rules:

new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba) → new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_compare7(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw613, h, ba)
new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba) → new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_compare7(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, zxw334, Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_lt4(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_sr(zxw4001, zxw3001) → new_primMulInt(zxw4001, zxw3001)
new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)
new_lt4(zxw490, zxw500) → new_esEs8(new_compare7(zxw490, zxw500), LT)
new_compare7(zxw49, zxw50) → new_primCmpInt(zxw49, zxw50)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Pos(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Neg(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)
new_lt21(zxw112, zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_esEs8(new_compare7(zxw112, new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT)

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_lt4(x0, x1)
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_compare7(x0, x1)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_sr(x0, x1)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sIZE_RATIO
new_sizeFM0(EmptyFM, x0, x1)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_lt21(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

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

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

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

new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw613, h, ba)
new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba) → new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_compare7(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, zxw334, Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_lt4(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_sr(zxw4001, zxw3001) → new_primMulInt(zxw4001, zxw3001)
new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)
new_lt4(zxw490, zxw500) → new_esEs8(new_compare7(zxw490, zxw500), LT)
new_compare7(zxw49, zxw50) → new_primCmpInt(zxw49, zxw50)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Pos(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Neg(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_lt4(x0, x1)
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_compare7(x0, x1)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_sr(x0, x1)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sIZE_RATIO
new_sizeFM0(EmptyFM, x0, x1)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_lt21(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

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

new_lt21(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
                                            ↳ UsableRulesProof
                                              ↳ QDP
                                                ↳ QReductionProof
                                                  ↳ QDP
                                                    ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw613, h, ba)
new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba) → new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_compare7(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, zxw334, Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_lt4(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_sr(zxw4001, zxw3001) → new_primMulInt(zxw4001, zxw3001)
new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)
new_lt4(zxw490, zxw500) → new_esEs8(new_compare7(zxw490, zxw500), LT)
new_compare7(zxw49, zxw50) → new_primCmpInt(zxw49, zxw50)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Pos(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Neg(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_lt4(x0, x1)
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_compare7(x0, x1)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_sr(x0, x1)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sIZE_RATIO
new_sizeFM0(EmptyFM, x0, x1)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba) → new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_compare7(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba) at position [11,0] we obtained the following new rules:

new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba) → new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ 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(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw613, h, ba)
new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba) → new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, zxw334, Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_lt4(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_sr(zxw4001, zxw3001) → new_primMulInt(zxw4001, zxw3001)
new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)
new_lt4(zxw490, zxw500) → new_esEs8(new_compare7(zxw490, zxw500), LT)
new_compare7(zxw49, zxw50) → new_primCmpInt(zxw49, zxw50)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Pos(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Neg(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_lt4(x0, x1)
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_compare7(x0, x1)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_sr(x0, x1)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sIZE_RATIO
new_sizeFM0(EmptyFM, x0, x1)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_lt4(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), h, ba) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_compare7(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ 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(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw613, h, ba)
new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba) → new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_compare7(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, zxw334, Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_sr(zxw4001, zxw3001) → new_primMulInt(zxw4001, zxw3001)
new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)
new_lt4(zxw490, zxw500) → new_esEs8(new_compare7(zxw490, zxw500), LT)
new_compare7(zxw49, zxw50) → new_primCmpInt(zxw49, zxw50)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Pos(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Neg(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_lt4(x0, x1)
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_compare7(x0, x1)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_sr(x0, x1)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sIZE_RATIO
new_sizeFM0(EmptyFM, x0, x1)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

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

↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ 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
                                            ↳ 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(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw613, h, ba)
new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba) → new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_compare7(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, zxw334, Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_sr(zxw4001, zxw3001) → new_primMulInt(zxw4001, zxw3001)
new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)
new_compare7(zxw49, zxw50) → new_primCmpInt(zxw49, zxw50)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Pos(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Neg(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_lt4(x0, x1)
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_compare7(x0, x1)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_sr(x0, x1)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sIZE_RATIO
new_sizeFM0(EmptyFM, x0, x1)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

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

new_lt4(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
                                            ↳ 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(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw613, h, ba)
new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba) → new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_compare7(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, zxw334, Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_sr(zxw4001, zxw3001) → new_primMulInt(zxw4001, zxw3001)
new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)
new_compare7(zxw49, zxw50) → new_primCmpInt(zxw49, zxw50)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Pos(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Neg(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_compare7(x0, x1)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_sr(x0, x1)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sIZE_RATIO
new_sizeFM0(EmptyFM, x0, x1)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba) → new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba) at position [11,0,0] we obtained the following new rules:

new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba) → new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ 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_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba) → new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw613, h, ba)
new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_compare7(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, zxw334, Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_sr(zxw4001, zxw3001) → new_primMulInt(zxw4001, zxw3001)
new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)
new_compare7(zxw49, zxw50) → new_primCmpInt(zxw49, zxw50)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Pos(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Neg(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_compare7(x0, x1)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_sr(x0, x1)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sIZE_RATIO
new_sizeFM0(EmptyFM, x0, x1)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_compare7(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ 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(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw613, h, ba)
new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba) → new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, zxw334, Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_sr(zxw4001, zxw3001) → new_primMulInt(zxw4001, zxw3001)
new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)
new_compare7(zxw49, zxw50) → new_primCmpInt(zxw49, zxw50)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Pos(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Neg(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_compare7(x0, x1)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_sr(x0, x1)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sIZE_RATIO
new_sizeFM0(EmptyFM, x0, x1)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

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

↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ 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
                                            ↳ 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_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba) → new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw613, h, ba)
new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, zxw334, Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_sr(zxw4001, zxw3001) → new_primMulInt(zxw4001, zxw3001)
new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Pos(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Neg(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_compare7(x0, x1)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_sr(x0, x1)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sIZE_RATIO
new_sizeFM0(EmptyFM, x0, x1)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

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

new_compare7(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
                                            ↳ 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(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw613, h, ba)
new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba) → new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, zxw334, Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_sr(zxw4001, zxw3001) → new_primMulInt(zxw4001, zxw3001)
new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Pos(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Neg(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_sr(x0, x1)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sIZE_RATIO
new_sizeFM0(EmptyFM, x0, x1)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba) → new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba) at position [11,0,0,0] we obtained the following new rules:

new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba) → new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ 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(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw613, h, ba)
new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba) → new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, zxw334, Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_sr(zxw4001, zxw3001) → new_primMulInt(zxw4001, zxw3001)
new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Pos(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Neg(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_sr(x0, x1)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sIZE_RATIO
new_sizeFM0(EmptyFM, x0, x1)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba) at position [11,0,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ 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(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw613, h, ba)
new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)
new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba) → new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, zxw334, Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_sr(zxw4001, zxw3001) → new_primMulInt(zxw4001, zxw3001)
new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Pos(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Neg(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_sr(x0, x1)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sIZE_RATIO
new_sizeFM0(EmptyFM, x0, x1)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

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

↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ 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
                                            ↳ 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(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw613, h, ba)
new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)
new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba) → new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, zxw334, Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)

The TRS R consists of the following rules:

new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)
new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_primMulInt(Neg(zxw40010), Pos(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Neg(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_sr(x0, x1)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sIZE_RATIO
new_sizeFM0(EmptyFM, x0, x1)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

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

new_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
                                            ↳ 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(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw613, h, ba)
new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba) → new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, zxw334, Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)

The TRS R consists of the following rules:

new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)
new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_primMulInt(Neg(zxw40010), Pos(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Neg(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sIZE_RATIO
new_sizeFM0(EmptyFM, x0, x1)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba) at position [11,0,0,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw613, h, ba)
new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba) → new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, zxw334, Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)
new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_primMulInt(Neg(zxw40010), Pos(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Neg(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sIZE_RATIO
new_sizeFM0(EmptyFM, x0, x1)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

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

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

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

new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw613, h, ba)
new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba) → new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, zxw334, Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sIZE_RATIO
new_sizeFM0(EmptyFM, x0, x1)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

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

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

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

new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw613, h, ba)
new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba) → new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, zxw334, Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sizeFM0(EmptyFM, x0, x1)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba) → new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba) at position [11,0,0,1] we obtained the following new rules:

new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba) → new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)), new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw613, h, ba)
new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, zxw334, Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)
new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba) → new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)), new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sizeFM0(EmptyFM, x0, x1)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba) at position [11,0,0,1] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM0(Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)), new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)



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

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

new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM0(Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)), new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw613, h, ba)
new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, zxw334, Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba) → new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)), new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sizeFM0(EmptyFM, x0, x1)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba) → new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)), new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba) at position [11,0,0,1] we obtained the following new rules:

new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba) → new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw332), new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ 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
                                                                                                        ↳ 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(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba) → new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw332), new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw613, h, ba)
new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM0(Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)), new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, zxw334, Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)

The TRS R consists of the following rules:

new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sizeFM0(EmptyFM, x0, x1)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM0(Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)), new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba) at position [11,0,0,1] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw612), new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ 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
                                                                                                        ↳ 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(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw613, h, ba)
new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba) → new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw332), new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, zxw334, Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw612), new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sizeFM0(EmptyFM, x0, x1)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba) → new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw332), new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba) at position [11,0,1] we obtained the following new rules:

new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba) → new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw332), new_sizeFM0(Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)), LT), h, ba)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ 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
                                                                                                        ↳ 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(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw613, h, ba)
new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba) → new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw332), new_sizeFM0(Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, zxw334, Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw612), new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sizeFM0(EmptyFM, x0, x1)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

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

↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ 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
                                            ↳ 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
                                                                                                        ↳ 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(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw613, h, ba)
new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba) → new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw332), new_sizeFM0(Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, zxw334, Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw612), new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sizeFM0(EmptyFM, x0, x1)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

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

new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ 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
                                                                                                        ↳ 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(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw613, h, ba)
new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba) → new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw332), new_sizeFM0(Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, zxw334, Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw612), new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sizeFM0(EmptyFM, x0, x1)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba) → new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw332), new_sizeFM0(Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)), LT), h, ba) at position [11,0,1] we obtained the following new rules:

new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba) → new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw332), zxw612), LT), h, ba)



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

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

new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba) → new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw332), zxw612), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw613, h, ba)
new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, zxw334, Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw612), new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sizeFM0(EmptyFM, x0, x1)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw612), new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT), h, ba) at position [11,0,1] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw612), new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)), LT), h, ba)



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

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

new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba) → new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw332), zxw612), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw613, h, ba)
new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, zxw334, Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw612), new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sizeFM0(EmptyFM, x0, x1)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

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

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

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

new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba) → new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw332), zxw612), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw613, h, ba)
new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, zxw334, Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw612), new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sizeFM0(EmptyFM, x0, x1)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

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

new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)



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

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

new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba) → new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw332), zxw612), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw613, h, ba)
new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, zxw334, Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw612), new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sizeFM0(EmptyFM, x0, x1)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpNat1(Succ(x0), Succ(x1))
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw612), new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)), LT), h, ba) at position [11,0,1] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw612), zxw332), LT), h, ba)



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

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

new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba) → new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw332), zxw612), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw613, h, ba)
new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, zxw334, Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw612), zxw332), LT), h, ba)

The TRS R consists of the following rules:

new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sizeFM0(EmptyFM, x0, x1)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpNat1(Succ(x0), Succ(x1))
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

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

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

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

new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba) → new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw332), zxw612), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw613, h, ba)
new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, zxw334, Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw612), zxw332), LT), h, ba)

The TRS R consists of the following rules:

new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_sizeFM0(EmptyFM, x0, x1)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primCmpNat1(Succ(x0), Succ(x1))
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

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

new_sizeFM0(EmptyFM, x0, x1)
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)



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

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

new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba) → new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw332), zxw612), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw613, h, ba)
new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, zxw334, Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw612), zxw332), LT), h, ba)

The TRS R consists of the following rules:

new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpNat1(Succ(x0), Succ(x1))
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

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_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, zxw334, Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
The remaining pairs can at least be oriented weakly.

new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba) → new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw332), zxw612), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw613, h, ba)
new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw612), zxw332), LT), h, ba)
Used ordering: Polynomial interpretation [25]:

POL(Branch(x1, x2, x3, x4, x5)) = x2 + x3 + x4 + x5   
POL(EQ) = 0   
POL(False) = 0   
POL(GT) = 0   
POL(LT) = 1   
POL(Neg(x1)) = 1   
POL(Pos(x1)) = 1   
POL(Succ(x1)) = 0   
POL(True) = 1   
POL(Zero) = 0   
POL(new_esEs8(x1, x2)) = x1   
POL(new_mkVBalBranch0(x1, x2, x3, x4, x5)) = x2   
POL(new_mkVBalBranch3MkVBalBranch10(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = x10 + x12 + x9   
POL(new_mkVBalBranch3MkVBalBranch20(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = x10 + x7 + x8 + x9   
POL(new_primCmpInt(x1, x2)) = x2   
POL(new_primCmpNat0(x1, x2)) = 1   
POL(new_primCmpNat1(x1, x2)) = 1   
POL(new_primCmpNat2(x1, x2)) = 1   
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:

new_primCmpNat1(Zero, Zero) → EQ
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(EQ, LT) → False
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_esEs8(LT, LT) → True
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT



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

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

new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba) → new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw332), zxw612), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw613, h, ba)
new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch10(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw612), zxw332), LT), h, ba)

The TRS R consists of the following rules:

new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpNat1(Succ(x0), Succ(x1))
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

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

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

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

new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba) → new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw332), zxw612), LT), h, ba)
new_mkVBalBranch3MkVBalBranch20(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkVBalBranch0(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw613, h, ba)

The TRS R consists of the following rules:

new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)

The set Q consists of the following terms:

new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Zero, Zero)
new_primPlusNat1(Zero, Succ(x0))
new_esEs8(LT, LT)
new_primCmpNat0(Zero, x0)
new_primCmpNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_primCmpNat2(x0, Succ(x1))
new_primMulNat0(Succ(x0), Zero)
new_primCmpNat0(Succ(x0), x1)
new_primCmpNat1(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpNat1(Zero, Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_esEs8(EQ, EQ)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_primCmpNat1(Succ(x0), Succ(x1))
new_primCmpNat2(x0, Zero)
new_esEs8(GT, GT)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, x0)

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

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



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ 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_splitGT2(zxw300, zxw31, zxw32, zxw33, Branch(zxw340, zxw341, zxw342, zxw343, zxw344), True, h, ba) → new_splitGT3(zxw340, zxw341, zxw342, zxw343, zxw344, Nothing, h, ba)
new_splitGT11(zxw31, zxw32, zxw33, zxw34, zxw400, True, h, ba) → new_splitGT0(zxw33, zxw400, h, ba)
new_splitGT0(Branch(zxw340, zxw341, zxw342, zxw343, zxw344), zxw400, h, ba) → new_splitGT3(zxw340, zxw341, zxw342, zxw343, zxw344, Just(zxw400), h, ba)
new_splitGT(Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba) → new_splitGT3(zxw340, zxw341, zxw342, zxw343, zxw344, Nothing, h, ba)
new_splitGT3(Just(zxw300), zxw31, zxw32, zxw33, zxw34, Just(zxw400), h, ba) → new_splitGT21(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs8(new_compare26(Just(zxw400), Just(zxw300), new_esEs29(zxw400, zxw300, h), h), GT), h, ba)
new_splitGT1(zxw31, zxw32, zxw33, zxw34, True, h, ba) → new_splitGT(zxw33, h, ba)
new_splitGT3(Just(zxw300), zxw31, zxw32, zxw33, zxw34, Nothing, h, ba) → new_splitGT2(zxw300, zxw31, zxw32, zxw33, zxw34, new_esEs8(new_compare26(Nothing, Just(zxw300), False, h), GT), h, ba)
new_splitGT2(zxw300, zxw31, zxw32, zxw33, zxw34, False, h, ba) → new_splitGT10(zxw300, zxw31, zxw32, zxw33, zxw34, new_esEs8(new_compare34(zxw300, h), LT), h, ba)
new_splitGT3(Nothing, zxw31, zxw32, zxw33, zxw34, Nothing, h, ba) → new_splitGT1(zxw31, zxw32, zxw33, zxw34, new_esEs8(new_compare33(h), LT), h, ba)
new_splitGT20(zxw31, zxw32, zxw33, Branch(zxw340, zxw341, zxw342, zxw343, zxw344), zxw400, True, h, ba) → new_splitGT3(zxw340, zxw341, zxw342, zxw343, zxw344, Just(zxw400), h, ba)
new_splitGT10(zxw300, zxw31, zxw32, zxw33, zxw34, True, h, ba) → new_splitGT(zxw33, h, ba)
new_splitGT12(zxw30, zxw31, zxw32, zxw33, zxw34, zxw35, True, bb, bc) → new_splitGT0(zxw33, zxw35, bb, bc)
new_splitGT21(zxw30, zxw31, zxw32, zxw33, zxw34, zxw35, True, bb, bc) → new_splitGT0(zxw34, zxw35, bb, bc)
new_splitGT3(Nothing, zxw31, zxw32, zxw33, zxw34, Just(zxw400), h, ba) → new_splitGT20(zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs8(new_compare26(Just(zxw400), Nothing, False, h), GT), h, ba)
new_splitGT21(zxw30, zxw31, zxw32, zxw33, zxw34, zxw35, False, bb, bc) → new_splitGT12(zxw30, zxw31, zxw32, zxw33, zxw34, zxw35, new_esEs8(new_compare36(zxw35, zxw30, bb), LT), bb, bc)
new_splitGT20(zxw31, zxw32, zxw33, zxw34, zxw400, False, h, ba) → new_splitGT11(zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs8(new_compare35(zxw400, h), LT), h, ba)

The TRS R consists of the following rules:

new_esEs6(Right(zxw4000), Right(zxw3000), cdc, ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_esEs29(zxw400, zxw300, ty_Integer) → new_esEs17(zxw400, zxw300)
new_esEs28(zxw4000, zxw3000, ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_esEs7(Just(zxw4000), Just(zxw3000), app(ty_Maybe, bge)) → new_esEs7(zxw4000, zxw3000, bge)
new_ltEs19(zxw4900, zxw5000, ty_Integer) → new_ltEs16(zxw4900, zxw5000)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_@0, cbg) → new_ltEs14(zxw49000, zxw50000)
new_esEs27(zxw49000, zxw50000, app(ty_[], che)) → new_esEs16(zxw49000, zxw50000, che)
new_ltEs4(EQ, GT) → True
new_esEs22(zxw4000, zxw3000, ty_@0) → new_esEs20(zxw4000, zxw3000)
new_compare15(zxw49000, zxw50000, True, be, bf) → LT
new_esEs6(Right(zxw4000), Right(zxw3000), cdc, ty_Float) → new_esEs19(zxw4000, zxw3000)
new_ltEs9(@2(zxw49000, zxw49001), @2(zxw50000, zxw50001), bec, bed) → new_pePe(new_lt10(zxw49000, zxw50000, bec), new_asAs(new_esEs23(zxw49000, zxw50000, bec), new_ltEs18(zxw49001, zxw50001, bed)))
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Integer, cca) → new_esEs17(zxw4000, zxw3000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_esEs23(zxw49000, zxw50000, app(app(ty_@2, gc), gd)) → new_esEs4(zxw49000, zxw50000, gc, gd)
new_compare29(zxw49000, zxw50000, ty_Char) → new_compare12(zxw49000, zxw50000)
new_esEs22(zxw4000, zxw3000, ty_Float) → new_esEs19(zxw4000, zxw3000)
new_esEs6(Right(zxw4000), Right(zxw3000), cdc, ty_Int) → new_esEs13(zxw4000, zxw3000)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Bool) → new_ltEs5(zxw49000, zxw50000)
new_lt19(zxw49001, zxw50001, ty_Integer) → new_lt5(zxw49001, zxw50001)
new_compare33(h) → new_compare26(Nothing, Nothing, True, h)
new_esEs12(zxw4000, zxw3000, ty_Bool) → new_esEs9(zxw4000, zxw3000)
new_esEs27(zxw49000, zxw50000, app(ty_Maybe, chd)) → new_esEs7(zxw49000, zxw50000, chd)
new_esEs12(zxw4000, zxw3000, ty_Char) → new_esEs15(zxw4000, zxw3000)
new_esEs11(zxw4001, zxw3001, app(ty_[], dh)) → new_esEs16(zxw4001, zxw3001, dh)
new_compare12(Char(zxw49000), Char(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_ltEs19(zxw4900, zxw5000, ty_Double) → new_ltEs11(zxw4900, zxw5000)
new_compare29(zxw49000, zxw50000, ty_Double) → new_compare16(zxw49000, zxw50000)
new_ltEs20(zxw49002, zxw50002, ty_Bool) → new_ltEs5(zxw49002, zxw50002)
new_esEs23(zxw49000, zxw50000, ty_Float) → new_esEs19(zxw49000, zxw50000)
new_lt19(zxw49001, zxw50001, ty_Ordering) → new_lt14(zxw49001, zxw50001)
new_lt19(zxw49001, zxw50001, ty_Int) → new_lt4(zxw49001, zxw50001)
new_esEs7(Just(zxw4000), Just(zxw3000), app(app(ty_Either, bhc), bhd)) → new_esEs6(zxw4000, zxw3000, bhc, bhd)
new_primMulNat0(Zero, Zero) → Zero
new_ltEs7(Left(zxw49000), Right(zxw50000), cbf, cbg) → True
new_compare26(Just(zxw4900), Nothing, False, bcg) → GT
new_esEs26(zxw49001, zxw50001, app(ty_[], cgc)) → new_esEs16(zxw49001, zxw50001, cgc)
new_esEs27(zxw49000, zxw50000, ty_Bool) → new_esEs9(zxw49000, zxw50000)
new_ltEs18(zxw49001, zxw50001, ty_Integer) → new_ltEs16(zxw49001, zxw50001)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_ltEs18(zxw49001, zxw50001, app(ty_[], beh)) → new_ltEs13(zxw49001, zxw50001, beh)
new_ltEs20(zxw49002, zxw50002, app(ty_Maybe, ceh)) → new_ltEs8(zxw49002, zxw50002, ceh)
new_esEs11(zxw4001, zxw3001, ty_Char) → new_esEs15(zxw4001, zxw3001)
new_esEs11(zxw4001, zxw3001, ty_Float) → new_esEs19(zxw4001, zxw3001)
new_esEs29(zxw400, zxw300, ty_@0) → new_esEs20(zxw400, zxw300)
new_lt8(zxw49000, zxw50000) → new_esEs8(new_compare16(zxw49000, zxw50000), LT)
new_esEs26(zxw49001, zxw50001, ty_Char) → new_esEs15(zxw49001, zxw50001)
new_lt20(zxw49000, zxw50000, app(app(ty_@2, chb), chc)) → new_lt11(zxw49000, zxw50000, chb, chc)
new_esEs29(zxw400, zxw300, app(ty_Maybe, bgd)) → new_esEs7(zxw400, zxw300, bgd)
new_esEs23(zxw49000, zxw50000, ty_Char) → new_esEs15(zxw49000, zxw50000)
new_esEs23(zxw49000, zxw50000, ty_Bool) → new_esEs9(zxw49000, zxw50000)
new_esEs27(zxw49000, zxw50000, ty_Char) → new_esEs15(zxw49000, zxw50000)
new_compare26(Nothing, Just(zxw5000), False, bcg) → LT
new_lt10(zxw49000, zxw50000, ty_Float) → new_lt7(zxw49000, zxw50000)
new_esEs21(zxw4001, zxw3001, ty_Double) → new_esEs18(zxw4001, zxw3001)
new_ltEs19(zxw4900, zxw5000, ty_Int) → new_ltEs10(zxw4900, zxw5000)
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_lt9(zxw49000, zxw50000, bg) → new_esEs8(new_compare0(zxw49000, zxw50000, bg), LT)
new_compare210(zxw49000, zxw50000, False, bfh, bga, bgb) → new_compare110(zxw49000, zxw50000, new_ltEs15(zxw49000, zxw50000, bfh, bga, bgb), bfh, bga, bgb)
new_esEs22(zxw4000, zxw3000, app(ty_Ratio, bbf)) → new_esEs14(zxw4000, zxw3000, bbf)
new_esEs21(zxw4001, zxw3001, app(ty_Ratio, bad)) → new_esEs14(zxw4001, zxw3001, bad)
new_esEs30(zxw20, zxw15, ty_Bool) → new_esEs9(zxw20, zxw15)
new_esEs7(Just(zxw4000), Just(zxw3000), app(app(ty_@2, bhe), bhf)) → new_esEs4(zxw4000, zxw3000, bhe, bhf)
new_esEs25(zxw4000, zxw3000, ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Bool) → new_esEs9(zxw4000, zxw3000)
new_esEs30(zxw20, zxw15, ty_Float) → new_esEs19(zxw20, zxw15)
new_ltEs20(zxw49002, zxw50002, ty_Integer) → new_ltEs16(zxw49002, zxw50002)
new_esEs21(zxw4001, zxw3001, app(app(ty_Either, bba), bbb)) → new_esEs6(zxw4001, zxw3001, bba, bbb)
new_ltEs7(Left(zxw49000), Left(zxw50000), app(app(app(ty_@3, dba), dbb), dbc), cbg) → new_ltEs15(zxw49000, zxw50000, dba, dbb, dbc)
new_esEs29(zxw400, zxw300, ty_Bool) → new_esEs9(zxw400, zxw300)
new_ltEs14(zxw4900, zxw5000) → new_fsEs(new_compare31(zxw4900, zxw5000))
new_compare24(zxw49000, zxw50000, False) → new_compare13(zxw49000, zxw50000, new_ltEs5(zxw49000, zxw50000))
new_esEs7(Just(zxw4000), Just(zxw3000), app(ty_Ratio, bgf)) → new_esEs14(zxw4000, zxw3000, bgf)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbf, app(app(ty_@2, dbg), dbh)) → new_ltEs9(zxw49000, zxw50000, dbg, dbh)
new_lt4(zxw490, zxw500) → new_esEs8(new_compare7(zxw490, zxw500), LT)
new_esEs28(zxw4000, zxw3000, app(app(app(ty_@3, ddd), dde), ddf)) → new_esEs5(zxw4000, zxw3000, ddd, dde, ddf)
new_esEs28(zxw4000, zxw3000, ty_Bool) → new_esEs9(zxw4000, zxw3000)
new_compare19(zxw490, zxw500, bcg) → new_compare26(zxw490, zxw500, new_esEs7(zxw490, zxw500, bcg), bcg)
new_esEs17(Integer(zxw4000), Integer(zxw3000)) → new_primEqInt(zxw4000, zxw3000)
new_pePe(False, zxw213) → zxw213
new_lt12(zxw490, zxw500, bcg) → new_esEs8(new_compare19(zxw490, zxw500, bcg), LT)
new_esEs20(@0, @0) → True
new_esEs6(Right(zxw4000), Right(zxw3000), cdc, app(ty_Ratio, cde)) → new_esEs14(zxw4000, zxw3000, cde)
new_esEs6(Left(zxw4000), Left(zxw3000), app(app(ty_@2, cda), cdb), cca) → new_esEs4(zxw4000, zxw3000, cda, cdb)
new_compare23(zxw49000, zxw50000, True) → EQ
new_esEs11(zxw4001, zxw3001, ty_Int) → new_esEs13(zxw4001, zxw3001)
new_lt19(zxw49001, zxw50001, app(ty_[], cgc)) → new_lt9(zxw49001, zxw50001, cgc)
new_compare29(zxw49000, zxw50000, ty_@0) → new_compare31(zxw49000, zxw50000)
new_compare26(Nothing, Nothing, False, bcg) → LT
new_esEs10(zxw4002, zxw3002, app(ty_Maybe, cc)) → new_esEs7(zxw4002, zxw3002, cc)
new_ltEs16(zxw4900, zxw5000) → new_fsEs(new_compare9(zxw4900, zxw5000))
new_esEs22(zxw4000, zxw3000, app(app(ty_@2, bce), bcf)) → new_esEs4(zxw4000, zxw3000, bce, bcf)
new_esEs23(zxw49000, zxw50000, app(ty_Maybe, bfg)) → new_esEs7(zxw49000, zxw50000, bfg)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbf, app(ty_Ratio, dch)) → new_ltEs17(zxw49000, zxw50000, dch)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Char, cbg) → new_ltEs12(zxw49000, zxw50000)
new_esEs28(zxw4000, zxw3000, ty_@0) → new_esEs20(zxw4000, zxw3000)
new_esEs10(zxw4002, zxw3002, app(app(app(ty_@3, cf), cg), da)) → new_esEs5(zxw4002, zxw3002, cf, cg, da)
new_ltEs20(zxw49002, zxw50002, app(ty_[], cfa)) → new_ltEs13(zxw49002, zxw50002, cfa)
new_esEs27(zxw49000, zxw50000, ty_Float) → new_esEs19(zxw49000, zxw50000)
new_ltEs20(zxw49002, zxw50002, app(app(app(ty_@3, cfb), cfc), cfd)) → new_ltEs15(zxw49002, zxw50002, cfb, cfc, cfd)
new_esEs22(zxw4000, zxw3000, ty_Ordering) → new_esEs8(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Bool) → new_esEs9(zxw4000, zxw3000)
new_compare6(zxw49000, zxw50000) → new_compare23(zxw49000, zxw50000, new_esEs8(zxw49000, zxw50000))
new_esEs29(zxw400, zxw300, app(app(ty_@2, baa), bab)) → new_esEs4(zxw400, zxw300, baa, bab)
new_esEs12(zxw4000, zxw3000, app(ty_[], fb)) → new_esEs16(zxw4000, zxw3000, fb)
new_compare32(zxw49000, zxw50000, be, bf) → new_compare25(zxw49000, zxw50000, new_esEs6(zxw49000, zxw50000, be, bf), be, bf)
new_compare29(zxw49000, zxw50000, ty_Int) → new_compare7(zxw49000, zxw50000)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Bool, cca) → new_esEs9(zxw4000, zxw3000)
new_ltEs8(Nothing, Just(zxw50000), ge) → True
new_ltEs7(Left(zxw49000), Left(zxw50000), app(app(ty_@2, dae), daf), cbg) → new_ltEs9(zxw49000, zxw50000, dae, daf)
new_esEs6(Right(zxw4000), Left(zxw3000), cdc, cca) → False
new_esEs6(Left(zxw4000), Right(zxw3000), cdc, cca) → False
new_esEs8(LT, LT) → True
new_lt20(zxw49000, zxw50000, ty_@0) → new_lt15(zxw49000, zxw50000)
new_esEs10(zxw4002, zxw3002, ty_Integer) → new_esEs17(zxw4002, zxw3002)
new_esEs28(zxw4000, zxw3000, ty_Float) → new_esEs19(zxw4000, zxw3000)
new_compare29(zxw49000, zxw50000, app(app(app(ty_@3, cad), cae), caf)) → new_compare28(zxw49000, zxw50000, cad, cae, caf)
new_lt19(zxw49001, zxw50001, ty_@0) → new_lt15(zxw49001, zxw50001)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbf, ty_Bool) → new_ltEs5(zxw49000, zxw50000)
new_ltEs5(True, False) → False
new_lt19(zxw49001, zxw50001, app(app(ty_@2, cfh), cga)) → new_lt11(zxw49001, zxw50001, cfh, cga)
new_compare0([], [], bhg) → EQ
new_pePe(True, zxw213) → True
new_primEqNat0(Zero, Zero) → True
new_compare34(zxw300, h) → new_compare26(Nothing, Just(zxw300), False, h)
new_esEs14(:%(zxw4000, zxw4001), :%(zxw3000, zxw3001), cbb) → new_asAs(new_esEs25(zxw4000, zxw3000, cbb), new_esEs24(zxw4001, zxw3001, cbb))
new_lt10(zxw49000, zxw50000, ty_Double) → new_lt8(zxw49000, zxw50000)
new_ltEs20(zxw49002, zxw50002, ty_Ordering) → new_ltEs4(zxw49002, zxw50002)
new_compare27(zxw49000, zxw50000, False, gc, gd) → new_compare17(zxw49000, zxw50000, new_ltEs9(zxw49000, zxw50000, gc, gd), gc, gd)
new_compare11(zxw180, zxw181, True, bd) → LT
new_esEs23(zxw49000, zxw50000, app(app(ty_Either, be), bf)) → new_esEs6(zxw49000, zxw50000, be, bf)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_@0, cca) → new_esEs20(zxw4000, zxw3000)
new_esEs6(Right(zxw4000), Right(zxw3000), cdc, ty_Bool) → new_esEs9(zxw4000, zxw3000)
new_esEs12(zxw4000, zxw3000, ty_Int) → new_esEs13(zxw4000, zxw3000)
new_lt20(zxw49000, zxw50000, app(ty_[], che)) → new_lt9(zxw49000, zxw50000, che)
new_esEs6(Right(zxw4000), Right(zxw3000), cdc, app(app(ty_Either, ceb), cec)) → new_esEs6(zxw4000, zxw3000, ceb, cec)
new_compare26(Just(zxw4900), Just(zxw5000), False, bcg) → new_compare11(zxw4900, zxw5000, new_ltEs19(zxw4900, zxw5000, bcg), bcg)
new_ltEs5(True, True) → True
new_ltEs7(Left(zxw49000), Left(zxw50000), app(ty_Maybe, dag), cbg) → new_ltEs8(zxw49000, zxw50000, dag)
new_esEs29(zxw400, zxw300, ty_Int) → new_esEs13(zxw400, zxw300)
new_compare36(zxw20, zxw15, bch) → new_compare26(Just(zxw20), Just(zxw15), new_esEs30(zxw20, zxw15, bch), bch)
new_ltEs20(zxw49002, zxw50002, app(app(ty_@2, cef), ceg)) → new_ltEs9(zxw49002, zxw50002, cef, ceg)
new_esEs15(Char(zxw4000), Char(zxw3000)) → new_primEqNat0(zxw4000, zxw3000)
new_sr(zxw4001, zxw3001) → new_primMulInt(zxw4001, zxw3001)
new_ltEs18(zxw49001, zxw50001, ty_Int) → new_ltEs10(zxw49001, zxw50001)
new_esEs25(zxw4000, zxw3000, ty_Int) → new_esEs13(zxw4000, zxw3000)
new_compare7(zxw49, zxw50) → new_primCmpInt(zxw49, zxw50)
new_primCmpNat1(Zero, Zero) → EQ
new_esEs7(Just(zxw4000), Just(zxw3000), app(ty_[], bgg)) → new_esEs16(zxw4000, zxw3000, bgg)
new_lt10(zxw49000, zxw50000, ty_Int) → new_lt4(zxw49000, zxw50000)
new_esEs28(zxw4000, zxw3000, app(app(ty_Either, ddg), ddh)) → new_esEs6(zxw4000, zxw3000, ddg, ddh)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbf, app(ty_Maybe, dca)) → new_ltEs8(zxw49000, zxw50000, dca)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbf, ty_Integer) → new_ltEs16(zxw49000, zxw50000)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbf, app(app(app(ty_@3, dcc), dcd), dce)) → new_ltEs15(zxw49000, zxw50000, dcc, dcd, dce)
new_esEs26(zxw49001, zxw50001, ty_Ordering) → new_esEs8(zxw49001, zxw50001)
new_esEs8(GT, GT) → True
new_esEs27(zxw49000, zxw50000, ty_@0) → new_esEs20(zxw49000, zxw50000)
new_esEs13(zxw400, zxw300) → new_primEqInt(zxw400, zxw300)
new_lt13(zxw49000, zxw50000) → new_esEs8(new_compare18(zxw49000, zxw50000), LT)
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_lt20(zxw49000, zxw50000, ty_Ordering) → new_lt14(zxw49000, zxw50000)
new_esEs11(zxw4001, zxw3001, ty_Ordering) → new_esEs8(zxw4001, zxw3001)
new_esEs11(zxw4001, zxw3001, app(app(ty_@2, ef), eg)) → new_esEs4(zxw4001, zxw3001, ef, eg)
new_lt10(zxw49000, zxw50000, app(app(ty_@2, gc), gd)) → new_lt11(zxw49000, zxw50000, gc, gd)
new_compare23(zxw49000, zxw50000, False) → new_compare10(zxw49000, zxw50000, new_ltEs4(zxw49000, zxw50000))
new_esEs8(LT, GT) → False
new_esEs8(GT, LT) → False
new_ltEs19(zxw4900, zxw5000, app(app(app(ty_@3, cbc), cbd), cbe)) → new_ltEs15(zxw4900, zxw5000, cbc, cbd, cbe)
new_lt20(zxw49000, zxw50000, app(app(ty_Either, daa), dab)) → new_lt17(zxw49000, zxw50000, daa, dab)
new_esEs26(zxw49001, zxw50001, ty_Bool) → new_esEs9(zxw49001, zxw50001)
new_ltEs11(zxw4900, zxw5000) → new_fsEs(new_compare16(zxw4900, zxw5000))
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_compare17(zxw49000, zxw50000, True, gc, gd) → LT
new_primEqInt(Neg(Succ(zxw40000)), Neg(Succ(zxw30000))) → new_primEqNat0(zxw40000, zxw30000)
new_ltEs5(False, False) → True
new_esEs23(zxw49000, zxw50000, ty_Ordering) → new_esEs8(zxw49000, zxw50000)
new_ltEs18(zxw49001, zxw50001, app(app(ty_Either, bfd), bfe)) → new_ltEs7(zxw49001, zxw50001, bfd, bfe)
new_esEs28(zxw4000, zxw3000, ty_Char) → new_esEs15(zxw4000, zxw3000)
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)
new_ltEs19(zxw4900, zxw5000, app(ty_Ratio, hh)) → new_ltEs17(zxw4900, zxw5000, hh)
new_esEs10(zxw4002, zxw3002, ty_Bool) → new_esEs9(zxw4002, zxw3002)
new_lt20(zxw49000, zxw50000, ty_Char) → new_lt6(zxw49000, zxw50000)
new_compare13(zxw49000, zxw50000, False) → GT
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Bool, cbg) → new_ltEs5(zxw49000, zxw50000)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Int, cbg) → new_ltEs10(zxw49000, zxw50000)
new_lt11(zxw49000, zxw50000, gc, gd) → new_esEs8(new_compare30(zxw49000, zxw50000, gc, gd), LT)
new_esEs21(zxw4001, zxw3001, ty_Char) → new_esEs15(zxw4001, zxw3001)
new_lt20(zxw49000, zxw50000, ty_Int) → new_lt4(zxw49000, zxw50000)
new_primCompAux1(zxw49000, zxw50000, zxw214, bhg) → new_primCompAux0(zxw214, new_compare29(zxw49000, zxw50000, bhg))
new_esEs7(Just(zxw4000), Just(zxw3000), ty_@0) → new_esEs20(zxw4000, zxw3000)
new_lt16(zxw49000, zxw50000, bfh, bga, bgb) → new_esEs8(new_compare28(zxw49000, zxw50000, bfh, bga, bgb), LT)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_ltEs7(Right(zxw49000), Left(zxw50000), cbf, cbg) → False
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Ordering) → new_esEs8(zxw4000, zxw3000)
new_ltEs7(Left(zxw49000), Left(zxw50000), app(ty_[], dah), cbg) → new_ltEs13(zxw49000, zxw50000, dah)
new_ltEs19(zxw4900, zxw5000, ty_Ordering) → new_ltEs4(zxw4900, zxw5000)
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_ltEs20(zxw49002, zxw50002, ty_Char) → new_ltEs12(zxw49002, zxw50002)
new_esEs11(zxw4001, zxw3001, app(app(app(ty_@3, ea), eb), ec)) → new_esEs5(zxw4001, zxw3001, ea, eb, ec)
new_ltEs20(zxw49002, zxw50002, app(ty_Ratio, cfg)) → new_ltEs17(zxw49002, zxw50002, cfg)
new_ltEs18(zxw49001, zxw50001, ty_@0) → new_ltEs14(zxw49001, zxw50001)
new_primEqInt(Neg(Succ(zxw40000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(zxw30000))) → False
new_ltEs19(zxw4900, zxw5000, ty_Char) → new_ltEs12(zxw4900, zxw5000)
new_esEs12(zxw4000, zxw3000, ty_Double) → new_esEs18(zxw4000, zxw3000)
new_primCompAux0(zxw218, GT) → GT
new_esEs8(EQ, EQ) → True
new_esEs6(Left(zxw4000), Left(zxw3000), app(ty_Ratio, ccb), cca) → new_esEs14(zxw4000, zxw3000, ccb)
new_ltEs8(Just(zxw49000), Just(zxw50000), app(app(ty_Either, he), hf)) → new_ltEs7(zxw49000, zxw50000, he, hf)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Integer, cbg) → new_ltEs16(zxw49000, zxw50000)
new_esEs6(Right(zxw4000), Right(zxw3000), cdc, app(ty_[], cdf)) → new_esEs16(zxw4000, zxw3000, cdf)
new_esEs23(zxw49000, zxw50000, ty_Integer) → new_esEs17(zxw49000, zxw50000)
new_esEs29(zxw400, zxw300, app(ty_[], dad)) → new_esEs16(zxw400, zxw300, dad)
new_esEs28(zxw4000, zxw3000, ty_Int) → new_esEs13(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, app(app(app(ty_@3, bbh), bca), bcb)) → new_esEs5(zxw4000, zxw3000, bbh, bca, bcb)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_ltEs18(zxw49001, zxw50001, ty_Ordering) → new_ltEs4(zxw49001, zxw50001)
new_ltEs4(EQ, LT) → False
new_esEs12(zxw4000, zxw3000, app(ty_Maybe, eh)) → new_esEs7(zxw4000, zxw3000, eh)
new_lt20(zxw49000, zxw50000, ty_Double) → new_lt8(zxw49000, zxw50000)
new_esEs10(zxw4002, zxw3002, ty_Float) → new_esEs19(zxw4002, zxw3002)
new_esEs11(zxw4001, zxw3001, ty_Bool) → new_esEs9(zxw4001, zxw3001)
new_compare11(zxw180, zxw181, False, bd) → GT
new_esEs26(zxw49001, zxw50001, ty_Integer) → new_esEs17(zxw49001, zxw50001)
new_lt10(zxw49000, zxw50000, ty_Ordering) → new_lt14(zxw49000, zxw50000)
new_ltEs18(zxw49001, zxw50001, ty_Bool) → new_ltEs5(zxw49001, zxw50001)
new_esEs12(zxw4000, zxw3000, app(app(app(ty_@3, fc), fd), ff)) → new_esEs5(zxw4000, zxw3000, fc, fd, ff)
new_primEqInt(Pos(Succ(zxw40000)), Pos(Succ(zxw30000))) → new_primEqNat0(zxw40000, zxw30000)
new_compare27(zxw49000, zxw50000, True, gc, gd) → EQ
new_esEs6(Left(zxw4000), Left(zxw3000), app(app(app(ty_@3, ccd), cce), ccf), cca) → new_esEs5(zxw4000, zxw3000, ccd, cce, ccf)
new_lt18(zxw49000, zxw50000, bgc) → new_esEs8(new_compare8(zxw49000, zxw50000, bgc), LT)
new_ltEs18(zxw49001, zxw50001, app(app(app(ty_@3, bfa), bfb), bfc)) → new_ltEs15(zxw49001, zxw50001, bfa, bfb, bfc)
new_lt10(zxw49000, zxw50000, app(ty_Maybe, bfg)) → new_lt12(zxw49000, zxw50000, bfg)
new_esEs26(zxw49001, zxw50001, ty_Int) → new_esEs13(zxw49001, zxw50001)
new_ltEs8(Just(zxw49000), Just(zxw50000), app(app(ty_@2, gf), gg)) → new_ltEs9(zxw49000, zxw50000, gf, gg)
new_primEqNat0(Succ(zxw40000), Succ(zxw30000)) → new_primEqNat0(zxw40000, zxw30000)
new_compare29(zxw49000, zxw50000, app(ty_[], cac)) → new_compare0(zxw49000, zxw50000, cac)
new_esEs27(zxw49000, zxw50000, ty_Ordering) → new_esEs8(zxw49000, zxw50000)
new_esEs27(zxw49000, zxw50000, ty_Integer) → new_esEs17(zxw49000, zxw50000)
new_esEs23(zxw49000, zxw50000, app(ty_Ratio, bgc)) → new_esEs14(zxw49000, zxw50000, bgc)
new_ltEs18(zxw49001, zxw50001, ty_Float) → new_ltEs6(zxw49001, zxw50001)
new_esEs22(zxw4000, zxw3000, ty_Int) → new_esEs13(zxw4000, zxw3000)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbf, app(ty_[], dcb)) → new_ltEs13(zxw49000, zxw50000, dcb)
new_ltEs4(GT, EQ) → False
new_lt7(zxw49000, zxw50000) → new_esEs8(new_compare14(zxw49000, zxw50000), LT)
new_lt10(zxw49000, zxw50000, app(app(app(ty_@3, bfh), bga), bgb)) → new_lt16(zxw49000, zxw50000, bfh, bga, bgb)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Int) → new_esEs13(zxw4000, zxw3000)
new_ltEs19(zxw4900, zxw5000, app(app(ty_Either, cbf), cbg)) → new_ltEs7(zxw4900, zxw5000, cbf, cbg)
new_ltEs8(Just(zxw49000), Nothing, ge) → False
new_esEs21(zxw4001, zxw3001, ty_Float) → new_esEs19(zxw4001, zxw3001)
new_esEs26(zxw49001, zxw50001, app(app(ty_@2, cfh), cga)) → new_esEs4(zxw49001, zxw50001, cfh, cga)
new_esEs27(zxw49000, zxw50000, app(app(app(ty_@3, chf), chg), chh)) → new_esEs5(zxw49000, zxw50000, chf, chg, chh)
new_ltEs13(zxw4900, zxw5000, bhg) → new_fsEs(new_compare0(zxw4900, zxw5000, bhg))
new_esEs22(zxw4000, zxw3000, ty_Char) → new_esEs15(zxw4000, zxw3000)
new_esEs30(zxw20, zxw15, app(ty_Ratio, bdb)) → new_esEs14(zxw20, zxw15, bdb)
new_ltEs18(zxw49001, zxw50001, ty_Double) → new_ltEs11(zxw49001, zxw50001)
new_esEs7(Nothing, Nothing, bgd) → True
new_esEs28(zxw4000, zxw3000, ty_Ordering) → new_esEs8(zxw4000, zxw3000)
new_lt10(zxw49000, zxw50000, app(app(ty_Either, be), bf)) → new_lt17(zxw49000, zxw50000, be, bf)
new_esEs8(EQ, LT) → False
new_esEs8(LT, EQ) → False
new_esEs10(zxw4002, zxw3002, ty_Char) → new_esEs15(zxw4002, zxw3002)
new_primEqInt(Pos(Succ(zxw40000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(zxw30000))) → False
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Double, cbg) → new_ltEs11(zxw49000, zxw50000)
new_ltEs4(EQ, EQ) → True
new_esEs6(Right(zxw4000), Right(zxw3000), cdc, app(ty_Maybe, cdd)) → new_esEs7(zxw4000, zxw3000, cdd)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbf, ty_Ordering) → new_ltEs4(zxw49000, zxw50000)
new_esEs29(zxw400, zxw300, ty_Double) → new_esEs18(zxw400, zxw300)
new_esEs30(zxw20, zxw15, ty_@0) → new_esEs20(zxw20, zxw15)
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_ltEs20(zxw49002, zxw50002, ty_@0) → new_ltEs14(zxw49002, zxw50002)
new_esEs23(zxw49000, zxw50000, ty_@0) → new_esEs20(zxw49000, zxw50000)
new_esEs6(Right(zxw4000), Right(zxw3000), cdc, ty_@0) → new_esEs20(zxw4000, zxw3000)
new_compare210(zxw49000, zxw50000, True, bfh, bga, bgb) → EQ
new_ltEs4(GT, LT) → False
new_sr0(Integer(zxw500000), Integer(zxw490010)) → Integer(new_primMulInt(zxw500000, zxw490010))
new_compare13(zxw49000, zxw50000, True) → LT
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_compare14(Float(zxw49000, zxw49001), Float(zxw50000, zxw50001)) → new_compare7(new_sr(zxw49000, zxw50000), new_sr(zxw49001, zxw50001))
new_primEqInt(Pos(Succ(zxw40000)), Neg(zxw3000)) → False
new_primEqInt(Neg(Succ(zxw40000)), Pos(zxw3000)) → False
new_esEs7(Just(zxw4000), Nothing, bgd) → False
new_esEs7(Nothing, Just(zxw3000), bgd) → False
new_esEs18(Double(zxw4000, zxw4001), Double(zxw3000, zxw3001)) → new_esEs13(new_sr(zxw4000, zxw3000), new_sr(zxw4001, zxw3001))
new_ltEs5(False, True) → True
new_esEs26(zxw49001, zxw50001, ty_Double) → new_esEs18(zxw49001, zxw50001)
new_compare28(zxw49000, zxw50000, bfh, bga, bgb) → new_compare210(zxw49000, zxw50000, new_esEs5(zxw49000, zxw50000, bfh, bga, bgb), bfh, bga, bgb)
new_esEs11(zxw4001, zxw3001, ty_Double) → new_esEs18(zxw4001, zxw3001)
new_ltEs6(zxw4900, zxw5000) → new_fsEs(new_compare14(zxw4900, zxw5000))
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Ordering, cbg) → new_ltEs4(zxw49000, zxw50000)
new_primEqInt(Pos(Zero), Neg(Succ(zxw30000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(zxw30000))) → False
new_ltEs19(zxw4900, zxw5000, app(app(ty_@2, bec), bed)) → new_ltEs9(zxw4900, zxw5000, bec, bed)
new_ltEs20(zxw49002, zxw50002, ty_Float) → new_ltEs6(zxw49002, zxw50002)
new_compare29(zxw49000, zxw50000, app(app(ty_@2, bhh), caa)) → new_compare30(zxw49000, zxw50000, bhh, caa)
new_compare24(zxw49000, zxw50000, True) → EQ
new_esEs27(zxw49000, zxw50000, ty_Int) → new_esEs13(zxw49000, zxw50000)
new_ltEs18(zxw49001, zxw50001, app(app(ty_@2, bee), bef)) → new_ltEs9(zxw49001, zxw50001, bee, bef)
new_esEs6(Right(zxw4000), Right(zxw3000), cdc, ty_Double) → new_esEs18(zxw4000, zxw3000)
new_lt20(zxw49000, zxw50000, ty_Bool) → new_lt13(zxw49000, zxw50000)
new_primCmpNat0(Zero, zxw4900) → LT
new_ltEs7(Right(zxw49000), Right(zxw50000), cbf, ty_Char) → new_ltEs12(zxw49000, zxw50000)
new_esEs8(EQ, GT) → False
new_esEs8(GT, EQ) → False
new_esEs10(zxw4002, zxw3002, app(ty_[], ce)) → new_esEs16(zxw4002, zxw3002, ce)
new_lt15(zxw49000, zxw50000) → new_esEs8(new_compare31(zxw49000, zxw50000), LT)
new_compare17(zxw49000, zxw50000, False, gc, gd) → GT
new_compare29(zxw49000, zxw50000, ty_Float) → new_compare14(zxw49000, zxw50000)
new_esEs30(zxw20, zxw15, ty_Double) → new_esEs18(zxw20, zxw15)
new_esEs28(zxw4000, zxw3000, app(ty_Ratio, ddb)) → new_esEs14(zxw4000, zxw3000, ddb)
new_compare26(zxw490, zxw500, True, bcg) → EQ
new_primCompAux0(zxw218, LT) → LT
new_esEs11(zxw4001, zxw3001, ty_@0) → new_esEs20(zxw4001, zxw3001)
new_esEs30(zxw20, zxw15, app(app(ty_Either, bdg), bdh)) → new_esEs6(zxw20, zxw15, bdg, bdh)
new_esEs12(zxw4000, zxw3000, ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_not(False) → True
new_esEs6(Left(zxw4000), Left(zxw3000), app(app(ty_Either, ccg), cch), cca) → new_esEs6(zxw4000, zxw3000, ccg, cch)
new_esEs28(zxw4000, zxw3000, app(ty_[], ddc)) → new_esEs16(zxw4000, zxw3000, ddc)
new_esEs24(zxw4001, zxw3001, ty_Int) → new_esEs13(zxw4001, zxw3001)
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_esEs26(zxw49001, zxw50001, app(ty_Ratio, cha)) → new_esEs14(zxw49001, zxw50001, cha)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Double) → new_ltEs11(zxw49000, zxw50000)
new_esEs11(zxw4001, zxw3001, app(app(ty_Either, ed), ee)) → new_esEs6(zxw4001, zxw3001, ed, ee)
new_esEs21(zxw4001, zxw3001, ty_@0) → new_esEs20(zxw4001, zxw3001)
new_lt19(zxw49001, zxw50001, ty_Float) → new_lt7(zxw49001, zxw50001)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbf, ty_Int) → new_ltEs10(zxw49000, zxw50000)
new_compare0(:(zxw49000, zxw49001), [], bhg) → GT
new_esEs12(zxw4000, zxw3000, ty_Float) → new_esEs19(zxw4000, zxw3000)
new_ltEs8(Just(zxw49000), Just(zxw50000), app(ty_[], ha)) → new_ltEs13(zxw49000, zxw50000, ha)
new_lt14(zxw49000, zxw50000) → new_esEs8(new_compare6(zxw49000, zxw50000), LT)
new_ltEs19(zxw4900, zxw5000, ty_Float) → new_ltEs6(zxw4900, zxw5000)
new_esEs27(zxw49000, zxw50000, app(app(ty_Either, daa), dab)) → new_esEs6(zxw49000, zxw50000, daa, dab)
new_lt19(zxw49001, zxw50001, app(ty_Ratio, cha)) → new_lt18(zxw49001, zxw50001, cha)
new_esEs9(True, True) → True
new_lt19(zxw49001, zxw50001, app(app(app(ty_@3, cgd), cge), cgf)) → new_lt16(zxw49001, zxw50001, cgd, cge, cgf)
new_lt19(zxw49001, zxw50001, ty_Char) → new_lt6(zxw49001, zxw50001)
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Double, cca) → new_esEs18(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, app(ty_Maybe, dda)) → new_esEs7(zxw4000, zxw3000, dda)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_esEs21(zxw4001, zxw3001, app(app(app(ty_@3, baf), bag), bah)) → new_esEs5(zxw4001, zxw3001, baf, bag, bah)
new_esEs22(zxw4000, zxw3000, app(ty_[], bbg)) → new_esEs16(zxw4000, zxw3000, bbg)
new_esEs21(zxw4001, zxw3001, app(ty_Maybe, bac)) → new_esEs7(zxw4001, zxw3001, bac)
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_esEs22(zxw4000, zxw3000, ty_Double) → new_esEs18(zxw4000, zxw3000)
new_esEs21(zxw4001, zxw3001, app(app(ty_@2, bbc), bbd)) → new_esEs4(zxw4001, zxw3001, bbc, bbd)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_@0) → new_ltEs14(zxw49000, zxw50000)
new_esEs19(Float(zxw4000, zxw4001), Float(zxw3000, zxw3001)) → new_esEs13(new_sr(zxw4000, zxw3000), new_sr(zxw4001, zxw3001))
new_ltEs19(zxw4900, zxw5000, app(ty_Maybe, ge)) → new_ltEs8(zxw4900, zxw5000, ge)
new_primMulInt(Neg(zxw40010), Neg(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_esEs29(zxw400, zxw300, ty_Char) → new_esEs15(zxw400, zxw300)
new_esEs30(zxw20, zxw15, app(ty_Maybe, bda)) → new_esEs7(zxw20, zxw15, bda)
new_primEqNat0(Zero, Succ(zxw30000)) → False
new_primEqNat0(Succ(zxw40000), Zero) → False
new_compare25(zxw49000, zxw50000, True, be, bf) → EQ
new_ltEs7(Left(zxw49000), Left(zxw50000), app(app(ty_Either, dbd), dbe), cbg) → new_ltEs7(zxw49000, zxw50000, dbd, dbe)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_lt10(zxw49000, zxw50000, app(ty_Ratio, bgc)) → new_lt18(zxw49000, zxw50000, bgc)
new_esEs12(zxw4000, zxw3000, ty_@0) → new_esEs20(zxw4000, zxw3000)
new_esEs21(zxw4001, zxw3001, ty_Bool) → new_esEs9(zxw4001, zxw3001)
new_esEs5(@3(zxw4000, zxw4001, zxw4002), @3(zxw3000, zxw3001, zxw3002), bh, ca, cb) → new_asAs(new_esEs12(zxw4000, zxw3000, bh), new_asAs(new_esEs11(zxw4001, zxw3001, ca), new_esEs10(zxw4002, zxw3002, cb)))
new_esEs16(:(zxw4000, zxw4001), [], dad) → False
new_esEs16([], :(zxw3000, zxw3001), dad) → False
new_lt10(zxw49000, zxw50000, ty_Integer) → new_lt5(zxw49000, zxw50000)
new_lt6(zxw49000, zxw50000) → new_esEs8(new_compare12(zxw49000, zxw50000), LT)
new_esEs29(zxw400, zxw300, app(app(ty_Either, cdc), cca)) → new_esEs6(zxw400, zxw300, cdc, cca)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_ltEs4(LT, GT) → True
new_esEs23(zxw49000, zxw50000, ty_Double) → new_esEs18(zxw49000, zxw50000)
new_compare25(zxw49000, zxw50000, False, be, bf) → new_compare15(zxw49000, zxw50000, new_ltEs7(zxw49000, zxw50000, be, bf), be, bf)
new_esEs29(zxw400, zxw300, app(app(app(ty_@3, bh), ca), cb)) → new_esEs5(zxw400, zxw300, bh, ca, cb)
new_lt19(zxw49001, zxw50001, app(app(ty_Either, cgg), cgh)) → new_lt17(zxw49001, zxw50001, cgg, cgh)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_esEs6(Left(zxw4000), Left(zxw3000), app(ty_Maybe, cbh), cca) → new_esEs7(zxw4000, zxw3000, cbh)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Ordering, cca) → new_esEs8(zxw4000, zxw3000)
new_esEs16(:(zxw4000, zxw4001), :(zxw3000, zxw3001), dad) → new_asAs(new_esEs28(zxw4000, zxw3000, dad), new_esEs16(zxw4001, zxw3001, dad))
new_ltEs8(Just(zxw49000), Just(zxw50000), app(ty_Ratio, hg)) → new_ltEs17(zxw49000, zxw50000, hg)
new_compare0(:(zxw49000, zxw49001), :(zxw50000, zxw50001), bhg) → new_primCompAux1(zxw49000, zxw50000, new_compare0(zxw49001, zxw50001, bhg), bhg)
new_esEs11(zxw4001, zxw3001, app(ty_Maybe, df)) → new_esEs7(zxw4001, zxw3001, df)
new_esEs6(Right(zxw4000), Right(zxw3000), cdc, app(app(ty_@2, ced), cee)) → new_esEs4(zxw4000, zxw3000, ced, cee)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Float) → new_ltEs6(zxw49000, zxw50000)
new_compare15(zxw49000, zxw50000, False, be, bf) → GT
new_compare29(zxw49000, zxw50000, app(app(ty_Either, cag), cah)) → new_compare32(zxw49000, zxw50000, cag, cah)
new_lt20(zxw49000, zxw50000, ty_Float) → new_lt7(zxw49000, zxw50000)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Char) → new_esEs15(zxw4000, zxw3000)
new_esEs23(zxw49000, zxw50000, ty_Int) → new_esEs13(zxw49000, zxw50000)
new_esEs30(zxw20, zxw15, app(ty_[], bdc)) → new_esEs16(zxw20, zxw15, bdc)
new_esEs7(Just(zxw4000), Just(zxw3000), app(app(app(ty_@3, bgh), bha), bhb)) → new_esEs5(zxw4000, zxw3000, bgh, bha, bhb)
new_esEs9(True, False) → False
new_esEs9(False, True) → False
new_compare29(zxw49000, zxw50000, app(ty_Ratio, cba)) → new_compare8(zxw49000, zxw50000, cba)
new_esEs10(zxw4002, zxw3002, app(app(ty_@2, dd), de)) → new_esEs4(zxw4002, zxw3002, dd, de)
new_esEs11(zxw4001, zxw3001, app(ty_Ratio, dg)) → new_esEs14(zxw4001, zxw3001, dg)
new_compare29(zxw49000, zxw50000, ty_Ordering) → new_compare6(zxw49000, zxw50000)
new_esEs21(zxw4001, zxw3001, ty_Integer) → new_esEs17(zxw4001, zxw3001)
new_esEs27(zxw49000, zxw50000, ty_Double) → new_esEs18(zxw49000, zxw50000)
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs27(zxw49000, zxw50000, app(ty_Ratio, dac)) → new_esEs14(zxw49000, zxw50000, dac)
new_ltEs4(LT, EQ) → True
new_esEs6(Right(zxw4000), Right(zxw3000), cdc, ty_Char) → new_esEs15(zxw4000, zxw3000)
new_esEs10(zxw4002, zxw3002, ty_Double) → new_esEs18(zxw4002, zxw3002)
new_compare31(@0, @0) → EQ
new_esEs12(zxw4000, zxw3000, app(app(ty_Either, fg), fh)) → new_esEs6(zxw4000, zxw3000, fg, fh)
new_ltEs8(Just(zxw49000), Just(zxw50000), app(ty_Maybe, gh)) → new_ltEs8(zxw49000, zxw50000, gh)
new_lt19(zxw49001, zxw50001, ty_Bool) → new_lt13(zxw49001, zxw50001)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbf, app(app(ty_Either, dcf), dcg)) → new_ltEs7(zxw49000, zxw50000, dcf, dcg)
new_esEs28(zxw4000, zxw3000, app(app(ty_@2, dea), deb)) → new_esEs4(zxw4000, zxw3000, dea, deb)
new_compare9(Integer(zxw49000), Integer(zxw50000)) → new_primCmpInt(zxw49000, zxw50000)
new_asAs(False, zxw187) → False
new_primMulInt(Neg(zxw40010), Pos(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Double) → new_esEs18(zxw4000, zxw3000)
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Ordering) → new_ltEs4(zxw49000, zxw50000)
new_esEs21(zxw4001, zxw3001, ty_Ordering) → new_esEs8(zxw4001, zxw3001)
new_primCmpNat2(zxw4900, Zero) → GT
new_ltEs20(zxw49002, zxw50002, ty_Double) → new_ltEs11(zxw49002, zxw50002)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Char, cca) → new_esEs15(zxw4000, zxw3000)
new_esEs26(zxw49001, zxw50001, app(ty_Maybe, cgb)) → new_esEs7(zxw49001, zxw50001, cgb)
new_esEs10(zxw4002, zxw3002, ty_@0) → new_esEs20(zxw4002, zxw3002)
new_lt19(zxw49001, zxw50001, ty_Double) → new_lt8(zxw49001, zxw50001)
new_esEs28(zxw4000, zxw3000, ty_Double) → new_esEs18(zxw4000, zxw3000)
new_compare110(zxw49000, zxw50000, True, bfh, bga, bgb) → LT
new_esEs24(zxw4001, zxw3001, ty_Integer) → new_esEs17(zxw4001, zxw3001)
new_lt19(zxw49001, zxw50001, app(ty_Maybe, cgb)) → new_lt12(zxw49001, zxw50001, cgb)
new_ltEs18(zxw49001, zxw50001, app(ty_Ratio, bff)) → new_ltEs17(zxw49001, zxw50001, bff)
new_ltEs18(zxw49001, zxw50001, ty_Char) → new_ltEs12(zxw49001, zxw50001)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Float, cca) → new_esEs19(zxw4000, zxw3000)
new_esEs21(zxw4001, zxw3001, ty_Int) → new_esEs13(zxw4001, zxw3001)
new_lt20(zxw49000, zxw50000, app(ty_Ratio, dac)) → new_lt18(zxw49000, zxw50000, dac)
new_ltEs19(zxw4900, zxw5000, ty_@0) → new_ltEs14(zxw4900, zxw5000)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbf, ty_Double) → new_ltEs11(zxw49000, zxw50000)
new_lt17(zxw49000, zxw50000, be, bf) → new_esEs8(new_compare32(zxw49000, zxw50000, be, bf), LT)
new_esEs9(False, False) → True
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Int) → new_ltEs10(zxw49000, zxw50000)
new_esEs30(zxw20, zxw15, ty_Int) → new_esEs13(zxw20, zxw15)
new_ltEs19(zxw4900, zxw5000, ty_Bool) → new_ltEs5(zxw4900, zxw5000)
new_compare29(zxw49000, zxw50000, ty_Integer) → new_compare9(zxw49000, zxw50000)
new_esEs29(zxw400, zxw300, ty_Float) → new_esEs19(zxw400, zxw300)
new_lt20(zxw49000, zxw50000, app(app(app(ty_@3, chf), chg), chh)) → new_lt16(zxw49000, zxw50000, chf, chg, chh)
new_esEs4(@2(zxw4000, zxw4001), @2(zxw3000, zxw3001), baa, bab) → new_asAs(new_esEs22(zxw4000, zxw3000, baa), new_esEs21(zxw4001, zxw3001, bab))
new_ltEs20(zxw49002, zxw50002, app(app(ty_Either, cfe), cff)) → new_ltEs7(zxw49002, zxw50002, cfe, cff)
new_esEs27(zxw49000, zxw50000, app(app(ty_@2, chb), chc)) → new_esEs4(zxw49000, zxw50000, chb, chc)
new_lt20(zxw49000, zxw50000, ty_Integer) → new_lt5(zxw49000, zxw50000)
new_compare35(zxw400, h) → new_compare26(Just(zxw400), Nothing, False, h)
new_ltEs18(zxw49001, zxw50001, app(ty_Maybe, beg)) → new_ltEs8(zxw49001, zxw50001, beg)
new_compare8(:%(zxw49000, zxw49001), :%(zxw50000, zxw50001), ty_Integer) → new_compare9(new_sr0(zxw49000, zxw50001), new_sr0(zxw50000, zxw49001))
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Float, cbg) → new_ltEs6(zxw49000, zxw50000)
new_ltEs4(LT, LT) → True
new_esEs16([], [], dad) → True
new_ltEs20(zxw49002, zxw50002, ty_Int) → new_ltEs10(zxw49002, zxw50002)
new_ltEs8(Nothing, Nothing, ge) → True
new_lt10(zxw49000, zxw50000, ty_Char) → new_lt6(zxw49000, zxw50000)
new_lt10(zxw49000, zxw50000, ty_Bool) → new_lt13(zxw49000, zxw50000)
new_esEs22(zxw4000, zxw3000, app(app(ty_Either, bcc), bcd)) → new_esEs6(zxw4000, zxw3000, bcc, bcd)
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_lt5(zxw49000, zxw50000) → new_esEs8(new_compare9(zxw49000, zxw50000), LT)
new_esEs26(zxw49001, zxw50001, ty_Float) → new_esEs19(zxw49001, zxw50001)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Int, cca) → new_esEs13(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_esEs10(zxw4002, zxw3002, ty_Int) → new_esEs13(zxw4002, zxw3002)
new_lt10(zxw49000, zxw50000, app(ty_[], bg)) → new_lt9(zxw49000, zxw50000, bg)
new_esEs12(zxw4000, zxw3000, app(ty_Ratio, fa)) → new_esEs14(zxw4000, zxw3000, fa)
new_ltEs15(@3(zxw49000, zxw49001, zxw49002), @3(zxw50000, zxw50001, zxw50002), cbc, cbd, cbe) → new_pePe(new_lt20(zxw49000, zxw50000, cbc), new_asAs(new_esEs27(zxw49000, zxw50000, cbc), new_pePe(new_lt19(zxw49001, zxw50001, cbd), new_asAs(new_esEs26(zxw49001, zxw50001, cbd), new_ltEs20(zxw49002, zxw50002, cbe)))))
new_ltEs10(zxw4900, zxw5000) → new_fsEs(new_compare7(zxw4900, zxw5000))
new_esEs30(zxw20, zxw15, ty_Ordering) → new_esEs8(zxw20, zxw15)
new_esEs10(zxw4002, zxw3002, app(ty_Ratio, cd)) → new_esEs14(zxw4002, zxw3002, cd)
new_ltEs12(zxw4900, zxw5000) → new_fsEs(new_compare12(zxw4900, zxw5000))
new_esEs10(zxw4002, zxw3002, ty_Ordering) → new_esEs8(zxw4002, zxw3002)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbf, ty_Float) → new_ltEs6(zxw49000, zxw50000)
new_esEs23(zxw49000, zxw50000, app(ty_[], bg)) → new_esEs16(zxw49000, zxw50000, bg)
new_esEs11(zxw4001, zxw3001, ty_Integer) → new_esEs17(zxw4001, zxw3001)
new_esEs26(zxw49001, zxw50001, app(app(ty_Either, cgg), cgh)) → new_esEs6(zxw49001, zxw50001, cgg, cgh)
new_compare16(Double(zxw49000, zxw49001), Double(zxw50000, zxw50001)) → new_compare7(new_sr(zxw49000, zxw50000), new_sr(zxw49001, zxw50001))
new_compare0([], :(zxw50000, zxw50001), bhg) → LT
new_primPlusNat1(Zero, Zero) → Zero
new_esEs12(zxw4000, zxw3000, ty_Ordering) → new_esEs8(zxw4000, zxw3000)
new_lt10(zxw49000, zxw50000, ty_@0) → new_lt15(zxw49000, zxw50000)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Char) → new_ltEs12(zxw49000, zxw50000)
new_asAs(True, zxw187) → zxw187
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_esEs30(zxw20, zxw15, ty_Integer) → new_esEs17(zxw20, zxw15)
new_esEs26(zxw49001, zxw50001, app(app(app(ty_@3, cgd), cge), cgf)) → new_esEs5(zxw49001, zxw50001, cgd, cge, cgf)
new_esEs10(zxw4002, zxw3002, app(app(ty_Either, db), dc)) → new_esEs6(zxw4002, zxw3002, db, dc)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Integer) → new_ltEs16(zxw49000, zxw50000)
new_compare30(zxw49000, zxw50000, gc, gd) → new_compare27(zxw49000, zxw50000, new_esEs4(zxw49000, zxw50000, gc, gd), gc, gd)
new_compare29(zxw49000, zxw50000, ty_Bool) → new_compare18(zxw49000, zxw50000)
new_fsEs(zxw202) → new_not(new_esEs8(zxw202, GT))
new_esEs23(zxw49000, zxw50000, app(app(app(ty_@3, bfh), bga), bgb)) → new_esEs5(zxw49000, zxw50000, bfh, bga, bgb)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Float) → new_esEs19(zxw4000, zxw3000)
new_compare10(zxw49000, zxw50000, True) → LT
new_esEs29(zxw400, zxw300, app(ty_Ratio, cbb)) → new_esEs14(zxw400, zxw300, cbb)
new_esEs30(zxw20, zxw15, app(app(app(ty_@3, bdd), bde), bdf)) → new_esEs5(zxw20, zxw15, bdd, bde, bdf)
new_compare29(zxw49000, zxw50000, app(ty_Maybe, cab)) → new_compare19(zxw49000, zxw50000, cab)
new_ltEs4(GT, GT) → True
new_esEs26(zxw49001, zxw50001, ty_@0) → new_esEs20(zxw49001, zxw50001)
new_compare110(zxw49000, zxw50000, False, bfh, bga, bgb) → GT
new_ltEs7(Left(zxw49000), Left(zxw50000), app(ty_Ratio, dbf), cbg) → new_ltEs17(zxw49000, zxw50000, dbf)
new_compare10(zxw49000, zxw50000, False) → GT
new_ltEs8(Just(zxw49000), Just(zxw50000), app(app(app(ty_@3, hb), hc), hd)) → new_ltEs15(zxw49000, zxw50000, hb, hc, hd)
new_esEs21(zxw4001, zxw3001, app(ty_[], bae)) → new_esEs16(zxw4001, zxw3001, bae)
new_compare18(zxw49000, zxw50000) → new_compare24(zxw49000, zxw50000, new_esEs9(zxw49000, zxw50000))
new_esEs6(Right(zxw4000), Right(zxw3000), cdc, ty_Ordering) → new_esEs8(zxw4000, zxw3000)
new_esEs6(Left(zxw4000), Left(zxw3000), app(ty_[], ccc), cca) → new_esEs16(zxw4000, zxw3000, ccc)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs6(Right(zxw4000), Right(zxw3000), cdc, app(app(app(ty_@3, cdg), cdh), cea)) → new_esEs5(zxw4000, zxw3000, cdg, cdh, cea)
new_primCompAux0(zxw218, EQ) → zxw218
new_esEs29(zxw400, zxw300, ty_Ordering) → new_esEs8(zxw400, zxw300)
new_lt20(zxw49000, zxw50000, app(ty_Maybe, chd)) → new_lt12(zxw49000, zxw50000, chd)
new_esEs12(zxw4000, zxw3000, app(app(ty_@2, ga), gb)) → new_esEs4(zxw4000, zxw3000, ga, gb)
new_ltEs19(zxw4900, zxw5000, app(ty_[], bhg)) → new_ltEs13(zxw4900, zxw5000, bhg)
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_esEs22(zxw4000, zxw3000, app(ty_Maybe, bbe)) → new_esEs7(zxw4000, zxw3000, bbe)
new_esEs30(zxw20, zxw15, ty_Char) → new_esEs15(zxw20, zxw15)
new_esEs30(zxw20, zxw15, app(app(ty_@2, bea), beb)) → new_esEs4(zxw20, zxw15, bea, beb)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbf, ty_@0) → new_ltEs14(zxw49000, zxw50000)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_compare8(:%(zxw49000, zxw49001), :%(zxw50000, zxw50001), ty_Int) → new_compare7(new_sr(zxw49000, zxw50001), new_sr(zxw50000, zxw49001))
new_ltEs17(zxw4900, zxw5000, hh) → new_fsEs(new_compare8(zxw4900, zxw5000, hh))
new_not(True) → False

The set Q consists of the following terms:

new_esEs17(Integer(x0), Integer(x1))
new_esEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Integer)
new_lt10(x0, x1, ty_Double)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_compare18(x0, x1)
new_compare29(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Double)
new_pePe(False, x0)
new_lt10(x0, x1, app(app(ty_Either, x2), x3))
new_lt17(x0, x1, x2, x3)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Left(x0), Left(x1), ty_Bool, x2)
new_compare7(x0, x1)
new_esEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_compare110(x0, x1, False, x2, x3, x4)
new_primMulNat0(Succ(x0), Zero)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs7(Just(x0), Just(x1), ty_Double)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_ltEs8(Just(x0), Just(x1), ty_Integer)
new_esEs10(x0, x1, ty_Int)
new_ltEs10(x0, x1)
new_esEs28(x0, x1, ty_Int)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs12(x0, x1, ty_Char)
new_compare25(x0, x1, True, x2, x3)
new_primMulNat0(Succ(x0), Succ(x1))
new_ltEs7(Left(x0), Left(x1), ty_Integer, x2)
new_esEs6(Left(x0), Left(x1), ty_Int, x2)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Int)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs16(x0, x1)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_compare13(x0, x1, True)
new_esEs10(x0, x1, ty_Ordering)
new_compare29(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs19(x0, x1, ty_Float)
new_compare0([], :(x0, x1), x2)
new_esEs11(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_Int)
new_esEs6(Left(x0), Left(x1), ty_@0, x2)
new_ltEs8(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare11(x0, x1, True, x2)
new_ltEs19(x0, x1, ty_Ordering)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs8(GT, GT)
new_compare11(x0, x1, False, x2)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_compare17(x0, x1, True, x2, x3)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCompAux1(x0, x1, x2, x3)
new_esEs8(LT, LT)
new_esEs29(x0, x1, ty_@0)
new_compare29(x0, x1, ty_Double)
new_esEs18(Double(x0, x1), Double(x2, x3))
new_primCmpNat0(Zero, x0)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_lt11(x0, x1, x2, x3)
new_ltEs8(Just(x0), Just(x1), ty_Bool)
new_esEs11(x0, x1, ty_@0)
new_primCmpNat1(Zero, Succ(x0))
new_esEs25(x0, x1, ty_Int)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_sr(x0, x1)
new_ltEs5(False, False)
new_ltEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_compare6(x0, x1)
new_lt10(x0, x1, ty_Ordering)
new_esEs6(Right(x0), Left(x1), x2, x3)
new_esEs6(Left(x0), Right(x1), x2, x3)
new_compare29(x0, x1, ty_Int)
new_esEs30(x0, x1, ty_Bool)
new_ltEs15(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs26(x0, x1, ty_Integer)
new_primEqNat0(Zero, Succ(x0))
new_primCmpNat1(Zero, Zero)
new_esEs7(Nothing, Nothing, x0)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs7(Left(x0), Left(x1), ty_Bool, x2)
new_compare16(Double(x0, x1), Double(x2, x3))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_lt7(x0, x1)
new_esEs28(x0, x1, ty_@0)
new_ltEs20(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Integer)
new_esEs16(:(x0, x1), :(x2, x3), x4)
new_esEs23(x0, x1, ty_Integer)
new_esEs11(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Double)
new_ltEs19(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_Char)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_compare15(x0, x1, True, x2, x3)
new_esEs24(x0, x1, ty_Int)
new_esEs6(Left(x0), Left(x1), ty_Char, x2)
new_esEs6(Left(x0), Left(x1), ty_Integer, x2)
new_primEqNat0(Zero, Zero)
new_compare32(x0, x1, x2, x3)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs8(Just(x0), Just(x1), app(ty_Maybe, x2))
new_compare36(x0, x1, x2)
new_ltEs8(Just(x0), Just(x1), ty_Double)
new_ltEs8(Just(x0), Just(x1), ty_Ordering)
new_ltEs19(x0, x1, ty_@0)
new_compare110(x0, x1, True, x2, x3, x4)
new_compare24(x0, x1, False)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs7(Just(x0), Nothing, x1)
new_esEs29(x0, x1, ty_Bool)
new_esEs9(True, True)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_lt18(x0, x1, x2)
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt4(x0, x1)
new_primMulNat0(Zero, Zero)
new_ltEs13(x0, x1, x2)
new_esEs23(x0, x1, ty_Char)
new_esEs30(x0, x1, ty_Ordering)
new_esEs10(x0, x1, ty_@0)
new_lt10(x0, x1, app(ty_Ratio, x2))
new_lt10(x0, x1, ty_Char)
new_esEs30(x0, x1, ty_Int)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_Integer)
new_fsEs(x0)
new_ltEs4(GT, GT)
new_lt8(x0, x1)
new_esEs30(x0, x1, ty_@0)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs10(x0, x1, ty_Float)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs28(x0, x1, ty_Double)
new_esEs29(x0, x1, ty_Char)
new_compare29(x0, x1, app(ty_[], x2))
new_esEs6(Right(x0), Right(x1), x2, ty_Float)
new_compare27(x0, x1, True, x2, x3)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_lt10(x0, x1, ty_Int)
new_esEs10(x0, x1, ty_Bool)
new_lt16(x0, x1, x2, x3, x4)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs23(x0, x1, ty_Ordering)
new_esEs7(Just(x0), Just(x1), ty_Int)
new_esEs10(x0, x1, ty_Char)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_lt10(x0, x1, app(ty_[], x2))
new_compare33(x0)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_pePe(True, x0)
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, ty_Int)
new_primPlusNat0(Zero, x0)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_lt10(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, ty_Int)
new_compare210(x0, x1, True, x2, x3, x4)
new_lt6(x0, x1)
new_esEs26(x0, x1, ty_Bool)
new_compare24(x0, x1, True)
new_ltEs18(x0, x1, ty_Integer)
new_compare15(x0, x1, False, x2, x3)
new_compare14(Float(x0, x1), Float(x2, x3))
new_ltEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(x0, x1)
new_esEs29(x0, x1, ty_Integer)
new_esEs12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primPlusNat1(Zero, Zero)
new_primCompAux0(x0, GT)
new_compare23(x0, x1, True)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_lt19(x0, x1, app(ty_[], x2))
new_lt15(x0, x1)
new_ltEs7(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs29(x0, x1, ty_Ordering)
new_compare19(x0, x1, x2)
new_compare13(x0, x1, False)
new_compare26(Nothing, Just(x0), False, x1)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_lt20(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_@0)
new_compare30(x0, x1, x2, x3)
new_primPlusNat0(Succ(x0), x1)
new_esEs12(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs4(EQ, EQ)
new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs19(x0, x1, ty_Char)
new_ltEs7(Right(x0), Right(x1), x2, ty_Char)
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_ltEs11(x0, x1)
new_esEs12(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Integer)
new_compare29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Char)
new_esEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs8(Nothing, Just(x0), x1)
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs8(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Just(x0), Just(x1), ty_Char)
new_ltEs7(Left(x0), Left(x1), ty_@0, x2)
new_lt9(x0, x1, x2)
new_esEs10(x0, x1, app(ty_[], x2))
new_esEs12(x0, x1, ty_Float)
new_compare31(@0, @0)
new_esEs7(Just(x0), Just(x1), ty_Float)
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs16([], :(x0, x1), x2)
new_primCmpNat2(x0, Zero)
new_ltEs4(LT, EQ)
new_ltEs4(EQ, LT)
new_esEs12(x0, x1, ty_Int)
new_lt19(x0, x1, ty_Double)
new_esEs6(Right(x0), Right(x1), x2, ty_Integer)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_primMulInt(Pos(x0), Pos(x1))
new_lt20(x0, x1, ty_Bool)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_ltEs7(Right(x0), Right(x1), x2, ty_Int)
new_ltEs18(x0, x1, app(ty_[], x2))
new_esEs30(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_@0)
new_esEs10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs7(Right(x0), Right(x1), x2, ty_Double)
new_asAs(True, x0)
new_primEqNat0(Succ(x0), Zero)
new_compare26(Just(x0), Nothing, False, x1)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs7(Left(x0), Left(x1), ty_Int, x2)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_esEs12(x0, x1, app(ty_[], x2))
new_esEs13(x0, x1)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_ltEs7(Left(x0), Right(x1), x2, x3)
new_ltEs7(Right(x0), Left(x1), x2, x3)
new_esEs14(:%(x0, x1), :%(x2, x3), x4)
new_compare26(x0, x1, True, x2)
new_esEs21(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Integer)
new_ltEs7(Left(x0), Left(x1), ty_Double, x2)
new_ltEs8(Nothing, Nothing, x0)
new_lt20(x0, x1, ty_@0)
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_Bool)
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Char)
new_compare26(Just(x0), Just(x1), False, x2)
new_esEs28(x0, x1, ty_Ordering)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, app(ty_Ratio, x2))
new_compare34(x0, x1)
new_lt20(x0, x1, ty_Ordering)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_lt12(x0, x1, x2)
new_esEs10(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_esEs12(x0, x1, app(ty_Maybe, x2))
new_esEs30(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, ty_Bool)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs27(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_Double)
new_esEs25(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(ty_[], x2))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_lt10(x0, x1, ty_Bool)
new_primPlusNat1(Succ(x0), Zero)
new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs22(x0, x1, ty_Float)
new_ltEs4(LT, LT)
new_esEs10(x0, x1, ty_Integer)
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Integer)
new_compare29(x0, x1, app(app(ty_@2, x2), x3))
new_compare23(x0, x1, False)
new_esEs21(x0, x1, app(ty_[], x2))
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs11(x0, x1, ty_Bool)
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_compare29(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_Double)
new_esEs21(x0, x1, ty_Bool)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, ty_Double)
new_esEs26(x0, x1, ty_Ordering)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs7(Nothing, Just(x0), x1)
new_primPlusNat1(Zero, Succ(x0))
new_ltEs12(x0, x1)
new_compare10(x0, x1, False)
new_lt10(x0, x1, app(app(ty_@2, x2), x3))
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Left(x0), Left(x1), ty_Float, x2)
new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_primCmpNat0(Succ(x0), x1)
new_lt10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, ty_@0)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs8(GT, EQ)
new_esEs8(EQ, GT)
new_esEs22(x0, x1, ty_Bool)
new_lt19(x0, x1, ty_Float)
new_lt19(x0, x1, ty_Integer)
new_ltEs8(Just(x0), Just(x1), ty_Char)
new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Left(x0), Left(x1), ty_Double, x2)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_ltEs8(Just(x0), Just(x1), ty_Float)
new_lt5(x0, x1)
new_compare29(x0, x1, ty_Ordering)
new_ltEs18(x0, x1, ty_Bool)
new_compare28(x0, x1, x2, x3, x4)
new_esEs11(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_@0)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, ty_Int)
new_esEs11(x0, x1, ty_Char)
new_esEs10(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Float)
new_lt19(x0, x1, ty_Ordering)
new_compare29(x0, x1, ty_Integer)
new_compare25(x0, x1, False, x2, x3)
new_esEs6(Right(x0), Right(x1), x2, ty_Char)
new_esEs26(x0, x1, app(ty_[], x2))
new_ltEs18(x0, x1, ty_Float)
new_ltEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs9(False, False)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs21(x0, x1, ty_Double)
new_esEs12(x0, x1, ty_Ordering)
new_ltEs8(Just(x0), Nothing, x1)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs22(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpNat1(Succ(x0), Succ(x1))
new_esEs10(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_@0)
new_ltEs6(x0, x1)
new_lt10(x0, x1, ty_Float)
new_esEs22(x0, x1, ty_Int)
new_ltEs7(Left(x0), Left(x1), ty_Char, x2)
new_compare17(x0, x1, False, x2, x3)
new_ltEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs21(x0, x1, ty_Float)
new_esEs29(x0, x1, ty_Double)
new_primCompAux0(x0, EQ)
new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare26(Nothing, Nothing, False, x0)
new_compare27(x0, x1, False, x2, x3)
new_esEs21(x0, x1, ty_Integer)
new_primCmpNat1(Succ(x0), Zero)
new_ltEs18(x0, x1, ty_@0)
new_esEs22(x0, x1, ty_Double)
new_ltEs7(Right(x0), Right(x1), x2, ty_@0)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, ty_Bool)
new_esEs16([], [], x0)
new_compare29(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, app(ty_[], x2))
new_lt13(x0, x1)
new_esEs23(x0, x1, ty_Bool)
new_ltEs5(True, True)
new_ltEs7(Right(x0), Right(x1), x2, ty_Integer)
new_lt19(x0, x1, ty_Int)
new_compare35(x0, x1)
new_lt19(x0, x1, ty_Char)
new_ltEs4(EQ, GT)
new_ltEs4(GT, EQ)
new_esEs6(Right(x0), Right(x1), x2, ty_@0)
new_not(True)
new_esEs11(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Float)
new_compare0(:(x0, x1), [], x2)
new_esEs28(x0, x1, ty_Char)
new_lt19(x0, x1, ty_@0)
new_esEs10(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, ty_Ordering)
new_ltEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs26(x0, x1, ty_Char)
new_ltEs18(x0, x1, ty_Int)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_ltEs20(x0, x1, ty_Ordering)
new_not(False)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_lt14(x0, x1)
new_compare12(Char(x0), Char(x1))
new_esEs15(Char(x0), Char(x1))
new_esEs11(x0, x1, app(ty_[], x2))
new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_compare10(x0, x1, True)
new_lt10(x0, x1, ty_@0)
new_asAs(False, x0)
new_esEs22(x0, x1, ty_Ordering)
new_ltEs18(x0, x1, ty_Char)
new_esEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs17(x0, x1, x2)
new_compare29(x0, x1, ty_Float)
new_lt19(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_Char)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_ltEs8(Just(x0), Just(x1), ty_@0)
new_esEs20(@0, @0)
new_ltEs8(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs7(Left(x0), Left(x1), ty_Float, x2)
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Int)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_esEs16(:(x0, x1), [], x2)
new_ltEs19(x0, x1, ty_Double)
new_esEs9(True, False)
new_esEs9(False, True)
new_esEs22(x0, x1, ty_Char)
new_ltEs7(Right(x0), Right(x1), x2, ty_Float)
new_ltEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare29(x0, x1, ty_Bool)
new_ltEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs30(x0, x1, ty_Double)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, ty_Integer)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs11(x0, x1, ty_Double)
new_ltEs20(x0, x1, ty_Float)
new_primCompAux0(x0, LT)
new_primCmpNat2(x0, Succ(x1))
new_esEs11(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs12(x0, x1, ty_Integer)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs10(x0, x1, ty_Double)
new_ltEs8(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_sr0(Integer(x0), Integer(x1))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs29(x0, x1, ty_Float)
new_ltEs8(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_primEqInt(Pos(Zero), Pos(Zero))
new_ltEs18(x0, x1, ty_Double)
new_esEs12(x0, x1, ty_Double)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_compare0(:(x0, x1), :(x2, x3), x4)
new_esEs29(x0, x1, ty_Int)
new_esEs12(x0, x1, ty_Bool)
new_compare9(Integer(x0), Integer(x1))
new_lt10(x0, x1, ty_Integer)
new_esEs30(x0, x1, ty_Char)
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs19(Float(x0, x1), Float(x2, x3))
new_primMulNat0(Zero, Succ(x0))
new_compare0([], [], x0)
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Just(x0), Just(x1), ty_@0)
new_ltEs4(GT, LT)
new_ltEs4(LT, GT)
new_ltEs5(True, False)
new_ltEs5(False, True)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs9(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs27(x0, x1, app(ty_[], x2))
new_ltEs8(Just(x0), Just(x1), ty_Int)
new_esEs12(x0, x1, app(app(ty_Either, x2), x3))
new_compare29(x0, x1, ty_@0)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Float)
new_esEs23(x0, x1, ty_Float)
new_compare210(x0, x1, False, x2, x3, x4)
new_esEs30(x0, x1, ty_Float)
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))

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_splitGT11(zxw31, zxw32, zxw33, zxw34, zxw400, True, h, ba) → new_splitGT0(zxw33, zxw400, h, ba)
new_splitGT20(zxw31, zxw32, zxw33, Branch(zxw340, zxw341, zxw342, zxw343, zxw344), zxw400, True, h, ba) → new_splitGT3(zxw340, zxw341, zxw342, zxw343, zxw344, Just(zxw400), h, ba)
new_splitGT0(Branch(zxw340, zxw341, zxw342, zxw343, zxw344), zxw400, h, ba) → new_splitGT3(zxw340, zxw341, zxw342, zxw343, zxw344, Just(zxw400), h, ba)
new_splitGT12(zxw30, zxw31, zxw32, zxw33, zxw34, zxw35, True, bb, bc) → new_splitGT0(zxw33, zxw35, bb, bc)
new_splitGT21(zxw30, zxw31, zxw32, zxw33, zxw34, zxw35, True, bb, bc) → new_splitGT0(zxw34, zxw35, bb, bc)
new_splitGT3(Nothing, zxw31, zxw32, zxw33, zxw34, Just(zxw400), h, ba) → new_splitGT20(zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs8(new_compare26(Just(zxw400), Nothing, False, h), GT), h, ba)
new_splitGT21(zxw30, zxw31, zxw32, zxw33, zxw34, zxw35, False, bb, bc) → new_splitGT12(zxw30, zxw31, zxw32, zxw33, zxw34, zxw35, new_esEs8(new_compare36(zxw35, zxw30, bb), LT), bb, bc)
new_splitGT3(Just(zxw300), zxw31, zxw32, zxw33, zxw34, Just(zxw400), h, ba) → new_splitGT21(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs8(new_compare26(Just(zxw400), Just(zxw300), new_esEs29(zxw400, zxw300, h), h), GT), h, ba)
new_splitGT20(zxw31, zxw32, zxw33, zxw34, zxw400, False, h, ba) → new_splitGT11(zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs8(new_compare35(zxw400, h), LT), h, ba)

The TRS R consists of the following rules:

new_esEs6(Right(zxw4000), Right(zxw3000), cdc, ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_esEs29(zxw400, zxw300, ty_Integer) → new_esEs17(zxw400, zxw300)
new_esEs28(zxw4000, zxw3000, ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_esEs7(Just(zxw4000), Just(zxw3000), app(ty_Maybe, bge)) → new_esEs7(zxw4000, zxw3000, bge)
new_ltEs19(zxw4900, zxw5000, ty_Integer) → new_ltEs16(zxw4900, zxw5000)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_@0, cbg) → new_ltEs14(zxw49000, zxw50000)
new_esEs27(zxw49000, zxw50000, app(ty_[], che)) → new_esEs16(zxw49000, zxw50000, che)
new_ltEs4(EQ, GT) → True
new_esEs22(zxw4000, zxw3000, ty_@0) → new_esEs20(zxw4000, zxw3000)
new_compare15(zxw49000, zxw50000, True, be, bf) → LT
new_esEs6(Right(zxw4000), Right(zxw3000), cdc, ty_Float) → new_esEs19(zxw4000, zxw3000)
new_ltEs9(@2(zxw49000, zxw49001), @2(zxw50000, zxw50001), bec, bed) → new_pePe(new_lt10(zxw49000, zxw50000, bec), new_asAs(new_esEs23(zxw49000, zxw50000, bec), new_ltEs18(zxw49001, zxw50001, bed)))
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Integer, cca) → new_esEs17(zxw4000, zxw3000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_esEs23(zxw49000, zxw50000, app(app(ty_@2, gc), gd)) → new_esEs4(zxw49000, zxw50000, gc, gd)
new_compare29(zxw49000, zxw50000, ty_Char) → new_compare12(zxw49000, zxw50000)
new_esEs22(zxw4000, zxw3000, ty_Float) → new_esEs19(zxw4000, zxw3000)
new_esEs6(Right(zxw4000), Right(zxw3000), cdc, ty_Int) → new_esEs13(zxw4000, zxw3000)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Bool) → new_ltEs5(zxw49000, zxw50000)
new_lt19(zxw49001, zxw50001, ty_Integer) → new_lt5(zxw49001, zxw50001)
new_compare33(h) → new_compare26(Nothing, Nothing, True, h)
new_esEs12(zxw4000, zxw3000, ty_Bool) → new_esEs9(zxw4000, zxw3000)
new_esEs27(zxw49000, zxw50000, app(ty_Maybe, chd)) → new_esEs7(zxw49000, zxw50000, chd)
new_esEs12(zxw4000, zxw3000, ty_Char) → new_esEs15(zxw4000, zxw3000)
new_esEs11(zxw4001, zxw3001, app(ty_[], dh)) → new_esEs16(zxw4001, zxw3001, dh)
new_compare12(Char(zxw49000), Char(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_ltEs19(zxw4900, zxw5000, ty_Double) → new_ltEs11(zxw4900, zxw5000)
new_compare29(zxw49000, zxw50000, ty_Double) → new_compare16(zxw49000, zxw50000)
new_ltEs20(zxw49002, zxw50002, ty_Bool) → new_ltEs5(zxw49002, zxw50002)
new_esEs23(zxw49000, zxw50000, ty_Float) → new_esEs19(zxw49000, zxw50000)
new_lt19(zxw49001, zxw50001, ty_Ordering) → new_lt14(zxw49001, zxw50001)
new_lt19(zxw49001, zxw50001, ty_Int) → new_lt4(zxw49001, zxw50001)
new_esEs7(Just(zxw4000), Just(zxw3000), app(app(ty_Either, bhc), bhd)) → new_esEs6(zxw4000, zxw3000, bhc, bhd)
new_primMulNat0(Zero, Zero) → Zero
new_ltEs7(Left(zxw49000), Right(zxw50000), cbf, cbg) → True
new_compare26(Just(zxw4900), Nothing, False, bcg) → GT
new_esEs26(zxw49001, zxw50001, app(ty_[], cgc)) → new_esEs16(zxw49001, zxw50001, cgc)
new_esEs27(zxw49000, zxw50000, ty_Bool) → new_esEs9(zxw49000, zxw50000)
new_ltEs18(zxw49001, zxw50001, ty_Integer) → new_ltEs16(zxw49001, zxw50001)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_ltEs18(zxw49001, zxw50001, app(ty_[], beh)) → new_ltEs13(zxw49001, zxw50001, beh)
new_ltEs20(zxw49002, zxw50002, app(ty_Maybe, ceh)) → new_ltEs8(zxw49002, zxw50002, ceh)
new_esEs11(zxw4001, zxw3001, ty_Char) → new_esEs15(zxw4001, zxw3001)
new_esEs11(zxw4001, zxw3001, ty_Float) → new_esEs19(zxw4001, zxw3001)
new_esEs29(zxw400, zxw300, ty_@0) → new_esEs20(zxw400, zxw300)
new_lt8(zxw49000, zxw50000) → new_esEs8(new_compare16(zxw49000, zxw50000), LT)
new_esEs26(zxw49001, zxw50001, ty_Char) → new_esEs15(zxw49001, zxw50001)
new_lt20(zxw49000, zxw50000, app(app(ty_@2, chb), chc)) → new_lt11(zxw49000, zxw50000, chb, chc)
new_esEs29(zxw400, zxw300, app(ty_Maybe, bgd)) → new_esEs7(zxw400, zxw300, bgd)
new_esEs23(zxw49000, zxw50000, ty_Char) → new_esEs15(zxw49000, zxw50000)
new_esEs23(zxw49000, zxw50000, ty_Bool) → new_esEs9(zxw49000, zxw50000)
new_esEs27(zxw49000, zxw50000, ty_Char) → new_esEs15(zxw49000, zxw50000)
new_compare26(Nothing, Just(zxw5000), False, bcg) → LT
new_lt10(zxw49000, zxw50000, ty_Float) → new_lt7(zxw49000, zxw50000)
new_esEs21(zxw4001, zxw3001, ty_Double) → new_esEs18(zxw4001, zxw3001)
new_ltEs19(zxw4900, zxw5000, ty_Int) → new_ltEs10(zxw4900, zxw5000)
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_lt9(zxw49000, zxw50000, bg) → new_esEs8(new_compare0(zxw49000, zxw50000, bg), LT)
new_compare210(zxw49000, zxw50000, False, bfh, bga, bgb) → new_compare110(zxw49000, zxw50000, new_ltEs15(zxw49000, zxw50000, bfh, bga, bgb), bfh, bga, bgb)
new_esEs22(zxw4000, zxw3000, app(ty_Ratio, bbf)) → new_esEs14(zxw4000, zxw3000, bbf)
new_esEs21(zxw4001, zxw3001, app(ty_Ratio, bad)) → new_esEs14(zxw4001, zxw3001, bad)
new_esEs30(zxw20, zxw15, ty_Bool) → new_esEs9(zxw20, zxw15)
new_esEs7(Just(zxw4000), Just(zxw3000), app(app(ty_@2, bhe), bhf)) → new_esEs4(zxw4000, zxw3000, bhe, bhf)
new_esEs25(zxw4000, zxw3000, ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Bool) → new_esEs9(zxw4000, zxw3000)
new_esEs30(zxw20, zxw15, ty_Float) → new_esEs19(zxw20, zxw15)
new_ltEs20(zxw49002, zxw50002, ty_Integer) → new_ltEs16(zxw49002, zxw50002)
new_esEs21(zxw4001, zxw3001, app(app(ty_Either, bba), bbb)) → new_esEs6(zxw4001, zxw3001, bba, bbb)
new_ltEs7(Left(zxw49000), Left(zxw50000), app(app(app(ty_@3, dba), dbb), dbc), cbg) → new_ltEs15(zxw49000, zxw50000, dba, dbb, dbc)
new_esEs29(zxw400, zxw300, ty_Bool) → new_esEs9(zxw400, zxw300)
new_ltEs14(zxw4900, zxw5000) → new_fsEs(new_compare31(zxw4900, zxw5000))
new_compare24(zxw49000, zxw50000, False) → new_compare13(zxw49000, zxw50000, new_ltEs5(zxw49000, zxw50000))
new_esEs7(Just(zxw4000), Just(zxw3000), app(ty_Ratio, bgf)) → new_esEs14(zxw4000, zxw3000, bgf)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbf, app(app(ty_@2, dbg), dbh)) → new_ltEs9(zxw49000, zxw50000, dbg, dbh)
new_lt4(zxw490, zxw500) → new_esEs8(new_compare7(zxw490, zxw500), LT)
new_esEs28(zxw4000, zxw3000, app(app(app(ty_@3, ddd), dde), ddf)) → new_esEs5(zxw4000, zxw3000, ddd, dde, ddf)
new_esEs28(zxw4000, zxw3000, ty_Bool) → new_esEs9(zxw4000, zxw3000)
new_compare19(zxw490, zxw500, bcg) → new_compare26(zxw490, zxw500, new_esEs7(zxw490, zxw500, bcg), bcg)
new_esEs17(Integer(zxw4000), Integer(zxw3000)) → new_primEqInt(zxw4000, zxw3000)
new_pePe(False, zxw213) → zxw213
new_lt12(zxw490, zxw500, bcg) → new_esEs8(new_compare19(zxw490, zxw500, bcg), LT)
new_esEs20(@0, @0) → True
new_esEs6(Right(zxw4000), Right(zxw3000), cdc, app(ty_Ratio, cde)) → new_esEs14(zxw4000, zxw3000, cde)
new_esEs6(Left(zxw4000), Left(zxw3000), app(app(ty_@2, cda), cdb), cca) → new_esEs4(zxw4000, zxw3000, cda, cdb)
new_compare23(zxw49000, zxw50000, True) → EQ
new_esEs11(zxw4001, zxw3001, ty_Int) → new_esEs13(zxw4001, zxw3001)
new_lt19(zxw49001, zxw50001, app(ty_[], cgc)) → new_lt9(zxw49001, zxw50001, cgc)
new_compare29(zxw49000, zxw50000, ty_@0) → new_compare31(zxw49000, zxw50000)
new_compare26(Nothing, Nothing, False, bcg) → LT
new_esEs10(zxw4002, zxw3002, app(ty_Maybe, cc)) → new_esEs7(zxw4002, zxw3002, cc)
new_ltEs16(zxw4900, zxw5000) → new_fsEs(new_compare9(zxw4900, zxw5000))
new_esEs22(zxw4000, zxw3000, app(app(ty_@2, bce), bcf)) → new_esEs4(zxw4000, zxw3000, bce, bcf)
new_esEs23(zxw49000, zxw50000, app(ty_Maybe, bfg)) → new_esEs7(zxw49000, zxw50000, bfg)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbf, app(ty_Ratio, dch)) → new_ltEs17(zxw49000, zxw50000, dch)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Char, cbg) → new_ltEs12(zxw49000, zxw50000)
new_esEs28(zxw4000, zxw3000, ty_@0) → new_esEs20(zxw4000, zxw3000)
new_esEs10(zxw4002, zxw3002, app(app(app(ty_@3, cf), cg), da)) → new_esEs5(zxw4002, zxw3002, cf, cg, da)
new_ltEs20(zxw49002, zxw50002, app(ty_[], cfa)) → new_ltEs13(zxw49002, zxw50002, cfa)
new_esEs27(zxw49000, zxw50000, ty_Float) → new_esEs19(zxw49000, zxw50000)
new_ltEs20(zxw49002, zxw50002, app(app(app(ty_@3, cfb), cfc), cfd)) → new_ltEs15(zxw49002, zxw50002, cfb, cfc, cfd)
new_esEs22(zxw4000, zxw3000, ty_Ordering) → new_esEs8(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Bool) → new_esEs9(zxw4000, zxw3000)
new_compare6(zxw49000, zxw50000) → new_compare23(zxw49000, zxw50000, new_esEs8(zxw49000, zxw50000))
new_esEs29(zxw400, zxw300, app(app(ty_@2, baa), bab)) → new_esEs4(zxw400, zxw300, baa, bab)
new_esEs12(zxw4000, zxw3000, app(ty_[], fb)) → new_esEs16(zxw4000, zxw3000, fb)
new_compare32(zxw49000, zxw50000, be, bf) → new_compare25(zxw49000, zxw50000, new_esEs6(zxw49000, zxw50000, be, bf), be, bf)
new_compare29(zxw49000, zxw50000, ty_Int) → new_compare7(zxw49000, zxw50000)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Bool, cca) → new_esEs9(zxw4000, zxw3000)
new_ltEs8(Nothing, Just(zxw50000), ge) → True
new_ltEs7(Left(zxw49000), Left(zxw50000), app(app(ty_@2, dae), daf), cbg) → new_ltEs9(zxw49000, zxw50000, dae, daf)
new_esEs6(Right(zxw4000), Left(zxw3000), cdc, cca) → False
new_esEs6(Left(zxw4000), Right(zxw3000), cdc, cca) → False
new_esEs8(LT, LT) → True
new_lt20(zxw49000, zxw50000, ty_@0) → new_lt15(zxw49000, zxw50000)
new_esEs10(zxw4002, zxw3002, ty_Integer) → new_esEs17(zxw4002, zxw3002)
new_esEs28(zxw4000, zxw3000, ty_Float) → new_esEs19(zxw4000, zxw3000)
new_compare29(zxw49000, zxw50000, app(app(app(ty_@3, cad), cae), caf)) → new_compare28(zxw49000, zxw50000, cad, cae, caf)
new_lt19(zxw49001, zxw50001, ty_@0) → new_lt15(zxw49001, zxw50001)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbf, ty_Bool) → new_ltEs5(zxw49000, zxw50000)
new_ltEs5(True, False) → False
new_lt19(zxw49001, zxw50001, app(app(ty_@2, cfh), cga)) → new_lt11(zxw49001, zxw50001, cfh, cga)
new_compare0([], [], bhg) → EQ
new_pePe(True, zxw213) → True
new_primEqNat0(Zero, Zero) → True
new_compare34(zxw300, h) → new_compare26(Nothing, Just(zxw300), False, h)
new_esEs14(:%(zxw4000, zxw4001), :%(zxw3000, zxw3001), cbb) → new_asAs(new_esEs25(zxw4000, zxw3000, cbb), new_esEs24(zxw4001, zxw3001, cbb))
new_lt10(zxw49000, zxw50000, ty_Double) → new_lt8(zxw49000, zxw50000)
new_ltEs20(zxw49002, zxw50002, ty_Ordering) → new_ltEs4(zxw49002, zxw50002)
new_compare27(zxw49000, zxw50000, False, gc, gd) → new_compare17(zxw49000, zxw50000, new_ltEs9(zxw49000, zxw50000, gc, gd), gc, gd)
new_compare11(zxw180, zxw181, True, bd) → LT
new_esEs23(zxw49000, zxw50000, app(app(ty_Either, be), bf)) → new_esEs6(zxw49000, zxw50000, be, bf)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_@0, cca) → new_esEs20(zxw4000, zxw3000)
new_esEs6(Right(zxw4000), Right(zxw3000), cdc, ty_Bool) → new_esEs9(zxw4000, zxw3000)
new_esEs12(zxw4000, zxw3000, ty_Int) → new_esEs13(zxw4000, zxw3000)
new_lt20(zxw49000, zxw50000, app(ty_[], che)) → new_lt9(zxw49000, zxw50000, che)
new_esEs6(Right(zxw4000), Right(zxw3000), cdc, app(app(ty_Either, ceb), cec)) → new_esEs6(zxw4000, zxw3000, ceb, cec)
new_compare26(Just(zxw4900), Just(zxw5000), False, bcg) → new_compare11(zxw4900, zxw5000, new_ltEs19(zxw4900, zxw5000, bcg), bcg)
new_ltEs5(True, True) → True
new_ltEs7(Left(zxw49000), Left(zxw50000), app(ty_Maybe, dag), cbg) → new_ltEs8(zxw49000, zxw50000, dag)
new_esEs29(zxw400, zxw300, ty_Int) → new_esEs13(zxw400, zxw300)
new_compare36(zxw20, zxw15, bch) → new_compare26(Just(zxw20), Just(zxw15), new_esEs30(zxw20, zxw15, bch), bch)
new_ltEs20(zxw49002, zxw50002, app(app(ty_@2, cef), ceg)) → new_ltEs9(zxw49002, zxw50002, cef, ceg)
new_esEs15(Char(zxw4000), Char(zxw3000)) → new_primEqNat0(zxw4000, zxw3000)
new_sr(zxw4001, zxw3001) → new_primMulInt(zxw4001, zxw3001)
new_ltEs18(zxw49001, zxw50001, ty_Int) → new_ltEs10(zxw49001, zxw50001)
new_esEs25(zxw4000, zxw3000, ty_Int) → new_esEs13(zxw4000, zxw3000)
new_compare7(zxw49, zxw50) → new_primCmpInt(zxw49, zxw50)
new_primCmpNat1(Zero, Zero) → EQ
new_esEs7(Just(zxw4000), Just(zxw3000), app(ty_[], bgg)) → new_esEs16(zxw4000, zxw3000, bgg)
new_lt10(zxw49000, zxw50000, ty_Int) → new_lt4(zxw49000, zxw50000)
new_esEs28(zxw4000, zxw3000, app(app(ty_Either, ddg), ddh)) → new_esEs6(zxw4000, zxw3000, ddg, ddh)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbf, app(ty_Maybe, dca)) → new_ltEs8(zxw49000, zxw50000, dca)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbf, ty_Integer) → new_ltEs16(zxw49000, zxw50000)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbf, app(app(app(ty_@3, dcc), dcd), dce)) → new_ltEs15(zxw49000, zxw50000, dcc, dcd, dce)
new_esEs26(zxw49001, zxw50001, ty_Ordering) → new_esEs8(zxw49001, zxw50001)
new_esEs8(GT, GT) → True
new_esEs27(zxw49000, zxw50000, ty_@0) → new_esEs20(zxw49000, zxw50000)
new_esEs13(zxw400, zxw300) → new_primEqInt(zxw400, zxw300)
new_lt13(zxw49000, zxw50000) → new_esEs8(new_compare18(zxw49000, zxw50000), LT)
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_lt20(zxw49000, zxw50000, ty_Ordering) → new_lt14(zxw49000, zxw50000)
new_esEs11(zxw4001, zxw3001, ty_Ordering) → new_esEs8(zxw4001, zxw3001)
new_esEs11(zxw4001, zxw3001, app(app(ty_@2, ef), eg)) → new_esEs4(zxw4001, zxw3001, ef, eg)
new_lt10(zxw49000, zxw50000, app(app(ty_@2, gc), gd)) → new_lt11(zxw49000, zxw50000, gc, gd)
new_compare23(zxw49000, zxw50000, False) → new_compare10(zxw49000, zxw50000, new_ltEs4(zxw49000, zxw50000))
new_esEs8(LT, GT) → False
new_esEs8(GT, LT) → False
new_ltEs19(zxw4900, zxw5000, app(app(app(ty_@3, cbc), cbd), cbe)) → new_ltEs15(zxw4900, zxw5000, cbc, cbd, cbe)
new_lt20(zxw49000, zxw50000, app(app(ty_Either, daa), dab)) → new_lt17(zxw49000, zxw50000, daa, dab)
new_esEs26(zxw49001, zxw50001, ty_Bool) → new_esEs9(zxw49001, zxw50001)
new_ltEs11(zxw4900, zxw5000) → new_fsEs(new_compare16(zxw4900, zxw5000))
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_compare17(zxw49000, zxw50000, True, gc, gd) → LT
new_primEqInt(Neg(Succ(zxw40000)), Neg(Succ(zxw30000))) → new_primEqNat0(zxw40000, zxw30000)
new_ltEs5(False, False) → True
new_esEs23(zxw49000, zxw50000, ty_Ordering) → new_esEs8(zxw49000, zxw50000)
new_ltEs18(zxw49001, zxw50001, app(app(ty_Either, bfd), bfe)) → new_ltEs7(zxw49001, zxw50001, bfd, bfe)
new_esEs28(zxw4000, zxw3000, ty_Char) → new_esEs15(zxw4000, zxw3000)
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)
new_ltEs19(zxw4900, zxw5000, app(ty_Ratio, hh)) → new_ltEs17(zxw4900, zxw5000, hh)
new_esEs10(zxw4002, zxw3002, ty_Bool) → new_esEs9(zxw4002, zxw3002)
new_lt20(zxw49000, zxw50000, ty_Char) → new_lt6(zxw49000, zxw50000)
new_compare13(zxw49000, zxw50000, False) → GT
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Bool, cbg) → new_ltEs5(zxw49000, zxw50000)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Int, cbg) → new_ltEs10(zxw49000, zxw50000)
new_lt11(zxw49000, zxw50000, gc, gd) → new_esEs8(new_compare30(zxw49000, zxw50000, gc, gd), LT)
new_esEs21(zxw4001, zxw3001, ty_Char) → new_esEs15(zxw4001, zxw3001)
new_lt20(zxw49000, zxw50000, ty_Int) → new_lt4(zxw49000, zxw50000)
new_primCompAux1(zxw49000, zxw50000, zxw214, bhg) → new_primCompAux0(zxw214, new_compare29(zxw49000, zxw50000, bhg))
new_esEs7(Just(zxw4000), Just(zxw3000), ty_@0) → new_esEs20(zxw4000, zxw3000)
new_lt16(zxw49000, zxw50000, bfh, bga, bgb) → new_esEs8(new_compare28(zxw49000, zxw50000, bfh, bga, bgb), LT)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_ltEs7(Right(zxw49000), Left(zxw50000), cbf, cbg) → False
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Ordering) → new_esEs8(zxw4000, zxw3000)
new_ltEs7(Left(zxw49000), Left(zxw50000), app(ty_[], dah), cbg) → new_ltEs13(zxw49000, zxw50000, dah)
new_ltEs19(zxw4900, zxw5000, ty_Ordering) → new_ltEs4(zxw4900, zxw5000)
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_ltEs20(zxw49002, zxw50002, ty_Char) → new_ltEs12(zxw49002, zxw50002)
new_esEs11(zxw4001, zxw3001, app(app(app(ty_@3, ea), eb), ec)) → new_esEs5(zxw4001, zxw3001, ea, eb, ec)
new_ltEs20(zxw49002, zxw50002, app(ty_Ratio, cfg)) → new_ltEs17(zxw49002, zxw50002, cfg)
new_ltEs18(zxw49001, zxw50001, ty_@0) → new_ltEs14(zxw49001, zxw50001)
new_primEqInt(Neg(Succ(zxw40000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(zxw30000))) → False
new_ltEs19(zxw4900, zxw5000, ty_Char) → new_ltEs12(zxw4900, zxw5000)
new_esEs12(zxw4000, zxw3000, ty_Double) → new_esEs18(zxw4000, zxw3000)
new_primCompAux0(zxw218, GT) → GT
new_esEs8(EQ, EQ) → True
new_esEs6(Left(zxw4000), Left(zxw3000), app(ty_Ratio, ccb), cca) → new_esEs14(zxw4000, zxw3000, ccb)
new_ltEs8(Just(zxw49000), Just(zxw50000), app(app(ty_Either, he), hf)) → new_ltEs7(zxw49000, zxw50000, he, hf)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Integer, cbg) → new_ltEs16(zxw49000, zxw50000)
new_esEs6(Right(zxw4000), Right(zxw3000), cdc, app(ty_[], cdf)) → new_esEs16(zxw4000, zxw3000, cdf)
new_esEs23(zxw49000, zxw50000, ty_Integer) → new_esEs17(zxw49000, zxw50000)
new_esEs29(zxw400, zxw300, app(ty_[], dad)) → new_esEs16(zxw400, zxw300, dad)
new_esEs28(zxw4000, zxw3000, ty_Int) → new_esEs13(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, app(app(app(ty_@3, bbh), bca), bcb)) → new_esEs5(zxw4000, zxw3000, bbh, bca, bcb)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_ltEs18(zxw49001, zxw50001, ty_Ordering) → new_ltEs4(zxw49001, zxw50001)
new_ltEs4(EQ, LT) → False
new_esEs12(zxw4000, zxw3000, app(ty_Maybe, eh)) → new_esEs7(zxw4000, zxw3000, eh)
new_lt20(zxw49000, zxw50000, ty_Double) → new_lt8(zxw49000, zxw50000)
new_esEs10(zxw4002, zxw3002, ty_Float) → new_esEs19(zxw4002, zxw3002)
new_esEs11(zxw4001, zxw3001, ty_Bool) → new_esEs9(zxw4001, zxw3001)
new_compare11(zxw180, zxw181, False, bd) → GT
new_esEs26(zxw49001, zxw50001, ty_Integer) → new_esEs17(zxw49001, zxw50001)
new_lt10(zxw49000, zxw50000, ty_Ordering) → new_lt14(zxw49000, zxw50000)
new_ltEs18(zxw49001, zxw50001, ty_Bool) → new_ltEs5(zxw49001, zxw50001)
new_esEs12(zxw4000, zxw3000, app(app(app(ty_@3, fc), fd), ff)) → new_esEs5(zxw4000, zxw3000, fc, fd, ff)
new_primEqInt(Pos(Succ(zxw40000)), Pos(Succ(zxw30000))) → new_primEqNat0(zxw40000, zxw30000)
new_compare27(zxw49000, zxw50000, True, gc, gd) → EQ
new_esEs6(Left(zxw4000), Left(zxw3000), app(app(app(ty_@3, ccd), cce), ccf), cca) → new_esEs5(zxw4000, zxw3000, ccd, cce, ccf)
new_lt18(zxw49000, zxw50000, bgc) → new_esEs8(new_compare8(zxw49000, zxw50000, bgc), LT)
new_ltEs18(zxw49001, zxw50001, app(app(app(ty_@3, bfa), bfb), bfc)) → new_ltEs15(zxw49001, zxw50001, bfa, bfb, bfc)
new_lt10(zxw49000, zxw50000, app(ty_Maybe, bfg)) → new_lt12(zxw49000, zxw50000, bfg)
new_esEs26(zxw49001, zxw50001, ty_Int) → new_esEs13(zxw49001, zxw50001)
new_ltEs8(Just(zxw49000), Just(zxw50000), app(app(ty_@2, gf), gg)) → new_ltEs9(zxw49000, zxw50000, gf, gg)
new_primEqNat0(Succ(zxw40000), Succ(zxw30000)) → new_primEqNat0(zxw40000, zxw30000)
new_compare29(zxw49000, zxw50000, app(ty_[], cac)) → new_compare0(zxw49000, zxw50000, cac)
new_esEs27(zxw49000, zxw50000, ty_Ordering) → new_esEs8(zxw49000, zxw50000)
new_esEs27(zxw49000, zxw50000, ty_Integer) → new_esEs17(zxw49000, zxw50000)
new_esEs23(zxw49000, zxw50000, app(ty_Ratio, bgc)) → new_esEs14(zxw49000, zxw50000, bgc)
new_ltEs18(zxw49001, zxw50001, ty_Float) → new_ltEs6(zxw49001, zxw50001)
new_esEs22(zxw4000, zxw3000, ty_Int) → new_esEs13(zxw4000, zxw3000)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbf, app(ty_[], dcb)) → new_ltEs13(zxw49000, zxw50000, dcb)
new_ltEs4(GT, EQ) → False
new_lt7(zxw49000, zxw50000) → new_esEs8(new_compare14(zxw49000, zxw50000), LT)
new_lt10(zxw49000, zxw50000, app(app(app(ty_@3, bfh), bga), bgb)) → new_lt16(zxw49000, zxw50000, bfh, bga, bgb)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Int) → new_esEs13(zxw4000, zxw3000)
new_ltEs19(zxw4900, zxw5000, app(app(ty_Either, cbf), cbg)) → new_ltEs7(zxw4900, zxw5000, cbf, cbg)
new_ltEs8(Just(zxw49000), Nothing, ge) → False
new_esEs21(zxw4001, zxw3001, ty_Float) → new_esEs19(zxw4001, zxw3001)
new_esEs26(zxw49001, zxw50001, app(app(ty_@2, cfh), cga)) → new_esEs4(zxw49001, zxw50001, cfh, cga)
new_esEs27(zxw49000, zxw50000, app(app(app(ty_@3, chf), chg), chh)) → new_esEs5(zxw49000, zxw50000, chf, chg, chh)
new_ltEs13(zxw4900, zxw5000, bhg) → new_fsEs(new_compare0(zxw4900, zxw5000, bhg))
new_esEs22(zxw4000, zxw3000, ty_Char) → new_esEs15(zxw4000, zxw3000)
new_esEs30(zxw20, zxw15, app(ty_Ratio, bdb)) → new_esEs14(zxw20, zxw15, bdb)
new_ltEs18(zxw49001, zxw50001, ty_Double) → new_ltEs11(zxw49001, zxw50001)
new_esEs7(Nothing, Nothing, bgd) → True
new_esEs28(zxw4000, zxw3000, ty_Ordering) → new_esEs8(zxw4000, zxw3000)
new_lt10(zxw49000, zxw50000, app(app(ty_Either, be), bf)) → new_lt17(zxw49000, zxw50000, be, bf)
new_esEs8(EQ, LT) → False
new_esEs8(LT, EQ) → False
new_esEs10(zxw4002, zxw3002, ty_Char) → new_esEs15(zxw4002, zxw3002)
new_primEqInt(Pos(Succ(zxw40000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(zxw30000))) → False
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Double, cbg) → new_ltEs11(zxw49000, zxw50000)
new_ltEs4(EQ, EQ) → True
new_esEs6(Right(zxw4000), Right(zxw3000), cdc, app(ty_Maybe, cdd)) → new_esEs7(zxw4000, zxw3000, cdd)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbf, ty_Ordering) → new_ltEs4(zxw49000, zxw50000)
new_esEs29(zxw400, zxw300, ty_Double) → new_esEs18(zxw400, zxw300)
new_esEs30(zxw20, zxw15, ty_@0) → new_esEs20(zxw20, zxw15)
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_ltEs20(zxw49002, zxw50002, ty_@0) → new_ltEs14(zxw49002, zxw50002)
new_esEs23(zxw49000, zxw50000, ty_@0) → new_esEs20(zxw49000, zxw50000)
new_esEs6(Right(zxw4000), Right(zxw3000), cdc, ty_@0) → new_esEs20(zxw4000, zxw3000)
new_compare210(zxw49000, zxw50000, True, bfh, bga, bgb) → EQ
new_ltEs4(GT, LT) → False
new_sr0(Integer(zxw500000), Integer(zxw490010)) → Integer(new_primMulInt(zxw500000, zxw490010))
new_compare13(zxw49000, zxw50000, True) → LT
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_compare14(Float(zxw49000, zxw49001), Float(zxw50000, zxw50001)) → new_compare7(new_sr(zxw49000, zxw50000), new_sr(zxw49001, zxw50001))
new_primEqInt(Pos(Succ(zxw40000)), Neg(zxw3000)) → False
new_primEqInt(Neg(Succ(zxw40000)), Pos(zxw3000)) → False
new_esEs7(Just(zxw4000), Nothing, bgd) → False
new_esEs7(Nothing, Just(zxw3000), bgd) → False
new_esEs18(Double(zxw4000, zxw4001), Double(zxw3000, zxw3001)) → new_esEs13(new_sr(zxw4000, zxw3000), new_sr(zxw4001, zxw3001))
new_ltEs5(False, True) → True
new_esEs26(zxw49001, zxw50001, ty_Double) → new_esEs18(zxw49001, zxw50001)
new_compare28(zxw49000, zxw50000, bfh, bga, bgb) → new_compare210(zxw49000, zxw50000, new_esEs5(zxw49000, zxw50000, bfh, bga, bgb), bfh, bga, bgb)
new_esEs11(zxw4001, zxw3001, ty_Double) → new_esEs18(zxw4001, zxw3001)
new_ltEs6(zxw4900, zxw5000) → new_fsEs(new_compare14(zxw4900, zxw5000))
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Ordering, cbg) → new_ltEs4(zxw49000, zxw50000)
new_primEqInt(Pos(Zero), Neg(Succ(zxw30000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(zxw30000))) → False
new_ltEs19(zxw4900, zxw5000, app(app(ty_@2, bec), bed)) → new_ltEs9(zxw4900, zxw5000, bec, bed)
new_ltEs20(zxw49002, zxw50002, ty_Float) → new_ltEs6(zxw49002, zxw50002)
new_compare29(zxw49000, zxw50000, app(app(ty_@2, bhh), caa)) → new_compare30(zxw49000, zxw50000, bhh, caa)
new_compare24(zxw49000, zxw50000, True) → EQ
new_esEs27(zxw49000, zxw50000, ty_Int) → new_esEs13(zxw49000, zxw50000)
new_ltEs18(zxw49001, zxw50001, app(app(ty_@2, bee), bef)) → new_ltEs9(zxw49001, zxw50001, bee, bef)
new_esEs6(Right(zxw4000), Right(zxw3000), cdc, ty_Double) → new_esEs18(zxw4000, zxw3000)
new_lt20(zxw49000, zxw50000, ty_Bool) → new_lt13(zxw49000, zxw50000)
new_primCmpNat0(Zero, zxw4900) → LT
new_ltEs7(Right(zxw49000), Right(zxw50000), cbf, ty_Char) → new_ltEs12(zxw49000, zxw50000)
new_esEs8(EQ, GT) → False
new_esEs8(GT, EQ) → False
new_esEs10(zxw4002, zxw3002, app(ty_[], ce)) → new_esEs16(zxw4002, zxw3002, ce)
new_lt15(zxw49000, zxw50000) → new_esEs8(new_compare31(zxw49000, zxw50000), LT)
new_compare17(zxw49000, zxw50000, False, gc, gd) → GT
new_compare29(zxw49000, zxw50000, ty_Float) → new_compare14(zxw49000, zxw50000)
new_esEs30(zxw20, zxw15, ty_Double) → new_esEs18(zxw20, zxw15)
new_esEs28(zxw4000, zxw3000, app(ty_Ratio, ddb)) → new_esEs14(zxw4000, zxw3000, ddb)
new_compare26(zxw490, zxw500, True, bcg) → EQ
new_primCompAux0(zxw218, LT) → LT
new_esEs11(zxw4001, zxw3001, ty_@0) → new_esEs20(zxw4001, zxw3001)
new_esEs30(zxw20, zxw15, app(app(ty_Either, bdg), bdh)) → new_esEs6(zxw20, zxw15, bdg, bdh)
new_esEs12(zxw4000, zxw3000, ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_not(False) → True
new_esEs6(Left(zxw4000), Left(zxw3000), app(app(ty_Either, ccg), cch), cca) → new_esEs6(zxw4000, zxw3000, ccg, cch)
new_esEs28(zxw4000, zxw3000, app(ty_[], ddc)) → new_esEs16(zxw4000, zxw3000, ddc)
new_esEs24(zxw4001, zxw3001, ty_Int) → new_esEs13(zxw4001, zxw3001)
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_esEs26(zxw49001, zxw50001, app(ty_Ratio, cha)) → new_esEs14(zxw49001, zxw50001, cha)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Double) → new_ltEs11(zxw49000, zxw50000)
new_esEs11(zxw4001, zxw3001, app(app(ty_Either, ed), ee)) → new_esEs6(zxw4001, zxw3001, ed, ee)
new_esEs21(zxw4001, zxw3001, ty_@0) → new_esEs20(zxw4001, zxw3001)
new_lt19(zxw49001, zxw50001, ty_Float) → new_lt7(zxw49001, zxw50001)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbf, ty_Int) → new_ltEs10(zxw49000, zxw50000)
new_compare0(:(zxw49000, zxw49001), [], bhg) → GT
new_esEs12(zxw4000, zxw3000, ty_Float) → new_esEs19(zxw4000, zxw3000)
new_ltEs8(Just(zxw49000), Just(zxw50000), app(ty_[], ha)) → new_ltEs13(zxw49000, zxw50000, ha)
new_lt14(zxw49000, zxw50000) → new_esEs8(new_compare6(zxw49000, zxw50000), LT)
new_ltEs19(zxw4900, zxw5000, ty_Float) → new_ltEs6(zxw4900, zxw5000)
new_esEs27(zxw49000, zxw50000, app(app(ty_Either, daa), dab)) → new_esEs6(zxw49000, zxw50000, daa, dab)
new_lt19(zxw49001, zxw50001, app(ty_Ratio, cha)) → new_lt18(zxw49001, zxw50001, cha)
new_esEs9(True, True) → True
new_lt19(zxw49001, zxw50001, app(app(app(ty_@3, cgd), cge), cgf)) → new_lt16(zxw49001, zxw50001, cgd, cge, cgf)
new_lt19(zxw49001, zxw50001, ty_Char) → new_lt6(zxw49001, zxw50001)
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Double, cca) → new_esEs18(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, app(ty_Maybe, dda)) → new_esEs7(zxw4000, zxw3000, dda)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_esEs21(zxw4001, zxw3001, app(app(app(ty_@3, baf), bag), bah)) → new_esEs5(zxw4001, zxw3001, baf, bag, bah)
new_esEs22(zxw4000, zxw3000, app(ty_[], bbg)) → new_esEs16(zxw4000, zxw3000, bbg)
new_esEs21(zxw4001, zxw3001, app(ty_Maybe, bac)) → new_esEs7(zxw4001, zxw3001, bac)
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_esEs22(zxw4000, zxw3000, ty_Double) → new_esEs18(zxw4000, zxw3000)
new_esEs21(zxw4001, zxw3001, app(app(ty_@2, bbc), bbd)) → new_esEs4(zxw4001, zxw3001, bbc, bbd)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_@0) → new_ltEs14(zxw49000, zxw50000)
new_esEs19(Float(zxw4000, zxw4001), Float(zxw3000, zxw3001)) → new_esEs13(new_sr(zxw4000, zxw3000), new_sr(zxw4001, zxw3001))
new_ltEs19(zxw4900, zxw5000, app(ty_Maybe, ge)) → new_ltEs8(zxw4900, zxw5000, ge)
new_primMulInt(Neg(zxw40010), Neg(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_esEs29(zxw400, zxw300, ty_Char) → new_esEs15(zxw400, zxw300)
new_esEs30(zxw20, zxw15, app(ty_Maybe, bda)) → new_esEs7(zxw20, zxw15, bda)
new_primEqNat0(Zero, Succ(zxw30000)) → False
new_primEqNat0(Succ(zxw40000), Zero) → False
new_compare25(zxw49000, zxw50000, True, be, bf) → EQ
new_ltEs7(Left(zxw49000), Left(zxw50000), app(app(ty_Either, dbd), dbe), cbg) → new_ltEs7(zxw49000, zxw50000, dbd, dbe)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_lt10(zxw49000, zxw50000, app(ty_Ratio, bgc)) → new_lt18(zxw49000, zxw50000, bgc)
new_esEs12(zxw4000, zxw3000, ty_@0) → new_esEs20(zxw4000, zxw3000)
new_esEs21(zxw4001, zxw3001, ty_Bool) → new_esEs9(zxw4001, zxw3001)
new_esEs5(@3(zxw4000, zxw4001, zxw4002), @3(zxw3000, zxw3001, zxw3002), bh, ca, cb) → new_asAs(new_esEs12(zxw4000, zxw3000, bh), new_asAs(new_esEs11(zxw4001, zxw3001, ca), new_esEs10(zxw4002, zxw3002, cb)))
new_esEs16(:(zxw4000, zxw4001), [], dad) → False
new_esEs16([], :(zxw3000, zxw3001), dad) → False
new_lt10(zxw49000, zxw50000, ty_Integer) → new_lt5(zxw49000, zxw50000)
new_lt6(zxw49000, zxw50000) → new_esEs8(new_compare12(zxw49000, zxw50000), LT)
new_esEs29(zxw400, zxw300, app(app(ty_Either, cdc), cca)) → new_esEs6(zxw400, zxw300, cdc, cca)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_ltEs4(LT, GT) → True
new_esEs23(zxw49000, zxw50000, ty_Double) → new_esEs18(zxw49000, zxw50000)
new_compare25(zxw49000, zxw50000, False, be, bf) → new_compare15(zxw49000, zxw50000, new_ltEs7(zxw49000, zxw50000, be, bf), be, bf)
new_esEs29(zxw400, zxw300, app(app(app(ty_@3, bh), ca), cb)) → new_esEs5(zxw400, zxw300, bh, ca, cb)
new_lt19(zxw49001, zxw50001, app(app(ty_Either, cgg), cgh)) → new_lt17(zxw49001, zxw50001, cgg, cgh)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_esEs6(Left(zxw4000), Left(zxw3000), app(ty_Maybe, cbh), cca) → new_esEs7(zxw4000, zxw3000, cbh)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Ordering, cca) → new_esEs8(zxw4000, zxw3000)
new_esEs16(:(zxw4000, zxw4001), :(zxw3000, zxw3001), dad) → new_asAs(new_esEs28(zxw4000, zxw3000, dad), new_esEs16(zxw4001, zxw3001, dad))
new_ltEs8(Just(zxw49000), Just(zxw50000), app(ty_Ratio, hg)) → new_ltEs17(zxw49000, zxw50000, hg)
new_compare0(:(zxw49000, zxw49001), :(zxw50000, zxw50001), bhg) → new_primCompAux1(zxw49000, zxw50000, new_compare0(zxw49001, zxw50001, bhg), bhg)
new_esEs11(zxw4001, zxw3001, app(ty_Maybe, df)) → new_esEs7(zxw4001, zxw3001, df)
new_esEs6(Right(zxw4000), Right(zxw3000), cdc, app(app(ty_@2, ced), cee)) → new_esEs4(zxw4000, zxw3000, ced, cee)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Float) → new_ltEs6(zxw49000, zxw50000)
new_compare15(zxw49000, zxw50000, False, be, bf) → GT
new_compare29(zxw49000, zxw50000, app(app(ty_Either, cag), cah)) → new_compare32(zxw49000, zxw50000, cag, cah)
new_lt20(zxw49000, zxw50000, ty_Float) → new_lt7(zxw49000, zxw50000)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Char) → new_esEs15(zxw4000, zxw3000)
new_esEs23(zxw49000, zxw50000, ty_Int) → new_esEs13(zxw49000, zxw50000)
new_esEs30(zxw20, zxw15, app(ty_[], bdc)) → new_esEs16(zxw20, zxw15, bdc)
new_esEs7(Just(zxw4000), Just(zxw3000), app(app(app(ty_@3, bgh), bha), bhb)) → new_esEs5(zxw4000, zxw3000, bgh, bha, bhb)
new_esEs9(True, False) → False
new_esEs9(False, True) → False
new_compare29(zxw49000, zxw50000, app(ty_Ratio, cba)) → new_compare8(zxw49000, zxw50000, cba)
new_esEs10(zxw4002, zxw3002, app(app(ty_@2, dd), de)) → new_esEs4(zxw4002, zxw3002, dd, de)
new_esEs11(zxw4001, zxw3001, app(ty_Ratio, dg)) → new_esEs14(zxw4001, zxw3001, dg)
new_compare29(zxw49000, zxw50000, ty_Ordering) → new_compare6(zxw49000, zxw50000)
new_esEs21(zxw4001, zxw3001, ty_Integer) → new_esEs17(zxw4001, zxw3001)
new_esEs27(zxw49000, zxw50000, ty_Double) → new_esEs18(zxw49000, zxw50000)
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs27(zxw49000, zxw50000, app(ty_Ratio, dac)) → new_esEs14(zxw49000, zxw50000, dac)
new_ltEs4(LT, EQ) → True
new_esEs6(Right(zxw4000), Right(zxw3000), cdc, ty_Char) → new_esEs15(zxw4000, zxw3000)
new_esEs10(zxw4002, zxw3002, ty_Double) → new_esEs18(zxw4002, zxw3002)
new_compare31(@0, @0) → EQ
new_esEs12(zxw4000, zxw3000, app(app(ty_Either, fg), fh)) → new_esEs6(zxw4000, zxw3000, fg, fh)
new_ltEs8(Just(zxw49000), Just(zxw50000), app(ty_Maybe, gh)) → new_ltEs8(zxw49000, zxw50000, gh)
new_lt19(zxw49001, zxw50001, ty_Bool) → new_lt13(zxw49001, zxw50001)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbf, app(app(ty_Either, dcf), dcg)) → new_ltEs7(zxw49000, zxw50000, dcf, dcg)
new_esEs28(zxw4000, zxw3000, app(app(ty_@2, dea), deb)) → new_esEs4(zxw4000, zxw3000, dea, deb)
new_compare9(Integer(zxw49000), Integer(zxw50000)) → new_primCmpInt(zxw49000, zxw50000)
new_asAs(False, zxw187) → False
new_primMulInt(Neg(zxw40010), Pos(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Double) → new_esEs18(zxw4000, zxw3000)
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Ordering) → new_ltEs4(zxw49000, zxw50000)
new_esEs21(zxw4001, zxw3001, ty_Ordering) → new_esEs8(zxw4001, zxw3001)
new_primCmpNat2(zxw4900, Zero) → GT
new_ltEs20(zxw49002, zxw50002, ty_Double) → new_ltEs11(zxw49002, zxw50002)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Char, cca) → new_esEs15(zxw4000, zxw3000)
new_esEs26(zxw49001, zxw50001, app(ty_Maybe, cgb)) → new_esEs7(zxw49001, zxw50001, cgb)
new_esEs10(zxw4002, zxw3002, ty_@0) → new_esEs20(zxw4002, zxw3002)
new_lt19(zxw49001, zxw50001, ty_Double) → new_lt8(zxw49001, zxw50001)
new_esEs28(zxw4000, zxw3000, ty_Double) → new_esEs18(zxw4000, zxw3000)
new_compare110(zxw49000, zxw50000, True, bfh, bga, bgb) → LT
new_esEs24(zxw4001, zxw3001, ty_Integer) → new_esEs17(zxw4001, zxw3001)
new_lt19(zxw49001, zxw50001, app(ty_Maybe, cgb)) → new_lt12(zxw49001, zxw50001, cgb)
new_ltEs18(zxw49001, zxw50001, app(ty_Ratio, bff)) → new_ltEs17(zxw49001, zxw50001, bff)
new_ltEs18(zxw49001, zxw50001, ty_Char) → new_ltEs12(zxw49001, zxw50001)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Float, cca) → new_esEs19(zxw4000, zxw3000)
new_esEs21(zxw4001, zxw3001, ty_Int) → new_esEs13(zxw4001, zxw3001)
new_lt20(zxw49000, zxw50000, app(ty_Ratio, dac)) → new_lt18(zxw49000, zxw50000, dac)
new_ltEs19(zxw4900, zxw5000, ty_@0) → new_ltEs14(zxw4900, zxw5000)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbf, ty_Double) → new_ltEs11(zxw49000, zxw50000)
new_lt17(zxw49000, zxw50000, be, bf) → new_esEs8(new_compare32(zxw49000, zxw50000, be, bf), LT)
new_esEs9(False, False) → True
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Int) → new_ltEs10(zxw49000, zxw50000)
new_esEs30(zxw20, zxw15, ty_Int) → new_esEs13(zxw20, zxw15)
new_ltEs19(zxw4900, zxw5000, ty_Bool) → new_ltEs5(zxw4900, zxw5000)
new_compare29(zxw49000, zxw50000, ty_Integer) → new_compare9(zxw49000, zxw50000)
new_esEs29(zxw400, zxw300, ty_Float) → new_esEs19(zxw400, zxw300)
new_lt20(zxw49000, zxw50000, app(app(app(ty_@3, chf), chg), chh)) → new_lt16(zxw49000, zxw50000, chf, chg, chh)
new_esEs4(@2(zxw4000, zxw4001), @2(zxw3000, zxw3001), baa, bab) → new_asAs(new_esEs22(zxw4000, zxw3000, baa), new_esEs21(zxw4001, zxw3001, bab))
new_ltEs20(zxw49002, zxw50002, app(app(ty_Either, cfe), cff)) → new_ltEs7(zxw49002, zxw50002, cfe, cff)
new_esEs27(zxw49000, zxw50000, app(app(ty_@2, chb), chc)) → new_esEs4(zxw49000, zxw50000, chb, chc)
new_lt20(zxw49000, zxw50000, ty_Integer) → new_lt5(zxw49000, zxw50000)
new_compare35(zxw400, h) → new_compare26(Just(zxw400), Nothing, False, h)
new_ltEs18(zxw49001, zxw50001, app(ty_Maybe, beg)) → new_ltEs8(zxw49001, zxw50001, beg)
new_compare8(:%(zxw49000, zxw49001), :%(zxw50000, zxw50001), ty_Integer) → new_compare9(new_sr0(zxw49000, zxw50001), new_sr0(zxw50000, zxw49001))
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Float, cbg) → new_ltEs6(zxw49000, zxw50000)
new_ltEs4(LT, LT) → True
new_esEs16([], [], dad) → True
new_ltEs20(zxw49002, zxw50002, ty_Int) → new_ltEs10(zxw49002, zxw50002)
new_ltEs8(Nothing, Nothing, ge) → True
new_lt10(zxw49000, zxw50000, ty_Char) → new_lt6(zxw49000, zxw50000)
new_lt10(zxw49000, zxw50000, ty_Bool) → new_lt13(zxw49000, zxw50000)
new_esEs22(zxw4000, zxw3000, app(app(ty_Either, bcc), bcd)) → new_esEs6(zxw4000, zxw3000, bcc, bcd)
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_lt5(zxw49000, zxw50000) → new_esEs8(new_compare9(zxw49000, zxw50000), LT)
new_esEs26(zxw49001, zxw50001, ty_Float) → new_esEs19(zxw49001, zxw50001)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Int, cca) → new_esEs13(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_esEs10(zxw4002, zxw3002, ty_Int) → new_esEs13(zxw4002, zxw3002)
new_lt10(zxw49000, zxw50000, app(ty_[], bg)) → new_lt9(zxw49000, zxw50000, bg)
new_esEs12(zxw4000, zxw3000, app(ty_Ratio, fa)) → new_esEs14(zxw4000, zxw3000, fa)
new_ltEs15(@3(zxw49000, zxw49001, zxw49002), @3(zxw50000, zxw50001, zxw50002), cbc, cbd, cbe) → new_pePe(new_lt20(zxw49000, zxw50000, cbc), new_asAs(new_esEs27(zxw49000, zxw50000, cbc), new_pePe(new_lt19(zxw49001, zxw50001, cbd), new_asAs(new_esEs26(zxw49001, zxw50001, cbd), new_ltEs20(zxw49002, zxw50002, cbe)))))
new_ltEs10(zxw4900, zxw5000) → new_fsEs(new_compare7(zxw4900, zxw5000))
new_esEs30(zxw20, zxw15, ty_Ordering) → new_esEs8(zxw20, zxw15)
new_esEs10(zxw4002, zxw3002, app(ty_Ratio, cd)) → new_esEs14(zxw4002, zxw3002, cd)
new_ltEs12(zxw4900, zxw5000) → new_fsEs(new_compare12(zxw4900, zxw5000))
new_esEs10(zxw4002, zxw3002, ty_Ordering) → new_esEs8(zxw4002, zxw3002)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbf, ty_Float) → new_ltEs6(zxw49000, zxw50000)
new_esEs23(zxw49000, zxw50000, app(ty_[], bg)) → new_esEs16(zxw49000, zxw50000, bg)
new_esEs11(zxw4001, zxw3001, ty_Integer) → new_esEs17(zxw4001, zxw3001)
new_esEs26(zxw49001, zxw50001, app(app(ty_Either, cgg), cgh)) → new_esEs6(zxw49001, zxw50001, cgg, cgh)
new_compare16(Double(zxw49000, zxw49001), Double(zxw50000, zxw50001)) → new_compare7(new_sr(zxw49000, zxw50000), new_sr(zxw49001, zxw50001))
new_compare0([], :(zxw50000, zxw50001), bhg) → LT
new_primPlusNat1(Zero, Zero) → Zero
new_esEs12(zxw4000, zxw3000, ty_Ordering) → new_esEs8(zxw4000, zxw3000)
new_lt10(zxw49000, zxw50000, ty_@0) → new_lt15(zxw49000, zxw50000)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Char) → new_ltEs12(zxw49000, zxw50000)
new_asAs(True, zxw187) → zxw187
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_esEs30(zxw20, zxw15, ty_Integer) → new_esEs17(zxw20, zxw15)
new_esEs26(zxw49001, zxw50001, app(app(app(ty_@3, cgd), cge), cgf)) → new_esEs5(zxw49001, zxw50001, cgd, cge, cgf)
new_esEs10(zxw4002, zxw3002, app(app(ty_Either, db), dc)) → new_esEs6(zxw4002, zxw3002, db, dc)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Integer) → new_ltEs16(zxw49000, zxw50000)
new_compare30(zxw49000, zxw50000, gc, gd) → new_compare27(zxw49000, zxw50000, new_esEs4(zxw49000, zxw50000, gc, gd), gc, gd)
new_compare29(zxw49000, zxw50000, ty_Bool) → new_compare18(zxw49000, zxw50000)
new_fsEs(zxw202) → new_not(new_esEs8(zxw202, GT))
new_esEs23(zxw49000, zxw50000, app(app(app(ty_@3, bfh), bga), bgb)) → new_esEs5(zxw49000, zxw50000, bfh, bga, bgb)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Float) → new_esEs19(zxw4000, zxw3000)
new_compare10(zxw49000, zxw50000, True) → LT
new_esEs29(zxw400, zxw300, app(ty_Ratio, cbb)) → new_esEs14(zxw400, zxw300, cbb)
new_esEs30(zxw20, zxw15, app(app(app(ty_@3, bdd), bde), bdf)) → new_esEs5(zxw20, zxw15, bdd, bde, bdf)
new_compare29(zxw49000, zxw50000, app(ty_Maybe, cab)) → new_compare19(zxw49000, zxw50000, cab)
new_ltEs4(GT, GT) → True
new_esEs26(zxw49001, zxw50001, ty_@0) → new_esEs20(zxw49001, zxw50001)
new_compare110(zxw49000, zxw50000, False, bfh, bga, bgb) → GT
new_ltEs7(Left(zxw49000), Left(zxw50000), app(ty_Ratio, dbf), cbg) → new_ltEs17(zxw49000, zxw50000, dbf)
new_compare10(zxw49000, zxw50000, False) → GT
new_ltEs8(Just(zxw49000), Just(zxw50000), app(app(app(ty_@3, hb), hc), hd)) → new_ltEs15(zxw49000, zxw50000, hb, hc, hd)
new_esEs21(zxw4001, zxw3001, app(ty_[], bae)) → new_esEs16(zxw4001, zxw3001, bae)
new_compare18(zxw49000, zxw50000) → new_compare24(zxw49000, zxw50000, new_esEs9(zxw49000, zxw50000))
new_esEs6(Right(zxw4000), Right(zxw3000), cdc, ty_Ordering) → new_esEs8(zxw4000, zxw3000)
new_esEs6(Left(zxw4000), Left(zxw3000), app(ty_[], ccc), cca) → new_esEs16(zxw4000, zxw3000, ccc)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs6(Right(zxw4000), Right(zxw3000), cdc, app(app(app(ty_@3, cdg), cdh), cea)) → new_esEs5(zxw4000, zxw3000, cdg, cdh, cea)
new_primCompAux0(zxw218, EQ) → zxw218
new_esEs29(zxw400, zxw300, ty_Ordering) → new_esEs8(zxw400, zxw300)
new_lt20(zxw49000, zxw50000, app(ty_Maybe, chd)) → new_lt12(zxw49000, zxw50000, chd)
new_esEs12(zxw4000, zxw3000, app(app(ty_@2, ga), gb)) → new_esEs4(zxw4000, zxw3000, ga, gb)
new_ltEs19(zxw4900, zxw5000, app(ty_[], bhg)) → new_ltEs13(zxw4900, zxw5000, bhg)
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_esEs22(zxw4000, zxw3000, app(ty_Maybe, bbe)) → new_esEs7(zxw4000, zxw3000, bbe)
new_esEs30(zxw20, zxw15, ty_Char) → new_esEs15(zxw20, zxw15)
new_esEs30(zxw20, zxw15, app(app(ty_@2, bea), beb)) → new_esEs4(zxw20, zxw15, bea, beb)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbf, ty_@0) → new_ltEs14(zxw49000, zxw50000)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_compare8(:%(zxw49000, zxw49001), :%(zxw50000, zxw50001), ty_Int) → new_compare7(new_sr(zxw49000, zxw50001), new_sr(zxw50000, zxw49001))
new_ltEs17(zxw4900, zxw5000, hh) → new_fsEs(new_compare8(zxw4900, zxw5000, hh))
new_not(True) → False

The set Q consists of the following terms:

new_esEs17(Integer(x0), Integer(x1))
new_esEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Integer)
new_lt10(x0, x1, ty_Double)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_compare18(x0, x1)
new_compare29(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Double)
new_pePe(False, x0)
new_lt10(x0, x1, app(app(ty_Either, x2), x3))
new_lt17(x0, x1, x2, x3)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Left(x0), Left(x1), ty_Bool, x2)
new_compare7(x0, x1)
new_esEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_compare110(x0, x1, False, x2, x3, x4)
new_primMulNat0(Succ(x0), Zero)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs7(Just(x0), Just(x1), ty_Double)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_ltEs8(Just(x0), Just(x1), ty_Integer)
new_esEs10(x0, x1, ty_Int)
new_ltEs10(x0, x1)
new_esEs28(x0, x1, ty_Int)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs12(x0, x1, ty_Char)
new_compare25(x0, x1, True, x2, x3)
new_primMulNat0(Succ(x0), Succ(x1))
new_ltEs7(Left(x0), Left(x1), ty_Integer, x2)
new_esEs6(Left(x0), Left(x1), ty_Int, x2)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Int)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs16(x0, x1)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_compare13(x0, x1, True)
new_esEs10(x0, x1, ty_Ordering)
new_compare29(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs19(x0, x1, ty_Float)
new_compare0([], :(x0, x1), x2)
new_esEs11(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_Int)
new_esEs6(Left(x0), Left(x1), ty_@0, x2)
new_ltEs8(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare11(x0, x1, True, x2)
new_ltEs19(x0, x1, ty_Ordering)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs8(GT, GT)
new_compare11(x0, x1, False, x2)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_compare17(x0, x1, True, x2, x3)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCompAux1(x0, x1, x2, x3)
new_esEs8(LT, LT)
new_esEs29(x0, x1, ty_@0)
new_compare29(x0, x1, ty_Double)
new_esEs18(Double(x0, x1), Double(x2, x3))
new_primCmpNat0(Zero, x0)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_lt11(x0, x1, x2, x3)
new_ltEs8(Just(x0), Just(x1), ty_Bool)
new_esEs11(x0, x1, ty_@0)
new_primCmpNat1(Zero, Succ(x0))
new_esEs25(x0, x1, ty_Int)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_sr(x0, x1)
new_ltEs5(False, False)
new_ltEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_compare6(x0, x1)
new_lt10(x0, x1, ty_Ordering)
new_esEs6(Right(x0), Left(x1), x2, x3)
new_esEs6(Left(x0), Right(x1), x2, x3)
new_compare29(x0, x1, ty_Int)
new_esEs30(x0, x1, ty_Bool)
new_ltEs15(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs26(x0, x1, ty_Integer)
new_primEqNat0(Zero, Succ(x0))
new_primCmpNat1(Zero, Zero)
new_esEs7(Nothing, Nothing, x0)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs7(Left(x0), Left(x1), ty_Bool, x2)
new_compare16(Double(x0, x1), Double(x2, x3))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_lt7(x0, x1)
new_esEs28(x0, x1, ty_@0)
new_ltEs20(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Integer)
new_esEs16(:(x0, x1), :(x2, x3), x4)
new_esEs23(x0, x1, ty_Integer)
new_esEs11(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Double)
new_ltEs19(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_Char)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_compare15(x0, x1, True, x2, x3)
new_esEs24(x0, x1, ty_Int)
new_esEs6(Left(x0), Left(x1), ty_Char, x2)
new_esEs6(Left(x0), Left(x1), ty_Integer, x2)
new_primEqNat0(Zero, Zero)
new_compare32(x0, x1, x2, x3)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs8(Just(x0), Just(x1), app(ty_Maybe, x2))
new_compare36(x0, x1, x2)
new_ltEs8(Just(x0), Just(x1), ty_Double)
new_ltEs8(Just(x0), Just(x1), ty_Ordering)
new_ltEs19(x0, x1, ty_@0)
new_compare110(x0, x1, True, x2, x3, x4)
new_compare24(x0, x1, False)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs7(Just(x0), Nothing, x1)
new_esEs29(x0, x1, ty_Bool)
new_esEs9(True, True)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_lt18(x0, x1, x2)
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt4(x0, x1)
new_primMulNat0(Zero, Zero)
new_ltEs13(x0, x1, x2)
new_esEs23(x0, x1, ty_Char)
new_esEs30(x0, x1, ty_Ordering)
new_esEs10(x0, x1, ty_@0)
new_lt10(x0, x1, app(ty_Ratio, x2))
new_lt10(x0, x1, ty_Char)
new_esEs30(x0, x1, ty_Int)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_Integer)
new_fsEs(x0)
new_ltEs4(GT, GT)
new_lt8(x0, x1)
new_esEs30(x0, x1, ty_@0)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs10(x0, x1, ty_Float)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs28(x0, x1, ty_Double)
new_esEs29(x0, x1, ty_Char)
new_compare29(x0, x1, app(ty_[], x2))
new_esEs6(Right(x0), Right(x1), x2, ty_Float)
new_compare27(x0, x1, True, x2, x3)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_lt10(x0, x1, ty_Int)
new_esEs10(x0, x1, ty_Bool)
new_lt16(x0, x1, x2, x3, x4)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs23(x0, x1, ty_Ordering)
new_esEs7(Just(x0), Just(x1), ty_Int)
new_esEs10(x0, x1, ty_Char)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_lt10(x0, x1, app(ty_[], x2))
new_compare33(x0)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_pePe(True, x0)
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, ty_Int)
new_primPlusNat0(Zero, x0)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_lt10(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, ty_Int)
new_compare210(x0, x1, True, x2, x3, x4)
new_lt6(x0, x1)
new_esEs26(x0, x1, ty_Bool)
new_compare24(x0, x1, True)
new_ltEs18(x0, x1, ty_Integer)
new_compare15(x0, x1, False, x2, x3)
new_compare14(Float(x0, x1), Float(x2, x3))
new_ltEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(x0, x1)
new_esEs29(x0, x1, ty_Integer)
new_esEs12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primPlusNat1(Zero, Zero)
new_primCompAux0(x0, GT)
new_compare23(x0, x1, True)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_lt19(x0, x1, app(ty_[], x2))
new_lt15(x0, x1)
new_ltEs7(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs29(x0, x1, ty_Ordering)
new_compare19(x0, x1, x2)
new_compare13(x0, x1, False)
new_compare26(Nothing, Just(x0), False, x1)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_lt20(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_@0)
new_compare30(x0, x1, x2, x3)
new_primPlusNat0(Succ(x0), x1)
new_esEs12(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs4(EQ, EQ)
new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs19(x0, x1, ty_Char)
new_ltEs7(Right(x0), Right(x1), x2, ty_Char)
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_ltEs11(x0, x1)
new_esEs12(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Integer)
new_compare29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Char)
new_esEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs8(Nothing, Just(x0), x1)
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs8(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Just(x0), Just(x1), ty_Char)
new_ltEs7(Left(x0), Left(x1), ty_@0, x2)
new_lt9(x0, x1, x2)
new_esEs10(x0, x1, app(ty_[], x2))
new_esEs12(x0, x1, ty_Float)
new_compare31(@0, @0)
new_esEs7(Just(x0), Just(x1), ty_Float)
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs16([], :(x0, x1), x2)
new_primCmpNat2(x0, Zero)
new_ltEs4(LT, EQ)
new_ltEs4(EQ, LT)
new_esEs12(x0, x1, ty_Int)
new_lt19(x0, x1, ty_Double)
new_esEs6(Right(x0), Right(x1), x2, ty_Integer)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_primMulInt(Pos(x0), Pos(x1))
new_lt20(x0, x1, ty_Bool)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_ltEs7(Right(x0), Right(x1), x2, ty_Int)
new_ltEs18(x0, x1, app(ty_[], x2))
new_esEs30(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_@0)
new_esEs10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs7(Right(x0), Right(x1), x2, ty_Double)
new_asAs(True, x0)
new_primEqNat0(Succ(x0), Zero)
new_compare26(Just(x0), Nothing, False, x1)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs7(Left(x0), Left(x1), ty_Int, x2)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_esEs12(x0, x1, app(ty_[], x2))
new_esEs13(x0, x1)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_ltEs7(Left(x0), Right(x1), x2, x3)
new_ltEs7(Right(x0), Left(x1), x2, x3)
new_esEs14(:%(x0, x1), :%(x2, x3), x4)
new_compare26(x0, x1, True, x2)
new_esEs21(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Integer)
new_ltEs7(Left(x0), Left(x1), ty_Double, x2)
new_ltEs8(Nothing, Nothing, x0)
new_lt20(x0, x1, ty_@0)
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_Bool)
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Char)
new_compare26(Just(x0), Just(x1), False, x2)
new_esEs28(x0, x1, ty_Ordering)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, app(ty_Ratio, x2))
new_compare34(x0, x1)
new_lt20(x0, x1, ty_Ordering)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_lt12(x0, x1, x2)
new_esEs10(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_esEs12(x0, x1, app(ty_Maybe, x2))
new_esEs30(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, ty_Bool)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs27(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_Double)
new_esEs25(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(ty_[], x2))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_lt10(x0, x1, ty_Bool)
new_primPlusNat1(Succ(x0), Zero)
new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs22(x0, x1, ty_Float)
new_ltEs4(LT, LT)
new_esEs10(x0, x1, ty_Integer)
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Integer)
new_compare29(x0, x1, app(app(ty_@2, x2), x3))
new_compare23(x0, x1, False)
new_esEs21(x0, x1, app(ty_[], x2))
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs11(x0, x1, ty_Bool)
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_compare29(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_Double)
new_esEs21(x0, x1, ty_Bool)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, ty_Double)
new_esEs26(x0, x1, ty_Ordering)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs7(Nothing, Just(x0), x1)
new_primPlusNat1(Zero, Succ(x0))
new_ltEs12(x0, x1)
new_compare10(x0, x1, False)
new_lt10(x0, x1, app(app(ty_@2, x2), x3))
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Left(x0), Left(x1), ty_Float, x2)
new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_primCmpNat0(Succ(x0), x1)
new_lt10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, ty_@0)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs8(GT, EQ)
new_esEs8(EQ, GT)
new_esEs22(x0, x1, ty_Bool)
new_lt19(x0, x1, ty_Float)
new_lt19(x0, x1, ty_Integer)
new_ltEs8(Just(x0), Just(x1), ty_Char)
new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Left(x0), Left(x1), ty_Double, x2)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_ltEs8(Just(x0), Just(x1), ty_Float)
new_lt5(x0, x1)
new_compare29(x0, x1, ty_Ordering)
new_ltEs18(x0, x1, ty_Bool)
new_compare28(x0, x1, x2, x3, x4)
new_esEs11(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_@0)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, ty_Int)
new_esEs11(x0, x1, ty_Char)
new_esEs10(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Float)
new_lt19(x0, x1, ty_Ordering)
new_compare29(x0, x1, ty_Integer)
new_compare25(x0, x1, False, x2, x3)
new_esEs6(Right(x0), Right(x1), x2, ty_Char)
new_esEs26(x0, x1, app(ty_[], x2))
new_ltEs18(x0, x1, ty_Float)
new_ltEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs9(False, False)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs21(x0, x1, ty_Double)
new_esEs12(x0, x1, ty_Ordering)
new_ltEs8(Just(x0), Nothing, x1)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs22(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpNat1(Succ(x0), Succ(x1))
new_esEs10(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_@0)
new_ltEs6(x0, x1)
new_lt10(x0, x1, ty_Float)
new_esEs22(x0, x1, ty_Int)
new_ltEs7(Left(x0), Left(x1), ty_Char, x2)
new_compare17(x0, x1, False, x2, x3)
new_ltEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs21(x0, x1, ty_Float)
new_esEs29(x0, x1, ty_Double)
new_primCompAux0(x0, EQ)
new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare26(Nothing, Nothing, False, x0)
new_compare27(x0, x1, False, x2, x3)
new_esEs21(x0, x1, ty_Integer)
new_primCmpNat1(Succ(x0), Zero)
new_ltEs18(x0, x1, ty_@0)
new_esEs22(x0, x1, ty_Double)
new_ltEs7(Right(x0), Right(x1), x2, ty_@0)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, ty_Bool)
new_esEs16([], [], x0)
new_compare29(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, app(ty_[], x2))
new_lt13(x0, x1)
new_esEs23(x0, x1, ty_Bool)
new_ltEs5(True, True)
new_ltEs7(Right(x0), Right(x1), x2, ty_Integer)
new_lt19(x0, x1, ty_Int)
new_compare35(x0, x1)
new_lt19(x0, x1, ty_Char)
new_ltEs4(EQ, GT)
new_ltEs4(GT, EQ)
new_esEs6(Right(x0), Right(x1), x2, ty_@0)
new_not(True)
new_esEs11(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Float)
new_compare0(:(x0, x1), [], x2)
new_esEs28(x0, x1, ty_Char)
new_lt19(x0, x1, ty_@0)
new_esEs10(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, ty_Ordering)
new_ltEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs26(x0, x1, ty_Char)
new_ltEs18(x0, x1, ty_Int)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_ltEs20(x0, x1, ty_Ordering)
new_not(False)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_lt14(x0, x1)
new_compare12(Char(x0), Char(x1))
new_esEs15(Char(x0), Char(x1))
new_esEs11(x0, x1, app(ty_[], x2))
new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_compare10(x0, x1, True)
new_lt10(x0, x1, ty_@0)
new_asAs(False, x0)
new_esEs22(x0, x1, ty_Ordering)
new_ltEs18(x0, x1, ty_Char)
new_esEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs17(x0, x1, x2)
new_compare29(x0, x1, ty_Float)
new_lt19(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_Char)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_ltEs8(Just(x0), Just(x1), ty_@0)
new_esEs20(@0, @0)
new_ltEs8(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs7(Left(x0), Left(x1), ty_Float, x2)
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Int)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_esEs16(:(x0, x1), [], x2)
new_ltEs19(x0, x1, ty_Double)
new_esEs9(True, False)
new_esEs9(False, True)
new_esEs22(x0, x1, ty_Char)
new_ltEs7(Right(x0), Right(x1), x2, ty_Float)
new_ltEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare29(x0, x1, ty_Bool)
new_ltEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs30(x0, x1, ty_Double)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, ty_Integer)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs11(x0, x1, ty_Double)
new_ltEs20(x0, x1, ty_Float)
new_primCompAux0(x0, LT)
new_primCmpNat2(x0, Succ(x1))
new_esEs11(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs12(x0, x1, ty_Integer)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs10(x0, x1, ty_Double)
new_ltEs8(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_sr0(Integer(x0), Integer(x1))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs29(x0, x1, ty_Float)
new_ltEs8(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_primEqInt(Pos(Zero), Pos(Zero))
new_ltEs18(x0, x1, ty_Double)
new_esEs12(x0, x1, ty_Double)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_compare0(:(x0, x1), :(x2, x3), x4)
new_esEs29(x0, x1, ty_Int)
new_esEs12(x0, x1, ty_Bool)
new_compare9(Integer(x0), Integer(x1))
new_lt10(x0, x1, ty_Integer)
new_esEs30(x0, x1, ty_Char)
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs19(Float(x0, x1), Float(x2, x3))
new_primMulNat0(Zero, Succ(x0))
new_compare0([], [], x0)
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Just(x0), Just(x1), ty_@0)
new_ltEs4(GT, LT)
new_ltEs4(LT, GT)
new_ltEs5(True, False)
new_ltEs5(False, True)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs9(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs27(x0, x1, app(ty_[], x2))
new_ltEs8(Just(x0), Just(x1), ty_Int)
new_esEs12(x0, x1, app(app(ty_Either, x2), x3))
new_compare29(x0, x1, ty_@0)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Float)
new_esEs23(x0, x1, ty_Float)
new_compare210(x0, x1, False, x2, x3, x4)
new_esEs30(x0, x1, ty_Float)
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))

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

↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ 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_splitGT11(zxw31, zxw32, zxw33, zxw34, zxw400, True, h, ba) → new_splitGT0(zxw33, zxw400, h, ba)
new_splitGT20(zxw31, zxw32, zxw33, Branch(zxw340, zxw341, zxw342, zxw343, zxw344), zxw400, True, h, ba) → new_splitGT3(zxw340, zxw341, zxw342, zxw343, zxw344, Just(zxw400), h, ba)
new_splitGT0(Branch(zxw340, zxw341, zxw342, zxw343, zxw344), zxw400, h, ba) → new_splitGT3(zxw340, zxw341, zxw342, zxw343, zxw344, Just(zxw400), h, ba)
new_splitGT12(zxw30, zxw31, zxw32, zxw33, zxw34, zxw35, True, bb, bc) → new_splitGT0(zxw33, zxw35, bb, bc)
new_splitGT21(zxw30, zxw31, zxw32, zxw33, zxw34, zxw35, True, bb, bc) → new_splitGT0(zxw34, zxw35, bb, bc)
new_splitGT3(Nothing, zxw31, zxw32, zxw33, zxw34, Just(zxw400), h, ba) → new_splitGT20(zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs8(new_compare26(Just(zxw400), Nothing, False, h), GT), h, ba)
new_splitGT21(zxw30, zxw31, zxw32, zxw33, zxw34, zxw35, False, bb, bc) → new_splitGT12(zxw30, zxw31, zxw32, zxw33, zxw34, zxw35, new_esEs8(new_compare36(zxw35, zxw30, bb), LT), bb, bc)
new_splitGT3(Just(zxw300), zxw31, zxw32, zxw33, zxw34, Just(zxw400), h, ba) → new_splitGT21(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs8(new_compare26(Just(zxw400), Just(zxw300), new_esEs29(zxw400, zxw300, h), h), GT), h, ba)
new_splitGT20(zxw31, zxw32, zxw33, zxw34, zxw400, False, h, ba) → new_splitGT11(zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs8(new_compare35(zxw400, h), LT), h, ba)

The TRS R consists of the following rules:

new_compare36(zxw20, zxw15, bch) → new_compare26(Just(zxw20), Just(zxw15), new_esEs30(zxw20, zxw15, bch), bch)
new_esEs8(LT, LT) → True
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs30(zxw20, zxw15, ty_Bool) → new_esEs9(zxw20, zxw15)
new_esEs30(zxw20, zxw15, ty_Float) → new_esEs19(zxw20, zxw15)
new_esEs30(zxw20, zxw15, app(ty_Ratio, bdb)) → new_esEs14(zxw20, zxw15, bdb)
new_esEs30(zxw20, zxw15, ty_@0) → new_esEs20(zxw20, zxw15)
new_esEs30(zxw20, zxw15, ty_Double) → new_esEs18(zxw20, zxw15)
new_esEs30(zxw20, zxw15, app(app(ty_Either, bdg), bdh)) → new_esEs6(zxw20, zxw15, bdg, bdh)
new_esEs30(zxw20, zxw15, app(ty_Maybe, bda)) → new_esEs7(zxw20, zxw15, bda)
new_esEs30(zxw20, zxw15, app(ty_[], bdc)) → new_esEs16(zxw20, zxw15, bdc)
new_esEs30(zxw20, zxw15, ty_Int) → new_esEs13(zxw20, zxw15)
new_esEs30(zxw20, zxw15, ty_Ordering) → new_esEs8(zxw20, zxw15)
new_esEs30(zxw20, zxw15, ty_Integer) → new_esEs17(zxw20, zxw15)
new_esEs30(zxw20, zxw15, app(app(app(ty_@3, bdd), bde), bdf)) → new_esEs5(zxw20, zxw15, bdd, bde, bdf)
new_esEs30(zxw20, zxw15, ty_Char) → new_esEs15(zxw20, zxw15)
new_esEs30(zxw20, zxw15, app(app(ty_@2, bea), beb)) → new_esEs4(zxw20, zxw15, bea, beb)
new_compare26(Just(zxw4900), Just(zxw5000), False, bcg) → new_compare11(zxw4900, zxw5000, new_ltEs19(zxw4900, zxw5000, bcg), bcg)
new_compare26(zxw490, zxw500, True, bcg) → EQ
new_ltEs19(zxw4900, zxw5000, ty_Integer) → new_ltEs16(zxw4900, zxw5000)
new_ltEs19(zxw4900, zxw5000, ty_Double) → new_ltEs11(zxw4900, zxw5000)
new_ltEs19(zxw4900, zxw5000, ty_Int) → new_ltEs10(zxw4900, zxw5000)
new_ltEs19(zxw4900, zxw5000, app(app(app(ty_@3, cbc), cbd), cbe)) → new_ltEs15(zxw4900, zxw5000, cbc, cbd, cbe)
new_ltEs19(zxw4900, zxw5000, app(ty_Ratio, hh)) → new_ltEs17(zxw4900, zxw5000, hh)
new_ltEs19(zxw4900, zxw5000, ty_Ordering) → new_ltEs4(zxw4900, zxw5000)
new_ltEs19(zxw4900, zxw5000, ty_Char) → new_ltEs12(zxw4900, zxw5000)
new_ltEs19(zxw4900, zxw5000, app(app(ty_Either, cbf), cbg)) → new_ltEs7(zxw4900, zxw5000, cbf, cbg)
new_ltEs19(zxw4900, zxw5000, app(app(ty_@2, bec), bed)) → new_ltEs9(zxw4900, zxw5000, bec, bed)
new_ltEs19(zxw4900, zxw5000, ty_Float) → new_ltEs6(zxw4900, zxw5000)
new_ltEs19(zxw4900, zxw5000, app(ty_Maybe, ge)) → new_ltEs8(zxw4900, zxw5000, ge)
new_ltEs19(zxw4900, zxw5000, ty_@0) → new_ltEs14(zxw4900, zxw5000)
new_ltEs19(zxw4900, zxw5000, ty_Bool) → new_ltEs5(zxw4900, zxw5000)
new_ltEs19(zxw4900, zxw5000, app(ty_[], bhg)) → new_ltEs13(zxw4900, zxw5000, bhg)
new_compare11(zxw180, zxw181, True, bd) → LT
new_compare11(zxw180, zxw181, False, bd) → GT
new_ltEs13(zxw4900, zxw5000, bhg) → new_fsEs(new_compare0(zxw4900, zxw5000, bhg))
new_compare0([], [], bhg) → EQ
new_compare0(:(zxw49000, zxw49001), [], bhg) → GT
new_compare0(:(zxw49000, zxw49001), :(zxw50000, zxw50001), bhg) → new_primCompAux1(zxw49000, zxw50000, new_compare0(zxw49001, zxw50001, bhg), bhg)
new_compare0([], :(zxw50000, zxw50001), bhg) → LT
new_fsEs(zxw202) → new_not(new_esEs8(zxw202, GT))
new_esEs8(GT, GT) → True
new_esEs8(LT, GT) → False
new_esEs8(EQ, GT) → False
new_not(False) → True
new_not(True) → False
new_primCompAux1(zxw49000, zxw50000, zxw214, bhg) → new_primCompAux0(zxw214, new_compare29(zxw49000, zxw50000, bhg))
new_compare29(zxw49000, zxw50000, ty_Char) → new_compare12(zxw49000, zxw50000)
new_compare29(zxw49000, zxw50000, ty_Double) → new_compare16(zxw49000, zxw50000)
new_compare29(zxw49000, zxw50000, ty_@0) → new_compare31(zxw49000, zxw50000)
new_compare29(zxw49000, zxw50000, ty_Int) → new_compare7(zxw49000, zxw50000)
new_compare29(zxw49000, zxw50000, app(app(app(ty_@3, cad), cae), caf)) → new_compare28(zxw49000, zxw50000, cad, cae, caf)
new_compare29(zxw49000, zxw50000, app(ty_[], cac)) → new_compare0(zxw49000, zxw50000, cac)
new_compare29(zxw49000, zxw50000, app(app(ty_@2, bhh), caa)) → new_compare30(zxw49000, zxw50000, bhh, caa)
new_compare29(zxw49000, zxw50000, ty_Float) → new_compare14(zxw49000, zxw50000)
new_compare29(zxw49000, zxw50000, app(app(ty_Either, cag), cah)) → new_compare32(zxw49000, zxw50000, cag, cah)
new_compare29(zxw49000, zxw50000, app(ty_Ratio, cba)) → new_compare8(zxw49000, zxw50000, cba)
new_compare29(zxw49000, zxw50000, ty_Ordering) → new_compare6(zxw49000, zxw50000)
new_compare29(zxw49000, zxw50000, ty_Integer) → new_compare9(zxw49000, zxw50000)
new_compare29(zxw49000, zxw50000, ty_Bool) → new_compare18(zxw49000, zxw50000)
new_compare29(zxw49000, zxw50000, app(ty_Maybe, cab)) → new_compare19(zxw49000, zxw50000, cab)
new_primCompAux0(zxw218, GT) → GT
new_primCompAux0(zxw218, LT) → LT
new_primCompAux0(zxw218, EQ) → zxw218
new_compare19(zxw490, zxw500, bcg) → new_compare26(zxw490, zxw500, new_esEs7(zxw490, zxw500, bcg), bcg)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_esEs7(Just(zxw4000), Just(zxw3000), app(app(ty_@2, bhe), bhf)) → new_esEs4(zxw4000, zxw3000, bhe, bhf)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Bool) → new_esEs9(zxw4000, zxw3000)
new_esEs7(Just(zxw4000), Just(zxw3000), app(ty_Ratio, bgf)) → new_esEs14(zxw4000, zxw3000, bgf)
new_esEs7(Just(zxw4000), Just(zxw3000), app(ty_[], bgg)) → new_esEs16(zxw4000, zxw3000, bgg)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_@0) → new_esEs20(zxw4000, zxw3000)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Ordering) → new_esEs8(zxw4000, zxw3000)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Int) → new_esEs13(zxw4000, zxw3000)
new_esEs7(Nothing, Nothing, bgd) → True
new_esEs7(Just(zxw4000), Nothing, bgd) → False
new_esEs7(Nothing, Just(zxw3000), bgd) → False
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Char) → new_esEs15(zxw4000, zxw3000)
new_esEs7(Just(zxw4000), Just(zxw3000), app(app(app(ty_@3, bgh), bha), bhb)) → new_esEs5(zxw4000, zxw3000, bgh, bha, bhb)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Double) → new_esEs18(zxw4000, zxw3000)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Float) → new_esEs19(zxw4000, zxw3000)
new_compare26(Just(zxw4900), Nothing, False, bcg) → GT
new_compare26(Nothing, Just(zxw5000), False, bcg) → LT
new_compare26(Nothing, Nothing, False, bcg) → LT
new_esEs6(Left(zxw4000), Left(zxw3000), app(ty_Maybe, cbh), cca) → new_esEs7(zxw4000, zxw3000, cbh)
new_esEs7(Just(zxw4000), Just(zxw3000), app(ty_Maybe, bge)) → new_esEs7(zxw4000, zxw3000, bge)
new_esEs6(Right(zxw4000), Right(zxw3000), cdc, app(ty_Maybe, cdd)) → new_esEs7(zxw4000, zxw3000, cdd)
new_esEs6(Left(zxw4000), Left(zxw3000), app(app(ty_Either, ccg), cch), cca) → new_esEs6(zxw4000, zxw3000, ccg, cch)
new_esEs6(Right(zxw4000), Right(zxw3000), cdc, app(app(ty_Either, ceb), cec)) → new_esEs6(zxw4000, zxw3000, ceb, cec)
new_esEs7(Just(zxw4000), Just(zxw3000), app(app(ty_Either, bhc), bhd)) → new_esEs6(zxw4000, zxw3000, bhc, bhd)
new_esEs6(Right(zxw4000), Right(zxw3000), cdc, ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_esEs6(Right(zxw4000), Right(zxw3000), cdc, ty_Float) → new_esEs19(zxw4000, zxw3000)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Integer, cca) → new_esEs17(zxw4000, zxw3000)
new_esEs6(Right(zxw4000), Right(zxw3000), cdc, ty_Int) → new_esEs13(zxw4000, zxw3000)
new_esEs6(Right(zxw4000), Right(zxw3000), cdc, app(ty_Ratio, cde)) → new_esEs14(zxw4000, zxw3000, cde)
new_esEs6(Left(zxw4000), Left(zxw3000), app(app(ty_@2, cda), cdb), cca) → new_esEs4(zxw4000, zxw3000, cda, cdb)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Bool, cca) → new_esEs9(zxw4000, zxw3000)
new_esEs6(Right(zxw4000), Left(zxw3000), cdc, cca) → False
new_esEs6(Left(zxw4000), Right(zxw3000), cdc, cca) → False
new_esEs6(Left(zxw4000), Left(zxw3000), ty_@0, cca) → new_esEs20(zxw4000, zxw3000)
new_esEs6(Right(zxw4000), Right(zxw3000), cdc, ty_Bool) → new_esEs9(zxw4000, zxw3000)
new_esEs6(Left(zxw4000), Left(zxw3000), app(ty_Ratio, ccb), cca) → new_esEs14(zxw4000, zxw3000, ccb)
new_esEs6(Right(zxw4000), Right(zxw3000), cdc, app(ty_[], cdf)) → new_esEs16(zxw4000, zxw3000, cdf)
new_esEs6(Left(zxw4000), Left(zxw3000), app(app(app(ty_@3, ccd), cce), ccf), cca) → new_esEs5(zxw4000, zxw3000, ccd, cce, ccf)
new_esEs6(Right(zxw4000), Right(zxw3000), cdc, ty_@0) → new_esEs20(zxw4000, zxw3000)
new_esEs6(Right(zxw4000), Right(zxw3000), cdc, ty_Double) → new_esEs18(zxw4000, zxw3000)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Double, cca) → new_esEs18(zxw4000, zxw3000)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Ordering, cca) → new_esEs8(zxw4000, zxw3000)
new_esEs6(Right(zxw4000), Right(zxw3000), cdc, app(app(ty_@2, ced), cee)) → new_esEs4(zxw4000, zxw3000, ced, cee)
new_esEs6(Right(zxw4000), Right(zxw3000), cdc, ty_Char) → new_esEs15(zxw4000, zxw3000)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Char, cca) → new_esEs15(zxw4000, zxw3000)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Float, cca) → new_esEs19(zxw4000, zxw3000)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Int, cca) → new_esEs13(zxw4000, zxw3000)
new_esEs6(Right(zxw4000), Right(zxw3000), cdc, ty_Ordering) → new_esEs8(zxw4000, zxw3000)
new_esEs6(Left(zxw4000), Left(zxw3000), app(ty_[], ccc), cca) → new_esEs16(zxw4000, zxw3000, ccc)
new_esEs6(Right(zxw4000), Right(zxw3000), cdc, app(app(app(ty_@3, cdg), cdh), cea)) → new_esEs5(zxw4000, zxw3000, cdg, cdh, cea)
new_esEs5(@3(zxw4000, zxw4001, zxw4002), @3(zxw3000, zxw3001, zxw3002), bh, ca, cb) → new_asAs(new_esEs12(zxw4000, zxw3000, bh), new_asAs(new_esEs11(zxw4001, zxw3001, ca), new_esEs10(zxw4002, zxw3002, cb)))
new_esEs12(zxw4000, zxw3000, ty_Bool) → new_esEs9(zxw4000, zxw3000)
new_esEs12(zxw4000, zxw3000, ty_Char) → new_esEs15(zxw4000, zxw3000)
new_esEs12(zxw4000, zxw3000, app(ty_[], fb)) → new_esEs16(zxw4000, zxw3000, fb)
new_esEs12(zxw4000, zxw3000, ty_Int) → new_esEs13(zxw4000, zxw3000)
new_esEs12(zxw4000, zxw3000, ty_Double) → new_esEs18(zxw4000, zxw3000)
new_esEs12(zxw4000, zxw3000, app(ty_Maybe, eh)) → new_esEs7(zxw4000, zxw3000, eh)
new_esEs12(zxw4000, zxw3000, app(app(app(ty_@3, fc), fd), ff)) → new_esEs5(zxw4000, zxw3000, fc, fd, ff)
new_esEs12(zxw4000, zxw3000, ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_esEs12(zxw4000, zxw3000, ty_Float) → new_esEs19(zxw4000, zxw3000)
new_esEs12(zxw4000, zxw3000, ty_@0) → new_esEs20(zxw4000, zxw3000)
new_esEs12(zxw4000, zxw3000, app(app(ty_Either, fg), fh)) → new_esEs6(zxw4000, zxw3000, fg, fh)
new_esEs12(zxw4000, zxw3000, app(ty_Ratio, fa)) → new_esEs14(zxw4000, zxw3000, fa)
new_esEs12(zxw4000, zxw3000, ty_Ordering) → new_esEs8(zxw4000, zxw3000)
new_esEs12(zxw4000, zxw3000, app(app(ty_@2, ga), gb)) → new_esEs4(zxw4000, zxw3000, ga, gb)
new_esEs11(zxw4001, zxw3001, app(ty_[], dh)) → new_esEs16(zxw4001, zxw3001, dh)
new_esEs11(zxw4001, zxw3001, ty_Char) → new_esEs15(zxw4001, zxw3001)
new_esEs11(zxw4001, zxw3001, ty_Float) → new_esEs19(zxw4001, zxw3001)
new_esEs11(zxw4001, zxw3001, ty_Int) → new_esEs13(zxw4001, zxw3001)
new_esEs11(zxw4001, zxw3001, ty_Ordering) → new_esEs8(zxw4001, zxw3001)
new_esEs11(zxw4001, zxw3001, app(app(ty_@2, ef), eg)) → new_esEs4(zxw4001, zxw3001, ef, eg)
new_esEs11(zxw4001, zxw3001, app(app(app(ty_@3, ea), eb), ec)) → new_esEs5(zxw4001, zxw3001, ea, eb, ec)
new_esEs11(zxw4001, zxw3001, ty_Bool) → new_esEs9(zxw4001, zxw3001)
new_esEs11(zxw4001, zxw3001, ty_Double) → new_esEs18(zxw4001, zxw3001)
new_esEs11(zxw4001, zxw3001, ty_@0) → new_esEs20(zxw4001, zxw3001)
new_esEs11(zxw4001, zxw3001, app(app(ty_Either, ed), ee)) → new_esEs6(zxw4001, zxw3001, ed, ee)
new_esEs11(zxw4001, zxw3001, app(ty_Maybe, df)) → new_esEs7(zxw4001, zxw3001, df)
new_esEs11(zxw4001, zxw3001, app(ty_Ratio, dg)) → new_esEs14(zxw4001, zxw3001, dg)
new_esEs11(zxw4001, zxw3001, ty_Integer) → new_esEs17(zxw4001, zxw3001)
new_esEs10(zxw4002, zxw3002, app(ty_Maybe, cc)) → new_esEs7(zxw4002, zxw3002, cc)
new_esEs10(zxw4002, zxw3002, app(app(app(ty_@3, cf), cg), da)) → new_esEs5(zxw4002, zxw3002, cf, cg, da)
new_esEs10(zxw4002, zxw3002, ty_Integer) → new_esEs17(zxw4002, zxw3002)
new_esEs10(zxw4002, zxw3002, ty_Bool) → new_esEs9(zxw4002, zxw3002)
new_esEs10(zxw4002, zxw3002, ty_Float) → new_esEs19(zxw4002, zxw3002)
new_esEs10(zxw4002, zxw3002, ty_Char) → new_esEs15(zxw4002, zxw3002)
new_esEs10(zxw4002, zxw3002, app(ty_[], ce)) → new_esEs16(zxw4002, zxw3002, ce)
new_esEs10(zxw4002, zxw3002, app(app(ty_@2, dd), de)) → new_esEs4(zxw4002, zxw3002, dd, de)
new_esEs10(zxw4002, zxw3002, ty_Double) → new_esEs18(zxw4002, zxw3002)
new_esEs10(zxw4002, zxw3002, ty_@0) → new_esEs20(zxw4002, zxw3002)
new_esEs10(zxw4002, zxw3002, ty_Int) → new_esEs13(zxw4002, zxw3002)
new_esEs10(zxw4002, zxw3002, app(ty_Ratio, cd)) → new_esEs14(zxw4002, zxw3002, cd)
new_esEs10(zxw4002, zxw3002, ty_Ordering) → new_esEs8(zxw4002, zxw3002)
new_esEs10(zxw4002, zxw3002, app(app(ty_Either, db), dc)) → new_esEs6(zxw4002, zxw3002, db, dc)
new_asAs(False, zxw187) → False
new_asAs(True, zxw187) → zxw187
new_esEs8(EQ, EQ) → True
new_esEs8(LT, EQ) → False
new_esEs8(GT, EQ) → False
new_esEs14(:%(zxw4000, zxw4001), :%(zxw3000, zxw3001), cbb) → new_asAs(new_esEs25(zxw4000, zxw3000, cbb), new_esEs24(zxw4001, zxw3001, cbb))
new_esEs25(zxw4000, zxw3000, ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_esEs25(zxw4000, zxw3000, ty_Int) → new_esEs13(zxw4000, zxw3000)
new_esEs24(zxw4001, zxw3001, ty_Int) → new_esEs13(zxw4001, zxw3001)
new_esEs24(zxw4001, zxw3001, ty_Integer) → new_esEs17(zxw4001, zxw3001)
new_esEs17(Integer(zxw4000), Integer(zxw3000)) → new_primEqInt(zxw4000, zxw3000)
new_primEqInt(Neg(Succ(zxw40000)), Neg(Succ(zxw30000))) → new_primEqNat0(zxw40000, zxw30000)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Succ(zxw40000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(zxw30000))) → False
new_primEqInt(Pos(Succ(zxw40000)), Pos(Succ(zxw30000))) → new_primEqNat0(zxw40000, zxw30000)
new_primEqInt(Pos(Succ(zxw40000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(zxw30000))) → False
new_primEqInt(Pos(Succ(zxw40000)), Neg(zxw3000)) → False
new_primEqInt(Neg(Succ(zxw40000)), Pos(zxw3000)) → False
new_primEqInt(Pos(Zero), Neg(Succ(zxw30000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(zxw30000))) → False
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(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_esEs13(zxw400, zxw300) → new_primEqInt(zxw400, zxw300)
new_esEs20(@0, @0) → True
new_esEs18(Double(zxw4000, zxw4001), Double(zxw3000, zxw3001)) → new_esEs13(new_sr(zxw4000, zxw3000), new_sr(zxw4001, zxw3001))
new_sr(zxw4001, zxw3001) → new_primMulInt(zxw4001, zxw3001)
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Neg(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Pos(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulNat0(Zero, Zero) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_esEs4(@2(zxw4000, zxw4001), @2(zxw3000, zxw3001), baa, bab) → new_asAs(new_esEs22(zxw4000, zxw3000, baa), new_esEs21(zxw4001, zxw3001, bab))
new_esEs22(zxw4000, zxw3000, ty_@0) → new_esEs20(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Float) → new_esEs19(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, app(ty_Ratio, bbf)) → new_esEs14(zxw4000, zxw3000, bbf)
new_esEs22(zxw4000, zxw3000, app(app(ty_@2, bce), bcf)) → new_esEs4(zxw4000, zxw3000, bce, bcf)
new_esEs22(zxw4000, zxw3000, ty_Ordering) → new_esEs8(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Bool) → new_esEs9(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, app(app(app(ty_@3, bbh), bca), bcb)) → new_esEs5(zxw4000, zxw3000, bbh, bca, bcb)
new_esEs22(zxw4000, zxw3000, ty_Int) → new_esEs13(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Char) → new_esEs15(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, app(ty_[], bbg)) → new_esEs16(zxw4000, zxw3000, bbg)
new_esEs22(zxw4000, zxw3000, ty_Double) → new_esEs18(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, app(app(ty_Either, bcc), bcd)) → new_esEs6(zxw4000, zxw3000, bcc, bcd)
new_esEs22(zxw4000, zxw3000, ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, app(ty_Maybe, bbe)) → new_esEs7(zxw4000, zxw3000, bbe)
new_esEs21(zxw4001, zxw3001, ty_Double) → new_esEs18(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, app(ty_Ratio, bad)) → new_esEs14(zxw4001, zxw3001, bad)
new_esEs21(zxw4001, zxw3001, app(app(ty_Either, bba), bbb)) → new_esEs6(zxw4001, zxw3001, bba, bbb)
new_esEs21(zxw4001, zxw3001, ty_Char) → new_esEs15(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, ty_Float) → new_esEs19(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, ty_@0) → new_esEs20(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, app(app(app(ty_@3, baf), bag), bah)) → new_esEs5(zxw4001, zxw3001, baf, bag, bah)
new_esEs21(zxw4001, zxw3001, app(ty_Maybe, bac)) → new_esEs7(zxw4001, zxw3001, bac)
new_esEs21(zxw4001, zxw3001, app(app(ty_@2, bbc), bbd)) → new_esEs4(zxw4001, zxw3001, bbc, bbd)
new_esEs21(zxw4001, zxw3001, ty_Bool) → new_esEs9(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, ty_Integer) → new_esEs17(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, ty_Ordering) → new_esEs8(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, ty_Int) → new_esEs13(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, app(ty_[], bae)) → new_esEs16(zxw4001, zxw3001, bae)
new_esEs16(:(zxw4000, zxw4001), [], dad) → False
new_esEs16([], :(zxw3000, zxw3001), dad) → False
new_esEs16(:(zxw4000, zxw4001), :(zxw3000, zxw3001), dad) → new_asAs(new_esEs28(zxw4000, zxw3000, dad), new_esEs16(zxw4001, zxw3001, dad))
new_esEs16([], [], dad) → True
new_esEs28(zxw4000, zxw3000, ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, app(app(app(ty_@3, ddd), dde), ddf)) → new_esEs5(zxw4000, zxw3000, ddd, dde, ddf)
new_esEs28(zxw4000, zxw3000, ty_Bool) → new_esEs9(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_@0) → new_esEs20(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_Float) → new_esEs19(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, app(app(ty_Either, ddg), ddh)) → new_esEs6(zxw4000, zxw3000, ddg, ddh)
new_esEs28(zxw4000, zxw3000, ty_Char) → new_esEs15(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_Int) → new_esEs13(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_Ordering) → new_esEs8(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, app(ty_Ratio, ddb)) → new_esEs14(zxw4000, zxw3000, ddb)
new_esEs28(zxw4000, zxw3000, app(ty_[], ddc)) → new_esEs16(zxw4000, zxw3000, ddc)
new_esEs28(zxw4000, zxw3000, app(ty_Maybe, dda)) → new_esEs7(zxw4000, zxw3000, dda)
new_esEs28(zxw4000, zxw3000, app(app(ty_@2, dea), deb)) → new_esEs4(zxw4000, zxw3000, dea, deb)
new_esEs28(zxw4000, zxw3000, ty_Double) → new_esEs18(zxw4000, zxw3000)
new_esEs15(Char(zxw4000), Char(zxw3000)) → new_primEqNat0(zxw4000, zxw3000)
new_esEs19(Float(zxw4000, zxw4001), Float(zxw3000, zxw3001)) → new_esEs13(new_sr(zxw4000, zxw3000), new_sr(zxw4001, zxw3001))
new_esEs9(True, True) → True
new_esEs9(True, False) → False
new_esEs9(False, True) → False
new_esEs9(False, False) → True
new_compare18(zxw49000, zxw50000) → new_compare24(zxw49000, zxw50000, new_esEs9(zxw49000, zxw50000))
new_compare24(zxw49000, zxw50000, False) → new_compare13(zxw49000, zxw50000, new_ltEs5(zxw49000, zxw50000))
new_compare24(zxw49000, zxw50000, True) → EQ
new_ltEs5(True, False) → False
new_ltEs5(True, True) → True
new_ltEs5(False, False) → True
new_ltEs5(False, True) → True
new_compare13(zxw49000, zxw50000, False) → GT
new_compare13(zxw49000, zxw50000, True) → LT
new_compare9(Integer(zxw49000), Integer(zxw50000)) → new_primCmpInt(zxw49000, zxw50000)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_compare6(zxw49000, zxw50000) → new_compare23(zxw49000, zxw50000, new_esEs8(zxw49000, zxw50000))
new_compare23(zxw49000, zxw50000, True) → EQ
new_compare23(zxw49000, zxw50000, False) → new_compare10(zxw49000, zxw50000, new_ltEs4(zxw49000, zxw50000))
new_ltEs4(EQ, GT) → True
new_ltEs4(EQ, LT) → False
new_ltEs4(GT, EQ) → False
new_ltEs4(EQ, EQ) → True
new_ltEs4(GT, LT) → False
new_ltEs4(LT, GT) → True
new_ltEs4(LT, EQ) → True
new_ltEs4(LT, LT) → True
new_ltEs4(GT, GT) → True
new_compare10(zxw49000, zxw50000, True) → LT
new_compare10(zxw49000, zxw50000, False) → GT
new_compare8(:%(zxw49000, zxw49001), :%(zxw50000, zxw50001), ty_Integer) → new_compare9(new_sr0(zxw49000, zxw50001), new_sr0(zxw50000, zxw49001))
new_compare8(:%(zxw49000, zxw49001), :%(zxw50000, zxw50001), ty_Int) → new_compare7(new_sr(zxw49000, zxw50001), new_sr(zxw50000, zxw49001))
new_compare7(zxw49, zxw50) → new_primCmpInt(zxw49, zxw50)
new_sr0(Integer(zxw500000), Integer(zxw490010)) → Integer(new_primMulInt(zxw500000, zxw490010))
new_compare32(zxw49000, zxw50000, be, bf) → new_compare25(zxw49000, zxw50000, new_esEs6(zxw49000, zxw50000, be, bf), be, bf)
new_compare25(zxw49000, zxw50000, True, be, bf) → EQ
new_compare25(zxw49000, zxw50000, False, be, bf) → new_compare15(zxw49000, zxw50000, new_ltEs7(zxw49000, zxw50000, be, bf), be, bf)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_@0, cbg) → new_ltEs14(zxw49000, zxw50000)
new_ltEs7(Left(zxw49000), Right(zxw50000), cbf, cbg) → True
new_ltEs7(Left(zxw49000), Left(zxw50000), app(app(app(ty_@3, dba), dbb), dbc), cbg) → new_ltEs15(zxw49000, zxw50000, dba, dbb, dbc)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbf, app(app(ty_@2, dbg), dbh)) → new_ltEs9(zxw49000, zxw50000, dbg, dbh)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbf, app(ty_Ratio, dch)) → new_ltEs17(zxw49000, zxw50000, dch)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Char, cbg) → new_ltEs12(zxw49000, zxw50000)
new_ltEs7(Left(zxw49000), Left(zxw50000), app(app(ty_@2, dae), daf), cbg) → new_ltEs9(zxw49000, zxw50000, dae, daf)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbf, ty_Bool) → new_ltEs5(zxw49000, zxw50000)
new_ltEs7(Left(zxw49000), Left(zxw50000), app(app(ty_Either, dbd), dbe), cbg) → new_ltEs7(zxw49000, zxw50000, dbd, dbe)
new_ltEs7(Left(zxw49000), Left(zxw50000), app(ty_Maybe, dag), cbg) → new_ltEs8(zxw49000, zxw50000, dag)
new_ltEs8(Just(zxw49000), Just(zxw50000), app(app(ty_Either, he), hf)) → new_ltEs7(zxw49000, zxw50000, he, hf)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbf, app(ty_Maybe, dca)) → new_ltEs8(zxw49000, zxw50000, dca)
new_ltEs8(Just(zxw49000), Just(zxw50000), app(ty_Maybe, gh)) → new_ltEs8(zxw49000, zxw50000, gh)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbf, app(app(ty_Either, dcf), dcg)) → new_ltEs7(zxw49000, zxw50000, dcf, dcg)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbf, ty_Integer) → new_ltEs16(zxw49000, zxw50000)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbf, app(app(app(ty_@3, dcc), dcd), dce)) → new_ltEs15(zxw49000, zxw50000, dcc, dcd, dce)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Bool, cbg) → new_ltEs5(zxw49000, zxw50000)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Int, cbg) → new_ltEs10(zxw49000, zxw50000)
new_ltEs7(Right(zxw49000), Left(zxw50000), cbf, cbg) → False
new_ltEs7(Left(zxw49000), Left(zxw50000), app(ty_[], dah), cbg) → new_ltEs13(zxw49000, zxw50000, dah)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Integer, cbg) → new_ltEs16(zxw49000, zxw50000)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbf, app(ty_[], dcb)) → new_ltEs13(zxw49000, zxw50000, dcb)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Double, cbg) → new_ltEs11(zxw49000, zxw50000)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbf, ty_Ordering) → new_ltEs4(zxw49000, zxw50000)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Ordering, cbg) → new_ltEs4(zxw49000, zxw50000)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbf, ty_Char) → new_ltEs12(zxw49000, zxw50000)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbf, ty_Int) → new_ltEs10(zxw49000, zxw50000)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbf, ty_Double) → new_ltEs11(zxw49000, zxw50000)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Float, cbg) → new_ltEs6(zxw49000, zxw50000)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbf, ty_Float) → new_ltEs6(zxw49000, zxw50000)
new_ltEs7(Left(zxw49000), Left(zxw50000), app(ty_Ratio, dbf), cbg) → new_ltEs17(zxw49000, zxw50000, dbf)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbf, ty_@0) → new_ltEs14(zxw49000, zxw50000)
new_compare15(zxw49000, zxw50000, True, be, bf) → LT
new_compare15(zxw49000, zxw50000, False, be, bf) → GT
new_ltEs14(zxw4900, zxw5000) → new_fsEs(new_compare31(zxw4900, zxw5000))
new_compare31(@0, @0) → EQ
new_ltEs17(zxw4900, zxw5000, hh) → new_fsEs(new_compare8(zxw4900, zxw5000, hh))
new_ltEs6(zxw4900, zxw5000) → new_fsEs(new_compare14(zxw4900, zxw5000))
new_compare14(Float(zxw49000, zxw49001), Float(zxw50000, zxw50001)) → new_compare7(new_sr(zxw49000, zxw50000), new_sr(zxw49001, zxw50001))
new_ltEs11(zxw4900, zxw5000) → new_fsEs(new_compare16(zxw4900, zxw5000))
new_compare16(Double(zxw49000, zxw49001), Double(zxw50000, zxw50001)) → new_compare7(new_sr(zxw49000, zxw50000), new_sr(zxw49001, zxw50001))
new_ltEs10(zxw4900, zxw5000) → new_fsEs(new_compare7(zxw4900, zxw5000))
new_ltEs12(zxw4900, zxw5000) → new_fsEs(new_compare12(zxw4900, zxw5000))
new_compare12(Char(zxw49000), Char(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_ltEs16(zxw4900, zxw5000) → new_fsEs(new_compare9(zxw4900, zxw5000))
new_ltEs15(@3(zxw49000, zxw49001, zxw49002), @3(zxw50000, zxw50001, zxw50002), cbc, cbd, cbe) → new_pePe(new_lt20(zxw49000, zxw50000, cbc), new_asAs(new_esEs27(zxw49000, zxw50000, cbc), new_pePe(new_lt19(zxw49001, zxw50001, cbd), new_asAs(new_esEs26(zxw49001, zxw50001, cbd), new_ltEs20(zxw49002, zxw50002, cbe)))))
new_lt20(zxw49000, zxw50000, app(app(ty_@2, chb), chc)) → new_lt11(zxw49000, zxw50000, chb, chc)
new_lt20(zxw49000, zxw50000, ty_@0) → new_lt15(zxw49000, zxw50000)
new_lt20(zxw49000, zxw50000, app(ty_[], che)) → new_lt9(zxw49000, zxw50000, che)
new_lt20(zxw49000, zxw50000, ty_Ordering) → new_lt14(zxw49000, zxw50000)
new_lt20(zxw49000, zxw50000, app(app(ty_Either, daa), dab)) → new_lt17(zxw49000, zxw50000, daa, dab)
new_lt20(zxw49000, zxw50000, ty_Char) → new_lt6(zxw49000, zxw50000)
new_lt20(zxw49000, zxw50000, ty_Int) → new_lt4(zxw49000, zxw50000)
new_lt20(zxw49000, zxw50000, ty_Double) → new_lt8(zxw49000, zxw50000)
new_lt20(zxw49000, zxw50000, ty_Bool) → new_lt13(zxw49000, zxw50000)
new_lt20(zxw49000, zxw50000, ty_Float) → new_lt7(zxw49000, zxw50000)
new_lt20(zxw49000, zxw50000, app(ty_Ratio, dac)) → new_lt18(zxw49000, zxw50000, dac)
new_lt20(zxw49000, zxw50000, app(app(app(ty_@3, chf), chg), chh)) → new_lt16(zxw49000, zxw50000, chf, chg, chh)
new_lt20(zxw49000, zxw50000, ty_Integer) → new_lt5(zxw49000, zxw50000)
new_lt20(zxw49000, zxw50000, app(ty_Maybe, chd)) → new_lt12(zxw49000, zxw50000, chd)
new_esEs27(zxw49000, zxw50000, app(ty_[], che)) → new_esEs16(zxw49000, zxw50000, che)
new_esEs27(zxw49000, zxw50000, app(ty_Maybe, chd)) → new_esEs7(zxw49000, zxw50000, chd)
new_esEs27(zxw49000, zxw50000, ty_Bool) → new_esEs9(zxw49000, zxw50000)
new_esEs27(zxw49000, zxw50000, ty_Char) → new_esEs15(zxw49000, zxw50000)
new_esEs27(zxw49000, zxw50000, ty_Float) → new_esEs19(zxw49000, zxw50000)
new_esEs27(zxw49000, zxw50000, ty_@0) → new_esEs20(zxw49000, zxw50000)
new_esEs27(zxw49000, zxw50000, ty_Ordering) → new_esEs8(zxw49000, zxw50000)
new_esEs27(zxw49000, zxw50000, ty_Integer) → new_esEs17(zxw49000, zxw50000)
new_esEs27(zxw49000, zxw50000, app(app(app(ty_@3, chf), chg), chh)) → new_esEs5(zxw49000, zxw50000, chf, chg, chh)
new_esEs27(zxw49000, zxw50000, ty_Int) → new_esEs13(zxw49000, zxw50000)
new_esEs27(zxw49000, zxw50000, app(app(ty_Either, daa), dab)) → new_esEs6(zxw49000, zxw50000, daa, dab)
new_esEs27(zxw49000, zxw50000, ty_Double) → new_esEs18(zxw49000, zxw50000)
new_esEs27(zxw49000, zxw50000, app(ty_Ratio, dac)) → new_esEs14(zxw49000, zxw50000, dac)
new_esEs27(zxw49000, zxw50000, app(app(ty_@2, chb), chc)) → new_esEs4(zxw49000, zxw50000, chb, chc)
new_lt19(zxw49001, zxw50001, ty_Integer) → new_lt5(zxw49001, zxw50001)
new_lt19(zxw49001, zxw50001, ty_Ordering) → new_lt14(zxw49001, zxw50001)
new_lt19(zxw49001, zxw50001, ty_Int) → new_lt4(zxw49001, zxw50001)
new_lt19(zxw49001, zxw50001, app(ty_[], cgc)) → new_lt9(zxw49001, zxw50001, cgc)
new_lt19(zxw49001, zxw50001, ty_@0) → new_lt15(zxw49001, zxw50001)
new_lt19(zxw49001, zxw50001, app(app(ty_@2, cfh), cga)) → new_lt11(zxw49001, zxw50001, cfh, cga)
new_lt19(zxw49001, zxw50001, ty_Float) → new_lt7(zxw49001, zxw50001)
new_lt19(zxw49001, zxw50001, app(ty_Ratio, cha)) → new_lt18(zxw49001, zxw50001, cha)
new_lt19(zxw49001, zxw50001, app(app(app(ty_@3, cgd), cge), cgf)) → new_lt16(zxw49001, zxw50001, cgd, cge, cgf)
new_lt19(zxw49001, zxw50001, ty_Char) → new_lt6(zxw49001, zxw50001)
new_lt19(zxw49001, zxw50001, app(app(ty_Either, cgg), cgh)) → new_lt17(zxw49001, zxw50001, cgg, cgh)
new_lt19(zxw49001, zxw50001, ty_Bool) → new_lt13(zxw49001, zxw50001)
new_lt19(zxw49001, zxw50001, ty_Double) → new_lt8(zxw49001, zxw50001)
new_lt19(zxw49001, zxw50001, app(ty_Maybe, cgb)) → new_lt12(zxw49001, zxw50001, cgb)
new_esEs26(zxw49001, zxw50001, app(ty_[], cgc)) → new_esEs16(zxw49001, zxw50001, cgc)
new_esEs26(zxw49001, zxw50001, ty_Char) → new_esEs15(zxw49001, zxw50001)
new_esEs26(zxw49001, zxw50001, ty_Ordering) → new_esEs8(zxw49001, zxw50001)
new_esEs26(zxw49001, zxw50001, ty_Bool) → new_esEs9(zxw49001, zxw50001)
new_esEs26(zxw49001, zxw50001, ty_Integer) → new_esEs17(zxw49001, zxw50001)
new_esEs26(zxw49001, zxw50001, ty_Int) → new_esEs13(zxw49001, zxw50001)
new_esEs26(zxw49001, zxw50001, app(app(ty_@2, cfh), cga)) → new_esEs4(zxw49001, zxw50001, cfh, cga)
new_esEs26(zxw49001, zxw50001, ty_Double) → new_esEs18(zxw49001, zxw50001)
new_esEs26(zxw49001, zxw50001, app(ty_Ratio, cha)) → new_esEs14(zxw49001, zxw50001, cha)
new_esEs26(zxw49001, zxw50001, app(ty_Maybe, cgb)) → new_esEs7(zxw49001, zxw50001, cgb)
new_esEs26(zxw49001, zxw50001, ty_Float) → new_esEs19(zxw49001, zxw50001)
new_esEs26(zxw49001, zxw50001, app(app(ty_Either, cgg), cgh)) → new_esEs6(zxw49001, zxw50001, cgg, cgh)
new_esEs26(zxw49001, zxw50001, app(app(app(ty_@3, cgd), cge), cgf)) → new_esEs5(zxw49001, zxw50001, cgd, cge, cgf)
new_esEs26(zxw49001, zxw50001, ty_@0) → new_esEs20(zxw49001, zxw50001)
new_ltEs20(zxw49002, zxw50002, ty_Bool) → new_ltEs5(zxw49002, zxw50002)
new_ltEs20(zxw49002, zxw50002, app(ty_Maybe, ceh)) → new_ltEs8(zxw49002, zxw50002, ceh)
new_ltEs20(zxw49002, zxw50002, ty_Integer) → new_ltEs16(zxw49002, zxw50002)
new_ltEs20(zxw49002, zxw50002, app(ty_[], cfa)) → new_ltEs13(zxw49002, zxw50002, cfa)
new_ltEs20(zxw49002, zxw50002, app(app(app(ty_@3, cfb), cfc), cfd)) → new_ltEs15(zxw49002, zxw50002, cfb, cfc, cfd)
new_ltEs20(zxw49002, zxw50002, ty_Ordering) → new_ltEs4(zxw49002, zxw50002)
new_ltEs20(zxw49002, zxw50002, app(app(ty_@2, cef), ceg)) → new_ltEs9(zxw49002, zxw50002, cef, ceg)
new_ltEs20(zxw49002, zxw50002, ty_Char) → new_ltEs12(zxw49002, zxw50002)
new_ltEs20(zxw49002, zxw50002, app(ty_Ratio, cfg)) → new_ltEs17(zxw49002, zxw50002, cfg)
new_ltEs20(zxw49002, zxw50002, ty_@0) → new_ltEs14(zxw49002, zxw50002)
new_ltEs20(zxw49002, zxw50002, ty_Float) → new_ltEs6(zxw49002, zxw50002)
new_ltEs20(zxw49002, zxw50002, ty_Double) → new_ltEs11(zxw49002, zxw50002)
new_ltEs20(zxw49002, zxw50002, app(app(ty_Either, cfe), cff)) → new_ltEs7(zxw49002, zxw50002, cfe, cff)
new_ltEs20(zxw49002, zxw50002, ty_Int) → new_ltEs10(zxw49002, zxw50002)
new_pePe(False, zxw213) → zxw213
new_pePe(True, zxw213) → True
new_ltEs9(@2(zxw49000, zxw49001), @2(zxw50000, zxw50001), bec, bed) → new_pePe(new_lt10(zxw49000, zxw50000, bec), new_asAs(new_esEs23(zxw49000, zxw50000, bec), new_ltEs18(zxw49001, zxw50001, bed)))
new_lt10(zxw49000, zxw50000, ty_Float) → new_lt7(zxw49000, zxw50000)
new_lt10(zxw49000, zxw50000, ty_Double) → new_lt8(zxw49000, zxw50000)
new_lt10(zxw49000, zxw50000, ty_Int) → new_lt4(zxw49000, zxw50000)
new_lt10(zxw49000, zxw50000, app(app(ty_@2, gc), gd)) → new_lt11(zxw49000, zxw50000, gc, gd)
new_lt10(zxw49000, zxw50000, ty_Ordering) → new_lt14(zxw49000, zxw50000)
new_lt10(zxw49000, zxw50000, app(ty_Maybe, bfg)) → new_lt12(zxw49000, zxw50000, bfg)
new_lt10(zxw49000, zxw50000, app(app(app(ty_@3, bfh), bga), bgb)) → new_lt16(zxw49000, zxw50000, bfh, bga, bgb)
new_lt10(zxw49000, zxw50000, app(app(ty_Either, be), bf)) → new_lt17(zxw49000, zxw50000, be, bf)
new_lt10(zxw49000, zxw50000, app(ty_Ratio, bgc)) → new_lt18(zxw49000, zxw50000, bgc)
new_lt10(zxw49000, zxw50000, ty_Integer) → new_lt5(zxw49000, zxw50000)
new_lt10(zxw49000, zxw50000, ty_Char) → new_lt6(zxw49000, zxw50000)
new_lt10(zxw49000, zxw50000, ty_Bool) → new_lt13(zxw49000, zxw50000)
new_lt10(zxw49000, zxw50000, app(ty_[], bg)) → new_lt9(zxw49000, zxw50000, bg)
new_lt10(zxw49000, zxw50000, ty_@0) → new_lt15(zxw49000, zxw50000)
new_esEs23(zxw49000, zxw50000, app(app(ty_@2, gc), gd)) → new_esEs4(zxw49000, zxw50000, gc, gd)
new_esEs23(zxw49000, zxw50000, ty_Float) → new_esEs19(zxw49000, zxw50000)
new_esEs23(zxw49000, zxw50000, ty_Char) → new_esEs15(zxw49000, zxw50000)
new_esEs23(zxw49000, zxw50000, ty_Bool) → new_esEs9(zxw49000, zxw50000)
new_esEs23(zxw49000, zxw50000, app(ty_Maybe, bfg)) → new_esEs7(zxw49000, zxw50000, bfg)
new_esEs23(zxw49000, zxw50000, app(app(ty_Either, be), bf)) → new_esEs6(zxw49000, zxw50000, be, bf)
new_esEs23(zxw49000, zxw50000, ty_Ordering) → new_esEs8(zxw49000, zxw50000)
new_esEs23(zxw49000, zxw50000, ty_Integer) → new_esEs17(zxw49000, zxw50000)
new_esEs23(zxw49000, zxw50000, app(ty_Ratio, bgc)) → new_esEs14(zxw49000, zxw50000, bgc)
new_esEs23(zxw49000, zxw50000, ty_@0) → new_esEs20(zxw49000, zxw50000)
new_esEs23(zxw49000, zxw50000, ty_Double) → new_esEs18(zxw49000, zxw50000)
new_esEs23(zxw49000, zxw50000, ty_Int) → new_esEs13(zxw49000, zxw50000)
new_esEs23(zxw49000, zxw50000, app(ty_[], bg)) → new_esEs16(zxw49000, zxw50000, bg)
new_esEs23(zxw49000, zxw50000, app(app(app(ty_@3, bfh), bga), bgb)) → new_esEs5(zxw49000, zxw50000, bfh, bga, bgb)
new_ltEs18(zxw49001, zxw50001, ty_Integer) → new_ltEs16(zxw49001, zxw50001)
new_ltEs18(zxw49001, zxw50001, app(ty_[], beh)) → new_ltEs13(zxw49001, zxw50001, beh)
new_ltEs18(zxw49001, zxw50001, ty_Int) → new_ltEs10(zxw49001, zxw50001)
new_ltEs18(zxw49001, zxw50001, app(app(ty_Either, bfd), bfe)) → new_ltEs7(zxw49001, zxw50001, bfd, bfe)
new_ltEs18(zxw49001, zxw50001, ty_@0) → new_ltEs14(zxw49001, zxw50001)
new_ltEs18(zxw49001, zxw50001, ty_Ordering) → new_ltEs4(zxw49001, zxw50001)
new_ltEs18(zxw49001, zxw50001, ty_Bool) → new_ltEs5(zxw49001, zxw50001)
new_ltEs18(zxw49001, zxw50001, app(app(app(ty_@3, bfa), bfb), bfc)) → new_ltEs15(zxw49001, zxw50001, bfa, bfb, bfc)
new_ltEs18(zxw49001, zxw50001, ty_Float) → new_ltEs6(zxw49001, zxw50001)
new_ltEs18(zxw49001, zxw50001, ty_Double) → new_ltEs11(zxw49001, zxw50001)
new_ltEs18(zxw49001, zxw50001, app(app(ty_@2, bee), bef)) → new_ltEs9(zxw49001, zxw50001, bee, bef)
new_ltEs18(zxw49001, zxw50001, app(ty_Ratio, bff)) → new_ltEs17(zxw49001, zxw50001, bff)
new_ltEs18(zxw49001, zxw50001, ty_Char) → new_ltEs12(zxw49001, zxw50001)
new_ltEs18(zxw49001, zxw50001, app(ty_Maybe, beg)) → new_ltEs8(zxw49001, zxw50001, beg)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Bool) → new_ltEs5(zxw49000, zxw50000)
new_ltEs8(Nothing, Just(zxw50000), ge) → True
new_ltEs8(Just(zxw49000), Just(zxw50000), app(app(ty_@2, gf), gg)) → new_ltEs9(zxw49000, zxw50000, gf, gg)
new_ltEs8(Just(zxw49000), Nothing, ge) → False
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Double) → new_ltEs11(zxw49000, zxw50000)
new_ltEs8(Just(zxw49000), Just(zxw50000), app(ty_[], ha)) → new_ltEs13(zxw49000, zxw50000, ha)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_@0) → new_ltEs14(zxw49000, zxw50000)
new_ltEs8(Just(zxw49000), Just(zxw50000), app(ty_Ratio, hg)) → new_ltEs17(zxw49000, zxw50000, hg)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Float) → new_ltEs6(zxw49000, zxw50000)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Ordering) → new_ltEs4(zxw49000, zxw50000)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Int) → new_ltEs10(zxw49000, zxw50000)
new_ltEs8(Nothing, Nothing, ge) → True
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Char) → new_ltEs12(zxw49000, zxw50000)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Integer) → new_ltEs16(zxw49000, zxw50000)
new_ltEs8(Just(zxw49000), Just(zxw50000), app(app(app(ty_@3, hb), hc), hd)) → new_ltEs15(zxw49000, zxw50000, hb, hc, hd)
new_lt15(zxw49000, zxw50000) → new_esEs8(new_compare31(zxw49000, zxw50000), LT)
new_lt9(zxw49000, zxw50000, bg) → new_esEs8(new_compare0(zxw49000, zxw50000, bg), LT)
new_lt13(zxw49000, zxw50000) → new_esEs8(new_compare18(zxw49000, zxw50000), LT)
new_lt6(zxw49000, zxw50000) → new_esEs8(new_compare12(zxw49000, zxw50000), LT)
new_lt5(zxw49000, zxw50000) → new_esEs8(new_compare9(zxw49000, zxw50000), LT)
new_lt18(zxw49000, zxw50000, bgc) → new_esEs8(new_compare8(zxw49000, zxw50000, bgc), LT)
new_lt17(zxw49000, zxw50000, be, bf) → new_esEs8(new_compare32(zxw49000, zxw50000, be, bf), LT)
new_lt16(zxw49000, zxw50000, bfh, bga, bgb) → new_esEs8(new_compare28(zxw49000, zxw50000, bfh, bga, bgb), LT)
new_compare28(zxw49000, zxw50000, bfh, bga, bgb) → new_compare210(zxw49000, zxw50000, new_esEs5(zxw49000, zxw50000, bfh, bga, bgb), bfh, bga, bgb)
new_compare210(zxw49000, zxw50000, False, bfh, bga, bgb) → new_compare110(zxw49000, zxw50000, new_ltEs15(zxw49000, zxw50000, bfh, bga, bgb), bfh, bga, bgb)
new_compare210(zxw49000, zxw50000, True, bfh, bga, bgb) → EQ
new_compare110(zxw49000, zxw50000, True, bfh, bga, bgb) → LT
new_compare110(zxw49000, zxw50000, False, bfh, bga, bgb) → GT
new_lt12(zxw490, zxw500, bcg) → new_esEs8(new_compare19(zxw490, zxw500, bcg), LT)
new_lt14(zxw49000, zxw50000) → new_esEs8(new_compare6(zxw49000, zxw50000), LT)
new_lt11(zxw49000, zxw50000, gc, gd) → new_esEs8(new_compare30(zxw49000, zxw50000, gc, gd), LT)
new_compare30(zxw49000, zxw50000, gc, gd) → new_compare27(zxw49000, zxw50000, new_esEs4(zxw49000, zxw50000, gc, gd), gc, gd)
new_compare27(zxw49000, zxw50000, False, gc, gd) → new_compare17(zxw49000, zxw50000, new_ltEs9(zxw49000, zxw50000, gc, gd), gc, gd)
new_compare27(zxw49000, zxw50000, True, gc, gd) → EQ
new_compare17(zxw49000, zxw50000, True, gc, gd) → LT
new_compare17(zxw49000, zxw50000, False, gc, gd) → GT
new_lt4(zxw490, zxw500) → new_esEs8(new_compare7(zxw490, zxw500), LT)
new_lt8(zxw49000, zxw50000) → new_esEs8(new_compare16(zxw49000, zxw50000), LT)
new_lt7(zxw49000, zxw50000) → new_esEs8(new_compare14(zxw49000, zxw50000), LT)
new_esEs29(zxw400, zxw300, ty_Integer) → new_esEs17(zxw400, zxw300)
new_esEs29(zxw400, zxw300, ty_@0) → new_esEs20(zxw400, zxw300)
new_esEs29(zxw400, zxw300, app(ty_Maybe, bgd)) → new_esEs7(zxw400, zxw300, bgd)
new_esEs29(zxw400, zxw300, ty_Bool) → new_esEs9(zxw400, zxw300)
new_esEs29(zxw400, zxw300, app(app(ty_@2, baa), bab)) → new_esEs4(zxw400, zxw300, baa, bab)
new_esEs29(zxw400, zxw300, ty_Int) → new_esEs13(zxw400, zxw300)
new_esEs29(zxw400, zxw300, app(ty_[], dad)) → new_esEs16(zxw400, zxw300, dad)
new_esEs29(zxw400, zxw300, ty_Double) → new_esEs18(zxw400, zxw300)
new_esEs29(zxw400, zxw300, ty_Char) → new_esEs15(zxw400, zxw300)
new_esEs29(zxw400, zxw300, app(app(ty_Either, cdc), cca)) → new_esEs6(zxw400, zxw300, cdc, cca)
new_esEs29(zxw400, zxw300, app(app(app(ty_@3, bh), ca), cb)) → new_esEs5(zxw400, zxw300, bh, ca, cb)
new_esEs29(zxw400, zxw300, ty_Float) → new_esEs19(zxw400, zxw300)
new_esEs29(zxw400, zxw300, app(ty_Ratio, cbb)) → new_esEs14(zxw400, zxw300, cbb)
new_esEs29(zxw400, zxw300, ty_Ordering) → new_esEs8(zxw400, zxw300)
new_compare35(zxw400, h) → new_compare26(Just(zxw400), Nothing, False, h)

The set Q consists of the following terms:

new_esEs17(Integer(x0), Integer(x1))
new_esEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Integer)
new_lt10(x0, x1, ty_Double)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_compare18(x0, x1)
new_compare29(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Double)
new_pePe(False, x0)
new_lt10(x0, x1, app(app(ty_Either, x2), x3))
new_lt17(x0, x1, x2, x3)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Left(x0), Left(x1), ty_Bool, x2)
new_compare7(x0, x1)
new_esEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_compare110(x0, x1, False, x2, x3, x4)
new_primMulNat0(Succ(x0), Zero)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs7(Just(x0), Just(x1), ty_Double)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_ltEs8(Just(x0), Just(x1), ty_Integer)
new_esEs10(x0, x1, ty_Int)
new_ltEs10(x0, x1)
new_esEs28(x0, x1, ty_Int)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs12(x0, x1, ty_Char)
new_compare25(x0, x1, True, x2, x3)
new_primMulNat0(Succ(x0), Succ(x1))
new_ltEs7(Left(x0), Left(x1), ty_Integer, x2)
new_esEs6(Left(x0), Left(x1), ty_Int, x2)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Int)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs16(x0, x1)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_compare13(x0, x1, True)
new_esEs10(x0, x1, ty_Ordering)
new_compare29(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs19(x0, x1, ty_Float)
new_compare0([], :(x0, x1), x2)
new_esEs11(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_Int)
new_esEs6(Left(x0), Left(x1), ty_@0, x2)
new_ltEs8(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare11(x0, x1, True, x2)
new_ltEs19(x0, x1, ty_Ordering)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs8(GT, GT)
new_compare11(x0, x1, False, x2)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_compare17(x0, x1, True, x2, x3)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCompAux1(x0, x1, x2, x3)
new_esEs8(LT, LT)
new_esEs29(x0, x1, ty_@0)
new_compare29(x0, x1, ty_Double)
new_esEs18(Double(x0, x1), Double(x2, x3))
new_primCmpNat0(Zero, x0)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_lt11(x0, x1, x2, x3)
new_ltEs8(Just(x0), Just(x1), ty_Bool)
new_esEs11(x0, x1, ty_@0)
new_primCmpNat1(Zero, Succ(x0))
new_esEs25(x0, x1, ty_Int)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_sr(x0, x1)
new_ltEs5(False, False)
new_ltEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_compare6(x0, x1)
new_lt10(x0, x1, ty_Ordering)
new_esEs6(Right(x0), Left(x1), x2, x3)
new_esEs6(Left(x0), Right(x1), x2, x3)
new_compare29(x0, x1, ty_Int)
new_esEs30(x0, x1, ty_Bool)
new_ltEs15(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs26(x0, x1, ty_Integer)
new_primEqNat0(Zero, Succ(x0))
new_primCmpNat1(Zero, Zero)
new_esEs7(Nothing, Nothing, x0)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs7(Left(x0), Left(x1), ty_Bool, x2)
new_compare16(Double(x0, x1), Double(x2, x3))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_lt7(x0, x1)
new_esEs28(x0, x1, ty_@0)
new_ltEs20(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Integer)
new_esEs16(:(x0, x1), :(x2, x3), x4)
new_esEs23(x0, x1, ty_Integer)
new_esEs11(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Double)
new_ltEs19(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_Char)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_compare15(x0, x1, True, x2, x3)
new_esEs24(x0, x1, ty_Int)
new_esEs6(Left(x0), Left(x1), ty_Char, x2)
new_esEs6(Left(x0), Left(x1), ty_Integer, x2)
new_primEqNat0(Zero, Zero)
new_compare32(x0, x1, x2, x3)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs8(Just(x0), Just(x1), app(ty_Maybe, x2))
new_compare36(x0, x1, x2)
new_ltEs8(Just(x0), Just(x1), ty_Double)
new_ltEs8(Just(x0), Just(x1), ty_Ordering)
new_ltEs19(x0, x1, ty_@0)
new_compare110(x0, x1, True, x2, x3, x4)
new_compare24(x0, x1, False)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs7(Just(x0), Nothing, x1)
new_esEs29(x0, x1, ty_Bool)
new_esEs9(True, True)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_lt18(x0, x1, x2)
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt4(x0, x1)
new_primMulNat0(Zero, Zero)
new_ltEs13(x0, x1, x2)
new_esEs23(x0, x1, ty_Char)
new_esEs30(x0, x1, ty_Ordering)
new_esEs10(x0, x1, ty_@0)
new_lt10(x0, x1, app(ty_Ratio, x2))
new_lt10(x0, x1, ty_Char)
new_esEs30(x0, x1, ty_Int)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_Integer)
new_fsEs(x0)
new_ltEs4(GT, GT)
new_lt8(x0, x1)
new_esEs30(x0, x1, ty_@0)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs10(x0, x1, ty_Float)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs28(x0, x1, ty_Double)
new_esEs29(x0, x1, ty_Char)
new_compare29(x0, x1, app(ty_[], x2))
new_esEs6(Right(x0), Right(x1), x2, ty_Float)
new_compare27(x0, x1, True, x2, x3)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_lt10(x0, x1, ty_Int)
new_esEs10(x0, x1, ty_Bool)
new_lt16(x0, x1, x2, x3, x4)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs23(x0, x1, ty_Ordering)
new_esEs7(Just(x0), Just(x1), ty_Int)
new_esEs10(x0, x1, ty_Char)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_lt10(x0, x1, app(ty_[], x2))
new_compare33(x0)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_pePe(True, x0)
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, ty_Int)
new_primPlusNat0(Zero, x0)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_lt10(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, ty_Int)
new_compare210(x0, x1, True, x2, x3, x4)
new_lt6(x0, x1)
new_esEs26(x0, x1, ty_Bool)
new_compare24(x0, x1, True)
new_ltEs18(x0, x1, ty_Integer)
new_compare15(x0, x1, False, x2, x3)
new_compare14(Float(x0, x1), Float(x2, x3))
new_ltEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(x0, x1)
new_esEs29(x0, x1, ty_Integer)
new_esEs12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primPlusNat1(Zero, Zero)
new_primCompAux0(x0, GT)
new_compare23(x0, x1, True)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_lt19(x0, x1, app(ty_[], x2))
new_lt15(x0, x1)
new_ltEs7(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs29(x0, x1, ty_Ordering)
new_compare19(x0, x1, x2)
new_compare13(x0, x1, False)
new_compare26(Nothing, Just(x0), False, x1)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_lt20(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_@0)
new_compare30(x0, x1, x2, x3)
new_primPlusNat0(Succ(x0), x1)
new_esEs12(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs4(EQ, EQ)
new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs19(x0, x1, ty_Char)
new_ltEs7(Right(x0), Right(x1), x2, ty_Char)
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_ltEs11(x0, x1)
new_esEs12(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Integer)
new_compare29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Char)
new_esEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs8(Nothing, Just(x0), x1)
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs8(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Just(x0), Just(x1), ty_Char)
new_ltEs7(Left(x0), Left(x1), ty_@0, x2)
new_lt9(x0, x1, x2)
new_esEs10(x0, x1, app(ty_[], x2))
new_esEs12(x0, x1, ty_Float)
new_compare31(@0, @0)
new_esEs7(Just(x0), Just(x1), ty_Float)
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs16([], :(x0, x1), x2)
new_primCmpNat2(x0, Zero)
new_ltEs4(LT, EQ)
new_ltEs4(EQ, LT)
new_esEs12(x0, x1, ty_Int)
new_lt19(x0, x1, ty_Double)
new_esEs6(Right(x0), Right(x1), x2, ty_Integer)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_primMulInt(Pos(x0), Pos(x1))
new_lt20(x0, x1, ty_Bool)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_ltEs7(Right(x0), Right(x1), x2, ty_Int)
new_ltEs18(x0, x1, app(ty_[], x2))
new_esEs30(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_@0)
new_esEs10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs7(Right(x0), Right(x1), x2, ty_Double)
new_asAs(True, x0)
new_primEqNat0(Succ(x0), Zero)
new_compare26(Just(x0), Nothing, False, x1)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs7(Left(x0), Left(x1), ty_Int, x2)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_esEs12(x0, x1, app(ty_[], x2))
new_esEs13(x0, x1)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_ltEs7(Left(x0), Right(x1), x2, x3)
new_ltEs7(Right(x0), Left(x1), x2, x3)
new_esEs14(:%(x0, x1), :%(x2, x3), x4)
new_compare26(x0, x1, True, x2)
new_esEs21(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Integer)
new_ltEs7(Left(x0), Left(x1), ty_Double, x2)
new_ltEs8(Nothing, Nothing, x0)
new_lt20(x0, x1, ty_@0)
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_Bool)
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Char)
new_compare26(Just(x0), Just(x1), False, x2)
new_esEs28(x0, x1, ty_Ordering)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, app(ty_Ratio, x2))
new_compare34(x0, x1)
new_lt20(x0, x1, ty_Ordering)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_lt12(x0, x1, x2)
new_esEs10(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_esEs12(x0, x1, app(ty_Maybe, x2))
new_esEs30(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, ty_Bool)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs27(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_Double)
new_esEs25(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(ty_[], x2))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_lt10(x0, x1, ty_Bool)
new_primPlusNat1(Succ(x0), Zero)
new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs22(x0, x1, ty_Float)
new_ltEs4(LT, LT)
new_esEs10(x0, x1, ty_Integer)
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Integer)
new_compare29(x0, x1, app(app(ty_@2, x2), x3))
new_compare23(x0, x1, False)
new_esEs21(x0, x1, app(ty_[], x2))
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs11(x0, x1, ty_Bool)
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_compare29(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_Double)
new_esEs21(x0, x1, ty_Bool)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, ty_Double)
new_esEs26(x0, x1, ty_Ordering)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs7(Nothing, Just(x0), x1)
new_primPlusNat1(Zero, Succ(x0))
new_ltEs12(x0, x1)
new_compare10(x0, x1, False)
new_lt10(x0, x1, app(app(ty_@2, x2), x3))
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Left(x0), Left(x1), ty_Float, x2)
new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_primCmpNat0(Succ(x0), x1)
new_lt10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, ty_@0)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs8(GT, EQ)
new_esEs8(EQ, GT)
new_esEs22(x0, x1, ty_Bool)
new_lt19(x0, x1, ty_Float)
new_lt19(x0, x1, ty_Integer)
new_ltEs8(Just(x0), Just(x1), ty_Char)
new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Left(x0), Left(x1), ty_Double, x2)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_ltEs8(Just(x0), Just(x1), ty_Float)
new_lt5(x0, x1)
new_compare29(x0, x1, ty_Ordering)
new_ltEs18(x0, x1, ty_Bool)
new_compare28(x0, x1, x2, x3, x4)
new_esEs11(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_@0)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, ty_Int)
new_esEs11(x0, x1, ty_Char)
new_esEs10(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Float)
new_lt19(x0, x1, ty_Ordering)
new_compare29(x0, x1, ty_Integer)
new_compare25(x0, x1, False, x2, x3)
new_esEs6(Right(x0), Right(x1), x2, ty_Char)
new_esEs26(x0, x1, app(ty_[], x2))
new_ltEs18(x0, x1, ty_Float)
new_ltEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs9(False, False)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs21(x0, x1, ty_Double)
new_esEs12(x0, x1, ty_Ordering)
new_ltEs8(Just(x0), Nothing, x1)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs22(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpNat1(Succ(x0), Succ(x1))
new_esEs10(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_@0)
new_ltEs6(x0, x1)
new_lt10(x0, x1, ty_Float)
new_esEs22(x0, x1, ty_Int)
new_ltEs7(Left(x0), Left(x1), ty_Char, x2)
new_compare17(x0, x1, False, x2, x3)
new_ltEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs21(x0, x1, ty_Float)
new_esEs29(x0, x1, ty_Double)
new_primCompAux0(x0, EQ)
new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare26(Nothing, Nothing, False, x0)
new_compare27(x0, x1, False, x2, x3)
new_esEs21(x0, x1, ty_Integer)
new_primCmpNat1(Succ(x0), Zero)
new_ltEs18(x0, x1, ty_@0)
new_esEs22(x0, x1, ty_Double)
new_ltEs7(Right(x0), Right(x1), x2, ty_@0)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, ty_Bool)
new_esEs16([], [], x0)
new_compare29(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, app(ty_[], x2))
new_lt13(x0, x1)
new_esEs23(x0, x1, ty_Bool)
new_ltEs5(True, True)
new_ltEs7(Right(x0), Right(x1), x2, ty_Integer)
new_lt19(x0, x1, ty_Int)
new_compare35(x0, x1)
new_lt19(x0, x1, ty_Char)
new_ltEs4(EQ, GT)
new_ltEs4(GT, EQ)
new_esEs6(Right(x0), Right(x1), x2, ty_@0)
new_not(True)
new_esEs11(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Float)
new_compare0(:(x0, x1), [], x2)
new_esEs28(x0, x1, ty_Char)
new_lt19(x0, x1, ty_@0)
new_esEs10(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, ty_Ordering)
new_ltEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs26(x0, x1, ty_Char)
new_ltEs18(x0, x1, ty_Int)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_ltEs20(x0, x1, ty_Ordering)
new_not(False)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_lt14(x0, x1)
new_compare12(Char(x0), Char(x1))
new_esEs15(Char(x0), Char(x1))
new_esEs11(x0, x1, app(ty_[], x2))
new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_compare10(x0, x1, True)
new_lt10(x0, x1, ty_@0)
new_asAs(False, x0)
new_esEs22(x0, x1, ty_Ordering)
new_ltEs18(x0, x1, ty_Char)
new_esEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs17(x0, x1, x2)
new_compare29(x0, x1, ty_Float)
new_lt19(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_Char)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_ltEs8(Just(x0), Just(x1), ty_@0)
new_esEs20(@0, @0)
new_ltEs8(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs7(Left(x0), Left(x1), ty_Float, x2)
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Int)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_esEs16(:(x0, x1), [], x2)
new_ltEs19(x0, x1, ty_Double)
new_esEs9(True, False)
new_esEs9(False, True)
new_esEs22(x0, x1, ty_Char)
new_ltEs7(Right(x0), Right(x1), x2, ty_Float)
new_ltEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare29(x0, x1, ty_Bool)
new_ltEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs30(x0, x1, ty_Double)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, ty_Integer)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs11(x0, x1, ty_Double)
new_ltEs20(x0, x1, ty_Float)
new_primCompAux0(x0, LT)
new_primCmpNat2(x0, Succ(x1))
new_esEs11(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs12(x0, x1, ty_Integer)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs10(x0, x1, ty_Double)
new_ltEs8(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_sr0(Integer(x0), Integer(x1))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs29(x0, x1, ty_Float)
new_ltEs8(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_primEqInt(Pos(Zero), Pos(Zero))
new_ltEs18(x0, x1, ty_Double)
new_esEs12(x0, x1, ty_Double)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_compare0(:(x0, x1), :(x2, x3), x4)
new_esEs29(x0, x1, ty_Int)
new_esEs12(x0, x1, ty_Bool)
new_compare9(Integer(x0), Integer(x1))
new_lt10(x0, x1, ty_Integer)
new_esEs30(x0, x1, ty_Char)
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs19(Float(x0, x1), Float(x2, x3))
new_primMulNat0(Zero, Succ(x0))
new_compare0([], [], x0)
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Just(x0), Just(x1), ty_@0)
new_ltEs4(GT, LT)
new_ltEs4(LT, GT)
new_ltEs5(True, False)
new_ltEs5(False, True)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs9(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs27(x0, x1, app(ty_[], x2))
new_ltEs8(Just(x0), Just(x1), ty_Int)
new_esEs12(x0, x1, app(app(ty_Either, x2), x3))
new_compare29(x0, x1, ty_@0)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Float)
new_esEs23(x0, x1, ty_Float)
new_compare210(x0, x1, False, x2, x3, x4)
new_esEs30(x0, x1, ty_Float)
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))

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

new_compare33(x0)
new_compare34(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
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ AND
                                        ↳ QDP
                                          ↳ UsableRulesProof
                                            ↳ QDP
                                              ↳ QReductionProof
                                                ↳ QDP
                                                  ↳ QDPSizeChangeProof
                                        ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_splitGT20(zxw31, zxw32, zxw33, Branch(zxw340, zxw341, zxw342, zxw343, zxw344), zxw400, True, h, ba) → new_splitGT3(zxw340, zxw341, zxw342, zxw343, zxw344, Just(zxw400), h, ba)
new_splitGT11(zxw31, zxw32, zxw33, zxw34, zxw400, True, h, ba) → new_splitGT0(zxw33, zxw400, h, ba)
new_splitGT0(Branch(zxw340, zxw341, zxw342, zxw343, zxw344), zxw400, h, ba) → new_splitGT3(zxw340, zxw341, zxw342, zxw343, zxw344, Just(zxw400), h, ba)
new_splitGT12(zxw30, zxw31, zxw32, zxw33, zxw34, zxw35, True, bb, bc) → new_splitGT0(zxw33, zxw35, bb, bc)
new_splitGT21(zxw30, zxw31, zxw32, zxw33, zxw34, zxw35, True, bb, bc) → new_splitGT0(zxw34, zxw35, bb, bc)
new_splitGT3(Just(zxw300), zxw31, zxw32, zxw33, zxw34, Just(zxw400), h, ba) → new_splitGT21(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs8(new_compare26(Just(zxw400), Just(zxw300), new_esEs29(zxw400, zxw300, h), h), GT), h, ba)
new_splitGT21(zxw30, zxw31, zxw32, zxw33, zxw34, zxw35, False, bb, bc) → new_splitGT12(zxw30, zxw31, zxw32, zxw33, zxw34, zxw35, new_esEs8(new_compare36(zxw35, zxw30, bb), LT), bb, bc)
new_splitGT3(Nothing, zxw31, zxw32, zxw33, zxw34, Just(zxw400), h, ba) → new_splitGT20(zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs8(new_compare26(Just(zxw400), Nothing, False, h), GT), h, ba)
new_splitGT20(zxw31, zxw32, zxw33, zxw34, zxw400, False, h, ba) → new_splitGT11(zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs8(new_compare35(zxw400, h), LT), h, ba)

The TRS R consists of the following rules:

new_compare36(zxw20, zxw15, bch) → new_compare26(Just(zxw20), Just(zxw15), new_esEs30(zxw20, zxw15, bch), bch)
new_esEs8(LT, LT) → True
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs30(zxw20, zxw15, ty_Bool) → new_esEs9(zxw20, zxw15)
new_esEs30(zxw20, zxw15, ty_Float) → new_esEs19(zxw20, zxw15)
new_esEs30(zxw20, zxw15, app(ty_Ratio, bdb)) → new_esEs14(zxw20, zxw15, bdb)
new_esEs30(zxw20, zxw15, ty_@0) → new_esEs20(zxw20, zxw15)
new_esEs30(zxw20, zxw15, ty_Double) → new_esEs18(zxw20, zxw15)
new_esEs30(zxw20, zxw15, app(app(ty_Either, bdg), bdh)) → new_esEs6(zxw20, zxw15, bdg, bdh)
new_esEs30(zxw20, zxw15, app(ty_Maybe, bda)) → new_esEs7(zxw20, zxw15, bda)
new_esEs30(zxw20, zxw15, app(ty_[], bdc)) → new_esEs16(zxw20, zxw15, bdc)
new_esEs30(zxw20, zxw15, ty_Int) → new_esEs13(zxw20, zxw15)
new_esEs30(zxw20, zxw15, ty_Ordering) → new_esEs8(zxw20, zxw15)
new_esEs30(zxw20, zxw15, ty_Integer) → new_esEs17(zxw20, zxw15)
new_esEs30(zxw20, zxw15, app(app(app(ty_@3, bdd), bde), bdf)) → new_esEs5(zxw20, zxw15, bdd, bde, bdf)
new_esEs30(zxw20, zxw15, ty_Char) → new_esEs15(zxw20, zxw15)
new_esEs30(zxw20, zxw15, app(app(ty_@2, bea), beb)) → new_esEs4(zxw20, zxw15, bea, beb)
new_compare26(Just(zxw4900), Just(zxw5000), False, bcg) → new_compare11(zxw4900, zxw5000, new_ltEs19(zxw4900, zxw5000, bcg), bcg)
new_compare26(zxw490, zxw500, True, bcg) → EQ
new_ltEs19(zxw4900, zxw5000, ty_Integer) → new_ltEs16(zxw4900, zxw5000)
new_ltEs19(zxw4900, zxw5000, ty_Double) → new_ltEs11(zxw4900, zxw5000)
new_ltEs19(zxw4900, zxw5000, ty_Int) → new_ltEs10(zxw4900, zxw5000)
new_ltEs19(zxw4900, zxw5000, app(app(app(ty_@3, cbc), cbd), cbe)) → new_ltEs15(zxw4900, zxw5000, cbc, cbd, cbe)
new_ltEs19(zxw4900, zxw5000, app(ty_Ratio, hh)) → new_ltEs17(zxw4900, zxw5000, hh)
new_ltEs19(zxw4900, zxw5000, ty_Ordering) → new_ltEs4(zxw4900, zxw5000)
new_ltEs19(zxw4900, zxw5000, ty_Char) → new_ltEs12(zxw4900, zxw5000)
new_ltEs19(zxw4900, zxw5000, app(app(ty_Either, cbf), cbg)) → new_ltEs7(zxw4900, zxw5000, cbf, cbg)
new_ltEs19(zxw4900, zxw5000, app(app(ty_@2, bec), bed)) → new_ltEs9(zxw4900, zxw5000, bec, bed)
new_ltEs19(zxw4900, zxw5000, ty_Float) → new_ltEs6(zxw4900, zxw5000)
new_ltEs19(zxw4900, zxw5000, app(ty_Maybe, ge)) → new_ltEs8(zxw4900, zxw5000, ge)
new_ltEs19(zxw4900, zxw5000, ty_@0) → new_ltEs14(zxw4900, zxw5000)
new_ltEs19(zxw4900, zxw5000, ty_Bool) → new_ltEs5(zxw4900, zxw5000)
new_ltEs19(zxw4900, zxw5000, app(ty_[], bhg)) → new_ltEs13(zxw4900, zxw5000, bhg)
new_compare11(zxw180, zxw181, True, bd) → LT
new_compare11(zxw180, zxw181, False, bd) → GT
new_ltEs13(zxw4900, zxw5000, bhg) → new_fsEs(new_compare0(zxw4900, zxw5000, bhg))
new_compare0([], [], bhg) → EQ
new_compare0(:(zxw49000, zxw49001), [], bhg) → GT
new_compare0(:(zxw49000, zxw49001), :(zxw50000, zxw50001), bhg) → new_primCompAux1(zxw49000, zxw50000, new_compare0(zxw49001, zxw50001, bhg), bhg)
new_compare0([], :(zxw50000, zxw50001), bhg) → LT
new_fsEs(zxw202) → new_not(new_esEs8(zxw202, GT))
new_esEs8(GT, GT) → True
new_esEs8(LT, GT) → False
new_esEs8(EQ, GT) → False
new_not(False) → True
new_not(True) → False
new_primCompAux1(zxw49000, zxw50000, zxw214, bhg) → new_primCompAux0(zxw214, new_compare29(zxw49000, zxw50000, bhg))
new_compare29(zxw49000, zxw50000, ty_Char) → new_compare12(zxw49000, zxw50000)
new_compare29(zxw49000, zxw50000, ty_Double) → new_compare16(zxw49000, zxw50000)
new_compare29(zxw49000, zxw50000, ty_@0) → new_compare31(zxw49000, zxw50000)
new_compare29(zxw49000, zxw50000, ty_Int) → new_compare7(zxw49000, zxw50000)
new_compare29(zxw49000, zxw50000, app(app(app(ty_@3, cad), cae), caf)) → new_compare28(zxw49000, zxw50000, cad, cae, caf)
new_compare29(zxw49000, zxw50000, app(ty_[], cac)) → new_compare0(zxw49000, zxw50000, cac)
new_compare29(zxw49000, zxw50000, app(app(ty_@2, bhh), caa)) → new_compare30(zxw49000, zxw50000, bhh, caa)
new_compare29(zxw49000, zxw50000, ty_Float) → new_compare14(zxw49000, zxw50000)
new_compare29(zxw49000, zxw50000, app(app(ty_Either, cag), cah)) → new_compare32(zxw49000, zxw50000, cag, cah)
new_compare29(zxw49000, zxw50000, app(ty_Ratio, cba)) → new_compare8(zxw49000, zxw50000, cba)
new_compare29(zxw49000, zxw50000, ty_Ordering) → new_compare6(zxw49000, zxw50000)
new_compare29(zxw49000, zxw50000, ty_Integer) → new_compare9(zxw49000, zxw50000)
new_compare29(zxw49000, zxw50000, ty_Bool) → new_compare18(zxw49000, zxw50000)
new_compare29(zxw49000, zxw50000, app(ty_Maybe, cab)) → new_compare19(zxw49000, zxw50000, cab)
new_primCompAux0(zxw218, GT) → GT
new_primCompAux0(zxw218, LT) → LT
new_primCompAux0(zxw218, EQ) → zxw218
new_compare19(zxw490, zxw500, bcg) → new_compare26(zxw490, zxw500, new_esEs7(zxw490, zxw500, bcg), bcg)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_esEs7(Just(zxw4000), Just(zxw3000), app(app(ty_@2, bhe), bhf)) → new_esEs4(zxw4000, zxw3000, bhe, bhf)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Bool) → new_esEs9(zxw4000, zxw3000)
new_esEs7(Just(zxw4000), Just(zxw3000), app(ty_Ratio, bgf)) → new_esEs14(zxw4000, zxw3000, bgf)
new_esEs7(Just(zxw4000), Just(zxw3000), app(ty_[], bgg)) → new_esEs16(zxw4000, zxw3000, bgg)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_@0) → new_esEs20(zxw4000, zxw3000)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Ordering) → new_esEs8(zxw4000, zxw3000)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Int) → new_esEs13(zxw4000, zxw3000)
new_esEs7(Nothing, Nothing, bgd) → True
new_esEs7(Just(zxw4000), Nothing, bgd) → False
new_esEs7(Nothing, Just(zxw3000), bgd) → False
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Char) → new_esEs15(zxw4000, zxw3000)
new_esEs7(Just(zxw4000), Just(zxw3000), app(app(app(ty_@3, bgh), bha), bhb)) → new_esEs5(zxw4000, zxw3000, bgh, bha, bhb)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Double) → new_esEs18(zxw4000, zxw3000)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Float) → new_esEs19(zxw4000, zxw3000)
new_compare26(Just(zxw4900), Nothing, False, bcg) → GT
new_compare26(Nothing, Just(zxw5000), False, bcg) → LT
new_compare26(Nothing, Nothing, False, bcg) → LT
new_esEs6(Left(zxw4000), Left(zxw3000), app(ty_Maybe, cbh), cca) → new_esEs7(zxw4000, zxw3000, cbh)
new_esEs7(Just(zxw4000), Just(zxw3000), app(ty_Maybe, bge)) → new_esEs7(zxw4000, zxw3000, bge)
new_esEs6(Right(zxw4000), Right(zxw3000), cdc, app(ty_Maybe, cdd)) → new_esEs7(zxw4000, zxw3000, cdd)
new_esEs6(Left(zxw4000), Left(zxw3000), app(app(ty_Either, ccg), cch), cca) → new_esEs6(zxw4000, zxw3000, ccg, cch)
new_esEs6(Right(zxw4000), Right(zxw3000), cdc, app(app(ty_Either, ceb), cec)) → new_esEs6(zxw4000, zxw3000, ceb, cec)
new_esEs7(Just(zxw4000), Just(zxw3000), app(app(ty_Either, bhc), bhd)) → new_esEs6(zxw4000, zxw3000, bhc, bhd)
new_esEs6(Right(zxw4000), Right(zxw3000), cdc, ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_esEs6(Right(zxw4000), Right(zxw3000), cdc, ty_Float) → new_esEs19(zxw4000, zxw3000)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Integer, cca) → new_esEs17(zxw4000, zxw3000)
new_esEs6(Right(zxw4000), Right(zxw3000), cdc, ty_Int) → new_esEs13(zxw4000, zxw3000)
new_esEs6(Right(zxw4000), Right(zxw3000), cdc, app(ty_Ratio, cde)) → new_esEs14(zxw4000, zxw3000, cde)
new_esEs6(Left(zxw4000), Left(zxw3000), app(app(ty_@2, cda), cdb), cca) → new_esEs4(zxw4000, zxw3000, cda, cdb)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Bool, cca) → new_esEs9(zxw4000, zxw3000)
new_esEs6(Right(zxw4000), Left(zxw3000), cdc, cca) → False
new_esEs6(Left(zxw4000), Right(zxw3000), cdc, cca) → False
new_esEs6(Left(zxw4000), Left(zxw3000), ty_@0, cca) → new_esEs20(zxw4000, zxw3000)
new_esEs6(Right(zxw4000), Right(zxw3000), cdc, ty_Bool) → new_esEs9(zxw4000, zxw3000)
new_esEs6(Left(zxw4000), Left(zxw3000), app(ty_Ratio, ccb), cca) → new_esEs14(zxw4000, zxw3000, ccb)
new_esEs6(Right(zxw4000), Right(zxw3000), cdc, app(ty_[], cdf)) → new_esEs16(zxw4000, zxw3000, cdf)
new_esEs6(Left(zxw4000), Left(zxw3000), app(app(app(ty_@3, ccd), cce), ccf), cca) → new_esEs5(zxw4000, zxw3000, ccd, cce, ccf)
new_esEs6(Right(zxw4000), Right(zxw3000), cdc, ty_@0) → new_esEs20(zxw4000, zxw3000)
new_esEs6(Right(zxw4000), Right(zxw3000), cdc, ty_Double) → new_esEs18(zxw4000, zxw3000)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Double, cca) → new_esEs18(zxw4000, zxw3000)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Ordering, cca) → new_esEs8(zxw4000, zxw3000)
new_esEs6(Right(zxw4000), Right(zxw3000), cdc, app(app(ty_@2, ced), cee)) → new_esEs4(zxw4000, zxw3000, ced, cee)
new_esEs6(Right(zxw4000), Right(zxw3000), cdc, ty_Char) → new_esEs15(zxw4000, zxw3000)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Char, cca) → new_esEs15(zxw4000, zxw3000)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Float, cca) → new_esEs19(zxw4000, zxw3000)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Int, cca) → new_esEs13(zxw4000, zxw3000)
new_esEs6(Right(zxw4000), Right(zxw3000), cdc, ty_Ordering) → new_esEs8(zxw4000, zxw3000)
new_esEs6(Left(zxw4000), Left(zxw3000), app(ty_[], ccc), cca) → new_esEs16(zxw4000, zxw3000, ccc)
new_esEs6(Right(zxw4000), Right(zxw3000), cdc, app(app(app(ty_@3, cdg), cdh), cea)) → new_esEs5(zxw4000, zxw3000, cdg, cdh, cea)
new_esEs5(@3(zxw4000, zxw4001, zxw4002), @3(zxw3000, zxw3001, zxw3002), bh, ca, cb) → new_asAs(new_esEs12(zxw4000, zxw3000, bh), new_asAs(new_esEs11(zxw4001, zxw3001, ca), new_esEs10(zxw4002, zxw3002, cb)))
new_esEs12(zxw4000, zxw3000, ty_Bool) → new_esEs9(zxw4000, zxw3000)
new_esEs12(zxw4000, zxw3000, ty_Char) → new_esEs15(zxw4000, zxw3000)
new_esEs12(zxw4000, zxw3000, app(ty_[], fb)) → new_esEs16(zxw4000, zxw3000, fb)
new_esEs12(zxw4000, zxw3000, ty_Int) → new_esEs13(zxw4000, zxw3000)
new_esEs12(zxw4000, zxw3000, ty_Double) → new_esEs18(zxw4000, zxw3000)
new_esEs12(zxw4000, zxw3000, app(ty_Maybe, eh)) → new_esEs7(zxw4000, zxw3000, eh)
new_esEs12(zxw4000, zxw3000, app(app(app(ty_@3, fc), fd), ff)) → new_esEs5(zxw4000, zxw3000, fc, fd, ff)
new_esEs12(zxw4000, zxw3000, ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_esEs12(zxw4000, zxw3000, ty_Float) → new_esEs19(zxw4000, zxw3000)
new_esEs12(zxw4000, zxw3000, ty_@0) → new_esEs20(zxw4000, zxw3000)
new_esEs12(zxw4000, zxw3000, app(app(ty_Either, fg), fh)) → new_esEs6(zxw4000, zxw3000, fg, fh)
new_esEs12(zxw4000, zxw3000, app(ty_Ratio, fa)) → new_esEs14(zxw4000, zxw3000, fa)
new_esEs12(zxw4000, zxw3000, ty_Ordering) → new_esEs8(zxw4000, zxw3000)
new_esEs12(zxw4000, zxw3000, app(app(ty_@2, ga), gb)) → new_esEs4(zxw4000, zxw3000, ga, gb)
new_esEs11(zxw4001, zxw3001, app(ty_[], dh)) → new_esEs16(zxw4001, zxw3001, dh)
new_esEs11(zxw4001, zxw3001, ty_Char) → new_esEs15(zxw4001, zxw3001)
new_esEs11(zxw4001, zxw3001, ty_Float) → new_esEs19(zxw4001, zxw3001)
new_esEs11(zxw4001, zxw3001, ty_Int) → new_esEs13(zxw4001, zxw3001)
new_esEs11(zxw4001, zxw3001, ty_Ordering) → new_esEs8(zxw4001, zxw3001)
new_esEs11(zxw4001, zxw3001, app(app(ty_@2, ef), eg)) → new_esEs4(zxw4001, zxw3001, ef, eg)
new_esEs11(zxw4001, zxw3001, app(app(app(ty_@3, ea), eb), ec)) → new_esEs5(zxw4001, zxw3001, ea, eb, ec)
new_esEs11(zxw4001, zxw3001, ty_Bool) → new_esEs9(zxw4001, zxw3001)
new_esEs11(zxw4001, zxw3001, ty_Double) → new_esEs18(zxw4001, zxw3001)
new_esEs11(zxw4001, zxw3001, ty_@0) → new_esEs20(zxw4001, zxw3001)
new_esEs11(zxw4001, zxw3001, app(app(ty_Either, ed), ee)) → new_esEs6(zxw4001, zxw3001, ed, ee)
new_esEs11(zxw4001, zxw3001, app(ty_Maybe, df)) → new_esEs7(zxw4001, zxw3001, df)
new_esEs11(zxw4001, zxw3001, app(ty_Ratio, dg)) → new_esEs14(zxw4001, zxw3001, dg)
new_esEs11(zxw4001, zxw3001, ty_Integer) → new_esEs17(zxw4001, zxw3001)
new_esEs10(zxw4002, zxw3002, app(ty_Maybe, cc)) → new_esEs7(zxw4002, zxw3002, cc)
new_esEs10(zxw4002, zxw3002, app(app(app(ty_@3, cf), cg), da)) → new_esEs5(zxw4002, zxw3002, cf, cg, da)
new_esEs10(zxw4002, zxw3002, ty_Integer) → new_esEs17(zxw4002, zxw3002)
new_esEs10(zxw4002, zxw3002, ty_Bool) → new_esEs9(zxw4002, zxw3002)
new_esEs10(zxw4002, zxw3002, ty_Float) → new_esEs19(zxw4002, zxw3002)
new_esEs10(zxw4002, zxw3002, ty_Char) → new_esEs15(zxw4002, zxw3002)
new_esEs10(zxw4002, zxw3002, app(ty_[], ce)) → new_esEs16(zxw4002, zxw3002, ce)
new_esEs10(zxw4002, zxw3002, app(app(ty_@2, dd), de)) → new_esEs4(zxw4002, zxw3002, dd, de)
new_esEs10(zxw4002, zxw3002, ty_Double) → new_esEs18(zxw4002, zxw3002)
new_esEs10(zxw4002, zxw3002, ty_@0) → new_esEs20(zxw4002, zxw3002)
new_esEs10(zxw4002, zxw3002, ty_Int) → new_esEs13(zxw4002, zxw3002)
new_esEs10(zxw4002, zxw3002, app(ty_Ratio, cd)) → new_esEs14(zxw4002, zxw3002, cd)
new_esEs10(zxw4002, zxw3002, ty_Ordering) → new_esEs8(zxw4002, zxw3002)
new_esEs10(zxw4002, zxw3002, app(app(ty_Either, db), dc)) → new_esEs6(zxw4002, zxw3002, db, dc)
new_asAs(False, zxw187) → False
new_asAs(True, zxw187) → zxw187
new_esEs8(EQ, EQ) → True
new_esEs8(LT, EQ) → False
new_esEs8(GT, EQ) → False
new_esEs14(:%(zxw4000, zxw4001), :%(zxw3000, zxw3001), cbb) → new_asAs(new_esEs25(zxw4000, zxw3000, cbb), new_esEs24(zxw4001, zxw3001, cbb))
new_esEs25(zxw4000, zxw3000, ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_esEs25(zxw4000, zxw3000, ty_Int) → new_esEs13(zxw4000, zxw3000)
new_esEs24(zxw4001, zxw3001, ty_Int) → new_esEs13(zxw4001, zxw3001)
new_esEs24(zxw4001, zxw3001, ty_Integer) → new_esEs17(zxw4001, zxw3001)
new_esEs17(Integer(zxw4000), Integer(zxw3000)) → new_primEqInt(zxw4000, zxw3000)
new_primEqInt(Neg(Succ(zxw40000)), Neg(Succ(zxw30000))) → new_primEqNat0(zxw40000, zxw30000)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Succ(zxw40000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(zxw30000))) → False
new_primEqInt(Pos(Succ(zxw40000)), Pos(Succ(zxw30000))) → new_primEqNat0(zxw40000, zxw30000)
new_primEqInt(Pos(Succ(zxw40000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(zxw30000))) → False
new_primEqInt(Pos(Succ(zxw40000)), Neg(zxw3000)) → False
new_primEqInt(Neg(Succ(zxw40000)), Pos(zxw3000)) → False
new_primEqInt(Pos(Zero), Neg(Succ(zxw30000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(zxw30000))) → False
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(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_esEs13(zxw400, zxw300) → new_primEqInt(zxw400, zxw300)
new_esEs20(@0, @0) → True
new_esEs18(Double(zxw4000, zxw4001), Double(zxw3000, zxw3001)) → new_esEs13(new_sr(zxw4000, zxw3000), new_sr(zxw4001, zxw3001))
new_sr(zxw4001, zxw3001) → new_primMulInt(zxw4001, zxw3001)
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Neg(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Pos(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulNat0(Zero, Zero) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_esEs4(@2(zxw4000, zxw4001), @2(zxw3000, zxw3001), baa, bab) → new_asAs(new_esEs22(zxw4000, zxw3000, baa), new_esEs21(zxw4001, zxw3001, bab))
new_esEs22(zxw4000, zxw3000, ty_@0) → new_esEs20(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Float) → new_esEs19(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, app(ty_Ratio, bbf)) → new_esEs14(zxw4000, zxw3000, bbf)
new_esEs22(zxw4000, zxw3000, app(app(ty_@2, bce), bcf)) → new_esEs4(zxw4000, zxw3000, bce, bcf)
new_esEs22(zxw4000, zxw3000, ty_Ordering) → new_esEs8(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Bool) → new_esEs9(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, app(app(app(ty_@3, bbh), bca), bcb)) → new_esEs5(zxw4000, zxw3000, bbh, bca, bcb)
new_esEs22(zxw4000, zxw3000, ty_Int) → new_esEs13(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Char) → new_esEs15(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, app(ty_[], bbg)) → new_esEs16(zxw4000, zxw3000, bbg)
new_esEs22(zxw4000, zxw3000, ty_Double) → new_esEs18(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, app(app(ty_Either, bcc), bcd)) → new_esEs6(zxw4000, zxw3000, bcc, bcd)
new_esEs22(zxw4000, zxw3000, ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, app(ty_Maybe, bbe)) → new_esEs7(zxw4000, zxw3000, bbe)
new_esEs21(zxw4001, zxw3001, ty_Double) → new_esEs18(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, app(ty_Ratio, bad)) → new_esEs14(zxw4001, zxw3001, bad)
new_esEs21(zxw4001, zxw3001, app(app(ty_Either, bba), bbb)) → new_esEs6(zxw4001, zxw3001, bba, bbb)
new_esEs21(zxw4001, zxw3001, ty_Char) → new_esEs15(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, ty_Float) → new_esEs19(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, ty_@0) → new_esEs20(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, app(app(app(ty_@3, baf), bag), bah)) → new_esEs5(zxw4001, zxw3001, baf, bag, bah)
new_esEs21(zxw4001, zxw3001, app(ty_Maybe, bac)) → new_esEs7(zxw4001, zxw3001, bac)
new_esEs21(zxw4001, zxw3001, app(app(ty_@2, bbc), bbd)) → new_esEs4(zxw4001, zxw3001, bbc, bbd)
new_esEs21(zxw4001, zxw3001, ty_Bool) → new_esEs9(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, ty_Integer) → new_esEs17(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, ty_Ordering) → new_esEs8(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, ty_Int) → new_esEs13(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, app(ty_[], bae)) → new_esEs16(zxw4001, zxw3001, bae)
new_esEs16(:(zxw4000, zxw4001), [], dad) → False
new_esEs16([], :(zxw3000, zxw3001), dad) → False
new_esEs16(:(zxw4000, zxw4001), :(zxw3000, zxw3001), dad) → new_asAs(new_esEs28(zxw4000, zxw3000, dad), new_esEs16(zxw4001, zxw3001, dad))
new_esEs16([], [], dad) → True
new_esEs28(zxw4000, zxw3000, ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, app(app(app(ty_@3, ddd), dde), ddf)) → new_esEs5(zxw4000, zxw3000, ddd, dde, ddf)
new_esEs28(zxw4000, zxw3000, ty_Bool) → new_esEs9(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_@0) → new_esEs20(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_Float) → new_esEs19(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, app(app(ty_Either, ddg), ddh)) → new_esEs6(zxw4000, zxw3000, ddg, ddh)
new_esEs28(zxw4000, zxw3000, ty_Char) → new_esEs15(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_Int) → new_esEs13(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_Ordering) → new_esEs8(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, app(ty_Ratio, ddb)) → new_esEs14(zxw4000, zxw3000, ddb)
new_esEs28(zxw4000, zxw3000, app(ty_[], ddc)) → new_esEs16(zxw4000, zxw3000, ddc)
new_esEs28(zxw4000, zxw3000, app(ty_Maybe, dda)) → new_esEs7(zxw4000, zxw3000, dda)
new_esEs28(zxw4000, zxw3000, app(app(ty_@2, dea), deb)) → new_esEs4(zxw4000, zxw3000, dea, deb)
new_esEs28(zxw4000, zxw3000, ty_Double) → new_esEs18(zxw4000, zxw3000)
new_esEs15(Char(zxw4000), Char(zxw3000)) → new_primEqNat0(zxw4000, zxw3000)
new_esEs19(Float(zxw4000, zxw4001), Float(zxw3000, zxw3001)) → new_esEs13(new_sr(zxw4000, zxw3000), new_sr(zxw4001, zxw3001))
new_esEs9(True, True) → True
new_esEs9(True, False) → False
new_esEs9(False, True) → False
new_esEs9(False, False) → True
new_compare18(zxw49000, zxw50000) → new_compare24(zxw49000, zxw50000, new_esEs9(zxw49000, zxw50000))
new_compare24(zxw49000, zxw50000, False) → new_compare13(zxw49000, zxw50000, new_ltEs5(zxw49000, zxw50000))
new_compare24(zxw49000, zxw50000, True) → EQ
new_ltEs5(True, False) → False
new_ltEs5(True, True) → True
new_ltEs5(False, False) → True
new_ltEs5(False, True) → True
new_compare13(zxw49000, zxw50000, False) → GT
new_compare13(zxw49000, zxw50000, True) → LT
new_compare9(Integer(zxw49000), Integer(zxw50000)) → new_primCmpInt(zxw49000, zxw50000)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_compare6(zxw49000, zxw50000) → new_compare23(zxw49000, zxw50000, new_esEs8(zxw49000, zxw50000))
new_compare23(zxw49000, zxw50000, True) → EQ
new_compare23(zxw49000, zxw50000, False) → new_compare10(zxw49000, zxw50000, new_ltEs4(zxw49000, zxw50000))
new_ltEs4(EQ, GT) → True
new_ltEs4(EQ, LT) → False
new_ltEs4(GT, EQ) → False
new_ltEs4(EQ, EQ) → True
new_ltEs4(GT, LT) → False
new_ltEs4(LT, GT) → True
new_ltEs4(LT, EQ) → True
new_ltEs4(LT, LT) → True
new_ltEs4(GT, GT) → True
new_compare10(zxw49000, zxw50000, True) → LT
new_compare10(zxw49000, zxw50000, False) → GT
new_compare8(:%(zxw49000, zxw49001), :%(zxw50000, zxw50001), ty_Integer) → new_compare9(new_sr0(zxw49000, zxw50001), new_sr0(zxw50000, zxw49001))
new_compare8(:%(zxw49000, zxw49001), :%(zxw50000, zxw50001), ty_Int) → new_compare7(new_sr(zxw49000, zxw50001), new_sr(zxw50000, zxw49001))
new_compare7(zxw49, zxw50) → new_primCmpInt(zxw49, zxw50)
new_sr0(Integer(zxw500000), Integer(zxw490010)) → Integer(new_primMulInt(zxw500000, zxw490010))
new_compare32(zxw49000, zxw50000, be, bf) → new_compare25(zxw49000, zxw50000, new_esEs6(zxw49000, zxw50000, be, bf), be, bf)
new_compare25(zxw49000, zxw50000, True, be, bf) → EQ
new_compare25(zxw49000, zxw50000, False, be, bf) → new_compare15(zxw49000, zxw50000, new_ltEs7(zxw49000, zxw50000, be, bf), be, bf)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_@0, cbg) → new_ltEs14(zxw49000, zxw50000)
new_ltEs7(Left(zxw49000), Right(zxw50000), cbf, cbg) → True
new_ltEs7(Left(zxw49000), Left(zxw50000), app(app(app(ty_@3, dba), dbb), dbc), cbg) → new_ltEs15(zxw49000, zxw50000, dba, dbb, dbc)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbf, app(app(ty_@2, dbg), dbh)) → new_ltEs9(zxw49000, zxw50000, dbg, dbh)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbf, app(ty_Ratio, dch)) → new_ltEs17(zxw49000, zxw50000, dch)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Char, cbg) → new_ltEs12(zxw49000, zxw50000)
new_ltEs7(Left(zxw49000), Left(zxw50000), app(app(ty_@2, dae), daf), cbg) → new_ltEs9(zxw49000, zxw50000, dae, daf)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbf, ty_Bool) → new_ltEs5(zxw49000, zxw50000)
new_ltEs7(Left(zxw49000), Left(zxw50000), app(app(ty_Either, dbd), dbe), cbg) → new_ltEs7(zxw49000, zxw50000, dbd, dbe)
new_ltEs7(Left(zxw49000), Left(zxw50000), app(ty_Maybe, dag), cbg) → new_ltEs8(zxw49000, zxw50000, dag)
new_ltEs8(Just(zxw49000), Just(zxw50000), app(app(ty_Either, he), hf)) → new_ltEs7(zxw49000, zxw50000, he, hf)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbf, app(ty_Maybe, dca)) → new_ltEs8(zxw49000, zxw50000, dca)
new_ltEs8(Just(zxw49000), Just(zxw50000), app(ty_Maybe, gh)) → new_ltEs8(zxw49000, zxw50000, gh)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbf, app(app(ty_Either, dcf), dcg)) → new_ltEs7(zxw49000, zxw50000, dcf, dcg)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbf, ty_Integer) → new_ltEs16(zxw49000, zxw50000)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbf, app(app(app(ty_@3, dcc), dcd), dce)) → new_ltEs15(zxw49000, zxw50000, dcc, dcd, dce)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Bool, cbg) → new_ltEs5(zxw49000, zxw50000)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Int, cbg) → new_ltEs10(zxw49000, zxw50000)
new_ltEs7(Right(zxw49000), Left(zxw50000), cbf, cbg) → False
new_ltEs7(Left(zxw49000), Left(zxw50000), app(ty_[], dah), cbg) → new_ltEs13(zxw49000, zxw50000, dah)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Integer, cbg) → new_ltEs16(zxw49000, zxw50000)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbf, app(ty_[], dcb)) → new_ltEs13(zxw49000, zxw50000, dcb)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Double, cbg) → new_ltEs11(zxw49000, zxw50000)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbf, ty_Ordering) → new_ltEs4(zxw49000, zxw50000)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Ordering, cbg) → new_ltEs4(zxw49000, zxw50000)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbf, ty_Char) → new_ltEs12(zxw49000, zxw50000)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbf, ty_Int) → new_ltEs10(zxw49000, zxw50000)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbf, ty_Double) → new_ltEs11(zxw49000, zxw50000)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Float, cbg) → new_ltEs6(zxw49000, zxw50000)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbf, ty_Float) → new_ltEs6(zxw49000, zxw50000)
new_ltEs7(Left(zxw49000), Left(zxw50000), app(ty_Ratio, dbf), cbg) → new_ltEs17(zxw49000, zxw50000, dbf)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbf, ty_@0) → new_ltEs14(zxw49000, zxw50000)
new_compare15(zxw49000, zxw50000, True, be, bf) → LT
new_compare15(zxw49000, zxw50000, False, be, bf) → GT
new_ltEs14(zxw4900, zxw5000) → new_fsEs(new_compare31(zxw4900, zxw5000))
new_compare31(@0, @0) → EQ
new_ltEs17(zxw4900, zxw5000, hh) → new_fsEs(new_compare8(zxw4900, zxw5000, hh))
new_ltEs6(zxw4900, zxw5000) → new_fsEs(new_compare14(zxw4900, zxw5000))
new_compare14(Float(zxw49000, zxw49001), Float(zxw50000, zxw50001)) → new_compare7(new_sr(zxw49000, zxw50000), new_sr(zxw49001, zxw50001))
new_ltEs11(zxw4900, zxw5000) → new_fsEs(new_compare16(zxw4900, zxw5000))
new_compare16(Double(zxw49000, zxw49001), Double(zxw50000, zxw50001)) → new_compare7(new_sr(zxw49000, zxw50000), new_sr(zxw49001, zxw50001))
new_ltEs10(zxw4900, zxw5000) → new_fsEs(new_compare7(zxw4900, zxw5000))
new_ltEs12(zxw4900, zxw5000) → new_fsEs(new_compare12(zxw4900, zxw5000))
new_compare12(Char(zxw49000), Char(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_ltEs16(zxw4900, zxw5000) → new_fsEs(new_compare9(zxw4900, zxw5000))
new_ltEs15(@3(zxw49000, zxw49001, zxw49002), @3(zxw50000, zxw50001, zxw50002), cbc, cbd, cbe) → new_pePe(new_lt20(zxw49000, zxw50000, cbc), new_asAs(new_esEs27(zxw49000, zxw50000, cbc), new_pePe(new_lt19(zxw49001, zxw50001, cbd), new_asAs(new_esEs26(zxw49001, zxw50001, cbd), new_ltEs20(zxw49002, zxw50002, cbe)))))
new_lt20(zxw49000, zxw50000, app(app(ty_@2, chb), chc)) → new_lt11(zxw49000, zxw50000, chb, chc)
new_lt20(zxw49000, zxw50000, ty_@0) → new_lt15(zxw49000, zxw50000)
new_lt20(zxw49000, zxw50000, app(ty_[], che)) → new_lt9(zxw49000, zxw50000, che)
new_lt20(zxw49000, zxw50000, ty_Ordering) → new_lt14(zxw49000, zxw50000)
new_lt20(zxw49000, zxw50000, app(app(ty_Either, daa), dab)) → new_lt17(zxw49000, zxw50000, daa, dab)
new_lt20(zxw49000, zxw50000, ty_Char) → new_lt6(zxw49000, zxw50000)
new_lt20(zxw49000, zxw50000, ty_Int) → new_lt4(zxw49000, zxw50000)
new_lt20(zxw49000, zxw50000, ty_Double) → new_lt8(zxw49000, zxw50000)
new_lt20(zxw49000, zxw50000, ty_Bool) → new_lt13(zxw49000, zxw50000)
new_lt20(zxw49000, zxw50000, ty_Float) → new_lt7(zxw49000, zxw50000)
new_lt20(zxw49000, zxw50000, app(ty_Ratio, dac)) → new_lt18(zxw49000, zxw50000, dac)
new_lt20(zxw49000, zxw50000, app(app(app(ty_@3, chf), chg), chh)) → new_lt16(zxw49000, zxw50000, chf, chg, chh)
new_lt20(zxw49000, zxw50000, ty_Integer) → new_lt5(zxw49000, zxw50000)
new_lt20(zxw49000, zxw50000, app(ty_Maybe, chd)) → new_lt12(zxw49000, zxw50000, chd)
new_esEs27(zxw49000, zxw50000, app(ty_[], che)) → new_esEs16(zxw49000, zxw50000, che)
new_esEs27(zxw49000, zxw50000, app(ty_Maybe, chd)) → new_esEs7(zxw49000, zxw50000, chd)
new_esEs27(zxw49000, zxw50000, ty_Bool) → new_esEs9(zxw49000, zxw50000)
new_esEs27(zxw49000, zxw50000, ty_Char) → new_esEs15(zxw49000, zxw50000)
new_esEs27(zxw49000, zxw50000, ty_Float) → new_esEs19(zxw49000, zxw50000)
new_esEs27(zxw49000, zxw50000, ty_@0) → new_esEs20(zxw49000, zxw50000)
new_esEs27(zxw49000, zxw50000, ty_Ordering) → new_esEs8(zxw49000, zxw50000)
new_esEs27(zxw49000, zxw50000, ty_Integer) → new_esEs17(zxw49000, zxw50000)
new_esEs27(zxw49000, zxw50000, app(app(app(ty_@3, chf), chg), chh)) → new_esEs5(zxw49000, zxw50000, chf, chg, chh)
new_esEs27(zxw49000, zxw50000, ty_Int) → new_esEs13(zxw49000, zxw50000)
new_esEs27(zxw49000, zxw50000, app(app(ty_Either, daa), dab)) → new_esEs6(zxw49000, zxw50000, daa, dab)
new_esEs27(zxw49000, zxw50000, ty_Double) → new_esEs18(zxw49000, zxw50000)
new_esEs27(zxw49000, zxw50000, app(ty_Ratio, dac)) → new_esEs14(zxw49000, zxw50000, dac)
new_esEs27(zxw49000, zxw50000, app(app(ty_@2, chb), chc)) → new_esEs4(zxw49000, zxw50000, chb, chc)
new_lt19(zxw49001, zxw50001, ty_Integer) → new_lt5(zxw49001, zxw50001)
new_lt19(zxw49001, zxw50001, ty_Ordering) → new_lt14(zxw49001, zxw50001)
new_lt19(zxw49001, zxw50001, ty_Int) → new_lt4(zxw49001, zxw50001)
new_lt19(zxw49001, zxw50001, app(ty_[], cgc)) → new_lt9(zxw49001, zxw50001, cgc)
new_lt19(zxw49001, zxw50001, ty_@0) → new_lt15(zxw49001, zxw50001)
new_lt19(zxw49001, zxw50001, app(app(ty_@2, cfh), cga)) → new_lt11(zxw49001, zxw50001, cfh, cga)
new_lt19(zxw49001, zxw50001, ty_Float) → new_lt7(zxw49001, zxw50001)
new_lt19(zxw49001, zxw50001, app(ty_Ratio, cha)) → new_lt18(zxw49001, zxw50001, cha)
new_lt19(zxw49001, zxw50001, app(app(app(ty_@3, cgd), cge), cgf)) → new_lt16(zxw49001, zxw50001, cgd, cge, cgf)
new_lt19(zxw49001, zxw50001, ty_Char) → new_lt6(zxw49001, zxw50001)
new_lt19(zxw49001, zxw50001, app(app(ty_Either, cgg), cgh)) → new_lt17(zxw49001, zxw50001, cgg, cgh)
new_lt19(zxw49001, zxw50001, ty_Bool) → new_lt13(zxw49001, zxw50001)
new_lt19(zxw49001, zxw50001, ty_Double) → new_lt8(zxw49001, zxw50001)
new_lt19(zxw49001, zxw50001, app(ty_Maybe, cgb)) → new_lt12(zxw49001, zxw50001, cgb)
new_esEs26(zxw49001, zxw50001, app(ty_[], cgc)) → new_esEs16(zxw49001, zxw50001, cgc)
new_esEs26(zxw49001, zxw50001, ty_Char) → new_esEs15(zxw49001, zxw50001)
new_esEs26(zxw49001, zxw50001, ty_Ordering) → new_esEs8(zxw49001, zxw50001)
new_esEs26(zxw49001, zxw50001, ty_Bool) → new_esEs9(zxw49001, zxw50001)
new_esEs26(zxw49001, zxw50001, ty_Integer) → new_esEs17(zxw49001, zxw50001)
new_esEs26(zxw49001, zxw50001, ty_Int) → new_esEs13(zxw49001, zxw50001)
new_esEs26(zxw49001, zxw50001, app(app(ty_@2, cfh), cga)) → new_esEs4(zxw49001, zxw50001, cfh, cga)
new_esEs26(zxw49001, zxw50001, ty_Double) → new_esEs18(zxw49001, zxw50001)
new_esEs26(zxw49001, zxw50001, app(ty_Ratio, cha)) → new_esEs14(zxw49001, zxw50001, cha)
new_esEs26(zxw49001, zxw50001, app(ty_Maybe, cgb)) → new_esEs7(zxw49001, zxw50001, cgb)
new_esEs26(zxw49001, zxw50001, ty_Float) → new_esEs19(zxw49001, zxw50001)
new_esEs26(zxw49001, zxw50001, app(app(ty_Either, cgg), cgh)) → new_esEs6(zxw49001, zxw50001, cgg, cgh)
new_esEs26(zxw49001, zxw50001, app(app(app(ty_@3, cgd), cge), cgf)) → new_esEs5(zxw49001, zxw50001, cgd, cge, cgf)
new_esEs26(zxw49001, zxw50001, ty_@0) → new_esEs20(zxw49001, zxw50001)
new_ltEs20(zxw49002, zxw50002, ty_Bool) → new_ltEs5(zxw49002, zxw50002)
new_ltEs20(zxw49002, zxw50002, app(ty_Maybe, ceh)) → new_ltEs8(zxw49002, zxw50002, ceh)
new_ltEs20(zxw49002, zxw50002, ty_Integer) → new_ltEs16(zxw49002, zxw50002)
new_ltEs20(zxw49002, zxw50002, app(ty_[], cfa)) → new_ltEs13(zxw49002, zxw50002, cfa)
new_ltEs20(zxw49002, zxw50002, app(app(app(ty_@3, cfb), cfc), cfd)) → new_ltEs15(zxw49002, zxw50002, cfb, cfc, cfd)
new_ltEs20(zxw49002, zxw50002, ty_Ordering) → new_ltEs4(zxw49002, zxw50002)
new_ltEs20(zxw49002, zxw50002, app(app(ty_@2, cef), ceg)) → new_ltEs9(zxw49002, zxw50002, cef, ceg)
new_ltEs20(zxw49002, zxw50002, ty_Char) → new_ltEs12(zxw49002, zxw50002)
new_ltEs20(zxw49002, zxw50002, app(ty_Ratio, cfg)) → new_ltEs17(zxw49002, zxw50002, cfg)
new_ltEs20(zxw49002, zxw50002, ty_@0) → new_ltEs14(zxw49002, zxw50002)
new_ltEs20(zxw49002, zxw50002, ty_Float) → new_ltEs6(zxw49002, zxw50002)
new_ltEs20(zxw49002, zxw50002, ty_Double) → new_ltEs11(zxw49002, zxw50002)
new_ltEs20(zxw49002, zxw50002, app(app(ty_Either, cfe), cff)) → new_ltEs7(zxw49002, zxw50002, cfe, cff)
new_ltEs20(zxw49002, zxw50002, ty_Int) → new_ltEs10(zxw49002, zxw50002)
new_pePe(False, zxw213) → zxw213
new_pePe(True, zxw213) → True
new_ltEs9(@2(zxw49000, zxw49001), @2(zxw50000, zxw50001), bec, bed) → new_pePe(new_lt10(zxw49000, zxw50000, bec), new_asAs(new_esEs23(zxw49000, zxw50000, bec), new_ltEs18(zxw49001, zxw50001, bed)))
new_lt10(zxw49000, zxw50000, ty_Float) → new_lt7(zxw49000, zxw50000)
new_lt10(zxw49000, zxw50000, ty_Double) → new_lt8(zxw49000, zxw50000)
new_lt10(zxw49000, zxw50000, ty_Int) → new_lt4(zxw49000, zxw50000)
new_lt10(zxw49000, zxw50000, app(app(ty_@2, gc), gd)) → new_lt11(zxw49000, zxw50000, gc, gd)
new_lt10(zxw49000, zxw50000, ty_Ordering) → new_lt14(zxw49000, zxw50000)
new_lt10(zxw49000, zxw50000, app(ty_Maybe, bfg)) → new_lt12(zxw49000, zxw50000, bfg)
new_lt10(zxw49000, zxw50000, app(app(app(ty_@3, bfh), bga), bgb)) → new_lt16(zxw49000, zxw50000, bfh, bga, bgb)
new_lt10(zxw49000, zxw50000, app(app(ty_Either, be), bf)) → new_lt17(zxw49000, zxw50000, be, bf)
new_lt10(zxw49000, zxw50000, app(ty_Ratio, bgc)) → new_lt18(zxw49000, zxw50000, bgc)
new_lt10(zxw49000, zxw50000, ty_Integer) → new_lt5(zxw49000, zxw50000)
new_lt10(zxw49000, zxw50000, ty_Char) → new_lt6(zxw49000, zxw50000)
new_lt10(zxw49000, zxw50000, ty_Bool) → new_lt13(zxw49000, zxw50000)
new_lt10(zxw49000, zxw50000, app(ty_[], bg)) → new_lt9(zxw49000, zxw50000, bg)
new_lt10(zxw49000, zxw50000, ty_@0) → new_lt15(zxw49000, zxw50000)
new_esEs23(zxw49000, zxw50000, app(app(ty_@2, gc), gd)) → new_esEs4(zxw49000, zxw50000, gc, gd)
new_esEs23(zxw49000, zxw50000, ty_Float) → new_esEs19(zxw49000, zxw50000)
new_esEs23(zxw49000, zxw50000, ty_Char) → new_esEs15(zxw49000, zxw50000)
new_esEs23(zxw49000, zxw50000, ty_Bool) → new_esEs9(zxw49000, zxw50000)
new_esEs23(zxw49000, zxw50000, app(ty_Maybe, bfg)) → new_esEs7(zxw49000, zxw50000, bfg)
new_esEs23(zxw49000, zxw50000, app(app(ty_Either, be), bf)) → new_esEs6(zxw49000, zxw50000, be, bf)
new_esEs23(zxw49000, zxw50000, ty_Ordering) → new_esEs8(zxw49000, zxw50000)
new_esEs23(zxw49000, zxw50000, ty_Integer) → new_esEs17(zxw49000, zxw50000)
new_esEs23(zxw49000, zxw50000, app(ty_Ratio, bgc)) → new_esEs14(zxw49000, zxw50000, bgc)
new_esEs23(zxw49000, zxw50000, ty_@0) → new_esEs20(zxw49000, zxw50000)
new_esEs23(zxw49000, zxw50000, ty_Double) → new_esEs18(zxw49000, zxw50000)
new_esEs23(zxw49000, zxw50000, ty_Int) → new_esEs13(zxw49000, zxw50000)
new_esEs23(zxw49000, zxw50000, app(ty_[], bg)) → new_esEs16(zxw49000, zxw50000, bg)
new_esEs23(zxw49000, zxw50000, app(app(app(ty_@3, bfh), bga), bgb)) → new_esEs5(zxw49000, zxw50000, bfh, bga, bgb)
new_ltEs18(zxw49001, zxw50001, ty_Integer) → new_ltEs16(zxw49001, zxw50001)
new_ltEs18(zxw49001, zxw50001, app(ty_[], beh)) → new_ltEs13(zxw49001, zxw50001, beh)
new_ltEs18(zxw49001, zxw50001, ty_Int) → new_ltEs10(zxw49001, zxw50001)
new_ltEs18(zxw49001, zxw50001, app(app(ty_Either, bfd), bfe)) → new_ltEs7(zxw49001, zxw50001, bfd, bfe)
new_ltEs18(zxw49001, zxw50001, ty_@0) → new_ltEs14(zxw49001, zxw50001)
new_ltEs18(zxw49001, zxw50001, ty_Ordering) → new_ltEs4(zxw49001, zxw50001)
new_ltEs18(zxw49001, zxw50001, ty_Bool) → new_ltEs5(zxw49001, zxw50001)
new_ltEs18(zxw49001, zxw50001, app(app(app(ty_@3, bfa), bfb), bfc)) → new_ltEs15(zxw49001, zxw50001, bfa, bfb, bfc)
new_ltEs18(zxw49001, zxw50001, ty_Float) → new_ltEs6(zxw49001, zxw50001)
new_ltEs18(zxw49001, zxw50001, ty_Double) → new_ltEs11(zxw49001, zxw50001)
new_ltEs18(zxw49001, zxw50001, app(app(ty_@2, bee), bef)) → new_ltEs9(zxw49001, zxw50001, bee, bef)
new_ltEs18(zxw49001, zxw50001, app(ty_Ratio, bff)) → new_ltEs17(zxw49001, zxw50001, bff)
new_ltEs18(zxw49001, zxw50001, ty_Char) → new_ltEs12(zxw49001, zxw50001)
new_ltEs18(zxw49001, zxw50001, app(ty_Maybe, beg)) → new_ltEs8(zxw49001, zxw50001, beg)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Bool) → new_ltEs5(zxw49000, zxw50000)
new_ltEs8(Nothing, Just(zxw50000), ge) → True
new_ltEs8(Just(zxw49000), Just(zxw50000), app(app(ty_@2, gf), gg)) → new_ltEs9(zxw49000, zxw50000, gf, gg)
new_ltEs8(Just(zxw49000), Nothing, ge) → False
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Double) → new_ltEs11(zxw49000, zxw50000)
new_ltEs8(Just(zxw49000), Just(zxw50000), app(ty_[], ha)) → new_ltEs13(zxw49000, zxw50000, ha)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_@0) → new_ltEs14(zxw49000, zxw50000)
new_ltEs8(Just(zxw49000), Just(zxw50000), app(ty_Ratio, hg)) → new_ltEs17(zxw49000, zxw50000, hg)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Float) → new_ltEs6(zxw49000, zxw50000)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Ordering) → new_ltEs4(zxw49000, zxw50000)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Int) → new_ltEs10(zxw49000, zxw50000)
new_ltEs8(Nothing, Nothing, ge) → True
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Char) → new_ltEs12(zxw49000, zxw50000)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Integer) → new_ltEs16(zxw49000, zxw50000)
new_ltEs8(Just(zxw49000), Just(zxw50000), app(app(app(ty_@3, hb), hc), hd)) → new_ltEs15(zxw49000, zxw50000, hb, hc, hd)
new_lt15(zxw49000, zxw50000) → new_esEs8(new_compare31(zxw49000, zxw50000), LT)
new_lt9(zxw49000, zxw50000, bg) → new_esEs8(new_compare0(zxw49000, zxw50000, bg), LT)
new_lt13(zxw49000, zxw50000) → new_esEs8(new_compare18(zxw49000, zxw50000), LT)
new_lt6(zxw49000, zxw50000) → new_esEs8(new_compare12(zxw49000, zxw50000), LT)
new_lt5(zxw49000, zxw50000) → new_esEs8(new_compare9(zxw49000, zxw50000), LT)
new_lt18(zxw49000, zxw50000, bgc) → new_esEs8(new_compare8(zxw49000, zxw50000, bgc), LT)
new_lt17(zxw49000, zxw50000, be, bf) → new_esEs8(new_compare32(zxw49000, zxw50000, be, bf), LT)
new_lt16(zxw49000, zxw50000, bfh, bga, bgb) → new_esEs8(new_compare28(zxw49000, zxw50000, bfh, bga, bgb), LT)
new_compare28(zxw49000, zxw50000, bfh, bga, bgb) → new_compare210(zxw49000, zxw50000, new_esEs5(zxw49000, zxw50000, bfh, bga, bgb), bfh, bga, bgb)
new_compare210(zxw49000, zxw50000, False, bfh, bga, bgb) → new_compare110(zxw49000, zxw50000, new_ltEs15(zxw49000, zxw50000, bfh, bga, bgb), bfh, bga, bgb)
new_compare210(zxw49000, zxw50000, True, bfh, bga, bgb) → EQ
new_compare110(zxw49000, zxw50000, True, bfh, bga, bgb) → LT
new_compare110(zxw49000, zxw50000, False, bfh, bga, bgb) → GT
new_lt12(zxw490, zxw500, bcg) → new_esEs8(new_compare19(zxw490, zxw500, bcg), LT)
new_lt14(zxw49000, zxw50000) → new_esEs8(new_compare6(zxw49000, zxw50000), LT)
new_lt11(zxw49000, zxw50000, gc, gd) → new_esEs8(new_compare30(zxw49000, zxw50000, gc, gd), LT)
new_compare30(zxw49000, zxw50000, gc, gd) → new_compare27(zxw49000, zxw50000, new_esEs4(zxw49000, zxw50000, gc, gd), gc, gd)
new_compare27(zxw49000, zxw50000, False, gc, gd) → new_compare17(zxw49000, zxw50000, new_ltEs9(zxw49000, zxw50000, gc, gd), gc, gd)
new_compare27(zxw49000, zxw50000, True, gc, gd) → EQ
new_compare17(zxw49000, zxw50000, True, gc, gd) → LT
new_compare17(zxw49000, zxw50000, False, gc, gd) → GT
new_lt4(zxw490, zxw500) → new_esEs8(new_compare7(zxw490, zxw500), LT)
new_lt8(zxw49000, zxw50000) → new_esEs8(new_compare16(zxw49000, zxw50000), LT)
new_lt7(zxw49000, zxw50000) → new_esEs8(new_compare14(zxw49000, zxw50000), LT)
new_esEs29(zxw400, zxw300, ty_Integer) → new_esEs17(zxw400, zxw300)
new_esEs29(zxw400, zxw300, ty_@0) → new_esEs20(zxw400, zxw300)
new_esEs29(zxw400, zxw300, app(ty_Maybe, bgd)) → new_esEs7(zxw400, zxw300, bgd)
new_esEs29(zxw400, zxw300, ty_Bool) → new_esEs9(zxw400, zxw300)
new_esEs29(zxw400, zxw300, app(app(ty_@2, baa), bab)) → new_esEs4(zxw400, zxw300, baa, bab)
new_esEs29(zxw400, zxw300, ty_Int) → new_esEs13(zxw400, zxw300)
new_esEs29(zxw400, zxw300, app(ty_[], dad)) → new_esEs16(zxw400, zxw300, dad)
new_esEs29(zxw400, zxw300, ty_Double) → new_esEs18(zxw400, zxw300)
new_esEs29(zxw400, zxw300, ty_Char) → new_esEs15(zxw400, zxw300)
new_esEs29(zxw400, zxw300, app(app(ty_Either, cdc), cca)) → new_esEs6(zxw400, zxw300, cdc, cca)
new_esEs29(zxw400, zxw300, app(app(app(ty_@3, bh), ca), cb)) → new_esEs5(zxw400, zxw300, bh, ca, cb)
new_esEs29(zxw400, zxw300, ty_Float) → new_esEs19(zxw400, zxw300)
new_esEs29(zxw400, zxw300, app(ty_Ratio, cbb)) → new_esEs14(zxw400, zxw300, cbb)
new_esEs29(zxw400, zxw300, ty_Ordering) → new_esEs8(zxw400, zxw300)
new_compare35(zxw400, h) → new_compare26(Just(zxw400), Nothing, False, h)

The set Q consists of the following terms:

new_esEs17(Integer(x0), Integer(x1))
new_esEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Integer)
new_lt10(x0, x1, ty_Double)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_compare18(x0, x1)
new_compare29(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Double)
new_pePe(False, x0)
new_lt10(x0, x1, app(app(ty_Either, x2), x3))
new_lt17(x0, x1, x2, x3)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Left(x0), Left(x1), ty_Bool, x2)
new_compare7(x0, x1)
new_esEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_compare110(x0, x1, False, x2, x3, x4)
new_primMulNat0(Succ(x0), Zero)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs7(Just(x0), Just(x1), ty_Double)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_ltEs8(Just(x0), Just(x1), ty_Integer)
new_esEs10(x0, x1, ty_Int)
new_ltEs10(x0, x1)
new_esEs28(x0, x1, ty_Int)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs12(x0, x1, ty_Char)
new_compare25(x0, x1, True, x2, x3)
new_primMulNat0(Succ(x0), Succ(x1))
new_ltEs7(Left(x0), Left(x1), ty_Integer, x2)
new_esEs6(Left(x0), Left(x1), ty_Int, x2)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Int)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs16(x0, x1)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_compare13(x0, x1, True)
new_esEs10(x0, x1, ty_Ordering)
new_compare29(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs19(x0, x1, ty_Float)
new_compare0([], :(x0, x1), x2)
new_esEs11(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_Int)
new_esEs6(Left(x0), Left(x1), ty_@0, x2)
new_ltEs8(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare11(x0, x1, True, x2)
new_ltEs19(x0, x1, ty_Ordering)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs8(GT, GT)
new_compare11(x0, x1, False, x2)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_compare17(x0, x1, True, x2, x3)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCompAux1(x0, x1, x2, x3)
new_esEs8(LT, LT)
new_esEs29(x0, x1, ty_@0)
new_compare29(x0, x1, ty_Double)
new_esEs18(Double(x0, x1), Double(x2, x3))
new_primCmpNat0(Zero, x0)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_lt11(x0, x1, x2, x3)
new_ltEs8(Just(x0), Just(x1), ty_Bool)
new_esEs11(x0, x1, ty_@0)
new_primCmpNat1(Zero, Succ(x0))
new_esEs25(x0, x1, ty_Int)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_sr(x0, x1)
new_ltEs5(False, False)
new_ltEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_compare6(x0, x1)
new_lt10(x0, x1, ty_Ordering)
new_esEs6(Right(x0), Left(x1), x2, x3)
new_esEs6(Left(x0), Right(x1), x2, x3)
new_compare29(x0, x1, ty_Int)
new_esEs30(x0, x1, ty_Bool)
new_ltEs15(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs26(x0, x1, ty_Integer)
new_primEqNat0(Zero, Succ(x0))
new_primCmpNat1(Zero, Zero)
new_esEs7(Nothing, Nothing, x0)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs7(Left(x0), Left(x1), ty_Bool, x2)
new_compare16(Double(x0, x1), Double(x2, x3))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_lt7(x0, x1)
new_esEs28(x0, x1, ty_@0)
new_ltEs20(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Integer)
new_esEs16(:(x0, x1), :(x2, x3), x4)
new_esEs23(x0, x1, ty_Integer)
new_esEs11(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Double)
new_ltEs19(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_Char)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_compare15(x0, x1, True, x2, x3)
new_esEs24(x0, x1, ty_Int)
new_esEs6(Left(x0), Left(x1), ty_Char, x2)
new_esEs6(Left(x0), Left(x1), ty_Integer, x2)
new_primEqNat0(Zero, Zero)
new_compare32(x0, x1, x2, x3)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs8(Just(x0), Just(x1), app(ty_Maybe, x2))
new_compare36(x0, x1, x2)
new_ltEs8(Just(x0), Just(x1), ty_Double)
new_ltEs8(Just(x0), Just(x1), ty_Ordering)
new_ltEs19(x0, x1, ty_@0)
new_compare110(x0, x1, True, x2, x3, x4)
new_compare24(x0, x1, False)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs7(Just(x0), Nothing, x1)
new_esEs29(x0, x1, ty_Bool)
new_esEs9(True, True)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_lt18(x0, x1, x2)
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt4(x0, x1)
new_primMulNat0(Zero, Zero)
new_ltEs13(x0, x1, x2)
new_esEs23(x0, x1, ty_Char)
new_esEs30(x0, x1, ty_Ordering)
new_esEs10(x0, x1, ty_@0)
new_lt10(x0, x1, app(ty_Ratio, x2))
new_lt10(x0, x1, ty_Char)
new_esEs30(x0, x1, ty_Int)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_Integer)
new_fsEs(x0)
new_ltEs4(GT, GT)
new_lt8(x0, x1)
new_esEs30(x0, x1, ty_@0)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs10(x0, x1, ty_Float)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs28(x0, x1, ty_Double)
new_esEs29(x0, x1, ty_Char)
new_compare29(x0, x1, app(ty_[], x2))
new_esEs6(Right(x0), Right(x1), x2, ty_Float)
new_compare27(x0, x1, True, x2, x3)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_lt10(x0, x1, ty_Int)
new_esEs10(x0, x1, ty_Bool)
new_lt16(x0, x1, x2, x3, x4)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs23(x0, x1, ty_Ordering)
new_esEs7(Just(x0), Just(x1), ty_Int)
new_esEs10(x0, x1, ty_Char)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_lt10(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_pePe(True, x0)
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, ty_Int)
new_primPlusNat0(Zero, x0)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_lt10(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, ty_Int)
new_compare210(x0, x1, True, x2, x3, x4)
new_lt6(x0, x1)
new_esEs26(x0, x1, ty_Bool)
new_compare24(x0, x1, True)
new_ltEs18(x0, x1, ty_Integer)
new_compare15(x0, x1, False, x2, x3)
new_compare14(Float(x0, x1), Float(x2, x3))
new_ltEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(x0, x1)
new_esEs29(x0, x1, ty_Integer)
new_esEs12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primPlusNat1(Zero, Zero)
new_primCompAux0(x0, GT)
new_compare23(x0, x1, True)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_lt19(x0, x1, app(ty_[], x2))
new_lt15(x0, x1)
new_ltEs7(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs29(x0, x1, ty_Ordering)
new_compare19(x0, x1, x2)
new_compare13(x0, x1, False)
new_compare26(Nothing, Just(x0), False, x1)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_lt20(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_@0)
new_compare30(x0, x1, x2, x3)
new_primPlusNat0(Succ(x0), x1)
new_esEs12(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs4(EQ, EQ)
new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs19(x0, x1, ty_Char)
new_ltEs7(Right(x0), Right(x1), x2, ty_Char)
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_ltEs11(x0, x1)
new_esEs12(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Integer)
new_compare29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Char)
new_esEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs8(Nothing, Just(x0), x1)
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs8(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Just(x0), Just(x1), ty_Char)
new_ltEs7(Left(x0), Left(x1), ty_@0, x2)
new_lt9(x0, x1, x2)
new_esEs10(x0, x1, app(ty_[], x2))
new_esEs12(x0, x1, ty_Float)
new_compare31(@0, @0)
new_esEs7(Just(x0), Just(x1), ty_Float)
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs16([], :(x0, x1), x2)
new_primCmpNat2(x0, Zero)
new_ltEs4(LT, EQ)
new_ltEs4(EQ, LT)
new_esEs12(x0, x1, ty_Int)
new_lt19(x0, x1, ty_Double)
new_esEs6(Right(x0), Right(x1), x2, ty_Integer)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_primMulInt(Pos(x0), Pos(x1))
new_lt20(x0, x1, ty_Bool)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_ltEs7(Right(x0), Right(x1), x2, ty_Int)
new_ltEs18(x0, x1, app(ty_[], x2))
new_esEs30(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_@0)
new_esEs10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs7(Right(x0), Right(x1), x2, ty_Double)
new_asAs(True, x0)
new_primEqNat0(Succ(x0), Zero)
new_compare26(Just(x0), Nothing, False, x1)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs7(Left(x0), Left(x1), ty_Int, x2)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_esEs12(x0, x1, app(ty_[], x2))
new_esEs13(x0, x1)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_ltEs7(Left(x0), Right(x1), x2, x3)
new_ltEs7(Right(x0), Left(x1), x2, x3)
new_esEs14(:%(x0, x1), :%(x2, x3), x4)
new_compare26(x0, x1, True, x2)
new_esEs21(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Integer)
new_ltEs7(Left(x0), Left(x1), ty_Double, x2)
new_ltEs8(Nothing, Nothing, x0)
new_lt20(x0, x1, ty_@0)
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_Bool)
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Char)
new_compare26(Just(x0), Just(x1), False, x2)
new_esEs28(x0, x1, ty_Ordering)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Ordering)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_lt12(x0, x1, x2)
new_esEs10(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_esEs12(x0, x1, app(ty_Maybe, x2))
new_esEs30(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, ty_Bool)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs27(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_Double)
new_esEs25(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(ty_[], x2))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_lt10(x0, x1, ty_Bool)
new_primPlusNat1(Succ(x0), Zero)
new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs22(x0, x1, ty_Float)
new_ltEs4(LT, LT)
new_esEs10(x0, x1, ty_Integer)
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Integer)
new_compare29(x0, x1, app(app(ty_@2, x2), x3))
new_compare23(x0, x1, False)
new_esEs21(x0, x1, app(ty_[], x2))
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs11(x0, x1, ty_Bool)
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_compare29(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_Double)
new_esEs21(x0, x1, ty_Bool)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, ty_Double)
new_esEs26(x0, x1, ty_Ordering)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs7(Nothing, Just(x0), x1)
new_primPlusNat1(Zero, Succ(x0))
new_ltEs12(x0, x1)
new_compare10(x0, x1, False)
new_lt10(x0, x1, app(app(ty_@2, x2), x3))
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Left(x0), Left(x1), ty_Float, x2)
new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_primCmpNat0(Succ(x0), x1)
new_lt10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, ty_@0)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs8(GT, EQ)
new_esEs8(EQ, GT)
new_esEs22(x0, x1, ty_Bool)
new_lt19(x0, x1, ty_Float)
new_lt19(x0, x1, ty_Integer)
new_ltEs8(Just(x0), Just(x1), ty_Char)
new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Left(x0), Left(x1), ty_Double, x2)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_ltEs8(Just(x0), Just(x1), ty_Float)
new_lt5(x0, x1)
new_compare29(x0, x1, ty_Ordering)
new_ltEs18(x0, x1, ty_Bool)
new_compare28(x0, x1, x2, x3, x4)
new_esEs11(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_@0)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, ty_Int)
new_esEs11(x0, x1, ty_Char)
new_esEs10(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Float)
new_lt19(x0, x1, ty_Ordering)
new_compare29(x0, x1, ty_Integer)
new_compare25(x0, x1, False, x2, x3)
new_esEs6(Right(x0), Right(x1), x2, ty_Char)
new_esEs26(x0, x1, app(ty_[], x2))
new_ltEs18(x0, x1, ty_Float)
new_ltEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs9(False, False)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs21(x0, x1, ty_Double)
new_esEs12(x0, x1, ty_Ordering)
new_ltEs8(Just(x0), Nothing, x1)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs22(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpNat1(Succ(x0), Succ(x1))
new_esEs10(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_@0)
new_ltEs6(x0, x1)
new_lt10(x0, x1, ty_Float)
new_esEs22(x0, x1, ty_Int)
new_ltEs7(Left(x0), Left(x1), ty_Char, x2)
new_compare17(x0, x1, False, x2, x3)
new_ltEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs21(x0, x1, ty_Float)
new_esEs29(x0, x1, ty_Double)
new_primCompAux0(x0, EQ)
new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare26(Nothing, Nothing, False, x0)
new_compare27(x0, x1, False, x2, x3)
new_esEs21(x0, x1, ty_Integer)
new_primCmpNat1(Succ(x0), Zero)
new_ltEs18(x0, x1, ty_@0)
new_esEs22(x0, x1, ty_Double)
new_ltEs7(Right(x0), Right(x1), x2, ty_@0)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, ty_Bool)
new_esEs16([], [], x0)
new_compare29(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, app(ty_[], x2))
new_lt13(x0, x1)
new_esEs23(x0, x1, ty_Bool)
new_ltEs5(True, True)
new_ltEs7(Right(x0), Right(x1), x2, ty_Integer)
new_lt19(x0, x1, ty_Int)
new_compare35(x0, x1)
new_lt19(x0, x1, ty_Char)
new_ltEs4(EQ, GT)
new_ltEs4(GT, EQ)
new_esEs6(Right(x0), Right(x1), x2, ty_@0)
new_not(True)
new_esEs11(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Float)
new_compare0(:(x0, x1), [], x2)
new_esEs28(x0, x1, ty_Char)
new_lt19(x0, x1, ty_@0)
new_esEs10(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, ty_Ordering)
new_ltEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs26(x0, x1, ty_Char)
new_ltEs18(x0, x1, ty_Int)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_ltEs20(x0, x1, ty_Ordering)
new_not(False)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_lt14(x0, x1)
new_compare12(Char(x0), Char(x1))
new_esEs15(Char(x0), Char(x1))
new_esEs11(x0, x1, app(ty_[], x2))
new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_compare10(x0, x1, True)
new_lt10(x0, x1, ty_@0)
new_asAs(False, x0)
new_esEs22(x0, x1, ty_Ordering)
new_ltEs18(x0, x1, ty_Char)
new_esEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs17(x0, x1, x2)
new_compare29(x0, x1, ty_Float)
new_lt19(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_Char)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_ltEs8(Just(x0), Just(x1), ty_@0)
new_esEs20(@0, @0)
new_ltEs8(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs7(Left(x0), Left(x1), ty_Float, x2)
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Int)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_esEs16(:(x0, x1), [], x2)
new_ltEs19(x0, x1, ty_Double)
new_esEs9(True, False)
new_esEs9(False, True)
new_esEs22(x0, x1, ty_Char)
new_ltEs7(Right(x0), Right(x1), x2, ty_Float)
new_ltEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare29(x0, x1, ty_Bool)
new_ltEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs30(x0, x1, ty_Double)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, ty_Integer)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs11(x0, x1, ty_Double)
new_ltEs20(x0, x1, ty_Float)
new_primCompAux0(x0, LT)
new_primCmpNat2(x0, Succ(x1))
new_esEs11(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs12(x0, x1, ty_Integer)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs10(x0, x1, ty_Double)
new_ltEs8(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_sr0(Integer(x0), Integer(x1))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs29(x0, x1, ty_Float)
new_ltEs8(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_primEqInt(Pos(Zero), Pos(Zero))
new_ltEs18(x0, x1, ty_Double)
new_esEs12(x0, x1, ty_Double)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_compare0(:(x0, x1), :(x2, x3), x4)
new_esEs29(x0, x1, ty_Int)
new_esEs12(x0, x1, ty_Bool)
new_compare9(Integer(x0), Integer(x1))
new_lt10(x0, x1, ty_Integer)
new_esEs30(x0, x1, ty_Char)
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs19(Float(x0, x1), Float(x2, x3))
new_primMulNat0(Zero, Succ(x0))
new_compare0([], [], x0)
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Just(x0), Just(x1), ty_@0)
new_ltEs4(GT, LT)
new_ltEs4(LT, GT)
new_ltEs5(True, False)
new_ltEs5(False, True)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs9(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs27(x0, x1, app(ty_[], x2))
new_ltEs8(Just(x0), Just(x1), ty_Int)
new_esEs12(x0, x1, app(app(ty_Either, x2), x3))
new_compare29(x0, x1, ty_@0)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Float)
new_esEs23(x0, x1, ty_Float)
new_compare210(x0, x1, False, x2, x3, x4)
new_esEs30(x0, x1, ty_Float)
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))

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

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



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ 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_splitGT3(Nothing, zxw31, zxw32, zxw33, zxw34, Nothing, h, ba) → new_splitGT1(zxw31, zxw32, zxw33, zxw34, new_esEs8(new_compare33(h), LT), h, ba)
new_splitGT2(zxw300, zxw31, zxw32, zxw33, Branch(zxw340, zxw341, zxw342, zxw343, zxw344), True, h, ba) → new_splitGT3(zxw340, zxw341, zxw342, zxw343, zxw344, Nothing, h, ba)
new_splitGT10(zxw300, zxw31, zxw32, zxw33, zxw34, True, h, ba) → new_splitGT(zxw33, h, ba)
new_splitGT(Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba) → new_splitGT3(zxw340, zxw341, zxw342, zxw343, zxw344, Nothing, h, ba)
new_splitGT1(zxw31, zxw32, zxw33, zxw34, True, h, ba) → new_splitGT(zxw33, h, ba)
new_splitGT2(zxw300, zxw31, zxw32, zxw33, zxw34, False, h, ba) → new_splitGT10(zxw300, zxw31, zxw32, zxw33, zxw34, new_esEs8(new_compare34(zxw300, h), LT), h, ba)
new_splitGT3(Just(zxw300), zxw31, zxw32, zxw33, zxw34, Nothing, h, ba) → new_splitGT2(zxw300, zxw31, zxw32, zxw33, zxw34, new_esEs8(new_compare26(Nothing, Just(zxw300), False, h), GT), h, ba)

The TRS R consists of the following rules:

new_esEs6(Right(zxw4000), Right(zxw3000), cdc, ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_esEs29(zxw400, zxw300, ty_Integer) → new_esEs17(zxw400, zxw300)
new_esEs28(zxw4000, zxw3000, ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_esEs7(Just(zxw4000), Just(zxw3000), app(ty_Maybe, bge)) → new_esEs7(zxw4000, zxw3000, bge)
new_ltEs19(zxw4900, zxw5000, ty_Integer) → new_ltEs16(zxw4900, zxw5000)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_@0, cbg) → new_ltEs14(zxw49000, zxw50000)
new_esEs27(zxw49000, zxw50000, app(ty_[], che)) → new_esEs16(zxw49000, zxw50000, che)
new_ltEs4(EQ, GT) → True
new_esEs22(zxw4000, zxw3000, ty_@0) → new_esEs20(zxw4000, zxw3000)
new_compare15(zxw49000, zxw50000, True, be, bf) → LT
new_esEs6(Right(zxw4000), Right(zxw3000), cdc, ty_Float) → new_esEs19(zxw4000, zxw3000)
new_ltEs9(@2(zxw49000, zxw49001), @2(zxw50000, zxw50001), bec, bed) → new_pePe(new_lt10(zxw49000, zxw50000, bec), new_asAs(new_esEs23(zxw49000, zxw50000, bec), new_ltEs18(zxw49001, zxw50001, bed)))
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Integer, cca) → new_esEs17(zxw4000, zxw3000)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_esEs23(zxw49000, zxw50000, app(app(ty_@2, gc), gd)) → new_esEs4(zxw49000, zxw50000, gc, gd)
new_compare29(zxw49000, zxw50000, ty_Char) → new_compare12(zxw49000, zxw50000)
new_esEs22(zxw4000, zxw3000, ty_Float) → new_esEs19(zxw4000, zxw3000)
new_esEs6(Right(zxw4000), Right(zxw3000), cdc, ty_Int) → new_esEs13(zxw4000, zxw3000)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Bool) → new_ltEs5(zxw49000, zxw50000)
new_lt19(zxw49001, zxw50001, ty_Integer) → new_lt5(zxw49001, zxw50001)
new_compare33(h) → new_compare26(Nothing, Nothing, True, h)
new_esEs12(zxw4000, zxw3000, ty_Bool) → new_esEs9(zxw4000, zxw3000)
new_esEs27(zxw49000, zxw50000, app(ty_Maybe, chd)) → new_esEs7(zxw49000, zxw50000, chd)
new_esEs12(zxw4000, zxw3000, ty_Char) → new_esEs15(zxw4000, zxw3000)
new_esEs11(zxw4001, zxw3001, app(ty_[], dh)) → new_esEs16(zxw4001, zxw3001, dh)
new_compare12(Char(zxw49000), Char(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_ltEs19(zxw4900, zxw5000, ty_Double) → new_ltEs11(zxw4900, zxw5000)
new_compare29(zxw49000, zxw50000, ty_Double) → new_compare16(zxw49000, zxw50000)
new_ltEs20(zxw49002, zxw50002, ty_Bool) → new_ltEs5(zxw49002, zxw50002)
new_esEs23(zxw49000, zxw50000, ty_Float) → new_esEs19(zxw49000, zxw50000)
new_lt19(zxw49001, zxw50001, ty_Ordering) → new_lt14(zxw49001, zxw50001)
new_lt19(zxw49001, zxw50001, ty_Int) → new_lt4(zxw49001, zxw50001)
new_esEs7(Just(zxw4000), Just(zxw3000), app(app(ty_Either, bhc), bhd)) → new_esEs6(zxw4000, zxw3000, bhc, bhd)
new_primMulNat0(Zero, Zero) → Zero
new_ltEs7(Left(zxw49000), Right(zxw50000), cbf, cbg) → True
new_compare26(Just(zxw4900), Nothing, False, bcg) → GT
new_esEs26(zxw49001, zxw50001, app(ty_[], cgc)) → new_esEs16(zxw49001, zxw50001, cgc)
new_esEs27(zxw49000, zxw50000, ty_Bool) → new_esEs9(zxw49000, zxw50000)
new_ltEs18(zxw49001, zxw50001, ty_Integer) → new_ltEs16(zxw49001, zxw50001)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_ltEs18(zxw49001, zxw50001, app(ty_[], beh)) → new_ltEs13(zxw49001, zxw50001, beh)
new_ltEs20(zxw49002, zxw50002, app(ty_Maybe, ceh)) → new_ltEs8(zxw49002, zxw50002, ceh)
new_esEs11(zxw4001, zxw3001, ty_Char) → new_esEs15(zxw4001, zxw3001)
new_esEs11(zxw4001, zxw3001, ty_Float) → new_esEs19(zxw4001, zxw3001)
new_esEs29(zxw400, zxw300, ty_@0) → new_esEs20(zxw400, zxw300)
new_lt8(zxw49000, zxw50000) → new_esEs8(new_compare16(zxw49000, zxw50000), LT)
new_esEs26(zxw49001, zxw50001, ty_Char) → new_esEs15(zxw49001, zxw50001)
new_lt20(zxw49000, zxw50000, app(app(ty_@2, chb), chc)) → new_lt11(zxw49000, zxw50000, chb, chc)
new_esEs29(zxw400, zxw300, app(ty_Maybe, bgd)) → new_esEs7(zxw400, zxw300, bgd)
new_esEs23(zxw49000, zxw50000, ty_Char) → new_esEs15(zxw49000, zxw50000)
new_esEs23(zxw49000, zxw50000, ty_Bool) → new_esEs9(zxw49000, zxw50000)
new_esEs27(zxw49000, zxw50000, ty_Char) → new_esEs15(zxw49000, zxw50000)
new_compare26(Nothing, Just(zxw5000), False, bcg) → LT
new_lt10(zxw49000, zxw50000, ty_Float) → new_lt7(zxw49000, zxw50000)
new_esEs21(zxw4001, zxw3001, ty_Double) → new_esEs18(zxw4001, zxw3001)
new_ltEs19(zxw4900, zxw5000, ty_Int) → new_ltEs10(zxw4900, zxw5000)
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_lt9(zxw49000, zxw50000, bg) → new_esEs8(new_compare0(zxw49000, zxw50000, bg), LT)
new_compare210(zxw49000, zxw50000, False, bfh, bga, bgb) → new_compare110(zxw49000, zxw50000, new_ltEs15(zxw49000, zxw50000, bfh, bga, bgb), bfh, bga, bgb)
new_esEs22(zxw4000, zxw3000, app(ty_Ratio, bbf)) → new_esEs14(zxw4000, zxw3000, bbf)
new_esEs21(zxw4001, zxw3001, app(ty_Ratio, bad)) → new_esEs14(zxw4001, zxw3001, bad)
new_esEs30(zxw20, zxw15, ty_Bool) → new_esEs9(zxw20, zxw15)
new_esEs7(Just(zxw4000), Just(zxw3000), app(app(ty_@2, bhe), bhf)) → new_esEs4(zxw4000, zxw3000, bhe, bhf)
new_esEs25(zxw4000, zxw3000, ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Bool) → new_esEs9(zxw4000, zxw3000)
new_esEs30(zxw20, zxw15, ty_Float) → new_esEs19(zxw20, zxw15)
new_ltEs20(zxw49002, zxw50002, ty_Integer) → new_ltEs16(zxw49002, zxw50002)
new_esEs21(zxw4001, zxw3001, app(app(ty_Either, bba), bbb)) → new_esEs6(zxw4001, zxw3001, bba, bbb)
new_ltEs7(Left(zxw49000), Left(zxw50000), app(app(app(ty_@3, dba), dbb), dbc), cbg) → new_ltEs15(zxw49000, zxw50000, dba, dbb, dbc)
new_esEs29(zxw400, zxw300, ty_Bool) → new_esEs9(zxw400, zxw300)
new_ltEs14(zxw4900, zxw5000) → new_fsEs(new_compare31(zxw4900, zxw5000))
new_compare24(zxw49000, zxw50000, False) → new_compare13(zxw49000, zxw50000, new_ltEs5(zxw49000, zxw50000))
new_esEs7(Just(zxw4000), Just(zxw3000), app(ty_Ratio, bgf)) → new_esEs14(zxw4000, zxw3000, bgf)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbf, app(app(ty_@2, dbg), dbh)) → new_ltEs9(zxw49000, zxw50000, dbg, dbh)
new_lt4(zxw490, zxw500) → new_esEs8(new_compare7(zxw490, zxw500), LT)
new_esEs28(zxw4000, zxw3000, app(app(app(ty_@3, ddd), dde), ddf)) → new_esEs5(zxw4000, zxw3000, ddd, dde, ddf)
new_esEs28(zxw4000, zxw3000, ty_Bool) → new_esEs9(zxw4000, zxw3000)
new_compare19(zxw490, zxw500, bcg) → new_compare26(zxw490, zxw500, new_esEs7(zxw490, zxw500, bcg), bcg)
new_esEs17(Integer(zxw4000), Integer(zxw3000)) → new_primEqInt(zxw4000, zxw3000)
new_pePe(False, zxw213) → zxw213
new_lt12(zxw490, zxw500, bcg) → new_esEs8(new_compare19(zxw490, zxw500, bcg), LT)
new_esEs20(@0, @0) → True
new_esEs6(Right(zxw4000), Right(zxw3000), cdc, app(ty_Ratio, cde)) → new_esEs14(zxw4000, zxw3000, cde)
new_esEs6(Left(zxw4000), Left(zxw3000), app(app(ty_@2, cda), cdb), cca) → new_esEs4(zxw4000, zxw3000, cda, cdb)
new_compare23(zxw49000, zxw50000, True) → EQ
new_esEs11(zxw4001, zxw3001, ty_Int) → new_esEs13(zxw4001, zxw3001)
new_lt19(zxw49001, zxw50001, app(ty_[], cgc)) → new_lt9(zxw49001, zxw50001, cgc)
new_compare29(zxw49000, zxw50000, ty_@0) → new_compare31(zxw49000, zxw50000)
new_compare26(Nothing, Nothing, False, bcg) → LT
new_esEs10(zxw4002, zxw3002, app(ty_Maybe, cc)) → new_esEs7(zxw4002, zxw3002, cc)
new_ltEs16(zxw4900, zxw5000) → new_fsEs(new_compare9(zxw4900, zxw5000))
new_esEs22(zxw4000, zxw3000, app(app(ty_@2, bce), bcf)) → new_esEs4(zxw4000, zxw3000, bce, bcf)
new_esEs23(zxw49000, zxw50000, app(ty_Maybe, bfg)) → new_esEs7(zxw49000, zxw50000, bfg)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbf, app(ty_Ratio, dch)) → new_ltEs17(zxw49000, zxw50000, dch)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Char, cbg) → new_ltEs12(zxw49000, zxw50000)
new_esEs28(zxw4000, zxw3000, ty_@0) → new_esEs20(zxw4000, zxw3000)
new_esEs10(zxw4002, zxw3002, app(app(app(ty_@3, cf), cg), da)) → new_esEs5(zxw4002, zxw3002, cf, cg, da)
new_ltEs20(zxw49002, zxw50002, app(ty_[], cfa)) → new_ltEs13(zxw49002, zxw50002, cfa)
new_esEs27(zxw49000, zxw50000, ty_Float) → new_esEs19(zxw49000, zxw50000)
new_ltEs20(zxw49002, zxw50002, app(app(app(ty_@3, cfb), cfc), cfd)) → new_ltEs15(zxw49002, zxw50002, cfb, cfc, cfd)
new_esEs22(zxw4000, zxw3000, ty_Ordering) → new_esEs8(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Bool) → new_esEs9(zxw4000, zxw3000)
new_compare6(zxw49000, zxw50000) → new_compare23(zxw49000, zxw50000, new_esEs8(zxw49000, zxw50000))
new_esEs29(zxw400, zxw300, app(app(ty_@2, baa), bab)) → new_esEs4(zxw400, zxw300, baa, bab)
new_esEs12(zxw4000, zxw3000, app(ty_[], fb)) → new_esEs16(zxw4000, zxw3000, fb)
new_compare32(zxw49000, zxw50000, be, bf) → new_compare25(zxw49000, zxw50000, new_esEs6(zxw49000, zxw50000, be, bf), be, bf)
new_compare29(zxw49000, zxw50000, ty_Int) → new_compare7(zxw49000, zxw50000)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Bool, cca) → new_esEs9(zxw4000, zxw3000)
new_ltEs8(Nothing, Just(zxw50000), ge) → True
new_ltEs7(Left(zxw49000), Left(zxw50000), app(app(ty_@2, dae), daf), cbg) → new_ltEs9(zxw49000, zxw50000, dae, daf)
new_esEs6(Right(zxw4000), Left(zxw3000), cdc, cca) → False
new_esEs6(Left(zxw4000), Right(zxw3000), cdc, cca) → False
new_esEs8(LT, LT) → True
new_lt20(zxw49000, zxw50000, ty_@0) → new_lt15(zxw49000, zxw50000)
new_esEs10(zxw4002, zxw3002, ty_Integer) → new_esEs17(zxw4002, zxw3002)
new_esEs28(zxw4000, zxw3000, ty_Float) → new_esEs19(zxw4000, zxw3000)
new_compare29(zxw49000, zxw50000, app(app(app(ty_@3, cad), cae), caf)) → new_compare28(zxw49000, zxw50000, cad, cae, caf)
new_lt19(zxw49001, zxw50001, ty_@0) → new_lt15(zxw49001, zxw50001)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbf, ty_Bool) → new_ltEs5(zxw49000, zxw50000)
new_ltEs5(True, False) → False
new_lt19(zxw49001, zxw50001, app(app(ty_@2, cfh), cga)) → new_lt11(zxw49001, zxw50001, cfh, cga)
new_compare0([], [], bhg) → EQ
new_pePe(True, zxw213) → True
new_primEqNat0(Zero, Zero) → True
new_compare34(zxw300, h) → new_compare26(Nothing, Just(zxw300), False, h)
new_esEs14(:%(zxw4000, zxw4001), :%(zxw3000, zxw3001), cbb) → new_asAs(new_esEs25(zxw4000, zxw3000, cbb), new_esEs24(zxw4001, zxw3001, cbb))
new_lt10(zxw49000, zxw50000, ty_Double) → new_lt8(zxw49000, zxw50000)
new_ltEs20(zxw49002, zxw50002, ty_Ordering) → new_ltEs4(zxw49002, zxw50002)
new_compare27(zxw49000, zxw50000, False, gc, gd) → new_compare17(zxw49000, zxw50000, new_ltEs9(zxw49000, zxw50000, gc, gd), gc, gd)
new_compare11(zxw180, zxw181, True, bd) → LT
new_esEs23(zxw49000, zxw50000, app(app(ty_Either, be), bf)) → new_esEs6(zxw49000, zxw50000, be, bf)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_@0, cca) → new_esEs20(zxw4000, zxw3000)
new_esEs6(Right(zxw4000), Right(zxw3000), cdc, ty_Bool) → new_esEs9(zxw4000, zxw3000)
new_esEs12(zxw4000, zxw3000, ty_Int) → new_esEs13(zxw4000, zxw3000)
new_lt20(zxw49000, zxw50000, app(ty_[], che)) → new_lt9(zxw49000, zxw50000, che)
new_esEs6(Right(zxw4000), Right(zxw3000), cdc, app(app(ty_Either, ceb), cec)) → new_esEs6(zxw4000, zxw3000, ceb, cec)
new_compare26(Just(zxw4900), Just(zxw5000), False, bcg) → new_compare11(zxw4900, zxw5000, new_ltEs19(zxw4900, zxw5000, bcg), bcg)
new_ltEs5(True, True) → True
new_ltEs7(Left(zxw49000), Left(zxw50000), app(ty_Maybe, dag), cbg) → new_ltEs8(zxw49000, zxw50000, dag)
new_esEs29(zxw400, zxw300, ty_Int) → new_esEs13(zxw400, zxw300)
new_compare36(zxw20, zxw15, bch) → new_compare26(Just(zxw20), Just(zxw15), new_esEs30(zxw20, zxw15, bch), bch)
new_ltEs20(zxw49002, zxw50002, app(app(ty_@2, cef), ceg)) → new_ltEs9(zxw49002, zxw50002, cef, ceg)
new_esEs15(Char(zxw4000), Char(zxw3000)) → new_primEqNat0(zxw4000, zxw3000)
new_sr(zxw4001, zxw3001) → new_primMulInt(zxw4001, zxw3001)
new_ltEs18(zxw49001, zxw50001, ty_Int) → new_ltEs10(zxw49001, zxw50001)
new_esEs25(zxw4000, zxw3000, ty_Int) → new_esEs13(zxw4000, zxw3000)
new_compare7(zxw49, zxw50) → new_primCmpInt(zxw49, zxw50)
new_primCmpNat1(Zero, Zero) → EQ
new_esEs7(Just(zxw4000), Just(zxw3000), app(ty_[], bgg)) → new_esEs16(zxw4000, zxw3000, bgg)
new_lt10(zxw49000, zxw50000, ty_Int) → new_lt4(zxw49000, zxw50000)
new_esEs28(zxw4000, zxw3000, app(app(ty_Either, ddg), ddh)) → new_esEs6(zxw4000, zxw3000, ddg, ddh)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbf, app(ty_Maybe, dca)) → new_ltEs8(zxw49000, zxw50000, dca)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbf, ty_Integer) → new_ltEs16(zxw49000, zxw50000)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbf, app(app(app(ty_@3, dcc), dcd), dce)) → new_ltEs15(zxw49000, zxw50000, dcc, dcd, dce)
new_esEs26(zxw49001, zxw50001, ty_Ordering) → new_esEs8(zxw49001, zxw50001)
new_esEs8(GT, GT) → True
new_esEs27(zxw49000, zxw50000, ty_@0) → new_esEs20(zxw49000, zxw50000)
new_esEs13(zxw400, zxw300) → new_primEqInt(zxw400, zxw300)
new_lt13(zxw49000, zxw50000) → new_esEs8(new_compare18(zxw49000, zxw50000), LT)
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_lt20(zxw49000, zxw50000, ty_Ordering) → new_lt14(zxw49000, zxw50000)
new_esEs11(zxw4001, zxw3001, ty_Ordering) → new_esEs8(zxw4001, zxw3001)
new_esEs11(zxw4001, zxw3001, app(app(ty_@2, ef), eg)) → new_esEs4(zxw4001, zxw3001, ef, eg)
new_lt10(zxw49000, zxw50000, app(app(ty_@2, gc), gd)) → new_lt11(zxw49000, zxw50000, gc, gd)
new_compare23(zxw49000, zxw50000, False) → new_compare10(zxw49000, zxw50000, new_ltEs4(zxw49000, zxw50000))
new_esEs8(LT, GT) → False
new_esEs8(GT, LT) → False
new_ltEs19(zxw4900, zxw5000, app(app(app(ty_@3, cbc), cbd), cbe)) → new_ltEs15(zxw4900, zxw5000, cbc, cbd, cbe)
new_lt20(zxw49000, zxw50000, app(app(ty_Either, daa), dab)) → new_lt17(zxw49000, zxw50000, daa, dab)
new_esEs26(zxw49001, zxw50001, ty_Bool) → new_esEs9(zxw49001, zxw50001)
new_ltEs11(zxw4900, zxw5000) → new_fsEs(new_compare16(zxw4900, zxw5000))
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_compare17(zxw49000, zxw50000, True, gc, gd) → LT
new_primEqInt(Neg(Succ(zxw40000)), Neg(Succ(zxw30000))) → new_primEqNat0(zxw40000, zxw30000)
new_ltEs5(False, False) → True
new_esEs23(zxw49000, zxw50000, ty_Ordering) → new_esEs8(zxw49000, zxw50000)
new_ltEs18(zxw49001, zxw50001, app(app(ty_Either, bfd), bfe)) → new_ltEs7(zxw49001, zxw50001, bfd, bfe)
new_esEs28(zxw4000, zxw3000, ty_Char) → new_esEs15(zxw4000, zxw3000)
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)
new_ltEs19(zxw4900, zxw5000, app(ty_Ratio, hh)) → new_ltEs17(zxw4900, zxw5000, hh)
new_esEs10(zxw4002, zxw3002, ty_Bool) → new_esEs9(zxw4002, zxw3002)
new_lt20(zxw49000, zxw50000, ty_Char) → new_lt6(zxw49000, zxw50000)
new_compare13(zxw49000, zxw50000, False) → GT
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Bool, cbg) → new_ltEs5(zxw49000, zxw50000)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Int, cbg) → new_ltEs10(zxw49000, zxw50000)
new_lt11(zxw49000, zxw50000, gc, gd) → new_esEs8(new_compare30(zxw49000, zxw50000, gc, gd), LT)
new_esEs21(zxw4001, zxw3001, ty_Char) → new_esEs15(zxw4001, zxw3001)
new_lt20(zxw49000, zxw50000, ty_Int) → new_lt4(zxw49000, zxw50000)
new_primCompAux1(zxw49000, zxw50000, zxw214, bhg) → new_primCompAux0(zxw214, new_compare29(zxw49000, zxw50000, bhg))
new_esEs7(Just(zxw4000), Just(zxw3000), ty_@0) → new_esEs20(zxw4000, zxw3000)
new_lt16(zxw49000, zxw50000, bfh, bga, bgb) → new_esEs8(new_compare28(zxw49000, zxw50000, bfh, bga, bgb), LT)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_ltEs7(Right(zxw49000), Left(zxw50000), cbf, cbg) → False
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Ordering) → new_esEs8(zxw4000, zxw3000)
new_ltEs7(Left(zxw49000), Left(zxw50000), app(ty_[], dah), cbg) → new_ltEs13(zxw49000, zxw50000, dah)
new_ltEs19(zxw4900, zxw5000, ty_Ordering) → new_ltEs4(zxw4900, zxw5000)
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_ltEs20(zxw49002, zxw50002, ty_Char) → new_ltEs12(zxw49002, zxw50002)
new_esEs11(zxw4001, zxw3001, app(app(app(ty_@3, ea), eb), ec)) → new_esEs5(zxw4001, zxw3001, ea, eb, ec)
new_ltEs20(zxw49002, zxw50002, app(ty_Ratio, cfg)) → new_ltEs17(zxw49002, zxw50002, cfg)
new_ltEs18(zxw49001, zxw50001, ty_@0) → new_ltEs14(zxw49001, zxw50001)
new_primEqInt(Neg(Succ(zxw40000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(zxw30000))) → False
new_ltEs19(zxw4900, zxw5000, ty_Char) → new_ltEs12(zxw4900, zxw5000)
new_esEs12(zxw4000, zxw3000, ty_Double) → new_esEs18(zxw4000, zxw3000)
new_primCompAux0(zxw218, GT) → GT
new_esEs8(EQ, EQ) → True
new_esEs6(Left(zxw4000), Left(zxw3000), app(ty_Ratio, ccb), cca) → new_esEs14(zxw4000, zxw3000, ccb)
new_ltEs8(Just(zxw49000), Just(zxw50000), app(app(ty_Either, he), hf)) → new_ltEs7(zxw49000, zxw50000, he, hf)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Integer, cbg) → new_ltEs16(zxw49000, zxw50000)
new_esEs6(Right(zxw4000), Right(zxw3000), cdc, app(ty_[], cdf)) → new_esEs16(zxw4000, zxw3000, cdf)
new_esEs23(zxw49000, zxw50000, ty_Integer) → new_esEs17(zxw49000, zxw50000)
new_esEs29(zxw400, zxw300, app(ty_[], dad)) → new_esEs16(zxw400, zxw300, dad)
new_esEs28(zxw4000, zxw3000, ty_Int) → new_esEs13(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, app(app(app(ty_@3, bbh), bca), bcb)) → new_esEs5(zxw4000, zxw3000, bbh, bca, bcb)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_ltEs18(zxw49001, zxw50001, ty_Ordering) → new_ltEs4(zxw49001, zxw50001)
new_ltEs4(EQ, LT) → False
new_esEs12(zxw4000, zxw3000, app(ty_Maybe, eh)) → new_esEs7(zxw4000, zxw3000, eh)
new_lt20(zxw49000, zxw50000, ty_Double) → new_lt8(zxw49000, zxw50000)
new_esEs10(zxw4002, zxw3002, ty_Float) → new_esEs19(zxw4002, zxw3002)
new_esEs11(zxw4001, zxw3001, ty_Bool) → new_esEs9(zxw4001, zxw3001)
new_compare11(zxw180, zxw181, False, bd) → GT
new_esEs26(zxw49001, zxw50001, ty_Integer) → new_esEs17(zxw49001, zxw50001)
new_lt10(zxw49000, zxw50000, ty_Ordering) → new_lt14(zxw49000, zxw50000)
new_ltEs18(zxw49001, zxw50001, ty_Bool) → new_ltEs5(zxw49001, zxw50001)
new_esEs12(zxw4000, zxw3000, app(app(app(ty_@3, fc), fd), ff)) → new_esEs5(zxw4000, zxw3000, fc, fd, ff)
new_primEqInt(Pos(Succ(zxw40000)), Pos(Succ(zxw30000))) → new_primEqNat0(zxw40000, zxw30000)
new_compare27(zxw49000, zxw50000, True, gc, gd) → EQ
new_esEs6(Left(zxw4000), Left(zxw3000), app(app(app(ty_@3, ccd), cce), ccf), cca) → new_esEs5(zxw4000, zxw3000, ccd, cce, ccf)
new_lt18(zxw49000, zxw50000, bgc) → new_esEs8(new_compare8(zxw49000, zxw50000, bgc), LT)
new_ltEs18(zxw49001, zxw50001, app(app(app(ty_@3, bfa), bfb), bfc)) → new_ltEs15(zxw49001, zxw50001, bfa, bfb, bfc)
new_lt10(zxw49000, zxw50000, app(ty_Maybe, bfg)) → new_lt12(zxw49000, zxw50000, bfg)
new_esEs26(zxw49001, zxw50001, ty_Int) → new_esEs13(zxw49001, zxw50001)
new_ltEs8(Just(zxw49000), Just(zxw50000), app(app(ty_@2, gf), gg)) → new_ltEs9(zxw49000, zxw50000, gf, gg)
new_primEqNat0(Succ(zxw40000), Succ(zxw30000)) → new_primEqNat0(zxw40000, zxw30000)
new_compare29(zxw49000, zxw50000, app(ty_[], cac)) → new_compare0(zxw49000, zxw50000, cac)
new_esEs27(zxw49000, zxw50000, ty_Ordering) → new_esEs8(zxw49000, zxw50000)
new_esEs27(zxw49000, zxw50000, ty_Integer) → new_esEs17(zxw49000, zxw50000)
new_esEs23(zxw49000, zxw50000, app(ty_Ratio, bgc)) → new_esEs14(zxw49000, zxw50000, bgc)
new_ltEs18(zxw49001, zxw50001, ty_Float) → new_ltEs6(zxw49001, zxw50001)
new_esEs22(zxw4000, zxw3000, ty_Int) → new_esEs13(zxw4000, zxw3000)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbf, app(ty_[], dcb)) → new_ltEs13(zxw49000, zxw50000, dcb)
new_ltEs4(GT, EQ) → False
new_lt7(zxw49000, zxw50000) → new_esEs8(new_compare14(zxw49000, zxw50000), LT)
new_lt10(zxw49000, zxw50000, app(app(app(ty_@3, bfh), bga), bgb)) → new_lt16(zxw49000, zxw50000, bfh, bga, bgb)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Int) → new_esEs13(zxw4000, zxw3000)
new_ltEs19(zxw4900, zxw5000, app(app(ty_Either, cbf), cbg)) → new_ltEs7(zxw4900, zxw5000, cbf, cbg)
new_ltEs8(Just(zxw49000), Nothing, ge) → False
new_esEs21(zxw4001, zxw3001, ty_Float) → new_esEs19(zxw4001, zxw3001)
new_esEs26(zxw49001, zxw50001, app(app(ty_@2, cfh), cga)) → new_esEs4(zxw49001, zxw50001, cfh, cga)
new_esEs27(zxw49000, zxw50000, app(app(app(ty_@3, chf), chg), chh)) → new_esEs5(zxw49000, zxw50000, chf, chg, chh)
new_ltEs13(zxw4900, zxw5000, bhg) → new_fsEs(new_compare0(zxw4900, zxw5000, bhg))
new_esEs22(zxw4000, zxw3000, ty_Char) → new_esEs15(zxw4000, zxw3000)
new_esEs30(zxw20, zxw15, app(ty_Ratio, bdb)) → new_esEs14(zxw20, zxw15, bdb)
new_ltEs18(zxw49001, zxw50001, ty_Double) → new_ltEs11(zxw49001, zxw50001)
new_esEs7(Nothing, Nothing, bgd) → True
new_esEs28(zxw4000, zxw3000, ty_Ordering) → new_esEs8(zxw4000, zxw3000)
new_lt10(zxw49000, zxw50000, app(app(ty_Either, be), bf)) → new_lt17(zxw49000, zxw50000, be, bf)
new_esEs8(EQ, LT) → False
new_esEs8(LT, EQ) → False
new_esEs10(zxw4002, zxw3002, ty_Char) → new_esEs15(zxw4002, zxw3002)
new_primEqInt(Pos(Succ(zxw40000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(zxw30000))) → False
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Double, cbg) → new_ltEs11(zxw49000, zxw50000)
new_ltEs4(EQ, EQ) → True
new_esEs6(Right(zxw4000), Right(zxw3000), cdc, app(ty_Maybe, cdd)) → new_esEs7(zxw4000, zxw3000, cdd)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbf, ty_Ordering) → new_ltEs4(zxw49000, zxw50000)
new_esEs29(zxw400, zxw300, ty_Double) → new_esEs18(zxw400, zxw300)
new_esEs30(zxw20, zxw15, ty_@0) → new_esEs20(zxw20, zxw15)
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_ltEs20(zxw49002, zxw50002, ty_@0) → new_ltEs14(zxw49002, zxw50002)
new_esEs23(zxw49000, zxw50000, ty_@0) → new_esEs20(zxw49000, zxw50000)
new_esEs6(Right(zxw4000), Right(zxw3000), cdc, ty_@0) → new_esEs20(zxw4000, zxw3000)
new_compare210(zxw49000, zxw50000, True, bfh, bga, bgb) → EQ
new_ltEs4(GT, LT) → False
new_sr0(Integer(zxw500000), Integer(zxw490010)) → Integer(new_primMulInt(zxw500000, zxw490010))
new_compare13(zxw49000, zxw50000, True) → LT
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_compare14(Float(zxw49000, zxw49001), Float(zxw50000, zxw50001)) → new_compare7(new_sr(zxw49000, zxw50000), new_sr(zxw49001, zxw50001))
new_primEqInt(Pos(Succ(zxw40000)), Neg(zxw3000)) → False
new_primEqInt(Neg(Succ(zxw40000)), Pos(zxw3000)) → False
new_esEs7(Just(zxw4000), Nothing, bgd) → False
new_esEs7(Nothing, Just(zxw3000), bgd) → False
new_esEs18(Double(zxw4000, zxw4001), Double(zxw3000, zxw3001)) → new_esEs13(new_sr(zxw4000, zxw3000), new_sr(zxw4001, zxw3001))
new_ltEs5(False, True) → True
new_esEs26(zxw49001, zxw50001, ty_Double) → new_esEs18(zxw49001, zxw50001)
new_compare28(zxw49000, zxw50000, bfh, bga, bgb) → new_compare210(zxw49000, zxw50000, new_esEs5(zxw49000, zxw50000, bfh, bga, bgb), bfh, bga, bgb)
new_esEs11(zxw4001, zxw3001, ty_Double) → new_esEs18(zxw4001, zxw3001)
new_ltEs6(zxw4900, zxw5000) → new_fsEs(new_compare14(zxw4900, zxw5000))
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Ordering, cbg) → new_ltEs4(zxw49000, zxw50000)
new_primEqInt(Pos(Zero), Neg(Succ(zxw30000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(zxw30000))) → False
new_ltEs19(zxw4900, zxw5000, app(app(ty_@2, bec), bed)) → new_ltEs9(zxw4900, zxw5000, bec, bed)
new_ltEs20(zxw49002, zxw50002, ty_Float) → new_ltEs6(zxw49002, zxw50002)
new_compare29(zxw49000, zxw50000, app(app(ty_@2, bhh), caa)) → new_compare30(zxw49000, zxw50000, bhh, caa)
new_compare24(zxw49000, zxw50000, True) → EQ
new_esEs27(zxw49000, zxw50000, ty_Int) → new_esEs13(zxw49000, zxw50000)
new_ltEs18(zxw49001, zxw50001, app(app(ty_@2, bee), bef)) → new_ltEs9(zxw49001, zxw50001, bee, bef)
new_esEs6(Right(zxw4000), Right(zxw3000), cdc, ty_Double) → new_esEs18(zxw4000, zxw3000)
new_lt20(zxw49000, zxw50000, ty_Bool) → new_lt13(zxw49000, zxw50000)
new_primCmpNat0(Zero, zxw4900) → LT
new_ltEs7(Right(zxw49000), Right(zxw50000), cbf, ty_Char) → new_ltEs12(zxw49000, zxw50000)
new_esEs8(EQ, GT) → False
new_esEs8(GT, EQ) → False
new_esEs10(zxw4002, zxw3002, app(ty_[], ce)) → new_esEs16(zxw4002, zxw3002, ce)
new_lt15(zxw49000, zxw50000) → new_esEs8(new_compare31(zxw49000, zxw50000), LT)
new_compare17(zxw49000, zxw50000, False, gc, gd) → GT
new_compare29(zxw49000, zxw50000, ty_Float) → new_compare14(zxw49000, zxw50000)
new_esEs30(zxw20, zxw15, ty_Double) → new_esEs18(zxw20, zxw15)
new_esEs28(zxw4000, zxw3000, app(ty_Ratio, ddb)) → new_esEs14(zxw4000, zxw3000, ddb)
new_compare26(zxw490, zxw500, True, bcg) → EQ
new_primCompAux0(zxw218, LT) → LT
new_esEs11(zxw4001, zxw3001, ty_@0) → new_esEs20(zxw4001, zxw3001)
new_esEs30(zxw20, zxw15, app(app(ty_Either, bdg), bdh)) → new_esEs6(zxw20, zxw15, bdg, bdh)
new_esEs12(zxw4000, zxw3000, ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_not(False) → True
new_esEs6(Left(zxw4000), Left(zxw3000), app(app(ty_Either, ccg), cch), cca) → new_esEs6(zxw4000, zxw3000, ccg, cch)
new_esEs28(zxw4000, zxw3000, app(ty_[], ddc)) → new_esEs16(zxw4000, zxw3000, ddc)
new_esEs24(zxw4001, zxw3001, ty_Int) → new_esEs13(zxw4001, zxw3001)
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_esEs26(zxw49001, zxw50001, app(ty_Ratio, cha)) → new_esEs14(zxw49001, zxw50001, cha)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Double) → new_ltEs11(zxw49000, zxw50000)
new_esEs11(zxw4001, zxw3001, app(app(ty_Either, ed), ee)) → new_esEs6(zxw4001, zxw3001, ed, ee)
new_esEs21(zxw4001, zxw3001, ty_@0) → new_esEs20(zxw4001, zxw3001)
new_lt19(zxw49001, zxw50001, ty_Float) → new_lt7(zxw49001, zxw50001)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbf, ty_Int) → new_ltEs10(zxw49000, zxw50000)
new_compare0(:(zxw49000, zxw49001), [], bhg) → GT
new_esEs12(zxw4000, zxw3000, ty_Float) → new_esEs19(zxw4000, zxw3000)
new_ltEs8(Just(zxw49000), Just(zxw50000), app(ty_[], ha)) → new_ltEs13(zxw49000, zxw50000, ha)
new_lt14(zxw49000, zxw50000) → new_esEs8(new_compare6(zxw49000, zxw50000), LT)
new_ltEs19(zxw4900, zxw5000, ty_Float) → new_ltEs6(zxw4900, zxw5000)
new_esEs27(zxw49000, zxw50000, app(app(ty_Either, daa), dab)) → new_esEs6(zxw49000, zxw50000, daa, dab)
new_lt19(zxw49001, zxw50001, app(ty_Ratio, cha)) → new_lt18(zxw49001, zxw50001, cha)
new_esEs9(True, True) → True
new_lt19(zxw49001, zxw50001, app(app(app(ty_@3, cgd), cge), cgf)) → new_lt16(zxw49001, zxw50001, cgd, cge, cgf)
new_lt19(zxw49001, zxw50001, ty_Char) → new_lt6(zxw49001, zxw50001)
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Double, cca) → new_esEs18(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, app(ty_Maybe, dda)) → new_esEs7(zxw4000, zxw3000, dda)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_esEs21(zxw4001, zxw3001, app(app(app(ty_@3, baf), bag), bah)) → new_esEs5(zxw4001, zxw3001, baf, bag, bah)
new_esEs22(zxw4000, zxw3000, app(ty_[], bbg)) → new_esEs16(zxw4000, zxw3000, bbg)
new_esEs21(zxw4001, zxw3001, app(ty_Maybe, bac)) → new_esEs7(zxw4001, zxw3001, bac)
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_esEs22(zxw4000, zxw3000, ty_Double) → new_esEs18(zxw4000, zxw3000)
new_esEs21(zxw4001, zxw3001, app(app(ty_@2, bbc), bbd)) → new_esEs4(zxw4001, zxw3001, bbc, bbd)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_@0) → new_ltEs14(zxw49000, zxw50000)
new_esEs19(Float(zxw4000, zxw4001), Float(zxw3000, zxw3001)) → new_esEs13(new_sr(zxw4000, zxw3000), new_sr(zxw4001, zxw3001))
new_ltEs19(zxw4900, zxw5000, app(ty_Maybe, ge)) → new_ltEs8(zxw4900, zxw5000, ge)
new_primMulInt(Neg(zxw40010), Neg(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_esEs29(zxw400, zxw300, ty_Char) → new_esEs15(zxw400, zxw300)
new_esEs30(zxw20, zxw15, app(ty_Maybe, bda)) → new_esEs7(zxw20, zxw15, bda)
new_primEqNat0(Zero, Succ(zxw30000)) → False
new_primEqNat0(Succ(zxw40000), Zero) → False
new_compare25(zxw49000, zxw50000, True, be, bf) → EQ
new_ltEs7(Left(zxw49000), Left(zxw50000), app(app(ty_Either, dbd), dbe), cbg) → new_ltEs7(zxw49000, zxw50000, dbd, dbe)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_lt10(zxw49000, zxw50000, app(ty_Ratio, bgc)) → new_lt18(zxw49000, zxw50000, bgc)
new_esEs12(zxw4000, zxw3000, ty_@0) → new_esEs20(zxw4000, zxw3000)
new_esEs21(zxw4001, zxw3001, ty_Bool) → new_esEs9(zxw4001, zxw3001)
new_esEs5(@3(zxw4000, zxw4001, zxw4002), @3(zxw3000, zxw3001, zxw3002), bh, ca, cb) → new_asAs(new_esEs12(zxw4000, zxw3000, bh), new_asAs(new_esEs11(zxw4001, zxw3001, ca), new_esEs10(zxw4002, zxw3002, cb)))
new_esEs16(:(zxw4000, zxw4001), [], dad) → False
new_esEs16([], :(zxw3000, zxw3001), dad) → False
new_lt10(zxw49000, zxw50000, ty_Integer) → new_lt5(zxw49000, zxw50000)
new_lt6(zxw49000, zxw50000) → new_esEs8(new_compare12(zxw49000, zxw50000), LT)
new_esEs29(zxw400, zxw300, app(app(ty_Either, cdc), cca)) → new_esEs6(zxw400, zxw300, cdc, cca)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_ltEs4(LT, GT) → True
new_esEs23(zxw49000, zxw50000, ty_Double) → new_esEs18(zxw49000, zxw50000)
new_compare25(zxw49000, zxw50000, False, be, bf) → new_compare15(zxw49000, zxw50000, new_ltEs7(zxw49000, zxw50000, be, bf), be, bf)
new_esEs29(zxw400, zxw300, app(app(app(ty_@3, bh), ca), cb)) → new_esEs5(zxw400, zxw300, bh, ca, cb)
new_lt19(zxw49001, zxw50001, app(app(ty_Either, cgg), cgh)) → new_lt17(zxw49001, zxw50001, cgg, cgh)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_esEs6(Left(zxw4000), Left(zxw3000), app(ty_Maybe, cbh), cca) → new_esEs7(zxw4000, zxw3000, cbh)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Ordering, cca) → new_esEs8(zxw4000, zxw3000)
new_esEs16(:(zxw4000, zxw4001), :(zxw3000, zxw3001), dad) → new_asAs(new_esEs28(zxw4000, zxw3000, dad), new_esEs16(zxw4001, zxw3001, dad))
new_ltEs8(Just(zxw49000), Just(zxw50000), app(ty_Ratio, hg)) → new_ltEs17(zxw49000, zxw50000, hg)
new_compare0(:(zxw49000, zxw49001), :(zxw50000, zxw50001), bhg) → new_primCompAux1(zxw49000, zxw50000, new_compare0(zxw49001, zxw50001, bhg), bhg)
new_esEs11(zxw4001, zxw3001, app(ty_Maybe, df)) → new_esEs7(zxw4001, zxw3001, df)
new_esEs6(Right(zxw4000), Right(zxw3000), cdc, app(app(ty_@2, ced), cee)) → new_esEs4(zxw4000, zxw3000, ced, cee)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Float) → new_ltEs6(zxw49000, zxw50000)
new_compare15(zxw49000, zxw50000, False, be, bf) → GT
new_compare29(zxw49000, zxw50000, app(app(ty_Either, cag), cah)) → new_compare32(zxw49000, zxw50000, cag, cah)
new_lt20(zxw49000, zxw50000, ty_Float) → new_lt7(zxw49000, zxw50000)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Char) → new_esEs15(zxw4000, zxw3000)
new_esEs23(zxw49000, zxw50000, ty_Int) → new_esEs13(zxw49000, zxw50000)
new_esEs30(zxw20, zxw15, app(ty_[], bdc)) → new_esEs16(zxw20, zxw15, bdc)
new_esEs7(Just(zxw4000), Just(zxw3000), app(app(app(ty_@3, bgh), bha), bhb)) → new_esEs5(zxw4000, zxw3000, bgh, bha, bhb)
new_esEs9(True, False) → False
new_esEs9(False, True) → False
new_compare29(zxw49000, zxw50000, app(ty_Ratio, cba)) → new_compare8(zxw49000, zxw50000, cba)
new_esEs10(zxw4002, zxw3002, app(app(ty_@2, dd), de)) → new_esEs4(zxw4002, zxw3002, dd, de)
new_esEs11(zxw4001, zxw3001, app(ty_Ratio, dg)) → new_esEs14(zxw4001, zxw3001, dg)
new_compare29(zxw49000, zxw50000, ty_Ordering) → new_compare6(zxw49000, zxw50000)
new_esEs21(zxw4001, zxw3001, ty_Integer) → new_esEs17(zxw4001, zxw3001)
new_esEs27(zxw49000, zxw50000, ty_Double) → new_esEs18(zxw49000, zxw50000)
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs27(zxw49000, zxw50000, app(ty_Ratio, dac)) → new_esEs14(zxw49000, zxw50000, dac)
new_ltEs4(LT, EQ) → True
new_esEs6(Right(zxw4000), Right(zxw3000), cdc, ty_Char) → new_esEs15(zxw4000, zxw3000)
new_esEs10(zxw4002, zxw3002, ty_Double) → new_esEs18(zxw4002, zxw3002)
new_compare31(@0, @0) → EQ
new_esEs12(zxw4000, zxw3000, app(app(ty_Either, fg), fh)) → new_esEs6(zxw4000, zxw3000, fg, fh)
new_ltEs8(Just(zxw49000), Just(zxw50000), app(ty_Maybe, gh)) → new_ltEs8(zxw49000, zxw50000, gh)
new_lt19(zxw49001, zxw50001, ty_Bool) → new_lt13(zxw49001, zxw50001)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbf, app(app(ty_Either, dcf), dcg)) → new_ltEs7(zxw49000, zxw50000, dcf, dcg)
new_esEs28(zxw4000, zxw3000, app(app(ty_@2, dea), deb)) → new_esEs4(zxw4000, zxw3000, dea, deb)
new_compare9(Integer(zxw49000), Integer(zxw50000)) → new_primCmpInt(zxw49000, zxw50000)
new_asAs(False, zxw187) → False
new_primMulInt(Neg(zxw40010), Pos(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Double) → new_esEs18(zxw4000, zxw3000)
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Ordering) → new_ltEs4(zxw49000, zxw50000)
new_esEs21(zxw4001, zxw3001, ty_Ordering) → new_esEs8(zxw4001, zxw3001)
new_primCmpNat2(zxw4900, Zero) → GT
new_ltEs20(zxw49002, zxw50002, ty_Double) → new_ltEs11(zxw49002, zxw50002)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Char, cca) → new_esEs15(zxw4000, zxw3000)
new_esEs26(zxw49001, zxw50001, app(ty_Maybe, cgb)) → new_esEs7(zxw49001, zxw50001, cgb)
new_esEs10(zxw4002, zxw3002, ty_@0) → new_esEs20(zxw4002, zxw3002)
new_lt19(zxw49001, zxw50001, ty_Double) → new_lt8(zxw49001, zxw50001)
new_esEs28(zxw4000, zxw3000, ty_Double) → new_esEs18(zxw4000, zxw3000)
new_compare110(zxw49000, zxw50000, True, bfh, bga, bgb) → LT
new_esEs24(zxw4001, zxw3001, ty_Integer) → new_esEs17(zxw4001, zxw3001)
new_lt19(zxw49001, zxw50001, app(ty_Maybe, cgb)) → new_lt12(zxw49001, zxw50001, cgb)
new_ltEs18(zxw49001, zxw50001, app(ty_Ratio, bff)) → new_ltEs17(zxw49001, zxw50001, bff)
new_ltEs18(zxw49001, zxw50001, ty_Char) → new_ltEs12(zxw49001, zxw50001)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Float, cca) → new_esEs19(zxw4000, zxw3000)
new_esEs21(zxw4001, zxw3001, ty_Int) → new_esEs13(zxw4001, zxw3001)
new_lt20(zxw49000, zxw50000, app(ty_Ratio, dac)) → new_lt18(zxw49000, zxw50000, dac)
new_ltEs19(zxw4900, zxw5000, ty_@0) → new_ltEs14(zxw4900, zxw5000)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbf, ty_Double) → new_ltEs11(zxw49000, zxw50000)
new_lt17(zxw49000, zxw50000, be, bf) → new_esEs8(new_compare32(zxw49000, zxw50000, be, bf), LT)
new_esEs9(False, False) → True
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Int) → new_ltEs10(zxw49000, zxw50000)
new_esEs30(zxw20, zxw15, ty_Int) → new_esEs13(zxw20, zxw15)
new_ltEs19(zxw4900, zxw5000, ty_Bool) → new_ltEs5(zxw4900, zxw5000)
new_compare29(zxw49000, zxw50000, ty_Integer) → new_compare9(zxw49000, zxw50000)
new_esEs29(zxw400, zxw300, ty_Float) → new_esEs19(zxw400, zxw300)
new_lt20(zxw49000, zxw50000, app(app(app(ty_@3, chf), chg), chh)) → new_lt16(zxw49000, zxw50000, chf, chg, chh)
new_esEs4(@2(zxw4000, zxw4001), @2(zxw3000, zxw3001), baa, bab) → new_asAs(new_esEs22(zxw4000, zxw3000, baa), new_esEs21(zxw4001, zxw3001, bab))
new_ltEs20(zxw49002, zxw50002, app(app(ty_Either, cfe), cff)) → new_ltEs7(zxw49002, zxw50002, cfe, cff)
new_esEs27(zxw49000, zxw50000, app(app(ty_@2, chb), chc)) → new_esEs4(zxw49000, zxw50000, chb, chc)
new_lt20(zxw49000, zxw50000, ty_Integer) → new_lt5(zxw49000, zxw50000)
new_compare35(zxw400, h) → new_compare26(Just(zxw400), Nothing, False, h)
new_ltEs18(zxw49001, zxw50001, app(ty_Maybe, beg)) → new_ltEs8(zxw49001, zxw50001, beg)
new_compare8(:%(zxw49000, zxw49001), :%(zxw50000, zxw50001), ty_Integer) → new_compare9(new_sr0(zxw49000, zxw50001), new_sr0(zxw50000, zxw49001))
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Float, cbg) → new_ltEs6(zxw49000, zxw50000)
new_ltEs4(LT, LT) → True
new_esEs16([], [], dad) → True
new_ltEs20(zxw49002, zxw50002, ty_Int) → new_ltEs10(zxw49002, zxw50002)
new_ltEs8(Nothing, Nothing, ge) → True
new_lt10(zxw49000, zxw50000, ty_Char) → new_lt6(zxw49000, zxw50000)
new_lt10(zxw49000, zxw50000, ty_Bool) → new_lt13(zxw49000, zxw50000)
new_esEs22(zxw4000, zxw3000, app(app(ty_Either, bcc), bcd)) → new_esEs6(zxw4000, zxw3000, bcc, bcd)
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_lt5(zxw49000, zxw50000) → new_esEs8(new_compare9(zxw49000, zxw50000), LT)
new_esEs26(zxw49001, zxw50001, ty_Float) → new_esEs19(zxw49001, zxw50001)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Int, cca) → new_esEs13(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_esEs10(zxw4002, zxw3002, ty_Int) → new_esEs13(zxw4002, zxw3002)
new_lt10(zxw49000, zxw50000, app(ty_[], bg)) → new_lt9(zxw49000, zxw50000, bg)
new_esEs12(zxw4000, zxw3000, app(ty_Ratio, fa)) → new_esEs14(zxw4000, zxw3000, fa)
new_ltEs15(@3(zxw49000, zxw49001, zxw49002), @3(zxw50000, zxw50001, zxw50002), cbc, cbd, cbe) → new_pePe(new_lt20(zxw49000, zxw50000, cbc), new_asAs(new_esEs27(zxw49000, zxw50000, cbc), new_pePe(new_lt19(zxw49001, zxw50001, cbd), new_asAs(new_esEs26(zxw49001, zxw50001, cbd), new_ltEs20(zxw49002, zxw50002, cbe)))))
new_ltEs10(zxw4900, zxw5000) → new_fsEs(new_compare7(zxw4900, zxw5000))
new_esEs30(zxw20, zxw15, ty_Ordering) → new_esEs8(zxw20, zxw15)
new_esEs10(zxw4002, zxw3002, app(ty_Ratio, cd)) → new_esEs14(zxw4002, zxw3002, cd)
new_ltEs12(zxw4900, zxw5000) → new_fsEs(new_compare12(zxw4900, zxw5000))
new_esEs10(zxw4002, zxw3002, ty_Ordering) → new_esEs8(zxw4002, zxw3002)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbf, ty_Float) → new_ltEs6(zxw49000, zxw50000)
new_esEs23(zxw49000, zxw50000, app(ty_[], bg)) → new_esEs16(zxw49000, zxw50000, bg)
new_esEs11(zxw4001, zxw3001, ty_Integer) → new_esEs17(zxw4001, zxw3001)
new_esEs26(zxw49001, zxw50001, app(app(ty_Either, cgg), cgh)) → new_esEs6(zxw49001, zxw50001, cgg, cgh)
new_compare16(Double(zxw49000, zxw49001), Double(zxw50000, zxw50001)) → new_compare7(new_sr(zxw49000, zxw50000), new_sr(zxw49001, zxw50001))
new_compare0([], :(zxw50000, zxw50001), bhg) → LT
new_primPlusNat1(Zero, Zero) → Zero
new_esEs12(zxw4000, zxw3000, ty_Ordering) → new_esEs8(zxw4000, zxw3000)
new_lt10(zxw49000, zxw50000, ty_@0) → new_lt15(zxw49000, zxw50000)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Char) → new_ltEs12(zxw49000, zxw50000)
new_asAs(True, zxw187) → zxw187
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_esEs30(zxw20, zxw15, ty_Integer) → new_esEs17(zxw20, zxw15)
new_esEs26(zxw49001, zxw50001, app(app(app(ty_@3, cgd), cge), cgf)) → new_esEs5(zxw49001, zxw50001, cgd, cge, cgf)
new_esEs10(zxw4002, zxw3002, app(app(ty_Either, db), dc)) → new_esEs6(zxw4002, zxw3002, db, dc)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Integer) → new_ltEs16(zxw49000, zxw50000)
new_compare30(zxw49000, zxw50000, gc, gd) → new_compare27(zxw49000, zxw50000, new_esEs4(zxw49000, zxw50000, gc, gd), gc, gd)
new_compare29(zxw49000, zxw50000, ty_Bool) → new_compare18(zxw49000, zxw50000)
new_fsEs(zxw202) → new_not(new_esEs8(zxw202, GT))
new_esEs23(zxw49000, zxw50000, app(app(app(ty_@3, bfh), bga), bgb)) → new_esEs5(zxw49000, zxw50000, bfh, bga, bgb)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Float) → new_esEs19(zxw4000, zxw3000)
new_compare10(zxw49000, zxw50000, True) → LT
new_esEs29(zxw400, zxw300, app(ty_Ratio, cbb)) → new_esEs14(zxw400, zxw300, cbb)
new_esEs30(zxw20, zxw15, app(app(app(ty_@3, bdd), bde), bdf)) → new_esEs5(zxw20, zxw15, bdd, bde, bdf)
new_compare29(zxw49000, zxw50000, app(ty_Maybe, cab)) → new_compare19(zxw49000, zxw50000, cab)
new_ltEs4(GT, GT) → True
new_esEs26(zxw49001, zxw50001, ty_@0) → new_esEs20(zxw49001, zxw50001)
new_compare110(zxw49000, zxw50000, False, bfh, bga, bgb) → GT
new_ltEs7(Left(zxw49000), Left(zxw50000), app(ty_Ratio, dbf), cbg) → new_ltEs17(zxw49000, zxw50000, dbf)
new_compare10(zxw49000, zxw50000, False) → GT
new_ltEs8(Just(zxw49000), Just(zxw50000), app(app(app(ty_@3, hb), hc), hd)) → new_ltEs15(zxw49000, zxw50000, hb, hc, hd)
new_esEs21(zxw4001, zxw3001, app(ty_[], bae)) → new_esEs16(zxw4001, zxw3001, bae)
new_compare18(zxw49000, zxw50000) → new_compare24(zxw49000, zxw50000, new_esEs9(zxw49000, zxw50000))
new_esEs6(Right(zxw4000), Right(zxw3000), cdc, ty_Ordering) → new_esEs8(zxw4000, zxw3000)
new_esEs6(Left(zxw4000), Left(zxw3000), app(ty_[], ccc), cca) → new_esEs16(zxw4000, zxw3000, ccc)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs6(Right(zxw4000), Right(zxw3000), cdc, app(app(app(ty_@3, cdg), cdh), cea)) → new_esEs5(zxw4000, zxw3000, cdg, cdh, cea)
new_primCompAux0(zxw218, EQ) → zxw218
new_esEs29(zxw400, zxw300, ty_Ordering) → new_esEs8(zxw400, zxw300)
new_lt20(zxw49000, zxw50000, app(ty_Maybe, chd)) → new_lt12(zxw49000, zxw50000, chd)
new_esEs12(zxw4000, zxw3000, app(app(ty_@2, ga), gb)) → new_esEs4(zxw4000, zxw3000, ga, gb)
new_ltEs19(zxw4900, zxw5000, app(ty_[], bhg)) → new_ltEs13(zxw4900, zxw5000, bhg)
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_esEs22(zxw4000, zxw3000, app(ty_Maybe, bbe)) → new_esEs7(zxw4000, zxw3000, bbe)
new_esEs30(zxw20, zxw15, ty_Char) → new_esEs15(zxw20, zxw15)
new_esEs30(zxw20, zxw15, app(app(ty_@2, bea), beb)) → new_esEs4(zxw20, zxw15, bea, beb)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbf, ty_@0) → new_ltEs14(zxw49000, zxw50000)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_compare8(:%(zxw49000, zxw49001), :%(zxw50000, zxw50001), ty_Int) → new_compare7(new_sr(zxw49000, zxw50001), new_sr(zxw50000, zxw49001))
new_ltEs17(zxw4900, zxw5000, hh) → new_fsEs(new_compare8(zxw4900, zxw5000, hh))
new_not(True) → False

The set Q consists of the following terms:

new_esEs17(Integer(x0), Integer(x1))
new_esEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Integer)
new_lt10(x0, x1, ty_Double)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_compare18(x0, x1)
new_compare29(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Double)
new_pePe(False, x0)
new_lt10(x0, x1, app(app(ty_Either, x2), x3))
new_lt17(x0, x1, x2, x3)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Left(x0), Left(x1), ty_Bool, x2)
new_compare7(x0, x1)
new_esEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_compare110(x0, x1, False, x2, x3, x4)
new_primMulNat0(Succ(x0), Zero)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs7(Just(x0), Just(x1), ty_Double)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_ltEs8(Just(x0), Just(x1), ty_Integer)
new_esEs10(x0, x1, ty_Int)
new_ltEs10(x0, x1)
new_esEs28(x0, x1, ty_Int)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs12(x0, x1, ty_Char)
new_compare25(x0, x1, True, x2, x3)
new_primMulNat0(Succ(x0), Succ(x1))
new_ltEs7(Left(x0), Left(x1), ty_Integer, x2)
new_esEs6(Left(x0), Left(x1), ty_Int, x2)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Int)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs16(x0, x1)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_compare13(x0, x1, True)
new_esEs10(x0, x1, ty_Ordering)
new_compare29(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs19(x0, x1, ty_Float)
new_compare0([], :(x0, x1), x2)
new_esEs11(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_Int)
new_esEs6(Left(x0), Left(x1), ty_@0, x2)
new_ltEs8(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare11(x0, x1, True, x2)
new_ltEs19(x0, x1, ty_Ordering)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs8(GT, GT)
new_compare11(x0, x1, False, x2)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_compare17(x0, x1, True, x2, x3)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCompAux1(x0, x1, x2, x3)
new_esEs8(LT, LT)
new_esEs29(x0, x1, ty_@0)
new_compare29(x0, x1, ty_Double)
new_esEs18(Double(x0, x1), Double(x2, x3))
new_primCmpNat0(Zero, x0)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_lt11(x0, x1, x2, x3)
new_ltEs8(Just(x0), Just(x1), ty_Bool)
new_esEs11(x0, x1, ty_@0)
new_primCmpNat1(Zero, Succ(x0))
new_esEs25(x0, x1, ty_Int)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_sr(x0, x1)
new_ltEs5(False, False)
new_ltEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_compare6(x0, x1)
new_lt10(x0, x1, ty_Ordering)
new_esEs6(Right(x0), Left(x1), x2, x3)
new_esEs6(Left(x0), Right(x1), x2, x3)
new_compare29(x0, x1, ty_Int)
new_esEs30(x0, x1, ty_Bool)
new_ltEs15(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs26(x0, x1, ty_Integer)
new_primEqNat0(Zero, Succ(x0))
new_primCmpNat1(Zero, Zero)
new_esEs7(Nothing, Nothing, x0)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs7(Left(x0), Left(x1), ty_Bool, x2)
new_compare16(Double(x0, x1), Double(x2, x3))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_lt7(x0, x1)
new_esEs28(x0, x1, ty_@0)
new_ltEs20(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Integer)
new_esEs16(:(x0, x1), :(x2, x3), x4)
new_esEs23(x0, x1, ty_Integer)
new_esEs11(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Double)
new_ltEs19(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_Char)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_compare15(x0, x1, True, x2, x3)
new_esEs24(x0, x1, ty_Int)
new_esEs6(Left(x0), Left(x1), ty_Char, x2)
new_esEs6(Left(x0), Left(x1), ty_Integer, x2)
new_primEqNat0(Zero, Zero)
new_compare32(x0, x1, x2, x3)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs8(Just(x0), Just(x1), app(ty_Maybe, x2))
new_compare36(x0, x1, x2)
new_ltEs8(Just(x0), Just(x1), ty_Double)
new_ltEs8(Just(x0), Just(x1), ty_Ordering)
new_ltEs19(x0, x1, ty_@0)
new_compare110(x0, x1, True, x2, x3, x4)
new_compare24(x0, x1, False)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs7(Just(x0), Nothing, x1)
new_esEs29(x0, x1, ty_Bool)
new_esEs9(True, True)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_lt18(x0, x1, x2)
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt4(x0, x1)
new_primMulNat0(Zero, Zero)
new_ltEs13(x0, x1, x2)
new_esEs23(x0, x1, ty_Char)
new_esEs30(x0, x1, ty_Ordering)
new_esEs10(x0, x1, ty_@0)
new_lt10(x0, x1, app(ty_Ratio, x2))
new_lt10(x0, x1, ty_Char)
new_esEs30(x0, x1, ty_Int)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_Integer)
new_fsEs(x0)
new_ltEs4(GT, GT)
new_lt8(x0, x1)
new_esEs30(x0, x1, ty_@0)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs10(x0, x1, ty_Float)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs28(x0, x1, ty_Double)
new_esEs29(x0, x1, ty_Char)
new_compare29(x0, x1, app(ty_[], x2))
new_esEs6(Right(x0), Right(x1), x2, ty_Float)
new_compare27(x0, x1, True, x2, x3)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_lt10(x0, x1, ty_Int)
new_esEs10(x0, x1, ty_Bool)
new_lt16(x0, x1, x2, x3, x4)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs23(x0, x1, ty_Ordering)
new_esEs7(Just(x0), Just(x1), ty_Int)
new_esEs10(x0, x1, ty_Char)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_lt10(x0, x1, app(ty_[], x2))
new_compare33(x0)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_pePe(True, x0)
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, ty_Int)
new_primPlusNat0(Zero, x0)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_lt10(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, ty_Int)
new_compare210(x0, x1, True, x2, x3, x4)
new_lt6(x0, x1)
new_esEs26(x0, x1, ty_Bool)
new_compare24(x0, x1, True)
new_ltEs18(x0, x1, ty_Integer)
new_compare15(x0, x1, False, x2, x3)
new_compare14(Float(x0, x1), Float(x2, x3))
new_ltEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(x0, x1)
new_esEs29(x0, x1, ty_Integer)
new_esEs12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primPlusNat1(Zero, Zero)
new_primCompAux0(x0, GT)
new_compare23(x0, x1, True)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_lt19(x0, x1, app(ty_[], x2))
new_lt15(x0, x1)
new_ltEs7(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs29(x0, x1, ty_Ordering)
new_compare19(x0, x1, x2)
new_compare13(x0, x1, False)
new_compare26(Nothing, Just(x0), False, x1)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_lt20(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_@0)
new_compare30(x0, x1, x2, x3)
new_primPlusNat0(Succ(x0), x1)
new_esEs12(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs4(EQ, EQ)
new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs19(x0, x1, ty_Char)
new_ltEs7(Right(x0), Right(x1), x2, ty_Char)
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_ltEs11(x0, x1)
new_esEs12(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Integer)
new_compare29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Char)
new_esEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs8(Nothing, Just(x0), x1)
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs8(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Just(x0), Just(x1), ty_Char)
new_ltEs7(Left(x0), Left(x1), ty_@0, x2)
new_lt9(x0, x1, x2)
new_esEs10(x0, x1, app(ty_[], x2))
new_esEs12(x0, x1, ty_Float)
new_compare31(@0, @0)
new_esEs7(Just(x0), Just(x1), ty_Float)
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs16([], :(x0, x1), x2)
new_primCmpNat2(x0, Zero)
new_ltEs4(LT, EQ)
new_ltEs4(EQ, LT)
new_esEs12(x0, x1, ty_Int)
new_lt19(x0, x1, ty_Double)
new_esEs6(Right(x0), Right(x1), x2, ty_Integer)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_primMulInt(Pos(x0), Pos(x1))
new_lt20(x0, x1, ty_Bool)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_ltEs7(Right(x0), Right(x1), x2, ty_Int)
new_ltEs18(x0, x1, app(ty_[], x2))
new_esEs30(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_@0)
new_esEs10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs7(Right(x0), Right(x1), x2, ty_Double)
new_asAs(True, x0)
new_primEqNat0(Succ(x0), Zero)
new_compare26(Just(x0), Nothing, False, x1)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs7(Left(x0), Left(x1), ty_Int, x2)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_esEs12(x0, x1, app(ty_[], x2))
new_esEs13(x0, x1)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_ltEs7(Left(x0), Right(x1), x2, x3)
new_ltEs7(Right(x0), Left(x1), x2, x3)
new_esEs14(:%(x0, x1), :%(x2, x3), x4)
new_compare26(x0, x1, True, x2)
new_esEs21(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Integer)
new_ltEs7(Left(x0), Left(x1), ty_Double, x2)
new_ltEs8(Nothing, Nothing, x0)
new_lt20(x0, x1, ty_@0)
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_Bool)
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Char)
new_compare26(Just(x0), Just(x1), False, x2)
new_esEs28(x0, x1, ty_Ordering)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, app(ty_Ratio, x2))
new_compare34(x0, x1)
new_lt20(x0, x1, ty_Ordering)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_lt12(x0, x1, x2)
new_esEs10(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_esEs12(x0, x1, app(ty_Maybe, x2))
new_esEs30(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, ty_Bool)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs27(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_Double)
new_esEs25(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(ty_[], x2))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_lt10(x0, x1, ty_Bool)
new_primPlusNat1(Succ(x0), Zero)
new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs22(x0, x1, ty_Float)
new_ltEs4(LT, LT)
new_esEs10(x0, x1, ty_Integer)
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Integer)
new_compare29(x0, x1, app(app(ty_@2, x2), x3))
new_compare23(x0, x1, False)
new_esEs21(x0, x1, app(ty_[], x2))
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs11(x0, x1, ty_Bool)
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_compare29(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_Double)
new_esEs21(x0, x1, ty_Bool)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, ty_Double)
new_esEs26(x0, x1, ty_Ordering)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs7(Nothing, Just(x0), x1)
new_primPlusNat1(Zero, Succ(x0))
new_ltEs12(x0, x1)
new_compare10(x0, x1, False)
new_lt10(x0, x1, app(app(ty_@2, x2), x3))
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Left(x0), Left(x1), ty_Float, x2)
new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_primCmpNat0(Succ(x0), x1)
new_lt10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, ty_@0)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs8(GT, EQ)
new_esEs8(EQ, GT)
new_esEs22(x0, x1, ty_Bool)
new_lt19(x0, x1, ty_Float)
new_lt19(x0, x1, ty_Integer)
new_ltEs8(Just(x0), Just(x1), ty_Char)
new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Left(x0), Left(x1), ty_Double, x2)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_ltEs8(Just(x0), Just(x1), ty_Float)
new_lt5(x0, x1)
new_compare29(x0, x1, ty_Ordering)
new_ltEs18(x0, x1, ty_Bool)
new_compare28(x0, x1, x2, x3, x4)
new_esEs11(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_@0)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, ty_Int)
new_esEs11(x0, x1, ty_Char)
new_esEs10(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Float)
new_lt19(x0, x1, ty_Ordering)
new_compare29(x0, x1, ty_Integer)
new_compare25(x0, x1, False, x2, x3)
new_esEs6(Right(x0), Right(x1), x2, ty_Char)
new_esEs26(x0, x1, app(ty_[], x2))
new_ltEs18(x0, x1, ty_Float)
new_ltEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs9(False, False)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs21(x0, x1, ty_Double)
new_esEs12(x0, x1, ty_Ordering)
new_ltEs8(Just(x0), Nothing, x1)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs22(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpNat1(Succ(x0), Succ(x1))
new_esEs10(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_@0)
new_ltEs6(x0, x1)
new_lt10(x0, x1, ty_Float)
new_esEs22(x0, x1, ty_Int)
new_ltEs7(Left(x0), Left(x1), ty_Char, x2)
new_compare17(x0, x1, False, x2, x3)
new_ltEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs21(x0, x1, ty_Float)
new_esEs29(x0, x1, ty_Double)
new_primCompAux0(x0, EQ)
new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare26(Nothing, Nothing, False, x0)
new_compare27(x0, x1, False, x2, x3)
new_esEs21(x0, x1, ty_Integer)
new_primCmpNat1(Succ(x0), Zero)
new_ltEs18(x0, x1, ty_@0)
new_esEs22(x0, x1, ty_Double)
new_ltEs7(Right(x0), Right(x1), x2, ty_@0)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, ty_Bool)
new_esEs16([], [], x0)
new_compare29(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, app(ty_[], x2))
new_lt13(x0, x1)
new_esEs23(x0, x1, ty_Bool)
new_ltEs5(True, True)
new_ltEs7(Right(x0), Right(x1), x2, ty_Integer)
new_lt19(x0, x1, ty_Int)
new_compare35(x0, x1)
new_lt19(x0, x1, ty_Char)
new_ltEs4(EQ, GT)
new_ltEs4(GT, EQ)
new_esEs6(Right(x0), Right(x1), x2, ty_@0)
new_not(True)
new_esEs11(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Float)
new_compare0(:(x0, x1), [], x2)
new_esEs28(x0, x1, ty_Char)
new_lt19(x0, x1, ty_@0)
new_esEs10(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, ty_Ordering)
new_ltEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs26(x0, x1, ty_Char)
new_ltEs18(x0, x1, ty_Int)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_ltEs20(x0, x1, ty_Ordering)
new_not(False)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_lt14(x0, x1)
new_compare12(Char(x0), Char(x1))
new_esEs15(Char(x0), Char(x1))
new_esEs11(x0, x1, app(ty_[], x2))
new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_compare10(x0, x1, True)
new_lt10(x0, x1, ty_@0)
new_asAs(False, x0)
new_esEs22(x0, x1, ty_Ordering)
new_ltEs18(x0, x1, ty_Char)
new_esEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs17(x0, x1, x2)
new_compare29(x0, x1, ty_Float)
new_lt19(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_Char)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_ltEs8(Just(x0), Just(x1), ty_@0)
new_esEs20(@0, @0)
new_ltEs8(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs7(Left(x0), Left(x1), ty_Float, x2)
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Int)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_esEs16(:(x0, x1), [], x2)
new_ltEs19(x0, x1, ty_Double)
new_esEs9(True, False)
new_esEs9(False, True)
new_esEs22(x0, x1, ty_Char)
new_ltEs7(Right(x0), Right(x1), x2, ty_Float)
new_ltEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare29(x0, x1, ty_Bool)
new_ltEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs30(x0, x1, ty_Double)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, ty_Integer)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs11(x0, x1, ty_Double)
new_ltEs20(x0, x1, ty_Float)
new_primCompAux0(x0, LT)
new_primCmpNat2(x0, Succ(x1))
new_esEs11(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs12(x0, x1, ty_Integer)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs10(x0, x1, ty_Double)
new_ltEs8(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_sr0(Integer(x0), Integer(x1))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs29(x0, x1, ty_Float)
new_ltEs8(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_primEqInt(Pos(Zero), Pos(Zero))
new_ltEs18(x0, x1, ty_Double)
new_esEs12(x0, x1, ty_Double)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_compare0(:(x0, x1), :(x2, x3), x4)
new_esEs29(x0, x1, ty_Int)
new_esEs12(x0, x1, ty_Bool)
new_compare9(Integer(x0), Integer(x1))
new_lt10(x0, x1, ty_Integer)
new_esEs30(x0, x1, ty_Char)
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs19(Float(x0, x1), Float(x2, x3))
new_primMulNat0(Zero, Succ(x0))
new_compare0([], [], x0)
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Just(x0), Just(x1), ty_@0)
new_ltEs4(GT, LT)
new_ltEs4(LT, GT)
new_ltEs5(True, False)
new_ltEs5(False, True)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs9(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs27(x0, x1, app(ty_[], x2))
new_ltEs8(Just(x0), Just(x1), ty_Int)
new_esEs12(x0, x1, app(app(ty_Either, x2), x3))
new_compare29(x0, x1, ty_@0)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Float)
new_esEs23(x0, x1, ty_Float)
new_compare210(x0, x1, False, x2, x3, x4)
new_esEs30(x0, x1, ty_Float)
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))

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

↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ 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_splitGT3(Nothing, zxw31, zxw32, zxw33, zxw34, Nothing, h, ba) → new_splitGT1(zxw31, zxw32, zxw33, zxw34, new_esEs8(new_compare33(h), LT), h, ba)
new_splitGT2(zxw300, zxw31, zxw32, zxw33, Branch(zxw340, zxw341, zxw342, zxw343, zxw344), True, h, ba) → new_splitGT3(zxw340, zxw341, zxw342, zxw343, zxw344, Nothing, h, ba)
new_splitGT10(zxw300, zxw31, zxw32, zxw33, zxw34, True, h, ba) → new_splitGT(zxw33, h, ba)
new_splitGT(Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba) → new_splitGT3(zxw340, zxw341, zxw342, zxw343, zxw344, Nothing, h, ba)
new_splitGT1(zxw31, zxw32, zxw33, zxw34, True, h, ba) → new_splitGT(zxw33, h, ba)
new_splitGT2(zxw300, zxw31, zxw32, zxw33, zxw34, False, h, ba) → new_splitGT10(zxw300, zxw31, zxw32, zxw33, zxw34, new_esEs8(new_compare34(zxw300, h), LT), h, ba)
new_splitGT3(Just(zxw300), zxw31, zxw32, zxw33, zxw34, Nothing, h, ba) → new_splitGT2(zxw300, zxw31, zxw32, zxw33, zxw34, new_esEs8(new_compare26(Nothing, Just(zxw300), False, h), GT), h, ba)

The TRS R consists of the following rules:

new_compare26(Nothing, Just(zxw5000), False, bcg) → LT
new_esEs8(GT, GT) → True
new_esEs8(LT, GT) → False
new_esEs8(EQ, GT) → False
new_compare34(zxw300, h) → new_compare26(Nothing, Just(zxw300), False, h)
new_esEs8(LT, LT) → True
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_compare33(h) → new_compare26(Nothing, Nothing, True, h)
new_compare26(zxw490, zxw500, True, bcg) → EQ

The set Q consists of the following terms:

new_esEs17(Integer(x0), Integer(x1))
new_esEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Integer)
new_lt10(x0, x1, ty_Double)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_compare18(x0, x1)
new_compare29(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Double)
new_pePe(False, x0)
new_lt10(x0, x1, app(app(ty_Either, x2), x3))
new_lt17(x0, x1, x2, x3)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Left(x0), Left(x1), ty_Bool, x2)
new_compare7(x0, x1)
new_esEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_compare110(x0, x1, False, x2, x3, x4)
new_primMulNat0(Succ(x0), Zero)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs7(Just(x0), Just(x1), ty_Double)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_ltEs8(Just(x0), Just(x1), ty_Integer)
new_esEs10(x0, x1, ty_Int)
new_ltEs10(x0, x1)
new_esEs28(x0, x1, ty_Int)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs12(x0, x1, ty_Char)
new_compare25(x0, x1, True, x2, x3)
new_primMulNat0(Succ(x0), Succ(x1))
new_ltEs7(Left(x0), Left(x1), ty_Integer, x2)
new_esEs6(Left(x0), Left(x1), ty_Int, x2)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Int)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs16(x0, x1)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_compare13(x0, x1, True)
new_esEs10(x0, x1, ty_Ordering)
new_compare29(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs19(x0, x1, ty_Float)
new_compare0([], :(x0, x1), x2)
new_esEs11(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_Int)
new_esEs6(Left(x0), Left(x1), ty_@0, x2)
new_ltEs8(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare11(x0, x1, True, x2)
new_ltEs19(x0, x1, ty_Ordering)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs8(GT, GT)
new_compare11(x0, x1, False, x2)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_compare17(x0, x1, True, x2, x3)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCompAux1(x0, x1, x2, x3)
new_esEs8(LT, LT)
new_esEs29(x0, x1, ty_@0)
new_compare29(x0, x1, ty_Double)
new_esEs18(Double(x0, x1), Double(x2, x3))
new_primCmpNat0(Zero, x0)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_lt11(x0, x1, x2, x3)
new_ltEs8(Just(x0), Just(x1), ty_Bool)
new_esEs11(x0, x1, ty_@0)
new_primCmpNat1(Zero, Succ(x0))
new_esEs25(x0, x1, ty_Int)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_sr(x0, x1)
new_ltEs5(False, False)
new_ltEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_compare6(x0, x1)
new_lt10(x0, x1, ty_Ordering)
new_esEs6(Right(x0), Left(x1), x2, x3)
new_esEs6(Left(x0), Right(x1), x2, x3)
new_compare29(x0, x1, ty_Int)
new_esEs30(x0, x1, ty_Bool)
new_ltEs15(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs26(x0, x1, ty_Integer)
new_primEqNat0(Zero, Succ(x0))
new_primCmpNat1(Zero, Zero)
new_esEs7(Nothing, Nothing, x0)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs7(Left(x0), Left(x1), ty_Bool, x2)
new_compare16(Double(x0, x1), Double(x2, x3))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_lt7(x0, x1)
new_esEs28(x0, x1, ty_@0)
new_ltEs20(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Integer)
new_esEs16(:(x0, x1), :(x2, x3), x4)
new_esEs23(x0, x1, ty_Integer)
new_esEs11(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Double)
new_ltEs19(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_Char)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_compare15(x0, x1, True, x2, x3)
new_esEs24(x0, x1, ty_Int)
new_esEs6(Left(x0), Left(x1), ty_Char, x2)
new_esEs6(Left(x0), Left(x1), ty_Integer, x2)
new_primEqNat0(Zero, Zero)
new_compare32(x0, x1, x2, x3)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs8(Just(x0), Just(x1), app(ty_Maybe, x2))
new_compare36(x0, x1, x2)
new_ltEs8(Just(x0), Just(x1), ty_Double)
new_ltEs8(Just(x0), Just(x1), ty_Ordering)
new_ltEs19(x0, x1, ty_@0)
new_compare110(x0, x1, True, x2, x3, x4)
new_compare24(x0, x1, False)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs7(Just(x0), Nothing, x1)
new_esEs29(x0, x1, ty_Bool)
new_esEs9(True, True)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_lt18(x0, x1, x2)
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt4(x0, x1)
new_primMulNat0(Zero, Zero)
new_ltEs13(x0, x1, x2)
new_esEs23(x0, x1, ty_Char)
new_esEs30(x0, x1, ty_Ordering)
new_esEs10(x0, x1, ty_@0)
new_lt10(x0, x1, app(ty_Ratio, x2))
new_lt10(x0, x1, ty_Char)
new_esEs30(x0, x1, ty_Int)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_Integer)
new_fsEs(x0)
new_ltEs4(GT, GT)
new_lt8(x0, x1)
new_esEs30(x0, x1, ty_@0)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs10(x0, x1, ty_Float)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs28(x0, x1, ty_Double)
new_esEs29(x0, x1, ty_Char)
new_compare29(x0, x1, app(ty_[], x2))
new_esEs6(Right(x0), Right(x1), x2, ty_Float)
new_compare27(x0, x1, True, x2, x3)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_lt10(x0, x1, ty_Int)
new_esEs10(x0, x1, ty_Bool)
new_lt16(x0, x1, x2, x3, x4)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs23(x0, x1, ty_Ordering)
new_esEs7(Just(x0), Just(x1), ty_Int)
new_esEs10(x0, x1, ty_Char)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_lt10(x0, x1, app(ty_[], x2))
new_compare33(x0)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_pePe(True, x0)
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, ty_Int)
new_primPlusNat0(Zero, x0)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_lt10(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, ty_Int)
new_compare210(x0, x1, True, x2, x3, x4)
new_lt6(x0, x1)
new_esEs26(x0, x1, ty_Bool)
new_compare24(x0, x1, True)
new_ltEs18(x0, x1, ty_Integer)
new_compare15(x0, x1, False, x2, x3)
new_compare14(Float(x0, x1), Float(x2, x3))
new_ltEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(x0, x1)
new_esEs29(x0, x1, ty_Integer)
new_esEs12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primPlusNat1(Zero, Zero)
new_primCompAux0(x0, GT)
new_compare23(x0, x1, True)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_lt19(x0, x1, app(ty_[], x2))
new_lt15(x0, x1)
new_ltEs7(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs29(x0, x1, ty_Ordering)
new_compare19(x0, x1, x2)
new_compare13(x0, x1, False)
new_compare26(Nothing, Just(x0), False, x1)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_lt20(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_@0)
new_compare30(x0, x1, x2, x3)
new_primPlusNat0(Succ(x0), x1)
new_esEs12(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs4(EQ, EQ)
new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs19(x0, x1, ty_Char)
new_ltEs7(Right(x0), Right(x1), x2, ty_Char)
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_ltEs11(x0, x1)
new_esEs12(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Integer)
new_compare29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Char)
new_esEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs8(Nothing, Just(x0), x1)
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs8(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Just(x0), Just(x1), ty_Char)
new_ltEs7(Left(x0), Left(x1), ty_@0, x2)
new_lt9(x0, x1, x2)
new_esEs10(x0, x1, app(ty_[], x2))
new_esEs12(x0, x1, ty_Float)
new_compare31(@0, @0)
new_esEs7(Just(x0), Just(x1), ty_Float)
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs16([], :(x0, x1), x2)
new_primCmpNat2(x0, Zero)
new_ltEs4(LT, EQ)
new_ltEs4(EQ, LT)
new_esEs12(x0, x1, ty_Int)
new_lt19(x0, x1, ty_Double)
new_esEs6(Right(x0), Right(x1), x2, ty_Integer)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_primMulInt(Pos(x0), Pos(x1))
new_lt20(x0, x1, ty_Bool)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_ltEs7(Right(x0), Right(x1), x2, ty_Int)
new_ltEs18(x0, x1, app(ty_[], x2))
new_esEs30(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_@0)
new_esEs10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs7(Right(x0), Right(x1), x2, ty_Double)
new_asAs(True, x0)
new_primEqNat0(Succ(x0), Zero)
new_compare26(Just(x0), Nothing, False, x1)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs7(Left(x0), Left(x1), ty_Int, x2)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_esEs12(x0, x1, app(ty_[], x2))
new_esEs13(x0, x1)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_ltEs7(Left(x0), Right(x1), x2, x3)
new_ltEs7(Right(x0), Left(x1), x2, x3)
new_esEs14(:%(x0, x1), :%(x2, x3), x4)
new_compare26(x0, x1, True, x2)
new_esEs21(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Integer)
new_ltEs7(Left(x0), Left(x1), ty_Double, x2)
new_ltEs8(Nothing, Nothing, x0)
new_lt20(x0, x1, ty_@0)
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_Bool)
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Char)
new_compare26(Just(x0), Just(x1), False, x2)
new_esEs28(x0, x1, ty_Ordering)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, app(ty_Ratio, x2))
new_compare34(x0, x1)
new_lt20(x0, x1, ty_Ordering)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_lt12(x0, x1, x2)
new_esEs10(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_esEs12(x0, x1, app(ty_Maybe, x2))
new_esEs30(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, ty_Bool)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs27(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_Double)
new_esEs25(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(ty_[], x2))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_lt10(x0, x1, ty_Bool)
new_primPlusNat1(Succ(x0), Zero)
new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs22(x0, x1, ty_Float)
new_ltEs4(LT, LT)
new_esEs10(x0, x1, ty_Integer)
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Integer)
new_compare29(x0, x1, app(app(ty_@2, x2), x3))
new_compare23(x0, x1, False)
new_esEs21(x0, x1, app(ty_[], x2))
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs11(x0, x1, ty_Bool)
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_compare29(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_Double)
new_esEs21(x0, x1, ty_Bool)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, ty_Double)
new_esEs26(x0, x1, ty_Ordering)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs7(Nothing, Just(x0), x1)
new_primPlusNat1(Zero, Succ(x0))
new_ltEs12(x0, x1)
new_compare10(x0, x1, False)
new_lt10(x0, x1, app(app(ty_@2, x2), x3))
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Left(x0), Left(x1), ty_Float, x2)
new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_primCmpNat0(Succ(x0), x1)
new_lt10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, ty_@0)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs8(GT, EQ)
new_esEs8(EQ, GT)
new_esEs22(x0, x1, ty_Bool)
new_lt19(x0, x1, ty_Float)
new_lt19(x0, x1, ty_Integer)
new_ltEs8(Just(x0), Just(x1), ty_Char)
new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Left(x0), Left(x1), ty_Double, x2)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_ltEs8(Just(x0), Just(x1), ty_Float)
new_lt5(x0, x1)
new_compare29(x0, x1, ty_Ordering)
new_ltEs18(x0, x1, ty_Bool)
new_compare28(x0, x1, x2, x3, x4)
new_esEs11(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_@0)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, ty_Int)
new_esEs11(x0, x1, ty_Char)
new_esEs10(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Float)
new_lt19(x0, x1, ty_Ordering)
new_compare29(x0, x1, ty_Integer)
new_compare25(x0, x1, False, x2, x3)
new_esEs6(Right(x0), Right(x1), x2, ty_Char)
new_esEs26(x0, x1, app(ty_[], x2))
new_ltEs18(x0, x1, ty_Float)
new_ltEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs9(False, False)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs21(x0, x1, ty_Double)
new_esEs12(x0, x1, ty_Ordering)
new_ltEs8(Just(x0), Nothing, x1)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs22(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpNat1(Succ(x0), Succ(x1))
new_esEs10(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_@0)
new_ltEs6(x0, x1)
new_lt10(x0, x1, ty_Float)
new_esEs22(x0, x1, ty_Int)
new_ltEs7(Left(x0), Left(x1), ty_Char, x2)
new_compare17(x0, x1, False, x2, x3)
new_ltEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs21(x0, x1, ty_Float)
new_esEs29(x0, x1, ty_Double)
new_primCompAux0(x0, EQ)
new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare26(Nothing, Nothing, False, x0)
new_compare27(x0, x1, False, x2, x3)
new_esEs21(x0, x1, ty_Integer)
new_primCmpNat1(Succ(x0), Zero)
new_ltEs18(x0, x1, ty_@0)
new_esEs22(x0, x1, ty_Double)
new_ltEs7(Right(x0), Right(x1), x2, ty_@0)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, ty_Bool)
new_esEs16([], [], x0)
new_compare29(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, app(ty_[], x2))
new_lt13(x0, x1)
new_esEs23(x0, x1, ty_Bool)
new_ltEs5(True, True)
new_ltEs7(Right(x0), Right(x1), x2, ty_Integer)
new_lt19(x0, x1, ty_Int)
new_compare35(x0, x1)
new_lt19(x0, x1, ty_Char)
new_ltEs4(EQ, GT)
new_ltEs4(GT, EQ)
new_esEs6(Right(x0), Right(x1), x2, ty_@0)
new_not(True)
new_esEs11(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Float)
new_compare0(:(x0, x1), [], x2)
new_esEs28(x0, x1, ty_Char)
new_lt19(x0, x1, ty_@0)
new_esEs10(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, ty_Ordering)
new_ltEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs26(x0, x1, ty_Char)
new_ltEs18(x0, x1, ty_Int)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_ltEs20(x0, x1, ty_Ordering)
new_not(False)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_lt14(x0, x1)
new_compare12(Char(x0), Char(x1))
new_esEs15(Char(x0), Char(x1))
new_esEs11(x0, x1, app(ty_[], x2))
new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_compare10(x0, x1, True)
new_lt10(x0, x1, ty_@0)
new_asAs(False, x0)
new_esEs22(x0, x1, ty_Ordering)
new_ltEs18(x0, x1, ty_Char)
new_esEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs17(x0, x1, x2)
new_compare29(x0, x1, ty_Float)
new_lt19(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_Char)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_ltEs8(Just(x0), Just(x1), ty_@0)
new_esEs20(@0, @0)
new_ltEs8(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs7(Left(x0), Left(x1), ty_Float, x2)
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Int)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_esEs16(:(x0, x1), [], x2)
new_ltEs19(x0, x1, ty_Double)
new_esEs9(True, False)
new_esEs9(False, True)
new_esEs22(x0, x1, ty_Char)
new_ltEs7(Right(x0), Right(x1), x2, ty_Float)
new_ltEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare29(x0, x1, ty_Bool)
new_ltEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs30(x0, x1, ty_Double)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, ty_Integer)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs11(x0, x1, ty_Double)
new_ltEs20(x0, x1, ty_Float)
new_primCompAux0(x0, LT)
new_primCmpNat2(x0, Succ(x1))
new_esEs11(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs12(x0, x1, ty_Integer)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs10(x0, x1, ty_Double)
new_ltEs8(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_sr0(Integer(x0), Integer(x1))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs29(x0, x1, ty_Float)
new_ltEs8(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_primEqInt(Pos(Zero), Pos(Zero))
new_ltEs18(x0, x1, ty_Double)
new_esEs12(x0, x1, ty_Double)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_compare0(:(x0, x1), :(x2, x3), x4)
new_esEs29(x0, x1, ty_Int)
new_esEs12(x0, x1, ty_Bool)
new_compare9(Integer(x0), Integer(x1))
new_lt10(x0, x1, ty_Integer)
new_esEs30(x0, x1, ty_Char)
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs19(Float(x0, x1), Float(x2, x3))
new_primMulNat0(Zero, Succ(x0))
new_compare0([], [], x0)
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Just(x0), Just(x1), ty_@0)
new_ltEs4(GT, LT)
new_ltEs4(LT, GT)
new_ltEs5(True, False)
new_ltEs5(False, True)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs9(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs27(x0, x1, app(ty_[], x2))
new_ltEs8(Just(x0), Just(x1), ty_Int)
new_esEs12(x0, x1, app(app(ty_Either, x2), x3))
new_compare29(x0, x1, ty_@0)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Float)
new_esEs23(x0, x1, ty_Float)
new_compare210(x0, x1, False, x2, x3, x4)
new_esEs30(x0, x1, ty_Float)
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))

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

new_esEs17(Integer(x0), Integer(x1))
new_esEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Integer)
new_lt10(x0, x1, ty_Double)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_compare18(x0, x1)
new_compare29(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Double)
new_pePe(False, x0)
new_lt10(x0, x1, app(app(ty_Either, x2), x3))
new_lt17(x0, x1, x2, x3)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Left(x0), Left(x1), ty_Bool, x2)
new_compare7(x0, x1)
new_esEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_compare110(x0, x1, False, x2, x3, x4)
new_primMulNat0(Succ(x0), Zero)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs7(Just(x0), Just(x1), ty_Double)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_ltEs8(Just(x0), Just(x1), ty_Integer)
new_esEs10(x0, x1, ty_Int)
new_ltEs10(x0, x1)
new_esEs28(x0, x1, ty_Int)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs12(x0, x1, ty_Char)
new_compare25(x0, x1, True, x2, x3)
new_primMulNat0(Succ(x0), Succ(x1))
new_ltEs7(Left(x0), Left(x1), ty_Integer, x2)
new_esEs6(Left(x0), Left(x1), ty_Int, x2)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Int)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs16(x0, x1)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_compare13(x0, x1, True)
new_esEs10(x0, x1, ty_Ordering)
new_compare29(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs19(x0, x1, ty_Float)
new_compare0([], :(x0, x1), x2)
new_esEs11(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_Int)
new_esEs6(Left(x0), Left(x1), ty_@0, x2)
new_ltEs8(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare11(x0, x1, True, x2)
new_ltEs19(x0, x1, ty_Ordering)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_compare11(x0, x1, False, x2)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_compare17(x0, x1, True, x2, x3)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCompAux1(x0, x1, x2, x3)
new_esEs29(x0, x1, ty_@0)
new_compare29(x0, x1, ty_Double)
new_esEs18(Double(x0, x1), Double(x2, x3))
new_primCmpNat0(Zero, x0)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_lt11(x0, x1, x2, x3)
new_ltEs8(Just(x0), Just(x1), ty_Bool)
new_esEs11(x0, x1, ty_@0)
new_primCmpNat1(Zero, Succ(x0))
new_esEs25(x0, x1, ty_Int)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_sr(x0, x1)
new_ltEs5(False, False)
new_ltEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_compare6(x0, x1)
new_lt10(x0, x1, ty_Ordering)
new_esEs6(Right(x0), Left(x1), x2, x3)
new_esEs6(Left(x0), Right(x1), x2, x3)
new_compare29(x0, x1, ty_Int)
new_esEs30(x0, x1, ty_Bool)
new_ltEs15(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs26(x0, x1, ty_Integer)
new_primEqNat0(Zero, Succ(x0))
new_primCmpNat1(Zero, Zero)
new_esEs7(Nothing, Nothing, x0)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs7(Left(x0), Left(x1), ty_Bool, x2)
new_compare16(Double(x0, x1), Double(x2, x3))
new_lt7(x0, x1)
new_esEs28(x0, x1, ty_@0)
new_ltEs20(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Integer)
new_esEs16(:(x0, x1), :(x2, x3), x4)
new_esEs23(x0, x1, ty_Integer)
new_esEs11(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Double)
new_ltEs19(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_Char)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_compare15(x0, x1, True, x2, x3)
new_esEs24(x0, x1, ty_Int)
new_esEs6(Left(x0), Left(x1), ty_Char, x2)
new_esEs6(Left(x0), Left(x1), ty_Integer, x2)
new_primEqNat0(Zero, Zero)
new_compare32(x0, x1, x2, x3)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs8(Just(x0), Just(x1), app(ty_Maybe, x2))
new_compare36(x0, x1, x2)
new_ltEs8(Just(x0), Just(x1), ty_Double)
new_ltEs8(Just(x0), Just(x1), ty_Ordering)
new_ltEs19(x0, x1, ty_@0)
new_compare110(x0, x1, True, x2, x3, x4)
new_compare24(x0, x1, False)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs7(Just(x0), Nothing, x1)
new_esEs29(x0, x1, ty_Bool)
new_esEs9(True, True)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_lt18(x0, x1, x2)
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt4(x0, x1)
new_primMulNat0(Zero, Zero)
new_ltEs13(x0, x1, x2)
new_esEs23(x0, x1, ty_Char)
new_esEs30(x0, x1, ty_Ordering)
new_esEs10(x0, x1, ty_@0)
new_lt10(x0, x1, app(ty_Ratio, x2))
new_lt10(x0, x1, ty_Char)
new_esEs30(x0, x1, ty_Int)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_Integer)
new_fsEs(x0)
new_ltEs4(GT, GT)
new_lt8(x0, x1)
new_esEs30(x0, x1, ty_@0)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs10(x0, x1, ty_Float)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs28(x0, x1, ty_Double)
new_esEs29(x0, x1, ty_Char)
new_compare29(x0, x1, app(ty_[], x2))
new_esEs6(Right(x0), Right(x1), x2, ty_Float)
new_compare27(x0, x1, True, x2, x3)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_lt10(x0, x1, ty_Int)
new_esEs10(x0, x1, ty_Bool)
new_lt16(x0, x1, x2, x3, x4)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs23(x0, x1, ty_Ordering)
new_esEs7(Just(x0), Just(x1), ty_Int)
new_esEs10(x0, x1, ty_Char)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_lt10(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_pePe(True, x0)
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, ty_Int)
new_primPlusNat0(Zero, x0)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_lt10(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, ty_Int)
new_compare210(x0, x1, True, x2, x3, x4)
new_lt6(x0, x1)
new_esEs26(x0, x1, ty_Bool)
new_compare24(x0, x1, True)
new_ltEs18(x0, x1, ty_Integer)
new_compare15(x0, x1, False, x2, x3)
new_compare14(Float(x0, x1), Float(x2, x3))
new_ltEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(x0, x1)
new_esEs29(x0, x1, ty_Integer)
new_esEs12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primPlusNat1(Zero, Zero)
new_primCompAux0(x0, GT)
new_compare23(x0, x1, True)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_lt19(x0, x1, app(ty_[], x2))
new_lt15(x0, x1)
new_ltEs7(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs29(x0, x1, ty_Ordering)
new_compare19(x0, x1, x2)
new_compare13(x0, x1, False)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_lt20(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_@0)
new_compare30(x0, x1, x2, x3)
new_primPlusNat0(Succ(x0), x1)
new_esEs12(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs4(EQ, EQ)
new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs19(x0, x1, ty_Char)
new_ltEs7(Right(x0), Right(x1), x2, ty_Char)
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_ltEs11(x0, x1)
new_esEs12(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Integer)
new_compare29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Char)
new_esEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs8(Nothing, Just(x0), x1)
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs8(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Just(x0), Just(x1), ty_Char)
new_ltEs7(Left(x0), Left(x1), ty_@0, x2)
new_lt9(x0, x1, x2)
new_esEs10(x0, x1, app(ty_[], x2))
new_esEs12(x0, x1, ty_Float)
new_compare31(@0, @0)
new_esEs7(Just(x0), Just(x1), ty_Float)
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs16([], :(x0, x1), x2)
new_primCmpNat2(x0, Zero)
new_ltEs4(LT, EQ)
new_ltEs4(EQ, LT)
new_esEs12(x0, x1, ty_Int)
new_lt19(x0, x1, ty_Double)
new_esEs6(Right(x0), Right(x1), x2, ty_Integer)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_primMulInt(Pos(x0), Pos(x1))
new_lt20(x0, x1, ty_Bool)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_ltEs7(Right(x0), Right(x1), x2, ty_Int)
new_ltEs18(x0, x1, app(ty_[], x2))
new_esEs30(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_@0)
new_esEs10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs7(Right(x0), Right(x1), x2, ty_Double)
new_asAs(True, x0)
new_primEqNat0(Succ(x0), Zero)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs7(Left(x0), Left(x1), ty_Int, x2)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_esEs12(x0, x1, app(ty_[], x2))
new_esEs13(x0, x1)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_ltEs7(Left(x0), Right(x1), x2, x3)
new_ltEs7(Right(x0), Left(x1), x2, x3)
new_esEs14(:%(x0, x1), :%(x2, x3), x4)
new_esEs21(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Integer)
new_ltEs7(Left(x0), Left(x1), ty_Double, x2)
new_ltEs8(Nothing, Nothing, x0)
new_lt20(x0, x1, ty_@0)
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_Bool)
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Char)
new_esEs28(x0, x1, ty_Ordering)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Ordering)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_lt12(x0, x1, x2)
new_esEs10(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_esEs12(x0, x1, app(ty_Maybe, x2))
new_esEs30(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, ty_Bool)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs27(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_Double)
new_esEs25(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(ty_[], x2))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_lt10(x0, x1, ty_Bool)
new_primPlusNat1(Succ(x0), Zero)
new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs22(x0, x1, ty_Float)
new_ltEs4(LT, LT)
new_esEs10(x0, x1, ty_Integer)
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Integer)
new_compare29(x0, x1, app(app(ty_@2, x2), x3))
new_compare23(x0, x1, False)
new_esEs21(x0, x1, app(ty_[], x2))
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs11(x0, x1, ty_Bool)
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_compare29(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_Double)
new_esEs21(x0, x1, ty_Bool)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, ty_Double)
new_esEs26(x0, x1, ty_Ordering)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs7(Nothing, Just(x0), x1)
new_primPlusNat1(Zero, Succ(x0))
new_ltEs12(x0, x1)
new_compare10(x0, x1, False)
new_lt10(x0, x1, app(app(ty_@2, x2), x3))
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Left(x0), Left(x1), ty_Float, x2)
new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_primCmpNat0(Succ(x0), x1)
new_lt10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, ty_@0)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs22(x0, x1, ty_Bool)
new_lt19(x0, x1, ty_Float)
new_lt19(x0, x1, ty_Integer)
new_ltEs8(Just(x0), Just(x1), ty_Char)
new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Left(x0), Left(x1), ty_Double, x2)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_ltEs8(Just(x0), Just(x1), ty_Float)
new_lt5(x0, x1)
new_compare29(x0, x1, ty_Ordering)
new_ltEs18(x0, x1, ty_Bool)
new_compare28(x0, x1, x2, x3, x4)
new_esEs11(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_@0)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, ty_Int)
new_esEs11(x0, x1, ty_Char)
new_esEs10(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Float)
new_lt19(x0, x1, ty_Ordering)
new_compare29(x0, x1, ty_Integer)
new_compare25(x0, x1, False, x2, x3)
new_esEs6(Right(x0), Right(x1), x2, ty_Char)
new_esEs26(x0, x1, app(ty_[], x2))
new_ltEs18(x0, x1, ty_Float)
new_ltEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs9(False, False)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs21(x0, x1, ty_Double)
new_esEs12(x0, x1, ty_Ordering)
new_ltEs8(Just(x0), Nothing, x1)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs22(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpNat1(Succ(x0), Succ(x1))
new_esEs10(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_@0)
new_ltEs6(x0, x1)
new_lt10(x0, x1, ty_Float)
new_esEs22(x0, x1, ty_Int)
new_ltEs7(Left(x0), Left(x1), ty_Char, x2)
new_compare17(x0, x1, False, x2, x3)
new_ltEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs21(x0, x1, ty_Float)
new_esEs29(x0, x1, ty_Double)
new_primCompAux0(x0, EQ)
new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare27(x0, x1, False, x2, x3)
new_esEs21(x0, x1, ty_Integer)
new_primCmpNat1(Succ(x0), Zero)
new_ltEs18(x0, x1, ty_@0)
new_esEs22(x0, x1, ty_Double)
new_ltEs7(Right(x0), Right(x1), x2, ty_@0)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, ty_Bool)
new_esEs16([], [], x0)
new_compare29(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, app(ty_[], x2))
new_lt13(x0, x1)
new_esEs23(x0, x1, ty_Bool)
new_ltEs5(True, True)
new_ltEs7(Right(x0), Right(x1), x2, ty_Integer)
new_lt19(x0, x1, ty_Int)
new_compare35(x0, x1)
new_lt19(x0, x1, ty_Char)
new_ltEs4(EQ, GT)
new_ltEs4(GT, EQ)
new_esEs6(Right(x0), Right(x1), x2, ty_@0)
new_not(True)
new_esEs11(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Float)
new_compare0(:(x0, x1), [], x2)
new_esEs28(x0, x1, ty_Char)
new_lt19(x0, x1, ty_@0)
new_esEs10(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, ty_Ordering)
new_ltEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs26(x0, x1, ty_Char)
new_ltEs18(x0, x1, ty_Int)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_ltEs20(x0, x1, ty_Ordering)
new_not(False)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_lt14(x0, x1)
new_compare12(Char(x0), Char(x1))
new_esEs15(Char(x0), Char(x1))
new_esEs11(x0, x1, app(ty_[], x2))
new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_compare10(x0, x1, True)
new_lt10(x0, x1, ty_@0)
new_asAs(False, x0)
new_esEs22(x0, x1, ty_Ordering)
new_ltEs18(x0, x1, ty_Char)
new_esEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs17(x0, x1, x2)
new_compare29(x0, x1, ty_Float)
new_lt19(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_Char)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_ltEs8(Just(x0), Just(x1), ty_@0)
new_esEs20(@0, @0)
new_ltEs8(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs7(Left(x0), Left(x1), ty_Float, x2)
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Int)
new_esEs16(:(x0, x1), [], x2)
new_ltEs19(x0, x1, ty_Double)
new_esEs9(True, False)
new_esEs9(False, True)
new_esEs22(x0, x1, ty_Char)
new_ltEs7(Right(x0), Right(x1), x2, ty_Float)
new_ltEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare29(x0, x1, ty_Bool)
new_ltEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs30(x0, x1, ty_Double)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, ty_Integer)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs11(x0, x1, ty_Double)
new_ltEs20(x0, x1, ty_Float)
new_primCompAux0(x0, LT)
new_primCmpNat2(x0, Succ(x1))
new_esEs11(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs12(x0, x1, ty_Integer)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs10(x0, x1, ty_Double)
new_ltEs8(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_sr0(Integer(x0), Integer(x1))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs29(x0, x1, ty_Float)
new_ltEs8(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_primEqInt(Pos(Zero), Pos(Zero))
new_ltEs18(x0, x1, ty_Double)
new_esEs12(x0, x1, ty_Double)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_compare0(:(x0, x1), :(x2, x3), x4)
new_esEs29(x0, x1, ty_Int)
new_esEs12(x0, x1, ty_Bool)
new_compare9(Integer(x0), Integer(x1))
new_lt10(x0, x1, ty_Integer)
new_esEs30(x0, x1, ty_Char)
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs19(Float(x0, x1), Float(x2, x3))
new_primMulNat0(Zero, Succ(x0))
new_compare0([], [], x0)
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Just(x0), Just(x1), ty_@0)
new_ltEs4(GT, LT)
new_ltEs4(LT, GT)
new_ltEs5(True, False)
new_ltEs5(False, True)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs9(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs27(x0, x1, app(ty_[], x2))
new_ltEs8(Just(x0), Just(x1), ty_Int)
new_esEs12(x0, x1, app(app(ty_Either, x2), x3))
new_compare29(x0, x1, ty_@0)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Float)
new_esEs23(x0, x1, ty_Float)
new_compare210(x0, x1, False, x2, x3, x4)
new_esEs30(x0, x1, ty_Float)
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))



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

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

new_splitGT2(zxw300, zxw31, zxw32, zxw33, Branch(zxw340, zxw341, zxw342, zxw343, zxw344), True, h, ba) → new_splitGT3(zxw340, zxw341, zxw342, zxw343, zxw344, Nothing, h, ba)
new_splitGT3(Nothing, zxw31, zxw32, zxw33, zxw34, Nothing, h, ba) → new_splitGT1(zxw31, zxw32, zxw33, zxw34, new_esEs8(new_compare33(h), LT), h, ba)
new_splitGT10(zxw300, zxw31, zxw32, zxw33, zxw34, True, h, ba) → new_splitGT(zxw33, h, ba)
new_splitGT(Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba) → new_splitGT3(zxw340, zxw341, zxw342, zxw343, zxw344, Nothing, h, ba)
new_splitGT1(zxw31, zxw32, zxw33, zxw34, True, h, ba) → new_splitGT(zxw33, h, ba)
new_splitGT3(Just(zxw300), zxw31, zxw32, zxw33, zxw34, Nothing, h, ba) → new_splitGT2(zxw300, zxw31, zxw32, zxw33, zxw34, new_esEs8(new_compare26(Nothing, Just(zxw300), False, h), GT), h, ba)
new_splitGT2(zxw300, zxw31, zxw32, zxw33, zxw34, False, h, ba) → new_splitGT10(zxw300, zxw31, zxw32, zxw33, zxw34, new_esEs8(new_compare34(zxw300, h), LT), h, ba)

The TRS R consists of the following rules:

new_compare26(Nothing, Just(zxw5000), False, bcg) → LT
new_esEs8(GT, GT) → True
new_esEs8(LT, GT) → False
new_esEs8(EQ, GT) → False
new_compare34(zxw300, h) → new_compare26(Nothing, Just(zxw300), False, h)
new_esEs8(LT, LT) → True
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_compare33(h) → new_compare26(Nothing, Nothing, True, h)
new_compare26(zxw490, zxw500, True, bcg) → EQ

The set Q consists of the following terms:

new_esEs8(GT, GT)
new_esEs8(LT, LT)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_compare33(x0)
new_compare26(Nothing, Just(x0), False, x1)
new_compare26(Just(x0), Nothing, False, x1)
new_compare26(x0, x1, True, x2)
new_compare26(Just(x0), Just(x1), False, x2)
new_compare34(x0, x1)
new_esEs8(EQ, EQ)
new_esEs8(GT, EQ)
new_esEs8(EQ, GT)
new_compare26(Nothing, Nothing, False, x0)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)

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_splitLT12(zxw15, zxw16, zxw17, zxw18, zxw19, zxw20, True, bb, bc) → new_splitLT0(zxw19, zxw20, bb, bc)
new_splitLT2(zxw300, zxw31, zxw32, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw34, True, h, ba) → new_splitLT3(zxw330, zxw331, zxw332, zxw333, zxw334, Nothing, h, ba)
new_splitLT1(zxw31, zxw32, zxw33, zxw34, True, h, ba) → new_splitLT(zxw34, h, ba)
new_splitLT3(Nothing, zxw31, zxw32, zxw33, zxw34, Nothing, h, ba) → new_splitLT1(zxw31, zxw32, zxw33, zxw34, new_esEs8(new_compare33(h), GT), h, ba)
new_splitLT21(zxw15, zxw16, zxw17, zxw18, zxw19, zxw20, False, bb, bc) → new_splitLT12(zxw15, zxw16, zxw17, zxw18, zxw19, zxw20, new_esEs8(new_compare36(zxw20, zxw15, bb), GT), bb, bc)
new_splitLT20(zxw31, zxw32, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw34, zxw400, True, h, ba) → new_splitLT3(zxw330, zxw331, zxw332, zxw333, zxw334, Just(zxw400), h, ba)
new_splitLT2(zxw300, zxw31, zxw32, zxw33, zxw34, False, h, ba) → new_splitLT10(zxw300, zxw31, zxw32, zxw33, zxw34, new_esEs8(new_compare34(zxw300, h), GT), h, ba)
new_splitLT21(zxw15, zxw16, zxw17, zxw18, zxw19, zxw20, True, bb, bc) → new_splitLT0(zxw18, zxw20, bb, bc)
new_splitLT(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba) → new_splitLT3(zxw330, zxw331, zxw332, zxw333, zxw334, Nothing, h, ba)
new_splitLT3(Just(zxw300), zxw31, zxw32, zxw33, zxw34, Just(zxw400), h, ba) → new_splitLT21(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs8(new_compare26(Just(zxw400), Just(zxw300), new_esEs31(zxw400, zxw300, h), h), LT), h, ba)
new_splitLT20(zxw31, zxw32, zxw33, zxw34, zxw400, False, h, ba) → new_splitLT11(zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs8(new_compare35(zxw400, h), GT), h, ba)
new_splitLT3(Just(zxw300), zxw31, zxw32, zxw33, zxw34, Nothing, h, ba) → new_splitLT2(zxw300, zxw31, zxw32, zxw33, zxw34, new_esEs8(new_compare26(Nothing, Just(zxw300), False, h), LT), h, ba)
new_splitLT0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw400, h, ba) → new_splitLT3(zxw330, zxw331, zxw332, zxw333, zxw334, Just(zxw400), h, ba)
new_splitLT10(zxw300, zxw31, zxw32, zxw33, zxw34, True, h, ba) → new_splitLT(zxw34, h, ba)
new_splitLT11(zxw31, zxw32, zxw33, zxw34, zxw400, True, h, ba) → new_splitLT0(zxw34, zxw400, h, ba)
new_splitLT3(Nothing, zxw31, zxw32, zxw33, zxw34, Just(zxw400), h, ba) → new_splitLT20(zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs8(new_compare26(Just(zxw400), Nothing, False, h), LT), h, ba)

The TRS R consists of the following rules:

new_esEs6(Right(zxw4000), Right(zxw3000), ce, ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_esEs7(Just(zxw4000), Just(zxw3000), app(ty_Maybe, bgh)) → new_esEs7(zxw4000, zxw3000, bgh)
new_ltEs19(zxw4900, zxw5000, ty_Integer) → new_ltEs16(zxw4900, zxw5000)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_@0, cca) → new_ltEs14(zxw49000, zxw50000)
new_esEs27(zxw49000, zxw50000, app(ty_[], che)) → new_esEs16(zxw49000, zxw50000, che)
new_ltEs4(EQ, GT) → True
new_esEs22(zxw4000, zxw3000, ty_@0) → new_esEs20(zxw4000, zxw3000)
new_compare15(zxw49000, zxw50000, True, be, bf) → LT
new_ltEs9(@2(zxw49000, zxw49001), @2(zxw50000, zxw50001), beg, beh) → new_pePe(new_lt10(zxw49000, zxw50000, beg), new_asAs(new_esEs23(zxw49000, zxw50000, beg), new_ltEs18(zxw49001, zxw50001, beh)))
new_esEs6(Right(zxw4000), Right(zxw3000), ce, ty_Float) → new_esEs19(zxw4000, zxw3000)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Integer, cf) → new_esEs17(zxw4000, zxw3000)
new_esEs31(zxw400, zxw300, ty_Ordering) → new_esEs8(zxw400, zxw300)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_esEs23(zxw49000, zxw50000, app(app(ty_@2, hb), hc)) → new_esEs4(zxw49000, zxw50000, hb, hc)
new_compare29(zxw49000, zxw50000, ty_Char) → new_compare12(zxw49000, zxw50000)
new_esEs22(zxw4000, zxw3000, ty_Float) → new_esEs19(zxw4000, zxw3000)
new_esEs6(Right(zxw4000), Right(zxw3000), ce, ty_Int) → new_esEs13(zxw4000, zxw3000)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Bool) → new_ltEs5(zxw49000, zxw50000)
new_lt19(zxw49001, zxw50001, ty_Integer) → new_lt5(zxw49001, zxw50001)
new_compare33(h) → new_compare26(Nothing, Nothing, True, h)
new_esEs12(zxw4000, zxw3000, ty_Bool) → new_esEs9(zxw4000, zxw3000)
new_esEs27(zxw49000, zxw50000, app(ty_Maybe, chd)) → new_esEs7(zxw49000, zxw50000, chd)
new_esEs11(zxw4001, zxw3001, app(ty_[], eg)) → new_esEs16(zxw4001, zxw3001, eg)
new_esEs12(zxw4000, zxw3000, ty_Char) → new_esEs15(zxw4000, zxw3000)
new_compare12(Char(zxw49000), Char(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_ltEs19(zxw4900, zxw5000, ty_Double) → new_ltEs11(zxw4900, zxw5000)
new_esEs31(zxw400, zxw300, app(app(app(ty_@3, cb), cc), cd)) → new_esEs5(zxw400, zxw300, cb, cc, cd)
new_compare29(zxw49000, zxw50000, ty_Double) → new_compare16(zxw49000, zxw50000)
new_ltEs20(zxw49002, zxw50002, ty_Bool) → new_ltEs5(zxw49002, zxw50002)
new_esEs23(zxw49000, zxw50000, ty_Float) → new_esEs19(zxw49000, zxw50000)
new_lt19(zxw49001, zxw50001, ty_Ordering) → new_lt14(zxw49001, zxw50001)
new_lt19(zxw49001, zxw50001, ty_Int) → new_lt4(zxw49001, zxw50001)
new_esEs7(Just(zxw4000), Just(zxw3000), app(app(ty_Either, bhf), bhg)) → new_esEs6(zxw4000, zxw3000, bhf, bhg)
new_primMulNat0(Zero, Zero) → Zero
new_ltEs7(Left(zxw49000), Right(zxw50000), cbh, cca) → True
new_compare26(Just(zxw4900), Nothing, False, bdd) → GT
new_esEs26(zxw49001, zxw50001, app(ty_[], cgc)) → new_esEs16(zxw49001, zxw50001, cgc)
new_esEs27(zxw49000, zxw50000, ty_Bool) → new_esEs9(zxw49000, zxw50000)
new_ltEs18(zxw49001, zxw50001, ty_Integer) → new_ltEs16(zxw49001, zxw50001)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_ltEs18(zxw49001, zxw50001, app(ty_[], bfd)) → new_ltEs13(zxw49001, zxw50001, bfd)
new_ltEs20(zxw49002, zxw50002, app(ty_Maybe, ceh)) → new_ltEs8(zxw49002, zxw50002, ceh)
new_esEs11(zxw4001, zxw3001, ty_Char) → new_esEs15(zxw4001, zxw3001)
new_esEs11(zxw4001, zxw3001, ty_Float) → new_esEs19(zxw4001, zxw3001)
new_lt8(zxw49000, zxw50000) → new_esEs8(new_compare16(zxw49000, zxw50000), LT)
new_esEs26(zxw49001, zxw50001, ty_Char) → new_esEs15(zxw49001, zxw50001)
new_lt20(zxw49000, zxw50000, app(app(ty_@2, chb), chc)) → new_lt11(zxw49000, zxw50000, chb, chc)
new_esEs23(zxw49000, zxw50000, ty_Char) → new_esEs15(zxw49000, zxw50000)
new_esEs23(zxw49000, zxw50000, ty_Bool) → new_esEs9(zxw49000, zxw50000)
new_esEs27(zxw49000, zxw50000, ty_Char) → new_esEs15(zxw49000, zxw50000)
new_compare26(Nothing, Just(zxw5000), False, bdd) → LT
new_lt10(zxw49000, zxw50000, ty_Float) → new_lt7(zxw49000, zxw50000)
new_esEs21(zxw4001, zxw3001, ty_Double) → new_esEs18(zxw4001, zxw3001)
new_ltEs19(zxw4900, zxw5000, ty_Int) → new_ltEs10(zxw4900, zxw5000)
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_lt9(zxw49000, zxw50000, db) → new_esEs8(new_compare0(zxw49000, zxw50000, db), LT)
new_compare210(zxw49000, zxw50000, False, bgd, bge, bgf) → new_compare110(zxw49000, zxw50000, new_ltEs15(zxw49000, zxw50000, bgd, bge, bgf), bgd, bge, bgf)
new_esEs22(zxw4000, zxw3000, app(ty_Ratio, bcc)) → new_esEs14(zxw4000, zxw3000, bcc)
new_esEs21(zxw4001, zxw3001, app(ty_Ratio, bba)) → new_esEs14(zxw4001, zxw3001, bba)
new_esEs30(zxw20, zxw15, ty_Bool) → new_esEs9(zxw20, zxw15)
new_esEs7(Just(zxw4000), Just(zxw3000), app(app(ty_@2, bhh), caa)) → new_esEs4(zxw4000, zxw3000, bhh, caa)
new_esEs25(zxw4000, zxw3000, ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Bool) → new_esEs9(zxw4000, zxw3000)
new_esEs30(zxw20, zxw15, ty_Float) → new_esEs19(zxw20, zxw15)
new_ltEs20(zxw49002, zxw50002, ty_Integer) → new_ltEs16(zxw49002, zxw50002)
new_esEs21(zxw4001, zxw3001, app(app(ty_Either, bbf), bbg)) → new_esEs6(zxw4001, zxw3001, bbf, bbg)
new_ltEs7(Left(zxw49000), Left(zxw50000), app(app(app(ty_@3, dah), dba), dbb), cca) → new_ltEs15(zxw49000, zxw50000, dah, dba, dbb)
new_ltEs14(zxw4900, zxw5000) → new_fsEs(new_compare31(zxw4900, zxw5000))
new_compare24(zxw49000, zxw50000, False) → new_compare13(zxw49000, zxw50000, new_ltEs5(zxw49000, zxw50000))
new_esEs7(Just(zxw4000), Just(zxw3000), app(ty_Ratio, bha)) → new_esEs14(zxw4000, zxw3000, bha)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbh, app(app(ty_@2, dbf), dbg)) → new_ltEs9(zxw49000, zxw50000, dbf, dbg)
new_lt4(zxw490, zxw500) → new_esEs8(new_compare7(zxw490, zxw500), LT)
new_esEs28(zxw4000, zxw3000, app(app(app(ty_@3, ddc), ddd), dde)) → new_esEs5(zxw4000, zxw3000, ddc, ddd, dde)
new_esEs28(zxw4000, zxw3000, ty_Bool) → new_esEs9(zxw4000, zxw3000)
new_compare19(zxw490, zxw500, bdd) → new_compare26(zxw490, zxw500, new_esEs7(zxw490, zxw500, bdd), bdd)
new_esEs17(Integer(zxw4000), Integer(zxw3000)) → new_primEqInt(zxw4000, zxw3000)
new_pePe(False, zxw213) → zxw213
new_lt12(zxw490, zxw500, bdd) → new_esEs8(new_compare19(zxw490, zxw500, bdd), LT)
new_esEs31(zxw400, zxw300, app(ty_[], ca)) → new_esEs16(zxw400, zxw300, ca)
new_esEs20(@0, @0) → True
new_esEs6(Left(zxw4000), Left(zxw3000), app(app(ty_@2, cdb), cdc), cf) → new_esEs4(zxw4000, zxw3000, cdb, cdc)
new_esEs31(zxw400, zxw300, ty_Bool) → new_esEs9(zxw400, zxw300)
new_esEs6(Right(zxw4000), Right(zxw3000), ce, app(ty_Ratio, cde)) → new_esEs14(zxw4000, zxw3000, cde)
new_compare23(zxw49000, zxw50000, True) → EQ
new_esEs11(zxw4001, zxw3001, ty_Int) → new_esEs13(zxw4001, zxw3001)
new_lt19(zxw49001, zxw50001, app(ty_[], cgc)) → new_lt9(zxw49001, zxw50001, cgc)
new_compare29(zxw49000, zxw50000, ty_@0) → new_compare31(zxw49000, zxw50000)
new_compare26(Nothing, Nothing, False, bdd) → LT
new_esEs10(zxw4002, zxw3002, app(ty_Maybe, dc)) → new_esEs7(zxw4002, zxw3002, dc)
new_ltEs16(zxw4900, zxw5000) → new_fsEs(new_compare9(zxw4900, zxw5000))
new_esEs22(zxw4000, zxw3000, app(app(ty_@2, bdb), bdc)) → new_esEs4(zxw4000, zxw3000, bdb, bdc)
new_esEs23(zxw49000, zxw50000, app(ty_Maybe, bgc)) → new_esEs7(zxw49000, zxw50000, bgc)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbh, app(ty_Ratio, dcg)) → new_ltEs17(zxw49000, zxw50000, dcg)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Char, cca) → new_ltEs12(zxw49000, zxw50000)
new_esEs28(zxw4000, zxw3000, ty_@0) → new_esEs20(zxw4000, zxw3000)
new_esEs10(zxw4002, zxw3002, app(app(app(ty_@3, df), dg), dh)) → new_esEs5(zxw4002, zxw3002, df, dg, dh)
new_ltEs20(zxw49002, zxw50002, app(ty_[], cfa)) → new_ltEs13(zxw49002, zxw50002, cfa)
new_esEs27(zxw49000, zxw50000, ty_Float) → new_esEs19(zxw49000, zxw50000)
new_ltEs20(zxw49002, zxw50002, app(app(app(ty_@3, cfb), cfc), cfd)) → new_ltEs15(zxw49002, zxw50002, cfb, cfc, cfd)
new_esEs22(zxw4000, zxw3000, ty_Ordering) → new_esEs8(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Bool) → new_esEs9(zxw4000, zxw3000)
new_compare6(zxw49000, zxw50000) → new_compare23(zxw49000, zxw50000, new_esEs8(zxw49000, zxw50000))
new_esEs12(zxw4000, zxw3000, app(ty_[], gb)) → new_esEs16(zxw4000, zxw3000, gb)
new_compare32(zxw49000, zxw50000, be, bf) → new_compare25(zxw49000, zxw50000, new_esEs6(zxw49000, zxw50000, be, bf), be, bf)
new_compare29(zxw49000, zxw50000, ty_Int) → new_compare7(zxw49000, zxw50000)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Bool, cf) → new_esEs9(zxw4000, zxw3000)
new_ltEs8(Nothing, Just(zxw50000), hd) → True
new_esEs31(zxw400, zxw300, app(app(ty_@2, cg), da)) → new_esEs4(zxw400, zxw300, cg, da)
new_ltEs7(Left(zxw49000), Left(zxw50000), app(app(ty_@2, dad), dae), cca) → new_ltEs9(zxw49000, zxw50000, dad, dae)
new_esEs6(Right(zxw4000), Left(zxw3000), ce, cf) → False
new_esEs6(Left(zxw4000), Right(zxw3000), ce, cf) → False
new_esEs8(LT, LT) → True
new_lt20(zxw49000, zxw50000, ty_@0) → new_lt15(zxw49000, zxw50000)
new_esEs10(zxw4002, zxw3002, ty_Integer) → new_esEs17(zxw4002, zxw3002)
new_esEs28(zxw4000, zxw3000, ty_Float) → new_esEs19(zxw4000, zxw3000)
new_compare29(zxw49000, zxw50000, app(app(app(ty_@3, cag), cah), cba)) → new_compare28(zxw49000, zxw50000, cag, cah, cba)
new_lt19(zxw49001, zxw50001, ty_@0) → new_lt15(zxw49001, zxw50001)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbh, ty_Bool) → new_ltEs5(zxw49000, zxw50000)
new_ltEs5(True, False) → False
new_lt19(zxw49001, zxw50001, app(app(ty_@2, cfh), cga)) → new_lt11(zxw49001, zxw50001, cfh, cga)
new_compare0([], [], cab) → EQ
new_pePe(True, zxw213) → True
new_primEqNat0(Zero, Zero) → True
new_compare34(zxw300, h) → new_compare26(Nothing, Just(zxw300), False, h)
new_esEs14(:%(zxw4000, zxw4001), :%(zxw3000, zxw3001), bh) → new_asAs(new_esEs25(zxw4000, zxw3000, bh), new_esEs24(zxw4001, zxw3001, bh))
new_lt10(zxw49000, zxw50000, ty_Double) → new_lt8(zxw49000, zxw50000)
new_ltEs20(zxw49002, zxw50002, ty_Ordering) → new_ltEs4(zxw49002, zxw50002)
new_compare27(zxw49000, zxw50000, False, hb, hc) → new_compare17(zxw49000, zxw50000, new_ltEs9(zxw49000, zxw50000, hb, hc), hb, hc)
new_compare11(zxw180, zxw181, True, bd) → LT
new_esEs23(zxw49000, zxw50000, app(app(ty_Either, be), bf)) → new_esEs6(zxw49000, zxw50000, be, bf)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_@0, cf) → new_esEs20(zxw4000, zxw3000)
new_esEs6(Right(zxw4000), Right(zxw3000), ce, ty_Bool) → new_esEs9(zxw4000, zxw3000)
new_esEs12(zxw4000, zxw3000, ty_Int) → new_esEs13(zxw4000, zxw3000)
new_lt20(zxw49000, zxw50000, app(ty_[], che)) → new_lt9(zxw49000, zxw50000, che)
new_esEs6(Right(zxw4000), Right(zxw3000), ce, app(app(ty_Either, ceb), cec)) → new_esEs6(zxw4000, zxw3000, ceb, cec)
new_compare26(Just(zxw4900), Just(zxw5000), False, bdd) → new_compare11(zxw4900, zxw5000, new_ltEs19(zxw4900, zxw5000, bdd), bdd)
new_ltEs5(True, True) → True
new_ltEs7(Left(zxw49000), Left(zxw50000), app(ty_Maybe, daf), cca) → new_ltEs8(zxw49000, zxw50000, daf)
new_compare36(zxw20, zxw15, bb) → new_compare26(Just(zxw20), Just(zxw15), new_esEs30(zxw20, zxw15, bb), bb)
new_ltEs20(zxw49002, zxw50002, app(app(ty_@2, cef), ceg)) → new_ltEs9(zxw49002, zxw50002, cef, ceg)
new_esEs15(Char(zxw4000), Char(zxw3000)) → new_primEqNat0(zxw4000, zxw3000)
new_sr(zxw4001, zxw3001) → new_primMulInt(zxw4001, zxw3001)
new_ltEs18(zxw49001, zxw50001, ty_Int) → new_ltEs10(zxw49001, zxw50001)
new_esEs25(zxw4000, zxw3000, ty_Int) → new_esEs13(zxw4000, zxw3000)
new_compare7(zxw49, zxw50) → new_primCmpInt(zxw49, zxw50)
new_primCmpNat1(Zero, Zero) → EQ
new_esEs7(Just(zxw4000), Just(zxw3000), app(ty_[], bhb)) → new_esEs16(zxw4000, zxw3000, bhb)
new_lt10(zxw49000, zxw50000, ty_Int) → new_lt4(zxw49000, zxw50000)
new_esEs28(zxw4000, zxw3000, app(app(ty_Either, ddf), ddg)) → new_esEs6(zxw4000, zxw3000, ddf, ddg)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbh, app(ty_Maybe, dbh)) → new_ltEs8(zxw49000, zxw50000, dbh)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbh, ty_Integer) → new_ltEs16(zxw49000, zxw50000)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbh, app(app(app(ty_@3, dcb), dcc), dcd)) → new_ltEs15(zxw49000, zxw50000, dcb, dcc, dcd)
new_esEs26(zxw49001, zxw50001, ty_Ordering) → new_esEs8(zxw49001, zxw50001)
new_esEs8(GT, GT) → True
new_esEs27(zxw49000, zxw50000, ty_@0) → new_esEs20(zxw49000, zxw50000)
new_esEs13(zxw400, zxw300) → new_primEqInt(zxw400, zxw300)
new_lt13(zxw49000, zxw50000) → new_esEs8(new_compare18(zxw49000, zxw50000), LT)
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_lt20(zxw49000, zxw50000, ty_Ordering) → new_lt14(zxw49000, zxw50000)
new_esEs11(zxw4001, zxw3001, app(app(ty_@2, ff), fg)) → new_esEs4(zxw4001, zxw3001, ff, fg)
new_esEs11(zxw4001, zxw3001, ty_Ordering) → new_esEs8(zxw4001, zxw3001)
new_lt10(zxw49000, zxw50000, app(app(ty_@2, hb), hc)) → new_lt11(zxw49000, zxw50000, hb, hc)
new_compare23(zxw49000, zxw50000, False) → new_compare10(zxw49000, zxw50000, new_ltEs4(zxw49000, zxw50000))
new_esEs8(LT, GT) → False
new_esEs8(GT, LT) → False
new_ltEs19(zxw4900, zxw5000, app(app(app(ty_@3, cbe), cbf), cbg)) → new_ltEs15(zxw4900, zxw5000, cbe, cbf, cbg)
new_lt20(zxw49000, zxw50000, app(app(ty_Either, daa), dab)) → new_lt17(zxw49000, zxw50000, daa, dab)
new_esEs26(zxw49001, zxw50001, ty_Bool) → new_esEs9(zxw49001, zxw50001)
new_ltEs11(zxw4900, zxw5000) → new_fsEs(new_compare16(zxw4900, zxw5000))
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_compare17(zxw49000, zxw50000, True, hb, hc) → LT
new_primEqInt(Neg(Succ(zxw40000)), Neg(Succ(zxw30000))) → new_primEqNat0(zxw40000, zxw30000)
new_ltEs5(False, False) → True
new_esEs23(zxw49000, zxw50000, ty_Ordering) → new_esEs8(zxw49000, zxw50000)
new_ltEs18(zxw49001, zxw50001, app(app(ty_Either, bfh), bga)) → new_ltEs7(zxw49001, zxw50001, bfh, bga)
new_esEs28(zxw4000, zxw3000, ty_Char) → new_esEs15(zxw4000, zxw3000)
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)
new_ltEs19(zxw4900, zxw5000, app(ty_Ratio, bag)) → new_ltEs17(zxw4900, zxw5000, bag)
new_esEs10(zxw4002, zxw3002, ty_Bool) → new_esEs9(zxw4002, zxw3002)
new_lt20(zxw49000, zxw50000, ty_Char) → new_lt6(zxw49000, zxw50000)
new_compare13(zxw49000, zxw50000, False) → GT
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Bool, cca) → new_ltEs5(zxw49000, zxw50000)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Int, cca) → new_ltEs10(zxw49000, zxw50000)
new_lt11(zxw49000, zxw50000, hb, hc) → new_esEs8(new_compare30(zxw49000, zxw50000, hb, hc), LT)
new_esEs21(zxw4001, zxw3001, ty_Char) → new_esEs15(zxw4001, zxw3001)
new_lt20(zxw49000, zxw50000, ty_Int) → new_lt4(zxw49000, zxw50000)
new_primCompAux1(zxw49000, zxw50000, zxw214, cab) → new_primCompAux0(zxw214, new_compare29(zxw49000, zxw50000, cab))
new_esEs7(Just(zxw4000), Just(zxw3000), ty_@0) → new_esEs20(zxw4000, zxw3000)
new_lt16(zxw49000, zxw50000, bgd, bge, bgf) → new_esEs8(new_compare28(zxw49000, zxw50000, bgd, bge, bgf), LT)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_ltEs7(Right(zxw49000), Left(zxw50000), cbh, cca) → False
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Ordering) → new_esEs8(zxw4000, zxw3000)
new_ltEs7(Left(zxw49000), Left(zxw50000), app(ty_[], dag), cca) → new_ltEs13(zxw49000, zxw50000, dag)
new_ltEs19(zxw4900, zxw5000, ty_Ordering) → new_ltEs4(zxw4900, zxw5000)
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_ltEs20(zxw49002, zxw50002, ty_Char) → new_ltEs12(zxw49002, zxw50002)
new_esEs11(zxw4001, zxw3001, app(app(app(ty_@3, eh), fa), fb)) → new_esEs5(zxw4001, zxw3001, eh, fa, fb)
new_ltEs20(zxw49002, zxw50002, app(ty_Ratio, cfg)) → new_ltEs17(zxw49002, zxw50002, cfg)
new_ltEs18(zxw49001, zxw50001, ty_@0) → new_ltEs14(zxw49001, zxw50001)
new_primEqInt(Neg(Succ(zxw40000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(zxw30000))) → False
new_ltEs19(zxw4900, zxw5000, ty_Char) → new_ltEs12(zxw4900, zxw5000)
new_esEs12(zxw4000, zxw3000, ty_Double) → new_esEs18(zxw4000, zxw3000)
new_primCompAux0(zxw218, GT) → GT
new_esEs8(EQ, EQ) → True
new_esEs6(Left(zxw4000), Left(zxw3000), app(ty_Ratio, ccc), cf) → new_esEs14(zxw4000, zxw3000, ccc)
new_ltEs8(Just(zxw49000), Just(zxw50000), app(app(ty_Either, bad), bae)) → new_ltEs7(zxw49000, zxw50000, bad, bae)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Integer, cca) → new_ltEs16(zxw49000, zxw50000)
new_esEs6(Right(zxw4000), Right(zxw3000), ce, app(ty_[], cdf)) → new_esEs16(zxw4000, zxw3000, cdf)
new_esEs23(zxw49000, zxw50000, ty_Integer) → new_esEs17(zxw49000, zxw50000)
new_esEs28(zxw4000, zxw3000, ty_Int) → new_esEs13(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, app(app(app(ty_@3, bce), bcf), bcg)) → new_esEs5(zxw4000, zxw3000, bce, bcf, bcg)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_ltEs18(zxw49001, zxw50001, ty_Ordering) → new_ltEs4(zxw49001, zxw50001)
new_ltEs4(EQ, LT) → False
new_esEs12(zxw4000, zxw3000, app(ty_Maybe, fh)) → new_esEs7(zxw4000, zxw3000, fh)
new_lt20(zxw49000, zxw50000, ty_Double) → new_lt8(zxw49000, zxw50000)
new_esEs10(zxw4002, zxw3002, ty_Float) → new_esEs19(zxw4002, zxw3002)
new_compare11(zxw180, zxw181, False, bd) → GT
new_esEs11(zxw4001, zxw3001, ty_Bool) → new_esEs9(zxw4001, zxw3001)
new_esEs26(zxw49001, zxw50001, ty_Integer) → new_esEs17(zxw49001, zxw50001)
new_lt10(zxw49000, zxw50000, ty_Ordering) → new_lt14(zxw49000, zxw50000)
new_ltEs18(zxw49001, zxw50001, ty_Bool) → new_ltEs5(zxw49001, zxw50001)
new_primEqInt(Pos(Succ(zxw40000)), Pos(Succ(zxw30000))) → new_primEqNat0(zxw40000, zxw30000)
new_esEs12(zxw4000, zxw3000, app(app(app(ty_@3, gc), gd), ge)) → new_esEs5(zxw4000, zxw3000, gc, gd, ge)
new_compare27(zxw49000, zxw50000, True, hb, hc) → EQ
new_esEs6(Left(zxw4000), Left(zxw3000), app(app(app(ty_@3, cce), ccf), ccg), cf) → new_esEs5(zxw4000, zxw3000, cce, ccf, ccg)
new_lt18(zxw49000, zxw50000, bgg) → new_esEs8(new_compare8(zxw49000, zxw50000, bgg), LT)
new_ltEs18(zxw49001, zxw50001, app(app(app(ty_@3, bfe), bff), bfg)) → new_ltEs15(zxw49001, zxw50001, bfe, bff, bfg)
new_esEs31(zxw400, zxw300, ty_Double) → new_esEs18(zxw400, zxw300)
new_lt10(zxw49000, zxw50000, app(ty_Maybe, bgc)) → new_lt12(zxw49000, zxw50000, bgc)
new_esEs26(zxw49001, zxw50001, ty_Int) → new_esEs13(zxw49001, zxw50001)
new_ltEs8(Just(zxw49000), Just(zxw50000), app(app(ty_@2, he), hf)) → new_ltEs9(zxw49000, zxw50000, he, hf)
new_primEqNat0(Succ(zxw40000), Succ(zxw30000)) → new_primEqNat0(zxw40000, zxw30000)
new_compare29(zxw49000, zxw50000, app(ty_[], caf)) → new_compare0(zxw49000, zxw50000, caf)
new_esEs27(zxw49000, zxw50000, ty_Ordering) → new_esEs8(zxw49000, zxw50000)
new_esEs27(zxw49000, zxw50000, ty_Integer) → new_esEs17(zxw49000, zxw50000)
new_esEs23(zxw49000, zxw50000, app(ty_Ratio, bgg)) → new_esEs14(zxw49000, zxw50000, bgg)
new_ltEs18(zxw49001, zxw50001, ty_Float) → new_ltEs6(zxw49001, zxw50001)
new_esEs22(zxw4000, zxw3000, ty_Int) → new_esEs13(zxw4000, zxw3000)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbh, app(ty_[], dca)) → new_ltEs13(zxw49000, zxw50000, dca)
new_ltEs4(GT, EQ) → False
new_lt7(zxw49000, zxw50000) → new_esEs8(new_compare14(zxw49000, zxw50000), LT)
new_lt10(zxw49000, zxw50000, app(app(app(ty_@3, bgd), bge), bgf)) → new_lt16(zxw49000, zxw50000, bgd, bge, bgf)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Int) → new_esEs13(zxw4000, zxw3000)
new_ltEs19(zxw4900, zxw5000, app(app(ty_Either, cbh), cca)) → new_ltEs7(zxw4900, zxw5000, cbh, cca)
new_ltEs8(Just(zxw49000), Nothing, hd) → False
new_esEs21(zxw4001, zxw3001, ty_Float) → new_esEs19(zxw4001, zxw3001)
new_esEs26(zxw49001, zxw50001, app(app(ty_@2, cfh), cga)) → new_esEs4(zxw49001, zxw50001, cfh, cga)
new_esEs27(zxw49000, zxw50000, app(app(app(ty_@3, chf), chg), chh)) → new_esEs5(zxw49000, zxw50000, chf, chg, chh)
new_ltEs13(zxw4900, zxw5000, cab) → new_fsEs(new_compare0(zxw4900, zxw5000, cab))
new_esEs22(zxw4000, zxw3000, ty_Char) → new_esEs15(zxw4000, zxw3000)
new_esEs30(zxw20, zxw15, app(ty_Ratio, bdf)) → new_esEs14(zxw20, zxw15, bdf)
new_ltEs18(zxw49001, zxw50001, ty_Double) → new_ltEs11(zxw49001, zxw50001)
new_esEs7(Nothing, Nothing, bg) → True
new_esEs28(zxw4000, zxw3000, ty_Ordering) → new_esEs8(zxw4000, zxw3000)
new_lt10(zxw49000, zxw50000, app(app(ty_Either, be), bf)) → new_lt17(zxw49000, zxw50000, be, bf)
new_esEs8(EQ, LT) → False
new_esEs8(LT, EQ) → False
new_esEs10(zxw4002, zxw3002, ty_Char) → new_esEs15(zxw4002, zxw3002)
new_primEqInt(Pos(Succ(zxw40000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(zxw30000))) → False
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Double, cca) → new_ltEs11(zxw49000, zxw50000)
new_ltEs4(EQ, EQ) → True
new_esEs6(Right(zxw4000), Right(zxw3000), ce, app(ty_Maybe, cdd)) → new_esEs7(zxw4000, zxw3000, cdd)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbh, ty_Ordering) → new_ltEs4(zxw49000, zxw50000)
new_esEs30(zxw20, zxw15, ty_@0) → new_esEs20(zxw20, zxw15)
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_ltEs20(zxw49002, zxw50002, ty_@0) → new_ltEs14(zxw49002, zxw50002)
new_esEs23(zxw49000, zxw50000, ty_@0) → new_esEs20(zxw49000, zxw50000)
new_compare210(zxw49000, zxw50000, True, bgd, bge, bgf) → EQ
new_esEs6(Right(zxw4000), Right(zxw3000), ce, ty_@0) → new_esEs20(zxw4000, zxw3000)
new_ltEs4(GT, LT) → False
new_sr0(Integer(zxw500000), Integer(zxw490010)) → Integer(new_primMulInt(zxw500000, zxw490010))
new_compare13(zxw49000, zxw50000, True) → LT
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_compare14(Float(zxw49000, zxw49001), Float(zxw50000, zxw50001)) → new_compare7(new_sr(zxw49000, zxw50000), new_sr(zxw49001, zxw50001))
new_primEqInt(Pos(Succ(zxw40000)), Neg(zxw3000)) → False
new_primEqInt(Neg(Succ(zxw40000)), Pos(zxw3000)) → False
new_esEs7(Just(zxw4000), Nothing, bg) → False
new_esEs7(Nothing, Just(zxw3000), bg) → False
new_esEs18(Double(zxw4000, zxw4001), Double(zxw3000, zxw3001)) → new_esEs13(new_sr(zxw4000, zxw3000), new_sr(zxw4001, zxw3001))
new_ltEs5(False, True) → True
new_esEs26(zxw49001, zxw50001, ty_Double) → new_esEs18(zxw49001, zxw50001)
new_compare28(zxw49000, zxw50000, bgd, bge, bgf) → new_compare210(zxw49000, zxw50000, new_esEs5(zxw49000, zxw50000, bgd, bge, bgf), bgd, bge, bgf)
new_esEs11(zxw4001, zxw3001, ty_Double) → new_esEs18(zxw4001, zxw3001)
new_ltEs6(zxw4900, zxw5000) → new_fsEs(new_compare14(zxw4900, zxw5000))
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Ordering, cca) → new_ltEs4(zxw49000, zxw50000)
new_esEs31(zxw400, zxw300, ty_Integer) → new_esEs17(zxw400, zxw300)
new_primEqInt(Pos(Zero), Neg(Succ(zxw30000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(zxw30000))) → False
new_ltEs19(zxw4900, zxw5000, app(app(ty_@2, beg), beh)) → new_ltEs9(zxw4900, zxw5000, beg, beh)
new_ltEs20(zxw49002, zxw50002, ty_Float) → new_ltEs6(zxw49002, zxw50002)
new_compare29(zxw49000, zxw50000, app(app(ty_@2, cac), cad)) → new_compare30(zxw49000, zxw50000, cac, cad)
new_compare24(zxw49000, zxw50000, True) → EQ
new_esEs27(zxw49000, zxw50000, ty_Int) → new_esEs13(zxw49000, zxw50000)
new_ltEs18(zxw49001, zxw50001, app(app(ty_@2, bfa), bfb)) → new_ltEs9(zxw49001, zxw50001, bfa, bfb)
new_esEs6(Right(zxw4000), Right(zxw3000), ce, ty_Double) → new_esEs18(zxw4000, zxw3000)
new_lt20(zxw49000, zxw50000, ty_Bool) → new_lt13(zxw49000, zxw50000)
new_primCmpNat0(Zero, zxw4900) → LT
new_ltEs7(Right(zxw49000), Right(zxw50000), cbh, ty_Char) → new_ltEs12(zxw49000, zxw50000)
new_esEs8(EQ, GT) → False
new_esEs8(GT, EQ) → False
new_esEs10(zxw4002, zxw3002, app(ty_[], de)) → new_esEs16(zxw4002, zxw3002, de)
new_lt15(zxw49000, zxw50000) → new_esEs8(new_compare31(zxw49000, zxw50000), LT)
new_esEs31(zxw400, zxw300, ty_Int) → new_esEs13(zxw400, zxw300)
new_compare17(zxw49000, zxw50000, False, hb, hc) → GT
new_compare29(zxw49000, zxw50000, ty_Float) → new_compare14(zxw49000, zxw50000)
new_esEs30(zxw20, zxw15, ty_Double) → new_esEs18(zxw20, zxw15)
new_esEs28(zxw4000, zxw3000, app(ty_Ratio, dda)) → new_esEs14(zxw4000, zxw3000, dda)
new_compare26(zxw490, zxw500, True, bdd) → EQ
new_primCompAux0(zxw218, LT) → LT
new_esEs11(zxw4001, zxw3001, ty_@0) → new_esEs20(zxw4001, zxw3001)
new_esEs30(zxw20, zxw15, app(app(ty_Either, bec), bed)) → new_esEs6(zxw20, zxw15, bec, bed)
new_esEs12(zxw4000, zxw3000, ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_not(False) → True
new_esEs6(Left(zxw4000), Left(zxw3000), app(app(ty_Either, cch), cda), cf) → new_esEs6(zxw4000, zxw3000, cch, cda)
new_esEs28(zxw4000, zxw3000, app(ty_[], ddb)) → new_esEs16(zxw4000, zxw3000, ddb)
new_esEs24(zxw4001, zxw3001, ty_Int) → new_esEs13(zxw4001, zxw3001)
new_esEs31(zxw400, zxw300, ty_Char) → new_esEs15(zxw400, zxw300)
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_esEs26(zxw49001, zxw50001, app(ty_Ratio, cha)) → new_esEs14(zxw49001, zxw50001, cha)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Double) → new_ltEs11(zxw49000, zxw50000)
new_esEs11(zxw4001, zxw3001, app(app(ty_Either, fc), fd)) → new_esEs6(zxw4001, zxw3001, fc, fd)
new_esEs21(zxw4001, zxw3001, ty_@0) → new_esEs20(zxw4001, zxw3001)
new_esEs31(zxw400, zxw300, app(ty_Ratio, bh)) → new_esEs14(zxw400, zxw300, bh)
new_lt19(zxw49001, zxw50001, ty_Float) → new_lt7(zxw49001, zxw50001)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbh, ty_Int) → new_ltEs10(zxw49000, zxw50000)
new_compare0(:(zxw49000, zxw49001), [], cab) → GT
new_esEs12(zxw4000, zxw3000, ty_Float) → new_esEs19(zxw4000, zxw3000)
new_ltEs8(Just(zxw49000), Just(zxw50000), app(ty_[], hh)) → new_ltEs13(zxw49000, zxw50000, hh)
new_lt14(zxw49000, zxw50000) → new_esEs8(new_compare6(zxw49000, zxw50000), LT)
new_ltEs19(zxw4900, zxw5000, ty_Float) → new_ltEs6(zxw4900, zxw5000)
new_esEs27(zxw49000, zxw50000, app(app(ty_Either, daa), dab)) → new_esEs6(zxw49000, zxw50000, daa, dab)
new_lt19(zxw49001, zxw50001, app(ty_Ratio, cha)) → new_lt18(zxw49001, zxw50001, cha)
new_esEs9(True, True) → True
new_lt19(zxw49001, zxw50001, app(app(app(ty_@3, cgd), cge), cgf)) → new_lt16(zxw49001, zxw50001, cgd, cge, cgf)
new_lt19(zxw49001, zxw50001, ty_Char) → new_lt6(zxw49001, zxw50001)
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Double, cf) → new_esEs18(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, app(ty_Maybe, dch)) → new_esEs7(zxw4000, zxw3000, dch)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_esEs21(zxw4001, zxw3001, app(app(app(ty_@3, bbc), bbd), bbe)) → new_esEs5(zxw4001, zxw3001, bbc, bbd, bbe)
new_esEs22(zxw4000, zxw3000, app(ty_[], bcd)) → new_esEs16(zxw4000, zxw3000, bcd)
new_esEs21(zxw4001, zxw3001, app(ty_Maybe, bah)) → new_esEs7(zxw4001, zxw3001, bah)
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_esEs22(zxw4000, zxw3000, ty_Double) → new_esEs18(zxw4000, zxw3000)
new_esEs21(zxw4001, zxw3001, app(app(ty_@2, bbh), bca)) → new_esEs4(zxw4001, zxw3001, bbh, bca)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_@0) → new_ltEs14(zxw49000, zxw50000)
new_esEs31(zxw400, zxw300, ty_@0) → new_esEs20(zxw400, zxw300)
new_esEs19(Float(zxw4000, zxw4001), Float(zxw3000, zxw3001)) → new_esEs13(new_sr(zxw4000, zxw3000), new_sr(zxw4001, zxw3001))
new_ltEs19(zxw4900, zxw5000, app(ty_Maybe, hd)) → new_ltEs8(zxw4900, zxw5000, hd)
new_primMulInt(Neg(zxw40010), Neg(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_esEs30(zxw20, zxw15, app(ty_Maybe, bde)) → new_esEs7(zxw20, zxw15, bde)
new_primEqNat0(Zero, Succ(zxw30000)) → False
new_primEqNat0(Succ(zxw40000), Zero) → False
new_compare25(zxw49000, zxw50000, True, be, bf) → EQ
new_ltEs7(Left(zxw49000), Left(zxw50000), app(app(ty_Either, dbc), dbd), cca) → new_ltEs7(zxw49000, zxw50000, dbc, dbd)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_lt10(zxw49000, zxw50000, app(ty_Ratio, bgg)) → new_lt18(zxw49000, zxw50000, bgg)
new_esEs12(zxw4000, zxw3000, ty_@0) → new_esEs20(zxw4000, zxw3000)
new_esEs21(zxw4001, zxw3001, ty_Bool) → new_esEs9(zxw4001, zxw3001)
new_esEs5(@3(zxw4000, zxw4001, zxw4002), @3(zxw3000, zxw3001, zxw3002), cb, cc, cd) → new_asAs(new_esEs12(zxw4000, zxw3000, cb), new_asAs(new_esEs11(zxw4001, zxw3001, cc), new_esEs10(zxw4002, zxw3002, cd)))
new_esEs16(:(zxw4000, zxw4001), [], ca) → False
new_esEs16([], :(zxw3000, zxw3001), ca) → False
new_lt10(zxw49000, zxw50000, ty_Integer) → new_lt5(zxw49000, zxw50000)
new_lt6(zxw49000, zxw50000) → new_esEs8(new_compare12(zxw49000, zxw50000), LT)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_ltEs4(LT, GT) → True
new_esEs23(zxw49000, zxw50000, ty_Double) → new_esEs18(zxw49000, zxw50000)
new_compare25(zxw49000, zxw50000, False, be, bf) → new_compare15(zxw49000, zxw50000, new_ltEs7(zxw49000, zxw50000, be, bf), be, bf)
new_lt19(zxw49001, zxw50001, app(app(ty_Either, cgg), cgh)) → new_lt17(zxw49001, zxw50001, cgg, cgh)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_esEs6(Left(zxw4000), Left(zxw3000), app(ty_Maybe, ccb), cf) → new_esEs7(zxw4000, zxw3000, ccb)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Ordering, cf) → new_esEs8(zxw4000, zxw3000)
new_esEs16(:(zxw4000, zxw4001), :(zxw3000, zxw3001), ca) → new_asAs(new_esEs28(zxw4000, zxw3000, ca), new_esEs16(zxw4001, zxw3001, ca))
new_ltEs8(Just(zxw49000), Just(zxw50000), app(ty_Ratio, baf)) → new_ltEs17(zxw49000, zxw50000, baf)
new_compare0(:(zxw49000, zxw49001), :(zxw50000, zxw50001), cab) → new_primCompAux1(zxw49000, zxw50000, new_compare0(zxw49001, zxw50001, cab), cab)
new_esEs11(zxw4001, zxw3001, app(ty_Maybe, ee)) → new_esEs7(zxw4001, zxw3001, ee)
new_esEs6(Right(zxw4000), Right(zxw3000), ce, app(app(ty_@2, ced), cee)) → new_esEs4(zxw4000, zxw3000, ced, cee)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Float) → new_ltEs6(zxw49000, zxw50000)
new_compare15(zxw49000, zxw50000, False, be, bf) → GT
new_compare29(zxw49000, zxw50000, app(app(ty_Either, cbb), cbc)) → new_compare32(zxw49000, zxw50000, cbb, cbc)
new_lt20(zxw49000, zxw50000, ty_Float) → new_lt7(zxw49000, zxw50000)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Char) → new_esEs15(zxw4000, zxw3000)
new_esEs23(zxw49000, zxw50000, ty_Int) → new_esEs13(zxw49000, zxw50000)
new_esEs30(zxw20, zxw15, app(ty_[], bdg)) → new_esEs16(zxw20, zxw15, bdg)
new_esEs7(Just(zxw4000), Just(zxw3000), app(app(app(ty_@3, bhc), bhd), bhe)) → new_esEs5(zxw4000, zxw3000, bhc, bhd, bhe)
new_esEs9(True, False) → False
new_esEs9(False, True) → False
new_compare29(zxw49000, zxw50000, app(ty_Ratio, cbd)) → new_compare8(zxw49000, zxw50000, cbd)
new_esEs10(zxw4002, zxw3002, app(app(ty_@2, ec), ed)) → new_esEs4(zxw4002, zxw3002, ec, ed)
new_esEs11(zxw4001, zxw3001, app(ty_Ratio, ef)) → new_esEs14(zxw4001, zxw3001, ef)
new_compare29(zxw49000, zxw50000, ty_Ordering) → new_compare6(zxw49000, zxw50000)
new_esEs21(zxw4001, zxw3001, ty_Integer) → new_esEs17(zxw4001, zxw3001)
new_esEs27(zxw49000, zxw50000, ty_Double) → new_esEs18(zxw49000, zxw50000)
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs27(zxw49000, zxw50000, app(ty_Ratio, dac)) → new_esEs14(zxw49000, zxw50000, dac)
new_ltEs4(LT, EQ) → True
new_esEs6(Right(zxw4000), Right(zxw3000), ce, ty_Char) → new_esEs15(zxw4000, zxw3000)
new_esEs10(zxw4002, zxw3002, ty_Double) → new_esEs18(zxw4002, zxw3002)
new_compare31(@0, @0) → EQ
new_esEs31(zxw400, zxw300, ty_Float) → new_esEs19(zxw400, zxw300)
new_esEs12(zxw4000, zxw3000, app(app(ty_Either, gf), gg)) → new_esEs6(zxw4000, zxw3000, gf, gg)
new_ltEs8(Just(zxw49000), Just(zxw50000), app(ty_Maybe, hg)) → new_ltEs8(zxw49000, zxw50000, hg)
new_lt19(zxw49001, zxw50001, ty_Bool) → new_lt13(zxw49001, zxw50001)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbh, app(app(ty_Either, dce), dcf)) → new_ltEs7(zxw49000, zxw50000, dce, dcf)
new_esEs28(zxw4000, zxw3000, app(app(ty_@2, ddh), dea)) → new_esEs4(zxw4000, zxw3000, ddh, dea)
new_compare9(Integer(zxw49000), Integer(zxw50000)) → new_primCmpInt(zxw49000, zxw50000)
new_asAs(False, zxw187) → False
new_primMulInt(Neg(zxw40010), Pos(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Double) → new_esEs18(zxw4000, zxw3000)
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Ordering) → new_ltEs4(zxw49000, zxw50000)
new_esEs21(zxw4001, zxw3001, ty_Ordering) → new_esEs8(zxw4001, zxw3001)
new_primCmpNat2(zxw4900, Zero) → GT
new_ltEs20(zxw49002, zxw50002, ty_Double) → new_ltEs11(zxw49002, zxw50002)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Char, cf) → new_esEs15(zxw4000, zxw3000)
new_esEs26(zxw49001, zxw50001, app(ty_Maybe, cgb)) → new_esEs7(zxw49001, zxw50001, cgb)
new_esEs10(zxw4002, zxw3002, ty_@0) → new_esEs20(zxw4002, zxw3002)
new_lt19(zxw49001, zxw50001, ty_Double) → new_lt8(zxw49001, zxw50001)
new_esEs28(zxw4000, zxw3000, ty_Double) → new_esEs18(zxw4000, zxw3000)
new_compare110(zxw49000, zxw50000, True, bgd, bge, bgf) → LT
new_esEs24(zxw4001, zxw3001, ty_Integer) → new_esEs17(zxw4001, zxw3001)
new_lt19(zxw49001, zxw50001, app(ty_Maybe, cgb)) → new_lt12(zxw49001, zxw50001, cgb)
new_ltEs18(zxw49001, zxw50001, app(ty_Ratio, bgb)) → new_ltEs17(zxw49001, zxw50001, bgb)
new_ltEs18(zxw49001, zxw50001, ty_Char) → new_ltEs12(zxw49001, zxw50001)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Float, cf) → new_esEs19(zxw4000, zxw3000)
new_esEs21(zxw4001, zxw3001, ty_Int) → new_esEs13(zxw4001, zxw3001)
new_lt20(zxw49000, zxw50000, app(ty_Ratio, dac)) → new_lt18(zxw49000, zxw50000, dac)
new_ltEs19(zxw4900, zxw5000, ty_@0) → new_ltEs14(zxw4900, zxw5000)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbh, ty_Double) → new_ltEs11(zxw49000, zxw50000)
new_lt17(zxw49000, zxw50000, be, bf) → new_esEs8(new_compare32(zxw49000, zxw50000, be, bf), LT)
new_esEs9(False, False) → True
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Int) → new_ltEs10(zxw49000, zxw50000)
new_esEs30(zxw20, zxw15, ty_Int) → new_esEs13(zxw20, zxw15)
new_ltEs19(zxw4900, zxw5000, ty_Bool) → new_ltEs5(zxw4900, zxw5000)
new_esEs31(zxw400, zxw300, app(app(ty_Either, ce), cf)) → new_esEs6(zxw400, zxw300, ce, cf)
new_compare29(zxw49000, zxw50000, ty_Integer) → new_compare9(zxw49000, zxw50000)
new_lt20(zxw49000, zxw50000, app(app(app(ty_@3, chf), chg), chh)) → new_lt16(zxw49000, zxw50000, chf, chg, chh)
new_esEs4(@2(zxw4000, zxw4001), @2(zxw3000, zxw3001), cg, da) → new_asAs(new_esEs22(zxw4000, zxw3000, cg), new_esEs21(zxw4001, zxw3001, da))
new_ltEs20(zxw49002, zxw50002, app(app(ty_Either, cfe), cff)) → new_ltEs7(zxw49002, zxw50002, cfe, cff)
new_esEs27(zxw49000, zxw50000, app(app(ty_@2, chb), chc)) → new_esEs4(zxw49000, zxw50000, chb, chc)
new_lt20(zxw49000, zxw50000, ty_Integer) → new_lt5(zxw49000, zxw50000)
new_compare35(zxw400, h) → new_compare26(Just(zxw400), Nothing, False, h)
new_ltEs18(zxw49001, zxw50001, app(ty_Maybe, bfc)) → new_ltEs8(zxw49001, zxw50001, bfc)
new_compare8(:%(zxw49000, zxw49001), :%(zxw50000, zxw50001), ty_Integer) → new_compare9(new_sr0(zxw49000, zxw50001), new_sr0(zxw50000, zxw49001))
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Float, cca) → new_ltEs6(zxw49000, zxw50000)
new_ltEs4(LT, LT) → True
new_esEs16([], [], ca) → True
new_ltEs20(zxw49002, zxw50002, ty_Int) → new_ltEs10(zxw49002, zxw50002)
new_ltEs8(Nothing, Nothing, hd) → True
new_lt10(zxw49000, zxw50000, ty_Char) → new_lt6(zxw49000, zxw50000)
new_lt10(zxw49000, zxw50000, ty_Bool) → new_lt13(zxw49000, zxw50000)
new_esEs22(zxw4000, zxw3000, app(app(ty_Either, bch), bda)) → new_esEs6(zxw4000, zxw3000, bch, bda)
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_lt5(zxw49000, zxw50000) → new_esEs8(new_compare9(zxw49000, zxw50000), LT)
new_esEs26(zxw49001, zxw50001, ty_Float) → new_esEs19(zxw49001, zxw50001)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Int, cf) → new_esEs13(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_esEs10(zxw4002, zxw3002, ty_Int) → new_esEs13(zxw4002, zxw3002)
new_lt10(zxw49000, zxw50000, app(ty_[], db)) → new_lt9(zxw49000, zxw50000, db)
new_esEs12(zxw4000, zxw3000, app(ty_Ratio, ga)) → new_esEs14(zxw4000, zxw3000, ga)
new_ltEs15(@3(zxw49000, zxw49001, zxw49002), @3(zxw50000, zxw50001, zxw50002), cbe, cbf, cbg) → new_pePe(new_lt20(zxw49000, zxw50000, cbe), new_asAs(new_esEs27(zxw49000, zxw50000, cbe), new_pePe(new_lt19(zxw49001, zxw50001, cbf), new_asAs(new_esEs26(zxw49001, zxw50001, cbf), new_ltEs20(zxw49002, zxw50002, cbg)))))
new_ltEs10(zxw4900, zxw5000) → new_fsEs(new_compare7(zxw4900, zxw5000))
new_esEs30(zxw20, zxw15, ty_Ordering) → new_esEs8(zxw20, zxw15)
new_esEs10(zxw4002, zxw3002, app(ty_Ratio, dd)) → new_esEs14(zxw4002, zxw3002, dd)
new_ltEs12(zxw4900, zxw5000) → new_fsEs(new_compare12(zxw4900, zxw5000))
new_esEs10(zxw4002, zxw3002, ty_Ordering) → new_esEs8(zxw4002, zxw3002)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbh, ty_Float) → new_ltEs6(zxw49000, zxw50000)
new_esEs23(zxw49000, zxw50000, app(ty_[], db)) → new_esEs16(zxw49000, zxw50000, db)
new_esEs11(zxw4001, zxw3001, ty_Integer) → new_esEs17(zxw4001, zxw3001)
new_esEs26(zxw49001, zxw50001, app(app(ty_Either, cgg), cgh)) → new_esEs6(zxw49001, zxw50001, cgg, cgh)
new_compare16(Double(zxw49000, zxw49001), Double(zxw50000, zxw50001)) → new_compare7(new_sr(zxw49000, zxw50000), new_sr(zxw49001, zxw50001))
new_compare0([], :(zxw50000, zxw50001), cab) → LT
new_primPlusNat1(Zero, Zero) → Zero
new_esEs12(zxw4000, zxw3000, ty_Ordering) → new_esEs8(zxw4000, zxw3000)
new_lt10(zxw49000, zxw50000, ty_@0) → new_lt15(zxw49000, zxw50000)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Char) → new_ltEs12(zxw49000, zxw50000)
new_asAs(True, zxw187) → zxw187
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_esEs30(zxw20, zxw15, ty_Integer) → new_esEs17(zxw20, zxw15)
new_esEs26(zxw49001, zxw50001, app(app(app(ty_@3, cgd), cge), cgf)) → new_esEs5(zxw49001, zxw50001, cgd, cge, cgf)
new_esEs31(zxw400, zxw300, app(ty_Maybe, bg)) → new_esEs7(zxw400, zxw300, bg)
new_esEs10(zxw4002, zxw3002, app(app(ty_Either, ea), eb)) → new_esEs6(zxw4002, zxw3002, ea, eb)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Integer) → new_ltEs16(zxw49000, zxw50000)
new_compare30(zxw49000, zxw50000, hb, hc) → new_compare27(zxw49000, zxw50000, new_esEs4(zxw49000, zxw50000, hb, hc), hb, hc)
new_compare29(zxw49000, zxw50000, ty_Bool) → new_compare18(zxw49000, zxw50000)
new_fsEs(zxw202) → new_not(new_esEs8(zxw202, GT))
new_esEs23(zxw49000, zxw50000, app(app(app(ty_@3, bgd), bge), bgf)) → new_esEs5(zxw49000, zxw50000, bgd, bge, bgf)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Float) → new_esEs19(zxw4000, zxw3000)
new_compare10(zxw49000, zxw50000, True) → LT
new_esEs30(zxw20, zxw15, app(app(app(ty_@3, bdh), bea), beb)) → new_esEs5(zxw20, zxw15, bdh, bea, beb)
new_compare29(zxw49000, zxw50000, app(ty_Maybe, cae)) → new_compare19(zxw49000, zxw50000, cae)
new_ltEs4(GT, GT) → True
new_esEs26(zxw49001, zxw50001, ty_@0) → new_esEs20(zxw49001, zxw50001)
new_compare110(zxw49000, zxw50000, False, bgd, bge, bgf) → GT
new_ltEs7(Left(zxw49000), Left(zxw50000), app(ty_Ratio, dbe), cca) → new_ltEs17(zxw49000, zxw50000, dbe)
new_compare10(zxw49000, zxw50000, False) → GT
new_ltEs8(Just(zxw49000), Just(zxw50000), app(app(app(ty_@3, baa), bab), bac)) → new_ltEs15(zxw49000, zxw50000, baa, bab, bac)
new_esEs21(zxw4001, zxw3001, app(ty_[], bbb)) → new_esEs16(zxw4001, zxw3001, bbb)
new_compare18(zxw49000, zxw50000) → new_compare24(zxw49000, zxw50000, new_esEs9(zxw49000, zxw50000))
new_esEs6(Left(zxw4000), Left(zxw3000), app(ty_[], ccd), cf) → new_esEs16(zxw4000, zxw3000, ccd)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs6(Right(zxw4000), Right(zxw3000), ce, ty_Ordering) → new_esEs8(zxw4000, zxw3000)
new_esEs6(Right(zxw4000), Right(zxw3000), ce, app(app(app(ty_@3, cdg), cdh), cea)) → new_esEs5(zxw4000, zxw3000, cdg, cdh, cea)
new_primCompAux0(zxw218, EQ) → zxw218
new_lt20(zxw49000, zxw50000, app(ty_Maybe, chd)) → new_lt12(zxw49000, zxw50000, chd)
new_esEs12(zxw4000, zxw3000, app(app(ty_@2, gh), ha)) → new_esEs4(zxw4000, zxw3000, gh, ha)
new_ltEs19(zxw4900, zxw5000, app(ty_[], cab)) → new_ltEs13(zxw4900, zxw5000, cab)
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_esEs22(zxw4000, zxw3000, app(ty_Maybe, bcb)) → new_esEs7(zxw4000, zxw3000, bcb)
new_esEs30(zxw20, zxw15, ty_Char) → new_esEs15(zxw20, zxw15)
new_esEs30(zxw20, zxw15, app(app(ty_@2, bee), bef)) → new_esEs4(zxw20, zxw15, bee, bef)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbh, ty_@0) → new_ltEs14(zxw49000, zxw50000)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_compare8(:%(zxw49000, zxw49001), :%(zxw50000, zxw50001), ty_Int) → new_compare7(new_sr(zxw49000, zxw50001), new_sr(zxw50000, zxw49001))
new_ltEs17(zxw4900, zxw5000, bag) → new_fsEs(new_compare8(zxw4900, zxw5000, bag))
new_not(True) → False

The set Q consists of the following terms:

new_esEs17(Integer(x0), Integer(x1))
new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_ltEs7(Right(x0), Right(x1), x2, ty_Bool)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Integer)
new_lt10(x0, x1, ty_Double)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_compare18(x0, x1)
new_compare29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare29(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Double)
new_pePe(False, x0)
new_lt10(x0, x1, app(app(ty_Either, x2), x3))
new_compare29(x0, x1, app(app(ty_Either, x2), x3))
new_lt17(x0, x1, x2, x3)
new_esEs31(x0, x1, ty_Double)
new_esEs10(x0, x1, app(ty_[], x2))
new_ltEs8(Nothing, Nothing, x0)
new_compare210(x0, x1, True, x2, x3, x4)
new_compare7(x0, x1)
new_primMulNat0(Succ(x0), Zero)
new_esEs31(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(ty_[], x2))
new_esEs7(Just(x0), Just(x1), ty_Double)
new_ltEs8(Just(x0), Just(x1), ty_Integer)
new_esEs10(x0, x1, ty_Int)
new_ltEs10(x0, x1)
new_esEs28(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Ordering)
new_esEs31(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs12(x0, x1, ty_Char)
new_compare25(x0, x1, True, x2, x3)
new_primMulNat0(Succ(x0), Succ(x1))
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare8(:%(x0, x1), :%(x2, x3), ty_Int)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_ltEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs16(x0, x1)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_lt10(x0, x1, app(ty_Ratio, x2))
new_ltEs8(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs6(Right(x0), Right(x1), x2, ty_Char)
new_compare13(x0, x1, True)
new_ltEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs10(x0, x1, ty_Ordering)
new_esEs31(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, ty_Float)
new_esEs11(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_Int)
new_esEs31(x0, x1, ty_Int)
new_compare11(x0, x1, True, x2)
new_ltEs19(x0, x1, ty_Ordering)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_lt10(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(GT, GT)
new_compare11(x0, x1, False, x2)
new_esEs8(LT, LT)
new_compare29(x0, x1, ty_Double)
new_esEs18(Double(x0, x1), Double(x2, x3))
new_primCmpNat0(Zero, x0)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_ltEs8(Just(x0), Just(x1), ty_Bool)
new_ltEs8(Just(x0), Just(x1), app(ty_[], x2))
new_esEs11(x0, x1, ty_@0)
new_primCmpNat1(Zero, Succ(x0))
new_esEs31(x0, x1, app(ty_Maybe, x2))
new_esEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, ty_Int)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_sr(x0, x1)
new_ltEs5(False, False)
new_compare17(x0, x1, False, x2, x3)
new_ltEs8(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare6(x0, x1)
new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt10(x0, x1, ty_Ordering)
new_compare28(x0, x1, x2, x3, x4)
new_compare29(x0, x1, ty_Int)
new_esEs30(x0, x1, ty_Bool)
new_compare19(x0, x1, x2)
new_esEs26(x0, x1, ty_Integer)
new_primEqNat0(Zero, Succ(x0))
new_primCmpNat1(Zero, Zero)
new_compare16(Double(x0, x1), Double(x2, x3))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_lt7(x0, x1)
new_esEs28(x0, x1, ty_@0)
new_ltEs20(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_Integer)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Double)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_Char)
new_lt12(x0, x1, x2)
new_ltEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_compare15(x0, x1, True, x2, x3)
new_esEs24(x0, x1, ty_Int)
new_compare26(Just(x0), Just(x1), False, x2)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_primEqNat0(Zero, Zero)
new_compare32(x0, x1, x2, x3)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs30(x0, x1, app(ty_[], x2))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs7(Left(x0), Left(x1), ty_Char, x2)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_ltEs8(Just(x0), Just(x1), ty_Double)
new_ltEs8(Just(x0), Just(x1), ty_Ordering)
new_ltEs19(x0, x1, ty_@0)
new_compare24(x0, x1, False)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs9(True, True)
new_compare27(x0, x1, True, x2, x3)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_lt4(x0, x1)
new_ltEs8(Nothing, Just(x0), x1)
new_primMulNat0(Zero, Zero)
new_esEs23(x0, x1, ty_Char)
new_esEs30(x0, x1, ty_Ordering)
new_compare29(x0, x1, app(app(ty_@2, x2), x3))
new_esEs10(x0, x1, ty_@0)
new_lt10(x0, x1, ty_Char)
new_ltEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs30(x0, x1, ty_Int)
new_compare26(Just(x0), Nothing, False, x1)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_Integer)
new_fsEs(x0)
new_ltEs4(GT, GT)
new_lt8(x0, x1)
new_esEs6(Right(x0), Right(x1), x2, ty_Integer)
new_esEs30(x0, x1, ty_@0)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(x0, x1, ty_Float)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs28(x0, x1, ty_Double)
new_ltEs8(Just(x0), Nothing, x1)
new_esEs31(x0, x1, app(app(ty_Either, x2), x3))
new_esEs11(x0, x1, app(ty_Ratio, x2))
new_ltEs8(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt10(x0, x1, ty_Int)
new_esEs10(x0, x1, ty_Bool)
new_ltEs18(x0, x1, app(ty_[], x2))
new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs10(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs23(x0, x1, ty_Ordering)
new_esEs7(Just(x0), Just(x1), ty_Int)
new_esEs10(x0, x1, ty_Char)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_compare33(x0)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt10(x0, x1, app(ty_Maybe, x2))
new_pePe(True, x0)
new_ltEs15(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_primPlusNat0(Zero, x0)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_compare26(Nothing, Nothing, False, x0)
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Int)
new_lt6(x0, x1)
new_esEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs26(x0, x1, ty_Bool)
new_compare24(x0, x1, True)
new_ltEs18(x0, x1, ty_Integer)
new_esEs10(x0, x1, app(ty_Maybe, x2))
new_compare15(x0, x1, False, x2, x3)
new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_compare14(Float(x0, x1), Float(x2, x3))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs7(Right(x0), Left(x1), x2, x3)
new_ltEs7(Left(x0), Right(x1), x2, x3)
new_lt10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_compare110(x0, x1, False, x2, x3, x4)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_ltEs14(x0, x1)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_primPlusNat1(Zero, Zero)
new_esEs11(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Right(x0), Left(x1), x2, x3)
new_esEs6(Left(x0), Right(x1), x2, x3)
new_primCompAux0(x0, GT)
new_ltEs7(Right(x0), Right(x1), x2, ty_Char)
new_esEs6(Left(x0), Left(x1), ty_Int, x2)
new_compare23(x0, x1, True)
new_esEs31(x0, x1, ty_Float)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_compare29(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, app(ty_[], x2))
new_lt15(x0, x1)
new_esEs6(Left(x0), Left(x1), ty_Integer, x2)
new_esEs14(:%(x0, x1), :%(x2, x3), x4)
new_compare13(x0, x1, False)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_lt20(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_@0)
new_esEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_primPlusNat0(Succ(x0), x1)
new_ltEs4(EQ, EQ)
new_esEs31(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, ty_Char)
new_esEs6(Right(x0), Right(x1), x2, ty_Int)
new_ltEs11(x0, x1)
new_compare29(x0, x1, app(ty_Ratio, x2))
new_esEs12(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Integer)
new_ltEs20(x0, x1, ty_Char)
new_esEs7(Just(x0), Just(x1), ty_Char)
new_esEs12(x0, x1, ty_Float)
new_compare31(@0, @0)
new_ltEs7(Left(x0), Left(x1), ty_Int, x2)
new_esEs7(Just(x0), Just(x1), ty_Float)
new_compare36(x0, x1, x2)
new_primCmpNat2(x0, Zero)
new_ltEs4(LT, EQ)
new_ltEs4(EQ, LT)
new_esEs12(x0, x1, ty_Int)
new_ltEs13(x0, x1, x2)
new_lt19(x0, x1, ty_Double)
new_esEs12(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, app(ty_Ratio, x2))
new_ltEs7(Left(x0), Left(x1), ty_@0, x2)
new_esEs21(x0, x1, app(ty_[], x2))
new_primMulInt(Pos(x0), Pos(x1))
new_lt20(x0, x1, ty_Bool)
new_esEs30(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_@0)
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_asAs(True, x0)
new_primEqNat0(Succ(x0), Zero)
new_ltEs8(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Right(x0), Right(x1), x2, ty_Bool)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_ltEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs13(x0, x1)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs21(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Integer)
new_lt20(x0, x1, ty_@0)
new_esEs12(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, ty_Bool)
new_lt20(x0, x1, ty_Char)
new_esEs6(Left(x0), Left(x1), ty_Float, x2)
new_esEs12(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_Ordering)
new_compare34(x0, x1)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Ordering)
new_esEs6(Right(x0), Right(x1), x2, ty_Float)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_compare26(Nothing, Just(x0), False, x1)
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_ltEs20(x0, x1, ty_Bool)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs12(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs27(x0, x1, ty_Int)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Double)
new_esEs25(x0, x1, ty_Integer)
new_ltEs7(Right(x0), Right(x1), x2, ty_Integer)
new_primMulInt(Neg(x0), Neg(x1))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs31(x0, x1, ty_Bool)
new_lt10(x0, x1, ty_Bool)
new_primPlusNat1(Succ(x0), Zero)
new_esEs22(x0, x1, ty_Float)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs6(Left(x0), Left(x1), ty_@0, x2)
new_ltEs4(LT, LT)
new_lt11(x0, x1, x2, x3)
new_esEs10(x0, x1, ty_Integer)
new_esEs31(x0, x1, ty_Ordering)
new_esEs12(x0, x1, app(app(ty_@2, x2), x3))
new_esEs16([], [], x0)
new_ltEs19(x0, x1, ty_Integer)
new_compare23(x0, x1, False)
new_lt16(x0, x1, x2, x3, x4)
new_compare29(x0, x1, app(ty_[], x2))
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs11(x0, x1, ty_Bool)
new_esEs11(x0, x1, app(app(ty_Either, x2), x3))
new_esEs16([], :(x0, x1), x2)
new_esEs23(x0, x1, ty_Double)
new_esEs21(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_Ordering)
new_ltEs9(@2(x0, x1), @2(x2, x3), x4, x5)
new_primPlusNat1(Zero, Succ(x0))
new_ltEs12(x0, x1)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_compare10(x0, x1, False)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_primCmpNat0(Succ(x0), x1)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, ty_@0)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs8(GT, EQ)
new_esEs8(EQ, GT)
new_esEs22(x0, x1, ty_Bool)
new_lt19(x0, x1, ty_Float)
new_ltEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_lt19(x0, x1, ty_Integer)
new_ltEs8(Just(x0), Just(x1), ty_Char)
new_esEs7(Nothing, Just(x0), x1)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt18(x0, x1, x2)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs16(:(x0, x1), :(x2, x3), x4)
new_ltEs8(Just(x0), Just(x1), ty_Float)
new_ltEs7(Left(x0), Left(x1), ty_Float, x2)
new_lt5(x0, x1)
new_compare29(x0, x1, ty_Ordering)
new_ltEs18(x0, x1, ty_Bool)
new_esEs11(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_@0)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, ty_Int)
new_esEs11(x0, x1, ty_Char)
new_ltEs7(Left(x0), Left(x1), ty_Double, x2)
new_esEs27(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Float)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_lt19(x0, x1, ty_Ordering)
new_compare29(x0, x1, ty_Integer)
new_compare25(x0, x1, False, x2, x3)
new_esEs26(x0, x1, app(ty_[], x2))
new_ltEs18(x0, x1, ty_Float)
new_esEs9(False, False)
new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs21(x0, x1, ty_Double)
new_esEs12(x0, x1, ty_Ordering)
new_primCompAux1(x0, x1, x2, x3)
new_ltEs17(x0, x1, x2)
new_compare0([], :(x0, x1), x2)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpNat1(Succ(x0), Succ(x1))
new_esEs26(x0, x1, ty_@0)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs6(x0, x1)
new_lt10(x0, x1, ty_Float)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs22(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Float)
new_primCompAux0(x0, EQ)
new_esEs10(x0, x1, app(app(ty_Either, x2), x3))
new_compare210(x0, x1, False, x2, x3, x4)
new_esEs21(x0, x1, ty_Integer)
new_primCmpNat1(Succ(x0), Zero)
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_esEs6(Left(x0), Left(x1), ty_Bool, x2)
new_esEs7(Nothing, Nothing, x0)
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, ty_@0)
new_esEs12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, ty_Double)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_lt13(x0, x1)
new_esEs23(x0, x1, ty_Bool)
new_ltEs5(True, True)
new_ltEs7(Right(x0), Right(x1), x2, ty_Int)
new_lt19(x0, x1, ty_Int)
new_compare35(x0, x1)
new_lt19(x0, x1, ty_Char)
new_ltEs4(EQ, GT)
new_ltEs4(GT, EQ)
new_esEs31(x0, x1, ty_Integer)
new_not(True)
new_esEs11(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Float)
new_ltEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs11(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, ty_Char)
new_lt19(x0, x1, ty_@0)
new_compare26(x0, x1, True, x2)
new_esEs21(x0, x1, ty_Ordering)
new_ltEs8(Just(x0), Just(x1), app(ty_Maybe, x2))
new_compare0([], [], x0)
new_esEs26(x0, x1, ty_Char)
new_esEs7(Just(x0), Nothing, x1)
new_esEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs18(x0, x1, ty_Int)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Ordering)
new_not(False)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_lt14(x0, x1)
new_compare12(Char(x0), Char(x1))
new_esEs15(Char(x0), Char(x1))
new_esEs10(x0, x1, app(ty_Ratio, x2))
new_compare10(x0, x1, True)
new_lt10(x0, x1, ty_@0)
new_asAs(False, x0)
new_esEs22(x0, x1, ty_Ordering)
new_ltEs18(x0, x1, ty_Char)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_compare29(x0, x1, ty_Float)
new_compare17(x0, x1, True, x2, x3)
new_lt19(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_Char)
new_esEs31(x0, x1, ty_Char)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_ltEs8(Just(x0), Just(x1), ty_@0)
new_esEs20(@0, @0)
new_esEs6(Right(x0), Right(x1), x2, ty_Double)
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_ltEs7(Right(x0), Right(x1), x2, ty_Double)
new_esEs22(x0, x1, app(ty_[], x2))
new_ltEs7(Left(x0), Left(x1), ty_Integer, x2)
new_esEs23(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Int)
new_compare0(:(x0, x1), [], x2)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_ltEs19(x0, x1, ty_Double)
new_esEs9(True, False)
new_esEs9(False, True)
new_esEs22(x0, x1, ty_Char)
new_compare29(x0, x1, ty_Bool)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs7(Right(x0), Right(x1), x2, ty_Float)
new_esEs30(x0, x1, ty_Double)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, ty_Integer)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs11(x0, x1, ty_Double)
new_ltEs20(x0, x1, ty_Float)
new_primCompAux0(x0, LT)
new_primCmpNat2(x0, Succ(x1))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs11(x0, x1, app(ty_[], x2))
new_ltEs7(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs12(x0, x1, ty_Integer)
new_esEs6(Left(x0), Left(x1), ty_Double, x2)
new_esEs10(x0, x1, ty_Double)
new_esEs6(Right(x0), Right(x1), x2, ty_@0)
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_sr0(Integer(x0), Integer(x1))
new_lt10(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs6(Left(x0), Left(x1), ty_Char, x2)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Pos(Zero), Pos(Zero))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_compare30(x0, x1, x2, x3)
new_ltEs18(x0, x1, ty_Double)
new_esEs12(x0, x1, ty_Double)
new_compare110(x0, x1, True, x2, x3, x4)
new_esEs12(x0, x1, ty_Bool)
new_lt9(x0, x1, x2)
new_compare9(Integer(x0), Integer(x1))
new_lt10(x0, x1, ty_Integer)
new_esEs30(x0, x1, ty_Char)
new_esEs19(Float(x0, x1), Float(x2, x3))
new_primMulNat0(Zero, Succ(x0))
new_esEs7(Just(x0), Just(x1), ty_@0)
new_ltEs4(GT, LT)
new_ltEs4(LT, GT)
new_ltEs5(True, False)
new_ltEs5(False, True)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, app(ty_[], x2))
new_ltEs7(Right(x0), Right(x1), x2, ty_@0)
new_ltEs8(Just(x0), Just(x1), ty_Int)
new_compare29(x0, x1, ty_@0)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Float)
new_compare27(x0, x1, False, x2, x3)
new_esEs23(x0, x1, ty_Float)
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs30(x0, x1, ty_Float)
new_esEs16(:(x0, x1), [], x2)

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_splitLT(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba) → new_splitLT3(zxw330, zxw331, zxw332, zxw333, zxw334, Nothing, h, ba)
new_splitLT2(zxw300, zxw31, zxw32, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw34, True, h, ba) → new_splitLT3(zxw330, zxw331, zxw332, zxw333, zxw334, Nothing, h, ba)
new_splitLT3(Just(zxw300), zxw31, zxw32, zxw33, zxw34, Nothing, h, ba) → new_splitLT2(zxw300, zxw31, zxw32, zxw33, zxw34, new_esEs8(new_compare26(Nothing, Just(zxw300), False, h), LT), h, ba)
new_splitLT1(zxw31, zxw32, zxw33, zxw34, True, h, ba) → new_splitLT(zxw34, h, ba)
new_splitLT3(Nothing, zxw31, zxw32, zxw33, zxw34, Nothing, h, ba) → new_splitLT1(zxw31, zxw32, zxw33, zxw34, new_esEs8(new_compare33(h), GT), h, ba)
new_splitLT10(zxw300, zxw31, zxw32, zxw33, zxw34, True, h, ba) → new_splitLT(zxw34, h, ba)
new_splitLT2(zxw300, zxw31, zxw32, zxw33, zxw34, False, h, ba) → new_splitLT10(zxw300, zxw31, zxw32, zxw33, zxw34, new_esEs8(new_compare34(zxw300, h), GT), h, ba)

The TRS R consists of the following rules:

new_esEs6(Right(zxw4000), Right(zxw3000), ce, ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_esEs7(Just(zxw4000), Just(zxw3000), app(ty_Maybe, bgh)) → new_esEs7(zxw4000, zxw3000, bgh)
new_ltEs19(zxw4900, zxw5000, ty_Integer) → new_ltEs16(zxw4900, zxw5000)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_@0, cca) → new_ltEs14(zxw49000, zxw50000)
new_esEs27(zxw49000, zxw50000, app(ty_[], che)) → new_esEs16(zxw49000, zxw50000, che)
new_ltEs4(EQ, GT) → True
new_esEs22(zxw4000, zxw3000, ty_@0) → new_esEs20(zxw4000, zxw3000)
new_compare15(zxw49000, zxw50000, True, be, bf) → LT
new_ltEs9(@2(zxw49000, zxw49001), @2(zxw50000, zxw50001), beg, beh) → new_pePe(new_lt10(zxw49000, zxw50000, beg), new_asAs(new_esEs23(zxw49000, zxw50000, beg), new_ltEs18(zxw49001, zxw50001, beh)))
new_esEs6(Right(zxw4000), Right(zxw3000), ce, ty_Float) → new_esEs19(zxw4000, zxw3000)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Integer, cf) → new_esEs17(zxw4000, zxw3000)
new_esEs31(zxw400, zxw300, ty_Ordering) → new_esEs8(zxw400, zxw300)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_esEs23(zxw49000, zxw50000, app(app(ty_@2, hb), hc)) → new_esEs4(zxw49000, zxw50000, hb, hc)
new_compare29(zxw49000, zxw50000, ty_Char) → new_compare12(zxw49000, zxw50000)
new_esEs22(zxw4000, zxw3000, ty_Float) → new_esEs19(zxw4000, zxw3000)
new_esEs6(Right(zxw4000), Right(zxw3000), ce, ty_Int) → new_esEs13(zxw4000, zxw3000)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Bool) → new_ltEs5(zxw49000, zxw50000)
new_lt19(zxw49001, zxw50001, ty_Integer) → new_lt5(zxw49001, zxw50001)
new_compare33(h) → new_compare26(Nothing, Nothing, True, h)
new_esEs12(zxw4000, zxw3000, ty_Bool) → new_esEs9(zxw4000, zxw3000)
new_esEs27(zxw49000, zxw50000, app(ty_Maybe, chd)) → new_esEs7(zxw49000, zxw50000, chd)
new_esEs11(zxw4001, zxw3001, app(ty_[], eg)) → new_esEs16(zxw4001, zxw3001, eg)
new_esEs12(zxw4000, zxw3000, ty_Char) → new_esEs15(zxw4000, zxw3000)
new_compare12(Char(zxw49000), Char(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_ltEs19(zxw4900, zxw5000, ty_Double) → new_ltEs11(zxw4900, zxw5000)
new_esEs31(zxw400, zxw300, app(app(app(ty_@3, cb), cc), cd)) → new_esEs5(zxw400, zxw300, cb, cc, cd)
new_compare29(zxw49000, zxw50000, ty_Double) → new_compare16(zxw49000, zxw50000)
new_ltEs20(zxw49002, zxw50002, ty_Bool) → new_ltEs5(zxw49002, zxw50002)
new_esEs23(zxw49000, zxw50000, ty_Float) → new_esEs19(zxw49000, zxw50000)
new_lt19(zxw49001, zxw50001, ty_Ordering) → new_lt14(zxw49001, zxw50001)
new_lt19(zxw49001, zxw50001, ty_Int) → new_lt4(zxw49001, zxw50001)
new_esEs7(Just(zxw4000), Just(zxw3000), app(app(ty_Either, bhf), bhg)) → new_esEs6(zxw4000, zxw3000, bhf, bhg)
new_primMulNat0(Zero, Zero) → Zero
new_ltEs7(Left(zxw49000), Right(zxw50000), cbh, cca) → True
new_compare26(Just(zxw4900), Nothing, False, bdd) → GT
new_esEs26(zxw49001, zxw50001, app(ty_[], cgc)) → new_esEs16(zxw49001, zxw50001, cgc)
new_esEs27(zxw49000, zxw50000, ty_Bool) → new_esEs9(zxw49000, zxw50000)
new_ltEs18(zxw49001, zxw50001, ty_Integer) → new_ltEs16(zxw49001, zxw50001)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_ltEs18(zxw49001, zxw50001, app(ty_[], bfd)) → new_ltEs13(zxw49001, zxw50001, bfd)
new_ltEs20(zxw49002, zxw50002, app(ty_Maybe, ceh)) → new_ltEs8(zxw49002, zxw50002, ceh)
new_esEs11(zxw4001, zxw3001, ty_Char) → new_esEs15(zxw4001, zxw3001)
new_esEs11(zxw4001, zxw3001, ty_Float) → new_esEs19(zxw4001, zxw3001)
new_lt8(zxw49000, zxw50000) → new_esEs8(new_compare16(zxw49000, zxw50000), LT)
new_esEs26(zxw49001, zxw50001, ty_Char) → new_esEs15(zxw49001, zxw50001)
new_lt20(zxw49000, zxw50000, app(app(ty_@2, chb), chc)) → new_lt11(zxw49000, zxw50000, chb, chc)
new_esEs23(zxw49000, zxw50000, ty_Char) → new_esEs15(zxw49000, zxw50000)
new_esEs23(zxw49000, zxw50000, ty_Bool) → new_esEs9(zxw49000, zxw50000)
new_esEs27(zxw49000, zxw50000, ty_Char) → new_esEs15(zxw49000, zxw50000)
new_compare26(Nothing, Just(zxw5000), False, bdd) → LT
new_lt10(zxw49000, zxw50000, ty_Float) → new_lt7(zxw49000, zxw50000)
new_esEs21(zxw4001, zxw3001, ty_Double) → new_esEs18(zxw4001, zxw3001)
new_ltEs19(zxw4900, zxw5000, ty_Int) → new_ltEs10(zxw4900, zxw5000)
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_lt9(zxw49000, zxw50000, db) → new_esEs8(new_compare0(zxw49000, zxw50000, db), LT)
new_compare210(zxw49000, zxw50000, False, bgd, bge, bgf) → new_compare110(zxw49000, zxw50000, new_ltEs15(zxw49000, zxw50000, bgd, bge, bgf), bgd, bge, bgf)
new_esEs22(zxw4000, zxw3000, app(ty_Ratio, bcc)) → new_esEs14(zxw4000, zxw3000, bcc)
new_esEs21(zxw4001, zxw3001, app(ty_Ratio, bba)) → new_esEs14(zxw4001, zxw3001, bba)
new_esEs30(zxw20, zxw15, ty_Bool) → new_esEs9(zxw20, zxw15)
new_esEs7(Just(zxw4000), Just(zxw3000), app(app(ty_@2, bhh), caa)) → new_esEs4(zxw4000, zxw3000, bhh, caa)
new_esEs25(zxw4000, zxw3000, ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Bool) → new_esEs9(zxw4000, zxw3000)
new_esEs30(zxw20, zxw15, ty_Float) → new_esEs19(zxw20, zxw15)
new_ltEs20(zxw49002, zxw50002, ty_Integer) → new_ltEs16(zxw49002, zxw50002)
new_esEs21(zxw4001, zxw3001, app(app(ty_Either, bbf), bbg)) → new_esEs6(zxw4001, zxw3001, bbf, bbg)
new_ltEs7(Left(zxw49000), Left(zxw50000), app(app(app(ty_@3, dah), dba), dbb), cca) → new_ltEs15(zxw49000, zxw50000, dah, dba, dbb)
new_ltEs14(zxw4900, zxw5000) → new_fsEs(new_compare31(zxw4900, zxw5000))
new_compare24(zxw49000, zxw50000, False) → new_compare13(zxw49000, zxw50000, new_ltEs5(zxw49000, zxw50000))
new_esEs7(Just(zxw4000), Just(zxw3000), app(ty_Ratio, bha)) → new_esEs14(zxw4000, zxw3000, bha)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbh, app(app(ty_@2, dbf), dbg)) → new_ltEs9(zxw49000, zxw50000, dbf, dbg)
new_lt4(zxw490, zxw500) → new_esEs8(new_compare7(zxw490, zxw500), LT)
new_esEs28(zxw4000, zxw3000, app(app(app(ty_@3, ddc), ddd), dde)) → new_esEs5(zxw4000, zxw3000, ddc, ddd, dde)
new_esEs28(zxw4000, zxw3000, ty_Bool) → new_esEs9(zxw4000, zxw3000)
new_compare19(zxw490, zxw500, bdd) → new_compare26(zxw490, zxw500, new_esEs7(zxw490, zxw500, bdd), bdd)
new_esEs17(Integer(zxw4000), Integer(zxw3000)) → new_primEqInt(zxw4000, zxw3000)
new_pePe(False, zxw213) → zxw213
new_lt12(zxw490, zxw500, bdd) → new_esEs8(new_compare19(zxw490, zxw500, bdd), LT)
new_esEs31(zxw400, zxw300, app(ty_[], ca)) → new_esEs16(zxw400, zxw300, ca)
new_esEs20(@0, @0) → True
new_esEs6(Left(zxw4000), Left(zxw3000), app(app(ty_@2, cdb), cdc), cf) → new_esEs4(zxw4000, zxw3000, cdb, cdc)
new_esEs31(zxw400, zxw300, ty_Bool) → new_esEs9(zxw400, zxw300)
new_esEs6(Right(zxw4000), Right(zxw3000), ce, app(ty_Ratio, cde)) → new_esEs14(zxw4000, zxw3000, cde)
new_compare23(zxw49000, zxw50000, True) → EQ
new_esEs11(zxw4001, zxw3001, ty_Int) → new_esEs13(zxw4001, zxw3001)
new_lt19(zxw49001, zxw50001, app(ty_[], cgc)) → new_lt9(zxw49001, zxw50001, cgc)
new_compare29(zxw49000, zxw50000, ty_@0) → new_compare31(zxw49000, zxw50000)
new_compare26(Nothing, Nothing, False, bdd) → LT
new_esEs10(zxw4002, zxw3002, app(ty_Maybe, dc)) → new_esEs7(zxw4002, zxw3002, dc)
new_ltEs16(zxw4900, zxw5000) → new_fsEs(new_compare9(zxw4900, zxw5000))
new_esEs22(zxw4000, zxw3000, app(app(ty_@2, bdb), bdc)) → new_esEs4(zxw4000, zxw3000, bdb, bdc)
new_esEs23(zxw49000, zxw50000, app(ty_Maybe, bgc)) → new_esEs7(zxw49000, zxw50000, bgc)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbh, app(ty_Ratio, dcg)) → new_ltEs17(zxw49000, zxw50000, dcg)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Char, cca) → new_ltEs12(zxw49000, zxw50000)
new_esEs28(zxw4000, zxw3000, ty_@0) → new_esEs20(zxw4000, zxw3000)
new_esEs10(zxw4002, zxw3002, app(app(app(ty_@3, df), dg), dh)) → new_esEs5(zxw4002, zxw3002, df, dg, dh)
new_ltEs20(zxw49002, zxw50002, app(ty_[], cfa)) → new_ltEs13(zxw49002, zxw50002, cfa)
new_esEs27(zxw49000, zxw50000, ty_Float) → new_esEs19(zxw49000, zxw50000)
new_ltEs20(zxw49002, zxw50002, app(app(app(ty_@3, cfb), cfc), cfd)) → new_ltEs15(zxw49002, zxw50002, cfb, cfc, cfd)
new_esEs22(zxw4000, zxw3000, ty_Ordering) → new_esEs8(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Bool) → new_esEs9(zxw4000, zxw3000)
new_compare6(zxw49000, zxw50000) → new_compare23(zxw49000, zxw50000, new_esEs8(zxw49000, zxw50000))
new_esEs12(zxw4000, zxw3000, app(ty_[], gb)) → new_esEs16(zxw4000, zxw3000, gb)
new_compare32(zxw49000, zxw50000, be, bf) → new_compare25(zxw49000, zxw50000, new_esEs6(zxw49000, zxw50000, be, bf), be, bf)
new_compare29(zxw49000, zxw50000, ty_Int) → new_compare7(zxw49000, zxw50000)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Bool, cf) → new_esEs9(zxw4000, zxw3000)
new_ltEs8(Nothing, Just(zxw50000), hd) → True
new_esEs31(zxw400, zxw300, app(app(ty_@2, cg), da)) → new_esEs4(zxw400, zxw300, cg, da)
new_ltEs7(Left(zxw49000), Left(zxw50000), app(app(ty_@2, dad), dae), cca) → new_ltEs9(zxw49000, zxw50000, dad, dae)
new_esEs6(Right(zxw4000), Left(zxw3000), ce, cf) → False
new_esEs6(Left(zxw4000), Right(zxw3000), ce, cf) → False
new_esEs8(LT, LT) → True
new_lt20(zxw49000, zxw50000, ty_@0) → new_lt15(zxw49000, zxw50000)
new_esEs10(zxw4002, zxw3002, ty_Integer) → new_esEs17(zxw4002, zxw3002)
new_esEs28(zxw4000, zxw3000, ty_Float) → new_esEs19(zxw4000, zxw3000)
new_compare29(zxw49000, zxw50000, app(app(app(ty_@3, cag), cah), cba)) → new_compare28(zxw49000, zxw50000, cag, cah, cba)
new_lt19(zxw49001, zxw50001, ty_@0) → new_lt15(zxw49001, zxw50001)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbh, ty_Bool) → new_ltEs5(zxw49000, zxw50000)
new_ltEs5(True, False) → False
new_lt19(zxw49001, zxw50001, app(app(ty_@2, cfh), cga)) → new_lt11(zxw49001, zxw50001, cfh, cga)
new_compare0([], [], cab) → EQ
new_pePe(True, zxw213) → True
new_primEqNat0(Zero, Zero) → True
new_compare34(zxw300, h) → new_compare26(Nothing, Just(zxw300), False, h)
new_esEs14(:%(zxw4000, zxw4001), :%(zxw3000, zxw3001), bh) → new_asAs(new_esEs25(zxw4000, zxw3000, bh), new_esEs24(zxw4001, zxw3001, bh))
new_lt10(zxw49000, zxw50000, ty_Double) → new_lt8(zxw49000, zxw50000)
new_ltEs20(zxw49002, zxw50002, ty_Ordering) → new_ltEs4(zxw49002, zxw50002)
new_compare27(zxw49000, zxw50000, False, hb, hc) → new_compare17(zxw49000, zxw50000, new_ltEs9(zxw49000, zxw50000, hb, hc), hb, hc)
new_compare11(zxw180, zxw181, True, bd) → LT
new_esEs23(zxw49000, zxw50000, app(app(ty_Either, be), bf)) → new_esEs6(zxw49000, zxw50000, be, bf)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_@0, cf) → new_esEs20(zxw4000, zxw3000)
new_esEs6(Right(zxw4000), Right(zxw3000), ce, ty_Bool) → new_esEs9(zxw4000, zxw3000)
new_esEs12(zxw4000, zxw3000, ty_Int) → new_esEs13(zxw4000, zxw3000)
new_lt20(zxw49000, zxw50000, app(ty_[], che)) → new_lt9(zxw49000, zxw50000, che)
new_esEs6(Right(zxw4000), Right(zxw3000), ce, app(app(ty_Either, ceb), cec)) → new_esEs6(zxw4000, zxw3000, ceb, cec)
new_compare26(Just(zxw4900), Just(zxw5000), False, bdd) → new_compare11(zxw4900, zxw5000, new_ltEs19(zxw4900, zxw5000, bdd), bdd)
new_ltEs5(True, True) → True
new_ltEs7(Left(zxw49000), Left(zxw50000), app(ty_Maybe, daf), cca) → new_ltEs8(zxw49000, zxw50000, daf)
new_compare36(zxw20, zxw15, bb) → new_compare26(Just(zxw20), Just(zxw15), new_esEs30(zxw20, zxw15, bb), bb)
new_ltEs20(zxw49002, zxw50002, app(app(ty_@2, cef), ceg)) → new_ltEs9(zxw49002, zxw50002, cef, ceg)
new_esEs15(Char(zxw4000), Char(zxw3000)) → new_primEqNat0(zxw4000, zxw3000)
new_sr(zxw4001, zxw3001) → new_primMulInt(zxw4001, zxw3001)
new_ltEs18(zxw49001, zxw50001, ty_Int) → new_ltEs10(zxw49001, zxw50001)
new_esEs25(zxw4000, zxw3000, ty_Int) → new_esEs13(zxw4000, zxw3000)
new_compare7(zxw49, zxw50) → new_primCmpInt(zxw49, zxw50)
new_primCmpNat1(Zero, Zero) → EQ
new_esEs7(Just(zxw4000), Just(zxw3000), app(ty_[], bhb)) → new_esEs16(zxw4000, zxw3000, bhb)
new_lt10(zxw49000, zxw50000, ty_Int) → new_lt4(zxw49000, zxw50000)
new_esEs28(zxw4000, zxw3000, app(app(ty_Either, ddf), ddg)) → new_esEs6(zxw4000, zxw3000, ddf, ddg)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbh, app(ty_Maybe, dbh)) → new_ltEs8(zxw49000, zxw50000, dbh)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbh, ty_Integer) → new_ltEs16(zxw49000, zxw50000)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbh, app(app(app(ty_@3, dcb), dcc), dcd)) → new_ltEs15(zxw49000, zxw50000, dcb, dcc, dcd)
new_esEs26(zxw49001, zxw50001, ty_Ordering) → new_esEs8(zxw49001, zxw50001)
new_esEs8(GT, GT) → True
new_esEs27(zxw49000, zxw50000, ty_@0) → new_esEs20(zxw49000, zxw50000)
new_esEs13(zxw400, zxw300) → new_primEqInt(zxw400, zxw300)
new_lt13(zxw49000, zxw50000) → new_esEs8(new_compare18(zxw49000, zxw50000), LT)
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_lt20(zxw49000, zxw50000, ty_Ordering) → new_lt14(zxw49000, zxw50000)
new_esEs11(zxw4001, zxw3001, app(app(ty_@2, ff), fg)) → new_esEs4(zxw4001, zxw3001, ff, fg)
new_esEs11(zxw4001, zxw3001, ty_Ordering) → new_esEs8(zxw4001, zxw3001)
new_lt10(zxw49000, zxw50000, app(app(ty_@2, hb), hc)) → new_lt11(zxw49000, zxw50000, hb, hc)
new_compare23(zxw49000, zxw50000, False) → new_compare10(zxw49000, zxw50000, new_ltEs4(zxw49000, zxw50000))
new_esEs8(LT, GT) → False
new_esEs8(GT, LT) → False
new_ltEs19(zxw4900, zxw5000, app(app(app(ty_@3, cbe), cbf), cbg)) → new_ltEs15(zxw4900, zxw5000, cbe, cbf, cbg)
new_lt20(zxw49000, zxw50000, app(app(ty_Either, daa), dab)) → new_lt17(zxw49000, zxw50000, daa, dab)
new_esEs26(zxw49001, zxw50001, ty_Bool) → new_esEs9(zxw49001, zxw50001)
new_ltEs11(zxw4900, zxw5000) → new_fsEs(new_compare16(zxw4900, zxw5000))
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_compare17(zxw49000, zxw50000, True, hb, hc) → LT
new_primEqInt(Neg(Succ(zxw40000)), Neg(Succ(zxw30000))) → new_primEqNat0(zxw40000, zxw30000)
new_ltEs5(False, False) → True
new_esEs23(zxw49000, zxw50000, ty_Ordering) → new_esEs8(zxw49000, zxw50000)
new_ltEs18(zxw49001, zxw50001, app(app(ty_Either, bfh), bga)) → new_ltEs7(zxw49001, zxw50001, bfh, bga)
new_esEs28(zxw4000, zxw3000, ty_Char) → new_esEs15(zxw4000, zxw3000)
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)
new_ltEs19(zxw4900, zxw5000, app(ty_Ratio, bag)) → new_ltEs17(zxw4900, zxw5000, bag)
new_esEs10(zxw4002, zxw3002, ty_Bool) → new_esEs9(zxw4002, zxw3002)
new_lt20(zxw49000, zxw50000, ty_Char) → new_lt6(zxw49000, zxw50000)
new_compare13(zxw49000, zxw50000, False) → GT
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Bool, cca) → new_ltEs5(zxw49000, zxw50000)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Int, cca) → new_ltEs10(zxw49000, zxw50000)
new_lt11(zxw49000, zxw50000, hb, hc) → new_esEs8(new_compare30(zxw49000, zxw50000, hb, hc), LT)
new_esEs21(zxw4001, zxw3001, ty_Char) → new_esEs15(zxw4001, zxw3001)
new_lt20(zxw49000, zxw50000, ty_Int) → new_lt4(zxw49000, zxw50000)
new_primCompAux1(zxw49000, zxw50000, zxw214, cab) → new_primCompAux0(zxw214, new_compare29(zxw49000, zxw50000, cab))
new_esEs7(Just(zxw4000), Just(zxw3000), ty_@0) → new_esEs20(zxw4000, zxw3000)
new_lt16(zxw49000, zxw50000, bgd, bge, bgf) → new_esEs8(new_compare28(zxw49000, zxw50000, bgd, bge, bgf), LT)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_ltEs7(Right(zxw49000), Left(zxw50000), cbh, cca) → False
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Ordering) → new_esEs8(zxw4000, zxw3000)
new_ltEs7(Left(zxw49000), Left(zxw50000), app(ty_[], dag), cca) → new_ltEs13(zxw49000, zxw50000, dag)
new_ltEs19(zxw4900, zxw5000, ty_Ordering) → new_ltEs4(zxw4900, zxw5000)
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_ltEs20(zxw49002, zxw50002, ty_Char) → new_ltEs12(zxw49002, zxw50002)
new_esEs11(zxw4001, zxw3001, app(app(app(ty_@3, eh), fa), fb)) → new_esEs5(zxw4001, zxw3001, eh, fa, fb)
new_ltEs20(zxw49002, zxw50002, app(ty_Ratio, cfg)) → new_ltEs17(zxw49002, zxw50002, cfg)
new_ltEs18(zxw49001, zxw50001, ty_@0) → new_ltEs14(zxw49001, zxw50001)
new_primEqInt(Neg(Succ(zxw40000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(zxw30000))) → False
new_ltEs19(zxw4900, zxw5000, ty_Char) → new_ltEs12(zxw4900, zxw5000)
new_esEs12(zxw4000, zxw3000, ty_Double) → new_esEs18(zxw4000, zxw3000)
new_primCompAux0(zxw218, GT) → GT
new_esEs8(EQ, EQ) → True
new_esEs6(Left(zxw4000), Left(zxw3000), app(ty_Ratio, ccc), cf) → new_esEs14(zxw4000, zxw3000, ccc)
new_ltEs8(Just(zxw49000), Just(zxw50000), app(app(ty_Either, bad), bae)) → new_ltEs7(zxw49000, zxw50000, bad, bae)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Integer, cca) → new_ltEs16(zxw49000, zxw50000)
new_esEs6(Right(zxw4000), Right(zxw3000), ce, app(ty_[], cdf)) → new_esEs16(zxw4000, zxw3000, cdf)
new_esEs23(zxw49000, zxw50000, ty_Integer) → new_esEs17(zxw49000, zxw50000)
new_esEs28(zxw4000, zxw3000, ty_Int) → new_esEs13(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, app(app(app(ty_@3, bce), bcf), bcg)) → new_esEs5(zxw4000, zxw3000, bce, bcf, bcg)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_ltEs18(zxw49001, zxw50001, ty_Ordering) → new_ltEs4(zxw49001, zxw50001)
new_ltEs4(EQ, LT) → False
new_esEs12(zxw4000, zxw3000, app(ty_Maybe, fh)) → new_esEs7(zxw4000, zxw3000, fh)
new_lt20(zxw49000, zxw50000, ty_Double) → new_lt8(zxw49000, zxw50000)
new_esEs10(zxw4002, zxw3002, ty_Float) → new_esEs19(zxw4002, zxw3002)
new_compare11(zxw180, zxw181, False, bd) → GT
new_esEs11(zxw4001, zxw3001, ty_Bool) → new_esEs9(zxw4001, zxw3001)
new_esEs26(zxw49001, zxw50001, ty_Integer) → new_esEs17(zxw49001, zxw50001)
new_lt10(zxw49000, zxw50000, ty_Ordering) → new_lt14(zxw49000, zxw50000)
new_ltEs18(zxw49001, zxw50001, ty_Bool) → new_ltEs5(zxw49001, zxw50001)
new_primEqInt(Pos(Succ(zxw40000)), Pos(Succ(zxw30000))) → new_primEqNat0(zxw40000, zxw30000)
new_esEs12(zxw4000, zxw3000, app(app(app(ty_@3, gc), gd), ge)) → new_esEs5(zxw4000, zxw3000, gc, gd, ge)
new_compare27(zxw49000, zxw50000, True, hb, hc) → EQ
new_esEs6(Left(zxw4000), Left(zxw3000), app(app(app(ty_@3, cce), ccf), ccg), cf) → new_esEs5(zxw4000, zxw3000, cce, ccf, ccg)
new_lt18(zxw49000, zxw50000, bgg) → new_esEs8(new_compare8(zxw49000, zxw50000, bgg), LT)
new_ltEs18(zxw49001, zxw50001, app(app(app(ty_@3, bfe), bff), bfg)) → new_ltEs15(zxw49001, zxw50001, bfe, bff, bfg)
new_esEs31(zxw400, zxw300, ty_Double) → new_esEs18(zxw400, zxw300)
new_lt10(zxw49000, zxw50000, app(ty_Maybe, bgc)) → new_lt12(zxw49000, zxw50000, bgc)
new_esEs26(zxw49001, zxw50001, ty_Int) → new_esEs13(zxw49001, zxw50001)
new_ltEs8(Just(zxw49000), Just(zxw50000), app(app(ty_@2, he), hf)) → new_ltEs9(zxw49000, zxw50000, he, hf)
new_primEqNat0(Succ(zxw40000), Succ(zxw30000)) → new_primEqNat0(zxw40000, zxw30000)
new_compare29(zxw49000, zxw50000, app(ty_[], caf)) → new_compare0(zxw49000, zxw50000, caf)
new_esEs27(zxw49000, zxw50000, ty_Ordering) → new_esEs8(zxw49000, zxw50000)
new_esEs27(zxw49000, zxw50000, ty_Integer) → new_esEs17(zxw49000, zxw50000)
new_esEs23(zxw49000, zxw50000, app(ty_Ratio, bgg)) → new_esEs14(zxw49000, zxw50000, bgg)
new_ltEs18(zxw49001, zxw50001, ty_Float) → new_ltEs6(zxw49001, zxw50001)
new_esEs22(zxw4000, zxw3000, ty_Int) → new_esEs13(zxw4000, zxw3000)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbh, app(ty_[], dca)) → new_ltEs13(zxw49000, zxw50000, dca)
new_ltEs4(GT, EQ) → False
new_lt7(zxw49000, zxw50000) → new_esEs8(new_compare14(zxw49000, zxw50000), LT)
new_lt10(zxw49000, zxw50000, app(app(app(ty_@3, bgd), bge), bgf)) → new_lt16(zxw49000, zxw50000, bgd, bge, bgf)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Int) → new_esEs13(zxw4000, zxw3000)
new_ltEs19(zxw4900, zxw5000, app(app(ty_Either, cbh), cca)) → new_ltEs7(zxw4900, zxw5000, cbh, cca)
new_ltEs8(Just(zxw49000), Nothing, hd) → False
new_esEs21(zxw4001, zxw3001, ty_Float) → new_esEs19(zxw4001, zxw3001)
new_esEs26(zxw49001, zxw50001, app(app(ty_@2, cfh), cga)) → new_esEs4(zxw49001, zxw50001, cfh, cga)
new_esEs27(zxw49000, zxw50000, app(app(app(ty_@3, chf), chg), chh)) → new_esEs5(zxw49000, zxw50000, chf, chg, chh)
new_ltEs13(zxw4900, zxw5000, cab) → new_fsEs(new_compare0(zxw4900, zxw5000, cab))
new_esEs22(zxw4000, zxw3000, ty_Char) → new_esEs15(zxw4000, zxw3000)
new_esEs30(zxw20, zxw15, app(ty_Ratio, bdf)) → new_esEs14(zxw20, zxw15, bdf)
new_ltEs18(zxw49001, zxw50001, ty_Double) → new_ltEs11(zxw49001, zxw50001)
new_esEs7(Nothing, Nothing, bg) → True
new_esEs28(zxw4000, zxw3000, ty_Ordering) → new_esEs8(zxw4000, zxw3000)
new_lt10(zxw49000, zxw50000, app(app(ty_Either, be), bf)) → new_lt17(zxw49000, zxw50000, be, bf)
new_esEs8(EQ, LT) → False
new_esEs8(LT, EQ) → False
new_esEs10(zxw4002, zxw3002, ty_Char) → new_esEs15(zxw4002, zxw3002)
new_primEqInt(Pos(Succ(zxw40000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(zxw30000))) → False
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Double, cca) → new_ltEs11(zxw49000, zxw50000)
new_ltEs4(EQ, EQ) → True
new_esEs6(Right(zxw4000), Right(zxw3000), ce, app(ty_Maybe, cdd)) → new_esEs7(zxw4000, zxw3000, cdd)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbh, ty_Ordering) → new_ltEs4(zxw49000, zxw50000)
new_esEs30(zxw20, zxw15, ty_@0) → new_esEs20(zxw20, zxw15)
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_ltEs20(zxw49002, zxw50002, ty_@0) → new_ltEs14(zxw49002, zxw50002)
new_esEs23(zxw49000, zxw50000, ty_@0) → new_esEs20(zxw49000, zxw50000)
new_compare210(zxw49000, zxw50000, True, bgd, bge, bgf) → EQ
new_esEs6(Right(zxw4000), Right(zxw3000), ce, ty_@0) → new_esEs20(zxw4000, zxw3000)
new_ltEs4(GT, LT) → False
new_sr0(Integer(zxw500000), Integer(zxw490010)) → Integer(new_primMulInt(zxw500000, zxw490010))
new_compare13(zxw49000, zxw50000, True) → LT
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_compare14(Float(zxw49000, zxw49001), Float(zxw50000, zxw50001)) → new_compare7(new_sr(zxw49000, zxw50000), new_sr(zxw49001, zxw50001))
new_primEqInt(Pos(Succ(zxw40000)), Neg(zxw3000)) → False
new_primEqInt(Neg(Succ(zxw40000)), Pos(zxw3000)) → False
new_esEs7(Just(zxw4000), Nothing, bg) → False
new_esEs7(Nothing, Just(zxw3000), bg) → False
new_esEs18(Double(zxw4000, zxw4001), Double(zxw3000, zxw3001)) → new_esEs13(new_sr(zxw4000, zxw3000), new_sr(zxw4001, zxw3001))
new_ltEs5(False, True) → True
new_esEs26(zxw49001, zxw50001, ty_Double) → new_esEs18(zxw49001, zxw50001)
new_compare28(zxw49000, zxw50000, bgd, bge, bgf) → new_compare210(zxw49000, zxw50000, new_esEs5(zxw49000, zxw50000, bgd, bge, bgf), bgd, bge, bgf)
new_esEs11(zxw4001, zxw3001, ty_Double) → new_esEs18(zxw4001, zxw3001)
new_ltEs6(zxw4900, zxw5000) → new_fsEs(new_compare14(zxw4900, zxw5000))
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Ordering, cca) → new_ltEs4(zxw49000, zxw50000)
new_esEs31(zxw400, zxw300, ty_Integer) → new_esEs17(zxw400, zxw300)
new_primEqInt(Pos(Zero), Neg(Succ(zxw30000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(zxw30000))) → False
new_ltEs19(zxw4900, zxw5000, app(app(ty_@2, beg), beh)) → new_ltEs9(zxw4900, zxw5000, beg, beh)
new_ltEs20(zxw49002, zxw50002, ty_Float) → new_ltEs6(zxw49002, zxw50002)
new_compare29(zxw49000, zxw50000, app(app(ty_@2, cac), cad)) → new_compare30(zxw49000, zxw50000, cac, cad)
new_compare24(zxw49000, zxw50000, True) → EQ
new_esEs27(zxw49000, zxw50000, ty_Int) → new_esEs13(zxw49000, zxw50000)
new_ltEs18(zxw49001, zxw50001, app(app(ty_@2, bfa), bfb)) → new_ltEs9(zxw49001, zxw50001, bfa, bfb)
new_esEs6(Right(zxw4000), Right(zxw3000), ce, ty_Double) → new_esEs18(zxw4000, zxw3000)
new_lt20(zxw49000, zxw50000, ty_Bool) → new_lt13(zxw49000, zxw50000)
new_primCmpNat0(Zero, zxw4900) → LT
new_ltEs7(Right(zxw49000), Right(zxw50000), cbh, ty_Char) → new_ltEs12(zxw49000, zxw50000)
new_esEs8(EQ, GT) → False
new_esEs8(GT, EQ) → False
new_esEs10(zxw4002, zxw3002, app(ty_[], de)) → new_esEs16(zxw4002, zxw3002, de)
new_lt15(zxw49000, zxw50000) → new_esEs8(new_compare31(zxw49000, zxw50000), LT)
new_esEs31(zxw400, zxw300, ty_Int) → new_esEs13(zxw400, zxw300)
new_compare17(zxw49000, zxw50000, False, hb, hc) → GT
new_compare29(zxw49000, zxw50000, ty_Float) → new_compare14(zxw49000, zxw50000)
new_esEs30(zxw20, zxw15, ty_Double) → new_esEs18(zxw20, zxw15)
new_esEs28(zxw4000, zxw3000, app(ty_Ratio, dda)) → new_esEs14(zxw4000, zxw3000, dda)
new_compare26(zxw490, zxw500, True, bdd) → EQ
new_primCompAux0(zxw218, LT) → LT
new_esEs11(zxw4001, zxw3001, ty_@0) → new_esEs20(zxw4001, zxw3001)
new_esEs30(zxw20, zxw15, app(app(ty_Either, bec), bed)) → new_esEs6(zxw20, zxw15, bec, bed)
new_esEs12(zxw4000, zxw3000, ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_not(False) → True
new_esEs6(Left(zxw4000), Left(zxw3000), app(app(ty_Either, cch), cda), cf) → new_esEs6(zxw4000, zxw3000, cch, cda)
new_esEs28(zxw4000, zxw3000, app(ty_[], ddb)) → new_esEs16(zxw4000, zxw3000, ddb)
new_esEs24(zxw4001, zxw3001, ty_Int) → new_esEs13(zxw4001, zxw3001)
new_esEs31(zxw400, zxw300, ty_Char) → new_esEs15(zxw400, zxw300)
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_esEs26(zxw49001, zxw50001, app(ty_Ratio, cha)) → new_esEs14(zxw49001, zxw50001, cha)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Double) → new_ltEs11(zxw49000, zxw50000)
new_esEs11(zxw4001, zxw3001, app(app(ty_Either, fc), fd)) → new_esEs6(zxw4001, zxw3001, fc, fd)
new_esEs21(zxw4001, zxw3001, ty_@0) → new_esEs20(zxw4001, zxw3001)
new_esEs31(zxw400, zxw300, app(ty_Ratio, bh)) → new_esEs14(zxw400, zxw300, bh)
new_lt19(zxw49001, zxw50001, ty_Float) → new_lt7(zxw49001, zxw50001)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbh, ty_Int) → new_ltEs10(zxw49000, zxw50000)
new_compare0(:(zxw49000, zxw49001), [], cab) → GT
new_esEs12(zxw4000, zxw3000, ty_Float) → new_esEs19(zxw4000, zxw3000)
new_ltEs8(Just(zxw49000), Just(zxw50000), app(ty_[], hh)) → new_ltEs13(zxw49000, zxw50000, hh)
new_lt14(zxw49000, zxw50000) → new_esEs8(new_compare6(zxw49000, zxw50000), LT)
new_ltEs19(zxw4900, zxw5000, ty_Float) → new_ltEs6(zxw4900, zxw5000)
new_esEs27(zxw49000, zxw50000, app(app(ty_Either, daa), dab)) → new_esEs6(zxw49000, zxw50000, daa, dab)
new_lt19(zxw49001, zxw50001, app(ty_Ratio, cha)) → new_lt18(zxw49001, zxw50001, cha)
new_esEs9(True, True) → True
new_lt19(zxw49001, zxw50001, app(app(app(ty_@3, cgd), cge), cgf)) → new_lt16(zxw49001, zxw50001, cgd, cge, cgf)
new_lt19(zxw49001, zxw50001, ty_Char) → new_lt6(zxw49001, zxw50001)
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Double, cf) → new_esEs18(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, app(ty_Maybe, dch)) → new_esEs7(zxw4000, zxw3000, dch)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_esEs21(zxw4001, zxw3001, app(app(app(ty_@3, bbc), bbd), bbe)) → new_esEs5(zxw4001, zxw3001, bbc, bbd, bbe)
new_esEs22(zxw4000, zxw3000, app(ty_[], bcd)) → new_esEs16(zxw4000, zxw3000, bcd)
new_esEs21(zxw4001, zxw3001, app(ty_Maybe, bah)) → new_esEs7(zxw4001, zxw3001, bah)
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_esEs22(zxw4000, zxw3000, ty_Double) → new_esEs18(zxw4000, zxw3000)
new_esEs21(zxw4001, zxw3001, app(app(ty_@2, bbh), bca)) → new_esEs4(zxw4001, zxw3001, bbh, bca)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_@0) → new_ltEs14(zxw49000, zxw50000)
new_esEs31(zxw400, zxw300, ty_@0) → new_esEs20(zxw400, zxw300)
new_esEs19(Float(zxw4000, zxw4001), Float(zxw3000, zxw3001)) → new_esEs13(new_sr(zxw4000, zxw3000), new_sr(zxw4001, zxw3001))
new_ltEs19(zxw4900, zxw5000, app(ty_Maybe, hd)) → new_ltEs8(zxw4900, zxw5000, hd)
new_primMulInt(Neg(zxw40010), Neg(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_esEs30(zxw20, zxw15, app(ty_Maybe, bde)) → new_esEs7(zxw20, zxw15, bde)
new_primEqNat0(Zero, Succ(zxw30000)) → False
new_primEqNat0(Succ(zxw40000), Zero) → False
new_compare25(zxw49000, zxw50000, True, be, bf) → EQ
new_ltEs7(Left(zxw49000), Left(zxw50000), app(app(ty_Either, dbc), dbd), cca) → new_ltEs7(zxw49000, zxw50000, dbc, dbd)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_lt10(zxw49000, zxw50000, app(ty_Ratio, bgg)) → new_lt18(zxw49000, zxw50000, bgg)
new_esEs12(zxw4000, zxw3000, ty_@0) → new_esEs20(zxw4000, zxw3000)
new_esEs21(zxw4001, zxw3001, ty_Bool) → new_esEs9(zxw4001, zxw3001)
new_esEs5(@3(zxw4000, zxw4001, zxw4002), @3(zxw3000, zxw3001, zxw3002), cb, cc, cd) → new_asAs(new_esEs12(zxw4000, zxw3000, cb), new_asAs(new_esEs11(zxw4001, zxw3001, cc), new_esEs10(zxw4002, zxw3002, cd)))
new_esEs16(:(zxw4000, zxw4001), [], ca) → False
new_esEs16([], :(zxw3000, zxw3001), ca) → False
new_lt10(zxw49000, zxw50000, ty_Integer) → new_lt5(zxw49000, zxw50000)
new_lt6(zxw49000, zxw50000) → new_esEs8(new_compare12(zxw49000, zxw50000), LT)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_ltEs4(LT, GT) → True
new_esEs23(zxw49000, zxw50000, ty_Double) → new_esEs18(zxw49000, zxw50000)
new_compare25(zxw49000, zxw50000, False, be, bf) → new_compare15(zxw49000, zxw50000, new_ltEs7(zxw49000, zxw50000, be, bf), be, bf)
new_lt19(zxw49001, zxw50001, app(app(ty_Either, cgg), cgh)) → new_lt17(zxw49001, zxw50001, cgg, cgh)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_esEs6(Left(zxw4000), Left(zxw3000), app(ty_Maybe, ccb), cf) → new_esEs7(zxw4000, zxw3000, ccb)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Ordering, cf) → new_esEs8(zxw4000, zxw3000)
new_esEs16(:(zxw4000, zxw4001), :(zxw3000, zxw3001), ca) → new_asAs(new_esEs28(zxw4000, zxw3000, ca), new_esEs16(zxw4001, zxw3001, ca))
new_ltEs8(Just(zxw49000), Just(zxw50000), app(ty_Ratio, baf)) → new_ltEs17(zxw49000, zxw50000, baf)
new_compare0(:(zxw49000, zxw49001), :(zxw50000, zxw50001), cab) → new_primCompAux1(zxw49000, zxw50000, new_compare0(zxw49001, zxw50001, cab), cab)
new_esEs11(zxw4001, zxw3001, app(ty_Maybe, ee)) → new_esEs7(zxw4001, zxw3001, ee)
new_esEs6(Right(zxw4000), Right(zxw3000), ce, app(app(ty_@2, ced), cee)) → new_esEs4(zxw4000, zxw3000, ced, cee)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Float) → new_ltEs6(zxw49000, zxw50000)
new_compare15(zxw49000, zxw50000, False, be, bf) → GT
new_compare29(zxw49000, zxw50000, app(app(ty_Either, cbb), cbc)) → new_compare32(zxw49000, zxw50000, cbb, cbc)
new_lt20(zxw49000, zxw50000, ty_Float) → new_lt7(zxw49000, zxw50000)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Char) → new_esEs15(zxw4000, zxw3000)
new_esEs23(zxw49000, zxw50000, ty_Int) → new_esEs13(zxw49000, zxw50000)
new_esEs30(zxw20, zxw15, app(ty_[], bdg)) → new_esEs16(zxw20, zxw15, bdg)
new_esEs7(Just(zxw4000), Just(zxw3000), app(app(app(ty_@3, bhc), bhd), bhe)) → new_esEs5(zxw4000, zxw3000, bhc, bhd, bhe)
new_esEs9(True, False) → False
new_esEs9(False, True) → False
new_compare29(zxw49000, zxw50000, app(ty_Ratio, cbd)) → new_compare8(zxw49000, zxw50000, cbd)
new_esEs10(zxw4002, zxw3002, app(app(ty_@2, ec), ed)) → new_esEs4(zxw4002, zxw3002, ec, ed)
new_esEs11(zxw4001, zxw3001, app(ty_Ratio, ef)) → new_esEs14(zxw4001, zxw3001, ef)
new_compare29(zxw49000, zxw50000, ty_Ordering) → new_compare6(zxw49000, zxw50000)
new_esEs21(zxw4001, zxw3001, ty_Integer) → new_esEs17(zxw4001, zxw3001)
new_esEs27(zxw49000, zxw50000, ty_Double) → new_esEs18(zxw49000, zxw50000)
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs27(zxw49000, zxw50000, app(ty_Ratio, dac)) → new_esEs14(zxw49000, zxw50000, dac)
new_ltEs4(LT, EQ) → True
new_esEs6(Right(zxw4000), Right(zxw3000), ce, ty_Char) → new_esEs15(zxw4000, zxw3000)
new_esEs10(zxw4002, zxw3002, ty_Double) → new_esEs18(zxw4002, zxw3002)
new_compare31(@0, @0) → EQ
new_esEs31(zxw400, zxw300, ty_Float) → new_esEs19(zxw400, zxw300)
new_esEs12(zxw4000, zxw3000, app(app(ty_Either, gf), gg)) → new_esEs6(zxw4000, zxw3000, gf, gg)
new_ltEs8(Just(zxw49000), Just(zxw50000), app(ty_Maybe, hg)) → new_ltEs8(zxw49000, zxw50000, hg)
new_lt19(zxw49001, zxw50001, ty_Bool) → new_lt13(zxw49001, zxw50001)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbh, app(app(ty_Either, dce), dcf)) → new_ltEs7(zxw49000, zxw50000, dce, dcf)
new_esEs28(zxw4000, zxw3000, app(app(ty_@2, ddh), dea)) → new_esEs4(zxw4000, zxw3000, ddh, dea)
new_compare9(Integer(zxw49000), Integer(zxw50000)) → new_primCmpInt(zxw49000, zxw50000)
new_asAs(False, zxw187) → False
new_primMulInt(Neg(zxw40010), Pos(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Double) → new_esEs18(zxw4000, zxw3000)
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Ordering) → new_ltEs4(zxw49000, zxw50000)
new_esEs21(zxw4001, zxw3001, ty_Ordering) → new_esEs8(zxw4001, zxw3001)
new_primCmpNat2(zxw4900, Zero) → GT
new_ltEs20(zxw49002, zxw50002, ty_Double) → new_ltEs11(zxw49002, zxw50002)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Char, cf) → new_esEs15(zxw4000, zxw3000)
new_esEs26(zxw49001, zxw50001, app(ty_Maybe, cgb)) → new_esEs7(zxw49001, zxw50001, cgb)
new_esEs10(zxw4002, zxw3002, ty_@0) → new_esEs20(zxw4002, zxw3002)
new_lt19(zxw49001, zxw50001, ty_Double) → new_lt8(zxw49001, zxw50001)
new_esEs28(zxw4000, zxw3000, ty_Double) → new_esEs18(zxw4000, zxw3000)
new_compare110(zxw49000, zxw50000, True, bgd, bge, bgf) → LT
new_esEs24(zxw4001, zxw3001, ty_Integer) → new_esEs17(zxw4001, zxw3001)
new_lt19(zxw49001, zxw50001, app(ty_Maybe, cgb)) → new_lt12(zxw49001, zxw50001, cgb)
new_ltEs18(zxw49001, zxw50001, app(ty_Ratio, bgb)) → new_ltEs17(zxw49001, zxw50001, bgb)
new_ltEs18(zxw49001, zxw50001, ty_Char) → new_ltEs12(zxw49001, zxw50001)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Float, cf) → new_esEs19(zxw4000, zxw3000)
new_esEs21(zxw4001, zxw3001, ty_Int) → new_esEs13(zxw4001, zxw3001)
new_lt20(zxw49000, zxw50000, app(ty_Ratio, dac)) → new_lt18(zxw49000, zxw50000, dac)
new_ltEs19(zxw4900, zxw5000, ty_@0) → new_ltEs14(zxw4900, zxw5000)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbh, ty_Double) → new_ltEs11(zxw49000, zxw50000)
new_lt17(zxw49000, zxw50000, be, bf) → new_esEs8(new_compare32(zxw49000, zxw50000, be, bf), LT)
new_esEs9(False, False) → True
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Int) → new_ltEs10(zxw49000, zxw50000)
new_esEs30(zxw20, zxw15, ty_Int) → new_esEs13(zxw20, zxw15)
new_ltEs19(zxw4900, zxw5000, ty_Bool) → new_ltEs5(zxw4900, zxw5000)
new_esEs31(zxw400, zxw300, app(app(ty_Either, ce), cf)) → new_esEs6(zxw400, zxw300, ce, cf)
new_compare29(zxw49000, zxw50000, ty_Integer) → new_compare9(zxw49000, zxw50000)
new_lt20(zxw49000, zxw50000, app(app(app(ty_@3, chf), chg), chh)) → new_lt16(zxw49000, zxw50000, chf, chg, chh)
new_esEs4(@2(zxw4000, zxw4001), @2(zxw3000, zxw3001), cg, da) → new_asAs(new_esEs22(zxw4000, zxw3000, cg), new_esEs21(zxw4001, zxw3001, da))
new_ltEs20(zxw49002, zxw50002, app(app(ty_Either, cfe), cff)) → new_ltEs7(zxw49002, zxw50002, cfe, cff)
new_esEs27(zxw49000, zxw50000, app(app(ty_@2, chb), chc)) → new_esEs4(zxw49000, zxw50000, chb, chc)
new_lt20(zxw49000, zxw50000, ty_Integer) → new_lt5(zxw49000, zxw50000)
new_compare35(zxw400, h) → new_compare26(Just(zxw400), Nothing, False, h)
new_ltEs18(zxw49001, zxw50001, app(ty_Maybe, bfc)) → new_ltEs8(zxw49001, zxw50001, bfc)
new_compare8(:%(zxw49000, zxw49001), :%(zxw50000, zxw50001), ty_Integer) → new_compare9(new_sr0(zxw49000, zxw50001), new_sr0(zxw50000, zxw49001))
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Float, cca) → new_ltEs6(zxw49000, zxw50000)
new_ltEs4(LT, LT) → True
new_esEs16([], [], ca) → True
new_ltEs20(zxw49002, zxw50002, ty_Int) → new_ltEs10(zxw49002, zxw50002)
new_ltEs8(Nothing, Nothing, hd) → True
new_lt10(zxw49000, zxw50000, ty_Char) → new_lt6(zxw49000, zxw50000)
new_lt10(zxw49000, zxw50000, ty_Bool) → new_lt13(zxw49000, zxw50000)
new_esEs22(zxw4000, zxw3000, app(app(ty_Either, bch), bda)) → new_esEs6(zxw4000, zxw3000, bch, bda)
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_lt5(zxw49000, zxw50000) → new_esEs8(new_compare9(zxw49000, zxw50000), LT)
new_esEs26(zxw49001, zxw50001, ty_Float) → new_esEs19(zxw49001, zxw50001)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Int, cf) → new_esEs13(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_esEs10(zxw4002, zxw3002, ty_Int) → new_esEs13(zxw4002, zxw3002)
new_lt10(zxw49000, zxw50000, app(ty_[], db)) → new_lt9(zxw49000, zxw50000, db)
new_esEs12(zxw4000, zxw3000, app(ty_Ratio, ga)) → new_esEs14(zxw4000, zxw3000, ga)
new_ltEs15(@3(zxw49000, zxw49001, zxw49002), @3(zxw50000, zxw50001, zxw50002), cbe, cbf, cbg) → new_pePe(new_lt20(zxw49000, zxw50000, cbe), new_asAs(new_esEs27(zxw49000, zxw50000, cbe), new_pePe(new_lt19(zxw49001, zxw50001, cbf), new_asAs(new_esEs26(zxw49001, zxw50001, cbf), new_ltEs20(zxw49002, zxw50002, cbg)))))
new_ltEs10(zxw4900, zxw5000) → new_fsEs(new_compare7(zxw4900, zxw5000))
new_esEs30(zxw20, zxw15, ty_Ordering) → new_esEs8(zxw20, zxw15)
new_esEs10(zxw4002, zxw3002, app(ty_Ratio, dd)) → new_esEs14(zxw4002, zxw3002, dd)
new_ltEs12(zxw4900, zxw5000) → new_fsEs(new_compare12(zxw4900, zxw5000))
new_esEs10(zxw4002, zxw3002, ty_Ordering) → new_esEs8(zxw4002, zxw3002)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbh, ty_Float) → new_ltEs6(zxw49000, zxw50000)
new_esEs23(zxw49000, zxw50000, app(ty_[], db)) → new_esEs16(zxw49000, zxw50000, db)
new_esEs11(zxw4001, zxw3001, ty_Integer) → new_esEs17(zxw4001, zxw3001)
new_esEs26(zxw49001, zxw50001, app(app(ty_Either, cgg), cgh)) → new_esEs6(zxw49001, zxw50001, cgg, cgh)
new_compare16(Double(zxw49000, zxw49001), Double(zxw50000, zxw50001)) → new_compare7(new_sr(zxw49000, zxw50000), new_sr(zxw49001, zxw50001))
new_compare0([], :(zxw50000, zxw50001), cab) → LT
new_primPlusNat1(Zero, Zero) → Zero
new_esEs12(zxw4000, zxw3000, ty_Ordering) → new_esEs8(zxw4000, zxw3000)
new_lt10(zxw49000, zxw50000, ty_@0) → new_lt15(zxw49000, zxw50000)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Char) → new_ltEs12(zxw49000, zxw50000)
new_asAs(True, zxw187) → zxw187
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_esEs30(zxw20, zxw15, ty_Integer) → new_esEs17(zxw20, zxw15)
new_esEs26(zxw49001, zxw50001, app(app(app(ty_@3, cgd), cge), cgf)) → new_esEs5(zxw49001, zxw50001, cgd, cge, cgf)
new_esEs31(zxw400, zxw300, app(ty_Maybe, bg)) → new_esEs7(zxw400, zxw300, bg)
new_esEs10(zxw4002, zxw3002, app(app(ty_Either, ea), eb)) → new_esEs6(zxw4002, zxw3002, ea, eb)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Integer) → new_ltEs16(zxw49000, zxw50000)
new_compare30(zxw49000, zxw50000, hb, hc) → new_compare27(zxw49000, zxw50000, new_esEs4(zxw49000, zxw50000, hb, hc), hb, hc)
new_compare29(zxw49000, zxw50000, ty_Bool) → new_compare18(zxw49000, zxw50000)
new_fsEs(zxw202) → new_not(new_esEs8(zxw202, GT))
new_esEs23(zxw49000, zxw50000, app(app(app(ty_@3, bgd), bge), bgf)) → new_esEs5(zxw49000, zxw50000, bgd, bge, bgf)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Float) → new_esEs19(zxw4000, zxw3000)
new_compare10(zxw49000, zxw50000, True) → LT
new_esEs30(zxw20, zxw15, app(app(app(ty_@3, bdh), bea), beb)) → new_esEs5(zxw20, zxw15, bdh, bea, beb)
new_compare29(zxw49000, zxw50000, app(ty_Maybe, cae)) → new_compare19(zxw49000, zxw50000, cae)
new_ltEs4(GT, GT) → True
new_esEs26(zxw49001, zxw50001, ty_@0) → new_esEs20(zxw49001, zxw50001)
new_compare110(zxw49000, zxw50000, False, bgd, bge, bgf) → GT
new_ltEs7(Left(zxw49000), Left(zxw50000), app(ty_Ratio, dbe), cca) → new_ltEs17(zxw49000, zxw50000, dbe)
new_compare10(zxw49000, zxw50000, False) → GT
new_ltEs8(Just(zxw49000), Just(zxw50000), app(app(app(ty_@3, baa), bab), bac)) → new_ltEs15(zxw49000, zxw50000, baa, bab, bac)
new_esEs21(zxw4001, zxw3001, app(ty_[], bbb)) → new_esEs16(zxw4001, zxw3001, bbb)
new_compare18(zxw49000, zxw50000) → new_compare24(zxw49000, zxw50000, new_esEs9(zxw49000, zxw50000))
new_esEs6(Left(zxw4000), Left(zxw3000), app(ty_[], ccd), cf) → new_esEs16(zxw4000, zxw3000, ccd)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs6(Right(zxw4000), Right(zxw3000), ce, ty_Ordering) → new_esEs8(zxw4000, zxw3000)
new_esEs6(Right(zxw4000), Right(zxw3000), ce, app(app(app(ty_@3, cdg), cdh), cea)) → new_esEs5(zxw4000, zxw3000, cdg, cdh, cea)
new_primCompAux0(zxw218, EQ) → zxw218
new_lt20(zxw49000, zxw50000, app(ty_Maybe, chd)) → new_lt12(zxw49000, zxw50000, chd)
new_esEs12(zxw4000, zxw3000, app(app(ty_@2, gh), ha)) → new_esEs4(zxw4000, zxw3000, gh, ha)
new_ltEs19(zxw4900, zxw5000, app(ty_[], cab)) → new_ltEs13(zxw4900, zxw5000, cab)
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_esEs22(zxw4000, zxw3000, app(ty_Maybe, bcb)) → new_esEs7(zxw4000, zxw3000, bcb)
new_esEs30(zxw20, zxw15, ty_Char) → new_esEs15(zxw20, zxw15)
new_esEs30(zxw20, zxw15, app(app(ty_@2, bee), bef)) → new_esEs4(zxw20, zxw15, bee, bef)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbh, ty_@0) → new_ltEs14(zxw49000, zxw50000)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_compare8(:%(zxw49000, zxw49001), :%(zxw50000, zxw50001), ty_Int) → new_compare7(new_sr(zxw49000, zxw50001), new_sr(zxw50000, zxw49001))
new_ltEs17(zxw4900, zxw5000, bag) → new_fsEs(new_compare8(zxw4900, zxw5000, bag))
new_not(True) → False

The set Q consists of the following terms:

new_esEs17(Integer(x0), Integer(x1))
new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_ltEs7(Right(x0), Right(x1), x2, ty_Bool)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Integer)
new_lt10(x0, x1, ty_Double)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_compare18(x0, x1)
new_compare29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare29(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Double)
new_pePe(False, x0)
new_lt10(x0, x1, app(app(ty_Either, x2), x3))
new_compare29(x0, x1, app(app(ty_Either, x2), x3))
new_lt17(x0, x1, x2, x3)
new_esEs31(x0, x1, ty_Double)
new_esEs10(x0, x1, app(ty_[], x2))
new_ltEs8(Nothing, Nothing, x0)
new_compare210(x0, x1, True, x2, x3, x4)
new_compare7(x0, x1)
new_primMulNat0(Succ(x0), Zero)
new_esEs31(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(ty_[], x2))
new_esEs7(Just(x0), Just(x1), ty_Double)
new_ltEs8(Just(x0), Just(x1), ty_Integer)
new_esEs10(x0, x1, ty_Int)
new_ltEs10(x0, x1)
new_esEs28(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Ordering)
new_esEs31(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs12(x0, x1, ty_Char)
new_compare25(x0, x1, True, x2, x3)
new_primMulNat0(Succ(x0), Succ(x1))
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare8(:%(x0, x1), :%(x2, x3), ty_Int)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_ltEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs16(x0, x1)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_lt10(x0, x1, app(ty_Ratio, x2))
new_ltEs8(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs6(Right(x0), Right(x1), x2, ty_Char)
new_compare13(x0, x1, True)
new_ltEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs10(x0, x1, ty_Ordering)
new_esEs31(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, ty_Float)
new_esEs11(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_Int)
new_esEs31(x0, x1, ty_Int)
new_compare11(x0, x1, True, x2)
new_ltEs19(x0, x1, ty_Ordering)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_lt10(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(GT, GT)
new_compare11(x0, x1, False, x2)
new_esEs8(LT, LT)
new_compare29(x0, x1, ty_Double)
new_esEs18(Double(x0, x1), Double(x2, x3))
new_primCmpNat0(Zero, x0)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_ltEs8(Just(x0), Just(x1), ty_Bool)
new_ltEs8(Just(x0), Just(x1), app(ty_[], x2))
new_esEs11(x0, x1, ty_@0)
new_primCmpNat1(Zero, Succ(x0))
new_esEs31(x0, x1, app(ty_Maybe, x2))
new_esEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, ty_Int)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_sr(x0, x1)
new_ltEs5(False, False)
new_compare17(x0, x1, False, x2, x3)
new_ltEs8(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare6(x0, x1)
new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt10(x0, x1, ty_Ordering)
new_compare28(x0, x1, x2, x3, x4)
new_compare29(x0, x1, ty_Int)
new_esEs30(x0, x1, ty_Bool)
new_compare19(x0, x1, x2)
new_esEs26(x0, x1, ty_Integer)
new_primEqNat0(Zero, Succ(x0))
new_primCmpNat1(Zero, Zero)
new_compare16(Double(x0, x1), Double(x2, x3))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_lt7(x0, x1)
new_esEs28(x0, x1, ty_@0)
new_ltEs20(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_Integer)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Double)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_Char)
new_lt12(x0, x1, x2)
new_ltEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_compare15(x0, x1, True, x2, x3)
new_esEs24(x0, x1, ty_Int)
new_compare26(Just(x0), Just(x1), False, x2)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_primEqNat0(Zero, Zero)
new_compare32(x0, x1, x2, x3)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs30(x0, x1, app(ty_[], x2))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs7(Left(x0), Left(x1), ty_Char, x2)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_ltEs8(Just(x0), Just(x1), ty_Double)
new_ltEs8(Just(x0), Just(x1), ty_Ordering)
new_ltEs19(x0, x1, ty_@0)
new_compare24(x0, x1, False)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs9(True, True)
new_compare27(x0, x1, True, x2, x3)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_lt4(x0, x1)
new_ltEs8(Nothing, Just(x0), x1)
new_primMulNat0(Zero, Zero)
new_esEs23(x0, x1, ty_Char)
new_esEs30(x0, x1, ty_Ordering)
new_compare29(x0, x1, app(app(ty_@2, x2), x3))
new_esEs10(x0, x1, ty_@0)
new_lt10(x0, x1, ty_Char)
new_ltEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs30(x0, x1, ty_Int)
new_compare26(Just(x0), Nothing, False, x1)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_Integer)
new_fsEs(x0)
new_ltEs4(GT, GT)
new_lt8(x0, x1)
new_esEs6(Right(x0), Right(x1), x2, ty_Integer)
new_esEs30(x0, x1, ty_@0)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(x0, x1, ty_Float)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs28(x0, x1, ty_Double)
new_ltEs8(Just(x0), Nothing, x1)
new_esEs31(x0, x1, app(app(ty_Either, x2), x3))
new_esEs11(x0, x1, app(ty_Ratio, x2))
new_ltEs8(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt10(x0, x1, ty_Int)
new_esEs10(x0, x1, ty_Bool)
new_ltEs18(x0, x1, app(ty_[], x2))
new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs10(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs23(x0, x1, ty_Ordering)
new_esEs7(Just(x0), Just(x1), ty_Int)
new_esEs10(x0, x1, ty_Char)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_compare33(x0)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt10(x0, x1, app(ty_Maybe, x2))
new_pePe(True, x0)
new_ltEs15(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_primPlusNat0(Zero, x0)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_compare26(Nothing, Nothing, False, x0)
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Int)
new_lt6(x0, x1)
new_esEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs26(x0, x1, ty_Bool)
new_compare24(x0, x1, True)
new_ltEs18(x0, x1, ty_Integer)
new_esEs10(x0, x1, app(ty_Maybe, x2))
new_compare15(x0, x1, False, x2, x3)
new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_compare14(Float(x0, x1), Float(x2, x3))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs7(Right(x0), Left(x1), x2, x3)
new_ltEs7(Left(x0), Right(x1), x2, x3)
new_lt10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_compare110(x0, x1, False, x2, x3, x4)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_ltEs14(x0, x1)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_primPlusNat1(Zero, Zero)
new_esEs11(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Right(x0), Left(x1), x2, x3)
new_esEs6(Left(x0), Right(x1), x2, x3)
new_primCompAux0(x0, GT)
new_ltEs7(Right(x0), Right(x1), x2, ty_Char)
new_esEs6(Left(x0), Left(x1), ty_Int, x2)
new_compare23(x0, x1, True)
new_esEs31(x0, x1, ty_Float)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_compare29(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, app(ty_[], x2))
new_lt15(x0, x1)
new_esEs6(Left(x0), Left(x1), ty_Integer, x2)
new_esEs14(:%(x0, x1), :%(x2, x3), x4)
new_compare13(x0, x1, False)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_lt20(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_@0)
new_esEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_primPlusNat0(Succ(x0), x1)
new_ltEs4(EQ, EQ)
new_esEs31(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, ty_Char)
new_esEs6(Right(x0), Right(x1), x2, ty_Int)
new_ltEs11(x0, x1)
new_compare29(x0, x1, app(ty_Ratio, x2))
new_esEs12(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Integer)
new_ltEs20(x0, x1, ty_Char)
new_esEs7(Just(x0), Just(x1), ty_Char)
new_esEs12(x0, x1, ty_Float)
new_compare31(@0, @0)
new_ltEs7(Left(x0), Left(x1), ty_Int, x2)
new_esEs7(Just(x0), Just(x1), ty_Float)
new_compare36(x0, x1, x2)
new_primCmpNat2(x0, Zero)
new_ltEs4(LT, EQ)
new_ltEs4(EQ, LT)
new_esEs12(x0, x1, ty_Int)
new_ltEs13(x0, x1, x2)
new_lt19(x0, x1, ty_Double)
new_esEs12(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, app(ty_Ratio, x2))
new_ltEs7(Left(x0), Left(x1), ty_@0, x2)
new_esEs21(x0, x1, app(ty_[], x2))
new_primMulInt(Pos(x0), Pos(x1))
new_lt20(x0, x1, ty_Bool)
new_esEs30(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_@0)
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_asAs(True, x0)
new_primEqNat0(Succ(x0), Zero)
new_ltEs8(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Right(x0), Right(x1), x2, ty_Bool)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_ltEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs13(x0, x1)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs21(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Integer)
new_lt20(x0, x1, ty_@0)
new_esEs12(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, ty_Bool)
new_lt20(x0, x1, ty_Char)
new_esEs6(Left(x0), Left(x1), ty_Float, x2)
new_esEs12(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_Ordering)
new_compare34(x0, x1)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Ordering)
new_esEs6(Right(x0), Right(x1), x2, ty_Float)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_compare26(Nothing, Just(x0), False, x1)
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_ltEs20(x0, x1, ty_Bool)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs12(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs27(x0, x1, ty_Int)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Double)
new_esEs25(x0, x1, ty_Integer)
new_ltEs7(Right(x0), Right(x1), x2, ty_Integer)
new_primMulInt(Neg(x0), Neg(x1))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs31(x0, x1, ty_Bool)
new_lt10(x0, x1, ty_Bool)
new_primPlusNat1(Succ(x0), Zero)
new_esEs22(x0, x1, ty_Float)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs6(Left(x0), Left(x1), ty_@0, x2)
new_ltEs4(LT, LT)
new_lt11(x0, x1, x2, x3)
new_esEs10(x0, x1, ty_Integer)
new_esEs31(x0, x1, ty_Ordering)
new_esEs12(x0, x1, app(app(ty_@2, x2), x3))
new_esEs16([], [], x0)
new_ltEs19(x0, x1, ty_Integer)
new_compare23(x0, x1, False)
new_lt16(x0, x1, x2, x3, x4)
new_compare29(x0, x1, app(ty_[], x2))
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs11(x0, x1, ty_Bool)
new_esEs11(x0, x1, app(app(ty_Either, x2), x3))
new_esEs16([], :(x0, x1), x2)
new_esEs23(x0, x1, ty_Double)
new_esEs21(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_Ordering)
new_ltEs9(@2(x0, x1), @2(x2, x3), x4, x5)
new_primPlusNat1(Zero, Succ(x0))
new_ltEs12(x0, x1)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_compare10(x0, x1, False)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_primCmpNat0(Succ(x0), x1)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, ty_@0)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs8(GT, EQ)
new_esEs8(EQ, GT)
new_esEs22(x0, x1, ty_Bool)
new_lt19(x0, x1, ty_Float)
new_ltEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_lt19(x0, x1, ty_Integer)
new_ltEs8(Just(x0), Just(x1), ty_Char)
new_esEs7(Nothing, Just(x0), x1)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt18(x0, x1, x2)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs16(:(x0, x1), :(x2, x3), x4)
new_ltEs8(Just(x0), Just(x1), ty_Float)
new_ltEs7(Left(x0), Left(x1), ty_Float, x2)
new_lt5(x0, x1)
new_compare29(x0, x1, ty_Ordering)
new_ltEs18(x0, x1, ty_Bool)
new_esEs11(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_@0)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, ty_Int)
new_esEs11(x0, x1, ty_Char)
new_ltEs7(Left(x0), Left(x1), ty_Double, x2)
new_esEs27(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Float)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_lt19(x0, x1, ty_Ordering)
new_compare29(x0, x1, ty_Integer)
new_compare25(x0, x1, False, x2, x3)
new_esEs26(x0, x1, app(ty_[], x2))
new_ltEs18(x0, x1, ty_Float)
new_esEs9(False, False)
new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs21(x0, x1, ty_Double)
new_esEs12(x0, x1, ty_Ordering)
new_primCompAux1(x0, x1, x2, x3)
new_ltEs17(x0, x1, x2)
new_compare0([], :(x0, x1), x2)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpNat1(Succ(x0), Succ(x1))
new_esEs26(x0, x1, ty_@0)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs6(x0, x1)
new_lt10(x0, x1, ty_Float)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs22(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Float)
new_primCompAux0(x0, EQ)
new_esEs10(x0, x1, app(app(ty_Either, x2), x3))
new_compare210(x0, x1, False, x2, x3, x4)
new_esEs21(x0, x1, ty_Integer)
new_primCmpNat1(Succ(x0), Zero)
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_esEs6(Left(x0), Left(x1), ty_Bool, x2)
new_esEs7(Nothing, Nothing, x0)
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, ty_@0)
new_esEs12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, ty_Double)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_lt13(x0, x1)
new_esEs23(x0, x1, ty_Bool)
new_ltEs5(True, True)
new_ltEs7(Right(x0), Right(x1), x2, ty_Int)
new_lt19(x0, x1, ty_Int)
new_compare35(x0, x1)
new_lt19(x0, x1, ty_Char)
new_ltEs4(EQ, GT)
new_ltEs4(GT, EQ)
new_esEs31(x0, x1, ty_Integer)
new_not(True)
new_esEs11(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Float)
new_ltEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs11(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, ty_Char)
new_lt19(x0, x1, ty_@0)
new_compare26(x0, x1, True, x2)
new_esEs21(x0, x1, ty_Ordering)
new_ltEs8(Just(x0), Just(x1), app(ty_Maybe, x2))
new_compare0([], [], x0)
new_esEs26(x0, x1, ty_Char)
new_esEs7(Just(x0), Nothing, x1)
new_esEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs18(x0, x1, ty_Int)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Ordering)
new_not(False)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_lt14(x0, x1)
new_compare12(Char(x0), Char(x1))
new_esEs15(Char(x0), Char(x1))
new_esEs10(x0, x1, app(ty_Ratio, x2))
new_compare10(x0, x1, True)
new_lt10(x0, x1, ty_@0)
new_asAs(False, x0)
new_esEs22(x0, x1, ty_Ordering)
new_ltEs18(x0, x1, ty_Char)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_compare29(x0, x1, ty_Float)
new_compare17(x0, x1, True, x2, x3)
new_lt19(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_Char)
new_esEs31(x0, x1, ty_Char)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_ltEs8(Just(x0), Just(x1), ty_@0)
new_esEs20(@0, @0)
new_esEs6(Right(x0), Right(x1), x2, ty_Double)
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_ltEs7(Right(x0), Right(x1), x2, ty_Double)
new_esEs22(x0, x1, app(ty_[], x2))
new_ltEs7(Left(x0), Left(x1), ty_Integer, x2)
new_esEs23(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Int)
new_compare0(:(x0, x1), [], x2)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_ltEs19(x0, x1, ty_Double)
new_esEs9(True, False)
new_esEs9(False, True)
new_esEs22(x0, x1, ty_Char)
new_compare29(x0, x1, ty_Bool)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs7(Right(x0), Right(x1), x2, ty_Float)
new_esEs30(x0, x1, ty_Double)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, ty_Integer)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs11(x0, x1, ty_Double)
new_ltEs20(x0, x1, ty_Float)
new_primCompAux0(x0, LT)
new_primCmpNat2(x0, Succ(x1))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs11(x0, x1, app(ty_[], x2))
new_ltEs7(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs12(x0, x1, ty_Integer)
new_esEs6(Left(x0), Left(x1), ty_Double, x2)
new_esEs10(x0, x1, ty_Double)
new_esEs6(Right(x0), Right(x1), x2, ty_@0)
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_sr0(Integer(x0), Integer(x1))
new_lt10(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs6(Left(x0), Left(x1), ty_Char, x2)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Pos(Zero), Pos(Zero))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_compare30(x0, x1, x2, x3)
new_ltEs18(x0, x1, ty_Double)
new_esEs12(x0, x1, ty_Double)
new_compare110(x0, x1, True, x2, x3, x4)
new_esEs12(x0, x1, ty_Bool)
new_lt9(x0, x1, x2)
new_compare9(Integer(x0), Integer(x1))
new_lt10(x0, x1, ty_Integer)
new_esEs30(x0, x1, ty_Char)
new_esEs19(Float(x0, x1), Float(x2, x3))
new_primMulNat0(Zero, Succ(x0))
new_esEs7(Just(x0), Just(x1), ty_@0)
new_ltEs4(GT, LT)
new_ltEs4(LT, GT)
new_ltEs5(True, False)
new_ltEs5(False, True)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, app(ty_[], x2))
new_ltEs7(Right(x0), Right(x1), x2, ty_@0)
new_ltEs8(Just(x0), Just(x1), ty_Int)
new_compare29(x0, x1, ty_@0)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Float)
new_compare27(x0, x1, False, x2, x3)
new_esEs23(x0, x1, ty_Float)
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs30(x0, x1, ty_Float)
new_esEs16(:(x0, x1), [], x2)

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_splitLT(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba) → new_splitLT3(zxw330, zxw331, zxw332, zxw333, zxw334, Nothing, h, ba)
new_splitLT2(zxw300, zxw31, zxw32, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw34, True, h, ba) → new_splitLT3(zxw330, zxw331, zxw332, zxw333, zxw334, Nothing, h, ba)
new_splitLT3(Just(zxw300), zxw31, zxw32, zxw33, zxw34, Nothing, h, ba) → new_splitLT2(zxw300, zxw31, zxw32, zxw33, zxw34, new_esEs8(new_compare26(Nothing, Just(zxw300), False, h), LT), h, ba)
new_splitLT1(zxw31, zxw32, zxw33, zxw34, True, h, ba) → new_splitLT(zxw34, h, ba)
new_splitLT3(Nothing, zxw31, zxw32, zxw33, zxw34, Nothing, h, ba) → new_splitLT1(zxw31, zxw32, zxw33, zxw34, new_esEs8(new_compare33(h), GT), h, ba)
new_splitLT10(zxw300, zxw31, zxw32, zxw33, zxw34, True, h, ba) → new_splitLT(zxw34, h, ba)
new_splitLT2(zxw300, zxw31, zxw32, zxw33, zxw34, False, h, ba) → new_splitLT10(zxw300, zxw31, zxw32, zxw33, zxw34, new_esEs8(new_compare34(zxw300, h), GT), h, ba)

The TRS R consists of the following rules:

new_compare26(Nothing, Just(zxw5000), False, bdd) → LT
new_esEs8(LT, LT) → True
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_compare34(zxw300, h) → new_compare26(Nothing, Just(zxw300), False, h)
new_esEs8(GT, GT) → True
new_esEs8(LT, GT) → False
new_esEs8(EQ, GT) → False
new_compare33(h) → new_compare26(Nothing, Nothing, True, h)
new_compare26(zxw490, zxw500, True, bdd) → EQ

The set Q consists of the following terms:

new_esEs17(Integer(x0), Integer(x1))
new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_ltEs7(Right(x0), Right(x1), x2, ty_Bool)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Integer)
new_lt10(x0, x1, ty_Double)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_compare18(x0, x1)
new_compare29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare29(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Double)
new_pePe(False, x0)
new_lt10(x0, x1, app(app(ty_Either, x2), x3))
new_compare29(x0, x1, app(app(ty_Either, x2), x3))
new_lt17(x0, x1, x2, x3)
new_esEs31(x0, x1, ty_Double)
new_esEs10(x0, x1, app(ty_[], x2))
new_ltEs8(Nothing, Nothing, x0)
new_compare210(x0, x1, True, x2, x3, x4)
new_compare7(x0, x1)
new_primMulNat0(Succ(x0), Zero)
new_esEs31(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(ty_[], x2))
new_esEs7(Just(x0), Just(x1), ty_Double)
new_ltEs8(Just(x0), Just(x1), ty_Integer)
new_esEs10(x0, x1, ty_Int)
new_ltEs10(x0, x1)
new_esEs28(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Ordering)
new_esEs31(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs12(x0, x1, ty_Char)
new_compare25(x0, x1, True, x2, x3)
new_primMulNat0(Succ(x0), Succ(x1))
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare8(:%(x0, x1), :%(x2, x3), ty_Int)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_ltEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs16(x0, x1)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_lt10(x0, x1, app(ty_Ratio, x2))
new_ltEs8(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs6(Right(x0), Right(x1), x2, ty_Char)
new_compare13(x0, x1, True)
new_ltEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs10(x0, x1, ty_Ordering)
new_esEs31(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, ty_Float)
new_esEs11(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_Int)
new_esEs31(x0, x1, ty_Int)
new_compare11(x0, x1, True, x2)
new_ltEs19(x0, x1, ty_Ordering)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_lt10(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(GT, GT)
new_compare11(x0, x1, False, x2)
new_esEs8(LT, LT)
new_compare29(x0, x1, ty_Double)
new_esEs18(Double(x0, x1), Double(x2, x3))
new_primCmpNat0(Zero, x0)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_ltEs8(Just(x0), Just(x1), ty_Bool)
new_ltEs8(Just(x0), Just(x1), app(ty_[], x2))
new_esEs11(x0, x1, ty_@0)
new_primCmpNat1(Zero, Succ(x0))
new_esEs31(x0, x1, app(ty_Maybe, x2))
new_esEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, ty_Int)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_sr(x0, x1)
new_ltEs5(False, False)
new_compare17(x0, x1, False, x2, x3)
new_ltEs8(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare6(x0, x1)
new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt10(x0, x1, ty_Ordering)
new_compare28(x0, x1, x2, x3, x4)
new_compare29(x0, x1, ty_Int)
new_esEs30(x0, x1, ty_Bool)
new_compare19(x0, x1, x2)
new_esEs26(x0, x1, ty_Integer)
new_primEqNat0(Zero, Succ(x0))
new_primCmpNat1(Zero, Zero)
new_compare16(Double(x0, x1), Double(x2, x3))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_lt7(x0, x1)
new_esEs28(x0, x1, ty_@0)
new_ltEs20(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_Integer)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Double)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_Char)
new_lt12(x0, x1, x2)
new_ltEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_compare15(x0, x1, True, x2, x3)
new_esEs24(x0, x1, ty_Int)
new_compare26(Just(x0), Just(x1), False, x2)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_primEqNat0(Zero, Zero)
new_compare32(x0, x1, x2, x3)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs30(x0, x1, app(ty_[], x2))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs7(Left(x0), Left(x1), ty_Char, x2)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_ltEs8(Just(x0), Just(x1), ty_Double)
new_ltEs8(Just(x0), Just(x1), ty_Ordering)
new_ltEs19(x0, x1, ty_@0)
new_compare24(x0, x1, False)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs9(True, True)
new_compare27(x0, x1, True, x2, x3)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_lt4(x0, x1)
new_ltEs8(Nothing, Just(x0), x1)
new_primMulNat0(Zero, Zero)
new_esEs23(x0, x1, ty_Char)
new_esEs30(x0, x1, ty_Ordering)
new_compare29(x0, x1, app(app(ty_@2, x2), x3))
new_esEs10(x0, x1, ty_@0)
new_lt10(x0, x1, ty_Char)
new_ltEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs30(x0, x1, ty_Int)
new_compare26(Just(x0), Nothing, False, x1)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_Integer)
new_fsEs(x0)
new_ltEs4(GT, GT)
new_lt8(x0, x1)
new_esEs6(Right(x0), Right(x1), x2, ty_Integer)
new_esEs30(x0, x1, ty_@0)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(x0, x1, ty_Float)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs28(x0, x1, ty_Double)
new_ltEs8(Just(x0), Nothing, x1)
new_esEs31(x0, x1, app(app(ty_Either, x2), x3))
new_esEs11(x0, x1, app(ty_Ratio, x2))
new_ltEs8(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt10(x0, x1, ty_Int)
new_esEs10(x0, x1, ty_Bool)
new_ltEs18(x0, x1, app(ty_[], x2))
new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs10(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs23(x0, x1, ty_Ordering)
new_esEs7(Just(x0), Just(x1), ty_Int)
new_esEs10(x0, x1, ty_Char)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_compare33(x0)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt10(x0, x1, app(ty_Maybe, x2))
new_pePe(True, x0)
new_ltEs15(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_primPlusNat0(Zero, x0)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_compare26(Nothing, Nothing, False, x0)
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Int)
new_lt6(x0, x1)
new_esEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs26(x0, x1, ty_Bool)
new_compare24(x0, x1, True)
new_ltEs18(x0, x1, ty_Integer)
new_esEs10(x0, x1, app(ty_Maybe, x2))
new_compare15(x0, x1, False, x2, x3)
new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_compare14(Float(x0, x1), Float(x2, x3))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs7(Right(x0), Left(x1), x2, x3)
new_ltEs7(Left(x0), Right(x1), x2, x3)
new_lt10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_compare110(x0, x1, False, x2, x3, x4)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_ltEs14(x0, x1)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_primPlusNat1(Zero, Zero)
new_esEs11(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Right(x0), Left(x1), x2, x3)
new_esEs6(Left(x0), Right(x1), x2, x3)
new_primCompAux0(x0, GT)
new_ltEs7(Right(x0), Right(x1), x2, ty_Char)
new_esEs6(Left(x0), Left(x1), ty_Int, x2)
new_compare23(x0, x1, True)
new_esEs31(x0, x1, ty_Float)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_compare29(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, app(ty_[], x2))
new_lt15(x0, x1)
new_esEs6(Left(x0), Left(x1), ty_Integer, x2)
new_esEs14(:%(x0, x1), :%(x2, x3), x4)
new_compare13(x0, x1, False)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_lt20(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_@0)
new_esEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_primPlusNat0(Succ(x0), x1)
new_ltEs4(EQ, EQ)
new_esEs31(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, ty_Char)
new_esEs6(Right(x0), Right(x1), x2, ty_Int)
new_ltEs11(x0, x1)
new_compare29(x0, x1, app(ty_Ratio, x2))
new_esEs12(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Integer)
new_ltEs20(x0, x1, ty_Char)
new_esEs7(Just(x0), Just(x1), ty_Char)
new_esEs12(x0, x1, ty_Float)
new_compare31(@0, @0)
new_ltEs7(Left(x0), Left(x1), ty_Int, x2)
new_esEs7(Just(x0), Just(x1), ty_Float)
new_compare36(x0, x1, x2)
new_primCmpNat2(x0, Zero)
new_ltEs4(LT, EQ)
new_ltEs4(EQ, LT)
new_esEs12(x0, x1, ty_Int)
new_ltEs13(x0, x1, x2)
new_lt19(x0, x1, ty_Double)
new_esEs12(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, app(ty_Ratio, x2))
new_ltEs7(Left(x0), Left(x1), ty_@0, x2)
new_esEs21(x0, x1, app(ty_[], x2))
new_primMulInt(Pos(x0), Pos(x1))
new_lt20(x0, x1, ty_Bool)
new_esEs30(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_@0)
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_asAs(True, x0)
new_primEqNat0(Succ(x0), Zero)
new_ltEs8(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Right(x0), Right(x1), x2, ty_Bool)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_ltEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs13(x0, x1)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs21(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Integer)
new_lt20(x0, x1, ty_@0)
new_esEs12(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, ty_Bool)
new_lt20(x0, x1, ty_Char)
new_esEs6(Left(x0), Left(x1), ty_Float, x2)
new_esEs12(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_Ordering)
new_compare34(x0, x1)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Ordering)
new_esEs6(Right(x0), Right(x1), x2, ty_Float)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_compare26(Nothing, Just(x0), False, x1)
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_ltEs20(x0, x1, ty_Bool)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs12(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs27(x0, x1, ty_Int)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Double)
new_esEs25(x0, x1, ty_Integer)
new_ltEs7(Right(x0), Right(x1), x2, ty_Integer)
new_primMulInt(Neg(x0), Neg(x1))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs31(x0, x1, ty_Bool)
new_lt10(x0, x1, ty_Bool)
new_primPlusNat1(Succ(x0), Zero)
new_esEs22(x0, x1, ty_Float)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs6(Left(x0), Left(x1), ty_@0, x2)
new_ltEs4(LT, LT)
new_lt11(x0, x1, x2, x3)
new_esEs10(x0, x1, ty_Integer)
new_esEs31(x0, x1, ty_Ordering)
new_esEs12(x0, x1, app(app(ty_@2, x2), x3))
new_esEs16([], [], x0)
new_ltEs19(x0, x1, ty_Integer)
new_compare23(x0, x1, False)
new_lt16(x0, x1, x2, x3, x4)
new_compare29(x0, x1, app(ty_[], x2))
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs11(x0, x1, ty_Bool)
new_esEs11(x0, x1, app(app(ty_Either, x2), x3))
new_esEs16([], :(x0, x1), x2)
new_esEs23(x0, x1, ty_Double)
new_esEs21(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_Ordering)
new_ltEs9(@2(x0, x1), @2(x2, x3), x4, x5)
new_primPlusNat1(Zero, Succ(x0))
new_ltEs12(x0, x1)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_compare10(x0, x1, False)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_primCmpNat0(Succ(x0), x1)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, ty_@0)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs8(GT, EQ)
new_esEs8(EQ, GT)
new_esEs22(x0, x1, ty_Bool)
new_lt19(x0, x1, ty_Float)
new_ltEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_lt19(x0, x1, ty_Integer)
new_ltEs8(Just(x0), Just(x1), ty_Char)
new_esEs7(Nothing, Just(x0), x1)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt18(x0, x1, x2)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs16(:(x0, x1), :(x2, x3), x4)
new_ltEs8(Just(x0), Just(x1), ty_Float)
new_ltEs7(Left(x0), Left(x1), ty_Float, x2)
new_lt5(x0, x1)
new_compare29(x0, x1, ty_Ordering)
new_ltEs18(x0, x1, ty_Bool)
new_esEs11(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_@0)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, ty_Int)
new_esEs11(x0, x1, ty_Char)
new_ltEs7(Left(x0), Left(x1), ty_Double, x2)
new_esEs27(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Float)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_lt19(x0, x1, ty_Ordering)
new_compare29(x0, x1, ty_Integer)
new_compare25(x0, x1, False, x2, x3)
new_esEs26(x0, x1, app(ty_[], x2))
new_ltEs18(x0, x1, ty_Float)
new_esEs9(False, False)
new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs21(x0, x1, ty_Double)
new_esEs12(x0, x1, ty_Ordering)
new_primCompAux1(x0, x1, x2, x3)
new_ltEs17(x0, x1, x2)
new_compare0([], :(x0, x1), x2)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpNat1(Succ(x0), Succ(x1))
new_esEs26(x0, x1, ty_@0)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs6(x0, x1)
new_lt10(x0, x1, ty_Float)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs22(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Float)
new_primCompAux0(x0, EQ)
new_esEs10(x0, x1, app(app(ty_Either, x2), x3))
new_compare210(x0, x1, False, x2, x3, x4)
new_esEs21(x0, x1, ty_Integer)
new_primCmpNat1(Succ(x0), Zero)
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_esEs6(Left(x0), Left(x1), ty_Bool, x2)
new_esEs7(Nothing, Nothing, x0)
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, ty_@0)
new_esEs12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, ty_Double)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_lt13(x0, x1)
new_esEs23(x0, x1, ty_Bool)
new_ltEs5(True, True)
new_ltEs7(Right(x0), Right(x1), x2, ty_Int)
new_lt19(x0, x1, ty_Int)
new_compare35(x0, x1)
new_lt19(x0, x1, ty_Char)
new_ltEs4(EQ, GT)
new_ltEs4(GT, EQ)
new_esEs31(x0, x1, ty_Integer)
new_not(True)
new_esEs11(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Float)
new_ltEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs11(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, ty_Char)
new_lt19(x0, x1, ty_@0)
new_compare26(x0, x1, True, x2)
new_esEs21(x0, x1, ty_Ordering)
new_ltEs8(Just(x0), Just(x1), app(ty_Maybe, x2))
new_compare0([], [], x0)
new_esEs26(x0, x1, ty_Char)
new_esEs7(Just(x0), Nothing, x1)
new_esEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs18(x0, x1, ty_Int)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Ordering)
new_not(False)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_lt14(x0, x1)
new_compare12(Char(x0), Char(x1))
new_esEs15(Char(x0), Char(x1))
new_esEs10(x0, x1, app(ty_Ratio, x2))
new_compare10(x0, x1, True)
new_lt10(x0, x1, ty_@0)
new_asAs(False, x0)
new_esEs22(x0, x1, ty_Ordering)
new_ltEs18(x0, x1, ty_Char)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_compare29(x0, x1, ty_Float)
new_compare17(x0, x1, True, x2, x3)
new_lt19(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_Char)
new_esEs31(x0, x1, ty_Char)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_ltEs8(Just(x0), Just(x1), ty_@0)
new_esEs20(@0, @0)
new_esEs6(Right(x0), Right(x1), x2, ty_Double)
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_ltEs7(Right(x0), Right(x1), x2, ty_Double)
new_esEs22(x0, x1, app(ty_[], x2))
new_ltEs7(Left(x0), Left(x1), ty_Integer, x2)
new_esEs23(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Int)
new_compare0(:(x0, x1), [], x2)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_ltEs19(x0, x1, ty_Double)
new_esEs9(True, False)
new_esEs9(False, True)
new_esEs22(x0, x1, ty_Char)
new_compare29(x0, x1, ty_Bool)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs7(Right(x0), Right(x1), x2, ty_Float)
new_esEs30(x0, x1, ty_Double)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, ty_Integer)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs11(x0, x1, ty_Double)
new_ltEs20(x0, x1, ty_Float)
new_primCompAux0(x0, LT)
new_primCmpNat2(x0, Succ(x1))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs11(x0, x1, app(ty_[], x2))
new_ltEs7(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs12(x0, x1, ty_Integer)
new_esEs6(Left(x0), Left(x1), ty_Double, x2)
new_esEs10(x0, x1, ty_Double)
new_esEs6(Right(x0), Right(x1), x2, ty_@0)
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_sr0(Integer(x0), Integer(x1))
new_lt10(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs6(Left(x0), Left(x1), ty_Char, x2)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Pos(Zero), Pos(Zero))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_compare30(x0, x1, x2, x3)
new_ltEs18(x0, x1, ty_Double)
new_esEs12(x0, x1, ty_Double)
new_compare110(x0, x1, True, x2, x3, x4)
new_esEs12(x0, x1, ty_Bool)
new_lt9(x0, x1, x2)
new_compare9(Integer(x0), Integer(x1))
new_lt10(x0, x1, ty_Integer)
new_esEs30(x0, x1, ty_Char)
new_esEs19(Float(x0, x1), Float(x2, x3))
new_primMulNat0(Zero, Succ(x0))
new_esEs7(Just(x0), Just(x1), ty_@0)
new_ltEs4(GT, LT)
new_ltEs4(LT, GT)
new_ltEs5(True, False)
new_ltEs5(False, True)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, app(ty_[], x2))
new_ltEs7(Right(x0), Right(x1), x2, ty_@0)
new_ltEs8(Just(x0), Just(x1), ty_Int)
new_compare29(x0, x1, ty_@0)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Float)
new_compare27(x0, x1, False, x2, x3)
new_esEs23(x0, x1, ty_Float)
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs30(x0, x1, ty_Float)
new_esEs16(:(x0, x1), [], x2)

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_esEs17(Integer(x0), Integer(x1))
new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_ltEs7(Right(x0), Right(x1), x2, ty_Bool)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Integer)
new_lt10(x0, x1, ty_Double)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_compare18(x0, x1)
new_compare29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare29(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Double)
new_pePe(False, x0)
new_lt10(x0, x1, app(app(ty_Either, x2), x3))
new_compare29(x0, x1, app(app(ty_Either, x2), x3))
new_lt17(x0, x1, x2, x3)
new_esEs31(x0, x1, ty_Double)
new_esEs10(x0, x1, app(ty_[], x2))
new_ltEs8(Nothing, Nothing, x0)
new_compare210(x0, x1, True, x2, x3, x4)
new_compare7(x0, x1)
new_primMulNat0(Succ(x0), Zero)
new_esEs31(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(ty_[], x2))
new_esEs7(Just(x0), Just(x1), ty_Double)
new_ltEs8(Just(x0), Just(x1), ty_Integer)
new_esEs10(x0, x1, ty_Int)
new_ltEs10(x0, x1)
new_esEs28(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Ordering)
new_esEs31(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs12(x0, x1, ty_Char)
new_compare25(x0, x1, True, x2, x3)
new_primMulNat0(Succ(x0), Succ(x1))
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare8(:%(x0, x1), :%(x2, x3), ty_Int)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_ltEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs16(x0, x1)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_lt10(x0, x1, app(ty_Ratio, x2))
new_ltEs8(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs6(Right(x0), Right(x1), x2, ty_Char)
new_compare13(x0, x1, True)
new_ltEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs10(x0, x1, ty_Ordering)
new_esEs31(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, ty_Float)
new_esEs11(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_Int)
new_esEs31(x0, x1, ty_Int)
new_compare11(x0, x1, True, x2)
new_ltEs19(x0, x1, ty_Ordering)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_lt10(x0, x1, app(app(ty_@2, x2), x3))
new_compare11(x0, x1, False, x2)
new_compare29(x0, x1, ty_Double)
new_esEs18(Double(x0, x1), Double(x2, x3))
new_primCmpNat0(Zero, x0)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_ltEs8(Just(x0), Just(x1), ty_Bool)
new_ltEs8(Just(x0), Just(x1), app(ty_[], x2))
new_esEs11(x0, x1, ty_@0)
new_primCmpNat1(Zero, Succ(x0))
new_esEs31(x0, x1, app(ty_Maybe, x2))
new_esEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, ty_Int)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_sr(x0, x1)
new_ltEs5(False, False)
new_compare17(x0, x1, False, x2, x3)
new_ltEs8(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare6(x0, x1)
new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt10(x0, x1, ty_Ordering)
new_compare28(x0, x1, x2, x3, x4)
new_compare29(x0, x1, ty_Int)
new_esEs30(x0, x1, ty_Bool)
new_compare19(x0, x1, x2)
new_esEs26(x0, x1, ty_Integer)
new_primEqNat0(Zero, Succ(x0))
new_primCmpNat1(Zero, Zero)
new_compare16(Double(x0, x1), Double(x2, x3))
new_lt7(x0, x1)
new_esEs28(x0, x1, ty_@0)
new_ltEs20(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_Integer)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Double)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_Char)
new_lt12(x0, x1, x2)
new_ltEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_compare15(x0, x1, True, x2, x3)
new_esEs24(x0, x1, ty_Int)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_primEqNat0(Zero, Zero)
new_compare32(x0, x1, x2, x3)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs30(x0, x1, app(ty_[], x2))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs7(Left(x0), Left(x1), ty_Char, x2)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_ltEs8(Just(x0), Just(x1), ty_Double)
new_ltEs8(Just(x0), Just(x1), ty_Ordering)
new_ltEs19(x0, x1, ty_@0)
new_compare24(x0, x1, False)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs9(True, True)
new_compare27(x0, x1, True, x2, x3)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_lt4(x0, x1)
new_ltEs8(Nothing, Just(x0), x1)
new_primMulNat0(Zero, Zero)
new_esEs23(x0, x1, ty_Char)
new_esEs30(x0, x1, ty_Ordering)
new_compare29(x0, x1, app(app(ty_@2, x2), x3))
new_esEs10(x0, x1, ty_@0)
new_lt10(x0, x1, ty_Char)
new_ltEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs30(x0, x1, ty_Int)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_Integer)
new_fsEs(x0)
new_ltEs4(GT, GT)
new_lt8(x0, x1)
new_esEs6(Right(x0), Right(x1), x2, ty_Integer)
new_esEs30(x0, x1, ty_@0)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(x0, x1, ty_Float)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs28(x0, x1, ty_Double)
new_ltEs8(Just(x0), Nothing, x1)
new_esEs31(x0, x1, app(app(ty_Either, x2), x3))
new_esEs11(x0, x1, app(ty_Ratio, x2))
new_ltEs8(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt10(x0, x1, ty_Int)
new_esEs10(x0, x1, ty_Bool)
new_ltEs18(x0, x1, app(ty_[], x2))
new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs10(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs23(x0, x1, ty_Ordering)
new_esEs7(Just(x0), Just(x1), ty_Int)
new_esEs10(x0, x1, ty_Char)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt10(x0, x1, app(ty_Maybe, x2))
new_pePe(True, x0)
new_ltEs15(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_primPlusNat0(Zero, x0)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Int)
new_lt6(x0, x1)
new_esEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs26(x0, x1, ty_Bool)
new_compare24(x0, x1, True)
new_ltEs18(x0, x1, ty_Integer)
new_esEs10(x0, x1, app(ty_Maybe, x2))
new_compare15(x0, x1, False, x2, x3)
new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_compare14(Float(x0, x1), Float(x2, x3))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs7(Right(x0), Left(x1), x2, x3)
new_ltEs7(Left(x0), Right(x1), x2, x3)
new_lt10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_compare110(x0, x1, False, x2, x3, x4)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_ltEs14(x0, x1)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_primPlusNat1(Zero, Zero)
new_esEs11(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Right(x0), Left(x1), x2, x3)
new_esEs6(Left(x0), Right(x1), x2, x3)
new_primCompAux0(x0, GT)
new_ltEs7(Right(x0), Right(x1), x2, ty_Char)
new_esEs6(Left(x0), Left(x1), ty_Int, x2)
new_compare23(x0, x1, True)
new_esEs31(x0, x1, ty_Float)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_compare29(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, app(ty_[], x2))
new_lt15(x0, x1)
new_esEs6(Left(x0), Left(x1), ty_Integer, x2)
new_esEs14(:%(x0, x1), :%(x2, x3), x4)
new_compare13(x0, x1, False)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_lt20(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_@0)
new_esEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_primPlusNat0(Succ(x0), x1)
new_ltEs4(EQ, EQ)
new_esEs31(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, ty_Char)
new_esEs6(Right(x0), Right(x1), x2, ty_Int)
new_ltEs11(x0, x1)
new_compare29(x0, x1, app(ty_Ratio, x2))
new_esEs12(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Integer)
new_ltEs20(x0, x1, ty_Char)
new_esEs7(Just(x0), Just(x1), ty_Char)
new_esEs12(x0, x1, ty_Float)
new_compare31(@0, @0)
new_ltEs7(Left(x0), Left(x1), ty_Int, x2)
new_esEs7(Just(x0), Just(x1), ty_Float)
new_compare36(x0, x1, x2)
new_primCmpNat2(x0, Zero)
new_ltEs4(LT, EQ)
new_ltEs4(EQ, LT)
new_esEs12(x0, x1, ty_Int)
new_ltEs13(x0, x1, x2)
new_lt19(x0, x1, ty_Double)
new_esEs12(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, app(ty_Ratio, x2))
new_ltEs7(Left(x0), Left(x1), ty_@0, x2)
new_esEs21(x0, x1, app(ty_[], x2))
new_primMulInt(Pos(x0), Pos(x1))
new_lt20(x0, x1, ty_Bool)
new_esEs30(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_@0)
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_asAs(True, x0)
new_primEqNat0(Succ(x0), Zero)
new_ltEs8(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Right(x0), Right(x1), x2, ty_Bool)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_ltEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs13(x0, x1)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs21(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Integer)
new_lt20(x0, x1, ty_@0)
new_esEs12(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, ty_Bool)
new_lt20(x0, x1, ty_Char)
new_esEs6(Left(x0), Left(x1), ty_Float, x2)
new_esEs12(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_Ordering)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Ordering)
new_esEs6(Right(x0), Right(x1), x2, ty_Float)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_ltEs20(x0, x1, ty_Bool)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs12(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs27(x0, x1, ty_Int)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Double)
new_esEs25(x0, x1, ty_Integer)
new_ltEs7(Right(x0), Right(x1), x2, ty_Integer)
new_primMulInt(Neg(x0), Neg(x1))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs31(x0, x1, ty_Bool)
new_lt10(x0, x1, ty_Bool)
new_primPlusNat1(Succ(x0), Zero)
new_esEs22(x0, x1, ty_Float)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs6(Left(x0), Left(x1), ty_@0, x2)
new_ltEs4(LT, LT)
new_lt11(x0, x1, x2, x3)
new_esEs10(x0, x1, ty_Integer)
new_esEs31(x0, x1, ty_Ordering)
new_esEs12(x0, x1, app(app(ty_@2, x2), x3))
new_esEs16([], [], x0)
new_ltEs19(x0, x1, ty_Integer)
new_compare23(x0, x1, False)
new_lt16(x0, x1, x2, x3, x4)
new_compare29(x0, x1, app(ty_[], x2))
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs11(x0, x1, ty_Bool)
new_esEs11(x0, x1, app(app(ty_Either, x2), x3))
new_esEs16([], :(x0, x1), x2)
new_esEs23(x0, x1, ty_Double)
new_esEs21(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_Ordering)
new_ltEs9(@2(x0, x1), @2(x2, x3), x4, x5)
new_primPlusNat1(Zero, Succ(x0))
new_ltEs12(x0, x1)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_compare10(x0, x1, False)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_primCmpNat0(Succ(x0), x1)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, ty_@0)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs22(x0, x1, ty_Bool)
new_lt19(x0, x1, ty_Float)
new_ltEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_lt19(x0, x1, ty_Integer)
new_ltEs8(Just(x0), Just(x1), ty_Char)
new_esEs7(Nothing, Just(x0), x1)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt18(x0, x1, x2)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs16(:(x0, x1), :(x2, x3), x4)
new_ltEs8(Just(x0), Just(x1), ty_Float)
new_ltEs7(Left(x0), Left(x1), ty_Float, x2)
new_lt5(x0, x1)
new_compare29(x0, x1, ty_Ordering)
new_ltEs18(x0, x1, ty_Bool)
new_esEs11(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_@0)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, ty_Int)
new_esEs11(x0, x1, ty_Char)
new_ltEs7(Left(x0), Left(x1), ty_Double, x2)
new_esEs27(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Float)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_lt19(x0, x1, ty_Ordering)
new_compare29(x0, x1, ty_Integer)
new_compare25(x0, x1, False, x2, x3)
new_esEs26(x0, x1, app(ty_[], x2))
new_ltEs18(x0, x1, ty_Float)
new_esEs9(False, False)
new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs21(x0, x1, ty_Double)
new_esEs12(x0, x1, ty_Ordering)
new_primCompAux1(x0, x1, x2, x3)
new_ltEs17(x0, x1, x2)
new_compare0([], :(x0, x1), x2)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpNat1(Succ(x0), Succ(x1))
new_esEs26(x0, x1, ty_@0)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs6(x0, x1)
new_lt10(x0, x1, ty_Float)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs22(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Float)
new_primCompAux0(x0, EQ)
new_esEs10(x0, x1, app(app(ty_Either, x2), x3))
new_compare210(x0, x1, False, x2, x3, x4)
new_esEs21(x0, x1, ty_Integer)
new_primCmpNat1(Succ(x0), Zero)
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_esEs6(Left(x0), Left(x1), ty_Bool, x2)
new_esEs7(Nothing, Nothing, x0)
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, ty_@0)
new_esEs12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, ty_Double)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_lt13(x0, x1)
new_esEs23(x0, x1, ty_Bool)
new_ltEs5(True, True)
new_ltEs7(Right(x0), Right(x1), x2, ty_Int)
new_lt19(x0, x1, ty_Int)
new_compare35(x0, x1)
new_lt19(x0, x1, ty_Char)
new_ltEs4(EQ, GT)
new_ltEs4(GT, EQ)
new_esEs31(x0, x1, ty_Integer)
new_not(True)
new_esEs11(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Float)
new_ltEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs11(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, ty_Char)
new_lt19(x0, x1, ty_@0)
new_esEs21(x0, x1, ty_Ordering)
new_ltEs8(Just(x0), Just(x1), app(ty_Maybe, x2))
new_compare0([], [], x0)
new_esEs26(x0, x1, ty_Char)
new_esEs7(Just(x0), Nothing, x1)
new_esEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs18(x0, x1, ty_Int)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Ordering)
new_not(False)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_lt14(x0, x1)
new_compare12(Char(x0), Char(x1))
new_esEs15(Char(x0), Char(x1))
new_esEs10(x0, x1, app(ty_Ratio, x2))
new_compare10(x0, x1, True)
new_lt10(x0, x1, ty_@0)
new_asAs(False, x0)
new_esEs22(x0, x1, ty_Ordering)
new_ltEs18(x0, x1, ty_Char)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_compare29(x0, x1, ty_Float)
new_compare17(x0, x1, True, x2, x3)
new_lt19(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_Char)
new_esEs31(x0, x1, ty_Char)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_ltEs8(Just(x0), Just(x1), ty_@0)
new_esEs20(@0, @0)
new_esEs6(Right(x0), Right(x1), x2, ty_Double)
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_ltEs7(Right(x0), Right(x1), x2, ty_Double)
new_esEs22(x0, x1, app(ty_[], x2))
new_ltEs7(Left(x0), Left(x1), ty_Integer, x2)
new_esEs23(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Int)
new_compare0(:(x0, x1), [], x2)
new_ltEs19(x0, x1, ty_Double)
new_esEs9(True, False)
new_esEs9(False, True)
new_esEs22(x0, x1, ty_Char)
new_compare29(x0, x1, ty_Bool)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs7(Right(x0), Right(x1), x2, ty_Float)
new_esEs30(x0, x1, ty_Double)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, ty_Integer)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs11(x0, x1, ty_Double)
new_ltEs20(x0, x1, ty_Float)
new_primCompAux0(x0, LT)
new_primCmpNat2(x0, Succ(x1))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs11(x0, x1, app(ty_[], x2))
new_ltEs7(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs12(x0, x1, ty_Integer)
new_esEs6(Left(x0), Left(x1), ty_Double, x2)
new_esEs10(x0, x1, ty_Double)
new_esEs6(Right(x0), Right(x1), x2, ty_@0)
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_sr0(Integer(x0), Integer(x1))
new_lt10(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs6(Left(x0), Left(x1), ty_Char, x2)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Pos(Zero), Pos(Zero))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_compare30(x0, x1, x2, x3)
new_ltEs18(x0, x1, ty_Double)
new_esEs12(x0, x1, ty_Double)
new_compare110(x0, x1, True, x2, x3, x4)
new_esEs12(x0, x1, ty_Bool)
new_lt9(x0, x1, x2)
new_compare9(Integer(x0), Integer(x1))
new_lt10(x0, x1, ty_Integer)
new_esEs30(x0, x1, ty_Char)
new_esEs19(Float(x0, x1), Float(x2, x3))
new_primMulNat0(Zero, Succ(x0))
new_esEs7(Just(x0), Just(x1), ty_@0)
new_ltEs4(GT, LT)
new_ltEs4(LT, GT)
new_ltEs5(True, False)
new_ltEs5(False, True)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, app(ty_[], x2))
new_ltEs7(Right(x0), Right(x1), x2, ty_@0)
new_ltEs8(Just(x0), Just(x1), ty_Int)
new_compare29(x0, x1, ty_@0)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Float)
new_compare27(x0, x1, False, x2, x3)
new_esEs23(x0, x1, ty_Float)
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs30(x0, x1, ty_Float)
new_esEs16(:(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
                                  ↳ 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_splitLT(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba) → new_splitLT3(zxw330, zxw331, zxw332, zxw333, zxw334, Nothing, h, ba)
new_splitLT2(zxw300, zxw31, zxw32, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw34, True, h, ba) → new_splitLT3(zxw330, zxw331, zxw332, zxw333, zxw334, Nothing, h, ba)
new_splitLT3(Just(zxw300), zxw31, zxw32, zxw33, zxw34, Nothing, h, ba) → new_splitLT2(zxw300, zxw31, zxw32, zxw33, zxw34, new_esEs8(new_compare26(Nothing, Just(zxw300), False, h), LT), h, ba)
new_splitLT1(zxw31, zxw32, zxw33, zxw34, True, h, ba) → new_splitLT(zxw34, h, ba)
new_splitLT3(Nothing, zxw31, zxw32, zxw33, zxw34, Nothing, h, ba) → new_splitLT1(zxw31, zxw32, zxw33, zxw34, new_esEs8(new_compare33(h), GT), h, ba)
new_splitLT10(zxw300, zxw31, zxw32, zxw33, zxw34, True, h, ba) → new_splitLT(zxw34, h, ba)
new_splitLT2(zxw300, zxw31, zxw32, zxw33, zxw34, False, h, ba) → new_splitLT10(zxw300, zxw31, zxw32, zxw33, zxw34, new_esEs8(new_compare34(zxw300, h), GT), h, ba)

The TRS R consists of the following rules:

new_compare26(Nothing, Just(zxw5000), False, bdd) → LT
new_esEs8(LT, LT) → True
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_compare34(zxw300, h) → new_compare26(Nothing, Just(zxw300), False, h)
new_esEs8(GT, GT) → True
new_esEs8(LT, GT) → False
new_esEs8(EQ, GT) → False
new_compare33(h) → new_compare26(Nothing, Nothing, True, h)
new_compare26(zxw490, zxw500, True, bdd) → EQ

The set Q consists of the following terms:

new_esEs8(GT, GT)
new_esEs8(LT, LT)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_compare26(Just(x0), Just(x1), False, x2)
new_compare26(Just(x0), Nothing, False, x1)
new_compare33(x0)
new_compare26(Nothing, Nothing, False, x0)
new_compare34(x0, x1)
new_esEs8(EQ, EQ)
new_compare26(Nothing, Just(x0), False, x1)
new_esEs8(GT, EQ)
new_esEs8(EQ, GT)
new_compare26(x0, x1, True, x2)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)

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_splitLT12(zxw15, zxw16, zxw17, zxw18, zxw19, zxw20, True, bb, bc) → new_splitLT0(zxw19, zxw20, bb, bc)
new_splitLT3(Just(zxw300), zxw31, zxw32, zxw33, zxw34, Just(zxw400), h, ba) → new_splitLT21(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs8(new_compare26(Just(zxw400), Just(zxw300), new_esEs31(zxw400, zxw300, h), h), LT), h, ba)
new_splitLT20(zxw31, zxw32, zxw33, zxw34, zxw400, False, h, ba) → new_splitLT11(zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs8(new_compare35(zxw400, h), GT), h, ba)
new_splitLT20(zxw31, zxw32, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw34, zxw400, True, h, ba) → new_splitLT3(zxw330, zxw331, zxw332, zxw333, zxw334, Just(zxw400), h, ba)
new_splitLT21(zxw15, zxw16, zxw17, zxw18, zxw19, zxw20, False, bb, bc) → new_splitLT12(zxw15, zxw16, zxw17, zxw18, zxw19, zxw20, new_esEs8(new_compare36(zxw20, zxw15, bb), GT), bb, bc)
new_splitLT0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw400, h, ba) → new_splitLT3(zxw330, zxw331, zxw332, zxw333, zxw334, Just(zxw400), h, ba)
new_splitLT11(zxw31, zxw32, zxw33, zxw34, zxw400, True, h, ba) → new_splitLT0(zxw34, zxw400, h, ba)
new_splitLT3(Nothing, zxw31, zxw32, zxw33, zxw34, Just(zxw400), h, ba) → new_splitLT20(zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs8(new_compare26(Just(zxw400), Nothing, False, h), LT), h, ba)
new_splitLT21(zxw15, zxw16, zxw17, zxw18, zxw19, zxw20, True, bb, bc) → new_splitLT0(zxw18, zxw20, bb, bc)

The TRS R consists of the following rules:

new_esEs6(Right(zxw4000), Right(zxw3000), ce, ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_esEs7(Just(zxw4000), Just(zxw3000), app(ty_Maybe, bgh)) → new_esEs7(zxw4000, zxw3000, bgh)
new_ltEs19(zxw4900, zxw5000, ty_Integer) → new_ltEs16(zxw4900, zxw5000)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_@0, cca) → new_ltEs14(zxw49000, zxw50000)
new_esEs27(zxw49000, zxw50000, app(ty_[], che)) → new_esEs16(zxw49000, zxw50000, che)
new_ltEs4(EQ, GT) → True
new_esEs22(zxw4000, zxw3000, ty_@0) → new_esEs20(zxw4000, zxw3000)
new_compare15(zxw49000, zxw50000, True, be, bf) → LT
new_ltEs9(@2(zxw49000, zxw49001), @2(zxw50000, zxw50001), beg, beh) → new_pePe(new_lt10(zxw49000, zxw50000, beg), new_asAs(new_esEs23(zxw49000, zxw50000, beg), new_ltEs18(zxw49001, zxw50001, beh)))
new_esEs6(Right(zxw4000), Right(zxw3000), ce, ty_Float) → new_esEs19(zxw4000, zxw3000)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Integer, cf) → new_esEs17(zxw4000, zxw3000)
new_esEs31(zxw400, zxw300, ty_Ordering) → new_esEs8(zxw400, zxw300)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_esEs23(zxw49000, zxw50000, app(app(ty_@2, hb), hc)) → new_esEs4(zxw49000, zxw50000, hb, hc)
new_compare29(zxw49000, zxw50000, ty_Char) → new_compare12(zxw49000, zxw50000)
new_esEs22(zxw4000, zxw3000, ty_Float) → new_esEs19(zxw4000, zxw3000)
new_esEs6(Right(zxw4000), Right(zxw3000), ce, ty_Int) → new_esEs13(zxw4000, zxw3000)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Bool) → new_ltEs5(zxw49000, zxw50000)
new_lt19(zxw49001, zxw50001, ty_Integer) → new_lt5(zxw49001, zxw50001)
new_compare33(h) → new_compare26(Nothing, Nothing, True, h)
new_esEs12(zxw4000, zxw3000, ty_Bool) → new_esEs9(zxw4000, zxw3000)
new_esEs27(zxw49000, zxw50000, app(ty_Maybe, chd)) → new_esEs7(zxw49000, zxw50000, chd)
new_esEs11(zxw4001, zxw3001, app(ty_[], eg)) → new_esEs16(zxw4001, zxw3001, eg)
new_esEs12(zxw4000, zxw3000, ty_Char) → new_esEs15(zxw4000, zxw3000)
new_compare12(Char(zxw49000), Char(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_ltEs19(zxw4900, zxw5000, ty_Double) → new_ltEs11(zxw4900, zxw5000)
new_esEs31(zxw400, zxw300, app(app(app(ty_@3, cb), cc), cd)) → new_esEs5(zxw400, zxw300, cb, cc, cd)
new_compare29(zxw49000, zxw50000, ty_Double) → new_compare16(zxw49000, zxw50000)
new_ltEs20(zxw49002, zxw50002, ty_Bool) → new_ltEs5(zxw49002, zxw50002)
new_esEs23(zxw49000, zxw50000, ty_Float) → new_esEs19(zxw49000, zxw50000)
new_lt19(zxw49001, zxw50001, ty_Ordering) → new_lt14(zxw49001, zxw50001)
new_lt19(zxw49001, zxw50001, ty_Int) → new_lt4(zxw49001, zxw50001)
new_esEs7(Just(zxw4000), Just(zxw3000), app(app(ty_Either, bhf), bhg)) → new_esEs6(zxw4000, zxw3000, bhf, bhg)
new_primMulNat0(Zero, Zero) → Zero
new_ltEs7(Left(zxw49000), Right(zxw50000), cbh, cca) → True
new_compare26(Just(zxw4900), Nothing, False, bdd) → GT
new_esEs26(zxw49001, zxw50001, app(ty_[], cgc)) → new_esEs16(zxw49001, zxw50001, cgc)
new_esEs27(zxw49000, zxw50000, ty_Bool) → new_esEs9(zxw49000, zxw50000)
new_ltEs18(zxw49001, zxw50001, ty_Integer) → new_ltEs16(zxw49001, zxw50001)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_ltEs18(zxw49001, zxw50001, app(ty_[], bfd)) → new_ltEs13(zxw49001, zxw50001, bfd)
new_ltEs20(zxw49002, zxw50002, app(ty_Maybe, ceh)) → new_ltEs8(zxw49002, zxw50002, ceh)
new_esEs11(zxw4001, zxw3001, ty_Char) → new_esEs15(zxw4001, zxw3001)
new_esEs11(zxw4001, zxw3001, ty_Float) → new_esEs19(zxw4001, zxw3001)
new_lt8(zxw49000, zxw50000) → new_esEs8(new_compare16(zxw49000, zxw50000), LT)
new_esEs26(zxw49001, zxw50001, ty_Char) → new_esEs15(zxw49001, zxw50001)
new_lt20(zxw49000, zxw50000, app(app(ty_@2, chb), chc)) → new_lt11(zxw49000, zxw50000, chb, chc)
new_esEs23(zxw49000, zxw50000, ty_Char) → new_esEs15(zxw49000, zxw50000)
new_esEs23(zxw49000, zxw50000, ty_Bool) → new_esEs9(zxw49000, zxw50000)
new_esEs27(zxw49000, zxw50000, ty_Char) → new_esEs15(zxw49000, zxw50000)
new_compare26(Nothing, Just(zxw5000), False, bdd) → LT
new_lt10(zxw49000, zxw50000, ty_Float) → new_lt7(zxw49000, zxw50000)
new_esEs21(zxw4001, zxw3001, ty_Double) → new_esEs18(zxw4001, zxw3001)
new_ltEs19(zxw4900, zxw5000, ty_Int) → new_ltEs10(zxw4900, zxw5000)
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_lt9(zxw49000, zxw50000, db) → new_esEs8(new_compare0(zxw49000, zxw50000, db), LT)
new_compare210(zxw49000, zxw50000, False, bgd, bge, bgf) → new_compare110(zxw49000, zxw50000, new_ltEs15(zxw49000, zxw50000, bgd, bge, bgf), bgd, bge, bgf)
new_esEs22(zxw4000, zxw3000, app(ty_Ratio, bcc)) → new_esEs14(zxw4000, zxw3000, bcc)
new_esEs21(zxw4001, zxw3001, app(ty_Ratio, bba)) → new_esEs14(zxw4001, zxw3001, bba)
new_esEs30(zxw20, zxw15, ty_Bool) → new_esEs9(zxw20, zxw15)
new_esEs7(Just(zxw4000), Just(zxw3000), app(app(ty_@2, bhh), caa)) → new_esEs4(zxw4000, zxw3000, bhh, caa)
new_esEs25(zxw4000, zxw3000, ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Bool) → new_esEs9(zxw4000, zxw3000)
new_esEs30(zxw20, zxw15, ty_Float) → new_esEs19(zxw20, zxw15)
new_ltEs20(zxw49002, zxw50002, ty_Integer) → new_ltEs16(zxw49002, zxw50002)
new_esEs21(zxw4001, zxw3001, app(app(ty_Either, bbf), bbg)) → new_esEs6(zxw4001, zxw3001, bbf, bbg)
new_ltEs7(Left(zxw49000), Left(zxw50000), app(app(app(ty_@3, dah), dba), dbb), cca) → new_ltEs15(zxw49000, zxw50000, dah, dba, dbb)
new_ltEs14(zxw4900, zxw5000) → new_fsEs(new_compare31(zxw4900, zxw5000))
new_compare24(zxw49000, zxw50000, False) → new_compare13(zxw49000, zxw50000, new_ltEs5(zxw49000, zxw50000))
new_esEs7(Just(zxw4000), Just(zxw3000), app(ty_Ratio, bha)) → new_esEs14(zxw4000, zxw3000, bha)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbh, app(app(ty_@2, dbf), dbg)) → new_ltEs9(zxw49000, zxw50000, dbf, dbg)
new_lt4(zxw490, zxw500) → new_esEs8(new_compare7(zxw490, zxw500), LT)
new_esEs28(zxw4000, zxw3000, app(app(app(ty_@3, ddc), ddd), dde)) → new_esEs5(zxw4000, zxw3000, ddc, ddd, dde)
new_esEs28(zxw4000, zxw3000, ty_Bool) → new_esEs9(zxw4000, zxw3000)
new_compare19(zxw490, zxw500, bdd) → new_compare26(zxw490, zxw500, new_esEs7(zxw490, zxw500, bdd), bdd)
new_esEs17(Integer(zxw4000), Integer(zxw3000)) → new_primEqInt(zxw4000, zxw3000)
new_pePe(False, zxw213) → zxw213
new_lt12(zxw490, zxw500, bdd) → new_esEs8(new_compare19(zxw490, zxw500, bdd), LT)
new_esEs31(zxw400, zxw300, app(ty_[], ca)) → new_esEs16(zxw400, zxw300, ca)
new_esEs20(@0, @0) → True
new_esEs6(Left(zxw4000), Left(zxw3000), app(app(ty_@2, cdb), cdc), cf) → new_esEs4(zxw4000, zxw3000, cdb, cdc)
new_esEs31(zxw400, zxw300, ty_Bool) → new_esEs9(zxw400, zxw300)
new_esEs6(Right(zxw4000), Right(zxw3000), ce, app(ty_Ratio, cde)) → new_esEs14(zxw4000, zxw3000, cde)
new_compare23(zxw49000, zxw50000, True) → EQ
new_esEs11(zxw4001, zxw3001, ty_Int) → new_esEs13(zxw4001, zxw3001)
new_lt19(zxw49001, zxw50001, app(ty_[], cgc)) → new_lt9(zxw49001, zxw50001, cgc)
new_compare29(zxw49000, zxw50000, ty_@0) → new_compare31(zxw49000, zxw50000)
new_compare26(Nothing, Nothing, False, bdd) → LT
new_esEs10(zxw4002, zxw3002, app(ty_Maybe, dc)) → new_esEs7(zxw4002, zxw3002, dc)
new_ltEs16(zxw4900, zxw5000) → new_fsEs(new_compare9(zxw4900, zxw5000))
new_esEs22(zxw4000, zxw3000, app(app(ty_@2, bdb), bdc)) → new_esEs4(zxw4000, zxw3000, bdb, bdc)
new_esEs23(zxw49000, zxw50000, app(ty_Maybe, bgc)) → new_esEs7(zxw49000, zxw50000, bgc)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbh, app(ty_Ratio, dcg)) → new_ltEs17(zxw49000, zxw50000, dcg)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Char, cca) → new_ltEs12(zxw49000, zxw50000)
new_esEs28(zxw4000, zxw3000, ty_@0) → new_esEs20(zxw4000, zxw3000)
new_esEs10(zxw4002, zxw3002, app(app(app(ty_@3, df), dg), dh)) → new_esEs5(zxw4002, zxw3002, df, dg, dh)
new_ltEs20(zxw49002, zxw50002, app(ty_[], cfa)) → new_ltEs13(zxw49002, zxw50002, cfa)
new_esEs27(zxw49000, zxw50000, ty_Float) → new_esEs19(zxw49000, zxw50000)
new_ltEs20(zxw49002, zxw50002, app(app(app(ty_@3, cfb), cfc), cfd)) → new_ltEs15(zxw49002, zxw50002, cfb, cfc, cfd)
new_esEs22(zxw4000, zxw3000, ty_Ordering) → new_esEs8(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Bool) → new_esEs9(zxw4000, zxw3000)
new_compare6(zxw49000, zxw50000) → new_compare23(zxw49000, zxw50000, new_esEs8(zxw49000, zxw50000))
new_esEs12(zxw4000, zxw3000, app(ty_[], gb)) → new_esEs16(zxw4000, zxw3000, gb)
new_compare32(zxw49000, zxw50000, be, bf) → new_compare25(zxw49000, zxw50000, new_esEs6(zxw49000, zxw50000, be, bf), be, bf)
new_compare29(zxw49000, zxw50000, ty_Int) → new_compare7(zxw49000, zxw50000)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Bool, cf) → new_esEs9(zxw4000, zxw3000)
new_ltEs8(Nothing, Just(zxw50000), hd) → True
new_esEs31(zxw400, zxw300, app(app(ty_@2, cg), da)) → new_esEs4(zxw400, zxw300, cg, da)
new_ltEs7(Left(zxw49000), Left(zxw50000), app(app(ty_@2, dad), dae), cca) → new_ltEs9(zxw49000, zxw50000, dad, dae)
new_esEs6(Right(zxw4000), Left(zxw3000), ce, cf) → False
new_esEs6(Left(zxw4000), Right(zxw3000), ce, cf) → False
new_esEs8(LT, LT) → True
new_lt20(zxw49000, zxw50000, ty_@0) → new_lt15(zxw49000, zxw50000)
new_esEs10(zxw4002, zxw3002, ty_Integer) → new_esEs17(zxw4002, zxw3002)
new_esEs28(zxw4000, zxw3000, ty_Float) → new_esEs19(zxw4000, zxw3000)
new_compare29(zxw49000, zxw50000, app(app(app(ty_@3, cag), cah), cba)) → new_compare28(zxw49000, zxw50000, cag, cah, cba)
new_lt19(zxw49001, zxw50001, ty_@0) → new_lt15(zxw49001, zxw50001)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbh, ty_Bool) → new_ltEs5(zxw49000, zxw50000)
new_ltEs5(True, False) → False
new_lt19(zxw49001, zxw50001, app(app(ty_@2, cfh), cga)) → new_lt11(zxw49001, zxw50001, cfh, cga)
new_compare0([], [], cab) → EQ
new_pePe(True, zxw213) → True
new_primEqNat0(Zero, Zero) → True
new_compare34(zxw300, h) → new_compare26(Nothing, Just(zxw300), False, h)
new_esEs14(:%(zxw4000, zxw4001), :%(zxw3000, zxw3001), bh) → new_asAs(new_esEs25(zxw4000, zxw3000, bh), new_esEs24(zxw4001, zxw3001, bh))
new_lt10(zxw49000, zxw50000, ty_Double) → new_lt8(zxw49000, zxw50000)
new_ltEs20(zxw49002, zxw50002, ty_Ordering) → new_ltEs4(zxw49002, zxw50002)
new_compare27(zxw49000, zxw50000, False, hb, hc) → new_compare17(zxw49000, zxw50000, new_ltEs9(zxw49000, zxw50000, hb, hc), hb, hc)
new_compare11(zxw180, zxw181, True, bd) → LT
new_esEs23(zxw49000, zxw50000, app(app(ty_Either, be), bf)) → new_esEs6(zxw49000, zxw50000, be, bf)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_@0, cf) → new_esEs20(zxw4000, zxw3000)
new_esEs6(Right(zxw4000), Right(zxw3000), ce, ty_Bool) → new_esEs9(zxw4000, zxw3000)
new_esEs12(zxw4000, zxw3000, ty_Int) → new_esEs13(zxw4000, zxw3000)
new_lt20(zxw49000, zxw50000, app(ty_[], che)) → new_lt9(zxw49000, zxw50000, che)
new_esEs6(Right(zxw4000), Right(zxw3000), ce, app(app(ty_Either, ceb), cec)) → new_esEs6(zxw4000, zxw3000, ceb, cec)
new_compare26(Just(zxw4900), Just(zxw5000), False, bdd) → new_compare11(zxw4900, zxw5000, new_ltEs19(zxw4900, zxw5000, bdd), bdd)
new_ltEs5(True, True) → True
new_ltEs7(Left(zxw49000), Left(zxw50000), app(ty_Maybe, daf), cca) → new_ltEs8(zxw49000, zxw50000, daf)
new_compare36(zxw20, zxw15, bb) → new_compare26(Just(zxw20), Just(zxw15), new_esEs30(zxw20, zxw15, bb), bb)
new_ltEs20(zxw49002, zxw50002, app(app(ty_@2, cef), ceg)) → new_ltEs9(zxw49002, zxw50002, cef, ceg)
new_esEs15(Char(zxw4000), Char(zxw3000)) → new_primEqNat0(zxw4000, zxw3000)
new_sr(zxw4001, zxw3001) → new_primMulInt(zxw4001, zxw3001)
new_ltEs18(zxw49001, zxw50001, ty_Int) → new_ltEs10(zxw49001, zxw50001)
new_esEs25(zxw4000, zxw3000, ty_Int) → new_esEs13(zxw4000, zxw3000)
new_compare7(zxw49, zxw50) → new_primCmpInt(zxw49, zxw50)
new_primCmpNat1(Zero, Zero) → EQ
new_esEs7(Just(zxw4000), Just(zxw3000), app(ty_[], bhb)) → new_esEs16(zxw4000, zxw3000, bhb)
new_lt10(zxw49000, zxw50000, ty_Int) → new_lt4(zxw49000, zxw50000)
new_esEs28(zxw4000, zxw3000, app(app(ty_Either, ddf), ddg)) → new_esEs6(zxw4000, zxw3000, ddf, ddg)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbh, app(ty_Maybe, dbh)) → new_ltEs8(zxw49000, zxw50000, dbh)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbh, ty_Integer) → new_ltEs16(zxw49000, zxw50000)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbh, app(app(app(ty_@3, dcb), dcc), dcd)) → new_ltEs15(zxw49000, zxw50000, dcb, dcc, dcd)
new_esEs26(zxw49001, zxw50001, ty_Ordering) → new_esEs8(zxw49001, zxw50001)
new_esEs8(GT, GT) → True
new_esEs27(zxw49000, zxw50000, ty_@0) → new_esEs20(zxw49000, zxw50000)
new_esEs13(zxw400, zxw300) → new_primEqInt(zxw400, zxw300)
new_lt13(zxw49000, zxw50000) → new_esEs8(new_compare18(zxw49000, zxw50000), LT)
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_lt20(zxw49000, zxw50000, ty_Ordering) → new_lt14(zxw49000, zxw50000)
new_esEs11(zxw4001, zxw3001, app(app(ty_@2, ff), fg)) → new_esEs4(zxw4001, zxw3001, ff, fg)
new_esEs11(zxw4001, zxw3001, ty_Ordering) → new_esEs8(zxw4001, zxw3001)
new_lt10(zxw49000, zxw50000, app(app(ty_@2, hb), hc)) → new_lt11(zxw49000, zxw50000, hb, hc)
new_compare23(zxw49000, zxw50000, False) → new_compare10(zxw49000, zxw50000, new_ltEs4(zxw49000, zxw50000))
new_esEs8(LT, GT) → False
new_esEs8(GT, LT) → False
new_ltEs19(zxw4900, zxw5000, app(app(app(ty_@3, cbe), cbf), cbg)) → new_ltEs15(zxw4900, zxw5000, cbe, cbf, cbg)
new_lt20(zxw49000, zxw50000, app(app(ty_Either, daa), dab)) → new_lt17(zxw49000, zxw50000, daa, dab)
new_esEs26(zxw49001, zxw50001, ty_Bool) → new_esEs9(zxw49001, zxw50001)
new_ltEs11(zxw4900, zxw5000) → new_fsEs(new_compare16(zxw4900, zxw5000))
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_compare17(zxw49000, zxw50000, True, hb, hc) → LT
new_primEqInt(Neg(Succ(zxw40000)), Neg(Succ(zxw30000))) → new_primEqNat0(zxw40000, zxw30000)
new_ltEs5(False, False) → True
new_esEs23(zxw49000, zxw50000, ty_Ordering) → new_esEs8(zxw49000, zxw50000)
new_ltEs18(zxw49001, zxw50001, app(app(ty_Either, bfh), bga)) → new_ltEs7(zxw49001, zxw50001, bfh, bga)
new_esEs28(zxw4000, zxw3000, ty_Char) → new_esEs15(zxw4000, zxw3000)
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)
new_ltEs19(zxw4900, zxw5000, app(ty_Ratio, bag)) → new_ltEs17(zxw4900, zxw5000, bag)
new_esEs10(zxw4002, zxw3002, ty_Bool) → new_esEs9(zxw4002, zxw3002)
new_lt20(zxw49000, zxw50000, ty_Char) → new_lt6(zxw49000, zxw50000)
new_compare13(zxw49000, zxw50000, False) → GT
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Bool, cca) → new_ltEs5(zxw49000, zxw50000)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Int, cca) → new_ltEs10(zxw49000, zxw50000)
new_lt11(zxw49000, zxw50000, hb, hc) → new_esEs8(new_compare30(zxw49000, zxw50000, hb, hc), LT)
new_esEs21(zxw4001, zxw3001, ty_Char) → new_esEs15(zxw4001, zxw3001)
new_lt20(zxw49000, zxw50000, ty_Int) → new_lt4(zxw49000, zxw50000)
new_primCompAux1(zxw49000, zxw50000, zxw214, cab) → new_primCompAux0(zxw214, new_compare29(zxw49000, zxw50000, cab))
new_esEs7(Just(zxw4000), Just(zxw3000), ty_@0) → new_esEs20(zxw4000, zxw3000)
new_lt16(zxw49000, zxw50000, bgd, bge, bgf) → new_esEs8(new_compare28(zxw49000, zxw50000, bgd, bge, bgf), LT)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_ltEs7(Right(zxw49000), Left(zxw50000), cbh, cca) → False
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Ordering) → new_esEs8(zxw4000, zxw3000)
new_ltEs7(Left(zxw49000), Left(zxw50000), app(ty_[], dag), cca) → new_ltEs13(zxw49000, zxw50000, dag)
new_ltEs19(zxw4900, zxw5000, ty_Ordering) → new_ltEs4(zxw4900, zxw5000)
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_ltEs20(zxw49002, zxw50002, ty_Char) → new_ltEs12(zxw49002, zxw50002)
new_esEs11(zxw4001, zxw3001, app(app(app(ty_@3, eh), fa), fb)) → new_esEs5(zxw4001, zxw3001, eh, fa, fb)
new_ltEs20(zxw49002, zxw50002, app(ty_Ratio, cfg)) → new_ltEs17(zxw49002, zxw50002, cfg)
new_ltEs18(zxw49001, zxw50001, ty_@0) → new_ltEs14(zxw49001, zxw50001)
new_primEqInt(Neg(Succ(zxw40000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(zxw30000))) → False
new_ltEs19(zxw4900, zxw5000, ty_Char) → new_ltEs12(zxw4900, zxw5000)
new_esEs12(zxw4000, zxw3000, ty_Double) → new_esEs18(zxw4000, zxw3000)
new_primCompAux0(zxw218, GT) → GT
new_esEs8(EQ, EQ) → True
new_esEs6(Left(zxw4000), Left(zxw3000), app(ty_Ratio, ccc), cf) → new_esEs14(zxw4000, zxw3000, ccc)
new_ltEs8(Just(zxw49000), Just(zxw50000), app(app(ty_Either, bad), bae)) → new_ltEs7(zxw49000, zxw50000, bad, bae)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Integer, cca) → new_ltEs16(zxw49000, zxw50000)
new_esEs6(Right(zxw4000), Right(zxw3000), ce, app(ty_[], cdf)) → new_esEs16(zxw4000, zxw3000, cdf)
new_esEs23(zxw49000, zxw50000, ty_Integer) → new_esEs17(zxw49000, zxw50000)
new_esEs28(zxw4000, zxw3000, ty_Int) → new_esEs13(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, app(app(app(ty_@3, bce), bcf), bcg)) → new_esEs5(zxw4000, zxw3000, bce, bcf, bcg)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_ltEs18(zxw49001, zxw50001, ty_Ordering) → new_ltEs4(zxw49001, zxw50001)
new_ltEs4(EQ, LT) → False
new_esEs12(zxw4000, zxw3000, app(ty_Maybe, fh)) → new_esEs7(zxw4000, zxw3000, fh)
new_lt20(zxw49000, zxw50000, ty_Double) → new_lt8(zxw49000, zxw50000)
new_esEs10(zxw4002, zxw3002, ty_Float) → new_esEs19(zxw4002, zxw3002)
new_compare11(zxw180, zxw181, False, bd) → GT
new_esEs11(zxw4001, zxw3001, ty_Bool) → new_esEs9(zxw4001, zxw3001)
new_esEs26(zxw49001, zxw50001, ty_Integer) → new_esEs17(zxw49001, zxw50001)
new_lt10(zxw49000, zxw50000, ty_Ordering) → new_lt14(zxw49000, zxw50000)
new_ltEs18(zxw49001, zxw50001, ty_Bool) → new_ltEs5(zxw49001, zxw50001)
new_primEqInt(Pos(Succ(zxw40000)), Pos(Succ(zxw30000))) → new_primEqNat0(zxw40000, zxw30000)
new_esEs12(zxw4000, zxw3000, app(app(app(ty_@3, gc), gd), ge)) → new_esEs5(zxw4000, zxw3000, gc, gd, ge)
new_compare27(zxw49000, zxw50000, True, hb, hc) → EQ
new_esEs6(Left(zxw4000), Left(zxw3000), app(app(app(ty_@3, cce), ccf), ccg), cf) → new_esEs5(zxw4000, zxw3000, cce, ccf, ccg)
new_lt18(zxw49000, zxw50000, bgg) → new_esEs8(new_compare8(zxw49000, zxw50000, bgg), LT)
new_ltEs18(zxw49001, zxw50001, app(app(app(ty_@3, bfe), bff), bfg)) → new_ltEs15(zxw49001, zxw50001, bfe, bff, bfg)
new_esEs31(zxw400, zxw300, ty_Double) → new_esEs18(zxw400, zxw300)
new_lt10(zxw49000, zxw50000, app(ty_Maybe, bgc)) → new_lt12(zxw49000, zxw50000, bgc)
new_esEs26(zxw49001, zxw50001, ty_Int) → new_esEs13(zxw49001, zxw50001)
new_ltEs8(Just(zxw49000), Just(zxw50000), app(app(ty_@2, he), hf)) → new_ltEs9(zxw49000, zxw50000, he, hf)
new_primEqNat0(Succ(zxw40000), Succ(zxw30000)) → new_primEqNat0(zxw40000, zxw30000)
new_compare29(zxw49000, zxw50000, app(ty_[], caf)) → new_compare0(zxw49000, zxw50000, caf)
new_esEs27(zxw49000, zxw50000, ty_Ordering) → new_esEs8(zxw49000, zxw50000)
new_esEs27(zxw49000, zxw50000, ty_Integer) → new_esEs17(zxw49000, zxw50000)
new_esEs23(zxw49000, zxw50000, app(ty_Ratio, bgg)) → new_esEs14(zxw49000, zxw50000, bgg)
new_ltEs18(zxw49001, zxw50001, ty_Float) → new_ltEs6(zxw49001, zxw50001)
new_esEs22(zxw4000, zxw3000, ty_Int) → new_esEs13(zxw4000, zxw3000)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbh, app(ty_[], dca)) → new_ltEs13(zxw49000, zxw50000, dca)
new_ltEs4(GT, EQ) → False
new_lt7(zxw49000, zxw50000) → new_esEs8(new_compare14(zxw49000, zxw50000), LT)
new_lt10(zxw49000, zxw50000, app(app(app(ty_@3, bgd), bge), bgf)) → new_lt16(zxw49000, zxw50000, bgd, bge, bgf)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Int) → new_esEs13(zxw4000, zxw3000)
new_ltEs19(zxw4900, zxw5000, app(app(ty_Either, cbh), cca)) → new_ltEs7(zxw4900, zxw5000, cbh, cca)
new_ltEs8(Just(zxw49000), Nothing, hd) → False
new_esEs21(zxw4001, zxw3001, ty_Float) → new_esEs19(zxw4001, zxw3001)
new_esEs26(zxw49001, zxw50001, app(app(ty_@2, cfh), cga)) → new_esEs4(zxw49001, zxw50001, cfh, cga)
new_esEs27(zxw49000, zxw50000, app(app(app(ty_@3, chf), chg), chh)) → new_esEs5(zxw49000, zxw50000, chf, chg, chh)
new_ltEs13(zxw4900, zxw5000, cab) → new_fsEs(new_compare0(zxw4900, zxw5000, cab))
new_esEs22(zxw4000, zxw3000, ty_Char) → new_esEs15(zxw4000, zxw3000)
new_esEs30(zxw20, zxw15, app(ty_Ratio, bdf)) → new_esEs14(zxw20, zxw15, bdf)
new_ltEs18(zxw49001, zxw50001, ty_Double) → new_ltEs11(zxw49001, zxw50001)
new_esEs7(Nothing, Nothing, bg) → True
new_esEs28(zxw4000, zxw3000, ty_Ordering) → new_esEs8(zxw4000, zxw3000)
new_lt10(zxw49000, zxw50000, app(app(ty_Either, be), bf)) → new_lt17(zxw49000, zxw50000, be, bf)
new_esEs8(EQ, LT) → False
new_esEs8(LT, EQ) → False
new_esEs10(zxw4002, zxw3002, ty_Char) → new_esEs15(zxw4002, zxw3002)
new_primEqInt(Pos(Succ(zxw40000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(zxw30000))) → False
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Double, cca) → new_ltEs11(zxw49000, zxw50000)
new_ltEs4(EQ, EQ) → True
new_esEs6(Right(zxw4000), Right(zxw3000), ce, app(ty_Maybe, cdd)) → new_esEs7(zxw4000, zxw3000, cdd)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbh, ty_Ordering) → new_ltEs4(zxw49000, zxw50000)
new_esEs30(zxw20, zxw15, ty_@0) → new_esEs20(zxw20, zxw15)
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_ltEs20(zxw49002, zxw50002, ty_@0) → new_ltEs14(zxw49002, zxw50002)
new_esEs23(zxw49000, zxw50000, ty_@0) → new_esEs20(zxw49000, zxw50000)
new_compare210(zxw49000, zxw50000, True, bgd, bge, bgf) → EQ
new_esEs6(Right(zxw4000), Right(zxw3000), ce, ty_@0) → new_esEs20(zxw4000, zxw3000)
new_ltEs4(GT, LT) → False
new_sr0(Integer(zxw500000), Integer(zxw490010)) → Integer(new_primMulInt(zxw500000, zxw490010))
new_compare13(zxw49000, zxw50000, True) → LT
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_compare14(Float(zxw49000, zxw49001), Float(zxw50000, zxw50001)) → new_compare7(new_sr(zxw49000, zxw50000), new_sr(zxw49001, zxw50001))
new_primEqInt(Pos(Succ(zxw40000)), Neg(zxw3000)) → False
new_primEqInt(Neg(Succ(zxw40000)), Pos(zxw3000)) → False
new_esEs7(Just(zxw4000), Nothing, bg) → False
new_esEs7(Nothing, Just(zxw3000), bg) → False
new_esEs18(Double(zxw4000, zxw4001), Double(zxw3000, zxw3001)) → new_esEs13(new_sr(zxw4000, zxw3000), new_sr(zxw4001, zxw3001))
new_ltEs5(False, True) → True
new_esEs26(zxw49001, zxw50001, ty_Double) → new_esEs18(zxw49001, zxw50001)
new_compare28(zxw49000, zxw50000, bgd, bge, bgf) → new_compare210(zxw49000, zxw50000, new_esEs5(zxw49000, zxw50000, bgd, bge, bgf), bgd, bge, bgf)
new_esEs11(zxw4001, zxw3001, ty_Double) → new_esEs18(zxw4001, zxw3001)
new_ltEs6(zxw4900, zxw5000) → new_fsEs(new_compare14(zxw4900, zxw5000))
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Ordering, cca) → new_ltEs4(zxw49000, zxw50000)
new_esEs31(zxw400, zxw300, ty_Integer) → new_esEs17(zxw400, zxw300)
new_primEqInt(Pos(Zero), Neg(Succ(zxw30000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(zxw30000))) → False
new_ltEs19(zxw4900, zxw5000, app(app(ty_@2, beg), beh)) → new_ltEs9(zxw4900, zxw5000, beg, beh)
new_ltEs20(zxw49002, zxw50002, ty_Float) → new_ltEs6(zxw49002, zxw50002)
new_compare29(zxw49000, zxw50000, app(app(ty_@2, cac), cad)) → new_compare30(zxw49000, zxw50000, cac, cad)
new_compare24(zxw49000, zxw50000, True) → EQ
new_esEs27(zxw49000, zxw50000, ty_Int) → new_esEs13(zxw49000, zxw50000)
new_ltEs18(zxw49001, zxw50001, app(app(ty_@2, bfa), bfb)) → new_ltEs9(zxw49001, zxw50001, bfa, bfb)
new_esEs6(Right(zxw4000), Right(zxw3000), ce, ty_Double) → new_esEs18(zxw4000, zxw3000)
new_lt20(zxw49000, zxw50000, ty_Bool) → new_lt13(zxw49000, zxw50000)
new_primCmpNat0(Zero, zxw4900) → LT
new_ltEs7(Right(zxw49000), Right(zxw50000), cbh, ty_Char) → new_ltEs12(zxw49000, zxw50000)
new_esEs8(EQ, GT) → False
new_esEs8(GT, EQ) → False
new_esEs10(zxw4002, zxw3002, app(ty_[], de)) → new_esEs16(zxw4002, zxw3002, de)
new_lt15(zxw49000, zxw50000) → new_esEs8(new_compare31(zxw49000, zxw50000), LT)
new_esEs31(zxw400, zxw300, ty_Int) → new_esEs13(zxw400, zxw300)
new_compare17(zxw49000, zxw50000, False, hb, hc) → GT
new_compare29(zxw49000, zxw50000, ty_Float) → new_compare14(zxw49000, zxw50000)
new_esEs30(zxw20, zxw15, ty_Double) → new_esEs18(zxw20, zxw15)
new_esEs28(zxw4000, zxw3000, app(ty_Ratio, dda)) → new_esEs14(zxw4000, zxw3000, dda)
new_compare26(zxw490, zxw500, True, bdd) → EQ
new_primCompAux0(zxw218, LT) → LT
new_esEs11(zxw4001, zxw3001, ty_@0) → new_esEs20(zxw4001, zxw3001)
new_esEs30(zxw20, zxw15, app(app(ty_Either, bec), bed)) → new_esEs6(zxw20, zxw15, bec, bed)
new_esEs12(zxw4000, zxw3000, ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_not(False) → True
new_esEs6(Left(zxw4000), Left(zxw3000), app(app(ty_Either, cch), cda), cf) → new_esEs6(zxw4000, zxw3000, cch, cda)
new_esEs28(zxw4000, zxw3000, app(ty_[], ddb)) → new_esEs16(zxw4000, zxw3000, ddb)
new_esEs24(zxw4001, zxw3001, ty_Int) → new_esEs13(zxw4001, zxw3001)
new_esEs31(zxw400, zxw300, ty_Char) → new_esEs15(zxw400, zxw300)
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_esEs26(zxw49001, zxw50001, app(ty_Ratio, cha)) → new_esEs14(zxw49001, zxw50001, cha)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Double) → new_ltEs11(zxw49000, zxw50000)
new_esEs11(zxw4001, zxw3001, app(app(ty_Either, fc), fd)) → new_esEs6(zxw4001, zxw3001, fc, fd)
new_esEs21(zxw4001, zxw3001, ty_@0) → new_esEs20(zxw4001, zxw3001)
new_esEs31(zxw400, zxw300, app(ty_Ratio, bh)) → new_esEs14(zxw400, zxw300, bh)
new_lt19(zxw49001, zxw50001, ty_Float) → new_lt7(zxw49001, zxw50001)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbh, ty_Int) → new_ltEs10(zxw49000, zxw50000)
new_compare0(:(zxw49000, zxw49001), [], cab) → GT
new_esEs12(zxw4000, zxw3000, ty_Float) → new_esEs19(zxw4000, zxw3000)
new_ltEs8(Just(zxw49000), Just(zxw50000), app(ty_[], hh)) → new_ltEs13(zxw49000, zxw50000, hh)
new_lt14(zxw49000, zxw50000) → new_esEs8(new_compare6(zxw49000, zxw50000), LT)
new_ltEs19(zxw4900, zxw5000, ty_Float) → new_ltEs6(zxw4900, zxw5000)
new_esEs27(zxw49000, zxw50000, app(app(ty_Either, daa), dab)) → new_esEs6(zxw49000, zxw50000, daa, dab)
new_lt19(zxw49001, zxw50001, app(ty_Ratio, cha)) → new_lt18(zxw49001, zxw50001, cha)
new_esEs9(True, True) → True
new_lt19(zxw49001, zxw50001, app(app(app(ty_@3, cgd), cge), cgf)) → new_lt16(zxw49001, zxw50001, cgd, cge, cgf)
new_lt19(zxw49001, zxw50001, ty_Char) → new_lt6(zxw49001, zxw50001)
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Double, cf) → new_esEs18(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, app(ty_Maybe, dch)) → new_esEs7(zxw4000, zxw3000, dch)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_esEs21(zxw4001, zxw3001, app(app(app(ty_@3, bbc), bbd), bbe)) → new_esEs5(zxw4001, zxw3001, bbc, bbd, bbe)
new_esEs22(zxw4000, zxw3000, app(ty_[], bcd)) → new_esEs16(zxw4000, zxw3000, bcd)
new_esEs21(zxw4001, zxw3001, app(ty_Maybe, bah)) → new_esEs7(zxw4001, zxw3001, bah)
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_esEs22(zxw4000, zxw3000, ty_Double) → new_esEs18(zxw4000, zxw3000)
new_esEs21(zxw4001, zxw3001, app(app(ty_@2, bbh), bca)) → new_esEs4(zxw4001, zxw3001, bbh, bca)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_@0) → new_ltEs14(zxw49000, zxw50000)
new_esEs31(zxw400, zxw300, ty_@0) → new_esEs20(zxw400, zxw300)
new_esEs19(Float(zxw4000, zxw4001), Float(zxw3000, zxw3001)) → new_esEs13(new_sr(zxw4000, zxw3000), new_sr(zxw4001, zxw3001))
new_ltEs19(zxw4900, zxw5000, app(ty_Maybe, hd)) → new_ltEs8(zxw4900, zxw5000, hd)
new_primMulInt(Neg(zxw40010), Neg(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_esEs30(zxw20, zxw15, app(ty_Maybe, bde)) → new_esEs7(zxw20, zxw15, bde)
new_primEqNat0(Zero, Succ(zxw30000)) → False
new_primEqNat0(Succ(zxw40000), Zero) → False
new_compare25(zxw49000, zxw50000, True, be, bf) → EQ
new_ltEs7(Left(zxw49000), Left(zxw50000), app(app(ty_Either, dbc), dbd), cca) → new_ltEs7(zxw49000, zxw50000, dbc, dbd)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_lt10(zxw49000, zxw50000, app(ty_Ratio, bgg)) → new_lt18(zxw49000, zxw50000, bgg)
new_esEs12(zxw4000, zxw3000, ty_@0) → new_esEs20(zxw4000, zxw3000)
new_esEs21(zxw4001, zxw3001, ty_Bool) → new_esEs9(zxw4001, zxw3001)
new_esEs5(@3(zxw4000, zxw4001, zxw4002), @3(zxw3000, zxw3001, zxw3002), cb, cc, cd) → new_asAs(new_esEs12(zxw4000, zxw3000, cb), new_asAs(new_esEs11(zxw4001, zxw3001, cc), new_esEs10(zxw4002, zxw3002, cd)))
new_esEs16(:(zxw4000, zxw4001), [], ca) → False
new_esEs16([], :(zxw3000, zxw3001), ca) → False
new_lt10(zxw49000, zxw50000, ty_Integer) → new_lt5(zxw49000, zxw50000)
new_lt6(zxw49000, zxw50000) → new_esEs8(new_compare12(zxw49000, zxw50000), LT)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_ltEs4(LT, GT) → True
new_esEs23(zxw49000, zxw50000, ty_Double) → new_esEs18(zxw49000, zxw50000)
new_compare25(zxw49000, zxw50000, False, be, bf) → new_compare15(zxw49000, zxw50000, new_ltEs7(zxw49000, zxw50000, be, bf), be, bf)
new_lt19(zxw49001, zxw50001, app(app(ty_Either, cgg), cgh)) → new_lt17(zxw49001, zxw50001, cgg, cgh)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_esEs6(Left(zxw4000), Left(zxw3000), app(ty_Maybe, ccb), cf) → new_esEs7(zxw4000, zxw3000, ccb)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Ordering, cf) → new_esEs8(zxw4000, zxw3000)
new_esEs16(:(zxw4000, zxw4001), :(zxw3000, zxw3001), ca) → new_asAs(new_esEs28(zxw4000, zxw3000, ca), new_esEs16(zxw4001, zxw3001, ca))
new_ltEs8(Just(zxw49000), Just(zxw50000), app(ty_Ratio, baf)) → new_ltEs17(zxw49000, zxw50000, baf)
new_compare0(:(zxw49000, zxw49001), :(zxw50000, zxw50001), cab) → new_primCompAux1(zxw49000, zxw50000, new_compare0(zxw49001, zxw50001, cab), cab)
new_esEs11(zxw4001, zxw3001, app(ty_Maybe, ee)) → new_esEs7(zxw4001, zxw3001, ee)
new_esEs6(Right(zxw4000), Right(zxw3000), ce, app(app(ty_@2, ced), cee)) → new_esEs4(zxw4000, zxw3000, ced, cee)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Float) → new_ltEs6(zxw49000, zxw50000)
new_compare15(zxw49000, zxw50000, False, be, bf) → GT
new_compare29(zxw49000, zxw50000, app(app(ty_Either, cbb), cbc)) → new_compare32(zxw49000, zxw50000, cbb, cbc)
new_lt20(zxw49000, zxw50000, ty_Float) → new_lt7(zxw49000, zxw50000)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Char) → new_esEs15(zxw4000, zxw3000)
new_esEs23(zxw49000, zxw50000, ty_Int) → new_esEs13(zxw49000, zxw50000)
new_esEs30(zxw20, zxw15, app(ty_[], bdg)) → new_esEs16(zxw20, zxw15, bdg)
new_esEs7(Just(zxw4000), Just(zxw3000), app(app(app(ty_@3, bhc), bhd), bhe)) → new_esEs5(zxw4000, zxw3000, bhc, bhd, bhe)
new_esEs9(True, False) → False
new_esEs9(False, True) → False
new_compare29(zxw49000, zxw50000, app(ty_Ratio, cbd)) → new_compare8(zxw49000, zxw50000, cbd)
new_esEs10(zxw4002, zxw3002, app(app(ty_@2, ec), ed)) → new_esEs4(zxw4002, zxw3002, ec, ed)
new_esEs11(zxw4001, zxw3001, app(ty_Ratio, ef)) → new_esEs14(zxw4001, zxw3001, ef)
new_compare29(zxw49000, zxw50000, ty_Ordering) → new_compare6(zxw49000, zxw50000)
new_esEs21(zxw4001, zxw3001, ty_Integer) → new_esEs17(zxw4001, zxw3001)
new_esEs27(zxw49000, zxw50000, ty_Double) → new_esEs18(zxw49000, zxw50000)
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs27(zxw49000, zxw50000, app(ty_Ratio, dac)) → new_esEs14(zxw49000, zxw50000, dac)
new_ltEs4(LT, EQ) → True
new_esEs6(Right(zxw4000), Right(zxw3000), ce, ty_Char) → new_esEs15(zxw4000, zxw3000)
new_esEs10(zxw4002, zxw3002, ty_Double) → new_esEs18(zxw4002, zxw3002)
new_compare31(@0, @0) → EQ
new_esEs31(zxw400, zxw300, ty_Float) → new_esEs19(zxw400, zxw300)
new_esEs12(zxw4000, zxw3000, app(app(ty_Either, gf), gg)) → new_esEs6(zxw4000, zxw3000, gf, gg)
new_ltEs8(Just(zxw49000), Just(zxw50000), app(ty_Maybe, hg)) → new_ltEs8(zxw49000, zxw50000, hg)
new_lt19(zxw49001, zxw50001, ty_Bool) → new_lt13(zxw49001, zxw50001)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbh, app(app(ty_Either, dce), dcf)) → new_ltEs7(zxw49000, zxw50000, dce, dcf)
new_esEs28(zxw4000, zxw3000, app(app(ty_@2, ddh), dea)) → new_esEs4(zxw4000, zxw3000, ddh, dea)
new_compare9(Integer(zxw49000), Integer(zxw50000)) → new_primCmpInt(zxw49000, zxw50000)
new_asAs(False, zxw187) → False
new_primMulInt(Neg(zxw40010), Pos(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Double) → new_esEs18(zxw4000, zxw3000)
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Ordering) → new_ltEs4(zxw49000, zxw50000)
new_esEs21(zxw4001, zxw3001, ty_Ordering) → new_esEs8(zxw4001, zxw3001)
new_primCmpNat2(zxw4900, Zero) → GT
new_ltEs20(zxw49002, zxw50002, ty_Double) → new_ltEs11(zxw49002, zxw50002)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Char, cf) → new_esEs15(zxw4000, zxw3000)
new_esEs26(zxw49001, zxw50001, app(ty_Maybe, cgb)) → new_esEs7(zxw49001, zxw50001, cgb)
new_esEs10(zxw4002, zxw3002, ty_@0) → new_esEs20(zxw4002, zxw3002)
new_lt19(zxw49001, zxw50001, ty_Double) → new_lt8(zxw49001, zxw50001)
new_esEs28(zxw4000, zxw3000, ty_Double) → new_esEs18(zxw4000, zxw3000)
new_compare110(zxw49000, zxw50000, True, bgd, bge, bgf) → LT
new_esEs24(zxw4001, zxw3001, ty_Integer) → new_esEs17(zxw4001, zxw3001)
new_lt19(zxw49001, zxw50001, app(ty_Maybe, cgb)) → new_lt12(zxw49001, zxw50001, cgb)
new_ltEs18(zxw49001, zxw50001, app(ty_Ratio, bgb)) → new_ltEs17(zxw49001, zxw50001, bgb)
new_ltEs18(zxw49001, zxw50001, ty_Char) → new_ltEs12(zxw49001, zxw50001)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Float, cf) → new_esEs19(zxw4000, zxw3000)
new_esEs21(zxw4001, zxw3001, ty_Int) → new_esEs13(zxw4001, zxw3001)
new_lt20(zxw49000, zxw50000, app(ty_Ratio, dac)) → new_lt18(zxw49000, zxw50000, dac)
new_ltEs19(zxw4900, zxw5000, ty_@0) → new_ltEs14(zxw4900, zxw5000)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbh, ty_Double) → new_ltEs11(zxw49000, zxw50000)
new_lt17(zxw49000, zxw50000, be, bf) → new_esEs8(new_compare32(zxw49000, zxw50000, be, bf), LT)
new_esEs9(False, False) → True
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Int) → new_ltEs10(zxw49000, zxw50000)
new_esEs30(zxw20, zxw15, ty_Int) → new_esEs13(zxw20, zxw15)
new_ltEs19(zxw4900, zxw5000, ty_Bool) → new_ltEs5(zxw4900, zxw5000)
new_esEs31(zxw400, zxw300, app(app(ty_Either, ce), cf)) → new_esEs6(zxw400, zxw300, ce, cf)
new_compare29(zxw49000, zxw50000, ty_Integer) → new_compare9(zxw49000, zxw50000)
new_lt20(zxw49000, zxw50000, app(app(app(ty_@3, chf), chg), chh)) → new_lt16(zxw49000, zxw50000, chf, chg, chh)
new_esEs4(@2(zxw4000, zxw4001), @2(zxw3000, zxw3001), cg, da) → new_asAs(new_esEs22(zxw4000, zxw3000, cg), new_esEs21(zxw4001, zxw3001, da))
new_ltEs20(zxw49002, zxw50002, app(app(ty_Either, cfe), cff)) → new_ltEs7(zxw49002, zxw50002, cfe, cff)
new_esEs27(zxw49000, zxw50000, app(app(ty_@2, chb), chc)) → new_esEs4(zxw49000, zxw50000, chb, chc)
new_lt20(zxw49000, zxw50000, ty_Integer) → new_lt5(zxw49000, zxw50000)
new_compare35(zxw400, h) → new_compare26(Just(zxw400), Nothing, False, h)
new_ltEs18(zxw49001, zxw50001, app(ty_Maybe, bfc)) → new_ltEs8(zxw49001, zxw50001, bfc)
new_compare8(:%(zxw49000, zxw49001), :%(zxw50000, zxw50001), ty_Integer) → new_compare9(new_sr0(zxw49000, zxw50001), new_sr0(zxw50000, zxw49001))
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Float, cca) → new_ltEs6(zxw49000, zxw50000)
new_ltEs4(LT, LT) → True
new_esEs16([], [], ca) → True
new_ltEs20(zxw49002, zxw50002, ty_Int) → new_ltEs10(zxw49002, zxw50002)
new_ltEs8(Nothing, Nothing, hd) → True
new_lt10(zxw49000, zxw50000, ty_Char) → new_lt6(zxw49000, zxw50000)
new_lt10(zxw49000, zxw50000, ty_Bool) → new_lt13(zxw49000, zxw50000)
new_esEs22(zxw4000, zxw3000, app(app(ty_Either, bch), bda)) → new_esEs6(zxw4000, zxw3000, bch, bda)
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_lt5(zxw49000, zxw50000) → new_esEs8(new_compare9(zxw49000, zxw50000), LT)
new_esEs26(zxw49001, zxw50001, ty_Float) → new_esEs19(zxw49001, zxw50001)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Int, cf) → new_esEs13(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_esEs10(zxw4002, zxw3002, ty_Int) → new_esEs13(zxw4002, zxw3002)
new_lt10(zxw49000, zxw50000, app(ty_[], db)) → new_lt9(zxw49000, zxw50000, db)
new_esEs12(zxw4000, zxw3000, app(ty_Ratio, ga)) → new_esEs14(zxw4000, zxw3000, ga)
new_ltEs15(@3(zxw49000, zxw49001, zxw49002), @3(zxw50000, zxw50001, zxw50002), cbe, cbf, cbg) → new_pePe(new_lt20(zxw49000, zxw50000, cbe), new_asAs(new_esEs27(zxw49000, zxw50000, cbe), new_pePe(new_lt19(zxw49001, zxw50001, cbf), new_asAs(new_esEs26(zxw49001, zxw50001, cbf), new_ltEs20(zxw49002, zxw50002, cbg)))))
new_ltEs10(zxw4900, zxw5000) → new_fsEs(new_compare7(zxw4900, zxw5000))
new_esEs30(zxw20, zxw15, ty_Ordering) → new_esEs8(zxw20, zxw15)
new_esEs10(zxw4002, zxw3002, app(ty_Ratio, dd)) → new_esEs14(zxw4002, zxw3002, dd)
new_ltEs12(zxw4900, zxw5000) → new_fsEs(new_compare12(zxw4900, zxw5000))
new_esEs10(zxw4002, zxw3002, ty_Ordering) → new_esEs8(zxw4002, zxw3002)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbh, ty_Float) → new_ltEs6(zxw49000, zxw50000)
new_esEs23(zxw49000, zxw50000, app(ty_[], db)) → new_esEs16(zxw49000, zxw50000, db)
new_esEs11(zxw4001, zxw3001, ty_Integer) → new_esEs17(zxw4001, zxw3001)
new_esEs26(zxw49001, zxw50001, app(app(ty_Either, cgg), cgh)) → new_esEs6(zxw49001, zxw50001, cgg, cgh)
new_compare16(Double(zxw49000, zxw49001), Double(zxw50000, zxw50001)) → new_compare7(new_sr(zxw49000, zxw50000), new_sr(zxw49001, zxw50001))
new_compare0([], :(zxw50000, zxw50001), cab) → LT
new_primPlusNat1(Zero, Zero) → Zero
new_esEs12(zxw4000, zxw3000, ty_Ordering) → new_esEs8(zxw4000, zxw3000)
new_lt10(zxw49000, zxw50000, ty_@0) → new_lt15(zxw49000, zxw50000)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Char) → new_ltEs12(zxw49000, zxw50000)
new_asAs(True, zxw187) → zxw187
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_esEs30(zxw20, zxw15, ty_Integer) → new_esEs17(zxw20, zxw15)
new_esEs26(zxw49001, zxw50001, app(app(app(ty_@3, cgd), cge), cgf)) → new_esEs5(zxw49001, zxw50001, cgd, cge, cgf)
new_esEs31(zxw400, zxw300, app(ty_Maybe, bg)) → new_esEs7(zxw400, zxw300, bg)
new_esEs10(zxw4002, zxw3002, app(app(ty_Either, ea), eb)) → new_esEs6(zxw4002, zxw3002, ea, eb)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Integer) → new_ltEs16(zxw49000, zxw50000)
new_compare30(zxw49000, zxw50000, hb, hc) → new_compare27(zxw49000, zxw50000, new_esEs4(zxw49000, zxw50000, hb, hc), hb, hc)
new_compare29(zxw49000, zxw50000, ty_Bool) → new_compare18(zxw49000, zxw50000)
new_fsEs(zxw202) → new_not(new_esEs8(zxw202, GT))
new_esEs23(zxw49000, zxw50000, app(app(app(ty_@3, bgd), bge), bgf)) → new_esEs5(zxw49000, zxw50000, bgd, bge, bgf)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Float) → new_esEs19(zxw4000, zxw3000)
new_compare10(zxw49000, zxw50000, True) → LT
new_esEs30(zxw20, zxw15, app(app(app(ty_@3, bdh), bea), beb)) → new_esEs5(zxw20, zxw15, bdh, bea, beb)
new_compare29(zxw49000, zxw50000, app(ty_Maybe, cae)) → new_compare19(zxw49000, zxw50000, cae)
new_ltEs4(GT, GT) → True
new_esEs26(zxw49001, zxw50001, ty_@0) → new_esEs20(zxw49001, zxw50001)
new_compare110(zxw49000, zxw50000, False, bgd, bge, bgf) → GT
new_ltEs7(Left(zxw49000), Left(zxw50000), app(ty_Ratio, dbe), cca) → new_ltEs17(zxw49000, zxw50000, dbe)
new_compare10(zxw49000, zxw50000, False) → GT
new_ltEs8(Just(zxw49000), Just(zxw50000), app(app(app(ty_@3, baa), bab), bac)) → new_ltEs15(zxw49000, zxw50000, baa, bab, bac)
new_esEs21(zxw4001, zxw3001, app(ty_[], bbb)) → new_esEs16(zxw4001, zxw3001, bbb)
new_compare18(zxw49000, zxw50000) → new_compare24(zxw49000, zxw50000, new_esEs9(zxw49000, zxw50000))
new_esEs6(Left(zxw4000), Left(zxw3000), app(ty_[], ccd), cf) → new_esEs16(zxw4000, zxw3000, ccd)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs6(Right(zxw4000), Right(zxw3000), ce, ty_Ordering) → new_esEs8(zxw4000, zxw3000)
new_esEs6(Right(zxw4000), Right(zxw3000), ce, app(app(app(ty_@3, cdg), cdh), cea)) → new_esEs5(zxw4000, zxw3000, cdg, cdh, cea)
new_primCompAux0(zxw218, EQ) → zxw218
new_lt20(zxw49000, zxw50000, app(ty_Maybe, chd)) → new_lt12(zxw49000, zxw50000, chd)
new_esEs12(zxw4000, zxw3000, app(app(ty_@2, gh), ha)) → new_esEs4(zxw4000, zxw3000, gh, ha)
new_ltEs19(zxw4900, zxw5000, app(ty_[], cab)) → new_ltEs13(zxw4900, zxw5000, cab)
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_esEs22(zxw4000, zxw3000, app(ty_Maybe, bcb)) → new_esEs7(zxw4000, zxw3000, bcb)
new_esEs30(zxw20, zxw15, ty_Char) → new_esEs15(zxw20, zxw15)
new_esEs30(zxw20, zxw15, app(app(ty_@2, bee), bef)) → new_esEs4(zxw20, zxw15, bee, bef)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbh, ty_@0) → new_ltEs14(zxw49000, zxw50000)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_compare8(:%(zxw49000, zxw49001), :%(zxw50000, zxw50001), ty_Int) → new_compare7(new_sr(zxw49000, zxw50001), new_sr(zxw50000, zxw49001))
new_ltEs17(zxw4900, zxw5000, bag) → new_fsEs(new_compare8(zxw4900, zxw5000, bag))
new_not(True) → False

The set Q consists of the following terms:

new_esEs17(Integer(x0), Integer(x1))
new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_ltEs7(Right(x0), Right(x1), x2, ty_Bool)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Integer)
new_lt10(x0, x1, ty_Double)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_compare18(x0, x1)
new_compare29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare29(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Double)
new_pePe(False, x0)
new_lt10(x0, x1, app(app(ty_Either, x2), x3))
new_compare29(x0, x1, app(app(ty_Either, x2), x3))
new_lt17(x0, x1, x2, x3)
new_esEs31(x0, x1, ty_Double)
new_esEs10(x0, x1, app(ty_[], x2))
new_ltEs8(Nothing, Nothing, x0)
new_compare210(x0, x1, True, x2, x3, x4)
new_compare7(x0, x1)
new_primMulNat0(Succ(x0), Zero)
new_esEs31(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(ty_[], x2))
new_esEs7(Just(x0), Just(x1), ty_Double)
new_ltEs8(Just(x0), Just(x1), ty_Integer)
new_esEs10(x0, x1, ty_Int)
new_ltEs10(x0, x1)
new_esEs28(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Ordering)
new_esEs31(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs12(x0, x1, ty_Char)
new_compare25(x0, x1, True, x2, x3)
new_primMulNat0(Succ(x0), Succ(x1))
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare8(:%(x0, x1), :%(x2, x3), ty_Int)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_ltEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs16(x0, x1)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_lt10(x0, x1, app(ty_Ratio, x2))
new_ltEs8(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs6(Right(x0), Right(x1), x2, ty_Char)
new_compare13(x0, x1, True)
new_ltEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs10(x0, x1, ty_Ordering)
new_esEs31(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, ty_Float)
new_esEs11(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_Int)
new_esEs31(x0, x1, ty_Int)
new_compare11(x0, x1, True, x2)
new_ltEs19(x0, x1, ty_Ordering)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_lt10(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(GT, GT)
new_compare11(x0, x1, False, x2)
new_esEs8(LT, LT)
new_compare29(x0, x1, ty_Double)
new_esEs18(Double(x0, x1), Double(x2, x3))
new_primCmpNat0(Zero, x0)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_ltEs8(Just(x0), Just(x1), ty_Bool)
new_ltEs8(Just(x0), Just(x1), app(ty_[], x2))
new_esEs11(x0, x1, ty_@0)
new_primCmpNat1(Zero, Succ(x0))
new_esEs31(x0, x1, app(ty_Maybe, x2))
new_esEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, ty_Int)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_sr(x0, x1)
new_ltEs5(False, False)
new_compare17(x0, x1, False, x2, x3)
new_ltEs8(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare6(x0, x1)
new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt10(x0, x1, ty_Ordering)
new_compare28(x0, x1, x2, x3, x4)
new_compare29(x0, x1, ty_Int)
new_esEs30(x0, x1, ty_Bool)
new_compare19(x0, x1, x2)
new_esEs26(x0, x1, ty_Integer)
new_primEqNat0(Zero, Succ(x0))
new_primCmpNat1(Zero, Zero)
new_compare16(Double(x0, x1), Double(x2, x3))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_lt7(x0, x1)
new_esEs28(x0, x1, ty_@0)
new_ltEs20(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_Integer)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Double)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_Char)
new_lt12(x0, x1, x2)
new_ltEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_compare15(x0, x1, True, x2, x3)
new_esEs24(x0, x1, ty_Int)
new_compare26(Just(x0), Just(x1), False, x2)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_primEqNat0(Zero, Zero)
new_compare32(x0, x1, x2, x3)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs30(x0, x1, app(ty_[], x2))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs7(Left(x0), Left(x1), ty_Char, x2)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_ltEs8(Just(x0), Just(x1), ty_Double)
new_ltEs8(Just(x0), Just(x1), ty_Ordering)
new_ltEs19(x0, x1, ty_@0)
new_compare24(x0, x1, False)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs9(True, True)
new_compare27(x0, x1, True, x2, x3)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_lt4(x0, x1)
new_ltEs8(Nothing, Just(x0), x1)
new_primMulNat0(Zero, Zero)
new_esEs23(x0, x1, ty_Char)
new_esEs30(x0, x1, ty_Ordering)
new_compare29(x0, x1, app(app(ty_@2, x2), x3))
new_esEs10(x0, x1, ty_@0)
new_lt10(x0, x1, ty_Char)
new_ltEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs30(x0, x1, ty_Int)
new_compare26(Just(x0), Nothing, False, x1)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_Integer)
new_fsEs(x0)
new_ltEs4(GT, GT)
new_lt8(x0, x1)
new_esEs6(Right(x0), Right(x1), x2, ty_Integer)
new_esEs30(x0, x1, ty_@0)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(x0, x1, ty_Float)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs28(x0, x1, ty_Double)
new_ltEs8(Just(x0), Nothing, x1)
new_esEs31(x0, x1, app(app(ty_Either, x2), x3))
new_esEs11(x0, x1, app(ty_Ratio, x2))
new_ltEs8(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt10(x0, x1, ty_Int)
new_esEs10(x0, x1, ty_Bool)
new_ltEs18(x0, x1, app(ty_[], x2))
new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs10(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs23(x0, x1, ty_Ordering)
new_esEs7(Just(x0), Just(x1), ty_Int)
new_esEs10(x0, x1, ty_Char)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_compare33(x0)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt10(x0, x1, app(ty_Maybe, x2))
new_pePe(True, x0)
new_ltEs15(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_primPlusNat0(Zero, x0)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_compare26(Nothing, Nothing, False, x0)
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Int)
new_lt6(x0, x1)
new_esEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs26(x0, x1, ty_Bool)
new_compare24(x0, x1, True)
new_ltEs18(x0, x1, ty_Integer)
new_esEs10(x0, x1, app(ty_Maybe, x2))
new_compare15(x0, x1, False, x2, x3)
new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_compare14(Float(x0, x1), Float(x2, x3))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs7(Right(x0), Left(x1), x2, x3)
new_ltEs7(Left(x0), Right(x1), x2, x3)
new_lt10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_compare110(x0, x1, False, x2, x3, x4)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_ltEs14(x0, x1)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_primPlusNat1(Zero, Zero)
new_esEs11(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Right(x0), Left(x1), x2, x3)
new_esEs6(Left(x0), Right(x1), x2, x3)
new_primCompAux0(x0, GT)
new_ltEs7(Right(x0), Right(x1), x2, ty_Char)
new_esEs6(Left(x0), Left(x1), ty_Int, x2)
new_compare23(x0, x1, True)
new_esEs31(x0, x1, ty_Float)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_compare29(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, app(ty_[], x2))
new_lt15(x0, x1)
new_esEs6(Left(x0), Left(x1), ty_Integer, x2)
new_esEs14(:%(x0, x1), :%(x2, x3), x4)
new_compare13(x0, x1, False)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_lt20(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_@0)
new_esEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_primPlusNat0(Succ(x0), x1)
new_ltEs4(EQ, EQ)
new_esEs31(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, ty_Char)
new_esEs6(Right(x0), Right(x1), x2, ty_Int)
new_ltEs11(x0, x1)
new_compare29(x0, x1, app(ty_Ratio, x2))
new_esEs12(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Integer)
new_ltEs20(x0, x1, ty_Char)
new_esEs7(Just(x0), Just(x1), ty_Char)
new_esEs12(x0, x1, ty_Float)
new_compare31(@0, @0)
new_ltEs7(Left(x0), Left(x1), ty_Int, x2)
new_esEs7(Just(x0), Just(x1), ty_Float)
new_compare36(x0, x1, x2)
new_primCmpNat2(x0, Zero)
new_ltEs4(LT, EQ)
new_ltEs4(EQ, LT)
new_esEs12(x0, x1, ty_Int)
new_ltEs13(x0, x1, x2)
new_lt19(x0, x1, ty_Double)
new_esEs12(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, app(ty_Ratio, x2))
new_ltEs7(Left(x0), Left(x1), ty_@0, x2)
new_esEs21(x0, x1, app(ty_[], x2))
new_primMulInt(Pos(x0), Pos(x1))
new_lt20(x0, x1, ty_Bool)
new_esEs30(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_@0)
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_asAs(True, x0)
new_primEqNat0(Succ(x0), Zero)
new_ltEs8(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Right(x0), Right(x1), x2, ty_Bool)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_ltEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs13(x0, x1)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs21(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Integer)
new_lt20(x0, x1, ty_@0)
new_esEs12(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, ty_Bool)
new_lt20(x0, x1, ty_Char)
new_esEs6(Left(x0), Left(x1), ty_Float, x2)
new_esEs12(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_Ordering)
new_compare34(x0, x1)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Ordering)
new_esEs6(Right(x0), Right(x1), x2, ty_Float)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_compare26(Nothing, Just(x0), False, x1)
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_ltEs20(x0, x1, ty_Bool)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs12(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs27(x0, x1, ty_Int)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Double)
new_esEs25(x0, x1, ty_Integer)
new_ltEs7(Right(x0), Right(x1), x2, ty_Integer)
new_primMulInt(Neg(x0), Neg(x1))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs31(x0, x1, ty_Bool)
new_lt10(x0, x1, ty_Bool)
new_primPlusNat1(Succ(x0), Zero)
new_esEs22(x0, x1, ty_Float)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs6(Left(x0), Left(x1), ty_@0, x2)
new_ltEs4(LT, LT)
new_lt11(x0, x1, x2, x3)
new_esEs10(x0, x1, ty_Integer)
new_esEs31(x0, x1, ty_Ordering)
new_esEs12(x0, x1, app(app(ty_@2, x2), x3))
new_esEs16([], [], x0)
new_ltEs19(x0, x1, ty_Integer)
new_compare23(x0, x1, False)
new_lt16(x0, x1, x2, x3, x4)
new_compare29(x0, x1, app(ty_[], x2))
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs11(x0, x1, ty_Bool)
new_esEs11(x0, x1, app(app(ty_Either, x2), x3))
new_esEs16([], :(x0, x1), x2)
new_esEs23(x0, x1, ty_Double)
new_esEs21(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_Ordering)
new_ltEs9(@2(x0, x1), @2(x2, x3), x4, x5)
new_primPlusNat1(Zero, Succ(x0))
new_ltEs12(x0, x1)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_compare10(x0, x1, False)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_primCmpNat0(Succ(x0), x1)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, ty_@0)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs8(GT, EQ)
new_esEs8(EQ, GT)
new_esEs22(x0, x1, ty_Bool)
new_lt19(x0, x1, ty_Float)
new_ltEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_lt19(x0, x1, ty_Integer)
new_ltEs8(Just(x0), Just(x1), ty_Char)
new_esEs7(Nothing, Just(x0), x1)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt18(x0, x1, x2)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs16(:(x0, x1), :(x2, x3), x4)
new_ltEs8(Just(x0), Just(x1), ty_Float)
new_ltEs7(Left(x0), Left(x1), ty_Float, x2)
new_lt5(x0, x1)
new_compare29(x0, x1, ty_Ordering)
new_ltEs18(x0, x1, ty_Bool)
new_esEs11(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_@0)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, ty_Int)
new_esEs11(x0, x1, ty_Char)
new_ltEs7(Left(x0), Left(x1), ty_Double, x2)
new_esEs27(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Float)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_lt19(x0, x1, ty_Ordering)
new_compare29(x0, x1, ty_Integer)
new_compare25(x0, x1, False, x2, x3)
new_esEs26(x0, x1, app(ty_[], x2))
new_ltEs18(x0, x1, ty_Float)
new_esEs9(False, False)
new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs21(x0, x1, ty_Double)
new_esEs12(x0, x1, ty_Ordering)
new_primCompAux1(x0, x1, x2, x3)
new_ltEs17(x0, x1, x2)
new_compare0([], :(x0, x1), x2)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpNat1(Succ(x0), Succ(x1))
new_esEs26(x0, x1, ty_@0)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs6(x0, x1)
new_lt10(x0, x1, ty_Float)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs22(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Float)
new_primCompAux0(x0, EQ)
new_esEs10(x0, x1, app(app(ty_Either, x2), x3))
new_compare210(x0, x1, False, x2, x3, x4)
new_esEs21(x0, x1, ty_Integer)
new_primCmpNat1(Succ(x0), Zero)
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_esEs6(Left(x0), Left(x1), ty_Bool, x2)
new_esEs7(Nothing, Nothing, x0)
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, ty_@0)
new_esEs12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, ty_Double)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_lt13(x0, x1)
new_esEs23(x0, x1, ty_Bool)
new_ltEs5(True, True)
new_ltEs7(Right(x0), Right(x1), x2, ty_Int)
new_lt19(x0, x1, ty_Int)
new_compare35(x0, x1)
new_lt19(x0, x1, ty_Char)
new_ltEs4(EQ, GT)
new_ltEs4(GT, EQ)
new_esEs31(x0, x1, ty_Integer)
new_not(True)
new_esEs11(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Float)
new_ltEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs11(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, ty_Char)
new_lt19(x0, x1, ty_@0)
new_compare26(x0, x1, True, x2)
new_esEs21(x0, x1, ty_Ordering)
new_ltEs8(Just(x0), Just(x1), app(ty_Maybe, x2))
new_compare0([], [], x0)
new_esEs26(x0, x1, ty_Char)
new_esEs7(Just(x0), Nothing, x1)
new_esEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs18(x0, x1, ty_Int)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Ordering)
new_not(False)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_lt14(x0, x1)
new_compare12(Char(x0), Char(x1))
new_esEs15(Char(x0), Char(x1))
new_esEs10(x0, x1, app(ty_Ratio, x2))
new_compare10(x0, x1, True)
new_lt10(x0, x1, ty_@0)
new_asAs(False, x0)
new_esEs22(x0, x1, ty_Ordering)
new_ltEs18(x0, x1, ty_Char)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_compare29(x0, x1, ty_Float)
new_compare17(x0, x1, True, x2, x3)
new_lt19(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_Char)
new_esEs31(x0, x1, ty_Char)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_ltEs8(Just(x0), Just(x1), ty_@0)
new_esEs20(@0, @0)
new_esEs6(Right(x0), Right(x1), x2, ty_Double)
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_ltEs7(Right(x0), Right(x1), x2, ty_Double)
new_esEs22(x0, x1, app(ty_[], x2))
new_ltEs7(Left(x0), Left(x1), ty_Integer, x2)
new_esEs23(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Int)
new_compare0(:(x0, x1), [], x2)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_ltEs19(x0, x1, ty_Double)
new_esEs9(True, False)
new_esEs9(False, True)
new_esEs22(x0, x1, ty_Char)
new_compare29(x0, x1, ty_Bool)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs7(Right(x0), Right(x1), x2, ty_Float)
new_esEs30(x0, x1, ty_Double)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, ty_Integer)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs11(x0, x1, ty_Double)
new_ltEs20(x0, x1, ty_Float)
new_primCompAux0(x0, LT)
new_primCmpNat2(x0, Succ(x1))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs11(x0, x1, app(ty_[], x2))
new_ltEs7(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs12(x0, x1, ty_Integer)
new_esEs6(Left(x0), Left(x1), ty_Double, x2)
new_esEs10(x0, x1, ty_Double)
new_esEs6(Right(x0), Right(x1), x2, ty_@0)
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_sr0(Integer(x0), Integer(x1))
new_lt10(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs6(Left(x0), Left(x1), ty_Char, x2)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Pos(Zero), Pos(Zero))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_compare30(x0, x1, x2, x3)
new_ltEs18(x0, x1, ty_Double)
new_esEs12(x0, x1, ty_Double)
new_compare110(x0, x1, True, x2, x3, x4)
new_esEs12(x0, x1, ty_Bool)
new_lt9(x0, x1, x2)
new_compare9(Integer(x0), Integer(x1))
new_lt10(x0, x1, ty_Integer)
new_esEs30(x0, x1, ty_Char)
new_esEs19(Float(x0, x1), Float(x2, x3))
new_primMulNat0(Zero, Succ(x0))
new_esEs7(Just(x0), Just(x1), ty_@0)
new_ltEs4(GT, LT)
new_ltEs4(LT, GT)
new_ltEs5(True, False)
new_ltEs5(False, True)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, app(ty_[], x2))
new_ltEs7(Right(x0), Right(x1), x2, ty_@0)
new_ltEs8(Just(x0), Just(x1), ty_Int)
new_compare29(x0, x1, ty_@0)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Float)
new_compare27(x0, x1, False, x2, x3)
new_esEs23(x0, x1, ty_Float)
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs30(x0, x1, ty_Float)
new_esEs16(:(x0, x1), [], x2)

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_splitLT12(zxw15, zxw16, zxw17, zxw18, zxw19, zxw20, True, bb, bc) → new_splitLT0(zxw19, zxw20, bb, bc)
new_splitLT3(Just(zxw300), zxw31, zxw32, zxw33, zxw34, Just(zxw400), h, ba) → new_splitLT21(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs8(new_compare26(Just(zxw400), Just(zxw300), new_esEs31(zxw400, zxw300, h), h), LT), h, ba)
new_splitLT20(zxw31, zxw32, zxw33, zxw34, zxw400, False, h, ba) → new_splitLT11(zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs8(new_compare35(zxw400, h), GT), h, ba)
new_splitLT20(zxw31, zxw32, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw34, zxw400, True, h, ba) → new_splitLT3(zxw330, zxw331, zxw332, zxw333, zxw334, Just(zxw400), h, ba)
new_splitLT21(zxw15, zxw16, zxw17, zxw18, zxw19, zxw20, False, bb, bc) → new_splitLT12(zxw15, zxw16, zxw17, zxw18, zxw19, zxw20, new_esEs8(new_compare36(zxw20, zxw15, bb), GT), bb, bc)
new_splitLT0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw400, h, ba) → new_splitLT3(zxw330, zxw331, zxw332, zxw333, zxw334, Just(zxw400), h, ba)
new_splitLT11(zxw31, zxw32, zxw33, zxw34, zxw400, True, h, ba) → new_splitLT0(zxw34, zxw400, h, ba)
new_splitLT3(Nothing, zxw31, zxw32, zxw33, zxw34, Just(zxw400), h, ba) → new_splitLT20(zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs8(new_compare26(Just(zxw400), Nothing, False, h), LT), h, ba)
new_splitLT21(zxw15, zxw16, zxw17, zxw18, zxw19, zxw20, True, bb, bc) → new_splitLT0(zxw18, zxw20, bb, bc)

The TRS R consists of the following rules:

new_compare26(Just(zxw4900), Nothing, False, bdd) → GT
new_esEs8(LT, LT) → True
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs31(zxw400, zxw300, ty_Ordering) → new_esEs8(zxw400, zxw300)
new_esEs31(zxw400, zxw300, app(app(app(ty_@3, cb), cc), cd)) → new_esEs5(zxw400, zxw300, cb, cc, cd)
new_esEs31(zxw400, zxw300, app(ty_[], ca)) → new_esEs16(zxw400, zxw300, ca)
new_esEs31(zxw400, zxw300, ty_Bool) → new_esEs9(zxw400, zxw300)
new_esEs31(zxw400, zxw300, app(app(ty_@2, cg), da)) → new_esEs4(zxw400, zxw300, cg, da)
new_esEs31(zxw400, zxw300, ty_Double) → new_esEs18(zxw400, zxw300)
new_esEs31(zxw400, zxw300, ty_Integer) → new_esEs17(zxw400, zxw300)
new_esEs31(zxw400, zxw300, ty_Int) → new_esEs13(zxw400, zxw300)
new_esEs31(zxw400, zxw300, ty_Char) → new_esEs15(zxw400, zxw300)
new_esEs31(zxw400, zxw300, app(ty_Ratio, bh)) → new_esEs14(zxw400, zxw300, bh)
new_esEs31(zxw400, zxw300, ty_@0) → new_esEs20(zxw400, zxw300)
new_esEs31(zxw400, zxw300, ty_Float) → new_esEs19(zxw400, zxw300)
new_esEs31(zxw400, zxw300, app(app(ty_Either, ce), cf)) → new_esEs6(zxw400, zxw300, ce, cf)
new_esEs31(zxw400, zxw300, app(ty_Maybe, bg)) → new_esEs7(zxw400, zxw300, bg)
new_compare26(Just(zxw4900), Just(zxw5000), False, bdd) → new_compare11(zxw4900, zxw5000, new_ltEs19(zxw4900, zxw5000, bdd), bdd)
new_compare26(zxw490, zxw500, True, bdd) → EQ
new_ltEs19(zxw4900, zxw5000, ty_Integer) → new_ltEs16(zxw4900, zxw5000)
new_ltEs19(zxw4900, zxw5000, ty_Double) → new_ltEs11(zxw4900, zxw5000)
new_ltEs19(zxw4900, zxw5000, ty_Int) → new_ltEs10(zxw4900, zxw5000)
new_ltEs19(zxw4900, zxw5000, app(app(app(ty_@3, cbe), cbf), cbg)) → new_ltEs15(zxw4900, zxw5000, cbe, cbf, cbg)
new_ltEs19(zxw4900, zxw5000, app(ty_Ratio, bag)) → new_ltEs17(zxw4900, zxw5000, bag)
new_ltEs19(zxw4900, zxw5000, ty_Ordering) → new_ltEs4(zxw4900, zxw5000)
new_ltEs19(zxw4900, zxw5000, ty_Char) → new_ltEs12(zxw4900, zxw5000)
new_ltEs19(zxw4900, zxw5000, app(app(ty_Either, cbh), cca)) → new_ltEs7(zxw4900, zxw5000, cbh, cca)
new_ltEs19(zxw4900, zxw5000, app(app(ty_@2, beg), beh)) → new_ltEs9(zxw4900, zxw5000, beg, beh)
new_ltEs19(zxw4900, zxw5000, ty_Float) → new_ltEs6(zxw4900, zxw5000)
new_ltEs19(zxw4900, zxw5000, app(ty_Maybe, hd)) → new_ltEs8(zxw4900, zxw5000, hd)
new_ltEs19(zxw4900, zxw5000, ty_@0) → new_ltEs14(zxw4900, zxw5000)
new_ltEs19(zxw4900, zxw5000, ty_Bool) → new_ltEs5(zxw4900, zxw5000)
new_ltEs19(zxw4900, zxw5000, app(ty_[], cab)) → new_ltEs13(zxw4900, zxw5000, cab)
new_compare11(zxw180, zxw181, True, bd) → LT
new_compare11(zxw180, zxw181, False, bd) → GT
new_ltEs13(zxw4900, zxw5000, cab) → new_fsEs(new_compare0(zxw4900, zxw5000, cab))
new_compare0([], [], cab) → EQ
new_compare0(:(zxw49000, zxw49001), [], cab) → GT
new_compare0(:(zxw49000, zxw49001), :(zxw50000, zxw50001), cab) → new_primCompAux1(zxw49000, zxw50000, new_compare0(zxw49001, zxw50001, cab), cab)
new_compare0([], :(zxw50000, zxw50001), cab) → LT
new_fsEs(zxw202) → new_not(new_esEs8(zxw202, GT))
new_esEs8(GT, GT) → True
new_esEs8(LT, GT) → False
new_esEs8(EQ, GT) → False
new_not(False) → True
new_not(True) → False
new_primCompAux1(zxw49000, zxw50000, zxw214, cab) → new_primCompAux0(zxw214, new_compare29(zxw49000, zxw50000, cab))
new_compare29(zxw49000, zxw50000, ty_Char) → new_compare12(zxw49000, zxw50000)
new_compare29(zxw49000, zxw50000, ty_Double) → new_compare16(zxw49000, zxw50000)
new_compare29(zxw49000, zxw50000, ty_@0) → new_compare31(zxw49000, zxw50000)
new_compare29(zxw49000, zxw50000, ty_Int) → new_compare7(zxw49000, zxw50000)
new_compare29(zxw49000, zxw50000, app(app(app(ty_@3, cag), cah), cba)) → new_compare28(zxw49000, zxw50000, cag, cah, cba)
new_compare29(zxw49000, zxw50000, app(ty_[], caf)) → new_compare0(zxw49000, zxw50000, caf)
new_compare29(zxw49000, zxw50000, app(app(ty_@2, cac), cad)) → new_compare30(zxw49000, zxw50000, cac, cad)
new_compare29(zxw49000, zxw50000, ty_Float) → new_compare14(zxw49000, zxw50000)
new_compare29(zxw49000, zxw50000, app(app(ty_Either, cbb), cbc)) → new_compare32(zxw49000, zxw50000, cbb, cbc)
new_compare29(zxw49000, zxw50000, app(ty_Ratio, cbd)) → new_compare8(zxw49000, zxw50000, cbd)
new_compare29(zxw49000, zxw50000, ty_Ordering) → new_compare6(zxw49000, zxw50000)
new_compare29(zxw49000, zxw50000, ty_Integer) → new_compare9(zxw49000, zxw50000)
new_compare29(zxw49000, zxw50000, ty_Bool) → new_compare18(zxw49000, zxw50000)
new_compare29(zxw49000, zxw50000, app(ty_Maybe, cae)) → new_compare19(zxw49000, zxw50000, cae)
new_primCompAux0(zxw218, GT) → GT
new_primCompAux0(zxw218, LT) → LT
new_primCompAux0(zxw218, EQ) → zxw218
new_compare19(zxw490, zxw500, bdd) → new_compare26(zxw490, zxw500, new_esEs7(zxw490, zxw500, bdd), bdd)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_esEs7(Just(zxw4000), Just(zxw3000), app(app(ty_@2, bhh), caa)) → new_esEs4(zxw4000, zxw3000, bhh, caa)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Bool) → new_esEs9(zxw4000, zxw3000)
new_esEs7(Just(zxw4000), Just(zxw3000), app(ty_Ratio, bha)) → new_esEs14(zxw4000, zxw3000, bha)
new_esEs7(Just(zxw4000), Just(zxw3000), app(ty_[], bhb)) → new_esEs16(zxw4000, zxw3000, bhb)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_@0) → new_esEs20(zxw4000, zxw3000)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Ordering) → new_esEs8(zxw4000, zxw3000)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Int) → new_esEs13(zxw4000, zxw3000)
new_esEs7(Nothing, Nothing, bg) → True
new_esEs7(Just(zxw4000), Nothing, bg) → False
new_esEs7(Nothing, Just(zxw3000), bg) → False
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Char) → new_esEs15(zxw4000, zxw3000)
new_esEs7(Just(zxw4000), Just(zxw3000), app(app(app(ty_@3, bhc), bhd), bhe)) → new_esEs5(zxw4000, zxw3000, bhc, bhd, bhe)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Double) → new_esEs18(zxw4000, zxw3000)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Float) → new_esEs19(zxw4000, zxw3000)
new_compare26(Nothing, Just(zxw5000), False, bdd) → LT
new_compare26(Nothing, Nothing, False, bdd) → LT
new_esEs6(Left(zxw4000), Left(zxw3000), app(ty_Maybe, ccb), cf) → new_esEs7(zxw4000, zxw3000, ccb)
new_esEs7(Just(zxw4000), Just(zxw3000), app(ty_Maybe, bgh)) → new_esEs7(zxw4000, zxw3000, bgh)
new_esEs6(Right(zxw4000), Right(zxw3000), ce, app(ty_Maybe, cdd)) → new_esEs7(zxw4000, zxw3000, cdd)
new_esEs6(Left(zxw4000), Left(zxw3000), app(app(ty_Either, cch), cda), cf) → new_esEs6(zxw4000, zxw3000, cch, cda)
new_esEs6(Right(zxw4000), Right(zxw3000), ce, app(app(ty_Either, ceb), cec)) → new_esEs6(zxw4000, zxw3000, ceb, cec)
new_esEs7(Just(zxw4000), Just(zxw3000), app(app(ty_Either, bhf), bhg)) → new_esEs6(zxw4000, zxw3000, bhf, bhg)
new_esEs6(Right(zxw4000), Right(zxw3000), ce, ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_esEs6(Right(zxw4000), Right(zxw3000), ce, ty_Float) → new_esEs19(zxw4000, zxw3000)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Integer, cf) → new_esEs17(zxw4000, zxw3000)
new_esEs6(Right(zxw4000), Right(zxw3000), ce, ty_Int) → new_esEs13(zxw4000, zxw3000)
new_esEs6(Left(zxw4000), Left(zxw3000), app(app(ty_@2, cdb), cdc), cf) → new_esEs4(zxw4000, zxw3000, cdb, cdc)
new_esEs6(Right(zxw4000), Right(zxw3000), ce, app(ty_Ratio, cde)) → new_esEs14(zxw4000, zxw3000, cde)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Bool, cf) → new_esEs9(zxw4000, zxw3000)
new_esEs6(Right(zxw4000), Left(zxw3000), ce, cf) → False
new_esEs6(Left(zxw4000), Right(zxw3000), ce, cf) → False
new_esEs6(Left(zxw4000), Left(zxw3000), ty_@0, cf) → new_esEs20(zxw4000, zxw3000)
new_esEs6(Right(zxw4000), Right(zxw3000), ce, ty_Bool) → new_esEs9(zxw4000, zxw3000)
new_esEs6(Left(zxw4000), Left(zxw3000), app(ty_Ratio, ccc), cf) → new_esEs14(zxw4000, zxw3000, ccc)
new_esEs6(Right(zxw4000), Right(zxw3000), ce, app(ty_[], cdf)) → new_esEs16(zxw4000, zxw3000, cdf)
new_esEs6(Left(zxw4000), Left(zxw3000), app(app(app(ty_@3, cce), ccf), ccg), cf) → new_esEs5(zxw4000, zxw3000, cce, ccf, ccg)
new_esEs6(Right(zxw4000), Right(zxw3000), ce, ty_@0) → new_esEs20(zxw4000, zxw3000)
new_esEs6(Right(zxw4000), Right(zxw3000), ce, ty_Double) → new_esEs18(zxw4000, zxw3000)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Double, cf) → new_esEs18(zxw4000, zxw3000)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Ordering, cf) → new_esEs8(zxw4000, zxw3000)
new_esEs6(Right(zxw4000), Right(zxw3000), ce, app(app(ty_@2, ced), cee)) → new_esEs4(zxw4000, zxw3000, ced, cee)
new_esEs6(Right(zxw4000), Right(zxw3000), ce, ty_Char) → new_esEs15(zxw4000, zxw3000)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Char, cf) → new_esEs15(zxw4000, zxw3000)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Float, cf) → new_esEs19(zxw4000, zxw3000)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Int, cf) → new_esEs13(zxw4000, zxw3000)
new_esEs6(Left(zxw4000), Left(zxw3000), app(ty_[], ccd), cf) → new_esEs16(zxw4000, zxw3000, ccd)
new_esEs6(Right(zxw4000), Right(zxw3000), ce, ty_Ordering) → new_esEs8(zxw4000, zxw3000)
new_esEs6(Right(zxw4000), Right(zxw3000), ce, app(app(app(ty_@3, cdg), cdh), cea)) → new_esEs5(zxw4000, zxw3000, cdg, cdh, cea)
new_esEs5(@3(zxw4000, zxw4001, zxw4002), @3(zxw3000, zxw3001, zxw3002), cb, cc, cd) → new_asAs(new_esEs12(zxw4000, zxw3000, cb), new_asAs(new_esEs11(zxw4001, zxw3001, cc), new_esEs10(zxw4002, zxw3002, cd)))
new_esEs12(zxw4000, zxw3000, ty_Bool) → new_esEs9(zxw4000, zxw3000)
new_esEs12(zxw4000, zxw3000, ty_Char) → new_esEs15(zxw4000, zxw3000)
new_esEs12(zxw4000, zxw3000, app(ty_[], gb)) → new_esEs16(zxw4000, zxw3000, gb)
new_esEs12(zxw4000, zxw3000, ty_Int) → new_esEs13(zxw4000, zxw3000)
new_esEs12(zxw4000, zxw3000, ty_Double) → new_esEs18(zxw4000, zxw3000)
new_esEs12(zxw4000, zxw3000, app(ty_Maybe, fh)) → new_esEs7(zxw4000, zxw3000, fh)
new_esEs12(zxw4000, zxw3000, app(app(app(ty_@3, gc), gd), ge)) → new_esEs5(zxw4000, zxw3000, gc, gd, ge)
new_esEs12(zxw4000, zxw3000, ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_esEs12(zxw4000, zxw3000, ty_Float) → new_esEs19(zxw4000, zxw3000)
new_esEs12(zxw4000, zxw3000, ty_@0) → new_esEs20(zxw4000, zxw3000)
new_esEs12(zxw4000, zxw3000, app(app(ty_Either, gf), gg)) → new_esEs6(zxw4000, zxw3000, gf, gg)
new_esEs12(zxw4000, zxw3000, app(ty_Ratio, ga)) → new_esEs14(zxw4000, zxw3000, ga)
new_esEs12(zxw4000, zxw3000, ty_Ordering) → new_esEs8(zxw4000, zxw3000)
new_esEs12(zxw4000, zxw3000, app(app(ty_@2, gh), ha)) → new_esEs4(zxw4000, zxw3000, gh, ha)
new_esEs11(zxw4001, zxw3001, app(ty_[], eg)) → new_esEs16(zxw4001, zxw3001, eg)
new_esEs11(zxw4001, zxw3001, ty_Char) → new_esEs15(zxw4001, zxw3001)
new_esEs11(zxw4001, zxw3001, ty_Float) → new_esEs19(zxw4001, zxw3001)
new_esEs11(zxw4001, zxw3001, ty_Int) → new_esEs13(zxw4001, zxw3001)
new_esEs11(zxw4001, zxw3001, app(app(ty_@2, ff), fg)) → new_esEs4(zxw4001, zxw3001, ff, fg)
new_esEs11(zxw4001, zxw3001, ty_Ordering) → new_esEs8(zxw4001, zxw3001)
new_esEs11(zxw4001, zxw3001, app(app(app(ty_@3, eh), fa), fb)) → new_esEs5(zxw4001, zxw3001, eh, fa, fb)
new_esEs11(zxw4001, zxw3001, ty_Bool) → new_esEs9(zxw4001, zxw3001)
new_esEs11(zxw4001, zxw3001, ty_Double) → new_esEs18(zxw4001, zxw3001)
new_esEs11(zxw4001, zxw3001, ty_@0) → new_esEs20(zxw4001, zxw3001)
new_esEs11(zxw4001, zxw3001, app(app(ty_Either, fc), fd)) → new_esEs6(zxw4001, zxw3001, fc, fd)
new_esEs11(zxw4001, zxw3001, app(ty_Maybe, ee)) → new_esEs7(zxw4001, zxw3001, ee)
new_esEs11(zxw4001, zxw3001, app(ty_Ratio, ef)) → new_esEs14(zxw4001, zxw3001, ef)
new_esEs11(zxw4001, zxw3001, ty_Integer) → new_esEs17(zxw4001, zxw3001)
new_esEs10(zxw4002, zxw3002, app(ty_Maybe, dc)) → new_esEs7(zxw4002, zxw3002, dc)
new_esEs10(zxw4002, zxw3002, app(app(app(ty_@3, df), dg), dh)) → new_esEs5(zxw4002, zxw3002, df, dg, dh)
new_esEs10(zxw4002, zxw3002, ty_Integer) → new_esEs17(zxw4002, zxw3002)
new_esEs10(zxw4002, zxw3002, ty_Bool) → new_esEs9(zxw4002, zxw3002)
new_esEs10(zxw4002, zxw3002, ty_Float) → new_esEs19(zxw4002, zxw3002)
new_esEs10(zxw4002, zxw3002, ty_Char) → new_esEs15(zxw4002, zxw3002)
new_esEs10(zxw4002, zxw3002, app(ty_[], de)) → new_esEs16(zxw4002, zxw3002, de)
new_esEs10(zxw4002, zxw3002, app(app(ty_@2, ec), ed)) → new_esEs4(zxw4002, zxw3002, ec, ed)
new_esEs10(zxw4002, zxw3002, ty_Double) → new_esEs18(zxw4002, zxw3002)
new_esEs10(zxw4002, zxw3002, ty_@0) → new_esEs20(zxw4002, zxw3002)
new_esEs10(zxw4002, zxw3002, ty_Int) → new_esEs13(zxw4002, zxw3002)
new_esEs10(zxw4002, zxw3002, app(ty_Ratio, dd)) → new_esEs14(zxw4002, zxw3002, dd)
new_esEs10(zxw4002, zxw3002, ty_Ordering) → new_esEs8(zxw4002, zxw3002)
new_esEs10(zxw4002, zxw3002, app(app(ty_Either, ea), eb)) → new_esEs6(zxw4002, zxw3002, ea, eb)
new_asAs(False, zxw187) → False
new_asAs(True, zxw187) → zxw187
new_esEs8(EQ, EQ) → True
new_esEs8(LT, EQ) → False
new_esEs8(GT, EQ) → False
new_esEs14(:%(zxw4000, zxw4001), :%(zxw3000, zxw3001), bh) → new_asAs(new_esEs25(zxw4000, zxw3000, bh), new_esEs24(zxw4001, zxw3001, bh))
new_esEs25(zxw4000, zxw3000, ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_esEs25(zxw4000, zxw3000, ty_Int) → new_esEs13(zxw4000, zxw3000)
new_esEs24(zxw4001, zxw3001, ty_Int) → new_esEs13(zxw4001, zxw3001)
new_esEs24(zxw4001, zxw3001, ty_Integer) → new_esEs17(zxw4001, zxw3001)
new_esEs17(Integer(zxw4000), Integer(zxw3000)) → new_primEqInt(zxw4000, zxw3000)
new_primEqInt(Neg(Succ(zxw40000)), Neg(Succ(zxw30000))) → new_primEqNat0(zxw40000, zxw30000)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Succ(zxw40000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(zxw30000))) → False
new_primEqInt(Pos(Succ(zxw40000)), Pos(Succ(zxw30000))) → new_primEqNat0(zxw40000, zxw30000)
new_primEqInt(Pos(Succ(zxw40000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(zxw30000))) → False
new_primEqInt(Pos(Succ(zxw40000)), Neg(zxw3000)) → False
new_primEqInt(Neg(Succ(zxw40000)), Pos(zxw3000)) → False
new_primEqInt(Pos(Zero), Neg(Succ(zxw30000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(zxw30000))) → False
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(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_esEs13(zxw400, zxw300) → new_primEqInt(zxw400, zxw300)
new_esEs20(@0, @0) → True
new_esEs18(Double(zxw4000, zxw4001), Double(zxw3000, zxw3001)) → new_esEs13(new_sr(zxw4000, zxw3000), new_sr(zxw4001, zxw3001))
new_sr(zxw4001, zxw3001) → new_primMulInt(zxw4001, zxw3001)
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Neg(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Pos(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulNat0(Zero, Zero) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_esEs4(@2(zxw4000, zxw4001), @2(zxw3000, zxw3001), cg, da) → new_asAs(new_esEs22(zxw4000, zxw3000, cg), new_esEs21(zxw4001, zxw3001, da))
new_esEs22(zxw4000, zxw3000, ty_@0) → new_esEs20(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Float) → new_esEs19(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, app(ty_Ratio, bcc)) → new_esEs14(zxw4000, zxw3000, bcc)
new_esEs22(zxw4000, zxw3000, app(app(ty_@2, bdb), bdc)) → new_esEs4(zxw4000, zxw3000, bdb, bdc)
new_esEs22(zxw4000, zxw3000, ty_Ordering) → new_esEs8(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Bool) → new_esEs9(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, app(app(app(ty_@3, bce), bcf), bcg)) → new_esEs5(zxw4000, zxw3000, bce, bcf, bcg)
new_esEs22(zxw4000, zxw3000, ty_Int) → new_esEs13(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Char) → new_esEs15(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, app(ty_[], bcd)) → new_esEs16(zxw4000, zxw3000, bcd)
new_esEs22(zxw4000, zxw3000, ty_Double) → new_esEs18(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, app(app(ty_Either, bch), bda)) → new_esEs6(zxw4000, zxw3000, bch, bda)
new_esEs22(zxw4000, zxw3000, ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, app(ty_Maybe, bcb)) → new_esEs7(zxw4000, zxw3000, bcb)
new_esEs21(zxw4001, zxw3001, ty_Double) → new_esEs18(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, app(ty_Ratio, bba)) → new_esEs14(zxw4001, zxw3001, bba)
new_esEs21(zxw4001, zxw3001, app(app(ty_Either, bbf), bbg)) → new_esEs6(zxw4001, zxw3001, bbf, bbg)
new_esEs21(zxw4001, zxw3001, ty_Char) → new_esEs15(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, ty_Float) → new_esEs19(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, ty_@0) → new_esEs20(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, app(app(app(ty_@3, bbc), bbd), bbe)) → new_esEs5(zxw4001, zxw3001, bbc, bbd, bbe)
new_esEs21(zxw4001, zxw3001, app(ty_Maybe, bah)) → new_esEs7(zxw4001, zxw3001, bah)
new_esEs21(zxw4001, zxw3001, app(app(ty_@2, bbh), bca)) → new_esEs4(zxw4001, zxw3001, bbh, bca)
new_esEs21(zxw4001, zxw3001, ty_Bool) → new_esEs9(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, ty_Integer) → new_esEs17(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, ty_Ordering) → new_esEs8(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, ty_Int) → new_esEs13(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, app(ty_[], bbb)) → new_esEs16(zxw4001, zxw3001, bbb)
new_esEs16(:(zxw4000, zxw4001), [], ca) → False
new_esEs16([], :(zxw3000, zxw3001), ca) → False
new_esEs16(:(zxw4000, zxw4001), :(zxw3000, zxw3001), ca) → new_asAs(new_esEs28(zxw4000, zxw3000, ca), new_esEs16(zxw4001, zxw3001, ca))
new_esEs16([], [], ca) → True
new_esEs28(zxw4000, zxw3000, ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, app(app(app(ty_@3, ddc), ddd), dde)) → new_esEs5(zxw4000, zxw3000, ddc, ddd, dde)
new_esEs28(zxw4000, zxw3000, ty_Bool) → new_esEs9(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_@0) → new_esEs20(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_Float) → new_esEs19(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, app(app(ty_Either, ddf), ddg)) → new_esEs6(zxw4000, zxw3000, ddf, ddg)
new_esEs28(zxw4000, zxw3000, ty_Char) → new_esEs15(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_Int) → new_esEs13(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_Ordering) → new_esEs8(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, app(ty_Ratio, dda)) → new_esEs14(zxw4000, zxw3000, dda)
new_esEs28(zxw4000, zxw3000, app(ty_[], ddb)) → new_esEs16(zxw4000, zxw3000, ddb)
new_esEs28(zxw4000, zxw3000, app(ty_Maybe, dch)) → new_esEs7(zxw4000, zxw3000, dch)
new_esEs28(zxw4000, zxw3000, app(app(ty_@2, ddh), dea)) → new_esEs4(zxw4000, zxw3000, ddh, dea)
new_esEs28(zxw4000, zxw3000, ty_Double) → new_esEs18(zxw4000, zxw3000)
new_esEs15(Char(zxw4000), Char(zxw3000)) → new_primEqNat0(zxw4000, zxw3000)
new_esEs19(Float(zxw4000, zxw4001), Float(zxw3000, zxw3001)) → new_esEs13(new_sr(zxw4000, zxw3000), new_sr(zxw4001, zxw3001))
new_esEs9(True, True) → True
new_esEs9(True, False) → False
new_esEs9(False, True) → False
new_esEs9(False, False) → True
new_compare18(zxw49000, zxw50000) → new_compare24(zxw49000, zxw50000, new_esEs9(zxw49000, zxw50000))
new_compare24(zxw49000, zxw50000, False) → new_compare13(zxw49000, zxw50000, new_ltEs5(zxw49000, zxw50000))
new_compare24(zxw49000, zxw50000, True) → EQ
new_ltEs5(True, False) → False
new_ltEs5(True, True) → True
new_ltEs5(False, False) → True
new_ltEs5(False, True) → True
new_compare13(zxw49000, zxw50000, False) → GT
new_compare13(zxw49000, zxw50000, True) → LT
new_compare9(Integer(zxw49000), Integer(zxw50000)) → new_primCmpInt(zxw49000, zxw50000)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_compare6(zxw49000, zxw50000) → new_compare23(zxw49000, zxw50000, new_esEs8(zxw49000, zxw50000))
new_compare23(zxw49000, zxw50000, True) → EQ
new_compare23(zxw49000, zxw50000, False) → new_compare10(zxw49000, zxw50000, new_ltEs4(zxw49000, zxw50000))
new_ltEs4(EQ, GT) → True
new_ltEs4(EQ, LT) → False
new_ltEs4(GT, EQ) → False
new_ltEs4(EQ, EQ) → True
new_ltEs4(GT, LT) → False
new_ltEs4(LT, GT) → True
new_ltEs4(LT, EQ) → True
new_ltEs4(LT, LT) → True
new_ltEs4(GT, GT) → True
new_compare10(zxw49000, zxw50000, True) → LT
new_compare10(zxw49000, zxw50000, False) → GT
new_compare8(:%(zxw49000, zxw49001), :%(zxw50000, zxw50001), ty_Integer) → new_compare9(new_sr0(zxw49000, zxw50001), new_sr0(zxw50000, zxw49001))
new_compare8(:%(zxw49000, zxw49001), :%(zxw50000, zxw50001), ty_Int) → new_compare7(new_sr(zxw49000, zxw50001), new_sr(zxw50000, zxw49001))
new_compare7(zxw49, zxw50) → new_primCmpInt(zxw49, zxw50)
new_sr0(Integer(zxw500000), Integer(zxw490010)) → Integer(new_primMulInt(zxw500000, zxw490010))
new_compare32(zxw49000, zxw50000, be, bf) → new_compare25(zxw49000, zxw50000, new_esEs6(zxw49000, zxw50000, be, bf), be, bf)
new_compare25(zxw49000, zxw50000, True, be, bf) → EQ
new_compare25(zxw49000, zxw50000, False, be, bf) → new_compare15(zxw49000, zxw50000, new_ltEs7(zxw49000, zxw50000, be, bf), be, bf)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_@0, cca) → new_ltEs14(zxw49000, zxw50000)
new_ltEs7(Left(zxw49000), Right(zxw50000), cbh, cca) → True
new_ltEs7(Left(zxw49000), Left(zxw50000), app(app(app(ty_@3, dah), dba), dbb), cca) → new_ltEs15(zxw49000, zxw50000, dah, dba, dbb)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbh, app(app(ty_@2, dbf), dbg)) → new_ltEs9(zxw49000, zxw50000, dbf, dbg)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbh, app(ty_Ratio, dcg)) → new_ltEs17(zxw49000, zxw50000, dcg)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Char, cca) → new_ltEs12(zxw49000, zxw50000)
new_ltEs7(Left(zxw49000), Left(zxw50000), app(app(ty_@2, dad), dae), cca) → new_ltEs9(zxw49000, zxw50000, dad, dae)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbh, ty_Bool) → new_ltEs5(zxw49000, zxw50000)
new_ltEs7(Left(zxw49000), Left(zxw50000), app(app(ty_Either, dbc), dbd), cca) → new_ltEs7(zxw49000, zxw50000, dbc, dbd)
new_ltEs7(Left(zxw49000), Left(zxw50000), app(ty_Maybe, daf), cca) → new_ltEs8(zxw49000, zxw50000, daf)
new_ltEs8(Just(zxw49000), Just(zxw50000), app(app(ty_Either, bad), bae)) → new_ltEs7(zxw49000, zxw50000, bad, bae)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbh, app(ty_Maybe, dbh)) → new_ltEs8(zxw49000, zxw50000, dbh)
new_ltEs8(Just(zxw49000), Just(zxw50000), app(ty_Maybe, hg)) → new_ltEs8(zxw49000, zxw50000, hg)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbh, app(app(ty_Either, dce), dcf)) → new_ltEs7(zxw49000, zxw50000, dce, dcf)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbh, ty_Integer) → new_ltEs16(zxw49000, zxw50000)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbh, app(app(app(ty_@3, dcb), dcc), dcd)) → new_ltEs15(zxw49000, zxw50000, dcb, dcc, dcd)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Bool, cca) → new_ltEs5(zxw49000, zxw50000)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Int, cca) → new_ltEs10(zxw49000, zxw50000)
new_ltEs7(Right(zxw49000), Left(zxw50000), cbh, cca) → False
new_ltEs7(Left(zxw49000), Left(zxw50000), app(ty_[], dag), cca) → new_ltEs13(zxw49000, zxw50000, dag)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Integer, cca) → new_ltEs16(zxw49000, zxw50000)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbh, app(ty_[], dca)) → new_ltEs13(zxw49000, zxw50000, dca)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Double, cca) → new_ltEs11(zxw49000, zxw50000)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbh, ty_Ordering) → new_ltEs4(zxw49000, zxw50000)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Ordering, cca) → new_ltEs4(zxw49000, zxw50000)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbh, ty_Char) → new_ltEs12(zxw49000, zxw50000)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbh, ty_Int) → new_ltEs10(zxw49000, zxw50000)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbh, ty_Double) → new_ltEs11(zxw49000, zxw50000)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Float, cca) → new_ltEs6(zxw49000, zxw50000)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbh, ty_Float) → new_ltEs6(zxw49000, zxw50000)
new_ltEs7(Left(zxw49000), Left(zxw50000), app(ty_Ratio, dbe), cca) → new_ltEs17(zxw49000, zxw50000, dbe)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbh, ty_@0) → new_ltEs14(zxw49000, zxw50000)
new_compare15(zxw49000, zxw50000, True, be, bf) → LT
new_compare15(zxw49000, zxw50000, False, be, bf) → GT
new_ltEs14(zxw4900, zxw5000) → new_fsEs(new_compare31(zxw4900, zxw5000))
new_compare31(@0, @0) → EQ
new_ltEs17(zxw4900, zxw5000, bag) → new_fsEs(new_compare8(zxw4900, zxw5000, bag))
new_ltEs6(zxw4900, zxw5000) → new_fsEs(new_compare14(zxw4900, zxw5000))
new_compare14(Float(zxw49000, zxw49001), Float(zxw50000, zxw50001)) → new_compare7(new_sr(zxw49000, zxw50000), new_sr(zxw49001, zxw50001))
new_ltEs11(zxw4900, zxw5000) → new_fsEs(new_compare16(zxw4900, zxw5000))
new_compare16(Double(zxw49000, zxw49001), Double(zxw50000, zxw50001)) → new_compare7(new_sr(zxw49000, zxw50000), new_sr(zxw49001, zxw50001))
new_ltEs10(zxw4900, zxw5000) → new_fsEs(new_compare7(zxw4900, zxw5000))
new_ltEs12(zxw4900, zxw5000) → new_fsEs(new_compare12(zxw4900, zxw5000))
new_compare12(Char(zxw49000), Char(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_ltEs16(zxw4900, zxw5000) → new_fsEs(new_compare9(zxw4900, zxw5000))
new_ltEs15(@3(zxw49000, zxw49001, zxw49002), @3(zxw50000, zxw50001, zxw50002), cbe, cbf, cbg) → new_pePe(new_lt20(zxw49000, zxw50000, cbe), new_asAs(new_esEs27(zxw49000, zxw50000, cbe), new_pePe(new_lt19(zxw49001, zxw50001, cbf), new_asAs(new_esEs26(zxw49001, zxw50001, cbf), new_ltEs20(zxw49002, zxw50002, cbg)))))
new_lt20(zxw49000, zxw50000, app(app(ty_@2, chb), chc)) → new_lt11(zxw49000, zxw50000, chb, chc)
new_lt20(zxw49000, zxw50000, ty_@0) → new_lt15(zxw49000, zxw50000)
new_lt20(zxw49000, zxw50000, app(ty_[], che)) → new_lt9(zxw49000, zxw50000, che)
new_lt20(zxw49000, zxw50000, ty_Ordering) → new_lt14(zxw49000, zxw50000)
new_lt20(zxw49000, zxw50000, app(app(ty_Either, daa), dab)) → new_lt17(zxw49000, zxw50000, daa, dab)
new_lt20(zxw49000, zxw50000, ty_Char) → new_lt6(zxw49000, zxw50000)
new_lt20(zxw49000, zxw50000, ty_Int) → new_lt4(zxw49000, zxw50000)
new_lt20(zxw49000, zxw50000, ty_Double) → new_lt8(zxw49000, zxw50000)
new_lt20(zxw49000, zxw50000, ty_Bool) → new_lt13(zxw49000, zxw50000)
new_lt20(zxw49000, zxw50000, ty_Float) → new_lt7(zxw49000, zxw50000)
new_lt20(zxw49000, zxw50000, app(ty_Ratio, dac)) → new_lt18(zxw49000, zxw50000, dac)
new_lt20(zxw49000, zxw50000, app(app(app(ty_@3, chf), chg), chh)) → new_lt16(zxw49000, zxw50000, chf, chg, chh)
new_lt20(zxw49000, zxw50000, ty_Integer) → new_lt5(zxw49000, zxw50000)
new_lt20(zxw49000, zxw50000, app(ty_Maybe, chd)) → new_lt12(zxw49000, zxw50000, chd)
new_esEs27(zxw49000, zxw50000, app(ty_[], che)) → new_esEs16(zxw49000, zxw50000, che)
new_esEs27(zxw49000, zxw50000, app(ty_Maybe, chd)) → new_esEs7(zxw49000, zxw50000, chd)
new_esEs27(zxw49000, zxw50000, ty_Bool) → new_esEs9(zxw49000, zxw50000)
new_esEs27(zxw49000, zxw50000, ty_Char) → new_esEs15(zxw49000, zxw50000)
new_esEs27(zxw49000, zxw50000, ty_Float) → new_esEs19(zxw49000, zxw50000)
new_esEs27(zxw49000, zxw50000, ty_@0) → new_esEs20(zxw49000, zxw50000)
new_esEs27(zxw49000, zxw50000, ty_Ordering) → new_esEs8(zxw49000, zxw50000)
new_esEs27(zxw49000, zxw50000, ty_Integer) → new_esEs17(zxw49000, zxw50000)
new_esEs27(zxw49000, zxw50000, app(app(app(ty_@3, chf), chg), chh)) → new_esEs5(zxw49000, zxw50000, chf, chg, chh)
new_esEs27(zxw49000, zxw50000, ty_Int) → new_esEs13(zxw49000, zxw50000)
new_esEs27(zxw49000, zxw50000, app(app(ty_Either, daa), dab)) → new_esEs6(zxw49000, zxw50000, daa, dab)
new_esEs27(zxw49000, zxw50000, ty_Double) → new_esEs18(zxw49000, zxw50000)
new_esEs27(zxw49000, zxw50000, app(ty_Ratio, dac)) → new_esEs14(zxw49000, zxw50000, dac)
new_esEs27(zxw49000, zxw50000, app(app(ty_@2, chb), chc)) → new_esEs4(zxw49000, zxw50000, chb, chc)
new_lt19(zxw49001, zxw50001, ty_Integer) → new_lt5(zxw49001, zxw50001)
new_lt19(zxw49001, zxw50001, ty_Ordering) → new_lt14(zxw49001, zxw50001)
new_lt19(zxw49001, zxw50001, ty_Int) → new_lt4(zxw49001, zxw50001)
new_lt19(zxw49001, zxw50001, app(ty_[], cgc)) → new_lt9(zxw49001, zxw50001, cgc)
new_lt19(zxw49001, zxw50001, ty_@0) → new_lt15(zxw49001, zxw50001)
new_lt19(zxw49001, zxw50001, app(app(ty_@2, cfh), cga)) → new_lt11(zxw49001, zxw50001, cfh, cga)
new_lt19(zxw49001, zxw50001, ty_Float) → new_lt7(zxw49001, zxw50001)
new_lt19(zxw49001, zxw50001, app(ty_Ratio, cha)) → new_lt18(zxw49001, zxw50001, cha)
new_lt19(zxw49001, zxw50001, app(app(app(ty_@3, cgd), cge), cgf)) → new_lt16(zxw49001, zxw50001, cgd, cge, cgf)
new_lt19(zxw49001, zxw50001, ty_Char) → new_lt6(zxw49001, zxw50001)
new_lt19(zxw49001, zxw50001, app(app(ty_Either, cgg), cgh)) → new_lt17(zxw49001, zxw50001, cgg, cgh)
new_lt19(zxw49001, zxw50001, ty_Bool) → new_lt13(zxw49001, zxw50001)
new_lt19(zxw49001, zxw50001, ty_Double) → new_lt8(zxw49001, zxw50001)
new_lt19(zxw49001, zxw50001, app(ty_Maybe, cgb)) → new_lt12(zxw49001, zxw50001, cgb)
new_esEs26(zxw49001, zxw50001, app(ty_[], cgc)) → new_esEs16(zxw49001, zxw50001, cgc)
new_esEs26(zxw49001, zxw50001, ty_Char) → new_esEs15(zxw49001, zxw50001)
new_esEs26(zxw49001, zxw50001, ty_Ordering) → new_esEs8(zxw49001, zxw50001)
new_esEs26(zxw49001, zxw50001, ty_Bool) → new_esEs9(zxw49001, zxw50001)
new_esEs26(zxw49001, zxw50001, ty_Integer) → new_esEs17(zxw49001, zxw50001)
new_esEs26(zxw49001, zxw50001, ty_Int) → new_esEs13(zxw49001, zxw50001)
new_esEs26(zxw49001, zxw50001, app(app(ty_@2, cfh), cga)) → new_esEs4(zxw49001, zxw50001, cfh, cga)
new_esEs26(zxw49001, zxw50001, ty_Double) → new_esEs18(zxw49001, zxw50001)
new_esEs26(zxw49001, zxw50001, app(ty_Ratio, cha)) → new_esEs14(zxw49001, zxw50001, cha)
new_esEs26(zxw49001, zxw50001, app(ty_Maybe, cgb)) → new_esEs7(zxw49001, zxw50001, cgb)
new_esEs26(zxw49001, zxw50001, ty_Float) → new_esEs19(zxw49001, zxw50001)
new_esEs26(zxw49001, zxw50001, app(app(ty_Either, cgg), cgh)) → new_esEs6(zxw49001, zxw50001, cgg, cgh)
new_esEs26(zxw49001, zxw50001, app(app(app(ty_@3, cgd), cge), cgf)) → new_esEs5(zxw49001, zxw50001, cgd, cge, cgf)
new_esEs26(zxw49001, zxw50001, ty_@0) → new_esEs20(zxw49001, zxw50001)
new_ltEs20(zxw49002, zxw50002, ty_Bool) → new_ltEs5(zxw49002, zxw50002)
new_ltEs20(zxw49002, zxw50002, app(ty_Maybe, ceh)) → new_ltEs8(zxw49002, zxw50002, ceh)
new_ltEs20(zxw49002, zxw50002, ty_Integer) → new_ltEs16(zxw49002, zxw50002)
new_ltEs20(zxw49002, zxw50002, app(ty_[], cfa)) → new_ltEs13(zxw49002, zxw50002, cfa)
new_ltEs20(zxw49002, zxw50002, app(app(app(ty_@3, cfb), cfc), cfd)) → new_ltEs15(zxw49002, zxw50002, cfb, cfc, cfd)
new_ltEs20(zxw49002, zxw50002, ty_Ordering) → new_ltEs4(zxw49002, zxw50002)
new_ltEs20(zxw49002, zxw50002, app(app(ty_@2, cef), ceg)) → new_ltEs9(zxw49002, zxw50002, cef, ceg)
new_ltEs20(zxw49002, zxw50002, ty_Char) → new_ltEs12(zxw49002, zxw50002)
new_ltEs20(zxw49002, zxw50002, app(ty_Ratio, cfg)) → new_ltEs17(zxw49002, zxw50002, cfg)
new_ltEs20(zxw49002, zxw50002, ty_@0) → new_ltEs14(zxw49002, zxw50002)
new_ltEs20(zxw49002, zxw50002, ty_Float) → new_ltEs6(zxw49002, zxw50002)
new_ltEs20(zxw49002, zxw50002, ty_Double) → new_ltEs11(zxw49002, zxw50002)
new_ltEs20(zxw49002, zxw50002, app(app(ty_Either, cfe), cff)) → new_ltEs7(zxw49002, zxw50002, cfe, cff)
new_ltEs20(zxw49002, zxw50002, ty_Int) → new_ltEs10(zxw49002, zxw50002)
new_pePe(False, zxw213) → zxw213
new_pePe(True, zxw213) → True
new_ltEs9(@2(zxw49000, zxw49001), @2(zxw50000, zxw50001), beg, beh) → new_pePe(new_lt10(zxw49000, zxw50000, beg), new_asAs(new_esEs23(zxw49000, zxw50000, beg), new_ltEs18(zxw49001, zxw50001, beh)))
new_lt10(zxw49000, zxw50000, ty_Float) → new_lt7(zxw49000, zxw50000)
new_lt10(zxw49000, zxw50000, ty_Double) → new_lt8(zxw49000, zxw50000)
new_lt10(zxw49000, zxw50000, ty_Int) → new_lt4(zxw49000, zxw50000)
new_lt10(zxw49000, zxw50000, app(app(ty_@2, hb), hc)) → new_lt11(zxw49000, zxw50000, hb, hc)
new_lt10(zxw49000, zxw50000, ty_Ordering) → new_lt14(zxw49000, zxw50000)
new_lt10(zxw49000, zxw50000, app(ty_Maybe, bgc)) → new_lt12(zxw49000, zxw50000, bgc)
new_lt10(zxw49000, zxw50000, app(app(app(ty_@3, bgd), bge), bgf)) → new_lt16(zxw49000, zxw50000, bgd, bge, bgf)
new_lt10(zxw49000, zxw50000, app(app(ty_Either, be), bf)) → new_lt17(zxw49000, zxw50000, be, bf)
new_lt10(zxw49000, zxw50000, app(ty_Ratio, bgg)) → new_lt18(zxw49000, zxw50000, bgg)
new_lt10(zxw49000, zxw50000, ty_Integer) → new_lt5(zxw49000, zxw50000)
new_lt10(zxw49000, zxw50000, ty_Char) → new_lt6(zxw49000, zxw50000)
new_lt10(zxw49000, zxw50000, ty_Bool) → new_lt13(zxw49000, zxw50000)
new_lt10(zxw49000, zxw50000, app(ty_[], db)) → new_lt9(zxw49000, zxw50000, db)
new_lt10(zxw49000, zxw50000, ty_@0) → new_lt15(zxw49000, zxw50000)
new_esEs23(zxw49000, zxw50000, app(app(ty_@2, hb), hc)) → new_esEs4(zxw49000, zxw50000, hb, hc)
new_esEs23(zxw49000, zxw50000, ty_Float) → new_esEs19(zxw49000, zxw50000)
new_esEs23(zxw49000, zxw50000, ty_Char) → new_esEs15(zxw49000, zxw50000)
new_esEs23(zxw49000, zxw50000, ty_Bool) → new_esEs9(zxw49000, zxw50000)
new_esEs23(zxw49000, zxw50000, app(ty_Maybe, bgc)) → new_esEs7(zxw49000, zxw50000, bgc)
new_esEs23(zxw49000, zxw50000, app(app(ty_Either, be), bf)) → new_esEs6(zxw49000, zxw50000, be, bf)
new_esEs23(zxw49000, zxw50000, ty_Ordering) → new_esEs8(zxw49000, zxw50000)
new_esEs23(zxw49000, zxw50000, ty_Integer) → new_esEs17(zxw49000, zxw50000)
new_esEs23(zxw49000, zxw50000, app(ty_Ratio, bgg)) → new_esEs14(zxw49000, zxw50000, bgg)
new_esEs23(zxw49000, zxw50000, ty_@0) → new_esEs20(zxw49000, zxw50000)
new_esEs23(zxw49000, zxw50000, ty_Double) → new_esEs18(zxw49000, zxw50000)
new_esEs23(zxw49000, zxw50000, ty_Int) → new_esEs13(zxw49000, zxw50000)
new_esEs23(zxw49000, zxw50000, app(ty_[], db)) → new_esEs16(zxw49000, zxw50000, db)
new_esEs23(zxw49000, zxw50000, app(app(app(ty_@3, bgd), bge), bgf)) → new_esEs5(zxw49000, zxw50000, bgd, bge, bgf)
new_ltEs18(zxw49001, zxw50001, ty_Integer) → new_ltEs16(zxw49001, zxw50001)
new_ltEs18(zxw49001, zxw50001, app(ty_[], bfd)) → new_ltEs13(zxw49001, zxw50001, bfd)
new_ltEs18(zxw49001, zxw50001, ty_Int) → new_ltEs10(zxw49001, zxw50001)
new_ltEs18(zxw49001, zxw50001, app(app(ty_Either, bfh), bga)) → new_ltEs7(zxw49001, zxw50001, bfh, bga)
new_ltEs18(zxw49001, zxw50001, ty_@0) → new_ltEs14(zxw49001, zxw50001)
new_ltEs18(zxw49001, zxw50001, ty_Ordering) → new_ltEs4(zxw49001, zxw50001)
new_ltEs18(zxw49001, zxw50001, ty_Bool) → new_ltEs5(zxw49001, zxw50001)
new_ltEs18(zxw49001, zxw50001, app(app(app(ty_@3, bfe), bff), bfg)) → new_ltEs15(zxw49001, zxw50001, bfe, bff, bfg)
new_ltEs18(zxw49001, zxw50001, ty_Float) → new_ltEs6(zxw49001, zxw50001)
new_ltEs18(zxw49001, zxw50001, ty_Double) → new_ltEs11(zxw49001, zxw50001)
new_ltEs18(zxw49001, zxw50001, app(app(ty_@2, bfa), bfb)) → new_ltEs9(zxw49001, zxw50001, bfa, bfb)
new_ltEs18(zxw49001, zxw50001, app(ty_Ratio, bgb)) → new_ltEs17(zxw49001, zxw50001, bgb)
new_ltEs18(zxw49001, zxw50001, ty_Char) → new_ltEs12(zxw49001, zxw50001)
new_ltEs18(zxw49001, zxw50001, app(ty_Maybe, bfc)) → new_ltEs8(zxw49001, zxw50001, bfc)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Bool) → new_ltEs5(zxw49000, zxw50000)
new_ltEs8(Nothing, Just(zxw50000), hd) → True
new_ltEs8(Just(zxw49000), Just(zxw50000), app(app(ty_@2, he), hf)) → new_ltEs9(zxw49000, zxw50000, he, hf)
new_ltEs8(Just(zxw49000), Nothing, hd) → False
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Double) → new_ltEs11(zxw49000, zxw50000)
new_ltEs8(Just(zxw49000), Just(zxw50000), app(ty_[], hh)) → new_ltEs13(zxw49000, zxw50000, hh)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_@0) → new_ltEs14(zxw49000, zxw50000)
new_ltEs8(Just(zxw49000), Just(zxw50000), app(ty_Ratio, baf)) → new_ltEs17(zxw49000, zxw50000, baf)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Float) → new_ltEs6(zxw49000, zxw50000)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Ordering) → new_ltEs4(zxw49000, zxw50000)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Int) → new_ltEs10(zxw49000, zxw50000)
new_ltEs8(Nothing, Nothing, hd) → True
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Char) → new_ltEs12(zxw49000, zxw50000)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Integer) → new_ltEs16(zxw49000, zxw50000)
new_ltEs8(Just(zxw49000), Just(zxw50000), app(app(app(ty_@3, baa), bab), bac)) → new_ltEs15(zxw49000, zxw50000, baa, bab, bac)
new_lt15(zxw49000, zxw50000) → new_esEs8(new_compare31(zxw49000, zxw50000), LT)
new_lt9(zxw49000, zxw50000, db) → new_esEs8(new_compare0(zxw49000, zxw50000, db), LT)
new_lt13(zxw49000, zxw50000) → new_esEs8(new_compare18(zxw49000, zxw50000), LT)
new_lt6(zxw49000, zxw50000) → new_esEs8(new_compare12(zxw49000, zxw50000), LT)
new_lt5(zxw49000, zxw50000) → new_esEs8(new_compare9(zxw49000, zxw50000), LT)
new_lt18(zxw49000, zxw50000, bgg) → new_esEs8(new_compare8(zxw49000, zxw50000, bgg), LT)
new_lt17(zxw49000, zxw50000, be, bf) → new_esEs8(new_compare32(zxw49000, zxw50000, be, bf), LT)
new_lt16(zxw49000, zxw50000, bgd, bge, bgf) → new_esEs8(new_compare28(zxw49000, zxw50000, bgd, bge, bgf), LT)
new_compare28(zxw49000, zxw50000, bgd, bge, bgf) → new_compare210(zxw49000, zxw50000, new_esEs5(zxw49000, zxw50000, bgd, bge, bgf), bgd, bge, bgf)
new_compare210(zxw49000, zxw50000, False, bgd, bge, bgf) → new_compare110(zxw49000, zxw50000, new_ltEs15(zxw49000, zxw50000, bgd, bge, bgf), bgd, bge, bgf)
new_compare210(zxw49000, zxw50000, True, bgd, bge, bgf) → EQ
new_compare110(zxw49000, zxw50000, True, bgd, bge, bgf) → LT
new_compare110(zxw49000, zxw50000, False, bgd, bge, bgf) → GT
new_lt12(zxw490, zxw500, bdd) → new_esEs8(new_compare19(zxw490, zxw500, bdd), LT)
new_lt14(zxw49000, zxw50000) → new_esEs8(new_compare6(zxw49000, zxw50000), LT)
new_lt11(zxw49000, zxw50000, hb, hc) → new_esEs8(new_compare30(zxw49000, zxw50000, hb, hc), LT)
new_compare30(zxw49000, zxw50000, hb, hc) → new_compare27(zxw49000, zxw50000, new_esEs4(zxw49000, zxw50000, hb, hc), hb, hc)
new_compare27(zxw49000, zxw50000, False, hb, hc) → new_compare17(zxw49000, zxw50000, new_ltEs9(zxw49000, zxw50000, hb, hc), hb, hc)
new_compare27(zxw49000, zxw50000, True, hb, hc) → EQ
new_compare17(zxw49000, zxw50000, True, hb, hc) → LT
new_compare17(zxw49000, zxw50000, False, hb, hc) → GT
new_lt4(zxw490, zxw500) → new_esEs8(new_compare7(zxw490, zxw500), LT)
new_lt8(zxw49000, zxw50000) → new_esEs8(new_compare16(zxw49000, zxw50000), LT)
new_lt7(zxw49000, zxw50000) → new_esEs8(new_compare14(zxw49000, zxw50000), LT)
new_compare36(zxw20, zxw15, bb) → new_compare26(Just(zxw20), Just(zxw15), new_esEs30(zxw20, zxw15, bb), bb)
new_esEs30(zxw20, zxw15, ty_Bool) → new_esEs9(zxw20, zxw15)
new_esEs30(zxw20, zxw15, ty_Float) → new_esEs19(zxw20, zxw15)
new_esEs30(zxw20, zxw15, app(ty_Ratio, bdf)) → new_esEs14(zxw20, zxw15, bdf)
new_esEs30(zxw20, zxw15, ty_@0) → new_esEs20(zxw20, zxw15)
new_esEs30(zxw20, zxw15, ty_Double) → new_esEs18(zxw20, zxw15)
new_esEs30(zxw20, zxw15, app(app(ty_Either, bec), bed)) → new_esEs6(zxw20, zxw15, bec, bed)
new_esEs30(zxw20, zxw15, app(ty_Maybe, bde)) → new_esEs7(zxw20, zxw15, bde)
new_esEs30(zxw20, zxw15, app(ty_[], bdg)) → new_esEs16(zxw20, zxw15, bdg)
new_esEs30(zxw20, zxw15, ty_Int) → new_esEs13(zxw20, zxw15)
new_esEs30(zxw20, zxw15, ty_Ordering) → new_esEs8(zxw20, zxw15)
new_esEs30(zxw20, zxw15, ty_Integer) → new_esEs17(zxw20, zxw15)
new_esEs30(zxw20, zxw15, app(app(app(ty_@3, bdh), bea), beb)) → new_esEs5(zxw20, zxw15, bdh, bea, beb)
new_esEs30(zxw20, zxw15, ty_Char) → new_esEs15(zxw20, zxw15)
new_esEs30(zxw20, zxw15, app(app(ty_@2, bee), bef)) → new_esEs4(zxw20, zxw15, bee, bef)
new_compare35(zxw400, h) → new_compare26(Just(zxw400), Nothing, False, h)

The set Q consists of the following terms:

new_esEs17(Integer(x0), Integer(x1))
new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_ltEs7(Right(x0), Right(x1), x2, ty_Bool)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Integer)
new_lt10(x0, x1, ty_Double)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_compare18(x0, x1)
new_compare29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare29(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Double)
new_pePe(False, x0)
new_lt10(x0, x1, app(app(ty_Either, x2), x3))
new_compare29(x0, x1, app(app(ty_Either, x2), x3))
new_lt17(x0, x1, x2, x3)
new_esEs31(x0, x1, ty_Double)
new_esEs10(x0, x1, app(ty_[], x2))
new_ltEs8(Nothing, Nothing, x0)
new_compare210(x0, x1, True, x2, x3, x4)
new_compare7(x0, x1)
new_primMulNat0(Succ(x0), Zero)
new_esEs31(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(ty_[], x2))
new_esEs7(Just(x0), Just(x1), ty_Double)
new_ltEs8(Just(x0), Just(x1), ty_Integer)
new_esEs10(x0, x1, ty_Int)
new_ltEs10(x0, x1)
new_esEs28(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Ordering)
new_esEs31(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs12(x0, x1, ty_Char)
new_compare25(x0, x1, True, x2, x3)
new_primMulNat0(Succ(x0), Succ(x1))
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare8(:%(x0, x1), :%(x2, x3), ty_Int)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_ltEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs16(x0, x1)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_lt10(x0, x1, app(ty_Ratio, x2))
new_ltEs8(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs6(Right(x0), Right(x1), x2, ty_Char)
new_compare13(x0, x1, True)
new_ltEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs10(x0, x1, ty_Ordering)
new_esEs31(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, ty_Float)
new_esEs11(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_Int)
new_esEs31(x0, x1, ty_Int)
new_compare11(x0, x1, True, x2)
new_ltEs19(x0, x1, ty_Ordering)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_lt10(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(GT, GT)
new_compare11(x0, x1, False, x2)
new_esEs8(LT, LT)
new_compare29(x0, x1, ty_Double)
new_esEs18(Double(x0, x1), Double(x2, x3))
new_primCmpNat0(Zero, x0)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_ltEs8(Just(x0), Just(x1), ty_Bool)
new_ltEs8(Just(x0), Just(x1), app(ty_[], x2))
new_esEs11(x0, x1, ty_@0)
new_primCmpNat1(Zero, Succ(x0))
new_esEs31(x0, x1, app(ty_Maybe, x2))
new_esEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, ty_Int)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_sr(x0, x1)
new_ltEs5(False, False)
new_compare17(x0, x1, False, x2, x3)
new_ltEs8(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare6(x0, x1)
new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt10(x0, x1, ty_Ordering)
new_compare28(x0, x1, x2, x3, x4)
new_compare29(x0, x1, ty_Int)
new_esEs30(x0, x1, ty_Bool)
new_compare19(x0, x1, x2)
new_esEs26(x0, x1, ty_Integer)
new_primEqNat0(Zero, Succ(x0))
new_primCmpNat1(Zero, Zero)
new_compare16(Double(x0, x1), Double(x2, x3))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_lt7(x0, x1)
new_esEs28(x0, x1, ty_@0)
new_ltEs20(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_Integer)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Double)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_Char)
new_lt12(x0, x1, x2)
new_ltEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_compare15(x0, x1, True, x2, x3)
new_esEs24(x0, x1, ty_Int)
new_compare26(Just(x0), Just(x1), False, x2)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_primEqNat0(Zero, Zero)
new_compare32(x0, x1, x2, x3)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs30(x0, x1, app(ty_[], x2))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs7(Left(x0), Left(x1), ty_Char, x2)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_ltEs8(Just(x0), Just(x1), ty_Double)
new_ltEs8(Just(x0), Just(x1), ty_Ordering)
new_ltEs19(x0, x1, ty_@0)
new_compare24(x0, x1, False)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs9(True, True)
new_compare27(x0, x1, True, x2, x3)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_lt4(x0, x1)
new_ltEs8(Nothing, Just(x0), x1)
new_primMulNat0(Zero, Zero)
new_esEs23(x0, x1, ty_Char)
new_esEs30(x0, x1, ty_Ordering)
new_compare29(x0, x1, app(app(ty_@2, x2), x3))
new_esEs10(x0, x1, ty_@0)
new_lt10(x0, x1, ty_Char)
new_ltEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs30(x0, x1, ty_Int)
new_compare26(Just(x0), Nothing, False, x1)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_Integer)
new_fsEs(x0)
new_ltEs4(GT, GT)
new_lt8(x0, x1)
new_esEs6(Right(x0), Right(x1), x2, ty_Integer)
new_esEs30(x0, x1, ty_@0)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(x0, x1, ty_Float)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs28(x0, x1, ty_Double)
new_ltEs8(Just(x0), Nothing, x1)
new_esEs31(x0, x1, app(app(ty_Either, x2), x3))
new_esEs11(x0, x1, app(ty_Ratio, x2))
new_ltEs8(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt10(x0, x1, ty_Int)
new_esEs10(x0, x1, ty_Bool)
new_ltEs18(x0, x1, app(ty_[], x2))
new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs10(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs23(x0, x1, ty_Ordering)
new_esEs7(Just(x0), Just(x1), ty_Int)
new_esEs10(x0, x1, ty_Char)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_compare33(x0)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt10(x0, x1, app(ty_Maybe, x2))
new_pePe(True, x0)
new_ltEs15(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_primPlusNat0(Zero, x0)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_compare26(Nothing, Nothing, False, x0)
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Int)
new_lt6(x0, x1)
new_esEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs26(x0, x1, ty_Bool)
new_compare24(x0, x1, True)
new_ltEs18(x0, x1, ty_Integer)
new_esEs10(x0, x1, app(ty_Maybe, x2))
new_compare15(x0, x1, False, x2, x3)
new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_compare14(Float(x0, x1), Float(x2, x3))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs7(Right(x0), Left(x1), x2, x3)
new_ltEs7(Left(x0), Right(x1), x2, x3)
new_lt10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_compare110(x0, x1, False, x2, x3, x4)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_ltEs14(x0, x1)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_primPlusNat1(Zero, Zero)
new_esEs11(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Right(x0), Left(x1), x2, x3)
new_esEs6(Left(x0), Right(x1), x2, x3)
new_primCompAux0(x0, GT)
new_ltEs7(Right(x0), Right(x1), x2, ty_Char)
new_esEs6(Left(x0), Left(x1), ty_Int, x2)
new_compare23(x0, x1, True)
new_esEs31(x0, x1, ty_Float)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_compare29(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, app(ty_[], x2))
new_lt15(x0, x1)
new_esEs6(Left(x0), Left(x1), ty_Integer, x2)
new_esEs14(:%(x0, x1), :%(x2, x3), x4)
new_compare13(x0, x1, False)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_lt20(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_@0)
new_esEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_primPlusNat0(Succ(x0), x1)
new_ltEs4(EQ, EQ)
new_esEs31(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, ty_Char)
new_esEs6(Right(x0), Right(x1), x2, ty_Int)
new_ltEs11(x0, x1)
new_compare29(x0, x1, app(ty_Ratio, x2))
new_esEs12(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Integer)
new_ltEs20(x0, x1, ty_Char)
new_esEs7(Just(x0), Just(x1), ty_Char)
new_esEs12(x0, x1, ty_Float)
new_compare31(@0, @0)
new_ltEs7(Left(x0), Left(x1), ty_Int, x2)
new_esEs7(Just(x0), Just(x1), ty_Float)
new_compare36(x0, x1, x2)
new_primCmpNat2(x0, Zero)
new_ltEs4(LT, EQ)
new_ltEs4(EQ, LT)
new_esEs12(x0, x1, ty_Int)
new_ltEs13(x0, x1, x2)
new_lt19(x0, x1, ty_Double)
new_esEs12(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, app(ty_Ratio, x2))
new_ltEs7(Left(x0), Left(x1), ty_@0, x2)
new_esEs21(x0, x1, app(ty_[], x2))
new_primMulInt(Pos(x0), Pos(x1))
new_lt20(x0, x1, ty_Bool)
new_esEs30(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_@0)
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_asAs(True, x0)
new_primEqNat0(Succ(x0), Zero)
new_ltEs8(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Right(x0), Right(x1), x2, ty_Bool)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_ltEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs13(x0, x1)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs21(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Integer)
new_lt20(x0, x1, ty_@0)
new_esEs12(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, ty_Bool)
new_lt20(x0, x1, ty_Char)
new_esEs6(Left(x0), Left(x1), ty_Float, x2)
new_esEs12(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_Ordering)
new_compare34(x0, x1)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Ordering)
new_esEs6(Right(x0), Right(x1), x2, ty_Float)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_compare26(Nothing, Just(x0), False, x1)
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_ltEs20(x0, x1, ty_Bool)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs12(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs27(x0, x1, ty_Int)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Double)
new_esEs25(x0, x1, ty_Integer)
new_ltEs7(Right(x0), Right(x1), x2, ty_Integer)
new_primMulInt(Neg(x0), Neg(x1))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs31(x0, x1, ty_Bool)
new_lt10(x0, x1, ty_Bool)
new_primPlusNat1(Succ(x0), Zero)
new_esEs22(x0, x1, ty_Float)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs6(Left(x0), Left(x1), ty_@0, x2)
new_ltEs4(LT, LT)
new_lt11(x0, x1, x2, x3)
new_esEs10(x0, x1, ty_Integer)
new_esEs31(x0, x1, ty_Ordering)
new_esEs12(x0, x1, app(app(ty_@2, x2), x3))
new_esEs16([], [], x0)
new_ltEs19(x0, x1, ty_Integer)
new_compare23(x0, x1, False)
new_lt16(x0, x1, x2, x3, x4)
new_compare29(x0, x1, app(ty_[], x2))
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs11(x0, x1, ty_Bool)
new_esEs11(x0, x1, app(app(ty_Either, x2), x3))
new_esEs16([], :(x0, x1), x2)
new_esEs23(x0, x1, ty_Double)
new_esEs21(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_Ordering)
new_ltEs9(@2(x0, x1), @2(x2, x3), x4, x5)
new_primPlusNat1(Zero, Succ(x0))
new_ltEs12(x0, x1)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_compare10(x0, x1, False)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_primCmpNat0(Succ(x0), x1)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, ty_@0)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs8(GT, EQ)
new_esEs8(EQ, GT)
new_esEs22(x0, x1, ty_Bool)
new_lt19(x0, x1, ty_Float)
new_ltEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_lt19(x0, x1, ty_Integer)
new_ltEs8(Just(x0), Just(x1), ty_Char)
new_esEs7(Nothing, Just(x0), x1)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt18(x0, x1, x2)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs16(:(x0, x1), :(x2, x3), x4)
new_ltEs8(Just(x0), Just(x1), ty_Float)
new_ltEs7(Left(x0), Left(x1), ty_Float, x2)
new_lt5(x0, x1)
new_compare29(x0, x1, ty_Ordering)
new_ltEs18(x0, x1, ty_Bool)
new_esEs11(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_@0)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, ty_Int)
new_esEs11(x0, x1, ty_Char)
new_ltEs7(Left(x0), Left(x1), ty_Double, x2)
new_esEs27(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Float)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_lt19(x0, x1, ty_Ordering)
new_compare29(x0, x1, ty_Integer)
new_compare25(x0, x1, False, x2, x3)
new_esEs26(x0, x1, app(ty_[], x2))
new_ltEs18(x0, x1, ty_Float)
new_esEs9(False, False)
new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs21(x0, x1, ty_Double)
new_esEs12(x0, x1, ty_Ordering)
new_primCompAux1(x0, x1, x2, x3)
new_ltEs17(x0, x1, x2)
new_compare0([], :(x0, x1), x2)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpNat1(Succ(x0), Succ(x1))
new_esEs26(x0, x1, ty_@0)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs6(x0, x1)
new_lt10(x0, x1, ty_Float)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs22(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Float)
new_primCompAux0(x0, EQ)
new_esEs10(x0, x1, app(app(ty_Either, x2), x3))
new_compare210(x0, x1, False, x2, x3, x4)
new_esEs21(x0, x1, ty_Integer)
new_primCmpNat1(Succ(x0), Zero)
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_esEs6(Left(x0), Left(x1), ty_Bool, x2)
new_esEs7(Nothing, Nothing, x0)
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, ty_@0)
new_esEs12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, ty_Double)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_lt13(x0, x1)
new_esEs23(x0, x1, ty_Bool)
new_ltEs5(True, True)
new_ltEs7(Right(x0), Right(x1), x2, ty_Int)
new_lt19(x0, x1, ty_Int)
new_compare35(x0, x1)
new_lt19(x0, x1, ty_Char)
new_ltEs4(EQ, GT)
new_ltEs4(GT, EQ)
new_esEs31(x0, x1, ty_Integer)
new_not(True)
new_esEs11(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Float)
new_ltEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs11(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, ty_Char)
new_lt19(x0, x1, ty_@0)
new_compare26(x0, x1, True, x2)
new_esEs21(x0, x1, ty_Ordering)
new_ltEs8(Just(x0), Just(x1), app(ty_Maybe, x2))
new_compare0([], [], x0)
new_esEs26(x0, x1, ty_Char)
new_esEs7(Just(x0), Nothing, x1)
new_esEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs18(x0, x1, ty_Int)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Ordering)
new_not(False)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_lt14(x0, x1)
new_compare12(Char(x0), Char(x1))
new_esEs15(Char(x0), Char(x1))
new_esEs10(x0, x1, app(ty_Ratio, x2))
new_compare10(x0, x1, True)
new_lt10(x0, x1, ty_@0)
new_asAs(False, x0)
new_esEs22(x0, x1, ty_Ordering)
new_ltEs18(x0, x1, ty_Char)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_compare29(x0, x1, ty_Float)
new_compare17(x0, x1, True, x2, x3)
new_lt19(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_Char)
new_esEs31(x0, x1, ty_Char)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_ltEs8(Just(x0), Just(x1), ty_@0)
new_esEs20(@0, @0)
new_esEs6(Right(x0), Right(x1), x2, ty_Double)
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_ltEs7(Right(x0), Right(x1), x2, ty_Double)
new_esEs22(x0, x1, app(ty_[], x2))
new_ltEs7(Left(x0), Left(x1), ty_Integer, x2)
new_esEs23(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Int)
new_compare0(:(x0, x1), [], x2)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_ltEs19(x0, x1, ty_Double)
new_esEs9(True, False)
new_esEs9(False, True)
new_esEs22(x0, x1, ty_Char)
new_compare29(x0, x1, ty_Bool)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs7(Right(x0), Right(x1), x2, ty_Float)
new_esEs30(x0, x1, ty_Double)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, ty_Integer)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs11(x0, x1, ty_Double)
new_ltEs20(x0, x1, ty_Float)
new_primCompAux0(x0, LT)
new_primCmpNat2(x0, Succ(x1))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs11(x0, x1, app(ty_[], x2))
new_ltEs7(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs12(x0, x1, ty_Integer)
new_esEs6(Left(x0), Left(x1), ty_Double, x2)
new_esEs10(x0, x1, ty_Double)
new_esEs6(Right(x0), Right(x1), x2, ty_@0)
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_sr0(Integer(x0), Integer(x1))
new_lt10(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs6(Left(x0), Left(x1), ty_Char, x2)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Pos(Zero), Pos(Zero))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_compare30(x0, x1, x2, x3)
new_ltEs18(x0, x1, ty_Double)
new_esEs12(x0, x1, ty_Double)
new_compare110(x0, x1, True, x2, x3, x4)
new_esEs12(x0, x1, ty_Bool)
new_lt9(x0, x1, x2)
new_compare9(Integer(x0), Integer(x1))
new_lt10(x0, x1, ty_Integer)
new_esEs30(x0, x1, ty_Char)
new_esEs19(Float(x0, x1), Float(x2, x3))
new_primMulNat0(Zero, Succ(x0))
new_esEs7(Just(x0), Just(x1), ty_@0)
new_ltEs4(GT, LT)
new_ltEs4(LT, GT)
new_ltEs5(True, False)
new_ltEs5(False, True)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, app(ty_[], x2))
new_ltEs7(Right(x0), Right(x1), x2, ty_@0)
new_ltEs8(Just(x0), Just(x1), ty_Int)
new_compare29(x0, x1, ty_@0)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Float)
new_compare27(x0, x1, False, x2, x3)
new_esEs23(x0, x1, ty_Float)
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs30(x0, x1, ty_Float)
new_esEs16(:(x0, x1), [], x2)

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_compare33(x0)
new_compare34(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
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ AND
                                        ↳ QDP
                                        ↳ QDP
                                          ↳ UsableRulesProof
                                            ↳ QDP
                                              ↳ QReductionProof
                                                ↳ QDP
                                                  ↳ QDPSizeChangeProof
                                  ↳ QDP

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

new_splitLT12(zxw15, zxw16, zxw17, zxw18, zxw19, zxw20, True, bb, bc) → new_splitLT0(zxw19, zxw20, bb, bc)
new_splitLT3(Just(zxw300), zxw31, zxw32, zxw33, zxw34, Just(zxw400), h, ba) → new_splitLT21(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs8(new_compare26(Just(zxw400), Just(zxw300), new_esEs31(zxw400, zxw300, h), h), LT), h, ba)
new_splitLT20(zxw31, zxw32, zxw33, zxw34, zxw400, False, h, ba) → new_splitLT11(zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs8(new_compare35(zxw400, h), GT), h, ba)
new_splitLT0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw400, h, ba) → new_splitLT3(zxw330, zxw331, zxw332, zxw333, zxw334, Just(zxw400), h, ba)
new_splitLT21(zxw15, zxw16, zxw17, zxw18, zxw19, zxw20, False, bb, bc) → new_splitLT12(zxw15, zxw16, zxw17, zxw18, zxw19, zxw20, new_esEs8(new_compare36(zxw20, zxw15, bb), GT), bb, bc)
new_splitLT20(zxw31, zxw32, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw34, zxw400, True, h, ba) → new_splitLT3(zxw330, zxw331, zxw332, zxw333, zxw334, Just(zxw400), h, ba)
new_splitLT3(Nothing, zxw31, zxw32, zxw33, zxw34, Just(zxw400), h, ba) → new_splitLT20(zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs8(new_compare26(Just(zxw400), Nothing, False, h), LT), h, ba)
new_splitLT11(zxw31, zxw32, zxw33, zxw34, zxw400, True, h, ba) → new_splitLT0(zxw34, zxw400, h, ba)
new_splitLT21(zxw15, zxw16, zxw17, zxw18, zxw19, zxw20, True, bb, bc) → new_splitLT0(zxw18, zxw20, bb, bc)

The TRS R consists of the following rules:

new_compare26(Just(zxw4900), Nothing, False, bdd) → GT
new_esEs8(LT, LT) → True
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs31(zxw400, zxw300, ty_Ordering) → new_esEs8(zxw400, zxw300)
new_esEs31(zxw400, zxw300, app(app(app(ty_@3, cb), cc), cd)) → new_esEs5(zxw400, zxw300, cb, cc, cd)
new_esEs31(zxw400, zxw300, app(ty_[], ca)) → new_esEs16(zxw400, zxw300, ca)
new_esEs31(zxw400, zxw300, ty_Bool) → new_esEs9(zxw400, zxw300)
new_esEs31(zxw400, zxw300, app(app(ty_@2, cg), da)) → new_esEs4(zxw400, zxw300, cg, da)
new_esEs31(zxw400, zxw300, ty_Double) → new_esEs18(zxw400, zxw300)
new_esEs31(zxw400, zxw300, ty_Integer) → new_esEs17(zxw400, zxw300)
new_esEs31(zxw400, zxw300, ty_Int) → new_esEs13(zxw400, zxw300)
new_esEs31(zxw400, zxw300, ty_Char) → new_esEs15(zxw400, zxw300)
new_esEs31(zxw400, zxw300, app(ty_Ratio, bh)) → new_esEs14(zxw400, zxw300, bh)
new_esEs31(zxw400, zxw300, ty_@0) → new_esEs20(zxw400, zxw300)
new_esEs31(zxw400, zxw300, ty_Float) → new_esEs19(zxw400, zxw300)
new_esEs31(zxw400, zxw300, app(app(ty_Either, ce), cf)) → new_esEs6(zxw400, zxw300, ce, cf)
new_esEs31(zxw400, zxw300, app(ty_Maybe, bg)) → new_esEs7(zxw400, zxw300, bg)
new_compare26(Just(zxw4900), Just(zxw5000), False, bdd) → new_compare11(zxw4900, zxw5000, new_ltEs19(zxw4900, zxw5000, bdd), bdd)
new_compare26(zxw490, zxw500, True, bdd) → EQ
new_ltEs19(zxw4900, zxw5000, ty_Integer) → new_ltEs16(zxw4900, zxw5000)
new_ltEs19(zxw4900, zxw5000, ty_Double) → new_ltEs11(zxw4900, zxw5000)
new_ltEs19(zxw4900, zxw5000, ty_Int) → new_ltEs10(zxw4900, zxw5000)
new_ltEs19(zxw4900, zxw5000, app(app(app(ty_@3, cbe), cbf), cbg)) → new_ltEs15(zxw4900, zxw5000, cbe, cbf, cbg)
new_ltEs19(zxw4900, zxw5000, app(ty_Ratio, bag)) → new_ltEs17(zxw4900, zxw5000, bag)
new_ltEs19(zxw4900, zxw5000, ty_Ordering) → new_ltEs4(zxw4900, zxw5000)
new_ltEs19(zxw4900, zxw5000, ty_Char) → new_ltEs12(zxw4900, zxw5000)
new_ltEs19(zxw4900, zxw5000, app(app(ty_Either, cbh), cca)) → new_ltEs7(zxw4900, zxw5000, cbh, cca)
new_ltEs19(zxw4900, zxw5000, app(app(ty_@2, beg), beh)) → new_ltEs9(zxw4900, zxw5000, beg, beh)
new_ltEs19(zxw4900, zxw5000, ty_Float) → new_ltEs6(zxw4900, zxw5000)
new_ltEs19(zxw4900, zxw5000, app(ty_Maybe, hd)) → new_ltEs8(zxw4900, zxw5000, hd)
new_ltEs19(zxw4900, zxw5000, ty_@0) → new_ltEs14(zxw4900, zxw5000)
new_ltEs19(zxw4900, zxw5000, ty_Bool) → new_ltEs5(zxw4900, zxw5000)
new_ltEs19(zxw4900, zxw5000, app(ty_[], cab)) → new_ltEs13(zxw4900, zxw5000, cab)
new_compare11(zxw180, zxw181, True, bd) → LT
new_compare11(zxw180, zxw181, False, bd) → GT
new_ltEs13(zxw4900, zxw5000, cab) → new_fsEs(new_compare0(zxw4900, zxw5000, cab))
new_compare0([], [], cab) → EQ
new_compare0(:(zxw49000, zxw49001), [], cab) → GT
new_compare0(:(zxw49000, zxw49001), :(zxw50000, zxw50001), cab) → new_primCompAux1(zxw49000, zxw50000, new_compare0(zxw49001, zxw50001, cab), cab)
new_compare0([], :(zxw50000, zxw50001), cab) → LT
new_fsEs(zxw202) → new_not(new_esEs8(zxw202, GT))
new_esEs8(GT, GT) → True
new_esEs8(LT, GT) → False
new_esEs8(EQ, GT) → False
new_not(False) → True
new_not(True) → False
new_primCompAux1(zxw49000, zxw50000, zxw214, cab) → new_primCompAux0(zxw214, new_compare29(zxw49000, zxw50000, cab))
new_compare29(zxw49000, zxw50000, ty_Char) → new_compare12(zxw49000, zxw50000)
new_compare29(zxw49000, zxw50000, ty_Double) → new_compare16(zxw49000, zxw50000)
new_compare29(zxw49000, zxw50000, ty_@0) → new_compare31(zxw49000, zxw50000)
new_compare29(zxw49000, zxw50000, ty_Int) → new_compare7(zxw49000, zxw50000)
new_compare29(zxw49000, zxw50000, app(app(app(ty_@3, cag), cah), cba)) → new_compare28(zxw49000, zxw50000, cag, cah, cba)
new_compare29(zxw49000, zxw50000, app(ty_[], caf)) → new_compare0(zxw49000, zxw50000, caf)
new_compare29(zxw49000, zxw50000, app(app(ty_@2, cac), cad)) → new_compare30(zxw49000, zxw50000, cac, cad)
new_compare29(zxw49000, zxw50000, ty_Float) → new_compare14(zxw49000, zxw50000)
new_compare29(zxw49000, zxw50000, app(app(ty_Either, cbb), cbc)) → new_compare32(zxw49000, zxw50000, cbb, cbc)
new_compare29(zxw49000, zxw50000, app(ty_Ratio, cbd)) → new_compare8(zxw49000, zxw50000, cbd)
new_compare29(zxw49000, zxw50000, ty_Ordering) → new_compare6(zxw49000, zxw50000)
new_compare29(zxw49000, zxw50000, ty_Integer) → new_compare9(zxw49000, zxw50000)
new_compare29(zxw49000, zxw50000, ty_Bool) → new_compare18(zxw49000, zxw50000)
new_compare29(zxw49000, zxw50000, app(ty_Maybe, cae)) → new_compare19(zxw49000, zxw50000, cae)
new_primCompAux0(zxw218, GT) → GT
new_primCompAux0(zxw218, LT) → LT
new_primCompAux0(zxw218, EQ) → zxw218
new_compare19(zxw490, zxw500, bdd) → new_compare26(zxw490, zxw500, new_esEs7(zxw490, zxw500, bdd), bdd)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_esEs7(Just(zxw4000), Just(zxw3000), app(app(ty_@2, bhh), caa)) → new_esEs4(zxw4000, zxw3000, bhh, caa)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Bool) → new_esEs9(zxw4000, zxw3000)
new_esEs7(Just(zxw4000), Just(zxw3000), app(ty_Ratio, bha)) → new_esEs14(zxw4000, zxw3000, bha)
new_esEs7(Just(zxw4000), Just(zxw3000), app(ty_[], bhb)) → new_esEs16(zxw4000, zxw3000, bhb)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_@0) → new_esEs20(zxw4000, zxw3000)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Ordering) → new_esEs8(zxw4000, zxw3000)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Int) → new_esEs13(zxw4000, zxw3000)
new_esEs7(Nothing, Nothing, bg) → True
new_esEs7(Just(zxw4000), Nothing, bg) → False
new_esEs7(Nothing, Just(zxw3000), bg) → False
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Char) → new_esEs15(zxw4000, zxw3000)
new_esEs7(Just(zxw4000), Just(zxw3000), app(app(app(ty_@3, bhc), bhd), bhe)) → new_esEs5(zxw4000, zxw3000, bhc, bhd, bhe)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Double) → new_esEs18(zxw4000, zxw3000)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Float) → new_esEs19(zxw4000, zxw3000)
new_compare26(Nothing, Just(zxw5000), False, bdd) → LT
new_compare26(Nothing, Nothing, False, bdd) → LT
new_esEs6(Left(zxw4000), Left(zxw3000), app(ty_Maybe, ccb), cf) → new_esEs7(zxw4000, zxw3000, ccb)
new_esEs7(Just(zxw4000), Just(zxw3000), app(ty_Maybe, bgh)) → new_esEs7(zxw4000, zxw3000, bgh)
new_esEs6(Right(zxw4000), Right(zxw3000), ce, app(ty_Maybe, cdd)) → new_esEs7(zxw4000, zxw3000, cdd)
new_esEs6(Left(zxw4000), Left(zxw3000), app(app(ty_Either, cch), cda), cf) → new_esEs6(zxw4000, zxw3000, cch, cda)
new_esEs6(Right(zxw4000), Right(zxw3000), ce, app(app(ty_Either, ceb), cec)) → new_esEs6(zxw4000, zxw3000, ceb, cec)
new_esEs7(Just(zxw4000), Just(zxw3000), app(app(ty_Either, bhf), bhg)) → new_esEs6(zxw4000, zxw3000, bhf, bhg)
new_esEs6(Right(zxw4000), Right(zxw3000), ce, ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_esEs6(Right(zxw4000), Right(zxw3000), ce, ty_Float) → new_esEs19(zxw4000, zxw3000)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Integer, cf) → new_esEs17(zxw4000, zxw3000)
new_esEs6(Right(zxw4000), Right(zxw3000), ce, ty_Int) → new_esEs13(zxw4000, zxw3000)
new_esEs6(Left(zxw4000), Left(zxw3000), app(app(ty_@2, cdb), cdc), cf) → new_esEs4(zxw4000, zxw3000, cdb, cdc)
new_esEs6(Right(zxw4000), Right(zxw3000), ce, app(ty_Ratio, cde)) → new_esEs14(zxw4000, zxw3000, cde)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Bool, cf) → new_esEs9(zxw4000, zxw3000)
new_esEs6(Right(zxw4000), Left(zxw3000), ce, cf) → False
new_esEs6(Left(zxw4000), Right(zxw3000), ce, cf) → False
new_esEs6(Left(zxw4000), Left(zxw3000), ty_@0, cf) → new_esEs20(zxw4000, zxw3000)
new_esEs6(Right(zxw4000), Right(zxw3000), ce, ty_Bool) → new_esEs9(zxw4000, zxw3000)
new_esEs6(Left(zxw4000), Left(zxw3000), app(ty_Ratio, ccc), cf) → new_esEs14(zxw4000, zxw3000, ccc)
new_esEs6(Right(zxw4000), Right(zxw3000), ce, app(ty_[], cdf)) → new_esEs16(zxw4000, zxw3000, cdf)
new_esEs6(Left(zxw4000), Left(zxw3000), app(app(app(ty_@3, cce), ccf), ccg), cf) → new_esEs5(zxw4000, zxw3000, cce, ccf, ccg)
new_esEs6(Right(zxw4000), Right(zxw3000), ce, ty_@0) → new_esEs20(zxw4000, zxw3000)
new_esEs6(Right(zxw4000), Right(zxw3000), ce, ty_Double) → new_esEs18(zxw4000, zxw3000)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Double, cf) → new_esEs18(zxw4000, zxw3000)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Ordering, cf) → new_esEs8(zxw4000, zxw3000)
new_esEs6(Right(zxw4000), Right(zxw3000), ce, app(app(ty_@2, ced), cee)) → new_esEs4(zxw4000, zxw3000, ced, cee)
new_esEs6(Right(zxw4000), Right(zxw3000), ce, ty_Char) → new_esEs15(zxw4000, zxw3000)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Char, cf) → new_esEs15(zxw4000, zxw3000)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Float, cf) → new_esEs19(zxw4000, zxw3000)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Int, cf) → new_esEs13(zxw4000, zxw3000)
new_esEs6(Left(zxw4000), Left(zxw3000), app(ty_[], ccd), cf) → new_esEs16(zxw4000, zxw3000, ccd)
new_esEs6(Right(zxw4000), Right(zxw3000), ce, ty_Ordering) → new_esEs8(zxw4000, zxw3000)
new_esEs6(Right(zxw4000), Right(zxw3000), ce, app(app(app(ty_@3, cdg), cdh), cea)) → new_esEs5(zxw4000, zxw3000, cdg, cdh, cea)
new_esEs5(@3(zxw4000, zxw4001, zxw4002), @3(zxw3000, zxw3001, zxw3002), cb, cc, cd) → new_asAs(new_esEs12(zxw4000, zxw3000, cb), new_asAs(new_esEs11(zxw4001, zxw3001, cc), new_esEs10(zxw4002, zxw3002, cd)))
new_esEs12(zxw4000, zxw3000, ty_Bool) → new_esEs9(zxw4000, zxw3000)
new_esEs12(zxw4000, zxw3000, ty_Char) → new_esEs15(zxw4000, zxw3000)
new_esEs12(zxw4000, zxw3000, app(ty_[], gb)) → new_esEs16(zxw4000, zxw3000, gb)
new_esEs12(zxw4000, zxw3000, ty_Int) → new_esEs13(zxw4000, zxw3000)
new_esEs12(zxw4000, zxw3000, ty_Double) → new_esEs18(zxw4000, zxw3000)
new_esEs12(zxw4000, zxw3000, app(ty_Maybe, fh)) → new_esEs7(zxw4000, zxw3000, fh)
new_esEs12(zxw4000, zxw3000, app(app(app(ty_@3, gc), gd), ge)) → new_esEs5(zxw4000, zxw3000, gc, gd, ge)
new_esEs12(zxw4000, zxw3000, ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_esEs12(zxw4000, zxw3000, ty_Float) → new_esEs19(zxw4000, zxw3000)
new_esEs12(zxw4000, zxw3000, ty_@0) → new_esEs20(zxw4000, zxw3000)
new_esEs12(zxw4000, zxw3000, app(app(ty_Either, gf), gg)) → new_esEs6(zxw4000, zxw3000, gf, gg)
new_esEs12(zxw4000, zxw3000, app(ty_Ratio, ga)) → new_esEs14(zxw4000, zxw3000, ga)
new_esEs12(zxw4000, zxw3000, ty_Ordering) → new_esEs8(zxw4000, zxw3000)
new_esEs12(zxw4000, zxw3000, app(app(ty_@2, gh), ha)) → new_esEs4(zxw4000, zxw3000, gh, ha)
new_esEs11(zxw4001, zxw3001, app(ty_[], eg)) → new_esEs16(zxw4001, zxw3001, eg)
new_esEs11(zxw4001, zxw3001, ty_Char) → new_esEs15(zxw4001, zxw3001)
new_esEs11(zxw4001, zxw3001, ty_Float) → new_esEs19(zxw4001, zxw3001)
new_esEs11(zxw4001, zxw3001, ty_Int) → new_esEs13(zxw4001, zxw3001)
new_esEs11(zxw4001, zxw3001, app(app(ty_@2, ff), fg)) → new_esEs4(zxw4001, zxw3001, ff, fg)
new_esEs11(zxw4001, zxw3001, ty_Ordering) → new_esEs8(zxw4001, zxw3001)
new_esEs11(zxw4001, zxw3001, app(app(app(ty_@3, eh), fa), fb)) → new_esEs5(zxw4001, zxw3001, eh, fa, fb)
new_esEs11(zxw4001, zxw3001, ty_Bool) → new_esEs9(zxw4001, zxw3001)
new_esEs11(zxw4001, zxw3001, ty_Double) → new_esEs18(zxw4001, zxw3001)
new_esEs11(zxw4001, zxw3001, ty_@0) → new_esEs20(zxw4001, zxw3001)
new_esEs11(zxw4001, zxw3001, app(app(ty_Either, fc), fd)) → new_esEs6(zxw4001, zxw3001, fc, fd)
new_esEs11(zxw4001, zxw3001, app(ty_Maybe, ee)) → new_esEs7(zxw4001, zxw3001, ee)
new_esEs11(zxw4001, zxw3001, app(ty_Ratio, ef)) → new_esEs14(zxw4001, zxw3001, ef)
new_esEs11(zxw4001, zxw3001, ty_Integer) → new_esEs17(zxw4001, zxw3001)
new_esEs10(zxw4002, zxw3002, app(ty_Maybe, dc)) → new_esEs7(zxw4002, zxw3002, dc)
new_esEs10(zxw4002, zxw3002, app(app(app(ty_@3, df), dg), dh)) → new_esEs5(zxw4002, zxw3002, df, dg, dh)
new_esEs10(zxw4002, zxw3002, ty_Integer) → new_esEs17(zxw4002, zxw3002)
new_esEs10(zxw4002, zxw3002, ty_Bool) → new_esEs9(zxw4002, zxw3002)
new_esEs10(zxw4002, zxw3002, ty_Float) → new_esEs19(zxw4002, zxw3002)
new_esEs10(zxw4002, zxw3002, ty_Char) → new_esEs15(zxw4002, zxw3002)
new_esEs10(zxw4002, zxw3002, app(ty_[], de)) → new_esEs16(zxw4002, zxw3002, de)
new_esEs10(zxw4002, zxw3002, app(app(ty_@2, ec), ed)) → new_esEs4(zxw4002, zxw3002, ec, ed)
new_esEs10(zxw4002, zxw3002, ty_Double) → new_esEs18(zxw4002, zxw3002)
new_esEs10(zxw4002, zxw3002, ty_@0) → new_esEs20(zxw4002, zxw3002)
new_esEs10(zxw4002, zxw3002, ty_Int) → new_esEs13(zxw4002, zxw3002)
new_esEs10(zxw4002, zxw3002, app(ty_Ratio, dd)) → new_esEs14(zxw4002, zxw3002, dd)
new_esEs10(zxw4002, zxw3002, ty_Ordering) → new_esEs8(zxw4002, zxw3002)
new_esEs10(zxw4002, zxw3002, app(app(ty_Either, ea), eb)) → new_esEs6(zxw4002, zxw3002, ea, eb)
new_asAs(False, zxw187) → False
new_asAs(True, zxw187) → zxw187
new_esEs8(EQ, EQ) → True
new_esEs8(LT, EQ) → False
new_esEs8(GT, EQ) → False
new_esEs14(:%(zxw4000, zxw4001), :%(zxw3000, zxw3001), bh) → new_asAs(new_esEs25(zxw4000, zxw3000, bh), new_esEs24(zxw4001, zxw3001, bh))
new_esEs25(zxw4000, zxw3000, ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_esEs25(zxw4000, zxw3000, ty_Int) → new_esEs13(zxw4000, zxw3000)
new_esEs24(zxw4001, zxw3001, ty_Int) → new_esEs13(zxw4001, zxw3001)
new_esEs24(zxw4001, zxw3001, ty_Integer) → new_esEs17(zxw4001, zxw3001)
new_esEs17(Integer(zxw4000), Integer(zxw3000)) → new_primEqInt(zxw4000, zxw3000)
new_primEqInt(Neg(Succ(zxw40000)), Neg(Succ(zxw30000))) → new_primEqNat0(zxw40000, zxw30000)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Succ(zxw40000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(zxw30000))) → False
new_primEqInt(Pos(Succ(zxw40000)), Pos(Succ(zxw30000))) → new_primEqNat0(zxw40000, zxw30000)
new_primEqInt(Pos(Succ(zxw40000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(zxw30000))) → False
new_primEqInt(Pos(Succ(zxw40000)), Neg(zxw3000)) → False
new_primEqInt(Neg(Succ(zxw40000)), Pos(zxw3000)) → False
new_primEqInt(Pos(Zero), Neg(Succ(zxw30000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(zxw30000))) → False
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(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_esEs13(zxw400, zxw300) → new_primEqInt(zxw400, zxw300)
new_esEs20(@0, @0) → True
new_esEs18(Double(zxw4000, zxw4001), Double(zxw3000, zxw3001)) → new_esEs13(new_sr(zxw4000, zxw3000), new_sr(zxw4001, zxw3001))
new_sr(zxw4001, zxw3001) → new_primMulInt(zxw4001, zxw3001)
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Neg(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Pos(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulNat0(Zero, Zero) → Zero
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_primPlusNat1(Zero, Zero) → Zero
new_esEs4(@2(zxw4000, zxw4001), @2(zxw3000, zxw3001), cg, da) → new_asAs(new_esEs22(zxw4000, zxw3000, cg), new_esEs21(zxw4001, zxw3001, da))
new_esEs22(zxw4000, zxw3000, ty_@0) → new_esEs20(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Float) → new_esEs19(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, app(ty_Ratio, bcc)) → new_esEs14(zxw4000, zxw3000, bcc)
new_esEs22(zxw4000, zxw3000, app(app(ty_@2, bdb), bdc)) → new_esEs4(zxw4000, zxw3000, bdb, bdc)
new_esEs22(zxw4000, zxw3000, ty_Ordering) → new_esEs8(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Bool) → new_esEs9(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, app(app(app(ty_@3, bce), bcf), bcg)) → new_esEs5(zxw4000, zxw3000, bce, bcf, bcg)
new_esEs22(zxw4000, zxw3000, ty_Int) → new_esEs13(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Char) → new_esEs15(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, app(ty_[], bcd)) → new_esEs16(zxw4000, zxw3000, bcd)
new_esEs22(zxw4000, zxw3000, ty_Double) → new_esEs18(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, app(app(ty_Either, bch), bda)) → new_esEs6(zxw4000, zxw3000, bch, bda)
new_esEs22(zxw4000, zxw3000, ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, app(ty_Maybe, bcb)) → new_esEs7(zxw4000, zxw3000, bcb)
new_esEs21(zxw4001, zxw3001, ty_Double) → new_esEs18(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, app(ty_Ratio, bba)) → new_esEs14(zxw4001, zxw3001, bba)
new_esEs21(zxw4001, zxw3001, app(app(ty_Either, bbf), bbg)) → new_esEs6(zxw4001, zxw3001, bbf, bbg)
new_esEs21(zxw4001, zxw3001, ty_Char) → new_esEs15(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, ty_Float) → new_esEs19(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, ty_@0) → new_esEs20(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, app(app(app(ty_@3, bbc), bbd), bbe)) → new_esEs5(zxw4001, zxw3001, bbc, bbd, bbe)
new_esEs21(zxw4001, zxw3001, app(ty_Maybe, bah)) → new_esEs7(zxw4001, zxw3001, bah)
new_esEs21(zxw4001, zxw3001, app(app(ty_@2, bbh), bca)) → new_esEs4(zxw4001, zxw3001, bbh, bca)
new_esEs21(zxw4001, zxw3001, ty_Bool) → new_esEs9(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, ty_Integer) → new_esEs17(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, ty_Ordering) → new_esEs8(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, ty_Int) → new_esEs13(zxw4001, zxw3001)
new_esEs21(zxw4001, zxw3001, app(ty_[], bbb)) → new_esEs16(zxw4001, zxw3001, bbb)
new_esEs16(:(zxw4000, zxw4001), [], ca) → False
new_esEs16([], :(zxw3000, zxw3001), ca) → False
new_esEs16(:(zxw4000, zxw4001), :(zxw3000, zxw3001), ca) → new_asAs(new_esEs28(zxw4000, zxw3000, ca), new_esEs16(zxw4001, zxw3001, ca))
new_esEs16([], [], ca) → True
new_esEs28(zxw4000, zxw3000, ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, app(app(app(ty_@3, ddc), ddd), dde)) → new_esEs5(zxw4000, zxw3000, ddc, ddd, dde)
new_esEs28(zxw4000, zxw3000, ty_Bool) → new_esEs9(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_@0) → new_esEs20(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_Float) → new_esEs19(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, app(app(ty_Either, ddf), ddg)) → new_esEs6(zxw4000, zxw3000, ddf, ddg)
new_esEs28(zxw4000, zxw3000, ty_Char) → new_esEs15(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_Int) → new_esEs13(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, ty_Ordering) → new_esEs8(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, app(ty_Ratio, dda)) → new_esEs14(zxw4000, zxw3000, dda)
new_esEs28(zxw4000, zxw3000, app(ty_[], ddb)) → new_esEs16(zxw4000, zxw3000, ddb)
new_esEs28(zxw4000, zxw3000, app(ty_Maybe, dch)) → new_esEs7(zxw4000, zxw3000, dch)
new_esEs28(zxw4000, zxw3000, app(app(ty_@2, ddh), dea)) → new_esEs4(zxw4000, zxw3000, ddh, dea)
new_esEs28(zxw4000, zxw3000, ty_Double) → new_esEs18(zxw4000, zxw3000)
new_esEs15(Char(zxw4000), Char(zxw3000)) → new_primEqNat0(zxw4000, zxw3000)
new_esEs19(Float(zxw4000, zxw4001), Float(zxw3000, zxw3001)) → new_esEs13(new_sr(zxw4000, zxw3000), new_sr(zxw4001, zxw3001))
new_esEs9(True, True) → True
new_esEs9(True, False) → False
new_esEs9(False, True) → False
new_esEs9(False, False) → True
new_compare18(zxw49000, zxw50000) → new_compare24(zxw49000, zxw50000, new_esEs9(zxw49000, zxw50000))
new_compare24(zxw49000, zxw50000, False) → new_compare13(zxw49000, zxw50000, new_ltEs5(zxw49000, zxw50000))
new_compare24(zxw49000, zxw50000, True) → EQ
new_ltEs5(True, False) → False
new_ltEs5(True, True) → True
new_ltEs5(False, False) → True
new_ltEs5(False, True) → True
new_compare13(zxw49000, zxw50000, False) → GT
new_compare13(zxw49000, zxw50000, True) → LT
new_compare9(Integer(zxw49000), Integer(zxw50000)) → new_primCmpInt(zxw49000, zxw50000)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_primCmpNat2(zxw4900, Zero) → GT
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_primCmpNat1(Zero, Zero) → EQ
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_primCmpNat0(Zero, zxw4900) → LT
new_compare6(zxw49000, zxw50000) → new_compare23(zxw49000, zxw50000, new_esEs8(zxw49000, zxw50000))
new_compare23(zxw49000, zxw50000, True) → EQ
new_compare23(zxw49000, zxw50000, False) → new_compare10(zxw49000, zxw50000, new_ltEs4(zxw49000, zxw50000))
new_ltEs4(EQ, GT) → True
new_ltEs4(EQ, LT) → False
new_ltEs4(GT, EQ) → False
new_ltEs4(EQ, EQ) → True
new_ltEs4(GT, LT) → False
new_ltEs4(LT, GT) → True
new_ltEs4(LT, EQ) → True
new_ltEs4(LT, LT) → True
new_ltEs4(GT, GT) → True
new_compare10(zxw49000, zxw50000, True) → LT
new_compare10(zxw49000, zxw50000, False) → GT
new_compare8(:%(zxw49000, zxw49001), :%(zxw50000, zxw50001), ty_Integer) → new_compare9(new_sr0(zxw49000, zxw50001), new_sr0(zxw50000, zxw49001))
new_compare8(:%(zxw49000, zxw49001), :%(zxw50000, zxw50001), ty_Int) → new_compare7(new_sr(zxw49000, zxw50001), new_sr(zxw50000, zxw49001))
new_compare7(zxw49, zxw50) → new_primCmpInt(zxw49, zxw50)
new_sr0(Integer(zxw500000), Integer(zxw490010)) → Integer(new_primMulInt(zxw500000, zxw490010))
new_compare32(zxw49000, zxw50000, be, bf) → new_compare25(zxw49000, zxw50000, new_esEs6(zxw49000, zxw50000, be, bf), be, bf)
new_compare25(zxw49000, zxw50000, True, be, bf) → EQ
new_compare25(zxw49000, zxw50000, False, be, bf) → new_compare15(zxw49000, zxw50000, new_ltEs7(zxw49000, zxw50000, be, bf), be, bf)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_@0, cca) → new_ltEs14(zxw49000, zxw50000)
new_ltEs7(Left(zxw49000), Right(zxw50000), cbh, cca) → True
new_ltEs7(Left(zxw49000), Left(zxw50000), app(app(app(ty_@3, dah), dba), dbb), cca) → new_ltEs15(zxw49000, zxw50000, dah, dba, dbb)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbh, app(app(ty_@2, dbf), dbg)) → new_ltEs9(zxw49000, zxw50000, dbf, dbg)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbh, app(ty_Ratio, dcg)) → new_ltEs17(zxw49000, zxw50000, dcg)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Char, cca) → new_ltEs12(zxw49000, zxw50000)
new_ltEs7(Left(zxw49000), Left(zxw50000), app(app(ty_@2, dad), dae), cca) → new_ltEs9(zxw49000, zxw50000, dad, dae)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbh, ty_Bool) → new_ltEs5(zxw49000, zxw50000)
new_ltEs7(Left(zxw49000), Left(zxw50000), app(app(ty_Either, dbc), dbd), cca) → new_ltEs7(zxw49000, zxw50000, dbc, dbd)
new_ltEs7(Left(zxw49000), Left(zxw50000), app(ty_Maybe, daf), cca) → new_ltEs8(zxw49000, zxw50000, daf)
new_ltEs8(Just(zxw49000), Just(zxw50000), app(app(ty_Either, bad), bae)) → new_ltEs7(zxw49000, zxw50000, bad, bae)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbh, app(ty_Maybe, dbh)) → new_ltEs8(zxw49000, zxw50000, dbh)
new_ltEs8(Just(zxw49000), Just(zxw50000), app(ty_Maybe, hg)) → new_ltEs8(zxw49000, zxw50000, hg)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbh, app(app(ty_Either, dce), dcf)) → new_ltEs7(zxw49000, zxw50000, dce, dcf)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbh, ty_Integer) → new_ltEs16(zxw49000, zxw50000)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbh, app(app(app(ty_@3, dcb), dcc), dcd)) → new_ltEs15(zxw49000, zxw50000, dcb, dcc, dcd)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Bool, cca) → new_ltEs5(zxw49000, zxw50000)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Int, cca) → new_ltEs10(zxw49000, zxw50000)
new_ltEs7(Right(zxw49000), Left(zxw50000), cbh, cca) → False
new_ltEs7(Left(zxw49000), Left(zxw50000), app(ty_[], dag), cca) → new_ltEs13(zxw49000, zxw50000, dag)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Integer, cca) → new_ltEs16(zxw49000, zxw50000)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbh, app(ty_[], dca)) → new_ltEs13(zxw49000, zxw50000, dca)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Double, cca) → new_ltEs11(zxw49000, zxw50000)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbh, ty_Ordering) → new_ltEs4(zxw49000, zxw50000)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Ordering, cca) → new_ltEs4(zxw49000, zxw50000)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbh, ty_Char) → new_ltEs12(zxw49000, zxw50000)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbh, ty_Int) → new_ltEs10(zxw49000, zxw50000)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbh, ty_Double) → new_ltEs11(zxw49000, zxw50000)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Float, cca) → new_ltEs6(zxw49000, zxw50000)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbh, ty_Float) → new_ltEs6(zxw49000, zxw50000)
new_ltEs7(Left(zxw49000), Left(zxw50000), app(ty_Ratio, dbe), cca) → new_ltEs17(zxw49000, zxw50000, dbe)
new_ltEs7(Right(zxw49000), Right(zxw50000), cbh, ty_@0) → new_ltEs14(zxw49000, zxw50000)
new_compare15(zxw49000, zxw50000, True, be, bf) → LT
new_compare15(zxw49000, zxw50000, False, be, bf) → GT
new_ltEs14(zxw4900, zxw5000) → new_fsEs(new_compare31(zxw4900, zxw5000))
new_compare31(@0, @0) → EQ
new_ltEs17(zxw4900, zxw5000, bag) → new_fsEs(new_compare8(zxw4900, zxw5000, bag))
new_ltEs6(zxw4900, zxw5000) → new_fsEs(new_compare14(zxw4900, zxw5000))
new_compare14(Float(zxw49000, zxw49001), Float(zxw50000, zxw50001)) → new_compare7(new_sr(zxw49000, zxw50000), new_sr(zxw49001, zxw50001))
new_ltEs11(zxw4900, zxw5000) → new_fsEs(new_compare16(zxw4900, zxw5000))
new_compare16(Double(zxw49000, zxw49001), Double(zxw50000, zxw50001)) → new_compare7(new_sr(zxw49000, zxw50000), new_sr(zxw49001, zxw50001))
new_ltEs10(zxw4900, zxw5000) → new_fsEs(new_compare7(zxw4900, zxw5000))
new_ltEs12(zxw4900, zxw5000) → new_fsEs(new_compare12(zxw4900, zxw5000))
new_compare12(Char(zxw49000), Char(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_ltEs16(zxw4900, zxw5000) → new_fsEs(new_compare9(zxw4900, zxw5000))
new_ltEs15(@3(zxw49000, zxw49001, zxw49002), @3(zxw50000, zxw50001, zxw50002), cbe, cbf, cbg) → new_pePe(new_lt20(zxw49000, zxw50000, cbe), new_asAs(new_esEs27(zxw49000, zxw50000, cbe), new_pePe(new_lt19(zxw49001, zxw50001, cbf), new_asAs(new_esEs26(zxw49001, zxw50001, cbf), new_ltEs20(zxw49002, zxw50002, cbg)))))
new_lt20(zxw49000, zxw50000, app(app(ty_@2, chb), chc)) → new_lt11(zxw49000, zxw50000, chb, chc)
new_lt20(zxw49000, zxw50000, ty_@0) → new_lt15(zxw49000, zxw50000)
new_lt20(zxw49000, zxw50000, app(ty_[], che)) → new_lt9(zxw49000, zxw50000, che)
new_lt20(zxw49000, zxw50000, ty_Ordering) → new_lt14(zxw49000, zxw50000)
new_lt20(zxw49000, zxw50000, app(app(ty_Either, daa), dab)) → new_lt17(zxw49000, zxw50000, daa, dab)
new_lt20(zxw49000, zxw50000, ty_Char) → new_lt6(zxw49000, zxw50000)
new_lt20(zxw49000, zxw50000, ty_Int) → new_lt4(zxw49000, zxw50000)
new_lt20(zxw49000, zxw50000, ty_Double) → new_lt8(zxw49000, zxw50000)
new_lt20(zxw49000, zxw50000, ty_Bool) → new_lt13(zxw49000, zxw50000)
new_lt20(zxw49000, zxw50000, ty_Float) → new_lt7(zxw49000, zxw50000)
new_lt20(zxw49000, zxw50000, app(ty_Ratio, dac)) → new_lt18(zxw49000, zxw50000, dac)
new_lt20(zxw49000, zxw50000, app(app(app(ty_@3, chf), chg), chh)) → new_lt16(zxw49000, zxw50000, chf, chg, chh)
new_lt20(zxw49000, zxw50000, ty_Integer) → new_lt5(zxw49000, zxw50000)
new_lt20(zxw49000, zxw50000, app(ty_Maybe, chd)) → new_lt12(zxw49000, zxw50000, chd)
new_esEs27(zxw49000, zxw50000, app(ty_[], che)) → new_esEs16(zxw49000, zxw50000, che)
new_esEs27(zxw49000, zxw50000, app(ty_Maybe, chd)) → new_esEs7(zxw49000, zxw50000, chd)
new_esEs27(zxw49000, zxw50000, ty_Bool) → new_esEs9(zxw49000, zxw50000)
new_esEs27(zxw49000, zxw50000, ty_Char) → new_esEs15(zxw49000, zxw50000)
new_esEs27(zxw49000, zxw50000, ty_Float) → new_esEs19(zxw49000, zxw50000)
new_esEs27(zxw49000, zxw50000, ty_@0) → new_esEs20(zxw49000, zxw50000)
new_esEs27(zxw49000, zxw50000, ty_Ordering) → new_esEs8(zxw49000, zxw50000)
new_esEs27(zxw49000, zxw50000, ty_Integer) → new_esEs17(zxw49000, zxw50000)
new_esEs27(zxw49000, zxw50000, app(app(app(ty_@3, chf), chg), chh)) → new_esEs5(zxw49000, zxw50000, chf, chg, chh)
new_esEs27(zxw49000, zxw50000, ty_Int) → new_esEs13(zxw49000, zxw50000)
new_esEs27(zxw49000, zxw50000, app(app(ty_Either, daa), dab)) → new_esEs6(zxw49000, zxw50000, daa, dab)
new_esEs27(zxw49000, zxw50000, ty_Double) → new_esEs18(zxw49000, zxw50000)
new_esEs27(zxw49000, zxw50000, app(ty_Ratio, dac)) → new_esEs14(zxw49000, zxw50000, dac)
new_esEs27(zxw49000, zxw50000, app(app(ty_@2, chb), chc)) → new_esEs4(zxw49000, zxw50000, chb, chc)
new_lt19(zxw49001, zxw50001, ty_Integer) → new_lt5(zxw49001, zxw50001)
new_lt19(zxw49001, zxw50001, ty_Ordering) → new_lt14(zxw49001, zxw50001)
new_lt19(zxw49001, zxw50001, ty_Int) → new_lt4(zxw49001, zxw50001)
new_lt19(zxw49001, zxw50001, app(ty_[], cgc)) → new_lt9(zxw49001, zxw50001, cgc)
new_lt19(zxw49001, zxw50001, ty_@0) → new_lt15(zxw49001, zxw50001)
new_lt19(zxw49001, zxw50001, app(app(ty_@2, cfh), cga)) → new_lt11(zxw49001, zxw50001, cfh, cga)
new_lt19(zxw49001, zxw50001, ty_Float) → new_lt7(zxw49001, zxw50001)
new_lt19(zxw49001, zxw50001, app(ty_Ratio, cha)) → new_lt18(zxw49001, zxw50001, cha)
new_lt19(zxw49001, zxw50001, app(app(app(ty_@3, cgd), cge), cgf)) → new_lt16(zxw49001, zxw50001, cgd, cge, cgf)
new_lt19(zxw49001, zxw50001, ty_Char) → new_lt6(zxw49001, zxw50001)
new_lt19(zxw49001, zxw50001, app(app(ty_Either, cgg), cgh)) → new_lt17(zxw49001, zxw50001, cgg, cgh)
new_lt19(zxw49001, zxw50001, ty_Bool) → new_lt13(zxw49001, zxw50001)
new_lt19(zxw49001, zxw50001, ty_Double) → new_lt8(zxw49001, zxw50001)
new_lt19(zxw49001, zxw50001, app(ty_Maybe, cgb)) → new_lt12(zxw49001, zxw50001, cgb)
new_esEs26(zxw49001, zxw50001, app(ty_[], cgc)) → new_esEs16(zxw49001, zxw50001, cgc)
new_esEs26(zxw49001, zxw50001, ty_Char) → new_esEs15(zxw49001, zxw50001)
new_esEs26(zxw49001, zxw50001, ty_Ordering) → new_esEs8(zxw49001, zxw50001)
new_esEs26(zxw49001, zxw50001, ty_Bool) → new_esEs9(zxw49001, zxw50001)
new_esEs26(zxw49001, zxw50001, ty_Integer) → new_esEs17(zxw49001, zxw50001)
new_esEs26(zxw49001, zxw50001, ty_Int) → new_esEs13(zxw49001, zxw50001)
new_esEs26(zxw49001, zxw50001, app(app(ty_@2, cfh), cga)) → new_esEs4(zxw49001, zxw50001, cfh, cga)
new_esEs26(zxw49001, zxw50001, ty_Double) → new_esEs18(zxw49001, zxw50001)
new_esEs26(zxw49001, zxw50001, app(ty_Ratio, cha)) → new_esEs14(zxw49001, zxw50001, cha)
new_esEs26(zxw49001, zxw50001, app(ty_Maybe, cgb)) → new_esEs7(zxw49001, zxw50001, cgb)
new_esEs26(zxw49001, zxw50001, ty_Float) → new_esEs19(zxw49001, zxw50001)
new_esEs26(zxw49001, zxw50001, app(app(ty_Either, cgg), cgh)) → new_esEs6(zxw49001, zxw50001, cgg, cgh)
new_esEs26(zxw49001, zxw50001, app(app(app(ty_@3, cgd), cge), cgf)) → new_esEs5(zxw49001, zxw50001, cgd, cge, cgf)
new_esEs26(zxw49001, zxw50001, ty_@0) → new_esEs20(zxw49001, zxw50001)
new_ltEs20(zxw49002, zxw50002, ty_Bool) → new_ltEs5(zxw49002, zxw50002)
new_ltEs20(zxw49002, zxw50002, app(ty_Maybe, ceh)) → new_ltEs8(zxw49002, zxw50002, ceh)
new_ltEs20(zxw49002, zxw50002, ty_Integer) → new_ltEs16(zxw49002, zxw50002)
new_ltEs20(zxw49002, zxw50002, app(ty_[], cfa)) → new_ltEs13(zxw49002, zxw50002, cfa)
new_ltEs20(zxw49002, zxw50002, app(app(app(ty_@3, cfb), cfc), cfd)) → new_ltEs15(zxw49002, zxw50002, cfb, cfc, cfd)
new_ltEs20(zxw49002, zxw50002, ty_Ordering) → new_ltEs4(zxw49002, zxw50002)
new_ltEs20(zxw49002, zxw50002, app(app(ty_@2, cef), ceg)) → new_ltEs9(zxw49002, zxw50002, cef, ceg)
new_ltEs20(zxw49002, zxw50002, ty_Char) → new_ltEs12(zxw49002, zxw50002)
new_ltEs20(zxw49002, zxw50002, app(ty_Ratio, cfg)) → new_ltEs17(zxw49002, zxw50002, cfg)
new_ltEs20(zxw49002, zxw50002, ty_@0) → new_ltEs14(zxw49002, zxw50002)
new_ltEs20(zxw49002, zxw50002, ty_Float) → new_ltEs6(zxw49002, zxw50002)
new_ltEs20(zxw49002, zxw50002, ty_Double) → new_ltEs11(zxw49002, zxw50002)
new_ltEs20(zxw49002, zxw50002, app(app(ty_Either, cfe), cff)) → new_ltEs7(zxw49002, zxw50002, cfe, cff)
new_ltEs20(zxw49002, zxw50002, ty_Int) → new_ltEs10(zxw49002, zxw50002)
new_pePe(False, zxw213) → zxw213
new_pePe(True, zxw213) → True
new_ltEs9(@2(zxw49000, zxw49001), @2(zxw50000, zxw50001), beg, beh) → new_pePe(new_lt10(zxw49000, zxw50000, beg), new_asAs(new_esEs23(zxw49000, zxw50000, beg), new_ltEs18(zxw49001, zxw50001, beh)))
new_lt10(zxw49000, zxw50000, ty_Float) → new_lt7(zxw49000, zxw50000)
new_lt10(zxw49000, zxw50000, ty_Double) → new_lt8(zxw49000, zxw50000)
new_lt10(zxw49000, zxw50000, ty_Int) → new_lt4(zxw49000, zxw50000)
new_lt10(zxw49000, zxw50000, app(app(ty_@2, hb), hc)) → new_lt11(zxw49000, zxw50000, hb, hc)
new_lt10(zxw49000, zxw50000, ty_Ordering) → new_lt14(zxw49000, zxw50000)
new_lt10(zxw49000, zxw50000, app(ty_Maybe, bgc)) → new_lt12(zxw49000, zxw50000, bgc)
new_lt10(zxw49000, zxw50000, app(app(app(ty_@3, bgd), bge), bgf)) → new_lt16(zxw49000, zxw50000, bgd, bge, bgf)
new_lt10(zxw49000, zxw50000, app(app(ty_Either, be), bf)) → new_lt17(zxw49000, zxw50000, be, bf)
new_lt10(zxw49000, zxw50000, app(ty_Ratio, bgg)) → new_lt18(zxw49000, zxw50000, bgg)
new_lt10(zxw49000, zxw50000, ty_Integer) → new_lt5(zxw49000, zxw50000)
new_lt10(zxw49000, zxw50000, ty_Char) → new_lt6(zxw49000, zxw50000)
new_lt10(zxw49000, zxw50000, ty_Bool) → new_lt13(zxw49000, zxw50000)
new_lt10(zxw49000, zxw50000, app(ty_[], db)) → new_lt9(zxw49000, zxw50000, db)
new_lt10(zxw49000, zxw50000, ty_@0) → new_lt15(zxw49000, zxw50000)
new_esEs23(zxw49000, zxw50000, app(app(ty_@2, hb), hc)) → new_esEs4(zxw49000, zxw50000, hb, hc)
new_esEs23(zxw49000, zxw50000, ty_Float) → new_esEs19(zxw49000, zxw50000)
new_esEs23(zxw49000, zxw50000, ty_Char) → new_esEs15(zxw49000, zxw50000)
new_esEs23(zxw49000, zxw50000, ty_Bool) → new_esEs9(zxw49000, zxw50000)
new_esEs23(zxw49000, zxw50000, app(ty_Maybe, bgc)) → new_esEs7(zxw49000, zxw50000, bgc)
new_esEs23(zxw49000, zxw50000, app(app(ty_Either, be), bf)) → new_esEs6(zxw49000, zxw50000, be, bf)
new_esEs23(zxw49000, zxw50000, ty_Ordering) → new_esEs8(zxw49000, zxw50000)
new_esEs23(zxw49000, zxw50000, ty_Integer) → new_esEs17(zxw49000, zxw50000)
new_esEs23(zxw49000, zxw50000, app(ty_Ratio, bgg)) → new_esEs14(zxw49000, zxw50000, bgg)
new_esEs23(zxw49000, zxw50000, ty_@0) → new_esEs20(zxw49000, zxw50000)
new_esEs23(zxw49000, zxw50000, ty_Double) → new_esEs18(zxw49000, zxw50000)
new_esEs23(zxw49000, zxw50000, ty_Int) → new_esEs13(zxw49000, zxw50000)
new_esEs23(zxw49000, zxw50000, app(ty_[], db)) → new_esEs16(zxw49000, zxw50000, db)
new_esEs23(zxw49000, zxw50000, app(app(app(ty_@3, bgd), bge), bgf)) → new_esEs5(zxw49000, zxw50000, bgd, bge, bgf)
new_ltEs18(zxw49001, zxw50001, ty_Integer) → new_ltEs16(zxw49001, zxw50001)
new_ltEs18(zxw49001, zxw50001, app(ty_[], bfd)) → new_ltEs13(zxw49001, zxw50001, bfd)
new_ltEs18(zxw49001, zxw50001, ty_Int) → new_ltEs10(zxw49001, zxw50001)
new_ltEs18(zxw49001, zxw50001, app(app(ty_Either, bfh), bga)) → new_ltEs7(zxw49001, zxw50001, bfh, bga)
new_ltEs18(zxw49001, zxw50001, ty_@0) → new_ltEs14(zxw49001, zxw50001)
new_ltEs18(zxw49001, zxw50001, ty_Ordering) → new_ltEs4(zxw49001, zxw50001)
new_ltEs18(zxw49001, zxw50001, ty_Bool) → new_ltEs5(zxw49001, zxw50001)
new_ltEs18(zxw49001, zxw50001, app(app(app(ty_@3, bfe), bff), bfg)) → new_ltEs15(zxw49001, zxw50001, bfe, bff, bfg)
new_ltEs18(zxw49001, zxw50001, ty_Float) → new_ltEs6(zxw49001, zxw50001)
new_ltEs18(zxw49001, zxw50001, ty_Double) → new_ltEs11(zxw49001, zxw50001)
new_ltEs18(zxw49001, zxw50001, app(app(ty_@2, bfa), bfb)) → new_ltEs9(zxw49001, zxw50001, bfa, bfb)
new_ltEs18(zxw49001, zxw50001, app(ty_Ratio, bgb)) → new_ltEs17(zxw49001, zxw50001, bgb)
new_ltEs18(zxw49001, zxw50001, ty_Char) → new_ltEs12(zxw49001, zxw50001)
new_ltEs18(zxw49001, zxw50001, app(ty_Maybe, bfc)) → new_ltEs8(zxw49001, zxw50001, bfc)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Bool) → new_ltEs5(zxw49000, zxw50000)
new_ltEs8(Nothing, Just(zxw50000), hd) → True
new_ltEs8(Just(zxw49000), Just(zxw50000), app(app(ty_@2, he), hf)) → new_ltEs9(zxw49000, zxw50000, he, hf)
new_ltEs8(Just(zxw49000), Nothing, hd) → False
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Double) → new_ltEs11(zxw49000, zxw50000)
new_ltEs8(Just(zxw49000), Just(zxw50000), app(ty_[], hh)) → new_ltEs13(zxw49000, zxw50000, hh)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_@0) → new_ltEs14(zxw49000, zxw50000)
new_ltEs8(Just(zxw49000), Just(zxw50000), app(ty_Ratio, baf)) → new_ltEs17(zxw49000, zxw50000, baf)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Float) → new_ltEs6(zxw49000, zxw50000)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Ordering) → new_ltEs4(zxw49000, zxw50000)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Int) → new_ltEs10(zxw49000, zxw50000)
new_ltEs8(Nothing, Nothing, hd) → True
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Char) → new_ltEs12(zxw49000, zxw50000)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Integer) → new_ltEs16(zxw49000, zxw50000)
new_ltEs8(Just(zxw49000), Just(zxw50000), app(app(app(ty_@3, baa), bab), bac)) → new_ltEs15(zxw49000, zxw50000, baa, bab, bac)
new_lt15(zxw49000, zxw50000) → new_esEs8(new_compare31(zxw49000, zxw50000), LT)
new_lt9(zxw49000, zxw50000, db) → new_esEs8(new_compare0(zxw49000, zxw50000, db), LT)
new_lt13(zxw49000, zxw50000) → new_esEs8(new_compare18(zxw49000, zxw50000), LT)
new_lt6(zxw49000, zxw50000) → new_esEs8(new_compare12(zxw49000, zxw50000), LT)
new_lt5(zxw49000, zxw50000) → new_esEs8(new_compare9(zxw49000, zxw50000), LT)
new_lt18(zxw49000, zxw50000, bgg) → new_esEs8(new_compare8(zxw49000, zxw50000, bgg), LT)
new_lt17(zxw49000, zxw50000, be, bf) → new_esEs8(new_compare32(zxw49000, zxw50000, be, bf), LT)
new_lt16(zxw49000, zxw50000, bgd, bge, bgf) → new_esEs8(new_compare28(zxw49000, zxw50000, bgd, bge, bgf), LT)
new_compare28(zxw49000, zxw50000, bgd, bge, bgf) → new_compare210(zxw49000, zxw50000, new_esEs5(zxw49000, zxw50000, bgd, bge, bgf), bgd, bge, bgf)
new_compare210(zxw49000, zxw50000, False, bgd, bge, bgf) → new_compare110(zxw49000, zxw50000, new_ltEs15(zxw49000, zxw50000, bgd, bge, bgf), bgd, bge, bgf)
new_compare210(zxw49000, zxw50000, True, bgd, bge, bgf) → EQ
new_compare110(zxw49000, zxw50000, True, bgd, bge, bgf) → LT
new_compare110(zxw49000, zxw50000, False, bgd, bge, bgf) → GT
new_lt12(zxw490, zxw500, bdd) → new_esEs8(new_compare19(zxw490, zxw500, bdd), LT)
new_lt14(zxw49000, zxw50000) → new_esEs8(new_compare6(zxw49000, zxw50000), LT)
new_lt11(zxw49000, zxw50000, hb, hc) → new_esEs8(new_compare30(zxw49000, zxw50000, hb, hc), LT)
new_compare30(zxw49000, zxw50000, hb, hc) → new_compare27(zxw49000, zxw50000, new_esEs4(zxw49000, zxw50000, hb, hc), hb, hc)
new_compare27(zxw49000, zxw50000, False, hb, hc) → new_compare17(zxw49000, zxw50000, new_ltEs9(zxw49000, zxw50000, hb, hc), hb, hc)
new_compare27(zxw49000, zxw50000, True, hb, hc) → EQ
new_compare17(zxw49000, zxw50000, True, hb, hc) → LT
new_compare17(zxw49000, zxw50000, False, hb, hc) → GT
new_lt4(zxw490, zxw500) → new_esEs8(new_compare7(zxw490, zxw500), LT)
new_lt8(zxw49000, zxw50000) → new_esEs8(new_compare16(zxw49000, zxw50000), LT)
new_lt7(zxw49000, zxw50000) → new_esEs8(new_compare14(zxw49000, zxw50000), LT)
new_compare36(zxw20, zxw15, bb) → new_compare26(Just(zxw20), Just(zxw15), new_esEs30(zxw20, zxw15, bb), bb)
new_esEs30(zxw20, zxw15, ty_Bool) → new_esEs9(zxw20, zxw15)
new_esEs30(zxw20, zxw15, ty_Float) → new_esEs19(zxw20, zxw15)
new_esEs30(zxw20, zxw15, app(ty_Ratio, bdf)) → new_esEs14(zxw20, zxw15, bdf)
new_esEs30(zxw20, zxw15, ty_@0) → new_esEs20(zxw20, zxw15)
new_esEs30(zxw20, zxw15, ty_Double) → new_esEs18(zxw20, zxw15)
new_esEs30(zxw20, zxw15, app(app(ty_Either, bec), bed)) → new_esEs6(zxw20, zxw15, bec, bed)
new_esEs30(zxw20, zxw15, app(ty_Maybe, bde)) → new_esEs7(zxw20, zxw15, bde)
new_esEs30(zxw20, zxw15, app(ty_[], bdg)) → new_esEs16(zxw20, zxw15, bdg)
new_esEs30(zxw20, zxw15, ty_Int) → new_esEs13(zxw20, zxw15)
new_esEs30(zxw20, zxw15, ty_Ordering) → new_esEs8(zxw20, zxw15)
new_esEs30(zxw20, zxw15, ty_Integer) → new_esEs17(zxw20, zxw15)
new_esEs30(zxw20, zxw15, app(app(app(ty_@3, bdh), bea), beb)) → new_esEs5(zxw20, zxw15, bdh, bea, beb)
new_esEs30(zxw20, zxw15, ty_Char) → new_esEs15(zxw20, zxw15)
new_esEs30(zxw20, zxw15, app(app(ty_@2, bee), bef)) → new_esEs4(zxw20, zxw15, bee, bef)
new_compare35(zxw400, h) → new_compare26(Just(zxw400), Nothing, False, h)

The set Q consists of the following terms:

new_esEs17(Integer(x0), Integer(x1))
new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_ltEs7(Right(x0), Right(x1), x2, ty_Bool)
new_compare8(:%(x0, x1), :%(x2, x3), ty_Integer)
new_lt10(x0, x1, ty_Double)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_compare18(x0, x1)
new_compare29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare29(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Double)
new_pePe(False, x0)
new_lt10(x0, x1, app(app(ty_Either, x2), x3))
new_compare29(x0, x1, app(app(ty_Either, x2), x3))
new_lt17(x0, x1, x2, x3)
new_esEs31(x0, x1, ty_Double)
new_esEs10(x0, x1, app(ty_[], x2))
new_ltEs8(Nothing, Nothing, x0)
new_compare210(x0, x1, True, x2, x3, x4)
new_compare7(x0, x1)
new_primMulNat0(Succ(x0), Zero)
new_esEs31(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(ty_[], x2))
new_esEs7(Just(x0), Just(x1), ty_Double)
new_ltEs8(Just(x0), Just(x1), ty_Integer)
new_esEs10(x0, x1, ty_Int)
new_ltEs10(x0, x1)
new_esEs28(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Ordering)
new_esEs31(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs12(x0, x1, ty_Char)
new_compare25(x0, x1, True, x2, x3)
new_primMulNat0(Succ(x0), Succ(x1))
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare8(:%(x0, x1), :%(x2, x3), ty_Int)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_ltEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs16(x0, x1)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_lt10(x0, x1, app(ty_Ratio, x2))
new_ltEs8(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs6(Right(x0), Right(x1), x2, ty_Char)
new_compare13(x0, x1, True)
new_ltEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs10(x0, x1, ty_Ordering)
new_esEs31(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, ty_Float)
new_esEs11(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_Int)
new_esEs31(x0, x1, ty_Int)
new_compare11(x0, x1, True, x2)
new_ltEs19(x0, x1, ty_Ordering)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_lt10(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(GT, GT)
new_compare11(x0, x1, False, x2)
new_esEs8(LT, LT)
new_compare29(x0, x1, ty_Double)
new_esEs18(Double(x0, x1), Double(x2, x3))
new_primCmpNat0(Zero, x0)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_ltEs8(Just(x0), Just(x1), ty_Bool)
new_ltEs8(Just(x0), Just(x1), app(ty_[], x2))
new_esEs11(x0, x1, ty_@0)
new_primCmpNat1(Zero, Succ(x0))
new_esEs31(x0, x1, app(ty_Maybe, x2))
new_esEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, ty_Int)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_sr(x0, x1)
new_ltEs5(False, False)
new_compare17(x0, x1, False, x2, x3)
new_ltEs8(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare6(x0, x1)
new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt10(x0, x1, ty_Ordering)
new_compare28(x0, x1, x2, x3, x4)
new_compare29(x0, x1, ty_Int)
new_esEs30(x0, x1, ty_Bool)
new_compare19(x0, x1, x2)
new_esEs26(x0, x1, ty_Integer)
new_primEqNat0(Zero, Succ(x0))
new_primCmpNat1(Zero, Zero)
new_compare16(Double(x0, x1), Double(x2, x3))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_lt7(x0, x1)
new_esEs28(x0, x1, ty_@0)
new_ltEs20(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_Integer)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Double)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_Char)
new_lt12(x0, x1, x2)
new_ltEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_compare15(x0, x1, True, x2, x3)
new_esEs24(x0, x1, ty_Int)
new_compare26(Just(x0), Just(x1), False, x2)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_primEqNat0(Zero, Zero)
new_compare32(x0, x1, x2, x3)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs30(x0, x1, app(ty_[], x2))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs7(Left(x0), Left(x1), ty_Char, x2)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_ltEs8(Just(x0), Just(x1), ty_Double)
new_ltEs8(Just(x0), Just(x1), ty_Ordering)
new_ltEs19(x0, x1, ty_@0)
new_compare24(x0, x1, False)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs9(True, True)
new_compare27(x0, x1, True, x2, x3)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_lt4(x0, x1)
new_ltEs8(Nothing, Just(x0), x1)
new_primMulNat0(Zero, Zero)
new_esEs23(x0, x1, ty_Char)
new_esEs30(x0, x1, ty_Ordering)
new_compare29(x0, x1, app(app(ty_@2, x2), x3))
new_esEs10(x0, x1, ty_@0)
new_lt10(x0, x1, ty_Char)
new_ltEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs30(x0, x1, ty_Int)
new_compare26(Just(x0), Nothing, False, x1)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_Integer)
new_fsEs(x0)
new_ltEs4(GT, GT)
new_lt8(x0, x1)
new_esEs6(Right(x0), Right(x1), x2, ty_Integer)
new_esEs30(x0, x1, ty_@0)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(x0, x1, ty_Float)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs28(x0, x1, ty_Double)
new_ltEs8(Just(x0), Nothing, x1)
new_esEs31(x0, x1, app(app(ty_Either, x2), x3))
new_esEs11(x0, x1, app(ty_Ratio, x2))
new_ltEs8(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt10(x0, x1, ty_Int)
new_esEs10(x0, x1, ty_Bool)
new_ltEs18(x0, x1, app(ty_[], x2))
new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs10(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs23(x0, x1, ty_Ordering)
new_esEs7(Just(x0), Just(x1), ty_Int)
new_esEs10(x0, x1, ty_Char)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt10(x0, x1, app(ty_Maybe, x2))
new_pePe(True, x0)
new_ltEs15(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_primPlusNat0(Zero, x0)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_compare26(Nothing, Nothing, False, x0)
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Int)
new_lt6(x0, x1)
new_esEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs26(x0, x1, ty_Bool)
new_compare24(x0, x1, True)
new_ltEs18(x0, x1, ty_Integer)
new_esEs10(x0, x1, app(ty_Maybe, x2))
new_compare15(x0, x1, False, x2, x3)
new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_compare14(Float(x0, x1), Float(x2, x3))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs7(Right(x0), Left(x1), x2, x3)
new_ltEs7(Left(x0), Right(x1), x2, x3)
new_lt10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_compare110(x0, x1, False, x2, x3, x4)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_ltEs14(x0, x1)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_primPlusNat1(Zero, Zero)
new_esEs11(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Right(x0), Left(x1), x2, x3)
new_esEs6(Left(x0), Right(x1), x2, x3)
new_primCompAux0(x0, GT)
new_ltEs7(Right(x0), Right(x1), x2, ty_Char)
new_esEs6(Left(x0), Left(x1), ty_Int, x2)
new_compare23(x0, x1, True)
new_esEs31(x0, x1, ty_Float)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_compare29(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, app(ty_[], x2))
new_lt15(x0, x1)
new_esEs6(Left(x0), Left(x1), ty_Integer, x2)
new_esEs14(:%(x0, x1), :%(x2, x3), x4)
new_compare13(x0, x1, False)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_lt20(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_@0)
new_esEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_primPlusNat0(Succ(x0), x1)
new_ltEs4(EQ, EQ)
new_esEs31(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, ty_Char)
new_esEs6(Right(x0), Right(x1), x2, ty_Int)
new_ltEs11(x0, x1)
new_compare29(x0, x1, app(ty_Ratio, x2))
new_esEs12(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Integer)
new_ltEs20(x0, x1, ty_Char)
new_esEs7(Just(x0), Just(x1), ty_Char)
new_esEs12(x0, x1, ty_Float)
new_compare31(@0, @0)
new_ltEs7(Left(x0), Left(x1), ty_Int, x2)
new_esEs7(Just(x0), Just(x1), ty_Float)
new_compare36(x0, x1, x2)
new_primCmpNat2(x0, Zero)
new_ltEs4(LT, EQ)
new_ltEs4(EQ, LT)
new_esEs12(x0, x1, ty_Int)
new_ltEs13(x0, x1, x2)
new_lt19(x0, x1, ty_Double)
new_esEs12(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, app(ty_Ratio, x2))
new_ltEs7(Left(x0), Left(x1), ty_@0, x2)
new_esEs21(x0, x1, app(ty_[], x2))
new_primMulInt(Pos(x0), Pos(x1))
new_lt20(x0, x1, ty_Bool)
new_esEs30(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_@0)
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_asAs(True, x0)
new_primEqNat0(Succ(x0), Zero)
new_ltEs8(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Right(x0), Right(x1), x2, ty_Bool)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_ltEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs13(x0, x1)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs21(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Integer)
new_lt20(x0, x1, ty_@0)
new_esEs12(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, ty_Bool)
new_lt20(x0, x1, ty_Char)
new_esEs6(Left(x0), Left(x1), ty_Float, x2)
new_esEs12(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_Ordering)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Ordering)
new_esEs6(Right(x0), Right(x1), x2, ty_Float)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_compare26(Nothing, Just(x0), False, x1)
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_ltEs20(x0, x1, ty_Bool)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs12(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs27(x0, x1, ty_Int)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Double)
new_esEs25(x0, x1, ty_Integer)
new_ltEs7(Right(x0), Right(x1), x2, ty_Integer)
new_primMulInt(Neg(x0), Neg(x1))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs31(x0, x1, ty_Bool)
new_lt10(x0, x1, ty_Bool)
new_primPlusNat1(Succ(x0), Zero)
new_esEs22(x0, x1, ty_Float)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs6(Left(x0), Left(x1), ty_@0, x2)
new_ltEs4(LT, LT)
new_lt11(x0, x1, x2, x3)
new_esEs10(x0, x1, ty_Integer)
new_esEs31(x0, x1, ty_Ordering)
new_esEs12(x0, x1, app(app(ty_@2, x2), x3))
new_esEs16([], [], x0)
new_ltEs19(x0, x1, ty_Integer)
new_compare23(x0, x1, False)
new_lt16(x0, x1, x2, x3, x4)
new_compare29(x0, x1, app(ty_[], x2))
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs11(x0, x1, ty_Bool)
new_esEs11(x0, x1, app(app(ty_Either, x2), x3))
new_esEs16([], :(x0, x1), x2)
new_esEs23(x0, x1, ty_Double)
new_esEs21(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_Ordering)
new_ltEs9(@2(x0, x1), @2(x2, x3), x4, x5)
new_primPlusNat1(Zero, Succ(x0))
new_ltEs12(x0, x1)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_compare10(x0, x1, False)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_primCmpNat0(Succ(x0), x1)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, ty_@0)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs8(GT, EQ)
new_esEs8(EQ, GT)
new_esEs22(x0, x1, ty_Bool)
new_lt19(x0, x1, ty_Float)
new_ltEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_lt19(x0, x1, ty_Integer)
new_ltEs8(Just(x0), Just(x1), ty_Char)
new_esEs7(Nothing, Just(x0), x1)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt18(x0, x1, x2)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs16(:(x0, x1), :(x2, x3), x4)
new_ltEs8(Just(x0), Just(x1), ty_Float)
new_ltEs7(Left(x0), Left(x1), ty_Float, x2)
new_lt5(x0, x1)
new_compare29(x0, x1, ty_Ordering)
new_ltEs18(x0, x1, ty_Bool)
new_esEs11(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_@0)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, ty_Int)
new_esEs11(x0, x1, ty_Char)
new_ltEs7(Left(x0), Left(x1), ty_Double, x2)
new_esEs27(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Float)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_lt19(x0, x1, ty_Ordering)
new_compare29(x0, x1, ty_Integer)
new_compare25(x0, x1, False, x2, x3)
new_esEs26(x0, x1, app(ty_[], x2))
new_ltEs18(x0, x1, ty_Float)
new_esEs9(False, False)
new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs21(x0, x1, ty_Double)
new_esEs12(x0, x1, ty_Ordering)
new_primCompAux1(x0, x1, x2, x3)
new_ltEs17(x0, x1, x2)
new_compare0([], :(x0, x1), x2)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpNat1(Succ(x0), Succ(x1))
new_esEs26(x0, x1, ty_@0)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs6(x0, x1)
new_lt10(x0, x1, ty_Float)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs22(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Float)
new_primCompAux0(x0, EQ)
new_esEs10(x0, x1, app(app(ty_Either, x2), x3))
new_compare210(x0, x1, False, x2, x3, x4)
new_esEs21(x0, x1, ty_Integer)
new_primCmpNat1(Succ(x0), Zero)
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_esEs6(Left(x0), Left(x1), ty_Bool, x2)
new_esEs7(Nothing, Nothing, x0)
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, ty_@0)
new_esEs12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, ty_Double)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_lt13(x0, x1)
new_esEs23(x0, x1, ty_Bool)
new_ltEs5(True, True)
new_ltEs7(Right(x0), Right(x1), x2, ty_Int)
new_lt19(x0, x1, ty_Int)
new_compare35(x0, x1)
new_lt19(x0, x1, ty_Char)
new_ltEs4(EQ, GT)
new_ltEs4(GT, EQ)
new_esEs31(x0, x1, ty_Integer)
new_not(True)
new_esEs11(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Float)
new_ltEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs11(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, ty_Char)
new_lt19(x0, x1, ty_@0)
new_compare26(x0, x1, True, x2)
new_esEs21(x0, x1, ty_Ordering)
new_ltEs8(Just(x0), Just(x1), app(ty_Maybe, x2))
new_compare0([], [], x0)
new_esEs26(x0, x1, ty_Char)
new_esEs7(Just(x0), Nothing, x1)
new_esEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs18(x0, x1, ty_Int)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Ordering)
new_not(False)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_lt14(x0, x1)
new_compare12(Char(x0), Char(x1))
new_esEs15(Char(x0), Char(x1))
new_esEs10(x0, x1, app(ty_Ratio, x2))
new_compare10(x0, x1, True)
new_lt10(x0, x1, ty_@0)
new_asAs(False, x0)
new_esEs22(x0, x1, ty_Ordering)
new_ltEs18(x0, x1, ty_Char)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_compare29(x0, x1, ty_Float)
new_compare17(x0, x1, True, x2, x3)
new_lt19(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_Char)
new_esEs31(x0, x1, ty_Char)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_ltEs8(Just(x0), Just(x1), ty_@0)
new_esEs20(@0, @0)
new_esEs6(Right(x0), Right(x1), x2, ty_Double)
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_ltEs7(Right(x0), Right(x1), x2, ty_Double)
new_esEs22(x0, x1, app(ty_[], x2))
new_ltEs7(Left(x0), Left(x1), ty_Integer, x2)
new_esEs23(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Int)
new_compare0(:(x0, x1), [], x2)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_ltEs19(x0, x1, ty_Double)
new_esEs9(True, False)
new_esEs9(False, True)
new_esEs22(x0, x1, ty_Char)
new_compare29(x0, x1, ty_Bool)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs7(Right(x0), Right(x1), x2, ty_Float)
new_esEs30(x0, x1, ty_Double)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, ty_Integer)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs11(x0, x1, ty_Double)
new_ltEs20(x0, x1, ty_Float)
new_primCompAux0(x0, LT)
new_primCmpNat2(x0, Succ(x1))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs11(x0, x1, app(ty_[], x2))
new_ltEs7(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs12(x0, x1, ty_Integer)
new_esEs6(Left(x0), Left(x1), ty_Double, x2)
new_esEs10(x0, x1, ty_Double)
new_esEs6(Right(x0), Right(x1), x2, ty_@0)
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_sr0(Integer(x0), Integer(x1))
new_lt10(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs6(Left(x0), Left(x1), ty_Char, x2)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Pos(Zero), Pos(Zero))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_compare30(x0, x1, x2, x3)
new_ltEs18(x0, x1, ty_Double)
new_esEs12(x0, x1, ty_Double)
new_compare110(x0, x1, True, x2, x3, x4)
new_esEs12(x0, x1, ty_Bool)
new_lt9(x0, x1, x2)
new_compare9(Integer(x0), Integer(x1))
new_lt10(x0, x1, ty_Integer)
new_esEs30(x0, x1, ty_Char)
new_esEs19(Float(x0, x1), Float(x2, x3))
new_primMulNat0(Zero, Succ(x0))
new_esEs7(Just(x0), Just(x1), ty_@0)
new_ltEs4(GT, LT)
new_ltEs4(LT, GT)
new_ltEs5(True, False)
new_ltEs5(False, True)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, app(ty_[], x2))
new_ltEs7(Right(x0), Right(x1), x2, ty_@0)
new_ltEs8(Just(x0), Just(x1), ty_Int)
new_compare29(x0, x1, ty_@0)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Float)
new_compare27(x0, x1, False, x2, x3)
new_esEs23(x0, x1, ty_Float)
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs30(x0, x1, ty_Float)
new_esEs16(:(x0, x1), [], x2)

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) → new_minusFM(new_splitLT30(zxw30, zxw31, zxw32, zxw33, zxw34, zxw40, h, ba), zxw43, h, ba, bb)
new_minusFM(Branch(zxw30, zxw31, zxw32, zxw33, zxw34), Branch(zxw40, zxw41, zxw42, zxw43, zxw44), h, ba, bb) → new_minusFM(new_splitGT30(zxw30, zxw31, zxw32, zxw33, zxw34, zxw40, h, ba), zxw44, h, ba, bb)

The TRS R consists of the following rules:

new_esEs6(Right(zxw4000), Right(zxw3000), hf, ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_esEs29(zxw400, zxw300, ty_Integer) → new_esEs17(zxw400, zxw300)
new_esEs28(zxw4000, zxw3000, ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_esEs7(Just(zxw4000), Just(zxw3000), app(ty_Maybe, bgf)) → new_esEs7(zxw4000, zxw3000, bgf)
new_splitLT30(Just(zxw300), zxw31, zxw32, zxw33, zxw34, Nothing, h, ba) → new_splitLT22(zxw300, zxw31, zxw32, zxw33, zxw34, new_esEs8(new_compare26(Nothing, Just(zxw300), False, h), LT), h, ba)
new_ltEs19(zxw4900, zxw5000, ty_Integer) → new_ltEs16(zxw4900, zxw5000)
new_addToFM_C4(EmptyFM, zxw300, zxw31, h, ba) → Branch(Just(zxw300), zxw31, Pos(Succ(Zero)), new_emptyFM(h, ba), new_emptyFM(h, ba))
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_@0, dcb) → new_ltEs14(zxw49000, zxw50000)
new_esEs27(zxw49000, zxw50000, app(ty_[], cgd)) → new_esEs16(zxw49000, zxw50000, cgd)
new_ltEs4(EQ, GT) → True
new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba)
new_splitGT22(zxw300, zxw31, zxw32, zxw33, zxw34, False, h, ba) → new_splitGT14(zxw300, zxw31, zxw32, zxw33, zxw34, new_esEs8(new_compare34(zxw300, h), LT), h, ba)
new_esEs22(zxw4000, zxw3000, ty_@0) → new_esEs20(zxw4000, zxw3000)
new_compare15(zxw49000, zxw50000, True, bgc, bgd) → LT
new_esEs6(Right(zxw4000), Right(zxw3000), hf, ty_Float) → new_esEs19(zxw4000, zxw3000)
new_ltEs9(@2(zxw49000, zxw49001), @2(zxw50000, zxw50001), beb, bec) → new_pePe(new_lt10(zxw49000, zxw50000, beb), new_asAs(new_esEs23(zxw49000, zxw50000, beb), new_ltEs18(zxw49001, zxw50001, bec)))
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Integer, hg) → new_esEs17(zxw4000, zxw3000)
new_splitLT30(Just(zxw300), zxw31, zxw32, zxw33, zxw34, Just(zxw400), h, ba) → new_splitLT23(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs8(new_compare26(Just(zxw400), Just(zxw300), new_esEs31(zxw400, zxw300, h), h), LT), h, ba)
new_esEs31(zxw400, zxw300, ty_Ordering) → new_esEs8(zxw400, zxw300)
new_primCmpNat1(Zero, Succ(zxw50000)) → LT
new_esEs23(zxw49000, zxw50000, app(app(ty_@2, ff), fg)) → new_esEs4(zxw49000, zxw50000, ff, fg)
new_esEs22(zxw4000, zxw3000, ty_Float) → new_esEs19(zxw4000, zxw3000)
new_compare29(zxw49000, zxw50000, ty_Char) → new_compare12(zxw49000, zxw50000)
new_esEs6(Right(zxw4000), Right(zxw3000), hf, ty_Int) → new_esEs13(zxw4000, zxw3000)
new_lt19(zxw49001, zxw50001, ty_Integer) → new_lt5(zxw49001, zxw50001)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Bool) → new_ltEs5(zxw49000, zxw50000)
new_compare33(h) → new_compare26(Nothing, Nothing, True, h)
new_esEs27(zxw49000, zxw50000, app(ty_Maybe, cgc)) → new_esEs7(zxw49000, zxw50000, cgc)
new_esEs12(zxw4000, zxw3000, ty_Bool) → new_esEs9(zxw4000, zxw3000)
new_esEs11(zxw4001, zxw3001, app(ty_[], dc)) → new_esEs16(zxw4001, zxw3001, dc)
new_esEs12(zxw4000, zxw3000, ty_Char) → new_esEs15(zxw4000, zxw3000)
new_compare12(Char(zxw49000), Char(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_ltEs19(zxw4900, zxw5000, ty_Double) → new_ltEs11(zxw4900, zxw5000)
new_sizeFM0(Branch(zxw540, zxw541, zxw542, zxw543, zxw544), h, ba) → zxw542
new_esEs31(zxw400, zxw300, app(app(app(ty_@3, bc), bd), be)) → new_esEs5(zxw400, zxw300, bc, bd, be)
new_ltEs20(zxw49002, zxw50002, ty_Bool) → new_ltEs5(zxw49002, zxw50002)
new_compare29(zxw49000, zxw50000, ty_Double) → new_compare16(zxw49000, zxw50000)
new_lt19(zxw49001, zxw50001, ty_Ordering) → new_lt14(zxw49001, zxw50001)
new_esEs23(zxw49000, zxw50000, ty_Float) → new_esEs19(zxw49000, zxw50000)
new_lt19(zxw49001, zxw50001, ty_Int) → new_lt4(zxw49001, zxw50001)
new_esEs7(Just(zxw4000), Just(zxw3000), app(app(ty_Either, bhd), bhe)) → new_esEs6(zxw4000, zxw3000, bhd, bhe)
new_primMulNat0(Zero, Zero) → Zero
new_ltEs7(Left(zxw49000), Right(zxw50000), dca, dcb) → True
new_compare26(Just(zxw4900), Nothing, False, bcf) → GT
new_esEs27(zxw49000, zxw50000, ty_Bool) → new_esEs9(zxw49000, zxw50000)
new_esEs26(zxw49001, zxw50001, app(ty_[], cfb)) → new_esEs16(zxw49001, zxw50001, cfb)
new_ltEs18(zxw49001, zxw50001, ty_Integer) → new_ltEs16(zxw49001, zxw50001)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_ltEs18(zxw49001, zxw50001, app(ty_[], beg)) → new_ltEs13(zxw49001, zxw50001, beg)
new_mkVBalBranch3MkVBalBranch22(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkBalBranch(zxw620, zxw621, new_mkVBalBranch1(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw623, h, ba), zxw624, h, ba)
new_splitLT15(zxw31, zxw32, zxw33, zxw34, zxw400, False, h, ba) → zxw33
new_ltEs20(zxw49002, zxw50002, app(ty_Maybe, cdg)) → new_ltEs8(zxw49002, zxw50002, cdg)
new_esEs11(zxw4001, zxw3001, ty_Char) → new_esEs15(zxw4001, zxw3001)
new_esEs11(zxw4001, zxw3001, ty_Float) → new_esEs19(zxw4001, zxw3001)
new_esEs29(zxw400, zxw300, ty_@0) → new_esEs20(zxw400, zxw300)
new_lt20(zxw49000, zxw50000, app(app(ty_@2, cga), cgb)) → new_lt11(zxw49000, zxw50000, cga, cgb)
new_esEs26(zxw49001, zxw50001, ty_Char) → new_esEs15(zxw49001, zxw50001)
new_lt8(zxw49000, zxw50000) → new_esEs8(new_compare16(zxw49000, zxw50000), LT)
new_splitLT14(zxw15, zxw16, zxw17, zxw18, zxw19, zxw20, False, bcg, caa) → zxw18
new_splitLT16(zxw31, zxw32, zxw33, zxw34, False, h, ba) → zxw33
new_addToFM_C12(zxw620, zxw621, zxw622, zxw623, zxw624, zxw300, zxw31, True, h, ba) → new_mkBalBranch(zxw620, zxw621, zxw623, new_addToFM_C4(zxw624, zxw300, zxw31, h, ba), h, ba)
new_splitLT24(zxw31, zxw32, zxw33, zxw34, zxw400, False, h, ba) → new_splitLT15(zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs8(new_compare35(zxw400, h), GT), h, ba)
new_esEs29(zxw400, zxw300, app(ty_Maybe, hc)) → new_esEs7(zxw400, zxw300, hc)
new_esEs23(zxw49000, zxw50000, ty_Char) → new_esEs15(zxw49000, zxw50000)
new_addToFM(zxw62, zxw300, zxw31, h, ba) → new_addToFM_C4(zxw62, zxw300, zxw31, h, ba)
new_mkBalBranch6MkBalBranch4(zxw50, zxw51, zxw54, zxw60, False, h, ba) → new_mkBalBranch6MkBalBranch3(zxw50, zxw51, zxw54, zxw60, new_gt(new_mkBalBranch6Size_l(zxw50, zxw51, zxw54, zxw60, h, ba), new_sr(new_sIZE_RATIO, new_mkBalBranch6Size_r(zxw50, zxw51, zxw54, zxw60, h, ba))), h, ba)
new_esEs23(zxw49000, zxw50000, ty_Bool) → new_esEs9(zxw49000, zxw50000)
new_esEs27(zxw49000, zxw50000, ty_Char) → new_esEs15(zxw49000, zxw50000)
new_lt10(zxw49000, zxw50000, ty_Float) → new_lt7(zxw49000, zxw50000)
new_compare26(Nothing, Just(zxw5000), False, bcf) → LT
new_esEs21(zxw4001, zxw3001, ty_Double) → new_esEs18(zxw4001, zxw3001)
new_ltEs19(zxw4900, zxw5000, ty_Int) → new_ltEs10(zxw4900, zxw5000)
new_primCmpNat1(Succ(zxw49000), Succ(zxw50000)) → new_primCmpNat1(zxw49000, zxw50000)
new_lt9(zxw49000, zxw50000, bfg) → new_esEs8(new_compare0(zxw49000, zxw50000, bfg), LT)
new_compare210(zxw49000, zxw50000, False, bfh, bga, bgb) → new_compare110(zxw49000, zxw50000, new_ltEs15(zxw49000, zxw50000, bfh, bga, bgb), bfh, bga, bgb)
new_esEs22(zxw4000, zxw3000, app(ty_Ratio, bbe)) → new_esEs14(zxw4000, zxw3000, bbe)
new_esEs21(zxw4001, zxw3001, app(ty_Ratio, bac)) → new_esEs14(zxw4001, zxw3001, bac)
new_esEs30(zxw20, zxw15, ty_Bool) → new_esEs9(zxw20, zxw15)
new_esEs7(Just(zxw4000), Just(zxw3000), app(app(ty_@2, bhf), bhg)) → new_esEs4(zxw4000, zxw3000, bhf, bhg)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Bool) → new_esEs9(zxw4000, zxw3000)
new_esEs30(zxw20, zxw15, ty_Float) → new_esEs19(zxw20, zxw15)
new_esEs25(zxw4000, zxw3000, ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_ltEs20(zxw49002, zxw50002, ty_Integer) → new_ltEs16(zxw49002, zxw50002)
new_esEs21(zxw4001, zxw3001, app(app(ty_Either, bah), bba)) → new_esEs6(zxw4001, zxw3001, bah, bba)
new_ltEs7(Left(zxw49000), Left(zxw50000), app(app(app(ty_@3, dcg), dch), dda), dcb) → new_ltEs15(zxw49000, zxw50000, dcg, dch, dda)
new_esEs29(zxw400, zxw300, ty_Bool) → new_esEs9(zxw400, zxw300)
new_ltEs14(zxw4900, zxw5000) → new_fsEs(new_compare31(zxw4900, zxw5000))
new_compare24(zxw49000, zxw50000, False) → new_compare13(zxw49000, zxw50000, new_ltEs5(zxw49000, zxw50000))
new_esEs7(Just(zxw4000), Just(zxw3000), app(ty_Ratio, bgg)) → new_esEs14(zxw4000, zxw3000, bgg)
new_ltEs7(Right(zxw49000), Right(zxw50000), dca, app(app(ty_@2, dde), ddf)) → new_ltEs9(zxw49000, zxw50000, dde, ddf)
new_lt4(zxw490, zxw500) → new_esEs8(new_compare7(zxw490, zxw500), LT)
new_esEs28(zxw4000, zxw3000, app(app(app(ty_@3, chf), chg), chh)) → new_esEs5(zxw4000, zxw3000, chf, chg, chh)
new_esEs28(zxw4000, zxw3000, ty_Bool) → new_esEs9(zxw4000, zxw3000)
new_mkVBalBranch1(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), EmptyFM, h, ba) → new_addToFM(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw300, zxw31, h, ba)
new_compare19(zxw490, zxw500, bcf) → new_compare26(zxw490, zxw500, new_esEs7(zxw490, zxw500, bcf), bcf)
new_esEs17(Integer(zxw4000), Integer(zxw3000)) → new_primEqInt(zxw4000, zxw3000)
new_pePe(False, zxw213) → zxw213
new_lt12(zxw490, zxw500, bcf) → new_esEs8(new_compare19(zxw490, zxw500, bcf), LT)
new_esEs31(zxw400, zxw300, app(ty_[], he)) → new_esEs16(zxw400, zxw300, he)
new_splitGT14(zxw300, zxw31, zxw32, zxw33, zxw34, True, h, ba) → new_mkVBalBranch1(zxw300, zxw31, new_splitGT4(zxw33, h, ba), zxw34, h, ba)
new_esEs20(@0, @0) → True
new_esEs6(Right(zxw4000), Right(zxw3000), hf, app(ty_Ratio, cca)) → new_esEs14(zxw4000, zxw3000, cca)
new_esEs6(Left(zxw4000), Left(zxw3000), app(app(ty_@2, cbf), cbg), hg) → new_esEs4(zxw4000, zxw3000, cbf, cbg)
new_esEs31(zxw400, zxw300, ty_Bool) → new_esEs9(zxw400, zxw300)
new_mkVBalBranch2(zxw31, EmptyFM, zxw61, h, ba) → new_addToFM1(zxw61, zxw31, h, ba)
new_compare23(zxw49000, zxw50000, True) → EQ
new_esEs11(zxw4001, zxw3001, ty_Int) → new_esEs13(zxw4001, zxw3001)
new_lt19(zxw49001, zxw50001, app(ty_[], cfb)) → new_lt9(zxw49001, zxw50001, cfb)
new_splitLT22(zxw300, zxw31, zxw32, zxw33, zxw34, False, h, ba) → new_splitLT13(zxw300, zxw31, zxw32, zxw33, zxw34, new_esEs8(new_compare34(zxw300, h), GT), h, ba)
new_compare29(zxw49000, zxw50000, ty_@0) → new_compare31(zxw49000, zxw50000)
new_compare26(Nothing, Nothing, False, bcf) → LT
new_esEs10(zxw4002, zxw3002, app(ty_Maybe, bf)) → new_esEs7(zxw4002, zxw3002, bf)
new_ltEs16(zxw4900, zxw5000) → new_fsEs(new_compare9(zxw4900, zxw5000))
new_esEs22(zxw4000, zxw3000, app(app(ty_@2, bcd), bce)) → new_esEs4(zxw4000, zxw3000, bcd, bce)
new_esEs23(zxw49000, zxw50000, app(ty_Maybe, bff)) → new_esEs7(zxw49000, zxw50000, bff)
new_ltEs7(Right(zxw49000), Right(zxw50000), dca, app(ty_Ratio, def)) → new_ltEs17(zxw49000, zxw50000, def)
new_esEs28(zxw4000, zxw3000, ty_@0) → new_esEs20(zxw4000, zxw3000)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Char, dcb) → new_ltEs12(zxw49000, zxw50000)
new_esEs27(zxw49000, zxw50000, ty_Float) → new_esEs19(zxw49000, zxw50000)
new_ltEs20(zxw49002, zxw50002, app(ty_[], cdh)) → new_ltEs13(zxw49002, zxw50002, cdh)
new_esEs10(zxw4002, zxw3002, app(app(app(ty_@3, ca), cb), cc)) → new_esEs5(zxw4002, zxw3002, ca, cb, cc)
new_ltEs20(zxw49002, zxw50002, app(app(app(ty_@3, cea), ceb), cec)) → new_ltEs15(zxw49002, zxw50002, cea, ceb, cec)
new_esEs22(zxw4000, zxw3000, ty_Ordering) → new_esEs8(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Bool) → new_esEs9(zxw4000, zxw3000)
new_compare6(zxw49000, zxw50000) → new_compare23(zxw49000, zxw50000, new_esEs8(zxw49000, zxw50000))
new_esEs29(zxw400, zxw300, app(app(ty_@2, hh), baa)) → new_esEs4(zxw400, zxw300, hh, baa)
new_esEs12(zxw4000, zxw3000, app(ty_[], ee)) → new_esEs16(zxw4000, zxw3000, ee)
new_compare32(zxw49000, zxw50000, bgc, bgd) → new_compare25(zxw49000, zxw50000, new_esEs6(zxw49000, zxw50000, bgc, bgd), bgc, bgd)
new_compare29(zxw49000, zxw50000, ty_Int) → new_compare7(zxw49000, zxw50000)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Bool, hg) → new_esEs9(zxw4000, zxw3000)
new_ltEs8(Nothing, Just(zxw50000), fh) → True
new_esEs31(zxw400, zxw300, app(app(ty_@2, hh), baa)) → new_esEs4(zxw400, zxw300, hh, baa)
new_ltEs7(Left(zxw49000), Left(zxw50000), app(app(ty_@2, dcc), dcd), dcb) → new_ltEs9(zxw49000, zxw50000, dcc, dcd)
new_esEs6(Right(zxw4000), Left(zxw3000), hf, hg) → False
new_esEs6(Left(zxw4000), Right(zxw3000), hf, hg) → False
new_esEs8(LT, LT) → True
new_lt20(zxw49000, zxw50000, ty_@0) → new_lt15(zxw49000, zxw50000)
new_esEs10(zxw4002, zxw3002, ty_Integer) → new_esEs17(zxw4002, zxw3002)
new_esEs28(zxw4000, zxw3000, ty_Float) → new_esEs19(zxw4000, zxw3000)
new_compare29(zxw49000, zxw50000, app(app(app(ty_@3, dbc), dbd), dbe)) → new_compare28(zxw49000, zxw50000, dbc, dbd, dbe)
new_lt19(zxw49001, zxw50001, ty_@0) → new_lt15(zxw49001, zxw50001)
new_ltEs7(Right(zxw49000), Right(zxw50000), dca, ty_Bool) → new_ltEs5(zxw49000, zxw50000)
new_ltEs5(True, False) → False
new_lt19(zxw49001, zxw50001, app(app(ty_@2, ceg), ceh)) → new_lt11(zxw49001, zxw50001, ceg, ceh)
new_compare0([], [], bhh) → EQ
new_pePe(True, zxw213) → True
new_primEqNat0(Zero, Zero) → True
new_compare34(zxw300, h) → new_compare26(Nothing, Just(zxw300), False, h)
new_esEs14(:%(zxw4000, zxw4001), :%(zxw3000, zxw3001), hd) → new_asAs(new_esEs25(zxw4000, zxw3000, hd), new_esEs24(zxw4001, zxw3001, hd))
new_lt10(zxw49000, zxw50000, ty_Double) → new_lt8(zxw49000, zxw50000)
new_mkBalBranch6MkBalBranch11(zxw50, zxw51, zxw54, zxw600, zxw601, zxw602, zxw603, Branch(zxw6040, zxw6041, zxw6042, zxw6043, zxw6044), False, h, ba) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))), zxw6040, zxw6041, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), zxw600, zxw601, zxw603, zxw6043, app(ty_Maybe, h), ba), new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), zxw50, zxw51, zxw6044, zxw54, app(ty_Maybe, h), ba), app(ty_Maybe, h), ba)
new_ltEs20(zxw49002, zxw50002, ty_Ordering) → new_ltEs4(zxw49002, zxw50002)
new_compare27(zxw49000, zxw50000, False, ff, fg) → new_compare17(zxw49000, zxw50000, new_ltEs9(zxw49000, zxw50000, ff, fg), ff, fg)
new_compare11(zxw180, zxw181, True, dae) → LT
new_esEs23(zxw49000, zxw50000, app(app(ty_Either, bgc), bgd)) → new_esEs6(zxw49000, zxw50000, bgc, bgd)
new_mkVBalBranch1(zxw300, zxw31, EmptyFM, zxw62, h, ba) → new_addToFM(zxw62, zxw300, zxw31, h, ba)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_@0, hg) → new_esEs20(zxw4000, zxw3000)
new_mkVBalBranch2(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba) → new_mkVBalBranch3MkVBalBranch21(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_lt21(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba), h, ba)
new_esEs6(Right(zxw4000), Right(zxw3000), hf, ty_Bool) → new_esEs9(zxw4000, zxw3000)
new_esEs12(zxw4000, zxw3000, ty_Int) → new_esEs13(zxw4000, zxw3000)
new_lt20(zxw49000, zxw50000, app(ty_[], cgd)) → new_lt9(zxw49000, zxw50000, cgd)
new_esEs6(Right(zxw4000), Right(zxw3000), hf, app(app(ty_Either, ccf), ccg)) → new_esEs6(zxw4000, zxw3000, ccf, ccg)
new_ltEs5(True, True) → True
new_compare26(Just(zxw4900), Just(zxw5000), False, bcf) → new_compare11(zxw4900, zxw5000, new_ltEs19(zxw4900, zxw5000, bcf), bcf)
new_ltEs7(Left(zxw49000), Left(zxw50000), app(ty_Maybe, dce), dcb) → new_ltEs8(zxw49000, zxw50000, dce)
new_esEs29(zxw400, zxw300, ty_Int) → new_esEs13(zxw400, zxw300)
new_compare36(zxw20, zxw15, bcg) → new_compare26(Just(zxw20), Just(zxw15), new_esEs30(zxw20, zxw15, bcg), bcg)
new_ltEs20(zxw49002, zxw50002, app(app(ty_@2, cde), cdf)) → new_ltEs9(zxw49002, zxw50002, cde, cdf)
new_esEs15(Char(zxw4000), Char(zxw3000)) → new_primEqNat0(zxw4000, zxw3000)
new_splitGT24(zxw30, zxw31, zxw32, zxw33, zxw34, zxw35, False, cab, cac) → new_splitGT16(zxw30, zxw31, zxw32, zxw33, zxw34, zxw35, new_esEs8(new_compare36(zxw35, zxw30, cab), LT), cab, cac)
new_ltEs18(zxw49001, zxw50001, ty_Int) → new_ltEs10(zxw49001, zxw50001)
new_sr(zxw4001, zxw3001) → new_primMulInt(zxw4001, zxw3001)
new_addToFM_C22(zxw610, zxw611, zxw612, zxw613, zxw614, zxw31, False, h, ba) → new_addToFM_C11(zxw610, zxw611, zxw612, zxw613, zxw614, zxw31, new_esEs8(new_compare19(Nothing, zxw610, h), GT), h, ba)
new_esEs25(zxw4000, zxw3000, ty_Int) → new_esEs13(zxw4000, zxw3000)
new_compare7(zxw49, zxw50) → new_primCmpInt(zxw49, zxw50)
new_primCmpNat1(Zero, Zero) → EQ
new_esEs7(Just(zxw4000), Just(zxw3000), app(ty_[], bgh)) → new_esEs16(zxw4000, zxw3000, bgh)
new_lt10(zxw49000, zxw50000, ty_Int) → new_lt4(zxw49000, zxw50000)
new_esEs28(zxw4000, zxw3000, app(app(ty_Either, daa), dab)) → new_esEs6(zxw4000, zxw3000, daa, dab)
new_ltEs7(Right(zxw49000), Right(zxw50000), dca, app(ty_Maybe, ddg)) → new_ltEs8(zxw49000, zxw50000, ddg)
new_ltEs7(Right(zxw49000), Right(zxw50000), dca, ty_Integer) → new_ltEs16(zxw49000, zxw50000)
new_primPlusInt(Neg(zxw1430), Neg(zxw1340)) → Neg(new_primPlusNat1(zxw1430, zxw1340))
new_ltEs7(Right(zxw49000), Right(zxw50000), dca, app(app(app(ty_@3, dea), deb), dec)) → new_ltEs15(zxw49000, zxw50000, dea, deb, dec)
new_esEs26(zxw49001, zxw50001, ty_Ordering) → new_esEs8(zxw49001, zxw50001)
new_mkVBalBranch3MkVBalBranch21(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkBalBranch(zxw610, zxw611, new_mkVBalBranch2(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw613, h, ba), zxw614, h, ba)
new_esEs8(GT, GT) → True
new_esEs27(zxw49000, zxw50000, ty_@0) → new_esEs20(zxw49000, zxw50000)
new_lt13(zxw49000, zxw50000) → new_esEs8(new_compare18(zxw49000, zxw50000), LT)
new_primPlusNat0(Succ(zxw1440), zxw300100) → Succ(Succ(new_primPlusNat1(zxw1440, zxw300100)))
new_esEs13(zxw400, zxw300) → new_primEqInt(zxw400, zxw300)
new_lt20(zxw49000, zxw50000, ty_Ordering) → new_lt14(zxw49000, zxw50000)
new_esEs11(zxw4001, zxw3001, app(app(ty_@2, ea), eb)) → new_esEs4(zxw4001, zxw3001, ea, eb)
new_esEs11(zxw4001, zxw3001, ty_Ordering) → new_esEs8(zxw4001, zxw3001)
new_lt10(zxw49000, zxw50000, app(app(ty_@2, ff), fg)) → new_lt11(zxw49000, zxw50000, ff, fg)
new_compare23(zxw49000, zxw50000, False) → new_compare10(zxw49000, zxw50000, new_ltEs4(zxw49000, zxw50000))
new_esEs8(LT, GT) → False
new_esEs8(GT, LT) → False
new_ltEs19(zxw4900, zxw5000, app(app(app(ty_@3, cdb), cdc), cdd)) → new_ltEs15(zxw4900, zxw5000, cdb, cdc, cdd)
new_lt20(zxw49000, zxw50000, app(app(ty_Either, cgh), cha)) → new_lt17(zxw49000, zxw50000, cgh, cha)
new_esEs26(zxw49001, zxw50001, ty_Bool) → new_esEs9(zxw49001, zxw50001)
new_ltEs11(zxw4900, zxw5000) → new_fsEs(new_compare16(zxw4900, zxw5000))
new_primCmpNat1(Succ(zxw49000), Zero) → GT
new_compare17(zxw49000, zxw50000, True, ff, fg) → LT
new_primEqInt(Neg(Succ(zxw40000)), Neg(Succ(zxw30000))) → new_primEqNat0(zxw40000, zxw30000)
new_splitGT13(zxw31, zxw32, zxw33, zxw34, True, h, ba) → new_mkVBalBranch2(zxw31, new_splitGT4(zxw33, h, ba), zxw34, h, ba)
new_esEs23(zxw49000, zxw50000, ty_Ordering) → new_esEs8(zxw49000, zxw50000)
new_ltEs5(False, False) → True
new_ltEs18(zxw49001, zxw50001, app(app(ty_Either, bfc), bfd)) → new_ltEs7(zxw49001, zxw50001, bfc, bfd)
new_sizeFM1(Branch(zxw2980, zxw2981, zxw2982, zxw2983, zxw2984), cad, cae) → zxw2982
new_esEs28(zxw4000, zxw3000, ty_Char) → new_esEs15(zxw4000, zxw3000)
new_primPlusNat1(Zero, Succ(zxw3001000)) → Succ(zxw3001000)
new_primPlusNat1(Succ(zxw14400), Zero) → Succ(zxw14400)
new_addToFM0(zxw611, zxw31, ba) → zxw31
new_esEs10(zxw4002, zxw3002, ty_Bool) → new_esEs9(zxw4002, zxw3002)
new_lt20(zxw49000, zxw50000, ty_Char) → new_lt6(zxw49000, zxw50000)
new_ltEs19(zxw4900, zxw5000, app(ty_Ratio, daf)) → new_ltEs17(zxw4900, zxw5000, daf)
new_compare13(zxw49000, zxw50000, False) → GT
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Bool, dcb) → new_ltEs5(zxw49000, zxw50000)
new_splitLT30(Nothing, zxw31, zxw32, zxw33, zxw34, Nothing, h, ba) → new_splitLT16(zxw31, zxw32, zxw33, zxw34, new_esEs8(new_compare33(h), GT), h, ba)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Int, dcb) → new_ltEs10(zxw49000, zxw50000)
new_esEs21(zxw4001, zxw3001, ty_Char) → new_esEs15(zxw4001, zxw3001)
new_lt11(zxw49000, zxw50000, ff, fg) → new_esEs8(new_compare30(zxw49000, zxw50000, ff, fg), LT)
new_lt20(zxw49000, zxw50000, ty_Int) → new_lt4(zxw49000, zxw50000)
new_primCompAux1(zxw49000, zxw50000, zxw214, bhh) → new_primCompAux0(zxw214, new_compare29(zxw49000, zxw50000, bhh))
new_esEs7(Just(zxw4000), Just(zxw3000), ty_@0) → new_esEs20(zxw4000, zxw3000)
new_lt16(zxw49000, zxw50000, bfh, bga, bgb) → new_esEs8(new_compare28(zxw49000, zxw50000, bfh, bga, bgb), LT)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_splitLT14(zxw15, zxw16, zxw17, zxw18, zxw19, zxw20, True, bcg, caa) → new_mkVBalBranch1(zxw15, zxw16, zxw18, new_splitLT5(zxw19, zxw20, bcg, caa), bcg, caa)
new_ltEs7(Right(zxw49000), Left(zxw50000), dca, dcb) → False
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Ordering) → new_esEs8(zxw4000, zxw3000)
new_mkBalBranch6MkBalBranch5(zxw50, zxw51, zxw54, zxw60, True, h, ba) → new_mkBranch(Zero, zxw50, zxw51, zxw60, zxw54, app(ty_Maybe, h), ba)
new_ltEs7(Left(zxw49000), Left(zxw50000), app(ty_[], dcf), dcb) → new_ltEs13(zxw49000, zxw50000, dcf)
new_ltEs19(zxw4900, zxw5000, ty_Ordering) → new_ltEs4(zxw4900, zxw5000)
new_ltEs20(zxw49002, zxw50002, ty_Char) → new_ltEs12(zxw49002, zxw50002)
new_primCmpNat0(Succ(zxw5000), zxw4900) → new_primCmpNat1(zxw5000, zxw4900)
new_ltEs20(zxw49002, zxw50002, app(ty_Ratio, cef)) → new_ltEs17(zxw49002, zxw50002, cef)
new_esEs11(zxw4001, zxw3001, app(app(app(ty_@3, dd), de), df)) → new_esEs5(zxw4001, zxw3001, dd, de, df)
new_ltEs18(zxw49001, zxw50001, ty_@0) → new_ltEs14(zxw49001, zxw50001)
new_addToFM_C3(Branch(zxw610, zxw611, zxw612, zxw613, zxw614), zxw31, h, ba) → new_addToFM_C22(zxw610, zxw611, zxw612, zxw613, zxw614, zxw31, new_lt12(Nothing, zxw610, h), h, ba)
new_primEqInt(Neg(Succ(zxw40000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(zxw30000))) → False
new_primCompAux0(zxw218, GT) → GT
new_esEs12(zxw4000, zxw3000, ty_Double) → new_esEs18(zxw4000, zxw3000)
new_ltEs19(zxw4900, zxw5000, ty_Char) → new_ltEs12(zxw4900, zxw5000)
new_esEs8(EQ, EQ) → True
new_esEs6(Left(zxw4000), Left(zxw3000), app(ty_Ratio, cag), hg) → new_esEs14(zxw4000, zxw3000, cag)
new_ltEs8(Just(zxw49000), Just(zxw50000), app(app(ty_Either, gh), ha)) → new_ltEs7(zxw49000, zxw50000, gh, ha)
new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_sizeFM0(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba)
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Integer, dcb) → new_ltEs16(zxw49000, zxw50000)
new_esEs6(Right(zxw4000), Right(zxw3000), hf, app(ty_[], ccb)) → new_esEs16(zxw4000, zxw3000, ccb)
new_splitGT22(zxw300, zxw31, zxw32, zxw33, zxw34, True, h, ba) → new_splitGT4(zxw34, h, ba)
new_esEs23(zxw49000, zxw50000, ty_Integer) → new_esEs17(zxw49000, zxw50000)
new_esEs29(zxw400, zxw300, app(ty_[], he)) → new_esEs16(zxw400, zxw300, he)
new_addToFM_C21(zxw620, zxw621, zxw622, zxw623, zxw624, zxw300, zxw31, False, h, ba) → new_addToFM_C12(zxw620, zxw621, zxw622, zxw623, zxw624, zxw300, zxw31, new_esEs8(new_compare19(Just(zxw300), zxw620, h), GT), h, ba)
new_esEs28(zxw4000, zxw3000, ty_Int) → new_esEs13(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, app(app(app(ty_@3, bbg), bbh), bca)) → new_esEs5(zxw4000, zxw3000, bbg, bbh, bca)
new_ltEs18(zxw49001, zxw50001, ty_Ordering) → new_ltEs4(zxw49001, zxw50001)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_ltEs4(EQ, LT) → False
new_esEs12(zxw4000, zxw3000, app(ty_Maybe, ec)) → new_esEs7(zxw4000, zxw3000, ec)
new_lt20(zxw49000, zxw50000, ty_Double) → new_lt8(zxw49000, zxw50000)
new_esEs10(zxw4002, zxw3002, ty_Float) → new_esEs19(zxw4002, zxw3002)
new_splitGT5(EmptyFM, zxw400, h, ba) → new_emptyFM(h, ba)
new_splitLT22(zxw300, zxw31, zxw32, zxw33, zxw34, True, h, ba) → new_splitLT4(zxw33, h, ba)
new_splitGT30(Just(zxw300), zxw31, zxw32, zxw33, zxw34, Just(zxw400), h, ba) → new_splitGT24(zxw300, zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs8(new_compare26(Just(zxw400), Just(zxw300), new_esEs29(zxw400, zxw300, h), h), GT), h, ba)
new_primMinusNat0(Succ(zxw14300), Zero) → Pos(Succ(zxw14300))
new_esEs11(zxw4001, zxw3001, ty_Bool) → new_esEs9(zxw4001, zxw3001)
new_compare11(zxw180, zxw181, False, dae) → GT
new_esEs26(zxw49001, zxw50001, ty_Integer) → new_esEs17(zxw49001, zxw50001)
new_ltEs18(zxw49001, zxw50001, ty_Bool) → new_ltEs5(zxw49001, zxw50001)
new_lt10(zxw49000, zxw50000, ty_Ordering) → new_lt14(zxw49000, zxw50000)
new_esEs12(zxw4000, zxw3000, app(app(app(ty_@3, ef), eg), eh)) → new_esEs5(zxw4000, zxw3000, ef, eg, eh)
new_primEqInt(Pos(Succ(zxw40000)), Pos(Succ(zxw30000))) → new_primEqNat0(zxw40000, zxw30000)
new_mkVBalBranch3MkVBalBranch11(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, False, h, ba) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Nothing, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw610, zxw611, zxw612, zxw613, zxw614), app(ty_Maybe, h), ba)
new_compare27(zxw49000, zxw50000, True, ff, fg) → EQ
new_splitGT16(zxw30, zxw31, zxw32, zxw33, zxw34, zxw35, True, cab, cac) → new_mkVBalBranch1(zxw30, zxw31, new_splitGT5(zxw33, zxw35, cab, cac), zxw34, cab, cac)
new_splitLT5(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw400, h, ba) → new_splitLT30(zxw330, zxw331, zxw332, zxw333, zxw334, Just(zxw400), h, ba)
new_esEs6(Left(zxw4000), Left(zxw3000), app(app(app(ty_@3, cba), cbb), cbc), hg) → new_esEs5(zxw4000, zxw3000, cba, cbb, cbc)
new_ltEs18(zxw49001, zxw50001, app(app(app(ty_@3, beh), bfa), bfb)) → new_ltEs15(zxw49001, zxw50001, beh, bfa, bfb)
new_lt18(zxw49000, zxw50000, bge) → new_esEs8(new_compare8(zxw49000, zxw50000, bge), LT)
new_esEs31(zxw400, zxw300, ty_Double) → new_esEs18(zxw400, zxw300)
new_mkVBalBranch2(zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), EmptyFM, h, ba) → new_addToFM1(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), zxw31, h, ba)
new_lt10(zxw49000, zxw50000, app(ty_Maybe, bff)) → new_lt12(zxw49000, zxw50000, bff)
new_mkBalBranch6MkBalBranch11(zxw50, zxw51, zxw54, zxw600, zxw601, zxw602, zxw603, zxw604, True, h, ba) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), zxw600, zxw601, zxw603, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), zxw50, zxw51, zxw604, zxw54, app(ty_Maybe, h), ba), app(ty_Maybe, h), ba)
new_esEs26(zxw49001, zxw50001, ty_Int) → new_esEs13(zxw49001, zxw50001)
new_ltEs8(Just(zxw49000), Just(zxw50000), app(app(ty_@2, ga), gb)) → new_ltEs9(zxw49000, zxw50000, ga, gb)
new_primEqNat0(Succ(zxw40000), Succ(zxw30000)) → new_primEqNat0(zxw40000, zxw30000)
new_compare29(zxw49000, zxw50000, app(ty_[], dbb)) → new_compare0(zxw49000, zxw50000, dbb)
new_esEs27(zxw49000, zxw50000, ty_Ordering) → new_esEs8(zxw49000, zxw50000)
new_esEs27(zxw49000, zxw50000, ty_Integer) → new_esEs17(zxw49000, zxw50000)
new_esEs23(zxw49000, zxw50000, app(ty_Ratio, bge)) → new_esEs14(zxw49000, zxw50000, bge)
new_ltEs18(zxw49001, zxw50001, ty_Float) → new_ltEs6(zxw49001, zxw50001)
new_esEs22(zxw4000, zxw3000, ty_Int) → new_esEs13(zxw4000, zxw3000)
new_ltEs7(Right(zxw49000), Right(zxw50000), dca, app(ty_[], ddh)) → new_ltEs13(zxw49000, zxw50000, ddh)
new_ltEs4(GT, EQ) → False
new_lt7(zxw49000, zxw50000) → new_esEs8(new_compare14(zxw49000, zxw50000), LT)
new_splitLT4(Branch(zxw330, zxw331, zxw332, zxw333, zxw334), h, ba) → new_splitLT30(zxw330, zxw331, zxw332, zxw333, zxw334, Nothing, h, ba)
new_lt10(zxw49000, zxw50000, app(app(app(ty_@3, bfh), bga), bgb)) → new_lt16(zxw49000, zxw50000, bfh, bga, bgb)
new_splitLT5(EmptyFM, zxw400, h, ba) → new_emptyFM(h, ba)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Int) → new_esEs13(zxw4000, zxw3000)
new_ltEs19(zxw4900, zxw5000, app(app(ty_Either, dca), dcb)) → new_ltEs7(zxw4900, zxw5000, dca, dcb)
new_ltEs8(Just(zxw49000), Nothing, fh) → False
new_esEs21(zxw4001, zxw3001, ty_Float) → new_esEs19(zxw4001, zxw3001)
new_esEs27(zxw49000, zxw50000, app(app(app(ty_@3, cge), cgf), cgg)) → new_esEs5(zxw49000, zxw50000, cge, cgf, cgg)
new_esEs26(zxw49001, zxw50001, app(app(ty_@2, ceg), ceh)) → new_esEs4(zxw49001, zxw50001, ceg, ceh)
new_splitGT13(zxw31, zxw32, zxw33, zxw34, False, h, ba) → zxw34
new_ltEs13(zxw4900, zxw5000, bhh) → new_fsEs(new_compare0(zxw4900, zxw5000, bhh))
new_esEs22(zxw4000, zxw3000, ty_Char) → new_esEs15(zxw4000, zxw3000)
new_esEs30(zxw20, zxw15, app(ty_Ratio, bda)) → new_esEs14(zxw20, zxw15, bda)
new_ltEs18(zxw49001, zxw50001, ty_Double) → new_ltEs11(zxw49001, zxw50001)
new_esEs7(Nothing, Nothing, hc) → True
new_esEs28(zxw4000, zxw3000, ty_Ordering) → new_esEs8(zxw4000, zxw3000)
new_lt10(zxw49000, zxw50000, app(app(ty_Either, bgc), bgd)) → new_lt17(zxw49000, zxw50000, bgc, bgd)
new_esEs8(LT, EQ) → False
new_esEs8(EQ, LT) → False
new_esEs10(zxw4002, zxw3002, ty_Char) → new_esEs15(zxw4002, zxw3002)
new_primEqInt(Pos(Succ(zxw40000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(zxw30000))) → False
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Double, dcb) → new_ltEs11(zxw49000, zxw50000)
new_ltEs4(EQ, EQ) → True
new_mkBalBranch6MkBalBranch01(zxw50, zxw51, zxw540, zxw541, zxw542, Branch(zxw5430, zxw5431, zxw5432, zxw5433, zxw5434), zxw544, zxw60, False, h, ba) → new_mkBranch(Succ(Succ(Succ(Succ(Zero)))), zxw5430, zxw5431, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Zero))))), zxw50, zxw51, zxw60, zxw5433, app(ty_Maybe, h), ba), new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))), zxw540, zxw541, zxw5434, zxw544, app(ty_Maybe, h), ba), app(ty_Maybe, h), ba)
new_splitLT30(Nothing, zxw31, zxw32, zxw33, zxw34, Just(zxw400), h, ba) → new_splitLT24(zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs8(new_compare26(Just(zxw400), Nothing, False, h), LT), h, ba)
new_addToFM_C3(EmptyFM, zxw31, h, ba) → Branch(Nothing, zxw31, Pos(Succ(Zero)), new_emptyFM(h, ba), new_emptyFM(h, ba))
new_esEs6(Right(zxw4000), Right(zxw3000), hf, app(ty_Maybe, cbh)) → new_esEs7(zxw4000, zxw3000, cbh)
new_splitGT16(zxw30, zxw31, zxw32, zxw33, zxw34, zxw35, False, cab, cac) → zxw34
new_ltEs7(Right(zxw49000), Right(zxw50000), dca, ty_Ordering) → new_ltEs4(zxw49000, zxw50000)
new_esEs29(zxw400, zxw300, ty_Double) → new_esEs18(zxw400, zxw300)
new_esEs30(zxw20, zxw15, ty_@0) → new_esEs20(zxw20, zxw15)
new_splitLT13(zxw300, zxw31, zxw32, zxw33, zxw34, False, h, ba) → zxw33
new_primCmpInt(Neg(Zero), Pos(Succ(zxw5000))) → LT
new_ltEs20(zxw49002, zxw50002, ty_@0) → new_ltEs14(zxw49002, zxw50002)
new_mkVBalBranch3MkVBalBranch11(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, True, h, ba) → new_mkBalBranch(zxw330, zxw331, zxw333, new_mkVBalBranch2(zxw31, zxw334, Branch(zxw610, zxw611, zxw612, zxw613, zxw614), h, ba), h, ba)
new_esEs23(zxw49000, zxw50000, ty_@0) → new_esEs20(zxw49000, zxw50000)
new_esEs6(Right(zxw4000), Right(zxw3000), hf, ty_@0) → new_esEs20(zxw4000, zxw3000)
new_compare210(zxw49000, zxw50000, True, bfh, bga, bgb) → EQ
new_ltEs4(GT, LT) → False
new_sr0(Integer(zxw500000), Integer(zxw490010)) → Integer(new_primMulInt(zxw500000, zxw490010))
new_compare13(zxw49000, zxw50000, True) → LT
new_mkVBalBranch1(zxw300, zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba) → new_mkVBalBranch3MkVBalBranch22(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_lt21(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba), h, ba)
new_primPlusNat1(Succ(zxw14400), Succ(zxw3001000)) → Succ(Succ(new_primPlusNat1(zxw14400, zxw3001000)))
new_compare14(Float(zxw49000, zxw49001), Float(zxw50000, zxw50001)) → new_compare7(new_sr(zxw49000, zxw50000), new_sr(zxw49001, zxw50001))
new_primEqInt(Pos(Succ(zxw40000)), Neg(zxw3000)) → False
new_primEqInt(Neg(Succ(zxw40000)), Pos(zxw3000)) → False
new_addToFM_C4(Branch(zxw620, zxw621, zxw622, zxw623, zxw624), zxw300, zxw31, h, ba) → new_addToFM_C21(zxw620, zxw621, zxw622, zxw623, zxw624, zxw300, zxw31, new_lt12(Just(zxw300), zxw620, h), h, ba)
new_addToFM_C12(zxw620, zxw621, zxw622, zxw623, zxw624, zxw300, zxw31, False, h, ba) → Branch(Just(zxw300), new_addToFM0(zxw621, zxw31, ba), zxw622, zxw623, zxw624)
new_esEs7(Just(zxw4000), Nothing, hc) → False
new_esEs7(Nothing, Just(zxw3000), hc) → False
new_esEs18(Double(zxw4000, zxw4001), Double(zxw3000, zxw3001)) → new_esEs13(new_sr(zxw4000, zxw3000), new_sr(zxw4001, zxw3001))
new_ltEs5(False, True) → True
new_esEs26(zxw49001, zxw50001, ty_Double) → new_esEs18(zxw49001, zxw50001)
new_primPlusInt(Neg(zxw1430), Pos(zxw1340)) → new_primMinusNat0(zxw1340, zxw1430)
new_primPlusInt(Pos(zxw1430), Neg(zxw1340)) → new_primMinusNat0(zxw1430, zxw1340)
new_mkBalBranch6MkBalBranch3(zxw50, zxw51, zxw54, EmptyFM, True, h, ba) → error([])
new_compare28(zxw49000, zxw50000, bfh, bga, bgb) → new_compare210(zxw49000, zxw50000, new_esEs5(zxw49000, zxw50000, bfh, bga, bgb), bfh, bga, bgb)
new_esEs11(zxw4001, zxw3001, ty_Double) → new_esEs18(zxw4001, zxw3001)
new_ltEs6(zxw4900, zxw5000) → new_fsEs(new_compare14(zxw4900, zxw5000))
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Ordering, dcb) → new_ltEs4(zxw49000, zxw50000)
new_primEqInt(Pos(Zero), Neg(Succ(zxw30000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(zxw30000))) → False
new_esEs31(zxw400, zxw300, ty_Integer) → new_esEs17(zxw400, zxw300)
new_ltEs19(zxw4900, zxw5000, app(app(ty_@2, beb), bec)) → new_ltEs9(zxw4900, zxw5000, beb, bec)
new_ltEs20(zxw49002, zxw50002, ty_Float) → new_ltEs6(zxw49002, zxw50002)
new_compare29(zxw49000, zxw50000, app(app(ty_@2, dag), dah)) → new_compare30(zxw49000, zxw50000, dag, dah)
new_compare24(zxw49000, zxw50000, True) → EQ
new_esEs27(zxw49000, zxw50000, ty_Int) → new_esEs13(zxw49000, zxw50000)
new_ltEs18(zxw49001, zxw50001, app(app(ty_@2, bed), bee)) → new_ltEs9(zxw49001, zxw50001, bed, bee)
new_esEs6(Right(zxw4000), Right(zxw3000), hf, ty_Double) → new_esEs18(zxw4000, zxw3000)
new_lt20(zxw49000, zxw50000, ty_Bool) → new_lt13(zxw49000, zxw50000)
new_primCmpNat0(Zero, zxw4900) → LT
new_mkVBalBranch3MkVBalBranch22(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch12(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, new_lt4(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_l(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), h, ba)
new_ltEs7(Right(zxw49000), Right(zxw50000), dca, ty_Char) → new_ltEs12(zxw49000, zxw50000)
new_esEs8(EQ, GT) → False
new_esEs8(GT, EQ) → False
new_mkVBalBranch3MkVBalBranch21(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, False, h, ba) → new_mkVBalBranch3MkVBalBranch11(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, zxw31, new_lt4(new_sr(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), new_mkVBalBranch3Size_l(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), h, ba)
new_emptyFM(h, ba) → EmptyFM
new_esEs10(zxw4002, zxw3002, app(ty_[], bh)) → new_esEs16(zxw4002, zxw3002, bh)
new_lt15(zxw49000, zxw50000) → new_esEs8(new_compare31(zxw49000, zxw50000), LT)
new_esEs31(zxw400, zxw300, ty_Int) → new_esEs13(zxw400, zxw300)
new_compare17(zxw49000, zxw50000, False, ff, fg) → GT
new_esEs30(zxw20, zxw15, ty_Double) → new_esEs18(zxw20, zxw15)
new_esEs28(zxw4000, zxw3000, app(ty_Ratio, chd)) → new_esEs14(zxw4000, zxw3000, chd)
new_compare29(zxw49000, zxw50000, ty_Float) → new_compare14(zxw49000, zxw50000)
new_compare26(zxw490, zxw500, True, bcf) → EQ
new_primCompAux0(zxw218, LT) → LT
new_esEs11(zxw4001, zxw3001, ty_@0) → new_esEs20(zxw4001, zxw3001)
new_esEs30(zxw20, zxw15, app(app(ty_Either, bdf), bdg)) → new_esEs6(zxw20, zxw15, bdf, bdg)
new_esEs12(zxw4000, zxw3000, ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_not(False) → True
new_esEs6(Left(zxw4000), Left(zxw3000), app(app(ty_Either, cbd), cbe), hg) → new_esEs6(zxw4000, zxw3000, cbd, cbe)
new_esEs28(zxw4000, zxw3000, app(ty_[], che)) → new_esEs16(zxw4000, zxw3000, che)
new_esEs24(zxw4001, zxw3001, ty_Int) → new_esEs13(zxw4001, zxw3001)
new_splitLT23(zxw15, zxw16, zxw17, zxw18, zxw19, zxw20, False, bcg, caa) → new_splitLT14(zxw15, zxw16, zxw17, zxw18, zxw19, zxw20, new_esEs8(new_compare36(zxw20, zxw15, bcg), GT), bcg, caa)
new_esEs31(zxw400, zxw300, ty_Char) → new_esEs15(zxw400, zxw300)
new_primPlusNat0(Zero, zxw300100) → Succ(zxw300100)
new_esEs26(zxw49001, zxw50001, app(ty_Ratio, cfh)) → new_esEs14(zxw49001, zxw50001, cfh)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Double) → new_ltEs11(zxw49000, zxw50000)
new_esEs11(zxw4001, zxw3001, app(app(ty_Either, dg), dh)) → new_esEs6(zxw4001, zxw3001, dg, dh)
new_esEs21(zxw4001, zxw3001, ty_@0) → new_esEs20(zxw4001, zxw3001)
new_splitGT4(EmptyFM, h, ba) → new_emptyFM(h, ba)
new_esEs31(zxw400, zxw300, app(ty_Ratio, hd)) → new_esEs14(zxw400, zxw300, hd)
new_addToFM_C22(zxw610, zxw611, zxw612, zxw613, zxw614, zxw31, True, h, ba) → new_mkBalBranch(zxw610, zxw611, new_addToFM_C3(zxw613, zxw31, h, ba), zxw614, h, ba)
new_lt19(zxw49001, zxw50001, ty_Float) → new_lt7(zxw49001, zxw50001)
new_ltEs7(Right(zxw49000), Right(zxw50000), dca, ty_Int) → new_ltEs10(zxw49000, zxw50000)
new_compare0(:(zxw49000, zxw49001), [], bhh) → GT
new_ltEs8(Just(zxw49000), Just(zxw50000), app(ty_[], gd)) → new_ltEs13(zxw49000, zxw50000, gd)
new_esEs12(zxw4000, zxw3000, ty_Float) → new_esEs19(zxw4000, zxw3000)
new_lt14(zxw49000, zxw50000) → new_esEs8(new_compare6(zxw49000, zxw50000), LT)
new_ltEs19(zxw4900, zxw5000, ty_Float) → new_ltEs6(zxw4900, zxw5000)
new_mkBalBranch6MkBalBranch3(zxw50, zxw51, zxw54, zxw60, False, h, ba) → new_mkBranch(Succ(Zero), zxw50, zxw51, zxw60, zxw54, app(ty_Maybe, h), ba)
new_esEs27(zxw49000, zxw50000, app(app(ty_Either, cgh), cha)) → new_esEs6(zxw49000, zxw50000, cgh, cha)
new_lt19(zxw49001, zxw50001, app(ty_Ratio, cfh)) → new_lt18(zxw49001, zxw50001, cfh)
new_esEs9(True, True) → True
new_lt19(zxw49001, zxw50001, app(app(app(ty_@3, cfc), cfd), cfe)) → new_lt16(zxw49001, zxw50001, cfc, cfd, cfe)
new_lt19(zxw49001, zxw50001, ty_Char) → new_lt6(zxw49001, zxw50001)
new_primCmpInt(Pos(Succ(zxw4900)), Neg(zxw500)) → GT
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Double, hg) → new_esEs18(zxw4000, zxw3000)
new_esEs28(zxw4000, zxw3000, app(ty_Maybe, chc)) → new_esEs7(zxw4000, zxw3000, chc)
new_splitGT30(Nothing, zxw31, zxw32, zxw33, zxw34, Just(zxw400), h, ba) → new_splitGT23(zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs8(new_compare26(Just(zxw400), Nothing, False, h), GT), h, ba)
new_esEs21(zxw4001, zxw3001, app(app(app(ty_@3, bae), baf), bag)) → new_esEs5(zxw4001, zxw3001, bae, baf, bag)
new_primCmpInt(Pos(Zero), Pos(Succ(zxw5000))) → new_primCmpNat0(Zero, zxw5000)
new_esEs22(zxw4000, zxw3000, app(ty_[], bbf)) → new_esEs16(zxw4000, zxw3000, bbf)
new_esEs21(zxw4001, zxw3001, app(ty_Maybe, bab)) → new_esEs7(zxw4001, zxw3001, bab)
new_splitGT30(Nothing, zxw31, zxw32, zxw33, zxw34, Nothing, h, ba) → new_splitGT13(zxw31, zxw32, zxw33, zxw34, new_esEs8(new_compare33(h), LT), h, ba)
new_esEs22(zxw4000, zxw3000, ty_Double) → new_esEs18(zxw4000, zxw3000)
new_primMulInt(Pos(zxw40010), Pos(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_esEs21(zxw4001, zxw3001, app(app(ty_@2, bbb), bbc)) → new_esEs4(zxw4001, zxw3001, bbb, bbc)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_@0) → new_ltEs14(zxw49000, zxw50000)
new_esEs31(zxw400, zxw300, ty_@0) → new_esEs20(zxw400, zxw300)
new_esEs19(Float(zxw4000, zxw4001), Float(zxw3000, zxw3001)) → new_esEs13(new_sr(zxw4000, zxw3000), new_sr(zxw4001, zxw3001))
new_primMulInt(Neg(zxw40010), Neg(zxw30010)) → Pos(new_primMulNat0(zxw40010, zxw30010))
new_ltEs19(zxw4900, zxw5000, app(ty_Maybe, fh)) → new_ltEs8(zxw4900, zxw5000, fh)
new_esEs29(zxw400, zxw300, ty_Char) → new_esEs15(zxw400, zxw300)
new_esEs30(zxw20, zxw15, app(ty_Maybe, bch)) → new_esEs7(zxw20, zxw15, bch)
new_primEqNat0(Zero, Succ(zxw30000)) → False
new_primEqNat0(Succ(zxw40000), Zero) → False
new_compare25(zxw49000, zxw50000, True, bgc, bgd) → EQ
new_ltEs7(Left(zxw49000), Left(zxw50000), app(app(ty_Either, ddb), ddc), dcb) → new_ltEs7(zxw49000, zxw50000, ddb, ddc)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_lt10(zxw49000, zxw50000, app(ty_Ratio, bge)) → new_lt18(zxw49000, zxw50000, bge)
new_esEs12(zxw4000, zxw3000, ty_@0) → new_esEs20(zxw4000, zxw3000)
new_esEs21(zxw4001, zxw3001, ty_Bool) → new_esEs9(zxw4001, zxw3001)
new_esEs5(@3(zxw4000, zxw4001, zxw4002), @3(zxw3000, zxw3001, zxw3002), bc, bd, be) → new_asAs(new_esEs12(zxw4000, zxw3000, bc), new_asAs(new_esEs11(zxw4001, zxw3001, bd), new_esEs10(zxw4002, zxw3002, be)))
new_esEs16(:(zxw4000, zxw4001), [], he) → False
new_esEs16([], :(zxw3000, zxw3001), he) → False
new_sizeFM0(EmptyFM, h, ba) → Pos(Zero)
new_splitGT14(zxw300, zxw31, zxw32, zxw33, zxw34, False, h, ba) → zxw34
new_esEs29(zxw400, zxw300, app(app(ty_Either, hf), hg)) → new_esEs6(zxw400, zxw300, hf, hg)
new_lt10(zxw49000, zxw50000, ty_Integer) → new_lt5(zxw49000, zxw50000)
new_lt6(zxw49000, zxw50000) → new_esEs8(new_compare12(zxw49000, zxw50000), LT)
new_primCmpInt(Neg(Zero), Neg(Succ(zxw5000))) → new_primCmpNat2(zxw5000, Zero)
new_ltEs4(LT, GT) → True
new_splitGT5(Branch(zxw340, zxw341, zxw342, zxw343, zxw344), zxw400, h, ba) → new_splitGT30(zxw340, zxw341, zxw342, zxw343, zxw344, Just(zxw400), h, ba)
new_esEs23(zxw49000, zxw50000, ty_Double) → new_esEs18(zxw49000, zxw50000)
new_compare25(zxw49000, zxw50000, False, bgc, bgd) → new_compare15(zxw49000, zxw50000, new_ltEs7(zxw49000, zxw50000, bgc, bgd), bgc, bgd)
new_esEs29(zxw400, zxw300, app(app(app(ty_@3, bc), bd), be)) → new_esEs5(zxw400, zxw300, bc, bd, be)
new_lt19(zxw49001, zxw50001, app(app(ty_Either, cff), cfg)) → new_lt17(zxw49001, zxw50001, cff, cfg)
new_splitGT23(zxw31, zxw32, zxw33, zxw34, zxw400, False, h, ba) → new_splitGT15(zxw31, zxw32, zxw33, zxw34, zxw400, new_esEs8(new_compare35(zxw400, h), LT), h, ba)
new_primMinusNat0(Zero, Zero) → Pos(Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zxw5000))) → GT
new_esEs6(Left(zxw4000), Left(zxw3000), app(ty_Maybe, caf), hg) → new_esEs7(zxw4000, zxw3000, caf)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Ordering, hg) → new_esEs8(zxw4000, zxw3000)
new_esEs16(:(zxw4000, zxw4001), :(zxw3000, zxw3001), he) → new_asAs(new_esEs28(zxw4000, zxw3000, he), new_esEs16(zxw4001, zxw3001, he))
new_ltEs8(Just(zxw49000), Just(zxw50000), app(ty_Ratio, hb)) → new_ltEs17(zxw49000, zxw50000, hb)
new_compare0(:(zxw49000, zxw49001), :(zxw50000, zxw50001), bhh) → new_primCompAux1(zxw49000, zxw50000, new_compare0(zxw49001, zxw50001, bhh), bhh)
new_esEs11(zxw4001, zxw3001, app(ty_Maybe, da)) → new_esEs7(zxw4001, zxw3001, da)
new_esEs6(Right(zxw4000), Right(zxw3000), hf, app(app(ty_@2, cch), cda)) → new_esEs4(zxw4000, zxw3000, cch, cda)
new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Float) → new_ltEs6(zxw49000, zxw50000)
new_compare15(zxw49000, zxw50000, False, bgc, bgd) → GT
new_splitLT24(zxw31, zxw32, zxw33, zxw34, zxw400, True, h, ba) → new_splitLT5(zxw33, zxw400, h, ba)
new_mkVBalBranch3MkVBalBranch12(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, True, h, ba) → new_mkBalBranch(zxw330, zxw331, zxw333, new_mkVBalBranch1(zxw300, zxw31, zxw334, Branch(zxw620, zxw621, zxw622, zxw623, zxw624), h, ba), h, ba)
new_mkBalBranch6MkBalBranch4(zxw50, zxw51, EmptyFM, zxw60, True, h, ba) → error([])
new_mkVBalBranch3MkVBalBranch12(zxw620, zxw621, zxw622, zxw623, zxw624, zxw330, zxw331, zxw332, zxw333, zxw334, zxw300, zxw31, False, h, ba) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Just(zxw300), zxw31, Branch(zxw330, zxw331, zxw332, zxw333, zxw334), Branch(zxw620, zxw621, zxw622, zxw623, zxw624), app(ty_Maybe, h), ba)
new_compare29(zxw49000, zxw50000, app(app(ty_Either, dbf), dbg)) → new_compare32(zxw49000, zxw50000, dbf, dbg)
new_splitGT24(zxw30, zxw31, zxw32, zxw33, zxw34, zxw35, True, cab, cac) → new_splitGT5(zxw34, zxw35, cab, cac)
new_splitLT4(EmptyFM, h, ba) → new_emptyFM(h, ba)
new_lt20(zxw49000, zxw50000, ty_Float) → new_lt7(zxw49000, zxw50000)
new_addToFM1(zxw61, zxw31, h, ba) → new_addToFM_C3(zxw61, zxw31, h, ba)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Char) → new_esEs15(zxw4000, zxw3000)
new_esEs23(zxw49000, zxw50000, ty_Int) → new_esEs13(zxw49000, zxw50000)
new_esEs30(zxw20, zxw15, app(ty_[], bdb)) → new_esEs16(zxw20, zxw15, bdb)
new_esEs7(Just(zxw4000), Just(zxw3000), app(app(app(ty_@3, bha), bhb), bhc)) → new_esEs5(zxw4000, zxw3000, bha, bhb, bhc)
new_esEs9(False, True) → False
new_esEs9(True, False) → False
new_esEs10(zxw4002, zxw3002, app(app(ty_@2, cf), cg)) → new_esEs4(zxw4002, zxw3002, cf, cg)
new_compare29(zxw49000, zxw50000, app(ty_Ratio, dbh)) → new_compare8(zxw49000, zxw50000, dbh)
new_esEs11(zxw4001, zxw3001, app(ty_Ratio, db)) → new_esEs14(zxw4001, zxw3001, db)
new_compare29(zxw49000, zxw50000, ty_Ordering) → new_compare6(zxw49000, zxw50000)
new_mkBalBranch6MkBalBranch3(zxw50, zxw51, zxw54, Branch(zxw600, zxw601, zxw602, zxw603, zxw604), True, h, ba) → new_mkBalBranch6MkBalBranch11(zxw50, zxw51, zxw54, zxw600, zxw601, zxw602, zxw603, zxw604, new_lt4(new_sizeFM0(zxw604, h, ba), new_sr(Pos(Succ(Succ(Zero))), new_sizeFM0(zxw603, h, ba))), h, ba)
new_esEs27(zxw49000, zxw50000, ty_Double) → new_esEs18(zxw49000, zxw50000)
new_esEs21(zxw4001, zxw3001, ty_Integer) → new_esEs17(zxw4001, zxw3001)
new_primPlusInt(Pos(zxw1430), Pos(zxw1340)) → Pos(new_primPlusNat1(zxw1430, zxw1340))
new_splitLT23(zxw15, zxw16, zxw17, zxw18, zxw19, zxw20, True, bcg, caa) → new_splitLT5(zxw18, zxw20, bcg, caa)
new_primCmpNat2(zxw4900, Succ(zxw5000)) → new_primCmpNat1(zxw4900, zxw5000)
new_esEs27(zxw49000, zxw50000, app(ty_Ratio, chb)) → new_esEs14(zxw49000, zxw50000, chb)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_ltEs4(LT, EQ) → True
new_esEs6(Right(zxw4000), Right(zxw3000), hf, ty_Char) → new_esEs15(zxw4000, zxw3000)
new_esEs10(zxw4002, zxw3002, ty_Double) → new_esEs18(zxw4002, zxw3002)
new_compare31(@0, @0) → EQ
new_esEs31(zxw400, zxw300, ty_Float) → new_esEs19(zxw400, zxw300)
new_lt19(zxw49001, zxw50001, ty_Bool) → new_lt13(zxw49001, zxw50001)
new_ltEs8(Just(zxw49000), Just(zxw50000), app(ty_Maybe, gc)) → new_ltEs8(zxw49000, zxw50000, gc)
new_esEs12(zxw4000, zxw3000, app(app(ty_Either, fa), fb)) → new_esEs6(zxw4000, zxw3000, fa, fb)
new_splitLT15(zxw31, zxw32, zxw33, zxw34, zxw400, True, h, ba) → new_mkVBalBranch2(zxw31, zxw33, new_splitLT5(zxw34, zxw400, h, ba), h, ba)
new_ltEs7(Right(zxw49000), Right(zxw50000), dca, app(app(ty_Either, ded), dee)) → new_ltEs7(zxw49000, zxw50000, ded, dee)
new_esEs28(zxw4000, zxw3000, app(app(ty_@2, dac), dad)) → new_esEs4(zxw4000, zxw3000, dac, dad)
new_compare9(Integer(zxw49000), Integer(zxw50000)) → new_primCmpInt(zxw49000, zxw50000)
new_asAs(False, zxw187) → False
new_primMulInt(Pos(zxw40010), Neg(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_primMulInt(Neg(zxw40010), Pos(zxw30010)) → Neg(new_primMulNat0(zxw40010, zxw30010))
new_sizeFM1(EmptyFM, cad, cae) → Pos(Zero)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Double) → new_esEs18(zxw4000, zxw3000)
new_primMulNat0(Succ(zxw400100), Zero) → Zero
new_primMulNat0(Zero, Succ(zxw300100)) → Zero
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Ordering) → new_ltEs4(zxw49000, zxw50000)
new_esEs21(zxw4001, zxw3001, ty_Ordering) → new_esEs8(zxw4001, zxw3001)
new_primCmpNat2(zxw4900, Zero) → GT
new_ltEs20(zxw49002, zxw50002, ty_Double) → new_ltEs11(zxw49002, zxw50002)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Char, hg) → new_esEs15(zxw4000, zxw3000)
new_esEs26(zxw49001, zxw50001, app(ty_Maybe, cfa)) → new_esEs7(zxw49001, zxw50001, cfa)
new_esEs10(zxw4002, zxw3002, ty_@0) → new_esEs20(zxw4002, zxw3002)
new_lt19(zxw49001, zxw50001, ty_Double) → new_lt8(zxw49001, zxw50001)
new_esEs28(zxw4000, zxw3000, ty_Double) → new_esEs18(zxw4000, zxw3000)
new_compare110(zxw49000, zxw50000, True, bfh, bga, bgb) → LT
new_esEs24(zxw4001, zxw3001, ty_Integer) → new_esEs17(zxw4001, zxw3001)
new_lt19(zxw49001, zxw50001, app(ty_Maybe, cfa)) → new_lt12(zxw49001, zxw50001, cfa)
new_ltEs18(zxw49001, zxw50001, app(ty_Ratio, bfe)) → new_ltEs17(zxw49001, zxw50001, bfe)
new_ltEs18(zxw49001, zxw50001, ty_Char) → new_ltEs12(zxw49001, zxw50001)
new_splitLT16(zxw31, zxw32, zxw33, zxw34, True, h, ba) → new_mkVBalBranch2(zxw31, zxw33, new_splitLT4(zxw34, h, ba), h, ba)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Float, hg) → new_esEs19(zxw4000, zxw3000)
new_esEs21(zxw4001, zxw3001, ty_Int) → new_esEs13(zxw4001, zxw3001)
new_mkBalBranch6MkBalBranch01(zxw50, zxw51, zxw540, zxw541, zxw542, EmptyFM, zxw544, zxw60, False, h, ba) → error([])
new_lt20(zxw49000, zxw50000, app(ty_Ratio, chb)) → new_lt18(zxw49000, zxw50000, chb)
new_splitLT13(zxw300, zxw31, zxw32, zxw33, zxw34, True, h, ba) → new_mkVBalBranch1(zxw300, zxw31, zxw33, new_splitLT4(zxw34, h, ba), h, ba)
new_ltEs19(zxw4900, zxw5000, ty_@0) → new_ltEs14(zxw4900, zxw5000)
new_ltEs7(Right(zxw49000), Right(zxw50000), dca, ty_Double) → new_ltEs11(zxw49000, zxw50000)
new_splitGT4(Branch(zxw340, zxw341, zxw342, zxw343, zxw344), h, ba) → new_splitGT30(zxw340, zxw341, zxw342, zxw343, zxw344, Nothing, h, ba)
new_splitGT23(zxw31, zxw32, zxw33, zxw34, zxw400, True, h, ba) → new_splitGT5(zxw34, zxw400, h, ba)
new_lt17(zxw49000, zxw50000, bgc, bgd) → new_esEs8(new_compare32(zxw49000, zxw50000, bgc, bgd), LT)
new_esEs9(False, False) → True
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Int) → new_ltEs10(zxw49000, zxw50000)
new_esEs30(zxw20, zxw15, ty_Int) → new_esEs13(zxw20, zxw15)
new_primMinusNat0(Zero, Succ(zxw13400)) → Neg(Succ(zxw13400))
new_ltEs19(zxw4900, zxw5000, ty_Bool) → new_ltEs5(zxw4900, zxw5000)
new_esEs31(zxw400, zxw300, app(app(ty_Either, hf), hg)) → new_esEs6(zxw400, zxw300, hf, hg)
new_mkBalBranch6MkBalBranch01(zxw50, zxw51, zxw540, zxw541, zxw542, zxw543, zxw544, zxw60, True, h, ba) → new_mkBranch(Succ(Succ(Zero)), zxw540, zxw541, new_mkBranch(Succ(Succ(Succ(Zero))), zxw50, zxw51, zxw60, zxw543, app(ty_Maybe, h), ba), zxw544, app(ty_Maybe, h), ba)
new_esEs29(zxw400, zxw300, ty_Float) → new_esEs19(zxw400, zxw300)
new_compare29(zxw49000, zxw50000, ty_Integer) → new_compare9(zxw49000, zxw50000)
new_lt20(zxw49000, zxw50000, app(app(app(ty_@3, cge), cgf), cgg)) → new_lt16(zxw49000, zxw50000, cge, cgf, cgg)
new_ltEs20(zxw49002, zxw50002, app(app(ty_Either, ced), cee)) → new_ltEs7(zxw49002, zxw50002, ced, cee)
new_esEs4(@2(zxw4000, zxw4001), @2(zxw3000, zxw3001), hh, baa) → new_asAs(new_esEs22(zxw4000, zxw3000, hh), new_esEs21(zxw4001, zxw3001, baa))
new_mkBalBranch6MkBalBranch4(zxw50, zxw51, Branch(zxw540, zxw541, zxw542, zxw543, zxw544), zxw60, True, h, ba) → new_mkBalBranch6MkBalBranch01(zxw50, zxw51, zxw540, zxw541, zxw542, zxw543, zxw544, zxw60, new_lt4(new_sizeFM0(zxw543, h, ba), new_sr(Pos(Succ(Succ(Zero))), new_sizeFM0(zxw544, h, ba))), h, ba)
new_esEs27(zxw49000, zxw50000, app(app(ty_@2, cga), cgb)) → new_esEs4(zxw49000, zxw50000, cga, cgb)
new_lt20(zxw49000, zxw50000, ty_Integer) → new_lt5(zxw49000, zxw50000)
new_ltEs18(zxw49001, zxw50001, app(ty_Maybe, bef)) → new_ltEs8(zxw49001, zxw50001, bef)
new_compare35(zxw400, h) → new_compare26(Just(zxw400), Nothing, False, h)
new_compare8(:%(zxw49000, zxw49001), :%(zxw50000, zxw50001), ty_Integer) → new_compare9(new_sr0(zxw49000, zxw50001), new_sr0(zxw50000, zxw49001))
new_ltEs7(Left(zxw49000), Left(zxw50000), ty_Float, dcb) → new_ltEs6(zxw49000, zxw50000)
new_ltEs4(LT, LT) → True
new_esEs16([], [], he) → True
new_ltEs20(zxw49002, zxw50002, ty_Int) → new_ltEs10(zxw49002, zxw50002)
new_addToFM_C11(zxw610, zxw611, zxw612, zxw613, zxw614, zxw31, True, h, ba) → new_mkBalBranch(zxw610, zxw611, zxw613, new_addToFM_C3(zxw614, zxw31, h, ba), h, ba)
new_ltEs8(Nothing, Nothing, fh) → True
new_lt10(zxw49000, zxw50000, ty_Char) → new_lt6(zxw49000, zxw50000)
new_lt10(zxw49000, zxw50000, ty_Bool) → new_lt13(zxw49000, zxw50000)
new_esEs22(zxw4000, zxw3000, app(app(ty_Either, bcb), bcc)) → new_esEs6(zxw4000, zxw3000, bcb, bcc)
new_primCmpInt(Neg(Succ(zxw4900)), Neg(zxw500)) → new_primCmpNat0(zxw500, zxw4900)
new_lt5(zxw49000, zxw50000) → new_esEs8(new_compare9(zxw49000, zxw50000), LT)
new_esEs26(zxw49001, zxw50001, ty_Float) → new_esEs19(zxw49001, zxw50001)
new_esEs6(Left(zxw4000), Left(zxw3000), ty_Int, hg) → new_esEs13(zxw4000, zxw3000)
new_esEs22(zxw4000, zxw3000, ty_Integer) → new_esEs17(zxw4000, zxw3000)
new_splitGT15(zxw31, zxw32, zxw33, zxw34, zxw400, False, h, ba) → zxw34
new_esEs10(zxw4002, zxw3002, ty_Int) → new_esEs13(zxw4002, zxw3002)
new_ltEs15(@3(zxw49000, zxw49001, zxw49002), @3(zxw50000, zxw50001, zxw50002), cdb, cdc, cdd) → new_pePe(new_lt20(zxw49000, zxw50000, cdb), new_asAs(new_esEs27(zxw49000, zxw50000, cdb), new_pePe(new_lt19(zxw49001, zxw50001, cdc), new_asAs(new_esEs26(zxw49001, zxw50001, cdc), new_ltEs20(zxw49002, zxw50002, cdd)))))
new_addToFM_C21(zxw620, zxw621, zxw622, zxw623, zxw624, zxw300, zxw31, True, h, ba) → new_mkBalBranch(zxw620, zxw621, new_addToFM_C4(zxw623, zxw300, zxw31, h, ba), zxw624, h, ba)
new_esEs12(zxw4000, zxw3000, app(ty_Ratio, ed)) → new_esEs14(zxw4000, zxw3000, ed)
new_lt10(zxw49000, zxw50000, app(ty_[], bfg)) → new_lt9(zxw49000, zxw50000, bfg)
new_ltEs10(zxw4900, zxw5000) → new_fsEs(new_compare7(zxw4900, zxw5000))
new_mkBalBranch6MkBalBranch11(zxw50, zxw51, zxw54, zxw600, zxw601, zxw602, zxw603, EmptyFM, False, h, ba) → error([])
new_esEs30(zxw20, zxw15, ty_Ordering) → new_esEs8(zxw20, zxw15)
new_lt21(zxw112, zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba) → new_esEs8(new_compare7(zxw112, new_mkVBalBranch3Size_r(zxw610, zxw611, zxw612, zxw613, zxw614, zxw330, zxw331, zxw332, zxw333, zxw334, h, ba)), LT)
new_esEs10(zxw4002, zxw3002, app(ty_Ratio, bg)) → new_esEs14(zxw4002, zxw3002, bg)
new_addToFM_C11(zxw610, zxw611, zxw612, zxw613, zxw614, zxw31, False, h, ba) → Branch(Nothing, new_addToFM0(zxw611, zxw31, ba), zxw612, zxw613, zxw614)
new_ltEs12(zxw4900, zxw5000) → new_fsEs(new_compare12(zxw4900, zxw5000))
new_esEs10(zxw4002, zxw3002, ty_Ordering) → new_esEs8(zxw4002, zxw3002)
new_ltEs7(Right(zxw49000), Right(zxw50000), dca, ty_Float) → new_ltEs6(zxw49000, zxw50000)
new_esEs23(zxw49000, zxw50000, app(ty_[], bfg)) → new_esEs16(zxw49000, zxw50000, bfg)
new_esEs26(zxw49001, zxw50001, app(app(ty_Either, cff), cfg)) → new_esEs6(zxw49001, zxw50001, cff, cfg)
new_esEs11(zxw4001, zxw3001, ty_Integer) → new_esEs17(zxw4001, zxw3001)
new_compare16(Double(zxw49000, zxw49001), Double(zxw50000, zxw50001)) → new_compare7(new_sr(zxw49000, zxw50000), new_sr(zxw49001, zxw50001))
new_compare0([], :(zxw50000, zxw50001), bhh) → LT
new_primPlusNat1(Zero, Zero) → Zero
new_esEs12(zxw4000, zxw3000, ty_Ordering) → new_esEs8(zxw4000, zxw3000)
new_lt10(zxw49000, zxw50000, ty_@0) → new_lt15(zxw49000, zxw50000)
new_mkBalBranch6Size_l(zxw50, zxw51, zxw54, zxw60, h, ba) → new_sizeFM0(zxw60, h, ba)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Char) → new_ltEs12(zxw49000, zxw50000)
new_asAs(True, zxw187) → zxw187
new_esEs26(zxw49001, zxw50001, app(app(app(ty_@3, cfc), cfd), cfe)) → new_esEs5(zxw49001, zxw50001, cfc, cfd, cfe)
new_esEs30(zxw20, zxw15, ty_Integer) → new_esEs17(zxw20, zxw15)
new_primMulNat0(Succ(zxw400100), Succ(zxw300100)) → new_primPlusNat0(new_primMulNat0(zxw400100, Succ(zxw300100)), zxw300100)
new_esEs31(zxw400, zxw300, app(ty_Maybe, hc)) → new_esEs7(zxw400, zxw300, hc)
new_ltEs8(Just(zxw49000), Just(zxw50000), ty_Integer) → new_ltEs16(zxw49000, zxw50000)
new_esEs10(zxw4002, zxw3002, app(app(ty_Either, cd), ce)) → new_esEs6(zxw4002, zxw3002, cd, ce)
new_compare30(zxw49000, zxw50000, ff, fg) → new_compare27(zxw49000, zxw50000, new_esEs4(zxw49000, zxw50000, ff, fg), ff, fg)
new_compare29(zxw49000, zxw50000, ty_Bool) → new_compare18(zxw49000, zxw50000)
new_fsEs(zxw202) → new_not(new_esEs8(zxw202, GT))
new_mkBranch(zxw294, zxw295, zxw296, zxw297, zxw298, cad, cae) → Branch(zxw295, zxw296, new_primPlusInt(new_primPlusInt(Pos(Succ(Zero)), new_sizeFM1(zxw297, cad, cae)), new_sizeFM1(zxw298, cad, cae)), zxw297, zxw298)
new_esEs23(zxw49000, zxw50000, app(app(app(ty_@3, bfh), bga), bgb)) → new_esEs5(zxw49000, zxw50000, bfh, bga, bgb)
new_esEs7(Just(zxw4000), Just(zxw3000), ty_Float) → new_esEs19(zxw4000, zxw3000)
new_esEs29(zxw400, zxw300, app(ty_Ratio, hd)) → new_esEs14(zxw400, zxw300, hd)
new_compare10(zxw49000, zxw50000, True) → LT
new_esEs30(zxw20, zxw15, app(app(app(ty_@3, bdc), bdd), bde)) → new_esEs5(zxw20, zxw15, bdc, bdd, bde)
new_compare29(zxw49000, zxw50000, app(ty_Maybe, dba)) → new_compare19(zxw49000, zxw50000, dba)
new_ltEs4(GT, GT) → True
new_esEs26(zxw49001, zxw50001, ty_@0) → new_esEs20(zxw49001, zxw50001)
new_mkBalBranch(zxw50, zxw51, zxw60, zxw54, h, ba) → new_mkBalBranch6MkBalBranch5(zxw50, zxw51, zxw54, zxw60, new_esEs8(new_primCmpInt(new_primPlusInt(new_mkBalBranch6Size_l(zxw50, zxw51, zxw54, zxw60, h, ba), new_mkBalBranch6Size_r(zxw50, zxw51, zxw54, zxw60, h, ba)), Pos(Succ(Succ(Zero)))), LT), h, ba)
new_compare110(zxw49000, zxw50000, False, bfh, bga, bgb) → GT
new_ltEs7(Left(zxw49000), Left(zxw50000), app(ty_Ratio, ddd), dcb) → new_ltEs17(zxw49000, zxw50000, ddd)
new_compare10(zxw49000, zxw50000, False) → GT
new_mkBalBranch6MkBalBranch5(zxw50, zxw51, zxw54, zxw60, False, h, ba) → new_mkBalBranch6MkBalBranch4(zxw50, zxw51, zxw54, zxw60, new_gt(new_mkBalBranch6Size_r(zxw50, zxw51, zxw54, zxw60, h, ba), new_sr(new_sIZE_RATIO, new_mkBalBranch6Size_l(zxw50, zxw51, zxw54, zxw60, h, ba))), h, ba)
new_ltEs8(Just(zxw49000), Just(zxw50000), app(app(app(ty_@3, ge), gf), gg)) → new_ltEs15(zxw49000, zxw50000, ge, gf, gg)
new_mkBalBranch6Size_r(zxw50, zxw51, zxw54, zxw60, h, ba) → new_sizeFM0(zxw54, h, ba)
new_esEs21(zxw4001, zxw3001, app(ty_[], bad)) → new_esEs16(zxw4001, zxw3001, bad)
new_compare18(zxw49000, zxw50000) → new_compare24(zxw49000, zxw50000, new_esEs9(zxw49000, zxw50000))
new_esEs6(Right(zxw4000), Right(zxw3000), hf, ty_Ordering) → new_esEs8(zxw4000, zxw3000)
new_esEs6(Left(zxw4000), Left(zxw3000), app(ty_[], cah), hg) → new_esEs16(zxw4000, zxw3000, cah)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs6(Right(zxw4000), Right(zxw3000), hf, app(app(app(ty_@3, ccc), ccd), cce)) → new_esEs5(zxw4000, zxw3000, ccc, ccd, cce)
new_primCompAux0(zxw218, EQ) → zxw218
new_splitGT15(zxw31, zxw32, zxw33, zxw34, zxw400, True, h, ba) → new_mkVBalBranch2(zxw31, new_splitGT5(zxw33, zxw400, h, ba), zxw34, h, ba)
new_esEs29(zxw400, zxw300, ty_Ordering) → new_esEs8(zxw400, zxw300)
new_splitGT30(Just(zxw300), zxw31, zxw32, zxw33, zxw34, Nothing, h, ba) → new_splitGT22(zxw300, zxw31, zxw32, zxw33, zxw34, new_esEs8(new_compare26(Nothing, Just(zxw300), False, h), GT), h, ba)
new_lt20(zxw49000, zxw50000, app(ty_Maybe, cgc)) → new_lt12(zxw49000, zxw50000, cgc)
new_esEs12(zxw4000, zxw3000, app(app(ty_@2, fc), fd)) → new_esEs4(zxw4000, zxw3000, fc, fd)
new_ltEs19(zxw4900, zxw5000, app(ty_[], bhh)) → new_ltEs13(zxw4900, zxw5000, bhh)
new_gt(zxw133, zxw132) → new_esEs8(new_compare7(zxw133, zxw132), GT)
new_primCmpInt(Pos(Succ(zxw4900)), Pos(zxw500)) → new_primCmpNat2(zxw4900, zxw500)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_esEs22(zxw4000, zxw3000, app(ty_Maybe, bbd)) → new_esEs7(zxw4000, zxw3000, bbd)
new_esEs30(zxw20, zxw15, ty_Char) → new_esEs15(zxw20, zxw15)
new_esEs30(zxw20, zxw15, app(app(ty_@2, bdh), bea)) → new_esEs4(zxw20, zxw15, bdh, bea)
new_ltEs7(Right(zxw49000), Right(zxw50000), dca, ty_@0) → new_ltEs14(zxw49000, zxw50000)
new_primCmpInt(Neg(Succ(zxw4900)), Pos(zxw500)) → LT
new_compare8(:%(zxw49000, zxw49001), :%(zxw50000, zxw50001), ty_Int) → new_compare7(new_sr(zxw49000, zxw50001), new_sr(zxw50000, zxw49001))
new_ltEs17(zxw4900, zxw5000, daf) → new_fsEs(new_compare8(zxw4900, zxw5000, daf))
new_not(True) → False
new_primMinusNat0(Succ(zxw14300), Succ(zxw13400)) → new_primMinusNat0(zxw14300, zxw13400)

The set Q consists of the following terms:

new_esEs17(Integer(x0), Integer(x1))
new_compare29(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, app(ty_[], x2))
new_ltEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_lt10(x0, x1, app(app(ty_Either, x2), x3))
new_addToFM0(x0, x1, x2)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_compare8(:%(x0, x1), :%(x2, x3), ty_Integer)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_lt10(x0, x1, ty_Double)
new_compare18(x0, x1)
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_compare29(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Double)
new_pePe(False, x0)
new_esEs31(x0, x1, ty_Double)
new_mkVBalBranch3MkVBalBranch12(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, True, x12, x13)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Left(x0), Left(x1), ty_@0, x2)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_primMinusNat0(Zero, Zero)
new_compare26(x0, x1, True, x2)
new_compare7(x0, x1)
new_compare110(x0, x1, False, x2, x3, x4)
new_primMulNat0(Succ(x0), Zero)
new_esEs7(Just(x0), Just(x1), ty_Double)
new_ltEs8(Just(x0), Just(x1), ty_Integer)
new_esEs10(x0, x1, ty_Int)
new_ltEs10(x0, x1)
new_mkBalBranch6MkBalBranch5(x0, x1, x2, x3, True, x4, x5)
new_esEs28(x0, x1, ty_Int)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_Ordering)
new_esEs31(x0, x1, ty_@0)
new_splitGT30(Nothing, x0, x1, x2, x3, Nothing, x4, x5)
new_compare32(x0, x1, x2, x3)
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_esEs12(x0, x1, ty_Char)
new_primMulNat0(Succ(x0), Succ(x1))
new_ltEs15(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_compare8(:%(x0, x1), :%(x2, x3), ty_Int)
new_ltEs7(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs8(Just(x0), Nothing, x1)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs6(Right(x0), Right(x1), x2, ty_Char)
new_ltEs7(Left(x0), Left(x1), ty_Float, x2)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs12(x0, x1, app(app(ty_@2, x2), x3))
new_lt19(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_splitLT24(x0, x1, x2, x3, x4, False, x5, x6)
new_ltEs7(Left(x0), Right(x1), x2, x3)
new_ltEs7(Right(x0), Left(x1), x2, x3)
new_ltEs16(x0, x1)
new_splitGT30(Just(x0), x1, x2, x3, x4, Nothing, x5, x6)
new_compare13(x0, x1, True)
new_esEs10(x0, x1, ty_Ordering)
new_compare26(Just(x0), Nothing, False, x1)
new_ltEs13(x0, x1, x2)
new_ltEs19(x0, x1, ty_Float)
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs11(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_Int)
new_esEs31(x0, x1, app(ty_Maybe, x2))
new_esEs31(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_Ordering)
new_splitGT22(x0, x1, x2, x3, x4, True, x5, x6)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_ltEs7(Right(x0), Right(x1), x2, ty_Bool)
new_mkVBalBranch1(x0, x1, Branch(x2, x3, x4, x5, x6), Branch(x7, x8, x9, x10, x11), x12, x13)
new_esEs8(GT, GT)
new_compare27(x0, x1, True, x2, x3)
new_mkVBalBranch2(x0, Branch(x1, x2, x3, x4, x5), Branch(x6, x7, x8, x9, x10), x11, x12)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(LT, LT)
new_esEs29(x0, x1, ty_@0)
new_compare29(x0, x1, ty_Double)
new_esEs18(Double(x0, x1), Double(x2, x3))
new_compare36(x0, x1, x2)
new_ltEs8(Nothing, Just(x0), x1)
new_primCmpNat0(Zero, x0)
new_addToFM1(x0, x1, x2, x3)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_compare29(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs8(Just(x0), Just(x1), ty_Bool)
new_esEs11(x0, x1, ty_@0)
new_primCmpNat1(Zero, Succ(x0))
new_ltEs7(Left(x0), Left(x1), ty_Integer, x2)
new_compare26(Just(x0), Just(x1), False, x2)
new_esEs25(x0, x1, ty_Int)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_sr(x0, x1)
new_ltEs5(False, False)
new_compare6(x0, x1)
new_lt10(x0, x1, ty_Ordering)
new_compare29(x0, x1, ty_Int)
new_esEs30(x0, x1, ty_Bool)
new_esEs11(x0, x1, app(app(ty_Either, x2), x3))
new_primEqNat0(Zero, Succ(x0))
new_esEs26(x0, x1, ty_Integer)
new_primCmpNat1(Zero, Zero)
new_mkBalBranch6MkBalBranch3(x0, x1, x2, Branch(x3, x4, x5, x6, x7), True, x8, x9)
new_ltEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs8(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs6(Right(x0), Left(x1), x2, x3)
new_esEs6(Left(x0), Right(x1), x2, x3)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_lt17(x0, x1, x2, x3)
new_compare16(Double(x0, x1), Double(x2, x3))
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_lt7(x0, x1)
new_ltEs8(Just(x0), Just(x1), app(ty_Ratio, x2))
new_sizeFM1(Branch(x0, x1, x2, x3, x4), x5, x6)
new_esEs28(x0, x1, ty_@0)
new_ltEs20(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Integer)
new_ltEs7(Right(x0), Right(x1), x2, ty_@0)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, ty_Integer)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_splitGT13(x0, x1, x2, x3, False, x4, x5)
new_lt20(x0, x1, ty_Double)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_Char)
new_ltEs7(Right(x0), Right(x1), x2, ty_Double)
new_addToFM_C21(x0, x1, x2, x3, x4, x5, x6, True, x7, x8)
new_esEs24(x0, x1, ty_Int)
new_primEqNat0(Zero, Zero)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs7(Left(x0), Left(x1), ty_Char, x2)
new_sizeFM1(EmptyFM, x0, x1)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_compare19(x0, x1, x2)
new_ltEs8(Just(x0), Just(x1), ty_Double)
new_ltEs8(Just(x0), Just(x1), ty_Ordering)
new_compare29(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, ty_@0)
new_compare110(x0, x1, True, x2, x3, x4)
new_compare24(x0, x1, False)
new_esEs29(x0, x1, ty_Bool)
new_esEs9(True, True)
new_mkBalBranch6MkBalBranch3(x0, x1, x2, EmptyFM, True, x3, x4)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_lt18(x0, x1, x2)
new_mkBalBranch6MkBalBranch11(x0, x1, x2, x3, x4, x5, x6, Branch(x7, x8, x9, x10, x11), False, x12, x13)
new_addToFM_C4(EmptyFM, x0, x1, x2, x3)
new_primPlusInt(Neg(x0), Neg(x1))
new_splitGT16(x0, x1, x2, x3, x4, x5, True, x6, x7)
new_splitLT16(x0, x1, x2, x3, True, x4, x5)
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_mkBalBranch6MkBalBranch11(x0, x1, x2, x3, x4, x5, x6, EmptyFM, False, x7, x8)
new_lt4(x0, x1)
new_primMulNat0(Zero, Zero)
new_esEs23(x0, x1, ty_Char)
new_primMinusNat0(Succ(x0), Succ(x1))
new_esEs30(x0, x1, ty_Ordering)
new_esEs10(x0, x1, ty_@0)
new_esEs7(Nothing, Nothing, x0)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs10(x0, x1, app(ty_Maybe, x2))
new_lt10(x0, x1, ty_Char)
new_esEs30(x0, x1, ty_Int)
new_mkVBalBranch2(x0, EmptyFM, x1, x2, x3)
new_ltEs18(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_Integer)
new_splitGT4(Branch(x0, x1, x2, x3, x4), x5, x6)
new_fsEs(x0)
new_esEs12(x0, x1, app(ty_[], x2))
new_ltEs4(GT, GT)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_lt8(x0, x1)
new_splitGT14(x0, x1, x2, x3, x4, False, x5, x6)
new_addToFM_C11(x0, x1, x2, x3, x4, x5, False, x6, x7)
new_esEs30(x0, x1, ty_@0)
new_primMinusNat0(Succ(x0), Zero)
new_sIZE_RATIO
new_esEs10(x0, x1, ty_Float)
new_sizeFM0(EmptyFM, x0, x1)
new_compare0(:(x0, x1), [], x2)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs28(x0, x1, ty_Double)
new_splitGT15(x0, x1, x2, x3, x4, False, x5, x6)
new_esEs29(x0, x1, ty_Char)
new_lt10(x0, x1, ty_Int)
new_esEs10(x0, x1, ty_Bool)
new_addToFM_C22(x0, x1, x2, x3, x4, x5, False, x6, x7)
new_lt16(x0, x1, x2, x3, x4)
new_esEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_addToFM_C3(EmptyFM, x0, x1, x2)
new_esEs23(x0, x1, ty_Ordering)
new_esEs10(x0, x1, app(ty_[], x2))
new_esEs7(Just(x0), Just(x1), ty_Int)
new_esEs10(x0, x1, ty_Char)
new_esEs6(Right(x0), Right(x1), x2, ty_Double)
new_addToFM_C22(x0, x1, x2, x3, x4, x5, True, x6, x7)
new_esEs6(Left(x0), Left(x1), ty_Int, x2)
new_compare33(x0)
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs6(Right(x0), Right(x1), x2, ty_Bool)
new_splitGT22(x0, x1, x2, x3, x4, False, x5, x6)
new_pePe(True, x0)
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_emptyFM(x0, x1)
new_mkBalBranch6MkBalBranch01(x0, x1, x2, x3, x4, EmptyFM, x5, x6, False, x7, x8)
new_primPlusNat0(Zero, x0)
new_compare11(x0, x1, True, x2)
new_ltEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs21(x0, x1, ty_Int)
new_lt6(x0, x1)
new_compare210(x0, x1, True, x2, x3, x4)
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, ty_Bool)
new_compare24(x0, x1, True)
new_ltEs18(x0, x1, ty_Integer)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_mkBalBranch6MkBalBranch01(x0, x1, x2, x3, x4, Branch(x5, x6, x7, x8, x9), x10, x11, False, x12, x13)
new_splitLT5(EmptyFM, x0, x1, x2)
new_compare14(Float(x0, x1), Float(x2, x3))
new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs16([], :(x0, x1), x2)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(x0, x1)
new_esEs29(x0, x1, ty_Integer)
new_gt(x0, x1)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_addToFM_C3(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_primPlusNat1(Zero, Zero)
new_ltEs9(@2(x0, x1), @2(x2, x3), x4, x5)
new_primCompAux0(x0, GT)
new_addToFM_C12(x0, x1, x2, x3, x4, x5, x6, True, x7, x8)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Left(x0), Left(x1), ty_Float, x2)
new_compare23(x0, x1, True)
new_esEs31(x0, x1, ty_Float)
new_lt19(x0, x1, app(ty_[], x2))
new_lt15(x0, x1)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs29(x0, x1, ty_Ordering)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_addToFM(x0, x1, x2, x3, x4)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_compare13(x0, x1, False)
new_esEs31(x0, x1, app(ty_Ratio, x2))
new_ltEs8(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_mkVBalBranch2(x0, Branch(x1, x2, x3, x4, x5), EmptyFM, x6, x7)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_lt20(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_@0)
new_primPlusNat0(Succ(x0), x1)
new_addToFM_C4(Branch(x0, x1, x2, x3, x4), x5, x6, x7, x8)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(EQ, EQ)
new_compare0([], [], x0)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, ty_Char)
new_ltEs11(x0, x1)
new_esEs12(x0, x1, ty_@0)
new_esEs24(x0, x1, ty_Integer)
new_esEs6(Right(x0), Right(x1), x2, ty_Int)
new_esEs31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Char)
new_primCompAux1(x0, x1, x2, x3)
new_primPlusInt(Pos(x0), Pos(x1))
new_esEs6(Left(x0), Left(x1), ty_Integer, x2)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Just(x0), Just(x1), ty_Char)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs12(x0, x1, ty_Float)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_compare31(@0, @0)
new_esEs7(Just(x0), Just(x1), ty_Float)
new_primCmpNat2(x0, Zero)
new_ltEs4(LT, EQ)
new_ltEs4(EQ, LT)
new_esEs12(x0, x1, ty_Int)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_mkBalBranch6MkBalBranch5(x0, x1, x2, x3, False, x4, x5)
new_lt19(x0, x1, ty_Double)
new_addToFM_C21(x0, x1, x2, x3, x4, x5, x6, False, x7, x8)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_splitLT13(x0, x1, x2, x3, x4, True, x5, x6)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Bool)
new_splitLT22(x0, x1, x2, x3, x4, True, x5, x6)
new_esEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_splitLT30(Just(x0), x1, x2, x3, x4, Nothing, x5, x6)
new_ltEs8(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs30(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Bool)
new_esEs31(x0, x1, app(app(ty_Either, x2), x3))
new_compare0(:(x0, x1), :(x2, x3), x4)
new_esEs27(x0, x1, ty_@0)
new_esEs7(Nothing, Just(x0), x1)
new_asAs(True, x0)
new_esEs30(x0, x1, app(ty_[], x2))
new_ltEs7(Right(x0), Right(x1), x2, ty_Integer)
new_primEqNat0(Succ(x0), Zero)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_mkBalBranch6MkBalBranch4(x0, x1, x2, x3, False, x4, x5)
new_mkBalBranch6MkBalBranch4(x0, x1, EmptyFM, x2, True, x3, x4)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_esEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_compare25(x0, x1, False, x2, x3)
new_esEs13(x0, x1)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs12(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs10(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs21(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Integer)
new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_lt20(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Bool)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_addToFM_C12(x0, x1, x2, x3, x4, x5, x6, False, x7, x8)
new_esEs31(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Char)
new_esEs28(x0, x1, ty_Ordering)
new_splitLT24(x0, x1, x2, x3, x4, True, x5, x6)
new_compare34(x0, x1)
new_esEs11(x0, x1, app(ty_[], x2))
new_compare30(x0, x1, x2, x3)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Ordering)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_compare0([], :(x0, x1), x2)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_ltEs20(x0, x1, ty_Bool)
new_ltEs18(x0, x1, app(ty_[], x2))
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs27(x0, x1, ty_Int)
new_splitLT14(x0, x1, x2, x3, x4, x5, False, x6, x7)
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_mkBalBranch6Size_l(x0, x1, x2, x3, x4, x5)
new_ltEs20(x0, x1, ty_Double)
new_esEs25(x0, x1, ty_Integer)
new_mkBalBranch6MkBalBranch01(x0, x1, x2, x3, x4, x5, x6, x7, True, x8, x9)
new_esEs6(Right(x0), Right(x1), x2, ty_@0)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs31(x0, x1, ty_Bool)
new_lt10(x0, x1, ty_Bool)
new_primPlusNat1(Succ(x0), Zero)
new_esEs22(x0, x1, ty_Float)
new_ltEs4(LT, LT)
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_esEs10(x0, x1, ty_Integer)
new_esEs31(x0, x1, ty_Ordering)
new_splitLT16(x0, x1, x2, x3, False, x4, x5)
new_ltEs19(x0, x1, ty_Integer)
new_compare23(x0, x1, False)
new_ltEs7(Left(x0), Left(x1), ty_Double, x2)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs11(x0, x1, ty_Bool)
new_ltEs7(Right(x0), Right(x1), x2, ty_Char)
new_esEs23(x0, x1, ty_Double)
new_compare25(x0, x1, True, x2, x3)
new_esEs21(x0, x1, ty_Bool)
new_esEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs26(x0, x1, ty_Ordering)
new_ltEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs16(:(x0, x1), [], x2)
new_primPlusNat1(Zero, Succ(x0))
new_ltEs12(x0, x1)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_compare10(x0, x1, False)
new_esEs10(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpNat0(Succ(x0), x1)
new_lt10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, ty_@0)
new_mkVBalBranch3MkVBalBranch21(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, True, x11, x12)
new_splitLT30(Just(x0), x1, x2, x3, x4, Just(x5), x6, x7)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs8(GT, EQ)
new_esEs8(EQ, GT)
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, ty_Float)
new_esEs22(x0, x1, ty_Bool)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_splitLT15(x0, x1, x2, x3, x4, False, x5, x6)
new_primMinusNat0(Zero, Succ(x0))
new_lt19(x0, x1, ty_Integer)
new_ltEs8(Just(x0), Just(x1), ty_Char)
new_ltEs7(Right(x0), Right(x1), x2, ty_Float)
new_esEs11(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_compare11(x0, x1, False, x2)
new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs8(Just(x0), Just(x1), ty_Float)
new_lt5(x0, x1)
new_compare29(x0, x1, ty_Ordering)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_ltEs18(x0, x1, ty_Bool)
new_compare28(x0, x1, x2, x3, x4)
new_esEs11(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_@0)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs6(Right(x0), Right(x1), x2, ty_Float)
new_mkVBalBranch3MkVBalBranch11(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, True, x11, x12)
new_ltEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs11(x0, x1, ty_Int)
new_esEs16([], [], x0)
new_splitGT30(Nothing, x0, x1, x2, x3, Just(x4), x5, x6)
new_ltEs7(Right(x0), Right(x1), x2, ty_Int)
new_esEs11(x0, x1, ty_Char)
new_splitGT5(EmptyFM, x0, x1, x2)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Float)
new_esEs6(Left(x0), Left(x1), ty_Double, x2)
new_lt19(x0, x1, ty_Ordering)
new_compare29(x0, x1, ty_Integer)
new_ltEs18(x0, x1, ty_Float)
new_esEs9(False, False)
new_esEs11(x0, x1, app(ty_Ratio, x2))
new_compare29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Double)
new_splitGT24(x0, x1, x2, x3, x4, x5, True, x6, x7)
new_esEs12(x0, x1, ty_Ordering)
new_ltEs8(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, app(ty_[], x2))
new_primCmpNat1(Succ(x0), Succ(x1))
new_esEs26(x0, x1, ty_@0)
new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs6(x0, x1)
new_lt10(x0, x1, ty_Float)
new_splitLT23(x0, x1, x2, x3, x4, x5, False, x6, x7)
new_esEs22(x0, x1, ty_Int)
new_esEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_lt10(x0, x1, app(app(ty_@2, x2), x3))
new_splitGT30(Just(x0), x1, x2, x3, x4, Just(x5), x6, x7)
new_esEs21(x0, x1, ty_Float)
new_esEs29(x0, x1, ty_Double)
new_compare15(x0, x1, False, x2, x3)
new_primCompAux0(x0, EQ)
new_splitGT24(x0, x1, x2, x3, x4, x5, False, x6, x7)
new_compare26(Nothing, Nothing, False, x0)
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_mkVBalBranch1(x0, x1, EmptyFM, x2, x3, x4)
new_lt9(x0, x1, x2)
new_esEs21(x0, x1, ty_Integer)
new_primCmpNat1(Succ(x0), Zero)
new_esEs22(x0, x1, ty_Double)
new_ltEs18(x0, x1, ty_@0)
new_esEs7(Just(x0), Nothing, x1)
new_compare29(x0, x1, app(app(ty_Either, x2), x3))
new_splitLT5(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_lt13(x0, x1)
new_esEs23(x0, x1, ty_Bool)
new_ltEs5(True, True)
new_splitLT23(x0, x1, x2, x3, x4, x5, True, x6, x7)
new_lt19(x0, x1, ty_Int)
new_compare35(x0, x1)
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1, ty_Char)
new_ltEs4(EQ, GT)
new_mkVBalBranch3MkVBalBranch22(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, True, x12, x13)
new_ltEs4(GT, EQ)
new_splitGT15(x0, x1, x2, x3, x4, True, x5, x6)
new_esEs31(x0, x1, ty_Integer)
new_not(True)
new_splitLT14(x0, x1, x2, x3, x4, x5, True, x6, x7)
new_mkBalBranch6Size_r(x0, x1, x2, x3, x4, x5)
new_esEs11(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Float)
new_esEs31(x0, x1, app(app(ty_@2, x2), x3))
new_mkBalBranch6MkBalBranch3(x0, x1, x2, x3, False, x4, x5)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Char)
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, ty_Ordering)
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs26(x0, x1, ty_Char)
new_compare26(Nothing, Just(x0), False, x1)
new_ltEs18(x0, x1, ty_Int)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_not(False)
new_ltEs20(x0, x1, ty_Ordering)
new_mkVBalBranch3MkVBalBranch21(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, False, x11, x12)
new_lt14(x0, x1)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_compare12(Char(x0), Char(x1))
new_esEs15(Char(x0), Char(x1))
new_lt21(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_compare10(x0, x1, True)
new_compare29(x0, x1, app(ty_Maybe, x2))
new_lt10(x0, x1, ty_@0)
new_asAs(False, x0)
new_esEs22(x0, x1, ty_Ordering)
new_ltEs18(x0, x1, ty_Char)
new_splitGT23(x0, x1, x2, x3, x4, False, x5, x6)
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs12(x0, x1, app(ty_Ratio, x2))
new_ltEs7(Left(x0), Left(x1), ty_@0, x2)
new_splitGT14(x0, x1, x2, x3, x4, True, x5, x6)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_compare29(x0, x1, ty_Float)
new_esEs6(Left(x0), Left(x1), ty_Char, x2)
new_lt19(x0, x1, ty_Bool)
new_esEs31(x0, x1, ty_Char)
new_esEs27(x0, x1, ty_Char)
new_lt11(x0, x1, x2, x3)
new_splitLT30(Nothing, x0, x1, x2, x3, Just(x4), x5, x6)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_ltEs8(Just(x0), Just(x1), ty_@0)
new_splitLT22(x0, x1, x2, x3, x4, False, x5, x6)
new_compare17(x0, x1, False, x2, x3)
new_esEs20(@0, @0)
new_splitGT5(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_splitGT23(x0, x1, x2, x3, x4, True, x5, x6)
new_lt10(x0, x1, app(ty_[], x2))
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_mkBalBranch(x0, x1, x2, x3, x4, x5)
new_esEs16(:(x0, x1), :(x2, x3), x4)
new_splitGT16(x0, x1, x2, x3, x4, x5, False, x6, x7)
new_esEs23(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Int)
new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_ltEs19(x0, x1, ty_Double)
new_esEs9(False, True)
new_esEs9(True, False)
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, ty_Char)
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs17(x0, x1, x2)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare29(x0, x1, ty_Bool)
new_mkVBalBranch1(x0, x1, Branch(x2, x3, x4, x5, x6), EmptyFM, x7, x8)
new_esEs30(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Integer)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs11(x0, x1, ty_Double)
new_mkBranch(x0, x1, x2, x3, x4, x5, x6)
new_ltEs20(x0, x1, ty_Float)
new_mkBalBranch6MkBalBranch11(x0, x1, x2, x3, x4, x5, x6, x7, True, x8, x9)
new_primCompAux0(x0, LT)
new_ltEs8(Just(x0), Just(x1), app(ty_[], x2))
new_mkVBalBranch3MkVBalBranch22(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, False, x12, x13)
new_ltEs8(Nothing, Nothing, x0)
new_primCmpNat2(x0, Succ(x1))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_splitGT13(x0, x1, x2, x3, True, x4, x5)
new_primPlusInt(Pos(x0), Neg(x1))
new_primPlusInt(Neg(x0), Pos(x1))
new_esEs12(x0, x1, ty_Integer)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_splitLT4(Branch(x0, x1, x2, x3, x4), x5, x6)
new_esEs10(x0, x1, ty_Double)
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_sr0(Integer(x0), Integer(x1))
new_addToFM_C11(x0, x1, x2, x3, x4, x5, True, x6, x7)
new_compare27(x0, x1, False, x2, x3)
new_esEs29(x0, x1, ty_Float)
new_compare15(x0, x1, True, x2, x3)
new_esEs12(x0, x1, app(ty_Maybe, x2))
new_compare17(x0, x1, True, x2, x3)
new_primEqInt(Pos(Zero), Pos(Zero))
new_splitGT4(EmptyFM, x0, x1)
new_ltEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs6(Left(x0), Left(x1), ty_Bool, x2)
new_esEs14(:%(x0, x1), :%(x2, x3), x4)
new_ltEs18(x0, x1, ty_Double)
new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs12(x0, x1, ty_Double)
new_esEs29(x0, x1, ty_Int)
new_esEs12(x0, x1, ty_Bool)
new_compare9(Integer(x0), Integer(x1))
new_lt10(x0, x1, ty_Integer)
new_ltEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_splitLT4(EmptyFM, x0, x1)
new_esEs30(x0, x1, ty_Char)
new_mkVBalBranch3MkVBalBranch11(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, False, x11, x12)
new_splitLT13(x0, x1, x2, x3, x4, False, x5, x6)
new_lt10(x0, x1, app(ty_Ratio, x2))
new_esEs19(Float(x0, x1), Float(x2, x3))
new_primMulNat0(Zero, Succ(x0))
new_esEs10(x0, x1, app(ty_Ratio, x2))
new_esEs7(Just(x0), Just(x1), ty_@0)
new_ltEs4(LT, GT)
new_ltEs4(GT, LT)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs11(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs5(True, False)
new_ltEs5(False, True)
new_mkVBalBranch3MkVBalBranch12(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, False, x12, x13)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_lt10(x0, x1, app(ty_Maybe, x2))
new_mkBalBranch6MkBalBranch4(x0, x1, Branch(x2, x3, x4, x5, x6), x7, True, x8, x9)
new_ltEs8(Just(x0), Just(x1), ty_Int)
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_compare29(x0, x1, ty_@0)
new_esEs6(Right(x0), Right(x1), x2, ty_Integer)
new_splitLT15(x0, x1, x2, x3, x4, True, x5, x6)
new_esEs27(x0, x1, ty_Float)
new_esEs23(x0, x1, ty_Float)
new_compare210(x0, x1, False, x2, x3, x4)
new_lt12(x0, x1, x2)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs30(x0, x1, ty_Float)
new_ltEs7(Left(x0), Left(x1), ty_Int, x2)
new_splitLT30(Nothing, x0, x1, x2, x3, Nothing, x4, x5)

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: