YES 43.963 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
  ((intersectFM_C :: Ord c => (d  ->  b  ->  a)  ->  FiniteMap (Maybe c) d  ->  FiniteMap (Maybe c) b  ->  FiniteMap (Maybe c) a) :: Ord c => (d  ->  b  ->  a)  ->  FiniteMap (Maybe c) d  ->  FiniteMap (Maybe c) b  ->  FiniteMap (Maybe c) a)

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

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

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

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

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

  emptyFM :: FiniteMap a b
emptyFM = EmptyFM

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

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

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

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

  glueBal :: Ord 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

  intersectFM_C :: Ord c => (a  ->  d  ->  b)  ->  FiniteMap c a  ->  FiniteMap c d  ->  FiniteMap c b
intersectFM_C combiner fm1 EmptyFM = emptyFM
intersectFM_C combiner EmptyFM fm2 = emptyFM
intersectFM_C combiner fm1 (Branch split_key elt2 _ left right) 
 | Maybe.isJust maybe_elt1 = 
mkVBalBranch split_key (combiner elt1 elt2) (intersectFM_C combiner lts left) (intersectFM_C combiner gts right)
 | otherwise = 
glueVBal (intersectFM_C combiner lts left) (intersectFM_C combiner gts right) where 
elt1 = (\(Just elt1) ->elt1) vv1
gts = splitGT fm1 split_key
lts = splitLT fm1 split_key
maybe_elt1 = lookupFM fm1 split_key
vv1 = maybe_elt1

  lookupFM :: Ord a => FiniteMap a b  ->  a  ->  Maybe b
lookupFM EmptyFM key = Nothing
lookupFM (Branch key elt _ fm_l fm_r) key_to_find 
 | key_to_find < key = 
lookupFM fm_l key_to_find
 | key_to_find > key = 
lookupFM fm_r key_to_find
 | otherwise = 
Just elt

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

  sIZE_RATIO :: Int
sIZE_RATIO = 5

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

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

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude
  isJust :: Maybe a  ->  Bool
isJust Nothing = False
isJust _ = True



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
\(Just elt1)→elt1

is transformed to
elt10 (Just elt1) = elt1

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

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

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

  
addToFM0 old new = new

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

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

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

  emptyFM :: FiniteMap a b
emptyFM = EmptyFM

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

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

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

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

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

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

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

  intersectFM_C :: Ord b => (d  ->  c  ->  a)  ->  FiniteMap b d  ->  FiniteMap b c  ->  FiniteMap b a
intersectFM_C combiner fm1 EmptyFM = emptyFM
intersectFM_C combiner EmptyFM fm2 = emptyFM
intersectFM_C combiner fm1 (Branch split_key elt2 _ left right) 
 | Maybe.isJust maybe_elt1 = 
mkVBalBranch split_key (combiner elt1 elt2) (intersectFM_C combiner lts left) (intersectFM_C combiner gts right)
 | otherwise = 
glueVBal (intersectFM_C combiner lts left) (intersectFM_C combiner gts right) where 
elt1 = elt10 vv1
elt10 (Just elt1) = elt1
gts = splitGT fm1 split_key
lts = splitLT fm1 split_key
maybe_elt1 = lookupFM fm1 split_key
vv1 = maybe_elt1

  lookupFM :: Ord a => FiniteMap a b  ->  a  ->  Maybe b
lookupFM EmptyFM key = Nothing
lookupFM (Branch key elt _ fm_l fm_r) key_to_find 
 | key_to_find < key = 
lookupFM fm_l key_to_find
 | key_to_find > key = 
lookupFM fm_r key_to_find
 | otherwise = 
Just elt

  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
  isJust :: Maybe a  ->  Bool
isJust Nothing = False
isJust _ = True



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

  intersectFM_C :: Ord c => (a  ->  b  ->  d)  ->  FiniteMap c a  ->  FiniteMap c b  ->  FiniteMap c d
intersectFM_C combiner fm1 EmptyFM = emptyFM
intersectFM_C combiner EmptyFM fm2 = emptyFM
intersectFM_C combiner fm1 (Branch split_key elt2 _ left right) 
 | Maybe.isJust maybe_elt1 = 
mkVBalBranch split_key (combiner elt1 elt2) (intersectFM_C combiner lts left) (intersectFM_C combiner gts right)
 | otherwise = 
glueVBal (intersectFM_C combiner lts left) (intersectFM_C combiner gts right) where 
elt1 = elt10 vv1
elt10 (Just elt1) = elt1
gts = splitGT fm1 split_key
lts = splitLT fm1 split_key
maybe_elt1 = lookupFM fm1 split_key
vv1 = maybe_elt1

  lookupFM :: Ord a => FiniteMap a b  ->  a  ->  Maybe b
lookupFM EmptyFM key = Nothing
lookupFM (Branch key elt _ fm_l fm_r) key_to_find 
 | key_to_find < key = 
lookupFM fm_l key_to_find
 | key_to_find > key = 
lookupFM fm_r key_to_find
 | otherwise = 
Just elt

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

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

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

  sIZE_RATIO :: Int
sIZE_RATIO = 5

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

  splitGT :: Ord 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
  isJust :: Maybe a  ->  Bool
isJust Nothing = False
isJust _ = True



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

  intersectFM_C :: Ord a => (d  ->  b  ->  c)  ->  FiniteMap a d  ->  FiniteMap a b  ->  FiniteMap a c
intersectFM_C combiner fm1 EmptyFM = emptyFM
intersectFM_C combiner EmptyFM fm2 = emptyFM
intersectFM_C combiner fm1 (Branch split_key elt2 _ left right) 
 | Maybe.isJust maybe_elt1 = 
mkVBalBranch split_key (combiner elt1 elt2) (intersectFM_C combiner lts left) (intersectFM_C combiner gts right)
 | otherwise = 
glueVBal (intersectFM_C combiner lts left) (intersectFM_C combiner gts right) where 
elt1 = elt10 vv1
elt10 (Just elt1) = elt1
gts = splitGT fm1 split_key
lts = splitLT fm1 split_key
maybe_elt1 = lookupFM fm1 split_key
vv1 = maybe_elt1

  lookupFM :: Ord b => FiniteMap b a  ->  b  ->  Maybe a
lookupFM EmptyFM key = Nothing
lookupFM (Branch key elt _ fm_l fm_r) key_to_find 
 | key_to_find < key = 
lookupFM fm_l key_to_find
 | key_to_find > key = 
lookupFM fm_r key_to_find
 | otherwise = 
Just elt

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

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

  sIZE_RATIO :: Int
sIZE_RATIO = 5

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

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

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude
  isJust :: Maybe a  ->  Bool
isJust Nothing = False
isJust _ = True



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
  ((intersectFM_C :: Ord a => (d  ->  b  ->  c)  ->  FiniteMap (Maybe a) d  ->  FiniteMap (Maybe a) b  ->  FiniteMap (Maybe a) c) :: Ord a => (d  ->  b  ->  c)  ->  FiniteMap (Maybe a) d  ->  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 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 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 wuw EmptyFM fm_r) = fm_r
deleteMin (Branch key elt wux fm_l fm_r) = mkBalBranch key elt (deleteMin fm_l) fm_r

  emptyFM :: FiniteMap b a
emptyFM = EmptyFM

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

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

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

  intersectFM_C :: Ord a => (c  ->  b  ->  d)  ->  FiniteMap a c  ->  FiniteMap a b  ->  FiniteMap a d
intersectFM_C combiner fm1 EmptyFM = emptyFM
intersectFM_C combiner EmptyFM fm2 = emptyFM
intersectFM_C combiner fm1 (Branch split_key elt2 wuy left right) 
 | Maybe.isJust maybe_elt1 = 
mkVBalBranch split_key (combiner elt1 elt2) (intersectFM_C combiner lts left) (intersectFM_C combiner gts right)
 | otherwise = 
glueVBal (intersectFM_C combiner lts left) (intersectFM_C combiner gts right) where 
elt1 = elt10 vv1
elt10 (Just elt1) = elt1
gts = splitGT fm1 split_key
lts = splitLT fm1 split_key
maybe_elt1 = lookupFM fm1 split_key
vv1 = maybe_elt1

  lookupFM :: Ord b => FiniteMap b a  ->  b  ->  Maybe a
lookupFM EmptyFM key = Nothing
lookupFM (Branch key elt wuv fm_l fm_r) key_to_find 
 | key_to_find < key = 
lookupFM fm_l key_to_find
 | key_to_find > key = 
lookupFM fm_r key_to_find
 | otherwise = 
Just elt

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

  mkBranch :: Ord 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 = 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 b => FiniteMap b a  ->  b  ->  FiniteMap b a
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 a => FiniteMap a b  ->  a  ->  FiniteMap a b
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
  isJust :: Maybe a  ->  Bool
isJust Nothing = False
isJust wuz = True



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

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

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 wzz xuu = splitLT3 wzz xuu

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

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)

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

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 xux xuy = splitGT3 xux xuy

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 xvw xvx = glueVBal3 xvw xvx

glueVBal5 EmptyFM fm2 = fm2
glueVBal5 xvz xwu = glueVBal4 xvz xwu

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 xwy xwz xxu xxv = mkVBalBranch3 xwy xwz xxu xxv

mkVBalBranch5 key elt EmptyFM fm_r = addToFM fm_r key elt
mkVBalBranch5 xxx xxy xxz xyu = mkVBalBranch4 xxx xxy xxz xyu

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)

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)

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)

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)

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

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

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

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

addToFM_C4 combiner EmptyFM key elt = unitFM key elt
addToFM_C4 xyz xzu xzv xzw = addToFM_C3 xyz xzu xzv xzw

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 xzy xzz = glueBal2 xzy xzz

glueBal4 EmptyFM fm2 = fm2
glueBal4 yuv yuw = glueBal3 yuv yuw

The following Function with conditions
lookupFM EmptyFM key = Nothing
lookupFM (Branch key elt wuv fm_l fm_r) key_to_find
 | key_to_find < key
 = lookupFM fm_l key_to_find
 | key_to_find > key
 = lookupFM fm_r key_to_find
 | otherwise
 = Just elt

is transformed to
lookupFM EmptyFM key = lookupFM4 EmptyFM key
lookupFM (Branch key elt wuv fm_l fm_r) key_to_find = lookupFM3 (Branch key elt wuv fm_l fm_r) key_to_find

lookupFM1 key elt wuv fm_l fm_r key_to_find True = lookupFM fm_r key_to_find
lookupFM1 key elt wuv fm_l fm_r key_to_find False = lookupFM0 key elt wuv fm_l fm_r key_to_find otherwise

lookupFM2 key elt wuv fm_l fm_r key_to_find True = lookupFM fm_l key_to_find
lookupFM2 key elt wuv fm_l fm_r key_to_find False = lookupFM1 key elt wuv fm_l fm_r key_to_find (key_to_find > key)

lookupFM0 key elt wuv fm_l fm_r key_to_find True = Just elt

lookupFM3 (Branch key elt wuv fm_l fm_r) key_to_find = lookupFM2 key elt wuv fm_l fm_r key_to_find (key_to_find < key)

lookupFM4 EmptyFM key = Nothing
lookupFM4 yuz yvu = lookupFM3 yuz yvu

The following Function with conditions
intersectFM_C combiner fm1 EmptyFM = emptyFM
intersectFM_C combiner EmptyFM fm2 = emptyFM
intersectFM_C combiner fm1 (Branch split_key elt2 wuy left right)
 | Maybe.isJust maybe_elt1
 = mkVBalBranch split_key (combiner elt1 elt2) (intersectFM_C combiner lts left) (intersectFM_C combiner gts right)
 | otherwise
 = glueVBal (intersectFM_C combiner lts left) (intersectFM_C combiner gts right)
where 
elt1  = elt10 vv1
elt10 (Just elt1) = elt1
gts  = splitGT fm1 split_key
lts  = splitLT fm1 split_key
maybe_elt1  = lookupFM fm1 split_key
vv1  = maybe_elt1

is transformed to
intersectFM_C combiner fm1 EmptyFM = intersectFM_C4 combiner fm1 EmptyFM
intersectFM_C combiner EmptyFM fm2 = intersectFM_C3 combiner EmptyFM fm2
intersectFM_C combiner fm1 (Branch split_key elt2 wuy left right) = intersectFM_C2 combiner fm1 (Branch split_key elt2 wuy left right)

intersectFM_C2 combiner fm1 (Branch split_key elt2 wuy left right) = 
intersectFM_C1 combiner fm1 split_key elt2 wuy left right (Maybe.isJust maybe_elt1)
where 
elt1  = elt10 vv1
elt10 (Just elt1) = elt1
gts  = splitGT fm1 split_key
intersectFM_C0 combiner fm1 split_key elt2 wuy left right True = glueVBal (intersectFM_C combiner lts left) (intersectFM_C combiner gts right)
intersectFM_C1 combiner fm1 split_key elt2 wuy left right True = mkVBalBranch split_key (combiner elt1 elt2) (intersectFM_C combiner lts left) (intersectFM_C combiner gts right)
intersectFM_C1 combiner fm1 split_key elt2 wuy left right False = intersectFM_C0 combiner fm1 split_key elt2 wuy left right otherwise
lts  = splitLT fm1 split_key
maybe_elt1  = lookupFM fm1 split_key
vv1  = maybe_elt1

intersectFM_C3 combiner EmptyFM fm2 = emptyFM
intersectFM_C3 yvx yvy yvz = intersectFM_C2 yvx yvy yvz

intersectFM_C4 combiner fm1 EmptyFM = emptyFM
intersectFM_C4 ywv yww ywx = intersectFM_C3 ywv yww ywx

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

is transformed to
compare x y = compare3 x y

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

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

compare0 x y True = GT

compare3 x y = compare2 x y (x == y)

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

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

gcd'0 x y = gcd' y (x `rem` y)

gcd'1 True x ywy = x
gcd'1 ywz yxu yxv = gcd'0 yxu yxv

gcd'2 x ywy = gcd'1 (ywy == 0) x ywy
gcd'2 yxw yxx = gcd'0 yxw yxx

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 yxy yxz = gcd3 yxy yxz
gcd x y = gcd0 x y

gcd0 x y = 
gcd' (abs x) (abs y)
where 
gcd' x ywy = gcd'2 x ywy
gcd' x y = gcd'0 x y
gcd'0 x y = gcd' y (x `rem` y)
gcd'1 True x ywy = x
gcd'1 ywz yxu yxv = gcd'0 yxu yxv
gcd'2 x ywy = gcd'1 (ywy == 0) x ywy
gcd'2 yxw yxx = gcd'0 yxw yxx

gcd1 True yxy yxz = error []
gcd1 yyu yyv yyw = gcd0 yyv yyw

gcd2 True yxy yxz = gcd1 (yxz == 0) yxy yxz
gcd2 yyx yyy yyz = gcd0 yyy yyz

gcd3 yxy yxz = gcd2 (yxy == 0) yxy yxz
gcd3 yzu yzv = gcd0 yzu yzv

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

is transformed to
absReal x = absReal2 x

absReal0 x True = `negate` x

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

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

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

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

  
addToFM0 old new = new

  addToFM_C :: Ord b => (a  ->  a  ->  a)  ->  FiniteMap b a  ->  b  ->  a  ->  FiniteMap b a
addToFM_C combiner EmptyFM key elt = 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 xyz xzu xzv xzw = addToFM_C3 xyz xzu xzv xzw

  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 wuw EmptyFM fm_r) = fm_r
deleteMin (Branch key elt wux fm_l fm_r) = mkBalBranch key elt (deleteMin fm_l) fm_r

  emptyFM :: FiniteMap a b
emptyFM = EmptyFM

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

  findMin :: FiniteMap 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 b a  ->  [(b,a)]
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 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 xzy xzz = glueBal2 xzy xzz

  
glueBal4 EmptyFM fm2 = fm2
glueBal4 yuv yuw = glueBal3 yuv yuw

  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 xvw xvx = glueVBal3 xvw xvx

  
glueVBal5 EmptyFM fm2 = fm2
glueVBal5 xvz xwu = glueVBal4 xvz xwu

  intersectFM_C :: Ord d => (b  ->  c  ->  a)  ->  FiniteMap d b  ->  FiniteMap d c  ->  FiniteMap d a
intersectFM_C combiner fm1 EmptyFM = intersectFM_C4 combiner fm1 EmptyFM
intersectFM_C combiner EmptyFM fm2 = intersectFM_C3 combiner EmptyFM fm2
intersectFM_C combiner fm1 (Branch split_key elt2 wuy left right) = intersectFM_C2 combiner fm1 (Branch split_key elt2 wuy left right)

  
intersectFM_C2 combiner fm1 (Branch split_key elt2 wuy left right) = 
intersectFM_C1 combiner fm1 split_key elt2 wuy left right (Maybe.isJust maybe_elt1) where 
elt1 = elt10 vv1
elt10 (Just elt1) = elt1
gts = splitGT fm1 split_key
intersectFM_C0 combiner fm1 split_key elt2 wuy left right True = glueVBal (intersectFM_C combiner lts left) (intersectFM_C combiner gts right)
intersectFM_C1 combiner fm1 split_key elt2 wuy left right True = mkVBalBranch split_key (combiner elt1 elt2) (intersectFM_C combiner lts left) (intersectFM_C combiner gts right)
intersectFM_C1 combiner fm1 split_key elt2 wuy left right False = intersectFM_C0 combiner fm1 split_key elt2 wuy left right otherwise
lts = splitLT fm1 split_key
maybe_elt1 = lookupFM fm1 split_key
vv1 = maybe_elt1

  
intersectFM_C3 combiner EmptyFM fm2 = emptyFM
intersectFM_C3 yvx yvy yvz = intersectFM_C2 yvx yvy yvz

  
intersectFM_C4 combiner fm1 EmptyFM = emptyFM
intersectFM_C4 ywv yww ywx = intersectFM_C3 ywv yww ywx

  lookupFM :: Ord a => FiniteMap a b  ->  a  ->  Maybe b
lookupFM EmptyFM key = lookupFM4 EmptyFM key
lookupFM (Branch key elt wuv fm_l fm_r) key_to_find = lookupFM3 (Branch key elt wuv fm_l fm_r) key_to_find

  
lookupFM0 key elt wuv fm_l fm_r key_to_find True = Just elt

  
lookupFM1 key elt wuv fm_l fm_r key_to_find True = lookupFM fm_r key_to_find
lookupFM1 key elt wuv fm_l fm_r key_to_find False = lookupFM0 key elt wuv fm_l fm_r key_to_find otherwise

  
lookupFM2 key elt wuv fm_l fm_r key_to_find True = lookupFM fm_l key_to_find
lookupFM2 key elt wuv fm_l fm_r key_to_find False = lookupFM1 key elt wuv fm_l fm_r key_to_find (key_to_find > key)

  
lookupFM3 (Branch key elt wuv fm_l fm_r) key_to_find = lookupFM2 key elt wuv fm_l fm_r key_to_find (key_to_find < key)

  
lookupFM4 EmptyFM key = Nothing
lookupFM4 yuz yvu = lookupFM3 yuz yvu

  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 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 = 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 xwy xwz xxu xxv = mkVBalBranch3 xwy xwz xxu xxv

  
mkVBalBranch5 key elt EmptyFM fm_r = addToFM fm_r key elt
mkVBalBranch5 xxx xxy xxz xyu = mkVBalBranch4 xxx xxy xxz xyu

  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 xux xuy = splitGT3 xux xuy

  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 wzz xuu = splitLT3 wzz xuu

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude
  isJust :: Maybe a  ->  Bool
isJust Nothing = False
isJust wuz = True



Let/Where Reductions:
The bindings of the following Let/Where expression
intersectFM_C1 combiner fm1 split_key elt2 wuy left right (Maybe.isJust maybe_elt1)
where 
elt1  = elt10 vv1
elt10 (Just elt1) = elt1
gts  = splitGT fm1 split_key
intersectFM_C0 combiner fm1 split_key elt2 wuy left right True = glueVBal (intersectFM_C combiner lts left) (intersectFM_C combiner gts right)
intersectFM_C1 combiner fm1 split_key elt2 wuy left right True = mkVBalBranch split_key (combiner elt1 elt2) (intersectFM_C combiner lts left) (intersectFM_C combiner gts right)
intersectFM_C1 combiner fm1 split_key elt2 wuy left right False = intersectFM_C0 combiner fm1 split_key elt2 wuy left right otherwise
lts  = splitLT fm1 split_key
maybe_elt1  = lookupFM fm1 split_key
vv1  = maybe_elt1

are unpacked to the following functions on top level
intersectFM_C2IntersectFM_C1 yzw yzx combiner fm1 split_key elt2 wuy left right True = mkVBalBranch split_key (combiner (intersectFM_C2Elt1 yzw yzx) elt2) (intersectFM_C combiner (intersectFM_C2Lts yzw yzx) left) (intersectFM_C combiner (intersectFM_C2Gts yzw yzx) right)
intersectFM_C2IntersectFM_C1 yzw yzx combiner fm1 split_key elt2 wuy left right False = intersectFM_C2IntersectFM_C0 yzw yzx combiner fm1 split_key elt2 wuy left right otherwise

intersectFM_C2Vv1 yzw yzx = intersectFM_C2Maybe_elt1 yzw yzx

intersectFM_C2IntersectFM_C0 yzw yzx combiner fm1 split_key elt2 wuy left right True = glueVBal (intersectFM_C combiner (intersectFM_C2Lts yzw yzx) left) (intersectFM_C combiner (intersectFM_C2Gts yzw yzx) right)

intersectFM_C2Elt10 yzw yzx (Just elt1) = elt1

intersectFM_C2Lts yzw yzx = splitLT yzw yzx

intersectFM_C2Elt1 yzw yzx = intersectFM_C2Elt10 yzw yzx (intersectFM_C2Vv1 yzw yzx)

intersectFM_C2Gts yzw yzx = splitGT yzw yzx

intersectFM_C2Maybe_elt1 yzw yzx = lookupFM yzw yzx

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_elt2 yzy yzz = glueBal2Mid_elt20 yzy yzz (glueBal2Vv3 yzy yzz)

glueBal2Mid_key1 yzy yzz = glueBal2Mid_key10 yzy yzz (glueBal2Vv2 yzy yzz)

glueBal2Mid_key20 yzy yzz (mid_key2,wuu) = mid_key2

glueBal2GlueBal0 yzy yzz fm1 fm2 True = mkBalBranch (glueBal2Mid_key1 yzy yzz) (glueBal2Mid_elt1 yzy yzz) (deleteMax fm1) fm2

glueBal2Vv2 yzy yzz = findMax yzy

glueBal2Mid_elt20 yzy yzz (vzy,mid_elt2) = mid_elt2

glueBal2Mid_elt1 yzy yzz = glueBal2Mid_elt10 yzy yzz (glueBal2Vv2 yzy yzz)

glueBal2GlueBal1 yzy yzz fm1 fm2 True = mkBalBranch (glueBal2Mid_key2 yzy yzz) (glueBal2Mid_elt2 yzy yzz) fm1 (deleteMin fm2)
glueBal2GlueBal1 yzy yzz fm1 fm2 False = glueBal2GlueBal0 yzy yzz fm1 fm2 otherwise

glueBal2Mid_elt10 yzy yzz (vzx,mid_elt1) = mid_elt1

glueBal2Mid_key2 yzy yzz = glueBal2Mid_key20 yzy yzz (glueBal2Vv3 yzy yzz)

glueBal2Mid_key10 yzy yzz (mid_key1,vzz) = mid_key1

glueBal2Vv3 yzy yzz = findMin yzz

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
mkBalBranch6MkBalBranch11 zuu zuv zuw zux fm_L fm_R vxw vxx vxy fm_ll fm_lr True = mkBalBranch6Single_R zuu zuv zuw zux fm_L fm_R
mkBalBranch6MkBalBranch11 zuu zuv zuw zux fm_L fm_R vxw vxx vxy fm_ll fm_lr False = mkBalBranch6MkBalBranch10 zuu zuv zuw zux fm_L fm_R vxw vxx vxy fm_ll fm_lr otherwise

mkBalBranch6MkBalBranch12 zuu zuv zuw zux fm_L fm_R (Branch vxw vxx vxy fm_ll fm_lr) = mkBalBranch6MkBalBranch11 zuu zuv zuw zux fm_L fm_R vxw vxx vxy fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll)

mkBalBranch6MkBalBranch02 zuu zuv zuw zux fm_L fm_R (Branch vyv vyw vyx fm_rl fm_rr) = mkBalBranch6MkBalBranch01 zuu zuv zuw zux fm_L fm_R vyv vyw vyx fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr)

mkBalBranch6MkBalBranch1 zuu zuv zuw zux fm_L fm_R (Branch vxw vxx vxy fm_ll fm_lr) = mkBalBranch6MkBalBranch12 zuu zuv zuw zux fm_L fm_R (Branch vxw vxx vxy fm_ll fm_lr)

mkBalBranch6Double_L zuu zuv zuw zux 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 zuu zuv fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr)

mkBalBranch6Size_r zuu zuv zuw zux = sizeFM zuw

mkBalBranch6Double_R zuu zuv zuw zux (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 zuu zuv fm_lrr fm_r)

mkBalBranch6MkBalBranch00 zuu zuv zuw zux fm_L fm_R vyv vyw vyx fm_rl fm_rr True = mkBalBranch6Double_L zuu zuv zuw zux fm_L fm_R

mkBalBranch6Single_L zuu zuv zuw zux fm_l (Branch key_r elt_r vyy fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 zuu zuv fm_l fm_rl) fm_rr

mkBalBranch6Single_R zuu zuv zuw zux (Branch key_l elt_l vwz fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 zuu zuv fm_lr fm_r)

mkBalBranch6MkBalBranch10 zuu zuv zuw zux fm_L fm_R vxw vxx vxy fm_ll fm_lr True = mkBalBranch6Double_R zuu zuv zuw zux fm_L fm_R

mkBalBranch6MkBalBranch5 zuu zuv zuw zux key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R
mkBalBranch6MkBalBranch5 zuu zuv zuw zux key elt fm_L fm_R False = mkBalBranch6MkBalBranch4 zuu zuv zuw zux key elt fm_L fm_R (mkBalBranch6Size_r zuu zuv zuw zux > sIZE_RATIO * mkBalBranch6Size_l zuu zuv zuw zux)

mkBalBranch6MkBalBranch01 zuu zuv zuw zux fm_L fm_R vyv vyw vyx fm_rl fm_rr True = mkBalBranch6Single_L zuu zuv zuw zux fm_L fm_R
mkBalBranch6MkBalBranch01 zuu zuv zuw zux fm_L fm_R vyv vyw vyx fm_rl fm_rr False = mkBalBranch6MkBalBranch00 zuu zuv zuw zux fm_L fm_R vyv vyw vyx fm_rl fm_rr otherwise

mkBalBranch6MkBalBranch4 zuu zuv zuw zux key elt fm_L fm_R True = mkBalBranch6MkBalBranch0 zuu zuv zuw zux fm_L fm_R fm_R
mkBalBranch6MkBalBranch4 zuu zuv zuw zux key elt fm_L fm_R False = mkBalBranch6MkBalBranch3 zuu zuv zuw zux key elt fm_L fm_R (mkBalBranch6Size_l zuu zuv zuw zux > sIZE_RATIO * mkBalBranch6Size_r zuu zuv zuw zux)

mkBalBranch6MkBalBranch2 zuu zuv zuw zux key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R

mkBalBranch6MkBalBranch0 zuu zuv zuw zux fm_L fm_R (Branch vyv vyw vyx fm_rl fm_rr) = mkBalBranch6MkBalBranch02 zuu zuv zuw zux fm_L fm_R (Branch vyv vyw vyx fm_rl fm_rr)

mkBalBranch6MkBalBranch3 zuu zuv zuw zux key elt fm_L fm_R True = mkBalBranch6MkBalBranch1 zuu zuv zuw zux fm_L fm_R fm_L
mkBalBranch6MkBalBranch3 zuu zuv zuw zux key elt fm_L fm_R False = mkBalBranch6MkBalBranch2 zuu zuv zuw zux key elt fm_L fm_R otherwise

mkBalBranch6Size_l zuu zuv zuw zux = sizeFM zux

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

are unpacked to the following functions on top level
glueVBal3Size_l zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv = sizeFM (Branch zuy zuz zvu zvv zvw)

glueVBal3GlueVBal2 zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv yy yz zu zv zw zy zz vuu vuv vuw True = mkBalBranch zy zz (glueVBal (Branch yy yz zu zv zw) vuv) vuw
glueVBal3GlueVBal2 zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv yy yz zu zv zw zy zz vuu vuv vuw False = glueVBal3GlueVBal1 zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv yy yz zu zv zw zy zz vuu vuv vuw (sIZE_RATIO * glueVBal3Size_r zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv < glueVBal3Size_l zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv)

glueVBal3GlueVBal0 zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv 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 zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv = sizeFM (Branch zvx zvy zvz zwu zwv)

glueVBal3GlueVBal1 zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv yy yz zu zv zw zy zz vuu vuv vuw True = mkBalBranch yy yz zv (glueVBal zw (Branch zy zz vuu vuv vuw))
glueVBal3GlueVBal1 zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv yy yz zu zv zw zy zz vuu vuv vuw False = glueVBal3GlueVBal0 zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv yy yz zu zv zw zy zz vuu vuv vuw otherwise

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
mkBranchRight_ok zww zwx zwy = mkBranchRight_ok0 zww zwx zwy zww zwx zww

mkBranchLeft_ok0 zww zwx zwy fm_l key EmptyFM = True
mkBranchLeft_ok0 zww zwx zwy fm_l key (Branch left_key vw vx vy vz) = mkBranchLeft_ok0Biggest_left_key fm_l < key

mkBranchLeft_ok zww zwx zwy = mkBranchLeft_ok0 zww zwx zwy zwy zwx zwy

mkBranchRight_ok0 zww zwx zwy fm_r key EmptyFM = True
mkBranchRight_ok0 zww zwx zwy fm_r key (Branch right_key wu wv ww wx) = key < mkBranchRight_ok0Smallest_right_key fm_r

mkBranchUnbox zww zwx zwy x = x

mkBranchRight_size zww zwx zwy = sizeFM zww

mkBranchLeft_size zww zwx zwy = sizeFM zwy

mkBranchBalance_ok zww zwx zwy = True

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

are unpacked to the following functions on top level
mkBranchResult zwz zxu zxv zxw = Branch zwz zxu (mkBranchUnbox zxv zwz zxw (1 + mkBranchLeft_size zxv zwz zxw + mkBranchRight_size zxv zwz zxw)) zxw zxv

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
mkVBalBranch3MkVBalBranch2 zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu 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 zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww False = mkVBalBranch3MkVBalBranch1 zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww (sIZE_RATIO * mkVBalBranch3Size_r zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu < mkVBalBranch3Size_l zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu)

mkVBalBranch3MkVBalBranch1 zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu 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 zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww False = mkVBalBranch3MkVBalBranch0 zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww otherwise

mkVBalBranch3Size_r zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu = sizeFM (Branch zxx zxy zxz zyu zyv)

mkVBalBranch3MkVBalBranch0 zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww True = mkBranch 13 key elt (Branch vuy vuz vvu vvv vvw) (Branch vvy vvz vwu vwv vww)

mkVBalBranch3Size_l zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu = sizeFM (Branch zyw zyx zyy zyz zzu)

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 zzv = fst (findMax zzv)

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 zzw = fst (findMin zzw)

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
reduce2Reduce1 zzx zzy x y True = error []
reduce2Reduce1 zzx zzy x y False = reduce2Reduce0 zzx zzy x y otherwise

reduce2D zzx zzy = gcd zzx zzy

reduce2Reduce0 zzx zzy x y True = x `quot` reduce2D zzx zzy :% (y `quot` reduce2D zzx zzy)

The bindings of the following Let/Where expression
gcd' (abs x) (abs y)
where 
gcd' x ywy = gcd'2 x ywy
gcd' x y = gcd'0 x y
gcd'0 x y = gcd' y (x `rem` y)
gcd'1 True x ywy = x
gcd'1 ywz yxu yxv = gcd'0 yxu yxv
gcd'2 x ywy = gcd'1 (ywy == 0) x ywy
gcd'2 yxw yxx = gcd'0 yxw yxx

are unpacked to the following functions on top level
gcd0Gcd'2 x ywy = gcd0Gcd'1 (ywy == 0) x ywy
gcd0Gcd'2 yxw yxx = gcd0Gcd'0 yxw yxx

gcd0Gcd'1 True x ywy = x
gcd0Gcd'1 ywz yxu yxv = gcd0Gcd'0 yxu yxv

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

gcd0Gcd' x ywy = gcd0Gcd'2 x ywy
gcd0Gcd' x y = gcd0Gcd'0 x y



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

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

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

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

  
addToFM0 old new = new

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

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

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

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

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

  
addToFM_C4 combiner EmptyFM key elt = unitFM key elt
addToFM_C4 xyz xzu xzv xzw = addToFM_C3 xyz xzu xzv xzw

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

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

  emptyFM :: FiniteMap a b
emptyFM = EmptyFM

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

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

  fmToList :: FiniteMap 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 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 yzy yzz fm1 fm2 True = mkBalBranch (glueBal2Mid_key1 yzy yzz) (glueBal2Mid_elt1 yzy yzz) (deleteMax fm1) fm2

  
glueBal2GlueBal1 yzy yzz fm1 fm2 True = mkBalBranch (glueBal2Mid_key2 yzy yzz) (glueBal2Mid_elt2 yzy yzz) fm1 (deleteMin fm2)
glueBal2GlueBal1 yzy yzz fm1 fm2 False = glueBal2GlueBal0 yzy yzz fm1 fm2 otherwise

  
glueBal2Mid_elt1 yzy yzz = glueBal2Mid_elt10 yzy yzz (glueBal2Vv2 yzy yzz)

  
glueBal2Mid_elt10 yzy yzz (vzx,mid_elt1) = mid_elt1

  
glueBal2Mid_elt2 yzy yzz = glueBal2Mid_elt20 yzy yzz (glueBal2Vv3 yzy yzz)

  
glueBal2Mid_elt20 yzy yzz (vzy,mid_elt2) = mid_elt2

  
glueBal2Mid_key1 yzy yzz = glueBal2Mid_key10 yzy yzz (glueBal2Vv2 yzy yzz)

  
glueBal2Mid_key10 yzy yzz (mid_key1,vzz) = mid_key1

  
glueBal2Mid_key2 yzy yzz = glueBal2Mid_key20 yzy yzz (glueBal2Vv3 yzy yzz)

  
glueBal2Mid_key20 yzy yzz (mid_key2,wuu) = mid_key2

  
glueBal2Vv2 yzy yzz = findMax yzy

  
glueBal2Vv3 yzy yzz = findMin yzz

  
glueBal3 fm1 EmptyFM = fm1
glueBal3 xzy xzz = glueBal2 xzy xzz

  
glueBal4 EmptyFM fm2 = fm2
glueBal4 yuv yuw = glueBal3 yuv yuw

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

  
glueVBal3GlueVBal0 zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv 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 zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv yy yz zu zv zw zy zz vuu vuv vuw True = mkBalBranch yy yz zv (glueVBal zw (Branch zy zz vuu vuv vuw))
glueVBal3GlueVBal1 zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv yy yz zu zv zw zy zz vuu vuv vuw False = glueVBal3GlueVBal0 zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv yy yz zu zv zw zy zz vuu vuv vuw otherwise

  
glueVBal3GlueVBal2 zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv yy yz zu zv zw zy zz vuu vuv vuw True = mkBalBranch zy zz (glueVBal (Branch yy yz zu zv zw) vuv) vuw
glueVBal3GlueVBal2 zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv yy yz zu zv zw zy zz vuu vuv vuw False = glueVBal3GlueVBal1 zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv yy yz zu zv zw zy zz vuu vuv vuw (sIZE_RATIO * glueVBal3Size_r zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv < glueVBal3Size_l zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv)

  
glueVBal3Size_l zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv = sizeFM (Branch zuy zuz zvu zvv zvw)

  
glueVBal3Size_r zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv = sizeFM (Branch zvx zvy zvz zwu zwv)

  
glueVBal4 fm1 EmptyFM = fm1
glueVBal4 xvw xvx = glueVBal3 xvw xvx

  
glueVBal5 EmptyFM fm2 = fm2
glueVBal5 xvz xwu = glueVBal4 xvz xwu

  intersectFM_C :: Ord c => (b  ->  d  ->  a)  ->  FiniteMap c b  ->  FiniteMap c d  ->  FiniteMap c a
intersectFM_C combiner fm1 EmptyFM = intersectFM_C4 combiner fm1 EmptyFM
intersectFM_C combiner EmptyFM fm2 = intersectFM_C3 combiner EmptyFM fm2
intersectFM_C combiner fm1 (Branch split_key elt2 wuy left right) = intersectFM_C2 combiner fm1 (Branch split_key elt2 wuy left right)

  
intersectFM_C2 combiner fm1 (Branch split_key elt2 wuy left right) = intersectFM_C2IntersectFM_C1 fm1 split_key combiner fm1 split_key elt2 wuy left right (Maybe.isJust (intersectFM_C2Maybe_elt1 fm1 split_key))

  
intersectFM_C2Elt1 yzw yzx = intersectFM_C2Elt10 yzw yzx (intersectFM_C2Vv1 yzw yzx)

  
intersectFM_C2Elt10 yzw yzx (Just elt1) = elt1

  
intersectFM_C2Gts yzw yzx = splitGT yzw yzx

  
intersectFM_C2IntersectFM_C0 yzw yzx combiner fm1 split_key elt2 wuy left right True = glueVBal (intersectFM_C combiner (intersectFM_C2Lts yzw yzx) left) (intersectFM_C combiner (intersectFM_C2Gts yzw yzx) right)

  
intersectFM_C2IntersectFM_C1 yzw yzx combiner fm1 split_key elt2 wuy left right True = mkVBalBranch split_key (combiner (intersectFM_C2Elt1 yzw yzx) elt2) (intersectFM_C combiner (intersectFM_C2Lts yzw yzx) left) (intersectFM_C combiner (intersectFM_C2Gts yzw yzx) right)
intersectFM_C2IntersectFM_C1 yzw yzx combiner fm1 split_key elt2 wuy left right False = intersectFM_C2IntersectFM_C0 yzw yzx combiner fm1 split_key elt2 wuy left right otherwise

  
intersectFM_C2Lts yzw yzx = splitLT yzw yzx

  
intersectFM_C2Maybe_elt1 yzw yzx = lookupFM yzw yzx

  
intersectFM_C2Vv1 yzw yzx = intersectFM_C2Maybe_elt1 yzw yzx

  
intersectFM_C3 combiner EmptyFM fm2 = emptyFM
intersectFM_C3 yvx yvy yvz = intersectFM_C2 yvx yvy yvz

  
intersectFM_C4 combiner fm1 EmptyFM = emptyFM
intersectFM_C4 ywv yww ywx = intersectFM_C3 ywv yww ywx

  lookupFM :: Ord b => FiniteMap b a  ->  b  ->  Maybe a
lookupFM EmptyFM key = lookupFM4 EmptyFM key
lookupFM (Branch key elt wuv fm_l fm_r) key_to_find = lookupFM3 (Branch key elt wuv fm_l fm_r) key_to_find

  
lookupFM0 key elt wuv fm_l fm_r key_to_find True = Just elt

  
lookupFM1 key elt wuv fm_l fm_r key_to_find True = lookupFM fm_r key_to_find
lookupFM1 key elt wuv fm_l fm_r key_to_find False = lookupFM0 key elt wuv fm_l fm_r key_to_find otherwise

  
lookupFM2 key elt wuv fm_l fm_r key_to_find True = lookupFM fm_l key_to_find
lookupFM2 key elt wuv fm_l fm_r key_to_find False = lookupFM1 key elt wuv fm_l fm_r key_to_find (key_to_find > key)

  
lookupFM3 (Branch key elt wuv fm_l fm_r) key_to_find = lookupFM2 key elt wuv fm_l fm_r key_to_find (key_to_find < key)

  
lookupFM4 EmptyFM key = Nothing
lookupFM4 yuz yvu = lookupFM3 yuz yvu

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

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

  
mkBalBranch6Double_L zuu zuv zuw zux 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 zuu zuv fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr)

  
mkBalBranch6Double_R zuu zuv zuw zux (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 zuu zuv fm_lrr fm_r)

  
mkBalBranch6MkBalBranch0 zuu zuv zuw zux fm_L fm_R (Branch vyv vyw vyx fm_rl fm_rr) = mkBalBranch6MkBalBranch02 zuu zuv zuw zux fm_L fm_R (Branch vyv vyw vyx fm_rl fm_rr)

  
mkBalBranch6MkBalBranch00 zuu zuv zuw zux fm_L fm_R vyv vyw vyx fm_rl fm_rr True = mkBalBranch6Double_L zuu zuv zuw zux fm_L fm_R

  
mkBalBranch6MkBalBranch01 zuu zuv zuw zux fm_L fm_R vyv vyw vyx fm_rl fm_rr True = mkBalBranch6Single_L zuu zuv zuw zux fm_L fm_R
mkBalBranch6MkBalBranch01 zuu zuv zuw zux fm_L fm_R vyv vyw vyx fm_rl fm_rr False = mkBalBranch6MkBalBranch00 zuu zuv zuw zux fm_L fm_R vyv vyw vyx fm_rl fm_rr otherwise

  
mkBalBranch6MkBalBranch02 zuu zuv zuw zux fm_L fm_R (Branch vyv vyw vyx fm_rl fm_rr) = mkBalBranch6MkBalBranch01 zuu zuv zuw zux fm_L fm_R vyv vyw vyx fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr)

  
mkBalBranch6MkBalBranch1 zuu zuv zuw zux fm_L fm_R (Branch vxw vxx vxy fm_ll fm_lr) = mkBalBranch6MkBalBranch12 zuu zuv zuw zux fm_L fm_R (Branch vxw vxx vxy fm_ll fm_lr)

  
mkBalBranch6MkBalBranch10 zuu zuv zuw zux fm_L fm_R vxw vxx vxy fm_ll fm_lr True = mkBalBranch6Double_R zuu zuv zuw zux fm_L fm_R

  
mkBalBranch6MkBalBranch11 zuu zuv zuw zux fm_L fm_R vxw vxx vxy fm_ll fm_lr True = mkBalBranch6Single_R zuu zuv zuw zux fm_L fm_R
mkBalBranch6MkBalBranch11 zuu zuv zuw zux fm_L fm_R vxw vxx vxy fm_ll fm_lr False = mkBalBranch6MkBalBranch10 zuu zuv zuw zux fm_L fm_R vxw vxx vxy fm_ll fm_lr otherwise

  
mkBalBranch6MkBalBranch12 zuu zuv zuw zux fm_L fm_R (Branch vxw vxx vxy fm_ll fm_lr) = mkBalBranch6MkBalBranch11 zuu zuv zuw zux fm_L fm_R vxw vxx vxy fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll)

  
mkBalBranch6MkBalBranch2 zuu zuv zuw zux key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R

  
mkBalBranch6MkBalBranch3 zuu zuv zuw zux key elt fm_L fm_R True = mkBalBranch6MkBalBranch1 zuu zuv zuw zux fm_L fm_R fm_L
mkBalBranch6MkBalBranch3 zuu zuv zuw zux key elt fm_L fm_R False = mkBalBranch6MkBalBranch2 zuu zuv zuw zux key elt fm_L fm_R otherwise

  
mkBalBranch6MkBalBranch4 zuu zuv zuw zux key elt fm_L fm_R True = mkBalBranch6MkBalBranch0 zuu zuv zuw zux fm_L fm_R fm_R
mkBalBranch6MkBalBranch4 zuu zuv zuw zux key elt fm_L fm_R False = mkBalBranch6MkBalBranch3 zuu zuv zuw zux key elt fm_L fm_R (mkBalBranch6Size_l zuu zuv zuw zux > sIZE_RATIO * mkBalBranch6Size_r zuu zuv zuw zux)

  
mkBalBranch6MkBalBranch5 zuu zuv zuw zux key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R
mkBalBranch6MkBalBranch5 zuu zuv zuw zux key elt fm_L fm_R False = mkBalBranch6MkBalBranch4 zuu zuv zuw zux key elt fm_L fm_R (mkBalBranch6Size_r zuu zuv zuw zux > sIZE_RATIO * mkBalBranch6Size_l zuu zuv zuw zux)

  
mkBalBranch6Single_L zuu zuv zuw zux fm_l (Branch key_r elt_r vyy fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 zuu zuv fm_l fm_rl) fm_rr

  
mkBalBranch6Single_R zuu zuv zuw zux (Branch key_l elt_l vwz fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 zuu zuv fm_lr fm_r)

  
mkBalBranch6Size_l zuu zuv zuw zux = sizeFM zux

  
mkBalBranch6Size_r zuu zuv zuw zux = sizeFM zuw

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

  
mkBranchBalance_ok zww zwx zwy = True

  
mkBranchLeft_ok zww zwx zwy = mkBranchLeft_ok0 zww zwx zwy zwy zwx zwy

  
mkBranchLeft_ok0 zww zwx zwy fm_l key EmptyFM = True
mkBranchLeft_ok0 zww zwx zwy fm_l key (Branch left_key vw vx vy vz) = mkBranchLeft_ok0Biggest_left_key fm_l < key

  
mkBranchLeft_ok0Biggest_left_key zzv = fst (findMax zzv)

  
mkBranchLeft_size zww zwx zwy = sizeFM zwy

  
mkBranchResult zwz zxu zxv zxw = Branch zwz zxu (mkBranchUnbox zxv zwz zxw (1 + mkBranchLeft_size zxv zwz zxw + mkBranchRight_size zxv zwz zxw)) zxw zxv

  
mkBranchRight_ok zww zwx zwy = mkBranchRight_ok0 zww zwx zwy zww zwx zww

  
mkBranchRight_ok0 zww zwx zwy fm_r key EmptyFM = True
mkBranchRight_ok0 zww zwx zwy fm_r key (Branch right_key wu wv ww wx) = key < mkBranchRight_ok0Smallest_right_key fm_r

  
mkBranchRight_ok0Smallest_right_key zzw = fst (findMin zzw)

  
mkBranchRight_size zww zwx zwy = sizeFM zww

  mkBranchUnbox :: Ord a =>  ->  (FiniteMap a b) ( ->  a ( ->  (FiniteMap a b) (Int  ->  Int)))
mkBranchUnbox zww zwx zwy 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 zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu 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 zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu 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 zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww False = mkVBalBranch3MkVBalBranch0 zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww otherwise

  
mkVBalBranch3MkVBalBranch2 zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu 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 zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww False = mkVBalBranch3MkVBalBranch1 zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww (sIZE_RATIO * mkVBalBranch3Size_r zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu < mkVBalBranch3Size_l zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu)

  
mkVBalBranch3Size_l zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu = sizeFM (Branch zyw zyx zyy zyz zzu)

  
mkVBalBranch3Size_r zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu = sizeFM (Branch zxx zxy zxz zyu zyv)

  
mkVBalBranch4 key elt fm_l EmptyFM = addToFM fm_l key elt
mkVBalBranch4 xwy xwz xxu xxv = mkVBalBranch3 xwy xwz xxu xxv

  
mkVBalBranch5 key elt EmptyFM fm_r = addToFM fm_r key elt
mkVBalBranch5 xxx xxy xxz xyu = mkVBalBranch4 xxx xxy xxz xyu

  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 xux xuy = splitGT3 xux xuy

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

  
splitLT0 key elt xx fm_l fm_r split_key True = fm_l

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

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

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

  
splitLT4 EmptyFM split_key = emptyFM
splitLT4 wzz xuu = splitLT3 wzz xuu

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude
  isJust :: Maybe a  ->  Bool
isJust Nothing = False
isJust wuz = True



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

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

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

  
addToFM0 old new = new

  addToFM_C :: Ord 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 xyz xzu xzv xzw = addToFM_C3 xyz xzu xzv xzw

  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 wuw EmptyFM fm_r) = fm_r
deleteMin (Branch key elt wux 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 b a  ->  [(b,a)]
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 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 yzy yzz fm1 fm2 True = mkBalBranch (glueBal2Mid_key1 yzy yzz) (glueBal2Mid_elt1 yzy yzz) (deleteMax fm1) fm2

  
glueBal2GlueBal1 yzy yzz fm1 fm2 True = mkBalBranch (glueBal2Mid_key2 yzy yzz) (glueBal2Mid_elt2 yzy yzz) fm1 (deleteMin fm2)
glueBal2GlueBal1 yzy yzz fm1 fm2 False = glueBal2GlueBal0 yzy yzz fm1 fm2 otherwise

  
glueBal2Mid_elt1 yzy yzz = glueBal2Mid_elt10 yzy yzz (glueBal2Vv2 yzy yzz)

  
glueBal2Mid_elt10 yzy yzz (vzx,mid_elt1) = mid_elt1

  
glueBal2Mid_elt2 yzy yzz = glueBal2Mid_elt20 yzy yzz (glueBal2Vv3 yzy yzz)

  
glueBal2Mid_elt20 yzy yzz (vzy,mid_elt2) = mid_elt2

  
glueBal2Mid_key1 yzy yzz = glueBal2Mid_key10 yzy yzz (glueBal2Vv2 yzy yzz)

  
glueBal2Mid_key10 yzy yzz (mid_key1,vzz) = mid_key1

  
glueBal2Mid_key2 yzy yzz = glueBal2Mid_key20 yzy yzz (glueBal2Vv3 yzy yzz)

  
glueBal2Mid_key20 yzy yzz (mid_key2,wuu) = mid_key2

  
glueBal2Vv2 yzy yzz = findMax yzy

  
glueBal2Vv3 yzy yzz = findMin yzz

  
glueBal3 fm1 EmptyFM = fm1
glueBal3 xzy xzz = glueBal2 xzy xzz

  
glueBal4 EmptyFM fm2 = fm2
glueBal4 yuv yuw = glueBal3 yuv yuw

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

  
glueVBal3GlueVBal0 zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv 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 zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv yy yz zu zv zw zy zz vuu vuv vuw True = mkBalBranch yy yz zv (glueVBal zw (Branch zy zz vuu vuv vuw))
glueVBal3GlueVBal1 zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv yy yz zu zv zw zy zz vuu vuv vuw False = glueVBal3GlueVBal0 zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv yy yz zu zv zw zy zz vuu vuv vuw otherwise

  
glueVBal3GlueVBal2 zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv yy yz zu zv zw zy zz vuu vuv vuw True = mkBalBranch zy zz (glueVBal (Branch yy yz zu zv zw) vuv) vuw
glueVBal3GlueVBal2 zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv yy yz zu zv zw zy zz vuu vuv vuw False = glueVBal3GlueVBal1 zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv yy yz zu zv zw zy zz vuu vuv vuw (sIZE_RATIO * glueVBal3Size_r zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv < glueVBal3Size_l zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv)

  
glueVBal3Size_l zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv = sizeFM (Branch zuy zuz zvu zvv zvw)

  
glueVBal3Size_r zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv = sizeFM (Branch zvx zvy zvz zwu zwv)

  
glueVBal4 fm1 EmptyFM = fm1
glueVBal4 xvw xvx = glueVBal3 xvw xvx

  
glueVBal5 EmptyFM fm2 = fm2
glueVBal5 xvz xwu = glueVBal4 xvz xwu

  intersectFM_C :: Ord a => (c  ->  b  ->  d)  ->  FiniteMap a c  ->  FiniteMap a b  ->  FiniteMap a d
intersectFM_C combiner fm1 EmptyFM = intersectFM_C4 combiner fm1 EmptyFM
intersectFM_C combiner EmptyFM fm2 = intersectFM_C3 combiner EmptyFM fm2
intersectFM_C combiner fm1 (Branch split_key elt2 wuy left right) = intersectFM_C2 combiner fm1 (Branch split_key elt2 wuy left right)

  
intersectFM_C2 combiner fm1 (Branch split_key elt2 wuy left right) = intersectFM_C2IntersectFM_C1 fm1 split_key combiner fm1 split_key elt2 wuy left right (Maybe.isJust (intersectFM_C2Maybe_elt1 fm1 split_key))

  
intersectFM_C2Elt1 yzw yzx = intersectFM_C2Elt10 yzw yzx (intersectFM_C2Vv1 yzw yzx)

  
intersectFM_C2Elt10 yzw yzx (Just elt1) = elt1

  
intersectFM_C2Gts yzw yzx = splitGT yzw yzx

  
intersectFM_C2IntersectFM_C0 yzw yzx combiner fm1 split_key elt2 wuy left right True = glueVBal (intersectFM_C combiner (intersectFM_C2Lts yzw yzx) left) (intersectFM_C combiner (intersectFM_C2Gts yzw yzx) right)

  
intersectFM_C2IntersectFM_C1 yzw yzx combiner fm1 split_key elt2 wuy left right True = mkVBalBranch split_key (combiner (intersectFM_C2Elt1 yzw yzx) elt2) (intersectFM_C combiner (intersectFM_C2Lts yzw yzx) left) (intersectFM_C combiner (intersectFM_C2Gts yzw yzx) right)
intersectFM_C2IntersectFM_C1 yzw yzx combiner fm1 split_key elt2 wuy left right False = intersectFM_C2IntersectFM_C0 yzw yzx combiner fm1 split_key elt2 wuy left right otherwise

  
intersectFM_C2Lts yzw yzx = splitLT yzw yzx

  
intersectFM_C2Maybe_elt1 yzw yzx = lookupFM yzw yzx

  
intersectFM_C2Vv1 yzw yzx = intersectFM_C2Maybe_elt1 yzw yzx

  
intersectFM_C3 combiner EmptyFM fm2 = emptyFM
intersectFM_C3 yvx yvy yvz = intersectFM_C2 yvx yvy yvz

  
intersectFM_C4 combiner fm1 EmptyFM = emptyFM
intersectFM_C4 ywv yww ywx = intersectFM_C3 ywv yww ywx

  lookupFM :: Ord a => FiniteMap a b  ->  a  ->  Maybe b
lookupFM EmptyFM key = lookupFM4 EmptyFM key
lookupFM (Branch key elt wuv fm_l fm_r) key_to_find = lookupFM3 (Branch key elt wuv fm_l fm_r) key_to_find

  
lookupFM0 key elt wuv fm_l fm_r key_to_find True = Just elt

  
lookupFM1 key elt wuv fm_l fm_r key_to_find True = lookupFM fm_r key_to_find
lookupFM1 key elt wuv fm_l fm_r key_to_find False = lookupFM0 key elt wuv fm_l fm_r key_to_find otherwise

  
lookupFM2 key elt wuv fm_l fm_r key_to_find True = lookupFM fm_l key_to_find
lookupFM2 key elt wuv fm_l fm_r key_to_find False = lookupFM1 key elt wuv fm_l fm_r key_to_find (key_to_find > key)

  
lookupFM3 (Branch key elt wuv fm_l fm_r) key_to_find = lookupFM2 key elt wuv fm_l fm_r key_to_find (key_to_find < key)

  
lookupFM4 EmptyFM key = Nothing
lookupFM4 yuz yvu = lookupFM3 yuz yvu

  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 zuu zuv zuw zux 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))))))) zuu zuv fm_l fm_rll) (mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) key_r elt_r fm_rlr fm_rr)

  
mkBalBranch6Double_R zuu zuv zuw zux (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))))))))))))) zuu zuv fm_lrr fm_r)

  
mkBalBranch6MkBalBranch0 zuu zuv zuw zux fm_L fm_R (Branch vyv vyw vyx fm_rl fm_rr) = mkBalBranch6MkBalBranch02 zuu zuv zuw zux fm_L fm_R (Branch vyv vyw vyx fm_rl fm_rr)

  
mkBalBranch6MkBalBranch00 zuu zuv zuw zux fm_L fm_R vyv vyw vyx fm_rl fm_rr True = mkBalBranch6Double_L zuu zuv zuw zux fm_L fm_R

  
mkBalBranch6MkBalBranch01 zuu zuv zuw zux fm_L fm_R vyv vyw vyx fm_rl fm_rr True = mkBalBranch6Single_L zuu zuv zuw zux fm_L fm_R
mkBalBranch6MkBalBranch01 zuu zuv zuw zux fm_L fm_R vyv vyw vyx fm_rl fm_rr False = mkBalBranch6MkBalBranch00 zuu zuv zuw zux fm_L fm_R vyv vyw vyx fm_rl fm_rr otherwise

  
mkBalBranch6MkBalBranch02 zuu zuv zuw zux fm_L fm_R (Branch vyv vyw vyx fm_rl fm_rr) = mkBalBranch6MkBalBranch01 zuu zuv zuw zux fm_L fm_R vyv vyw vyx fm_rl fm_rr (sizeFM fm_rl < Pos (Succ (Succ Zero)) * sizeFM fm_rr)

  
mkBalBranch6MkBalBranch1 zuu zuv zuw zux fm_L fm_R (Branch vxw vxx vxy fm_ll fm_lr) = mkBalBranch6MkBalBranch12 zuu zuv zuw zux fm_L fm_R (Branch vxw vxx vxy fm_ll fm_lr)

  
mkBalBranch6MkBalBranch10 zuu zuv zuw zux fm_L fm_R vxw vxx vxy fm_ll fm_lr True = mkBalBranch6Double_R zuu zuv zuw zux fm_L fm_R

  
mkBalBranch6MkBalBranch11 zuu zuv zuw zux fm_L fm_R vxw vxx vxy fm_ll fm_lr True = mkBalBranch6Single_R zuu zuv zuw zux fm_L fm_R
mkBalBranch6MkBalBranch11 zuu zuv zuw zux fm_L fm_R vxw vxx vxy fm_ll fm_lr False = mkBalBranch6MkBalBranch10 zuu zuv zuw zux fm_L fm_R vxw vxx vxy fm_ll fm_lr otherwise

  
mkBalBranch6MkBalBranch12 zuu zuv zuw zux fm_L fm_R (Branch vxw vxx vxy fm_ll fm_lr) = mkBalBranch6MkBalBranch11 zuu zuv zuw zux fm_L fm_R vxw vxx vxy fm_ll fm_lr (sizeFM fm_lr < Pos (Succ (Succ Zero)) * sizeFM fm_ll)

  
mkBalBranch6MkBalBranch2 zuu zuv zuw zux key elt fm_L fm_R True = mkBranch (Pos (Succ (Succ Zero))) key elt fm_L fm_R

  
mkBalBranch6MkBalBranch3 zuu zuv zuw zux key elt fm_L fm_R True = mkBalBranch6MkBalBranch1 zuu zuv zuw zux fm_L fm_R fm_L
mkBalBranch6MkBalBranch3 zuu zuv zuw zux key elt fm_L fm_R False = mkBalBranch6MkBalBranch2 zuu zuv zuw zux key elt fm_L fm_R otherwise

  
mkBalBranch6MkBalBranch4 zuu zuv zuw zux key elt fm_L fm_R True = mkBalBranch6MkBalBranch0 zuu zuv zuw zux fm_L fm_R fm_R
mkBalBranch6MkBalBranch4 zuu zuv zuw zux key elt fm_L fm_R False = mkBalBranch6MkBalBranch3 zuu zuv zuw zux key elt fm_L fm_R (mkBalBranch6Size_l zuu zuv zuw zux > sIZE_RATIO * mkBalBranch6Size_r zuu zuv zuw zux)

  
mkBalBranch6MkBalBranch5 zuu zuv zuw zux key elt fm_L fm_R True = mkBranch (Pos (Succ Zero)) key elt fm_L fm_R
mkBalBranch6MkBalBranch5 zuu zuv zuw zux key elt fm_L fm_R False = mkBalBranch6MkBalBranch4 zuu zuv zuw zux key elt fm_L fm_R (mkBalBranch6Size_r zuu zuv zuw zux > sIZE_RATIO * mkBalBranch6Size_l zuu zuv zuw zux)

  
mkBalBranch6Single_L zuu zuv zuw zux 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))))) zuu zuv fm_l fm_rl) fm_rr

  
mkBalBranch6Single_R zuu zuv zuw zux (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)))))))))) zuu zuv fm_lr fm_r)

  
mkBalBranch6Size_l zuu zuv zuw zux = sizeFM zux

  
mkBalBranch6Size_r zuu zuv zuw zux = sizeFM zuw

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

  
mkBranchBalance_ok zww zwx zwy = True

  
mkBranchLeft_ok zww zwx zwy = mkBranchLeft_ok0 zww zwx zwy zwy zwx zwy

  
mkBranchLeft_ok0 zww zwx zwy fm_l key EmptyFM = True
mkBranchLeft_ok0 zww zwx zwy fm_l key (Branch left_key vw vx vy vz) = mkBranchLeft_ok0Biggest_left_key fm_l < key

  
mkBranchLeft_ok0Biggest_left_key zzv = fst (findMax zzv)

  
mkBranchLeft_size zww zwx zwy = sizeFM zwy

  
mkBranchResult zwz zxu zxv zxw = Branch zwz zxu (mkBranchUnbox zxv zwz zxw (Pos (Succ Zero) + mkBranchLeft_size zxv zwz zxw + mkBranchRight_size zxv zwz zxw)) zxw zxv

  
mkBranchRight_ok zww zwx zwy = mkBranchRight_ok0 zww zwx zwy zww zwx zww

  
mkBranchRight_ok0 zww zwx zwy fm_r key EmptyFM = True
mkBranchRight_ok0 zww zwx zwy fm_r key (Branch right_key wu wv ww wx) = key < mkBranchRight_ok0Smallest_right_key fm_r

  
mkBranchRight_ok0Smallest_right_key zzw = fst (findMin zzw)

  
mkBranchRight_size zww zwx zwy = sizeFM zww

  mkBranchUnbox :: Ord a =>  ->  (FiniteMap a b) ( ->  a ( ->  (FiniteMap a b) (Int  ->  Int)))
mkBranchUnbox zww zwx zwy x = x

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

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

  
mkVBalBranch3MkVBalBranch0 zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu 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 zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu 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 zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww False = mkVBalBranch3MkVBalBranch0 zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww otherwise

  
mkVBalBranch3MkVBalBranch2 zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu 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 zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww False = mkVBalBranch3MkVBalBranch1 zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww (sIZE_RATIO * mkVBalBranch3Size_r zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu < mkVBalBranch3Size_l zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu)

  
mkVBalBranch3Size_l zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu = sizeFM (Branch zyw zyx zyy zyz zzu)

  
mkVBalBranch3Size_r zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu = sizeFM (Branch zxx zxy zxz zyu zyv)

  
mkVBalBranch4 key elt fm_l EmptyFM = addToFM fm_l key elt
mkVBalBranch4 xwy xwz xxu xxv = mkVBalBranch3 xwy xwz xxu xxv

  
mkVBalBranch5 key elt EmptyFM fm_r = addToFM fm_r key elt
mkVBalBranch5 xxx xxy xxz xyu = mkVBalBranch4 xxx xxy xxz xyu

  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 xux xuy = splitGT3 xux xuy

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

  
splitLT0 key elt xx fm_l fm_r split_key True = fm_l

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

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

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

  
splitLT4 EmptyFM split_key = emptyFM
splitLT4 wzz xuu = splitLT3 wzz xuu

  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
  isJust :: Maybe a  ->  Bool
isJust Nothing = False
isJust wuz = True



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_glueBal2Mid_key20(zzz575, zzz576, zzz577, zzz578, zzz579, zzz580, zzz581, zzz582, zzz583, zzz584, zzz585, zzz586, zzz587, Branch(zzz5880, zzz5881, zzz5882, zzz5883, zzz5884), zzz589, h, ba) → new_glueBal2Mid_key20(zzz575, zzz576, zzz577, zzz578, zzz579, zzz580, zzz581, zzz582, zzz583, zzz584, zzz5880, zzz5881, zzz5882, zzz5883, zzz5884, 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
                                    ↳ 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_elt20(zzz559, zzz560, zzz561, zzz562, zzz563, zzz564, zzz565, zzz566, zzz567, zzz568, zzz569, zzz570, zzz571, Branch(zzz5720, zzz5721, zzz5722, zzz5723, zzz5724), zzz573, h, ba) → new_glueBal2Mid_elt20(zzz559, zzz560, zzz561, zzz562, zzz563, zzz564, zzz565, zzz566, zzz567, zzz568, zzz5720, zzz5721, zzz5722, zzz5723, zzz5724, 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_key10(zzz608, zzz609, zzz610, zzz611, zzz612, zzz613, zzz614, zzz615, zzz616, zzz617, zzz618, zzz619, zzz620, zzz621, Branch(zzz6220, zzz6221, zzz6222, zzz6223, zzz6224), h, ba) → new_glueBal2Mid_key10(zzz608, zzz609, zzz610, zzz611, zzz612, zzz613, zzz614, zzz615, zzz616, zzz617, zzz6220, zzz6221, zzz6222, zzz6223, zzz6224, 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_elt10(zzz591, zzz592, zzz593, zzz594, zzz595, zzz596, zzz597, zzz598, zzz599, zzz600, zzz601, zzz602, zzz603, zzz604, Branch(zzz6050, zzz6051, zzz6052, zzz6053, zzz6054), h, ba) → new_glueBal2Mid_elt10(zzz591, zzz592, zzz593, zzz594, zzz595, zzz596, zzz597, zzz598, zzz599, zzz600, zzz6050, zzz6051, zzz6052, zzz6053, zzz6054, 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_primEqNat(Succ(zzz50000), Succ(zzz40000)) → new_primEqNat(zzz50000, zzz40000)

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_primCmpNat(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat(zzz5000000, zzz43000000)

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_primMinusNat(Succ(zzz154200), Succ(zzz44000)) → new_primMinusNat(zzz154200, zzz44000)

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_primPlusNat(Succ(zzz22100), Succ(zzz4000000)) → new_primPlusNat(zzz22100, zzz4000000)

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_primMulNat(Succ(zzz500000), Succ(zzz400000)) → new_primMulNat(zzz500000, Succ(zzz400000))

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_esEs3(Just(zzz5000), Just(zzz4000), app(app(ty_@2, bdd), bde)) → new_esEs0(zzz5000, zzz4000, bdd, bde)
new_esEs0(@2(zzz5000, zzz5001), @2(zzz4000, zzz4001), app(app(app(ty_@3, ff), fg), fh), fa) → new_esEs2(zzz5000, zzz4000, ff, fg, fh)
new_esEs2(@3(zzz5000, zzz5001, zzz5002), @3(zzz4000, zzz4001, zzz4002), app(app(app(ty_@3, bcf), bcg), bch), he, bba) → new_esEs2(zzz5000, zzz4000, bcf, bcg, bch)
new_esEs2(@3(zzz5000, zzz5001, zzz5002), @3(zzz4000, zzz4001, zzz4002), hd, app(app(ty_@2, bbb), bbc), bba) → new_esEs0(zzz5001, zzz4001, bbb, bbc)
new_esEs2(@3(zzz5000, zzz5001, zzz5002), @3(zzz4000, zzz4001, zzz4002), app(app(ty_Either, bca), bcb), he, bba) → new_esEs(zzz5000, zzz4000, bca, bcb)
new_esEs0(@2(zzz5000, zzz5001), @2(zzz4000, zzz4001), de, app(app(app(ty_@3, ec), ed), ee)) → new_esEs2(zzz5001, zzz4001, ec, ed, ee)
new_esEs2(@3(zzz5000, zzz5001, zzz5002), @3(zzz4000, zzz4001, zzz4002), hd, app(ty_Maybe, bbh), bba) → new_esEs3(zzz5001, zzz4001, bbh)
new_esEs2(@3(zzz5000, zzz5001, zzz5002), @3(zzz4000, zzz4001, zzz4002), hd, he, app(app(ty_@2, hh), baa)) → new_esEs0(zzz5002, zzz4002, hh, baa)
new_esEs(Right(zzz5000), Right(zzz4000), cb, app(ty_Maybe, dd)) → new_esEs3(zzz5000, zzz4000, dd)
new_esEs(Right(zzz5000), Right(zzz4000), cb, app(ty_[], cg)) → new_esEs1(zzz5000, zzz4000, cg)
new_esEs2(@3(zzz5000, zzz5001, zzz5002), @3(zzz4000, zzz4001, zzz4002), hd, he, app(ty_Maybe, baf)) → new_esEs3(zzz5002, zzz4002, baf)
new_esEs1(:(zzz5000, zzz5001), :(zzz4000, zzz4001), gb) → new_esEs1(zzz5001, zzz4001, gb)
new_esEs2(@3(zzz5000, zzz5001, zzz5002), @3(zzz4000, zzz4001, zzz4002), app(app(ty_@2, bcc), bcd), he, bba) → new_esEs0(zzz5000, zzz4000, bcc, bcd)
new_esEs2(@3(zzz5000, zzz5001, zzz5002), @3(zzz4000, zzz4001, zzz4002), hd, app(ty_[], bbd), bba) → new_esEs1(zzz5001, zzz4001, bbd)
new_esEs0(@2(zzz5000, zzz5001), @2(zzz4000, zzz4001), app(ty_[], fd), fa) → new_esEs1(zzz5000, zzz4000, fd)
new_esEs1(:(zzz5000, zzz5001), :(zzz4000, zzz4001), app(ty_[], gg)) → new_esEs1(zzz5000, zzz4000, gg)
new_esEs(Right(zzz5000), Right(zzz4000), cb, app(app(ty_@2, ce), cf)) → new_esEs0(zzz5000, zzz4000, ce, cf)
new_esEs0(@2(zzz5000, zzz5001), @2(zzz4000, zzz4001), app(app(ty_Either, eg), eh), fa) → new_esEs(zzz5000, zzz4000, eg, eh)
new_esEs0(@2(zzz5000, zzz5001), @2(zzz4000, zzz4001), de, app(app(ty_Either, df), dg)) → new_esEs(zzz5001, zzz4001, df, dg)
new_esEs2(@3(zzz5000, zzz5001, zzz5002), @3(zzz4000, zzz4001, zzz4002), hd, app(app(ty_Either, bag), bah), bba) → new_esEs(zzz5001, zzz4001, bag, bah)
new_esEs2(@3(zzz5000, zzz5001, zzz5002), @3(zzz4000, zzz4001, zzz4002), hd, he, app(app(ty_Either, hf), hg)) → new_esEs(zzz5002, zzz4002, hf, hg)
new_esEs(Right(zzz5000), Right(zzz4000), cb, app(app(ty_Either, cc), cd)) → new_esEs(zzz5000, zzz4000, cc, cd)
new_esEs0(@2(zzz5000, zzz5001), @2(zzz4000, zzz4001), de, app(ty_Maybe, ef)) → new_esEs3(zzz5001, zzz4001, ef)
new_esEs(Left(zzz5000), Left(zzz4000), app(app(ty_@2, bc), bd), bb) → new_esEs0(zzz5000, zzz4000, bc, bd)
new_esEs0(@2(zzz5000, zzz5001), @2(zzz4000, zzz4001), app(ty_Maybe, ga), fa) → new_esEs3(zzz5000, zzz4000, ga)
new_esEs2(@3(zzz5000, zzz5001, zzz5002), @3(zzz4000, zzz4001, zzz4002), hd, app(app(app(ty_@3, bbe), bbf), bbg), bba) → new_esEs2(zzz5001, zzz4001, bbe, bbf, bbg)
new_esEs3(Just(zzz5000), Just(zzz4000), app(app(app(ty_@3, bdg), bdh), bea)) → new_esEs2(zzz5000, zzz4000, bdg, bdh, bea)
new_esEs3(Just(zzz5000), Just(zzz4000), app(ty_Maybe, beb)) → new_esEs3(zzz5000, zzz4000, beb)
new_esEs2(@3(zzz5000, zzz5001, zzz5002), @3(zzz4000, zzz4001, zzz4002), app(ty_Maybe, bda), he, bba) → new_esEs3(zzz5000, zzz4000, bda)
new_esEs(Left(zzz5000), Left(zzz4000), app(ty_Maybe, ca), bb) → new_esEs3(zzz5000, zzz4000, ca)
new_esEs3(Just(zzz5000), Just(zzz4000), app(app(ty_Either, bdb), bdc)) → new_esEs(zzz5000, zzz4000, bdb, bdc)
new_esEs0(@2(zzz5000, zzz5001), @2(zzz4000, zzz4001), app(app(ty_@2, fb), fc), fa) → new_esEs0(zzz5000, zzz4000, fb, fc)
new_esEs2(@3(zzz5000, zzz5001, zzz5002), @3(zzz4000, zzz4001, zzz4002), hd, he, app(ty_[], bab)) → new_esEs1(zzz5002, zzz4002, bab)
new_esEs(Left(zzz5000), Left(zzz4000), app(ty_[], be), bb) → new_esEs1(zzz5000, zzz4000, be)
new_esEs(Left(zzz5000), Left(zzz4000), app(app(app(ty_@3, bf), bg), bh), bb) → new_esEs2(zzz5000, zzz4000, bf, bg, bh)
new_esEs(Right(zzz5000), Right(zzz4000), cb, app(app(app(ty_@3, da), db), dc)) → new_esEs2(zzz5000, zzz4000, da, db, dc)
new_esEs3(Just(zzz5000), Just(zzz4000), app(ty_[], bdf)) → new_esEs1(zzz5000, zzz4000, bdf)
new_esEs0(@2(zzz5000, zzz5001), @2(zzz4000, zzz4001), de, app(ty_[], eb)) → new_esEs1(zzz5001, zzz4001, eb)
new_esEs2(@3(zzz5000, zzz5001, zzz5002), @3(zzz4000, zzz4001, zzz4002), app(ty_[], bce), he, bba) → new_esEs1(zzz5000, zzz4000, bce)
new_esEs1(:(zzz5000, zzz5001), :(zzz4000, zzz4001), app(app(app(ty_@3, gh), ha), hb)) → new_esEs2(zzz5000, zzz4000, gh, ha, hb)
new_esEs0(@2(zzz5000, zzz5001), @2(zzz4000, zzz4001), de, app(app(ty_@2, dh), ea)) → new_esEs0(zzz5001, zzz4001, dh, ea)
new_esEs1(:(zzz5000, zzz5001), :(zzz4000, zzz4001), app(app(ty_Either, gc), gd)) → new_esEs(zzz5000, zzz4000, gc, gd)
new_esEs1(:(zzz5000, zzz5001), :(zzz4000, zzz4001), app(ty_Maybe, hc)) → new_esEs3(zzz5000, zzz4000, hc)
new_esEs1(:(zzz5000, zzz5001), :(zzz4000, zzz4001), app(app(ty_@2, ge), gf)) → new_esEs0(zzz5000, zzz4000, ge, gf)
new_esEs(Left(zzz5000), Left(zzz4000), app(app(ty_Either, h), ba), bb) → new_esEs(zzz5000, zzz4000, h, ba)
new_esEs2(@3(zzz5000, zzz5001, zzz5002), @3(zzz4000, zzz4001, zzz4002), hd, he, app(app(app(ty_@3, bac), bad), bae)) → new_esEs2(zzz5002, zzz4002, bac, bad, bae)

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_compare(:(zzz500000, zzz500001), :(zzz4300000, zzz4300001), bdb) → new_primCompAux(zzz500000, zzz4300000, new_compare4(zzz500001, zzz4300001, bdb), bdb)
new_compare22(Just(Just(zzz500000)), Just(Just(zzz4300000)), False, app(ty_Maybe, app(ty_Maybe, gg))) → new_ltEs1(zzz500000, zzz4300000, gg)
new_ltEs1(Just(zzz500000), Just(zzz4300000), app(app(app(ty_@3, gh), ha), hb)) → new_ltEs2(zzz500000, zzz4300000, gh, ha, hb)
new_ltEs0(@2(zzz500000, zzz500001), @2(zzz4300000, zzz4300001), eg, app(ty_Maybe, fd)) → new_ltEs1(zzz500001, zzz4300001, fd)
new_compare22(Just(@3(zzz500000, zzz500001, zzz500002)), Just(@3(zzz4300000, zzz4300001, zzz4300002)), False, app(app(app(ty_@3, app(app(app(ty_@3, bac), bad), bae)), hf), hg)) → new_lt2(zzz500000, zzz4300000, bac, bad, bae)
new_ltEs(Right(zzz500000), Right(zzz4300000), cb, app(app(ty_Either, cc), cd)) → new_ltEs(zzz500000, zzz4300000, cc, cd)
new_ltEs0(@2(zzz500000, zzz500001), @2(zzz4300000, zzz4300001), app(app(ty_Either, de), df), dg) → new_compare2(zzz500000, zzz4300000, new_esEs4(zzz500000, zzz4300000, de, df), de, df)
new_compare22(Just(@2(zzz500000, zzz500001)), Just(@2(zzz4300000, zzz4300001)), False, app(app(ty_@2, eg), app(app(app(ty_@3, ff), fg), fh))) → new_ltEs2(zzz500001, zzz4300001, ff, fg, fh)
new_compare22(Just(Right(zzz500000)), Just(Right(zzz4300000)), False, app(app(ty_Either, cb), app(ty_Maybe, cg))) → new_ltEs1(zzz500000, zzz4300000, cg)
new_ltEs0(@2(zzz500000, zzz500001), @2(zzz4300000, zzz4300001), app(app(app(ty_@3, ec), ed), ee), dg) → new_compare21(zzz500000, zzz4300000, new_esEs6(zzz500000, zzz4300000, ec, ed, ee), ec, ed, ee)
new_ltEs2(@3(zzz500000, zzz500001, zzz500002), @3(zzz4300000, zzz4300001, zzz4300002), bag, app(ty_[], bbh), hg) → new_lt3(zzz500001, zzz4300001, bbh)
new_ltEs2(@3(zzz500000, zzz500001, zzz500002), @3(zzz4300000, zzz4300001, zzz4300002), bag, app(app(app(ty_@3, bbe), bbf), bbg), hg) → new_lt2(zzz500001, zzz4300001, bbe, bbf, bbg)
new_compare22(Just(@3(zzz500000, zzz500001, zzz500002)), Just(@3(zzz4300000, zzz4300001, zzz4300002)), False, app(app(app(ty_@3, bag), app(app(app(ty_@3, bbe), bbf), bbg)), hg)) → new_lt2(zzz500001, zzz4300001, bbe, bbf, bbg)
new_compare22(Just(Just(zzz500000)), Just(Just(zzz4300000)), False, app(ty_Maybe, app(app(ty_Either, gc), gd))) → new_ltEs(zzz500000, zzz4300000, gc, gd)
new_compare22(Just(Just(zzz500000)), Just(Just(zzz4300000)), False, app(ty_Maybe, app(app(ty_@2, ge), gf))) → new_ltEs0(zzz500000, zzz4300000, ge, gf)
new_ltEs0(@2(zzz500000, zzz500001), @2(zzz4300000, zzz4300001), app(app(ty_@2, dh), ea), dg) → new_compare20(zzz500000, zzz4300000, new_esEs5(zzz500000, zzz4300000, dh, ea), dh, ea)
new_compare22(Just(@2(zzz500000, zzz500001)), Just(@2(zzz4300000, zzz4300001)), False, app(app(ty_@2, app(app(app(ty_@3, ec), ed), ee)), dg)) → new_compare21(zzz500000, zzz4300000, new_esEs6(zzz500000, zzz4300000, ec, ed, ee), ec, ed, ee)
new_compare22(Just(Right(zzz500000)), Just(Right(zzz4300000)), False, app(app(ty_Either, cb), app(app(app(ty_@3, da), db), dc))) → new_ltEs2(zzz500000, zzz4300000, da, db, dc)
new_ltEs3(:(zzz500000, zzz500001), :(zzz4300000, zzz4300001), bdb) → new_compare(zzz500001, zzz4300001, bdb)
new_primCompAux(zzz500000, zzz4300000, zzz220, app(ty_[], bec)) → new_compare(zzz500000, zzz4300000, bec)
new_compare22(Just(:(zzz500000, zzz500001)), Just(:(zzz4300000, zzz4300001)), False, app(ty_[], bdb)) → new_primCompAux(zzz500000, zzz4300000, new_compare4(zzz500001, zzz4300001, bdb), bdb)
new_ltEs0(@2(zzz500000, zzz500001), @2(zzz4300000, zzz4300001), app(ty_[], ef), dg) → new_compare(zzz500000, zzz4300000, ef)
new_compare22(Just(@3(zzz500000, zzz500001, zzz500002)), Just(@3(zzz4300000, zzz4300001, zzz4300002)), False, app(app(app(ty_@3, app(ty_[], baf)), hf), hg)) → new_lt3(zzz500000, zzz4300000, baf)
new_ltEs2(@3(zzz500000, zzz500001, zzz500002), @3(zzz4300000, zzz4300001, zzz4300002), bag, hf, app(ty_Maybe, bce)) → new_ltEs1(zzz500002, zzz4300002, bce)
new_lt0(zzz500000, zzz4300000, de, df) → new_compare2(zzz500000, zzz4300000, new_esEs4(zzz500000, zzz4300000, de, df), de, df)
new_lt(zzz5000, zzz43000, gb) → new_compare22(zzz5000, zzz43000, new_esEs7(zzz5000, zzz43000, gb), gb)
new_compare22(Just(:(zzz500000, zzz500001)), Just(:(zzz4300000, zzz4300001)), False, app(ty_[], bdb)) → new_compare(zzz500001, zzz4300001, bdb)
new_compare22(Just(@2(zzz500000, zzz500001)), Just(@2(zzz4300000, zzz4300001)), False, app(app(ty_@2, eg), app(app(ty_Either, eh), fa))) → new_ltEs(zzz500001, zzz4300001, eh, fa)
new_ltEs2(@3(zzz500000, zzz500001, zzz500002), @3(zzz4300000, zzz4300001, zzz4300002), bag, hf, app(ty_[], bda)) → new_ltEs3(zzz500002, zzz4300002, bda)
new_ltEs1(Just(zzz500000), Just(zzz4300000), app(app(ty_Either, gc), gd)) → new_ltEs(zzz500000, zzz4300000, gc, gd)
new_ltEs(Left(zzz500000), Left(zzz4300000), app(app(app(ty_@3, bf), bg), bh), bb) → new_ltEs2(zzz500000, zzz4300000, bf, bg, bh)
new_ltEs(Right(zzz500000), Right(zzz4300000), cb, app(ty_[], dd)) → new_ltEs3(zzz500000, zzz4300000, dd)
new_compare22(Just(@2(zzz500000, zzz500001)), Just(@2(zzz4300000, zzz4300001)), False, app(app(ty_@2, eg), app(ty_Maybe, fd))) → new_ltEs1(zzz500001, zzz4300001, fd)
new_compare22(Just(@3(zzz500000, zzz500001, zzz500002)), Just(@3(zzz4300000, zzz4300001, zzz4300002)), False, app(app(app(ty_@3, bag), hf), app(ty_Maybe, bce))) → new_ltEs1(zzz500002, zzz4300002, bce)
new_ltEs0(@2(zzz500000, zzz500001), @2(zzz4300000, zzz4300001), app(ty_Maybe, eb), dg) → new_lt(zzz500000, zzz4300000, eb)
new_primCompAux(zzz500000, zzz4300000, zzz220, app(app(app(ty_@3, bdh), bea), beb)) → new_compare5(zzz500000, zzz4300000, bdh, bea, beb)
new_ltEs3(:(zzz500000, zzz500001), :(zzz4300000, zzz4300001), bdb) → new_primCompAux(zzz500000, zzz4300000, new_compare4(zzz500001, zzz4300001, bdb), bdb)
new_compare22(Just(Left(zzz500000)), Just(Left(zzz4300000)), False, app(app(ty_Either, app(ty_Maybe, be)), bb)) → new_ltEs1(zzz500000, zzz4300000, be)
new_ltEs(Left(zzz500000), Left(zzz4300000), app(ty_Maybe, be), bb) → new_ltEs1(zzz500000, zzz4300000, be)
new_ltEs2(@3(zzz500000, zzz500001, zzz500002), @3(zzz4300000, zzz4300001, zzz4300002), bag, app(ty_Maybe, bbd), hg) → new_lt(zzz500001, zzz4300001, bbd)
new_ltEs0(@2(zzz500000, zzz500001), @2(zzz4300000, zzz4300001), eg, app(ty_[], ga)) → new_ltEs3(zzz500001, zzz4300001, ga)
new_compare0(zzz500000, zzz4300000, de, df) → new_compare2(zzz500000, zzz4300000, new_esEs4(zzz500000, zzz4300000, de, df), de, df)
new_compare1(zzz500000, zzz4300000, dh, ea) → new_compare20(zzz500000, zzz4300000, new_esEs5(zzz500000, zzz4300000, dh, ea), dh, ea)
new_compare22(Just(@3(zzz500000, zzz500001, zzz500002)), Just(@3(zzz4300000, zzz4300001, zzz4300002)), False, app(app(app(ty_@3, app(app(ty_@2, hh), baa)), hf), hg)) → new_lt1(zzz500000, zzz4300000, hh, baa)
new_compare22(Just(Left(zzz500000)), Just(Left(zzz4300000)), False, app(app(ty_Either, app(app(app(ty_@3, bf), bg), bh)), bb)) → new_ltEs2(zzz500000, zzz4300000, bf, bg, bh)
new_primCompAux(zzz500000, zzz4300000, zzz220, app(app(ty_@2, bde), bdf)) → new_compare1(zzz500000, zzz4300000, bde, bdf)
new_ltEs2(@3(zzz500000, zzz500001, zzz500002), @3(zzz4300000, zzz4300001, zzz4300002), bag, app(app(ty_Either, bah), bba), hg) → new_lt0(zzz500001, zzz4300001, bah, bba)
new_ltEs(Right(zzz500000), Right(zzz4300000), cb, app(ty_Maybe, cg)) → new_ltEs1(zzz500000, zzz4300000, cg)
new_compare22(Just(@3(zzz500000, zzz500001, zzz500002)), Just(@3(zzz4300000, zzz4300001, zzz4300002)), False, app(app(app(ty_@3, bag), hf), app(ty_[], bda))) → new_ltEs3(zzz500002, zzz4300002, bda)
new_compare21(zzz500000, zzz4300000, False, ec, ed, ee) → new_ltEs2(zzz500000, zzz4300000, ec, ed, ee)
new_compare22(Just(@3(zzz500000, zzz500001, zzz500002)), Just(@3(zzz4300000, zzz4300001, zzz4300002)), False, app(app(app(ty_@3, app(ty_Maybe, bab)), hf), hg)) → new_lt(zzz500000, zzz4300000, bab)
new_compare22(Just(@3(zzz500000, zzz500001, zzz500002)), Just(@3(zzz4300000, zzz4300001, zzz4300002)), False, app(app(app(ty_@3, bag), hf), app(app(app(ty_@3, bcf), bcg), bch))) → new_ltEs2(zzz500002, zzz4300002, bcf, bcg, bch)
new_compare22(Just(@3(zzz500000, zzz500001, zzz500002)), Just(@3(zzz4300000, zzz4300001, zzz4300002)), False, app(app(app(ty_@3, bag), app(app(ty_Either, bah), bba)), hg)) → new_lt0(zzz500001, zzz4300001, bah, bba)
new_compare22(Just(Right(zzz500000)), Just(Right(zzz4300000)), False, app(app(ty_Either, cb), app(app(ty_@2, ce), cf))) → new_ltEs0(zzz500000, zzz4300000, ce, cf)
new_compare2(zzz500000, zzz4300000, False, de, df) → new_ltEs(zzz500000, zzz4300000, de, df)
new_lt1(zzz500000, zzz4300000, dh, ea) → new_compare20(zzz500000, zzz4300000, new_esEs5(zzz500000, zzz4300000, dh, ea), dh, ea)
new_ltEs2(@3(zzz500000, zzz500001, zzz500002), @3(zzz4300000, zzz4300001, zzz4300002), bag, hf, app(app(app(ty_@3, bcf), bcg), bch)) → new_ltEs2(zzz500002, zzz4300002, bcf, bcg, bch)
new_ltEs2(@3(zzz500000, zzz500001, zzz500002), @3(zzz4300000, zzz4300001, zzz4300002), app(app(ty_@2, hh), baa), hf, hg) → new_lt1(zzz500000, zzz4300000, hh, baa)
new_ltEs(Left(zzz500000), Left(zzz4300000), app(app(ty_Either, h), ba), bb) → new_ltEs(zzz500000, zzz4300000, h, ba)
new_ltEs2(@3(zzz500000, zzz500001, zzz500002), @3(zzz4300000, zzz4300001, zzz4300002), app(ty_[], baf), hf, hg) → new_lt3(zzz500000, zzz4300000, baf)
new_compare22(Just(@3(zzz500000, zzz500001, zzz500002)), Just(@3(zzz4300000, zzz4300001, zzz4300002)), False, app(app(app(ty_@3, bag), hf), app(app(ty_@2, bcc), bcd))) → new_ltEs0(zzz500002, zzz4300002, bcc, bcd)
new_ltEs(Right(zzz500000), Right(zzz4300000), cb, app(app(ty_@2, ce), cf)) → new_ltEs0(zzz500000, zzz4300000, ce, cf)
new_compare22(Just(@2(zzz500000, zzz500001)), Just(@2(zzz4300000, zzz4300001)), False, app(app(ty_@2, app(ty_[], ef)), dg)) → new_compare(zzz500000, zzz4300000, ef)
new_compare22(Just(Right(zzz500000)), Just(Right(zzz4300000)), False, app(app(ty_Either, cb), app(ty_[], dd))) → new_ltEs3(zzz500000, zzz4300000, dd)
new_compare22(Just(@2(zzz500000, zzz500001)), Just(@2(zzz4300000, zzz4300001)), False, app(app(ty_@2, eg), app(ty_[], ga))) → new_ltEs3(zzz500001, zzz4300001, ga)
new_ltEs1(Just(zzz500000), Just(zzz4300000), app(ty_Maybe, gg)) → new_ltEs1(zzz500000, zzz4300000, gg)
new_primCompAux(zzz500000, zzz4300000, zzz220, app(app(ty_Either, bdc), bdd)) → new_compare0(zzz500000, zzz4300000, bdc, bdd)
new_compare22(Just(Left(zzz500000)), Just(Left(zzz4300000)), False, app(app(ty_Either, app(app(ty_@2, bc), bd)), bb)) → new_ltEs0(zzz500000, zzz4300000, bc, bd)
new_compare5(zzz500000, zzz4300000, ec, ed, ee) → new_compare21(zzz500000, zzz4300000, new_esEs6(zzz500000, zzz4300000, ec, ed, ee), ec, ed, ee)
new_compare22(Just(@2(zzz500000, zzz500001)), Just(@2(zzz4300000, zzz4300001)), False, app(app(ty_@2, app(app(ty_Either, de), df)), dg)) → new_compare2(zzz500000, zzz4300000, new_esEs4(zzz500000, zzz4300000, de, df), de, df)
new_compare22(Just(@3(zzz500000, zzz500001, zzz500002)), Just(@3(zzz4300000, zzz4300001, zzz4300002)), False, app(app(app(ty_@3, bag), app(ty_[], bbh)), hg)) → new_lt3(zzz500001, zzz4300001, bbh)
new_compare22(Just(Just(zzz500000)), Just(Just(zzz4300000)), False, app(ty_Maybe, app(app(app(ty_@3, gh), ha), hb))) → new_ltEs2(zzz500000, zzz4300000, gh, ha, hb)
new_compare3(zzz5000, zzz43000, gb) → new_compare22(zzz5000, zzz43000, new_esEs7(zzz5000, zzz43000, gb), gb)
new_compare20(zzz500000, zzz4300000, False, dh, ea) → new_ltEs0(zzz500000, zzz4300000, dh, ea)
new_compare22(Just(@3(zzz500000, zzz500001, zzz500002)), Just(@3(zzz4300000, zzz4300001, zzz4300002)), False, app(app(app(ty_@3, bag), app(app(ty_@2, bbb), bbc)), hg)) → new_lt1(zzz500001, zzz4300001, bbb, bbc)
new_ltEs0(@2(zzz500000, zzz500001), @2(zzz4300000, zzz4300001), eg, app(app(app(ty_@3, ff), fg), fh)) → new_ltEs2(zzz500001, zzz4300001, ff, fg, fh)
new_ltEs(Left(zzz500000), Left(zzz4300000), app(ty_[], ca), bb) → new_ltEs3(zzz500000, zzz4300000, ca)
new_compare22(Just(@2(zzz500000, zzz500001)), Just(@2(zzz4300000, zzz4300001)), False, app(app(ty_@2, app(ty_Maybe, eb)), dg)) → new_lt(zzz500000, zzz4300000, eb)
new_lt2(zzz500000, zzz4300000, ec, ed, ee) → new_compare21(zzz500000, zzz4300000, new_esEs6(zzz500000, zzz4300000, ec, ed, ee), ec, ed, ee)
new_ltEs0(@2(zzz500000, zzz500001), @2(zzz4300000, zzz4300001), eg, app(app(ty_Either, eh), fa)) → new_ltEs(zzz500001, zzz4300001, eh, fa)
new_ltEs0(@2(zzz500000, zzz500001), @2(zzz4300000, zzz4300001), eg, app(app(ty_@2, fb), fc)) → new_ltEs0(zzz500001, zzz4300001, fb, fc)
new_ltEs2(@3(zzz500000, zzz500001, zzz500002), @3(zzz4300000, zzz4300001, zzz4300002), bag, app(app(ty_@2, bbb), bbc), hg) → new_lt1(zzz500001, zzz4300001, bbb, bbc)
new_ltEs2(@3(zzz500000, zzz500001, zzz500002), @3(zzz4300000, zzz4300001, zzz4300002), bag, hf, app(app(ty_Either, bca), bcb)) → new_ltEs(zzz500002, zzz4300002, bca, bcb)
new_compare22(Just(Just(zzz500000)), Just(Just(zzz4300000)), False, app(ty_Maybe, app(ty_[], hc))) → new_ltEs3(zzz500000, zzz4300000, hc)
new_ltEs1(Just(zzz500000), Just(zzz4300000), app(app(ty_@2, ge), gf)) → new_ltEs0(zzz500000, zzz4300000, ge, gf)
new_ltEs2(@3(zzz500000, zzz500001, zzz500002), @3(zzz4300000, zzz4300001, zzz4300002), app(app(ty_Either, hd), he), hf, hg) → new_lt0(zzz500000, zzz4300000, hd, he)
new_compare22(Just(Left(zzz500000)), Just(Left(zzz4300000)), False, app(app(ty_Either, app(ty_[], ca)), bb)) → new_ltEs3(zzz500000, zzz4300000, ca)
new_compare(:(zzz500000, zzz500001), :(zzz4300000, zzz4300001), bdb) → new_compare(zzz500001, zzz4300001, bdb)
new_ltEs2(@3(zzz500000, zzz500001, zzz500002), @3(zzz4300000, zzz4300001, zzz4300002), app(ty_Maybe, bab), hf, hg) → new_lt(zzz500000, zzz4300000, bab)
new_lt3(zzz500000, zzz4300000, ef) → new_compare(zzz500000, zzz4300000, ef)
new_compare22(Just(@3(zzz500000, zzz500001, zzz500002)), Just(@3(zzz4300000, zzz4300001, zzz4300002)), False, app(app(app(ty_@3, app(app(ty_Either, hd), he)), hf), hg)) → new_lt0(zzz500000, zzz4300000, hd, he)
new_ltEs1(Just(zzz500000), Just(zzz4300000), app(ty_[], hc)) → new_ltEs3(zzz500000, zzz4300000, hc)
new_ltEs2(@3(zzz500000, zzz500001, zzz500002), @3(zzz4300000, zzz4300001, zzz4300002), app(app(app(ty_@3, bac), bad), bae), hf, hg) → new_lt2(zzz500000, zzz4300000, bac, bad, bae)
new_ltEs(Right(zzz500000), Right(zzz4300000), cb, app(app(app(ty_@3, da), db), dc)) → new_ltEs2(zzz500000, zzz4300000, da, db, dc)
new_compare22(Just(Left(zzz500000)), Just(Left(zzz4300000)), False, app(app(ty_Either, app(app(ty_Either, h), ba)), bb)) → new_ltEs(zzz500000, zzz4300000, h, ba)
new_ltEs2(@3(zzz500000, zzz500001, zzz500002), @3(zzz4300000, zzz4300001, zzz4300002), bag, hf, app(app(ty_@2, bcc), bcd)) → new_ltEs0(zzz500002, zzz4300002, bcc, bcd)
new_compare22(Just(@3(zzz500000, zzz500001, zzz500002)), Just(@3(zzz4300000, zzz4300001, zzz4300002)), False, app(app(app(ty_@3, bag), app(ty_Maybe, bbd)), hg)) → new_lt(zzz500001, zzz4300001, bbd)
new_compare22(Just(@2(zzz500000, zzz500001)), Just(@2(zzz4300000, zzz4300001)), False, app(app(ty_@2, app(app(ty_@2, dh), ea)), dg)) → new_compare20(zzz500000, zzz4300000, new_esEs5(zzz500000, zzz4300000, dh, ea), dh, ea)
new_compare22(Just(Right(zzz500000)), Just(Right(zzz4300000)), False, app(app(ty_Either, cb), app(app(ty_Either, cc), cd))) → new_ltEs(zzz500000, zzz4300000, cc, cd)
new_compare22(Just(@2(zzz500000, zzz500001)), Just(@2(zzz4300000, zzz4300001)), False, app(app(ty_@2, eg), app(app(ty_@2, fb), fc))) → new_ltEs0(zzz500001, zzz4300001, fb, fc)
new_primCompAux(zzz500000, zzz4300000, zzz220, app(ty_Maybe, bdg)) → new_compare3(zzz500000, zzz4300000, bdg)
new_compare22(Just(@3(zzz500000, zzz500001, zzz500002)), Just(@3(zzz4300000, zzz4300001, zzz4300002)), False, app(app(app(ty_@3, bag), hf), app(app(ty_Either, bca), bcb))) → new_ltEs(zzz500002, zzz4300002, bca, bcb)
new_ltEs(Left(zzz500000), Left(zzz4300000), app(app(ty_@2, bc), bd), bb) → new_ltEs0(zzz500000, zzz4300000, bc, bd)

The TRS R consists of the following rules:

new_lt19(zzz500000, zzz4300000, ty_Float) → new_lt6(zzz500000, zzz4300000)
new_ltEs18(zzz50000, zzz430000, app(ty_Ratio, cce)) → new_ltEs15(zzz50000, zzz430000, cce)
new_esEs7(Just(zzz5000), Just(zzz4000), app(ty_Maybe, bfg)) → new_esEs7(zzz5000, zzz4000, bfg)
new_esEs4(Right(zzz5000), Right(zzz4000), cea, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_esEs20(zzz5000, zzz4000, app(ty_Maybe, cbg)) → new_esEs7(zzz5000, zzz4000, cbg)
new_esEs12(:(zzz5000, zzz5001), :(zzz4000, zzz4001), caf) → new_asAs(new_esEs20(zzz5000, zzz4000, caf), new_esEs12(zzz5001, zzz4001, caf))
new_esEs7(Just(zzz5000), Just(zzz4000), app(ty_[], bfc)) → new_esEs12(zzz5000, zzz4000, bfc)
new_ltEs7(Right(zzz500000), Right(zzz4300000), cb, ty_Ordering) → new_ltEs10(zzz500000, zzz4300000)
new_lt19(zzz500000, zzz4300000, app(app(app(ty_@3, bac), bad), bae)) → new_lt8(zzz500000, zzz4300000, bac, bad, bae)
new_ltEs18(zzz50000, zzz430000, app(app(app(ty_@3, bag), hf), hg)) → new_ltEs16(zzz50000, zzz430000, bag, hf, hg)
new_lt20(zzz500001, zzz4300001, app(ty_[], bbh)) → new_lt18(zzz500001, zzz4300001, bbh)
new_esEs4(Right(zzz5000), Right(zzz4000), cea, ty_Char) → new_esEs11(zzz5000, zzz4000)
new_compare15(zzz500000, zzz4300000, True, dh, ea) → LT
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Bool, ccf) → new_esEs14(zzz5000, zzz4000)
new_ltEs18(zzz50000, zzz430000, app(ty_Maybe, bed)) → new_ltEs4(zzz50000, zzz430000, bed)
new_ltEs20(zzz500002, zzz4300002, ty_Ordering) → new_ltEs10(zzz500002, zzz4300002)
new_esEs4(Right(zzz5000), Right(zzz4000), cea, app(app(app(ty_@3, ceg), ceh), cfa)) → new_esEs6(zzz5000, zzz4000, ceg, ceh, cfa)
new_lt13(zzz500000, zzz4300000, app(app(app(ty_@3, ec), ed), ee)) → new_lt8(zzz500000, zzz4300000, ec, ed, ee)
new_lt15(zzz500000, zzz4300000) → new_esEs8(new_compare14(zzz500000, zzz4300000), LT)
new_lt20(zzz500001, zzz4300001, app(app(app(ty_@3, bbe), bbf), bbg)) → new_lt8(zzz500001, zzz4300001, bbe, bbf, bbg)
new_esEs27(zzz5001, zzz4001, app(ty_Maybe, dag)) → new_esEs7(zzz5001, zzz4001, dag)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Ordering) → new_ltEs10(zzz500000, zzz4300000)
new_esEs23(zzz500000, zzz4300000, ty_Bool) → new_esEs14(zzz500000, zzz4300000)
new_compare27(zzz500000, zzz4300000, False, de, df) → new_compare113(zzz500000, zzz4300000, new_ltEs7(zzz500000, zzz4300000, de, df), de, df)
new_lt19(zzz500000, zzz4300000, ty_Double) → new_lt15(zzz500000, zzz4300000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), app(ty_Maybe, be), bb) → new_ltEs4(zzz500000, zzz4300000, be)
new_ltEs7(Right(zzz500000), Right(zzz4300000), cb, ty_@0) → new_ltEs11(zzz500000, zzz4300000)
new_ltEs20(zzz500002, zzz4300002, app(ty_Ratio, cga)) → new_ltEs15(zzz500002, zzz4300002, cga)
new_lt13(zzz500000, zzz4300000, app(ty_[], ef)) → new_lt18(zzz500000, zzz4300000, ef)
new_esEs26(zzz5002, zzz4002, ty_Float) → new_esEs13(zzz5002, zzz4002)
new_ltEs7(Left(zzz500000), Right(zzz4300000), cb, bb) → True
new_primMulNat0(Zero, Zero) → Zero
new_esEs19(zzz5000, zzz4000, ty_Int) → new_esEs17(zzz5000, zzz4000)
new_sr(Integer(zzz43000000), Integer(zzz5000010)) → Integer(new_primMulInt(zzz43000000, zzz5000010))
new_ltEs20(zzz500002, zzz4300002, ty_Float) → new_ltEs12(zzz500002, zzz4300002)
new_ltEs20(zzz500002, zzz4300002, ty_@0) → new_ltEs11(zzz500002, zzz4300002)
new_esEs20(zzz5000, zzz4000, app(ty_Ratio, cbh)) → new_esEs16(zzz5000, zzz4000, cbh)
new_esEs18(zzz5001, zzz4001, ty_Double) → new_esEs9(zzz5001, zzz4001)
new_lt20(zzz500001, zzz4300001, ty_Float) → new_lt6(zzz500001, zzz4300001)
new_esEs23(zzz500000, zzz4300000, ty_Double) → new_esEs9(zzz500000, zzz4300000)
new_esEs4(Right(zzz5000), Right(zzz4000), cea, app(ty_[], cef)) → new_esEs12(zzz5000, zzz4000, cef)
new_esEs24(zzz500001, zzz4300001, ty_Integer) → new_esEs15(zzz500001, zzz4300001)
new_ltEs14(False, True) → True
new_ltEs19(zzz500001, zzz4300001, ty_Integer) → new_ltEs9(zzz500001, zzz4300001)
new_ltEs4(Just(zzz500000), Just(zzz4300000), app(app(ty_@2, ge), gf)) → new_ltEs13(zzz500000, zzz4300000, ge, gf)
new_esEs20(zzz5000, zzz4000, app(app(ty_Either, cag), cah)) → new_esEs4(zzz5000, zzz4000, cag, cah)
new_esEs12([], [], caf) → True
new_ltEs19(zzz500001, zzz4300001, ty_Ordering) → new_ltEs10(zzz500001, zzz4300001)
new_esEs24(zzz500001, zzz4300001, app(app(ty_@2, bbb), bbc)) → new_esEs5(zzz500001, zzz4300001, bbb, bbc)
new_lt12(zzz500000, zzz4300000) → new_esEs8(new_compare10(zzz500000, zzz4300000), LT)
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Ordering, bb) → new_ltEs10(zzz500000, zzz4300000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), cb, app(ty_Ratio, ccd)) → new_ltEs15(zzz500000, zzz4300000, ccd)
new_esEs15(Integer(zzz5000), Integer(zzz4000)) → new_primEqInt(zzz5000, zzz4000)
new_ltEs10(EQ, GT) → True
new_ltEs19(zzz500001, zzz4300001, app(ty_Maybe, fd)) → new_ltEs4(zzz500001, zzz4300001, fd)
new_esEs21(zzz5001, zzz4001, ty_Int) → new_esEs17(zzz5001, zzz4001)
new_ltEs7(Left(zzz500000), Left(zzz4300000), app(app(app(ty_@3, bf), bg), bh), bb) → new_ltEs16(zzz500000, zzz4300000, bf, bg, bh)
new_lt13(zzz500000, zzz4300000, ty_Char) → new_lt12(zzz500000, zzz4300000)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Ordering, ccf) → new_esEs8(zzz5000, zzz4000)
new_esEs24(zzz500001, zzz4300001, app(ty_[], bbh)) → new_esEs12(zzz500001, zzz4300001, bbh)
new_esEs25(zzz500000, zzz4300000, ty_Double) → new_esEs9(zzz500000, zzz4300000)
new_esEs25(zzz500000, zzz4300000, ty_Float) → new_esEs13(zzz500000, zzz4300000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), cb, app(ty_[], dd)) → new_ltEs17(zzz500000, zzz4300000, dd)
new_pePe(False, zzz218) → zzz218
new_lt14(zzz5000, zzz43000) → new_esEs8(new_compare8(zzz5000, zzz43000), LT)
new_esEs25(zzz500000, zzz4300000, app(app(ty_Either, hd), he)) → new_esEs4(zzz500000, zzz4300000, hd, he)
new_esEs12(:(zzz5000, zzz5001), [], caf) → False
new_esEs12([], :(zzz4000, zzz4001), caf) → False
new_esEs25(zzz500000, zzz4300000, ty_Char) → new_esEs11(zzz500000, zzz4300000)
new_esEs25(zzz500000, zzz4300000, ty_Bool) → new_esEs14(zzz500000, zzz4300000)
new_lt19(zzz500000, zzz4300000, ty_Ordering) → new_lt9(zzz500000, zzz4300000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), cb, app(app(ty_@2, ce), cf)) → new_ltEs13(zzz500000, zzz4300000, ce, cf)
new_esEs4(Right(zzz5000), Right(zzz4000), cea, app(ty_Ratio, cfc)) → new_esEs16(zzz5000, zzz4000, cfc)
new_compare23(zzz500000, zzz4300000, True) → EQ
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Float, bb) → new_ltEs12(zzz500000, zzz4300000)
new_lt19(zzz500000, zzz4300000, app(ty_Ratio, cfg)) → new_lt17(zzz500000, zzz4300000, cfg)
new_esEs24(zzz500001, zzz4300001, app(ty_Maybe, bbd)) → new_esEs7(zzz500001, zzz4300001, bbd)
new_ltEs4(Nothing, Just(zzz4300000), bed) → True
new_esEs23(zzz500000, zzz4300000, app(ty_Maybe, eb)) → new_esEs7(zzz500000, zzz4300000, eb)
new_compare30(zzz500000, zzz4300000, ty_Integer) → new_compare9(zzz500000, zzz4300000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(ty_Ratio, cdh), ccf) → new_esEs16(zzz5000, zzz4000, cdh)
new_ltEs7(Right(zzz500000), Right(zzz4300000), cb, ty_Char) → new_ltEs5(zzz500000, zzz4300000)
new_compare13(zzz500000, zzz4300000, ec, ed, ee) → new_compare24(zzz500000, zzz4300000, new_esEs6(zzz500000, zzz4300000, ec, ed, ee), ec, ed, ee)
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_lt4(zzz500000, zzz4300000) → new_esEs8(new_compare11(zzz500000, zzz4300000), LT)
new_esEs4(Right(zzz5000), Right(zzz4000), cea, ty_Integer) → new_esEs15(zzz5000, zzz4000)
new_esEs20(zzz5000, zzz4000, app(app(ty_@2, cba), cbb)) → new_esEs5(zzz5000, zzz4000, cba, cbb)
new_esEs28(zzz5000, zzz4000, app(ty_Ratio, dcb)) → new_esEs16(zzz5000, zzz4000, dcb)
new_compare30(zzz500000, zzz4300000, app(ty_Ratio, cfd)) → new_compare7(zzz500000, zzz4300000, cfd)
new_compare19(zzz500000, zzz4300000, True) → LT
new_compare6(zzz500000, zzz4300000) → new_compare23(zzz500000, zzz4300000, new_esEs8(zzz500000, zzz4300000))
new_ltEs18(zzz50000, zzz430000, ty_@0) → new_ltEs11(zzz50000, zzz430000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_ltEs19(zzz500001, zzz4300001, app(ty_Ratio, cff)) → new_ltEs15(zzz500001, zzz4300001, cff)
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Int) → new_esEs17(zzz5000, zzz4000)
new_ltEs20(zzz500002, zzz4300002, ty_Bool) → new_ltEs14(zzz500002, zzz4300002)
new_esEs27(zzz5001, zzz4001, ty_@0) → new_esEs10(zzz5001, zzz4001)
new_ltEs12(zzz50000, zzz430000) → new_fsEs(new_compare16(zzz50000, zzz430000))
new_esEs8(LT, LT) → True
new_lt19(zzz500000, zzz4300000, app(app(ty_@2, hh), baa)) → new_lt16(zzz500000, zzz4300000, hh, baa)
new_esEs25(zzz500000, zzz4300000, ty_Ordering) → new_esEs8(zzz500000, zzz4300000)
new_esEs19(zzz5000, zzz4000, app(ty_Maybe, gb)) → new_esEs7(zzz5000, zzz4000, gb)
new_esEs20(zzz5000, zzz4000, app(app(app(ty_@3, cbd), cbe), cbf)) → new_esEs6(zzz5000, zzz4000, cbd, cbe, cbf)
new_esEs18(zzz5001, zzz4001, app(ty_Ratio, bhd)) → new_esEs16(zzz5001, zzz4001, bhd)
new_pePe(True, zzz218) → True
new_primEqNat0(Zero, Zero) → True
new_lt20(zzz500001, zzz4300001, app(app(ty_Either, bah), bba)) → new_lt5(zzz500001, zzz4300001, bah, bba)
new_compare26(zzz500000, zzz4300000, True) → EQ
new_lt20(zzz500001, zzz4300001, ty_Bool) → new_lt7(zzz500001, zzz4300001)
new_esEs13(Float(zzz5000, zzz5001), Float(zzz4000, zzz4001)) → new_esEs17(new_sr0(zzz5000, zzz4000), new_sr0(zzz5001, zzz4001))
new_esEs19(zzz5000, zzz4000, app(ty_[], caa)) → new_esEs12(zzz5000, zzz4000, caa)
new_compare29(Nothing, Just(zzz430000), False, gb) → LT
new_esEs19(zzz5000, zzz4000, ty_Float) → new_esEs13(zzz5000, zzz4000)
new_compare30(zzz500000, zzz4300000, app(ty_Maybe, bdg)) → new_compare28(zzz500000, zzz4300000, bdg)
new_esEs18(zzz5001, zzz4001, app(app(ty_@2, bge), bgf)) → new_esEs5(zzz5001, zzz4001, bge, bgf)
new_esEs25(zzz500000, zzz4300000, ty_Int) → new_esEs17(zzz500000, zzz4300000)
new_esEs9(Double(zzz5000, zzz5001), Double(zzz4000, zzz4001)) → new_esEs17(new_sr0(zzz5000, zzz4000), new_sr0(zzz5001, zzz4001))
new_esEs26(zzz5002, zzz4002, ty_Ordering) → new_esEs8(zzz5002, zzz4002)
new_esEs8(GT, GT) → True
new_lt20(zzz500001, zzz4300001, app(ty_Maybe, bbd)) → new_lt11(zzz500001, zzz4300001, bbd)
new_esEs18(zzz5001, zzz4001, app(app(app(ty_@3, bgh), bha), bhb)) → new_esEs6(zzz5001, zzz4001, bgh, bha, bhb)
new_esEs25(zzz500000, zzz4300000, ty_@0) → new_esEs10(zzz500000, zzz4300000)
new_compare4([], [], bdb) → EQ
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_lt19(zzz500000, zzz4300000, ty_@0) → new_lt4(zzz500000, zzz4300000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(app(ty_@2, cda), cdb), ccf) → new_esEs5(zzz5000, zzz4000, cda, cdb)
new_ltEs7(Right(zzz500000), Right(zzz4300000), cb, ty_Integer) → new_ltEs9(zzz500000, zzz4300000)
new_esEs26(zzz5002, zzz4002, app(app(app(ty_@3, chb), chc), chd)) → new_esEs6(zzz5002, zzz4002, chb, chc, chd)
new_compare18(zzz500000, zzz4300000, dh, ea) → new_compare25(zzz500000, zzz4300000, new_esEs5(zzz500000, zzz4300000, dh, ea), dh, ea)
new_ltEs17(zzz50000, zzz430000, bdb) → new_fsEs(new_compare4(zzz50000, zzz430000, bdb))
new_esEs8(GT, LT) → False
new_esEs8(LT, GT) → False
new_compare30(zzz500000, zzz4300000, app(ty_[], bec)) → new_compare4(zzz500000, zzz4300000, bec)
new_compare30(zzz500000, zzz4300000, ty_Double) → new_compare14(zzz500000, zzz4300000)
new_ltEs13(@2(zzz500000, zzz500001), @2(zzz4300000, zzz4300001), eg, dg) → new_pePe(new_lt13(zzz500000, zzz4300000, eg), new_asAs(new_esEs23(zzz500000, zzz4300000, eg), new_ltEs19(zzz500001, zzz4300001, dg)))
new_esEs4(Right(zzz5000), Right(zzz4000), cea, app(app(ty_Either, ceb), cec)) → new_esEs4(zzz5000, zzz4000, ceb, cec)
new_esEs25(zzz500000, zzz4300000, app(ty_[], baf)) → new_esEs12(zzz500000, zzz4300000, baf)
new_compare24(zzz500000, zzz4300000, True, ec, ed, ee) → EQ
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Int, bb) → new_ltEs6(zzz500000, zzz4300000)
new_lt20(zzz500001, zzz4300001, ty_Ordering) → new_lt9(zzz500001, zzz4300001)
new_primEqInt(Neg(Succ(zzz50000)), Neg(Succ(zzz40000))) → new_primEqNat0(zzz50000, zzz40000)
new_esEs20(zzz5000, zzz4000, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_compare113(zzz500000, zzz4300000, True, de, df) → LT
new_esEs23(zzz500000, zzz4300000, ty_Ordering) → new_esEs8(zzz500000, zzz4300000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(app(ty_Either, ccg), cch), ccf) → new_esEs4(zzz5000, zzz4000, ccg, cch)
new_ltEs18(zzz50000, zzz430000, app(app(ty_Either, cb), bb)) → new_ltEs7(zzz50000, zzz430000, cb, bb)
new_esEs24(zzz500001, zzz4300001, ty_Bool) → new_esEs14(zzz500001, zzz4300001)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_lt19(zzz500000, zzz4300000, ty_Bool) → new_lt7(zzz500000, zzz4300000)
new_lt19(zzz500000, zzz4300000, ty_Integer) → new_lt10(zzz500000, zzz4300000)
new_ltEs4(Nothing, Nothing, bed) → True
new_lt13(zzz500000, zzz4300000, ty_Float) → new_lt6(zzz500000, zzz4300000)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_@0) → new_ltEs11(zzz500000, zzz4300000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Char, bb) → new_ltEs5(zzz500000, zzz4300000)
new_lt13(zzz500000, zzz4300000, ty_Int) → new_lt14(zzz500000, zzz4300000)
new_lt6(zzz500000, zzz4300000) → new_esEs8(new_compare16(zzz500000, zzz4300000), LT)
new_compare29(Just(zzz50000), Nothing, False, gb) → GT
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_ltEs7(Right(zzz500000), Left(zzz4300000), cb, bb) → False
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_esEs24(zzz500001, zzz4300001, app(app(app(ty_@3, bbe), bbf), bbg)) → new_esEs6(zzz500001, zzz4300001, bbe, bbf, bbg)
new_esEs23(zzz500000, zzz4300000, ty_Char) → new_esEs11(zzz500000, zzz4300000)
new_lt13(zzz500000, zzz4300000, ty_Bool) → new_lt7(zzz500000, zzz4300000)
new_esEs19(zzz5000, zzz4000, ty_Bool) → new_esEs14(zzz5000, zzz4000)
new_esEs20(zzz5000, zzz4000, ty_Float) → new_esEs13(zzz5000, zzz4000)
new_compare14(Double(zzz500000, zzz500001), Double(zzz4300000, zzz4300001)) → new_compare8(new_sr0(zzz500000, zzz4300000), new_sr0(zzz500001, zzz4300001))
new_compare12(zzz500000, zzz4300000, de, df) → new_compare27(zzz500000, zzz4300000, new_esEs4(zzz500000, zzz4300000, de, df), de, df)
new_compare8(zzz500, zzz4300) → new_primCmpInt(zzz500, zzz4300)
new_lt19(zzz500000, zzz4300000, ty_Char) → new_lt12(zzz500000, zzz4300000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), cb, app(app(app(ty_@3, da), db), dc)) → new_ltEs16(zzz500000, zzz4300000, da, db, dc)
new_primEqInt(Neg(Succ(zzz50000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(zzz40000))) → False
new_compare17(zzz500000, zzz4300000) → new_compare26(zzz500000, zzz4300000, new_esEs14(zzz500000, zzz4300000))
new_esEs8(EQ, EQ) → True
new_lt13(zzz500000, zzz4300000, ty_Double) → new_lt15(zzz500000, zzz4300000)
new_compare111(zzz200, zzz201, True, ccb) → LT
new_esEs20(zzz5000, zzz4000, ty_@0) → new_esEs10(zzz5000, zzz4000)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Char, ccf) → new_esEs11(zzz5000, zzz4000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_ltEs19(zzz500001, zzz4300001, ty_@0) → new_ltEs11(zzz500001, zzz4300001)
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_esEs18(zzz5001, zzz4001, ty_Char) → new_esEs11(zzz5001, zzz4001)
new_compare112(zzz500000, zzz4300000, True) → LT
new_esEs19(zzz5000, zzz4000, ty_Char) → new_esEs11(zzz5000, zzz4000)
new_compare30(zzz500000, zzz4300000, app(app(ty_Either, bdc), bdd)) → new_compare12(zzz500000, zzz4300000, bdc, bdd)
new_primEqInt(Pos(Succ(zzz50000)), Pos(Succ(zzz40000))) → new_primEqNat0(zzz50000, zzz40000)
new_ltEs18(zzz50000, zzz430000, ty_Double) → new_ltEs8(zzz50000, zzz430000)
new_compare27(zzz500000, zzz4300000, True, de, df) → EQ
new_lt10(zzz500000, zzz4300000) → new_esEs8(new_compare9(zzz500000, zzz4300000), LT)
new_esEs24(zzz500001, zzz4300001, app(ty_Ratio, cfh)) → new_esEs16(zzz500001, zzz4300001, cfh)
new_ltEs19(zzz500001, zzz4300001, ty_Bool) → new_ltEs14(zzz500001, zzz4300001)
new_esEs14(False, True) → False
new_esEs14(True, False) → False
new_esEs23(zzz500000, zzz4300000, app(ty_[], ef)) → new_esEs12(zzz500000, zzz4300000, ef)
new_ltEs4(Just(zzz500000), Just(zzz4300000), app(app(ty_Either, gc), gd)) → new_ltEs7(zzz500000, zzz4300000, gc, gd)
new_esEs26(zzz5002, zzz4002, ty_Integer) → new_esEs15(zzz5002, zzz4002)
new_ltEs10(GT, EQ) → False
new_lt17(zzz500000, zzz4300000, cfe) → new_esEs8(new_compare7(zzz500000, zzz4300000, cfe), LT)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Double) → new_ltEs8(zzz500000, zzz4300000)
new_esEs24(zzz500001, zzz4300001, ty_Int) → new_esEs17(zzz500001, zzz4300001)
new_primEqNat0(Succ(zzz50000), Succ(zzz40000)) → new_primEqNat0(zzz50000, zzz40000)
new_ltEs20(zzz500002, zzz4300002, app(ty_[], bda)) → new_ltEs17(zzz500002, zzz4300002, bda)
new_esEs27(zzz5001, zzz4001, ty_Ordering) → new_esEs8(zzz5001, zzz4001)
new_ltEs14(False, False) → True
new_compare11(@0, @0) → EQ
new_lt7(zzz500000, zzz4300000) → new_esEs8(new_compare17(zzz500000, zzz4300000), LT)
new_esEs19(zzz5000, zzz4000, app(app(app(ty_@3, cab), cac), cad)) → new_esEs6(zzz5000, zzz4000, cab, cac, cad)
new_ltEs9(zzz50000, zzz430000) → new_fsEs(new_compare9(zzz50000, zzz430000))
new_ltEs20(zzz500002, zzz4300002, ty_Char) → new_ltEs5(zzz500002, zzz4300002)
new_compare113(zzz500000, zzz4300000, False, de, df) → GT
new_ltEs7(Right(zzz500000), Right(zzz4300000), cb, ty_Bool) → new_ltEs14(zzz500000, zzz4300000)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Int) → new_ltEs6(zzz500000, zzz4300000)
new_primCompAux00(zzz225, LT) → LT
new_lt20(zzz500001, zzz4300001, ty_@0) → new_lt4(zzz500001, zzz4300001)
new_ltEs19(zzz500001, zzz4300001, app(ty_[], ga)) → new_ltEs17(zzz500001, zzz4300001, ga)
new_ltEs19(zzz500001, zzz4300001, app(app(ty_Either, eh), fa)) → new_ltEs7(zzz500001, zzz4300001, eh, fa)
new_compare7(:%(zzz500000, zzz500001), :%(zzz4300000, zzz4300001), ty_Int) → new_compare8(new_sr0(zzz500000, zzz4300001), new_sr0(zzz4300000, zzz500001))
new_esEs24(zzz500001, zzz4300001, ty_Ordering) → new_esEs8(zzz500001, zzz4300001)
new_ltEs8(zzz50000, zzz430000) → new_fsEs(new_compare14(zzz50000, zzz430000))
new_esEs7(Nothing, Nothing, bef) → True
new_esEs28(zzz5000, zzz4000, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_esEs8(EQ, LT) → False
new_esEs8(LT, EQ) → False
new_esEs18(zzz5001, zzz4001, app(ty_Maybe, bhc)) → new_esEs7(zzz5001, zzz4001, bhc)
new_primEqInt(Pos(Succ(zzz50000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(zzz40000))) → False
new_lt20(zzz500001, zzz4300001, app(ty_Ratio, cfh)) → new_lt17(zzz500001, zzz4300001, cfh)
new_compare30(zzz500000, zzz4300000, ty_Int) → new_compare8(zzz500000, zzz4300000)
new_compare24(zzz500000, zzz4300000, False, ec, ed, ee) → new_compare110(zzz500000, zzz4300000, new_ltEs16(zzz500000, zzz4300000, ec, ed, ee), ec, ed, ee)
new_esEs24(zzz500001, zzz4300001, ty_@0) → new_esEs10(zzz500001, zzz4300001)
new_primCmpNat0(Zero, Zero) → EQ
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Integer, bb) → new_ltEs9(zzz500000, zzz4300000)
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_esEs23(zzz500000, zzz4300000, app(app(ty_@2, dh), ea)) → new_esEs5(zzz500000, zzz4300000, dh, ea)
new_esEs4(Right(zzz5000), Right(zzz4000), cea, ty_@0) → new_esEs10(zzz5000, zzz4000)
new_ltEs10(LT, EQ) → True
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_compare19(zzz500000, zzz4300000, False) → GT
new_esEs27(zzz5001, zzz4001, ty_Double) → new_esEs9(zzz5001, zzz4001)
new_ltEs15(zzz50000, zzz430000, cce) → new_fsEs(new_compare7(zzz50000, zzz430000, cce))
new_esEs23(zzz500000, zzz4300000, ty_Float) → new_esEs13(zzz500000, zzz4300000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Integer) → new_esEs15(zzz5000, zzz4000)
new_compare29(Just(zzz50000), Just(zzz430000), False, gb) → new_compare111(zzz50000, zzz430000, new_ltEs18(zzz50000, zzz430000, gb), gb)
new_primEqInt(Pos(Succ(zzz50000)), Neg(zzz4000)) → False
new_primEqInt(Neg(Succ(zzz50000)), Pos(zzz4000)) → False
new_lt13(zzz500000, zzz4300000, app(ty_Ratio, cfe)) → new_lt17(zzz500000, zzz4300000, cfe)
new_esEs7(Nothing, Just(zzz4000), bef) → False
new_esEs7(Just(zzz5000), Nothing, bef) → False
new_esEs18(zzz5001, zzz4001, app(ty_[], bgg)) → new_esEs12(zzz5001, zzz4001, bgg)
new_esEs28(zzz5000, zzz4000, ty_Char) → new_esEs11(zzz5000, zzz4000)
new_ltEs10(GT, GT) → True
new_esEs26(zzz5002, zzz4002, app(ty_Ratio, chf)) → new_esEs16(zzz5002, zzz4002, chf)
new_esEs26(zzz5002, zzz4002, ty_Int) → new_esEs17(zzz5002, zzz4002)
new_esEs4(Right(zzz5000), Right(zzz4000), cea, ty_Bool) → new_esEs14(zzz5000, zzz4000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_@0, bb) → new_ltEs11(zzz500000, zzz4300000)
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primEqInt(Pos(Zero), Neg(Succ(zzz40000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(zzz40000))) → False
new_ltEs6(zzz50000, zzz430000) → new_fsEs(new_compare8(zzz50000, zzz430000))
new_esEs20(zzz5000, zzz4000, app(ty_[], cbc)) → new_esEs12(zzz5000, zzz4000, cbc)
new_esEs21(zzz5001, zzz4001, ty_Integer) → new_esEs15(zzz5001, zzz4001)
new_compare30(zzz500000, zzz4300000, app(app(ty_@2, bde), bdf)) → new_compare18(zzz500000, zzz4300000, bde, bdf)
new_primCompAux00(zzz225, EQ) → zzz225
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Double, ccf) → new_esEs9(zzz5000, zzz4000)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Integer, ccf) → new_esEs15(zzz5000, zzz4000)
new_esEs18(zzz5001, zzz4001, ty_Int) → new_esEs17(zzz5001, zzz4001)
new_lt16(zzz500000, zzz4300000, dh, ea) → new_esEs8(new_compare18(zzz500000, zzz4300000, dh, ea), LT)
new_esEs8(GT, EQ) → False
new_esEs8(EQ, GT) → False
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Double) → new_esEs9(zzz5000, zzz4000)
new_esEs26(zzz5002, zzz4002, ty_Char) → new_esEs11(zzz5002, zzz4002)
new_esEs27(zzz5001, zzz4001, app(ty_Ratio, dah)) → new_esEs16(zzz5001, zzz4001, dah)
new_esEs26(zzz5002, zzz4002, app(app(ty_@2, cgg), cgh)) → new_esEs5(zzz5002, zzz4002, cgg, cgh)
new_ltEs19(zzz500001, zzz4300001, app(app(ty_@2, fb), fc)) → new_ltEs13(zzz500001, zzz4300001, fb, fc)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Bool) → new_ltEs14(zzz500000, zzz4300000)
new_not(False) → True
new_esEs24(zzz500001, zzz4300001, ty_Double) → new_esEs9(zzz500001, zzz4300001)
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_ltEs5(zzz50000, zzz430000) → new_fsEs(new_compare10(zzz50000, zzz430000))
new_esEs25(zzz500000, zzz4300000, ty_Integer) → new_esEs15(zzz500000, zzz4300000)
new_esEs26(zzz5002, zzz4002, ty_Bool) → new_esEs14(zzz5002, zzz4002)
new_ltEs19(zzz500001, zzz4300001, ty_Int) → new_ltEs6(zzz500001, zzz4300001)
new_esEs25(zzz500000, zzz4300000, app(ty_Ratio, cfg)) → new_esEs16(zzz500000, zzz4300000, cfg)
new_esEs4(Right(zzz5000), Right(zzz4000), cea, ty_Int) → new_esEs17(zzz5000, zzz4000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Bool, bb) → new_ltEs14(zzz500000, zzz4300000)
new_esEs28(zzz5000, zzz4000, app(app(ty_@2, dbc), dbd)) → new_esEs5(zzz5000, zzz4000, dbc, dbd)
new_esEs23(zzz500000, zzz4300000, ty_@0) → new_esEs10(zzz500000, zzz4300000)
new_compare30(zzz500000, zzz4300000, ty_@0) → new_compare11(zzz500000, zzz4300000)
new_esEs18(zzz5001, zzz4001, app(app(ty_Either, bgc), bgd)) → new_esEs4(zzz5001, zzz4001, bgc, bgd)
new_lt18(zzz500000, zzz4300000, ef) → new_esEs8(new_compare4(zzz500000, zzz4300000, ef), LT)
new_ltEs18(zzz50000, zzz430000, ty_Int) → new_ltEs6(zzz50000, zzz430000)
new_esEs22(zzz5000, zzz4000, ty_Int) → new_esEs17(zzz5000, zzz4000)
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_esEs6(@3(zzz5000, zzz5001, zzz5002), @3(zzz4000, zzz4001, zzz4002), cgb, cgc, cgd) → new_asAs(new_esEs28(zzz5000, zzz4000, cgb), new_asAs(new_esEs27(zzz5001, zzz4001, cgc), new_esEs26(zzz5002, zzz4002, cgd)))
new_esEs28(zzz5000, zzz4000, app(ty_Maybe, dca)) → new_esEs7(zzz5000, zzz4000, dca)
new_esEs28(zzz5000, zzz4000, ty_Double) → new_esEs9(zzz5000, zzz4000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), cb, ty_Double) → new_ltEs8(zzz500000, zzz4300000)
new_lt20(zzz500001, zzz4300001, ty_Double) → new_lt15(zzz500001, zzz4300001)
new_lt20(zzz500001, zzz4300001, ty_Integer) → new_lt10(zzz500001, zzz4300001)
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_esEs26(zzz5002, zzz4002, ty_@0) → new_esEs10(zzz5002, zzz4002)
new_esEs18(zzz5001, zzz4001, ty_Float) → new_esEs13(zzz5001, zzz4001)
new_compare25(zzz500000, zzz4300000, False, dh, ea) → new_compare15(zzz500000, zzz4300000, new_ltEs13(zzz500000, zzz4300000, dh, ea), dh, ea)
new_esEs23(zzz500000, zzz4300000, app(app(ty_Either, de), df)) → new_esEs4(zzz500000, zzz4300000, de, df)
new_esEs20(zzz5000, zzz4000, ty_Char) → new_esEs11(zzz5000, zzz4000)
new_lt19(zzz500000, zzz4300000, app(ty_Maybe, bab)) → new_lt11(zzz500000, zzz4300000, bab)
new_esEs4(Left(zzz5000), Left(zzz4000), app(ty_Maybe, cdg), ccf) → new_esEs7(zzz5000, zzz4000, cdg)
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_esEs20(zzz5000, zzz4000, ty_Integer) → new_esEs15(zzz5000, zzz4000)
new_primEqNat0(Zero, Succ(zzz40000)) → False
new_primEqNat0(Succ(zzz50000), Zero) → False
new_esEs18(zzz5001, zzz4001, ty_Integer) → new_esEs15(zzz5001, zzz4001)
new_esEs17(zzz500, zzz400) → new_primEqInt(zzz500, zzz400)
new_lt5(zzz500000, zzz4300000, de, df) → new_esEs8(new_compare12(zzz500000, zzz4300000, de, df), LT)
new_compare25(zzz500000, zzz4300000, True, dh, ea) → EQ
new_esEs20(zzz5000, zzz4000, ty_Bool) → new_esEs14(zzz5000, zzz4000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), app(app(ty_Either, h), ba), bb) → new_ltEs7(zzz500000, zzz4300000, h, ba)
new_ltEs14(True, True) → True
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs24(zzz500001, zzz4300001, app(app(ty_Either, bah), bba)) → new_esEs4(zzz500001, zzz4300001, bah, bba)
new_esEs28(zzz5000, zzz4000, app(app(app(ty_@3, dbf), dbg), dbh)) → new_esEs6(zzz5000, zzz4000, dbf, dbg, dbh)
new_compare30(zzz500000, zzz4300000, ty_Bool) → new_compare17(zzz500000, zzz4300000)
new_esEs27(zzz5001, zzz4001, app(app(ty_Either, chg), chh)) → new_esEs4(zzz5001, zzz4001, chg, chh)
new_esEs27(zzz5001, zzz4001, app(app(app(ty_@3, dad), dae), daf)) → new_esEs6(zzz5001, zzz4001, dad, dae, daf)
new_compare4(:(zzz500000, zzz500001), [], bdb) → GT
new_ltEs18(zzz50000, zzz430000, app(ty_[], bdb)) → new_ltEs17(zzz50000, zzz430000, bdb)
new_esEs27(zzz5001, zzz4001, app(app(ty_@2, daa), dab)) → new_esEs5(zzz5001, zzz4001, daa, dab)
new_esEs27(zzz5001, zzz4001, ty_Int) → new_esEs17(zzz5001, zzz4001)
new_esEs23(zzz500000, zzz4300000, ty_Int) → new_esEs17(zzz500000, zzz4300000)
new_lt13(zzz500000, zzz4300000, ty_@0) → new_lt4(zzz500000, zzz4300000)
new_compare30(zzz500000, zzz4300000, ty_Char) → new_compare10(zzz500000, zzz4300000)
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_compare4([], :(zzz4300000, zzz4300001), bdb) → LT
new_sr0(zzz5000, zzz4000) → new_primMulInt(zzz5000, zzz4000)
new_lt19(zzz500000, zzz4300000, app(ty_[], baf)) → new_lt18(zzz500000, zzz4300000, baf)
new_compare15(zzz500000, zzz4300000, False, dh, ea) → GT
new_ltEs18(zzz50000, zzz430000, ty_Float) → new_ltEs12(zzz50000, zzz430000)
new_ltEs18(zzz50000, zzz430000, ty_Integer) → new_ltEs9(zzz50000, zzz430000)
new_ltEs19(zzz500001, zzz4300001, ty_Double) → new_ltEs8(zzz500001, zzz4300001)
new_compare30(zzz500000, zzz4300000, ty_Float) → new_compare16(zzz500000, zzz4300000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), app(ty_[], ca), bb) → new_ltEs17(zzz500000, zzz4300000, ca)
new_esEs11(Char(zzz5000), Char(zzz4000)) → new_primEqNat0(zzz5000, zzz4000)
new_esEs7(Just(zzz5000), Just(zzz4000), app(app(app(ty_@3, bfd), bfe), bff)) → new_esEs6(zzz5000, zzz4000, bfd, bfe, bff)
new_esEs25(zzz500000, zzz4300000, app(ty_Maybe, bab)) → new_esEs7(zzz500000, zzz4300000, bab)
new_compare29(Nothing, Nothing, False, gb) → LT
new_esEs23(zzz500000, zzz4300000, app(ty_Ratio, cfe)) → new_esEs16(zzz500000, zzz4300000, cfe)
new_lt13(zzz500000, zzz4300000, app(app(ty_Either, de), df)) → new_lt5(zzz500000, zzz4300000, de, df)
new_esEs16(:%(zzz5000, zzz5001), :%(zzz4000, zzz4001), cca) → new_asAs(new_esEs22(zzz5000, zzz4000, cca), new_esEs21(zzz5001, zzz4001, cca))
new_ltEs4(Just(zzz500000), Just(zzz4300000), app(ty_Maybe, gg)) → new_ltEs4(zzz500000, zzz4300000, gg)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Float) → new_ltEs12(zzz500000, zzz4300000)
new_primCompAux0(zzz500000, zzz4300000, zzz220, bdb) → new_primCompAux00(zzz220, new_compare30(zzz500000, zzz4300000, bdb))
new_esEs19(zzz5000, zzz4000, app(app(ty_@2, bhg), bhh)) → new_esEs5(zzz5000, zzz4000, bhg, bhh)
new_esEs19(zzz5000, zzz4000, app(ty_Ratio, cae)) → new_esEs16(zzz5000, zzz4000, cae)
new_esEs10(@0, @0) → True
new_compare29(zzz5000, zzz43000, True, gb) → EQ
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs27(zzz5001, zzz4001, ty_Float) → new_esEs13(zzz5001, zzz4001)
new_lt13(zzz500000, zzz4300000, ty_Integer) → new_lt10(zzz500000, zzz4300000)
new_compare28(zzz5000, zzz43000, gb) → new_compare29(zzz5000, zzz43000, new_esEs7(zzz5000, zzz43000, gb), gb)
new_esEs4(Right(zzz5000), Right(zzz4000), cea, app(app(ty_@2, ced), cee)) → new_esEs5(zzz5000, zzz4000, ced, cee)
new_esEs24(zzz500001, zzz4300001, ty_Char) → new_esEs11(zzz500001, zzz4300001)
new_esEs28(zzz5000, zzz4000, ty_@0) → new_esEs10(zzz5000, zzz4000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), cb, app(app(ty_Either, cc), cd)) → new_ltEs7(zzz500000, zzz4300000, cc, cd)
new_esEs28(zzz5000, zzz4000, ty_Int) → new_esEs17(zzz5000, zzz4000)
new_compare7(:%(zzz500000, zzz500001), :%(zzz4300000, zzz4300001), ty_Integer) → new_compare9(new_sr(zzz500000, zzz4300001), new_sr(zzz4300000, zzz500001))
new_compare9(Integer(zzz500000), Integer(zzz4300000)) → new_primCmpInt(zzz500000, zzz4300000)
new_compare23(zzz500000, zzz4300000, False) → new_compare112(zzz500000, zzz4300000, new_ltEs10(zzz500000, zzz4300000))
new_asAs(False, zzz207) → False
new_esEs4(Left(zzz5000), Left(zzz4000), ty_@0, ccf) → new_esEs10(zzz5000, zzz4000)
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_esEs26(zzz5002, zzz4002, ty_Double) → new_esEs9(zzz5002, zzz4002)
new_ltEs10(LT, GT) → True
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_ltEs4(Just(zzz500000), Just(zzz4300000), app(ty_Ratio, bee)) → new_ltEs15(zzz500000, zzz4300000, bee)
new_esEs23(zzz500000, zzz4300000, app(app(app(ty_@3, ec), ed), ee)) → new_esEs6(zzz500000, zzz4300000, ec, ed, ee)
new_lt8(zzz500000, zzz4300000, ec, ed, ee) → new_esEs8(new_compare13(zzz500000, zzz4300000, ec, ed, ee), LT)
new_lt11(zzz5000, zzz43000, gb) → new_esEs8(new_compare28(zzz5000, zzz43000, gb), LT)
new_esEs26(zzz5002, zzz4002, app(ty_[], cha)) → new_esEs12(zzz5002, zzz4002, cha)
new_compare4(:(zzz500000, zzz500001), :(zzz4300000, zzz4300001), bdb) → new_primCompAux0(zzz500000, zzz4300000, new_compare4(zzz500001, zzz4300001, bdb), bdb)
new_compare16(Float(zzz500000, zzz500001), Float(zzz4300000, zzz4300001)) → new_compare8(new_sr0(zzz500000, zzz4300000), new_sr0(zzz500001, zzz4300001))
new_esEs26(zzz5002, zzz4002, app(ty_Maybe, che)) → new_esEs7(zzz5002, zzz4002, che)
new_esEs28(zzz5000, zzz4000, ty_Bool) → new_esEs14(zzz5000, zzz4000)
new_compare110(zzz500000, zzz4300000, True, ec, ed, ee) → LT
new_lt19(zzz500000, zzz4300000, app(app(ty_Either, hd), he)) → new_lt5(zzz500000, zzz4300000, hd, he)
new_ltEs18(zzz50000, zzz430000, ty_Bool) → new_ltEs14(zzz50000, zzz430000)
new_esEs28(zzz5000, zzz4000, ty_Integer) → new_esEs15(zzz5000, zzz4000)
new_esEs18(zzz5001, zzz4001, ty_Ordering) → new_esEs8(zzz5001, zzz4001)
new_esEs19(zzz5000, zzz4000, ty_Double) → new_esEs9(zzz5000, zzz4000)
new_lt20(zzz500001, zzz4300001, app(app(ty_@2, bbb), bbc)) → new_lt16(zzz500001, zzz4300001, bbb, bbc)
new_esEs5(@2(zzz5000, zzz5001), @2(zzz4000, zzz4001), bga, bgb) → new_asAs(new_esEs19(zzz5000, zzz4000, bga), new_esEs18(zzz5001, zzz4001, bgb))
new_compare26(zzz500000, zzz4300000, False) → new_compare19(zzz500000, zzz4300000, new_ltEs14(zzz500000, zzz4300000))
new_esEs28(zzz5000, zzz4000, app(app(ty_Either, dba), dbb)) → new_esEs4(zzz5000, zzz4000, dba, dbb)
new_esEs4(Right(zzz5000), Right(zzz4000), cea, app(ty_Maybe, cfb)) → new_esEs7(zzz5000, zzz4000, cfb)
new_esEs7(Just(zzz5000), Just(zzz4000), ty_@0) → new_esEs10(zzz5000, zzz4000)
new_ltEs18(zzz50000, zzz430000, ty_Char) → new_ltEs5(zzz50000, zzz430000)
new_esEs28(zzz5000, zzz4000, ty_Float) → new_esEs13(zzz5000, zzz4000)
new_lt13(zzz500000, zzz4300000, ty_Ordering) → new_lt9(zzz500000, zzz4300000)
new_esEs25(zzz500000, zzz4300000, app(app(app(ty_@3, bac), bad), bae)) → new_esEs6(zzz500000, zzz4300000, bac, bad, bae)
new_ltEs10(EQ, EQ) → True
new_ltEs18(zzz50000, zzz430000, app(app(ty_@2, eg), dg)) → new_ltEs13(zzz50000, zzz430000, eg, dg)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Int, ccf) → new_esEs17(zzz5000, zzz4000)
new_esEs23(zzz500000, zzz4300000, ty_Integer) → new_esEs15(zzz500000, zzz4300000)
new_ltEs10(LT, LT) → True
new_esEs14(True, True) → True
new_compare111(zzz200, zzz201, False, ccb) → GT
new_esEs27(zzz5001, zzz4001, ty_Bool) → new_esEs14(zzz5001, zzz4001)
new_esEs7(Just(zzz5000), Just(zzz4000), app(app(ty_Either, beg), beh)) → new_esEs4(zzz5000, zzz4000, beg, beh)
new_compare10(Char(zzz500000), Char(zzz4300000)) → new_primCmpNat0(zzz500000, zzz4300000)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Float, ccf) → new_esEs13(zzz5000, zzz4000)
new_lt13(zzz500000, zzz4300000, app(app(ty_@2, dh), ea)) → new_lt16(zzz500000, zzz4300000, dh, ea)
new_ltEs7(Left(zzz500000), Left(zzz4300000), app(app(ty_@2, bc), bd), bb) → new_ltEs13(zzz500000, zzz4300000, bc, bd)
new_esEs7(Just(zzz5000), Just(zzz4000), app(ty_Ratio, bfh)) → new_esEs16(zzz5000, zzz4000, bfh)
new_lt13(zzz500000, zzz4300000, app(ty_Maybe, eb)) → new_lt11(zzz500000, zzz4300000, eb)
new_ltEs20(zzz500002, zzz4300002, app(app(ty_Either, bca), bcb)) → new_ltEs7(zzz500002, zzz4300002, bca, bcb)
new_esEs18(zzz5001, zzz4001, ty_@0) → new_esEs10(zzz5001, zzz4001)
new_ltEs16(@3(zzz500000, zzz500001, zzz500002), @3(zzz4300000, zzz4300001, zzz4300002), bag, hf, hg) → new_pePe(new_lt19(zzz500000, zzz4300000, bag), new_asAs(new_esEs25(zzz500000, zzz4300000, bag), new_pePe(new_lt20(zzz500001, zzz4300001, hf), new_asAs(new_esEs24(zzz500001, zzz4300001, hf), new_ltEs20(zzz500002, zzz4300002, hg)))))
new_esEs4(Right(zzz5000), Right(zzz4000), cea, ty_Double) → new_esEs9(zzz5000, zzz4000)
new_ltEs14(True, False) → False
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_esEs20(zzz5000, zzz4000, ty_Int) → new_esEs17(zzz5000, zzz4000)
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_esEs25(zzz500000, zzz4300000, app(app(ty_@2, hh), baa)) → new_esEs5(zzz500000, zzz4300000, hh, baa)
new_ltEs20(zzz500002, zzz4300002, ty_Double) → new_ltEs8(zzz500002, zzz4300002)
new_ltEs7(Left(zzz500000), Left(zzz4300000), app(ty_Ratio, ccc), bb) → new_ltEs15(zzz500000, zzz4300000, ccc)
new_ltEs19(zzz500001, zzz4300001, app(app(app(ty_@3, ff), fg), fh)) → new_ltEs16(zzz500001, zzz4300001, ff, fg, fh)
new_ltEs20(zzz500002, zzz4300002, app(app(app(ty_@3, bcf), bcg), bch)) → new_ltEs16(zzz500002, zzz4300002, bcf, bcg, bch)
new_compare112(zzz500000, zzz4300000, False) → GT
new_ltEs10(EQ, LT) → False
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Float) → new_esEs13(zzz5000, zzz4000)
new_esEs14(False, False) → True
new_esEs7(Just(zzz5000), Just(zzz4000), app(app(ty_@2, bfa), bfb)) → new_esEs5(zzz5000, zzz4000, bfa, bfb)
new_lt20(zzz500001, zzz4300001, ty_Char) → new_lt12(zzz500001, zzz4300001)
new_lt9(zzz500000, zzz4300000) → new_esEs8(new_compare6(zzz500000, zzz4300000), LT)
new_ltEs10(GT, LT) → False
new_esEs18(zzz5001, zzz4001, ty_Bool) → new_esEs14(zzz5001, zzz4001)
new_esEs22(zzz5000, zzz4000, ty_Integer) → new_esEs15(zzz5000, zzz4000)
new_primPlusNat1(Zero, Zero) → Zero
new_compare30(zzz500000, zzz4300000, app(app(app(ty_@3, bdh), bea), beb)) → new_compare13(zzz500000, zzz4300000, bdh, bea, beb)
new_esEs19(zzz5000, zzz4000, ty_Integer) → new_esEs15(zzz5000, zzz4000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(ty_[], cdc), ccf) → new_esEs12(zzz5000, zzz4000, cdc)
new_esEs26(zzz5002, zzz4002, app(app(ty_Either, cge), cgf)) → new_esEs4(zzz5002, zzz4002, cge, cgf)
new_asAs(True, zzz207) → zzz207
new_esEs28(zzz5000, zzz4000, app(ty_[], dbe)) → new_esEs12(zzz5000, zzz4000, dbe)
new_esEs27(zzz5001, zzz4001, app(ty_[], dac)) → new_esEs12(zzz5001, zzz4001, dac)
new_esEs19(zzz5000, zzz4000, app(app(ty_Either, bhe), bhf)) → new_esEs4(zzz5000, zzz4000, bhe, bhf)
new_ltEs4(Just(zzz500000), Nothing, bed) → False
new_esEs20(zzz5000, zzz4000, ty_Double) → new_esEs9(zzz5000, zzz4000)
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_ltEs4(Just(zzz500000), Just(zzz4300000), app(ty_[], hc)) → new_ltEs17(zzz500000, zzz4300000, hc)
new_esEs4(Right(zzz5000), Left(zzz4000), cea, ccf) → False
new_esEs4(Left(zzz5000), Right(zzz4000), cea, ccf) → False
new_ltEs19(zzz500001, zzz4300001, ty_Float) → new_ltEs12(zzz500001, zzz4300001)
new_ltEs20(zzz500002, zzz4300002, app(ty_Maybe, bce)) → new_ltEs4(zzz500002, zzz4300002, bce)
new_esEs4(Left(zzz5000), Left(zzz4000), app(app(app(ty_@3, cdd), cde), cdf), ccf) → new_esEs6(zzz5000, zzz4000, cdd, cde, cdf)
new_ltEs19(zzz500001, zzz4300001, ty_Char) → new_ltEs5(zzz500001, zzz4300001)
new_fsEs(zzz210) → new_not(new_esEs8(zzz210, GT))
new_esEs19(zzz5000, zzz4000, ty_@0) → new_esEs10(zzz5000, zzz4000)
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Bool) → new_esEs14(zzz5000, zzz4000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Double, bb) → new_ltEs8(zzz500000, zzz4300000)
new_esEs24(zzz500001, zzz4300001, ty_Float) → new_esEs13(zzz500001, zzz4300001)
new_ltEs11(zzz50000, zzz430000) → new_fsEs(new_compare11(zzz50000, zzz430000))
new_lt20(zzz500001, zzz4300001, ty_Int) → new_lt14(zzz500001, zzz4300001)
new_esEs4(Right(zzz5000), Right(zzz4000), cea, ty_Float) → new_esEs13(zzz5000, zzz4000)
new_esEs19(zzz5000, zzz4000, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_ltEs20(zzz500002, zzz4300002, app(app(ty_@2, bcc), bcd)) → new_ltEs13(zzz500002, zzz4300002, bcc, bcd)
new_esEs27(zzz5001, zzz4001, ty_Char) → new_esEs11(zzz5001, zzz4001)
new_ltEs20(zzz500002, zzz4300002, ty_Int) → new_ltEs6(zzz500002, zzz4300002)
new_compare110(zzz500000, zzz4300000, False, ec, ed, ee) → GT
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Char) → new_ltEs5(zzz500000, zzz4300000)
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Char) → new_esEs11(zzz5000, zzz4000)
new_primCompAux00(zzz225, GT) → GT
new_ltEs20(zzz500002, zzz4300002, ty_Integer) → new_ltEs9(zzz500002, zzz4300002)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_ltEs7(Right(zzz500000), Right(zzz4300000), cb, app(ty_Maybe, cg)) → new_ltEs4(zzz500000, zzz4300000, cg)
new_lt19(zzz500000, zzz4300000, ty_Int) → new_lt14(zzz500000, zzz4300000)
new_ltEs4(Just(zzz500000), Just(zzz4300000), app(app(app(ty_@3, gh), ha), hb)) → new_ltEs16(zzz500000, zzz4300000, gh, ha, hb)
new_ltEs18(zzz50000, zzz430000, ty_Ordering) → new_ltEs10(zzz50000, zzz430000)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Integer) → new_ltEs9(zzz500000, zzz4300000)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_compare30(zzz500000, zzz4300000, ty_Ordering) → new_compare6(zzz500000, zzz4300000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), cb, ty_Float) → new_ltEs12(zzz500000, zzz4300000)
new_esEs27(zzz5001, zzz4001, ty_Integer) → new_esEs15(zzz5001, zzz4001)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_ltEs7(Right(zzz500000), Right(zzz4300000), cb, ty_Int) → new_ltEs6(zzz500000, zzz4300000)
new_not(True) → False

The set Q consists of the following terms:

new_compare23(x0, x1, True)
new_lt14(x0, x1)
new_ltEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_asAs(True, x0)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_compare19(x0, x1, True)
new_esEs26(x0, x1, ty_@0)
new_ltEs4(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs18(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_Ordering)
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs18(x0, x1, ty_Int)
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, app(ty_[], x2))
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_primPlusNat1(Zero, Succ(x0))
new_compare30(x0, x1, ty_@0)
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Ordering)
new_esEs9(Double(x0, x1), Double(x2, x3))
new_primMulNat0(Succ(x0), Zero)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_lt19(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1, ty_Double)
new_primMulInt(Neg(x0), Neg(x1))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, ty_Integer)
new_ltEs18(x0, x1, app(ty_[], x2))
new_ltEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs24(x0, x1, ty_@0)
new_compare30(x0, x1, app(app(ty_@2, x2), x3))
new_primPlusNat1(Succ(x0), Zero)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, ty_Int)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Left(x0), Left(x1), ty_Double, x2)
new_ltEs7(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs10(LT, LT)
new_ltEs15(x0, x1, x2)
new_esEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs7(Left(x0), Left(x1), ty_Double, x2)
new_esEs4(Right(x0), Right(x1), x2, ty_@0)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Bool)
new_esEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs27(x0, x1, ty_Int)
new_esEs18(x0, x1, ty_Char)
new_esEs24(x0, x1, ty_Char)
new_ltEs14(True, False)
new_ltEs14(False, True)
new_esEs25(x0, x1, ty_Double)
new_ltEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_pePe(False, x0)
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs19(x0, x1, ty_Char)
new_esEs25(x0, x1, ty_Char)
new_ltEs13(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs7(Just(x0), Just(x1), ty_Double)
new_esEs8(GT, GT)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_@0)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_lt9(x0, x1)
new_lt19(x0, x1, ty_Ordering)
new_lt13(x0, x1, app(app(ty_@2, x2), x3))
new_esEs11(Char(x0), Char(x1))
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs4(Left(x0), Left(x1), ty_Float, x2)
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs12(:(x0, x1), [], x2)
new_esEs8(LT, LT)
new_lt13(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_sr0(x0, x1)
new_compare6(x0, x1)
new_compare30(x0, x1, ty_Double)
new_esEs7(Just(x0), Just(x1), ty_Char)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare19(x0, x1, False)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_compare29(Nothing, Just(x0), False, x1)
new_esEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs26(x0, x1, ty_Double)
new_ltEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_esEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs17(x0, x1)
new_ltEs19(x0, x1, ty_Char)
new_primCompAux0(x0, x1, x2, x3)
new_compare110(x0, x1, True, x2, x3, x4)
new_esEs14(True, True)
new_compare26(x0, x1, True)
new_lt20(x0, x1, ty_Char)
new_esEs28(x0, x1, app(ty_[], x2))
new_ltEs4(Nothing, Just(x0), x1)
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_compare112(x0, x1, False)
new_esEs18(x0, x1, ty_Bool)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs20(x0, x1, ty_Float)
new_primEqNat0(Zero, Zero)
new_ltEs4(Just(x0), Just(x1), ty_Double)
new_esEs4(Right(x0), Right(x1), x2, ty_Double)
new_esEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_compare30(x0, x1, ty_Char)
new_ltEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs20(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Double)
new_lt19(x0, x1, ty_Bool)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Integer)
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_lt16(x0, x1, x2, x3)
new_compare17(x0, x1)
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_primPlusNat0(Zero, x0)
new_esEs12(:(x0, x1), :(x2, x3), x4)
new_ltEs20(x0, x1, ty_Int)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_primMulNat0(Zero, Zero)
new_primCmpNat0(Succ(x0), Zero)
new_compare16(Float(x0, x1), Float(x2, x3))
new_ltEs20(x0, x1, ty_Integer)
new_compare30(x0, x1, ty_Ordering)
new_ltEs7(Left(x0), Left(x1), ty_@0, x2)
new_esEs26(x0, x1, ty_Integer)
new_lt17(x0, x1, x2)
new_ltEs10(EQ, LT)
new_ltEs10(LT, EQ)
new_lt4(x0, x1)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_compare4([], :(x0, x1), x2)
new_esEs19(x0, x1, ty_Bool)
new_compare15(x0, x1, False, x2, x3)
new_compare113(x0, x1, False, x2, x3)
new_esEs28(x0, x1, ty_@0)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs4(Right(x0), Right(x1), x2, ty_Integer)
new_lt7(x0, x1)
new_esEs23(x0, x1, ty_Float)
new_esEs7(Nothing, Nothing, x0)
new_lt20(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_Double)
new_compare29(Nothing, Nothing, False, x0)
new_compare4(:(x0, x1), :(x2, x3), x4)
new_ltEs18(x0, x1, ty_@0)
new_compare13(x0, x1, x2, x3, x4)
new_esEs18(x0, x1, app(ty_Maybe, x2))
new_ltEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs23(x0, x1, ty_Char)
new_compare15(x0, x1, True, x2, x3)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, ty_Int)
new_ltEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_compare9(Integer(x0), Integer(x1))
new_ltEs20(x0, x1, ty_Ordering)
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_esEs24(x0, x1, ty_Bool)
new_esEs4(Right(x0), Right(x1), x2, ty_Bool)
new_esEs4(Left(x0), Left(x1), ty_Bool, x2)
new_esEs26(x0, x1, ty_Char)
new_lt13(x0, x1, app(ty_Maybe, x2))
new_compare30(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, app(ty_[], x2))
new_lt19(x0, x1, app(ty_Maybe, x2))
new_esEs20(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_fsEs(x0)
new_ltEs11(x0, x1)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_Double)
new_lt13(x0, x1, ty_@0)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs4(Right(x0), Right(x1), x2, ty_Int)
new_esEs7(Just(x0), Just(x1), ty_Int)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_compare26(x0, x1, False)
new_ltEs18(x0, x1, ty_Double)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs25(x0, x1, ty_Bool)
new_ltEs7(Left(x0), Left(x1), ty_Bool, x2)
new_esEs19(x0, x1, app(ty_[], x2))
new_primPlusNat1(Zero, Zero)
new_esEs28(x0, x1, ty_Float)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs19(x0, x1, app(ty_[], x2))
new_lt12(x0, x1)
new_compare7(:%(x0, x1), :%(x2, x3), ty_Int)
new_lt5(x0, x1, x2, x3)
new_esEs4(Right(x0), Right(x1), x2, ty_Char)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs4(Right(x0), Left(x1), x2, x3)
new_esEs4(Left(x0), Right(x1), x2, x3)
new_compare27(x0, x1, False, x2, x3)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_ltEs4(Just(x0), Just(x1), ty_Int)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_compare11(@0, @0)
new_primMulNat0(Zero, Succ(x0))
new_esEs26(x0, x1, ty_Bool)
new_asAs(False, x0)
new_esEs12([], :(x0, x1), x2)
new_ltEs4(Just(x0), Just(x1), ty_Bool)
new_ltEs8(x0, x1)
new_ltEs18(x0, x1, ty_Int)
new_ltEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Float)
new_esEs27(x0, x1, ty_Double)
new_ltEs19(x0, x1, ty_Ordering)
new_compare29(x0, x1, True, x2)
new_ltEs4(Just(x0), Just(x1), ty_Ordering)
new_esEs18(x0, x1, ty_Double)
new_ltEs10(GT, LT)
new_ltEs10(LT, GT)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, ty_Double)
new_esEs10(@0, @0)
new_lt13(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare14(Double(x0, x1), Double(x2, x3))
new_lt13(x0, x1, app(ty_Ratio, x2))
new_compare30(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_Integer)
new_ltEs18(x0, x1, ty_Float)
new_ltEs4(Just(x0), Nothing, x1)
new_ltEs7(Right(x0), Right(x1), x2, ty_Char)
new_compare8(x0, x1)
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs20(x0, x1, ty_Char)
new_esEs18(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Integer)
new_esEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_pePe(True, x0)
new_esEs27(x0, x1, ty_Float)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_primCompAux00(x0, EQ)
new_compare25(x0, x1, True, x2, x3)
new_lt19(x0, x1, ty_Float)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_primEqNat0(Succ(x0), Zero)
new_esEs28(x0, x1, ty_Int)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs16(:%(x0, x1), :%(x2, x3), x4)
new_esEs18(x0, x1, ty_Ordering)
new_esEs25(x0, x1, ty_Int)
new_ltEs4(Just(x0), Just(x1), ty_@0)
new_ltEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_compare23(x0, x1, False)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_ltEs7(Right(x0), Right(x1), x2, ty_Integer)
new_compare112(x0, x1, True)
new_esEs7(Nothing, Just(x0), x1)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs18(x0, x1, app(ty_[], x2))
new_esEs19(x0, x1, ty_Double)
new_esEs13(Float(x0, x1), Float(x2, x3))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Zero), Neg(Zero))
new_compare29(Just(x0), Nothing, False, x1)
new_lt13(x0, x1, ty_Char)
new_lt11(x0, x1, x2)
new_ltEs20(x0, x1, ty_Char)
new_esEs15(Integer(x0), Integer(x1))
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_ltEs12(x0, x1)
new_lt20(x0, x1, ty_@0)
new_compare25(x0, x1, False, x2, x3)
new_esEs27(x0, x1, ty_@0)
new_esEs14(True, False)
new_esEs14(False, True)
new_ltEs4(Just(x0), Just(x1), ty_Float)
new_lt18(x0, x1, x2)
new_compare24(x0, x1, False, x2, x3, x4)
new_ltEs6(x0, x1)
new_esEs22(x0, x1, ty_Int)
new_esEs20(x0, x1, ty_Double)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs9(x0, x1)
new_compare30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs19(x0, x1, ty_@0)
new_ltEs7(Right(x0), Right(x1), x2, ty_Bool)
new_compare30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Ordering)
new_esEs27(x0, x1, ty_Integer)
new_lt20(x0, x1, ty_Float)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_compare30(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Integer)
new_primCmpNat0(Succ(x0), Succ(x1))
new_lt19(x0, x1, ty_Char)
new_ltEs4(Nothing, Nothing, x0)
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_Integer)
new_esEs28(x0, x1, ty_Ordering)
new_compare4(:(x0, x1), [], x2)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_esEs21(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_ltEs7(Right(x0), Right(x1), x2, ty_Int)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs7(Right(x0), Right(x1), x2, ty_Double)
new_lt20(x0, x1, ty_Bool)
new_ltEs7(Left(x0), Left(x1), ty_Float, x2)
new_esEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_primPlusNat0(Succ(x0), x1)
new_compare113(x0, x1, True, x2, x3)
new_esEs20(x0, x1, ty_@0)
new_esEs24(x0, x1, app(ty_[], x2))
new_ltEs18(x0, x1, ty_Integer)
new_lt8(x0, x1, x2, x3, x4)
new_esEs7(Just(x0), Just(x1), ty_Float)
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_esEs19(x0, x1, ty_Float)
new_ltEs20(x0, x1, ty_Bool)
new_primCmpNat0(Zero, Zero)
new_esEs19(x0, x1, ty_Ordering)
new_lt13(x0, x1, ty_Bool)
new_esEs7(Just(x0), Nothing, x1)
new_ltEs19(x0, x1, ty_Float)
new_lt10(x0, x1)
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_compare28(x0, x1, x2)
new_compare7(:%(x0, x1), :%(x2, x3), ty_Integer)
new_ltEs16(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs18(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs7(Right(x0), Right(x1), x2, ty_Float)
new_esEs25(x0, x1, ty_Ordering)
new_esEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Float)
new_ltEs7(Right(x0), Right(x1), x2, ty_@0)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs10(GT, GT)
new_esEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs14(True, True)
new_esEs4(Left(x0), Left(x1), ty_Int, x2)
new_ltEs14(False, False)
new_esEs12([], [], x0)
new_compare4([], [], x0)
new_esEs24(x0, x1, ty_Ordering)
new_ltEs17(x0, x1, x2)
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_lt19(x0, x1, ty_@0)
new_esEs18(x0, x1, ty_Float)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, ty_Char)
new_not(True)
new_esEs19(x0, x1, ty_Int)
new_esEs7(Just(x0), Just(x1), ty_@0)
new_compare30(x0, x1, ty_Integer)
new_ltEs5(x0, x1)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Double)
new_esEs4(Left(x0), Left(x1), ty_Char, x2)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_compare12(x0, x1, x2, x3)
new_ltEs4(Just(x0), Just(x1), ty_Integer)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_ltEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_not(False)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs25(x0, x1, ty_Integer)
new_esEs4(Right(x0), Right(x1), x2, ty_Float)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_compare27(x0, x1, True, x2, x3)
new_primCompAux00(x0, LT)
new_lt6(x0, x1)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_ltEs10(EQ, GT)
new_ltEs10(GT, EQ)
new_ltEs19(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Float)
new_compare110(x0, x1, False, x2, x3, x4)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_lt19(x0, x1, app(ty_[], x2))
new_ltEs7(Left(x0), Left(x1), ty_Char, x2)
new_esEs27(x0, x1, app(ty_[], x2))
new_ltEs7(Right(x0), Left(x1), x2, x3)
new_ltEs7(Left(x0), Right(x1), x2, x3)
new_ltEs18(x0, x1, ty_Char)
new_lt13(x0, x1, app(ty_[], x2))
new_compare30(x0, x1, app(ty_[], x2))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs19(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_sr(Integer(x0), Integer(x1))
new_esEs27(x0, x1, ty_Char)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs20(x0, x1, ty_Bool)
new_esEs4(Left(x0), Left(x1), ty_@0, x2)
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs18(x0, x1, app(app(ty_@2, x2), x3))
new_compare24(x0, x1, True, x2, x3, x4)
new_ltEs4(Just(x0), Just(x1), ty_Char)
new_compare111(x0, x1, True, x2)
new_esEs18(x0, x1, ty_@0)
new_lt13(x0, x1, ty_Double)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_compare111(x0, x1, False, x2)
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, ty_Bool)
new_lt13(x0, x1, ty_Ordering)
new_ltEs18(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Ordering)
new_compare30(x0, x1, ty_Float)
new_lt13(x0, x1, ty_Integer)
new_compare30(x0, x1, app(ty_Maybe, x2))
new_esEs14(False, False)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_compare10(Char(x0), Char(x1))
new_esEs4(Left(x0), Left(x1), ty_Integer, x2)
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs24(x0, x1, ty_Integer)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Double)
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_ltEs20(x0, x1, ty_Float)
new_ltEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_lt13(x0, x1, ty_Int)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_lt13(x0, x1, ty_Float)
new_lt20(x0, x1, ty_Integer)
new_primCmpNat0(Zero, Succ(x0))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, ty_Int)
new_primCompAux00(x0, GT)
new_ltEs20(x0, x1, ty_@0)
new_lt15(x0, x1)
new_primEqNat0(Zero, Succ(x0))
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs7(Left(x0), Left(x1), ty_Int, x2)
new_compare18(x0, x1, x2, x3)
new_esEs27(x0, x1, ty_Bool)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare29(Just(x0), Just(x1), False, x2)
new_ltEs19(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_@0)
new_esEs18(x0, x1, ty_Integer)
new_ltEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs10(EQ, EQ)
new_esEs24(x0, x1, app(ty_Maybe, 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
                                    ↳ 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_intersectFM_C2Elt101(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, h, ba) → new_intersectFM_C2Elt102(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_lt11(Just(zzz542), zzz543, ba), h, ba)
new_intersectFM_C2Elt102(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, False, h, ba) → new_intersectFM_C2Elt10(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, new_gt(Just(zzz542), zzz543, ba), h, ba)
new_intersectFM_C2Elt10(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, zzz546, zzz547, True, h, ba) → new_intersectFM_C2Elt100(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz547, h, ba)
new_intersectFM_C2Elt102(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz543, zzz544, zzz545, Branch(zzz5460, zzz5461, zzz5462, zzz5463, zzz5464), zzz547, True, h, ba) → new_intersectFM_C2Elt101(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz5460, zzz5461, zzz5462, zzz5463, zzz5464, h, ba)
new_intersectFM_C2Elt100(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, Branch(zzz5460, zzz5461, zzz5462, zzz5463, zzz5464), h, ba) → new_intersectFM_C2Elt101(zzz537, zzz538, zzz539, zzz540, zzz541, zzz542, zzz5460, zzz5461, zzz5462, zzz5463, zzz5464, h, ba)

The TRS R consists of the following rules:

new_lt19(zzz500000, zzz4300000, ty_Float) → new_lt6(zzz500000, zzz4300000)
new_ltEs18(zzz50000, zzz430000, app(ty_Ratio, bef)) → new_ltEs15(zzz50000, zzz430000, bef)
new_esEs7(Just(zzz5000), Just(zzz4000), app(ty_Maybe, dh)) → new_esEs7(zzz5000, zzz4000, dh)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_esEs20(zzz5000, zzz4000, app(ty_Maybe, bba)) → new_esEs7(zzz5000, zzz4000, bba)
new_esEs12(:(zzz5000, zzz5001), :(zzz4000, zzz4001), hh) → new_asAs(new_esEs20(zzz5000, zzz4000, hh), new_esEs12(zzz5001, zzz4001, hh))
new_esEs7(Just(zzz5000), Just(zzz4000), app(ty_[], dd)) → new_esEs12(zzz5000, zzz4000, dd)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, ty_Ordering) → new_ltEs10(zzz500000, zzz4300000)
new_lt19(zzz500000, zzz4300000, app(app(app(ty_@3, cde), cdf), cdg)) → new_lt8(zzz500000, zzz4300000, cde, cdf, cdg)
new_ltEs18(zzz50000, zzz430000, app(app(app(ty_@3, beg), beh), bfa)) → new_ltEs16(zzz50000, zzz430000, beg, beh, bfa)
new_lt20(zzz500001, zzz4300001, app(ty_[], cfb)) → new_lt18(zzz500001, zzz4300001, cfb)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, ty_Char) → new_esEs11(zzz5000, zzz4000)
new_compare15(zzz500000, zzz4300000, True, hf, hg) → LT
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Bool, bfb) → new_esEs14(zzz5000, zzz4000)
new_ltEs18(zzz50000, zzz430000, app(ty_Maybe, bb)) → new_ltEs4(zzz50000, zzz430000, bb)
new_ltEs20(zzz500002, zzz4300002, ty_Ordering) → new_ltEs10(zzz500002, zzz4300002)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, app(app(app(ty_@3, bhc), bhd), bhe)) → new_esEs6(zzz5000, zzz4000, bhc, bhd, bhe)
new_lt13(zzz500000, zzz4300000, app(app(app(ty_@3, hc), hd), he)) → new_lt8(zzz500000, zzz4300000, hc, hd, he)
new_lt15(zzz500000, zzz4300000) → new_esEs8(new_compare14(zzz500000, zzz4300000), LT)
new_lt20(zzz500001, zzz4300001, app(app(app(ty_@3, ceg), ceh), cfa)) → new_lt8(zzz500001, zzz4300001, ceg, ceh, cfa)
new_esEs27(zzz5001, zzz4001, app(ty_Maybe, dbb)) → new_esEs7(zzz5001, zzz4001, dbb)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Ordering) → new_ltEs10(zzz500000, zzz4300000)
new_esEs23(zzz500000, zzz4300000, ty_Bool) → new_esEs14(zzz500000, zzz4300000)
new_compare27(zzz500000, zzz4300000, False, ha, hb) → new_compare113(zzz500000, zzz4300000, new_ltEs7(zzz500000, zzz4300000, ha, hb), ha, hb)
new_lt19(zzz500000, zzz4300000, ty_Double) → new_lt15(zzz500000, zzz4300000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), app(ty_Maybe, bcb), bbe) → new_ltEs4(zzz500000, zzz4300000, bcb)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, ty_@0) → new_ltEs11(zzz500000, zzz4300000)
new_ltEs20(zzz500002, zzz4300002, app(ty_Ratio, cfh)) → new_ltEs15(zzz500002, zzz4300002, cfh)
new_lt13(zzz500000, zzz4300000, app(ty_[], cbd)) → new_lt18(zzz500000, zzz4300000, cbd)
new_esEs26(zzz5002, zzz4002, ty_Float) → new_esEs13(zzz5002, zzz4002)
new_ltEs7(Left(zzz500000), Right(zzz4300000), bch, bbe) → True
new_primMulNat0(Zero, Zero) → Zero
new_esEs19(zzz5000, zzz4000, ty_Int) → new_esEs17(zzz5000, zzz4000)
new_sr(Integer(zzz43000000), Integer(zzz5000010)) → Integer(new_primMulInt(zzz43000000, zzz5000010))
new_ltEs20(zzz500002, zzz4300002, ty_Float) → new_ltEs12(zzz500002, zzz4300002)
new_ltEs20(zzz500002, zzz4300002, ty_@0) → new_ltEs11(zzz500002, zzz4300002)
new_esEs20(zzz5000, zzz4000, app(ty_Ratio, bbb)) → new_esEs16(zzz5000, zzz4000, bbb)
new_esEs18(zzz5001, zzz4001, ty_Double) → new_esEs9(zzz5001, zzz4001)
new_lt20(zzz500001, zzz4300001, ty_Float) → new_lt6(zzz500001, zzz4300001)
new_esEs23(zzz500000, zzz4300000, ty_Double) → new_esEs9(zzz500000, zzz4300000)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, app(ty_[], bhb)) → new_esEs12(zzz5000, zzz4000, bhb)
new_esEs24(zzz500001, zzz4300001, ty_Integer) → new_esEs15(zzz500001, zzz4300001)
new_ltEs14(False, True) → True
new_ltEs19(zzz500001, zzz4300001, ty_Integer) → new_ltEs9(zzz500001, zzz4300001)
new_ltEs4(Just(zzz500000), Just(zzz4300000), app(app(ty_@2, be), bf)) → new_ltEs13(zzz500000, zzz4300000, be, bf)
new_esEs20(zzz5000, zzz4000, app(app(ty_Either, baa), bab)) → new_esEs4(zzz5000, zzz4000, baa, bab)
new_esEs12([], [], hh) → True
new_ltEs19(zzz500001, zzz4300001, ty_Ordering) → new_ltEs10(zzz500001, zzz4300001)
new_esEs24(zzz500001, zzz4300001, app(app(ty_@2, cec), ced)) → new_esEs5(zzz500001, zzz4300001, cec, ced)
new_lt12(zzz500000, zzz4300000) → new_esEs8(new_compare10(zzz500000, zzz4300000), LT)
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Ordering, bbe) → new_ltEs10(zzz500000, zzz4300000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, app(ty_Ratio, bdf)) → new_ltEs15(zzz500000, zzz4300000, bdf)
new_esEs15(Integer(zzz5000), Integer(zzz4000)) → new_primEqInt(zzz5000, zzz4000)
new_ltEs10(EQ, GT) → True
new_ltEs19(zzz500001, zzz4300001, app(ty_Maybe, cca)) → new_ltEs4(zzz500001, zzz4300001, cca)
new_esEs21(zzz5001, zzz4001, ty_Int) → new_esEs17(zzz5001, zzz4001)
new_ltEs7(Left(zzz500000), Left(zzz4300000), app(app(app(ty_@3, bcd), bce), bcf), bbe) → new_ltEs16(zzz500000, zzz4300000, bcd, bce, bcf)
new_lt13(zzz500000, zzz4300000, ty_Char) → new_lt12(zzz500000, zzz4300000)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Ordering, bfb) → new_esEs8(zzz5000, zzz4000)
new_esEs24(zzz500001, zzz4300001, app(ty_[], cfb)) → new_esEs12(zzz500001, zzz4300001, cfb)
new_esEs25(zzz500000, zzz4300000, ty_Double) → new_esEs9(zzz500000, zzz4300000)
new_esEs25(zzz500000, zzz4300000, ty_Float) → new_esEs13(zzz500000, zzz4300000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, app(ty_[], beb)) → new_ltEs17(zzz500000, zzz4300000, beb)
new_pePe(False, zzz218) → zzz218
new_lt14(zzz5000, zzz43000) → new_esEs8(new_compare8(zzz5000, zzz43000), LT)
new_esEs25(zzz500000, zzz4300000, app(app(ty_Either, ccg), cch)) → new_esEs4(zzz500000, zzz4300000, ccg, cch)
new_esEs12(:(zzz5000, zzz5001), [], hh) → False
new_esEs12([], :(zzz4000, zzz4001), hh) → False
new_esEs25(zzz500000, zzz4300000, ty_Char) → new_esEs11(zzz500000, zzz4300000)
new_esEs25(zzz500000, zzz4300000, ty_Bool) → new_esEs14(zzz500000, zzz4300000)
new_lt19(zzz500000, zzz4300000, ty_Ordering) → new_lt9(zzz500000, zzz4300000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, app(app(ty_@2, bdc), bdd)) → new_ltEs13(zzz500000, zzz4300000, bdc, bdd)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, app(ty_Ratio, bhg)) → new_esEs16(zzz5000, zzz4000, bhg)
new_compare23(zzz500000, zzz4300000, True) → EQ
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Float, bbe) → new_ltEs12(zzz500000, zzz4300000)
new_lt19(zzz500000, zzz4300000, app(ty_Ratio, cdd)) → new_lt17(zzz500000, zzz4300000, cdd)
new_esEs24(zzz500001, zzz4300001, app(ty_Maybe, cee)) → new_esEs7(zzz500001, zzz4300001, cee)
new_ltEs4(Nothing, Just(zzz4300000), bb) → True
new_esEs23(zzz500000, zzz4300000, app(ty_Maybe, cbb)) → new_esEs7(zzz500000, zzz4300000, cbb)
new_compare30(zzz500000, zzz4300000, ty_Integer) → new_compare9(zzz500000, zzz4300000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(ty_Ratio, bgd), bfb) → new_esEs16(zzz5000, zzz4000, bgd)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, ty_Char) → new_ltEs5(zzz500000, zzz4300000)
new_compare13(zzz500000, zzz4300000, hc, hd, he) → new_compare24(zzz500000, zzz4300000, new_esEs6(zzz500000, zzz4300000, hc, hd, he), hc, hd, he)
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_lt4(zzz500000, zzz4300000) → new_esEs8(new_compare11(zzz500000, zzz4300000), LT)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, ty_Integer) → new_esEs15(zzz5000, zzz4000)
new_esEs20(zzz5000, zzz4000, app(app(ty_@2, bac), bad)) → new_esEs5(zzz5000, zzz4000, bac, bad)
new_esEs28(zzz5000, zzz4000, app(ty_Ratio, dce)) → new_esEs16(zzz5000, zzz4000, dce)
new_compare30(zzz500000, zzz4300000, app(ty_Ratio, cae)) → new_compare7(zzz500000, zzz4300000, cae)
new_compare19(zzz500000, zzz4300000, True) → LT
new_compare6(zzz500000, zzz4300000) → new_compare23(zzz500000, zzz4300000, new_esEs8(zzz500000, zzz4300000))
new_ltEs18(zzz50000, zzz430000, ty_@0) → new_ltEs11(zzz50000, zzz430000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_ltEs19(zzz500001, zzz4300001, app(ty_Ratio, ccb)) → new_ltEs15(zzz500001, zzz4300001, ccb)
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Int) → new_esEs17(zzz5000, zzz4000)
new_ltEs20(zzz500002, zzz4300002, ty_Bool) → new_ltEs14(zzz500002, zzz4300002)
new_esEs27(zzz5001, zzz4001, ty_@0) → new_esEs10(zzz5001, zzz4001)
new_ltEs12(zzz50000, zzz430000) → new_fsEs(new_compare16(zzz50000, zzz430000))
new_esEs8(LT, LT) → True
new_lt19(zzz500000, zzz4300000, app(app(ty_@2, cda), cdb)) → new_lt16(zzz500000, zzz4300000, cda, cdb)
new_esEs25(zzz500000, zzz4300000, ty_Ordering) → new_esEs8(zzz500000, zzz4300000)
new_esEs19(zzz5000, zzz4000, app(ty_Maybe, gg)) → new_esEs7(zzz5000, zzz4000, gg)
new_esEs20(zzz5000, zzz4000, app(app(app(ty_@3, baf), bag), bah)) → new_esEs6(zzz5000, zzz4000, baf, bag, bah)
new_esEs18(zzz5001, zzz4001, app(ty_Ratio, ff)) → new_esEs16(zzz5001, zzz4001, ff)
new_pePe(True, zzz218) → True
new_primEqNat0(Zero, Zero) → True
new_lt20(zzz500001, zzz4300001, app(app(ty_Either, cea), ceb)) → new_lt5(zzz500001, zzz4300001, cea, ceb)
new_compare26(zzz500000, zzz4300000, True) → EQ
new_lt20(zzz500001, zzz4300001, ty_Bool) → new_lt7(zzz500001, zzz4300001)
new_esEs13(Float(zzz5000, zzz5001), Float(zzz4000, zzz4001)) → new_esEs17(new_sr0(zzz5000, zzz4000), new_sr0(zzz5001, zzz4001))
new_esEs19(zzz5000, zzz4000, app(ty_[], gc)) → new_esEs12(zzz5000, zzz4000, gc)
new_compare29(Nothing, Just(zzz430000), False, gg) → LT
new_esEs19(zzz5000, zzz4000, ty_Float) → new_esEs13(zzz5000, zzz4000)
new_compare30(zzz500000, zzz4300000, app(ty_Maybe, cad)) → new_compare28(zzz500000, zzz4300000, cad)
new_esEs18(zzz5001, zzz4001, app(app(ty_@2, ef), eg)) → new_esEs5(zzz5001, zzz4001, ef, eg)
new_esEs25(zzz500000, zzz4300000, ty_Int) → new_esEs17(zzz500000, zzz4300000)
new_esEs9(Double(zzz5000, zzz5001), Double(zzz4000, zzz4001)) → new_esEs17(new_sr0(zzz5000, zzz4000), new_sr0(zzz5001, zzz4001))
new_esEs26(zzz5002, zzz4002, ty_Ordering) → new_esEs8(zzz5002, zzz4002)
new_esEs8(GT, GT) → True
new_lt20(zzz500001, zzz4300001, app(ty_Maybe, cee)) → new_lt11(zzz500001, zzz4300001, cee)
new_esEs18(zzz5001, zzz4001, app(app(app(ty_@3, fa), fb), fc)) → new_esEs6(zzz5001, zzz4001, fa, fb, fc)
new_esEs25(zzz500000, zzz4300000, ty_@0) → new_esEs10(zzz500000, zzz4300000)
new_compare4([], [], ce) → EQ
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_lt19(zzz500000, zzz4300000, ty_@0) → new_lt4(zzz500000, zzz4300000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(app(ty_@2, bfe), bff), bfb) → new_esEs5(zzz5000, zzz4000, bfe, bff)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, ty_Integer) → new_ltEs9(zzz500000, zzz4300000)
new_esEs26(zzz5002, zzz4002, app(app(app(ty_@3, che), chf), chg)) → new_esEs6(zzz5002, zzz4002, che, chf, chg)
new_compare18(zzz500000, zzz4300000, hf, hg) → new_compare25(zzz500000, zzz4300000, new_esEs5(zzz500000, zzz4300000, hf, hg), hf, hg)
new_ltEs17(zzz50000, zzz430000, ce) → new_fsEs(new_compare4(zzz50000, zzz430000, ce))
new_esEs8(GT, LT) → False
new_esEs8(LT, GT) → False
new_compare30(zzz500000, zzz4300000, app(ty_[], cba)) → new_compare4(zzz500000, zzz4300000, cba)
new_compare30(zzz500000, zzz4300000, ty_Double) → new_compare14(zzz500000, zzz4300000)
new_ltEs13(@2(zzz500000, zzz500001), @2(zzz4300000, zzz4300001), bed, bee) → new_pePe(new_lt13(zzz500000, zzz4300000, bed), new_asAs(new_esEs23(zzz500000, zzz4300000, bed), new_ltEs19(zzz500001, zzz4300001, bee)))
new_esEs4(Right(zzz5000), Right(zzz4000), bge, app(app(ty_Either, bgf), bgg)) → new_esEs4(zzz5000, zzz4000, bgf, bgg)
new_esEs25(zzz500000, zzz4300000, app(ty_[], cdh)) → new_esEs12(zzz500000, zzz4300000, cdh)
new_compare24(zzz500000, zzz4300000, True, hc, hd, he) → EQ
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Int, bbe) → new_ltEs6(zzz500000, zzz4300000)
new_lt20(zzz500001, zzz4300001, ty_Ordering) → new_lt9(zzz500001, zzz4300001)
new_primEqInt(Neg(Succ(zzz50000)), Neg(Succ(zzz40000))) → new_primEqNat0(zzz50000, zzz40000)
new_esEs20(zzz5000, zzz4000, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_compare113(zzz500000, zzz4300000, True, ha, hb) → LT
new_esEs23(zzz500000, zzz4300000, ty_Ordering) → new_esEs8(zzz500000, zzz4300000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(app(ty_Either, bfc), bfd), bfb) → new_esEs4(zzz5000, zzz4000, bfc, bfd)
new_ltEs18(zzz50000, zzz430000, app(app(ty_Either, bch), bbe)) → new_ltEs7(zzz50000, zzz430000, bch, bbe)
new_esEs24(zzz500001, zzz4300001, ty_Bool) → new_esEs14(zzz500001, zzz4300001)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_lt19(zzz500000, zzz4300000, ty_Bool) → new_lt7(zzz500000, zzz4300000)
new_lt19(zzz500000, zzz4300000, ty_Integer) → new_lt10(zzz500000, zzz4300000)
new_ltEs4(Nothing, Nothing, bb) → True
new_lt13(zzz500000, zzz4300000, ty_Float) → new_lt6(zzz500000, zzz4300000)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_@0) → new_ltEs11(zzz500000, zzz4300000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Char, bbe) → new_ltEs5(zzz500000, zzz4300000)
new_lt13(zzz500000, zzz4300000, ty_Int) → new_lt14(zzz500000, zzz4300000)
new_lt6(zzz500000, zzz4300000) → new_esEs8(new_compare16(zzz500000, zzz4300000), LT)
new_compare29(Just(zzz50000), Nothing, False, gg) → GT
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_ltEs7(Right(zzz500000), Left(zzz4300000), bch, bbe) → False
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_esEs24(zzz500001, zzz4300001, app(app(app(ty_@3, ceg), ceh), cfa)) → new_esEs6(zzz500001, zzz4300001, ceg, ceh, cfa)
new_esEs23(zzz500000, zzz4300000, ty_Char) → new_esEs11(zzz500000, zzz4300000)
new_lt13(zzz500000, zzz4300000, ty_Bool) → new_lt7(zzz500000, zzz4300000)
new_esEs19(zzz5000, zzz4000, ty_Bool) → new_esEs14(zzz5000, zzz4000)
new_esEs20(zzz5000, zzz4000, ty_Float) → new_esEs13(zzz5000, zzz4000)
new_compare14(Double(zzz500000, zzz500001), Double(zzz4300000, zzz4300001)) → new_compare8(new_sr0(zzz500000, zzz4300000), new_sr0(zzz500001, zzz4300001))
new_compare12(zzz500000, zzz4300000, ha, hb) → new_compare27(zzz500000, zzz4300000, new_esEs4(zzz500000, zzz4300000, ha, hb), ha, hb)
new_compare8(zzz500, zzz4300) → new_primCmpInt(zzz500, zzz4300)
new_lt19(zzz500000, zzz4300000, ty_Char) → new_lt12(zzz500000, zzz4300000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, app(app(app(ty_@3, bdg), bdh), bea)) → new_ltEs16(zzz500000, zzz4300000, bdg, bdh, bea)
new_primEqInt(Neg(Succ(zzz50000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(zzz40000))) → False
new_compare17(zzz500000, zzz4300000) → new_compare26(zzz500000, zzz4300000, new_esEs14(zzz500000, zzz4300000))
new_esEs8(EQ, EQ) → True
new_lt13(zzz500000, zzz4300000, ty_Double) → new_lt15(zzz500000, zzz4300000)
new_compare111(zzz200, zzz201, True, bbd) → LT
new_esEs20(zzz5000, zzz4000, ty_@0) → new_esEs10(zzz5000, zzz4000)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Char, bfb) → new_esEs11(zzz5000, zzz4000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_ltEs19(zzz500001, zzz4300001, ty_@0) → new_ltEs11(zzz500001, zzz4300001)
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_esEs18(zzz5001, zzz4001, ty_Char) → new_esEs11(zzz5001, zzz4001)
new_compare112(zzz500000, zzz4300000, True) → LT
new_esEs19(zzz5000, zzz4000, ty_Char) → new_esEs11(zzz5000, zzz4000)
new_compare30(zzz500000, zzz4300000, app(app(ty_Either, bhh), caa)) → new_compare12(zzz500000, zzz4300000, bhh, caa)
new_primEqInt(Pos(Succ(zzz50000)), Pos(Succ(zzz40000))) → new_primEqNat0(zzz50000, zzz40000)
new_ltEs18(zzz50000, zzz430000, ty_Double) → new_ltEs8(zzz50000, zzz430000)
new_compare27(zzz500000, zzz4300000, True, ha, hb) → EQ
new_lt10(zzz500000, zzz4300000) → new_esEs8(new_compare9(zzz500000, zzz4300000), LT)
new_esEs24(zzz500001, zzz4300001, app(ty_Ratio, cef)) → new_esEs16(zzz500001, zzz4300001, cef)
new_ltEs19(zzz500001, zzz4300001, ty_Bool) → new_ltEs14(zzz500001, zzz4300001)
new_esEs14(False, True) → False
new_esEs14(True, False) → False
new_esEs23(zzz500000, zzz4300000, app(ty_[], cbd)) → new_esEs12(zzz500000, zzz4300000, cbd)
new_ltEs4(Just(zzz500000), Just(zzz4300000), app(app(ty_Either, bc), bd)) → new_ltEs7(zzz500000, zzz4300000, bc, bd)
new_esEs26(zzz5002, zzz4002, ty_Integer) → new_esEs15(zzz5002, zzz4002)
new_ltEs10(GT, EQ) → False
new_lt17(zzz500000, zzz4300000, cbc) → new_esEs8(new_compare7(zzz500000, zzz4300000, cbc), LT)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Double) → new_ltEs8(zzz500000, zzz4300000)
new_esEs24(zzz500001, zzz4300001, ty_Int) → new_esEs17(zzz500001, zzz4300001)
new_primEqNat0(Succ(zzz50000), Succ(zzz40000)) → new_primEqNat0(zzz50000, zzz40000)
new_ltEs20(zzz500002, zzz4300002, app(ty_[], cgd)) → new_ltEs17(zzz500002, zzz4300002, cgd)
new_esEs27(zzz5001, zzz4001, ty_Ordering) → new_esEs8(zzz5001, zzz4001)
new_ltEs14(False, False) → True
new_compare11(@0, @0) → EQ
new_lt7(zzz500000, zzz4300000) → new_esEs8(new_compare17(zzz500000, zzz4300000), LT)
new_esEs19(zzz5000, zzz4000, app(app(app(ty_@3, gd), ge), gf)) → new_esEs6(zzz5000, zzz4000, gd, ge, gf)
new_ltEs9(zzz50000, zzz430000) → new_fsEs(new_compare9(zzz50000, zzz430000))
new_ltEs20(zzz500002, zzz4300002, ty_Char) → new_ltEs5(zzz500002, zzz4300002)
new_compare113(zzz500000, zzz4300000, False, ha, hb) → GT
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, ty_Bool) → new_ltEs14(zzz500000, zzz4300000)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Int) → new_ltEs6(zzz500000, zzz4300000)
new_primCompAux00(zzz225, LT) → LT
new_lt20(zzz500001, zzz4300001, ty_@0) → new_lt4(zzz500001, zzz4300001)
new_ltEs19(zzz500001, zzz4300001, app(ty_[], ccf)) → new_ltEs17(zzz500001, zzz4300001, ccf)
new_ltEs19(zzz500001, zzz4300001, app(app(ty_Either, cbe), cbf)) → new_ltEs7(zzz500001, zzz4300001, cbe, cbf)
new_compare7(:%(zzz500000, zzz500001), :%(zzz4300000, zzz4300001), ty_Int) → new_compare8(new_sr0(zzz500000, zzz4300001), new_sr0(zzz4300000, zzz500001))
new_esEs24(zzz500001, zzz4300001, ty_Ordering) → new_esEs8(zzz500001, zzz4300001)
new_ltEs8(zzz50000, zzz430000) → new_fsEs(new_compare14(zzz50000, zzz430000))
new_esEs7(Nothing, Nothing, cf) → True
new_esEs28(zzz5000, zzz4000, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_esEs8(EQ, LT) → False
new_esEs8(LT, EQ) → False
new_esEs18(zzz5001, zzz4001, app(ty_Maybe, fd)) → new_esEs7(zzz5001, zzz4001, fd)
new_primEqInt(Pos(Succ(zzz50000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(zzz40000))) → False
new_lt20(zzz500001, zzz4300001, app(ty_Ratio, cef)) → new_lt17(zzz500001, zzz4300001, cef)
new_compare30(zzz500000, zzz4300000, ty_Int) → new_compare8(zzz500000, zzz4300000)
new_compare24(zzz500000, zzz4300000, False, hc, hd, he) → new_compare110(zzz500000, zzz4300000, new_ltEs16(zzz500000, zzz4300000, hc, hd, he), hc, hd, he)
new_esEs24(zzz500001, zzz4300001, ty_@0) → new_esEs10(zzz500001, zzz4300001)
new_primCmpNat0(Zero, Zero) → EQ
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Integer, bbe) → new_ltEs9(zzz500000, zzz4300000)
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_esEs23(zzz500000, zzz4300000, app(app(ty_@2, hf), hg)) → new_esEs5(zzz500000, zzz4300000, hf, hg)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, ty_@0) → new_esEs10(zzz5000, zzz4000)
new_ltEs10(LT, EQ) → True
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_compare19(zzz500000, zzz4300000, False) → GT
new_esEs27(zzz5001, zzz4001, ty_Double) → new_esEs9(zzz5001, zzz4001)
new_ltEs15(zzz50000, zzz430000, bef) → new_fsEs(new_compare7(zzz50000, zzz430000, bef))
new_esEs23(zzz500000, zzz4300000, ty_Float) → new_esEs13(zzz500000, zzz4300000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Integer) → new_esEs15(zzz5000, zzz4000)
new_compare29(Just(zzz50000), Just(zzz430000), False, gg) → new_compare111(zzz50000, zzz430000, new_ltEs18(zzz50000, zzz430000, gg), gg)
new_primEqInt(Pos(Succ(zzz50000)), Neg(zzz4000)) → False
new_primEqInt(Neg(Succ(zzz50000)), Pos(zzz4000)) → False
new_lt13(zzz500000, zzz4300000, app(ty_Ratio, cbc)) → new_lt17(zzz500000, zzz4300000, cbc)
new_esEs7(Nothing, Just(zzz4000), cf) → False
new_esEs7(Just(zzz5000), Nothing, cf) → False
new_esEs18(zzz5001, zzz4001, app(ty_[], eh)) → new_esEs12(zzz5001, zzz4001, eh)
new_esEs28(zzz5000, zzz4000, ty_Char) → new_esEs11(zzz5000, zzz4000)
new_ltEs10(GT, GT) → True
new_esEs26(zzz5002, zzz4002, app(ty_Ratio, daa)) → new_esEs16(zzz5002, zzz4002, daa)
new_esEs26(zzz5002, zzz4002, ty_Int) → new_esEs17(zzz5002, zzz4002)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, ty_Bool) → new_esEs14(zzz5000, zzz4000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_@0, bbe) → new_ltEs11(zzz500000, zzz4300000)
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primEqInt(Pos(Zero), Neg(Succ(zzz40000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(zzz40000))) → False
new_ltEs6(zzz50000, zzz430000) → new_fsEs(new_compare8(zzz50000, zzz430000))
new_esEs20(zzz5000, zzz4000, app(ty_[], bae)) → new_esEs12(zzz5000, zzz4000, bae)
new_esEs21(zzz5001, zzz4001, ty_Integer) → new_esEs15(zzz5001, zzz4001)
new_compare30(zzz500000, zzz4300000, app(app(ty_@2, cab), cac)) → new_compare18(zzz500000, zzz4300000, cab, cac)
new_primCompAux00(zzz225, EQ) → zzz225
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Double, bfb) → new_esEs9(zzz5000, zzz4000)
new_gt(zzz440, zzz4440, bec) → new_esEs8(new_compare28(zzz440, zzz4440, bec), GT)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Integer, bfb) → new_esEs15(zzz5000, zzz4000)
new_esEs18(zzz5001, zzz4001, ty_Int) → new_esEs17(zzz5001, zzz4001)
new_lt16(zzz500000, zzz4300000, hf, hg) → new_esEs8(new_compare18(zzz500000, zzz4300000, hf, hg), LT)
new_esEs8(GT, EQ) → False
new_esEs8(EQ, GT) → False
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Double) → new_esEs9(zzz5000, zzz4000)
new_esEs26(zzz5002, zzz4002, ty_Char) → new_esEs11(zzz5002, zzz4002)
new_esEs27(zzz5001, zzz4001, app(ty_Ratio, dbc)) → new_esEs16(zzz5001, zzz4001, dbc)
new_esEs26(zzz5002, zzz4002, app(app(ty_@2, chb), chc)) → new_esEs5(zzz5002, zzz4002, chb, chc)
new_ltEs19(zzz500001, zzz4300001, app(app(ty_@2, cbg), cbh)) → new_ltEs13(zzz500001, zzz4300001, cbg, cbh)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Bool) → new_ltEs14(zzz500000, zzz4300000)
new_not(False) → True
new_esEs24(zzz500001, zzz4300001, ty_Double) → new_esEs9(zzz500001, zzz4300001)
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_ltEs5(zzz50000, zzz430000) → new_fsEs(new_compare10(zzz50000, zzz430000))
new_esEs25(zzz500000, zzz4300000, ty_Integer) → new_esEs15(zzz500000, zzz4300000)
new_esEs26(zzz5002, zzz4002, ty_Bool) → new_esEs14(zzz5002, zzz4002)
new_ltEs19(zzz500001, zzz4300001, ty_Int) → new_ltEs6(zzz500001, zzz4300001)
new_esEs25(zzz500000, zzz4300000, app(ty_Ratio, cdd)) → new_esEs16(zzz500000, zzz4300000, cdd)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, ty_Int) → new_esEs17(zzz5000, zzz4000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Bool, bbe) → new_ltEs14(zzz500000, zzz4300000)
new_esEs28(zzz5000, zzz4000, app(app(ty_@2, dbf), dbg)) → new_esEs5(zzz5000, zzz4000, dbf, dbg)
new_esEs23(zzz500000, zzz4300000, ty_@0) → new_esEs10(zzz500000, zzz4300000)
new_compare30(zzz500000, zzz4300000, ty_@0) → new_compare11(zzz500000, zzz4300000)
new_esEs18(zzz5001, zzz4001, app(app(ty_Either, ed), ee)) → new_esEs4(zzz5001, zzz4001, ed, ee)
new_lt18(zzz500000, zzz4300000, cbd) → new_esEs8(new_compare4(zzz500000, zzz4300000, cbd), LT)
new_ltEs18(zzz50000, zzz430000, ty_Int) → new_ltEs6(zzz50000, zzz430000)
new_esEs22(zzz5000, zzz4000, ty_Int) → new_esEs17(zzz5000, zzz4000)
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_esEs6(@3(zzz5000, zzz5001, zzz5002), @3(zzz4000, zzz4001, zzz4002), cge, cgf, cgg) → new_asAs(new_esEs28(zzz5000, zzz4000, cge), new_asAs(new_esEs27(zzz5001, zzz4001, cgf), new_esEs26(zzz5002, zzz4002, cgg)))
new_esEs28(zzz5000, zzz4000, app(ty_Maybe, dcd)) → new_esEs7(zzz5000, zzz4000, dcd)
new_esEs28(zzz5000, zzz4000, ty_Double) → new_esEs9(zzz5000, zzz4000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, ty_Double) → new_ltEs8(zzz500000, zzz4300000)
new_lt20(zzz500001, zzz4300001, ty_Double) → new_lt15(zzz500001, zzz4300001)
new_lt20(zzz500001, zzz4300001, ty_Integer) → new_lt10(zzz500001, zzz4300001)
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_esEs26(zzz5002, zzz4002, ty_@0) → new_esEs10(zzz5002, zzz4002)
new_esEs18(zzz5001, zzz4001, ty_Float) → new_esEs13(zzz5001, zzz4001)
new_compare25(zzz500000, zzz4300000, False, hf, hg) → new_compare15(zzz500000, zzz4300000, new_ltEs13(zzz500000, zzz4300000, hf, hg), hf, hg)
new_esEs23(zzz500000, zzz4300000, app(app(ty_Either, ha), hb)) → new_esEs4(zzz500000, zzz4300000, ha, hb)
new_esEs20(zzz5000, zzz4000, ty_Char) → new_esEs11(zzz5000, zzz4000)
new_lt19(zzz500000, zzz4300000, app(ty_Maybe, cdc)) → new_lt11(zzz500000, zzz4300000, cdc)
new_esEs4(Left(zzz5000), Left(zzz4000), app(ty_Maybe, bgc), bfb) → new_esEs7(zzz5000, zzz4000, bgc)
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_esEs20(zzz5000, zzz4000, ty_Integer) → new_esEs15(zzz5000, zzz4000)
new_primEqNat0(Zero, Succ(zzz40000)) → False
new_primEqNat0(Succ(zzz50000), Zero) → False
new_esEs18(zzz5001, zzz4001, ty_Integer) → new_esEs15(zzz5001, zzz4001)
new_esEs17(zzz500, zzz400) → new_primEqInt(zzz500, zzz400)
new_lt5(zzz500000, zzz4300000, ha, hb) → new_esEs8(new_compare12(zzz500000, zzz4300000, ha, hb), LT)
new_compare25(zzz500000, zzz4300000, True, hf, hg) → EQ
new_esEs20(zzz5000, zzz4000, ty_Bool) → new_esEs14(zzz5000, zzz4000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), app(app(ty_Either, bbf), bbg), bbe) → new_ltEs7(zzz500000, zzz4300000, bbf, bbg)
new_ltEs14(True, True) → True
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs24(zzz500001, zzz4300001, app(app(ty_Either, cea), ceb)) → new_esEs4(zzz500001, zzz4300001, cea, ceb)
new_esEs28(zzz5000, zzz4000, app(app(app(ty_@3, dca), dcb), dcc)) → new_esEs6(zzz5000, zzz4000, dca, dcb, dcc)
new_compare30(zzz500000, zzz4300000, ty_Bool) → new_compare17(zzz500000, zzz4300000)
new_esEs27(zzz5001, zzz4001, app(app(ty_Either, dab), dac)) → new_esEs4(zzz5001, zzz4001, dab, dac)
new_esEs27(zzz5001, zzz4001, app(app(app(ty_@3, dag), dah), dba)) → new_esEs6(zzz5001, zzz4001, dag, dah, dba)
new_compare4(:(zzz500000, zzz500001), [], ce) → GT
new_ltEs18(zzz50000, zzz430000, app(ty_[], ce)) → new_ltEs17(zzz50000, zzz430000, ce)
new_esEs27(zzz5001, zzz4001, app(app(ty_@2, dad), dae)) → new_esEs5(zzz5001, zzz4001, dad, dae)
new_esEs27(zzz5001, zzz4001, ty_Int) → new_esEs17(zzz5001, zzz4001)
new_esEs23(zzz500000, zzz4300000, ty_Int) → new_esEs17(zzz500000, zzz4300000)
new_lt13(zzz500000, zzz4300000, ty_@0) → new_lt4(zzz500000, zzz4300000)
new_compare30(zzz500000, zzz4300000, ty_Char) → new_compare10(zzz500000, zzz4300000)
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_compare4([], :(zzz4300000, zzz4300001), ce) → LT
new_sr0(zzz5000, zzz4000) → new_primMulInt(zzz5000, zzz4000)
new_lt19(zzz500000, zzz4300000, app(ty_[], cdh)) → new_lt18(zzz500000, zzz4300000, cdh)
new_compare15(zzz500000, zzz4300000, False, hf, hg) → GT
new_ltEs18(zzz50000, zzz430000, ty_Float) → new_ltEs12(zzz50000, zzz430000)
new_ltEs18(zzz50000, zzz430000, ty_Integer) → new_ltEs9(zzz50000, zzz430000)
new_ltEs19(zzz500001, zzz4300001, ty_Double) → new_ltEs8(zzz500001, zzz4300001)
new_compare30(zzz500000, zzz4300000, ty_Float) → new_compare16(zzz500000, zzz4300000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), app(ty_[], bcg), bbe) → new_ltEs17(zzz500000, zzz4300000, bcg)
new_esEs11(Char(zzz5000), Char(zzz4000)) → new_primEqNat0(zzz5000, zzz4000)
new_esEs7(Just(zzz5000), Just(zzz4000), app(app(app(ty_@3, de), df), dg)) → new_esEs6(zzz5000, zzz4000, de, df, dg)
new_esEs25(zzz500000, zzz4300000, app(ty_Maybe, cdc)) → new_esEs7(zzz500000, zzz4300000, cdc)
new_compare29(Nothing, Nothing, False, gg) → LT
new_esEs23(zzz500000, zzz4300000, app(ty_Ratio, cbc)) → new_esEs16(zzz500000, zzz4300000, cbc)
new_lt13(zzz500000, zzz4300000, app(app(ty_Either, ha), hb)) → new_lt5(zzz500000, zzz4300000, ha, hb)
new_esEs16(:%(zzz5000, zzz5001), :%(zzz4000, zzz4001), bbc) → new_asAs(new_esEs22(zzz5000, zzz4000, bbc), new_esEs21(zzz5001, zzz4001, bbc))
new_ltEs4(Just(zzz500000), Just(zzz4300000), app(ty_Maybe, bg)) → new_ltEs4(zzz500000, zzz4300000, bg)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Float) → new_ltEs12(zzz500000, zzz4300000)
new_primCompAux0(zzz500000, zzz4300000, zzz220, ce) → new_primCompAux00(zzz220, new_compare30(zzz500000, zzz4300000, ce))
new_esEs19(zzz5000, zzz4000, app(app(ty_@2, ga), gb)) → new_esEs5(zzz5000, zzz4000, ga, gb)
new_esEs19(zzz5000, zzz4000, app(ty_Ratio, gh)) → new_esEs16(zzz5000, zzz4000, gh)
new_esEs10(@0, @0) → True
new_compare29(zzz5000, zzz43000, True, gg) → EQ
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs27(zzz5001, zzz4001, ty_Float) → new_esEs13(zzz5001, zzz4001)
new_lt13(zzz500000, zzz4300000, ty_Integer) → new_lt10(zzz500000, zzz4300000)
new_compare28(zzz5000, zzz43000, gg) → new_compare29(zzz5000, zzz43000, new_esEs7(zzz5000, zzz43000, gg), gg)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, app(app(ty_@2, bgh), bha)) → new_esEs5(zzz5000, zzz4000, bgh, bha)
new_esEs24(zzz500001, zzz4300001, ty_Char) → new_esEs11(zzz500001, zzz4300001)
new_esEs28(zzz5000, zzz4000, ty_@0) → new_esEs10(zzz5000, zzz4000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, app(app(ty_Either, bda), bdb)) → new_ltEs7(zzz500000, zzz4300000, bda, bdb)
new_esEs28(zzz5000, zzz4000, ty_Int) → new_esEs17(zzz5000, zzz4000)
new_compare7(:%(zzz500000, zzz500001), :%(zzz4300000, zzz4300001), ty_Integer) → new_compare9(new_sr(zzz500000, zzz4300001), new_sr(zzz4300000, zzz500001))
new_compare9(Integer(zzz500000), Integer(zzz4300000)) → new_primCmpInt(zzz500000, zzz4300000)
new_compare23(zzz500000, zzz4300000, False) → new_compare112(zzz500000, zzz4300000, new_ltEs10(zzz500000, zzz4300000))
new_asAs(False, zzz207) → False
new_esEs4(Left(zzz5000), Left(zzz4000), ty_@0, bfb) → new_esEs10(zzz5000, zzz4000)
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_esEs26(zzz5002, zzz4002, ty_Double) → new_esEs9(zzz5002, zzz4002)
new_ltEs10(LT, GT) → True
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_ltEs4(Just(zzz500000), Just(zzz4300000), app(ty_Ratio, bh)) → new_ltEs15(zzz500000, zzz4300000, bh)
new_esEs23(zzz500000, zzz4300000, app(app(app(ty_@3, hc), hd), he)) → new_esEs6(zzz500000, zzz4300000, hc, hd, he)
new_lt8(zzz500000, zzz4300000, hc, hd, he) → new_esEs8(new_compare13(zzz500000, zzz4300000, hc, hd, he), LT)
new_lt11(zzz5000, zzz43000, gg) → new_esEs8(new_compare28(zzz5000, zzz43000, gg), LT)
new_esEs26(zzz5002, zzz4002, app(ty_[], chd)) → new_esEs12(zzz5002, zzz4002, chd)
new_compare4(:(zzz500000, zzz500001), :(zzz4300000, zzz4300001), ce) → new_primCompAux0(zzz500000, zzz4300000, new_compare4(zzz500001, zzz4300001, ce), ce)
new_compare16(Float(zzz500000, zzz500001), Float(zzz4300000, zzz4300001)) → new_compare8(new_sr0(zzz500000, zzz4300000), new_sr0(zzz500001, zzz4300001))
new_esEs26(zzz5002, zzz4002, app(ty_Maybe, chh)) → new_esEs7(zzz5002, zzz4002, chh)
new_esEs28(zzz5000, zzz4000, ty_Bool) → new_esEs14(zzz5000, zzz4000)
new_compare110(zzz500000, zzz4300000, True, hc, hd, he) → LT
new_lt19(zzz500000, zzz4300000, app(app(ty_Either, ccg), cch)) → new_lt5(zzz500000, zzz4300000, ccg, cch)
new_ltEs18(zzz50000, zzz430000, ty_Bool) → new_ltEs14(zzz50000, zzz430000)
new_esEs28(zzz5000, zzz4000, ty_Integer) → new_esEs15(zzz5000, zzz4000)
new_esEs18(zzz5001, zzz4001, ty_Ordering) → new_esEs8(zzz5001, zzz4001)
new_esEs19(zzz5000, zzz4000, ty_Double) → new_esEs9(zzz5000, zzz4000)
new_lt20(zzz500001, zzz4300001, app(app(ty_@2, cec), ced)) → new_lt16(zzz500001, zzz4300001, cec, ced)
new_esEs5(@2(zzz5000, zzz5001), @2(zzz4000, zzz4001), eb, ec) → new_asAs(new_esEs19(zzz5000, zzz4000, eb), new_esEs18(zzz5001, zzz4001, ec))
new_compare26(zzz500000, zzz4300000, False) → new_compare19(zzz500000, zzz4300000, new_ltEs14(zzz500000, zzz4300000))
new_esEs28(zzz5000, zzz4000, app(app(ty_Either, dbd), dbe)) → new_esEs4(zzz5000, zzz4000, dbd, dbe)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, app(ty_Maybe, bhf)) → new_esEs7(zzz5000, zzz4000, bhf)
new_esEs7(Just(zzz5000), Just(zzz4000), ty_@0) → new_esEs10(zzz5000, zzz4000)
new_ltEs18(zzz50000, zzz430000, ty_Char) → new_ltEs5(zzz50000, zzz430000)
new_esEs28(zzz5000, zzz4000, ty_Float) → new_esEs13(zzz5000, zzz4000)
new_lt13(zzz500000, zzz4300000, ty_Ordering) → new_lt9(zzz500000, zzz4300000)
new_esEs25(zzz500000, zzz4300000, app(app(app(ty_@3, cde), cdf), cdg)) → new_esEs6(zzz500000, zzz4300000, cde, cdf, cdg)
new_ltEs10(EQ, EQ) → True
new_ltEs18(zzz50000, zzz430000, app(app(ty_@2, bed), bee)) → new_ltEs13(zzz50000, zzz430000, bed, bee)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Int, bfb) → new_esEs17(zzz5000, zzz4000)
new_esEs23(zzz500000, zzz4300000, ty_Integer) → new_esEs15(zzz500000, zzz4300000)
new_ltEs10(LT, LT) → True
new_esEs14(True, True) → True
new_compare111(zzz200, zzz201, False, bbd) → GT
new_esEs27(zzz5001, zzz4001, ty_Bool) → new_esEs14(zzz5001, zzz4001)
new_esEs7(Just(zzz5000), Just(zzz4000), app(app(ty_Either, cg), da)) → new_esEs4(zzz5000, zzz4000, cg, da)
new_compare10(Char(zzz500000), Char(zzz4300000)) → new_primCmpNat0(zzz500000, zzz4300000)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Float, bfb) → new_esEs13(zzz5000, zzz4000)
new_lt13(zzz500000, zzz4300000, app(app(ty_@2, hf), hg)) → new_lt16(zzz500000, zzz4300000, hf, hg)
new_ltEs7(Left(zzz500000), Left(zzz4300000), app(app(ty_@2, bbh), bca), bbe) → new_ltEs13(zzz500000, zzz4300000, bbh, bca)
new_esEs7(Just(zzz5000), Just(zzz4000), app(ty_Ratio, ea)) → new_esEs16(zzz5000, zzz4000, ea)
new_lt13(zzz500000, zzz4300000, app(ty_Maybe, cbb)) → new_lt11(zzz500000, zzz4300000, cbb)
new_ltEs20(zzz500002, zzz4300002, app(app(ty_Either, cfc), cfd)) → new_ltEs7(zzz500002, zzz4300002, cfc, cfd)
new_esEs18(zzz5001, zzz4001, ty_@0) → new_esEs10(zzz5001, zzz4001)
new_ltEs16(@3(zzz500000, zzz500001, zzz500002), @3(zzz4300000, zzz4300001, zzz4300002), beg, beh, bfa) → new_pePe(new_lt19(zzz500000, zzz4300000, beg), new_asAs(new_esEs25(zzz500000, zzz4300000, beg), new_pePe(new_lt20(zzz500001, zzz4300001, beh), new_asAs(new_esEs24(zzz500001, zzz4300001, beh), new_ltEs20(zzz500002, zzz4300002, bfa)))))
new_esEs4(Right(zzz5000), Right(zzz4000), bge, ty_Double) → new_esEs9(zzz5000, zzz4000)
new_ltEs14(True, False) → False
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_esEs20(zzz5000, zzz4000, ty_Int) → new_esEs17(zzz5000, zzz4000)
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_esEs25(zzz500000, zzz4300000, app(app(ty_@2, cda), cdb)) → new_esEs5(zzz500000, zzz4300000, cda, cdb)
new_ltEs20(zzz500002, zzz4300002, ty_Double) → new_ltEs8(zzz500002, zzz4300002)
new_ltEs7(Left(zzz500000), Left(zzz4300000), app(ty_Ratio, bcc), bbe) → new_ltEs15(zzz500000, zzz4300000, bcc)
new_ltEs19(zzz500001, zzz4300001, app(app(app(ty_@3, ccc), ccd), cce)) → new_ltEs16(zzz500001, zzz4300001, ccc, ccd, cce)
new_ltEs20(zzz500002, zzz4300002, app(app(app(ty_@3, cga), cgb), cgc)) → new_ltEs16(zzz500002, zzz4300002, cga, cgb, cgc)
new_compare112(zzz500000, zzz4300000, False) → GT
new_ltEs10(EQ, LT) → False
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Float) → new_esEs13(zzz5000, zzz4000)
new_esEs14(False, False) → True
new_esEs7(Just(zzz5000), Just(zzz4000), app(app(ty_@2, db), dc)) → new_esEs5(zzz5000, zzz4000, db, dc)
new_lt20(zzz500001, zzz4300001, ty_Char) → new_lt12(zzz500001, zzz4300001)
new_lt9(zzz500000, zzz4300000) → new_esEs8(new_compare6(zzz500000, zzz4300000), LT)
new_ltEs10(GT, LT) → False
new_esEs18(zzz5001, zzz4001, ty_Bool) → new_esEs14(zzz5001, zzz4001)
new_esEs22(zzz5000, zzz4000, ty_Integer) → new_esEs15(zzz5000, zzz4000)
new_primPlusNat1(Zero, Zero) → Zero
new_compare30(zzz500000, zzz4300000, app(app(app(ty_@3, caf), cag), cah)) → new_compare13(zzz500000, zzz4300000, caf, cag, cah)
new_esEs19(zzz5000, zzz4000, ty_Integer) → new_esEs15(zzz5000, zzz4000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(ty_[], bfg), bfb) → new_esEs12(zzz5000, zzz4000, bfg)
new_esEs26(zzz5002, zzz4002, app(app(ty_Either, cgh), cha)) → new_esEs4(zzz5002, zzz4002, cgh, cha)
new_asAs(True, zzz207) → zzz207
new_esEs28(zzz5000, zzz4000, app(ty_[], dbh)) → new_esEs12(zzz5000, zzz4000, dbh)
new_esEs27(zzz5001, zzz4001, app(ty_[], daf)) → new_esEs12(zzz5001, zzz4001, daf)
new_esEs19(zzz5000, zzz4000, app(app(ty_Either, fg), fh)) → new_esEs4(zzz5000, zzz4000, fg, fh)
new_ltEs4(Just(zzz500000), Nothing, bb) → False
new_esEs20(zzz5000, zzz4000, ty_Double) → new_esEs9(zzz5000, zzz4000)
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_ltEs4(Just(zzz500000), Just(zzz4300000), app(ty_[], cd)) → new_ltEs17(zzz500000, zzz4300000, cd)
new_esEs4(Right(zzz5000), Left(zzz4000), bge, bfb) → False
new_esEs4(Left(zzz5000), Right(zzz4000), bge, bfb) → False
new_ltEs19(zzz500001, zzz4300001, ty_Float) → new_ltEs12(zzz500001, zzz4300001)
new_ltEs20(zzz500002, zzz4300002, app(ty_Maybe, cfg)) → new_ltEs4(zzz500002, zzz4300002, cfg)
new_esEs4(Left(zzz5000), Left(zzz4000), app(app(app(ty_@3, bfh), bga), bgb), bfb) → new_esEs6(zzz5000, zzz4000, bfh, bga, bgb)
new_ltEs19(zzz500001, zzz4300001, ty_Char) → new_ltEs5(zzz500001, zzz4300001)
new_fsEs(zzz210) → new_not(new_esEs8(zzz210, GT))
new_esEs19(zzz5000, zzz4000, ty_@0) → new_esEs10(zzz5000, zzz4000)
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Bool) → new_esEs14(zzz5000, zzz4000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Double, bbe) → new_ltEs8(zzz500000, zzz4300000)
new_esEs24(zzz500001, zzz4300001, ty_Float) → new_esEs13(zzz500001, zzz4300001)
new_ltEs11(zzz50000, zzz430000) → new_fsEs(new_compare11(zzz50000, zzz430000))
new_lt20(zzz500001, zzz4300001, ty_Int) → new_lt14(zzz500001, zzz4300001)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, ty_Float) → new_esEs13(zzz5000, zzz4000)
new_esEs19(zzz5000, zzz4000, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_ltEs20(zzz500002, zzz4300002, app(app(ty_@2, cfe), cff)) → new_ltEs13(zzz500002, zzz4300002, cfe, cff)
new_esEs27(zzz5001, zzz4001, ty_Char) → new_esEs11(zzz5001, zzz4001)
new_ltEs20(zzz500002, zzz4300002, ty_Int) → new_ltEs6(zzz500002, zzz4300002)
new_compare110(zzz500000, zzz4300000, False, hc, hd, he) → GT
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Char) → new_ltEs5(zzz500000, zzz4300000)
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Char) → new_esEs11(zzz5000, zzz4000)
new_primCompAux00(zzz225, GT) → GT
new_ltEs20(zzz500002, zzz4300002, ty_Integer) → new_ltEs9(zzz500002, zzz4300002)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, app(ty_Maybe, bde)) → new_ltEs4(zzz500000, zzz4300000, bde)
new_lt19(zzz500000, zzz4300000, ty_Int) → new_lt14(zzz500000, zzz4300000)
new_ltEs4(Just(zzz500000), Just(zzz4300000), app(app(app(ty_@3, ca), cb), cc)) → new_ltEs16(zzz500000, zzz4300000, ca, cb, cc)
new_ltEs18(zzz50000, zzz430000, ty_Ordering) → new_ltEs10(zzz50000, zzz430000)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Integer) → new_ltEs9(zzz500000, zzz4300000)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_compare30(zzz500000, zzz4300000, ty_Ordering) → new_compare6(zzz500000, zzz4300000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, ty_Float) → new_ltEs12(zzz500000, zzz4300000)
new_esEs27(zzz5001, zzz4001, ty_Integer) → new_esEs15(zzz5001, zzz4001)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, ty_Int) → new_ltEs6(zzz500000, zzz4300000)
new_not(True) → False

The set Q consists of the following terms:

new_compare30(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_compare23(x0, x1, True)
new_lt11(x0, x1, x2)
new_lt14(x0, x1)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs18(x0, x1, app(app(ty_@2, x2), x3))
new_asAs(True, x0)
new_compare29(Nothing, Nothing, False, x0)
new_compare19(x0, x1, True)
new_esEs26(x0, x1, ty_@0)
new_ltEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs18(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_Ordering)
new_esEs18(x0, x1, ty_Int)
new_ltEs19(x0, x1, app(ty_[], x2))
new_primPlusNat1(Zero, Succ(x0))
new_compare29(Nothing, Just(x0), False, x1)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_compare30(x0, x1, ty_@0)
new_lt20(x0, x1, ty_Ordering)
new_esEs9(Double(x0, x1), Double(x2, x3))
new_ltEs7(Right(x0), Right(x1), x2, ty_@0)
new_primCompAux0(x0, x1, x2, x3)
new_primMulNat0(Succ(x0), Zero)
new_lt19(x0, x1, ty_Double)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_@0)
new_primPlusNat1(Succ(x0), Zero)
new_esEs21(x0, x1, ty_Int)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare4(:(x0, x1), :(x2, x3), x4)
new_ltEs10(LT, LT)
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_esEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs16(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs23(x0, x1, ty_Bool)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs27(x0, x1, ty_Int)
new_esEs4(Right(x0), Left(x1), x2, x3)
new_esEs4(Left(x0), Right(x1), x2, x3)
new_esEs18(x0, x1, ty_Char)
new_esEs24(x0, x1, ty_Char)
new_ltEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(True, False)
new_ltEs14(False, True)
new_esEs25(x0, x1, ty_Double)
new_pePe(False, x0)
new_esEs19(x0, x1, ty_Char)
new_esEs25(x0, x1, ty_Char)
new_compare27(x0, x1, True, x2, x3)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs7(Just(x0), Just(x1), ty_Double)
new_esEs8(GT, GT)
new_esEs23(x0, x1, ty_@0)
new_compare4([], :(x0, x1), x2)
new_lt9(x0, x1)
new_lt19(x0, x1, ty_Ordering)
new_esEs11(Char(x0), Char(x1))
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs4(Left(x0), Left(x1), ty_Int, x2)
new_esEs7(Nothing, Just(x0), x1)
new_esEs8(LT, LT)
new_sr0(x0, x1)
new_compare6(x0, x1)
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_compare30(x0, x1, ty_Double)
new_esEs7(Just(x0), Just(x1), ty_Char)
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, app(ty_[], x2))
new_lt13(x0, x1, app(ty_Ratio, x2))
new_compare19(x0, x1, False)
new_ltEs4(Nothing, Nothing, x0)
new_compare110(x0, x1, False, x2, x3, x4)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs26(x0, x1, ty_Double)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_lt18(x0, x1, x2)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_lt16(x0, x1, x2, x3)
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_compare111(x0, x1, False, x2)
new_compare4([], [], x0)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs7(Left(x0), Left(x1), ty_Char, x2)
new_ltEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs17(x0, x1)
new_ltEs19(x0, x1, ty_Char)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs14(True, True)
new_compare26(x0, x1, True)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Char)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare112(x0, x1, False)
new_esEs18(x0, x1, ty_Bool)
new_esEs20(x0, x1, ty_Float)
new_primEqNat0(Zero, Zero)
new_ltEs4(Just(x0), Just(x1), ty_Double)
new_compare30(x0, x1, ty_Char)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_ltEs7(Right(x0), Right(x1), x2, ty_Char)
new_esEs20(x0, x1, ty_Int)
new_lt13(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Double)
new_lt19(x0, x1, ty_Bool)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, ty_@0)
new_lt13(x0, x1, app(ty_[], x2))
new_esEs12([], :(x0, x1), x2)
new_esEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs28(x0, x1, ty_Integer)
new_compare17(x0, x1)
new_ltEs17(x0, x1, x2)
new_primPlusNat0(Zero, x0)
new_ltEs20(x0, x1, ty_Int)
new_compare13(x0, x1, x2, x3, x4)
new_primMulNat0(Zero, Zero)
new_esEs4(Right(x0), Right(x1), x2, ty_Float)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpNat0(Succ(x0), Zero)
new_compare16(Float(x0, x1), Float(x2, x3))
new_ltEs20(x0, x1, ty_Integer)
new_compare30(x0, x1, ty_Ordering)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs26(x0, x1, ty_Integer)
new_ltEs10(EQ, LT)
new_ltEs10(LT, EQ)
new_lt4(x0, x1)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_ltEs7(Left(x0), Left(x1), ty_@0, x2)
new_lt13(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs19(x0, x1, ty_Bool)
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs28(x0, x1, ty_@0)
new_primMulNat0(Succ(x0), Succ(x1))
new_lt7(x0, x1)
new_esEs23(x0, x1, ty_Float)
new_ltEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_Double)
new_compare113(x0, x1, False, x2, x3)
new_ltEs18(x0, x1, ty_@0)
new_compare15(x0, x1, True, x2, x3)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs23(x0, x1, ty_Char)
new_esEs24(x0, x1, ty_Int)
new_compare9(Integer(x0), Integer(x1))
new_esEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, ty_Ordering)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_ltEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_compare4(:(x0, x1), [], x2)
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_esEs24(x0, x1, ty_Bool)
new_ltEs13(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs26(x0, x1, ty_Char)
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_compare25(x0, x1, False, x2, x3)
new_esEs20(x0, x1, ty_Ordering)
new_esEs12(:(x0, x1), :(x2, x3), x4)
new_fsEs(x0)
new_lt8(x0, x1, x2, x3, x4)
new_ltEs11(x0, x1)
new_esEs23(x0, x1, ty_Double)
new_lt13(x0, x1, ty_@0)
new_ltEs7(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Just(x0), Just(x1), ty_Int)
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_compare26(x0, x1, False)
new_ltEs18(x0, x1, ty_Double)
new_ltEs7(Right(x0), Left(x1), x2, x3)
new_ltEs7(Left(x0), Right(x1), x2, x3)
new_ltEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs25(x0, x1, ty_Bool)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primPlusNat1(Zero, Zero)
new_esEs28(x0, x1, ty_Float)
new_ltEs7(Right(x0), Right(x1), x2, ty_Int)
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_lt12(x0, x1)
new_compare7(:%(x0, x1), :%(x2, x3), ty_Int)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_ltEs4(Just(x0), Just(x1), ty_Int)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_compare11(@0, @0)
new_esEs4(Right(x0), Right(x1), x2, ty_Integer)
new_primMulNat0(Zero, Succ(x0))
new_esEs26(x0, x1, ty_Bool)
new_asAs(False, x0)
new_esEs12(:(x0, x1), [], x2)
new_ltEs4(Just(x0), Just(x1), ty_Bool)
new_ltEs8(x0, x1)
new_ltEs18(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Float)
new_esEs27(x0, x1, ty_Double)
new_ltEs19(x0, x1, ty_Ordering)
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs4(Just(x0), Just(x1), ty_Ordering)
new_esEs4(Left(x0), Left(x1), ty_@0, x2)
new_esEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs18(x0, x1, ty_Double)
new_ltEs10(GT, LT)
new_esEs4(Left(x0), Left(x1), ty_Double, x2)
new_ltEs10(LT, GT)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs28(x0, x1, ty_Double)
new_esEs10(@0, @0)
new_compare14(Double(x0, x1), Double(x2, x3))
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_compare24(x0, x1, True, x2, x3, x4)
new_compare30(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_Integer)
new_ltEs18(x0, x1, ty_Float)
new_compare8(x0, x1)
new_lt13(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs20(x0, x1, ty_Char)
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs7(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs19(x0, x1, ty_Integer)
new_pePe(True, x0)
new_compare29(Just(x0), Just(x1), False, x2)
new_esEs27(x0, x1, ty_Float)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_primCompAux00(x0, EQ)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_lt19(x0, x1, ty_Float)
new_primEqNat0(Succ(x0), Zero)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_ltEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_lt17(x0, x1, x2)
new_esEs28(x0, x1, ty_Int)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_compare27(x0, x1, False, x2, x3)
new_esEs18(x0, x1, ty_Ordering)
new_esEs25(x0, x1, ty_Int)
new_esEs18(x0, x1, app(ty_Ratio, x2))
new_esEs7(Nothing, Nothing, x0)
new_ltEs15(x0, x1, x2)
new_ltEs4(Just(x0), Just(x1), ty_@0)
new_esEs19(x0, x1, app(ty_[], x2))
new_compare23(x0, x1, False)
new_compare30(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_ltEs4(Just(x0), Nothing, x1)
new_esEs8(EQ, EQ)
new_compare112(x0, x1, True)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs4(Right(x0), Right(x1), x2, ty_Int)
new_esEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs19(x0, x1, ty_Double)
new_esEs13(Float(x0, x1), Float(x2, x3))
new_primEqInt(Neg(Zero), Neg(Zero))
new_gt(x0, x1, x2)
new_lt13(x0, x1, ty_Char)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, ty_Char)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_esEs15(Integer(x0), Integer(x1))
new_ltEs12(x0, x1)
new_ltEs20(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_@0)
new_esEs14(True, False)
new_esEs14(False, True)
new_ltEs4(Just(x0), Just(x1), ty_Float)
new_ltEs7(Right(x0), Right(x1), x2, ty_Float)
new_esEs18(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, app(ty_[], x2))
new_ltEs6(x0, x1)
new_esEs22(x0, x1, ty_Int)
new_esEs20(x0, x1, ty_Double)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare110(x0, x1, True, x2, x3, x4)
new_ltEs9(x0, x1)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs19(x0, x1, ty_@0)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_lt19(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Ordering)
new_esEs27(x0, x1, ty_Integer)
new_esEs16(:%(x0, x1), :%(x2, x3), x4)
new_lt20(x0, x1, ty_Float)
new_compare25(x0, x1, True, x2, x3)
new_compare30(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Integer)
new_primCmpNat0(Succ(x0), Succ(x1))
new_lt19(x0, x1, ty_Char)
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_esEs20(x0, x1, ty_Integer)
new_esEs28(x0, x1, ty_Ordering)
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_esEs21(x0, x1, ty_Integer)
new_compare28(x0, x1, x2)
new_ltEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_esEs4(Right(x0), Right(x1), x2, ty_Double)
new_ltEs7(Right(x0), Right(x1), x2, ty_Double)
new_lt20(x0, x1, ty_Bool)
new_primPlusNat0(Succ(x0), x1)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_@0)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, ty_Integer)
new_compare30(x0, x1, app(ty_Maybe, x2))
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs7(Just(x0), Just(x1), ty_Float)
new_compare18(x0, x1, x2, x3)
new_esEs19(x0, x1, ty_Float)
new_ltEs20(x0, x1, ty_Bool)
new_primCmpNat0(Zero, Zero)
new_esEs4(Left(x0), Left(x1), ty_Integer, x2)
new_esEs19(x0, x1, ty_Ordering)
new_lt13(x0, x1, ty_Bool)
new_ltEs19(x0, x1, ty_Float)
new_esEs27(x0, x1, app(ty_[], x2))
new_ltEs7(Left(x0), Left(x1), ty_Double, x2)
new_esEs12([], [], x0)
new_lt10(x0, x1)
new_compare7(:%(x0, x1), :%(x2, x3), ty_Integer)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_compare113(x0, x1, True, x2, x3)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs20(x0, x1, app(ty_[], x2))
new_ltEs7(Left(x0), Left(x1), ty_Bool, x2)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, ty_Ordering)
new_esEs4(Left(x0), Left(x1), ty_Char, x2)
new_esEs26(x0, x1, ty_Float)
new_ltEs7(Left(x0), Left(x1), ty_Float, x2)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt5(x0, x1, x2, x3)
new_esEs28(x0, x1, app(ty_[], x2))
new_compare29(Just(x0), Nothing, False, x1)
new_ltEs10(GT, GT)
new_ltEs14(True, True)
new_ltEs14(False, False)
new_esEs24(x0, x1, ty_Ordering)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_lt19(x0, x1, ty_@0)
new_esEs18(x0, x1, ty_Float)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_lt13(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, ty_Char)
new_ltEs7(Left(x0), Left(x1), ty_Int, x2)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_esEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_not(True)
new_esEs19(x0, x1, ty_Int)
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Just(x0), Just(x1), ty_@0)
new_compare30(x0, x1, ty_Integer)
new_ltEs5(x0, x1)
new_compare30(x0, x1, app(ty_Ratio, x2))
new_esEs4(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs20(x0, x1, ty_Double)
new_esEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(Just(x0), Just(x1), ty_Integer)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_not(False)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Integer)
new_esEs4(Right(x0), Right(x1), x2, ty_@0)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_ltEs4(Just(x0), Just(x1), app(ty_[], x2))
new_primCompAux00(x0, LT)
new_lt6(x0, x1)
new_ltEs10(EQ, GT)
new_ltEs10(GT, EQ)
new_ltEs19(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Float)
new_esEs24(x0, x1, app(ty_[], x2))
new_ltEs18(x0, x1, ty_Char)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs19(x0, x1, ty_Integer)
new_esEs18(x0, x1, app(ty_[], x2))
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_sr(Integer(x0), Integer(x1))
new_esEs4(Right(x0), Right(x1), x2, ty_Char)
new_esEs27(x0, x1, ty_Char)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs20(x0, x1, ty_Bool)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(Just(x0), Just(x1), ty_Char)
new_esEs4(Left(x0), Left(x1), ty_Float, x2)
new_ltEs4(Nothing, Just(x0), x1)
new_esEs18(x0, x1, ty_@0)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_ltEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_lt13(x0, x1, ty_Double)
new_esEs18(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_Bool)
new_lt13(x0, x1, ty_Ordering)
new_compare12(x0, x1, x2, x3)
new_compare15(x0, x1, False, x2, x3)
new_ltEs18(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Ordering)
new_compare30(x0, x1, ty_Float)
new_esEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare111(x0, x1, True, x2)
new_lt13(x0, x1, ty_Integer)
new_lt19(x0, x1, app(ty_[], x2))
new_esEs14(False, False)
new_primEqInt(Pos(Zero), Pos(Zero))
new_compare30(x0, x1, app(ty_[], x2))
new_compare10(Char(x0), Char(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs24(x0, x1, ty_Integer)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Double)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs25(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, ty_Float)
new_lt13(x0, x1, ty_Int)
new_compare29(x0, x1, True, x2)
new_lt13(x0, x1, ty_Float)
new_lt20(x0, x1, ty_Integer)
new_primCmpNat0(Zero, Succ(x0))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_ltEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_Int)
new_primCompAux00(x0, GT)
new_ltEs20(x0, x1, ty_@0)
new_esEs4(Left(x0), Left(x1), ty_Bool, x2)
new_lt15(x0, x1)
new_ltEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primEqNat0(Zero, Succ(x0))
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs7(Left(x0), Left(x1), ty_Integer, x2)
new_esEs27(x0, x1, ty_Bool)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_@0)
new_compare24(x0, x1, False, x2, x3, x4)
new_esEs7(Just(x0), Nothing, x1)
new_esEs18(x0, x1, ty_Integer)
new_ltEs10(EQ, EQ)

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_intersectFM_C2Elt106(zzz523, zzz524, zzz525, zzz526, zzz527, zzz528, zzz529, zzz530, zzz531, zzz532, False, h, ba) → new_intersectFM_C2Elt103(zzz523, zzz524, zzz525, zzz526, zzz527, zzz528, zzz529, zzz530, zzz531, zzz532, new_gt(Just(zzz527), zzz528, ba), h, ba)
new_intersectFM_C2Elt105(zzz523, zzz524, zzz525, zzz526, zzz527, zzz528, zzz529, zzz530, zzz531, zzz532, h, ba) → new_intersectFM_C2Elt106(zzz523, zzz524, zzz525, zzz526, zzz527, zzz528, zzz529, zzz530, zzz531, zzz532, new_lt11(Just(zzz527), zzz528, ba), h, ba)
new_intersectFM_C2Elt106(zzz523, zzz524, zzz525, zzz526, zzz527, zzz528, zzz529, zzz530, Branch(zzz5310, zzz5311, zzz5312, zzz5313, zzz5314), zzz532, True, h, ba) → new_intersectFM_C2Elt105(zzz523, zzz524, zzz525, zzz526, zzz527, zzz5310, zzz5311, zzz5312, zzz5313, zzz5314, h, ba)
new_intersectFM_C2Elt104(zzz523, zzz524, zzz525, zzz526, zzz527, Branch(zzz5310, zzz5311, zzz5312, zzz5313, zzz5314), h, ba) → new_intersectFM_C2Elt105(zzz523, zzz524, zzz525, zzz526, zzz527, zzz5310, zzz5311, zzz5312, zzz5313, zzz5314, h, ba)
new_intersectFM_C2Elt103(zzz523, zzz524, zzz525, zzz526, zzz527, zzz528, zzz529, zzz530, zzz531, zzz532, True, h, ba) → new_intersectFM_C2Elt104(zzz523, zzz524, zzz525, zzz526, zzz527, zzz532, h, ba)

The TRS R consists of the following rules:

new_lt19(zzz500000, zzz4300000, ty_Float) → new_lt6(zzz500000, zzz4300000)
new_ltEs18(zzz50000, zzz430000, app(ty_Ratio, bef)) → new_ltEs15(zzz50000, zzz430000, bef)
new_esEs7(Just(zzz5000), Just(zzz4000), app(ty_Maybe, dh)) → new_esEs7(zzz5000, zzz4000, dh)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_esEs20(zzz5000, zzz4000, app(ty_Maybe, bba)) → new_esEs7(zzz5000, zzz4000, bba)
new_esEs12(:(zzz5000, zzz5001), :(zzz4000, zzz4001), hh) → new_asAs(new_esEs20(zzz5000, zzz4000, hh), new_esEs12(zzz5001, zzz4001, hh))
new_esEs7(Just(zzz5000), Just(zzz4000), app(ty_[], dd)) → new_esEs12(zzz5000, zzz4000, dd)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, ty_Ordering) → new_ltEs10(zzz500000, zzz4300000)
new_lt19(zzz500000, zzz4300000, app(app(app(ty_@3, cde), cdf), cdg)) → new_lt8(zzz500000, zzz4300000, cde, cdf, cdg)
new_ltEs18(zzz50000, zzz430000, app(app(app(ty_@3, beg), beh), bfa)) → new_ltEs16(zzz50000, zzz430000, beg, beh, bfa)
new_lt20(zzz500001, zzz4300001, app(ty_[], cfb)) → new_lt18(zzz500001, zzz4300001, cfb)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, ty_Char) → new_esEs11(zzz5000, zzz4000)
new_compare15(zzz500000, zzz4300000, True, hf, hg) → LT
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Bool, bfb) → new_esEs14(zzz5000, zzz4000)
new_ltEs18(zzz50000, zzz430000, app(ty_Maybe, bb)) → new_ltEs4(zzz50000, zzz430000, bb)
new_ltEs20(zzz500002, zzz4300002, ty_Ordering) → new_ltEs10(zzz500002, zzz4300002)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, app(app(app(ty_@3, bhc), bhd), bhe)) → new_esEs6(zzz5000, zzz4000, bhc, bhd, bhe)
new_lt13(zzz500000, zzz4300000, app(app(app(ty_@3, hc), hd), he)) → new_lt8(zzz500000, zzz4300000, hc, hd, he)
new_lt15(zzz500000, zzz4300000) → new_esEs8(new_compare14(zzz500000, zzz4300000), LT)
new_lt20(zzz500001, zzz4300001, app(app(app(ty_@3, ceg), ceh), cfa)) → new_lt8(zzz500001, zzz4300001, ceg, ceh, cfa)
new_esEs27(zzz5001, zzz4001, app(ty_Maybe, dbb)) → new_esEs7(zzz5001, zzz4001, dbb)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Ordering) → new_ltEs10(zzz500000, zzz4300000)
new_esEs23(zzz500000, zzz4300000, ty_Bool) → new_esEs14(zzz500000, zzz4300000)
new_compare27(zzz500000, zzz4300000, False, ha, hb) → new_compare113(zzz500000, zzz4300000, new_ltEs7(zzz500000, zzz4300000, ha, hb), ha, hb)
new_lt19(zzz500000, zzz4300000, ty_Double) → new_lt15(zzz500000, zzz4300000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), app(ty_Maybe, bcb), bbe) → new_ltEs4(zzz500000, zzz4300000, bcb)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, ty_@0) → new_ltEs11(zzz500000, zzz4300000)
new_ltEs20(zzz500002, zzz4300002, app(ty_Ratio, cfh)) → new_ltEs15(zzz500002, zzz4300002, cfh)
new_lt13(zzz500000, zzz4300000, app(ty_[], cbd)) → new_lt18(zzz500000, zzz4300000, cbd)
new_esEs26(zzz5002, zzz4002, ty_Float) → new_esEs13(zzz5002, zzz4002)
new_ltEs7(Left(zzz500000), Right(zzz4300000), bch, bbe) → True
new_primMulNat0(Zero, Zero) → Zero
new_esEs19(zzz5000, zzz4000, ty_Int) → new_esEs17(zzz5000, zzz4000)
new_sr(Integer(zzz43000000), Integer(zzz5000010)) → Integer(new_primMulInt(zzz43000000, zzz5000010))
new_ltEs20(zzz500002, zzz4300002, ty_Float) → new_ltEs12(zzz500002, zzz4300002)
new_ltEs20(zzz500002, zzz4300002, ty_@0) → new_ltEs11(zzz500002, zzz4300002)
new_esEs20(zzz5000, zzz4000, app(ty_Ratio, bbb)) → new_esEs16(zzz5000, zzz4000, bbb)
new_esEs18(zzz5001, zzz4001, ty_Double) → new_esEs9(zzz5001, zzz4001)
new_lt20(zzz500001, zzz4300001, ty_Float) → new_lt6(zzz500001, zzz4300001)
new_esEs23(zzz500000, zzz4300000, ty_Double) → new_esEs9(zzz500000, zzz4300000)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, app(ty_[], bhb)) → new_esEs12(zzz5000, zzz4000, bhb)
new_esEs24(zzz500001, zzz4300001, ty_Integer) → new_esEs15(zzz500001, zzz4300001)
new_ltEs14(False, True) → True
new_ltEs19(zzz500001, zzz4300001, ty_Integer) → new_ltEs9(zzz500001, zzz4300001)
new_ltEs4(Just(zzz500000), Just(zzz4300000), app(app(ty_@2, be), bf)) → new_ltEs13(zzz500000, zzz4300000, be, bf)
new_esEs20(zzz5000, zzz4000, app(app(ty_Either, baa), bab)) → new_esEs4(zzz5000, zzz4000, baa, bab)
new_esEs12([], [], hh) → True
new_ltEs19(zzz500001, zzz4300001, ty_Ordering) → new_ltEs10(zzz500001, zzz4300001)
new_esEs24(zzz500001, zzz4300001, app(app(ty_@2, cec), ced)) → new_esEs5(zzz500001, zzz4300001, cec, ced)
new_lt12(zzz500000, zzz4300000) → new_esEs8(new_compare10(zzz500000, zzz4300000), LT)
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Ordering, bbe) → new_ltEs10(zzz500000, zzz4300000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, app(ty_Ratio, bdf)) → new_ltEs15(zzz500000, zzz4300000, bdf)
new_esEs15(Integer(zzz5000), Integer(zzz4000)) → new_primEqInt(zzz5000, zzz4000)
new_ltEs10(EQ, GT) → True
new_ltEs19(zzz500001, zzz4300001, app(ty_Maybe, cca)) → new_ltEs4(zzz500001, zzz4300001, cca)
new_esEs21(zzz5001, zzz4001, ty_Int) → new_esEs17(zzz5001, zzz4001)
new_ltEs7(Left(zzz500000), Left(zzz4300000), app(app(app(ty_@3, bcd), bce), bcf), bbe) → new_ltEs16(zzz500000, zzz4300000, bcd, bce, bcf)
new_lt13(zzz500000, zzz4300000, ty_Char) → new_lt12(zzz500000, zzz4300000)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Ordering, bfb) → new_esEs8(zzz5000, zzz4000)
new_esEs24(zzz500001, zzz4300001, app(ty_[], cfb)) → new_esEs12(zzz500001, zzz4300001, cfb)
new_esEs25(zzz500000, zzz4300000, ty_Double) → new_esEs9(zzz500000, zzz4300000)
new_esEs25(zzz500000, zzz4300000, ty_Float) → new_esEs13(zzz500000, zzz4300000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, app(ty_[], beb)) → new_ltEs17(zzz500000, zzz4300000, beb)
new_pePe(False, zzz218) → zzz218
new_lt14(zzz5000, zzz43000) → new_esEs8(new_compare8(zzz5000, zzz43000), LT)
new_esEs25(zzz500000, zzz4300000, app(app(ty_Either, ccg), cch)) → new_esEs4(zzz500000, zzz4300000, ccg, cch)
new_esEs12(:(zzz5000, zzz5001), [], hh) → False
new_esEs12([], :(zzz4000, zzz4001), hh) → False
new_esEs25(zzz500000, zzz4300000, ty_Char) → new_esEs11(zzz500000, zzz4300000)
new_esEs25(zzz500000, zzz4300000, ty_Bool) → new_esEs14(zzz500000, zzz4300000)
new_lt19(zzz500000, zzz4300000, ty_Ordering) → new_lt9(zzz500000, zzz4300000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, app(app(ty_@2, bdc), bdd)) → new_ltEs13(zzz500000, zzz4300000, bdc, bdd)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, app(ty_Ratio, bhg)) → new_esEs16(zzz5000, zzz4000, bhg)
new_compare23(zzz500000, zzz4300000, True) → EQ
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Float, bbe) → new_ltEs12(zzz500000, zzz4300000)
new_lt19(zzz500000, zzz4300000, app(ty_Ratio, cdd)) → new_lt17(zzz500000, zzz4300000, cdd)
new_esEs24(zzz500001, zzz4300001, app(ty_Maybe, cee)) → new_esEs7(zzz500001, zzz4300001, cee)
new_ltEs4(Nothing, Just(zzz4300000), bb) → True
new_esEs23(zzz500000, zzz4300000, app(ty_Maybe, cbb)) → new_esEs7(zzz500000, zzz4300000, cbb)
new_compare30(zzz500000, zzz4300000, ty_Integer) → new_compare9(zzz500000, zzz4300000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(ty_Ratio, bgd), bfb) → new_esEs16(zzz5000, zzz4000, bgd)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, ty_Char) → new_ltEs5(zzz500000, zzz4300000)
new_compare13(zzz500000, zzz4300000, hc, hd, he) → new_compare24(zzz500000, zzz4300000, new_esEs6(zzz500000, zzz4300000, hc, hd, he), hc, hd, he)
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_lt4(zzz500000, zzz4300000) → new_esEs8(new_compare11(zzz500000, zzz4300000), LT)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, ty_Integer) → new_esEs15(zzz5000, zzz4000)
new_esEs20(zzz5000, zzz4000, app(app(ty_@2, bac), bad)) → new_esEs5(zzz5000, zzz4000, bac, bad)
new_esEs28(zzz5000, zzz4000, app(ty_Ratio, dce)) → new_esEs16(zzz5000, zzz4000, dce)
new_compare30(zzz500000, zzz4300000, app(ty_Ratio, cae)) → new_compare7(zzz500000, zzz4300000, cae)
new_compare19(zzz500000, zzz4300000, True) → LT
new_compare6(zzz500000, zzz4300000) → new_compare23(zzz500000, zzz4300000, new_esEs8(zzz500000, zzz4300000))
new_ltEs18(zzz50000, zzz430000, ty_@0) → new_ltEs11(zzz50000, zzz430000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_ltEs19(zzz500001, zzz4300001, app(ty_Ratio, ccb)) → new_ltEs15(zzz500001, zzz4300001, ccb)
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Int) → new_esEs17(zzz5000, zzz4000)
new_ltEs20(zzz500002, zzz4300002, ty_Bool) → new_ltEs14(zzz500002, zzz4300002)
new_esEs27(zzz5001, zzz4001, ty_@0) → new_esEs10(zzz5001, zzz4001)
new_ltEs12(zzz50000, zzz430000) → new_fsEs(new_compare16(zzz50000, zzz430000))
new_esEs8(LT, LT) → True
new_lt19(zzz500000, zzz4300000, app(app(ty_@2, cda), cdb)) → new_lt16(zzz500000, zzz4300000, cda, cdb)
new_esEs25(zzz500000, zzz4300000, ty_Ordering) → new_esEs8(zzz500000, zzz4300000)
new_esEs19(zzz5000, zzz4000, app(ty_Maybe, gg)) → new_esEs7(zzz5000, zzz4000, gg)
new_esEs20(zzz5000, zzz4000, app(app(app(ty_@3, baf), bag), bah)) → new_esEs6(zzz5000, zzz4000, baf, bag, bah)
new_esEs18(zzz5001, zzz4001, app(ty_Ratio, ff)) → new_esEs16(zzz5001, zzz4001, ff)
new_pePe(True, zzz218) → True
new_primEqNat0(Zero, Zero) → True
new_lt20(zzz500001, zzz4300001, app(app(ty_Either, cea), ceb)) → new_lt5(zzz500001, zzz4300001, cea, ceb)
new_compare26(zzz500000, zzz4300000, True) → EQ
new_lt20(zzz500001, zzz4300001, ty_Bool) → new_lt7(zzz500001, zzz4300001)
new_esEs13(Float(zzz5000, zzz5001), Float(zzz4000, zzz4001)) → new_esEs17(new_sr0(zzz5000, zzz4000), new_sr0(zzz5001, zzz4001))
new_esEs19(zzz5000, zzz4000, app(ty_[], gc)) → new_esEs12(zzz5000, zzz4000, gc)
new_compare29(Nothing, Just(zzz430000), False, gg) → LT
new_esEs19(zzz5000, zzz4000, ty_Float) → new_esEs13(zzz5000, zzz4000)
new_compare30(zzz500000, zzz4300000, app(ty_Maybe, cad)) → new_compare28(zzz500000, zzz4300000, cad)
new_esEs18(zzz5001, zzz4001, app(app(ty_@2, ef), eg)) → new_esEs5(zzz5001, zzz4001, ef, eg)
new_esEs25(zzz500000, zzz4300000, ty_Int) → new_esEs17(zzz500000, zzz4300000)
new_esEs9(Double(zzz5000, zzz5001), Double(zzz4000, zzz4001)) → new_esEs17(new_sr0(zzz5000, zzz4000), new_sr0(zzz5001, zzz4001))
new_esEs26(zzz5002, zzz4002, ty_Ordering) → new_esEs8(zzz5002, zzz4002)
new_esEs8(GT, GT) → True
new_lt20(zzz500001, zzz4300001, app(ty_Maybe, cee)) → new_lt11(zzz500001, zzz4300001, cee)
new_esEs18(zzz5001, zzz4001, app(app(app(ty_@3, fa), fb), fc)) → new_esEs6(zzz5001, zzz4001, fa, fb, fc)
new_esEs25(zzz500000, zzz4300000, ty_@0) → new_esEs10(zzz500000, zzz4300000)
new_compare4([], [], ce) → EQ
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_lt19(zzz500000, zzz4300000, ty_@0) → new_lt4(zzz500000, zzz4300000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(app(ty_@2, bfe), bff), bfb) → new_esEs5(zzz5000, zzz4000, bfe, bff)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, ty_Integer) → new_ltEs9(zzz500000, zzz4300000)
new_esEs26(zzz5002, zzz4002, app(app(app(ty_@3, che), chf), chg)) → new_esEs6(zzz5002, zzz4002, che, chf, chg)
new_compare18(zzz500000, zzz4300000, hf, hg) → new_compare25(zzz500000, zzz4300000, new_esEs5(zzz500000, zzz4300000, hf, hg), hf, hg)
new_ltEs17(zzz50000, zzz430000, ce) → new_fsEs(new_compare4(zzz50000, zzz430000, ce))
new_esEs8(GT, LT) → False
new_esEs8(LT, GT) → False
new_compare30(zzz500000, zzz4300000, app(ty_[], cba)) → new_compare4(zzz500000, zzz4300000, cba)
new_compare30(zzz500000, zzz4300000, ty_Double) → new_compare14(zzz500000, zzz4300000)
new_ltEs13(@2(zzz500000, zzz500001), @2(zzz4300000, zzz4300001), bed, bee) → new_pePe(new_lt13(zzz500000, zzz4300000, bed), new_asAs(new_esEs23(zzz500000, zzz4300000, bed), new_ltEs19(zzz500001, zzz4300001, bee)))
new_esEs4(Right(zzz5000), Right(zzz4000), bge, app(app(ty_Either, bgf), bgg)) → new_esEs4(zzz5000, zzz4000, bgf, bgg)
new_esEs25(zzz500000, zzz4300000, app(ty_[], cdh)) → new_esEs12(zzz500000, zzz4300000, cdh)
new_compare24(zzz500000, zzz4300000, True, hc, hd, he) → EQ
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Int, bbe) → new_ltEs6(zzz500000, zzz4300000)
new_lt20(zzz500001, zzz4300001, ty_Ordering) → new_lt9(zzz500001, zzz4300001)
new_primEqInt(Neg(Succ(zzz50000)), Neg(Succ(zzz40000))) → new_primEqNat0(zzz50000, zzz40000)
new_esEs20(zzz5000, zzz4000, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_compare113(zzz500000, zzz4300000, True, ha, hb) → LT
new_esEs23(zzz500000, zzz4300000, ty_Ordering) → new_esEs8(zzz500000, zzz4300000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(app(ty_Either, bfc), bfd), bfb) → new_esEs4(zzz5000, zzz4000, bfc, bfd)
new_ltEs18(zzz50000, zzz430000, app(app(ty_Either, bch), bbe)) → new_ltEs7(zzz50000, zzz430000, bch, bbe)
new_esEs24(zzz500001, zzz4300001, ty_Bool) → new_esEs14(zzz500001, zzz4300001)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_lt19(zzz500000, zzz4300000, ty_Bool) → new_lt7(zzz500000, zzz4300000)
new_lt19(zzz500000, zzz4300000, ty_Integer) → new_lt10(zzz500000, zzz4300000)
new_ltEs4(Nothing, Nothing, bb) → True
new_lt13(zzz500000, zzz4300000, ty_Float) → new_lt6(zzz500000, zzz4300000)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_@0) → new_ltEs11(zzz500000, zzz4300000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Char, bbe) → new_ltEs5(zzz500000, zzz4300000)
new_lt13(zzz500000, zzz4300000, ty_Int) → new_lt14(zzz500000, zzz4300000)
new_lt6(zzz500000, zzz4300000) → new_esEs8(new_compare16(zzz500000, zzz4300000), LT)
new_compare29(Just(zzz50000), Nothing, False, gg) → GT
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_ltEs7(Right(zzz500000), Left(zzz4300000), bch, bbe) → False
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_esEs24(zzz500001, zzz4300001, app(app(app(ty_@3, ceg), ceh), cfa)) → new_esEs6(zzz500001, zzz4300001, ceg, ceh, cfa)
new_esEs23(zzz500000, zzz4300000, ty_Char) → new_esEs11(zzz500000, zzz4300000)
new_lt13(zzz500000, zzz4300000, ty_Bool) → new_lt7(zzz500000, zzz4300000)
new_esEs19(zzz5000, zzz4000, ty_Bool) → new_esEs14(zzz5000, zzz4000)
new_esEs20(zzz5000, zzz4000, ty_Float) → new_esEs13(zzz5000, zzz4000)
new_compare14(Double(zzz500000, zzz500001), Double(zzz4300000, zzz4300001)) → new_compare8(new_sr0(zzz500000, zzz4300000), new_sr0(zzz500001, zzz4300001))
new_compare12(zzz500000, zzz4300000, ha, hb) → new_compare27(zzz500000, zzz4300000, new_esEs4(zzz500000, zzz4300000, ha, hb), ha, hb)
new_compare8(zzz500, zzz4300) → new_primCmpInt(zzz500, zzz4300)
new_lt19(zzz500000, zzz4300000, ty_Char) → new_lt12(zzz500000, zzz4300000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, app(app(app(ty_@3, bdg), bdh), bea)) → new_ltEs16(zzz500000, zzz4300000, bdg, bdh, bea)
new_primEqInt(Neg(Succ(zzz50000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(zzz40000))) → False
new_compare17(zzz500000, zzz4300000) → new_compare26(zzz500000, zzz4300000, new_esEs14(zzz500000, zzz4300000))
new_esEs8(EQ, EQ) → True
new_lt13(zzz500000, zzz4300000, ty_Double) → new_lt15(zzz500000, zzz4300000)
new_compare111(zzz200, zzz201, True, bbd) → LT
new_esEs20(zzz5000, zzz4000, ty_@0) → new_esEs10(zzz5000, zzz4000)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Char, bfb) → new_esEs11(zzz5000, zzz4000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_ltEs19(zzz500001, zzz4300001, ty_@0) → new_ltEs11(zzz500001, zzz4300001)
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_esEs18(zzz5001, zzz4001, ty_Char) → new_esEs11(zzz5001, zzz4001)
new_compare112(zzz500000, zzz4300000, True) → LT
new_esEs19(zzz5000, zzz4000, ty_Char) → new_esEs11(zzz5000, zzz4000)
new_compare30(zzz500000, zzz4300000, app(app(ty_Either, bhh), caa)) → new_compare12(zzz500000, zzz4300000, bhh, caa)
new_primEqInt(Pos(Succ(zzz50000)), Pos(Succ(zzz40000))) → new_primEqNat0(zzz50000, zzz40000)
new_ltEs18(zzz50000, zzz430000, ty_Double) → new_ltEs8(zzz50000, zzz430000)
new_compare27(zzz500000, zzz4300000, True, ha, hb) → EQ
new_lt10(zzz500000, zzz4300000) → new_esEs8(new_compare9(zzz500000, zzz4300000), LT)
new_esEs24(zzz500001, zzz4300001, app(ty_Ratio, cef)) → new_esEs16(zzz500001, zzz4300001, cef)
new_ltEs19(zzz500001, zzz4300001, ty_Bool) → new_ltEs14(zzz500001, zzz4300001)
new_esEs14(False, True) → False
new_esEs14(True, False) → False
new_esEs23(zzz500000, zzz4300000, app(ty_[], cbd)) → new_esEs12(zzz500000, zzz4300000, cbd)
new_ltEs4(Just(zzz500000), Just(zzz4300000), app(app(ty_Either, bc), bd)) → new_ltEs7(zzz500000, zzz4300000, bc, bd)
new_esEs26(zzz5002, zzz4002, ty_Integer) → new_esEs15(zzz5002, zzz4002)
new_ltEs10(GT, EQ) → False
new_lt17(zzz500000, zzz4300000, cbc) → new_esEs8(new_compare7(zzz500000, zzz4300000, cbc), LT)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Double) → new_ltEs8(zzz500000, zzz4300000)
new_esEs24(zzz500001, zzz4300001, ty_Int) → new_esEs17(zzz500001, zzz4300001)
new_primEqNat0(Succ(zzz50000), Succ(zzz40000)) → new_primEqNat0(zzz50000, zzz40000)
new_ltEs20(zzz500002, zzz4300002, app(ty_[], cgd)) → new_ltEs17(zzz500002, zzz4300002, cgd)
new_esEs27(zzz5001, zzz4001, ty_Ordering) → new_esEs8(zzz5001, zzz4001)
new_ltEs14(False, False) → True
new_compare11(@0, @0) → EQ
new_lt7(zzz500000, zzz4300000) → new_esEs8(new_compare17(zzz500000, zzz4300000), LT)
new_esEs19(zzz5000, zzz4000, app(app(app(ty_@3, gd), ge), gf)) → new_esEs6(zzz5000, zzz4000, gd, ge, gf)
new_ltEs9(zzz50000, zzz430000) → new_fsEs(new_compare9(zzz50000, zzz430000))
new_ltEs20(zzz500002, zzz4300002, ty_Char) → new_ltEs5(zzz500002, zzz4300002)
new_compare113(zzz500000, zzz4300000, False, ha, hb) → GT
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, ty_Bool) → new_ltEs14(zzz500000, zzz4300000)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Int) → new_ltEs6(zzz500000, zzz4300000)
new_primCompAux00(zzz225, LT) → LT
new_lt20(zzz500001, zzz4300001, ty_@0) → new_lt4(zzz500001, zzz4300001)
new_ltEs19(zzz500001, zzz4300001, app(ty_[], ccf)) → new_ltEs17(zzz500001, zzz4300001, ccf)
new_ltEs19(zzz500001, zzz4300001, app(app(ty_Either, cbe), cbf)) → new_ltEs7(zzz500001, zzz4300001, cbe, cbf)
new_compare7(:%(zzz500000, zzz500001), :%(zzz4300000, zzz4300001), ty_Int) → new_compare8(new_sr0(zzz500000, zzz4300001), new_sr0(zzz4300000, zzz500001))
new_esEs24(zzz500001, zzz4300001, ty_Ordering) → new_esEs8(zzz500001, zzz4300001)
new_ltEs8(zzz50000, zzz430000) → new_fsEs(new_compare14(zzz50000, zzz430000))
new_esEs7(Nothing, Nothing, cf) → True
new_esEs28(zzz5000, zzz4000, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_esEs8(EQ, LT) → False
new_esEs8(LT, EQ) → False
new_esEs18(zzz5001, zzz4001, app(ty_Maybe, fd)) → new_esEs7(zzz5001, zzz4001, fd)
new_primEqInt(Pos(Succ(zzz50000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(zzz40000))) → False
new_lt20(zzz500001, zzz4300001, app(ty_Ratio, cef)) → new_lt17(zzz500001, zzz4300001, cef)
new_compare30(zzz500000, zzz4300000, ty_Int) → new_compare8(zzz500000, zzz4300000)
new_compare24(zzz500000, zzz4300000, False, hc, hd, he) → new_compare110(zzz500000, zzz4300000, new_ltEs16(zzz500000, zzz4300000, hc, hd, he), hc, hd, he)
new_esEs24(zzz500001, zzz4300001, ty_@0) → new_esEs10(zzz500001, zzz4300001)
new_primCmpNat0(Zero, Zero) → EQ
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Integer, bbe) → new_ltEs9(zzz500000, zzz4300000)
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_esEs23(zzz500000, zzz4300000, app(app(ty_@2, hf), hg)) → new_esEs5(zzz500000, zzz4300000, hf, hg)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, ty_@0) → new_esEs10(zzz5000, zzz4000)
new_ltEs10(LT, EQ) → True
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_compare19(zzz500000, zzz4300000, False) → GT
new_esEs27(zzz5001, zzz4001, ty_Double) → new_esEs9(zzz5001, zzz4001)
new_ltEs15(zzz50000, zzz430000, bef) → new_fsEs(new_compare7(zzz50000, zzz430000, bef))
new_esEs23(zzz500000, zzz4300000, ty_Float) → new_esEs13(zzz500000, zzz4300000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Integer) → new_esEs15(zzz5000, zzz4000)
new_compare29(Just(zzz50000), Just(zzz430000), False, gg) → new_compare111(zzz50000, zzz430000, new_ltEs18(zzz50000, zzz430000, gg), gg)
new_primEqInt(Pos(Succ(zzz50000)), Neg(zzz4000)) → False
new_primEqInt(Neg(Succ(zzz50000)), Pos(zzz4000)) → False
new_lt13(zzz500000, zzz4300000, app(ty_Ratio, cbc)) → new_lt17(zzz500000, zzz4300000, cbc)
new_esEs7(Nothing, Just(zzz4000), cf) → False
new_esEs7(Just(zzz5000), Nothing, cf) → False
new_esEs18(zzz5001, zzz4001, app(ty_[], eh)) → new_esEs12(zzz5001, zzz4001, eh)
new_esEs28(zzz5000, zzz4000, ty_Char) → new_esEs11(zzz5000, zzz4000)
new_ltEs10(GT, GT) → True
new_esEs26(zzz5002, zzz4002, app(ty_Ratio, daa)) → new_esEs16(zzz5002, zzz4002, daa)
new_esEs26(zzz5002, zzz4002, ty_Int) → new_esEs17(zzz5002, zzz4002)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, ty_Bool) → new_esEs14(zzz5000, zzz4000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_@0, bbe) → new_ltEs11(zzz500000, zzz4300000)
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primEqInt(Pos(Zero), Neg(Succ(zzz40000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(zzz40000))) → False
new_ltEs6(zzz50000, zzz430000) → new_fsEs(new_compare8(zzz50000, zzz430000))
new_esEs20(zzz5000, zzz4000, app(ty_[], bae)) → new_esEs12(zzz5000, zzz4000, bae)
new_esEs21(zzz5001, zzz4001, ty_Integer) → new_esEs15(zzz5001, zzz4001)
new_compare30(zzz500000, zzz4300000, app(app(ty_@2, cab), cac)) → new_compare18(zzz500000, zzz4300000, cab, cac)
new_primCompAux00(zzz225, EQ) → zzz225
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Double, bfb) → new_esEs9(zzz5000, zzz4000)
new_gt(zzz440, zzz4440, bec) → new_esEs8(new_compare28(zzz440, zzz4440, bec), GT)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Integer, bfb) → new_esEs15(zzz5000, zzz4000)
new_esEs18(zzz5001, zzz4001, ty_Int) → new_esEs17(zzz5001, zzz4001)
new_lt16(zzz500000, zzz4300000, hf, hg) → new_esEs8(new_compare18(zzz500000, zzz4300000, hf, hg), LT)
new_esEs8(GT, EQ) → False
new_esEs8(EQ, GT) → False
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Double) → new_esEs9(zzz5000, zzz4000)
new_esEs26(zzz5002, zzz4002, ty_Char) → new_esEs11(zzz5002, zzz4002)
new_esEs27(zzz5001, zzz4001, app(ty_Ratio, dbc)) → new_esEs16(zzz5001, zzz4001, dbc)
new_esEs26(zzz5002, zzz4002, app(app(ty_@2, chb), chc)) → new_esEs5(zzz5002, zzz4002, chb, chc)
new_ltEs19(zzz500001, zzz4300001, app(app(ty_@2, cbg), cbh)) → new_ltEs13(zzz500001, zzz4300001, cbg, cbh)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Bool) → new_ltEs14(zzz500000, zzz4300000)
new_not(False) → True
new_esEs24(zzz500001, zzz4300001, ty_Double) → new_esEs9(zzz500001, zzz4300001)
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_ltEs5(zzz50000, zzz430000) → new_fsEs(new_compare10(zzz50000, zzz430000))
new_esEs25(zzz500000, zzz4300000, ty_Integer) → new_esEs15(zzz500000, zzz4300000)
new_esEs26(zzz5002, zzz4002, ty_Bool) → new_esEs14(zzz5002, zzz4002)
new_ltEs19(zzz500001, zzz4300001, ty_Int) → new_ltEs6(zzz500001, zzz4300001)
new_esEs25(zzz500000, zzz4300000, app(ty_Ratio, cdd)) → new_esEs16(zzz500000, zzz4300000, cdd)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, ty_Int) → new_esEs17(zzz5000, zzz4000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Bool, bbe) → new_ltEs14(zzz500000, zzz4300000)
new_esEs28(zzz5000, zzz4000, app(app(ty_@2, dbf), dbg)) → new_esEs5(zzz5000, zzz4000, dbf, dbg)
new_esEs23(zzz500000, zzz4300000, ty_@0) → new_esEs10(zzz500000, zzz4300000)
new_compare30(zzz500000, zzz4300000, ty_@0) → new_compare11(zzz500000, zzz4300000)
new_esEs18(zzz5001, zzz4001, app(app(ty_Either, ed), ee)) → new_esEs4(zzz5001, zzz4001, ed, ee)
new_lt18(zzz500000, zzz4300000, cbd) → new_esEs8(new_compare4(zzz500000, zzz4300000, cbd), LT)
new_ltEs18(zzz50000, zzz430000, ty_Int) → new_ltEs6(zzz50000, zzz430000)
new_esEs22(zzz5000, zzz4000, ty_Int) → new_esEs17(zzz5000, zzz4000)
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_esEs6(@3(zzz5000, zzz5001, zzz5002), @3(zzz4000, zzz4001, zzz4002), cge, cgf, cgg) → new_asAs(new_esEs28(zzz5000, zzz4000, cge), new_asAs(new_esEs27(zzz5001, zzz4001, cgf), new_esEs26(zzz5002, zzz4002, cgg)))
new_esEs28(zzz5000, zzz4000, app(ty_Maybe, dcd)) → new_esEs7(zzz5000, zzz4000, dcd)
new_esEs28(zzz5000, zzz4000, ty_Double) → new_esEs9(zzz5000, zzz4000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, ty_Double) → new_ltEs8(zzz500000, zzz4300000)
new_lt20(zzz500001, zzz4300001, ty_Double) → new_lt15(zzz500001, zzz4300001)
new_lt20(zzz500001, zzz4300001, ty_Integer) → new_lt10(zzz500001, zzz4300001)
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_esEs26(zzz5002, zzz4002, ty_@0) → new_esEs10(zzz5002, zzz4002)
new_esEs18(zzz5001, zzz4001, ty_Float) → new_esEs13(zzz5001, zzz4001)
new_compare25(zzz500000, zzz4300000, False, hf, hg) → new_compare15(zzz500000, zzz4300000, new_ltEs13(zzz500000, zzz4300000, hf, hg), hf, hg)
new_esEs23(zzz500000, zzz4300000, app(app(ty_Either, ha), hb)) → new_esEs4(zzz500000, zzz4300000, ha, hb)
new_esEs20(zzz5000, zzz4000, ty_Char) → new_esEs11(zzz5000, zzz4000)
new_lt19(zzz500000, zzz4300000, app(ty_Maybe, cdc)) → new_lt11(zzz500000, zzz4300000, cdc)
new_esEs4(Left(zzz5000), Left(zzz4000), app(ty_Maybe, bgc), bfb) → new_esEs7(zzz5000, zzz4000, bgc)
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_esEs20(zzz5000, zzz4000, ty_Integer) → new_esEs15(zzz5000, zzz4000)
new_primEqNat0(Zero, Succ(zzz40000)) → False
new_primEqNat0(Succ(zzz50000), Zero) → False
new_esEs18(zzz5001, zzz4001, ty_Integer) → new_esEs15(zzz5001, zzz4001)
new_esEs17(zzz500, zzz400) → new_primEqInt(zzz500, zzz400)
new_lt5(zzz500000, zzz4300000, ha, hb) → new_esEs8(new_compare12(zzz500000, zzz4300000, ha, hb), LT)
new_compare25(zzz500000, zzz4300000, True, hf, hg) → EQ
new_esEs20(zzz5000, zzz4000, ty_Bool) → new_esEs14(zzz5000, zzz4000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), app(app(ty_Either, bbf), bbg), bbe) → new_ltEs7(zzz500000, zzz4300000, bbf, bbg)
new_ltEs14(True, True) → True
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs24(zzz500001, zzz4300001, app(app(ty_Either, cea), ceb)) → new_esEs4(zzz500001, zzz4300001, cea, ceb)
new_esEs28(zzz5000, zzz4000, app(app(app(ty_@3, dca), dcb), dcc)) → new_esEs6(zzz5000, zzz4000, dca, dcb, dcc)
new_compare30(zzz500000, zzz4300000, ty_Bool) → new_compare17(zzz500000, zzz4300000)
new_esEs27(zzz5001, zzz4001, app(app(ty_Either, dab), dac)) → new_esEs4(zzz5001, zzz4001, dab, dac)
new_esEs27(zzz5001, zzz4001, app(app(app(ty_@3, dag), dah), dba)) → new_esEs6(zzz5001, zzz4001, dag, dah, dba)
new_compare4(:(zzz500000, zzz500001), [], ce) → GT
new_ltEs18(zzz50000, zzz430000, app(ty_[], ce)) → new_ltEs17(zzz50000, zzz430000, ce)
new_esEs27(zzz5001, zzz4001, app(app(ty_@2, dad), dae)) → new_esEs5(zzz5001, zzz4001, dad, dae)
new_esEs27(zzz5001, zzz4001, ty_Int) → new_esEs17(zzz5001, zzz4001)
new_esEs23(zzz500000, zzz4300000, ty_Int) → new_esEs17(zzz500000, zzz4300000)
new_lt13(zzz500000, zzz4300000, ty_@0) → new_lt4(zzz500000, zzz4300000)
new_compare30(zzz500000, zzz4300000, ty_Char) → new_compare10(zzz500000, zzz4300000)
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_compare4([], :(zzz4300000, zzz4300001), ce) → LT
new_sr0(zzz5000, zzz4000) → new_primMulInt(zzz5000, zzz4000)
new_lt19(zzz500000, zzz4300000, app(ty_[], cdh)) → new_lt18(zzz500000, zzz4300000, cdh)
new_compare15(zzz500000, zzz4300000, False, hf, hg) → GT
new_ltEs18(zzz50000, zzz430000, ty_Float) → new_ltEs12(zzz50000, zzz430000)
new_ltEs18(zzz50000, zzz430000, ty_Integer) → new_ltEs9(zzz50000, zzz430000)
new_ltEs19(zzz500001, zzz4300001, ty_Double) → new_ltEs8(zzz500001, zzz4300001)
new_compare30(zzz500000, zzz4300000, ty_Float) → new_compare16(zzz500000, zzz4300000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), app(ty_[], bcg), bbe) → new_ltEs17(zzz500000, zzz4300000, bcg)
new_esEs11(Char(zzz5000), Char(zzz4000)) → new_primEqNat0(zzz5000, zzz4000)
new_esEs7(Just(zzz5000), Just(zzz4000), app(app(app(ty_@3, de), df), dg)) → new_esEs6(zzz5000, zzz4000, de, df, dg)
new_esEs25(zzz500000, zzz4300000, app(ty_Maybe, cdc)) → new_esEs7(zzz500000, zzz4300000, cdc)
new_compare29(Nothing, Nothing, False, gg) → LT
new_esEs23(zzz500000, zzz4300000, app(ty_Ratio, cbc)) → new_esEs16(zzz500000, zzz4300000, cbc)
new_lt13(zzz500000, zzz4300000, app(app(ty_Either, ha), hb)) → new_lt5(zzz500000, zzz4300000, ha, hb)
new_esEs16(:%(zzz5000, zzz5001), :%(zzz4000, zzz4001), bbc) → new_asAs(new_esEs22(zzz5000, zzz4000, bbc), new_esEs21(zzz5001, zzz4001, bbc))
new_ltEs4(Just(zzz500000), Just(zzz4300000), app(ty_Maybe, bg)) → new_ltEs4(zzz500000, zzz4300000, bg)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Float) → new_ltEs12(zzz500000, zzz4300000)
new_primCompAux0(zzz500000, zzz4300000, zzz220, ce) → new_primCompAux00(zzz220, new_compare30(zzz500000, zzz4300000, ce))
new_esEs19(zzz5000, zzz4000, app(app(ty_@2, ga), gb)) → new_esEs5(zzz5000, zzz4000, ga, gb)
new_esEs19(zzz5000, zzz4000, app(ty_Ratio, gh)) → new_esEs16(zzz5000, zzz4000, gh)
new_esEs10(@0, @0) → True
new_compare29(zzz5000, zzz43000, True, gg) → EQ
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs27(zzz5001, zzz4001, ty_Float) → new_esEs13(zzz5001, zzz4001)
new_lt13(zzz500000, zzz4300000, ty_Integer) → new_lt10(zzz500000, zzz4300000)
new_compare28(zzz5000, zzz43000, gg) → new_compare29(zzz5000, zzz43000, new_esEs7(zzz5000, zzz43000, gg), gg)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, app(app(ty_@2, bgh), bha)) → new_esEs5(zzz5000, zzz4000, bgh, bha)
new_esEs24(zzz500001, zzz4300001, ty_Char) → new_esEs11(zzz500001, zzz4300001)
new_esEs28(zzz5000, zzz4000, ty_@0) → new_esEs10(zzz5000, zzz4000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, app(app(ty_Either, bda), bdb)) → new_ltEs7(zzz500000, zzz4300000, bda, bdb)
new_esEs28(zzz5000, zzz4000, ty_Int) → new_esEs17(zzz5000, zzz4000)
new_compare7(:%(zzz500000, zzz500001), :%(zzz4300000, zzz4300001), ty_Integer) → new_compare9(new_sr(zzz500000, zzz4300001), new_sr(zzz4300000, zzz500001))
new_compare9(Integer(zzz500000), Integer(zzz4300000)) → new_primCmpInt(zzz500000, zzz4300000)
new_compare23(zzz500000, zzz4300000, False) → new_compare112(zzz500000, zzz4300000, new_ltEs10(zzz500000, zzz4300000))
new_asAs(False, zzz207) → False
new_esEs4(Left(zzz5000), Left(zzz4000), ty_@0, bfb) → new_esEs10(zzz5000, zzz4000)
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_esEs26(zzz5002, zzz4002, ty_Double) → new_esEs9(zzz5002, zzz4002)
new_ltEs10(LT, GT) → True
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_ltEs4(Just(zzz500000), Just(zzz4300000), app(ty_Ratio, bh)) → new_ltEs15(zzz500000, zzz4300000, bh)
new_esEs23(zzz500000, zzz4300000, app(app(app(ty_@3, hc), hd), he)) → new_esEs6(zzz500000, zzz4300000, hc, hd, he)
new_lt8(zzz500000, zzz4300000, hc, hd, he) → new_esEs8(new_compare13(zzz500000, zzz4300000, hc, hd, he), LT)
new_lt11(zzz5000, zzz43000, gg) → new_esEs8(new_compare28(zzz5000, zzz43000, gg), LT)
new_esEs26(zzz5002, zzz4002, app(ty_[], chd)) → new_esEs12(zzz5002, zzz4002, chd)
new_compare4(:(zzz500000, zzz500001), :(zzz4300000, zzz4300001), ce) → new_primCompAux0(zzz500000, zzz4300000, new_compare4(zzz500001, zzz4300001, ce), ce)
new_compare16(Float(zzz500000, zzz500001), Float(zzz4300000, zzz4300001)) → new_compare8(new_sr0(zzz500000, zzz4300000), new_sr0(zzz500001, zzz4300001))
new_esEs26(zzz5002, zzz4002, app(ty_Maybe, chh)) → new_esEs7(zzz5002, zzz4002, chh)
new_esEs28(zzz5000, zzz4000, ty_Bool) → new_esEs14(zzz5000, zzz4000)
new_compare110(zzz500000, zzz4300000, True, hc, hd, he) → LT
new_lt19(zzz500000, zzz4300000, app(app(ty_Either, ccg), cch)) → new_lt5(zzz500000, zzz4300000, ccg, cch)
new_ltEs18(zzz50000, zzz430000, ty_Bool) → new_ltEs14(zzz50000, zzz430000)
new_esEs28(zzz5000, zzz4000, ty_Integer) → new_esEs15(zzz5000, zzz4000)
new_esEs18(zzz5001, zzz4001, ty_Ordering) → new_esEs8(zzz5001, zzz4001)
new_esEs19(zzz5000, zzz4000, ty_Double) → new_esEs9(zzz5000, zzz4000)
new_lt20(zzz500001, zzz4300001, app(app(ty_@2, cec), ced)) → new_lt16(zzz500001, zzz4300001, cec, ced)
new_esEs5(@2(zzz5000, zzz5001), @2(zzz4000, zzz4001), eb, ec) → new_asAs(new_esEs19(zzz5000, zzz4000, eb), new_esEs18(zzz5001, zzz4001, ec))
new_compare26(zzz500000, zzz4300000, False) → new_compare19(zzz500000, zzz4300000, new_ltEs14(zzz500000, zzz4300000))
new_esEs28(zzz5000, zzz4000, app(app(ty_Either, dbd), dbe)) → new_esEs4(zzz5000, zzz4000, dbd, dbe)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, app(ty_Maybe, bhf)) → new_esEs7(zzz5000, zzz4000, bhf)
new_esEs7(Just(zzz5000), Just(zzz4000), ty_@0) → new_esEs10(zzz5000, zzz4000)
new_ltEs18(zzz50000, zzz430000, ty_Char) → new_ltEs5(zzz50000, zzz430000)
new_esEs28(zzz5000, zzz4000, ty_Float) → new_esEs13(zzz5000, zzz4000)
new_lt13(zzz500000, zzz4300000, ty_Ordering) → new_lt9(zzz500000, zzz4300000)
new_esEs25(zzz500000, zzz4300000, app(app(app(ty_@3, cde), cdf), cdg)) → new_esEs6(zzz500000, zzz4300000, cde, cdf, cdg)
new_ltEs10(EQ, EQ) → True
new_ltEs18(zzz50000, zzz430000, app(app(ty_@2, bed), bee)) → new_ltEs13(zzz50000, zzz430000, bed, bee)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Int, bfb) → new_esEs17(zzz5000, zzz4000)
new_esEs23(zzz500000, zzz4300000, ty_Integer) → new_esEs15(zzz500000, zzz4300000)
new_ltEs10(LT, LT) → True
new_esEs14(True, True) → True
new_compare111(zzz200, zzz201, False, bbd) → GT
new_esEs27(zzz5001, zzz4001, ty_Bool) → new_esEs14(zzz5001, zzz4001)
new_esEs7(Just(zzz5000), Just(zzz4000), app(app(ty_Either, cg), da)) → new_esEs4(zzz5000, zzz4000, cg, da)
new_compare10(Char(zzz500000), Char(zzz4300000)) → new_primCmpNat0(zzz500000, zzz4300000)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Float, bfb) → new_esEs13(zzz5000, zzz4000)
new_lt13(zzz500000, zzz4300000, app(app(ty_@2, hf), hg)) → new_lt16(zzz500000, zzz4300000, hf, hg)
new_ltEs7(Left(zzz500000), Left(zzz4300000), app(app(ty_@2, bbh), bca), bbe) → new_ltEs13(zzz500000, zzz4300000, bbh, bca)
new_esEs7(Just(zzz5000), Just(zzz4000), app(ty_Ratio, ea)) → new_esEs16(zzz5000, zzz4000, ea)
new_lt13(zzz500000, zzz4300000, app(ty_Maybe, cbb)) → new_lt11(zzz500000, zzz4300000, cbb)
new_ltEs20(zzz500002, zzz4300002, app(app(ty_Either, cfc), cfd)) → new_ltEs7(zzz500002, zzz4300002, cfc, cfd)
new_esEs18(zzz5001, zzz4001, ty_@0) → new_esEs10(zzz5001, zzz4001)
new_ltEs16(@3(zzz500000, zzz500001, zzz500002), @3(zzz4300000, zzz4300001, zzz4300002), beg, beh, bfa) → new_pePe(new_lt19(zzz500000, zzz4300000, beg), new_asAs(new_esEs25(zzz500000, zzz4300000, beg), new_pePe(new_lt20(zzz500001, zzz4300001, beh), new_asAs(new_esEs24(zzz500001, zzz4300001, beh), new_ltEs20(zzz500002, zzz4300002, bfa)))))
new_esEs4(Right(zzz5000), Right(zzz4000), bge, ty_Double) → new_esEs9(zzz5000, zzz4000)
new_ltEs14(True, False) → False
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_esEs20(zzz5000, zzz4000, ty_Int) → new_esEs17(zzz5000, zzz4000)
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_esEs25(zzz500000, zzz4300000, app(app(ty_@2, cda), cdb)) → new_esEs5(zzz500000, zzz4300000, cda, cdb)
new_ltEs20(zzz500002, zzz4300002, ty_Double) → new_ltEs8(zzz500002, zzz4300002)
new_ltEs7(Left(zzz500000), Left(zzz4300000), app(ty_Ratio, bcc), bbe) → new_ltEs15(zzz500000, zzz4300000, bcc)
new_ltEs19(zzz500001, zzz4300001, app(app(app(ty_@3, ccc), ccd), cce)) → new_ltEs16(zzz500001, zzz4300001, ccc, ccd, cce)
new_ltEs20(zzz500002, zzz4300002, app(app(app(ty_@3, cga), cgb), cgc)) → new_ltEs16(zzz500002, zzz4300002, cga, cgb, cgc)
new_compare112(zzz500000, zzz4300000, False) → GT
new_ltEs10(EQ, LT) → False
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Float) → new_esEs13(zzz5000, zzz4000)
new_esEs14(False, False) → True
new_esEs7(Just(zzz5000), Just(zzz4000), app(app(ty_@2, db), dc)) → new_esEs5(zzz5000, zzz4000, db, dc)
new_lt20(zzz500001, zzz4300001, ty_Char) → new_lt12(zzz500001, zzz4300001)
new_lt9(zzz500000, zzz4300000) → new_esEs8(new_compare6(zzz500000, zzz4300000), LT)
new_ltEs10(GT, LT) → False
new_esEs18(zzz5001, zzz4001, ty_Bool) → new_esEs14(zzz5001, zzz4001)
new_esEs22(zzz5000, zzz4000, ty_Integer) → new_esEs15(zzz5000, zzz4000)
new_primPlusNat1(Zero, Zero) → Zero
new_compare30(zzz500000, zzz4300000, app(app(app(ty_@3, caf), cag), cah)) → new_compare13(zzz500000, zzz4300000, caf, cag, cah)
new_esEs19(zzz5000, zzz4000, ty_Integer) → new_esEs15(zzz5000, zzz4000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(ty_[], bfg), bfb) → new_esEs12(zzz5000, zzz4000, bfg)
new_esEs26(zzz5002, zzz4002, app(app(ty_Either, cgh), cha)) → new_esEs4(zzz5002, zzz4002, cgh, cha)
new_asAs(True, zzz207) → zzz207
new_esEs28(zzz5000, zzz4000, app(ty_[], dbh)) → new_esEs12(zzz5000, zzz4000, dbh)
new_esEs27(zzz5001, zzz4001, app(ty_[], daf)) → new_esEs12(zzz5001, zzz4001, daf)
new_esEs19(zzz5000, zzz4000, app(app(ty_Either, fg), fh)) → new_esEs4(zzz5000, zzz4000, fg, fh)
new_ltEs4(Just(zzz500000), Nothing, bb) → False
new_esEs20(zzz5000, zzz4000, ty_Double) → new_esEs9(zzz5000, zzz4000)
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_ltEs4(Just(zzz500000), Just(zzz4300000), app(ty_[], cd)) → new_ltEs17(zzz500000, zzz4300000, cd)
new_esEs4(Right(zzz5000), Left(zzz4000), bge, bfb) → False
new_esEs4(Left(zzz5000), Right(zzz4000), bge, bfb) → False
new_ltEs19(zzz500001, zzz4300001, ty_Float) → new_ltEs12(zzz500001, zzz4300001)
new_ltEs20(zzz500002, zzz4300002, app(ty_Maybe, cfg)) → new_ltEs4(zzz500002, zzz4300002, cfg)
new_esEs4(Left(zzz5000), Left(zzz4000), app(app(app(ty_@3, bfh), bga), bgb), bfb) → new_esEs6(zzz5000, zzz4000, bfh, bga, bgb)
new_ltEs19(zzz500001, zzz4300001, ty_Char) → new_ltEs5(zzz500001, zzz4300001)
new_fsEs(zzz210) → new_not(new_esEs8(zzz210, GT))
new_esEs19(zzz5000, zzz4000, ty_@0) → new_esEs10(zzz5000, zzz4000)
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Bool) → new_esEs14(zzz5000, zzz4000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Double, bbe) → new_ltEs8(zzz500000, zzz4300000)
new_esEs24(zzz500001, zzz4300001, ty_Float) → new_esEs13(zzz500001, zzz4300001)
new_ltEs11(zzz50000, zzz430000) → new_fsEs(new_compare11(zzz50000, zzz430000))
new_lt20(zzz500001, zzz4300001, ty_Int) → new_lt14(zzz500001, zzz4300001)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, ty_Float) → new_esEs13(zzz5000, zzz4000)
new_esEs19(zzz5000, zzz4000, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_ltEs20(zzz500002, zzz4300002, app(app(ty_@2, cfe), cff)) → new_ltEs13(zzz500002, zzz4300002, cfe, cff)
new_esEs27(zzz5001, zzz4001, ty_Char) → new_esEs11(zzz5001, zzz4001)
new_ltEs20(zzz500002, zzz4300002, ty_Int) → new_ltEs6(zzz500002, zzz4300002)
new_compare110(zzz500000, zzz4300000, False, hc, hd, he) → GT
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Char) → new_ltEs5(zzz500000, zzz4300000)
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Char) → new_esEs11(zzz5000, zzz4000)
new_primCompAux00(zzz225, GT) → GT
new_ltEs20(zzz500002, zzz4300002, ty_Integer) → new_ltEs9(zzz500002, zzz4300002)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, app(ty_Maybe, bde)) → new_ltEs4(zzz500000, zzz4300000, bde)
new_lt19(zzz500000, zzz4300000, ty_Int) → new_lt14(zzz500000, zzz4300000)
new_ltEs4(Just(zzz500000), Just(zzz4300000), app(app(app(ty_@3, ca), cb), cc)) → new_ltEs16(zzz500000, zzz4300000, ca, cb, cc)
new_ltEs18(zzz50000, zzz430000, ty_Ordering) → new_ltEs10(zzz50000, zzz430000)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Integer) → new_ltEs9(zzz500000, zzz4300000)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_compare30(zzz500000, zzz4300000, ty_Ordering) → new_compare6(zzz500000, zzz4300000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, ty_Float) → new_ltEs12(zzz500000, zzz4300000)
new_esEs27(zzz5001, zzz4001, ty_Integer) → new_esEs15(zzz5001, zzz4001)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, ty_Int) → new_ltEs6(zzz500000, zzz4300000)
new_not(True) → False

The set Q consists of the following terms:

new_compare30(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_compare23(x0, x1, True)
new_lt11(x0, x1, x2)
new_lt14(x0, x1)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs18(x0, x1, app(app(ty_@2, x2), x3))
new_asAs(True, x0)
new_compare29(Nothing, Nothing, False, x0)
new_compare19(x0, x1, True)
new_esEs26(x0, x1, ty_@0)
new_ltEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs18(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_Ordering)
new_esEs18(x0, x1, ty_Int)
new_ltEs19(x0, x1, app(ty_[], x2))
new_primPlusNat1(Zero, Succ(x0))
new_compare29(Nothing, Just(x0), False, x1)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_compare30(x0, x1, ty_@0)
new_lt20(x0, x1, ty_Ordering)
new_esEs9(Double(x0, x1), Double(x2, x3))
new_ltEs7(Right(x0), Right(x1), x2, ty_@0)
new_primCompAux0(x0, x1, x2, x3)
new_primMulNat0(Succ(x0), Zero)
new_lt19(x0, x1, ty_Double)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_@0)
new_primPlusNat1(Succ(x0), Zero)
new_esEs21(x0, x1, ty_Int)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare4(:(x0, x1), :(x2, x3), x4)
new_ltEs10(LT, LT)
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_esEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs16(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs23(x0, x1, ty_Bool)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs27(x0, x1, ty_Int)
new_esEs4(Right(x0), Left(x1), x2, x3)
new_esEs4(Left(x0), Right(x1), x2, x3)
new_esEs18(x0, x1, ty_Char)
new_esEs24(x0, x1, ty_Char)
new_ltEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(True, False)
new_ltEs14(False, True)
new_esEs25(x0, x1, ty_Double)
new_pePe(False, x0)
new_esEs19(x0, x1, ty_Char)
new_esEs25(x0, x1, ty_Char)
new_compare27(x0, x1, True, x2, x3)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs7(Just(x0), Just(x1), ty_Double)
new_esEs8(GT, GT)
new_esEs23(x0, x1, ty_@0)
new_compare4([], :(x0, x1), x2)
new_lt9(x0, x1)
new_lt19(x0, x1, ty_Ordering)
new_esEs11(Char(x0), Char(x1))
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs4(Left(x0), Left(x1), ty_Int, x2)
new_esEs7(Nothing, Just(x0), x1)
new_esEs8(LT, LT)
new_sr0(x0, x1)
new_compare6(x0, x1)
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_compare30(x0, x1, ty_Double)
new_esEs7(Just(x0), Just(x1), ty_Char)
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, app(ty_[], x2))
new_lt13(x0, x1, app(ty_Ratio, x2))
new_compare19(x0, x1, False)
new_ltEs4(Nothing, Nothing, x0)
new_compare110(x0, x1, False, x2, x3, x4)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs26(x0, x1, ty_Double)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_lt18(x0, x1, x2)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_lt16(x0, x1, x2, x3)
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_compare111(x0, x1, False, x2)
new_compare4([], [], x0)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs7(Left(x0), Left(x1), ty_Char, x2)
new_ltEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs17(x0, x1)
new_ltEs19(x0, x1, ty_Char)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs14(True, True)
new_compare26(x0, x1, True)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Char)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare112(x0, x1, False)
new_esEs18(x0, x1, ty_Bool)
new_esEs20(x0, x1, ty_Float)
new_primEqNat0(Zero, Zero)
new_ltEs4(Just(x0), Just(x1), ty_Double)
new_compare30(x0, x1, ty_Char)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_ltEs7(Right(x0), Right(x1), x2, ty_Char)
new_esEs20(x0, x1, ty_Int)
new_lt13(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Double)
new_lt19(x0, x1, ty_Bool)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, ty_@0)
new_lt13(x0, x1, app(ty_[], x2))
new_esEs12([], :(x0, x1), x2)
new_esEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs28(x0, x1, ty_Integer)
new_compare17(x0, x1)
new_ltEs17(x0, x1, x2)
new_primPlusNat0(Zero, x0)
new_ltEs20(x0, x1, ty_Int)
new_compare13(x0, x1, x2, x3, x4)
new_primMulNat0(Zero, Zero)
new_esEs4(Right(x0), Right(x1), x2, ty_Float)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpNat0(Succ(x0), Zero)
new_compare16(Float(x0, x1), Float(x2, x3))
new_ltEs20(x0, x1, ty_Integer)
new_compare30(x0, x1, ty_Ordering)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs26(x0, x1, ty_Integer)
new_ltEs10(EQ, LT)
new_ltEs10(LT, EQ)
new_lt4(x0, x1)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_ltEs7(Left(x0), Left(x1), ty_@0, x2)
new_lt13(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs19(x0, x1, ty_Bool)
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs28(x0, x1, ty_@0)
new_primMulNat0(Succ(x0), Succ(x1))
new_lt7(x0, x1)
new_esEs23(x0, x1, ty_Float)
new_ltEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_Double)
new_compare113(x0, x1, False, x2, x3)
new_ltEs18(x0, x1, ty_@0)
new_compare15(x0, x1, True, x2, x3)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs23(x0, x1, ty_Char)
new_esEs24(x0, x1, ty_Int)
new_compare9(Integer(x0), Integer(x1))
new_esEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, ty_Ordering)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_ltEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_compare4(:(x0, x1), [], x2)
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_esEs24(x0, x1, ty_Bool)
new_ltEs13(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs26(x0, x1, ty_Char)
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_compare25(x0, x1, False, x2, x3)
new_esEs20(x0, x1, ty_Ordering)
new_esEs12(:(x0, x1), :(x2, x3), x4)
new_fsEs(x0)
new_lt8(x0, x1, x2, x3, x4)
new_ltEs11(x0, x1)
new_esEs23(x0, x1, ty_Double)
new_lt13(x0, x1, ty_@0)
new_ltEs7(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Just(x0), Just(x1), ty_Int)
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_compare26(x0, x1, False)
new_ltEs18(x0, x1, ty_Double)
new_ltEs7(Right(x0), Left(x1), x2, x3)
new_ltEs7(Left(x0), Right(x1), x2, x3)
new_ltEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs25(x0, x1, ty_Bool)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primPlusNat1(Zero, Zero)
new_esEs28(x0, x1, ty_Float)
new_ltEs7(Right(x0), Right(x1), x2, ty_Int)
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_lt12(x0, x1)
new_compare7(:%(x0, x1), :%(x2, x3), ty_Int)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_ltEs4(Just(x0), Just(x1), ty_Int)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_compare11(@0, @0)
new_esEs4(Right(x0), Right(x1), x2, ty_Integer)
new_primMulNat0(Zero, Succ(x0))
new_esEs26(x0, x1, ty_Bool)
new_asAs(False, x0)
new_esEs12(:(x0, x1), [], x2)
new_ltEs4(Just(x0), Just(x1), ty_Bool)
new_ltEs8(x0, x1)
new_ltEs18(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Float)
new_esEs27(x0, x1, ty_Double)
new_ltEs19(x0, x1, ty_Ordering)
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs4(Just(x0), Just(x1), ty_Ordering)
new_esEs4(Left(x0), Left(x1), ty_@0, x2)
new_esEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs18(x0, x1, ty_Double)
new_ltEs10(GT, LT)
new_esEs4(Left(x0), Left(x1), ty_Double, x2)
new_ltEs10(LT, GT)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs28(x0, x1, ty_Double)
new_esEs10(@0, @0)
new_compare14(Double(x0, x1), Double(x2, x3))
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_compare24(x0, x1, True, x2, x3, x4)
new_compare30(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_Integer)
new_ltEs18(x0, x1, ty_Float)
new_compare8(x0, x1)
new_lt13(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs20(x0, x1, ty_Char)
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs7(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs19(x0, x1, ty_Integer)
new_pePe(True, x0)
new_compare29(Just(x0), Just(x1), False, x2)
new_esEs27(x0, x1, ty_Float)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_primCompAux00(x0, EQ)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_lt19(x0, x1, ty_Float)
new_primEqNat0(Succ(x0), Zero)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_ltEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_lt17(x0, x1, x2)
new_esEs28(x0, x1, ty_Int)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_compare27(x0, x1, False, x2, x3)
new_esEs18(x0, x1, ty_Ordering)
new_esEs25(x0, x1, ty_Int)
new_esEs18(x0, x1, app(ty_Ratio, x2))
new_esEs7(Nothing, Nothing, x0)
new_ltEs15(x0, x1, x2)
new_ltEs4(Just(x0), Just(x1), ty_@0)
new_esEs19(x0, x1, app(ty_[], x2))
new_compare23(x0, x1, False)
new_compare30(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_ltEs4(Just(x0), Nothing, x1)
new_esEs8(EQ, EQ)
new_compare112(x0, x1, True)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs4(Right(x0), Right(x1), x2, ty_Int)
new_esEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs19(x0, x1, ty_Double)
new_esEs13(Float(x0, x1), Float(x2, x3))
new_primEqInt(Neg(Zero), Neg(Zero))
new_gt(x0, x1, x2)
new_lt13(x0, x1, ty_Char)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, ty_Char)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_esEs15(Integer(x0), Integer(x1))
new_ltEs12(x0, x1)
new_ltEs20(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_@0)
new_esEs14(True, False)
new_esEs14(False, True)
new_ltEs4(Just(x0), Just(x1), ty_Float)
new_ltEs7(Right(x0), Right(x1), x2, ty_Float)
new_esEs18(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, app(ty_[], x2))
new_ltEs6(x0, x1)
new_esEs22(x0, x1, ty_Int)
new_esEs20(x0, x1, ty_Double)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare110(x0, x1, True, x2, x3, x4)
new_ltEs9(x0, x1)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs19(x0, x1, ty_@0)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_lt19(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Ordering)
new_esEs27(x0, x1, ty_Integer)
new_esEs16(:%(x0, x1), :%(x2, x3), x4)
new_lt20(x0, x1, ty_Float)
new_compare25(x0, x1, True, x2, x3)
new_compare30(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Integer)
new_primCmpNat0(Succ(x0), Succ(x1))
new_lt19(x0, x1, ty_Char)
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_esEs20(x0, x1, ty_Integer)
new_esEs28(x0, x1, ty_Ordering)
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_esEs21(x0, x1, ty_Integer)
new_compare28(x0, x1, x2)
new_ltEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_esEs4(Right(x0), Right(x1), x2, ty_Double)
new_ltEs7(Right(x0), Right(x1), x2, ty_Double)
new_lt20(x0, x1, ty_Bool)
new_primPlusNat0(Succ(x0), x1)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_@0)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, ty_Integer)
new_compare30(x0, x1, app(ty_Maybe, x2))
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs7(Just(x0), Just(x1), ty_Float)
new_compare18(x0, x1, x2, x3)
new_esEs19(x0, x1, ty_Float)
new_ltEs20(x0, x1, ty_Bool)
new_primCmpNat0(Zero, Zero)
new_esEs4(Left(x0), Left(x1), ty_Integer, x2)
new_esEs19(x0, x1, ty_Ordering)
new_lt13(x0, x1, ty_Bool)
new_ltEs19(x0, x1, ty_Float)
new_esEs27(x0, x1, app(ty_[], x2))
new_ltEs7(Left(x0), Left(x1), ty_Double, x2)
new_esEs12([], [], x0)
new_lt10(x0, x1)
new_compare7(:%(x0, x1), :%(x2, x3), ty_Integer)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_compare113(x0, x1, True, x2, x3)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs20(x0, x1, app(ty_[], x2))
new_ltEs7(Left(x0), Left(x1), ty_Bool, x2)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, ty_Ordering)
new_esEs4(Left(x0), Left(x1), ty_Char, x2)
new_esEs26(x0, x1, ty_Float)
new_ltEs7(Left(x0), Left(x1), ty_Float, x2)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt5(x0, x1, x2, x3)
new_esEs28(x0, x1, app(ty_[], x2))
new_compare29(Just(x0), Nothing, False, x1)
new_ltEs10(GT, GT)
new_ltEs14(True, True)
new_ltEs14(False, False)
new_esEs24(x0, x1, ty_Ordering)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_lt19(x0, x1, ty_@0)
new_esEs18(x0, x1, ty_Float)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_lt13(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, ty_Char)
new_ltEs7(Left(x0), Left(x1), ty_Int, x2)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_esEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_not(True)
new_esEs19(x0, x1, ty_Int)
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Just(x0), Just(x1), ty_@0)
new_compare30(x0, x1, ty_Integer)
new_ltEs5(x0, x1)
new_compare30(x0, x1, app(ty_Ratio, x2))
new_esEs4(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs20(x0, x1, ty_Double)
new_esEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(Just(x0), Just(x1), ty_Integer)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_not(False)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Integer)
new_esEs4(Right(x0), Right(x1), x2, ty_@0)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_ltEs4(Just(x0), Just(x1), app(ty_[], x2))
new_primCompAux00(x0, LT)
new_lt6(x0, x1)
new_ltEs10(EQ, GT)
new_ltEs10(GT, EQ)
new_ltEs19(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Float)
new_esEs24(x0, x1, app(ty_[], x2))
new_ltEs18(x0, x1, ty_Char)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs19(x0, x1, ty_Integer)
new_esEs18(x0, x1, app(ty_[], x2))
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_sr(Integer(x0), Integer(x1))
new_esEs4(Right(x0), Right(x1), x2, ty_Char)
new_esEs27(x0, x1, ty_Char)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs20(x0, x1, ty_Bool)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(Just(x0), Just(x1), ty_Char)
new_esEs4(Left(x0), Left(x1), ty_Float, x2)
new_ltEs4(Nothing, Just(x0), x1)
new_esEs18(x0, x1, ty_@0)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_ltEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_lt13(x0, x1, ty_Double)
new_esEs18(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_Bool)
new_lt13(x0, x1, ty_Ordering)
new_compare12(x0, x1, x2, x3)
new_compare15(x0, x1, False, x2, x3)
new_ltEs18(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Ordering)
new_compare30(x0, x1, ty_Float)
new_esEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare111(x0, x1, True, x2)
new_lt13(x0, x1, ty_Integer)
new_lt19(x0, x1, app(ty_[], x2))
new_esEs14(False, False)
new_primEqInt(Pos(Zero), Pos(Zero))
new_compare30(x0, x1, app(ty_[], x2))
new_compare10(Char(x0), Char(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs24(x0, x1, ty_Integer)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Double)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs25(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, ty_Float)
new_lt13(x0, x1, ty_Int)
new_compare29(x0, x1, True, x2)
new_lt13(x0, x1, ty_Float)
new_lt20(x0, x1, ty_Integer)
new_primCmpNat0(Zero, Succ(x0))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_ltEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_Int)
new_primCompAux00(x0, GT)
new_ltEs20(x0, x1, ty_@0)
new_esEs4(Left(x0), Left(x1), ty_Bool, x2)
new_lt15(x0, x1)
new_ltEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primEqNat0(Zero, Succ(x0))
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs7(Left(x0), Left(x1), ty_Integer, x2)
new_esEs27(x0, x1, ty_Bool)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_@0)
new_compare24(x0, x1, False, x2, x3, x4)
new_esEs7(Just(x0), Nothing, x1)
new_esEs18(x0, x1, ty_Integer)
new_ltEs10(EQ, EQ)

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_intersectFM_C2Elt1010(zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz519, Branch(zzz5200, zzz5201, zzz5202, zzz5203, zzz5204), zzz521, True, h, ba) → new_intersectFM_C2Elt109(zzz512, zzz513, zzz514, zzz515, zzz516, zzz5200, zzz5201, zzz5202, zzz5203, zzz5204, h, ba)
new_intersectFM_C2Elt1010(zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz519, zzz520, zzz521, False, h, ba) → new_intersectFM_C2Elt107(zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz519, zzz520, zzz521, new_gt(Nothing, zzz517, ba), h, ba)
new_intersectFM_C2Elt108(zzz512, zzz513, zzz514, zzz515, zzz516, Branch(zzz5200, zzz5201, zzz5202, zzz5203, zzz5204), h, ba) → new_intersectFM_C2Elt109(zzz512, zzz513, zzz514, zzz515, zzz516, zzz5200, zzz5201, zzz5202, zzz5203, zzz5204, h, ba)
new_intersectFM_C2Elt109(zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz519, zzz520, zzz521, h, ba) → new_intersectFM_C2Elt1010(zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz519, zzz520, zzz521, new_lt11(Nothing, zzz517, ba), h, ba)
new_intersectFM_C2Elt107(zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz519, zzz520, zzz521, True, h, ba) → new_intersectFM_C2Elt108(zzz512, zzz513, zzz514, zzz515, zzz516, zzz521, h, ba)

The TRS R consists of the following rules:

new_lt19(zzz500000, zzz4300000, ty_Float) → new_lt6(zzz500000, zzz4300000)
new_ltEs18(zzz50000, zzz430000, app(ty_Ratio, bef)) → new_ltEs15(zzz50000, zzz430000, bef)
new_esEs7(Just(zzz5000), Just(zzz4000), app(ty_Maybe, dh)) → new_esEs7(zzz5000, zzz4000, dh)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_esEs20(zzz5000, zzz4000, app(ty_Maybe, bba)) → new_esEs7(zzz5000, zzz4000, bba)
new_esEs12(:(zzz5000, zzz5001), :(zzz4000, zzz4001), hh) → new_asAs(new_esEs20(zzz5000, zzz4000, hh), new_esEs12(zzz5001, zzz4001, hh))
new_esEs7(Just(zzz5000), Just(zzz4000), app(ty_[], dd)) → new_esEs12(zzz5000, zzz4000, dd)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, ty_Ordering) → new_ltEs10(zzz500000, zzz4300000)
new_lt19(zzz500000, zzz4300000, app(app(app(ty_@3, cde), cdf), cdg)) → new_lt8(zzz500000, zzz4300000, cde, cdf, cdg)
new_ltEs18(zzz50000, zzz430000, app(app(app(ty_@3, beg), beh), bfa)) → new_ltEs16(zzz50000, zzz430000, beg, beh, bfa)
new_lt20(zzz500001, zzz4300001, app(ty_[], cfb)) → new_lt18(zzz500001, zzz4300001, cfb)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, ty_Char) → new_esEs11(zzz5000, zzz4000)
new_compare15(zzz500000, zzz4300000, True, hf, hg) → LT
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Bool, bfb) → new_esEs14(zzz5000, zzz4000)
new_ltEs18(zzz50000, zzz430000, app(ty_Maybe, bb)) → new_ltEs4(zzz50000, zzz430000, bb)
new_ltEs20(zzz500002, zzz4300002, ty_Ordering) → new_ltEs10(zzz500002, zzz4300002)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, app(app(app(ty_@3, bhc), bhd), bhe)) → new_esEs6(zzz5000, zzz4000, bhc, bhd, bhe)
new_lt13(zzz500000, zzz4300000, app(app(app(ty_@3, hc), hd), he)) → new_lt8(zzz500000, zzz4300000, hc, hd, he)
new_lt15(zzz500000, zzz4300000) → new_esEs8(new_compare14(zzz500000, zzz4300000), LT)
new_lt20(zzz500001, zzz4300001, app(app(app(ty_@3, ceg), ceh), cfa)) → new_lt8(zzz500001, zzz4300001, ceg, ceh, cfa)
new_esEs27(zzz5001, zzz4001, app(ty_Maybe, dbb)) → new_esEs7(zzz5001, zzz4001, dbb)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Ordering) → new_ltEs10(zzz500000, zzz4300000)
new_esEs23(zzz500000, zzz4300000, ty_Bool) → new_esEs14(zzz500000, zzz4300000)
new_compare27(zzz500000, zzz4300000, False, ha, hb) → new_compare113(zzz500000, zzz4300000, new_ltEs7(zzz500000, zzz4300000, ha, hb), ha, hb)
new_lt19(zzz500000, zzz4300000, ty_Double) → new_lt15(zzz500000, zzz4300000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), app(ty_Maybe, bcb), bbe) → new_ltEs4(zzz500000, zzz4300000, bcb)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, ty_@0) → new_ltEs11(zzz500000, zzz4300000)
new_ltEs20(zzz500002, zzz4300002, app(ty_Ratio, cfh)) → new_ltEs15(zzz500002, zzz4300002, cfh)
new_lt13(zzz500000, zzz4300000, app(ty_[], cbd)) → new_lt18(zzz500000, zzz4300000, cbd)
new_esEs26(zzz5002, zzz4002, ty_Float) → new_esEs13(zzz5002, zzz4002)
new_ltEs7(Left(zzz500000), Right(zzz4300000), bch, bbe) → True
new_primMulNat0(Zero, Zero) → Zero
new_esEs19(zzz5000, zzz4000, ty_Int) → new_esEs17(zzz5000, zzz4000)
new_sr(Integer(zzz43000000), Integer(zzz5000010)) → Integer(new_primMulInt(zzz43000000, zzz5000010))
new_ltEs20(zzz500002, zzz4300002, ty_Float) → new_ltEs12(zzz500002, zzz4300002)
new_ltEs20(zzz500002, zzz4300002, ty_@0) → new_ltEs11(zzz500002, zzz4300002)
new_esEs20(zzz5000, zzz4000, app(ty_Ratio, bbb)) → new_esEs16(zzz5000, zzz4000, bbb)
new_esEs18(zzz5001, zzz4001, ty_Double) → new_esEs9(zzz5001, zzz4001)
new_lt20(zzz500001, zzz4300001, ty_Float) → new_lt6(zzz500001, zzz4300001)
new_esEs23(zzz500000, zzz4300000, ty_Double) → new_esEs9(zzz500000, zzz4300000)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, app(ty_[], bhb)) → new_esEs12(zzz5000, zzz4000, bhb)
new_esEs24(zzz500001, zzz4300001, ty_Integer) → new_esEs15(zzz500001, zzz4300001)
new_ltEs14(False, True) → True
new_ltEs19(zzz500001, zzz4300001, ty_Integer) → new_ltEs9(zzz500001, zzz4300001)
new_ltEs4(Just(zzz500000), Just(zzz4300000), app(app(ty_@2, be), bf)) → new_ltEs13(zzz500000, zzz4300000, be, bf)
new_esEs20(zzz5000, zzz4000, app(app(ty_Either, baa), bab)) → new_esEs4(zzz5000, zzz4000, baa, bab)
new_esEs12([], [], hh) → True
new_ltEs19(zzz500001, zzz4300001, ty_Ordering) → new_ltEs10(zzz500001, zzz4300001)
new_esEs24(zzz500001, zzz4300001, app(app(ty_@2, cec), ced)) → new_esEs5(zzz500001, zzz4300001, cec, ced)
new_lt12(zzz500000, zzz4300000) → new_esEs8(new_compare10(zzz500000, zzz4300000), LT)
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Ordering, bbe) → new_ltEs10(zzz500000, zzz4300000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, app(ty_Ratio, bdf)) → new_ltEs15(zzz500000, zzz4300000, bdf)
new_esEs15(Integer(zzz5000), Integer(zzz4000)) → new_primEqInt(zzz5000, zzz4000)
new_ltEs10(EQ, GT) → True
new_ltEs19(zzz500001, zzz4300001, app(ty_Maybe, cca)) → new_ltEs4(zzz500001, zzz4300001, cca)
new_esEs21(zzz5001, zzz4001, ty_Int) → new_esEs17(zzz5001, zzz4001)
new_ltEs7(Left(zzz500000), Left(zzz4300000), app(app(app(ty_@3, bcd), bce), bcf), bbe) → new_ltEs16(zzz500000, zzz4300000, bcd, bce, bcf)
new_lt13(zzz500000, zzz4300000, ty_Char) → new_lt12(zzz500000, zzz4300000)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Ordering, bfb) → new_esEs8(zzz5000, zzz4000)
new_esEs24(zzz500001, zzz4300001, app(ty_[], cfb)) → new_esEs12(zzz500001, zzz4300001, cfb)
new_esEs25(zzz500000, zzz4300000, ty_Double) → new_esEs9(zzz500000, zzz4300000)
new_esEs25(zzz500000, zzz4300000, ty_Float) → new_esEs13(zzz500000, zzz4300000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, app(ty_[], beb)) → new_ltEs17(zzz500000, zzz4300000, beb)
new_pePe(False, zzz218) → zzz218
new_lt14(zzz5000, zzz43000) → new_esEs8(new_compare8(zzz5000, zzz43000), LT)
new_esEs25(zzz500000, zzz4300000, app(app(ty_Either, ccg), cch)) → new_esEs4(zzz500000, zzz4300000, ccg, cch)
new_esEs12(:(zzz5000, zzz5001), [], hh) → False
new_esEs12([], :(zzz4000, zzz4001), hh) → False
new_esEs25(zzz500000, zzz4300000, ty_Char) → new_esEs11(zzz500000, zzz4300000)
new_esEs25(zzz500000, zzz4300000, ty_Bool) → new_esEs14(zzz500000, zzz4300000)
new_lt19(zzz500000, zzz4300000, ty_Ordering) → new_lt9(zzz500000, zzz4300000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, app(app(ty_@2, bdc), bdd)) → new_ltEs13(zzz500000, zzz4300000, bdc, bdd)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, app(ty_Ratio, bhg)) → new_esEs16(zzz5000, zzz4000, bhg)
new_compare23(zzz500000, zzz4300000, True) → EQ
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Float, bbe) → new_ltEs12(zzz500000, zzz4300000)
new_lt19(zzz500000, zzz4300000, app(ty_Ratio, cdd)) → new_lt17(zzz500000, zzz4300000, cdd)
new_esEs24(zzz500001, zzz4300001, app(ty_Maybe, cee)) → new_esEs7(zzz500001, zzz4300001, cee)
new_ltEs4(Nothing, Just(zzz4300000), bb) → True
new_esEs23(zzz500000, zzz4300000, app(ty_Maybe, cbb)) → new_esEs7(zzz500000, zzz4300000, cbb)
new_compare30(zzz500000, zzz4300000, ty_Integer) → new_compare9(zzz500000, zzz4300000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(ty_Ratio, bgd), bfb) → new_esEs16(zzz5000, zzz4000, bgd)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, ty_Char) → new_ltEs5(zzz500000, zzz4300000)
new_compare13(zzz500000, zzz4300000, hc, hd, he) → new_compare24(zzz500000, zzz4300000, new_esEs6(zzz500000, zzz4300000, hc, hd, he), hc, hd, he)
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_lt4(zzz500000, zzz4300000) → new_esEs8(new_compare11(zzz500000, zzz4300000), LT)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, ty_Integer) → new_esEs15(zzz5000, zzz4000)
new_esEs20(zzz5000, zzz4000, app(app(ty_@2, bac), bad)) → new_esEs5(zzz5000, zzz4000, bac, bad)
new_esEs28(zzz5000, zzz4000, app(ty_Ratio, dce)) → new_esEs16(zzz5000, zzz4000, dce)
new_compare30(zzz500000, zzz4300000, app(ty_Ratio, cae)) → new_compare7(zzz500000, zzz4300000, cae)
new_compare19(zzz500000, zzz4300000, True) → LT
new_compare6(zzz500000, zzz4300000) → new_compare23(zzz500000, zzz4300000, new_esEs8(zzz500000, zzz4300000))
new_ltEs18(zzz50000, zzz430000, ty_@0) → new_ltEs11(zzz50000, zzz430000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_ltEs19(zzz500001, zzz4300001, app(ty_Ratio, ccb)) → new_ltEs15(zzz500001, zzz4300001, ccb)
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Int) → new_esEs17(zzz5000, zzz4000)
new_ltEs20(zzz500002, zzz4300002, ty_Bool) → new_ltEs14(zzz500002, zzz4300002)
new_esEs27(zzz5001, zzz4001, ty_@0) → new_esEs10(zzz5001, zzz4001)
new_ltEs12(zzz50000, zzz430000) → new_fsEs(new_compare16(zzz50000, zzz430000))
new_esEs8(LT, LT) → True
new_lt19(zzz500000, zzz4300000, app(app(ty_@2, cda), cdb)) → new_lt16(zzz500000, zzz4300000, cda, cdb)
new_esEs25(zzz500000, zzz4300000, ty_Ordering) → new_esEs8(zzz500000, zzz4300000)
new_esEs19(zzz5000, zzz4000, app(ty_Maybe, gg)) → new_esEs7(zzz5000, zzz4000, gg)
new_esEs20(zzz5000, zzz4000, app(app(app(ty_@3, baf), bag), bah)) → new_esEs6(zzz5000, zzz4000, baf, bag, bah)
new_esEs18(zzz5001, zzz4001, app(ty_Ratio, ff)) → new_esEs16(zzz5001, zzz4001, ff)
new_pePe(True, zzz218) → True
new_primEqNat0(Zero, Zero) → True
new_lt20(zzz500001, zzz4300001, app(app(ty_Either, cea), ceb)) → new_lt5(zzz500001, zzz4300001, cea, ceb)
new_compare26(zzz500000, zzz4300000, True) → EQ
new_lt20(zzz500001, zzz4300001, ty_Bool) → new_lt7(zzz500001, zzz4300001)
new_esEs13(Float(zzz5000, zzz5001), Float(zzz4000, zzz4001)) → new_esEs17(new_sr0(zzz5000, zzz4000), new_sr0(zzz5001, zzz4001))
new_esEs19(zzz5000, zzz4000, app(ty_[], gc)) → new_esEs12(zzz5000, zzz4000, gc)
new_compare29(Nothing, Just(zzz430000), False, gg) → LT
new_esEs19(zzz5000, zzz4000, ty_Float) → new_esEs13(zzz5000, zzz4000)
new_compare30(zzz500000, zzz4300000, app(ty_Maybe, cad)) → new_compare28(zzz500000, zzz4300000, cad)
new_esEs18(zzz5001, zzz4001, app(app(ty_@2, ef), eg)) → new_esEs5(zzz5001, zzz4001, ef, eg)
new_esEs25(zzz500000, zzz4300000, ty_Int) → new_esEs17(zzz500000, zzz4300000)
new_esEs9(Double(zzz5000, zzz5001), Double(zzz4000, zzz4001)) → new_esEs17(new_sr0(zzz5000, zzz4000), new_sr0(zzz5001, zzz4001))
new_esEs26(zzz5002, zzz4002, ty_Ordering) → new_esEs8(zzz5002, zzz4002)
new_esEs8(GT, GT) → True
new_lt20(zzz500001, zzz4300001, app(ty_Maybe, cee)) → new_lt11(zzz500001, zzz4300001, cee)
new_esEs18(zzz5001, zzz4001, app(app(app(ty_@3, fa), fb), fc)) → new_esEs6(zzz5001, zzz4001, fa, fb, fc)
new_esEs25(zzz500000, zzz4300000, ty_@0) → new_esEs10(zzz500000, zzz4300000)
new_compare4([], [], ce) → EQ
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_lt19(zzz500000, zzz4300000, ty_@0) → new_lt4(zzz500000, zzz4300000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(app(ty_@2, bfe), bff), bfb) → new_esEs5(zzz5000, zzz4000, bfe, bff)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, ty_Integer) → new_ltEs9(zzz500000, zzz4300000)
new_esEs26(zzz5002, zzz4002, app(app(app(ty_@3, che), chf), chg)) → new_esEs6(zzz5002, zzz4002, che, chf, chg)
new_compare18(zzz500000, zzz4300000, hf, hg) → new_compare25(zzz500000, zzz4300000, new_esEs5(zzz500000, zzz4300000, hf, hg), hf, hg)
new_ltEs17(zzz50000, zzz430000, ce) → new_fsEs(new_compare4(zzz50000, zzz430000, ce))
new_esEs8(GT, LT) → False
new_esEs8(LT, GT) → False
new_compare30(zzz500000, zzz4300000, app(ty_[], cba)) → new_compare4(zzz500000, zzz4300000, cba)
new_compare30(zzz500000, zzz4300000, ty_Double) → new_compare14(zzz500000, zzz4300000)
new_ltEs13(@2(zzz500000, zzz500001), @2(zzz4300000, zzz4300001), bed, bee) → new_pePe(new_lt13(zzz500000, zzz4300000, bed), new_asAs(new_esEs23(zzz500000, zzz4300000, bed), new_ltEs19(zzz500001, zzz4300001, bee)))
new_esEs4(Right(zzz5000), Right(zzz4000), bge, app(app(ty_Either, bgf), bgg)) → new_esEs4(zzz5000, zzz4000, bgf, bgg)
new_esEs25(zzz500000, zzz4300000, app(ty_[], cdh)) → new_esEs12(zzz500000, zzz4300000, cdh)
new_compare24(zzz500000, zzz4300000, True, hc, hd, he) → EQ
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Int, bbe) → new_ltEs6(zzz500000, zzz4300000)
new_lt20(zzz500001, zzz4300001, ty_Ordering) → new_lt9(zzz500001, zzz4300001)
new_primEqInt(Neg(Succ(zzz50000)), Neg(Succ(zzz40000))) → new_primEqNat0(zzz50000, zzz40000)
new_esEs20(zzz5000, zzz4000, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_compare113(zzz500000, zzz4300000, True, ha, hb) → LT
new_esEs23(zzz500000, zzz4300000, ty_Ordering) → new_esEs8(zzz500000, zzz4300000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(app(ty_Either, bfc), bfd), bfb) → new_esEs4(zzz5000, zzz4000, bfc, bfd)
new_ltEs18(zzz50000, zzz430000, app(app(ty_Either, bch), bbe)) → new_ltEs7(zzz50000, zzz430000, bch, bbe)
new_esEs24(zzz500001, zzz4300001, ty_Bool) → new_esEs14(zzz500001, zzz4300001)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_lt19(zzz500000, zzz4300000, ty_Bool) → new_lt7(zzz500000, zzz4300000)
new_lt19(zzz500000, zzz4300000, ty_Integer) → new_lt10(zzz500000, zzz4300000)
new_ltEs4(Nothing, Nothing, bb) → True
new_lt13(zzz500000, zzz4300000, ty_Float) → new_lt6(zzz500000, zzz4300000)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_@0) → new_ltEs11(zzz500000, zzz4300000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Char, bbe) → new_ltEs5(zzz500000, zzz4300000)
new_lt13(zzz500000, zzz4300000, ty_Int) → new_lt14(zzz500000, zzz4300000)
new_lt6(zzz500000, zzz4300000) → new_esEs8(new_compare16(zzz500000, zzz4300000), LT)
new_compare29(Just(zzz50000), Nothing, False, gg) → GT
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_ltEs7(Right(zzz500000), Left(zzz4300000), bch, bbe) → False
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_esEs24(zzz500001, zzz4300001, app(app(app(ty_@3, ceg), ceh), cfa)) → new_esEs6(zzz500001, zzz4300001, ceg, ceh, cfa)
new_esEs23(zzz500000, zzz4300000, ty_Char) → new_esEs11(zzz500000, zzz4300000)
new_lt13(zzz500000, zzz4300000, ty_Bool) → new_lt7(zzz500000, zzz4300000)
new_esEs19(zzz5000, zzz4000, ty_Bool) → new_esEs14(zzz5000, zzz4000)
new_esEs20(zzz5000, zzz4000, ty_Float) → new_esEs13(zzz5000, zzz4000)
new_compare14(Double(zzz500000, zzz500001), Double(zzz4300000, zzz4300001)) → new_compare8(new_sr0(zzz500000, zzz4300000), new_sr0(zzz500001, zzz4300001))
new_compare12(zzz500000, zzz4300000, ha, hb) → new_compare27(zzz500000, zzz4300000, new_esEs4(zzz500000, zzz4300000, ha, hb), ha, hb)
new_compare8(zzz500, zzz4300) → new_primCmpInt(zzz500, zzz4300)
new_lt19(zzz500000, zzz4300000, ty_Char) → new_lt12(zzz500000, zzz4300000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, app(app(app(ty_@3, bdg), bdh), bea)) → new_ltEs16(zzz500000, zzz4300000, bdg, bdh, bea)
new_primEqInt(Neg(Succ(zzz50000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(zzz40000))) → False
new_compare17(zzz500000, zzz4300000) → new_compare26(zzz500000, zzz4300000, new_esEs14(zzz500000, zzz4300000))
new_esEs8(EQ, EQ) → True
new_lt13(zzz500000, zzz4300000, ty_Double) → new_lt15(zzz500000, zzz4300000)
new_compare111(zzz200, zzz201, True, bbd) → LT
new_esEs20(zzz5000, zzz4000, ty_@0) → new_esEs10(zzz5000, zzz4000)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Char, bfb) → new_esEs11(zzz5000, zzz4000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_ltEs19(zzz500001, zzz4300001, ty_@0) → new_ltEs11(zzz500001, zzz4300001)
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_esEs18(zzz5001, zzz4001, ty_Char) → new_esEs11(zzz5001, zzz4001)
new_compare112(zzz500000, zzz4300000, True) → LT
new_esEs19(zzz5000, zzz4000, ty_Char) → new_esEs11(zzz5000, zzz4000)
new_compare30(zzz500000, zzz4300000, app(app(ty_Either, bhh), caa)) → new_compare12(zzz500000, zzz4300000, bhh, caa)
new_primEqInt(Pos(Succ(zzz50000)), Pos(Succ(zzz40000))) → new_primEqNat0(zzz50000, zzz40000)
new_ltEs18(zzz50000, zzz430000, ty_Double) → new_ltEs8(zzz50000, zzz430000)
new_compare27(zzz500000, zzz4300000, True, ha, hb) → EQ
new_lt10(zzz500000, zzz4300000) → new_esEs8(new_compare9(zzz500000, zzz4300000), LT)
new_esEs24(zzz500001, zzz4300001, app(ty_Ratio, cef)) → new_esEs16(zzz500001, zzz4300001, cef)
new_ltEs19(zzz500001, zzz4300001, ty_Bool) → new_ltEs14(zzz500001, zzz4300001)
new_esEs14(False, True) → False
new_esEs14(True, False) → False
new_esEs23(zzz500000, zzz4300000, app(ty_[], cbd)) → new_esEs12(zzz500000, zzz4300000, cbd)
new_ltEs4(Just(zzz500000), Just(zzz4300000), app(app(ty_Either, bc), bd)) → new_ltEs7(zzz500000, zzz4300000, bc, bd)
new_esEs26(zzz5002, zzz4002, ty_Integer) → new_esEs15(zzz5002, zzz4002)
new_ltEs10(GT, EQ) → False
new_lt17(zzz500000, zzz4300000, cbc) → new_esEs8(new_compare7(zzz500000, zzz4300000, cbc), LT)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Double) → new_ltEs8(zzz500000, zzz4300000)
new_esEs24(zzz500001, zzz4300001, ty_Int) → new_esEs17(zzz500001, zzz4300001)
new_primEqNat0(Succ(zzz50000), Succ(zzz40000)) → new_primEqNat0(zzz50000, zzz40000)
new_ltEs20(zzz500002, zzz4300002, app(ty_[], cgd)) → new_ltEs17(zzz500002, zzz4300002, cgd)
new_esEs27(zzz5001, zzz4001, ty_Ordering) → new_esEs8(zzz5001, zzz4001)
new_ltEs14(False, False) → True
new_compare11(@0, @0) → EQ
new_lt7(zzz500000, zzz4300000) → new_esEs8(new_compare17(zzz500000, zzz4300000), LT)
new_esEs19(zzz5000, zzz4000, app(app(app(ty_@3, gd), ge), gf)) → new_esEs6(zzz5000, zzz4000, gd, ge, gf)
new_ltEs9(zzz50000, zzz430000) → new_fsEs(new_compare9(zzz50000, zzz430000))
new_ltEs20(zzz500002, zzz4300002, ty_Char) → new_ltEs5(zzz500002, zzz4300002)
new_compare113(zzz500000, zzz4300000, False, ha, hb) → GT
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, ty_Bool) → new_ltEs14(zzz500000, zzz4300000)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Int) → new_ltEs6(zzz500000, zzz4300000)
new_primCompAux00(zzz225, LT) → LT
new_lt20(zzz500001, zzz4300001, ty_@0) → new_lt4(zzz500001, zzz4300001)
new_ltEs19(zzz500001, zzz4300001, app(ty_[], ccf)) → new_ltEs17(zzz500001, zzz4300001, ccf)
new_ltEs19(zzz500001, zzz4300001, app(app(ty_Either, cbe), cbf)) → new_ltEs7(zzz500001, zzz4300001, cbe, cbf)
new_compare7(:%(zzz500000, zzz500001), :%(zzz4300000, zzz4300001), ty_Int) → new_compare8(new_sr0(zzz500000, zzz4300001), new_sr0(zzz4300000, zzz500001))
new_esEs24(zzz500001, zzz4300001, ty_Ordering) → new_esEs8(zzz500001, zzz4300001)
new_ltEs8(zzz50000, zzz430000) → new_fsEs(new_compare14(zzz50000, zzz430000))
new_esEs7(Nothing, Nothing, cf) → True
new_esEs28(zzz5000, zzz4000, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_esEs8(EQ, LT) → False
new_esEs8(LT, EQ) → False
new_esEs18(zzz5001, zzz4001, app(ty_Maybe, fd)) → new_esEs7(zzz5001, zzz4001, fd)
new_primEqInt(Pos(Succ(zzz50000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(zzz40000))) → False
new_lt20(zzz500001, zzz4300001, app(ty_Ratio, cef)) → new_lt17(zzz500001, zzz4300001, cef)
new_compare30(zzz500000, zzz4300000, ty_Int) → new_compare8(zzz500000, zzz4300000)
new_compare24(zzz500000, zzz4300000, False, hc, hd, he) → new_compare110(zzz500000, zzz4300000, new_ltEs16(zzz500000, zzz4300000, hc, hd, he), hc, hd, he)
new_esEs24(zzz500001, zzz4300001, ty_@0) → new_esEs10(zzz500001, zzz4300001)
new_primCmpNat0(Zero, Zero) → EQ
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Integer, bbe) → new_ltEs9(zzz500000, zzz4300000)
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_esEs23(zzz500000, zzz4300000, app(app(ty_@2, hf), hg)) → new_esEs5(zzz500000, zzz4300000, hf, hg)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, ty_@0) → new_esEs10(zzz5000, zzz4000)
new_ltEs10(LT, EQ) → True
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_compare19(zzz500000, zzz4300000, False) → GT
new_esEs27(zzz5001, zzz4001, ty_Double) → new_esEs9(zzz5001, zzz4001)
new_ltEs15(zzz50000, zzz430000, bef) → new_fsEs(new_compare7(zzz50000, zzz430000, bef))
new_esEs23(zzz500000, zzz4300000, ty_Float) → new_esEs13(zzz500000, zzz4300000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Integer) → new_esEs15(zzz5000, zzz4000)
new_compare29(Just(zzz50000), Just(zzz430000), False, gg) → new_compare111(zzz50000, zzz430000, new_ltEs18(zzz50000, zzz430000, gg), gg)
new_primEqInt(Pos(Succ(zzz50000)), Neg(zzz4000)) → False
new_primEqInt(Neg(Succ(zzz50000)), Pos(zzz4000)) → False
new_lt13(zzz500000, zzz4300000, app(ty_Ratio, cbc)) → new_lt17(zzz500000, zzz4300000, cbc)
new_esEs7(Nothing, Just(zzz4000), cf) → False
new_esEs7(Just(zzz5000), Nothing, cf) → False
new_esEs18(zzz5001, zzz4001, app(ty_[], eh)) → new_esEs12(zzz5001, zzz4001, eh)
new_esEs28(zzz5000, zzz4000, ty_Char) → new_esEs11(zzz5000, zzz4000)
new_ltEs10(GT, GT) → True
new_esEs26(zzz5002, zzz4002, app(ty_Ratio, daa)) → new_esEs16(zzz5002, zzz4002, daa)
new_esEs26(zzz5002, zzz4002, ty_Int) → new_esEs17(zzz5002, zzz4002)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, ty_Bool) → new_esEs14(zzz5000, zzz4000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_@0, bbe) → new_ltEs11(zzz500000, zzz4300000)
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primEqInt(Pos(Zero), Neg(Succ(zzz40000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(zzz40000))) → False
new_ltEs6(zzz50000, zzz430000) → new_fsEs(new_compare8(zzz50000, zzz430000))
new_esEs20(zzz5000, zzz4000, app(ty_[], bae)) → new_esEs12(zzz5000, zzz4000, bae)
new_esEs21(zzz5001, zzz4001, ty_Integer) → new_esEs15(zzz5001, zzz4001)
new_compare30(zzz500000, zzz4300000, app(app(ty_@2, cab), cac)) → new_compare18(zzz500000, zzz4300000, cab, cac)
new_primCompAux00(zzz225, EQ) → zzz225
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Double, bfb) → new_esEs9(zzz5000, zzz4000)
new_gt(zzz440, zzz4440, bec) → new_esEs8(new_compare28(zzz440, zzz4440, bec), GT)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Integer, bfb) → new_esEs15(zzz5000, zzz4000)
new_esEs18(zzz5001, zzz4001, ty_Int) → new_esEs17(zzz5001, zzz4001)
new_lt16(zzz500000, zzz4300000, hf, hg) → new_esEs8(new_compare18(zzz500000, zzz4300000, hf, hg), LT)
new_esEs8(GT, EQ) → False
new_esEs8(EQ, GT) → False
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Double) → new_esEs9(zzz5000, zzz4000)
new_esEs26(zzz5002, zzz4002, ty_Char) → new_esEs11(zzz5002, zzz4002)
new_esEs27(zzz5001, zzz4001, app(ty_Ratio, dbc)) → new_esEs16(zzz5001, zzz4001, dbc)
new_esEs26(zzz5002, zzz4002, app(app(ty_@2, chb), chc)) → new_esEs5(zzz5002, zzz4002, chb, chc)
new_ltEs19(zzz500001, zzz4300001, app(app(ty_@2, cbg), cbh)) → new_ltEs13(zzz500001, zzz4300001, cbg, cbh)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Bool) → new_ltEs14(zzz500000, zzz4300000)
new_not(False) → True
new_esEs24(zzz500001, zzz4300001, ty_Double) → new_esEs9(zzz500001, zzz4300001)
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_ltEs5(zzz50000, zzz430000) → new_fsEs(new_compare10(zzz50000, zzz430000))
new_esEs25(zzz500000, zzz4300000, ty_Integer) → new_esEs15(zzz500000, zzz4300000)
new_esEs26(zzz5002, zzz4002, ty_Bool) → new_esEs14(zzz5002, zzz4002)
new_ltEs19(zzz500001, zzz4300001, ty_Int) → new_ltEs6(zzz500001, zzz4300001)
new_esEs25(zzz500000, zzz4300000, app(ty_Ratio, cdd)) → new_esEs16(zzz500000, zzz4300000, cdd)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, ty_Int) → new_esEs17(zzz5000, zzz4000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Bool, bbe) → new_ltEs14(zzz500000, zzz4300000)
new_esEs28(zzz5000, zzz4000, app(app(ty_@2, dbf), dbg)) → new_esEs5(zzz5000, zzz4000, dbf, dbg)
new_esEs23(zzz500000, zzz4300000, ty_@0) → new_esEs10(zzz500000, zzz4300000)
new_compare30(zzz500000, zzz4300000, ty_@0) → new_compare11(zzz500000, zzz4300000)
new_esEs18(zzz5001, zzz4001, app(app(ty_Either, ed), ee)) → new_esEs4(zzz5001, zzz4001, ed, ee)
new_lt18(zzz500000, zzz4300000, cbd) → new_esEs8(new_compare4(zzz500000, zzz4300000, cbd), LT)
new_ltEs18(zzz50000, zzz430000, ty_Int) → new_ltEs6(zzz50000, zzz430000)
new_esEs22(zzz5000, zzz4000, ty_Int) → new_esEs17(zzz5000, zzz4000)
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_esEs6(@3(zzz5000, zzz5001, zzz5002), @3(zzz4000, zzz4001, zzz4002), cge, cgf, cgg) → new_asAs(new_esEs28(zzz5000, zzz4000, cge), new_asAs(new_esEs27(zzz5001, zzz4001, cgf), new_esEs26(zzz5002, zzz4002, cgg)))
new_esEs28(zzz5000, zzz4000, app(ty_Maybe, dcd)) → new_esEs7(zzz5000, zzz4000, dcd)
new_esEs28(zzz5000, zzz4000, ty_Double) → new_esEs9(zzz5000, zzz4000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, ty_Double) → new_ltEs8(zzz500000, zzz4300000)
new_lt20(zzz500001, zzz4300001, ty_Double) → new_lt15(zzz500001, zzz4300001)
new_lt20(zzz500001, zzz4300001, ty_Integer) → new_lt10(zzz500001, zzz4300001)
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_esEs26(zzz5002, zzz4002, ty_@0) → new_esEs10(zzz5002, zzz4002)
new_esEs18(zzz5001, zzz4001, ty_Float) → new_esEs13(zzz5001, zzz4001)
new_compare25(zzz500000, zzz4300000, False, hf, hg) → new_compare15(zzz500000, zzz4300000, new_ltEs13(zzz500000, zzz4300000, hf, hg), hf, hg)
new_esEs23(zzz500000, zzz4300000, app(app(ty_Either, ha), hb)) → new_esEs4(zzz500000, zzz4300000, ha, hb)
new_esEs20(zzz5000, zzz4000, ty_Char) → new_esEs11(zzz5000, zzz4000)
new_lt19(zzz500000, zzz4300000, app(ty_Maybe, cdc)) → new_lt11(zzz500000, zzz4300000, cdc)
new_esEs4(Left(zzz5000), Left(zzz4000), app(ty_Maybe, bgc), bfb) → new_esEs7(zzz5000, zzz4000, bgc)
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_esEs20(zzz5000, zzz4000, ty_Integer) → new_esEs15(zzz5000, zzz4000)
new_primEqNat0(Zero, Succ(zzz40000)) → False
new_primEqNat0(Succ(zzz50000), Zero) → False
new_esEs18(zzz5001, zzz4001, ty_Integer) → new_esEs15(zzz5001, zzz4001)
new_esEs17(zzz500, zzz400) → new_primEqInt(zzz500, zzz400)
new_lt5(zzz500000, zzz4300000, ha, hb) → new_esEs8(new_compare12(zzz500000, zzz4300000, ha, hb), LT)
new_compare25(zzz500000, zzz4300000, True, hf, hg) → EQ
new_esEs20(zzz5000, zzz4000, ty_Bool) → new_esEs14(zzz5000, zzz4000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), app(app(ty_Either, bbf), bbg), bbe) → new_ltEs7(zzz500000, zzz4300000, bbf, bbg)
new_ltEs14(True, True) → True
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs24(zzz500001, zzz4300001, app(app(ty_Either, cea), ceb)) → new_esEs4(zzz500001, zzz4300001, cea, ceb)
new_esEs28(zzz5000, zzz4000, app(app(app(ty_@3, dca), dcb), dcc)) → new_esEs6(zzz5000, zzz4000, dca, dcb, dcc)
new_compare30(zzz500000, zzz4300000, ty_Bool) → new_compare17(zzz500000, zzz4300000)
new_esEs27(zzz5001, zzz4001, app(app(ty_Either, dab), dac)) → new_esEs4(zzz5001, zzz4001, dab, dac)
new_esEs27(zzz5001, zzz4001, app(app(app(ty_@3, dag), dah), dba)) → new_esEs6(zzz5001, zzz4001, dag, dah, dba)
new_compare4(:(zzz500000, zzz500001), [], ce) → GT
new_ltEs18(zzz50000, zzz430000, app(ty_[], ce)) → new_ltEs17(zzz50000, zzz430000, ce)
new_esEs27(zzz5001, zzz4001, app(app(ty_@2, dad), dae)) → new_esEs5(zzz5001, zzz4001, dad, dae)
new_esEs27(zzz5001, zzz4001, ty_Int) → new_esEs17(zzz5001, zzz4001)
new_esEs23(zzz500000, zzz4300000, ty_Int) → new_esEs17(zzz500000, zzz4300000)
new_lt13(zzz500000, zzz4300000, ty_@0) → new_lt4(zzz500000, zzz4300000)
new_compare30(zzz500000, zzz4300000, ty_Char) → new_compare10(zzz500000, zzz4300000)
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_compare4([], :(zzz4300000, zzz4300001), ce) → LT
new_sr0(zzz5000, zzz4000) → new_primMulInt(zzz5000, zzz4000)
new_lt19(zzz500000, zzz4300000, app(ty_[], cdh)) → new_lt18(zzz500000, zzz4300000, cdh)
new_compare15(zzz500000, zzz4300000, False, hf, hg) → GT
new_ltEs18(zzz50000, zzz430000, ty_Float) → new_ltEs12(zzz50000, zzz430000)
new_ltEs18(zzz50000, zzz430000, ty_Integer) → new_ltEs9(zzz50000, zzz430000)
new_ltEs19(zzz500001, zzz4300001, ty_Double) → new_ltEs8(zzz500001, zzz4300001)
new_compare30(zzz500000, zzz4300000, ty_Float) → new_compare16(zzz500000, zzz4300000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), app(ty_[], bcg), bbe) → new_ltEs17(zzz500000, zzz4300000, bcg)
new_esEs11(Char(zzz5000), Char(zzz4000)) → new_primEqNat0(zzz5000, zzz4000)
new_esEs7(Just(zzz5000), Just(zzz4000), app(app(app(ty_@3, de), df), dg)) → new_esEs6(zzz5000, zzz4000, de, df, dg)
new_esEs25(zzz500000, zzz4300000, app(ty_Maybe, cdc)) → new_esEs7(zzz500000, zzz4300000, cdc)
new_compare29(Nothing, Nothing, False, gg) → LT
new_esEs23(zzz500000, zzz4300000, app(ty_Ratio, cbc)) → new_esEs16(zzz500000, zzz4300000, cbc)
new_lt13(zzz500000, zzz4300000, app(app(ty_Either, ha), hb)) → new_lt5(zzz500000, zzz4300000, ha, hb)
new_esEs16(:%(zzz5000, zzz5001), :%(zzz4000, zzz4001), bbc) → new_asAs(new_esEs22(zzz5000, zzz4000, bbc), new_esEs21(zzz5001, zzz4001, bbc))
new_ltEs4(Just(zzz500000), Just(zzz4300000), app(ty_Maybe, bg)) → new_ltEs4(zzz500000, zzz4300000, bg)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Float) → new_ltEs12(zzz500000, zzz4300000)
new_primCompAux0(zzz500000, zzz4300000, zzz220, ce) → new_primCompAux00(zzz220, new_compare30(zzz500000, zzz4300000, ce))
new_esEs19(zzz5000, zzz4000, app(app(ty_@2, ga), gb)) → new_esEs5(zzz5000, zzz4000, ga, gb)
new_esEs19(zzz5000, zzz4000, app(ty_Ratio, gh)) → new_esEs16(zzz5000, zzz4000, gh)
new_esEs10(@0, @0) → True
new_compare29(zzz5000, zzz43000, True, gg) → EQ
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs27(zzz5001, zzz4001, ty_Float) → new_esEs13(zzz5001, zzz4001)
new_lt13(zzz500000, zzz4300000, ty_Integer) → new_lt10(zzz500000, zzz4300000)
new_compare28(zzz5000, zzz43000, gg) → new_compare29(zzz5000, zzz43000, new_esEs7(zzz5000, zzz43000, gg), gg)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, app(app(ty_@2, bgh), bha)) → new_esEs5(zzz5000, zzz4000, bgh, bha)
new_esEs24(zzz500001, zzz4300001, ty_Char) → new_esEs11(zzz500001, zzz4300001)
new_esEs28(zzz5000, zzz4000, ty_@0) → new_esEs10(zzz5000, zzz4000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, app(app(ty_Either, bda), bdb)) → new_ltEs7(zzz500000, zzz4300000, bda, bdb)
new_esEs28(zzz5000, zzz4000, ty_Int) → new_esEs17(zzz5000, zzz4000)
new_compare7(:%(zzz500000, zzz500001), :%(zzz4300000, zzz4300001), ty_Integer) → new_compare9(new_sr(zzz500000, zzz4300001), new_sr(zzz4300000, zzz500001))
new_compare9(Integer(zzz500000), Integer(zzz4300000)) → new_primCmpInt(zzz500000, zzz4300000)
new_compare23(zzz500000, zzz4300000, False) → new_compare112(zzz500000, zzz4300000, new_ltEs10(zzz500000, zzz4300000))
new_asAs(False, zzz207) → False
new_esEs4(Left(zzz5000), Left(zzz4000), ty_@0, bfb) → new_esEs10(zzz5000, zzz4000)
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_esEs26(zzz5002, zzz4002, ty_Double) → new_esEs9(zzz5002, zzz4002)
new_ltEs10(LT, GT) → True
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_ltEs4(Just(zzz500000), Just(zzz4300000), app(ty_Ratio, bh)) → new_ltEs15(zzz500000, zzz4300000, bh)
new_esEs23(zzz500000, zzz4300000, app(app(app(ty_@3, hc), hd), he)) → new_esEs6(zzz500000, zzz4300000, hc, hd, he)
new_lt8(zzz500000, zzz4300000, hc, hd, he) → new_esEs8(new_compare13(zzz500000, zzz4300000, hc, hd, he), LT)
new_lt11(zzz5000, zzz43000, gg) → new_esEs8(new_compare28(zzz5000, zzz43000, gg), LT)
new_esEs26(zzz5002, zzz4002, app(ty_[], chd)) → new_esEs12(zzz5002, zzz4002, chd)
new_compare4(:(zzz500000, zzz500001), :(zzz4300000, zzz4300001), ce) → new_primCompAux0(zzz500000, zzz4300000, new_compare4(zzz500001, zzz4300001, ce), ce)
new_compare16(Float(zzz500000, zzz500001), Float(zzz4300000, zzz4300001)) → new_compare8(new_sr0(zzz500000, zzz4300000), new_sr0(zzz500001, zzz4300001))
new_esEs26(zzz5002, zzz4002, app(ty_Maybe, chh)) → new_esEs7(zzz5002, zzz4002, chh)
new_esEs28(zzz5000, zzz4000, ty_Bool) → new_esEs14(zzz5000, zzz4000)
new_compare110(zzz500000, zzz4300000, True, hc, hd, he) → LT
new_lt19(zzz500000, zzz4300000, app(app(ty_Either, ccg), cch)) → new_lt5(zzz500000, zzz4300000, ccg, cch)
new_ltEs18(zzz50000, zzz430000, ty_Bool) → new_ltEs14(zzz50000, zzz430000)
new_esEs28(zzz5000, zzz4000, ty_Integer) → new_esEs15(zzz5000, zzz4000)
new_esEs18(zzz5001, zzz4001, ty_Ordering) → new_esEs8(zzz5001, zzz4001)
new_esEs19(zzz5000, zzz4000, ty_Double) → new_esEs9(zzz5000, zzz4000)
new_lt20(zzz500001, zzz4300001, app(app(ty_@2, cec), ced)) → new_lt16(zzz500001, zzz4300001, cec, ced)
new_esEs5(@2(zzz5000, zzz5001), @2(zzz4000, zzz4001), eb, ec) → new_asAs(new_esEs19(zzz5000, zzz4000, eb), new_esEs18(zzz5001, zzz4001, ec))
new_compare26(zzz500000, zzz4300000, False) → new_compare19(zzz500000, zzz4300000, new_ltEs14(zzz500000, zzz4300000))
new_esEs28(zzz5000, zzz4000, app(app(ty_Either, dbd), dbe)) → new_esEs4(zzz5000, zzz4000, dbd, dbe)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, app(ty_Maybe, bhf)) → new_esEs7(zzz5000, zzz4000, bhf)
new_esEs7(Just(zzz5000), Just(zzz4000), ty_@0) → new_esEs10(zzz5000, zzz4000)
new_ltEs18(zzz50000, zzz430000, ty_Char) → new_ltEs5(zzz50000, zzz430000)
new_esEs28(zzz5000, zzz4000, ty_Float) → new_esEs13(zzz5000, zzz4000)
new_lt13(zzz500000, zzz4300000, ty_Ordering) → new_lt9(zzz500000, zzz4300000)
new_esEs25(zzz500000, zzz4300000, app(app(app(ty_@3, cde), cdf), cdg)) → new_esEs6(zzz500000, zzz4300000, cde, cdf, cdg)
new_ltEs10(EQ, EQ) → True
new_ltEs18(zzz50000, zzz430000, app(app(ty_@2, bed), bee)) → new_ltEs13(zzz50000, zzz430000, bed, bee)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Int, bfb) → new_esEs17(zzz5000, zzz4000)
new_esEs23(zzz500000, zzz4300000, ty_Integer) → new_esEs15(zzz500000, zzz4300000)
new_ltEs10(LT, LT) → True
new_esEs14(True, True) → True
new_compare111(zzz200, zzz201, False, bbd) → GT
new_esEs27(zzz5001, zzz4001, ty_Bool) → new_esEs14(zzz5001, zzz4001)
new_esEs7(Just(zzz5000), Just(zzz4000), app(app(ty_Either, cg), da)) → new_esEs4(zzz5000, zzz4000, cg, da)
new_compare10(Char(zzz500000), Char(zzz4300000)) → new_primCmpNat0(zzz500000, zzz4300000)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Float, bfb) → new_esEs13(zzz5000, zzz4000)
new_lt13(zzz500000, zzz4300000, app(app(ty_@2, hf), hg)) → new_lt16(zzz500000, zzz4300000, hf, hg)
new_ltEs7(Left(zzz500000), Left(zzz4300000), app(app(ty_@2, bbh), bca), bbe) → new_ltEs13(zzz500000, zzz4300000, bbh, bca)
new_esEs7(Just(zzz5000), Just(zzz4000), app(ty_Ratio, ea)) → new_esEs16(zzz5000, zzz4000, ea)
new_lt13(zzz500000, zzz4300000, app(ty_Maybe, cbb)) → new_lt11(zzz500000, zzz4300000, cbb)
new_ltEs20(zzz500002, zzz4300002, app(app(ty_Either, cfc), cfd)) → new_ltEs7(zzz500002, zzz4300002, cfc, cfd)
new_esEs18(zzz5001, zzz4001, ty_@0) → new_esEs10(zzz5001, zzz4001)
new_ltEs16(@3(zzz500000, zzz500001, zzz500002), @3(zzz4300000, zzz4300001, zzz4300002), beg, beh, bfa) → new_pePe(new_lt19(zzz500000, zzz4300000, beg), new_asAs(new_esEs25(zzz500000, zzz4300000, beg), new_pePe(new_lt20(zzz500001, zzz4300001, beh), new_asAs(new_esEs24(zzz500001, zzz4300001, beh), new_ltEs20(zzz500002, zzz4300002, bfa)))))
new_esEs4(Right(zzz5000), Right(zzz4000), bge, ty_Double) → new_esEs9(zzz5000, zzz4000)
new_ltEs14(True, False) → False
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_esEs20(zzz5000, zzz4000, ty_Int) → new_esEs17(zzz5000, zzz4000)
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_esEs25(zzz500000, zzz4300000, app(app(ty_@2, cda), cdb)) → new_esEs5(zzz500000, zzz4300000, cda, cdb)
new_ltEs20(zzz500002, zzz4300002, ty_Double) → new_ltEs8(zzz500002, zzz4300002)
new_ltEs7(Left(zzz500000), Left(zzz4300000), app(ty_Ratio, bcc), bbe) → new_ltEs15(zzz500000, zzz4300000, bcc)
new_ltEs19(zzz500001, zzz4300001, app(app(app(ty_@3, ccc), ccd), cce)) → new_ltEs16(zzz500001, zzz4300001, ccc, ccd, cce)
new_ltEs20(zzz500002, zzz4300002, app(app(app(ty_@3, cga), cgb), cgc)) → new_ltEs16(zzz500002, zzz4300002, cga, cgb, cgc)
new_compare112(zzz500000, zzz4300000, False) → GT
new_ltEs10(EQ, LT) → False
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Float) → new_esEs13(zzz5000, zzz4000)
new_esEs14(False, False) → True
new_esEs7(Just(zzz5000), Just(zzz4000), app(app(ty_@2, db), dc)) → new_esEs5(zzz5000, zzz4000, db, dc)
new_lt20(zzz500001, zzz4300001, ty_Char) → new_lt12(zzz500001, zzz4300001)
new_lt9(zzz500000, zzz4300000) → new_esEs8(new_compare6(zzz500000, zzz4300000), LT)
new_ltEs10(GT, LT) → False
new_esEs18(zzz5001, zzz4001, ty_Bool) → new_esEs14(zzz5001, zzz4001)
new_esEs22(zzz5000, zzz4000, ty_Integer) → new_esEs15(zzz5000, zzz4000)
new_primPlusNat1(Zero, Zero) → Zero
new_compare30(zzz500000, zzz4300000, app(app(app(ty_@3, caf), cag), cah)) → new_compare13(zzz500000, zzz4300000, caf, cag, cah)
new_esEs19(zzz5000, zzz4000, ty_Integer) → new_esEs15(zzz5000, zzz4000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(ty_[], bfg), bfb) → new_esEs12(zzz5000, zzz4000, bfg)
new_esEs26(zzz5002, zzz4002, app(app(ty_Either, cgh), cha)) → new_esEs4(zzz5002, zzz4002, cgh, cha)
new_asAs(True, zzz207) → zzz207
new_esEs28(zzz5000, zzz4000, app(ty_[], dbh)) → new_esEs12(zzz5000, zzz4000, dbh)
new_esEs27(zzz5001, zzz4001, app(ty_[], daf)) → new_esEs12(zzz5001, zzz4001, daf)
new_esEs19(zzz5000, zzz4000, app(app(ty_Either, fg), fh)) → new_esEs4(zzz5000, zzz4000, fg, fh)
new_ltEs4(Just(zzz500000), Nothing, bb) → False
new_esEs20(zzz5000, zzz4000, ty_Double) → new_esEs9(zzz5000, zzz4000)
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_ltEs4(Just(zzz500000), Just(zzz4300000), app(ty_[], cd)) → new_ltEs17(zzz500000, zzz4300000, cd)
new_esEs4(Right(zzz5000), Left(zzz4000), bge, bfb) → False
new_esEs4(Left(zzz5000), Right(zzz4000), bge, bfb) → False
new_ltEs19(zzz500001, zzz4300001, ty_Float) → new_ltEs12(zzz500001, zzz4300001)
new_ltEs20(zzz500002, zzz4300002, app(ty_Maybe, cfg)) → new_ltEs4(zzz500002, zzz4300002, cfg)
new_esEs4(Left(zzz5000), Left(zzz4000), app(app(app(ty_@3, bfh), bga), bgb), bfb) → new_esEs6(zzz5000, zzz4000, bfh, bga, bgb)
new_ltEs19(zzz500001, zzz4300001, ty_Char) → new_ltEs5(zzz500001, zzz4300001)
new_fsEs(zzz210) → new_not(new_esEs8(zzz210, GT))
new_esEs19(zzz5000, zzz4000, ty_@0) → new_esEs10(zzz5000, zzz4000)
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Bool) → new_esEs14(zzz5000, zzz4000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Double, bbe) → new_ltEs8(zzz500000, zzz4300000)
new_esEs24(zzz500001, zzz4300001, ty_Float) → new_esEs13(zzz500001, zzz4300001)
new_ltEs11(zzz50000, zzz430000) → new_fsEs(new_compare11(zzz50000, zzz430000))
new_lt20(zzz500001, zzz4300001, ty_Int) → new_lt14(zzz500001, zzz4300001)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, ty_Float) → new_esEs13(zzz5000, zzz4000)
new_esEs19(zzz5000, zzz4000, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_ltEs20(zzz500002, zzz4300002, app(app(ty_@2, cfe), cff)) → new_ltEs13(zzz500002, zzz4300002, cfe, cff)
new_esEs27(zzz5001, zzz4001, ty_Char) → new_esEs11(zzz5001, zzz4001)
new_ltEs20(zzz500002, zzz4300002, ty_Int) → new_ltEs6(zzz500002, zzz4300002)
new_compare110(zzz500000, zzz4300000, False, hc, hd, he) → GT
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Char) → new_ltEs5(zzz500000, zzz4300000)
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Char) → new_esEs11(zzz5000, zzz4000)
new_primCompAux00(zzz225, GT) → GT
new_ltEs20(zzz500002, zzz4300002, ty_Integer) → new_ltEs9(zzz500002, zzz4300002)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, app(ty_Maybe, bde)) → new_ltEs4(zzz500000, zzz4300000, bde)
new_lt19(zzz500000, zzz4300000, ty_Int) → new_lt14(zzz500000, zzz4300000)
new_ltEs4(Just(zzz500000), Just(zzz4300000), app(app(app(ty_@3, ca), cb), cc)) → new_ltEs16(zzz500000, zzz4300000, ca, cb, cc)
new_ltEs18(zzz50000, zzz430000, ty_Ordering) → new_ltEs10(zzz50000, zzz430000)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Integer) → new_ltEs9(zzz500000, zzz4300000)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_compare30(zzz500000, zzz4300000, ty_Ordering) → new_compare6(zzz500000, zzz4300000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, ty_Float) → new_ltEs12(zzz500000, zzz4300000)
new_esEs27(zzz5001, zzz4001, ty_Integer) → new_esEs15(zzz5001, zzz4001)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, ty_Int) → new_ltEs6(zzz500000, zzz4300000)
new_not(True) → False

The set Q consists of the following terms:

new_compare30(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_compare23(x0, x1, True)
new_lt11(x0, x1, x2)
new_lt14(x0, x1)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs18(x0, x1, app(app(ty_@2, x2), x3))
new_asAs(True, x0)
new_compare29(Nothing, Nothing, False, x0)
new_compare19(x0, x1, True)
new_esEs26(x0, x1, ty_@0)
new_ltEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs18(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_Ordering)
new_esEs18(x0, x1, ty_Int)
new_ltEs19(x0, x1, app(ty_[], x2))
new_primPlusNat1(Zero, Succ(x0))
new_compare29(Nothing, Just(x0), False, x1)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_compare30(x0, x1, ty_@0)
new_lt20(x0, x1, ty_Ordering)
new_esEs9(Double(x0, x1), Double(x2, x3))
new_ltEs7(Right(x0), Right(x1), x2, ty_@0)
new_primCompAux0(x0, x1, x2, x3)
new_primMulNat0(Succ(x0), Zero)
new_lt19(x0, x1, ty_Double)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_@0)
new_primPlusNat1(Succ(x0), Zero)
new_esEs21(x0, x1, ty_Int)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare4(:(x0, x1), :(x2, x3), x4)
new_ltEs10(LT, LT)
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_esEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs16(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs23(x0, x1, ty_Bool)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs27(x0, x1, ty_Int)
new_esEs4(Right(x0), Left(x1), x2, x3)
new_esEs4(Left(x0), Right(x1), x2, x3)
new_esEs18(x0, x1, ty_Char)
new_esEs24(x0, x1, ty_Char)
new_ltEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(True, False)
new_ltEs14(False, True)
new_esEs25(x0, x1, ty_Double)
new_pePe(False, x0)
new_esEs19(x0, x1, ty_Char)
new_esEs25(x0, x1, ty_Char)
new_compare27(x0, x1, True, x2, x3)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs7(Just(x0), Just(x1), ty_Double)
new_esEs8(GT, GT)
new_esEs23(x0, x1, ty_@0)
new_compare4([], :(x0, x1), x2)
new_lt9(x0, x1)
new_lt19(x0, x1, ty_Ordering)
new_esEs11(Char(x0), Char(x1))
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs4(Left(x0), Left(x1), ty_Int, x2)
new_esEs7(Nothing, Just(x0), x1)
new_esEs8(LT, LT)
new_sr0(x0, x1)
new_compare6(x0, x1)
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_compare30(x0, x1, ty_Double)
new_esEs7(Just(x0), Just(x1), ty_Char)
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, app(ty_[], x2))
new_lt13(x0, x1, app(ty_Ratio, x2))
new_compare19(x0, x1, False)
new_ltEs4(Nothing, Nothing, x0)
new_compare110(x0, x1, False, x2, x3, x4)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs26(x0, x1, ty_Double)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_lt18(x0, x1, x2)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_lt16(x0, x1, x2, x3)
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_compare111(x0, x1, False, x2)
new_compare4([], [], x0)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs7(Left(x0), Left(x1), ty_Char, x2)
new_ltEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs17(x0, x1)
new_ltEs19(x0, x1, ty_Char)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs14(True, True)
new_compare26(x0, x1, True)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Char)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare112(x0, x1, False)
new_esEs18(x0, x1, ty_Bool)
new_esEs20(x0, x1, ty_Float)
new_primEqNat0(Zero, Zero)
new_ltEs4(Just(x0), Just(x1), ty_Double)
new_compare30(x0, x1, ty_Char)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_ltEs7(Right(x0), Right(x1), x2, ty_Char)
new_esEs20(x0, x1, ty_Int)
new_lt13(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Double)
new_lt19(x0, x1, ty_Bool)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, ty_@0)
new_lt13(x0, x1, app(ty_[], x2))
new_esEs12([], :(x0, x1), x2)
new_esEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs28(x0, x1, ty_Integer)
new_compare17(x0, x1)
new_ltEs17(x0, x1, x2)
new_primPlusNat0(Zero, x0)
new_ltEs20(x0, x1, ty_Int)
new_compare13(x0, x1, x2, x3, x4)
new_primMulNat0(Zero, Zero)
new_esEs4(Right(x0), Right(x1), x2, ty_Float)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpNat0(Succ(x0), Zero)
new_compare16(Float(x0, x1), Float(x2, x3))
new_ltEs20(x0, x1, ty_Integer)
new_compare30(x0, x1, ty_Ordering)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs26(x0, x1, ty_Integer)
new_ltEs10(EQ, LT)
new_ltEs10(LT, EQ)
new_lt4(x0, x1)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_ltEs7(Left(x0), Left(x1), ty_@0, x2)
new_lt13(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs19(x0, x1, ty_Bool)
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs28(x0, x1, ty_@0)
new_primMulNat0(Succ(x0), Succ(x1))
new_lt7(x0, x1)
new_esEs23(x0, x1, ty_Float)
new_ltEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_Double)
new_compare113(x0, x1, False, x2, x3)
new_ltEs18(x0, x1, ty_@0)
new_compare15(x0, x1, True, x2, x3)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs23(x0, x1, ty_Char)
new_esEs24(x0, x1, ty_Int)
new_compare9(Integer(x0), Integer(x1))
new_esEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, ty_Ordering)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_ltEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_compare4(:(x0, x1), [], x2)
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_esEs24(x0, x1, ty_Bool)
new_ltEs13(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs26(x0, x1, ty_Char)
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_compare25(x0, x1, False, x2, x3)
new_esEs20(x0, x1, ty_Ordering)
new_esEs12(:(x0, x1), :(x2, x3), x4)
new_fsEs(x0)
new_lt8(x0, x1, x2, x3, x4)
new_ltEs11(x0, x1)
new_esEs23(x0, x1, ty_Double)
new_lt13(x0, x1, ty_@0)
new_ltEs7(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Just(x0), Just(x1), ty_Int)
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_compare26(x0, x1, False)
new_ltEs18(x0, x1, ty_Double)
new_ltEs7(Right(x0), Left(x1), x2, x3)
new_ltEs7(Left(x0), Right(x1), x2, x3)
new_ltEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs25(x0, x1, ty_Bool)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primPlusNat1(Zero, Zero)
new_esEs28(x0, x1, ty_Float)
new_ltEs7(Right(x0), Right(x1), x2, ty_Int)
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_lt12(x0, x1)
new_compare7(:%(x0, x1), :%(x2, x3), ty_Int)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_ltEs4(Just(x0), Just(x1), ty_Int)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_compare11(@0, @0)
new_esEs4(Right(x0), Right(x1), x2, ty_Integer)
new_primMulNat0(Zero, Succ(x0))
new_esEs26(x0, x1, ty_Bool)
new_asAs(False, x0)
new_esEs12(:(x0, x1), [], x2)
new_ltEs4(Just(x0), Just(x1), ty_Bool)
new_ltEs8(x0, x1)
new_ltEs18(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Float)
new_esEs27(x0, x1, ty_Double)
new_ltEs19(x0, x1, ty_Ordering)
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs4(Just(x0), Just(x1), ty_Ordering)
new_esEs4(Left(x0), Left(x1), ty_@0, x2)
new_esEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs18(x0, x1, ty_Double)
new_ltEs10(GT, LT)
new_esEs4(Left(x0), Left(x1), ty_Double, x2)
new_ltEs10(LT, GT)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs28(x0, x1, ty_Double)
new_esEs10(@0, @0)
new_compare14(Double(x0, x1), Double(x2, x3))
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_compare24(x0, x1, True, x2, x3, x4)
new_compare30(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_Integer)
new_ltEs18(x0, x1, ty_Float)
new_compare8(x0, x1)
new_lt13(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs20(x0, x1, ty_Char)
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs7(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs19(x0, x1, ty_Integer)
new_pePe(True, x0)
new_compare29(Just(x0), Just(x1), False, x2)
new_esEs27(x0, x1, ty_Float)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_primCompAux00(x0, EQ)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_lt19(x0, x1, ty_Float)
new_primEqNat0(Succ(x0), Zero)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_ltEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_lt17(x0, x1, x2)
new_esEs28(x0, x1, ty_Int)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_compare27(x0, x1, False, x2, x3)
new_esEs18(x0, x1, ty_Ordering)
new_esEs25(x0, x1, ty_Int)
new_esEs18(x0, x1, app(ty_Ratio, x2))
new_esEs7(Nothing, Nothing, x0)
new_ltEs15(x0, x1, x2)
new_ltEs4(Just(x0), Just(x1), ty_@0)
new_esEs19(x0, x1, app(ty_[], x2))
new_compare23(x0, x1, False)
new_compare30(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_ltEs4(Just(x0), Nothing, x1)
new_esEs8(EQ, EQ)
new_compare112(x0, x1, True)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs4(Right(x0), Right(x1), x2, ty_Int)
new_esEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs19(x0, x1, ty_Double)
new_esEs13(Float(x0, x1), Float(x2, x3))
new_primEqInt(Neg(Zero), Neg(Zero))
new_gt(x0, x1, x2)
new_lt13(x0, x1, ty_Char)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, ty_Char)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_esEs15(Integer(x0), Integer(x1))
new_ltEs12(x0, x1)
new_ltEs20(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_@0)
new_esEs14(True, False)
new_esEs14(False, True)
new_ltEs4(Just(x0), Just(x1), ty_Float)
new_ltEs7(Right(x0), Right(x1), x2, ty_Float)
new_esEs18(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, app(ty_[], x2))
new_ltEs6(x0, x1)
new_esEs22(x0, x1, ty_Int)
new_esEs20(x0, x1, ty_Double)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare110(x0, x1, True, x2, x3, x4)
new_ltEs9(x0, x1)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs19(x0, x1, ty_@0)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_lt19(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Ordering)
new_esEs27(x0, x1, ty_Integer)
new_esEs16(:%(x0, x1), :%(x2, x3), x4)
new_lt20(x0, x1, ty_Float)
new_compare25(x0, x1, True, x2, x3)
new_compare30(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Integer)
new_primCmpNat0(Succ(x0), Succ(x1))
new_lt19(x0, x1, ty_Char)
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_esEs20(x0, x1, ty_Integer)
new_esEs28(x0, x1, ty_Ordering)
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_esEs21(x0, x1, ty_Integer)
new_compare28(x0, x1, x2)
new_ltEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_esEs4(Right(x0), Right(x1), x2, ty_Double)
new_ltEs7(Right(x0), Right(x1), x2, ty_Double)
new_lt20(x0, x1, ty_Bool)
new_primPlusNat0(Succ(x0), x1)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_@0)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, ty_Integer)
new_compare30(x0, x1, app(ty_Maybe, x2))
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs7(Just(x0), Just(x1), ty_Float)
new_compare18(x0, x1, x2, x3)
new_esEs19(x0, x1, ty_Float)
new_ltEs20(x0, x1, ty_Bool)
new_primCmpNat0(Zero, Zero)
new_esEs4(Left(x0), Left(x1), ty_Integer, x2)
new_esEs19(x0, x1, ty_Ordering)
new_lt13(x0, x1, ty_Bool)
new_ltEs19(x0, x1, ty_Float)
new_esEs27(x0, x1, app(ty_[], x2))
new_ltEs7(Left(x0), Left(x1), ty_Double, x2)
new_esEs12([], [], x0)
new_lt10(x0, x1)
new_compare7(:%(x0, x1), :%(x2, x3), ty_Integer)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_compare113(x0, x1, True, x2, x3)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs20(x0, x1, app(ty_[], x2))
new_ltEs7(Left(x0), Left(x1), ty_Bool, x2)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, ty_Ordering)
new_esEs4(Left(x0), Left(x1), ty_Char, x2)
new_esEs26(x0, x1, ty_Float)
new_ltEs7(Left(x0), Left(x1), ty_Float, x2)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt5(x0, x1, x2, x3)
new_esEs28(x0, x1, app(ty_[], x2))
new_compare29(Just(x0), Nothing, False, x1)
new_ltEs10(GT, GT)
new_ltEs14(True, True)
new_ltEs14(False, False)
new_esEs24(x0, x1, ty_Ordering)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_lt19(x0, x1, ty_@0)
new_esEs18(x0, x1, ty_Float)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_lt13(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, ty_Char)
new_ltEs7(Left(x0), Left(x1), ty_Int, x2)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_esEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_not(True)
new_esEs19(x0, x1, ty_Int)
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Just(x0), Just(x1), ty_@0)
new_compare30(x0, x1, ty_Integer)
new_ltEs5(x0, x1)
new_compare30(x0, x1, app(ty_Ratio, x2))
new_esEs4(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs20(x0, x1, ty_Double)
new_esEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(Just(x0), Just(x1), ty_Integer)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_not(False)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Integer)
new_esEs4(Right(x0), Right(x1), x2, ty_@0)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_ltEs4(Just(x0), Just(x1), app(ty_[], x2))
new_primCompAux00(x0, LT)
new_lt6(x0, x1)
new_ltEs10(EQ, GT)
new_ltEs10(GT, EQ)
new_ltEs19(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Float)
new_esEs24(x0, x1, app(ty_[], x2))
new_ltEs18(x0, x1, ty_Char)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs19(x0, x1, ty_Integer)
new_esEs18(x0, x1, app(ty_[], x2))
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_sr(Integer(x0), Integer(x1))
new_esEs4(Right(x0), Right(x1), x2, ty_Char)
new_esEs27(x0, x1, ty_Char)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs20(x0, x1, ty_Bool)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(Just(x0), Just(x1), ty_Char)
new_esEs4(Left(x0), Left(x1), ty_Float, x2)
new_ltEs4(Nothing, Just(x0), x1)
new_esEs18(x0, x1, ty_@0)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_ltEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_lt13(x0, x1, ty_Double)
new_esEs18(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_Bool)
new_lt13(x0, x1, ty_Ordering)
new_compare12(x0, x1, x2, x3)
new_compare15(x0, x1, False, x2, x3)
new_ltEs18(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Ordering)
new_compare30(x0, x1, ty_Float)
new_esEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare111(x0, x1, True, x2)
new_lt13(x0, x1, ty_Integer)
new_lt19(x0, x1, app(ty_[], x2))
new_esEs14(False, False)
new_primEqInt(Pos(Zero), Pos(Zero))
new_compare30(x0, x1, app(ty_[], x2))
new_compare10(Char(x0), Char(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs24(x0, x1, ty_Integer)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Double)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs25(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, ty_Float)
new_lt13(x0, x1, ty_Int)
new_compare29(x0, x1, True, x2)
new_lt13(x0, x1, ty_Float)
new_lt20(x0, x1, ty_Integer)
new_primCmpNat0(Zero, Succ(x0))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_ltEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_Int)
new_primCompAux00(x0, GT)
new_ltEs20(x0, x1, ty_@0)
new_esEs4(Left(x0), Left(x1), ty_Bool, x2)
new_lt15(x0, x1)
new_ltEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primEqNat0(Zero, Succ(x0))
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs7(Left(x0), Left(x1), ty_Integer, x2)
new_esEs27(x0, x1, ty_Bool)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_@0)
new_compare24(x0, x1, False, x2, x3, x4)
new_esEs7(Just(x0), Nothing, x1)
new_esEs18(x0, x1, ty_Integer)
new_ltEs10(EQ, EQ)

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_intersectFM_C2Elt1011(zzz492, zzz493, zzz494, zzz495, zzz496, zzz497, zzz498, zzz499, zzz500, True, h, ba) → new_intersectFM_C2Elt1012(zzz492, zzz493, zzz494, zzz495, zzz500, h, ba)
new_intersectFM_C2Elt1014(zzz492, zzz493, zzz494, zzz495, zzz496, zzz497, zzz498, Branch(zzz4990, zzz4991, zzz4992, zzz4993, zzz4994), zzz500, True, h, ba) → new_intersectFM_C2Elt1013(zzz492, zzz493, zzz494, zzz495, zzz4990, zzz4991, zzz4992, zzz4993, zzz4994, h, ba)
new_intersectFM_C2Elt1014(zzz492, zzz493, zzz494, zzz495, zzz496, zzz497, zzz498, zzz499, zzz500, False, h, ba) → new_intersectFM_C2Elt1011(zzz492, zzz493, zzz494, zzz495, zzz496, zzz497, zzz498, zzz499, zzz500, new_gt(Nothing, zzz496, ba), h, ba)
new_intersectFM_C2Elt1012(zzz492, zzz493, zzz494, zzz495, Branch(zzz4990, zzz4991, zzz4992, zzz4993, zzz4994), h, ba) → new_intersectFM_C2Elt1013(zzz492, zzz493, zzz494, zzz495, zzz4990, zzz4991, zzz4992, zzz4993, zzz4994, h, ba)
new_intersectFM_C2Elt1013(zzz492, zzz493, zzz494, zzz495, zzz496, zzz497, zzz498, zzz499, zzz500, h, ba) → new_intersectFM_C2Elt1014(zzz492, zzz493, zzz494, zzz495, zzz496, zzz497, zzz498, zzz499, zzz500, new_lt11(Nothing, zzz496, ba), h, ba)

The TRS R consists of the following rules:

new_lt19(zzz500000, zzz4300000, ty_Float) → new_lt6(zzz500000, zzz4300000)
new_ltEs18(zzz50000, zzz430000, app(ty_Ratio, bef)) → new_ltEs15(zzz50000, zzz430000, bef)
new_esEs7(Just(zzz5000), Just(zzz4000), app(ty_Maybe, dh)) → new_esEs7(zzz5000, zzz4000, dh)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_esEs20(zzz5000, zzz4000, app(ty_Maybe, bba)) → new_esEs7(zzz5000, zzz4000, bba)
new_esEs12(:(zzz5000, zzz5001), :(zzz4000, zzz4001), hh) → new_asAs(new_esEs20(zzz5000, zzz4000, hh), new_esEs12(zzz5001, zzz4001, hh))
new_esEs7(Just(zzz5000), Just(zzz4000), app(ty_[], dd)) → new_esEs12(zzz5000, zzz4000, dd)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, ty_Ordering) → new_ltEs10(zzz500000, zzz4300000)
new_lt19(zzz500000, zzz4300000, app(app(app(ty_@3, cde), cdf), cdg)) → new_lt8(zzz500000, zzz4300000, cde, cdf, cdg)
new_ltEs18(zzz50000, zzz430000, app(app(app(ty_@3, beg), beh), bfa)) → new_ltEs16(zzz50000, zzz430000, beg, beh, bfa)
new_lt20(zzz500001, zzz4300001, app(ty_[], cfb)) → new_lt18(zzz500001, zzz4300001, cfb)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, ty_Char) → new_esEs11(zzz5000, zzz4000)
new_compare15(zzz500000, zzz4300000, True, hf, hg) → LT
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Bool, bfb) → new_esEs14(zzz5000, zzz4000)
new_ltEs18(zzz50000, zzz430000, app(ty_Maybe, bb)) → new_ltEs4(zzz50000, zzz430000, bb)
new_ltEs20(zzz500002, zzz4300002, ty_Ordering) → new_ltEs10(zzz500002, zzz4300002)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, app(app(app(ty_@3, bhc), bhd), bhe)) → new_esEs6(zzz5000, zzz4000, bhc, bhd, bhe)
new_lt13(zzz500000, zzz4300000, app(app(app(ty_@3, hc), hd), he)) → new_lt8(zzz500000, zzz4300000, hc, hd, he)
new_lt15(zzz500000, zzz4300000) → new_esEs8(new_compare14(zzz500000, zzz4300000), LT)
new_lt20(zzz500001, zzz4300001, app(app(app(ty_@3, ceg), ceh), cfa)) → new_lt8(zzz500001, zzz4300001, ceg, ceh, cfa)
new_esEs27(zzz5001, zzz4001, app(ty_Maybe, dbb)) → new_esEs7(zzz5001, zzz4001, dbb)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Ordering) → new_ltEs10(zzz500000, zzz4300000)
new_esEs23(zzz500000, zzz4300000, ty_Bool) → new_esEs14(zzz500000, zzz4300000)
new_compare27(zzz500000, zzz4300000, False, ha, hb) → new_compare113(zzz500000, zzz4300000, new_ltEs7(zzz500000, zzz4300000, ha, hb), ha, hb)
new_lt19(zzz500000, zzz4300000, ty_Double) → new_lt15(zzz500000, zzz4300000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), app(ty_Maybe, bcb), bbe) → new_ltEs4(zzz500000, zzz4300000, bcb)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, ty_@0) → new_ltEs11(zzz500000, zzz4300000)
new_ltEs20(zzz500002, zzz4300002, app(ty_Ratio, cfh)) → new_ltEs15(zzz500002, zzz4300002, cfh)
new_lt13(zzz500000, zzz4300000, app(ty_[], cbd)) → new_lt18(zzz500000, zzz4300000, cbd)
new_esEs26(zzz5002, zzz4002, ty_Float) → new_esEs13(zzz5002, zzz4002)
new_ltEs7(Left(zzz500000), Right(zzz4300000), bch, bbe) → True
new_primMulNat0(Zero, Zero) → Zero
new_esEs19(zzz5000, zzz4000, ty_Int) → new_esEs17(zzz5000, zzz4000)
new_sr(Integer(zzz43000000), Integer(zzz5000010)) → Integer(new_primMulInt(zzz43000000, zzz5000010))
new_ltEs20(zzz500002, zzz4300002, ty_Float) → new_ltEs12(zzz500002, zzz4300002)
new_ltEs20(zzz500002, zzz4300002, ty_@0) → new_ltEs11(zzz500002, zzz4300002)
new_esEs20(zzz5000, zzz4000, app(ty_Ratio, bbb)) → new_esEs16(zzz5000, zzz4000, bbb)
new_esEs18(zzz5001, zzz4001, ty_Double) → new_esEs9(zzz5001, zzz4001)
new_lt20(zzz500001, zzz4300001, ty_Float) → new_lt6(zzz500001, zzz4300001)
new_esEs23(zzz500000, zzz4300000, ty_Double) → new_esEs9(zzz500000, zzz4300000)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, app(ty_[], bhb)) → new_esEs12(zzz5000, zzz4000, bhb)
new_esEs24(zzz500001, zzz4300001, ty_Integer) → new_esEs15(zzz500001, zzz4300001)
new_ltEs14(False, True) → True
new_ltEs19(zzz500001, zzz4300001, ty_Integer) → new_ltEs9(zzz500001, zzz4300001)
new_ltEs4(Just(zzz500000), Just(zzz4300000), app(app(ty_@2, be), bf)) → new_ltEs13(zzz500000, zzz4300000, be, bf)
new_esEs20(zzz5000, zzz4000, app(app(ty_Either, baa), bab)) → new_esEs4(zzz5000, zzz4000, baa, bab)
new_esEs12([], [], hh) → True
new_ltEs19(zzz500001, zzz4300001, ty_Ordering) → new_ltEs10(zzz500001, zzz4300001)
new_esEs24(zzz500001, zzz4300001, app(app(ty_@2, cec), ced)) → new_esEs5(zzz500001, zzz4300001, cec, ced)
new_lt12(zzz500000, zzz4300000) → new_esEs8(new_compare10(zzz500000, zzz4300000), LT)
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Ordering, bbe) → new_ltEs10(zzz500000, zzz4300000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, app(ty_Ratio, bdf)) → new_ltEs15(zzz500000, zzz4300000, bdf)
new_esEs15(Integer(zzz5000), Integer(zzz4000)) → new_primEqInt(zzz5000, zzz4000)
new_ltEs10(EQ, GT) → True
new_ltEs19(zzz500001, zzz4300001, app(ty_Maybe, cca)) → new_ltEs4(zzz500001, zzz4300001, cca)
new_esEs21(zzz5001, zzz4001, ty_Int) → new_esEs17(zzz5001, zzz4001)
new_ltEs7(Left(zzz500000), Left(zzz4300000), app(app(app(ty_@3, bcd), bce), bcf), bbe) → new_ltEs16(zzz500000, zzz4300000, bcd, bce, bcf)
new_lt13(zzz500000, zzz4300000, ty_Char) → new_lt12(zzz500000, zzz4300000)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Ordering, bfb) → new_esEs8(zzz5000, zzz4000)
new_esEs24(zzz500001, zzz4300001, app(ty_[], cfb)) → new_esEs12(zzz500001, zzz4300001, cfb)
new_esEs25(zzz500000, zzz4300000, ty_Double) → new_esEs9(zzz500000, zzz4300000)
new_esEs25(zzz500000, zzz4300000, ty_Float) → new_esEs13(zzz500000, zzz4300000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, app(ty_[], beb)) → new_ltEs17(zzz500000, zzz4300000, beb)
new_pePe(False, zzz218) → zzz218
new_lt14(zzz5000, zzz43000) → new_esEs8(new_compare8(zzz5000, zzz43000), LT)
new_esEs25(zzz500000, zzz4300000, app(app(ty_Either, ccg), cch)) → new_esEs4(zzz500000, zzz4300000, ccg, cch)
new_esEs12(:(zzz5000, zzz5001), [], hh) → False
new_esEs12([], :(zzz4000, zzz4001), hh) → False
new_esEs25(zzz500000, zzz4300000, ty_Char) → new_esEs11(zzz500000, zzz4300000)
new_esEs25(zzz500000, zzz4300000, ty_Bool) → new_esEs14(zzz500000, zzz4300000)
new_lt19(zzz500000, zzz4300000, ty_Ordering) → new_lt9(zzz500000, zzz4300000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, app(app(ty_@2, bdc), bdd)) → new_ltEs13(zzz500000, zzz4300000, bdc, bdd)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, app(ty_Ratio, bhg)) → new_esEs16(zzz5000, zzz4000, bhg)
new_compare23(zzz500000, zzz4300000, True) → EQ
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Float, bbe) → new_ltEs12(zzz500000, zzz4300000)
new_lt19(zzz500000, zzz4300000, app(ty_Ratio, cdd)) → new_lt17(zzz500000, zzz4300000, cdd)
new_esEs24(zzz500001, zzz4300001, app(ty_Maybe, cee)) → new_esEs7(zzz500001, zzz4300001, cee)
new_ltEs4(Nothing, Just(zzz4300000), bb) → True
new_esEs23(zzz500000, zzz4300000, app(ty_Maybe, cbb)) → new_esEs7(zzz500000, zzz4300000, cbb)
new_compare30(zzz500000, zzz4300000, ty_Integer) → new_compare9(zzz500000, zzz4300000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(ty_Ratio, bgd), bfb) → new_esEs16(zzz5000, zzz4000, bgd)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, ty_Char) → new_ltEs5(zzz500000, zzz4300000)
new_compare13(zzz500000, zzz4300000, hc, hd, he) → new_compare24(zzz500000, zzz4300000, new_esEs6(zzz500000, zzz4300000, hc, hd, he), hc, hd, he)
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_lt4(zzz500000, zzz4300000) → new_esEs8(new_compare11(zzz500000, zzz4300000), LT)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, ty_Integer) → new_esEs15(zzz5000, zzz4000)
new_esEs20(zzz5000, zzz4000, app(app(ty_@2, bac), bad)) → new_esEs5(zzz5000, zzz4000, bac, bad)
new_esEs28(zzz5000, zzz4000, app(ty_Ratio, dce)) → new_esEs16(zzz5000, zzz4000, dce)
new_compare30(zzz500000, zzz4300000, app(ty_Ratio, cae)) → new_compare7(zzz500000, zzz4300000, cae)
new_compare19(zzz500000, zzz4300000, True) → LT
new_compare6(zzz500000, zzz4300000) → new_compare23(zzz500000, zzz4300000, new_esEs8(zzz500000, zzz4300000))
new_ltEs18(zzz50000, zzz430000, ty_@0) → new_ltEs11(zzz50000, zzz430000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_ltEs19(zzz500001, zzz4300001, app(ty_Ratio, ccb)) → new_ltEs15(zzz500001, zzz4300001, ccb)
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Int) → new_esEs17(zzz5000, zzz4000)
new_ltEs20(zzz500002, zzz4300002, ty_Bool) → new_ltEs14(zzz500002, zzz4300002)
new_esEs27(zzz5001, zzz4001, ty_@0) → new_esEs10(zzz5001, zzz4001)
new_ltEs12(zzz50000, zzz430000) → new_fsEs(new_compare16(zzz50000, zzz430000))
new_esEs8(LT, LT) → True
new_lt19(zzz500000, zzz4300000, app(app(ty_@2, cda), cdb)) → new_lt16(zzz500000, zzz4300000, cda, cdb)
new_esEs25(zzz500000, zzz4300000, ty_Ordering) → new_esEs8(zzz500000, zzz4300000)
new_esEs19(zzz5000, zzz4000, app(ty_Maybe, gg)) → new_esEs7(zzz5000, zzz4000, gg)
new_esEs20(zzz5000, zzz4000, app(app(app(ty_@3, baf), bag), bah)) → new_esEs6(zzz5000, zzz4000, baf, bag, bah)
new_esEs18(zzz5001, zzz4001, app(ty_Ratio, ff)) → new_esEs16(zzz5001, zzz4001, ff)
new_pePe(True, zzz218) → True
new_primEqNat0(Zero, Zero) → True
new_lt20(zzz500001, zzz4300001, app(app(ty_Either, cea), ceb)) → new_lt5(zzz500001, zzz4300001, cea, ceb)
new_compare26(zzz500000, zzz4300000, True) → EQ
new_lt20(zzz500001, zzz4300001, ty_Bool) → new_lt7(zzz500001, zzz4300001)
new_esEs13(Float(zzz5000, zzz5001), Float(zzz4000, zzz4001)) → new_esEs17(new_sr0(zzz5000, zzz4000), new_sr0(zzz5001, zzz4001))
new_esEs19(zzz5000, zzz4000, app(ty_[], gc)) → new_esEs12(zzz5000, zzz4000, gc)
new_compare29(Nothing, Just(zzz430000), False, gg) → LT
new_esEs19(zzz5000, zzz4000, ty_Float) → new_esEs13(zzz5000, zzz4000)
new_compare30(zzz500000, zzz4300000, app(ty_Maybe, cad)) → new_compare28(zzz500000, zzz4300000, cad)
new_esEs18(zzz5001, zzz4001, app(app(ty_@2, ef), eg)) → new_esEs5(zzz5001, zzz4001, ef, eg)
new_esEs25(zzz500000, zzz4300000, ty_Int) → new_esEs17(zzz500000, zzz4300000)
new_esEs9(Double(zzz5000, zzz5001), Double(zzz4000, zzz4001)) → new_esEs17(new_sr0(zzz5000, zzz4000), new_sr0(zzz5001, zzz4001))
new_esEs26(zzz5002, zzz4002, ty_Ordering) → new_esEs8(zzz5002, zzz4002)
new_esEs8(GT, GT) → True
new_lt20(zzz500001, zzz4300001, app(ty_Maybe, cee)) → new_lt11(zzz500001, zzz4300001, cee)
new_esEs18(zzz5001, zzz4001, app(app(app(ty_@3, fa), fb), fc)) → new_esEs6(zzz5001, zzz4001, fa, fb, fc)
new_esEs25(zzz500000, zzz4300000, ty_@0) → new_esEs10(zzz500000, zzz4300000)
new_compare4([], [], ce) → EQ
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_lt19(zzz500000, zzz4300000, ty_@0) → new_lt4(zzz500000, zzz4300000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(app(ty_@2, bfe), bff), bfb) → new_esEs5(zzz5000, zzz4000, bfe, bff)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, ty_Integer) → new_ltEs9(zzz500000, zzz4300000)
new_esEs26(zzz5002, zzz4002, app(app(app(ty_@3, che), chf), chg)) → new_esEs6(zzz5002, zzz4002, che, chf, chg)
new_compare18(zzz500000, zzz4300000, hf, hg) → new_compare25(zzz500000, zzz4300000, new_esEs5(zzz500000, zzz4300000, hf, hg), hf, hg)
new_ltEs17(zzz50000, zzz430000, ce) → new_fsEs(new_compare4(zzz50000, zzz430000, ce))
new_esEs8(GT, LT) → False
new_esEs8(LT, GT) → False
new_compare30(zzz500000, zzz4300000, app(ty_[], cba)) → new_compare4(zzz500000, zzz4300000, cba)
new_compare30(zzz500000, zzz4300000, ty_Double) → new_compare14(zzz500000, zzz4300000)
new_ltEs13(@2(zzz500000, zzz500001), @2(zzz4300000, zzz4300001), bed, bee) → new_pePe(new_lt13(zzz500000, zzz4300000, bed), new_asAs(new_esEs23(zzz500000, zzz4300000, bed), new_ltEs19(zzz500001, zzz4300001, bee)))
new_esEs4(Right(zzz5000), Right(zzz4000), bge, app(app(ty_Either, bgf), bgg)) → new_esEs4(zzz5000, zzz4000, bgf, bgg)
new_esEs25(zzz500000, zzz4300000, app(ty_[], cdh)) → new_esEs12(zzz500000, zzz4300000, cdh)
new_compare24(zzz500000, zzz4300000, True, hc, hd, he) → EQ
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Int, bbe) → new_ltEs6(zzz500000, zzz4300000)
new_lt20(zzz500001, zzz4300001, ty_Ordering) → new_lt9(zzz500001, zzz4300001)
new_primEqInt(Neg(Succ(zzz50000)), Neg(Succ(zzz40000))) → new_primEqNat0(zzz50000, zzz40000)
new_esEs20(zzz5000, zzz4000, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_compare113(zzz500000, zzz4300000, True, ha, hb) → LT
new_esEs23(zzz500000, zzz4300000, ty_Ordering) → new_esEs8(zzz500000, zzz4300000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(app(ty_Either, bfc), bfd), bfb) → new_esEs4(zzz5000, zzz4000, bfc, bfd)
new_ltEs18(zzz50000, zzz430000, app(app(ty_Either, bch), bbe)) → new_ltEs7(zzz50000, zzz430000, bch, bbe)
new_esEs24(zzz500001, zzz4300001, ty_Bool) → new_esEs14(zzz500001, zzz4300001)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_lt19(zzz500000, zzz4300000, ty_Bool) → new_lt7(zzz500000, zzz4300000)
new_lt19(zzz500000, zzz4300000, ty_Integer) → new_lt10(zzz500000, zzz4300000)
new_ltEs4(Nothing, Nothing, bb) → True
new_lt13(zzz500000, zzz4300000, ty_Float) → new_lt6(zzz500000, zzz4300000)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_@0) → new_ltEs11(zzz500000, zzz4300000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Char, bbe) → new_ltEs5(zzz500000, zzz4300000)
new_lt13(zzz500000, zzz4300000, ty_Int) → new_lt14(zzz500000, zzz4300000)
new_lt6(zzz500000, zzz4300000) → new_esEs8(new_compare16(zzz500000, zzz4300000), LT)
new_compare29(Just(zzz50000), Nothing, False, gg) → GT
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_ltEs7(Right(zzz500000), Left(zzz4300000), bch, bbe) → False
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_esEs24(zzz500001, zzz4300001, app(app(app(ty_@3, ceg), ceh), cfa)) → new_esEs6(zzz500001, zzz4300001, ceg, ceh, cfa)
new_esEs23(zzz500000, zzz4300000, ty_Char) → new_esEs11(zzz500000, zzz4300000)
new_lt13(zzz500000, zzz4300000, ty_Bool) → new_lt7(zzz500000, zzz4300000)
new_esEs19(zzz5000, zzz4000, ty_Bool) → new_esEs14(zzz5000, zzz4000)
new_esEs20(zzz5000, zzz4000, ty_Float) → new_esEs13(zzz5000, zzz4000)
new_compare14(Double(zzz500000, zzz500001), Double(zzz4300000, zzz4300001)) → new_compare8(new_sr0(zzz500000, zzz4300000), new_sr0(zzz500001, zzz4300001))
new_compare12(zzz500000, zzz4300000, ha, hb) → new_compare27(zzz500000, zzz4300000, new_esEs4(zzz500000, zzz4300000, ha, hb), ha, hb)
new_compare8(zzz500, zzz4300) → new_primCmpInt(zzz500, zzz4300)
new_lt19(zzz500000, zzz4300000, ty_Char) → new_lt12(zzz500000, zzz4300000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, app(app(app(ty_@3, bdg), bdh), bea)) → new_ltEs16(zzz500000, zzz4300000, bdg, bdh, bea)
new_primEqInt(Neg(Succ(zzz50000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(zzz40000))) → False
new_compare17(zzz500000, zzz4300000) → new_compare26(zzz500000, zzz4300000, new_esEs14(zzz500000, zzz4300000))
new_esEs8(EQ, EQ) → True
new_lt13(zzz500000, zzz4300000, ty_Double) → new_lt15(zzz500000, zzz4300000)
new_compare111(zzz200, zzz201, True, bbd) → LT
new_esEs20(zzz5000, zzz4000, ty_@0) → new_esEs10(zzz5000, zzz4000)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Char, bfb) → new_esEs11(zzz5000, zzz4000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_ltEs19(zzz500001, zzz4300001, ty_@0) → new_ltEs11(zzz500001, zzz4300001)
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_esEs18(zzz5001, zzz4001, ty_Char) → new_esEs11(zzz5001, zzz4001)
new_compare112(zzz500000, zzz4300000, True) → LT
new_esEs19(zzz5000, zzz4000, ty_Char) → new_esEs11(zzz5000, zzz4000)
new_compare30(zzz500000, zzz4300000, app(app(ty_Either, bhh), caa)) → new_compare12(zzz500000, zzz4300000, bhh, caa)
new_primEqInt(Pos(Succ(zzz50000)), Pos(Succ(zzz40000))) → new_primEqNat0(zzz50000, zzz40000)
new_ltEs18(zzz50000, zzz430000, ty_Double) → new_ltEs8(zzz50000, zzz430000)
new_compare27(zzz500000, zzz4300000, True, ha, hb) → EQ
new_lt10(zzz500000, zzz4300000) → new_esEs8(new_compare9(zzz500000, zzz4300000), LT)
new_esEs24(zzz500001, zzz4300001, app(ty_Ratio, cef)) → new_esEs16(zzz500001, zzz4300001, cef)
new_ltEs19(zzz500001, zzz4300001, ty_Bool) → new_ltEs14(zzz500001, zzz4300001)
new_esEs14(False, True) → False
new_esEs14(True, False) → False
new_esEs23(zzz500000, zzz4300000, app(ty_[], cbd)) → new_esEs12(zzz500000, zzz4300000, cbd)
new_ltEs4(Just(zzz500000), Just(zzz4300000), app(app(ty_Either, bc), bd)) → new_ltEs7(zzz500000, zzz4300000, bc, bd)
new_esEs26(zzz5002, zzz4002, ty_Integer) → new_esEs15(zzz5002, zzz4002)
new_ltEs10(GT, EQ) → False
new_lt17(zzz500000, zzz4300000, cbc) → new_esEs8(new_compare7(zzz500000, zzz4300000, cbc), LT)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Double) → new_ltEs8(zzz500000, zzz4300000)
new_esEs24(zzz500001, zzz4300001, ty_Int) → new_esEs17(zzz500001, zzz4300001)
new_primEqNat0(Succ(zzz50000), Succ(zzz40000)) → new_primEqNat0(zzz50000, zzz40000)
new_ltEs20(zzz500002, zzz4300002, app(ty_[], cgd)) → new_ltEs17(zzz500002, zzz4300002, cgd)
new_esEs27(zzz5001, zzz4001, ty_Ordering) → new_esEs8(zzz5001, zzz4001)
new_ltEs14(False, False) → True
new_compare11(@0, @0) → EQ
new_lt7(zzz500000, zzz4300000) → new_esEs8(new_compare17(zzz500000, zzz4300000), LT)
new_esEs19(zzz5000, zzz4000, app(app(app(ty_@3, gd), ge), gf)) → new_esEs6(zzz5000, zzz4000, gd, ge, gf)
new_ltEs9(zzz50000, zzz430000) → new_fsEs(new_compare9(zzz50000, zzz430000))
new_ltEs20(zzz500002, zzz4300002, ty_Char) → new_ltEs5(zzz500002, zzz4300002)
new_compare113(zzz500000, zzz4300000, False, ha, hb) → GT
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, ty_Bool) → new_ltEs14(zzz500000, zzz4300000)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Int) → new_ltEs6(zzz500000, zzz4300000)
new_primCompAux00(zzz225, LT) → LT
new_lt20(zzz500001, zzz4300001, ty_@0) → new_lt4(zzz500001, zzz4300001)
new_ltEs19(zzz500001, zzz4300001, app(ty_[], ccf)) → new_ltEs17(zzz500001, zzz4300001, ccf)
new_ltEs19(zzz500001, zzz4300001, app(app(ty_Either, cbe), cbf)) → new_ltEs7(zzz500001, zzz4300001, cbe, cbf)
new_compare7(:%(zzz500000, zzz500001), :%(zzz4300000, zzz4300001), ty_Int) → new_compare8(new_sr0(zzz500000, zzz4300001), new_sr0(zzz4300000, zzz500001))
new_esEs24(zzz500001, zzz4300001, ty_Ordering) → new_esEs8(zzz500001, zzz4300001)
new_ltEs8(zzz50000, zzz430000) → new_fsEs(new_compare14(zzz50000, zzz430000))
new_esEs7(Nothing, Nothing, cf) → True
new_esEs28(zzz5000, zzz4000, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_esEs8(EQ, LT) → False
new_esEs8(LT, EQ) → False
new_esEs18(zzz5001, zzz4001, app(ty_Maybe, fd)) → new_esEs7(zzz5001, zzz4001, fd)
new_primEqInt(Pos(Succ(zzz50000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(zzz40000))) → False
new_lt20(zzz500001, zzz4300001, app(ty_Ratio, cef)) → new_lt17(zzz500001, zzz4300001, cef)
new_compare30(zzz500000, zzz4300000, ty_Int) → new_compare8(zzz500000, zzz4300000)
new_compare24(zzz500000, zzz4300000, False, hc, hd, he) → new_compare110(zzz500000, zzz4300000, new_ltEs16(zzz500000, zzz4300000, hc, hd, he), hc, hd, he)
new_esEs24(zzz500001, zzz4300001, ty_@0) → new_esEs10(zzz500001, zzz4300001)
new_primCmpNat0(Zero, Zero) → EQ
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Integer, bbe) → new_ltEs9(zzz500000, zzz4300000)
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_esEs23(zzz500000, zzz4300000, app(app(ty_@2, hf), hg)) → new_esEs5(zzz500000, zzz4300000, hf, hg)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, ty_@0) → new_esEs10(zzz5000, zzz4000)
new_ltEs10(LT, EQ) → True
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_compare19(zzz500000, zzz4300000, False) → GT
new_esEs27(zzz5001, zzz4001, ty_Double) → new_esEs9(zzz5001, zzz4001)
new_ltEs15(zzz50000, zzz430000, bef) → new_fsEs(new_compare7(zzz50000, zzz430000, bef))
new_esEs23(zzz500000, zzz4300000, ty_Float) → new_esEs13(zzz500000, zzz4300000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Integer) → new_esEs15(zzz5000, zzz4000)
new_compare29(Just(zzz50000), Just(zzz430000), False, gg) → new_compare111(zzz50000, zzz430000, new_ltEs18(zzz50000, zzz430000, gg), gg)
new_primEqInt(Pos(Succ(zzz50000)), Neg(zzz4000)) → False
new_primEqInt(Neg(Succ(zzz50000)), Pos(zzz4000)) → False
new_lt13(zzz500000, zzz4300000, app(ty_Ratio, cbc)) → new_lt17(zzz500000, zzz4300000, cbc)
new_esEs7(Nothing, Just(zzz4000), cf) → False
new_esEs7(Just(zzz5000), Nothing, cf) → False
new_esEs18(zzz5001, zzz4001, app(ty_[], eh)) → new_esEs12(zzz5001, zzz4001, eh)
new_esEs28(zzz5000, zzz4000, ty_Char) → new_esEs11(zzz5000, zzz4000)
new_ltEs10(GT, GT) → True
new_esEs26(zzz5002, zzz4002, app(ty_Ratio, daa)) → new_esEs16(zzz5002, zzz4002, daa)
new_esEs26(zzz5002, zzz4002, ty_Int) → new_esEs17(zzz5002, zzz4002)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, ty_Bool) → new_esEs14(zzz5000, zzz4000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_@0, bbe) → new_ltEs11(zzz500000, zzz4300000)
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primEqInt(Pos(Zero), Neg(Succ(zzz40000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(zzz40000))) → False
new_ltEs6(zzz50000, zzz430000) → new_fsEs(new_compare8(zzz50000, zzz430000))
new_esEs20(zzz5000, zzz4000, app(ty_[], bae)) → new_esEs12(zzz5000, zzz4000, bae)
new_esEs21(zzz5001, zzz4001, ty_Integer) → new_esEs15(zzz5001, zzz4001)
new_compare30(zzz500000, zzz4300000, app(app(ty_@2, cab), cac)) → new_compare18(zzz500000, zzz4300000, cab, cac)
new_primCompAux00(zzz225, EQ) → zzz225
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Double, bfb) → new_esEs9(zzz5000, zzz4000)
new_gt(zzz440, zzz4440, bec) → new_esEs8(new_compare28(zzz440, zzz4440, bec), GT)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Integer, bfb) → new_esEs15(zzz5000, zzz4000)
new_esEs18(zzz5001, zzz4001, ty_Int) → new_esEs17(zzz5001, zzz4001)
new_lt16(zzz500000, zzz4300000, hf, hg) → new_esEs8(new_compare18(zzz500000, zzz4300000, hf, hg), LT)
new_esEs8(GT, EQ) → False
new_esEs8(EQ, GT) → False
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Double) → new_esEs9(zzz5000, zzz4000)
new_esEs26(zzz5002, zzz4002, ty_Char) → new_esEs11(zzz5002, zzz4002)
new_esEs27(zzz5001, zzz4001, app(ty_Ratio, dbc)) → new_esEs16(zzz5001, zzz4001, dbc)
new_esEs26(zzz5002, zzz4002, app(app(ty_@2, chb), chc)) → new_esEs5(zzz5002, zzz4002, chb, chc)
new_ltEs19(zzz500001, zzz4300001, app(app(ty_@2, cbg), cbh)) → new_ltEs13(zzz500001, zzz4300001, cbg, cbh)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Bool) → new_ltEs14(zzz500000, zzz4300000)
new_not(False) → True
new_esEs24(zzz500001, zzz4300001, ty_Double) → new_esEs9(zzz500001, zzz4300001)
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_ltEs5(zzz50000, zzz430000) → new_fsEs(new_compare10(zzz50000, zzz430000))
new_esEs25(zzz500000, zzz4300000, ty_Integer) → new_esEs15(zzz500000, zzz4300000)
new_esEs26(zzz5002, zzz4002, ty_Bool) → new_esEs14(zzz5002, zzz4002)
new_ltEs19(zzz500001, zzz4300001, ty_Int) → new_ltEs6(zzz500001, zzz4300001)
new_esEs25(zzz500000, zzz4300000, app(ty_Ratio, cdd)) → new_esEs16(zzz500000, zzz4300000, cdd)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, ty_Int) → new_esEs17(zzz5000, zzz4000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Bool, bbe) → new_ltEs14(zzz500000, zzz4300000)
new_esEs28(zzz5000, zzz4000, app(app(ty_@2, dbf), dbg)) → new_esEs5(zzz5000, zzz4000, dbf, dbg)
new_esEs23(zzz500000, zzz4300000, ty_@0) → new_esEs10(zzz500000, zzz4300000)
new_compare30(zzz500000, zzz4300000, ty_@0) → new_compare11(zzz500000, zzz4300000)
new_esEs18(zzz5001, zzz4001, app(app(ty_Either, ed), ee)) → new_esEs4(zzz5001, zzz4001, ed, ee)
new_lt18(zzz500000, zzz4300000, cbd) → new_esEs8(new_compare4(zzz500000, zzz4300000, cbd), LT)
new_ltEs18(zzz50000, zzz430000, ty_Int) → new_ltEs6(zzz50000, zzz430000)
new_esEs22(zzz5000, zzz4000, ty_Int) → new_esEs17(zzz5000, zzz4000)
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_esEs6(@3(zzz5000, zzz5001, zzz5002), @3(zzz4000, zzz4001, zzz4002), cge, cgf, cgg) → new_asAs(new_esEs28(zzz5000, zzz4000, cge), new_asAs(new_esEs27(zzz5001, zzz4001, cgf), new_esEs26(zzz5002, zzz4002, cgg)))
new_esEs28(zzz5000, zzz4000, app(ty_Maybe, dcd)) → new_esEs7(zzz5000, zzz4000, dcd)
new_esEs28(zzz5000, zzz4000, ty_Double) → new_esEs9(zzz5000, zzz4000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, ty_Double) → new_ltEs8(zzz500000, zzz4300000)
new_lt20(zzz500001, zzz4300001, ty_Double) → new_lt15(zzz500001, zzz4300001)
new_lt20(zzz500001, zzz4300001, ty_Integer) → new_lt10(zzz500001, zzz4300001)
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_esEs26(zzz5002, zzz4002, ty_@0) → new_esEs10(zzz5002, zzz4002)
new_esEs18(zzz5001, zzz4001, ty_Float) → new_esEs13(zzz5001, zzz4001)
new_compare25(zzz500000, zzz4300000, False, hf, hg) → new_compare15(zzz500000, zzz4300000, new_ltEs13(zzz500000, zzz4300000, hf, hg), hf, hg)
new_esEs23(zzz500000, zzz4300000, app(app(ty_Either, ha), hb)) → new_esEs4(zzz500000, zzz4300000, ha, hb)
new_esEs20(zzz5000, zzz4000, ty_Char) → new_esEs11(zzz5000, zzz4000)
new_lt19(zzz500000, zzz4300000, app(ty_Maybe, cdc)) → new_lt11(zzz500000, zzz4300000, cdc)
new_esEs4(Left(zzz5000), Left(zzz4000), app(ty_Maybe, bgc), bfb) → new_esEs7(zzz5000, zzz4000, bgc)
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_esEs20(zzz5000, zzz4000, ty_Integer) → new_esEs15(zzz5000, zzz4000)
new_primEqNat0(Zero, Succ(zzz40000)) → False
new_primEqNat0(Succ(zzz50000), Zero) → False
new_esEs18(zzz5001, zzz4001, ty_Integer) → new_esEs15(zzz5001, zzz4001)
new_esEs17(zzz500, zzz400) → new_primEqInt(zzz500, zzz400)
new_lt5(zzz500000, zzz4300000, ha, hb) → new_esEs8(new_compare12(zzz500000, zzz4300000, ha, hb), LT)
new_compare25(zzz500000, zzz4300000, True, hf, hg) → EQ
new_esEs20(zzz5000, zzz4000, ty_Bool) → new_esEs14(zzz5000, zzz4000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), app(app(ty_Either, bbf), bbg), bbe) → new_ltEs7(zzz500000, zzz4300000, bbf, bbg)
new_ltEs14(True, True) → True
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs24(zzz500001, zzz4300001, app(app(ty_Either, cea), ceb)) → new_esEs4(zzz500001, zzz4300001, cea, ceb)
new_esEs28(zzz5000, zzz4000, app(app(app(ty_@3, dca), dcb), dcc)) → new_esEs6(zzz5000, zzz4000, dca, dcb, dcc)
new_compare30(zzz500000, zzz4300000, ty_Bool) → new_compare17(zzz500000, zzz4300000)
new_esEs27(zzz5001, zzz4001, app(app(ty_Either, dab), dac)) → new_esEs4(zzz5001, zzz4001, dab, dac)
new_esEs27(zzz5001, zzz4001, app(app(app(ty_@3, dag), dah), dba)) → new_esEs6(zzz5001, zzz4001, dag, dah, dba)
new_compare4(:(zzz500000, zzz500001), [], ce) → GT
new_ltEs18(zzz50000, zzz430000, app(ty_[], ce)) → new_ltEs17(zzz50000, zzz430000, ce)
new_esEs27(zzz5001, zzz4001, app(app(ty_@2, dad), dae)) → new_esEs5(zzz5001, zzz4001, dad, dae)
new_esEs27(zzz5001, zzz4001, ty_Int) → new_esEs17(zzz5001, zzz4001)
new_esEs23(zzz500000, zzz4300000, ty_Int) → new_esEs17(zzz500000, zzz4300000)
new_lt13(zzz500000, zzz4300000, ty_@0) → new_lt4(zzz500000, zzz4300000)
new_compare30(zzz500000, zzz4300000, ty_Char) → new_compare10(zzz500000, zzz4300000)
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_compare4([], :(zzz4300000, zzz4300001), ce) → LT
new_sr0(zzz5000, zzz4000) → new_primMulInt(zzz5000, zzz4000)
new_lt19(zzz500000, zzz4300000, app(ty_[], cdh)) → new_lt18(zzz500000, zzz4300000, cdh)
new_compare15(zzz500000, zzz4300000, False, hf, hg) → GT
new_ltEs18(zzz50000, zzz430000, ty_Float) → new_ltEs12(zzz50000, zzz430000)
new_ltEs18(zzz50000, zzz430000, ty_Integer) → new_ltEs9(zzz50000, zzz430000)
new_ltEs19(zzz500001, zzz4300001, ty_Double) → new_ltEs8(zzz500001, zzz4300001)
new_compare30(zzz500000, zzz4300000, ty_Float) → new_compare16(zzz500000, zzz4300000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), app(ty_[], bcg), bbe) → new_ltEs17(zzz500000, zzz4300000, bcg)
new_esEs11(Char(zzz5000), Char(zzz4000)) → new_primEqNat0(zzz5000, zzz4000)
new_esEs7(Just(zzz5000), Just(zzz4000), app(app(app(ty_@3, de), df), dg)) → new_esEs6(zzz5000, zzz4000, de, df, dg)
new_esEs25(zzz500000, zzz4300000, app(ty_Maybe, cdc)) → new_esEs7(zzz500000, zzz4300000, cdc)
new_compare29(Nothing, Nothing, False, gg) → LT
new_esEs23(zzz500000, zzz4300000, app(ty_Ratio, cbc)) → new_esEs16(zzz500000, zzz4300000, cbc)
new_lt13(zzz500000, zzz4300000, app(app(ty_Either, ha), hb)) → new_lt5(zzz500000, zzz4300000, ha, hb)
new_esEs16(:%(zzz5000, zzz5001), :%(zzz4000, zzz4001), bbc) → new_asAs(new_esEs22(zzz5000, zzz4000, bbc), new_esEs21(zzz5001, zzz4001, bbc))
new_ltEs4(Just(zzz500000), Just(zzz4300000), app(ty_Maybe, bg)) → new_ltEs4(zzz500000, zzz4300000, bg)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Float) → new_ltEs12(zzz500000, zzz4300000)
new_primCompAux0(zzz500000, zzz4300000, zzz220, ce) → new_primCompAux00(zzz220, new_compare30(zzz500000, zzz4300000, ce))
new_esEs19(zzz5000, zzz4000, app(app(ty_@2, ga), gb)) → new_esEs5(zzz5000, zzz4000, ga, gb)
new_esEs19(zzz5000, zzz4000, app(ty_Ratio, gh)) → new_esEs16(zzz5000, zzz4000, gh)
new_esEs10(@0, @0) → True
new_compare29(zzz5000, zzz43000, True, gg) → EQ
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs27(zzz5001, zzz4001, ty_Float) → new_esEs13(zzz5001, zzz4001)
new_lt13(zzz500000, zzz4300000, ty_Integer) → new_lt10(zzz500000, zzz4300000)
new_compare28(zzz5000, zzz43000, gg) → new_compare29(zzz5000, zzz43000, new_esEs7(zzz5000, zzz43000, gg), gg)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, app(app(ty_@2, bgh), bha)) → new_esEs5(zzz5000, zzz4000, bgh, bha)
new_esEs24(zzz500001, zzz4300001, ty_Char) → new_esEs11(zzz500001, zzz4300001)
new_esEs28(zzz5000, zzz4000, ty_@0) → new_esEs10(zzz5000, zzz4000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, app(app(ty_Either, bda), bdb)) → new_ltEs7(zzz500000, zzz4300000, bda, bdb)
new_esEs28(zzz5000, zzz4000, ty_Int) → new_esEs17(zzz5000, zzz4000)
new_compare7(:%(zzz500000, zzz500001), :%(zzz4300000, zzz4300001), ty_Integer) → new_compare9(new_sr(zzz500000, zzz4300001), new_sr(zzz4300000, zzz500001))
new_compare9(Integer(zzz500000), Integer(zzz4300000)) → new_primCmpInt(zzz500000, zzz4300000)
new_compare23(zzz500000, zzz4300000, False) → new_compare112(zzz500000, zzz4300000, new_ltEs10(zzz500000, zzz4300000))
new_asAs(False, zzz207) → False
new_esEs4(Left(zzz5000), Left(zzz4000), ty_@0, bfb) → new_esEs10(zzz5000, zzz4000)
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_esEs26(zzz5002, zzz4002, ty_Double) → new_esEs9(zzz5002, zzz4002)
new_ltEs10(LT, GT) → True
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_ltEs4(Just(zzz500000), Just(zzz4300000), app(ty_Ratio, bh)) → new_ltEs15(zzz500000, zzz4300000, bh)
new_esEs23(zzz500000, zzz4300000, app(app(app(ty_@3, hc), hd), he)) → new_esEs6(zzz500000, zzz4300000, hc, hd, he)
new_lt8(zzz500000, zzz4300000, hc, hd, he) → new_esEs8(new_compare13(zzz500000, zzz4300000, hc, hd, he), LT)
new_lt11(zzz5000, zzz43000, gg) → new_esEs8(new_compare28(zzz5000, zzz43000, gg), LT)
new_esEs26(zzz5002, zzz4002, app(ty_[], chd)) → new_esEs12(zzz5002, zzz4002, chd)
new_compare4(:(zzz500000, zzz500001), :(zzz4300000, zzz4300001), ce) → new_primCompAux0(zzz500000, zzz4300000, new_compare4(zzz500001, zzz4300001, ce), ce)
new_compare16(Float(zzz500000, zzz500001), Float(zzz4300000, zzz4300001)) → new_compare8(new_sr0(zzz500000, zzz4300000), new_sr0(zzz500001, zzz4300001))
new_esEs26(zzz5002, zzz4002, app(ty_Maybe, chh)) → new_esEs7(zzz5002, zzz4002, chh)
new_esEs28(zzz5000, zzz4000, ty_Bool) → new_esEs14(zzz5000, zzz4000)
new_compare110(zzz500000, zzz4300000, True, hc, hd, he) → LT
new_lt19(zzz500000, zzz4300000, app(app(ty_Either, ccg), cch)) → new_lt5(zzz500000, zzz4300000, ccg, cch)
new_ltEs18(zzz50000, zzz430000, ty_Bool) → new_ltEs14(zzz50000, zzz430000)
new_esEs28(zzz5000, zzz4000, ty_Integer) → new_esEs15(zzz5000, zzz4000)
new_esEs18(zzz5001, zzz4001, ty_Ordering) → new_esEs8(zzz5001, zzz4001)
new_esEs19(zzz5000, zzz4000, ty_Double) → new_esEs9(zzz5000, zzz4000)
new_lt20(zzz500001, zzz4300001, app(app(ty_@2, cec), ced)) → new_lt16(zzz500001, zzz4300001, cec, ced)
new_esEs5(@2(zzz5000, zzz5001), @2(zzz4000, zzz4001), eb, ec) → new_asAs(new_esEs19(zzz5000, zzz4000, eb), new_esEs18(zzz5001, zzz4001, ec))
new_compare26(zzz500000, zzz4300000, False) → new_compare19(zzz500000, zzz4300000, new_ltEs14(zzz500000, zzz4300000))
new_esEs28(zzz5000, zzz4000, app(app(ty_Either, dbd), dbe)) → new_esEs4(zzz5000, zzz4000, dbd, dbe)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, app(ty_Maybe, bhf)) → new_esEs7(zzz5000, zzz4000, bhf)
new_esEs7(Just(zzz5000), Just(zzz4000), ty_@0) → new_esEs10(zzz5000, zzz4000)
new_ltEs18(zzz50000, zzz430000, ty_Char) → new_ltEs5(zzz50000, zzz430000)
new_esEs28(zzz5000, zzz4000, ty_Float) → new_esEs13(zzz5000, zzz4000)
new_lt13(zzz500000, zzz4300000, ty_Ordering) → new_lt9(zzz500000, zzz4300000)
new_esEs25(zzz500000, zzz4300000, app(app(app(ty_@3, cde), cdf), cdg)) → new_esEs6(zzz500000, zzz4300000, cde, cdf, cdg)
new_ltEs10(EQ, EQ) → True
new_ltEs18(zzz50000, zzz430000, app(app(ty_@2, bed), bee)) → new_ltEs13(zzz50000, zzz430000, bed, bee)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Int, bfb) → new_esEs17(zzz5000, zzz4000)
new_esEs23(zzz500000, zzz4300000, ty_Integer) → new_esEs15(zzz500000, zzz4300000)
new_ltEs10(LT, LT) → True
new_esEs14(True, True) → True
new_compare111(zzz200, zzz201, False, bbd) → GT
new_esEs27(zzz5001, zzz4001, ty_Bool) → new_esEs14(zzz5001, zzz4001)
new_esEs7(Just(zzz5000), Just(zzz4000), app(app(ty_Either, cg), da)) → new_esEs4(zzz5000, zzz4000, cg, da)
new_compare10(Char(zzz500000), Char(zzz4300000)) → new_primCmpNat0(zzz500000, zzz4300000)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Float, bfb) → new_esEs13(zzz5000, zzz4000)
new_lt13(zzz500000, zzz4300000, app(app(ty_@2, hf), hg)) → new_lt16(zzz500000, zzz4300000, hf, hg)
new_ltEs7(Left(zzz500000), Left(zzz4300000), app(app(ty_@2, bbh), bca), bbe) → new_ltEs13(zzz500000, zzz4300000, bbh, bca)
new_esEs7(Just(zzz5000), Just(zzz4000), app(ty_Ratio, ea)) → new_esEs16(zzz5000, zzz4000, ea)
new_lt13(zzz500000, zzz4300000, app(ty_Maybe, cbb)) → new_lt11(zzz500000, zzz4300000, cbb)
new_ltEs20(zzz500002, zzz4300002, app(app(ty_Either, cfc), cfd)) → new_ltEs7(zzz500002, zzz4300002, cfc, cfd)
new_esEs18(zzz5001, zzz4001, ty_@0) → new_esEs10(zzz5001, zzz4001)
new_ltEs16(@3(zzz500000, zzz500001, zzz500002), @3(zzz4300000, zzz4300001, zzz4300002), beg, beh, bfa) → new_pePe(new_lt19(zzz500000, zzz4300000, beg), new_asAs(new_esEs25(zzz500000, zzz4300000, beg), new_pePe(new_lt20(zzz500001, zzz4300001, beh), new_asAs(new_esEs24(zzz500001, zzz4300001, beh), new_ltEs20(zzz500002, zzz4300002, bfa)))))
new_esEs4(Right(zzz5000), Right(zzz4000), bge, ty_Double) → new_esEs9(zzz5000, zzz4000)
new_ltEs14(True, False) → False
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_esEs20(zzz5000, zzz4000, ty_Int) → new_esEs17(zzz5000, zzz4000)
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_esEs25(zzz500000, zzz4300000, app(app(ty_@2, cda), cdb)) → new_esEs5(zzz500000, zzz4300000, cda, cdb)
new_ltEs20(zzz500002, zzz4300002, ty_Double) → new_ltEs8(zzz500002, zzz4300002)
new_ltEs7(Left(zzz500000), Left(zzz4300000), app(ty_Ratio, bcc), bbe) → new_ltEs15(zzz500000, zzz4300000, bcc)
new_ltEs19(zzz500001, zzz4300001, app(app(app(ty_@3, ccc), ccd), cce)) → new_ltEs16(zzz500001, zzz4300001, ccc, ccd, cce)
new_ltEs20(zzz500002, zzz4300002, app(app(app(ty_@3, cga), cgb), cgc)) → new_ltEs16(zzz500002, zzz4300002, cga, cgb, cgc)
new_compare112(zzz500000, zzz4300000, False) → GT
new_ltEs10(EQ, LT) → False
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Float) → new_esEs13(zzz5000, zzz4000)
new_esEs14(False, False) → True
new_esEs7(Just(zzz5000), Just(zzz4000), app(app(ty_@2, db), dc)) → new_esEs5(zzz5000, zzz4000, db, dc)
new_lt20(zzz500001, zzz4300001, ty_Char) → new_lt12(zzz500001, zzz4300001)
new_lt9(zzz500000, zzz4300000) → new_esEs8(new_compare6(zzz500000, zzz4300000), LT)
new_ltEs10(GT, LT) → False
new_esEs18(zzz5001, zzz4001, ty_Bool) → new_esEs14(zzz5001, zzz4001)
new_esEs22(zzz5000, zzz4000, ty_Integer) → new_esEs15(zzz5000, zzz4000)
new_primPlusNat1(Zero, Zero) → Zero
new_compare30(zzz500000, zzz4300000, app(app(app(ty_@3, caf), cag), cah)) → new_compare13(zzz500000, zzz4300000, caf, cag, cah)
new_esEs19(zzz5000, zzz4000, ty_Integer) → new_esEs15(zzz5000, zzz4000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(ty_[], bfg), bfb) → new_esEs12(zzz5000, zzz4000, bfg)
new_esEs26(zzz5002, zzz4002, app(app(ty_Either, cgh), cha)) → new_esEs4(zzz5002, zzz4002, cgh, cha)
new_asAs(True, zzz207) → zzz207
new_esEs28(zzz5000, zzz4000, app(ty_[], dbh)) → new_esEs12(zzz5000, zzz4000, dbh)
new_esEs27(zzz5001, zzz4001, app(ty_[], daf)) → new_esEs12(zzz5001, zzz4001, daf)
new_esEs19(zzz5000, zzz4000, app(app(ty_Either, fg), fh)) → new_esEs4(zzz5000, zzz4000, fg, fh)
new_ltEs4(Just(zzz500000), Nothing, bb) → False
new_esEs20(zzz5000, zzz4000, ty_Double) → new_esEs9(zzz5000, zzz4000)
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_ltEs4(Just(zzz500000), Just(zzz4300000), app(ty_[], cd)) → new_ltEs17(zzz500000, zzz4300000, cd)
new_esEs4(Right(zzz5000), Left(zzz4000), bge, bfb) → False
new_esEs4(Left(zzz5000), Right(zzz4000), bge, bfb) → False
new_ltEs19(zzz500001, zzz4300001, ty_Float) → new_ltEs12(zzz500001, zzz4300001)
new_ltEs20(zzz500002, zzz4300002, app(ty_Maybe, cfg)) → new_ltEs4(zzz500002, zzz4300002, cfg)
new_esEs4(Left(zzz5000), Left(zzz4000), app(app(app(ty_@3, bfh), bga), bgb), bfb) → new_esEs6(zzz5000, zzz4000, bfh, bga, bgb)
new_ltEs19(zzz500001, zzz4300001, ty_Char) → new_ltEs5(zzz500001, zzz4300001)
new_fsEs(zzz210) → new_not(new_esEs8(zzz210, GT))
new_esEs19(zzz5000, zzz4000, ty_@0) → new_esEs10(zzz5000, zzz4000)
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Bool) → new_esEs14(zzz5000, zzz4000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Double, bbe) → new_ltEs8(zzz500000, zzz4300000)
new_esEs24(zzz500001, zzz4300001, ty_Float) → new_esEs13(zzz500001, zzz4300001)
new_ltEs11(zzz50000, zzz430000) → new_fsEs(new_compare11(zzz50000, zzz430000))
new_lt20(zzz500001, zzz4300001, ty_Int) → new_lt14(zzz500001, zzz4300001)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, ty_Float) → new_esEs13(zzz5000, zzz4000)
new_esEs19(zzz5000, zzz4000, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_ltEs20(zzz500002, zzz4300002, app(app(ty_@2, cfe), cff)) → new_ltEs13(zzz500002, zzz4300002, cfe, cff)
new_esEs27(zzz5001, zzz4001, ty_Char) → new_esEs11(zzz5001, zzz4001)
new_ltEs20(zzz500002, zzz4300002, ty_Int) → new_ltEs6(zzz500002, zzz4300002)
new_compare110(zzz500000, zzz4300000, False, hc, hd, he) → GT
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Char) → new_ltEs5(zzz500000, zzz4300000)
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Char) → new_esEs11(zzz5000, zzz4000)
new_primCompAux00(zzz225, GT) → GT
new_ltEs20(zzz500002, zzz4300002, ty_Integer) → new_ltEs9(zzz500002, zzz4300002)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, app(ty_Maybe, bde)) → new_ltEs4(zzz500000, zzz4300000, bde)
new_lt19(zzz500000, zzz4300000, ty_Int) → new_lt14(zzz500000, zzz4300000)
new_ltEs4(Just(zzz500000), Just(zzz4300000), app(app(app(ty_@3, ca), cb), cc)) → new_ltEs16(zzz500000, zzz4300000, ca, cb, cc)
new_ltEs18(zzz50000, zzz430000, ty_Ordering) → new_ltEs10(zzz50000, zzz430000)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Integer) → new_ltEs9(zzz500000, zzz4300000)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_compare30(zzz500000, zzz4300000, ty_Ordering) → new_compare6(zzz500000, zzz4300000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, ty_Float) → new_ltEs12(zzz500000, zzz4300000)
new_esEs27(zzz5001, zzz4001, ty_Integer) → new_esEs15(zzz5001, zzz4001)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, ty_Int) → new_ltEs6(zzz500000, zzz4300000)
new_not(True) → False

The set Q consists of the following terms:

new_compare30(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_compare23(x0, x1, True)
new_lt11(x0, x1, x2)
new_lt14(x0, x1)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs18(x0, x1, app(app(ty_@2, x2), x3))
new_asAs(True, x0)
new_compare29(Nothing, Nothing, False, x0)
new_compare19(x0, x1, True)
new_esEs26(x0, x1, ty_@0)
new_ltEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs18(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_Ordering)
new_esEs18(x0, x1, ty_Int)
new_ltEs19(x0, x1, app(ty_[], x2))
new_primPlusNat1(Zero, Succ(x0))
new_compare29(Nothing, Just(x0), False, x1)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_compare30(x0, x1, ty_@0)
new_lt20(x0, x1, ty_Ordering)
new_esEs9(Double(x0, x1), Double(x2, x3))
new_ltEs7(Right(x0), Right(x1), x2, ty_@0)
new_primCompAux0(x0, x1, x2, x3)
new_primMulNat0(Succ(x0), Zero)
new_lt19(x0, x1, ty_Double)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_@0)
new_primPlusNat1(Succ(x0), Zero)
new_esEs21(x0, x1, ty_Int)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare4(:(x0, x1), :(x2, x3), x4)
new_ltEs10(LT, LT)
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_esEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs16(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs23(x0, x1, ty_Bool)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs27(x0, x1, ty_Int)
new_esEs4(Right(x0), Left(x1), x2, x3)
new_esEs4(Left(x0), Right(x1), x2, x3)
new_esEs18(x0, x1, ty_Char)
new_esEs24(x0, x1, ty_Char)
new_ltEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(True, False)
new_ltEs14(False, True)
new_esEs25(x0, x1, ty_Double)
new_pePe(False, x0)
new_esEs19(x0, x1, ty_Char)
new_esEs25(x0, x1, ty_Char)
new_compare27(x0, x1, True, x2, x3)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs7(Just(x0), Just(x1), ty_Double)
new_esEs8(GT, GT)
new_esEs23(x0, x1, ty_@0)
new_compare4([], :(x0, x1), x2)
new_lt9(x0, x1)
new_lt19(x0, x1, ty_Ordering)
new_esEs11(Char(x0), Char(x1))
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs4(Left(x0), Left(x1), ty_Int, x2)
new_esEs7(Nothing, Just(x0), x1)
new_esEs8(LT, LT)
new_sr0(x0, x1)
new_compare6(x0, x1)
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_compare30(x0, x1, ty_Double)
new_esEs7(Just(x0), Just(x1), ty_Char)
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, app(ty_[], x2))
new_lt13(x0, x1, app(ty_Ratio, x2))
new_compare19(x0, x1, False)
new_ltEs4(Nothing, Nothing, x0)
new_compare110(x0, x1, False, x2, x3, x4)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs26(x0, x1, ty_Double)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_lt18(x0, x1, x2)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_lt16(x0, x1, x2, x3)
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_compare111(x0, x1, False, x2)
new_compare4([], [], x0)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs7(Left(x0), Left(x1), ty_Char, x2)
new_ltEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs17(x0, x1)
new_ltEs19(x0, x1, ty_Char)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs14(True, True)
new_compare26(x0, x1, True)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Char)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare112(x0, x1, False)
new_esEs18(x0, x1, ty_Bool)
new_esEs20(x0, x1, ty_Float)
new_primEqNat0(Zero, Zero)
new_ltEs4(Just(x0), Just(x1), ty_Double)
new_compare30(x0, x1, ty_Char)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_ltEs7(Right(x0), Right(x1), x2, ty_Char)
new_esEs20(x0, x1, ty_Int)
new_lt13(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Double)
new_lt19(x0, x1, ty_Bool)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, ty_@0)
new_lt13(x0, x1, app(ty_[], x2))
new_esEs12([], :(x0, x1), x2)
new_esEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs28(x0, x1, ty_Integer)
new_compare17(x0, x1)
new_ltEs17(x0, x1, x2)
new_primPlusNat0(Zero, x0)
new_ltEs20(x0, x1, ty_Int)
new_compare13(x0, x1, x2, x3, x4)
new_primMulNat0(Zero, Zero)
new_esEs4(Right(x0), Right(x1), x2, ty_Float)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpNat0(Succ(x0), Zero)
new_compare16(Float(x0, x1), Float(x2, x3))
new_ltEs20(x0, x1, ty_Integer)
new_compare30(x0, x1, ty_Ordering)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs26(x0, x1, ty_Integer)
new_ltEs10(EQ, LT)
new_ltEs10(LT, EQ)
new_lt4(x0, x1)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_ltEs7(Left(x0), Left(x1), ty_@0, x2)
new_lt13(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs19(x0, x1, ty_Bool)
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs28(x0, x1, ty_@0)
new_primMulNat0(Succ(x0), Succ(x1))
new_lt7(x0, x1)
new_esEs23(x0, x1, ty_Float)
new_ltEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_Double)
new_compare113(x0, x1, False, x2, x3)
new_ltEs18(x0, x1, ty_@0)
new_compare15(x0, x1, True, x2, x3)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs23(x0, x1, ty_Char)
new_esEs24(x0, x1, ty_Int)
new_compare9(Integer(x0), Integer(x1))
new_esEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, ty_Ordering)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_ltEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_compare4(:(x0, x1), [], x2)
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_esEs24(x0, x1, ty_Bool)
new_ltEs13(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs26(x0, x1, ty_Char)
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_compare25(x0, x1, False, x2, x3)
new_esEs20(x0, x1, ty_Ordering)
new_esEs12(:(x0, x1), :(x2, x3), x4)
new_fsEs(x0)
new_lt8(x0, x1, x2, x3, x4)
new_ltEs11(x0, x1)
new_esEs23(x0, x1, ty_Double)
new_lt13(x0, x1, ty_@0)
new_ltEs7(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Just(x0), Just(x1), ty_Int)
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_compare26(x0, x1, False)
new_ltEs18(x0, x1, ty_Double)
new_ltEs7(Right(x0), Left(x1), x2, x3)
new_ltEs7(Left(x0), Right(x1), x2, x3)
new_ltEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs25(x0, x1, ty_Bool)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primPlusNat1(Zero, Zero)
new_esEs28(x0, x1, ty_Float)
new_ltEs7(Right(x0), Right(x1), x2, ty_Int)
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_lt12(x0, x1)
new_compare7(:%(x0, x1), :%(x2, x3), ty_Int)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_ltEs4(Just(x0), Just(x1), ty_Int)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_compare11(@0, @0)
new_esEs4(Right(x0), Right(x1), x2, ty_Integer)
new_primMulNat0(Zero, Succ(x0))
new_esEs26(x0, x1, ty_Bool)
new_asAs(False, x0)
new_esEs12(:(x0, x1), [], x2)
new_ltEs4(Just(x0), Just(x1), ty_Bool)
new_ltEs8(x0, x1)
new_ltEs18(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Float)
new_esEs27(x0, x1, ty_Double)
new_ltEs19(x0, x1, ty_Ordering)
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs4(Just(x0), Just(x1), ty_Ordering)
new_esEs4(Left(x0), Left(x1), ty_@0, x2)
new_esEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs18(x0, x1, ty_Double)
new_ltEs10(GT, LT)
new_esEs4(Left(x0), Left(x1), ty_Double, x2)
new_ltEs10(LT, GT)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs28(x0, x1, ty_Double)
new_esEs10(@0, @0)
new_compare14(Double(x0, x1), Double(x2, x3))
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_compare24(x0, x1, True, x2, x3, x4)
new_compare30(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_Integer)
new_ltEs18(x0, x1, ty_Float)
new_compare8(x0, x1)
new_lt13(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs20(x0, x1, ty_Char)
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs7(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs19(x0, x1, ty_Integer)
new_pePe(True, x0)
new_compare29(Just(x0), Just(x1), False, x2)
new_esEs27(x0, x1, ty_Float)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_primCompAux00(x0, EQ)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_lt19(x0, x1, ty_Float)
new_primEqNat0(Succ(x0), Zero)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_ltEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_lt17(x0, x1, x2)
new_esEs28(x0, x1, ty_Int)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_compare27(x0, x1, False, x2, x3)
new_esEs18(x0, x1, ty_Ordering)
new_esEs25(x0, x1, ty_Int)
new_esEs18(x0, x1, app(ty_Ratio, x2))
new_esEs7(Nothing, Nothing, x0)
new_ltEs15(x0, x1, x2)
new_ltEs4(Just(x0), Just(x1), ty_@0)
new_esEs19(x0, x1, app(ty_[], x2))
new_compare23(x0, x1, False)
new_compare30(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_ltEs4(Just(x0), Nothing, x1)
new_esEs8(EQ, EQ)
new_compare112(x0, x1, True)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs4(Right(x0), Right(x1), x2, ty_Int)
new_esEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs19(x0, x1, ty_Double)
new_esEs13(Float(x0, x1), Float(x2, x3))
new_primEqInt(Neg(Zero), Neg(Zero))
new_gt(x0, x1, x2)
new_lt13(x0, x1, ty_Char)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, ty_Char)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_esEs15(Integer(x0), Integer(x1))
new_ltEs12(x0, x1)
new_ltEs20(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_@0)
new_esEs14(True, False)
new_esEs14(False, True)
new_ltEs4(Just(x0), Just(x1), ty_Float)
new_ltEs7(Right(x0), Right(x1), x2, ty_Float)
new_esEs18(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, app(ty_[], x2))
new_ltEs6(x0, x1)
new_esEs22(x0, x1, ty_Int)
new_esEs20(x0, x1, ty_Double)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare110(x0, x1, True, x2, x3, x4)
new_ltEs9(x0, x1)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs19(x0, x1, ty_@0)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_lt19(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Ordering)
new_esEs27(x0, x1, ty_Integer)
new_esEs16(:%(x0, x1), :%(x2, x3), x4)
new_lt20(x0, x1, ty_Float)
new_compare25(x0, x1, True, x2, x3)
new_compare30(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Integer)
new_primCmpNat0(Succ(x0), Succ(x1))
new_lt19(x0, x1, ty_Char)
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_esEs20(x0, x1, ty_Integer)
new_esEs28(x0, x1, ty_Ordering)
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_esEs21(x0, x1, ty_Integer)
new_compare28(x0, x1, x2)
new_ltEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_esEs4(Right(x0), Right(x1), x2, ty_Double)
new_ltEs7(Right(x0), Right(x1), x2, ty_Double)
new_lt20(x0, x1, ty_Bool)
new_primPlusNat0(Succ(x0), x1)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_@0)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, ty_Integer)
new_compare30(x0, x1, app(ty_Maybe, x2))
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs7(Just(x0), Just(x1), ty_Float)
new_compare18(x0, x1, x2, x3)
new_esEs19(x0, x1, ty_Float)
new_ltEs20(x0, x1, ty_Bool)
new_primCmpNat0(Zero, Zero)
new_esEs4(Left(x0), Left(x1), ty_Integer, x2)
new_esEs19(x0, x1, ty_Ordering)
new_lt13(x0, x1, ty_Bool)
new_ltEs19(x0, x1, ty_Float)
new_esEs27(x0, x1, app(ty_[], x2))
new_ltEs7(Left(x0), Left(x1), ty_Double, x2)
new_esEs12([], [], x0)
new_lt10(x0, x1)
new_compare7(:%(x0, x1), :%(x2, x3), ty_Integer)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_compare113(x0, x1, True, x2, x3)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs20(x0, x1, app(ty_[], x2))
new_ltEs7(Left(x0), Left(x1), ty_Bool, x2)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, ty_Ordering)
new_esEs4(Left(x0), Left(x1), ty_Char, x2)
new_esEs26(x0, x1, ty_Float)
new_ltEs7(Left(x0), Left(x1), ty_Float, x2)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt5(x0, x1, x2, x3)
new_esEs28(x0, x1, app(ty_[], x2))
new_compare29(Just(x0), Nothing, False, x1)
new_ltEs10(GT, GT)
new_ltEs14(True, True)
new_ltEs14(False, False)
new_esEs24(x0, x1, ty_Ordering)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_lt19(x0, x1, ty_@0)
new_esEs18(x0, x1, ty_Float)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_lt13(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, ty_Char)
new_ltEs7(Left(x0), Left(x1), ty_Int, x2)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_esEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_not(True)
new_esEs19(x0, x1, ty_Int)
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Just(x0), Just(x1), ty_@0)
new_compare30(x0, x1, ty_Integer)
new_ltEs5(x0, x1)
new_compare30(x0, x1, app(ty_Ratio, x2))
new_esEs4(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs20(x0, x1, ty_Double)
new_esEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(Just(x0), Just(x1), ty_Integer)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_not(False)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Integer)
new_esEs4(Right(x0), Right(x1), x2, ty_@0)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_ltEs4(Just(x0), Just(x1), app(ty_[], x2))
new_primCompAux00(x0, LT)
new_lt6(x0, x1)
new_ltEs10(EQ, GT)
new_ltEs10(GT, EQ)
new_ltEs19(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Float)
new_esEs24(x0, x1, app(ty_[], x2))
new_ltEs18(x0, x1, ty_Char)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs19(x0, x1, ty_Integer)
new_esEs18(x0, x1, app(ty_[], x2))
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_sr(Integer(x0), Integer(x1))
new_esEs4(Right(x0), Right(x1), x2, ty_Char)
new_esEs27(x0, x1, ty_Char)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs20(x0, x1, ty_Bool)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(Just(x0), Just(x1), ty_Char)
new_esEs4(Left(x0), Left(x1), ty_Float, x2)
new_ltEs4(Nothing, Just(x0), x1)
new_esEs18(x0, x1, ty_@0)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_ltEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_lt13(x0, x1, ty_Double)
new_esEs18(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_Bool)
new_lt13(x0, x1, ty_Ordering)
new_compare12(x0, x1, x2, x3)
new_compare15(x0, x1, False, x2, x3)
new_ltEs18(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Ordering)
new_compare30(x0, x1, ty_Float)
new_esEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare111(x0, x1, True, x2)
new_lt13(x0, x1, ty_Integer)
new_lt19(x0, x1, app(ty_[], x2))
new_esEs14(False, False)
new_primEqInt(Pos(Zero), Pos(Zero))
new_compare30(x0, x1, app(ty_[], x2))
new_compare10(Char(x0), Char(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs24(x0, x1, ty_Integer)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Double)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs25(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, ty_Float)
new_lt13(x0, x1, ty_Int)
new_compare29(x0, x1, True, x2)
new_lt13(x0, x1, ty_Float)
new_lt20(x0, x1, ty_Integer)
new_primCmpNat0(Zero, Succ(x0))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_ltEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_Int)
new_primCompAux00(x0, GT)
new_ltEs20(x0, x1, ty_@0)
new_esEs4(Left(x0), Left(x1), ty_Bool, x2)
new_lt15(x0, x1)
new_ltEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primEqNat0(Zero, Succ(x0))
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs7(Left(x0), Left(x1), ty_Integer, x2)
new_esEs27(x0, x1, ty_Bool)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_@0)
new_compare24(x0, x1, False, x2, x3, x4)
new_esEs7(Just(x0), Nothing, x1)
new_esEs18(x0, x1, ty_Integer)
new_ltEs10(EQ, EQ)

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(zzz800, zzz801, zzz802, Branch(zzz8030, zzz8031, zzz8032, zzz8033, zzz8034), zzz804, h, ba) → new_deleteMin(zzz8030, zzz8031, zzz8032, zzz8033, zzz8034, 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(zzz810, zzz811, zzz812, zzz813, Branch(zzz8140, zzz8141, zzz8142, zzz8143, zzz8144), h, ba) → new_deleteMax(zzz8140, zzz8141, zzz8142, zzz8143, zzz8144, 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_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, True, h, ba) → new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), zzz803, h, ba)
new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba) → new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_lt14(new_sr0(new_sIZE_RATIO, new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), h, ba)
new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, True, h, ba) → new_glueVBal(zzz814, Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba)
new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, False, h, ba) → new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_lt14(new_sr0(new_sIZE_RATIO, new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), h, ba)

The TRS R consists of the following rules:

new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba) → new_sizeFM(zzz810, zzz811, zzz812, zzz813, zzz814, h, ba)
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_compare8(zzz500, zzz4300) → new_primCmpInt(zzz500, zzz4300)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_esEs8(EQ, EQ) → True
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba) → new_sizeFM(zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)
new_primPlusNat1(Zero, Zero) → Zero
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_lt14(zzz5000, zzz43000) → new_esEs8(new_compare8(zzz5000, zzz43000), LT)
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_esEs8(EQ, GT) → False
new_esEs8(GT, EQ) → False
new_primMulNat0(Zero, Zero) → Zero
new_esEs8(GT, GT) → True
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_esEs8(LT, GT) → False
new_esEs8(GT, LT) → False
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_sr0(zzz5000, zzz4000) → new_primMulInt(zzz5000, zzz4000)
new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_sizeFM(zzz760, zzz761, zzz762, zzz763, zzz764, h, ba) → zzz762
new_esEs8(LT, EQ) → False
new_esEs8(EQ, LT) → False
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_esEs8(LT, LT) → True
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz5000000), Zero) → GT

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primPlusNat0(Zero, x0)
new_lt14(x0, x1)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpNat0(Succ(x0), Zero)
new_compare8(x0, x1)
new_esEs8(LT, LT)
new_sr0(x0, x1)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_glueVBal3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primMulInt(Neg(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_esEs8(GT, GT)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_sIZE_RATIO

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_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, True, h, ba) → new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), zzz803, h, ba)
new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba) → new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_lt14(new_sr0(new_sIZE_RATIO, new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), h, ba)
new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, True, h, ba) → new_glueVBal(zzz814, Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba)
new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, False, h, ba) → new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_lt14(new_sr0(new_sIZE_RATIO, new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba) → new_sizeFM(zzz810, zzz811, zzz812, zzz813, zzz814, h, ba)
new_sr0(zzz5000, zzz4000) → new_primMulInt(zzz5000, zzz4000)
new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba) → new_sizeFM(zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)
new_lt14(zzz5000, zzz43000) → new_esEs8(new_compare8(zzz5000, zzz43000), LT)
new_compare8(zzz500, zzz4300) → new_primCmpInt(zzz500, zzz4300)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_sizeFM(zzz760, zzz761, zzz762, zzz763, zzz764, h, ba) → zzz762
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primPlusNat0(Zero, x0)
new_lt14(x0, x1)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpNat0(Succ(x0), Zero)
new_compare8(x0, x1)
new_esEs8(LT, LT)
new_sr0(x0, x1)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_glueVBal3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primMulInt(Neg(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_esEs8(GT, GT)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_sIZE_RATIO

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba) → new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_lt14(new_sr0(new_sIZE_RATIO, new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), h, ba) at position [10] we obtained the following new rules:

new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba) → new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_compare8(new_sr0(new_sIZE_RATIO, new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, 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_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, True, h, ba) → new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), zzz803, h, ba)
new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, True, h, ba) → new_glueVBal(zzz814, Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba)
new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, False, h, ba) → new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_lt14(new_sr0(new_sIZE_RATIO, new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), h, ba)
new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba) → new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_compare8(new_sr0(new_sIZE_RATIO, new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba) → new_sizeFM(zzz810, zzz811, zzz812, zzz813, zzz814, h, ba)
new_sr0(zzz5000, zzz4000) → new_primMulInt(zzz5000, zzz4000)
new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba) → new_sizeFM(zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)
new_lt14(zzz5000, zzz43000) → new_esEs8(new_compare8(zzz5000, zzz43000), LT)
new_compare8(zzz500, zzz4300) → new_primCmpInt(zzz500, zzz4300)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_sizeFM(zzz760, zzz761, zzz762, zzz763, zzz764, h, ba) → zzz762
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primPlusNat0(Zero, x0)
new_lt14(x0, x1)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpNat0(Succ(x0), Zero)
new_compare8(x0, x1)
new_esEs8(LT, LT)
new_sr0(x0, x1)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_glueVBal3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primMulInt(Neg(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_esEs8(GT, GT)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_sIZE_RATIO

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, False, h, ba) → new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_lt14(new_sr0(new_sIZE_RATIO, new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), h, ba) at position [10] we obtained the following new rules:

new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, False, h, ba) → new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_compare8(new_sr0(new_sIZE_RATIO, new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, 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_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, True, h, ba) → new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), zzz803, h, ba)
new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, True, h, ba) → new_glueVBal(zzz814, Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba)
new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba) → new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_compare8(new_sr0(new_sIZE_RATIO, new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), LT), h, ba)
new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, False, h, ba) → new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_compare8(new_sr0(new_sIZE_RATIO, new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba) → new_sizeFM(zzz810, zzz811, zzz812, zzz813, zzz814, h, ba)
new_sr0(zzz5000, zzz4000) → new_primMulInt(zzz5000, zzz4000)
new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba) → new_sizeFM(zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)
new_lt14(zzz5000, zzz43000) → new_esEs8(new_compare8(zzz5000, zzz43000), LT)
new_compare8(zzz500, zzz4300) → new_primCmpInt(zzz500, zzz4300)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_sizeFM(zzz760, zzz761, zzz762, zzz763, zzz764, h, ba) → zzz762
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primPlusNat0(Zero, x0)
new_lt14(x0, x1)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpNat0(Succ(x0), Zero)
new_compare8(x0, x1)
new_esEs8(LT, LT)
new_sr0(x0, x1)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_glueVBal3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primMulInt(Neg(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_esEs8(GT, GT)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_sIZE_RATIO

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_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, True, h, ba) → new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), zzz803, h, ba)
new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, True, h, ba) → new_glueVBal(zzz814, Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba)
new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba) → new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_compare8(new_sr0(new_sIZE_RATIO, new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), LT), h, ba)
new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, False, h, ba) → new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_compare8(new_sr0(new_sIZE_RATIO, new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba) → new_sizeFM(zzz810, zzz811, zzz812, zzz813, zzz814, h, ba)
new_sr0(zzz5000, zzz4000) → new_primMulInt(zzz5000, zzz4000)
new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba) → new_sizeFM(zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)
new_compare8(zzz500, zzz4300) → new_primCmpInt(zzz500, zzz4300)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_sizeFM(zzz760, zzz761, zzz762, zzz763, zzz764, h, ba) → zzz762
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primPlusNat0(Zero, x0)
new_lt14(x0, x1)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpNat0(Succ(x0), Zero)
new_compare8(x0, x1)
new_esEs8(LT, LT)
new_sr0(x0, x1)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_glueVBal3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primMulInt(Neg(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_esEs8(GT, GT)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_sIZE_RATIO

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_lt14(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_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, True, h, ba) → new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), zzz803, h, ba)
new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, True, h, ba) → new_glueVBal(zzz814, Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba)
new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba) → new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_compare8(new_sr0(new_sIZE_RATIO, new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), LT), h, ba)
new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, False, h, ba) → new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_compare8(new_sr0(new_sIZE_RATIO, new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba) → new_sizeFM(zzz810, zzz811, zzz812, zzz813, zzz814, h, ba)
new_sr0(zzz5000, zzz4000) → new_primMulInt(zzz5000, zzz4000)
new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba) → new_sizeFM(zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)
new_compare8(zzz500, zzz4300) → new_primCmpInt(zzz500, zzz4300)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_sizeFM(zzz760, zzz761, zzz762, zzz763, zzz764, h, ba) → zzz762
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primPlusNat0(Zero, x0)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpNat0(Succ(x0), Zero)
new_compare8(x0, x1)
new_esEs8(LT, LT)
new_sr0(x0, x1)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_glueVBal3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primMulInt(Neg(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_esEs8(GT, GT)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_sIZE_RATIO

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba) → new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_compare8(new_sr0(new_sIZE_RATIO, new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), LT), h, ba) at position [10,0] we obtained the following new rules:

new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba) → new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, 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_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, True, h, ba) → new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), zzz803, h, ba)
new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, True, h, ba) → new_glueVBal(zzz814, Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba)
new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba) → new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), LT), h, ba)
new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, False, h, ba) → new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_compare8(new_sr0(new_sIZE_RATIO, new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba) → new_sizeFM(zzz810, zzz811, zzz812, zzz813, zzz814, h, ba)
new_sr0(zzz5000, zzz4000) → new_primMulInt(zzz5000, zzz4000)
new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba) → new_sizeFM(zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)
new_compare8(zzz500, zzz4300) → new_primCmpInt(zzz500, zzz4300)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_sizeFM(zzz760, zzz761, zzz762, zzz763, zzz764, h, ba) → zzz762
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primPlusNat0(Zero, x0)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpNat0(Succ(x0), Zero)
new_compare8(x0, x1)
new_esEs8(LT, LT)
new_sr0(x0, x1)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_glueVBal3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primMulInt(Neg(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_esEs8(GT, GT)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_sIZE_RATIO

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, False, h, ba) → new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_compare8(new_sr0(new_sIZE_RATIO, new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), LT), h, ba) at position [10,0] we obtained the following new rules:

new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, False, h, ba) → new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, 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_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, True, h, ba) → new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), zzz803, h, ba)
new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, True, h, ba) → new_glueVBal(zzz814, Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba)
new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba) → new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), LT), h, ba)
new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, False, h, ba) → new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba) → new_sizeFM(zzz810, zzz811, zzz812, zzz813, zzz814, h, ba)
new_sr0(zzz5000, zzz4000) → new_primMulInt(zzz5000, zzz4000)
new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba) → new_sizeFM(zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)
new_compare8(zzz500, zzz4300) → new_primCmpInt(zzz500, zzz4300)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_sizeFM(zzz760, zzz761, zzz762, zzz763, zzz764, h, ba) → zzz762
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primPlusNat0(Zero, x0)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpNat0(Succ(x0), Zero)
new_compare8(x0, x1)
new_esEs8(LT, LT)
new_sr0(x0, x1)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_glueVBal3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primMulInt(Neg(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_esEs8(GT, GT)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_sIZE_RATIO

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_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, True, h, ba) → new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), zzz803, h, ba)
new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, True, h, ba) → new_glueVBal(zzz814, Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba)
new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba) → new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), LT), h, ba)
new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, False, h, ba) → new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba) → new_sizeFM(zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)
new_sr0(zzz5000, zzz4000) → new_primMulInt(zzz5000, zzz4000)
new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba) → new_sizeFM(zzz810, zzz811, zzz812, zzz813, zzz814, h, ba)
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_sizeFM(zzz760, zzz761, zzz762, zzz763, zzz764, h, ba) → zzz762
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primPlusNat0(Zero, x0)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpNat0(Succ(x0), Zero)
new_compare8(x0, x1)
new_esEs8(LT, LT)
new_sr0(x0, x1)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_glueVBal3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primMulInt(Neg(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_esEs8(GT, GT)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_sIZE_RATIO

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_compare8(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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, True, h, ba) → new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), zzz803, h, ba)
new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, True, h, ba) → new_glueVBal(zzz814, Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba)
new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba) → new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), LT), h, ba)
new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, False, h, ba) → new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba) → new_sizeFM(zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)
new_sr0(zzz5000, zzz4000) → new_primMulInt(zzz5000, zzz4000)
new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba) → new_sizeFM(zzz810, zzz811, zzz812, zzz813, zzz814, h, ba)
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_sizeFM(zzz760, zzz761, zzz762, zzz763, zzz764, h, ba) → zzz762
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primPlusNat0(Zero, x0)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, LT)
new_sr0(x0, x1)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_glueVBal3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primMulInt(Neg(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_esEs8(GT, GT)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_sIZE_RATIO

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba) → new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), LT), h, ba) at position [10,0,0] we obtained the following new rules:

new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba) → new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, 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_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, True, h, ba) → new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), zzz803, h, ba)
new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, True, h, ba) → new_glueVBal(zzz814, Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba)
new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, False, h, ba) → new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), LT), h, ba)
new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba) → new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba) → new_sizeFM(zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)
new_sr0(zzz5000, zzz4000) → new_primMulInt(zzz5000, zzz4000)
new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba) → new_sizeFM(zzz810, zzz811, zzz812, zzz813, zzz814, h, ba)
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_sizeFM(zzz760, zzz761, zzz762, zzz763, zzz764, h, ba) → zzz762
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primPlusNat0(Zero, x0)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, LT)
new_sr0(x0, x1)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_glueVBal3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primMulInt(Neg(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_esEs8(GT, GT)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_sIZE_RATIO

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, False, h, ba) → new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), LT), h, ba) at position [10,0,0] we obtained the following new rules:

new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, False, h, ba) → new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, 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
                                                                                ↳ UsableRulesProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, False, h, ba) → new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), LT), h, ba)
new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, True, h, ba) → new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), zzz803, h, ba)
new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, True, h, ba) → new_glueVBal(zzz814, Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba)
new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba) → new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba) → new_sizeFM(zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)
new_sr0(zzz5000, zzz4000) → new_primMulInt(zzz5000, zzz4000)
new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba) → new_sizeFM(zzz810, zzz811, zzz812, zzz813, zzz814, h, ba)
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_sizeFM(zzz760, zzz761, zzz762, zzz763, zzz764, h, ba) → zzz762
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primPlusNat0(Zero, x0)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, LT)
new_sr0(x0, x1)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_glueVBal3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primMulInt(Neg(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_esEs8(GT, GT)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_sIZE_RATIO

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

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

new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, False, h, ba) → new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), LT), h, ba)
new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, True, h, ba) → new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), zzz803, h, ba)
new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, True, h, ba) → new_glueVBal(zzz814, Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba)
new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba) → new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba) → new_sizeFM(zzz810, zzz811, zzz812, zzz813, zzz814, h, ba)
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba) → new_sizeFM(zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_sizeFM(zzz760, zzz761, zzz762, zzz763, zzz764, h, ba) → zzz762
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primPlusNat0(Zero, x0)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, LT)
new_sr0(x0, x1)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_glueVBal3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primMulInt(Neg(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_esEs8(GT, GT)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_sIZE_RATIO

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

new_sr0(x0, x1)



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

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

new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, False, h, ba) → new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), LT), h, ba)
new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, True, h, ba) → new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), zzz803, h, ba)
new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, True, h, ba) → new_glueVBal(zzz814, Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba)
new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba) → new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba) → new_sizeFM(zzz810, zzz811, zzz812, zzz813, zzz814, h, ba)
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba) → new_sizeFM(zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_sizeFM(zzz760, zzz761, zzz762, zzz763, zzz764, h, ba) → zzz762
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primPlusNat0(Zero, x0)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, LT)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_glueVBal3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primMulInt(Neg(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_esEs8(GT, GT)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_sIZE_RATIO

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, False, h, ba) → new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), LT), h, ba) at position [10,0,0,0] we obtained the following new rules:

new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, False, h, ba) → new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, 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
                                                                                ↳ 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_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, True, h, ba) → new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), zzz803, h, ba)
new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, True, h, ba) → new_glueVBal(zzz814, Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba)
new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, False, h, ba) → new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), LT), h, ba)
new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba) → new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba) → new_sizeFM(zzz810, zzz811, zzz812, zzz813, zzz814, h, ba)
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba) → new_sizeFM(zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_sizeFM(zzz760, zzz761, zzz762, zzz763, zzz764, h, ba) → zzz762
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primPlusNat0(Zero, x0)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, LT)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_glueVBal3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primMulInt(Neg(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_esEs8(GT, GT)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_sIZE_RATIO

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba) → new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), LT), h, ba) at position [10,0,0,0] we obtained the following new rules:

new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba) → new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, 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
                                                                                ↳ 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_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, True, h, ba) → new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), zzz803, h, ba)
new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba) → new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), LT), h, ba)
new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, True, h, ba) → new_glueVBal(zzz814, Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba)
new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, False, h, ba) → new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba) → new_sizeFM(zzz810, zzz811, zzz812, zzz813, zzz814, h, ba)
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba) → new_sizeFM(zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_sizeFM(zzz760, zzz761, zzz762, zzz763, zzz764, h, ba) → zzz762
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primPlusNat0(Zero, x0)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, LT)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_glueVBal3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primMulInt(Neg(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_esEs8(GT, GT)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_sIZE_RATIO

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
                                                                                ↳ 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_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, True, h, ba) → new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), zzz803, h, ba)
new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba) → new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), LT), h, ba)
new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, True, h, ba) → new_glueVBal(zzz814, Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba)
new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, False, h, ba) → new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba) → new_sizeFM(zzz810, zzz811, zzz812, zzz813, zzz814, h, ba)
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba) → new_sizeFM(zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_sizeFM(zzz760, zzz761, zzz762, zzz763, zzz764, h, ba) → zzz762
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primPlusNat0(Zero, x0)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, LT)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_glueVBal3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primMulInt(Neg(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_esEs8(GT, GT)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_sIZE_RATIO

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
                                                                            ↳ 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_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, True, h, ba) → new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), zzz803, h, ba)
new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, True, h, ba) → new_glueVBal(zzz814, Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba)
new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba) → new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), LT), h, ba)
new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, False, h, ba) → new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba) → new_sizeFM(zzz810, zzz811, zzz812, zzz813, zzz814, h, ba)
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba) → new_sizeFM(zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_sizeFM(zzz760, zzz761, zzz762, zzz763, zzz764, h, ba) → zzz762
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primPlusNat0(Zero, x0)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, LT)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_glueVBal3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primMulInt(Neg(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_esEs8(GT, GT)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba) → new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), LT), h, ba) at position [10,0,0,1] we obtained the following new rules:

new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba) → new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(zzz810, zzz811, zzz812, zzz813, zzz814, h, ba)), new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, 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
                                                                                ↳ 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_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, True, h, ba) → new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), zzz803, h, ba)
new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, True, h, ba) → new_glueVBal(zzz814, Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba)
new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, False, h, ba) → new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), LT), h, ba)
new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba) → new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(zzz810, zzz811, zzz812, zzz813, zzz814, h, ba)), new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba) → new_sizeFM(zzz810, zzz811, zzz812, zzz813, zzz814, h, ba)
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba) → new_sizeFM(zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_sizeFM(zzz760, zzz761, zzz762, zzz763, zzz764, h, ba) → zzz762
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primPlusNat0(Zero, x0)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, LT)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_glueVBal3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primMulInt(Neg(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_esEs8(GT, GT)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, False, h, ba) → new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), LT), h, ba) at position [10,0,0,1] we obtained the following new rules:

new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, False, h, ba) → new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, 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
                                                                                ↳ 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_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, False, h, ba) → new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), LT), h, ba)
new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, True, h, ba) → new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), zzz803, h, ba)
new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, True, h, ba) → new_glueVBal(zzz814, Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba)
new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba) → new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(zzz810, zzz811, zzz812, zzz813, zzz814, h, ba)), new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba) → new_sizeFM(zzz810, zzz811, zzz812, zzz813, zzz814, h, ba)
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba) → new_sizeFM(zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_sizeFM(zzz760, zzz761, zzz762, zzz763, zzz764, h, ba) → zzz762
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primPlusNat0(Zero, x0)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, LT)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_glueVBal3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primMulInt(Neg(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_esEs8(GT, GT)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba) → new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(zzz810, zzz811, zzz812, zzz813, zzz814, h, ba)), new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), LT), h, ba) at position [10,0,0,1] we obtained the following new rules:

new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba) → new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz812), new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, 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
                                                                                ↳ 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_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, True, h, ba) → new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), zzz803, h, ba)
new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, False, h, ba) → new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), LT), h, ba)
new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, True, h, ba) → new_glueVBal(zzz814, Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba)
new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba) → new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz812), new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba) → new_sizeFM(zzz810, zzz811, zzz812, zzz813, zzz814, h, ba)
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba) → new_sizeFM(zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_sizeFM(zzz760, zzz761, zzz762, zzz763, zzz764, h, ba) → zzz762
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primPlusNat0(Zero, x0)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, LT)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_glueVBal3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primMulInt(Neg(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_esEs8(GT, GT)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, False, h, ba) → new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), LT), h, ba) at position [10,0,0,1] we obtained the following new rules:

new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, False, h, ba) → new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz802), new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, 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
                                                                                ↳ 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
                                  ↳ QDP
                                  ↳ QDP

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

new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, True, h, ba) → new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), zzz803, h, ba)
new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, True, h, ba) → new_glueVBal(zzz814, Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba)
new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba) → new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz812), new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), LT), h, ba)
new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, False, h, ba) → new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz802), new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba) → new_sizeFM(zzz810, zzz811, zzz812, zzz813, zzz814, h, ba)
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba) → new_sizeFM(zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_sizeFM(zzz760, zzz761, zzz762, zzz763, zzz764, h, ba) → zzz762
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primPlusNat0(Zero, x0)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, LT)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_glueVBal3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primMulInt(Neg(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_esEs8(GT, GT)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba) → new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz812), new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), LT), h, ba) at position [10,0,1] we obtained the following new rules:

new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba) → new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz812), new_sizeFM(zzz800, zzz801, zzz802, zzz803, zzz804, 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
                                                                                ↳ 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
                                  ↳ QDP
                                  ↳ QDP

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

new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, True, h, ba) → new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), zzz803, h, ba)
new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, True, h, ba) → new_glueVBal(zzz814, Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba)
new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba) → new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz812), new_sizeFM(zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), LT), h, ba)
new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, False, h, ba) → new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz802), new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba) → new_sizeFM(zzz810, zzz811, zzz812, zzz813, zzz814, h, ba)
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_glueVBal3Size_r(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba) → new_sizeFM(zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_sizeFM(zzz760, zzz761, zzz762, zzz763, zzz764, h, ba) → zzz762
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primPlusNat0(Zero, x0)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, LT)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_glueVBal3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primMulInt(Neg(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_esEs8(GT, GT)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)

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
                                                                                ↳ 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
                                  ↳ QDP
                                  ↳ QDP

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

new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, True, h, ba) → new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), zzz803, h, ba)
new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, True, h, ba) → new_glueVBal(zzz814, Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba)
new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba) → new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz812), new_sizeFM(zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), LT), h, ba)
new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, False, h, ba) → new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz802), new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_sizeFM(zzz760, zzz761, zzz762, zzz763, zzz764, h, ba) → zzz762
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)
new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba) → new_sizeFM(zzz810, zzz811, zzz812, zzz813, zzz814, h, ba)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primPlusNat0(Zero, x0)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, LT)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_glueVBal3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primMulInt(Neg(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_esEs8(GT, GT)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)

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

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

new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, True, h, ba) → new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), zzz803, h, ba)
new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, True, h, ba) → new_glueVBal(zzz814, Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba)
new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba) → new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz812), new_sizeFM(zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), LT), h, ba)
new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, False, h, ba) → new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz802), new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_sizeFM(zzz760, zzz761, zzz762, zzz763, zzz764, h, ba) → zzz762
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)
new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba) → new_sizeFM(zzz810, zzz811, zzz812, zzz813, zzz814, h, ba)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primPlusNat0(Zero, x0)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, LT)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_glueVBal3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primMulInt(Neg(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_esEs8(GT, GT)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba) → new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz812), new_sizeFM(zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), LT), h, ba) at position [10,0,1] we obtained the following new rules:

new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba) → new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz812), zzz802), 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
                                                                                ↳ 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
                                                                                                                                        ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba) → new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz812), zzz802), LT), h, ba)
new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, True, h, ba) → new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), zzz803, h, ba)
new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, True, h, ba) → new_glueVBal(zzz814, Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba)
new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, False, h, ba) → new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz802), new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_sizeFM(zzz760, zzz761, zzz762, zzz763, zzz764, h, ba) → zzz762
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)
new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba) → new_sizeFM(zzz810, zzz811, zzz812, zzz813, zzz814, h, ba)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primPlusNat0(Zero, x0)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, LT)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_glueVBal3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primMulInt(Neg(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_esEs8(GT, GT)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, False, h, ba) → new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz802), new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba)), LT), h, ba) at position [10,0,1] we obtained the following new rules:

new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, False, h, ba) → new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz802), new_sizeFM(zzz810, zzz811, zzz812, zzz813, zzz814, 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
                                                                                ↳ 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
                                                                                                                                        ↳ Rewriting
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ UsableRulesProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, False, h, ba) → new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz802), new_sizeFM(zzz810, zzz811, zzz812, zzz813, zzz814, h, ba)), LT), h, ba)
new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba) → new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz812), zzz802), LT), h, ba)
new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, True, h, ba) → new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), zzz803, h, ba)
new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, True, h, ba) → new_glueVBal(zzz814, Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba)

The TRS R consists of the following rules:

new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_sizeFM(zzz760, zzz761, zzz762, zzz763, zzz764, h, ba) → zzz762
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)
new_glueVBal3Size_l(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, h, ba) → new_sizeFM(zzz810, zzz811, zzz812, zzz813, zzz814, h, ba)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primPlusNat0(Zero, x0)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, LT)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_glueVBal3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primMulInt(Neg(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_esEs8(GT, GT)

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

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

new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, False, h, ba) → new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz802), new_sizeFM(zzz810, zzz811, zzz812, zzz813, zzz814, h, ba)), LT), h, ba)
new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba) → new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz812), zzz802), LT), h, ba)
new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, True, h, ba) → new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), zzz803, h, ba)
new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, True, h, ba) → new_glueVBal(zzz814, Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba)

The TRS R consists of the following rules:

new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)
new_sizeFM(zzz760, zzz761, zzz762, zzz763, zzz764, h, ba) → zzz762

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primPlusNat0(Zero, x0)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, LT)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_glueVBal3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat1(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primMulInt(Neg(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_esEs8(GT, GT)

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_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
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ UsableRulesProof
                                                  ↳ QDP
                                                    ↳ QReductionProof
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ UsableRulesProof
                                                                                                  ↳ QDP
                                                                                                    ↳ QReductionProof
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ UsableRulesProof
                                                                                                                              ↳ QDP
                                                                                                                                ↳ QReductionProof
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ 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_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba) → new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz812), zzz802), LT), h, ba)
new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, False, h, ba) → new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz802), new_sizeFM(zzz810, zzz811, zzz812, zzz813, zzz814, h, ba)), LT), h, ba)
new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, True, h, ba) → new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), zzz803, h, ba)
new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, True, h, ba) → new_glueVBal(zzz814, Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba)

The TRS R consists of the following rules:

new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)
new_sizeFM(zzz760, zzz761, zzz762, zzz763, zzz764, h, ba) → zzz762

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, False, h, ba) → new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz802), new_sizeFM(zzz810, zzz811, zzz812, zzz813, zzz814, h, ba)), LT), h, ba) at position [10,0,1] we obtained the following new rules:

new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, False, h, ba) → new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz802), zzz812), 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
                                                                                ↳ 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
                                                                                                                                        ↳ Rewriting
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ QReductionProof
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ UsableRulesProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba) → new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz812), zzz802), LT), h, ba)
new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, True, h, ba) → new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), zzz803, h, ba)
new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, False, h, ba) → new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz802), zzz812), LT), h, ba)
new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, True, h, ba) → new_glueVBal(zzz814, Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba)

The TRS R consists of the following rules:

new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)
new_sizeFM(zzz760, zzz761, zzz762, zzz763, zzz764, h, ba) → zzz762

The set Q consists of the following terms:

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

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
                                                                                ↳ 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
                                                                                                                                        ↳ Rewriting
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ QReductionProof
                                                                                                                                                  ↳ 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_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba) → new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz812), zzz802), LT), h, ba)
new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, True, h, ba) → new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), zzz803, h, ba)
new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, False, h, ba) → new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz802), zzz812), LT), h, ba)
new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, True, h, ba) → new_glueVBal(zzz814, Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba)

The TRS R consists of the following rules:

new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

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

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

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



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ UsableRulesProof
                                                  ↳ QDP
                                                    ↳ QReductionProof
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ UsableRulesProof
                                                                                                  ↳ QDP
                                                                                                    ↳ QReductionProof
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ UsableRulesProof
                                                                                                                              ↳ QDP
                                                                                                                                ↳ QReductionProof
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ Rewriting
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ QReductionProof
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ 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_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba) → new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz812), zzz802), LT), h, ba)
new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, True, h, ba) → new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), zzz803, h, ba)
new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, True, h, ba) → new_glueVBal(zzz814, Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba)
new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, False, h, ba) → new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz802), zzz812), LT), h, ba)

The TRS R consists of the following rules:

new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

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

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(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, False, h, ba) → new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz802), zzz812), LT), h, ba)
The remaining pairs can at least be oriented weakly.

new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba) → new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz812), zzz802), LT), h, ba)
new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, True, h, ba) → new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), zzz803, h, ba)
new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, True, h, ba) → new_glueVBal(zzz814, Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba)
Used ordering: Polynomial interpretation [25]:

POL(Branch(x1, x2, x3, x4, x5)) = 1 + x2 + x5   
POL(EQ) = 0   
POL(False) = 0   
POL(GT) = 0   
POL(LT) = 0   
POL(Neg(x1)) = 0   
POL(Pos(x1)) = 0   
POL(Succ(x1)) = 0   
POL(True) = 0   
POL(Zero) = 0   
POL(new_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)) = x2 + x5   
POL(new_glueVBal3GlueVBal2(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = 1 + x2 + x5   
POL(new_primCmpInt(x1, x2)) = 0   
POL(new_primCmpNat0(x1, x2)) = 0   
POL(new_primMulInt(x1, x2)) = 0   
POL(new_primMulNat0(x1, x2)) = 0   
POL(new_primPlusNat0(x1, x2)) = 0   
POL(new_primPlusNat1(x1, x2)) = 0   

The following usable rules [17] were oriented: none



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ UsableRulesProof
                                                  ↳ QDP
                                                    ↳ QReductionProof
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ UsableRulesProof
                                                                                                  ↳ QDP
                                                                                                    ↳ QReductionProof
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ UsableRulesProof
                                                                                                                              ↳ QDP
                                                                                                                                ↳ QReductionProof
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ Rewriting
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ QReductionProof
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ 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_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba) → new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz812), zzz802), LT), h, ba)
new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, True, h, ba) → new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), zzz803, h, ba)
new_glueVBal3GlueVBal1(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, True, h, ba) → new_glueVBal(zzz814, Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba)

The TRS R consists of the following rules:

new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

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

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
                                                                                ↳ 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
                                                                                                                                        ↳ Rewriting
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ QReductionProof
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ UsableRulesProof
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ QReductionProof
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ QDPOrderProof
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ QDPSizeChangeProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), Branch(zzz800, zzz801, zzz802, zzz803, zzz804), h, ba) → new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz812), zzz802), LT), h, ba)
new_glueVBal3GlueVBal2(zzz810, zzz811, zzz812, zzz813, zzz814, zzz800, zzz801, zzz802, zzz803, zzz804, True, h, ba) → new_glueVBal(Branch(zzz810, zzz811, zzz812, zzz813, zzz814), zzz803, h, ba)

The TRS R consists of the following rules:

new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

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

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(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz440, zzz441, False, h, ba) → new_addToFM_C1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz440, zzz441, new_gt(zzz440, zzz4440, h), h, ba)
new_addToFM_C(Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), zzz440, zzz441, h, ba) → new_addToFM_C2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz440, zzz441, new_lt11(zzz440, zzz4440, h), h, ba)
new_addToFM_C1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz440, zzz441, True, h, ba) → new_addToFM_C(zzz4444, zzz440, zzz441, h, ba)
new_addToFM_C2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz440, zzz441, True, h, ba) → new_addToFM_C(zzz4443, zzz440, zzz441, h, ba)

The TRS R consists of the following rules:

new_lt19(zzz500000, zzz4300000, ty_Float) → new_lt6(zzz500000, zzz4300000)
new_ltEs18(zzz50000, zzz430000, app(ty_Ratio, bee)) → new_ltEs15(zzz50000, zzz430000, bee)
new_esEs7(Just(zzz5000), Just(zzz4000), app(ty_Maybe, dh)) → new_esEs7(zzz5000, zzz4000, dh)
new_esEs4(Right(zzz5000), Right(zzz4000), bgd, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_esEs20(zzz5000, zzz4000, app(ty_Maybe, bba)) → new_esEs7(zzz5000, zzz4000, bba)
new_esEs12(:(zzz5000, zzz5001), :(zzz4000, zzz4001), hh) → new_asAs(new_esEs20(zzz5000, zzz4000, hh), new_esEs12(zzz5001, zzz4001, hh))
new_esEs7(Just(zzz5000), Just(zzz4000), app(ty_[], dd)) → new_esEs12(zzz5000, zzz4000, dd)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, ty_Ordering) → new_ltEs10(zzz500000, zzz4300000)
new_lt19(zzz500000, zzz4300000, app(app(app(ty_@3, cdd), cde), cdf)) → new_lt8(zzz500000, zzz4300000, cdd, cde, cdf)
new_ltEs18(zzz50000, zzz430000, app(app(app(ty_@3, bef), beg), beh)) → new_ltEs16(zzz50000, zzz430000, bef, beg, beh)
new_lt20(zzz500001, zzz4300001, app(ty_[], cfa)) → new_lt18(zzz500001, zzz4300001, cfa)
new_esEs4(Right(zzz5000), Right(zzz4000), bgd, ty_Char) → new_esEs11(zzz5000, zzz4000)
new_compare15(zzz500000, zzz4300000, True, hf, hg) → LT
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Bool, bfa) → new_esEs14(zzz5000, zzz4000)
new_ltEs18(zzz50000, zzz430000, app(ty_Maybe, bb)) → new_ltEs4(zzz50000, zzz430000, bb)
new_ltEs20(zzz500002, zzz4300002, ty_Ordering) → new_ltEs10(zzz500002, zzz4300002)
new_esEs4(Right(zzz5000), Right(zzz4000), bgd, app(app(app(ty_@3, bhb), bhc), bhd)) → new_esEs6(zzz5000, zzz4000, bhb, bhc, bhd)
new_lt13(zzz500000, zzz4300000, app(app(app(ty_@3, hc), hd), he)) → new_lt8(zzz500000, zzz4300000, hc, hd, he)
new_lt15(zzz500000, zzz4300000) → new_esEs8(new_compare14(zzz500000, zzz4300000), LT)
new_lt20(zzz500001, zzz4300001, app(app(app(ty_@3, cef), ceg), ceh)) → new_lt8(zzz500001, zzz4300001, cef, ceg, ceh)
new_esEs27(zzz5001, zzz4001, app(ty_Maybe, dba)) → new_esEs7(zzz5001, zzz4001, dba)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Ordering) → new_ltEs10(zzz500000, zzz4300000)
new_esEs23(zzz500000, zzz4300000, ty_Bool) → new_esEs14(zzz500000, zzz4300000)
new_compare27(zzz500000, zzz4300000, False, ha, hb) → new_compare113(zzz500000, zzz4300000, new_ltEs7(zzz500000, zzz4300000, ha, hb), ha, hb)
new_lt19(zzz500000, zzz4300000, ty_Double) → new_lt15(zzz500000, zzz4300000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), app(ty_Maybe, bcb), bbe) → new_ltEs4(zzz500000, zzz4300000, bcb)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, ty_@0) → new_ltEs11(zzz500000, zzz4300000)
new_ltEs20(zzz500002, zzz4300002, app(ty_Ratio, cfg)) → new_ltEs15(zzz500002, zzz4300002, cfg)
new_lt13(zzz500000, zzz4300000, app(ty_[], cbc)) → new_lt18(zzz500000, zzz4300000, cbc)
new_esEs26(zzz5002, zzz4002, ty_Float) → new_esEs13(zzz5002, zzz4002)
new_ltEs7(Left(zzz500000), Right(zzz4300000), bch, bbe) → True
new_primMulNat0(Zero, Zero) → Zero
new_esEs19(zzz5000, zzz4000, ty_Int) → new_esEs17(zzz5000, zzz4000)
new_sr(Integer(zzz43000000), Integer(zzz5000010)) → Integer(new_primMulInt(zzz43000000, zzz5000010))
new_ltEs20(zzz500002, zzz4300002, ty_Float) → new_ltEs12(zzz500002, zzz4300002)
new_ltEs20(zzz500002, zzz4300002, ty_@0) → new_ltEs11(zzz500002, zzz4300002)
new_esEs20(zzz5000, zzz4000, app(ty_Ratio, bbb)) → new_esEs16(zzz5000, zzz4000, bbb)
new_esEs18(zzz5001, zzz4001, ty_Double) → new_esEs9(zzz5001, zzz4001)
new_lt20(zzz500001, zzz4300001, ty_Float) → new_lt6(zzz500001, zzz4300001)
new_esEs23(zzz500000, zzz4300000, ty_Double) → new_esEs9(zzz500000, zzz4300000)
new_esEs4(Right(zzz5000), Right(zzz4000), bgd, app(ty_[], bha)) → new_esEs12(zzz5000, zzz4000, bha)
new_esEs24(zzz500001, zzz4300001, ty_Integer) → new_esEs15(zzz500001, zzz4300001)
new_ltEs14(False, True) → True
new_ltEs19(zzz500001, zzz4300001, ty_Integer) → new_ltEs9(zzz500001, zzz4300001)
new_ltEs4(Just(zzz500000), Just(zzz4300000), app(app(ty_@2, be), bf)) → new_ltEs13(zzz500000, zzz4300000, be, bf)
new_esEs20(zzz5000, zzz4000, app(app(ty_Either, baa), bab)) → new_esEs4(zzz5000, zzz4000, baa, bab)
new_esEs12([], [], hh) → True
new_ltEs19(zzz500001, zzz4300001, ty_Ordering) → new_ltEs10(zzz500001, zzz4300001)
new_esEs24(zzz500001, zzz4300001, app(app(ty_@2, ceb), cec)) → new_esEs5(zzz500001, zzz4300001, ceb, cec)
new_lt12(zzz500000, zzz4300000) → new_esEs8(new_compare10(zzz500000, zzz4300000), LT)
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Ordering, bbe) → new_ltEs10(zzz500000, zzz4300000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, app(ty_Ratio, bdf)) → new_ltEs15(zzz500000, zzz4300000, bdf)
new_esEs15(Integer(zzz5000), Integer(zzz4000)) → new_primEqInt(zzz5000, zzz4000)
new_ltEs10(EQ, GT) → True
new_ltEs19(zzz500001, zzz4300001, app(ty_Maybe, cbh)) → new_ltEs4(zzz500001, zzz4300001, cbh)
new_esEs21(zzz5001, zzz4001, ty_Int) → new_esEs17(zzz5001, zzz4001)
new_ltEs7(Left(zzz500000), Left(zzz4300000), app(app(app(ty_@3, bcd), bce), bcf), bbe) → new_ltEs16(zzz500000, zzz4300000, bcd, bce, bcf)
new_lt13(zzz500000, zzz4300000, ty_Char) → new_lt12(zzz500000, zzz4300000)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Ordering, bfa) → new_esEs8(zzz5000, zzz4000)
new_esEs24(zzz500001, zzz4300001, app(ty_[], cfa)) → new_esEs12(zzz500001, zzz4300001, cfa)
new_esEs25(zzz500000, zzz4300000, ty_Double) → new_esEs9(zzz500000, zzz4300000)
new_esEs25(zzz500000, zzz4300000, ty_Float) → new_esEs13(zzz500000, zzz4300000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, app(ty_[], beb)) → new_ltEs17(zzz500000, zzz4300000, beb)
new_pePe(False, zzz218) → zzz218
new_lt14(zzz5000, zzz43000) → new_esEs8(new_compare8(zzz5000, zzz43000), LT)
new_esEs25(zzz500000, zzz4300000, app(app(ty_Either, ccf), ccg)) → new_esEs4(zzz500000, zzz4300000, ccf, ccg)
new_esEs12(:(zzz5000, zzz5001), [], hh) → False
new_esEs12([], :(zzz4000, zzz4001), hh) → False
new_esEs25(zzz500000, zzz4300000, ty_Char) → new_esEs11(zzz500000, zzz4300000)
new_esEs25(zzz500000, zzz4300000, ty_Bool) → new_esEs14(zzz500000, zzz4300000)
new_lt19(zzz500000, zzz4300000, ty_Ordering) → new_lt9(zzz500000, zzz4300000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, app(app(ty_@2, bdc), bdd)) → new_ltEs13(zzz500000, zzz4300000, bdc, bdd)
new_esEs4(Right(zzz5000), Right(zzz4000), bgd, app(ty_Ratio, bhf)) → new_esEs16(zzz5000, zzz4000, bhf)
new_compare23(zzz500000, zzz4300000, True) → EQ
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Float, bbe) → new_ltEs12(zzz500000, zzz4300000)
new_lt19(zzz500000, zzz4300000, app(ty_Ratio, cdc)) → new_lt17(zzz500000, zzz4300000, cdc)
new_esEs24(zzz500001, zzz4300001, app(ty_Maybe, ced)) → new_esEs7(zzz500001, zzz4300001, ced)
new_ltEs4(Nothing, Just(zzz4300000), bb) → True
new_esEs23(zzz500000, zzz4300000, app(ty_Maybe, cba)) → new_esEs7(zzz500000, zzz4300000, cba)
new_compare30(zzz500000, zzz4300000, ty_Integer) → new_compare9(zzz500000, zzz4300000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(ty_Ratio, bgc), bfa) → new_esEs16(zzz5000, zzz4000, bgc)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, ty_Char) → new_ltEs5(zzz500000, zzz4300000)
new_compare13(zzz500000, zzz4300000, hc, hd, he) → new_compare24(zzz500000, zzz4300000, new_esEs6(zzz500000, zzz4300000, hc, hd, he), hc, hd, he)
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_lt4(zzz500000, zzz4300000) → new_esEs8(new_compare11(zzz500000, zzz4300000), LT)
new_esEs4(Right(zzz5000), Right(zzz4000), bgd, ty_Integer) → new_esEs15(zzz5000, zzz4000)
new_esEs20(zzz5000, zzz4000, app(app(ty_@2, bac), bad)) → new_esEs5(zzz5000, zzz4000, bac, bad)
new_esEs28(zzz5000, zzz4000, app(ty_Ratio, dcd)) → new_esEs16(zzz5000, zzz4000, dcd)
new_compare30(zzz500000, zzz4300000, app(ty_Ratio, cad)) → new_compare7(zzz500000, zzz4300000, cad)
new_compare19(zzz500000, zzz4300000, True) → LT
new_compare6(zzz500000, zzz4300000) → new_compare23(zzz500000, zzz4300000, new_esEs8(zzz500000, zzz4300000))
new_ltEs18(zzz50000, zzz430000, ty_@0) → new_ltEs11(zzz50000, zzz430000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_ltEs19(zzz500001, zzz4300001, app(ty_Ratio, cca)) → new_ltEs15(zzz500001, zzz4300001, cca)
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Int) → new_esEs17(zzz5000, zzz4000)
new_ltEs20(zzz500002, zzz4300002, ty_Bool) → new_ltEs14(zzz500002, zzz4300002)
new_esEs27(zzz5001, zzz4001, ty_@0) → new_esEs10(zzz5001, zzz4001)
new_ltEs12(zzz50000, zzz430000) → new_fsEs(new_compare16(zzz50000, zzz430000))
new_esEs8(LT, LT) → True
new_lt19(zzz500000, zzz4300000, app(app(ty_@2, cch), cda)) → new_lt16(zzz500000, zzz4300000, cch, cda)
new_esEs25(zzz500000, zzz4300000, ty_Ordering) → new_esEs8(zzz500000, zzz4300000)
new_esEs19(zzz5000, zzz4000, app(ty_Maybe, gg)) → new_esEs7(zzz5000, zzz4000, gg)
new_esEs20(zzz5000, zzz4000, app(app(app(ty_@3, baf), bag), bah)) → new_esEs6(zzz5000, zzz4000, baf, bag, bah)
new_esEs18(zzz5001, zzz4001, app(ty_Ratio, ff)) → new_esEs16(zzz5001, zzz4001, ff)
new_pePe(True, zzz218) → True
new_primEqNat0(Zero, Zero) → True
new_lt20(zzz500001, zzz4300001, app(app(ty_Either, cdh), cea)) → new_lt5(zzz500001, zzz4300001, cdh, cea)
new_compare26(zzz500000, zzz4300000, True) → EQ
new_lt20(zzz500001, zzz4300001, ty_Bool) → new_lt7(zzz500001, zzz4300001)
new_esEs13(Float(zzz5000, zzz5001), Float(zzz4000, zzz4001)) → new_esEs17(new_sr0(zzz5000, zzz4000), new_sr0(zzz5001, zzz4001))
new_esEs19(zzz5000, zzz4000, app(ty_[], gc)) → new_esEs12(zzz5000, zzz4000, gc)
new_compare29(Nothing, Just(zzz430000), False, gg) → LT
new_esEs19(zzz5000, zzz4000, ty_Float) → new_esEs13(zzz5000, zzz4000)
new_compare30(zzz500000, zzz4300000, app(ty_Maybe, cac)) → new_compare28(zzz500000, zzz4300000, cac)
new_esEs18(zzz5001, zzz4001, app(app(ty_@2, ef), eg)) → new_esEs5(zzz5001, zzz4001, ef, eg)
new_esEs25(zzz500000, zzz4300000, ty_Int) → new_esEs17(zzz500000, zzz4300000)
new_esEs9(Double(zzz5000, zzz5001), Double(zzz4000, zzz4001)) → new_esEs17(new_sr0(zzz5000, zzz4000), new_sr0(zzz5001, zzz4001))
new_esEs26(zzz5002, zzz4002, ty_Ordering) → new_esEs8(zzz5002, zzz4002)
new_esEs8(GT, GT) → True
new_lt20(zzz500001, zzz4300001, app(ty_Maybe, ced)) → new_lt11(zzz500001, zzz4300001, ced)
new_esEs18(zzz5001, zzz4001, app(app(app(ty_@3, fa), fb), fc)) → new_esEs6(zzz5001, zzz4001, fa, fb, fc)
new_esEs25(zzz500000, zzz4300000, ty_@0) → new_esEs10(zzz500000, zzz4300000)
new_compare4([], [], ce) → EQ
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_lt19(zzz500000, zzz4300000, ty_@0) → new_lt4(zzz500000, zzz4300000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(app(ty_@2, bfd), bfe), bfa) → new_esEs5(zzz5000, zzz4000, bfd, bfe)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, ty_Integer) → new_ltEs9(zzz500000, zzz4300000)
new_esEs26(zzz5002, zzz4002, app(app(app(ty_@3, chd), che), chf)) → new_esEs6(zzz5002, zzz4002, chd, che, chf)
new_compare18(zzz500000, zzz4300000, hf, hg) → new_compare25(zzz500000, zzz4300000, new_esEs5(zzz500000, zzz4300000, hf, hg), hf, hg)
new_ltEs17(zzz50000, zzz430000, ce) → new_fsEs(new_compare4(zzz50000, zzz430000, ce))
new_esEs8(GT, LT) → False
new_esEs8(LT, GT) → False
new_compare30(zzz500000, zzz4300000, app(ty_[], cah)) → new_compare4(zzz500000, zzz4300000, cah)
new_compare30(zzz500000, zzz4300000, ty_Double) → new_compare14(zzz500000, zzz4300000)
new_ltEs13(@2(zzz500000, zzz500001), @2(zzz4300000, zzz4300001), bec, bed) → new_pePe(new_lt13(zzz500000, zzz4300000, bec), new_asAs(new_esEs23(zzz500000, zzz4300000, bec), new_ltEs19(zzz500001, zzz4300001, bed)))
new_esEs4(Right(zzz5000), Right(zzz4000), bgd, app(app(ty_Either, bge), bgf)) → new_esEs4(zzz5000, zzz4000, bge, bgf)
new_esEs25(zzz500000, zzz4300000, app(ty_[], cdg)) → new_esEs12(zzz500000, zzz4300000, cdg)
new_compare24(zzz500000, zzz4300000, True, hc, hd, he) → EQ
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Int, bbe) → new_ltEs6(zzz500000, zzz4300000)
new_lt20(zzz500001, zzz4300001, ty_Ordering) → new_lt9(zzz500001, zzz4300001)
new_primEqInt(Neg(Succ(zzz50000)), Neg(Succ(zzz40000))) → new_primEqNat0(zzz50000, zzz40000)
new_esEs20(zzz5000, zzz4000, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_compare113(zzz500000, zzz4300000, True, ha, hb) → LT
new_esEs23(zzz500000, zzz4300000, ty_Ordering) → new_esEs8(zzz500000, zzz4300000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(app(ty_Either, bfb), bfc), bfa) → new_esEs4(zzz5000, zzz4000, bfb, bfc)
new_ltEs18(zzz50000, zzz430000, app(app(ty_Either, bch), bbe)) → new_ltEs7(zzz50000, zzz430000, bch, bbe)
new_esEs24(zzz500001, zzz4300001, ty_Bool) → new_esEs14(zzz500001, zzz4300001)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_lt19(zzz500000, zzz4300000, ty_Bool) → new_lt7(zzz500000, zzz4300000)
new_lt19(zzz500000, zzz4300000, ty_Integer) → new_lt10(zzz500000, zzz4300000)
new_ltEs4(Nothing, Nothing, bb) → True
new_lt13(zzz500000, zzz4300000, ty_Float) → new_lt6(zzz500000, zzz4300000)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_@0) → new_ltEs11(zzz500000, zzz4300000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Char, bbe) → new_ltEs5(zzz500000, zzz4300000)
new_lt13(zzz500000, zzz4300000, ty_Int) → new_lt14(zzz500000, zzz4300000)
new_lt6(zzz500000, zzz4300000) → new_esEs8(new_compare16(zzz500000, zzz4300000), LT)
new_compare29(Just(zzz50000), Nothing, False, gg) → GT
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_ltEs7(Right(zzz500000), Left(zzz4300000), bch, bbe) → False
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_esEs24(zzz500001, zzz4300001, app(app(app(ty_@3, cef), ceg), ceh)) → new_esEs6(zzz500001, zzz4300001, cef, ceg, ceh)
new_esEs23(zzz500000, zzz4300000, ty_Char) → new_esEs11(zzz500000, zzz4300000)
new_lt13(zzz500000, zzz4300000, ty_Bool) → new_lt7(zzz500000, zzz4300000)
new_esEs19(zzz5000, zzz4000, ty_Bool) → new_esEs14(zzz5000, zzz4000)
new_esEs20(zzz5000, zzz4000, ty_Float) → new_esEs13(zzz5000, zzz4000)
new_compare14(Double(zzz500000, zzz500001), Double(zzz4300000, zzz4300001)) → new_compare8(new_sr0(zzz500000, zzz4300000), new_sr0(zzz500001, zzz4300001))
new_compare12(zzz500000, zzz4300000, ha, hb) → new_compare27(zzz500000, zzz4300000, new_esEs4(zzz500000, zzz4300000, ha, hb), ha, hb)
new_compare8(zzz500, zzz4300) → new_primCmpInt(zzz500, zzz4300)
new_lt19(zzz500000, zzz4300000, ty_Char) → new_lt12(zzz500000, zzz4300000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, app(app(app(ty_@3, bdg), bdh), bea)) → new_ltEs16(zzz500000, zzz4300000, bdg, bdh, bea)
new_primEqInt(Neg(Succ(zzz50000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(zzz40000))) → False
new_compare17(zzz500000, zzz4300000) → new_compare26(zzz500000, zzz4300000, new_esEs14(zzz500000, zzz4300000))
new_esEs8(EQ, EQ) → True
new_lt13(zzz500000, zzz4300000, ty_Double) → new_lt15(zzz500000, zzz4300000)
new_compare111(zzz200, zzz201, True, bbd) → LT
new_esEs20(zzz5000, zzz4000, ty_@0) → new_esEs10(zzz5000, zzz4000)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Char, bfa) → new_esEs11(zzz5000, zzz4000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_ltEs19(zzz500001, zzz4300001, ty_@0) → new_ltEs11(zzz500001, zzz4300001)
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_esEs18(zzz5001, zzz4001, ty_Char) → new_esEs11(zzz5001, zzz4001)
new_compare112(zzz500000, zzz4300000, True) → LT
new_esEs19(zzz5000, zzz4000, ty_Char) → new_esEs11(zzz5000, zzz4000)
new_compare30(zzz500000, zzz4300000, app(app(ty_Either, bhg), bhh)) → new_compare12(zzz500000, zzz4300000, bhg, bhh)
new_primEqInt(Pos(Succ(zzz50000)), Pos(Succ(zzz40000))) → new_primEqNat0(zzz50000, zzz40000)
new_ltEs18(zzz50000, zzz430000, ty_Double) → new_ltEs8(zzz50000, zzz430000)
new_compare27(zzz500000, zzz4300000, True, ha, hb) → EQ
new_lt10(zzz500000, zzz4300000) → new_esEs8(new_compare9(zzz500000, zzz4300000), LT)
new_esEs24(zzz500001, zzz4300001, app(ty_Ratio, cee)) → new_esEs16(zzz500001, zzz4300001, cee)
new_ltEs19(zzz500001, zzz4300001, ty_Bool) → new_ltEs14(zzz500001, zzz4300001)
new_esEs14(False, True) → False
new_esEs14(True, False) → False
new_esEs23(zzz500000, zzz4300000, app(ty_[], cbc)) → new_esEs12(zzz500000, zzz4300000, cbc)
new_ltEs4(Just(zzz500000), Just(zzz4300000), app(app(ty_Either, bc), bd)) → new_ltEs7(zzz500000, zzz4300000, bc, bd)
new_esEs26(zzz5002, zzz4002, ty_Integer) → new_esEs15(zzz5002, zzz4002)
new_ltEs10(GT, EQ) → False
new_lt17(zzz500000, zzz4300000, cbb) → new_esEs8(new_compare7(zzz500000, zzz4300000, cbb), LT)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Double) → new_ltEs8(zzz500000, zzz4300000)
new_esEs24(zzz500001, zzz4300001, ty_Int) → new_esEs17(zzz500001, zzz4300001)
new_primEqNat0(Succ(zzz50000), Succ(zzz40000)) → new_primEqNat0(zzz50000, zzz40000)
new_ltEs20(zzz500002, zzz4300002, app(ty_[], cgc)) → new_ltEs17(zzz500002, zzz4300002, cgc)
new_esEs27(zzz5001, zzz4001, ty_Ordering) → new_esEs8(zzz5001, zzz4001)
new_ltEs14(False, False) → True
new_compare11(@0, @0) → EQ
new_lt7(zzz500000, zzz4300000) → new_esEs8(new_compare17(zzz500000, zzz4300000), LT)
new_esEs19(zzz5000, zzz4000, app(app(app(ty_@3, gd), ge), gf)) → new_esEs6(zzz5000, zzz4000, gd, ge, gf)
new_ltEs9(zzz50000, zzz430000) → new_fsEs(new_compare9(zzz50000, zzz430000))
new_ltEs20(zzz500002, zzz4300002, ty_Char) → new_ltEs5(zzz500002, zzz4300002)
new_compare113(zzz500000, zzz4300000, False, ha, hb) → GT
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, ty_Bool) → new_ltEs14(zzz500000, zzz4300000)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Int) → new_ltEs6(zzz500000, zzz4300000)
new_primCompAux00(zzz225, LT) → LT
new_lt20(zzz500001, zzz4300001, ty_@0) → new_lt4(zzz500001, zzz4300001)
new_ltEs19(zzz500001, zzz4300001, app(ty_[], cce)) → new_ltEs17(zzz500001, zzz4300001, cce)
new_ltEs19(zzz500001, zzz4300001, app(app(ty_Either, cbd), cbe)) → new_ltEs7(zzz500001, zzz4300001, cbd, cbe)
new_compare7(:%(zzz500000, zzz500001), :%(zzz4300000, zzz4300001), ty_Int) → new_compare8(new_sr0(zzz500000, zzz4300001), new_sr0(zzz4300000, zzz500001))
new_esEs24(zzz500001, zzz4300001, ty_Ordering) → new_esEs8(zzz500001, zzz4300001)
new_ltEs8(zzz50000, zzz430000) → new_fsEs(new_compare14(zzz50000, zzz430000))
new_esEs7(Nothing, Nothing, cf) → True
new_esEs28(zzz5000, zzz4000, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_esEs8(EQ, LT) → False
new_esEs8(LT, EQ) → False
new_esEs18(zzz5001, zzz4001, app(ty_Maybe, fd)) → new_esEs7(zzz5001, zzz4001, fd)
new_primEqInt(Pos(Succ(zzz50000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(zzz40000))) → False
new_lt20(zzz500001, zzz4300001, app(ty_Ratio, cee)) → new_lt17(zzz500001, zzz4300001, cee)
new_compare30(zzz500000, zzz4300000, ty_Int) → new_compare8(zzz500000, zzz4300000)
new_compare24(zzz500000, zzz4300000, False, hc, hd, he) → new_compare110(zzz500000, zzz4300000, new_ltEs16(zzz500000, zzz4300000, hc, hd, he), hc, hd, he)
new_esEs24(zzz500001, zzz4300001, ty_@0) → new_esEs10(zzz500001, zzz4300001)
new_primCmpNat0(Zero, Zero) → EQ
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Integer, bbe) → new_ltEs9(zzz500000, zzz4300000)
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_esEs23(zzz500000, zzz4300000, app(app(ty_@2, hf), hg)) → new_esEs5(zzz500000, zzz4300000, hf, hg)
new_esEs4(Right(zzz5000), Right(zzz4000), bgd, ty_@0) → new_esEs10(zzz5000, zzz4000)
new_ltEs10(LT, EQ) → True
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_compare19(zzz500000, zzz4300000, False) → GT
new_esEs27(zzz5001, zzz4001, ty_Double) → new_esEs9(zzz5001, zzz4001)
new_ltEs15(zzz50000, zzz430000, bee) → new_fsEs(new_compare7(zzz50000, zzz430000, bee))
new_esEs23(zzz500000, zzz4300000, ty_Float) → new_esEs13(zzz500000, zzz4300000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Integer) → new_esEs15(zzz5000, zzz4000)
new_compare29(Just(zzz50000), Just(zzz430000), False, gg) → new_compare111(zzz50000, zzz430000, new_ltEs18(zzz50000, zzz430000, gg), gg)
new_primEqInt(Pos(Succ(zzz50000)), Neg(zzz4000)) → False
new_primEqInt(Neg(Succ(zzz50000)), Pos(zzz4000)) → False
new_lt13(zzz500000, zzz4300000, app(ty_Ratio, cbb)) → new_lt17(zzz500000, zzz4300000, cbb)
new_esEs7(Nothing, Just(zzz4000), cf) → False
new_esEs7(Just(zzz5000), Nothing, cf) → False
new_esEs18(zzz5001, zzz4001, app(ty_[], eh)) → new_esEs12(zzz5001, zzz4001, eh)
new_esEs28(zzz5000, zzz4000, ty_Char) → new_esEs11(zzz5000, zzz4000)
new_ltEs10(GT, GT) → True
new_esEs26(zzz5002, zzz4002, app(ty_Ratio, chh)) → new_esEs16(zzz5002, zzz4002, chh)
new_esEs26(zzz5002, zzz4002, ty_Int) → new_esEs17(zzz5002, zzz4002)
new_esEs4(Right(zzz5000), Right(zzz4000), bgd, ty_Bool) → new_esEs14(zzz5000, zzz4000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_@0, bbe) → new_ltEs11(zzz500000, zzz4300000)
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primEqInt(Pos(Zero), Neg(Succ(zzz40000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(zzz40000))) → False
new_ltEs6(zzz50000, zzz430000) → new_fsEs(new_compare8(zzz50000, zzz430000))
new_esEs20(zzz5000, zzz4000, app(ty_[], bae)) → new_esEs12(zzz5000, zzz4000, bae)
new_esEs21(zzz5001, zzz4001, ty_Integer) → new_esEs15(zzz5001, zzz4001)
new_compare30(zzz500000, zzz4300000, app(app(ty_@2, caa), cab)) → new_compare18(zzz500000, zzz4300000, caa, cab)
new_primCompAux00(zzz225, EQ) → zzz225
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Double, bfa) → new_esEs9(zzz5000, zzz4000)
new_gt(zzz440, zzz4440, h) → new_esEs8(new_compare28(zzz440, zzz4440, h), GT)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Integer, bfa) → new_esEs15(zzz5000, zzz4000)
new_esEs18(zzz5001, zzz4001, ty_Int) → new_esEs17(zzz5001, zzz4001)
new_lt16(zzz500000, zzz4300000, hf, hg) → new_esEs8(new_compare18(zzz500000, zzz4300000, hf, hg), LT)
new_esEs8(GT, EQ) → False
new_esEs8(EQ, GT) → False
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Double) → new_esEs9(zzz5000, zzz4000)
new_esEs26(zzz5002, zzz4002, ty_Char) → new_esEs11(zzz5002, zzz4002)
new_esEs27(zzz5001, zzz4001, app(ty_Ratio, dbb)) → new_esEs16(zzz5001, zzz4001, dbb)
new_esEs26(zzz5002, zzz4002, app(app(ty_@2, cha), chb)) → new_esEs5(zzz5002, zzz4002, cha, chb)
new_ltEs19(zzz500001, zzz4300001, app(app(ty_@2, cbf), cbg)) → new_ltEs13(zzz500001, zzz4300001, cbf, cbg)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Bool) → new_ltEs14(zzz500000, zzz4300000)
new_not(False) → True
new_esEs24(zzz500001, zzz4300001, ty_Double) → new_esEs9(zzz500001, zzz4300001)
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_ltEs5(zzz50000, zzz430000) → new_fsEs(new_compare10(zzz50000, zzz430000))
new_esEs25(zzz500000, zzz4300000, ty_Integer) → new_esEs15(zzz500000, zzz4300000)
new_esEs26(zzz5002, zzz4002, ty_Bool) → new_esEs14(zzz5002, zzz4002)
new_ltEs19(zzz500001, zzz4300001, ty_Int) → new_ltEs6(zzz500001, zzz4300001)
new_esEs25(zzz500000, zzz4300000, app(ty_Ratio, cdc)) → new_esEs16(zzz500000, zzz4300000, cdc)
new_esEs4(Right(zzz5000), Right(zzz4000), bgd, ty_Int) → new_esEs17(zzz5000, zzz4000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Bool, bbe) → new_ltEs14(zzz500000, zzz4300000)
new_esEs28(zzz5000, zzz4000, app(app(ty_@2, dbe), dbf)) → new_esEs5(zzz5000, zzz4000, dbe, dbf)
new_esEs23(zzz500000, zzz4300000, ty_@0) → new_esEs10(zzz500000, zzz4300000)
new_compare30(zzz500000, zzz4300000, ty_@0) → new_compare11(zzz500000, zzz4300000)
new_esEs18(zzz5001, zzz4001, app(app(ty_Either, ed), ee)) → new_esEs4(zzz5001, zzz4001, ed, ee)
new_lt18(zzz500000, zzz4300000, cbc) → new_esEs8(new_compare4(zzz500000, zzz4300000, cbc), LT)
new_ltEs18(zzz50000, zzz430000, ty_Int) → new_ltEs6(zzz50000, zzz430000)
new_esEs22(zzz5000, zzz4000, ty_Int) → new_esEs17(zzz5000, zzz4000)
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_esEs6(@3(zzz5000, zzz5001, zzz5002), @3(zzz4000, zzz4001, zzz4002), cgd, cge, cgf) → new_asAs(new_esEs28(zzz5000, zzz4000, cgd), new_asAs(new_esEs27(zzz5001, zzz4001, cge), new_esEs26(zzz5002, zzz4002, cgf)))
new_esEs28(zzz5000, zzz4000, app(ty_Maybe, dcc)) → new_esEs7(zzz5000, zzz4000, dcc)
new_esEs28(zzz5000, zzz4000, ty_Double) → new_esEs9(zzz5000, zzz4000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, ty_Double) → new_ltEs8(zzz500000, zzz4300000)
new_lt20(zzz500001, zzz4300001, ty_Double) → new_lt15(zzz500001, zzz4300001)
new_lt20(zzz500001, zzz4300001, ty_Integer) → new_lt10(zzz500001, zzz4300001)
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_esEs26(zzz5002, zzz4002, ty_@0) → new_esEs10(zzz5002, zzz4002)
new_esEs18(zzz5001, zzz4001, ty_Float) → new_esEs13(zzz5001, zzz4001)
new_compare25(zzz500000, zzz4300000, False, hf, hg) → new_compare15(zzz500000, zzz4300000, new_ltEs13(zzz500000, zzz4300000, hf, hg), hf, hg)
new_esEs23(zzz500000, zzz4300000, app(app(ty_Either, ha), hb)) → new_esEs4(zzz500000, zzz4300000, ha, hb)
new_esEs20(zzz5000, zzz4000, ty_Char) → new_esEs11(zzz5000, zzz4000)
new_lt19(zzz500000, zzz4300000, app(ty_Maybe, cdb)) → new_lt11(zzz500000, zzz4300000, cdb)
new_esEs4(Left(zzz5000), Left(zzz4000), app(ty_Maybe, bgb), bfa) → new_esEs7(zzz5000, zzz4000, bgb)
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_esEs20(zzz5000, zzz4000, ty_Integer) → new_esEs15(zzz5000, zzz4000)
new_primEqNat0(Zero, Succ(zzz40000)) → False
new_primEqNat0(Succ(zzz50000), Zero) → False
new_esEs18(zzz5001, zzz4001, ty_Integer) → new_esEs15(zzz5001, zzz4001)
new_esEs17(zzz500, zzz400) → new_primEqInt(zzz500, zzz400)
new_lt5(zzz500000, zzz4300000, ha, hb) → new_esEs8(new_compare12(zzz500000, zzz4300000, ha, hb), LT)
new_compare25(zzz500000, zzz4300000, True, hf, hg) → EQ
new_esEs20(zzz5000, zzz4000, ty_Bool) → new_esEs14(zzz5000, zzz4000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), app(app(ty_Either, bbf), bbg), bbe) → new_ltEs7(zzz500000, zzz4300000, bbf, bbg)
new_ltEs14(True, True) → True
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs24(zzz500001, zzz4300001, app(app(ty_Either, cdh), cea)) → new_esEs4(zzz500001, zzz4300001, cdh, cea)
new_esEs28(zzz5000, zzz4000, app(app(app(ty_@3, dbh), dca), dcb)) → new_esEs6(zzz5000, zzz4000, dbh, dca, dcb)
new_compare30(zzz500000, zzz4300000, ty_Bool) → new_compare17(zzz500000, zzz4300000)
new_esEs27(zzz5001, zzz4001, app(app(ty_Either, daa), dab)) → new_esEs4(zzz5001, zzz4001, daa, dab)
new_esEs27(zzz5001, zzz4001, app(app(app(ty_@3, daf), dag), dah)) → new_esEs6(zzz5001, zzz4001, daf, dag, dah)
new_compare4(:(zzz500000, zzz500001), [], ce) → GT
new_ltEs18(zzz50000, zzz430000, app(ty_[], ce)) → new_ltEs17(zzz50000, zzz430000, ce)
new_esEs27(zzz5001, zzz4001, app(app(ty_@2, dac), dad)) → new_esEs5(zzz5001, zzz4001, dac, dad)
new_esEs27(zzz5001, zzz4001, ty_Int) → new_esEs17(zzz5001, zzz4001)
new_esEs23(zzz500000, zzz4300000, ty_Int) → new_esEs17(zzz500000, zzz4300000)
new_lt13(zzz500000, zzz4300000, ty_@0) → new_lt4(zzz500000, zzz4300000)
new_compare30(zzz500000, zzz4300000, ty_Char) → new_compare10(zzz500000, zzz4300000)
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_compare4([], :(zzz4300000, zzz4300001), ce) → LT
new_sr0(zzz5000, zzz4000) → new_primMulInt(zzz5000, zzz4000)
new_lt19(zzz500000, zzz4300000, app(ty_[], cdg)) → new_lt18(zzz500000, zzz4300000, cdg)
new_compare15(zzz500000, zzz4300000, False, hf, hg) → GT
new_ltEs18(zzz50000, zzz430000, ty_Float) → new_ltEs12(zzz50000, zzz430000)
new_ltEs18(zzz50000, zzz430000, ty_Integer) → new_ltEs9(zzz50000, zzz430000)
new_ltEs19(zzz500001, zzz4300001, ty_Double) → new_ltEs8(zzz500001, zzz4300001)
new_compare30(zzz500000, zzz4300000, ty_Float) → new_compare16(zzz500000, zzz4300000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), app(ty_[], bcg), bbe) → new_ltEs17(zzz500000, zzz4300000, bcg)
new_esEs11(Char(zzz5000), Char(zzz4000)) → new_primEqNat0(zzz5000, zzz4000)
new_esEs7(Just(zzz5000), Just(zzz4000), app(app(app(ty_@3, de), df), dg)) → new_esEs6(zzz5000, zzz4000, de, df, dg)
new_esEs25(zzz500000, zzz4300000, app(ty_Maybe, cdb)) → new_esEs7(zzz500000, zzz4300000, cdb)
new_compare29(Nothing, Nothing, False, gg) → LT
new_esEs23(zzz500000, zzz4300000, app(ty_Ratio, cbb)) → new_esEs16(zzz500000, zzz4300000, cbb)
new_lt13(zzz500000, zzz4300000, app(app(ty_Either, ha), hb)) → new_lt5(zzz500000, zzz4300000, ha, hb)
new_esEs16(:%(zzz5000, zzz5001), :%(zzz4000, zzz4001), bbc) → new_asAs(new_esEs22(zzz5000, zzz4000, bbc), new_esEs21(zzz5001, zzz4001, bbc))
new_ltEs4(Just(zzz500000), Just(zzz4300000), app(ty_Maybe, bg)) → new_ltEs4(zzz500000, zzz4300000, bg)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Float) → new_ltEs12(zzz500000, zzz4300000)
new_primCompAux0(zzz500000, zzz4300000, zzz220, ce) → new_primCompAux00(zzz220, new_compare30(zzz500000, zzz4300000, ce))
new_esEs19(zzz5000, zzz4000, app(app(ty_@2, ga), gb)) → new_esEs5(zzz5000, zzz4000, ga, gb)
new_esEs19(zzz5000, zzz4000, app(ty_Ratio, gh)) → new_esEs16(zzz5000, zzz4000, gh)
new_esEs10(@0, @0) → True
new_compare29(zzz5000, zzz43000, True, gg) → EQ
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs27(zzz5001, zzz4001, ty_Float) → new_esEs13(zzz5001, zzz4001)
new_lt13(zzz500000, zzz4300000, ty_Integer) → new_lt10(zzz500000, zzz4300000)
new_compare28(zzz5000, zzz43000, gg) → new_compare29(zzz5000, zzz43000, new_esEs7(zzz5000, zzz43000, gg), gg)
new_esEs4(Right(zzz5000), Right(zzz4000), bgd, app(app(ty_@2, bgg), bgh)) → new_esEs5(zzz5000, zzz4000, bgg, bgh)
new_esEs24(zzz500001, zzz4300001, ty_Char) → new_esEs11(zzz500001, zzz4300001)
new_esEs28(zzz5000, zzz4000, ty_@0) → new_esEs10(zzz5000, zzz4000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, app(app(ty_Either, bda), bdb)) → new_ltEs7(zzz500000, zzz4300000, bda, bdb)
new_esEs28(zzz5000, zzz4000, ty_Int) → new_esEs17(zzz5000, zzz4000)
new_compare7(:%(zzz500000, zzz500001), :%(zzz4300000, zzz4300001), ty_Integer) → new_compare9(new_sr(zzz500000, zzz4300001), new_sr(zzz4300000, zzz500001))
new_compare9(Integer(zzz500000), Integer(zzz4300000)) → new_primCmpInt(zzz500000, zzz4300000)
new_compare23(zzz500000, zzz4300000, False) → new_compare112(zzz500000, zzz4300000, new_ltEs10(zzz500000, zzz4300000))
new_asAs(False, zzz207) → False
new_esEs4(Left(zzz5000), Left(zzz4000), ty_@0, bfa) → new_esEs10(zzz5000, zzz4000)
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_esEs26(zzz5002, zzz4002, ty_Double) → new_esEs9(zzz5002, zzz4002)
new_ltEs10(LT, GT) → True
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_ltEs4(Just(zzz500000), Just(zzz4300000), app(ty_Ratio, bh)) → new_ltEs15(zzz500000, zzz4300000, bh)
new_esEs23(zzz500000, zzz4300000, app(app(app(ty_@3, hc), hd), he)) → new_esEs6(zzz500000, zzz4300000, hc, hd, he)
new_lt8(zzz500000, zzz4300000, hc, hd, he) → new_esEs8(new_compare13(zzz500000, zzz4300000, hc, hd, he), LT)
new_lt11(zzz5000, zzz43000, gg) → new_esEs8(new_compare28(zzz5000, zzz43000, gg), LT)
new_esEs26(zzz5002, zzz4002, app(ty_[], chc)) → new_esEs12(zzz5002, zzz4002, chc)
new_compare4(:(zzz500000, zzz500001), :(zzz4300000, zzz4300001), ce) → new_primCompAux0(zzz500000, zzz4300000, new_compare4(zzz500001, zzz4300001, ce), ce)
new_compare16(Float(zzz500000, zzz500001), Float(zzz4300000, zzz4300001)) → new_compare8(new_sr0(zzz500000, zzz4300000), new_sr0(zzz500001, zzz4300001))
new_esEs26(zzz5002, zzz4002, app(ty_Maybe, chg)) → new_esEs7(zzz5002, zzz4002, chg)
new_esEs28(zzz5000, zzz4000, ty_Bool) → new_esEs14(zzz5000, zzz4000)
new_compare110(zzz500000, zzz4300000, True, hc, hd, he) → LT
new_lt19(zzz500000, zzz4300000, app(app(ty_Either, ccf), ccg)) → new_lt5(zzz500000, zzz4300000, ccf, ccg)
new_ltEs18(zzz50000, zzz430000, ty_Bool) → new_ltEs14(zzz50000, zzz430000)
new_esEs28(zzz5000, zzz4000, ty_Integer) → new_esEs15(zzz5000, zzz4000)
new_esEs18(zzz5001, zzz4001, ty_Ordering) → new_esEs8(zzz5001, zzz4001)
new_esEs19(zzz5000, zzz4000, ty_Double) → new_esEs9(zzz5000, zzz4000)
new_lt20(zzz500001, zzz4300001, app(app(ty_@2, ceb), cec)) → new_lt16(zzz500001, zzz4300001, ceb, cec)
new_esEs5(@2(zzz5000, zzz5001), @2(zzz4000, zzz4001), eb, ec) → new_asAs(new_esEs19(zzz5000, zzz4000, eb), new_esEs18(zzz5001, zzz4001, ec))
new_compare26(zzz500000, zzz4300000, False) → new_compare19(zzz500000, zzz4300000, new_ltEs14(zzz500000, zzz4300000))
new_esEs28(zzz5000, zzz4000, app(app(ty_Either, dbc), dbd)) → new_esEs4(zzz5000, zzz4000, dbc, dbd)
new_esEs4(Right(zzz5000), Right(zzz4000), bgd, app(ty_Maybe, bhe)) → new_esEs7(zzz5000, zzz4000, bhe)
new_esEs7(Just(zzz5000), Just(zzz4000), ty_@0) → new_esEs10(zzz5000, zzz4000)
new_ltEs18(zzz50000, zzz430000, ty_Char) → new_ltEs5(zzz50000, zzz430000)
new_esEs28(zzz5000, zzz4000, ty_Float) → new_esEs13(zzz5000, zzz4000)
new_lt13(zzz500000, zzz4300000, ty_Ordering) → new_lt9(zzz500000, zzz4300000)
new_esEs25(zzz500000, zzz4300000, app(app(app(ty_@3, cdd), cde), cdf)) → new_esEs6(zzz500000, zzz4300000, cdd, cde, cdf)
new_ltEs10(EQ, EQ) → True
new_ltEs18(zzz50000, zzz430000, app(app(ty_@2, bec), bed)) → new_ltEs13(zzz50000, zzz430000, bec, bed)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Int, bfa) → new_esEs17(zzz5000, zzz4000)
new_esEs23(zzz500000, zzz4300000, ty_Integer) → new_esEs15(zzz500000, zzz4300000)
new_ltEs10(LT, LT) → True
new_esEs14(True, True) → True
new_compare111(zzz200, zzz201, False, bbd) → GT
new_esEs27(zzz5001, zzz4001, ty_Bool) → new_esEs14(zzz5001, zzz4001)
new_esEs7(Just(zzz5000), Just(zzz4000), app(app(ty_Either, cg), da)) → new_esEs4(zzz5000, zzz4000, cg, da)
new_compare10(Char(zzz500000), Char(zzz4300000)) → new_primCmpNat0(zzz500000, zzz4300000)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Float, bfa) → new_esEs13(zzz5000, zzz4000)
new_lt13(zzz500000, zzz4300000, app(app(ty_@2, hf), hg)) → new_lt16(zzz500000, zzz4300000, hf, hg)
new_ltEs7(Left(zzz500000), Left(zzz4300000), app(app(ty_@2, bbh), bca), bbe) → new_ltEs13(zzz500000, zzz4300000, bbh, bca)
new_esEs7(Just(zzz5000), Just(zzz4000), app(ty_Ratio, ea)) → new_esEs16(zzz5000, zzz4000, ea)
new_lt13(zzz500000, zzz4300000, app(ty_Maybe, cba)) → new_lt11(zzz500000, zzz4300000, cba)
new_ltEs20(zzz500002, zzz4300002, app(app(ty_Either, cfb), cfc)) → new_ltEs7(zzz500002, zzz4300002, cfb, cfc)
new_esEs18(zzz5001, zzz4001, ty_@0) → new_esEs10(zzz5001, zzz4001)
new_ltEs16(@3(zzz500000, zzz500001, zzz500002), @3(zzz4300000, zzz4300001, zzz4300002), bef, beg, beh) → new_pePe(new_lt19(zzz500000, zzz4300000, bef), new_asAs(new_esEs25(zzz500000, zzz4300000, bef), new_pePe(new_lt20(zzz500001, zzz4300001, beg), new_asAs(new_esEs24(zzz500001, zzz4300001, beg), new_ltEs20(zzz500002, zzz4300002, beh)))))
new_esEs4(Right(zzz5000), Right(zzz4000), bgd, ty_Double) → new_esEs9(zzz5000, zzz4000)
new_ltEs14(True, False) → False
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_esEs20(zzz5000, zzz4000, ty_Int) → new_esEs17(zzz5000, zzz4000)
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_esEs25(zzz500000, zzz4300000, app(app(ty_@2, cch), cda)) → new_esEs5(zzz500000, zzz4300000, cch, cda)
new_ltEs20(zzz500002, zzz4300002, ty_Double) → new_ltEs8(zzz500002, zzz4300002)
new_ltEs7(Left(zzz500000), Left(zzz4300000), app(ty_Ratio, bcc), bbe) → new_ltEs15(zzz500000, zzz4300000, bcc)
new_ltEs19(zzz500001, zzz4300001, app(app(app(ty_@3, ccb), ccc), ccd)) → new_ltEs16(zzz500001, zzz4300001, ccb, ccc, ccd)
new_ltEs20(zzz500002, zzz4300002, app(app(app(ty_@3, cfh), cga), cgb)) → new_ltEs16(zzz500002, zzz4300002, cfh, cga, cgb)
new_compare112(zzz500000, zzz4300000, False) → GT
new_ltEs10(EQ, LT) → False
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Float) → new_esEs13(zzz5000, zzz4000)
new_esEs14(False, False) → True
new_esEs7(Just(zzz5000), Just(zzz4000), app(app(ty_@2, db), dc)) → new_esEs5(zzz5000, zzz4000, db, dc)
new_lt20(zzz500001, zzz4300001, ty_Char) → new_lt12(zzz500001, zzz4300001)
new_lt9(zzz500000, zzz4300000) → new_esEs8(new_compare6(zzz500000, zzz4300000), LT)
new_ltEs10(GT, LT) → False
new_esEs18(zzz5001, zzz4001, ty_Bool) → new_esEs14(zzz5001, zzz4001)
new_esEs22(zzz5000, zzz4000, ty_Integer) → new_esEs15(zzz5000, zzz4000)
new_primPlusNat1(Zero, Zero) → Zero
new_compare30(zzz500000, zzz4300000, app(app(app(ty_@3, cae), caf), cag)) → new_compare13(zzz500000, zzz4300000, cae, caf, cag)
new_esEs19(zzz5000, zzz4000, ty_Integer) → new_esEs15(zzz5000, zzz4000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(ty_[], bff), bfa) → new_esEs12(zzz5000, zzz4000, bff)
new_esEs26(zzz5002, zzz4002, app(app(ty_Either, cgg), cgh)) → new_esEs4(zzz5002, zzz4002, cgg, cgh)
new_asAs(True, zzz207) → zzz207
new_esEs28(zzz5000, zzz4000, app(ty_[], dbg)) → new_esEs12(zzz5000, zzz4000, dbg)
new_esEs27(zzz5001, zzz4001, app(ty_[], dae)) → new_esEs12(zzz5001, zzz4001, dae)
new_esEs19(zzz5000, zzz4000, app(app(ty_Either, fg), fh)) → new_esEs4(zzz5000, zzz4000, fg, fh)
new_ltEs4(Just(zzz500000), Nothing, bb) → False
new_esEs20(zzz5000, zzz4000, ty_Double) → new_esEs9(zzz5000, zzz4000)
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_ltEs4(Just(zzz500000), Just(zzz4300000), app(ty_[], cd)) → new_ltEs17(zzz500000, zzz4300000, cd)
new_esEs4(Right(zzz5000), Left(zzz4000), bgd, bfa) → False
new_esEs4(Left(zzz5000), Right(zzz4000), bgd, bfa) → False
new_ltEs19(zzz500001, zzz4300001, ty_Float) → new_ltEs12(zzz500001, zzz4300001)
new_ltEs20(zzz500002, zzz4300002, app(ty_Maybe, cff)) → new_ltEs4(zzz500002, zzz4300002, cff)
new_esEs4(Left(zzz5000), Left(zzz4000), app(app(app(ty_@3, bfg), bfh), bga), bfa) → new_esEs6(zzz5000, zzz4000, bfg, bfh, bga)
new_ltEs19(zzz500001, zzz4300001, ty_Char) → new_ltEs5(zzz500001, zzz4300001)
new_fsEs(zzz210) → new_not(new_esEs8(zzz210, GT))
new_esEs19(zzz5000, zzz4000, ty_@0) → new_esEs10(zzz5000, zzz4000)
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Bool) → new_esEs14(zzz5000, zzz4000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Double, bbe) → new_ltEs8(zzz500000, zzz4300000)
new_esEs24(zzz500001, zzz4300001, ty_Float) → new_esEs13(zzz500001, zzz4300001)
new_ltEs11(zzz50000, zzz430000) → new_fsEs(new_compare11(zzz50000, zzz430000))
new_lt20(zzz500001, zzz4300001, ty_Int) → new_lt14(zzz500001, zzz4300001)
new_esEs4(Right(zzz5000), Right(zzz4000), bgd, ty_Float) → new_esEs13(zzz5000, zzz4000)
new_esEs19(zzz5000, zzz4000, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_ltEs20(zzz500002, zzz4300002, app(app(ty_@2, cfd), cfe)) → new_ltEs13(zzz500002, zzz4300002, cfd, cfe)
new_esEs27(zzz5001, zzz4001, ty_Char) → new_esEs11(zzz5001, zzz4001)
new_ltEs20(zzz500002, zzz4300002, ty_Int) → new_ltEs6(zzz500002, zzz4300002)
new_compare110(zzz500000, zzz4300000, False, hc, hd, he) → GT
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Char) → new_ltEs5(zzz500000, zzz4300000)
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Char) → new_esEs11(zzz5000, zzz4000)
new_primCompAux00(zzz225, GT) → GT
new_ltEs20(zzz500002, zzz4300002, ty_Integer) → new_ltEs9(zzz500002, zzz4300002)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, app(ty_Maybe, bde)) → new_ltEs4(zzz500000, zzz4300000, bde)
new_lt19(zzz500000, zzz4300000, ty_Int) → new_lt14(zzz500000, zzz4300000)
new_ltEs4(Just(zzz500000), Just(zzz4300000), app(app(app(ty_@3, ca), cb), cc)) → new_ltEs16(zzz500000, zzz4300000, ca, cb, cc)
new_ltEs18(zzz50000, zzz430000, ty_Ordering) → new_ltEs10(zzz50000, zzz430000)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Integer) → new_ltEs9(zzz500000, zzz4300000)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_compare30(zzz500000, zzz4300000, ty_Ordering) → new_compare6(zzz500000, zzz4300000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, ty_Float) → new_ltEs12(zzz500000, zzz4300000)
new_esEs27(zzz5001, zzz4001, ty_Integer) → new_esEs15(zzz5001, zzz4001)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, ty_Int) → new_ltEs6(zzz500000, zzz4300000)
new_not(True) → False

The set Q consists of the following terms:

new_ltEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_compare23(x0, x1, True)
new_lt11(x0, x1, x2)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_lt14(x0, x1)
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs18(x0, x1, app(app(ty_@2, x2), x3))
new_asAs(True, x0)
new_compare29(Nothing, Nothing, False, x0)
new_compare19(x0, x1, True)
new_esEs26(x0, x1, ty_@0)
new_ltEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, app(ty_[], x2))
new_ltEs18(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_Ordering)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_lt13(x0, x1, app(ty_Ratio, x2))
new_esEs18(x0, x1, ty_Int)
new_primPlusNat1(Zero, Succ(x0))
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare29(Nothing, Just(x0), False, x1)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_compare30(x0, x1, ty_@0)
new_lt20(x0, x1, ty_Ordering)
new_esEs9(Double(x0, x1), Double(x2, x3))
new_ltEs7(Right(x0), Right(x1), x2, ty_@0)
new_primCompAux0(x0, x1, x2, x3)
new_primMulNat0(Succ(x0), Zero)
new_lt19(x0, x1, ty_Double)
new_primMulInt(Neg(x0), Neg(x1))
new_lt19(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_@0)
new_primPlusNat1(Succ(x0), Zero)
new_esEs21(x0, x1, ty_Int)
new_compare4(:(x0, x1), :(x2, x3), x4)
new_esEs4(Right(x0), Right(x1), x2, ty_Integer)
new_esEs4(Left(x0), Left(x1), ty_Double, x2)
new_ltEs10(LT, LT)
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs23(x0, x1, ty_Bool)
new_primPlusNat1(Succ(x0), Succ(x1))
new_compare30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, ty_Int)
new_esEs18(x0, x1, ty_Char)
new_esEs24(x0, x1, ty_Char)
new_ltEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(True, False)
new_ltEs14(False, True)
new_esEs25(x0, x1, ty_Double)
new_pePe(False, x0)
new_esEs19(x0, x1, ty_Char)
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Char)
new_compare27(x0, x1, True, x2, x3)
new_esEs7(Just(x0), Just(x1), ty_Double)
new_esEs8(GT, GT)
new_esEs23(x0, x1, ty_@0)
new_compare4([], :(x0, x1), x2)
new_lt9(x0, x1)
new_lt19(x0, x1, ty_Ordering)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs11(Char(x0), Char(x1))
new_esEs7(Nothing, Just(x0), x1)
new_esEs4(Right(x0), Right(x1), x2, ty_Bool)
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs8(LT, LT)
new_sr0(x0, x1)
new_compare6(x0, x1)
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_compare30(x0, x1, ty_Double)
new_esEs7(Just(x0), Just(x1), ty_Char)
new_esEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs18(x0, x1, app(ty_[], x2))
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare19(x0, x1, False)
new_ltEs4(Nothing, Nothing, x0)
new_compare110(x0, x1, False, x2, x3, x4)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs26(x0, x1, ty_Double)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs4(Right(x0), Right(x1), x2, ty_Float)
new_lt16(x0, x1, x2, x3)
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_compare111(x0, x1, False, x2)
new_compare4([], [], x0)
new_ltEs7(Left(x0), Left(x1), ty_Char, x2)
new_ltEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs17(x0, x1)
new_ltEs19(x0, x1, ty_Char)
new_esEs4(Left(x0), Left(x1), ty_Float, x2)
new_esEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs14(True, True)
new_compare26(x0, x1, True)
new_lt20(x0, x1, ty_Char)
new_compare112(x0, x1, False)
new_esEs18(x0, x1, ty_Bool)
new_esEs20(x0, x1, ty_Float)
new_primEqNat0(Zero, Zero)
new_ltEs4(Just(x0), Just(x1), ty_Double)
new_compare30(x0, x1, ty_Char)
new_lt20(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_ltEs7(Right(x0), Right(x1), x2, ty_Char)
new_gt(x0, x1, x2)
new_esEs20(x0, x1, ty_Int)
new_lt13(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Double)
new_lt19(x0, x1, ty_Bool)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, ty_@0)
new_esEs12([], :(x0, x1), x2)
new_esEs28(x0, x1, ty_Integer)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_compare17(x0, x1)
new_ltEs17(x0, x1, x2)
new_primPlusNat0(Zero, x0)
new_ltEs20(x0, x1, ty_Int)
new_compare13(x0, x1, x2, x3, x4)
new_primMulNat0(Zero, Zero)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpNat0(Succ(x0), Zero)
new_compare16(Float(x0, x1), Float(x2, x3))
new_ltEs20(x0, x1, ty_Integer)
new_compare30(x0, x1, ty_Ordering)
new_ltEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs26(x0, x1, ty_Integer)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs10(EQ, LT)
new_ltEs10(LT, EQ)
new_lt4(x0, x1)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_ltEs7(Left(x0), Left(x1), ty_@0, x2)
new_lt13(x0, x1, app(app(ty_@2, x2), x3))
new_esEs19(x0, x1, ty_Bool)
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs28(x0, x1, ty_@0)
new_primMulNat0(Succ(x0), Succ(x1))
new_lt7(x0, x1)
new_esEs23(x0, x1, ty_Float)
new_ltEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Int)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs19(x0, x1, ty_Double)
new_compare113(x0, x1, False, x2, x3)
new_ltEs18(x0, x1, ty_@0)
new_compare15(x0, x1, True, x2, x3)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs4(Right(x0), Right(x1), x2, ty_@0)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Char)
new_esEs24(x0, x1, ty_Int)
new_compare9(Integer(x0), Integer(x1))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, ty_Ordering)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_ltEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_compare4(:(x0, x1), [], x2)
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_esEs24(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_Char)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_compare25(x0, x1, False, x2, x3)
new_esEs20(x0, x1, ty_Ordering)
new_esEs12(:(x0, x1), :(x2, x3), x4)
new_compare30(x0, x1, app(ty_[], x2))
new_fsEs(x0)
new_lt8(x0, x1, x2, x3, x4)
new_ltEs11(x0, x1)
new_esEs23(x0, x1, ty_Double)
new_lt13(x0, x1, ty_@0)
new_ltEs7(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Just(x0), Just(x1), ty_Int)
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_compare26(x0, x1, False)
new_ltEs18(x0, x1, ty_Double)
new_ltEs7(Right(x0), Left(x1), x2, x3)
new_ltEs7(Left(x0), Right(x1), x2, x3)
new_ltEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs25(x0, x1, ty_Bool)
new_lt17(x0, x1, x2)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primPlusNat1(Zero, Zero)
new_esEs28(x0, x1, ty_Float)
new_ltEs7(Right(x0), Right(x1), x2, ty_Int)
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_lt12(x0, x1)
new_compare7(:%(x0, x1), :%(x2, x3), ty_Int)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_ltEs4(Just(x0), Just(x1), ty_Int)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_compare11(@0, @0)
new_primMulNat0(Zero, Succ(x0))
new_esEs26(x0, x1, ty_Bool)
new_asAs(False, x0)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs12(:(x0, x1), [], x2)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs4(Just(x0), Just(x1), ty_Bool)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1, app(ty_[], x2))
new_ltEs8(x0, x1)
new_ltEs18(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Float)
new_esEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_Double)
new_ltEs19(x0, x1, ty_Ordering)
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(Just(x0), Just(x1), ty_Ordering)
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs18(x0, x1, ty_Double)
new_ltEs10(GT, LT)
new_ltEs10(LT, GT)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs28(x0, x1, ty_Double)
new_esEs10(@0, @0)
new_compare14(Double(x0, x1), Double(x2, x3))
new_compare24(x0, x1, True, x2, x3, x4)
new_compare30(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_Integer)
new_compare30(x0, x1, app(ty_Maybe, x2))
new_ltEs18(x0, x1, ty_Float)
new_ltEs15(x0, x1, x2)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_compare8(x0, x1)
new_lt13(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs20(x0, x1, ty_Char)
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs7(Right(x0), Right(x1), x2, ty_Integer)
new_compare30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Integer)
new_pePe(True, x0)
new_compare29(Just(x0), Just(x1), False, x2)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_Float)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_esEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCompAux00(x0, EQ)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1, ty_Float)
new_primEqNat0(Succ(x0), Zero)
new_ltEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_compare30(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_Int)
new_compare27(x0, x1, False, x2, x3)
new_esEs18(x0, x1, ty_Ordering)
new_esEs25(x0, x1, ty_Int)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs18(x0, x1, app(ty_Ratio, x2))
new_esEs7(Nothing, Nothing, x0)
new_ltEs4(Just(x0), Just(x1), ty_@0)
new_esEs19(x0, x1, app(ty_[], x2))
new_compare23(x0, x1, False)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_ltEs4(Just(x0), Nothing, x1)
new_esEs8(EQ, EQ)
new_compare112(x0, x1, True)
new_esEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs19(x0, x1, ty_Double)
new_esEs13(Float(x0, x1), Float(x2, x3))
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs4(Right(x0), Right(x1), x2, ty_Double)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_lt13(x0, x1, ty_Char)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, ty_Char)
new_esEs15(Integer(x0), Integer(x1))
new_ltEs12(x0, x1)
new_lt20(x0, x1, ty_@0)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_@0)
new_esEs14(True, False)
new_esEs14(False, True)
new_ltEs4(Just(x0), Just(x1), ty_Float)
new_ltEs7(Right(x0), Right(x1), x2, ty_Float)
new_esEs18(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs6(x0, x1)
new_esEs22(x0, x1, ty_Int)
new_esEs20(x0, x1, ty_Double)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare110(x0, x1, True, x2, x3, x4)
new_ltEs9(x0, x1)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs19(x0, x1, ty_@0)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Ordering)
new_esEs27(x0, x1, ty_Integer)
new_esEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs16(:%(x0, x1), :%(x2, x3), x4)
new_lt20(x0, x1, ty_Float)
new_compare25(x0, x1, True, x2, x3)
new_compare30(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Integer)
new_primCmpNat0(Succ(x0), Succ(x1))
new_lt19(x0, x1, ty_Char)
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_esEs20(x0, x1, ty_Integer)
new_esEs28(x0, x1, ty_Ordering)
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_esEs21(x0, x1, ty_Integer)
new_compare28(x0, x1, x2)
new_ltEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_ltEs7(Right(x0), Right(x1), x2, ty_Double)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Bool)
new_primPlusNat0(Succ(x0), x1)
new_esEs20(x0, x1, ty_@0)
new_ltEs13(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs18(x0, x1, ty_Integer)
new_esEs4(Left(x0), Left(x1), ty_Int, x2)
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Just(x0), Just(x1), ty_Float)
new_compare18(x0, x1, x2, x3)
new_esEs19(x0, x1, ty_Float)
new_ltEs20(x0, x1, ty_Bool)
new_primCmpNat0(Zero, Zero)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs4(Left(x0), Left(x1), ty_Integer, x2)
new_esEs19(x0, x1, ty_Ordering)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_lt13(x0, x1, app(ty_Maybe, x2))
new_lt13(x0, x1, ty_Bool)
new_lt18(x0, x1, x2)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, ty_Float)
new_ltEs7(Left(x0), Left(x1), ty_Double, x2)
new_ltEs16(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs12([], [], x0)
new_lt10(x0, x1)
new_compare7(:%(x0, x1), :%(x2, x3), ty_Integer)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_compare113(x0, x1, True, x2, x3)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs20(x0, x1, app(ty_[], x2))
new_ltEs7(Left(x0), Left(x1), ty_Bool, x2)
new_esEs4(Left(x0), Left(x1), ty_Char, x2)
new_esEs25(x0, x1, ty_Ordering)
new_esEs27(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_Float)
new_ltEs7(Left(x0), Left(x1), ty_Float, x2)
new_lt5(x0, x1, x2, x3)
new_compare29(Just(x0), Nothing, False, x1)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs10(GT, GT)
new_esEs4(Right(x0), Right(x1), x2, ty_Int)
new_ltEs14(True, True)
new_ltEs14(False, False)
new_esEs24(x0, x1, ty_Ordering)
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_lt19(x0, x1, ty_@0)
new_esEs18(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Char)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs7(Left(x0), Left(x1), ty_Int, x2)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_not(True)
new_esEs19(x0, x1, ty_Int)
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Just(x0), Just(x1), ty_@0)
new_compare30(x0, x1, ty_Integer)
new_ltEs5(x0, x1)
new_ltEs20(x0, x1, ty_Double)
new_esEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(Just(x0), Just(x1), ty_Integer)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_not(False)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_Integer)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_ltEs4(Just(x0), Just(x1), app(ty_[], x2))
new_primCompAux00(x0, LT)
new_esEs4(Left(x0), Left(x1), ty_@0, x2)
new_lt6(x0, x1)
new_ltEs10(EQ, GT)
new_ltEs10(GT, EQ)
new_esEs4(Right(x0), Left(x1), x2, x3)
new_esEs4(Left(x0), Right(x1), x2, x3)
new_ltEs19(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Float)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_ltEs18(x0, x1, ty_Char)
new_esEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs19(x0, x1, ty_Integer)
new_esEs18(x0, x1, app(ty_[], x2))
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_sr(Integer(x0), Integer(x1))
new_esEs27(x0, x1, ty_Char)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs20(x0, x1, ty_Bool)
new_ltEs4(Just(x0), Just(x1), ty_Char)
new_ltEs4(Nothing, Just(x0), x1)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs18(x0, x1, ty_@0)
new_esEs24(x0, x1, app(ty_[], x2))
new_ltEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_lt13(x0, x1, ty_Double)
new_esEs18(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_lt13(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, ty_Bool)
new_lt13(x0, x1, ty_Ordering)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare12(x0, x1, x2, x3)
new_compare30(x0, x1, app(app(ty_Either, x2), x3))
new_compare15(x0, x1, False, x2, x3)
new_ltEs18(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Ordering)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_compare30(x0, x1, ty_Float)
new_compare111(x0, x1, True, x2)
new_lt13(x0, x1, ty_Integer)
new_esEs14(False, False)
new_primEqInt(Pos(Zero), Pos(Zero))
new_compare10(Char(x0), Char(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs24(x0, x1, ty_Integer)
new_esEs4(Right(x0), Right(x1), x2, ty_Char)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Double)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_ltEs20(x0, x1, ty_Float)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_lt13(x0, x1, ty_Int)
new_compare29(x0, x1, True, x2)
new_lt13(x0, x1, ty_Float)
new_lt20(x0, x1, ty_Integer)
new_primCmpNat0(Zero, Succ(x0))
new_ltEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs23(x0, x1, ty_Int)
new_primCompAux00(x0, GT)
new_ltEs20(x0, x1, ty_@0)
new_lt15(x0, x1)
new_ltEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primEqNat0(Zero, Succ(x0))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs7(Left(x0), Left(x1), ty_Integer, x2)
new_esEs27(x0, x1, ty_Bool)
new_ltEs19(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_@0)
new_compare24(x0, x1, False, x2, x3, x4)
new_esEs7(Just(x0), Nothing, x1)
new_esEs18(x0, x1, ty_Integer)
new_ltEs10(EQ, EQ)

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(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, True, h, ba) → new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), zzz4443, h, ba)
new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, True, h, ba) → new_mkVBalBranch(zzz440, zzz441, zzz3544, Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba)
new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba) → new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_lt14(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_lt14(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), h, ba)

The TRS R consists of the following rules:

new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_compare8(zzz500, zzz4300) → new_primCmpInt(zzz500, zzz4300)
new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba) → new_sizeFM(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, h, ba)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_esEs8(EQ, EQ) → True
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primPlusNat1(Zero, Zero) → Zero
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_lt14(zzz5000, zzz43000) → new_esEs8(new_compare8(zzz5000, zzz43000), LT)
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_esEs8(EQ, GT) → False
new_esEs8(GT, EQ) → False
new_primMulNat0(Zero, Zero) → Zero
new_esEs8(GT, GT) → True
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_esEs8(LT, GT) → False
new_esEs8(GT, LT) → False
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_sr0(zzz5000, zzz4000) → new_primMulInt(zzz5000, zzz4000)
new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba) → new_sizeFM(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_sizeFM(zzz760, zzz761, zzz762, zzz763, zzz764, h, bb) → zzz762
new_esEs8(LT, EQ) → False
new_esEs8(EQ, LT) → False
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_esEs8(LT, LT) → True
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz5000000), Zero) → GT

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primPlusNat0(Zero, x0)
new_lt14(x0, x1)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpNat0(Succ(x0), Zero)
new_compare8(x0, x1)
new_esEs8(LT, LT)
new_sr0(x0, x1)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_primPlusNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primMulInt(Neg(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_esEs8(GT, GT)
new_sIZE_RATIO

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(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, True, h, ba) → new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), zzz4443, h, ba)
new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, True, h, ba) → new_mkVBalBranch(zzz440, zzz441, zzz3544, Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba)
new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba) → new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_lt14(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), h, ba)
new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_lt14(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba) → new_sizeFM(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)
new_sr0(zzz5000, zzz4000) → new_primMulInt(zzz5000, zzz4000)
new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba) → new_sizeFM(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, h, ba)
new_lt14(zzz5000, zzz43000) → new_esEs8(new_compare8(zzz5000, zzz43000), LT)
new_compare8(zzz500, zzz4300) → new_primCmpInt(zzz500, zzz4300)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_sizeFM(zzz760, zzz761, zzz762, zzz763, zzz764, h, bb) → zzz762
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primPlusNat0(Zero, x0)
new_lt14(x0, x1)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpNat0(Succ(x0), Zero)
new_compare8(x0, x1)
new_esEs8(LT, LT)
new_sr0(x0, x1)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_primPlusNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primMulInt(Neg(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_esEs8(GT, GT)
new_sIZE_RATIO

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba) → new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_lt14(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), h, ba) at position [12] we obtained the following new rules:

new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba) → new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_compare8(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, 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
                                            ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba) → new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_compare8(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, True, h, ba) → new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), zzz4443, h, ba)
new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, True, h, ba) → new_mkVBalBranch(zzz440, zzz441, zzz3544, Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba)
new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_lt14(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), h, ba)

The TRS R consists of the following rules:

new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba) → new_sizeFM(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)
new_sr0(zzz5000, zzz4000) → new_primMulInt(zzz5000, zzz4000)
new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba) → new_sizeFM(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, h, ba)
new_lt14(zzz5000, zzz43000) → new_esEs8(new_compare8(zzz5000, zzz43000), LT)
new_compare8(zzz500, zzz4300) → new_primCmpInt(zzz500, zzz4300)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_sizeFM(zzz760, zzz761, zzz762, zzz763, zzz764, h, bb) → zzz762
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primPlusNat0(Zero, x0)
new_lt14(x0, x1)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpNat0(Succ(x0), Zero)
new_compare8(x0, x1)
new_esEs8(LT, LT)
new_sr0(x0, x1)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_primPlusNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primMulInt(Neg(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_esEs8(GT, GT)
new_sIZE_RATIO

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_lt14(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), h, ba) at position [12] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_compare8(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, 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
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ UsableRulesProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba) → new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_compare8(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, True, h, ba) → new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), zzz4443, h, ba)
new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, True, h, ba) → new_mkVBalBranch(zzz440, zzz441, zzz3544, Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba)
new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_compare8(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, 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(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba) → new_sizeFM(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)
new_sr0(zzz5000, zzz4000) → new_primMulInt(zzz5000, zzz4000)
new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba) → new_sizeFM(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, h, ba)
new_lt14(zzz5000, zzz43000) → new_esEs8(new_compare8(zzz5000, zzz43000), LT)
new_compare8(zzz500, zzz4300) → new_primCmpInt(zzz500, zzz4300)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_sizeFM(zzz760, zzz761, zzz762, zzz763, zzz764, h, bb) → zzz762
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primPlusNat0(Zero, x0)
new_lt14(x0, x1)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpNat0(Succ(x0), Zero)
new_compare8(x0, x1)
new_esEs8(LT, LT)
new_sr0(x0, x1)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_primPlusNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primMulInt(Neg(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_esEs8(GT, GT)
new_sIZE_RATIO

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

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

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

new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba) → new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_compare8(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, True, h, ba) → new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), zzz4443, h, ba)
new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, True, h, ba) → new_mkVBalBranch(zzz440, zzz441, zzz3544, Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba)
new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_compare8(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, 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(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba) → new_sizeFM(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)
new_sr0(zzz5000, zzz4000) → new_primMulInt(zzz5000, zzz4000)
new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba) → new_sizeFM(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, h, ba)
new_compare8(zzz500, zzz4300) → new_primCmpInt(zzz500, zzz4300)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_sizeFM(zzz760, zzz761, zzz762, zzz763, zzz764, h, bb) → zzz762
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primPlusNat0(Zero, x0)
new_lt14(x0, x1)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpNat0(Succ(x0), Zero)
new_compare8(x0, x1)
new_esEs8(LT, LT)
new_sr0(x0, x1)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_primPlusNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primMulInt(Neg(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_esEs8(GT, GT)
new_sIZE_RATIO

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_lt14(x0, x1)



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

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

new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba) → new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_compare8(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, True, h, ba) → new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), zzz4443, h, ba)
new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, True, h, ba) → new_mkVBalBranch(zzz440, zzz441, zzz3544, Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba)
new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_compare8(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, 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(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba) → new_sizeFM(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)
new_sr0(zzz5000, zzz4000) → new_primMulInt(zzz5000, zzz4000)
new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba) → new_sizeFM(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, h, ba)
new_compare8(zzz500, zzz4300) → new_primCmpInt(zzz500, zzz4300)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_sizeFM(zzz760, zzz761, zzz762, zzz763, zzz764, h, bb) → zzz762
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primPlusNat0(Zero, x0)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpNat0(Succ(x0), Zero)
new_compare8(x0, x1)
new_esEs8(LT, LT)
new_sr0(x0, x1)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_primPlusNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primMulInt(Neg(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_esEs8(GT, GT)
new_sIZE_RATIO

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba) → new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_compare8(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), LT), h, ba) at position [12,0] we obtained the following new rules:

new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba) → new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, 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
                                            ↳ 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(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, True, h, ba) → new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), zzz4443, h, ba)
new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba) → new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, True, h, ba) → new_mkVBalBranch(zzz440, zzz441, zzz3544, Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba)
new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_compare8(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, 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(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba) → new_sizeFM(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)
new_sr0(zzz5000, zzz4000) → new_primMulInt(zzz5000, zzz4000)
new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba) → new_sizeFM(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, h, ba)
new_compare8(zzz500, zzz4300) → new_primCmpInt(zzz500, zzz4300)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_sizeFM(zzz760, zzz761, zzz762, zzz763, zzz764, h, bb) → zzz762
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primPlusNat0(Zero, x0)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpNat0(Succ(x0), Zero)
new_compare8(x0, x1)
new_esEs8(LT, LT)
new_sr0(x0, x1)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_primPlusNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primMulInt(Neg(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_esEs8(GT, GT)
new_sIZE_RATIO

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_compare8(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), LT), h, ba) at position [12,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, 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
                                            ↳ 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(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, True, h, ba) → new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), zzz4443, h, ba)
new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba) → new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, True, h, ba) → new_mkVBalBranch(zzz440, zzz441, zzz3544, Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba)
new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, 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(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba) → new_sizeFM(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)
new_sr0(zzz5000, zzz4000) → new_primMulInt(zzz5000, zzz4000)
new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba) → new_sizeFM(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, h, ba)
new_compare8(zzz500, zzz4300) → new_primCmpInt(zzz500, zzz4300)
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_sizeFM(zzz760, zzz761, zzz762, zzz763, zzz764, h, bb) → zzz762
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primPlusNat0(Zero, x0)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpNat0(Succ(x0), Zero)
new_compare8(x0, x1)
new_esEs8(LT, LT)
new_sr0(x0, x1)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_primPlusNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primMulInt(Neg(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_esEs8(GT, GT)
new_sIZE_RATIO

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

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

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

new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, True, h, ba) → new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), zzz4443, h, ba)
new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba) → new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, True, h, ba) → new_mkVBalBranch(zzz440, zzz441, zzz3544, Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba)
new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, 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(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba) → new_sizeFM(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)
new_sr0(zzz5000, zzz4000) → new_primMulInt(zzz5000, zzz4000)
new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba) → new_sizeFM(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, h, ba)
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_sizeFM(zzz760, zzz761, zzz762, zzz763, zzz764, h, bb) → zzz762
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primPlusNat0(Zero, x0)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpNat0(Succ(x0), Zero)
new_compare8(x0, x1)
new_esEs8(LT, LT)
new_sr0(x0, x1)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_primPlusNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primMulInt(Neg(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_esEs8(GT, GT)
new_sIZE_RATIO

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_compare8(x0, x1)



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

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

new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, True, h, ba) → new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), zzz4443, h, ba)
new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba) → new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, True, h, ba) → new_mkVBalBranch(zzz440, zzz441, zzz3544, Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba)
new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, 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(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba) → new_sizeFM(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)
new_sr0(zzz5000, zzz4000) → new_primMulInt(zzz5000, zzz4000)
new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba) → new_sizeFM(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, h, ba)
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_sizeFM(zzz760, zzz761, zzz762, zzz763, zzz764, h, bb) → zzz762
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primPlusNat0(Zero, x0)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, LT)
new_sr0(x0, x1)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_primPlusNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primMulInt(Neg(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_esEs8(GT, GT)
new_sIZE_RATIO

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba) → new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), LT), h, ba) at position [12,0,0] we obtained the following new rules:

new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba) → new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, 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
                                            ↳ 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(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, True, h, ba) → new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), zzz4443, h, ba)
new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba) → new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, True, h, ba) → new_mkVBalBranch(zzz440, zzz441, zzz3544, Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba)
new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, 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(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba) → new_sizeFM(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)
new_sr0(zzz5000, zzz4000) → new_primMulInt(zzz5000, zzz4000)
new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba) → new_sizeFM(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, h, ba)
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_sizeFM(zzz760, zzz761, zzz762, zzz763, zzz764, h, bb) → zzz762
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primPlusNat0(Zero, x0)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, LT)
new_sr0(x0, x1)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_primPlusNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primMulInt(Neg(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_esEs8(GT, GT)
new_sIZE_RATIO

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), LT), h, ba) at position [12,0,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, 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
                                            ↳ 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(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, True, h, ba) → new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), zzz4443, h, ba)
new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba) → new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, True, h, ba) → new_mkVBalBranch(zzz440, zzz441, zzz3544, Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba)
new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, 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(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba) → new_sizeFM(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)
new_sr0(zzz5000, zzz4000) → new_primMulInt(zzz5000, zzz4000)
new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba) → new_sizeFM(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, h, ba)
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_sizeFM(zzz760, zzz761, zzz762, zzz763, zzz764, h, bb) → zzz762
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primPlusNat0(Zero, x0)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, LT)
new_sr0(x0, x1)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_primPlusNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primMulInt(Neg(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_esEs8(GT, GT)
new_sIZE_RATIO

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

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

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

new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, True, h, ba) → new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), zzz4443, h, ba)
new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba) → new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, True, h, ba) → new_mkVBalBranch(zzz440, zzz441, zzz3544, Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba)
new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, 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(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba) → new_sizeFM(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, h, ba)
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba) → new_sizeFM(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_sizeFM(zzz760, zzz761, zzz762, zzz763, zzz764, h, bb) → zzz762
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primPlusNat0(Zero, x0)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_primCmpNat0(Zero, Zero)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primMulNat0(Zero, Succ(x0))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpNat0(Succ(x0), Zero)
new_esEs8(LT, LT)
new_sr0(x0, x1)
new_primCmpNat0(Succ(x0), Succ(x1))
new_primCmpNat0(Zero, Succ(x0))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_primPlusNat1(Succ(x0), Succ(x1))
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_primPlusNat1(Zero, Succ(x0))
new_primPlusNat1(Zero, Zero)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_primMulNat0(Succ(x0), Zero)
new_primMulNat0(Succ(x0), Succ(x1))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primMulInt(Neg(x0), Neg(x1))
new_primPlusNat0(Succ(x0), x1)
new_esEs8(GT, GT)
new_sIZE_RATIO

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

new_sr0(x0, x1)



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

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

new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, True, h, ba) → new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), zzz4443, h, ba)
new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba) → new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, True, h, ba) → new_mkVBalBranch(zzz440, zzz441, zzz3544, Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba)
new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, 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(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba) → new_sizeFM(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, h, ba)
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba) → new_sizeFM(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_sizeFM(zzz760, zzz761, zzz762, zzz763, zzz764, h, bb) → zzz762
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba) → new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), LT), h, ba) at position [12,0,0,0] we obtained the following new rules:

new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba) → new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, 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
                                            ↳ 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(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba) → new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, True, h, ba) → new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), zzz4443, h, ba)
new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, True, h, ba) → new_mkVBalBranch(zzz440, zzz441, zzz3544, Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba)
new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, 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(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba) → new_sizeFM(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, h, ba)
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba) → new_sizeFM(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_sizeFM(zzz760, zzz761, zzz762, zzz763, zzz764, h, bb) → zzz762
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_primMulInt(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), LT), h, ba) at position [12,0,0,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, 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
                                            ↳ 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(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba) → new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, True, h, ba) → new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), zzz4443, h, ba)
new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, True, h, ba) → new_mkVBalBranch(zzz440, zzz441, zzz3544, Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba)
new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, 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(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba) → new_sizeFM(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, h, ba)
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba) → new_sizeFM(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_sizeFM(zzz760, zzz761, zzz762, zzz763, zzz764, h, bb) → zzz762
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

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

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

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

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

new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba) → new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, True, h, ba) → new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), zzz4443, h, ba)
new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, True, h, ba) → new_mkVBalBranch(zzz440, zzz441, zzz3544, Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba)
new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba) → new_sizeFM(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, h, ba)
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba) → new_sizeFM(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_sizeFM(zzz760, zzz761, zzz762, zzz763, zzz764, h, bb) → zzz762
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

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

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

new_sIZE_RATIO



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

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

new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba) → new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, True, h, ba) → new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), zzz4443, h, ba)
new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, True, h, ba) → new_mkVBalBranch(zzz440, zzz441, zzz3544, Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba)
new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba) → new_sizeFM(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, h, ba)
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba) → new_sizeFM(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_sizeFM(zzz760, zzz761, zzz762, zzz763, zzz764, h, bb) → zzz762
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba) → new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), LT), h, ba) at position [12,0,0,1] we obtained the following new rules:

new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba) → new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, 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
                                            ↳ 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(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, True, h, ba) → new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), zzz4443, h, ba)
new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba) → new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, True, h, ba) → new_mkVBalBranch(zzz440, zzz441, zzz3544, Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba)
new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba) → new_sizeFM(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, h, ba)
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba) → new_sizeFM(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_sizeFM(zzz760, zzz761, zzz762, zzz763, zzz764, h, bb) → zzz762
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), LT), h, ba) at position [12,0,0,1] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, h, ba)), new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, 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
                                            ↳ 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(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, True, h, ba) → new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), zzz4443, h, ba)
new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, h, ba)), new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), LT), h, ba)
new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba) → new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, True, h, ba) → new_mkVBalBranch(zzz440, zzz441, zzz3544, Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba)

The TRS R consists of the following rules:

new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba) → new_sizeFM(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, h, ba)
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba) → new_sizeFM(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_sizeFM(zzz760, zzz761, zzz762, zzz763, zzz764, h, bb) → zzz762
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba) → new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), LT), h, ba) at position [12,0,0,1] we obtained the following new rules:

new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba) → new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz3542), new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, 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
                                            ↳ 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(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, True, h, ba) → new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), zzz4443, h, ba)
new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, h, ba)), new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), LT), h, ba)
new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba) → new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz3542), new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, True, h, ba) → new_mkVBalBranch(zzz440, zzz441, zzz3544, Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba)

The TRS R consists of the following rules:

new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba) → new_sizeFM(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, h, ba)
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba) → new_sizeFM(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_sizeFM(zzz760, zzz761, zzz762, zzz763, zzz764, h, bb) → zzz762
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), new_sizeFM(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, h, ba)), new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), LT), h, ba) at position [12,0,0,1] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz4442), new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, 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
                                            ↳ 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(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz4442), new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, True, h, ba) → new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), zzz4443, h, ba)
new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba) → new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz3542), new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, True, h, ba) → new_mkVBalBranch(zzz440, zzz441, zzz3544, Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba)

The TRS R consists of the following rules:

new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba) → new_sizeFM(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, h, ba)
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba) → new_sizeFM(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_sizeFM(zzz760, zzz761, zzz762, zzz763, zzz764, h, bb) → zzz762
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba) → new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz3542), new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), LT), h, ba) at position [12,0,1] we obtained the following new rules:

new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba) → new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz3542), new_sizeFM(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, 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
                                            ↳ 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(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz4442), new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, True, h, ba) → new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), zzz4443, h, ba)
new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, True, h, ba) → new_mkVBalBranch(zzz440, zzz441, zzz3544, Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba)
new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba) → new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz3542), new_sizeFM(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba) → new_sizeFM(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, h, ba)
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba) → new_sizeFM(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_sizeFM(zzz760, zzz761, zzz762, zzz763, zzz764, h, bb) → zzz762
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

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

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

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

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

new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz4442), new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, True, h, ba) → new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), zzz4443, h, ba)
new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, True, h, ba) → new_mkVBalBranch(zzz440, zzz441, zzz3544, Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba)
new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba) → new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz3542), new_sizeFM(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_sizeFM(zzz760, zzz761, zzz762, zzz763, zzz764, h, bb) → zzz762
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)
new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba) → new_sizeFM(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)

The set Q consists of the following terms:

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

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
                                            ↳ 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(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz4442), new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, True, h, ba) → new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), zzz4443, h, ba)
new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, True, h, ba) → new_mkVBalBranch(zzz440, zzz441, zzz3544, Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba)
new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba) → new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz3542), new_sizeFM(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_sizeFM(zzz760, zzz761, zzz762, zzz763, zzz764, h, bb) → zzz762
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)
new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba) → new_sizeFM(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz4442), new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), LT), h, ba) at position [12,0,1] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz4442), new_sizeFM(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, 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
                                            ↳ 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(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, True, h, ba) → new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), zzz4443, h, ba)
new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz4442), new_sizeFM(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, True, h, ba) → new_mkVBalBranch(zzz440, zzz441, zzz3544, Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba)
new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba) → new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz3542), new_sizeFM(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_sizeFM(zzz760, zzz761, zzz762, zzz763, zzz764, h, bb) → zzz762
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)
new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba) → new_sizeFM(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)

The set Q consists of the following terms:

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

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

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

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

new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, True, h, ba) → new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), zzz4443, h, ba)
new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz4442), new_sizeFM(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, True, h, ba) → new_mkVBalBranch(zzz440, zzz441, zzz3544, Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba)
new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba) → new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz3542), new_sizeFM(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_sizeFM(zzz760, zzz761, zzz762, zzz763, zzz764, h, bb) → zzz762
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

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

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
                                            ↳ 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(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, True, h, ba) → new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), zzz4443, h, ba)
new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz4442), new_sizeFM(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, True, h, ba) → new_mkVBalBranch(zzz440, zzz441, zzz3544, Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba)
new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba) → new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz3542), new_sizeFM(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_sizeFM(zzz760, zzz761, zzz762, zzz763, zzz764, h, bb) → zzz762
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz4442), new_sizeFM(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, h, ba)), LT), h, ba) at position [12,0,1] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz4442), zzz3542), 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
                                            ↳ 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(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, True, h, ba) → new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), zzz4443, h, ba)
new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz4442), zzz3542), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, True, h, ba) → new_mkVBalBranch(zzz440, zzz441, zzz3544, Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba)
new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba) → new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz3542), new_sizeFM(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, h, ba)), LT), h, ba)

The TRS R consists of the following rules:

new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_sizeFM(zzz760, zzz761, zzz762, zzz763, zzz764, h, bb) → zzz762
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba) → new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz3542), new_sizeFM(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, h, ba)), LT), h, ba) at position [12,0,1] we obtained the following new rules:

new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba) → new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz3542), zzz4442), 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
                                            ↳ 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(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, True, h, ba) → new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), zzz4443, h, ba)
new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz4442), zzz3542), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, True, h, ba) → new_mkVBalBranch(zzz440, zzz441, zzz3544, Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba)
new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba) → new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz3542), zzz4442), LT), h, ba)

The TRS R consists of the following rules:

new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_sizeFM(zzz760, zzz761, zzz762, zzz763, zzz764, h, bb) → zzz762
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

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

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

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

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

new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, True, h, ba) → new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), zzz4443, h, ba)
new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz4442), zzz3542), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, True, h, ba) → new_mkVBalBranch(zzz440, zzz441, zzz3544, Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba)
new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba) → new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz3542), zzz4442), LT), h, ba)

The TRS R consists of the following rules:

new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

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

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

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



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ UsableRulesProof
                                                  ↳ QDP
                                                    ↳ QReductionProof
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ UsableRulesProof
                                                                                                  ↳ QDP
                                                                                                    ↳ QReductionProof
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ UsableRulesProof
                                                                                                                              ↳ QDP
                                                                                                                                ↳ QReductionProof
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ UsableRulesProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ QReductionProof
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ 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(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, True, h, ba) → new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), zzz4443, h, ba)
new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz4442), zzz3542), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, True, h, ba) → new_mkVBalBranch(zzz440, zzz441, zzz3544, Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba)
new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba) → new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz3542), zzz4442), LT), h, ba)

The TRS R consists of the following rules:

new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
We use the reduction pair processor [15].


The following pairs can be oriented strictly and are deleted.


new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba) → new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz3542), zzz4442), LT), h, ba)
The remaining pairs can at least be oriented weakly.

new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, True, h, ba) → new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), zzz4443, h, ba)
new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz4442), zzz3542), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, True, h, ba) → new_mkVBalBranch(zzz440, zzz441, zzz3544, Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba)
Used ordering: Polynomial interpretation [25]:

POL(Branch(x1, x2, x3, x4, x5)) = 1 + x1 + x2 + x4 + x5   
POL(EQ) = 0   
POL(False) = 1   
POL(GT) = 0   
POL(LT) = 1   
POL(Neg(x1)) = 0   
POL(Pos(x1)) = 1   
POL(Succ(x1)) = 0   
POL(True) = 1   
POL(Zero) = 0   
POL(new_esEs8(x1, x2)) = x2   
POL(new_mkVBalBranch(x1, x2, x3, x4, x5, x6)) = x3 + x4   
POL(new_mkVBalBranch3MkVBalBranch1(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15)) = 1 + x1 + x10 + x2 + x4 + x5 + x7 + x9   
POL(new_mkVBalBranch3MkVBalBranch2(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15)) = x1 + x10 + x13 + x2 + x4 + x5 + x6 + x7 + x9   
POL(new_primCmpInt(x1, x2)) = 0   
POL(new_primCmpNat0(x1, x2)) = 0   
POL(new_primMulInt(x1, x2)) = x1   
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_esEs8(EQ, LT) → False
new_esEs8(GT, LT) → False
new_esEs8(LT, LT) → True



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ UsableRulesProof
                                                  ↳ QDP
                                                    ↳ QReductionProof
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
                                                                ↳ UsableRulesProof
                                                                  ↳ QDP
                                                                    ↳ QReductionProof
                                                                      ↳ QDP
                                                                        ↳ Rewriting
                                                                          ↳ QDP
                                                                            ↳ Rewriting
                                                                              ↳ QDP
                                                                                ↳ UsableRulesProof
                                                                                  ↳ QDP
                                                                                    ↳ QReductionProof
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ UsableRulesProof
                                                                                                  ↳ QDP
                                                                                                    ↳ QReductionProof
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ UsableRulesProof
                                                                                                                              ↳ QDP
                                                                                                                                ↳ QReductionProof
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ UsableRulesProof
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ QReductionProof
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ 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(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, True, h, ba) → new_mkVBalBranch(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), zzz4443, h, ba)
new_mkVBalBranch3MkVBalBranch2(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, False, h, ba) → new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_esEs8(new_primCmpInt(new_primMulInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz4442), zzz3542), LT), h, ba)
new_mkVBalBranch3MkVBalBranch1(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, True, h, ba) → new_mkVBalBranch(zzz440, zzz441, zzz3544, Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba)

The TRS R consists of the following rules:

new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs8(GT, LT) → False
new_esEs8(EQ, LT) → False
new_esEs8(LT, LT) → True
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_primMulNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_primPlusNat1(Zero, Zero) → Zero
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 0 SCCs with 3 less nodes.

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

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

new_splitLT1(zzz2630, zzz2631, zzz2632, zzz2633, zzz2634, zzz265, True, h, ba) → new_splitLT(zzz2634, zzz265, h, ba)
new_splitLT2(zzz2630, zzz2631, zzz2632, zzz2633, zzz2634, zzz265, False, h, ba) → new_splitLT1(zzz2630, zzz2631, zzz2632, zzz2633, zzz2634, zzz265, new_gt0(zzz265, zzz2630, h), h, ba)
new_splitLT(Branch(zzz26330, zzz26331, zzz26332, zzz26333, zzz26334), zzz265, h, ba) → new_splitLT2(zzz26330, zzz26331, zzz26332, zzz26333, zzz26334, zzz265, new_lt11(Just(zzz265), zzz26330, h), h, ba)
new_splitLT2(zzz2630, zzz2631, zzz2632, Branch(zzz26330, zzz26331, zzz26332, zzz26333, zzz26334), zzz2634, zzz265, True, h, ba) → new_splitLT2(zzz26330, zzz26331, zzz26332, zzz26333, zzz26334, zzz265, new_lt11(Just(zzz265), zzz26330, h), h, ba)

The TRS R consists of the following rules:

new_lt19(zzz500000, zzz4300000, ty_Float) → new_lt6(zzz500000, zzz4300000)
new_ltEs18(zzz50000, zzz430000, app(ty_Ratio, bef)) → new_ltEs15(zzz50000, zzz430000, bef)
new_esEs7(Just(zzz5000), Just(zzz4000), app(ty_Maybe, ea)) → new_esEs7(zzz5000, zzz4000, ea)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_esEs20(zzz5000, zzz4000, app(ty_Maybe, bbb)) → new_esEs7(zzz5000, zzz4000, bbb)
new_esEs12(:(zzz5000, zzz5001), :(zzz4000, zzz4001), baa) → new_asAs(new_esEs20(zzz5000, zzz4000, baa), new_esEs12(zzz5001, zzz4001, baa))
new_esEs7(Just(zzz5000), Just(zzz4000), app(ty_[], de)) → new_esEs12(zzz5000, zzz4000, de)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bda, ty_Ordering) → new_ltEs10(zzz500000, zzz4300000)
new_lt19(zzz500000, zzz4300000, app(app(app(ty_@3, cdh), cea), ceb)) → new_lt8(zzz500000, zzz4300000, cdh, cea, ceb)
new_ltEs18(zzz50000, zzz430000, app(app(app(ty_@3, beg), beh), bfa)) → new_ltEs16(zzz50000, zzz430000, beg, beh, bfa)
new_lt20(zzz500001, zzz4300001, app(ty_[], cfe)) → new_lt18(zzz500001, zzz4300001, cfe)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, ty_Char) → new_esEs11(zzz5000, zzz4000)
new_compare15(zzz500000, zzz4300000, True, hg, hh) → LT
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Bool, bfb) → new_esEs14(zzz5000, zzz4000)
new_ltEs18(zzz50000, zzz430000, app(ty_Maybe, bb)) → new_ltEs4(zzz50000, zzz430000, bb)
new_ltEs20(zzz500002, zzz4300002, ty_Ordering) → new_ltEs10(zzz500002, zzz4300002)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, app(app(app(ty_@3, bhc), bhd), bhe)) → new_esEs6(zzz5000, zzz4000, bhc, bhd, bhe)
new_lt13(zzz500000, zzz4300000, app(app(app(ty_@3, hd), he), hf)) → new_lt8(zzz500000, zzz4300000, hd, he, hf)
new_lt15(zzz500000, zzz4300000) → new_esEs8(new_compare14(zzz500000, zzz4300000), LT)
new_lt20(zzz500001, zzz4300001, app(app(app(ty_@3, cfb), cfc), cfd)) → new_lt8(zzz500001, zzz4300001, cfb, cfc, cfd)
new_esEs27(zzz5001, zzz4001, app(ty_Maybe, dbb)) → new_esEs7(zzz5001, zzz4001, dbb)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Ordering) → new_ltEs10(zzz500000, zzz4300000)
new_esEs23(zzz500000, zzz4300000, ty_Bool) → new_esEs14(zzz500000, zzz4300000)
new_compare27(zzz500000, zzz4300000, False, hb, hc) → new_compare113(zzz500000, zzz4300000, new_ltEs7(zzz500000, zzz4300000, hb, hc), hb, hc)
new_lt19(zzz500000, zzz4300000, ty_Double) → new_lt15(zzz500000, zzz4300000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), app(ty_Maybe, bcc), bbf) → new_ltEs4(zzz500000, zzz4300000, bcc)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bda, ty_@0) → new_ltEs11(zzz500000, zzz4300000)
new_ltEs20(zzz500002, zzz4300002, app(ty_Ratio, cgc)) → new_ltEs15(zzz500002, zzz4300002, cgc)
new_lt13(zzz500000, zzz4300000, app(ty_[], cbg)) → new_lt18(zzz500000, zzz4300000, cbg)
new_esEs26(zzz5002, zzz4002, ty_Float) → new_esEs13(zzz5002, zzz4002)
new_ltEs7(Left(zzz500000), Right(zzz4300000), bda, bbf) → True
new_primMulNat0(Zero, Zero) → Zero
new_esEs29(zzz500, Just(zzz4300), ty_Integer) → new_esEs15(zzz500, zzz4300)
new_esEs19(zzz5000, zzz4000, ty_Int) → new_esEs17(zzz5000, zzz4000)
new_esEs29(zzz500, Just(zzz4300), ty_Double) → new_esEs9(zzz500, zzz4300)
new_sr(Integer(zzz43000000), Integer(zzz5000010)) → Integer(new_primMulInt(zzz43000000, zzz5000010))
new_ltEs20(zzz500002, zzz4300002, ty_Float) → new_ltEs12(zzz500002, zzz4300002)
new_ltEs20(zzz500002, zzz4300002, ty_@0) → new_ltEs11(zzz500002, zzz4300002)
new_esEs20(zzz5000, zzz4000, app(ty_Ratio, bbc)) → new_esEs16(zzz5000, zzz4000, bbc)
new_esEs18(zzz5001, zzz4001, ty_Double) → new_esEs9(zzz5001, zzz4001)
new_esEs23(zzz500000, zzz4300000, ty_Double) → new_esEs9(zzz500000, zzz4300000)
new_lt20(zzz500001, zzz4300001, ty_Float) → new_lt6(zzz500001, zzz4300001)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, app(ty_[], bhb)) → new_esEs12(zzz5000, zzz4000, bhb)
new_esEs24(zzz500001, zzz4300001, ty_Integer) → new_esEs15(zzz500001, zzz4300001)
new_ltEs14(False, True) → True
new_ltEs19(zzz500001, zzz4300001, ty_Integer) → new_ltEs9(zzz500001, zzz4300001)
new_esEs29(zzz500, Just(zzz4300), ty_Char) → new_esEs11(zzz500, zzz4300)
new_ltEs4(Just(zzz500000), Just(zzz4300000), app(app(ty_@2, be), bf)) → new_ltEs13(zzz500000, zzz4300000, be, bf)
new_esEs20(zzz5000, zzz4000, app(app(ty_Either, bab), bac)) → new_esEs4(zzz5000, zzz4000, bab, bac)
new_esEs12([], [], baa) → True
new_ltEs19(zzz500001, zzz4300001, ty_Ordering) → new_ltEs10(zzz500001, zzz4300001)
new_esEs24(zzz500001, zzz4300001, app(app(ty_@2, cef), ceg)) → new_esEs5(zzz500001, zzz4300001, cef, ceg)
new_lt12(zzz500000, zzz4300000) → new_esEs8(new_compare10(zzz500000, zzz4300000), LT)
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Ordering, bbf) → new_ltEs10(zzz500000, zzz4300000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bda, app(ty_Ratio, bdg)) → new_ltEs15(zzz500000, zzz4300000, bdg)
new_esEs15(Integer(zzz5000), Integer(zzz4000)) → new_primEqInt(zzz5000, zzz4000)
new_ltEs10(EQ, GT) → True
new_ltEs19(zzz500001, zzz4300001, app(ty_Maybe, ccd)) → new_ltEs4(zzz500001, zzz4300001, ccd)
new_esEs21(zzz5001, zzz4001, ty_Int) → new_esEs17(zzz5001, zzz4001)
new_ltEs7(Left(zzz500000), Left(zzz4300000), app(app(app(ty_@3, bce), bcf), bcg), bbf) → new_ltEs16(zzz500000, zzz4300000, bce, bcf, bcg)
new_lt13(zzz500000, zzz4300000, ty_Char) → new_lt12(zzz500000, zzz4300000)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Ordering, bfb) → new_esEs8(zzz5000, zzz4000)
new_esEs24(zzz500001, zzz4300001, app(ty_[], cfe)) → new_esEs12(zzz500001, zzz4300001, cfe)
new_esEs25(zzz500000, zzz4300000, ty_Double) → new_esEs9(zzz500000, zzz4300000)
new_esEs25(zzz500000, zzz4300000, ty_Float) → new_esEs13(zzz500000, zzz4300000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bda, app(ty_[], bec)) → new_ltEs17(zzz500000, zzz4300000, bec)
new_pePe(False, zzz218) → zzz218
new_lt14(zzz5000, zzz43000) → new_esEs8(new_compare8(zzz5000, zzz43000), LT)
new_esEs25(zzz500000, zzz4300000, app(app(ty_Either, cdb), cdc)) → new_esEs4(zzz500000, zzz4300000, cdb, cdc)
new_esEs12(:(zzz5000, zzz5001), [], baa) → False
new_esEs12([], :(zzz4000, zzz4001), baa) → False
new_esEs25(zzz500000, zzz4300000, ty_Char) → new_esEs11(zzz500000, zzz4300000)
new_esEs25(zzz500000, zzz4300000, ty_Bool) → new_esEs14(zzz500000, zzz4300000)
new_lt19(zzz500000, zzz4300000, ty_Ordering) → new_lt9(zzz500000, zzz4300000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bda, app(app(ty_@2, bdd), bde)) → new_ltEs13(zzz500000, zzz4300000, bdd, bde)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, app(ty_Ratio, bhg)) → new_esEs16(zzz5000, zzz4000, bhg)
new_compare23(zzz500000, zzz4300000, True) → EQ
new_esEs29(zzz500, Just(zzz4300), app(ty_[], baa)) → new_esEs12(zzz500, zzz4300, baa)
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Float, bbf) → new_ltEs12(zzz500000, zzz4300000)
new_lt19(zzz500000, zzz4300000, app(ty_Ratio, cdg)) → new_lt17(zzz500000, zzz4300000, cdg)
new_esEs24(zzz500001, zzz4300001, app(ty_Maybe, ceh)) → new_esEs7(zzz500001, zzz4300001, ceh)
new_ltEs4(Nothing, Just(zzz4300000), bb) → True
new_esEs23(zzz500000, zzz4300000, app(ty_Maybe, cbe)) → new_esEs7(zzz500000, zzz4300000, cbe)
new_compare30(zzz500000, zzz4300000, ty_Integer) → new_compare9(zzz500000, zzz4300000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(ty_Ratio, bgd), bfb) → new_esEs16(zzz5000, zzz4000, bgd)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bda, ty_Char) → new_ltEs5(zzz500000, zzz4300000)
new_compare13(zzz500000, zzz4300000, hd, he, hf) → new_compare24(zzz500000, zzz4300000, new_esEs6(zzz500000, zzz4300000, hd, he, hf), hd, he, hf)
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_lt4(zzz500000, zzz4300000) → new_esEs8(new_compare11(zzz500000, zzz4300000), LT)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, ty_Integer) → new_esEs15(zzz5000, zzz4000)
new_esEs20(zzz5000, zzz4000, app(app(ty_@2, bad), bae)) → new_esEs5(zzz5000, zzz4000, bad, bae)
new_esEs28(zzz5000, zzz4000, app(ty_Ratio, dce)) → new_esEs16(zzz5000, zzz4000, dce)
new_compare30(zzz500000, zzz4300000, app(ty_Ratio, cae)) → new_compare7(zzz500000, zzz4300000, cae)
new_compare19(zzz500000, zzz4300000, True) → LT
new_compare6(zzz500000, zzz4300000) → new_compare23(zzz500000, zzz4300000, new_esEs8(zzz500000, zzz4300000))
new_ltEs18(zzz50000, zzz430000, ty_@0) → new_ltEs11(zzz50000, zzz430000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_ltEs19(zzz500001, zzz4300001, app(ty_Ratio, cce)) → new_ltEs15(zzz500001, zzz4300001, cce)
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Int) → new_esEs17(zzz5000, zzz4000)
new_ltEs20(zzz500002, zzz4300002, ty_Bool) → new_ltEs14(zzz500002, zzz4300002)
new_esEs27(zzz5001, zzz4001, ty_@0) → new_esEs10(zzz5001, zzz4001)
new_ltEs12(zzz50000, zzz430000) → new_fsEs(new_compare16(zzz50000, zzz430000))
new_esEs8(LT, LT) → True
new_lt19(zzz500000, zzz4300000, app(app(ty_@2, cdd), cde)) → new_lt16(zzz500000, zzz4300000, cdd, cde)
new_esEs25(zzz500000, zzz4300000, ty_Ordering) → new_esEs8(zzz500000, zzz4300000)
new_esEs19(zzz5000, zzz4000, app(ty_Maybe, gh)) → new_esEs7(zzz5000, zzz4000, gh)
new_esEs20(zzz5000, zzz4000, app(app(app(ty_@3, bag), bah), bba)) → new_esEs6(zzz5000, zzz4000, bag, bah, bba)
new_esEs18(zzz5001, zzz4001, app(ty_Ratio, fg)) → new_esEs16(zzz5001, zzz4001, fg)
new_pePe(True, zzz218) → True
new_primEqNat0(Zero, Zero) → True
new_compare26(zzz500000, zzz4300000, True) → EQ
new_lt20(zzz500001, zzz4300001, app(app(ty_Either, ced), cee)) → new_lt5(zzz500001, zzz4300001, ced, cee)
new_esEs13(Float(zzz5000, zzz5001), Float(zzz4000, zzz4001)) → new_esEs17(new_sr0(zzz5000, zzz4000), new_sr0(zzz5001, zzz4001))
new_lt20(zzz500001, zzz4300001, ty_Bool) → new_lt7(zzz500001, zzz4300001)
new_esEs19(zzz5000, zzz4000, app(ty_[], gd)) → new_esEs12(zzz5000, zzz4000, gd)
new_compare29(Nothing, Just(zzz430000), False, gh) → LT
new_esEs19(zzz5000, zzz4000, ty_Float) → new_esEs13(zzz5000, zzz4000)
new_compare30(zzz500000, zzz4300000, app(ty_Maybe, cad)) → new_compare28(zzz500000, zzz4300000, cad)
new_esEs18(zzz5001, zzz4001, app(app(ty_@2, eg), eh)) → new_esEs5(zzz5001, zzz4001, eg, eh)
new_esEs25(zzz500000, zzz4300000, ty_Int) → new_esEs17(zzz500000, zzz4300000)
new_esEs9(Double(zzz5000, zzz5001), Double(zzz4000, zzz4001)) → new_esEs17(new_sr0(zzz5000, zzz4000), new_sr0(zzz5001, zzz4001))
new_esEs26(zzz5002, zzz4002, ty_Ordering) → new_esEs8(zzz5002, zzz4002)
new_esEs8(GT, GT) → True
new_esEs18(zzz5001, zzz4001, app(app(app(ty_@3, fb), fc), fd)) → new_esEs6(zzz5001, zzz4001, fb, fc, fd)
new_lt20(zzz500001, zzz4300001, app(ty_Maybe, ceh)) → new_lt11(zzz500001, zzz4300001, ceh)
new_esEs25(zzz500000, zzz4300000, ty_@0) → new_esEs10(zzz500000, zzz4300000)
new_compare4([], [], ce) → EQ
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_lt19(zzz500000, zzz4300000, ty_@0) → new_lt4(zzz500000, zzz4300000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(app(ty_@2, bfe), bff), bfb) → new_esEs5(zzz5000, zzz4000, bfe, bff)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bda, ty_Integer) → new_ltEs9(zzz500000, zzz4300000)
new_esEs26(zzz5002, zzz4002, app(app(app(ty_@3, che), chf), chg)) → new_esEs6(zzz5002, zzz4002, che, chf, chg)
new_compare18(zzz500000, zzz4300000, hg, hh) → new_compare25(zzz500000, zzz4300000, new_esEs5(zzz500000, zzz4300000, hg, hh), hg, hh)
new_ltEs17(zzz50000, zzz430000, ce) → new_fsEs(new_compare4(zzz50000, zzz430000, ce))
new_esEs8(GT, LT) → False
new_esEs8(LT, GT) → False
new_compare30(zzz500000, zzz4300000, app(ty_[], cba)) → new_compare4(zzz500000, zzz4300000, cba)
new_compare30(zzz500000, zzz4300000, ty_Double) → new_compare14(zzz500000, zzz4300000)
new_ltEs13(@2(zzz500000, zzz500001), @2(zzz4300000, zzz4300001), bed, bee) → new_pePe(new_lt13(zzz500000, zzz4300000, bed), new_asAs(new_esEs23(zzz500000, zzz4300000, bed), new_ltEs19(zzz500001, zzz4300001, bee)))
new_esEs4(Right(zzz5000), Right(zzz4000), bge, app(app(ty_Either, bgf), bgg)) → new_esEs4(zzz5000, zzz4000, bgf, bgg)
new_esEs25(zzz500000, zzz4300000, app(ty_[], cec)) → new_esEs12(zzz500000, zzz4300000, cec)
new_compare24(zzz500000, zzz4300000, True, hd, he, hf) → EQ
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Int, bbf) → new_ltEs6(zzz500000, zzz4300000)
new_lt20(zzz500001, zzz4300001, ty_Ordering) → new_lt9(zzz500001, zzz4300001)
new_primEqInt(Neg(Succ(zzz50000)), Neg(Succ(zzz40000))) → new_primEqNat0(zzz50000, zzz40000)
new_esEs20(zzz5000, zzz4000, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_compare113(zzz500000, zzz4300000, True, hb, hc) → LT
new_esEs23(zzz500000, zzz4300000, ty_Ordering) → new_esEs8(zzz500000, zzz4300000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(app(ty_Either, bfc), bfd), bfb) → new_esEs4(zzz5000, zzz4000, bfc, bfd)
new_ltEs18(zzz50000, zzz430000, app(app(ty_Either, bda), bbf)) → new_ltEs7(zzz50000, zzz430000, bda, bbf)
new_esEs24(zzz500001, zzz4300001, ty_Bool) → new_esEs14(zzz500001, zzz4300001)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_lt19(zzz500000, zzz4300000, ty_Bool) → new_lt7(zzz500000, zzz4300000)
new_lt19(zzz500000, zzz4300000, ty_Integer) → new_lt10(zzz500000, zzz4300000)
new_ltEs4(Nothing, Nothing, bb) → True
new_lt13(zzz500000, zzz4300000, ty_Float) → new_lt6(zzz500000, zzz4300000)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_@0) → new_ltEs11(zzz500000, zzz4300000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Char, bbf) → new_ltEs5(zzz500000, zzz4300000)
new_lt13(zzz500000, zzz4300000, ty_Int) → new_lt14(zzz500000, zzz4300000)
new_lt6(zzz500000, zzz4300000) → new_esEs8(new_compare16(zzz500000, zzz4300000), LT)
new_compare29(Just(zzz50000), Nothing, False, gh) → GT
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_ltEs7(Right(zzz500000), Left(zzz4300000), bda, bbf) → False
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_esEs24(zzz500001, zzz4300001, app(app(app(ty_@3, cfb), cfc), cfd)) → new_esEs6(zzz500001, zzz4300001, cfb, cfc, cfd)
new_esEs23(zzz500000, zzz4300000, ty_Char) → new_esEs11(zzz500000, zzz4300000)
new_lt13(zzz500000, zzz4300000, ty_Bool) → new_lt7(zzz500000, zzz4300000)
new_esEs19(zzz5000, zzz4000, ty_Bool) → new_esEs14(zzz5000, zzz4000)
new_esEs20(zzz5000, zzz4000, ty_Float) → new_esEs13(zzz5000, zzz4000)
new_compare14(Double(zzz500000, zzz500001), Double(zzz4300000, zzz4300001)) → new_compare8(new_sr0(zzz500000, zzz4300000), new_sr0(zzz500001, zzz4300001))
new_compare12(zzz500000, zzz4300000, hb, hc) → new_compare27(zzz500000, zzz4300000, new_esEs4(zzz500000, zzz4300000, hb, hc), hb, hc)
new_compare8(zzz500, zzz4300) → new_primCmpInt(zzz500, zzz4300)
new_lt19(zzz500000, zzz4300000, ty_Char) → new_lt12(zzz500000, zzz4300000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bda, app(app(app(ty_@3, bdh), bea), beb)) → new_ltEs16(zzz500000, zzz4300000, bdh, bea, beb)
new_primEqInt(Neg(Succ(zzz50000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(zzz40000))) → False
new_compare17(zzz500000, zzz4300000) → new_compare26(zzz500000, zzz4300000, new_esEs14(zzz500000, zzz4300000))
new_esEs8(EQ, EQ) → True
new_lt13(zzz500000, zzz4300000, ty_Double) → new_lt15(zzz500000, zzz4300000)
new_compare111(zzz200, zzz201, True, bbe) → LT
new_esEs20(zzz5000, zzz4000, ty_@0) → new_esEs10(zzz5000, zzz4000)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Char, bfb) → new_esEs11(zzz5000, zzz4000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_ltEs19(zzz500001, zzz4300001, ty_@0) → new_ltEs11(zzz500001, zzz4300001)
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_esEs18(zzz5001, zzz4001, ty_Char) → new_esEs11(zzz5001, zzz4001)
new_compare112(zzz500000, zzz4300000, True) → LT
new_esEs19(zzz5000, zzz4000, ty_Char) → new_esEs11(zzz5000, zzz4000)
new_compare30(zzz500000, zzz4300000, app(app(ty_Either, bhh), caa)) → new_compare12(zzz500000, zzz4300000, bhh, caa)
new_primEqInt(Pos(Succ(zzz50000)), Pos(Succ(zzz40000))) → new_primEqNat0(zzz50000, zzz40000)
new_ltEs18(zzz50000, zzz430000, ty_Double) → new_ltEs8(zzz50000, zzz430000)
new_compare27(zzz500000, zzz4300000, True, hb, hc) → EQ
new_lt10(zzz500000, zzz4300000) → new_esEs8(new_compare9(zzz500000, zzz4300000), LT)
new_esEs24(zzz500001, zzz4300001, app(ty_Ratio, cfa)) → new_esEs16(zzz500001, zzz4300001, cfa)
new_ltEs19(zzz500001, zzz4300001, ty_Bool) → new_ltEs14(zzz500001, zzz4300001)
new_esEs14(False, True) → False
new_esEs14(True, False) → False
new_esEs23(zzz500000, zzz4300000, app(ty_[], cbg)) → new_esEs12(zzz500000, zzz4300000, cbg)
new_ltEs4(Just(zzz500000), Just(zzz4300000), app(app(ty_Either, bc), bd)) → new_ltEs7(zzz500000, zzz4300000, bc, bd)
new_esEs29(zzz500, Just(zzz4300), app(ty_Maybe, cg)) → new_esEs7(zzz500, zzz4300, cg)
new_esEs26(zzz5002, zzz4002, ty_Integer) → new_esEs15(zzz5002, zzz4002)
new_ltEs10(GT, EQ) → False
new_lt17(zzz500000, zzz4300000, cbf) → new_esEs8(new_compare7(zzz500000, zzz4300000, cbf), LT)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Double) → new_ltEs8(zzz500000, zzz4300000)
new_esEs24(zzz500001, zzz4300001, ty_Int) → new_esEs17(zzz500001, zzz4300001)
new_primEqNat0(Succ(zzz50000), Succ(zzz40000)) → new_primEqNat0(zzz50000, zzz40000)
new_ltEs20(zzz500002, zzz4300002, app(ty_[], cgg)) → new_ltEs17(zzz500002, zzz4300002, cgg)
new_esEs27(zzz5001, zzz4001, ty_Ordering) → new_esEs8(zzz5001, zzz4001)
new_ltEs14(False, False) → True
new_compare11(@0, @0) → EQ
new_lt7(zzz500000, zzz4300000) → new_esEs8(new_compare17(zzz500000, zzz4300000), LT)
new_esEs19(zzz5000, zzz4000, app(app(app(ty_@3, ge), gf), gg)) → new_esEs6(zzz5000, zzz4000, ge, gf, gg)
new_ltEs9(zzz50000, zzz430000) → new_fsEs(new_compare9(zzz50000, zzz430000))
new_esEs29(zzz500, Nothing, cf) → False
new_ltEs20(zzz500002, zzz4300002, ty_Char) → new_ltEs5(zzz500002, zzz4300002)
new_compare113(zzz500000, zzz4300000, False, hb, hc) → GT
new_ltEs7(Right(zzz500000), Right(zzz4300000), bda, ty_Bool) → new_ltEs14(zzz500000, zzz4300000)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Int) → new_ltEs6(zzz500000, zzz4300000)
new_primCompAux00(zzz225, LT) → LT
new_ltEs19(zzz500001, zzz4300001, app(ty_[], cda)) → new_ltEs17(zzz500001, zzz4300001, cda)
new_ltEs19(zzz500001, zzz4300001, app(app(ty_Either, cbh), cca)) → new_ltEs7(zzz500001, zzz4300001, cbh, cca)
new_compare7(:%(zzz500000, zzz500001), :%(zzz4300000, zzz4300001), ty_Int) → new_compare8(new_sr0(zzz500000, zzz4300001), new_sr0(zzz4300000, zzz500001))
new_lt20(zzz500001, zzz4300001, ty_@0) → new_lt4(zzz500001, zzz4300001)
new_esEs24(zzz500001, zzz4300001, ty_Ordering) → new_esEs8(zzz500001, zzz4300001)
new_ltEs8(zzz50000, zzz430000) → new_fsEs(new_compare14(zzz50000, zzz430000))
new_esEs7(Nothing, Nothing, cg) → True
new_esEs28(zzz5000, zzz4000, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_esEs8(EQ, LT) → False
new_esEs8(LT, EQ) → False
new_esEs18(zzz5001, zzz4001, app(ty_Maybe, ff)) → new_esEs7(zzz5001, zzz4001, ff)
new_primEqInt(Pos(Succ(zzz50000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(zzz40000))) → False
new_compare30(zzz500000, zzz4300000, ty_Int) → new_compare8(zzz500000, zzz4300000)
new_lt20(zzz500001, zzz4300001, app(ty_Ratio, cfa)) → new_lt17(zzz500001, zzz4300001, cfa)
new_compare24(zzz500000, zzz4300000, False, hd, he, hf) → new_compare110(zzz500000, zzz4300000, new_ltEs16(zzz500000, zzz4300000, hd, he, hf), hd, he, hf)
new_esEs24(zzz500001, zzz4300001, ty_@0) → new_esEs10(zzz500001, zzz4300001)
new_primCmpNat0(Zero, Zero) → EQ
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Integer, bbf) → new_ltEs9(zzz500000, zzz4300000)
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_esEs23(zzz500000, zzz4300000, app(app(ty_@2, hg), hh)) → new_esEs5(zzz500000, zzz4300000, hg, hh)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, ty_@0) → new_esEs10(zzz5000, zzz4000)
new_ltEs10(LT, EQ) → True
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_compare19(zzz500000, zzz4300000, False) → GT
new_esEs27(zzz5001, zzz4001, ty_Double) → new_esEs9(zzz5001, zzz4001)
new_ltEs15(zzz50000, zzz430000, bef) → new_fsEs(new_compare7(zzz50000, zzz430000, bef))
new_esEs23(zzz500000, zzz4300000, ty_Float) → new_esEs13(zzz500000, zzz4300000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Integer) → new_esEs15(zzz5000, zzz4000)
new_compare29(Just(zzz50000), Just(zzz430000), False, gh) → new_compare111(zzz50000, zzz430000, new_ltEs18(zzz50000, zzz430000, gh), gh)
new_primEqInt(Pos(Succ(zzz50000)), Neg(zzz4000)) → False
new_primEqInt(Neg(Succ(zzz50000)), Pos(zzz4000)) → False
new_lt13(zzz500000, zzz4300000, app(ty_Ratio, cbf)) → new_lt17(zzz500000, zzz4300000, cbf)
new_esEs7(Nothing, Just(zzz4000), cg) → False
new_esEs7(Just(zzz5000), Nothing, cg) → False
new_esEs18(zzz5001, zzz4001, app(ty_[], fa)) → new_esEs12(zzz5001, zzz4001, fa)
new_esEs28(zzz5000, zzz4000, ty_Char) → new_esEs11(zzz5000, zzz4000)
new_ltEs10(GT, GT) → True
new_esEs26(zzz5002, zzz4002, app(ty_Ratio, daa)) → new_esEs16(zzz5002, zzz4002, daa)
new_esEs26(zzz5002, zzz4002, ty_Int) → new_esEs17(zzz5002, zzz4002)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, ty_Bool) → new_esEs14(zzz5000, zzz4000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_@0, bbf) → new_ltEs11(zzz500000, zzz4300000)
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primEqInt(Pos(Zero), Neg(Succ(zzz40000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(zzz40000))) → False
new_ltEs6(zzz50000, zzz430000) → new_fsEs(new_compare8(zzz50000, zzz430000))
new_esEs20(zzz5000, zzz4000, app(ty_[], baf)) → new_esEs12(zzz5000, zzz4000, baf)
new_esEs21(zzz5001, zzz4001, ty_Integer) → new_esEs15(zzz5001, zzz4001)
new_compare30(zzz500000, zzz4300000, app(app(ty_@2, cab), cac)) → new_compare18(zzz500000, zzz4300000, cab, cac)
new_primCompAux00(zzz225, EQ) → zzz225
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Double, bfb) → new_esEs9(zzz5000, zzz4000)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Integer, bfb) → new_esEs15(zzz5000, zzz4000)
new_esEs18(zzz5001, zzz4001, ty_Int) → new_esEs17(zzz5001, zzz4001)
new_lt16(zzz500000, zzz4300000, hg, hh) → new_esEs8(new_compare18(zzz500000, zzz4300000, hg, hh), LT)
new_esEs8(GT, EQ) → False
new_esEs8(EQ, GT) → False
new_esEs29(zzz500, Just(zzz4300), app(app(ty_@2, ec), ed)) → new_esEs5(zzz500, zzz4300, ec, ed)
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Double) → new_esEs9(zzz5000, zzz4000)
new_esEs26(zzz5002, zzz4002, ty_Char) → new_esEs11(zzz5002, zzz4002)
new_esEs27(zzz5001, zzz4001, app(ty_Ratio, dbc)) → new_esEs16(zzz5001, zzz4001, dbc)
new_esEs26(zzz5002, zzz4002, app(app(ty_@2, chb), chc)) → new_esEs5(zzz5002, zzz4002, chb, chc)
new_esEs29(zzz500, Just(zzz4300), ty_Bool) → new_esEs14(zzz500, zzz4300)
new_ltEs19(zzz500001, zzz4300001, app(app(ty_@2, ccb), ccc)) → new_ltEs13(zzz500001, zzz4300001, ccb, ccc)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Bool) → new_ltEs14(zzz500000, zzz4300000)
new_not(False) → True
new_esEs24(zzz500001, zzz4300001, ty_Double) → new_esEs9(zzz500001, zzz4300001)
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_ltEs5(zzz50000, zzz430000) → new_fsEs(new_compare10(zzz50000, zzz430000))
new_esEs25(zzz500000, zzz4300000, ty_Integer) → new_esEs15(zzz500000, zzz4300000)
new_esEs26(zzz5002, zzz4002, ty_Bool) → new_esEs14(zzz5002, zzz4002)
new_ltEs19(zzz500001, zzz4300001, ty_Int) → new_ltEs6(zzz500001, zzz4300001)
new_esEs25(zzz500000, zzz4300000, app(ty_Ratio, cdg)) → new_esEs16(zzz500000, zzz4300000, cdg)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, ty_Int) → new_esEs17(zzz5000, zzz4000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Bool, bbf) → new_ltEs14(zzz500000, zzz4300000)
new_esEs28(zzz5000, zzz4000, app(app(ty_@2, dbf), dbg)) → new_esEs5(zzz5000, zzz4000, dbf, dbg)
new_esEs23(zzz500000, zzz4300000, ty_@0) → new_esEs10(zzz500000, zzz4300000)
new_compare30(zzz500000, zzz4300000, ty_@0) → new_compare11(zzz500000, zzz4300000)
new_esEs18(zzz5001, zzz4001, app(app(ty_Either, ee), ef)) → new_esEs4(zzz5001, zzz4001, ee, ef)
new_lt18(zzz500000, zzz4300000, cbg) → new_esEs8(new_compare4(zzz500000, zzz4300000, cbg), LT)
new_ltEs18(zzz50000, zzz430000, ty_Int) → new_ltEs6(zzz50000, zzz430000)
new_esEs22(zzz5000, zzz4000, ty_Int) → new_esEs17(zzz5000, zzz4000)
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_esEs6(@3(zzz5000, zzz5001, zzz5002), @3(zzz4000, zzz4001, zzz4002), cbb, cbc, cbd) → new_asAs(new_esEs28(zzz5000, zzz4000, cbb), new_asAs(new_esEs27(zzz5001, zzz4001, cbc), new_esEs26(zzz5002, zzz4002, cbd)))
new_esEs28(zzz5000, zzz4000, app(ty_Maybe, dcd)) → new_esEs7(zzz5000, zzz4000, dcd)
new_esEs28(zzz5000, zzz4000, ty_Double) → new_esEs9(zzz5000, zzz4000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bda, ty_Double) → new_ltEs8(zzz500000, zzz4300000)
new_lt20(zzz500001, zzz4300001, ty_Double) → new_lt15(zzz500001, zzz4300001)
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_lt20(zzz500001, zzz4300001, ty_Integer) → new_lt10(zzz500001, zzz4300001)
new_esEs26(zzz5002, zzz4002, ty_@0) → new_esEs10(zzz5002, zzz4002)
new_esEs18(zzz5001, zzz4001, ty_Float) → new_esEs13(zzz5001, zzz4001)
new_compare25(zzz500000, zzz4300000, False, hg, hh) → new_compare15(zzz500000, zzz4300000, new_ltEs13(zzz500000, zzz4300000, hg, hh), hg, hh)
new_esEs23(zzz500000, zzz4300000, app(app(ty_Either, hb), hc)) → new_esEs4(zzz500000, zzz4300000, hb, hc)
new_esEs20(zzz5000, zzz4000, ty_Char) → new_esEs11(zzz5000, zzz4000)
new_lt19(zzz500000, zzz4300000, app(ty_Maybe, cdf)) → new_lt11(zzz500000, zzz4300000, cdf)
new_esEs4(Left(zzz5000), Left(zzz4000), app(ty_Maybe, bgc), bfb) → new_esEs7(zzz5000, zzz4000, bgc)
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_esEs20(zzz5000, zzz4000, ty_Integer) → new_esEs15(zzz5000, zzz4000)
new_primEqNat0(Zero, Succ(zzz40000)) → False
new_primEqNat0(Succ(zzz50000), Zero) → False
new_esEs18(zzz5001, zzz4001, ty_Integer) → new_esEs15(zzz5001, zzz4001)
new_esEs17(zzz500, zzz400) → new_primEqInt(zzz500, zzz400)
new_lt5(zzz500000, zzz4300000, hb, hc) → new_esEs8(new_compare12(zzz500000, zzz4300000, hb, hc), LT)
new_compare25(zzz500000, zzz4300000, True, hg, hh) → EQ
new_esEs20(zzz5000, zzz4000, ty_Bool) → new_esEs14(zzz5000, zzz4000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), app(app(ty_Either, bbg), bbh), bbf) → new_ltEs7(zzz500000, zzz4300000, bbg, bbh)
new_ltEs14(True, True) → True
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs24(zzz500001, zzz4300001, app(app(ty_Either, ced), cee)) → new_esEs4(zzz500001, zzz4300001, ced, cee)
new_esEs28(zzz5000, zzz4000, app(app(app(ty_@3, dca), dcb), dcc)) → new_esEs6(zzz5000, zzz4000, dca, dcb, dcc)
new_compare30(zzz500000, zzz4300000, ty_Bool) → new_compare17(zzz500000, zzz4300000)
new_esEs27(zzz5001, zzz4001, app(app(ty_Either, dab), dac)) → new_esEs4(zzz5001, zzz4001, dab, dac)
new_esEs27(zzz5001, zzz4001, app(app(app(ty_@3, dag), dah), dba)) → new_esEs6(zzz5001, zzz4001, dag, dah, dba)
new_compare4(:(zzz500000, zzz500001), [], ce) → GT
new_ltEs18(zzz50000, zzz430000, app(ty_[], ce)) → new_ltEs17(zzz50000, zzz430000, ce)
new_esEs27(zzz5001, zzz4001, app(app(ty_@2, dad), dae)) → new_esEs5(zzz5001, zzz4001, dad, dae)
new_esEs27(zzz5001, zzz4001, ty_Int) → new_esEs17(zzz5001, zzz4001)
new_esEs23(zzz500000, zzz4300000, ty_Int) → new_esEs17(zzz500000, zzz4300000)
new_lt13(zzz500000, zzz4300000, ty_@0) → new_lt4(zzz500000, zzz4300000)
new_compare30(zzz500000, zzz4300000, ty_Char) → new_compare10(zzz500000, zzz4300000)
new_esEs29(zzz500, Just(zzz4300), ty_@0) → new_esEs10(zzz500, zzz4300)
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_compare4([], :(zzz4300000, zzz4300001), ce) → LT
new_sr0(zzz5000, zzz4000) → new_primMulInt(zzz5000, zzz4000)
new_lt19(zzz500000, zzz4300000, app(ty_[], cec)) → new_lt18(zzz500000, zzz4300000, cec)
new_compare15(zzz500000, zzz4300000, False, hg, hh) → GT
new_ltEs18(zzz50000, zzz430000, ty_Float) → new_ltEs12(zzz50000, zzz430000)
new_ltEs18(zzz50000, zzz430000, ty_Integer) → new_ltEs9(zzz50000, zzz430000)
new_ltEs19(zzz500001, zzz4300001, ty_Double) → new_ltEs8(zzz500001, zzz4300001)
new_compare30(zzz500000, zzz4300000, ty_Float) → new_compare16(zzz500000, zzz4300000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), app(ty_[], bch), bbf) → new_ltEs17(zzz500000, zzz4300000, bch)
new_esEs11(Char(zzz5000), Char(zzz4000)) → new_primEqNat0(zzz5000, zzz4000)
new_esEs7(Just(zzz5000), Just(zzz4000), app(app(app(ty_@3, df), dg), dh)) → new_esEs6(zzz5000, zzz4000, df, dg, dh)
new_esEs25(zzz500000, zzz4300000, app(ty_Maybe, cdf)) → new_esEs7(zzz500000, zzz4300000, cdf)
new_compare29(Nothing, Nothing, False, gh) → LT
new_esEs23(zzz500000, zzz4300000, app(ty_Ratio, cbf)) → new_esEs16(zzz500000, zzz4300000, cbf)
new_lt13(zzz500000, zzz4300000, app(app(ty_Either, hb), hc)) → new_lt5(zzz500000, zzz4300000, hb, hc)
new_esEs16(:%(zzz5000, zzz5001), :%(zzz4000, zzz4001), bbd) → new_asAs(new_esEs22(zzz5000, zzz4000, bbd), new_esEs21(zzz5001, zzz4001, bbd))
new_ltEs4(Just(zzz500000), Just(zzz4300000), app(ty_Maybe, bg)) → new_ltEs4(zzz500000, zzz4300000, bg)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Float) → new_ltEs12(zzz500000, zzz4300000)
new_primCompAux0(zzz500000, zzz4300000, zzz220, ce) → new_primCompAux00(zzz220, new_compare30(zzz500000, zzz4300000, ce))
new_esEs19(zzz5000, zzz4000, app(app(ty_@2, gb), gc)) → new_esEs5(zzz5000, zzz4000, gb, gc)
new_esEs19(zzz5000, zzz4000, app(ty_Ratio, ha)) → new_esEs16(zzz5000, zzz4000, ha)
new_esEs10(@0, @0) → True
new_compare29(zzz5000, zzz43000, True, gh) → EQ
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs27(zzz5001, zzz4001, ty_Float) → new_esEs13(zzz5001, zzz4001)
new_lt13(zzz500000, zzz4300000, ty_Integer) → new_lt10(zzz500000, zzz4300000)
new_compare28(zzz5000, zzz43000, gh) → new_compare29(zzz5000, zzz43000, new_esEs7(zzz5000, zzz43000, gh), gh)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, app(app(ty_@2, bgh), bha)) → new_esEs5(zzz5000, zzz4000, bgh, bha)
new_esEs24(zzz500001, zzz4300001, ty_Char) → new_esEs11(zzz500001, zzz4300001)
new_esEs28(zzz5000, zzz4000, ty_@0) → new_esEs10(zzz5000, zzz4000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bda, app(app(ty_Either, bdb), bdc)) → new_ltEs7(zzz500000, zzz4300000, bdb, bdc)
new_esEs28(zzz5000, zzz4000, ty_Int) → new_esEs17(zzz5000, zzz4000)
new_compare7(:%(zzz500000, zzz500001), :%(zzz4300000, zzz4300001), ty_Integer) → new_compare9(new_sr(zzz500000, zzz4300001), new_sr(zzz4300000, zzz500001))
new_compare9(Integer(zzz500000), Integer(zzz4300000)) → new_primCmpInt(zzz500000, zzz4300000)
new_compare23(zzz500000, zzz4300000, False) → new_compare112(zzz500000, zzz4300000, new_ltEs10(zzz500000, zzz4300000))
new_asAs(False, zzz207) → False
new_esEs29(zzz500, Just(zzz4300), ty_Float) → new_esEs13(zzz500, zzz4300)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_@0, bfb) → new_esEs10(zzz5000, zzz4000)
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_esEs26(zzz5002, zzz4002, ty_Double) → new_esEs9(zzz5002, zzz4002)
new_ltEs10(LT, GT) → True
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_ltEs4(Just(zzz500000), Just(zzz4300000), app(ty_Ratio, bh)) → new_ltEs15(zzz500000, zzz4300000, bh)
new_esEs23(zzz500000, zzz4300000, app(app(app(ty_@3, hd), he), hf)) → new_esEs6(zzz500000, zzz4300000, hd, he, hf)
new_lt8(zzz500000, zzz4300000, hd, he, hf) → new_esEs8(new_compare13(zzz500000, zzz4300000, hd, he, hf), LT)
new_lt11(zzz5000, zzz43000, gh) → new_esEs8(new_compare28(zzz5000, zzz43000, gh), LT)
new_esEs29(zzz500, Just(zzz4300), ty_Int) → new_esEs17(zzz500, zzz4300)
new_esEs26(zzz5002, zzz4002, app(ty_[], chd)) → new_esEs12(zzz5002, zzz4002, chd)
new_compare4(:(zzz500000, zzz500001), :(zzz4300000, zzz4300001), ce) → new_primCompAux0(zzz500000, zzz4300000, new_compare4(zzz500001, zzz4300001, ce), ce)
new_compare16(Float(zzz500000, zzz500001), Float(zzz4300000, zzz4300001)) → new_compare8(new_sr0(zzz500000, zzz4300000), new_sr0(zzz500001, zzz4300001))
new_esEs26(zzz5002, zzz4002, app(ty_Maybe, chh)) → new_esEs7(zzz5002, zzz4002, chh)
new_esEs28(zzz5000, zzz4000, ty_Bool) → new_esEs14(zzz5000, zzz4000)
new_compare110(zzz500000, zzz4300000, True, hd, he, hf) → LT
new_lt19(zzz500000, zzz4300000, app(app(ty_Either, cdb), cdc)) → new_lt5(zzz500000, zzz4300000, cdb, cdc)
new_ltEs18(zzz50000, zzz430000, ty_Bool) → new_ltEs14(zzz50000, zzz430000)
new_esEs28(zzz5000, zzz4000, ty_Integer) → new_esEs15(zzz5000, zzz4000)
new_esEs18(zzz5001, zzz4001, ty_Ordering) → new_esEs8(zzz5001, zzz4001)
new_esEs19(zzz5000, zzz4000, ty_Double) → new_esEs9(zzz5000, zzz4000)
new_esEs5(@2(zzz5000, zzz5001), @2(zzz4000, zzz4001), ec, ed) → new_asAs(new_esEs19(zzz5000, zzz4000, ec), new_esEs18(zzz5001, zzz4001, ed))
new_compare26(zzz500000, zzz4300000, False) → new_compare19(zzz500000, zzz4300000, new_ltEs14(zzz500000, zzz4300000))
new_lt20(zzz500001, zzz4300001, app(app(ty_@2, cef), ceg)) → new_lt16(zzz500001, zzz4300001, cef, ceg)
new_esEs28(zzz5000, zzz4000, app(app(ty_Either, dbd), dbe)) → new_esEs4(zzz5000, zzz4000, dbd, dbe)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, app(ty_Maybe, bhf)) → new_esEs7(zzz5000, zzz4000, bhf)
new_esEs7(Just(zzz5000), Just(zzz4000), ty_@0) → new_esEs10(zzz5000, zzz4000)
new_ltEs18(zzz50000, zzz430000, ty_Char) → new_ltEs5(zzz50000, zzz430000)
new_esEs28(zzz5000, zzz4000, ty_Float) → new_esEs13(zzz5000, zzz4000)
new_lt13(zzz500000, zzz4300000, ty_Ordering) → new_lt9(zzz500000, zzz4300000)
new_esEs25(zzz500000, zzz4300000, app(app(app(ty_@3, cdh), cea), ceb)) → new_esEs6(zzz500000, zzz4300000, cdh, cea, ceb)
new_ltEs10(EQ, EQ) → True
new_ltEs18(zzz50000, zzz430000, app(app(ty_@2, bed), bee)) → new_ltEs13(zzz50000, zzz430000, bed, bee)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Int, bfb) → new_esEs17(zzz5000, zzz4000)
new_esEs23(zzz500000, zzz4300000, ty_Integer) → new_esEs15(zzz500000, zzz4300000)
new_ltEs10(LT, LT) → True
new_esEs14(True, True) → True
new_compare111(zzz200, zzz201, False, bbe) → GT
new_esEs27(zzz5001, zzz4001, ty_Bool) → new_esEs14(zzz5001, zzz4001)
new_esEs7(Just(zzz5000), Just(zzz4000), app(app(ty_Either, da), db)) → new_esEs4(zzz5000, zzz4000, da, db)
new_compare10(Char(zzz500000), Char(zzz4300000)) → new_primCmpNat0(zzz500000, zzz4300000)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Float, bfb) → new_esEs13(zzz5000, zzz4000)
new_lt13(zzz500000, zzz4300000, app(app(ty_@2, hg), hh)) → new_lt16(zzz500000, zzz4300000, hg, hh)
new_ltEs7(Left(zzz500000), Left(zzz4300000), app(app(ty_@2, bca), bcb), bbf) → new_ltEs13(zzz500000, zzz4300000, bca, bcb)
new_esEs7(Just(zzz5000), Just(zzz4000), app(ty_Ratio, eb)) → new_esEs16(zzz5000, zzz4000, eb)
new_lt13(zzz500000, zzz4300000, app(ty_Maybe, cbe)) → new_lt11(zzz500000, zzz4300000, cbe)
new_ltEs20(zzz500002, zzz4300002, app(app(ty_Either, cff), cfg)) → new_ltEs7(zzz500002, zzz4300002, cff, cfg)
new_esEs18(zzz5001, zzz4001, ty_@0) → new_esEs10(zzz5001, zzz4001)
new_ltEs16(@3(zzz500000, zzz500001, zzz500002), @3(zzz4300000, zzz4300001, zzz4300002), beg, beh, bfa) → new_pePe(new_lt19(zzz500000, zzz4300000, beg), new_asAs(new_esEs25(zzz500000, zzz4300000, beg), new_pePe(new_lt20(zzz500001, zzz4300001, beh), new_asAs(new_esEs24(zzz500001, zzz4300001, beh), new_ltEs20(zzz500002, zzz4300002, bfa)))))
new_esEs4(Right(zzz5000), Right(zzz4000), bge, ty_Double) → new_esEs9(zzz5000, zzz4000)
new_ltEs14(True, False) → False
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_esEs20(zzz5000, zzz4000, ty_Int) → new_esEs17(zzz5000, zzz4000)
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_esEs25(zzz500000, zzz4300000, app(app(ty_@2, cdd), cde)) → new_esEs5(zzz500000, zzz4300000, cdd, cde)
new_ltEs20(zzz500002, zzz4300002, ty_Double) → new_ltEs8(zzz500002, zzz4300002)
new_ltEs7(Left(zzz500000), Left(zzz4300000), app(ty_Ratio, bcd), bbf) → new_ltEs15(zzz500000, zzz4300000, bcd)
new_ltEs19(zzz500001, zzz4300001, app(app(app(ty_@3, ccf), ccg), cch)) → new_ltEs16(zzz500001, zzz4300001, ccf, ccg, cch)
new_ltEs20(zzz500002, zzz4300002, app(app(app(ty_@3, cgd), cge), cgf)) → new_ltEs16(zzz500002, zzz4300002, cgd, cge, cgf)
new_compare112(zzz500000, zzz4300000, False) → GT
new_esEs29(zzz500, Just(zzz4300), app(app(app(ty_@3, cbb), cbc), cbd)) → new_esEs6(zzz500, zzz4300, cbb, cbc, cbd)
new_ltEs10(EQ, LT) → False
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Float) → new_esEs13(zzz5000, zzz4000)
new_esEs14(False, False) → True
new_esEs7(Just(zzz5000), Just(zzz4000), app(app(ty_@2, dc), dd)) → new_esEs5(zzz5000, zzz4000, dc, dd)
new_lt20(zzz500001, zzz4300001, ty_Char) → new_lt12(zzz500001, zzz4300001)
new_esEs29(zzz500, Just(zzz4300), app(app(ty_Either, bge), bfb)) → new_esEs4(zzz500, zzz4300, bge, bfb)
new_lt9(zzz500000, zzz4300000) → new_esEs8(new_compare6(zzz500000, zzz4300000), LT)
new_ltEs10(GT, LT) → False
new_esEs18(zzz5001, zzz4001, ty_Bool) → new_esEs14(zzz5001, zzz4001)
new_esEs22(zzz5000, zzz4000, ty_Integer) → new_esEs15(zzz5000, zzz4000)
new_primPlusNat1(Zero, Zero) → Zero
new_compare30(zzz500000, zzz4300000, app(app(app(ty_@3, caf), cag), cah)) → new_compare13(zzz500000, zzz4300000, caf, cag, cah)
new_esEs19(zzz5000, zzz4000, ty_Integer) → new_esEs15(zzz5000, zzz4000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(ty_[], bfg), bfb) → new_esEs12(zzz5000, zzz4000, bfg)
new_esEs26(zzz5002, zzz4002, app(app(ty_Either, cgh), cha)) → new_esEs4(zzz5002, zzz4002, cgh, cha)
new_asAs(True, zzz207) → zzz207
new_esEs28(zzz5000, zzz4000, app(ty_[], dbh)) → new_esEs12(zzz5000, zzz4000, dbh)
new_esEs27(zzz5001, zzz4001, app(ty_[], daf)) → new_esEs12(zzz5001, zzz4001, daf)
new_esEs19(zzz5000, zzz4000, app(app(ty_Either, fh), ga)) → new_esEs4(zzz5000, zzz4000, fh, ga)
new_ltEs4(Just(zzz500000), Nothing, bb) → False
new_esEs20(zzz5000, zzz4000, ty_Double) → new_esEs9(zzz5000, zzz4000)
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_ltEs4(Just(zzz500000), Just(zzz4300000), app(ty_[], cd)) → new_ltEs17(zzz500000, zzz4300000, cd)
new_esEs29(zzz500, Just(zzz4300), ty_Ordering) → new_esEs8(zzz500, zzz4300)
new_esEs4(Right(zzz5000), Left(zzz4000), bge, bfb) → False
new_esEs4(Left(zzz5000), Right(zzz4000), bge, bfb) → False
new_ltEs19(zzz500001, zzz4300001, ty_Float) → new_ltEs12(zzz500001, zzz4300001)
new_ltEs20(zzz500002, zzz4300002, app(ty_Maybe, cgb)) → new_ltEs4(zzz500002, zzz4300002, cgb)
new_esEs4(Left(zzz5000), Left(zzz4000), app(app(app(ty_@3, bfh), bga), bgb), bfb) → new_esEs6(zzz5000, zzz4000, bfh, bga, bgb)
new_ltEs19(zzz500001, zzz4300001, ty_Char) → new_ltEs5(zzz500001, zzz4300001)
new_fsEs(zzz210) → new_not(new_esEs8(zzz210, GT))
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Double, bbf) → new_ltEs8(zzz500000, zzz4300000)
new_esEs19(zzz5000, zzz4000, ty_@0) → new_esEs10(zzz5000, zzz4000)
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Bool) → new_esEs14(zzz5000, zzz4000)
new_esEs24(zzz500001, zzz4300001, ty_Float) → new_esEs13(zzz500001, zzz4300001)
new_ltEs11(zzz50000, zzz430000) → new_fsEs(new_compare11(zzz50000, zzz430000))
new_lt20(zzz500001, zzz4300001, ty_Int) → new_lt14(zzz500001, zzz4300001)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, ty_Float) → new_esEs13(zzz5000, zzz4000)
new_esEs19(zzz5000, zzz4000, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_ltEs20(zzz500002, zzz4300002, app(app(ty_@2, cfh), cga)) → new_ltEs13(zzz500002, zzz4300002, cfh, cga)
new_esEs27(zzz5001, zzz4001, ty_Char) → new_esEs11(zzz5001, zzz4001)
new_ltEs20(zzz500002, zzz4300002, ty_Int) → new_ltEs6(zzz500002, zzz4300002)
new_compare110(zzz500000, zzz4300000, False, hd, he, hf) → GT
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Char) → new_ltEs5(zzz500000, zzz4300000)
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Char) → new_esEs11(zzz5000, zzz4000)
new_primCompAux00(zzz225, GT) → GT
new_ltEs20(zzz500002, zzz4300002, ty_Integer) → new_ltEs9(zzz500002, zzz4300002)
new_compare31(zzz500, zzz430, cf) → new_compare29(Just(zzz500), zzz430, new_esEs29(zzz500, zzz430, cf), cf)
new_esEs29(zzz500, Just(zzz4300), app(ty_Ratio, bbd)) → new_esEs16(zzz500, zzz4300, bbd)
new_gt0(zzz500, zzz430, cf) → new_esEs8(new_compare31(zzz500, zzz430, cf), GT)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_ltEs7(Right(zzz500000), Right(zzz4300000), bda, app(ty_Maybe, bdf)) → new_ltEs4(zzz500000, zzz4300000, bdf)
new_lt19(zzz500000, zzz4300000, ty_Int) → new_lt14(zzz500000, zzz4300000)
new_ltEs4(Just(zzz500000), Just(zzz4300000), app(app(app(ty_@3, ca), cb), cc)) → new_ltEs16(zzz500000, zzz4300000, ca, cb, cc)
new_ltEs18(zzz50000, zzz430000, ty_Ordering) → new_ltEs10(zzz50000, zzz430000)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Integer) → new_ltEs9(zzz500000, zzz4300000)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_compare30(zzz500000, zzz4300000, ty_Ordering) → new_compare6(zzz500000, zzz4300000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bda, ty_Float) → new_ltEs12(zzz500000, zzz4300000)
new_esEs27(zzz5001, zzz4001, ty_Integer) → new_esEs15(zzz5001, zzz4001)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_ltEs7(Right(zzz500000), Right(zzz4300000), bda, ty_Int) → new_ltEs6(zzz500000, zzz4300000)
new_not(True) → False

The set Q consists of the following terms:

new_compare30(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_compare23(x0, x1, True)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_lt14(x0, x1)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, app(ty_[], x2))
new_compare27(x0, x1, True, x2, x3)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs7(Left(x0), Left(x1), ty_Integer, x2)
new_asAs(True, x0)
new_compare19(x0, x1, True)
new_ltEs7(Left(x0), Left(x1), ty_Bool, x2)
new_compare18(x0, x1, x2, x3)
new_esEs18(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_@0)
new_ltEs7(Left(x0), Left(x1), ty_Double, x2)
new_ltEs18(x0, x1, ty_Bool)
new_ltEs7(Right(x0), Right(x1), x2, ty_Int)
new_esEs26(x0, x1, ty_Ordering)
new_esEs18(x0, x1, ty_Int)
new_primPlusNat1(Zero, Succ(x0))
new_compare30(x0, x1, ty_@0)
new_lt20(x0, x1, ty_Ordering)
new_esEs9(Double(x0, x1), Double(x2, x3))
new_primMulNat0(Succ(x0), Zero)
new_primCompAux0(x0, x1, x2, x3)
new_ltEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt19(x0, x1, ty_Double)
new_primMulInt(Neg(x0), Neg(x1))
new_compare111(x0, x1, True, x2)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1, ty_Integer)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, ty_@0)
new_primPlusNat1(Succ(x0), Zero)
new_esEs21(x0, x1, ty_Int)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare4(:(x0, x1), :(x2, x3), x4)
new_ltEs10(LT, LT)
new_esEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_lt19(x0, x1, app(ty_Ratio, x2))
new_ltEs16(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_compare113(x0, x1, True, x2, x3)
new_esEs23(x0, x1, ty_Bool)
new_esEs29(x0, Just(x1), app(ty_Ratio, x2))
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs27(x0, x1, ty_Int)
new_esEs4(Right(x0), Left(x1), x2, x3)
new_esEs4(Left(x0), Right(x1), x2, x3)
new_esEs18(x0, x1, ty_Char)
new_esEs29(x0, Just(x1), ty_Bool)
new_esEs24(x0, x1, ty_Char)
new_ltEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(True, False)
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs14(False, True)
new_esEs25(x0, x1, ty_Double)
new_pePe(False, x0)
new_lt19(x0, x1, app(ty_[], x2))
new_esEs19(x0, x1, ty_Char)
new_esEs25(x0, x1, ty_Char)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_ltEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs7(Just(x0), Just(x1), ty_Double)
new_esEs8(GT, GT)
new_esEs23(x0, x1, ty_@0)
new_compare4([], :(x0, x1), x2)
new_ltEs7(Left(x0), Left(x1), ty_Int, x2)
new_lt9(x0, x1)
new_lt19(x0, x1, ty_Ordering)
new_esEs11(Char(x0), Char(x1))
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs29(x0, Just(x1), ty_Integer)
new_esEs7(Nothing, Just(x0), x1)
new_esEs4(Left(x0), Left(x1), ty_Int, x2)
new_esEs8(LT, LT)
new_sr0(x0, x1)
new_compare6(x0, x1)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs7(Left(x0), Left(x1), ty_Float, x2)
new_compare30(x0, x1, ty_Double)
new_esEs7(Just(x0), Just(x1), ty_Char)
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, app(ty_[], x2))
new_compare19(x0, x1, False)
new_ltEs4(Nothing, Nothing, x0)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs26(x0, x1, ty_Double)
new_esEs29(x0, Just(x1), ty_@0)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_compare4([], [], x0)
new_esEs17(x0, x1)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, ty_Char)
new_compare113(x0, x1, False, x2, x3)
new_esEs14(True, True)
new_compare26(x0, x1, True)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Char)
new_esEs18(x0, x1, app(ty_Ratio, x2))
new_esEs12(:(x0, x1), [], x2)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare112(x0, x1, False)
new_compare15(x0, x1, True, x2, x3)
new_esEs18(x0, x1, ty_Bool)
new_esEs20(x0, x1, ty_Float)
new_primEqNat0(Zero, Zero)
new_ltEs4(Just(x0), Just(x1), ty_Double)
new_compare30(x0, x1, ty_Char)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_ltEs7(Right(x0), Right(x1), x2, ty_@0)
new_esEs20(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Double)
new_lt19(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_@0)
new_lt13(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_Integer)
new_compare17(x0, x1)
new_ltEs17(x0, x1, x2)
new_primPlusNat0(Zero, x0)
new_ltEs20(x0, x1, ty_Int)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs7(Right(x0), Right(x1), x2, ty_Integer)
new_compare110(x0, x1, False, x2, x3, x4)
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_primMulNat0(Zero, Zero)
new_esEs4(Right(x0), Right(x1), x2, ty_Float)
new_primCmpNat0(Succ(x0), Zero)
new_compare16(Float(x0, x1), Float(x2, x3))
new_ltEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs20(x0, x1, ty_Integer)
new_esEs29(x0, Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare30(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, ty_Integer)
new_ltEs10(EQ, LT)
new_ltEs10(LT, EQ)
new_lt4(x0, x1)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_lt19(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs19(x0, x1, ty_Bool)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Just(x0), Nothing, x1)
new_esEs28(x0, x1, ty_@0)
new_primMulNat0(Succ(x0), Succ(x1))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_lt18(x0, x1, x2)
new_lt7(x0, x1)
new_esEs23(x0, x1, ty_Float)
new_ltEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Int)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, ty_Double)
new_ltEs18(x0, x1, ty_@0)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs23(x0, x1, ty_Char)
new_ltEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs24(x0, x1, ty_Int)
new_compare9(Integer(x0), Integer(x1))
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs20(x0, x1, ty_Ordering)
new_compare4(:(x0, x1), [], x2)
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_esEs24(x0, x1, ty_Bool)
new_ltEs13(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, ty_Char)
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs20(x0, x1, ty_Ordering)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_fsEs(x0)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_compare111(x0, x1, False, x2)
new_ltEs11(x0, x1)
new_esEs23(x0, x1, ty_Double)
new_lt13(x0, x1, ty_@0)
new_lt17(x0, x1, x2)
new_esEs7(Just(x0), Just(x1), ty_Int)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_compare26(x0, x1, False)
new_esEs29(x0, Just(x1), ty_Char)
new_ltEs18(x0, x1, ty_Double)
new_esEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs25(x0, x1, ty_Bool)
new_primPlusNat1(Zero, Zero)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, ty_Float)
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_gt0(x0, x1, x2)
new_esEs29(x0, Just(x1), ty_Ordering)
new_compare29(x0, x1, True, x2)
new_lt12(x0, x1)
new_compare7(:%(x0, x1), :%(x2, x3), ty_Int)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs7(Nothing, Nothing, x0)
new_compare24(x0, x1, False, x2, x3, x4)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(Just(x0), Just(x1), ty_Int)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_compare11(@0, @0)
new_primMulNat0(Zero, Succ(x0))
new_esEs4(Right(x0), Right(x1), x2, ty_Integer)
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs26(x0, x1, ty_Bool)
new_asAs(False, x0)
new_esEs25(x0, x1, app(ty_[], x2))
new_ltEs4(Just(x0), Just(x1), ty_Bool)
new_compare31(x0, x1, x2)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs8(x0, x1)
new_ltEs18(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Float)
new_lt13(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, ty_Double)
new_ltEs19(x0, x1, ty_Ordering)
new_ltEs4(Just(x0), Just(x1), ty_Ordering)
new_esEs4(Left(x0), Left(x1), ty_@0, x2)
new_esEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs18(x0, x1, ty_Double)
new_ltEs10(GT, LT)
new_ltEs10(LT, GT)
new_esEs4(Left(x0), Left(x1), ty_Double, x2)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_compare29(Nothing, Nothing, False, x0)
new_esEs28(x0, x1, ty_Double)
new_lt11(x0, x1, x2)
new_esEs10(@0, @0)
new_compare14(Double(x0, x1), Double(x2, x3))
new_esEs29(x0, Just(x1), app(ty_Maybe, x2))
new_ltEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_compare30(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_Integer)
new_ltEs18(x0, x1, ty_Float)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs7(Left(x0), Left(x1), ty_Char, x2)
new_ltEs7(Right(x0), Right(x1), x2, ty_Char)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_compare28(x0, x1, x2)
new_compare8(x0, x1)
new_esEs20(x0, x1, ty_Char)
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, ty_Integer)
new_pePe(True, x0)
new_esEs27(x0, x1, ty_Float)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_primCompAux00(x0, EQ)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_lt19(x0, x1, ty_Float)
new_primEqNat0(Succ(x0), Zero)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, ty_Int)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs18(x0, x1, ty_Ordering)
new_esEs25(x0, x1, ty_Int)
new_ltEs15(x0, x1, x2)
new_ltEs4(Just(x0), Just(x1), ty_@0)
new_compare23(x0, x1, False)
new_compare30(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_ltEs4(Just(x0), Nothing, x1)
new_esEs8(EQ, EQ)
new_compare112(x0, x1, True)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs4(Right(x0), Right(x1), x2, ty_Int)
new_esEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs19(x0, x1, ty_Double)
new_esEs13(Float(x0, x1), Float(x2, x3))
new_esEs29(x0, Just(x1), ty_Double)
new_ltEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primEqInt(Neg(Zero), Neg(Zero))
new_lt13(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_Char)
new_esEs15(Integer(x0), Integer(x1))
new_ltEs12(x0, x1)
new_ltEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_lt20(x0, x1, ty_@0)
new_esEs18(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, ty_@0)
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs14(True, False)
new_esEs14(False, True)
new_ltEs4(Just(x0), Just(x1), ty_Float)
new_ltEs6(x0, x1)
new_esEs29(x0, Just(x1), app(ty_[], x2))
new_esEs22(x0, x1, ty_Int)
new_esEs29(x0, Nothing, x1)
new_esEs20(x0, x1, ty_Double)
new_ltEs9(x0, x1)
new_esEs12([], [], x0)
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs19(x0, x1, ty_@0)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_lt19(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Ordering)
new_esEs27(x0, x1, ty_Integer)
new_esEs29(x0, Just(x1), ty_Float)
new_lt16(x0, x1, x2, x3)
new_lt13(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Float)
new_compare25(x0, x1, False, x2, x3)
new_esEs19(x0, x1, app(ty_[], x2))
new_compare30(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Integer)
new_primCmpNat0(Succ(x0), Succ(x1))
new_lt19(x0, x1, ty_Char)
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_esEs20(x0, x1, ty_Integer)
new_esEs28(x0, x1, ty_Ordering)
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_esEs21(x0, x1, ty_Integer)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_esEs4(Right(x0), Right(x1), x2, ty_Double)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_compare29(Nothing, Just(x0), False, x1)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Bool)
new_compare12(x0, x1, x2, x3)
new_primPlusNat0(Succ(x0), x1)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs29(x0, Just(x1), app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, ty_@0)
new_ltEs7(Right(x0), Right(x1), x2, ty_Float)
new_ltEs18(x0, x1, ty_Integer)
new_compare30(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs7(Just(x0), Just(x1), ty_Float)
new_esEs19(x0, x1, ty_Float)
new_ltEs20(x0, x1, ty_Bool)
new_primCmpNat0(Zero, Zero)
new_esEs4(Left(x0), Left(x1), ty_Integer, x2)
new_esEs19(x0, x1, ty_Ordering)
new_lt13(x0, x1, ty_Bool)
new_ltEs19(x0, x1, ty_Float)
new_esEs27(x0, x1, app(ty_[], x2))
new_lt10(x0, x1)
new_compare25(x0, x1, True, x2, x3)
new_compare7(:%(x0, x1), :%(x2, x3), ty_Integer)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_lt13(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_compare24(x0, x1, True, x2, x3, x4)
new_esEs16(:%(x0, x1), :%(x2, x3), x4)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, ty_Ordering)
new_esEs4(Left(x0), Left(x1), ty_Char, x2)
new_esEs26(x0, x1, ty_Float)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_compare27(x0, x1, False, x2, x3)
new_esEs28(x0, x1, app(ty_[], x2))
new_ltEs10(GT, GT)
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(True, True)
new_ltEs14(False, False)
new_esEs24(x0, x1, ty_Ordering)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_ltEs7(Right(x0), Right(x1), x2, ty_Double)
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_lt19(x0, x1, ty_@0)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs18(x0, x1, ty_Float)
new_esEs18(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, ty_Char)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_esEs18(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_not(True)
new_esEs19(x0, x1, ty_Int)
new_esEs7(Just(x0), Just(x1), ty_@0)
new_compare30(x0, x1, ty_Integer)
new_ltEs5(x0, x1)
new_compare30(x0, x1, app(ty_Ratio, x2))
new_esEs4(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs20(x0, x1, ty_Double)
new_esEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_compare110(x0, x1, True, x2, x3, x4)
new_esEs12([], :(x0, x1), x2)
new_compare15(x0, x1, False, x2, x3)
new_ltEs4(Just(x0), Just(x1), ty_Integer)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_not(False)
new_esEs25(x0, x1, ty_Integer)
new_esEs4(Right(x0), Right(x1), x2, ty_@0)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_ltEs4(Just(x0), Just(x1), app(ty_[], x2))
new_primCompAux00(x0, LT)
new_lt6(x0, x1)
new_ltEs10(EQ, GT)
new_ltEs10(GT, EQ)
new_esEs12(:(x0, x1), :(x2, x3), x4)
new_ltEs19(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Float)
new_ltEs7(Right(x0), Right(x1), x2, ty_Bool)
new_esEs29(x0, Just(x1), app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, ty_Char)
new_lt8(x0, x1, x2, x3, x4)
new_ltEs7(Left(x0), Left(x1), ty_@0, x2)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs19(x0, x1, ty_Integer)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_sr(Integer(x0), Integer(x1))
new_esEs4(Right(x0), Right(x1), x2, ty_Char)
new_lt5(x0, x1, x2, x3)
new_esEs27(x0, x1, ty_Char)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs20(x0, x1, ty_Bool)
new_compare29(Just(x0), Just(x1), False, x2)
new_lt13(x0, x1, app(ty_Maybe, x2))
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_compare30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(Just(x0), Just(x1), ty_Char)
new_esEs4(Left(x0), Left(x1), ty_Float, x2)
new_ltEs4(Nothing, Just(x0), x1)
new_esEs18(x0, x1, ty_@0)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_lt13(x0, x1, ty_Double)
new_esEs20(x0, x1, app(ty_[], x2))
new_ltEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare29(Just(x0), Nothing, False, x1)
new_ltEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs28(x0, x1, ty_Bool)
new_lt13(x0, x1, ty_Ordering)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt13(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Ordering)
new_ltEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare30(x0, x1, ty_Float)
new_esEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_lt13(x0, x1, ty_Integer)
new_compare13(x0, x1, x2, x3, x4)
new_esEs14(False, False)
new_primEqInt(Pos(Zero), Pos(Zero))
new_compare30(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_compare10(Char(x0), Char(x1))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs24(x0, x1, ty_Integer)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Double)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_ltEs20(x0, x1, ty_Float)
new_lt13(x0, x1, ty_Int)
new_lt13(x0, x1, ty_Float)
new_lt20(x0, x1, ty_Integer)
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_primCmpNat0(Zero, Succ(x0))
new_ltEs7(Right(x0), Left(x1), x2, x3)
new_ltEs7(Left(x0), Right(x1), x2, x3)
new_esEs23(x0, x1, ty_Int)
new_primCompAux00(x0, GT)
new_ltEs20(x0, x1, ty_@0)
new_esEs4(Left(x0), Left(x1), ty_Bool, x2)
new_lt15(x0, x1)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs29(x0, Just(x1), ty_Int)
new_ltEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primEqNat0(Zero, Succ(x0))
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, ty_Bool)
new_ltEs19(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_@0)
new_esEs18(x0, x1, ty_Integer)
new_ltEs10(EQ, EQ)

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
                                    ↳ QDPSizeChangeProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_splitGT2(zzz2640, zzz2641, zzz2642, zzz2643, zzz2644, zzz265, False, h, ba) → new_splitGT1(zzz2640, zzz2641, zzz2642, zzz2643, zzz2644, zzz265, new_lt11(Just(zzz265), zzz2640, h), h, ba)
new_splitGT(Branch(zzz26440, zzz26441, zzz26442, zzz26443, zzz26444), zzz265, h, ba) → new_splitGT2(zzz26440, zzz26441, zzz26442, zzz26443, zzz26444, zzz265, new_gt(Just(zzz265), zzz26440, h), h, ba)
new_splitGT1(zzz2640, zzz2641, zzz2642, zzz2643, zzz2644, zzz265, True, h, ba) → new_splitGT(zzz2643, zzz265, h, ba)
new_splitGT2(zzz2640, zzz2641, zzz2642, zzz2643, Branch(zzz26440, zzz26441, zzz26442, zzz26443, zzz26444), zzz265, True, h, ba) → new_splitGT2(zzz26440, zzz26441, zzz26442, zzz26443, zzz26444, zzz265, new_gt(Just(zzz265), zzz26440, h), h, ba)

The TRS R consists of the following rules:

new_lt19(zzz500000, zzz4300000, ty_Float) → new_lt6(zzz500000, zzz4300000)
new_ltEs18(zzz50000, zzz430000, app(ty_Ratio, bef)) → new_ltEs15(zzz50000, zzz430000, bef)
new_esEs7(Just(zzz5000), Just(zzz4000), app(ty_Maybe, dh)) → new_esEs7(zzz5000, zzz4000, dh)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_esEs20(zzz5000, zzz4000, app(ty_Maybe, bba)) → new_esEs7(zzz5000, zzz4000, bba)
new_esEs12(:(zzz5000, zzz5001), :(zzz4000, zzz4001), hh) → new_asAs(new_esEs20(zzz5000, zzz4000, hh), new_esEs12(zzz5001, zzz4001, hh))
new_esEs7(Just(zzz5000), Just(zzz4000), app(ty_[], dd)) → new_esEs12(zzz5000, zzz4000, dd)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, ty_Ordering) → new_ltEs10(zzz500000, zzz4300000)
new_lt19(zzz500000, zzz4300000, app(app(app(ty_@3, cde), cdf), cdg)) → new_lt8(zzz500000, zzz4300000, cde, cdf, cdg)
new_ltEs18(zzz50000, zzz430000, app(app(app(ty_@3, beg), beh), bfa)) → new_ltEs16(zzz50000, zzz430000, beg, beh, bfa)
new_lt20(zzz500001, zzz4300001, app(ty_[], cfb)) → new_lt18(zzz500001, zzz4300001, cfb)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, ty_Char) → new_esEs11(zzz5000, zzz4000)
new_compare15(zzz500000, zzz4300000, True, hf, hg) → LT
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Bool, bfb) → new_esEs14(zzz5000, zzz4000)
new_ltEs18(zzz50000, zzz430000, app(ty_Maybe, bb)) → new_ltEs4(zzz50000, zzz430000, bb)
new_ltEs20(zzz500002, zzz4300002, ty_Ordering) → new_ltEs10(zzz500002, zzz4300002)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, app(app(app(ty_@3, bhc), bhd), bhe)) → new_esEs6(zzz5000, zzz4000, bhc, bhd, bhe)
new_lt13(zzz500000, zzz4300000, app(app(app(ty_@3, hc), hd), he)) → new_lt8(zzz500000, zzz4300000, hc, hd, he)
new_lt15(zzz500000, zzz4300000) → new_esEs8(new_compare14(zzz500000, zzz4300000), LT)
new_lt20(zzz500001, zzz4300001, app(app(app(ty_@3, ceg), ceh), cfa)) → new_lt8(zzz500001, zzz4300001, ceg, ceh, cfa)
new_esEs27(zzz5001, zzz4001, app(ty_Maybe, dbb)) → new_esEs7(zzz5001, zzz4001, dbb)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Ordering) → new_ltEs10(zzz500000, zzz4300000)
new_esEs23(zzz500000, zzz4300000, ty_Bool) → new_esEs14(zzz500000, zzz4300000)
new_compare27(zzz500000, zzz4300000, False, ha, hb) → new_compare113(zzz500000, zzz4300000, new_ltEs7(zzz500000, zzz4300000, ha, hb), ha, hb)
new_lt19(zzz500000, zzz4300000, ty_Double) → new_lt15(zzz500000, zzz4300000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), app(ty_Maybe, bcb), bbe) → new_ltEs4(zzz500000, zzz4300000, bcb)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, ty_@0) → new_ltEs11(zzz500000, zzz4300000)
new_ltEs20(zzz500002, zzz4300002, app(ty_Ratio, cfh)) → new_ltEs15(zzz500002, zzz4300002, cfh)
new_lt13(zzz500000, zzz4300000, app(ty_[], cbd)) → new_lt18(zzz500000, zzz4300000, cbd)
new_esEs26(zzz5002, zzz4002, ty_Float) → new_esEs13(zzz5002, zzz4002)
new_ltEs7(Left(zzz500000), Right(zzz4300000), bch, bbe) → True
new_primMulNat0(Zero, Zero) → Zero
new_esEs19(zzz5000, zzz4000, ty_Int) → new_esEs17(zzz5000, zzz4000)
new_sr(Integer(zzz43000000), Integer(zzz5000010)) → Integer(new_primMulInt(zzz43000000, zzz5000010))
new_ltEs20(zzz500002, zzz4300002, ty_Float) → new_ltEs12(zzz500002, zzz4300002)
new_ltEs20(zzz500002, zzz4300002, ty_@0) → new_ltEs11(zzz500002, zzz4300002)
new_esEs20(zzz5000, zzz4000, app(ty_Ratio, bbb)) → new_esEs16(zzz5000, zzz4000, bbb)
new_esEs18(zzz5001, zzz4001, ty_Double) → new_esEs9(zzz5001, zzz4001)
new_lt20(zzz500001, zzz4300001, ty_Float) → new_lt6(zzz500001, zzz4300001)
new_esEs23(zzz500000, zzz4300000, ty_Double) → new_esEs9(zzz500000, zzz4300000)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, app(ty_[], bhb)) → new_esEs12(zzz5000, zzz4000, bhb)
new_esEs24(zzz500001, zzz4300001, ty_Integer) → new_esEs15(zzz500001, zzz4300001)
new_ltEs14(False, True) → True
new_ltEs19(zzz500001, zzz4300001, ty_Integer) → new_ltEs9(zzz500001, zzz4300001)
new_ltEs4(Just(zzz500000), Just(zzz4300000), app(app(ty_@2, be), bf)) → new_ltEs13(zzz500000, zzz4300000, be, bf)
new_esEs20(zzz5000, zzz4000, app(app(ty_Either, baa), bab)) → new_esEs4(zzz5000, zzz4000, baa, bab)
new_esEs12([], [], hh) → True
new_ltEs19(zzz500001, zzz4300001, ty_Ordering) → new_ltEs10(zzz500001, zzz4300001)
new_esEs24(zzz500001, zzz4300001, app(app(ty_@2, cec), ced)) → new_esEs5(zzz500001, zzz4300001, cec, ced)
new_lt12(zzz500000, zzz4300000) → new_esEs8(new_compare10(zzz500000, zzz4300000), LT)
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Ordering, bbe) → new_ltEs10(zzz500000, zzz4300000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, app(ty_Ratio, bdf)) → new_ltEs15(zzz500000, zzz4300000, bdf)
new_esEs15(Integer(zzz5000), Integer(zzz4000)) → new_primEqInt(zzz5000, zzz4000)
new_ltEs10(EQ, GT) → True
new_ltEs19(zzz500001, zzz4300001, app(ty_Maybe, cca)) → new_ltEs4(zzz500001, zzz4300001, cca)
new_esEs21(zzz5001, zzz4001, ty_Int) → new_esEs17(zzz5001, zzz4001)
new_ltEs7(Left(zzz500000), Left(zzz4300000), app(app(app(ty_@3, bcd), bce), bcf), bbe) → new_ltEs16(zzz500000, zzz4300000, bcd, bce, bcf)
new_lt13(zzz500000, zzz4300000, ty_Char) → new_lt12(zzz500000, zzz4300000)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Ordering, bfb) → new_esEs8(zzz5000, zzz4000)
new_esEs24(zzz500001, zzz4300001, app(ty_[], cfb)) → new_esEs12(zzz500001, zzz4300001, cfb)
new_esEs25(zzz500000, zzz4300000, ty_Double) → new_esEs9(zzz500000, zzz4300000)
new_esEs25(zzz500000, zzz4300000, ty_Float) → new_esEs13(zzz500000, zzz4300000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, app(ty_[], beb)) → new_ltEs17(zzz500000, zzz4300000, beb)
new_pePe(False, zzz218) → zzz218
new_lt14(zzz5000, zzz43000) → new_esEs8(new_compare8(zzz5000, zzz43000), LT)
new_esEs25(zzz500000, zzz4300000, app(app(ty_Either, ccg), cch)) → new_esEs4(zzz500000, zzz4300000, ccg, cch)
new_esEs12(:(zzz5000, zzz5001), [], hh) → False
new_esEs12([], :(zzz4000, zzz4001), hh) → False
new_esEs25(zzz500000, zzz4300000, ty_Char) → new_esEs11(zzz500000, zzz4300000)
new_esEs25(zzz500000, zzz4300000, ty_Bool) → new_esEs14(zzz500000, zzz4300000)
new_lt19(zzz500000, zzz4300000, ty_Ordering) → new_lt9(zzz500000, zzz4300000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, app(app(ty_@2, bdc), bdd)) → new_ltEs13(zzz500000, zzz4300000, bdc, bdd)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, app(ty_Ratio, bhg)) → new_esEs16(zzz5000, zzz4000, bhg)
new_compare23(zzz500000, zzz4300000, True) → EQ
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Float, bbe) → new_ltEs12(zzz500000, zzz4300000)
new_lt19(zzz500000, zzz4300000, app(ty_Ratio, cdd)) → new_lt17(zzz500000, zzz4300000, cdd)
new_esEs24(zzz500001, zzz4300001, app(ty_Maybe, cee)) → new_esEs7(zzz500001, zzz4300001, cee)
new_ltEs4(Nothing, Just(zzz4300000), bb) → True
new_esEs23(zzz500000, zzz4300000, app(ty_Maybe, cbb)) → new_esEs7(zzz500000, zzz4300000, cbb)
new_compare30(zzz500000, zzz4300000, ty_Integer) → new_compare9(zzz500000, zzz4300000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(ty_Ratio, bgd), bfb) → new_esEs16(zzz5000, zzz4000, bgd)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, ty_Char) → new_ltEs5(zzz500000, zzz4300000)
new_compare13(zzz500000, zzz4300000, hc, hd, he) → new_compare24(zzz500000, zzz4300000, new_esEs6(zzz500000, zzz4300000, hc, hd, he), hc, hd, he)
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_lt4(zzz500000, zzz4300000) → new_esEs8(new_compare11(zzz500000, zzz4300000), LT)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, ty_Integer) → new_esEs15(zzz5000, zzz4000)
new_esEs20(zzz5000, zzz4000, app(app(ty_@2, bac), bad)) → new_esEs5(zzz5000, zzz4000, bac, bad)
new_esEs28(zzz5000, zzz4000, app(ty_Ratio, dce)) → new_esEs16(zzz5000, zzz4000, dce)
new_compare30(zzz500000, zzz4300000, app(ty_Ratio, cae)) → new_compare7(zzz500000, zzz4300000, cae)
new_compare19(zzz500000, zzz4300000, True) → LT
new_compare6(zzz500000, zzz4300000) → new_compare23(zzz500000, zzz4300000, new_esEs8(zzz500000, zzz4300000))
new_ltEs18(zzz50000, zzz430000, ty_@0) → new_ltEs11(zzz50000, zzz430000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_ltEs19(zzz500001, zzz4300001, app(ty_Ratio, ccb)) → new_ltEs15(zzz500001, zzz4300001, ccb)
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Int) → new_esEs17(zzz5000, zzz4000)
new_ltEs20(zzz500002, zzz4300002, ty_Bool) → new_ltEs14(zzz500002, zzz4300002)
new_esEs27(zzz5001, zzz4001, ty_@0) → new_esEs10(zzz5001, zzz4001)
new_ltEs12(zzz50000, zzz430000) → new_fsEs(new_compare16(zzz50000, zzz430000))
new_esEs8(LT, LT) → True
new_lt19(zzz500000, zzz4300000, app(app(ty_@2, cda), cdb)) → new_lt16(zzz500000, zzz4300000, cda, cdb)
new_esEs25(zzz500000, zzz4300000, ty_Ordering) → new_esEs8(zzz500000, zzz4300000)
new_esEs19(zzz5000, zzz4000, app(ty_Maybe, gg)) → new_esEs7(zzz5000, zzz4000, gg)
new_esEs20(zzz5000, zzz4000, app(app(app(ty_@3, baf), bag), bah)) → new_esEs6(zzz5000, zzz4000, baf, bag, bah)
new_esEs18(zzz5001, zzz4001, app(ty_Ratio, ff)) → new_esEs16(zzz5001, zzz4001, ff)
new_pePe(True, zzz218) → True
new_primEqNat0(Zero, Zero) → True
new_lt20(zzz500001, zzz4300001, app(app(ty_Either, cea), ceb)) → new_lt5(zzz500001, zzz4300001, cea, ceb)
new_compare26(zzz500000, zzz4300000, True) → EQ
new_lt20(zzz500001, zzz4300001, ty_Bool) → new_lt7(zzz500001, zzz4300001)
new_esEs13(Float(zzz5000, zzz5001), Float(zzz4000, zzz4001)) → new_esEs17(new_sr0(zzz5000, zzz4000), new_sr0(zzz5001, zzz4001))
new_esEs19(zzz5000, zzz4000, app(ty_[], gc)) → new_esEs12(zzz5000, zzz4000, gc)
new_compare29(Nothing, Just(zzz430000), False, gg) → LT
new_esEs19(zzz5000, zzz4000, ty_Float) → new_esEs13(zzz5000, zzz4000)
new_compare30(zzz500000, zzz4300000, app(ty_Maybe, cad)) → new_compare28(zzz500000, zzz4300000, cad)
new_esEs18(zzz5001, zzz4001, app(app(ty_@2, ef), eg)) → new_esEs5(zzz5001, zzz4001, ef, eg)
new_esEs25(zzz500000, zzz4300000, ty_Int) → new_esEs17(zzz500000, zzz4300000)
new_esEs9(Double(zzz5000, zzz5001), Double(zzz4000, zzz4001)) → new_esEs17(new_sr0(zzz5000, zzz4000), new_sr0(zzz5001, zzz4001))
new_esEs26(zzz5002, zzz4002, ty_Ordering) → new_esEs8(zzz5002, zzz4002)
new_esEs8(GT, GT) → True
new_lt20(zzz500001, zzz4300001, app(ty_Maybe, cee)) → new_lt11(zzz500001, zzz4300001, cee)
new_esEs18(zzz5001, zzz4001, app(app(app(ty_@3, fa), fb), fc)) → new_esEs6(zzz5001, zzz4001, fa, fb, fc)
new_esEs25(zzz500000, zzz4300000, ty_@0) → new_esEs10(zzz500000, zzz4300000)
new_compare4([], [], ce) → EQ
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_lt19(zzz500000, zzz4300000, ty_@0) → new_lt4(zzz500000, zzz4300000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(app(ty_@2, bfe), bff), bfb) → new_esEs5(zzz5000, zzz4000, bfe, bff)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, ty_Integer) → new_ltEs9(zzz500000, zzz4300000)
new_esEs26(zzz5002, zzz4002, app(app(app(ty_@3, che), chf), chg)) → new_esEs6(zzz5002, zzz4002, che, chf, chg)
new_compare18(zzz500000, zzz4300000, hf, hg) → new_compare25(zzz500000, zzz4300000, new_esEs5(zzz500000, zzz4300000, hf, hg), hf, hg)
new_ltEs17(zzz50000, zzz430000, ce) → new_fsEs(new_compare4(zzz50000, zzz430000, ce))
new_esEs8(GT, LT) → False
new_esEs8(LT, GT) → False
new_compare30(zzz500000, zzz4300000, app(ty_[], cba)) → new_compare4(zzz500000, zzz4300000, cba)
new_compare30(zzz500000, zzz4300000, ty_Double) → new_compare14(zzz500000, zzz4300000)
new_ltEs13(@2(zzz500000, zzz500001), @2(zzz4300000, zzz4300001), bed, bee) → new_pePe(new_lt13(zzz500000, zzz4300000, bed), new_asAs(new_esEs23(zzz500000, zzz4300000, bed), new_ltEs19(zzz500001, zzz4300001, bee)))
new_esEs4(Right(zzz5000), Right(zzz4000), bge, app(app(ty_Either, bgf), bgg)) → new_esEs4(zzz5000, zzz4000, bgf, bgg)
new_esEs25(zzz500000, zzz4300000, app(ty_[], cdh)) → new_esEs12(zzz500000, zzz4300000, cdh)
new_compare24(zzz500000, zzz4300000, True, hc, hd, he) → EQ
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Int, bbe) → new_ltEs6(zzz500000, zzz4300000)
new_lt20(zzz500001, zzz4300001, ty_Ordering) → new_lt9(zzz500001, zzz4300001)
new_primEqInt(Neg(Succ(zzz50000)), Neg(Succ(zzz40000))) → new_primEqNat0(zzz50000, zzz40000)
new_esEs20(zzz5000, zzz4000, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_compare113(zzz500000, zzz4300000, True, ha, hb) → LT
new_esEs23(zzz500000, zzz4300000, ty_Ordering) → new_esEs8(zzz500000, zzz4300000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(app(ty_Either, bfc), bfd), bfb) → new_esEs4(zzz5000, zzz4000, bfc, bfd)
new_ltEs18(zzz50000, zzz430000, app(app(ty_Either, bch), bbe)) → new_ltEs7(zzz50000, zzz430000, bch, bbe)
new_esEs24(zzz500001, zzz4300001, ty_Bool) → new_esEs14(zzz500001, zzz4300001)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_lt19(zzz500000, zzz4300000, ty_Bool) → new_lt7(zzz500000, zzz4300000)
new_lt19(zzz500000, zzz4300000, ty_Integer) → new_lt10(zzz500000, zzz4300000)
new_ltEs4(Nothing, Nothing, bb) → True
new_lt13(zzz500000, zzz4300000, ty_Float) → new_lt6(zzz500000, zzz4300000)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_@0) → new_ltEs11(zzz500000, zzz4300000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Char, bbe) → new_ltEs5(zzz500000, zzz4300000)
new_lt13(zzz500000, zzz4300000, ty_Int) → new_lt14(zzz500000, zzz4300000)
new_lt6(zzz500000, zzz4300000) → new_esEs8(new_compare16(zzz500000, zzz4300000), LT)
new_compare29(Just(zzz50000), Nothing, False, gg) → GT
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_ltEs7(Right(zzz500000), Left(zzz4300000), bch, bbe) → False
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_esEs24(zzz500001, zzz4300001, app(app(app(ty_@3, ceg), ceh), cfa)) → new_esEs6(zzz500001, zzz4300001, ceg, ceh, cfa)
new_esEs23(zzz500000, zzz4300000, ty_Char) → new_esEs11(zzz500000, zzz4300000)
new_lt13(zzz500000, zzz4300000, ty_Bool) → new_lt7(zzz500000, zzz4300000)
new_esEs19(zzz5000, zzz4000, ty_Bool) → new_esEs14(zzz5000, zzz4000)
new_esEs20(zzz5000, zzz4000, ty_Float) → new_esEs13(zzz5000, zzz4000)
new_compare14(Double(zzz500000, zzz500001), Double(zzz4300000, zzz4300001)) → new_compare8(new_sr0(zzz500000, zzz4300000), new_sr0(zzz500001, zzz4300001))
new_compare12(zzz500000, zzz4300000, ha, hb) → new_compare27(zzz500000, zzz4300000, new_esEs4(zzz500000, zzz4300000, ha, hb), ha, hb)
new_compare8(zzz500, zzz4300) → new_primCmpInt(zzz500, zzz4300)
new_lt19(zzz500000, zzz4300000, ty_Char) → new_lt12(zzz500000, zzz4300000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, app(app(app(ty_@3, bdg), bdh), bea)) → new_ltEs16(zzz500000, zzz4300000, bdg, bdh, bea)
new_primEqInt(Neg(Succ(zzz50000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(zzz40000))) → False
new_compare17(zzz500000, zzz4300000) → new_compare26(zzz500000, zzz4300000, new_esEs14(zzz500000, zzz4300000))
new_esEs8(EQ, EQ) → True
new_lt13(zzz500000, zzz4300000, ty_Double) → new_lt15(zzz500000, zzz4300000)
new_compare111(zzz200, zzz201, True, bbd) → LT
new_esEs20(zzz5000, zzz4000, ty_@0) → new_esEs10(zzz5000, zzz4000)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Char, bfb) → new_esEs11(zzz5000, zzz4000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_ltEs19(zzz500001, zzz4300001, ty_@0) → new_ltEs11(zzz500001, zzz4300001)
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_esEs18(zzz5001, zzz4001, ty_Char) → new_esEs11(zzz5001, zzz4001)
new_compare112(zzz500000, zzz4300000, True) → LT
new_esEs19(zzz5000, zzz4000, ty_Char) → new_esEs11(zzz5000, zzz4000)
new_compare30(zzz500000, zzz4300000, app(app(ty_Either, bhh), caa)) → new_compare12(zzz500000, zzz4300000, bhh, caa)
new_primEqInt(Pos(Succ(zzz50000)), Pos(Succ(zzz40000))) → new_primEqNat0(zzz50000, zzz40000)
new_ltEs18(zzz50000, zzz430000, ty_Double) → new_ltEs8(zzz50000, zzz430000)
new_compare27(zzz500000, zzz4300000, True, ha, hb) → EQ
new_lt10(zzz500000, zzz4300000) → new_esEs8(new_compare9(zzz500000, zzz4300000), LT)
new_esEs24(zzz500001, zzz4300001, app(ty_Ratio, cef)) → new_esEs16(zzz500001, zzz4300001, cef)
new_ltEs19(zzz500001, zzz4300001, ty_Bool) → new_ltEs14(zzz500001, zzz4300001)
new_esEs14(False, True) → False
new_esEs14(True, False) → False
new_esEs23(zzz500000, zzz4300000, app(ty_[], cbd)) → new_esEs12(zzz500000, zzz4300000, cbd)
new_ltEs4(Just(zzz500000), Just(zzz4300000), app(app(ty_Either, bc), bd)) → new_ltEs7(zzz500000, zzz4300000, bc, bd)
new_esEs26(zzz5002, zzz4002, ty_Integer) → new_esEs15(zzz5002, zzz4002)
new_ltEs10(GT, EQ) → False
new_lt17(zzz500000, zzz4300000, cbc) → new_esEs8(new_compare7(zzz500000, zzz4300000, cbc), LT)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Double) → new_ltEs8(zzz500000, zzz4300000)
new_esEs24(zzz500001, zzz4300001, ty_Int) → new_esEs17(zzz500001, zzz4300001)
new_primEqNat0(Succ(zzz50000), Succ(zzz40000)) → new_primEqNat0(zzz50000, zzz40000)
new_ltEs20(zzz500002, zzz4300002, app(ty_[], cgd)) → new_ltEs17(zzz500002, zzz4300002, cgd)
new_esEs27(zzz5001, zzz4001, ty_Ordering) → new_esEs8(zzz5001, zzz4001)
new_ltEs14(False, False) → True
new_compare11(@0, @0) → EQ
new_lt7(zzz500000, zzz4300000) → new_esEs8(new_compare17(zzz500000, zzz4300000), LT)
new_esEs19(zzz5000, zzz4000, app(app(app(ty_@3, gd), ge), gf)) → new_esEs6(zzz5000, zzz4000, gd, ge, gf)
new_ltEs9(zzz50000, zzz430000) → new_fsEs(new_compare9(zzz50000, zzz430000))
new_ltEs20(zzz500002, zzz4300002, ty_Char) → new_ltEs5(zzz500002, zzz4300002)
new_compare113(zzz500000, zzz4300000, False, ha, hb) → GT
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, ty_Bool) → new_ltEs14(zzz500000, zzz4300000)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Int) → new_ltEs6(zzz500000, zzz4300000)
new_primCompAux00(zzz225, LT) → LT
new_lt20(zzz500001, zzz4300001, ty_@0) → new_lt4(zzz500001, zzz4300001)
new_ltEs19(zzz500001, zzz4300001, app(ty_[], ccf)) → new_ltEs17(zzz500001, zzz4300001, ccf)
new_ltEs19(zzz500001, zzz4300001, app(app(ty_Either, cbe), cbf)) → new_ltEs7(zzz500001, zzz4300001, cbe, cbf)
new_compare7(:%(zzz500000, zzz500001), :%(zzz4300000, zzz4300001), ty_Int) → new_compare8(new_sr0(zzz500000, zzz4300001), new_sr0(zzz4300000, zzz500001))
new_esEs24(zzz500001, zzz4300001, ty_Ordering) → new_esEs8(zzz500001, zzz4300001)
new_ltEs8(zzz50000, zzz430000) → new_fsEs(new_compare14(zzz50000, zzz430000))
new_esEs7(Nothing, Nothing, cf) → True
new_esEs28(zzz5000, zzz4000, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_esEs8(EQ, LT) → False
new_esEs8(LT, EQ) → False
new_esEs18(zzz5001, zzz4001, app(ty_Maybe, fd)) → new_esEs7(zzz5001, zzz4001, fd)
new_primEqInt(Pos(Succ(zzz50000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(zzz40000))) → False
new_lt20(zzz500001, zzz4300001, app(ty_Ratio, cef)) → new_lt17(zzz500001, zzz4300001, cef)
new_compare30(zzz500000, zzz4300000, ty_Int) → new_compare8(zzz500000, zzz4300000)
new_compare24(zzz500000, zzz4300000, False, hc, hd, he) → new_compare110(zzz500000, zzz4300000, new_ltEs16(zzz500000, zzz4300000, hc, hd, he), hc, hd, he)
new_esEs24(zzz500001, zzz4300001, ty_@0) → new_esEs10(zzz500001, zzz4300001)
new_primCmpNat0(Zero, Zero) → EQ
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Integer, bbe) → new_ltEs9(zzz500000, zzz4300000)
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_esEs23(zzz500000, zzz4300000, app(app(ty_@2, hf), hg)) → new_esEs5(zzz500000, zzz4300000, hf, hg)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, ty_@0) → new_esEs10(zzz5000, zzz4000)
new_ltEs10(LT, EQ) → True
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_compare19(zzz500000, zzz4300000, False) → GT
new_esEs27(zzz5001, zzz4001, ty_Double) → new_esEs9(zzz5001, zzz4001)
new_ltEs15(zzz50000, zzz430000, bef) → new_fsEs(new_compare7(zzz50000, zzz430000, bef))
new_esEs23(zzz500000, zzz4300000, ty_Float) → new_esEs13(zzz500000, zzz4300000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Integer) → new_esEs15(zzz5000, zzz4000)
new_compare29(Just(zzz50000), Just(zzz430000), False, gg) → new_compare111(zzz50000, zzz430000, new_ltEs18(zzz50000, zzz430000, gg), gg)
new_primEqInt(Pos(Succ(zzz50000)), Neg(zzz4000)) → False
new_primEqInt(Neg(Succ(zzz50000)), Pos(zzz4000)) → False
new_lt13(zzz500000, zzz4300000, app(ty_Ratio, cbc)) → new_lt17(zzz500000, zzz4300000, cbc)
new_esEs7(Nothing, Just(zzz4000), cf) → False
new_esEs7(Just(zzz5000), Nothing, cf) → False
new_esEs18(zzz5001, zzz4001, app(ty_[], eh)) → new_esEs12(zzz5001, zzz4001, eh)
new_esEs28(zzz5000, zzz4000, ty_Char) → new_esEs11(zzz5000, zzz4000)
new_ltEs10(GT, GT) → True
new_esEs26(zzz5002, zzz4002, app(ty_Ratio, daa)) → new_esEs16(zzz5002, zzz4002, daa)
new_esEs26(zzz5002, zzz4002, ty_Int) → new_esEs17(zzz5002, zzz4002)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, ty_Bool) → new_esEs14(zzz5000, zzz4000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_@0, bbe) → new_ltEs11(zzz500000, zzz4300000)
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primEqInt(Pos(Zero), Neg(Succ(zzz40000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(zzz40000))) → False
new_ltEs6(zzz50000, zzz430000) → new_fsEs(new_compare8(zzz50000, zzz430000))
new_esEs20(zzz5000, zzz4000, app(ty_[], bae)) → new_esEs12(zzz5000, zzz4000, bae)
new_esEs21(zzz5001, zzz4001, ty_Integer) → new_esEs15(zzz5001, zzz4001)
new_compare30(zzz500000, zzz4300000, app(app(ty_@2, cab), cac)) → new_compare18(zzz500000, zzz4300000, cab, cac)
new_primCompAux00(zzz225, EQ) → zzz225
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Double, bfb) → new_esEs9(zzz5000, zzz4000)
new_gt(zzz440, zzz4440, bec) → new_esEs8(new_compare28(zzz440, zzz4440, bec), GT)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Integer, bfb) → new_esEs15(zzz5000, zzz4000)
new_esEs18(zzz5001, zzz4001, ty_Int) → new_esEs17(zzz5001, zzz4001)
new_lt16(zzz500000, zzz4300000, hf, hg) → new_esEs8(new_compare18(zzz500000, zzz4300000, hf, hg), LT)
new_esEs8(GT, EQ) → False
new_esEs8(EQ, GT) → False
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Double) → new_esEs9(zzz5000, zzz4000)
new_esEs26(zzz5002, zzz4002, ty_Char) → new_esEs11(zzz5002, zzz4002)
new_esEs27(zzz5001, zzz4001, app(ty_Ratio, dbc)) → new_esEs16(zzz5001, zzz4001, dbc)
new_esEs26(zzz5002, zzz4002, app(app(ty_@2, chb), chc)) → new_esEs5(zzz5002, zzz4002, chb, chc)
new_ltEs19(zzz500001, zzz4300001, app(app(ty_@2, cbg), cbh)) → new_ltEs13(zzz500001, zzz4300001, cbg, cbh)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Bool) → new_ltEs14(zzz500000, zzz4300000)
new_not(False) → True
new_esEs24(zzz500001, zzz4300001, ty_Double) → new_esEs9(zzz500001, zzz4300001)
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_ltEs5(zzz50000, zzz430000) → new_fsEs(new_compare10(zzz50000, zzz430000))
new_esEs25(zzz500000, zzz4300000, ty_Integer) → new_esEs15(zzz500000, zzz4300000)
new_esEs26(zzz5002, zzz4002, ty_Bool) → new_esEs14(zzz5002, zzz4002)
new_ltEs19(zzz500001, zzz4300001, ty_Int) → new_ltEs6(zzz500001, zzz4300001)
new_esEs25(zzz500000, zzz4300000, app(ty_Ratio, cdd)) → new_esEs16(zzz500000, zzz4300000, cdd)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, ty_Int) → new_esEs17(zzz5000, zzz4000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Bool, bbe) → new_ltEs14(zzz500000, zzz4300000)
new_esEs28(zzz5000, zzz4000, app(app(ty_@2, dbf), dbg)) → new_esEs5(zzz5000, zzz4000, dbf, dbg)
new_esEs23(zzz500000, zzz4300000, ty_@0) → new_esEs10(zzz500000, zzz4300000)
new_compare30(zzz500000, zzz4300000, ty_@0) → new_compare11(zzz500000, zzz4300000)
new_esEs18(zzz5001, zzz4001, app(app(ty_Either, ed), ee)) → new_esEs4(zzz5001, zzz4001, ed, ee)
new_lt18(zzz500000, zzz4300000, cbd) → new_esEs8(new_compare4(zzz500000, zzz4300000, cbd), LT)
new_ltEs18(zzz50000, zzz430000, ty_Int) → new_ltEs6(zzz50000, zzz430000)
new_esEs22(zzz5000, zzz4000, ty_Int) → new_esEs17(zzz5000, zzz4000)
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_esEs6(@3(zzz5000, zzz5001, zzz5002), @3(zzz4000, zzz4001, zzz4002), cge, cgf, cgg) → new_asAs(new_esEs28(zzz5000, zzz4000, cge), new_asAs(new_esEs27(zzz5001, zzz4001, cgf), new_esEs26(zzz5002, zzz4002, cgg)))
new_esEs28(zzz5000, zzz4000, app(ty_Maybe, dcd)) → new_esEs7(zzz5000, zzz4000, dcd)
new_esEs28(zzz5000, zzz4000, ty_Double) → new_esEs9(zzz5000, zzz4000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, ty_Double) → new_ltEs8(zzz500000, zzz4300000)
new_lt20(zzz500001, zzz4300001, ty_Double) → new_lt15(zzz500001, zzz4300001)
new_lt20(zzz500001, zzz4300001, ty_Integer) → new_lt10(zzz500001, zzz4300001)
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_esEs26(zzz5002, zzz4002, ty_@0) → new_esEs10(zzz5002, zzz4002)
new_esEs18(zzz5001, zzz4001, ty_Float) → new_esEs13(zzz5001, zzz4001)
new_compare25(zzz500000, zzz4300000, False, hf, hg) → new_compare15(zzz500000, zzz4300000, new_ltEs13(zzz500000, zzz4300000, hf, hg), hf, hg)
new_esEs23(zzz500000, zzz4300000, app(app(ty_Either, ha), hb)) → new_esEs4(zzz500000, zzz4300000, ha, hb)
new_esEs20(zzz5000, zzz4000, ty_Char) → new_esEs11(zzz5000, zzz4000)
new_lt19(zzz500000, zzz4300000, app(ty_Maybe, cdc)) → new_lt11(zzz500000, zzz4300000, cdc)
new_esEs4(Left(zzz5000), Left(zzz4000), app(ty_Maybe, bgc), bfb) → new_esEs7(zzz5000, zzz4000, bgc)
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_esEs20(zzz5000, zzz4000, ty_Integer) → new_esEs15(zzz5000, zzz4000)
new_primEqNat0(Zero, Succ(zzz40000)) → False
new_primEqNat0(Succ(zzz50000), Zero) → False
new_esEs18(zzz5001, zzz4001, ty_Integer) → new_esEs15(zzz5001, zzz4001)
new_esEs17(zzz500, zzz400) → new_primEqInt(zzz500, zzz400)
new_lt5(zzz500000, zzz4300000, ha, hb) → new_esEs8(new_compare12(zzz500000, zzz4300000, ha, hb), LT)
new_compare25(zzz500000, zzz4300000, True, hf, hg) → EQ
new_esEs20(zzz5000, zzz4000, ty_Bool) → new_esEs14(zzz5000, zzz4000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), app(app(ty_Either, bbf), bbg), bbe) → new_ltEs7(zzz500000, zzz4300000, bbf, bbg)
new_ltEs14(True, True) → True
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs24(zzz500001, zzz4300001, app(app(ty_Either, cea), ceb)) → new_esEs4(zzz500001, zzz4300001, cea, ceb)
new_esEs28(zzz5000, zzz4000, app(app(app(ty_@3, dca), dcb), dcc)) → new_esEs6(zzz5000, zzz4000, dca, dcb, dcc)
new_compare30(zzz500000, zzz4300000, ty_Bool) → new_compare17(zzz500000, zzz4300000)
new_esEs27(zzz5001, zzz4001, app(app(ty_Either, dab), dac)) → new_esEs4(zzz5001, zzz4001, dab, dac)
new_esEs27(zzz5001, zzz4001, app(app(app(ty_@3, dag), dah), dba)) → new_esEs6(zzz5001, zzz4001, dag, dah, dba)
new_compare4(:(zzz500000, zzz500001), [], ce) → GT
new_ltEs18(zzz50000, zzz430000, app(ty_[], ce)) → new_ltEs17(zzz50000, zzz430000, ce)
new_esEs27(zzz5001, zzz4001, app(app(ty_@2, dad), dae)) → new_esEs5(zzz5001, zzz4001, dad, dae)
new_esEs27(zzz5001, zzz4001, ty_Int) → new_esEs17(zzz5001, zzz4001)
new_esEs23(zzz500000, zzz4300000, ty_Int) → new_esEs17(zzz500000, zzz4300000)
new_lt13(zzz500000, zzz4300000, ty_@0) → new_lt4(zzz500000, zzz4300000)
new_compare30(zzz500000, zzz4300000, ty_Char) → new_compare10(zzz500000, zzz4300000)
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_compare4([], :(zzz4300000, zzz4300001), ce) → LT
new_sr0(zzz5000, zzz4000) → new_primMulInt(zzz5000, zzz4000)
new_lt19(zzz500000, zzz4300000, app(ty_[], cdh)) → new_lt18(zzz500000, zzz4300000, cdh)
new_compare15(zzz500000, zzz4300000, False, hf, hg) → GT
new_ltEs18(zzz50000, zzz430000, ty_Float) → new_ltEs12(zzz50000, zzz430000)
new_ltEs18(zzz50000, zzz430000, ty_Integer) → new_ltEs9(zzz50000, zzz430000)
new_ltEs19(zzz500001, zzz4300001, ty_Double) → new_ltEs8(zzz500001, zzz4300001)
new_compare30(zzz500000, zzz4300000, ty_Float) → new_compare16(zzz500000, zzz4300000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), app(ty_[], bcg), bbe) → new_ltEs17(zzz500000, zzz4300000, bcg)
new_esEs11(Char(zzz5000), Char(zzz4000)) → new_primEqNat0(zzz5000, zzz4000)
new_esEs7(Just(zzz5000), Just(zzz4000), app(app(app(ty_@3, de), df), dg)) → new_esEs6(zzz5000, zzz4000, de, df, dg)
new_esEs25(zzz500000, zzz4300000, app(ty_Maybe, cdc)) → new_esEs7(zzz500000, zzz4300000, cdc)
new_compare29(Nothing, Nothing, False, gg) → LT
new_esEs23(zzz500000, zzz4300000, app(ty_Ratio, cbc)) → new_esEs16(zzz500000, zzz4300000, cbc)
new_lt13(zzz500000, zzz4300000, app(app(ty_Either, ha), hb)) → new_lt5(zzz500000, zzz4300000, ha, hb)
new_esEs16(:%(zzz5000, zzz5001), :%(zzz4000, zzz4001), bbc) → new_asAs(new_esEs22(zzz5000, zzz4000, bbc), new_esEs21(zzz5001, zzz4001, bbc))
new_ltEs4(Just(zzz500000), Just(zzz4300000), app(ty_Maybe, bg)) → new_ltEs4(zzz500000, zzz4300000, bg)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Float) → new_ltEs12(zzz500000, zzz4300000)
new_primCompAux0(zzz500000, zzz4300000, zzz220, ce) → new_primCompAux00(zzz220, new_compare30(zzz500000, zzz4300000, ce))
new_esEs19(zzz5000, zzz4000, app(app(ty_@2, ga), gb)) → new_esEs5(zzz5000, zzz4000, ga, gb)
new_esEs19(zzz5000, zzz4000, app(ty_Ratio, gh)) → new_esEs16(zzz5000, zzz4000, gh)
new_esEs10(@0, @0) → True
new_compare29(zzz5000, zzz43000, True, gg) → EQ
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs27(zzz5001, zzz4001, ty_Float) → new_esEs13(zzz5001, zzz4001)
new_lt13(zzz500000, zzz4300000, ty_Integer) → new_lt10(zzz500000, zzz4300000)
new_compare28(zzz5000, zzz43000, gg) → new_compare29(zzz5000, zzz43000, new_esEs7(zzz5000, zzz43000, gg), gg)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, app(app(ty_@2, bgh), bha)) → new_esEs5(zzz5000, zzz4000, bgh, bha)
new_esEs24(zzz500001, zzz4300001, ty_Char) → new_esEs11(zzz500001, zzz4300001)
new_esEs28(zzz5000, zzz4000, ty_@0) → new_esEs10(zzz5000, zzz4000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, app(app(ty_Either, bda), bdb)) → new_ltEs7(zzz500000, zzz4300000, bda, bdb)
new_esEs28(zzz5000, zzz4000, ty_Int) → new_esEs17(zzz5000, zzz4000)
new_compare7(:%(zzz500000, zzz500001), :%(zzz4300000, zzz4300001), ty_Integer) → new_compare9(new_sr(zzz500000, zzz4300001), new_sr(zzz4300000, zzz500001))
new_compare9(Integer(zzz500000), Integer(zzz4300000)) → new_primCmpInt(zzz500000, zzz4300000)
new_compare23(zzz500000, zzz4300000, False) → new_compare112(zzz500000, zzz4300000, new_ltEs10(zzz500000, zzz4300000))
new_asAs(False, zzz207) → False
new_esEs4(Left(zzz5000), Left(zzz4000), ty_@0, bfb) → new_esEs10(zzz5000, zzz4000)
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_esEs26(zzz5002, zzz4002, ty_Double) → new_esEs9(zzz5002, zzz4002)
new_ltEs10(LT, GT) → True
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_ltEs4(Just(zzz500000), Just(zzz4300000), app(ty_Ratio, bh)) → new_ltEs15(zzz500000, zzz4300000, bh)
new_esEs23(zzz500000, zzz4300000, app(app(app(ty_@3, hc), hd), he)) → new_esEs6(zzz500000, zzz4300000, hc, hd, he)
new_lt8(zzz500000, zzz4300000, hc, hd, he) → new_esEs8(new_compare13(zzz500000, zzz4300000, hc, hd, he), LT)
new_lt11(zzz5000, zzz43000, gg) → new_esEs8(new_compare28(zzz5000, zzz43000, gg), LT)
new_esEs26(zzz5002, zzz4002, app(ty_[], chd)) → new_esEs12(zzz5002, zzz4002, chd)
new_compare4(:(zzz500000, zzz500001), :(zzz4300000, zzz4300001), ce) → new_primCompAux0(zzz500000, zzz4300000, new_compare4(zzz500001, zzz4300001, ce), ce)
new_compare16(Float(zzz500000, zzz500001), Float(zzz4300000, zzz4300001)) → new_compare8(new_sr0(zzz500000, zzz4300000), new_sr0(zzz500001, zzz4300001))
new_esEs26(zzz5002, zzz4002, app(ty_Maybe, chh)) → new_esEs7(zzz5002, zzz4002, chh)
new_esEs28(zzz5000, zzz4000, ty_Bool) → new_esEs14(zzz5000, zzz4000)
new_compare110(zzz500000, zzz4300000, True, hc, hd, he) → LT
new_lt19(zzz500000, zzz4300000, app(app(ty_Either, ccg), cch)) → new_lt5(zzz500000, zzz4300000, ccg, cch)
new_ltEs18(zzz50000, zzz430000, ty_Bool) → new_ltEs14(zzz50000, zzz430000)
new_esEs28(zzz5000, zzz4000, ty_Integer) → new_esEs15(zzz5000, zzz4000)
new_esEs18(zzz5001, zzz4001, ty_Ordering) → new_esEs8(zzz5001, zzz4001)
new_esEs19(zzz5000, zzz4000, ty_Double) → new_esEs9(zzz5000, zzz4000)
new_lt20(zzz500001, zzz4300001, app(app(ty_@2, cec), ced)) → new_lt16(zzz500001, zzz4300001, cec, ced)
new_esEs5(@2(zzz5000, zzz5001), @2(zzz4000, zzz4001), eb, ec) → new_asAs(new_esEs19(zzz5000, zzz4000, eb), new_esEs18(zzz5001, zzz4001, ec))
new_compare26(zzz500000, zzz4300000, False) → new_compare19(zzz500000, zzz4300000, new_ltEs14(zzz500000, zzz4300000))
new_esEs28(zzz5000, zzz4000, app(app(ty_Either, dbd), dbe)) → new_esEs4(zzz5000, zzz4000, dbd, dbe)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, app(ty_Maybe, bhf)) → new_esEs7(zzz5000, zzz4000, bhf)
new_esEs7(Just(zzz5000), Just(zzz4000), ty_@0) → new_esEs10(zzz5000, zzz4000)
new_ltEs18(zzz50000, zzz430000, ty_Char) → new_ltEs5(zzz50000, zzz430000)
new_esEs28(zzz5000, zzz4000, ty_Float) → new_esEs13(zzz5000, zzz4000)
new_lt13(zzz500000, zzz4300000, ty_Ordering) → new_lt9(zzz500000, zzz4300000)
new_esEs25(zzz500000, zzz4300000, app(app(app(ty_@3, cde), cdf), cdg)) → new_esEs6(zzz500000, zzz4300000, cde, cdf, cdg)
new_ltEs10(EQ, EQ) → True
new_ltEs18(zzz50000, zzz430000, app(app(ty_@2, bed), bee)) → new_ltEs13(zzz50000, zzz430000, bed, bee)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Int, bfb) → new_esEs17(zzz5000, zzz4000)
new_esEs23(zzz500000, zzz4300000, ty_Integer) → new_esEs15(zzz500000, zzz4300000)
new_ltEs10(LT, LT) → True
new_esEs14(True, True) → True
new_compare111(zzz200, zzz201, False, bbd) → GT
new_esEs27(zzz5001, zzz4001, ty_Bool) → new_esEs14(zzz5001, zzz4001)
new_esEs7(Just(zzz5000), Just(zzz4000), app(app(ty_Either, cg), da)) → new_esEs4(zzz5000, zzz4000, cg, da)
new_compare10(Char(zzz500000), Char(zzz4300000)) → new_primCmpNat0(zzz500000, zzz4300000)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Float, bfb) → new_esEs13(zzz5000, zzz4000)
new_lt13(zzz500000, zzz4300000, app(app(ty_@2, hf), hg)) → new_lt16(zzz500000, zzz4300000, hf, hg)
new_ltEs7(Left(zzz500000), Left(zzz4300000), app(app(ty_@2, bbh), bca), bbe) → new_ltEs13(zzz500000, zzz4300000, bbh, bca)
new_esEs7(Just(zzz5000), Just(zzz4000), app(ty_Ratio, ea)) → new_esEs16(zzz5000, zzz4000, ea)
new_lt13(zzz500000, zzz4300000, app(ty_Maybe, cbb)) → new_lt11(zzz500000, zzz4300000, cbb)
new_ltEs20(zzz500002, zzz4300002, app(app(ty_Either, cfc), cfd)) → new_ltEs7(zzz500002, zzz4300002, cfc, cfd)
new_esEs18(zzz5001, zzz4001, ty_@0) → new_esEs10(zzz5001, zzz4001)
new_ltEs16(@3(zzz500000, zzz500001, zzz500002), @3(zzz4300000, zzz4300001, zzz4300002), beg, beh, bfa) → new_pePe(new_lt19(zzz500000, zzz4300000, beg), new_asAs(new_esEs25(zzz500000, zzz4300000, beg), new_pePe(new_lt20(zzz500001, zzz4300001, beh), new_asAs(new_esEs24(zzz500001, zzz4300001, beh), new_ltEs20(zzz500002, zzz4300002, bfa)))))
new_esEs4(Right(zzz5000), Right(zzz4000), bge, ty_Double) → new_esEs9(zzz5000, zzz4000)
new_ltEs14(True, False) → False
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_esEs20(zzz5000, zzz4000, ty_Int) → new_esEs17(zzz5000, zzz4000)
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_esEs25(zzz500000, zzz4300000, app(app(ty_@2, cda), cdb)) → new_esEs5(zzz500000, zzz4300000, cda, cdb)
new_ltEs20(zzz500002, zzz4300002, ty_Double) → new_ltEs8(zzz500002, zzz4300002)
new_ltEs7(Left(zzz500000), Left(zzz4300000), app(ty_Ratio, bcc), bbe) → new_ltEs15(zzz500000, zzz4300000, bcc)
new_ltEs19(zzz500001, zzz4300001, app(app(app(ty_@3, ccc), ccd), cce)) → new_ltEs16(zzz500001, zzz4300001, ccc, ccd, cce)
new_ltEs20(zzz500002, zzz4300002, app(app(app(ty_@3, cga), cgb), cgc)) → new_ltEs16(zzz500002, zzz4300002, cga, cgb, cgc)
new_compare112(zzz500000, zzz4300000, False) → GT
new_ltEs10(EQ, LT) → False
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Float) → new_esEs13(zzz5000, zzz4000)
new_esEs14(False, False) → True
new_esEs7(Just(zzz5000), Just(zzz4000), app(app(ty_@2, db), dc)) → new_esEs5(zzz5000, zzz4000, db, dc)
new_lt20(zzz500001, zzz4300001, ty_Char) → new_lt12(zzz500001, zzz4300001)
new_lt9(zzz500000, zzz4300000) → new_esEs8(new_compare6(zzz500000, zzz4300000), LT)
new_ltEs10(GT, LT) → False
new_esEs18(zzz5001, zzz4001, ty_Bool) → new_esEs14(zzz5001, zzz4001)
new_esEs22(zzz5000, zzz4000, ty_Integer) → new_esEs15(zzz5000, zzz4000)
new_primPlusNat1(Zero, Zero) → Zero
new_compare30(zzz500000, zzz4300000, app(app(app(ty_@3, caf), cag), cah)) → new_compare13(zzz500000, zzz4300000, caf, cag, cah)
new_esEs19(zzz5000, zzz4000, ty_Integer) → new_esEs15(zzz5000, zzz4000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(ty_[], bfg), bfb) → new_esEs12(zzz5000, zzz4000, bfg)
new_esEs26(zzz5002, zzz4002, app(app(ty_Either, cgh), cha)) → new_esEs4(zzz5002, zzz4002, cgh, cha)
new_asAs(True, zzz207) → zzz207
new_esEs28(zzz5000, zzz4000, app(ty_[], dbh)) → new_esEs12(zzz5000, zzz4000, dbh)
new_esEs27(zzz5001, zzz4001, app(ty_[], daf)) → new_esEs12(zzz5001, zzz4001, daf)
new_esEs19(zzz5000, zzz4000, app(app(ty_Either, fg), fh)) → new_esEs4(zzz5000, zzz4000, fg, fh)
new_ltEs4(Just(zzz500000), Nothing, bb) → False
new_esEs20(zzz5000, zzz4000, ty_Double) → new_esEs9(zzz5000, zzz4000)
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_ltEs4(Just(zzz500000), Just(zzz4300000), app(ty_[], cd)) → new_ltEs17(zzz500000, zzz4300000, cd)
new_esEs4(Right(zzz5000), Left(zzz4000), bge, bfb) → False
new_esEs4(Left(zzz5000), Right(zzz4000), bge, bfb) → False
new_ltEs19(zzz500001, zzz4300001, ty_Float) → new_ltEs12(zzz500001, zzz4300001)
new_ltEs20(zzz500002, zzz4300002, app(ty_Maybe, cfg)) → new_ltEs4(zzz500002, zzz4300002, cfg)
new_esEs4(Left(zzz5000), Left(zzz4000), app(app(app(ty_@3, bfh), bga), bgb), bfb) → new_esEs6(zzz5000, zzz4000, bfh, bga, bgb)
new_ltEs19(zzz500001, zzz4300001, ty_Char) → new_ltEs5(zzz500001, zzz4300001)
new_fsEs(zzz210) → new_not(new_esEs8(zzz210, GT))
new_esEs19(zzz5000, zzz4000, ty_@0) → new_esEs10(zzz5000, zzz4000)
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Bool) → new_esEs14(zzz5000, zzz4000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Double, bbe) → new_ltEs8(zzz500000, zzz4300000)
new_esEs24(zzz500001, zzz4300001, ty_Float) → new_esEs13(zzz500001, zzz4300001)
new_ltEs11(zzz50000, zzz430000) → new_fsEs(new_compare11(zzz50000, zzz430000))
new_lt20(zzz500001, zzz4300001, ty_Int) → new_lt14(zzz500001, zzz4300001)
new_esEs4(Right(zzz5000), Right(zzz4000), bge, ty_Float) → new_esEs13(zzz5000, zzz4000)
new_esEs19(zzz5000, zzz4000, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_ltEs20(zzz500002, zzz4300002, app(app(ty_@2, cfe), cff)) → new_ltEs13(zzz500002, zzz4300002, cfe, cff)
new_esEs27(zzz5001, zzz4001, ty_Char) → new_esEs11(zzz5001, zzz4001)
new_ltEs20(zzz500002, zzz4300002, ty_Int) → new_ltEs6(zzz500002, zzz4300002)
new_compare110(zzz500000, zzz4300000, False, hc, hd, he) → GT
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Char) → new_ltEs5(zzz500000, zzz4300000)
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Char) → new_esEs11(zzz5000, zzz4000)
new_primCompAux00(zzz225, GT) → GT
new_ltEs20(zzz500002, zzz4300002, ty_Integer) → new_ltEs9(zzz500002, zzz4300002)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, app(ty_Maybe, bde)) → new_ltEs4(zzz500000, zzz4300000, bde)
new_lt19(zzz500000, zzz4300000, ty_Int) → new_lt14(zzz500000, zzz4300000)
new_ltEs4(Just(zzz500000), Just(zzz4300000), app(app(app(ty_@3, ca), cb), cc)) → new_ltEs16(zzz500000, zzz4300000, ca, cb, cc)
new_ltEs18(zzz50000, zzz430000, ty_Ordering) → new_ltEs10(zzz50000, zzz430000)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Integer) → new_ltEs9(zzz500000, zzz4300000)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_compare30(zzz500000, zzz4300000, ty_Ordering) → new_compare6(zzz500000, zzz4300000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, ty_Float) → new_ltEs12(zzz500000, zzz4300000)
new_esEs27(zzz5001, zzz4001, ty_Integer) → new_esEs15(zzz5001, zzz4001)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, ty_Int) → new_ltEs6(zzz500000, zzz4300000)
new_not(True) → False

The set Q consists of the following terms:

new_compare30(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_compare23(x0, x1, True)
new_lt11(x0, x1, x2)
new_lt14(x0, x1)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs18(x0, x1, app(app(ty_@2, x2), x3))
new_asAs(True, x0)
new_compare29(Nothing, Nothing, False, x0)
new_compare19(x0, x1, True)
new_esEs26(x0, x1, ty_@0)
new_ltEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs18(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_Ordering)
new_esEs18(x0, x1, ty_Int)
new_ltEs19(x0, x1, app(ty_[], x2))
new_primPlusNat1(Zero, Succ(x0))
new_compare29(Nothing, Just(x0), False, x1)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_compare30(x0, x1, ty_@0)
new_lt20(x0, x1, ty_Ordering)
new_esEs9(Double(x0, x1), Double(x2, x3))
new_ltEs7(Right(x0), Right(x1), x2, ty_@0)
new_primCompAux0(x0, x1, x2, x3)
new_primMulNat0(Succ(x0), Zero)
new_lt19(x0, x1, ty_Double)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_@0)
new_primPlusNat1(Succ(x0), Zero)
new_esEs21(x0, x1, ty_Int)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare4(:(x0, x1), :(x2, x3), x4)
new_ltEs10(LT, LT)
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_esEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs16(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs23(x0, x1, ty_Bool)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs27(x0, x1, ty_Int)
new_esEs4(Right(x0), Left(x1), x2, x3)
new_esEs4(Left(x0), Right(x1), x2, x3)
new_esEs18(x0, x1, ty_Char)
new_esEs24(x0, x1, ty_Char)
new_ltEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(True, False)
new_ltEs14(False, True)
new_esEs25(x0, x1, ty_Double)
new_pePe(False, x0)
new_esEs19(x0, x1, ty_Char)
new_esEs25(x0, x1, ty_Char)
new_compare27(x0, x1, True, x2, x3)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs7(Just(x0), Just(x1), ty_Double)
new_esEs8(GT, GT)
new_esEs23(x0, x1, ty_@0)
new_compare4([], :(x0, x1), x2)
new_lt9(x0, x1)
new_lt19(x0, x1, ty_Ordering)
new_esEs11(Char(x0), Char(x1))
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs4(Left(x0), Left(x1), ty_Int, x2)
new_esEs7(Nothing, Just(x0), x1)
new_esEs8(LT, LT)
new_sr0(x0, x1)
new_compare6(x0, x1)
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_compare30(x0, x1, ty_Double)
new_esEs7(Just(x0), Just(x1), ty_Char)
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, app(ty_[], x2))
new_lt13(x0, x1, app(ty_Ratio, x2))
new_compare19(x0, x1, False)
new_ltEs4(Nothing, Nothing, x0)
new_compare110(x0, x1, False, x2, x3, x4)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs26(x0, x1, ty_Double)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_lt18(x0, x1, x2)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_lt16(x0, x1, x2, x3)
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_compare111(x0, x1, False, x2)
new_compare4([], [], x0)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs7(Left(x0), Left(x1), ty_Char, x2)
new_ltEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs17(x0, x1)
new_ltEs19(x0, x1, ty_Char)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs14(True, True)
new_compare26(x0, x1, True)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Char)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare112(x0, x1, False)
new_esEs18(x0, x1, ty_Bool)
new_esEs20(x0, x1, ty_Float)
new_primEqNat0(Zero, Zero)
new_ltEs4(Just(x0), Just(x1), ty_Double)
new_compare30(x0, x1, ty_Char)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_ltEs7(Right(x0), Right(x1), x2, ty_Char)
new_esEs20(x0, x1, ty_Int)
new_lt13(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Double)
new_lt19(x0, x1, ty_Bool)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, ty_@0)
new_lt13(x0, x1, app(ty_[], x2))
new_esEs12([], :(x0, x1), x2)
new_esEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs28(x0, x1, ty_Integer)
new_compare17(x0, x1)
new_ltEs17(x0, x1, x2)
new_primPlusNat0(Zero, x0)
new_ltEs20(x0, x1, ty_Int)
new_compare13(x0, x1, x2, x3, x4)
new_primMulNat0(Zero, Zero)
new_esEs4(Right(x0), Right(x1), x2, ty_Float)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpNat0(Succ(x0), Zero)
new_compare16(Float(x0, x1), Float(x2, x3))
new_ltEs20(x0, x1, ty_Integer)
new_compare30(x0, x1, ty_Ordering)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs26(x0, x1, ty_Integer)
new_ltEs10(EQ, LT)
new_ltEs10(LT, EQ)
new_lt4(x0, x1)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_ltEs7(Left(x0), Left(x1), ty_@0, x2)
new_lt13(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs19(x0, x1, ty_Bool)
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs28(x0, x1, ty_@0)
new_primMulNat0(Succ(x0), Succ(x1))
new_lt7(x0, x1)
new_esEs23(x0, x1, ty_Float)
new_ltEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_Double)
new_compare113(x0, x1, False, x2, x3)
new_ltEs18(x0, x1, ty_@0)
new_compare15(x0, x1, True, x2, x3)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs23(x0, x1, ty_Char)
new_esEs24(x0, x1, ty_Int)
new_compare9(Integer(x0), Integer(x1))
new_esEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, ty_Ordering)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_ltEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_compare4(:(x0, x1), [], x2)
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_esEs24(x0, x1, ty_Bool)
new_ltEs13(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs26(x0, x1, ty_Char)
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_compare25(x0, x1, False, x2, x3)
new_esEs20(x0, x1, ty_Ordering)
new_esEs12(:(x0, x1), :(x2, x3), x4)
new_fsEs(x0)
new_lt8(x0, x1, x2, x3, x4)
new_ltEs11(x0, x1)
new_esEs23(x0, x1, ty_Double)
new_lt13(x0, x1, ty_@0)
new_ltEs7(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Just(x0), Just(x1), ty_Int)
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_compare26(x0, x1, False)
new_ltEs18(x0, x1, ty_Double)
new_ltEs7(Right(x0), Left(x1), x2, x3)
new_ltEs7(Left(x0), Right(x1), x2, x3)
new_ltEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs25(x0, x1, ty_Bool)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primPlusNat1(Zero, Zero)
new_esEs28(x0, x1, ty_Float)
new_ltEs7(Right(x0), Right(x1), x2, ty_Int)
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_lt12(x0, x1)
new_compare7(:%(x0, x1), :%(x2, x3), ty_Int)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_ltEs4(Just(x0), Just(x1), ty_Int)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_compare11(@0, @0)
new_esEs4(Right(x0), Right(x1), x2, ty_Integer)
new_primMulNat0(Zero, Succ(x0))
new_esEs26(x0, x1, ty_Bool)
new_asAs(False, x0)
new_esEs12(:(x0, x1), [], x2)
new_ltEs4(Just(x0), Just(x1), ty_Bool)
new_ltEs8(x0, x1)
new_ltEs18(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Float)
new_esEs27(x0, x1, ty_Double)
new_ltEs19(x0, x1, ty_Ordering)
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs4(Just(x0), Just(x1), ty_Ordering)
new_esEs4(Left(x0), Left(x1), ty_@0, x2)
new_esEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs18(x0, x1, ty_Double)
new_ltEs10(GT, LT)
new_esEs4(Left(x0), Left(x1), ty_Double, x2)
new_ltEs10(LT, GT)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs28(x0, x1, ty_Double)
new_esEs10(@0, @0)
new_compare14(Double(x0, x1), Double(x2, x3))
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_compare24(x0, x1, True, x2, x3, x4)
new_compare30(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_Integer)
new_ltEs18(x0, x1, ty_Float)
new_compare8(x0, x1)
new_lt13(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs20(x0, x1, ty_Char)
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs7(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs19(x0, x1, ty_Integer)
new_pePe(True, x0)
new_compare29(Just(x0), Just(x1), False, x2)
new_esEs27(x0, x1, ty_Float)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_primCompAux00(x0, EQ)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_lt19(x0, x1, ty_Float)
new_primEqNat0(Succ(x0), Zero)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_ltEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_lt17(x0, x1, x2)
new_esEs28(x0, x1, ty_Int)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_compare27(x0, x1, False, x2, x3)
new_esEs18(x0, x1, ty_Ordering)
new_esEs25(x0, x1, ty_Int)
new_esEs18(x0, x1, app(ty_Ratio, x2))
new_esEs7(Nothing, Nothing, x0)
new_ltEs15(x0, x1, x2)
new_ltEs4(Just(x0), Just(x1), ty_@0)
new_esEs19(x0, x1, app(ty_[], x2))
new_compare23(x0, x1, False)
new_compare30(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_ltEs4(Just(x0), Nothing, x1)
new_esEs8(EQ, EQ)
new_compare112(x0, x1, True)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs4(Right(x0), Right(x1), x2, ty_Int)
new_esEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs19(x0, x1, ty_Double)
new_esEs13(Float(x0, x1), Float(x2, x3))
new_primEqInt(Neg(Zero), Neg(Zero))
new_gt(x0, x1, x2)
new_lt13(x0, x1, ty_Char)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, ty_Char)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_esEs15(Integer(x0), Integer(x1))
new_ltEs12(x0, x1)
new_ltEs20(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_@0)
new_esEs14(True, False)
new_esEs14(False, True)
new_ltEs4(Just(x0), Just(x1), ty_Float)
new_ltEs7(Right(x0), Right(x1), x2, ty_Float)
new_esEs18(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, app(ty_[], x2))
new_ltEs6(x0, x1)
new_esEs22(x0, x1, ty_Int)
new_esEs20(x0, x1, ty_Double)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare110(x0, x1, True, x2, x3, x4)
new_ltEs9(x0, x1)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs19(x0, x1, ty_@0)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_lt19(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Ordering)
new_esEs27(x0, x1, ty_Integer)
new_esEs16(:%(x0, x1), :%(x2, x3), x4)
new_lt20(x0, x1, ty_Float)
new_compare25(x0, x1, True, x2, x3)
new_compare30(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Integer)
new_primCmpNat0(Succ(x0), Succ(x1))
new_lt19(x0, x1, ty_Char)
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_esEs20(x0, x1, ty_Integer)
new_esEs28(x0, x1, ty_Ordering)
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_esEs21(x0, x1, ty_Integer)
new_compare28(x0, x1, x2)
new_ltEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_esEs4(Right(x0), Right(x1), x2, ty_Double)
new_ltEs7(Right(x0), Right(x1), x2, ty_Double)
new_lt20(x0, x1, ty_Bool)
new_primPlusNat0(Succ(x0), x1)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_@0)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, ty_Integer)
new_compare30(x0, x1, app(ty_Maybe, x2))
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs7(Just(x0), Just(x1), ty_Float)
new_compare18(x0, x1, x2, x3)
new_esEs19(x0, x1, ty_Float)
new_ltEs20(x0, x1, ty_Bool)
new_primCmpNat0(Zero, Zero)
new_esEs4(Left(x0), Left(x1), ty_Integer, x2)
new_esEs19(x0, x1, ty_Ordering)
new_lt13(x0, x1, ty_Bool)
new_ltEs19(x0, x1, ty_Float)
new_esEs27(x0, x1, app(ty_[], x2))
new_ltEs7(Left(x0), Left(x1), ty_Double, x2)
new_esEs12([], [], x0)
new_lt10(x0, x1)
new_compare7(:%(x0, x1), :%(x2, x3), ty_Integer)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_compare113(x0, x1, True, x2, x3)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs20(x0, x1, app(ty_[], x2))
new_ltEs7(Left(x0), Left(x1), ty_Bool, x2)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, ty_Ordering)
new_esEs4(Left(x0), Left(x1), ty_Char, x2)
new_esEs26(x0, x1, ty_Float)
new_ltEs7(Left(x0), Left(x1), ty_Float, x2)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt5(x0, x1, x2, x3)
new_esEs28(x0, x1, app(ty_[], x2))
new_compare29(Just(x0), Nothing, False, x1)
new_ltEs10(GT, GT)
new_ltEs14(True, True)
new_ltEs14(False, False)
new_esEs24(x0, x1, ty_Ordering)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_lt19(x0, x1, ty_@0)
new_esEs18(x0, x1, ty_Float)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_lt13(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, ty_Char)
new_ltEs7(Left(x0), Left(x1), ty_Int, x2)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_esEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_not(True)
new_esEs19(x0, x1, ty_Int)
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Just(x0), Just(x1), ty_@0)
new_compare30(x0, x1, ty_Integer)
new_ltEs5(x0, x1)
new_compare30(x0, x1, app(ty_Ratio, x2))
new_esEs4(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs20(x0, x1, ty_Double)
new_esEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(Just(x0), Just(x1), ty_Integer)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_not(False)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Integer)
new_esEs4(Right(x0), Right(x1), x2, ty_@0)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_ltEs4(Just(x0), Just(x1), app(ty_[], x2))
new_primCompAux00(x0, LT)
new_lt6(x0, x1)
new_ltEs10(EQ, GT)
new_ltEs10(GT, EQ)
new_ltEs19(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Float)
new_esEs24(x0, x1, app(ty_[], x2))
new_ltEs18(x0, x1, ty_Char)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs19(x0, x1, ty_Integer)
new_esEs18(x0, x1, app(ty_[], x2))
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_sr(Integer(x0), Integer(x1))
new_esEs4(Right(x0), Right(x1), x2, ty_Char)
new_esEs27(x0, x1, ty_Char)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs20(x0, x1, ty_Bool)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(Just(x0), Just(x1), ty_Char)
new_esEs4(Left(x0), Left(x1), ty_Float, x2)
new_ltEs4(Nothing, Just(x0), x1)
new_esEs18(x0, x1, ty_@0)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_ltEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_lt13(x0, x1, ty_Double)
new_esEs18(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_Bool)
new_lt13(x0, x1, ty_Ordering)
new_compare12(x0, x1, x2, x3)
new_compare15(x0, x1, False, x2, x3)
new_ltEs18(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Ordering)
new_compare30(x0, x1, ty_Float)
new_esEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare111(x0, x1, True, x2)
new_lt13(x0, x1, ty_Integer)
new_lt19(x0, x1, app(ty_[], x2))
new_esEs14(False, False)
new_primEqInt(Pos(Zero), Pos(Zero))
new_compare30(x0, x1, app(ty_[], x2))
new_compare10(Char(x0), Char(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs24(x0, x1, ty_Integer)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Double)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs25(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, ty_Float)
new_lt13(x0, x1, ty_Int)
new_compare29(x0, x1, True, x2)
new_lt13(x0, x1, ty_Float)
new_lt20(x0, x1, ty_Integer)
new_primCmpNat0(Zero, Succ(x0))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_ltEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_Int)
new_primCompAux00(x0, GT)
new_ltEs20(x0, x1, ty_@0)
new_esEs4(Left(x0), Left(x1), ty_Bool, x2)
new_lt15(x0, x1)
new_ltEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primEqNat0(Zero, Succ(x0))
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs7(Left(x0), Left(x1), ty_Integer, x2)
new_esEs27(x0, x1, ty_Bool)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_@0)
new_compare24(x0, x1, False, x2, x3, x4)
new_esEs7(Just(x0), Nothing, x1)
new_esEs18(x0, x1, ty_Integer)
new_ltEs10(EQ, EQ)

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
                                    ↳ QDPSizeChangeProof
                                  ↳ QDP
                                  ↳ QDP

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

new_splitLT20(zzz430, zzz431, zzz432, Branch(zzz4330, zzz4331, zzz4332, zzz4333, zzz4334), zzz434, True, h, ba) → new_splitLT20(zzz4330, zzz4331, zzz4332, zzz4333, zzz4334, new_lt11(Nothing, zzz4330, h), h, ba)
new_splitLT0(Branch(zzz4330, zzz4331, zzz4332, zzz4333, zzz4334), h, ba) → new_splitLT20(zzz4330, zzz4331, zzz4332, zzz4333, zzz4334, new_lt11(Nothing, zzz4330, h), h, ba)
new_splitLT20(zzz430, zzz431, zzz432, zzz433, zzz434, False, h, ba) → new_splitLT10(zzz430, zzz431, zzz432, zzz433, zzz434, new_gt1(zzz430, h), h, ba)
new_splitLT10(zzz430, zzz431, zzz432, zzz433, zzz434, True, h, ba) → new_splitLT0(zzz434, h, ba)

The TRS R consists of the following rules:

new_lt19(zzz500000, zzz4300000, ty_Float) → new_lt6(zzz500000, zzz4300000)
new_ltEs18(zzz50000, zzz430000, app(ty_Ratio, bee)) → new_ltEs15(zzz50000, zzz430000, bee)
new_esEs7(Just(zzz5000), Just(zzz4000), app(ty_Maybe, dh)) → new_esEs7(zzz5000, zzz4000, dh)
new_esEs4(Right(zzz5000), Right(zzz4000), bgd, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_esEs20(zzz5000, zzz4000, app(ty_Maybe, bba)) → new_esEs7(zzz5000, zzz4000, bba)
new_esEs12(:(zzz5000, zzz5001), :(zzz4000, zzz4001), hh) → new_asAs(new_esEs20(zzz5000, zzz4000, hh), new_esEs12(zzz5001, zzz4001, hh))
new_esEs7(Just(zzz5000), Just(zzz4000), app(ty_[], dd)) → new_esEs12(zzz5000, zzz4000, dd)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, ty_Ordering) → new_ltEs10(zzz500000, zzz4300000)
new_lt19(zzz500000, zzz4300000, app(app(app(ty_@3, cdd), cde), cdf)) → new_lt8(zzz500000, zzz4300000, cdd, cde, cdf)
new_ltEs18(zzz50000, zzz430000, app(app(app(ty_@3, bef), beg), beh)) → new_ltEs16(zzz50000, zzz430000, bef, beg, beh)
new_lt20(zzz500001, zzz4300001, app(ty_[], cfa)) → new_lt18(zzz500001, zzz4300001, cfa)
new_esEs4(Right(zzz5000), Right(zzz4000), bgd, ty_Char) → new_esEs11(zzz5000, zzz4000)
new_compare15(zzz500000, zzz4300000, True, hf, hg) → LT
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Bool, bfa) → new_esEs14(zzz5000, zzz4000)
new_ltEs18(zzz50000, zzz430000, app(ty_Maybe, bb)) → new_ltEs4(zzz50000, zzz430000, bb)
new_ltEs20(zzz500002, zzz4300002, ty_Ordering) → new_ltEs10(zzz500002, zzz4300002)
new_esEs4(Right(zzz5000), Right(zzz4000), bgd, app(app(app(ty_@3, bhb), bhc), bhd)) → new_esEs6(zzz5000, zzz4000, bhb, bhc, bhd)
new_lt13(zzz500000, zzz4300000, app(app(app(ty_@3, hc), hd), he)) → new_lt8(zzz500000, zzz4300000, hc, hd, he)
new_compare32(zzz430, h) → new_compare29(Nothing, zzz430, new_esEs30(zzz430, h), h)
new_lt15(zzz500000, zzz4300000) → new_esEs8(new_compare14(zzz500000, zzz4300000), LT)
new_lt20(zzz500001, zzz4300001, app(app(app(ty_@3, cef), ceg), ceh)) → new_lt8(zzz500001, zzz4300001, cef, ceg, ceh)
new_esEs27(zzz5001, zzz4001, app(ty_Maybe, dba)) → new_esEs7(zzz5001, zzz4001, dba)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Ordering) → new_ltEs10(zzz500000, zzz4300000)
new_esEs23(zzz500000, zzz4300000, ty_Bool) → new_esEs14(zzz500000, zzz4300000)
new_compare27(zzz500000, zzz4300000, False, ha, hb) → new_compare113(zzz500000, zzz4300000, new_ltEs7(zzz500000, zzz4300000, ha, hb), ha, hb)
new_lt19(zzz500000, zzz4300000, ty_Double) → new_lt15(zzz500000, zzz4300000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), app(ty_Maybe, bcb), bbe) → new_ltEs4(zzz500000, zzz4300000, bcb)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, ty_@0) → new_ltEs11(zzz500000, zzz4300000)
new_ltEs20(zzz500002, zzz4300002, app(ty_Ratio, cfg)) → new_ltEs15(zzz500002, zzz4300002, cfg)
new_lt13(zzz500000, zzz4300000, app(ty_[], cbc)) → new_lt18(zzz500000, zzz4300000, cbc)
new_esEs26(zzz5002, zzz4002, ty_Float) → new_esEs13(zzz5002, zzz4002)
new_ltEs7(Left(zzz500000), Right(zzz4300000), bch, bbe) → True
new_primMulNat0(Zero, Zero) → Zero
new_esEs19(zzz5000, zzz4000, ty_Int) → new_esEs17(zzz5000, zzz4000)
new_sr(Integer(zzz43000000), Integer(zzz5000010)) → Integer(new_primMulInt(zzz43000000, zzz5000010))
new_ltEs20(zzz500002, zzz4300002, ty_Float) → new_ltEs12(zzz500002, zzz4300002)
new_ltEs20(zzz500002, zzz4300002, ty_@0) → new_ltEs11(zzz500002, zzz4300002)
new_esEs20(zzz5000, zzz4000, app(ty_Ratio, bbb)) → new_esEs16(zzz5000, zzz4000, bbb)
new_esEs18(zzz5001, zzz4001, ty_Double) → new_esEs9(zzz5001, zzz4001)
new_lt20(zzz500001, zzz4300001, ty_Float) → new_lt6(zzz500001, zzz4300001)
new_esEs23(zzz500000, zzz4300000, ty_Double) → new_esEs9(zzz500000, zzz4300000)
new_esEs4(Right(zzz5000), Right(zzz4000), bgd, app(ty_[], bha)) → new_esEs12(zzz5000, zzz4000, bha)
new_esEs24(zzz500001, zzz4300001, ty_Integer) → new_esEs15(zzz500001, zzz4300001)
new_ltEs14(False, True) → True
new_ltEs19(zzz500001, zzz4300001, ty_Integer) → new_ltEs9(zzz500001, zzz4300001)
new_ltEs4(Just(zzz500000), Just(zzz4300000), app(app(ty_@2, be), bf)) → new_ltEs13(zzz500000, zzz4300000, be, bf)
new_esEs20(zzz5000, zzz4000, app(app(ty_Either, baa), bab)) → new_esEs4(zzz5000, zzz4000, baa, bab)
new_esEs12([], [], hh) → True
new_ltEs19(zzz500001, zzz4300001, ty_Ordering) → new_ltEs10(zzz500001, zzz4300001)
new_esEs24(zzz500001, zzz4300001, app(app(ty_@2, ceb), cec)) → new_esEs5(zzz500001, zzz4300001, ceb, cec)
new_lt12(zzz500000, zzz4300000) → new_esEs8(new_compare10(zzz500000, zzz4300000), LT)
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Ordering, bbe) → new_ltEs10(zzz500000, zzz4300000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, app(ty_Ratio, bdf)) → new_ltEs15(zzz500000, zzz4300000, bdf)
new_esEs15(Integer(zzz5000), Integer(zzz4000)) → new_primEqInt(zzz5000, zzz4000)
new_ltEs10(EQ, GT) → True
new_ltEs19(zzz500001, zzz4300001, app(ty_Maybe, cbh)) → new_ltEs4(zzz500001, zzz4300001, cbh)
new_esEs21(zzz5001, zzz4001, ty_Int) → new_esEs17(zzz5001, zzz4001)
new_ltEs7(Left(zzz500000), Left(zzz4300000), app(app(app(ty_@3, bcd), bce), bcf), bbe) → new_ltEs16(zzz500000, zzz4300000, bcd, bce, bcf)
new_lt13(zzz500000, zzz4300000, ty_Char) → new_lt12(zzz500000, zzz4300000)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Ordering, bfa) → new_esEs8(zzz5000, zzz4000)
new_esEs24(zzz500001, zzz4300001, app(ty_[], cfa)) → new_esEs12(zzz500001, zzz4300001, cfa)
new_esEs25(zzz500000, zzz4300000, ty_Double) → new_esEs9(zzz500000, zzz4300000)
new_esEs25(zzz500000, zzz4300000, ty_Float) → new_esEs13(zzz500000, zzz4300000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, app(ty_[], beb)) → new_ltEs17(zzz500000, zzz4300000, beb)
new_pePe(False, zzz218) → zzz218
new_lt14(zzz5000, zzz43000) → new_esEs8(new_compare8(zzz5000, zzz43000), LT)
new_esEs25(zzz500000, zzz4300000, app(app(ty_Either, ccf), ccg)) → new_esEs4(zzz500000, zzz4300000, ccf, ccg)
new_esEs12(:(zzz5000, zzz5001), [], hh) → False
new_esEs12([], :(zzz4000, zzz4001), hh) → False
new_esEs25(zzz500000, zzz4300000, ty_Char) → new_esEs11(zzz500000, zzz4300000)
new_esEs25(zzz500000, zzz4300000, ty_Bool) → new_esEs14(zzz500000, zzz4300000)
new_lt19(zzz500000, zzz4300000, ty_Ordering) → new_lt9(zzz500000, zzz4300000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, app(app(ty_@2, bdc), bdd)) → new_ltEs13(zzz500000, zzz4300000, bdc, bdd)
new_esEs4(Right(zzz5000), Right(zzz4000), bgd, app(ty_Ratio, bhf)) → new_esEs16(zzz5000, zzz4000, bhf)
new_compare23(zzz500000, zzz4300000, True) → EQ
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Float, bbe) → new_ltEs12(zzz500000, zzz4300000)
new_lt19(zzz500000, zzz4300000, app(ty_Ratio, cdc)) → new_lt17(zzz500000, zzz4300000, cdc)
new_esEs24(zzz500001, zzz4300001, app(ty_Maybe, ced)) → new_esEs7(zzz500001, zzz4300001, ced)
new_ltEs4(Nothing, Just(zzz4300000), bb) → True
new_esEs23(zzz500000, zzz4300000, app(ty_Maybe, cba)) → new_esEs7(zzz500000, zzz4300000, cba)
new_compare30(zzz500000, zzz4300000, ty_Integer) → new_compare9(zzz500000, zzz4300000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(ty_Ratio, bgc), bfa) → new_esEs16(zzz5000, zzz4000, bgc)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, ty_Char) → new_ltEs5(zzz500000, zzz4300000)
new_compare13(zzz500000, zzz4300000, hc, hd, he) → new_compare24(zzz500000, zzz4300000, new_esEs6(zzz500000, zzz4300000, hc, hd, he), hc, hd, he)
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_lt4(zzz500000, zzz4300000) → new_esEs8(new_compare11(zzz500000, zzz4300000), LT)
new_esEs4(Right(zzz5000), Right(zzz4000), bgd, ty_Integer) → new_esEs15(zzz5000, zzz4000)
new_esEs20(zzz5000, zzz4000, app(app(ty_@2, bac), bad)) → new_esEs5(zzz5000, zzz4000, bac, bad)
new_esEs28(zzz5000, zzz4000, app(ty_Ratio, dcd)) → new_esEs16(zzz5000, zzz4000, dcd)
new_compare30(zzz500000, zzz4300000, app(ty_Ratio, cad)) → new_compare7(zzz500000, zzz4300000, cad)
new_compare19(zzz500000, zzz4300000, True) → LT
new_compare6(zzz500000, zzz4300000) → new_compare23(zzz500000, zzz4300000, new_esEs8(zzz500000, zzz4300000))
new_ltEs18(zzz50000, zzz430000, ty_@0) → new_ltEs11(zzz50000, zzz430000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_ltEs19(zzz500001, zzz4300001, app(ty_Ratio, cca)) → new_ltEs15(zzz500001, zzz4300001, cca)
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Int) → new_esEs17(zzz5000, zzz4000)
new_ltEs20(zzz500002, zzz4300002, ty_Bool) → new_ltEs14(zzz500002, zzz4300002)
new_esEs27(zzz5001, zzz4001, ty_@0) → new_esEs10(zzz5001, zzz4001)
new_ltEs12(zzz50000, zzz430000) → new_fsEs(new_compare16(zzz50000, zzz430000))
new_esEs8(LT, LT) → True
new_lt19(zzz500000, zzz4300000, app(app(ty_@2, cch), cda)) → new_lt16(zzz500000, zzz4300000, cch, cda)
new_esEs25(zzz500000, zzz4300000, ty_Ordering) → new_esEs8(zzz500000, zzz4300000)
new_esEs19(zzz5000, zzz4000, app(ty_Maybe, gg)) → new_esEs7(zzz5000, zzz4000, gg)
new_esEs20(zzz5000, zzz4000, app(app(app(ty_@3, baf), bag), bah)) → new_esEs6(zzz5000, zzz4000, baf, bag, bah)
new_esEs18(zzz5001, zzz4001, app(ty_Ratio, ff)) → new_esEs16(zzz5001, zzz4001, ff)
new_pePe(True, zzz218) → True
new_primEqNat0(Zero, Zero) → True
new_lt20(zzz500001, zzz4300001, app(app(ty_Either, cdh), cea)) → new_lt5(zzz500001, zzz4300001, cdh, cea)
new_compare26(zzz500000, zzz4300000, True) → EQ
new_lt20(zzz500001, zzz4300001, ty_Bool) → new_lt7(zzz500001, zzz4300001)
new_esEs13(Float(zzz5000, zzz5001), Float(zzz4000, zzz4001)) → new_esEs17(new_sr0(zzz5000, zzz4000), new_sr0(zzz5001, zzz4001))
new_esEs19(zzz5000, zzz4000, app(ty_[], gc)) → new_esEs12(zzz5000, zzz4000, gc)
new_compare29(Nothing, Just(zzz430000), False, gg) → LT
new_esEs19(zzz5000, zzz4000, ty_Float) → new_esEs13(zzz5000, zzz4000)
new_compare30(zzz500000, zzz4300000, app(ty_Maybe, cac)) → new_compare28(zzz500000, zzz4300000, cac)
new_esEs18(zzz5001, zzz4001, app(app(ty_@2, ef), eg)) → new_esEs5(zzz5001, zzz4001, ef, eg)
new_esEs25(zzz500000, zzz4300000, ty_Int) → new_esEs17(zzz500000, zzz4300000)
new_esEs9(Double(zzz5000, zzz5001), Double(zzz4000, zzz4001)) → new_esEs17(new_sr0(zzz5000, zzz4000), new_sr0(zzz5001, zzz4001))
new_esEs26(zzz5002, zzz4002, ty_Ordering) → new_esEs8(zzz5002, zzz4002)
new_esEs8(GT, GT) → True
new_lt20(zzz500001, zzz4300001, app(ty_Maybe, ced)) → new_lt11(zzz500001, zzz4300001, ced)
new_esEs18(zzz5001, zzz4001, app(app(app(ty_@3, fa), fb), fc)) → new_esEs6(zzz5001, zzz4001, fa, fb, fc)
new_esEs25(zzz500000, zzz4300000, ty_@0) → new_esEs10(zzz500000, zzz4300000)
new_compare4([], [], ce) → EQ
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_lt19(zzz500000, zzz4300000, ty_@0) → new_lt4(zzz500000, zzz4300000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(app(ty_@2, bfd), bfe), bfa) → new_esEs5(zzz5000, zzz4000, bfd, bfe)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, ty_Integer) → new_ltEs9(zzz500000, zzz4300000)
new_esEs26(zzz5002, zzz4002, app(app(app(ty_@3, chd), che), chf)) → new_esEs6(zzz5002, zzz4002, chd, che, chf)
new_compare18(zzz500000, zzz4300000, hf, hg) → new_compare25(zzz500000, zzz4300000, new_esEs5(zzz500000, zzz4300000, hf, hg), hf, hg)
new_ltEs17(zzz50000, zzz430000, ce) → new_fsEs(new_compare4(zzz50000, zzz430000, ce))
new_esEs8(GT, LT) → False
new_esEs8(LT, GT) → False
new_compare30(zzz500000, zzz4300000, app(ty_[], cah)) → new_compare4(zzz500000, zzz4300000, cah)
new_compare30(zzz500000, zzz4300000, ty_Double) → new_compare14(zzz500000, zzz4300000)
new_ltEs13(@2(zzz500000, zzz500001), @2(zzz4300000, zzz4300001), bec, bed) → new_pePe(new_lt13(zzz500000, zzz4300000, bec), new_asAs(new_esEs23(zzz500000, zzz4300000, bec), new_ltEs19(zzz500001, zzz4300001, bed)))
new_esEs4(Right(zzz5000), Right(zzz4000), bgd, app(app(ty_Either, bge), bgf)) → new_esEs4(zzz5000, zzz4000, bge, bgf)
new_esEs25(zzz500000, zzz4300000, app(ty_[], cdg)) → new_esEs12(zzz500000, zzz4300000, cdg)
new_compare24(zzz500000, zzz4300000, True, hc, hd, he) → EQ
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Int, bbe) → new_ltEs6(zzz500000, zzz4300000)
new_lt20(zzz500001, zzz4300001, ty_Ordering) → new_lt9(zzz500001, zzz4300001)
new_primEqInt(Neg(Succ(zzz50000)), Neg(Succ(zzz40000))) → new_primEqNat0(zzz50000, zzz40000)
new_esEs20(zzz5000, zzz4000, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_compare113(zzz500000, zzz4300000, True, ha, hb) → LT
new_esEs23(zzz500000, zzz4300000, ty_Ordering) → new_esEs8(zzz500000, zzz4300000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(app(ty_Either, bfb), bfc), bfa) → new_esEs4(zzz5000, zzz4000, bfb, bfc)
new_ltEs18(zzz50000, zzz430000, app(app(ty_Either, bch), bbe)) → new_ltEs7(zzz50000, zzz430000, bch, bbe)
new_esEs24(zzz500001, zzz4300001, ty_Bool) → new_esEs14(zzz500001, zzz4300001)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_lt19(zzz500000, zzz4300000, ty_Bool) → new_lt7(zzz500000, zzz4300000)
new_lt19(zzz500000, zzz4300000, ty_Integer) → new_lt10(zzz500000, zzz4300000)
new_ltEs4(Nothing, Nothing, bb) → True
new_lt13(zzz500000, zzz4300000, ty_Float) → new_lt6(zzz500000, zzz4300000)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_@0) → new_ltEs11(zzz500000, zzz4300000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Char, bbe) → new_ltEs5(zzz500000, zzz4300000)
new_lt13(zzz500000, zzz4300000, ty_Int) → new_lt14(zzz500000, zzz4300000)
new_lt6(zzz500000, zzz4300000) → new_esEs8(new_compare16(zzz500000, zzz4300000), LT)
new_compare29(Just(zzz50000), Nothing, False, gg) → GT
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_ltEs7(Right(zzz500000), Left(zzz4300000), bch, bbe) → False
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_esEs24(zzz500001, zzz4300001, app(app(app(ty_@3, cef), ceg), ceh)) → new_esEs6(zzz500001, zzz4300001, cef, ceg, ceh)
new_esEs23(zzz500000, zzz4300000, ty_Char) → new_esEs11(zzz500000, zzz4300000)
new_lt13(zzz500000, zzz4300000, ty_Bool) → new_lt7(zzz500000, zzz4300000)
new_esEs19(zzz5000, zzz4000, ty_Bool) → new_esEs14(zzz5000, zzz4000)
new_esEs20(zzz5000, zzz4000, ty_Float) → new_esEs13(zzz5000, zzz4000)
new_compare14(Double(zzz500000, zzz500001), Double(zzz4300000, zzz4300001)) → new_compare8(new_sr0(zzz500000, zzz4300000), new_sr0(zzz500001, zzz4300001))
new_compare12(zzz500000, zzz4300000, ha, hb) → new_compare27(zzz500000, zzz4300000, new_esEs4(zzz500000, zzz4300000, ha, hb), ha, hb)
new_compare8(zzz500, zzz4300) → new_primCmpInt(zzz500, zzz4300)
new_lt19(zzz500000, zzz4300000, ty_Char) → new_lt12(zzz500000, zzz4300000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, app(app(app(ty_@3, bdg), bdh), bea)) → new_ltEs16(zzz500000, zzz4300000, bdg, bdh, bea)
new_primEqInt(Neg(Succ(zzz50000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(zzz40000))) → False
new_compare17(zzz500000, zzz4300000) → new_compare26(zzz500000, zzz4300000, new_esEs14(zzz500000, zzz4300000))
new_esEs8(EQ, EQ) → True
new_lt13(zzz500000, zzz4300000, ty_Double) → new_lt15(zzz500000, zzz4300000)
new_compare111(zzz200, zzz201, True, bbd) → LT
new_esEs20(zzz5000, zzz4000, ty_@0) → new_esEs10(zzz5000, zzz4000)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Char, bfa) → new_esEs11(zzz5000, zzz4000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_ltEs19(zzz500001, zzz4300001, ty_@0) → new_ltEs11(zzz500001, zzz4300001)
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_esEs18(zzz5001, zzz4001, ty_Char) → new_esEs11(zzz5001, zzz4001)
new_compare112(zzz500000, zzz4300000, True) → LT
new_esEs19(zzz5000, zzz4000, ty_Char) → new_esEs11(zzz5000, zzz4000)
new_compare30(zzz500000, zzz4300000, app(app(ty_Either, bhg), bhh)) → new_compare12(zzz500000, zzz4300000, bhg, bhh)
new_primEqInt(Pos(Succ(zzz50000)), Pos(Succ(zzz40000))) → new_primEqNat0(zzz50000, zzz40000)
new_ltEs18(zzz50000, zzz430000, ty_Double) → new_ltEs8(zzz50000, zzz430000)
new_compare27(zzz500000, zzz4300000, True, ha, hb) → EQ
new_lt10(zzz500000, zzz4300000) → new_esEs8(new_compare9(zzz500000, zzz4300000), LT)
new_esEs24(zzz500001, zzz4300001, app(ty_Ratio, cee)) → new_esEs16(zzz500001, zzz4300001, cee)
new_ltEs19(zzz500001, zzz4300001, ty_Bool) → new_ltEs14(zzz500001, zzz4300001)
new_esEs14(False, True) → False
new_esEs14(True, False) → False
new_esEs23(zzz500000, zzz4300000, app(ty_[], cbc)) → new_esEs12(zzz500000, zzz4300000, cbc)
new_ltEs4(Just(zzz500000), Just(zzz4300000), app(app(ty_Either, bc), bd)) → new_ltEs7(zzz500000, zzz4300000, bc, bd)
new_esEs26(zzz5002, zzz4002, ty_Integer) → new_esEs15(zzz5002, zzz4002)
new_ltEs10(GT, EQ) → False
new_lt17(zzz500000, zzz4300000, cbb) → new_esEs8(new_compare7(zzz500000, zzz4300000, cbb), LT)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Double) → new_ltEs8(zzz500000, zzz4300000)
new_esEs24(zzz500001, zzz4300001, ty_Int) → new_esEs17(zzz500001, zzz4300001)
new_primEqNat0(Succ(zzz50000), Succ(zzz40000)) → new_primEqNat0(zzz50000, zzz40000)
new_ltEs20(zzz500002, zzz4300002, app(ty_[], cgc)) → new_ltEs17(zzz500002, zzz4300002, cgc)
new_esEs27(zzz5001, zzz4001, ty_Ordering) → new_esEs8(zzz5001, zzz4001)
new_ltEs14(False, False) → True
new_compare11(@0, @0) → EQ
new_lt7(zzz500000, zzz4300000) → new_esEs8(new_compare17(zzz500000, zzz4300000), LT)
new_esEs19(zzz5000, zzz4000, app(app(app(ty_@3, gd), ge), gf)) → new_esEs6(zzz5000, zzz4000, gd, ge, gf)
new_ltEs9(zzz50000, zzz430000) → new_fsEs(new_compare9(zzz50000, zzz430000))
new_ltEs20(zzz500002, zzz4300002, ty_Char) → new_ltEs5(zzz500002, zzz4300002)
new_compare113(zzz500000, zzz4300000, False, ha, hb) → GT
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, ty_Bool) → new_ltEs14(zzz500000, zzz4300000)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Int) → new_ltEs6(zzz500000, zzz4300000)
new_primCompAux00(zzz225, LT) → LT
new_lt20(zzz500001, zzz4300001, ty_@0) → new_lt4(zzz500001, zzz4300001)
new_ltEs19(zzz500001, zzz4300001, app(ty_[], cce)) → new_ltEs17(zzz500001, zzz4300001, cce)
new_ltEs19(zzz500001, zzz4300001, app(app(ty_Either, cbd), cbe)) → new_ltEs7(zzz500001, zzz4300001, cbd, cbe)
new_compare7(:%(zzz500000, zzz500001), :%(zzz4300000, zzz4300001), ty_Int) → new_compare8(new_sr0(zzz500000, zzz4300001), new_sr0(zzz4300000, zzz500001))
new_esEs24(zzz500001, zzz4300001, ty_Ordering) → new_esEs8(zzz500001, zzz4300001)
new_ltEs8(zzz50000, zzz430000) → new_fsEs(new_compare14(zzz50000, zzz430000))
new_esEs7(Nothing, Nothing, cf) → True
new_esEs28(zzz5000, zzz4000, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_esEs8(EQ, LT) → False
new_esEs8(LT, EQ) → False
new_esEs18(zzz5001, zzz4001, app(ty_Maybe, fd)) → new_esEs7(zzz5001, zzz4001, fd)
new_primEqInt(Pos(Succ(zzz50000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(zzz40000))) → False
new_lt20(zzz500001, zzz4300001, app(ty_Ratio, cee)) → new_lt17(zzz500001, zzz4300001, cee)
new_compare30(zzz500000, zzz4300000, ty_Int) → new_compare8(zzz500000, zzz4300000)
new_compare24(zzz500000, zzz4300000, False, hc, hd, he) → new_compare110(zzz500000, zzz4300000, new_ltEs16(zzz500000, zzz4300000, hc, hd, he), hc, hd, he)
new_esEs24(zzz500001, zzz4300001, ty_@0) → new_esEs10(zzz500001, zzz4300001)
new_primCmpNat0(Zero, Zero) → EQ
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Integer, bbe) → new_ltEs9(zzz500000, zzz4300000)
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_esEs23(zzz500000, zzz4300000, app(app(ty_@2, hf), hg)) → new_esEs5(zzz500000, zzz4300000, hf, hg)
new_esEs4(Right(zzz5000), Right(zzz4000), bgd, ty_@0) → new_esEs10(zzz5000, zzz4000)
new_ltEs10(LT, EQ) → True
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_compare19(zzz500000, zzz4300000, False) → GT
new_esEs27(zzz5001, zzz4001, ty_Double) → new_esEs9(zzz5001, zzz4001)
new_ltEs15(zzz50000, zzz430000, bee) → new_fsEs(new_compare7(zzz50000, zzz430000, bee))
new_esEs23(zzz500000, zzz4300000, ty_Float) → new_esEs13(zzz500000, zzz4300000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Integer) → new_esEs15(zzz5000, zzz4000)
new_compare29(Just(zzz50000), Just(zzz430000), False, gg) → new_compare111(zzz50000, zzz430000, new_ltEs18(zzz50000, zzz430000, gg), gg)
new_primEqInt(Pos(Succ(zzz50000)), Neg(zzz4000)) → False
new_primEqInt(Neg(Succ(zzz50000)), Pos(zzz4000)) → False
new_lt13(zzz500000, zzz4300000, app(ty_Ratio, cbb)) → new_lt17(zzz500000, zzz4300000, cbb)
new_esEs7(Nothing, Just(zzz4000), cf) → False
new_esEs7(Just(zzz5000), Nothing, cf) → False
new_esEs18(zzz5001, zzz4001, app(ty_[], eh)) → new_esEs12(zzz5001, zzz4001, eh)
new_esEs28(zzz5000, zzz4000, ty_Char) → new_esEs11(zzz5000, zzz4000)
new_ltEs10(GT, GT) → True
new_esEs26(zzz5002, zzz4002, app(ty_Ratio, chh)) → new_esEs16(zzz5002, zzz4002, chh)
new_esEs26(zzz5002, zzz4002, ty_Int) → new_esEs17(zzz5002, zzz4002)
new_esEs4(Right(zzz5000), Right(zzz4000), bgd, ty_Bool) → new_esEs14(zzz5000, zzz4000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_@0, bbe) → new_ltEs11(zzz500000, zzz4300000)
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primEqInt(Pos(Zero), Neg(Succ(zzz40000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(zzz40000))) → False
new_ltEs6(zzz50000, zzz430000) → new_fsEs(new_compare8(zzz50000, zzz430000))
new_esEs20(zzz5000, zzz4000, app(ty_[], bae)) → new_esEs12(zzz5000, zzz4000, bae)
new_esEs21(zzz5001, zzz4001, ty_Integer) → new_esEs15(zzz5001, zzz4001)
new_compare30(zzz500000, zzz4300000, app(app(ty_@2, caa), cab)) → new_compare18(zzz500000, zzz4300000, caa, cab)
new_primCompAux00(zzz225, EQ) → zzz225
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Double, bfa) → new_esEs9(zzz5000, zzz4000)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Integer, bfa) → new_esEs15(zzz5000, zzz4000)
new_esEs18(zzz5001, zzz4001, ty_Int) → new_esEs17(zzz5001, zzz4001)
new_lt16(zzz500000, zzz4300000, hf, hg) → new_esEs8(new_compare18(zzz500000, zzz4300000, hf, hg), LT)
new_esEs8(GT, EQ) → False
new_esEs8(EQ, GT) → False
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Double) → new_esEs9(zzz5000, zzz4000)
new_esEs26(zzz5002, zzz4002, ty_Char) → new_esEs11(zzz5002, zzz4002)
new_esEs27(zzz5001, zzz4001, app(ty_Ratio, dbb)) → new_esEs16(zzz5001, zzz4001, dbb)
new_esEs26(zzz5002, zzz4002, app(app(ty_@2, cha), chb)) → new_esEs5(zzz5002, zzz4002, cha, chb)
new_ltEs19(zzz500001, zzz4300001, app(app(ty_@2, cbf), cbg)) → new_ltEs13(zzz500001, zzz4300001, cbf, cbg)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Bool) → new_ltEs14(zzz500000, zzz4300000)
new_not(False) → True
new_esEs24(zzz500001, zzz4300001, ty_Double) → new_esEs9(zzz500001, zzz4300001)
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_ltEs5(zzz50000, zzz430000) → new_fsEs(new_compare10(zzz50000, zzz430000))
new_esEs25(zzz500000, zzz4300000, ty_Integer) → new_esEs15(zzz500000, zzz4300000)
new_esEs26(zzz5002, zzz4002, ty_Bool) → new_esEs14(zzz5002, zzz4002)
new_ltEs19(zzz500001, zzz4300001, ty_Int) → new_ltEs6(zzz500001, zzz4300001)
new_esEs25(zzz500000, zzz4300000, app(ty_Ratio, cdc)) → new_esEs16(zzz500000, zzz4300000, cdc)
new_esEs4(Right(zzz5000), Right(zzz4000), bgd, ty_Int) → new_esEs17(zzz5000, zzz4000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Bool, bbe) → new_ltEs14(zzz500000, zzz4300000)
new_esEs28(zzz5000, zzz4000, app(app(ty_@2, dbe), dbf)) → new_esEs5(zzz5000, zzz4000, dbe, dbf)
new_esEs23(zzz500000, zzz4300000, ty_@0) → new_esEs10(zzz500000, zzz4300000)
new_compare30(zzz500000, zzz4300000, ty_@0) → new_compare11(zzz500000, zzz4300000)
new_esEs18(zzz5001, zzz4001, app(app(ty_Either, ed), ee)) → new_esEs4(zzz5001, zzz4001, ed, ee)
new_lt18(zzz500000, zzz4300000, cbc) → new_esEs8(new_compare4(zzz500000, zzz4300000, cbc), LT)
new_ltEs18(zzz50000, zzz430000, ty_Int) → new_ltEs6(zzz50000, zzz430000)
new_esEs22(zzz5000, zzz4000, ty_Int) → new_esEs17(zzz5000, zzz4000)
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_esEs6(@3(zzz5000, zzz5001, zzz5002), @3(zzz4000, zzz4001, zzz4002), cgd, cge, cgf) → new_asAs(new_esEs28(zzz5000, zzz4000, cgd), new_asAs(new_esEs27(zzz5001, zzz4001, cge), new_esEs26(zzz5002, zzz4002, cgf)))
new_esEs28(zzz5000, zzz4000, app(ty_Maybe, dcc)) → new_esEs7(zzz5000, zzz4000, dcc)
new_esEs28(zzz5000, zzz4000, ty_Double) → new_esEs9(zzz5000, zzz4000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, ty_Double) → new_ltEs8(zzz500000, zzz4300000)
new_lt20(zzz500001, zzz4300001, ty_Double) → new_lt15(zzz500001, zzz4300001)
new_lt20(zzz500001, zzz4300001, ty_Integer) → new_lt10(zzz500001, zzz4300001)
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_esEs26(zzz5002, zzz4002, ty_@0) → new_esEs10(zzz5002, zzz4002)
new_esEs18(zzz5001, zzz4001, ty_Float) → new_esEs13(zzz5001, zzz4001)
new_compare25(zzz500000, zzz4300000, False, hf, hg) → new_compare15(zzz500000, zzz4300000, new_ltEs13(zzz500000, zzz4300000, hf, hg), hf, hg)
new_esEs23(zzz500000, zzz4300000, app(app(ty_Either, ha), hb)) → new_esEs4(zzz500000, zzz4300000, ha, hb)
new_esEs20(zzz5000, zzz4000, ty_Char) → new_esEs11(zzz5000, zzz4000)
new_lt19(zzz500000, zzz4300000, app(ty_Maybe, cdb)) → new_lt11(zzz500000, zzz4300000, cdb)
new_esEs4(Left(zzz5000), Left(zzz4000), app(ty_Maybe, bgb), bfa) → new_esEs7(zzz5000, zzz4000, bgb)
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_esEs20(zzz5000, zzz4000, ty_Integer) → new_esEs15(zzz5000, zzz4000)
new_primEqNat0(Zero, Succ(zzz40000)) → False
new_primEqNat0(Succ(zzz50000), Zero) → False
new_esEs18(zzz5001, zzz4001, ty_Integer) → new_esEs15(zzz5001, zzz4001)
new_esEs17(zzz500, zzz400) → new_primEqInt(zzz500, zzz400)
new_lt5(zzz500000, zzz4300000, ha, hb) → new_esEs8(new_compare12(zzz500000, zzz4300000, ha, hb), LT)
new_compare25(zzz500000, zzz4300000, True, hf, hg) → EQ
new_esEs20(zzz5000, zzz4000, ty_Bool) → new_esEs14(zzz5000, zzz4000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), app(app(ty_Either, bbf), bbg), bbe) → new_ltEs7(zzz500000, zzz4300000, bbf, bbg)
new_ltEs14(True, True) → True
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs24(zzz500001, zzz4300001, app(app(ty_Either, cdh), cea)) → new_esEs4(zzz500001, zzz4300001, cdh, cea)
new_esEs28(zzz5000, zzz4000, app(app(app(ty_@3, dbh), dca), dcb)) → new_esEs6(zzz5000, zzz4000, dbh, dca, dcb)
new_compare30(zzz500000, zzz4300000, ty_Bool) → new_compare17(zzz500000, zzz4300000)
new_esEs27(zzz5001, zzz4001, app(app(ty_Either, daa), dab)) → new_esEs4(zzz5001, zzz4001, daa, dab)
new_esEs27(zzz5001, zzz4001, app(app(app(ty_@3, daf), dag), dah)) → new_esEs6(zzz5001, zzz4001, daf, dag, dah)
new_compare4(:(zzz500000, zzz500001), [], ce) → GT
new_ltEs18(zzz50000, zzz430000, app(ty_[], ce)) → new_ltEs17(zzz50000, zzz430000, ce)
new_esEs27(zzz5001, zzz4001, app(app(ty_@2, dac), dad)) → new_esEs5(zzz5001, zzz4001, dac, dad)
new_esEs27(zzz5001, zzz4001, ty_Int) → new_esEs17(zzz5001, zzz4001)
new_esEs23(zzz500000, zzz4300000, ty_Int) → new_esEs17(zzz500000, zzz4300000)
new_lt13(zzz500000, zzz4300000, ty_@0) → new_lt4(zzz500000, zzz4300000)
new_compare30(zzz500000, zzz4300000, ty_Char) → new_compare10(zzz500000, zzz4300000)
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_compare4([], :(zzz4300000, zzz4300001), ce) → LT
new_sr0(zzz5000, zzz4000) → new_primMulInt(zzz5000, zzz4000)
new_lt19(zzz500000, zzz4300000, app(ty_[], cdg)) → new_lt18(zzz500000, zzz4300000, cdg)
new_compare15(zzz500000, zzz4300000, False, hf, hg) → GT
new_ltEs18(zzz50000, zzz430000, ty_Float) → new_ltEs12(zzz50000, zzz430000)
new_ltEs18(zzz50000, zzz430000, ty_Integer) → new_ltEs9(zzz50000, zzz430000)
new_ltEs19(zzz500001, zzz4300001, ty_Double) → new_ltEs8(zzz500001, zzz4300001)
new_compare30(zzz500000, zzz4300000, ty_Float) → new_compare16(zzz500000, zzz4300000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), app(ty_[], bcg), bbe) → new_ltEs17(zzz500000, zzz4300000, bcg)
new_esEs11(Char(zzz5000), Char(zzz4000)) → new_primEqNat0(zzz5000, zzz4000)
new_esEs7(Just(zzz5000), Just(zzz4000), app(app(app(ty_@3, de), df), dg)) → new_esEs6(zzz5000, zzz4000, de, df, dg)
new_esEs25(zzz500000, zzz4300000, app(ty_Maybe, cdb)) → new_esEs7(zzz500000, zzz4300000, cdb)
new_compare29(Nothing, Nothing, False, gg) → LT
new_esEs23(zzz500000, zzz4300000, app(ty_Ratio, cbb)) → new_esEs16(zzz500000, zzz4300000, cbb)
new_lt13(zzz500000, zzz4300000, app(app(ty_Either, ha), hb)) → new_lt5(zzz500000, zzz4300000, ha, hb)
new_esEs16(:%(zzz5000, zzz5001), :%(zzz4000, zzz4001), bbc) → new_asAs(new_esEs22(zzz5000, zzz4000, bbc), new_esEs21(zzz5001, zzz4001, bbc))
new_ltEs4(Just(zzz500000), Just(zzz4300000), app(ty_Maybe, bg)) → new_ltEs4(zzz500000, zzz4300000, bg)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Float) → new_ltEs12(zzz500000, zzz4300000)
new_primCompAux0(zzz500000, zzz4300000, zzz220, ce) → new_primCompAux00(zzz220, new_compare30(zzz500000, zzz4300000, ce))
new_esEs19(zzz5000, zzz4000, app(app(ty_@2, ga), gb)) → new_esEs5(zzz5000, zzz4000, ga, gb)
new_esEs19(zzz5000, zzz4000, app(ty_Ratio, gh)) → new_esEs16(zzz5000, zzz4000, gh)
new_esEs10(@0, @0) → True
new_compare29(zzz5000, zzz43000, True, gg) → EQ
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs27(zzz5001, zzz4001, ty_Float) → new_esEs13(zzz5001, zzz4001)
new_lt13(zzz500000, zzz4300000, ty_Integer) → new_lt10(zzz500000, zzz4300000)
new_compare28(zzz5000, zzz43000, gg) → new_compare29(zzz5000, zzz43000, new_esEs7(zzz5000, zzz43000, gg), gg)
new_esEs4(Right(zzz5000), Right(zzz4000), bgd, app(app(ty_@2, bgg), bgh)) → new_esEs5(zzz5000, zzz4000, bgg, bgh)
new_esEs24(zzz500001, zzz4300001, ty_Char) → new_esEs11(zzz500001, zzz4300001)
new_esEs28(zzz5000, zzz4000, ty_@0) → new_esEs10(zzz5000, zzz4000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, app(app(ty_Either, bda), bdb)) → new_ltEs7(zzz500000, zzz4300000, bda, bdb)
new_esEs28(zzz5000, zzz4000, ty_Int) → new_esEs17(zzz5000, zzz4000)
new_compare7(:%(zzz500000, zzz500001), :%(zzz4300000, zzz4300001), ty_Integer) → new_compare9(new_sr(zzz500000, zzz4300001), new_sr(zzz4300000, zzz500001))
new_compare9(Integer(zzz500000), Integer(zzz4300000)) → new_primCmpInt(zzz500000, zzz4300000)
new_compare23(zzz500000, zzz4300000, False) → new_compare112(zzz500000, zzz4300000, new_ltEs10(zzz500000, zzz4300000))
new_asAs(False, zzz207) → False
new_esEs4(Left(zzz5000), Left(zzz4000), ty_@0, bfa) → new_esEs10(zzz5000, zzz4000)
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_esEs26(zzz5002, zzz4002, ty_Double) → new_esEs9(zzz5002, zzz4002)
new_ltEs10(LT, GT) → True
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_ltEs4(Just(zzz500000), Just(zzz4300000), app(ty_Ratio, bh)) → new_ltEs15(zzz500000, zzz4300000, bh)
new_esEs23(zzz500000, zzz4300000, app(app(app(ty_@3, hc), hd), he)) → new_esEs6(zzz500000, zzz4300000, hc, hd, he)
new_lt8(zzz500000, zzz4300000, hc, hd, he) → new_esEs8(new_compare13(zzz500000, zzz4300000, hc, hd, he), LT)
new_lt11(zzz5000, zzz43000, gg) → new_esEs8(new_compare28(zzz5000, zzz43000, gg), LT)
new_esEs26(zzz5002, zzz4002, app(ty_[], chc)) → new_esEs12(zzz5002, zzz4002, chc)
new_compare4(:(zzz500000, zzz500001), :(zzz4300000, zzz4300001), ce) → new_primCompAux0(zzz500000, zzz4300000, new_compare4(zzz500001, zzz4300001, ce), ce)
new_compare16(Float(zzz500000, zzz500001), Float(zzz4300000, zzz4300001)) → new_compare8(new_sr0(zzz500000, zzz4300000), new_sr0(zzz500001, zzz4300001))
new_esEs26(zzz5002, zzz4002, app(ty_Maybe, chg)) → new_esEs7(zzz5002, zzz4002, chg)
new_esEs28(zzz5000, zzz4000, ty_Bool) → new_esEs14(zzz5000, zzz4000)
new_compare110(zzz500000, zzz4300000, True, hc, hd, he) → LT
new_lt19(zzz500000, zzz4300000, app(app(ty_Either, ccf), ccg)) → new_lt5(zzz500000, zzz4300000, ccf, ccg)
new_ltEs18(zzz50000, zzz430000, ty_Bool) → new_ltEs14(zzz50000, zzz430000)
new_esEs28(zzz5000, zzz4000, ty_Integer) → new_esEs15(zzz5000, zzz4000)
new_esEs18(zzz5001, zzz4001, ty_Ordering) → new_esEs8(zzz5001, zzz4001)
new_esEs19(zzz5000, zzz4000, ty_Double) → new_esEs9(zzz5000, zzz4000)
new_lt20(zzz500001, zzz4300001, app(app(ty_@2, ceb), cec)) → new_lt16(zzz500001, zzz4300001, ceb, cec)
new_esEs5(@2(zzz5000, zzz5001), @2(zzz4000, zzz4001), eb, ec) → new_asAs(new_esEs19(zzz5000, zzz4000, eb), new_esEs18(zzz5001, zzz4001, ec))
new_compare26(zzz500000, zzz4300000, False) → new_compare19(zzz500000, zzz4300000, new_ltEs14(zzz500000, zzz4300000))
new_esEs28(zzz5000, zzz4000, app(app(ty_Either, dbc), dbd)) → new_esEs4(zzz5000, zzz4000, dbc, dbd)
new_esEs4(Right(zzz5000), Right(zzz4000), bgd, app(ty_Maybe, bhe)) → new_esEs7(zzz5000, zzz4000, bhe)
new_esEs7(Just(zzz5000), Just(zzz4000), ty_@0) → new_esEs10(zzz5000, zzz4000)
new_ltEs18(zzz50000, zzz430000, ty_Char) → new_ltEs5(zzz50000, zzz430000)
new_esEs28(zzz5000, zzz4000, ty_Float) → new_esEs13(zzz5000, zzz4000)
new_lt13(zzz500000, zzz4300000, ty_Ordering) → new_lt9(zzz500000, zzz4300000)
new_esEs25(zzz500000, zzz4300000, app(app(app(ty_@3, cdd), cde), cdf)) → new_esEs6(zzz500000, zzz4300000, cdd, cde, cdf)
new_ltEs10(EQ, EQ) → True
new_ltEs18(zzz50000, zzz430000, app(app(ty_@2, bec), bed)) → new_ltEs13(zzz50000, zzz430000, bec, bed)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Int, bfa) → new_esEs17(zzz5000, zzz4000)
new_esEs23(zzz500000, zzz4300000, ty_Integer) → new_esEs15(zzz500000, zzz4300000)
new_ltEs10(LT, LT) → True
new_esEs14(True, True) → True
new_compare111(zzz200, zzz201, False, bbd) → GT
new_esEs27(zzz5001, zzz4001, ty_Bool) → new_esEs14(zzz5001, zzz4001)
new_esEs7(Just(zzz5000), Just(zzz4000), app(app(ty_Either, cg), da)) → new_esEs4(zzz5000, zzz4000, cg, da)
new_compare10(Char(zzz500000), Char(zzz4300000)) → new_primCmpNat0(zzz500000, zzz4300000)
new_esEs30(Just(zzz4300), h) → False
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Float, bfa) → new_esEs13(zzz5000, zzz4000)
new_lt13(zzz500000, zzz4300000, app(app(ty_@2, hf), hg)) → new_lt16(zzz500000, zzz4300000, hf, hg)
new_ltEs7(Left(zzz500000), Left(zzz4300000), app(app(ty_@2, bbh), bca), bbe) → new_ltEs13(zzz500000, zzz4300000, bbh, bca)
new_esEs7(Just(zzz5000), Just(zzz4000), app(ty_Ratio, ea)) → new_esEs16(zzz5000, zzz4000, ea)
new_lt13(zzz500000, zzz4300000, app(ty_Maybe, cba)) → new_lt11(zzz500000, zzz4300000, cba)
new_ltEs20(zzz500002, zzz4300002, app(app(ty_Either, cfb), cfc)) → new_ltEs7(zzz500002, zzz4300002, cfb, cfc)
new_esEs18(zzz5001, zzz4001, ty_@0) → new_esEs10(zzz5001, zzz4001)
new_ltEs16(@3(zzz500000, zzz500001, zzz500002), @3(zzz4300000, zzz4300001, zzz4300002), bef, beg, beh) → new_pePe(new_lt19(zzz500000, zzz4300000, bef), new_asAs(new_esEs25(zzz500000, zzz4300000, bef), new_pePe(new_lt20(zzz500001, zzz4300001, beg), new_asAs(new_esEs24(zzz500001, zzz4300001, beg), new_ltEs20(zzz500002, zzz4300002, beh)))))
new_esEs4(Right(zzz5000), Right(zzz4000), bgd, ty_Double) → new_esEs9(zzz5000, zzz4000)
new_ltEs14(True, False) → False
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_esEs20(zzz5000, zzz4000, ty_Int) → new_esEs17(zzz5000, zzz4000)
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_esEs25(zzz500000, zzz4300000, app(app(ty_@2, cch), cda)) → new_esEs5(zzz500000, zzz4300000, cch, cda)
new_ltEs20(zzz500002, zzz4300002, ty_Double) → new_ltEs8(zzz500002, zzz4300002)
new_ltEs7(Left(zzz500000), Left(zzz4300000), app(ty_Ratio, bcc), bbe) → new_ltEs15(zzz500000, zzz4300000, bcc)
new_gt1(zzz430, h) → new_esEs8(new_compare32(zzz430, h), GT)
new_ltEs19(zzz500001, zzz4300001, app(app(app(ty_@3, ccb), ccc), ccd)) → new_ltEs16(zzz500001, zzz4300001, ccb, ccc, ccd)
new_ltEs20(zzz500002, zzz4300002, app(app(app(ty_@3, cfh), cga), cgb)) → new_ltEs16(zzz500002, zzz4300002, cfh, cga, cgb)
new_compare112(zzz500000, zzz4300000, False) → GT
new_ltEs10(EQ, LT) → False
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Float) → new_esEs13(zzz5000, zzz4000)
new_esEs14(False, False) → True
new_esEs7(Just(zzz5000), Just(zzz4000), app(app(ty_@2, db), dc)) → new_esEs5(zzz5000, zzz4000, db, dc)
new_lt20(zzz500001, zzz4300001, ty_Char) → new_lt12(zzz500001, zzz4300001)
new_lt9(zzz500000, zzz4300000) → new_esEs8(new_compare6(zzz500000, zzz4300000), LT)
new_ltEs10(GT, LT) → False
new_esEs18(zzz5001, zzz4001, ty_Bool) → new_esEs14(zzz5001, zzz4001)
new_esEs22(zzz5000, zzz4000, ty_Integer) → new_esEs15(zzz5000, zzz4000)
new_primPlusNat1(Zero, Zero) → Zero
new_compare30(zzz500000, zzz4300000, app(app(app(ty_@3, cae), caf), cag)) → new_compare13(zzz500000, zzz4300000, cae, caf, cag)
new_esEs19(zzz5000, zzz4000, ty_Integer) → new_esEs15(zzz5000, zzz4000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(ty_[], bff), bfa) → new_esEs12(zzz5000, zzz4000, bff)
new_esEs26(zzz5002, zzz4002, app(app(ty_Either, cgg), cgh)) → new_esEs4(zzz5002, zzz4002, cgg, cgh)
new_asAs(True, zzz207) → zzz207
new_esEs28(zzz5000, zzz4000, app(ty_[], dbg)) → new_esEs12(zzz5000, zzz4000, dbg)
new_esEs27(zzz5001, zzz4001, app(ty_[], dae)) → new_esEs12(zzz5001, zzz4001, dae)
new_esEs19(zzz5000, zzz4000, app(app(ty_Either, fg), fh)) → new_esEs4(zzz5000, zzz4000, fg, fh)
new_ltEs4(Just(zzz500000), Nothing, bb) → False
new_esEs20(zzz5000, zzz4000, ty_Double) → new_esEs9(zzz5000, zzz4000)
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_ltEs4(Just(zzz500000), Just(zzz4300000), app(ty_[], cd)) → new_ltEs17(zzz500000, zzz4300000, cd)
new_esEs4(Right(zzz5000), Left(zzz4000), bgd, bfa) → False
new_esEs4(Left(zzz5000), Right(zzz4000), bgd, bfa) → False
new_ltEs19(zzz500001, zzz4300001, ty_Float) → new_ltEs12(zzz500001, zzz4300001)
new_ltEs20(zzz500002, zzz4300002, app(ty_Maybe, cff)) → new_ltEs4(zzz500002, zzz4300002, cff)
new_esEs4(Left(zzz5000), Left(zzz4000), app(app(app(ty_@3, bfg), bfh), bga), bfa) → new_esEs6(zzz5000, zzz4000, bfg, bfh, bga)
new_ltEs19(zzz500001, zzz4300001, ty_Char) → new_ltEs5(zzz500001, zzz4300001)
new_fsEs(zzz210) → new_not(new_esEs8(zzz210, GT))
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Double, bbe) → new_ltEs8(zzz500000, zzz4300000)
new_esEs19(zzz5000, zzz4000, ty_@0) → new_esEs10(zzz5000, zzz4000)
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Bool) → new_esEs14(zzz5000, zzz4000)
new_esEs24(zzz500001, zzz4300001, ty_Float) → new_esEs13(zzz500001, zzz4300001)
new_ltEs11(zzz50000, zzz430000) → new_fsEs(new_compare11(zzz50000, zzz430000))
new_lt20(zzz500001, zzz4300001, ty_Int) → new_lt14(zzz500001, zzz4300001)
new_esEs4(Right(zzz5000), Right(zzz4000), bgd, ty_Float) → new_esEs13(zzz5000, zzz4000)
new_esEs19(zzz5000, zzz4000, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_ltEs20(zzz500002, zzz4300002, app(app(ty_@2, cfd), cfe)) → new_ltEs13(zzz500002, zzz4300002, cfd, cfe)
new_esEs30(Nothing, h) → True
new_esEs27(zzz5001, zzz4001, ty_Char) → new_esEs11(zzz5001, zzz4001)
new_ltEs20(zzz500002, zzz4300002, ty_Int) → new_ltEs6(zzz500002, zzz4300002)
new_compare110(zzz500000, zzz4300000, False, hc, hd, he) → GT
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Char) → new_ltEs5(zzz500000, zzz4300000)
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Char) → new_esEs11(zzz5000, zzz4000)
new_primCompAux00(zzz225, GT) → GT
new_ltEs20(zzz500002, zzz4300002, ty_Integer) → new_ltEs9(zzz500002, zzz4300002)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, app(ty_Maybe, bde)) → new_ltEs4(zzz500000, zzz4300000, bde)
new_lt19(zzz500000, zzz4300000, ty_Int) → new_lt14(zzz500000, zzz4300000)
new_ltEs4(Just(zzz500000), Just(zzz4300000), app(app(app(ty_@3, ca), cb), cc)) → new_ltEs16(zzz500000, zzz4300000, ca, cb, cc)
new_ltEs18(zzz50000, zzz430000, ty_Ordering) → new_ltEs10(zzz50000, zzz430000)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Integer) → new_ltEs9(zzz500000, zzz4300000)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_compare30(zzz500000, zzz4300000, ty_Ordering) → new_compare6(zzz500000, zzz4300000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, ty_Float) → new_ltEs12(zzz500000, zzz4300000)
new_esEs27(zzz5001, zzz4001, ty_Integer) → new_esEs15(zzz5001, zzz4001)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, ty_Int) → new_ltEs6(zzz500000, zzz4300000)
new_not(True) → False

The set Q consists of the following terms:

new_ltEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_compare23(x0, x1, True)
new_lt11(x0, x1, x2)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_lt14(x0, x1)
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs18(x0, x1, app(app(ty_@2, x2), x3))
new_asAs(True, x0)
new_compare29(Nothing, Nothing, False, x0)
new_compare19(x0, x1, True)
new_esEs26(x0, x1, ty_@0)
new_ltEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, app(ty_[], x2))
new_ltEs18(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_Ordering)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_lt13(x0, x1, app(ty_Ratio, x2))
new_esEs18(x0, x1, ty_Int)
new_primPlusNat1(Zero, Succ(x0))
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare29(Nothing, Just(x0), False, x1)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_compare30(x0, x1, ty_@0)
new_lt20(x0, x1, ty_Ordering)
new_esEs9(Double(x0, x1), Double(x2, x3))
new_ltEs7(Right(x0), Right(x1), x2, ty_@0)
new_primCompAux0(x0, x1, x2, x3)
new_primMulNat0(Succ(x0), Zero)
new_lt19(x0, x1, ty_Double)
new_primMulInt(Neg(x0), Neg(x1))
new_lt19(x0, x1, ty_Integer)
new_esEs30(Just(x0), x1)
new_esEs24(x0, x1, ty_@0)
new_primPlusNat1(Succ(x0), Zero)
new_esEs21(x0, x1, ty_Int)
new_compare4(:(x0, x1), :(x2, x3), x4)
new_esEs4(Right(x0), Right(x1), x2, ty_Integer)
new_esEs4(Left(x0), Left(x1), ty_Double, x2)
new_ltEs10(LT, LT)
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs23(x0, x1, ty_Bool)
new_primPlusNat1(Succ(x0), Succ(x1))
new_compare30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, ty_Int)
new_esEs18(x0, x1, ty_Char)
new_esEs24(x0, x1, ty_Char)
new_ltEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(True, False)
new_ltEs14(False, True)
new_esEs25(x0, x1, ty_Double)
new_pePe(False, x0)
new_esEs19(x0, x1, ty_Char)
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Char)
new_compare27(x0, x1, True, x2, x3)
new_esEs7(Just(x0), Just(x1), ty_Double)
new_esEs8(GT, GT)
new_esEs23(x0, x1, ty_@0)
new_compare4([], :(x0, x1), x2)
new_lt9(x0, x1)
new_lt19(x0, x1, ty_Ordering)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs11(Char(x0), Char(x1))
new_esEs7(Nothing, Just(x0), x1)
new_esEs4(Right(x0), Right(x1), x2, ty_Bool)
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs8(LT, LT)
new_sr0(x0, x1)
new_compare6(x0, x1)
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_compare30(x0, x1, ty_Double)
new_esEs7(Just(x0), Just(x1), ty_Char)
new_esEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs18(x0, x1, app(ty_[], x2))
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare19(x0, x1, False)
new_ltEs4(Nothing, Nothing, x0)
new_compare110(x0, x1, False, x2, x3, x4)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs26(x0, x1, ty_Double)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs4(Right(x0), Right(x1), x2, ty_Float)
new_lt16(x0, x1, x2, x3)
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_compare111(x0, x1, False, x2)
new_compare4([], [], x0)
new_ltEs7(Left(x0), Left(x1), ty_Char, x2)
new_ltEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs17(x0, x1)
new_ltEs19(x0, x1, ty_Char)
new_esEs4(Left(x0), Left(x1), ty_Float, x2)
new_esEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs14(True, True)
new_compare26(x0, x1, True)
new_lt20(x0, x1, ty_Char)
new_compare112(x0, x1, False)
new_esEs18(x0, x1, ty_Bool)
new_esEs20(x0, x1, ty_Float)
new_primEqNat0(Zero, Zero)
new_ltEs4(Just(x0), Just(x1), ty_Double)
new_compare30(x0, x1, ty_Char)
new_lt20(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_ltEs7(Right(x0), Right(x1), x2, ty_Char)
new_esEs20(x0, x1, ty_Int)
new_lt13(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Double)
new_lt19(x0, x1, ty_Bool)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, ty_@0)
new_esEs12([], :(x0, x1), x2)
new_esEs28(x0, x1, ty_Integer)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_compare17(x0, x1)
new_ltEs17(x0, x1, x2)
new_primPlusNat0(Zero, x0)
new_ltEs20(x0, x1, ty_Int)
new_compare13(x0, x1, x2, x3, x4)
new_primMulNat0(Zero, Zero)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpNat0(Succ(x0), Zero)
new_compare16(Float(x0, x1), Float(x2, x3))
new_ltEs20(x0, x1, ty_Integer)
new_compare30(x0, x1, ty_Ordering)
new_ltEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs26(x0, x1, ty_Integer)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs10(EQ, LT)
new_ltEs10(LT, EQ)
new_lt4(x0, x1)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_ltEs7(Left(x0), Left(x1), ty_@0, x2)
new_lt13(x0, x1, app(app(ty_@2, x2), x3))
new_esEs19(x0, x1, ty_Bool)
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs28(x0, x1, ty_@0)
new_primMulNat0(Succ(x0), Succ(x1))
new_lt7(x0, x1)
new_esEs23(x0, x1, ty_Float)
new_ltEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Int)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs19(x0, x1, ty_Double)
new_compare113(x0, x1, False, x2, x3)
new_ltEs18(x0, x1, ty_@0)
new_compare15(x0, x1, True, x2, x3)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs4(Right(x0), Right(x1), x2, ty_@0)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Char)
new_esEs24(x0, x1, ty_Int)
new_compare9(Integer(x0), Integer(x1))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, ty_Ordering)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_ltEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_compare4(:(x0, x1), [], x2)
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_esEs24(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_Char)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_compare25(x0, x1, False, x2, x3)
new_esEs20(x0, x1, ty_Ordering)
new_esEs30(Nothing, x0)
new_esEs12(:(x0, x1), :(x2, x3), x4)
new_compare30(x0, x1, app(ty_[], x2))
new_fsEs(x0)
new_lt8(x0, x1, x2, x3, x4)
new_ltEs11(x0, x1)
new_esEs23(x0, x1, ty_Double)
new_lt13(x0, x1, ty_@0)
new_gt1(x0, x1)
new_ltEs7(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Just(x0), Just(x1), ty_Int)
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_compare26(x0, x1, False)
new_ltEs18(x0, x1, ty_Double)
new_ltEs7(Right(x0), Left(x1), x2, x3)
new_ltEs7(Left(x0), Right(x1), x2, x3)
new_ltEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs25(x0, x1, ty_Bool)
new_lt17(x0, x1, x2)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primPlusNat1(Zero, Zero)
new_esEs28(x0, x1, ty_Float)
new_ltEs7(Right(x0), Right(x1), x2, ty_Int)
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_lt12(x0, x1)
new_compare7(:%(x0, x1), :%(x2, x3), ty_Int)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_ltEs4(Just(x0), Just(x1), ty_Int)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_compare11(@0, @0)
new_primMulNat0(Zero, Succ(x0))
new_esEs26(x0, x1, ty_Bool)
new_asAs(False, x0)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs12(:(x0, x1), [], x2)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs4(Just(x0), Just(x1), ty_Bool)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1, app(ty_[], x2))
new_ltEs8(x0, x1)
new_ltEs18(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Float)
new_esEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_Double)
new_ltEs19(x0, x1, ty_Ordering)
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(Just(x0), Just(x1), ty_Ordering)
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs18(x0, x1, ty_Double)
new_ltEs10(GT, LT)
new_ltEs10(LT, GT)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs28(x0, x1, ty_Double)
new_esEs10(@0, @0)
new_compare14(Double(x0, x1), Double(x2, x3))
new_compare24(x0, x1, True, x2, x3, x4)
new_compare30(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_Integer)
new_compare30(x0, x1, app(ty_Maybe, x2))
new_ltEs18(x0, x1, ty_Float)
new_ltEs15(x0, x1, x2)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_compare8(x0, x1)
new_lt13(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs20(x0, x1, ty_Char)
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs7(Right(x0), Right(x1), x2, ty_Integer)
new_compare30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Integer)
new_pePe(True, x0)
new_compare29(Just(x0), Just(x1), False, x2)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_Float)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_esEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCompAux00(x0, EQ)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1, ty_Float)
new_primEqNat0(Succ(x0), Zero)
new_ltEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_compare30(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_Int)
new_compare27(x0, x1, False, x2, x3)
new_esEs18(x0, x1, ty_Ordering)
new_esEs25(x0, x1, ty_Int)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs18(x0, x1, app(ty_Ratio, x2))
new_esEs7(Nothing, Nothing, x0)
new_ltEs4(Just(x0), Just(x1), ty_@0)
new_esEs19(x0, x1, app(ty_[], x2))
new_compare23(x0, x1, False)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_ltEs4(Just(x0), Nothing, x1)
new_esEs8(EQ, EQ)
new_compare112(x0, x1, True)
new_esEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs19(x0, x1, ty_Double)
new_esEs13(Float(x0, x1), Float(x2, x3))
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs4(Right(x0), Right(x1), x2, ty_Double)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_lt13(x0, x1, ty_Char)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, ty_Char)
new_esEs15(Integer(x0), Integer(x1))
new_ltEs12(x0, x1)
new_lt20(x0, x1, ty_@0)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_@0)
new_esEs14(True, False)
new_esEs14(False, True)
new_ltEs4(Just(x0), Just(x1), ty_Float)
new_ltEs7(Right(x0), Right(x1), x2, ty_Float)
new_esEs18(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs6(x0, x1)
new_esEs22(x0, x1, ty_Int)
new_esEs20(x0, x1, ty_Double)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare110(x0, x1, True, x2, x3, x4)
new_ltEs9(x0, x1)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs19(x0, x1, ty_@0)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Ordering)
new_esEs27(x0, x1, ty_Integer)
new_esEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs16(:%(x0, x1), :%(x2, x3), x4)
new_lt20(x0, x1, ty_Float)
new_compare25(x0, x1, True, x2, x3)
new_compare30(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Integer)
new_primCmpNat0(Succ(x0), Succ(x1))
new_lt19(x0, x1, ty_Char)
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_esEs20(x0, x1, ty_Integer)
new_esEs28(x0, x1, ty_Ordering)
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_esEs21(x0, x1, ty_Integer)
new_compare28(x0, x1, x2)
new_ltEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_ltEs7(Right(x0), Right(x1), x2, ty_Double)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Bool)
new_primPlusNat0(Succ(x0), x1)
new_esEs20(x0, x1, ty_@0)
new_ltEs13(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs18(x0, x1, ty_Integer)
new_esEs4(Left(x0), Left(x1), ty_Int, x2)
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Just(x0), Just(x1), ty_Float)
new_compare18(x0, x1, x2, x3)
new_esEs19(x0, x1, ty_Float)
new_ltEs20(x0, x1, ty_Bool)
new_primCmpNat0(Zero, Zero)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs4(Left(x0), Left(x1), ty_Integer, x2)
new_esEs19(x0, x1, ty_Ordering)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_lt13(x0, x1, app(ty_Maybe, x2))
new_lt13(x0, x1, ty_Bool)
new_lt18(x0, x1, x2)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, ty_Float)
new_ltEs7(Left(x0), Left(x1), ty_Double, x2)
new_ltEs16(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs12([], [], x0)
new_lt10(x0, x1)
new_compare7(:%(x0, x1), :%(x2, x3), ty_Integer)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_compare113(x0, x1, True, x2, x3)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs20(x0, x1, app(ty_[], x2))
new_ltEs7(Left(x0), Left(x1), ty_Bool, x2)
new_esEs4(Left(x0), Left(x1), ty_Char, x2)
new_esEs25(x0, x1, ty_Ordering)
new_esEs27(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_Float)
new_ltEs7(Left(x0), Left(x1), ty_Float, x2)
new_lt5(x0, x1, x2, x3)
new_compare29(Just(x0), Nothing, False, x1)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs10(GT, GT)
new_esEs4(Right(x0), Right(x1), x2, ty_Int)
new_ltEs14(True, True)
new_ltEs14(False, False)
new_esEs24(x0, x1, ty_Ordering)
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_lt19(x0, x1, ty_@0)
new_esEs18(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Char)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs7(Left(x0), Left(x1), ty_Int, x2)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_not(True)
new_esEs19(x0, x1, ty_Int)
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Just(x0), Just(x1), ty_@0)
new_compare30(x0, x1, ty_Integer)
new_ltEs5(x0, x1)
new_ltEs20(x0, x1, ty_Double)
new_esEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(Just(x0), Just(x1), ty_Integer)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_not(False)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_Integer)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_ltEs4(Just(x0), Just(x1), app(ty_[], x2))
new_primCompAux00(x0, LT)
new_esEs4(Left(x0), Left(x1), ty_@0, x2)
new_lt6(x0, x1)
new_ltEs10(EQ, GT)
new_ltEs10(GT, EQ)
new_esEs4(Right(x0), Left(x1), x2, x3)
new_esEs4(Left(x0), Right(x1), x2, x3)
new_ltEs19(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Float)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_ltEs18(x0, x1, ty_Char)
new_esEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs19(x0, x1, ty_Integer)
new_esEs18(x0, x1, app(ty_[], x2))
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_sr(Integer(x0), Integer(x1))
new_esEs27(x0, x1, ty_Char)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs20(x0, x1, ty_Bool)
new_ltEs4(Just(x0), Just(x1), ty_Char)
new_ltEs4(Nothing, Just(x0), x1)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs18(x0, x1, ty_@0)
new_esEs24(x0, x1, app(ty_[], x2))
new_ltEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_lt13(x0, x1, ty_Double)
new_esEs18(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_lt13(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, ty_Bool)
new_lt13(x0, x1, ty_Ordering)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare12(x0, x1, x2, x3)
new_compare30(x0, x1, app(app(ty_Either, x2), x3))
new_compare15(x0, x1, False, x2, x3)
new_ltEs18(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Ordering)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_compare30(x0, x1, ty_Float)
new_compare111(x0, x1, True, x2)
new_lt13(x0, x1, ty_Integer)
new_esEs14(False, False)
new_primEqInt(Pos(Zero), Pos(Zero))
new_compare10(Char(x0), Char(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs24(x0, x1, ty_Integer)
new_esEs4(Right(x0), Right(x1), x2, ty_Char)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Double)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_ltEs20(x0, x1, ty_Float)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_lt13(x0, x1, ty_Int)
new_compare29(x0, x1, True, x2)
new_lt13(x0, x1, ty_Float)
new_lt20(x0, x1, ty_Integer)
new_primCmpNat0(Zero, Succ(x0))
new_ltEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs23(x0, x1, ty_Int)
new_primCompAux00(x0, GT)
new_ltEs20(x0, x1, ty_@0)
new_lt15(x0, x1)
new_ltEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primEqNat0(Zero, Succ(x0))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs7(Left(x0), Left(x1), ty_Integer, x2)
new_esEs27(x0, x1, ty_Bool)
new_ltEs19(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_@0)
new_compare24(x0, x1, False, x2, x3, x4)
new_compare32(x0, x1)
new_esEs7(Just(x0), Nothing, x1)
new_esEs18(x0, x1, ty_Integer)
new_ltEs10(EQ, EQ)

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
                                    ↳ QDPSizeChangeProof
                                  ↳ QDP

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

new_splitGT10(zzz440, zzz441, zzz442, zzz443, zzz444, True, h, ba) → new_splitGT0(zzz443, h, ba)
new_splitGT20(zzz440, zzz441, zzz442, zzz443, Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), True, h, ba) → new_splitGT20(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, new_gt1(zzz4440, h), h, ba)
new_splitGT20(zzz440, zzz441, zzz442, zzz443, zzz444, False, h, ba) → new_splitGT10(zzz440, zzz441, zzz442, zzz443, zzz444, new_lt11(Nothing, zzz440, h), h, ba)
new_splitGT0(Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), h, ba) → new_splitGT20(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, new_gt1(zzz4440, h), h, ba)

The TRS R consists of the following rules:

new_lt19(zzz500000, zzz4300000, ty_Float) → new_lt6(zzz500000, zzz4300000)
new_ltEs18(zzz50000, zzz430000, app(ty_Ratio, bee)) → new_ltEs15(zzz50000, zzz430000, bee)
new_esEs7(Just(zzz5000), Just(zzz4000), app(ty_Maybe, dh)) → new_esEs7(zzz5000, zzz4000, dh)
new_esEs4(Right(zzz5000), Right(zzz4000), bgd, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_esEs20(zzz5000, zzz4000, app(ty_Maybe, bba)) → new_esEs7(zzz5000, zzz4000, bba)
new_esEs12(:(zzz5000, zzz5001), :(zzz4000, zzz4001), hh) → new_asAs(new_esEs20(zzz5000, zzz4000, hh), new_esEs12(zzz5001, zzz4001, hh))
new_esEs7(Just(zzz5000), Just(zzz4000), app(ty_[], dd)) → new_esEs12(zzz5000, zzz4000, dd)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, ty_Ordering) → new_ltEs10(zzz500000, zzz4300000)
new_lt19(zzz500000, zzz4300000, app(app(app(ty_@3, cdd), cde), cdf)) → new_lt8(zzz500000, zzz4300000, cdd, cde, cdf)
new_ltEs18(zzz50000, zzz430000, app(app(app(ty_@3, bef), beg), beh)) → new_ltEs16(zzz50000, zzz430000, bef, beg, beh)
new_lt20(zzz500001, zzz4300001, app(ty_[], cfa)) → new_lt18(zzz500001, zzz4300001, cfa)
new_esEs4(Right(zzz5000), Right(zzz4000), bgd, ty_Char) → new_esEs11(zzz5000, zzz4000)
new_compare15(zzz500000, zzz4300000, True, hf, hg) → LT
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Bool, bfa) → new_esEs14(zzz5000, zzz4000)
new_ltEs18(zzz50000, zzz430000, app(ty_Maybe, bb)) → new_ltEs4(zzz50000, zzz430000, bb)
new_ltEs20(zzz500002, zzz4300002, ty_Ordering) → new_ltEs10(zzz500002, zzz4300002)
new_esEs4(Right(zzz5000), Right(zzz4000), bgd, app(app(app(ty_@3, bhb), bhc), bhd)) → new_esEs6(zzz5000, zzz4000, bhb, bhc, bhd)
new_lt13(zzz500000, zzz4300000, app(app(app(ty_@3, hc), hd), he)) → new_lt8(zzz500000, zzz4300000, hc, hd, he)
new_compare32(zzz430, h) → new_compare29(Nothing, zzz430, new_esEs30(zzz430, h), h)
new_lt15(zzz500000, zzz4300000) → new_esEs8(new_compare14(zzz500000, zzz4300000), LT)
new_lt20(zzz500001, zzz4300001, app(app(app(ty_@3, cef), ceg), ceh)) → new_lt8(zzz500001, zzz4300001, cef, ceg, ceh)
new_esEs27(zzz5001, zzz4001, app(ty_Maybe, dba)) → new_esEs7(zzz5001, zzz4001, dba)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Ordering) → new_ltEs10(zzz500000, zzz4300000)
new_esEs23(zzz500000, zzz4300000, ty_Bool) → new_esEs14(zzz500000, zzz4300000)
new_compare27(zzz500000, zzz4300000, False, ha, hb) → new_compare113(zzz500000, zzz4300000, new_ltEs7(zzz500000, zzz4300000, ha, hb), ha, hb)
new_lt19(zzz500000, zzz4300000, ty_Double) → new_lt15(zzz500000, zzz4300000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), app(ty_Maybe, bcb), bbe) → new_ltEs4(zzz500000, zzz4300000, bcb)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, ty_@0) → new_ltEs11(zzz500000, zzz4300000)
new_ltEs20(zzz500002, zzz4300002, app(ty_Ratio, cfg)) → new_ltEs15(zzz500002, zzz4300002, cfg)
new_lt13(zzz500000, zzz4300000, app(ty_[], cbc)) → new_lt18(zzz500000, zzz4300000, cbc)
new_esEs26(zzz5002, zzz4002, ty_Float) → new_esEs13(zzz5002, zzz4002)
new_ltEs7(Left(zzz500000), Right(zzz4300000), bch, bbe) → True
new_primMulNat0(Zero, Zero) → Zero
new_esEs19(zzz5000, zzz4000, ty_Int) → new_esEs17(zzz5000, zzz4000)
new_sr(Integer(zzz43000000), Integer(zzz5000010)) → Integer(new_primMulInt(zzz43000000, zzz5000010))
new_ltEs20(zzz500002, zzz4300002, ty_Float) → new_ltEs12(zzz500002, zzz4300002)
new_ltEs20(zzz500002, zzz4300002, ty_@0) → new_ltEs11(zzz500002, zzz4300002)
new_esEs20(zzz5000, zzz4000, app(ty_Ratio, bbb)) → new_esEs16(zzz5000, zzz4000, bbb)
new_esEs18(zzz5001, zzz4001, ty_Double) → new_esEs9(zzz5001, zzz4001)
new_lt20(zzz500001, zzz4300001, ty_Float) → new_lt6(zzz500001, zzz4300001)
new_esEs23(zzz500000, zzz4300000, ty_Double) → new_esEs9(zzz500000, zzz4300000)
new_esEs4(Right(zzz5000), Right(zzz4000), bgd, app(ty_[], bha)) → new_esEs12(zzz5000, zzz4000, bha)
new_esEs24(zzz500001, zzz4300001, ty_Integer) → new_esEs15(zzz500001, zzz4300001)
new_ltEs14(False, True) → True
new_ltEs19(zzz500001, zzz4300001, ty_Integer) → new_ltEs9(zzz500001, zzz4300001)
new_ltEs4(Just(zzz500000), Just(zzz4300000), app(app(ty_@2, be), bf)) → new_ltEs13(zzz500000, zzz4300000, be, bf)
new_esEs20(zzz5000, zzz4000, app(app(ty_Either, baa), bab)) → new_esEs4(zzz5000, zzz4000, baa, bab)
new_esEs12([], [], hh) → True
new_ltEs19(zzz500001, zzz4300001, ty_Ordering) → new_ltEs10(zzz500001, zzz4300001)
new_esEs24(zzz500001, zzz4300001, app(app(ty_@2, ceb), cec)) → new_esEs5(zzz500001, zzz4300001, ceb, cec)
new_lt12(zzz500000, zzz4300000) → new_esEs8(new_compare10(zzz500000, zzz4300000), LT)
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Ordering, bbe) → new_ltEs10(zzz500000, zzz4300000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, app(ty_Ratio, bdf)) → new_ltEs15(zzz500000, zzz4300000, bdf)
new_esEs15(Integer(zzz5000), Integer(zzz4000)) → new_primEqInt(zzz5000, zzz4000)
new_ltEs10(EQ, GT) → True
new_ltEs19(zzz500001, zzz4300001, app(ty_Maybe, cbh)) → new_ltEs4(zzz500001, zzz4300001, cbh)
new_esEs21(zzz5001, zzz4001, ty_Int) → new_esEs17(zzz5001, zzz4001)
new_ltEs7(Left(zzz500000), Left(zzz4300000), app(app(app(ty_@3, bcd), bce), bcf), bbe) → new_ltEs16(zzz500000, zzz4300000, bcd, bce, bcf)
new_lt13(zzz500000, zzz4300000, ty_Char) → new_lt12(zzz500000, zzz4300000)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Ordering, bfa) → new_esEs8(zzz5000, zzz4000)
new_esEs24(zzz500001, zzz4300001, app(ty_[], cfa)) → new_esEs12(zzz500001, zzz4300001, cfa)
new_esEs25(zzz500000, zzz4300000, ty_Double) → new_esEs9(zzz500000, zzz4300000)
new_esEs25(zzz500000, zzz4300000, ty_Float) → new_esEs13(zzz500000, zzz4300000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, app(ty_[], beb)) → new_ltEs17(zzz500000, zzz4300000, beb)
new_pePe(False, zzz218) → zzz218
new_lt14(zzz5000, zzz43000) → new_esEs8(new_compare8(zzz5000, zzz43000), LT)
new_esEs25(zzz500000, zzz4300000, app(app(ty_Either, ccf), ccg)) → new_esEs4(zzz500000, zzz4300000, ccf, ccg)
new_esEs12(:(zzz5000, zzz5001), [], hh) → False
new_esEs12([], :(zzz4000, zzz4001), hh) → False
new_esEs25(zzz500000, zzz4300000, ty_Char) → new_esEs11(zzz500000, zzz4300000)
new_esEs25(zzz500000, zzz4300000, ty_Bool) → new_esEs14(zzz500000, zzz4300000)
new_lt19(zzz500000, zzz4300000, ty_Ordering) → new_lt9(zzz500000, zzz4300000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, app(app(ty_@2, bdc), bdd)) → new_ltEs13(zzz500000, zzz4300000, bdc, bdd)
new_esEs4(Right(zzz5000), Right(zzz4000), bgd, app(ty_Ratio, bhf)) → new_esEs16(zzz5000, zzz4000, bhf)
new_compare23(zzz500000, zzz4300000, True) → EQ
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Float, bbe) → new_ltEs12(zzz500000, zzz4300000)
new_lt19(zzz500000, zzz4300000, app(ty_Ratio, cdc)) → new_lt17(zzz500000, zzz4300000, cdc)
new_esEs24(zzz500001, zzz4300001, app(ty_Maybe, ced)) → new_esEs7(zzz500001, zzz4300001, ced)
new_ltEs4(Nothing, Just(zzz4300000), bb) → True
new_esEs23(zzz500000, zzz4300000, app(ty_Maybe, cba)) → new_esEs7(zzz500000, zzz4300000, cba)
new_compare30(zzz500000, zzz4300000, ty_Integer) → new_compare9(zzz500000, zzz4300000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(ty_Ratio, bgc), bfa) → new_esEs16(zzz5000, zzz4000, bgc)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, ty_Char) → new_ltEs5(zzz500000, zzz4300000)
new_compare13(zzz500000, zzz4300000, hc, hd, he) → new_compare24(zzz500000, zzz4300000, new_esEs6(zzz500000, zzz4300000, hc, hd, he), hc, hd, he)
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_lt4(zzz500000, zzz4300000) → new_esEs8(new_compare11(zzz500000, zzz4300000), LT)
new_esEs4(Right(zzz5000), Right(zzz4000), bgd, ty_Integer) → new_esEs15(zzz5000, zzz4000)
new_esEs20(zzz5000, zzz4000, app(app(ty_@2, bac), bad)) → new_esEs5(zzz5000, zzz4000, bac, bad)
new_esEs28(zzz5000, zzz4000, app(ty_Ratio, dcd)) → new_esEs16(zzz5000, zzz4000, dcd)
new_compare30(zzz500000, zzz4300000, app(ty_Ratio, cad)) → new_compare7(zzz500000, zzz4300000, cad)
new_compare19(zzz500000, zzz4300000, True) → LT
new_compare6(zzz500000, zzz4300000) → new_compare23(zzz500000, zzz4300000, new_esEs8(zzz500000, zzz4300000))
new_ltEs18(zzz50000, zzz430000, ty_@0) → new_ltEs11(zzz50000, zzz430000)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_ltEs19(zzz500001, zzz4300001, app(ty_Ratio, cca)) → new_ltEs15(zzz500001, zzz4300001, cca)
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Int) → new_esEs17(zzz5000, zzz4000)
new_ltEs20(zzz500002, zzz4300002, ty_Bool) → new_ltEs14(zzz500002, zzz4300002)
new_esEs27(zzz5001, zzz4001, ty_@0) → new_esEs10(zzz5001, zzz4001)
new_ltEs12(zzz50000, zzz430000) → new_fsEs(new_compare16(zzz50000, zzz430000))
new_esEs8(LT, LT) → True
new_lt19(zzz500000, zzz4300000, app(app(ty_@2, cch), cda)) → new_lt16(zzz500000, zzz4300000, cch, cda)
new_esEs25(zzz500000, zzz4300000, ty_Ordering) → new_esEs8(zzz500000, zzz4300000)
new_esEs19(zzz5000, zzz4000, app(ty_Maybe, gg)) → new_esEs7(zzz5000, zzz4000, gg)
new_esEs20(zzz5000, zzz4000, app(app(app(ty_@3, baf), bag), bah)) → new_esEs6(zzz5000, zzz4000, baf, bag, bah)
new_esEs18(zzz5001, zzz4001, app(ty_Ratio, ff)) → new_esEs16(zzz5001, zzz4001, ff)
new_pePe(True, zzz218) → True
new_primEqNat0(Zero, Zero) → True
new_lt20(zzz500001, zzz4300001, app(app(ty_Either, cdh), cea)) → new_lt5(zzz500001, zzz4300001, cdh, cea)
new_compare26(zzz500000, zzz4300000, True) → EQ
new_lt20(zzz500001, zzz4300001, ty_Bool) → new_lt7(zzz500001, zzz4300001)
new_esEs13(Float(zzz5000, zzz5001), Float(zzz4000, zzz4001)) → new_esEs17(new_sr0(zzz5000, zzz4000), new_sr0(zzz5001, zzz4001))
new_esEs19(zzz5000, zzz4000, app(ty_[], gc)) → new_esEs12(zzz5000, zzz4000, gc)
new_compare29(Nothing, Just(zzz430000), False, gg) → LT
new_esEs19(zzz5000, zzz4000, ty_Float) → new_esEs13(zzz5000, zzz4000)
new_compare30(zzz500000, zzz4300000, app(ty_Maybe, cac)) → new_compare28(zzz500000, zzz4300000, cac)
new_esEs18(zzz5001, zzz4001, app(app(ty_@2, ef), eg)) → new_esEs5(zzz5001, zzz4001, ef, eg)
new_esEs25(zzz500000, zzz4300000, ty_Int) → new_esEs17(zzz500000, zzz4300000)
new_esEs9(Double(zzz5000, zzz5001), Double(zzz4000, zzz4001)) → new_esEs17(new_sr0(zzz5000, zzz4000), new_sr0(zzz5001, zzz4001))
new_esEs26(zzz5002, zzz4002, ty_Ordering) → new_esEs8(zzz5002, zzz4002)
new_esEs8(GT, GT) → True
new_lt20(zzz500001, zzz4300001, app(ty_Maybe, ced)) → new_lt11(zzz500001, zzz4300001, ced)
new_esEs18(zzz5001, zzz4001, app(app(app(ty_@3, fa), fb), fc)) → new_esEs6(zzz5001, zzz4001, fa, fb, fc)
new_esEs25(zzz500000, zzz4300000, ty_@0) → new_esEs10(zzz500000, zzz4300000)
new_compare4([], [], ce) → EQ
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_lt19(zzz500000, zzz4300000, ty_@0) → new_lt4(zzz500000, zzz4300000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(app(ty_@2, bfd), bfe), bfa) → new_esEs5(zzz5000, zzz4000, bfd, bfe)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, ty_Integer) → new_ltEs9(zzz500000, zzz4300000)
new_esEs26(zzz5002, zzz4002, app(app(app(ty_@3, chd), che), chf)) → new_esEs6(zzz5002, zzz4002, chd, che, chf)
new_compare18(zzz500000, zzz4300000, hf, hg) → new_compare25(zzz500000, zzz4300000, new_esEs5(zzz500000, zzz4300000, hf, hg), hf, hg)
new_ltEs17(zzz50000, zzz430000, ce) → new_fsEs(new_compare4(zzz50000, zzz430000, ce))
new_esEs8(GT, LT) → False
new_esEs8(LT, GT) → False
new_compare30(zzz500000, zzz4300000, app(ty_[], cah)) → new_compare4(zzz500000, zzz4300000, cah)
new_compare30(zzz500000, zzz4300000, ty_Double) → new_compare14(zzz500000, zzz4300000)
new_ltEs13(@2(zzz500000, zzz500001), @2(zzz4300000, zzz4300001), bec, bed) → new_pePe(new_lt13(zzz500000, zzz4300000, bec), new_asAs(new_esEs23(zzz500000, zzz4300000, bec), new_ltEs19(zzz500001, zzz4300001, bed)))
new_esEs4(Right(zzz5000), Right(zzz4000), bgd, app(app(ty_Either, bge), bgf)) → new_esEs4(zzz5000, zzz4000, bge, bgf)
new_esEs25(zzz500000, zzz4300000, app(ty_[], cdg)) → new_esEs12(zzz500000, zzz4300000, cdg)
new_compare24(zzz500000, zzz4300000, True, hc, hd, he) → EQ
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Int, bbe) → new_ltEs6(zzz500000, zzz4300000)
new_lt20(zzz500001, zzz4300001, ty_Ordering) → new_lt9(zzz500001, zzz4300001)
new_primEqInt(Neg(Succ(zzz50000)), Neg(Succ(zzz40000))) → new_primEqNat0(zzz50000, zzz40000)
new_esEs20(zzz5000, zzz4000, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_compare113(zzz500000, zzz4300000, True, ha, hb) → LT
new_esEs23(zzz500000, zzz4300000, ty_Ordering) → new_esEs8(zzz500000, zzz4300000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(app(ty_Either, bfb), bfc), bfa) → new_esEs4(zzz5000, zzz4000, bfb, bfc)
new_ltEs18(zzz50000, zzz430000, app(app(ty_Either, bch), bbe)) → new_ltEs7(zzz50000, zzz430000, bch, bbe)
new_esEs24(zzz500001, zzz4300001, ty_Bool) → new_esEs14(zzz500001, zzz4300001)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_lt19(zzz500000, zzz4300000, ty_Bool) → new_lt7(zzz500000, zzz4300000)
new_lt19(zzz500000, zzz4300000, ty_Integer) → new_lt10(zzz500000, zzz4300000)
new_ltEs4(Nothing, Nothing, bb) → True
new_lt13(zzz500000, zzz4300000, ty_Float) → new_lt6(zzz500000, zzz4300000)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_@0) → new_ltEs11(zzz500000, zzz4300000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Char, bbe) → new_ltEs5(zzz500000, zzz4300000)
new_lt13(zzz500000, zzz4300000, ty_Int) → new_lt14(zzz500000, zzz4300000)
new_lt6(zzz500000, zzz4300000) → new_esEs8(new_compare16(zzz500000, zzz4300000), LT)
new_compare29(Just(zzz50000), Nothing, False, gg) → GT
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_ltEs7(Right(zzz500000), Left(zzz4300000), bch, bbe) → False
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_esEs24(zzz500001, zzz4300001, app(app(app(ty_@3, cef), ceg), ceh)) → new_esEs6(zzz500001, zzz4300001, cef, ceg, ceh)
new_esEs23(zzz500000, zzz4300000, ty_Char) → new_esEs11(zzz500000, zzz4300000)
new_lt13(zzz500000, zzz4300000, ty_Bool) → new_lt7(zzz500000, zzz4300000)
new_esEs19(zzz5000, zzz4000, ty_Bool) → new_esEs14(zzz5000, zzz4000)
new_esEs20(zzz5000, zzz4000, ty_Float) → new_esEs13(zzz5000, zzz4000)
new_compare14(Double(zzz500000, zzz500001), Double(zzz4300000, zzz4300001)) → new_compare8(new_sr0(zzz500000, zzz4300000), new_sr0(zzz500001, zzz4300001))
new_compare12(zzz500000, zzz4300000, ha, hb) → new_compare27(zzz500000, zzz4300000, new_esEs4(zzz500000, zzz4300000, ha, hb), ha, hb)
new_compare8(zzz500, zzz4300) → new_primCmpInt(zzz500, zzz4300)
new_lt19(zzz500000, zzz4300000, ty_Char) → new_lt12(zzz500000, zzz4300000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, app(app(app(ty_@3, bdg), bdh), bea)) → new_ltEs16(zzz500000, zzz4300000, bdg, bdh, bea)
new_primEqInt(Neg(Succ(zzz50000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(zzz40000))) → False
new_compare17(zzz500000, zzz4300000) → new_compare26(zzz500000, zzz4300000, new_esEs14(zzz500000, zzz4300000))
new_esEs8(EQ, EQ) → True
new_lt13(zzz500000, zzz4300000, ty_Double) → new_lt15(zzz500000, zzz4300000)
new_compare111(zzz200, zzz201, True, bbd) → LT
new_esEs20(zzz5000, zzz4000, ty_@0) → new_esEs10(zzz5000, zzz4000)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Char, bfa) → new_esEs11(zzz5000, zzz4000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_ltEs19(zzz500001, zzz4300001, ty_@0) → new_ltEs11(zzz500001, zzz4300001)
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_esEs18(zzz5001, zzz4001, ty_Char) → new_esEs11(zzz5001, zzz4001)
new_compare112(zzz500000, zzz4300000, True) → LT
new_esEs19(zzz5000, zzz4000, ty_Char) → new_esEs11(zzz5000, zzz4000)
new_compare30(zzz500000, zzz4300000, app(app(ty_Either, bhg), bhh)) → new_compare12(zzz500000, zzz4300000, bhg, bhh)
new_primEqInt(Pos(Succ(zzz50000)), Pos(Succ(zzz40000))) → new_primEqNat0(zzz50000, zzz40000)
new_ltEs18(zzz50000, zzz430000, ty_Double) → new_ltEs8(zzz50000, zzz430000)
new_compare27(zzz500000, zzz4300000, True, ha, hb) → EQ
new_lt10(zzz500000, zzz4300000) → new_esEs8(new_compare9(zzz500000, zzz4300000), LT)
new_esEs24(zzz500001, zzz4300001, app(ty_Ratio, cee)) → new_esEs16(zzz500001, zzz4300001, cee)
new_ltEs19(zzz500001, zzz4300001, ty_Bool) → new_ltEs14(zzz500001, zzz4300001)
new_esEs14(False, True) → False
new_esEs14(True, False) → False
new_esEs23(zzz500000, zzz4300000, app(ty_[], cbc)) → new_esEs12(zzz500000, zzz4300000, cbc)
new_ltEs4(Just(zzz500000), Just(zzz4300000), app(app(ty_Either, bc), bd)) → new_ltEs7(zzz500000, zzz4300000, bc, bd)
new_esEs26(zzz5002, zzz4002, ty_Integer) → new_esEs15(zzz5002, zzz4002)
new_ltEs10(GT, EQ) → False
new_lt17(zzz500000, zzz4300000, cbb) → new_esEs8(new_compare7(zzz500000, zzz4300000, cbb), LT)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Double) → new_ltEs8(zzz500000, zzz4300000)
new_esEs24(zzz500001, zzz4300001, ty_Int) → new_esEs17(zzz500001, zzz4300001)
new_primEqNat0(Succ(zzz50000), Succ(zzz40000)) → new_primEqNat0(zzz50000, zzz40000)
new_ltEs20(zzz500002, zzz4300002, app(ty_[], cgc)) → new_ltEs17(zzz500002, zzz4300002, cgc)
new_esEs27(zzz5001, zzz4001, ty_Ordering) → new_esEs8(zzz5001, zzz4001)
new_ltEs14(False, False) → True
new_compare11(@0, @0) → EQ
new_lt7(zzz500000, zzz4300000) → new_esEs8(new_compare17(zzz500000, zzz4300000), LT)
new_esEs19(zzz5000, zzz4000, app(app(app(ty_@3, gd), ge), gf)) → new_esEs6(zzz5000, zzz4000, gd, ge, gf)
new_ltEs9(zzz50000, zzz430000) → new_fsEs(new_compare9(zzz50000, zzz430000))
new_ltEs20(zzz500002, zzz4300002, ty_Char) → new_ltEs5(zzz500002, zzz4300002)
new_compare113(zzz500000, zzz4300000, False, ha, hb) → GT
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, ty_Bool) → new_ltEs14(zzz500000, zzz4300000)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Int) → new_ltEs6(zzz500000, zzz4300000)
new_primCompAux00(zzz225, LT) → LT
new_lt20(zzz500001, zzz4300001, ty_@0) → new_lt4(zzz500001, zzz4300001)
new_ltEs19(zzz500001, zzz4300001, app(ty_[], cce)) → new_ltEs17(zzz500001, zzz4300001, cce)
new_ltEs19(zzz500001, zzz4300001, app(app(ty_Either, cbd), cbe)) → new_ltEs7(zzz500001, zzz4300001, cbd, cbe)
new_compare7(:%(zzz500000, zzz500001), :%(zzz4300000, zzz4300001), ty_Int) → new_compare8(new_sr0(zzz500000, zzz4300001), new_sr0(zzz4300000, zzz500001))
new_esEs24(zzz500001, zzz4300001, ty_Ordering) → new_esEs8(zzz500001, zzz4300001)
new_ltEs8(zzz50000, zzz430000) → new_fsEs(new_compare14(zzz50000, zzz430000))
new_esEs7(Nothing, Nothing, cf) → True
new_esEs28(zzz5000, zzz4000, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_esEs8(EQ, LT) → False
new_esEs8(LT, EQ) → False
new_esEs18(zzz5001, zzz4001, app(ty_Maybe, fd)) → new_esEs7(zzz5001, zzz4001, fd)
new_primEqInt(Pos(Succ(zzz50000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(zzz40000))) → False
new_lt20(zzz500001, zzz4300001, app(ty_Ratio, cee)) → new_lt17(zzz500001, zzz4300001, cee)
new_compare30(zzz500000, zzz4300000, ty_Int) → new_compare8(zzz500000, zzz4300000)
new_compare24(zzz500000, zzz4300000, False, hc, hd, he) → new_compare110(zzz500000, zzz4300000, new_ltEs16(zzz500000, zzz4300000, hc, hd, he), hc, hd, he)
new_esEs24(zzz500001, zzz4300001, ty_@0) → new_esEs10(zzz500001, zzz4300001)
new_primCmpNat0(Zero, Zero) → EQ
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Integer, bbe) → new_ltEs9(zzz500000, zzz4300000)
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_esEs23(zzz500000, zzz4300000, app(app(ty_@2, hf), hg)) → new_esEs5(zzz500000, zzz4300000, hf, hg)
new_esEs4(Right(zzz5000), Right(zzz4000), bgd, ty_@0) → new_esEs10(zzz5000, zzz4000)
new_ltEs10(LT, EQ) → True
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_compare19(zzz500000, zzz4300000, False) → GT
new_esEs27(zzz5001, zzz4001, ty_Double) → new_esEs9(zzz5001, zzz4001)
new_ltEs15(zzz50000, zzz430000, bee) → new_fsEs(new_compare7(zzz50000, zzz430000, bee))
new_esEs23(zzz500000, zzz4300000, ty_Float) → new_esEs13(zzz500000, zzz4300000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Integer) → new_esEs15(zzz5000, zzz4000)
new_compare29(Just(zzz50000), Just(zzz430000), False, gg) → new_compare111(zzz50000, zzz430000, new_ltEs18(zzz50000, zzz430000, gg), gg)
new_primEqInt(Pos(Succ(zzz50000)), Neg(zzz4000)) → False
new_primEqInt(Neg(Succ(zzz50000)), Pos(zzz4000)) → False
new_lt13(zzz500000, zzz4300000, app(ty_Ratio, cbb)) → new_lt17(zzz500000, zzz4300000, cbb)
new_esEs7(Nothing, Just(zzz4000), cf) → False
new_esEs7(Just(zzz5000), Nothing, cf) → False
new_esEs18(zzz5001, zzz4001, app(ty_[], eh)) → new_esEs12(zzz5001, zzz4001, eh)
new_esEs28(zzz5000, zzz4000, ty_Char) → new_esEs11(zzz5000, zzz4000)
new_ltEs10(GT, GT) → True
new_esEs26(zzz5002, zzz4002, app(ty_Ratio, chh)) → new_esEs16(zzz5002, zzz4002, chh)
new_esEs26(zzz5002, zzz4002, ty_Int) → new_esEs17(zzz5002, zzz4002)
new_esEs4(Right(zzz5000), Right(zzz4000), bgd, ty_Bool) → new_esEs14(zzz5000, zzz4000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_@0, bbe) → new_ltEs11(zzz500000, zzz4300000)
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_primEqInt(Pos(Zero), Neg(Succ(zzz40000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(zzz40000))) → False
new_ltEs6(zzz50000, zzz430000) → new_fsEs(new_compare8(zzz50000, zzz430000))
new_esEs20(zzz5000, zzz4000, app(ty_[], bae)) → new_esEs12(zzz5000, zzz4000, bae)
new_esEs21(zzz5001, zzz4001, ty_Integer) → new_esEs15(zzz5001, zzz4001)
new_compare30(zzz500000, zzz4300000, app(app(ty_@2, caa), cab)) → new_compare18(zzz500000, zzz4300000, caa, cab)
new_primCompAux00(zzz225, EQ) → zzz225
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Double, bfa) → new_esEs9(zzz5000, zzz4000)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Integer, bfa) → new_esEs15(zzz5000, zzz4000)
new_esEs18(zzz5001, zzz4001, ty_Int) → new_esEs17(zzz5001, zzz4001)
new_lt16(zzz500000, zzz4300000, hf, hg) → new_esEs8(new_compare18(zzz500000, zzz4300000, hf, hg), LT)
new_esEs8(GT, EQ) → False
new_esEs8(EQ, GT) → False
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Double) → new_esEs9(zzz5000, zzz4000)
new_esEs26(zzz5002, zzz4002, ty_Char) → new_esEs11(zzz5002, zzz4002)
new_esEs27(zzz5001, zzz4001, app(ty_Ratio, dbb)) → new_esEs16(zzz5001, zzz4001, dbb)
new_esEs26(zzz5002, zzz4002, app(app(ty_@2, cha), chb)) → new_esEs5(zzz5002, zzz4002, cha, chb)
new_ltEs19(zzz500001, zzz4300001, app(app(ty_@2, cbf), cbg)) → new_ltEs13(zzz500001, zzz4300001, cbf, cbg)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Bool) → new_ltEs14(zzz500000, zzz4300000)
new_not(False) → True
new_esEs24(zzz500001, zzz4300001, ty_Double) → new_esEs9(zzz500001, zzz4300001)
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_ltEs5(zzz50000, zzz430000) → new_fsEs(new_compare10(zzz50000, zzz430000))
new_esEs25(zzz500000, zzz4300000, ty_Integer) → new_esEs15(zzz500000, zzz4300000)
new_esEs26(zzz5002, zzz4002, ty_Bool) → new_esEs14(zzz5002, zzz4002)
new_ltEs19(zzz500001, zzz4300001, ty_Int) → new_ltEs6(zzz500001, zzz4300001)
new_esEs25(zzz500000, zzz4300000, app(ty_Ratio, cdc)) → new_esEs16(zzz500000, zzz4300000, cdc)
new_esEs4(Right(zzz5000), Right(zzz4000), bgd, ty_Int) → new_esEs17(zzz5000, zzz4000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Bool, bbe) → new_ltEs14(zzz500000, zzz4300000)
new_esEs28(zzz5000, zzz4000, app(app(ty_@2, dbe), dbf)) → new_esEs5(zzz5000, zzz4000, dbe, dbf)
new_esEs23(zzz500000, zzz4300000, ty_@0) → new_esEs10(zzz500000, zzz4300000)
new_compare30(zzz500000, zzz4300000, ty_@0) → new_compare11(zzz500000, zzz4300000)
new_esEs18(zzz5001, zzz4001, app(app(ty_Either, ed), ee)) → new_esEs4(zzz5001, zzz4001, ed, ee)
new_lt18(zzz500000, zzz4300000, cbc) → new_esEs8(new_compare4(zzz500000, zzz4300000, cbc), LT)
new_ltEs18(zzz50000, zzz430000, ty_Int) → new_ltEs6(zzz50000, zzz430000)
new_esEs22(zzz5000, zzz4000, ty_Int) → new_esEs17(zzz5000, zzz4000)
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_esEs6(@3(zzz5000, zzz5001, zzz5002), @3(zzz4000, zzz4001, zzz4002), cgd, cge, cgf) → new_asAs(new_esEs28(zzz5000, zzz4000, cgd), new_asAs(new_esEs27(zzz5001, zzz4001, cge), new_esEs26(zzz5002, zzz4002, cgf)))
new_esEs28(zzz5000, zzz4000, app(ty_Maybe, dcc)) → new_esEs7(zzz5000, zzz4000, dcc)
new_esEs28(zzz5000, zzz4000, ty_Double) → new_esEs9(zzz5000, zzz4000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, ty_Double) → new_ltEs8(zzz500000, zzz4300000)
new_lt20(zzz500001, zzz4300001, ty_Double) → new_lt15(zzz500001, zzz4300001)
new_lt20(zzz500001, zzz4300001, ty_Integer) → new_lt10(zzz500001, zzz4300001)
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_esEs26(zzz5002, zzz4002, ty_@0) → new_esEs10(zzz5002, zzz4002)
new_esEs18(zzz5001, zzz4001, ty_Float) → new_esEs13(zzz5001, zzz4001)
new_compare25(zzz500000, zzz4300000, False, hf, hg) → new_compare15(zzz500000, zzz4300000, new_ltEs13(zzz500000, zzz4300000, hf, hg), hf, hg)
new_esEs23(zzz500000, zzz4300000, app(app(ty_Either, ha), hb)) → new_esEs4(zzz500000, zzz4300000, ha, hb)
new_esEs20(zzz5000, zzz4000, ty_Char) → new_esEs11(zzz5000, zzz4000)
new_lt19(zzz500000, zzz4300000, app(ty_Maybe, cdb)) → new_lt11(zzz500000, zzz4300000, cdb)
new_esEs4(Left(zzz5000), Left(zzz4000), app(ty_Maybe, bgb), bfa) → new_esEs7(zzz5000, zzz4000, bgb)
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_esEs20(zzz5000, zzz4000, ty_Integer) → new_esEs15(zzz5000, zzz4000)
new_primEqNat0(Zero, Succ(zzz40000)) → False
new_primEqNat0(Succ(zzz50000), Zero) → False
new_esEs18(zzz5001, zzz4001, ty_Integer) → new_esEs15(zzz5001, zzz4001)
new_esEs17(zzz500, zzz400) → new_primEqInt(zzz500, zzz400)
new_lt5(zzz500000, zzz4300000, ha, hb) → new_esEs8(new_compare12(zzz500000, zzz4300000, ha, hb), LT)
new_compare25(zzz500000, zzz4300000, True, hf, hg) → EQ
new_esEs20(zzz5000, zzz4000, ty_Bool) → new_esEs14(zzz5000, zzz4000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), app(app(ty_Either, bbf), bbg), bbe) → new_ltEs7(zzz500000, zzz4300000, bbf, bbg)
new_ltEs14(True, True) → True
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs24(zzz500001, zzz4300001, app(app(ty_Either, cdh), cea)) → new_esEs4(zzz500001, zzz4300001, cdh, cea)
new_esEs28(zzz5000, zzz4000, app(app(app(ty_@3, dbh), dca), dcb)) → new_esEs6(zzz5000, zzz4000, dbh, dca, dcb)
new_compare30(zzz500000, zzz4300000, ty_Bool) → new_compare17(zzz500000, zzz4300000)
new_esEs27(zzz5001, zzz4001, app(app(ty_Either, daa), dab)) → new_esEs4(zzz5001, zzz4001, daa, dab)
new_esEs27(zzz5001, zzz4001, app(app(app(ty_@3, daf), dag), dah)) → new_esEs6(zzz5001, zzz4001, daf, dag, dah)
new_compare4(:(zzz500000, zzz500001), [], ce) → GT
new_ltEs18(zzz50000, zzz430000, app(ty_[], ce)) → new_ltEs17(zzz50000, zzz430000, ce)
new_esEs27(zzz5001, zzz4001, app(app(ty_@2, dac), dad)) → new_esEs5(zzz5001, zzz4001, dac, dad)
new_esEs27(zzz5001, zzz4001, ty_Int) → new_esEs17(zzz5001, zzz4001)
new_esEs23(zzz500000, zzz4300000, ty_Int) → new_esEs17(zzz500000, zzz4300000)
new_lt13(zzz500000, zzz4300000, ty_@0) → new_lt4(zzz500000, zzz4300000)
new_compare30(zzz500000, zzz4300000, ty_Char) → new_compare10(zzz500000, zzz4300000)
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_compare4([], :(zzz4300000, zzz4300001), ce) → LT
new_sr0(zzz5000, zzz4000) → new_primMulInt(zzz5000, zzz4000)
new_lt19(zzz500000, zzz4300000, app(ty_[], cdg)) → new_lt18(zzz500000, zzz4300000, cdg)
new_compare15(zzz500000, zzz4300000, False, hf, hg) → GT
new_ltEs18(zzz50000, zzz430000, ty_Float) → new_ltEs12(zzz50000, zzz430000)
new_ltEs18(zzz50000, zzz430000, ty_Integer) → new_ltEs9(zzz50000, zzz430000)
new_ltEs19(zzz500001, zzz4300001, ty_Double) → new_ltEs8(zzz500001, zzz4300001)
new_compare30(zzz500000, zzz4300000, ty_Float) → new_compare16(zzz500000, zzz4300000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), app(ty_[], bcg), bbe) → new_ltEs17(zzz500000, zzz4300000, bcg)
new_esEs11(Char(zzz5000), Char(zzz4000)) → new_primEqNat0(zzz5000, zzz4000)
new_esEs7(Just(zzz5000), Just(zzz4000), app(app(app(ty_@3, de), df), dg)) → new_esEs6(zzz5000, zzz4000, de, df, dg)
new_esEs25(zzz500000, zzz4300000, app(ty_Maybe, cdb)) → new_esEs7(zzz500000, zzz4300000, cdb)
new_compare29(Nothing, Nothing, False, gg) → LT
new_esEs23(zzz500000, zzz4300000, app(ty_Ratio, cbb)) → new_esEs16(zzz500000, zzz4300000, cbb)
new_lt13(zzz500000, zzz4300000, app(app(ty_Either, ha), hb)) → new_lt5(zzz500000, zzz4300000, ha, hb)
new_esEs16(:%(zzz5000, zzz5001), :%(zzz4000, zzz4001), bbc) → new_asAs(new_esEs22(zzz5000, zzz4000, bbc), new_esEs21(zzz5001, zzz4001, bbc))
new_ltEs4(Just(zzz500000), Just(zzz4300000), app(ty_Maybe, bg)) → new_ltEs4(zzz500000, zzz4300000, bg)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Float) → new_ltEs12(zzz500000, zzz4300000)
new_primCompAux0(zzz500000, zzz4300000, zzz220, ce) → new_primCompAux00(zzz220, new_compare30(zzz500000, zzz4300000, ce))
new_esEs19(zzz5000, zzz4000, app(app(ty_@2, ga), gb)) → new_esEs5(zzz5000, zzz4000, ga, gb)
new_esEs19(zzz5000, zzz4000, app(ty_Ratio, gh)) → new_esEs16(zzz5000, zzz4000, gh)
new_esEs10(@0, @0) → True
new_compare29(zzz5000, zzz43000, True, gg) → EQ
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs27(zzz5001, zzz4001, ty_Float) → new_esEs13(zzz5001, zzz4001)
new_lt13(zzz500000, zzz4300000, ty_Integer) → new_lt10(zzz500000, zzz4300000)
new_compare28(zzz5000, zzz43000, gg) → new_compare29(zzz5000, zzz43000, new_esEs7(zzz5000, zzz43000, gg), gg)
new_esEs4(Right(zzz5000), Right(zzz4000), bgd, app(app(ty_@2, bgg), bgh)) → new_esEs5(zzz5000, zzz4000, bgg, bgh)
new_esEs24(zzz500001, zzz4300001, ty_Char) → new_esEs11(zzz500001, zzz4300001)
new_esEs28(zzz5000, zzz4000, ty_@0) → new_esEs10(zzz5000, zzz4000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, app(app(ty_Either, bda), bdb)) → new_ltEs7(zzz500000, zzz4300000, bda, bdb)
new_esEs28(zzz5000, zzz4000, ty_Int) → new_esEs17(zzz5000, zzz4000)
new_compare7(:%(zzz500000, zzz500001), :%(zzz4300000, zzz4300001), ty_Integer) → new_compare9(new_sr(zzz500000, zzz4300001), new_sr(zzz4300000, zzz500001))
new_compare9(Integer(zzz500000), Integer(zzz4300000)) → new_primCmpInt(zzz500000, zzz4300000)
new_compare23(zzz500000, zzz4300000, False) → new_compare112(zzz500000, zzz4300000, new_ltEs10(zzz500000, zzz4300000))
new_asAs(False, zzz207) → False
new_esEs4(Left(zzz5000), Left(zzz4000), ty_@0, bfa) → new_esEs10(zzz5000, zzz4000)
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_esEs26(zzz5002, zzz4002, ty_Double) → new_esEs9(zzz5002, zzz4002)
new_ltEs10(LT, GT) → True
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_ltEs4(Just(zzz500000), Just(zzz4300000), app(ty_Ratio, bh)) → new_ltEs15(zzz500000, zzz4300000, bh)
new_esEs23(zzz500000, zzz4300000, app(app(app(ty_@3, hc), hd), he)) → new_esEs6(zzz500000, zzz4300000, hc, hd, he)
new_lt8(zzz500000, zzz4300000, hc, hd, he) → new_esEs8(new_compare13(zzz500000, zzz4300000, hc, hd, he), LT)
new_lt11(zzz5000, zzz43000, gg) → new_esEs8(new_compare28(zzz5000, zzz43000, gg), LT)
new_esEs26(zzz5002, zzz4002, app(ty_[], chc)) → new_esEs12(zzz5002, zzz4002, chc)
new_compare4(:(zzz500000, zzz500001), :(zzz4300000, zzz4300001), ce) → new_primCompAux0(zzz500000, zzz4300000, new_compare4(zzz500001, zzz4300001, ce), ce)
new_compare16(Float(zzz500000, zzz500001), Float(zzz4300000, zzz4300001)) → new_compare8(new_sr0(zzz500000, zzz4300000), new_sr0(zzz500001, zzz4300001))
new_esEs26(zzz5002, zzz4002, app(ty_Maybe, chg)) → new_esEs7(zzz5002, zzz4002, chg)
new_esEs28(zzz5000, zzz4000, ty_Bool) → new_esEs14(zzz5000, zzz4000)
new_compare110(zzz500000, zzz4300000, True, hc, hd, he) → LT
new_lt19(zzz500000, zzz4300000, app(app(ty_Either, ccf), ccg)) → new_lt5(zzz500000, zzz4300000, ccf, ccg)
new_ltEs18(zzz50000, zzz430000, ty_Bool) → new_ltEs14(zzz50000, zzz430000)
new_esEs28(zzz5000, zzz4000, ty_Integer) → new_esEs15(zzz5000, zzz4000)
new_esEs18(zzz5001, zzz4001, ty_Ordering) → new_esEs8(zzz5001, zzz4001)
new_esEs19(zzz5000, zzz4000, ty_Double) → new_esEs9(zzz5000, zzz4000)
new_lt20(zzz500001, zzz4300001, app(app(ty_@2, ceb), cec)) → new_lt16(zzz500001, zzz4300001, ceb, cec)
new_esEs5(@2(zzz5000, zzz5001), @2(zzz4000, zzz4001), eb, ec) → new_asAs(new_esEs19(zzz5000, zzz4000, eb), new_esEs18(zzz5001, zzz4001, ec))
new_compare26(zzz500000, zzz4300000, False) → new_compare19(zzz500000, zzz4300000, new_ltEs14(zzz500000, zzz4300000))
new_esEs28(zzz5000, zzz4000, app(app(ty_Either, dbc), dbd)) → new_esEs4(zzz5000, zzz4000, dbc, dbd)
new_esEs4(Right(zzz5000), Right(zzz4000), bgd, app(ty_Maybe, bhe)) → new_esEs7(zzz5000, zzz4000, bhe)
new_esEs7(Just(zzz5000), Just(zzz4000), ty_@0) → new_esEs10(zzz5000, zzz4000)
new_ltEs18(zzz50000, zzz430000, ty_Char) → new_ltEs5(zzz50000, zzz430000)
new_esEs28(zzz5000, zzz4000, ty_Float) → new_esEs13(zzz5000, zzz4000)
new_lt13(zzz500000, zzz4300000, ty_Ordering) → new_lt9(zzz500000, zzz4300000)
new_esEs25(zzz500000, zzz4300000, app(app(app(ty_@3, cdd), cde), cdf)) → new_esEs6(zzz500000, zzz4300000, cdd, cde, cdf)
new_ltEs10(EQ, EQ) → True
new_ltEs18(zzz50000, zzz430000, app(app(ty_@2, bec), bed)) → new_ltEs13(zzz50000, zzz430000, bec, bed)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Int, bfa) → new_esEs17(zzz5000, zzz4000)
new_esEs23(zzz500000, zzz4300000, ty_Integer) → new_esEs15(zzz500000, zzz4300000)
new_ltEs10(LT, LT) → True
new_esEs14(True, True) → True
new_compare111(zzz200, zzz201, False, bbd) → GT
new_esEs27(zzz5001, zzz4001, ty_Bool) → new_esEs14(zzz5001, zzz4001)
new_esEs7(Just(zzz5000), Just(zzz4000), app(app(ty_Either, cg), da)) → new_esEs4(zzz5000, zzz4000, cg, da)
new_compare10(Char(zzz500000), Char(zzz4300000)) → new_primCmpNat0(zzz500000, zzz4300000)
new_esEs30(Just(zzz4300), h) → False
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Float, bfa) → new_esEs13(zzz5000, zzz4000)
new_lt13(zzz500000, zzz4300000, app(app(ty_@2, hf), hg)) → new_lt16(zzz500000, zzz4300000, hf, hg)
new_ltEs7(Left(zzz500000), Left(zzz4300000), app(app(ty_@2, bbh), bca), bbe) → new_ltEs13(zzz500000, zzz4300000, bbh, bca)
new_esEs7(Just(zzz5000), Just(zzz4000), app(ty_Ratio, ea)) → new_esEs16(zzz5000, zzz4000, ea)
new_lt13(zzz500000, zzz4300000, app(ty_Maybe, cba)) → new_lt11(zzz500000, zzz4300000, cba)
new_ltEs20(zzz500002, zzz4300002, app(app(ty_Either, cfb), cfc)) → new_ltEs7(zzz500002, zzz4300002, cfb, cfc)
new_esEs18(zzz5001, zzz4001, ty_@0) → new_esEs10(zzz5001, zzz4001)
new_ltEs16(@3(zzz500000, zzz500001, zzz500002), @3(zzz4300000, zzz4300001, zzz4300002), bef, beg, beh) → new_pePe(new_lt19(zzz500000, zzz4300000, bef), new_asAs(new_esEs25(zzz500000, zzz4300000, bef), new_pePe(new_lt20(zzz500001, zzz4300001, beg), new_asAs(new_esEs24(zzz500001, zzz4300001, beg), new_ltEs20(zzz500002, zzz4300002, beh)))))
new_esEs4(Right(zzz5000), Right(zzz4000), bgd, ty_Double) → new_esEs9(zzz5000, zzz4000)
new_ltEs14(True, False) → False
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_esEs20(zzz5000, zzz4000, ty_Int) → new_esEs17(zzz5000, zzz4000)
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_esEs25(zzz500000, zzz4300000, app(app(ty_@2, cch), cda)) → new_esEs5(zzz500000, zzz4300000, cch, cda)
new_ltEs20(zzz500002, zzz4300002, ty_Double) → new_ltEs8(zzz500002, zzz4300002)
new_ltEs7(Left(zzz500000), Left(zzz4300000), app(ty_Ratio, bcc), bbe) → new_ltEs15(zzz500000, zzz4300000, bcc)
new_gt1(zzz430, h) → new_esEs8(new_compare32(zzz430, h), GT)
new_ltEs19(zzz500001, zzz4300001, app(app(app(ty_@3, ccb), ccc), ccd)) → new_ltEs16(zzz500001, zzz4300001, ccb, ccc, ccd)
new_ltEs20(zzz500002, zzz4300002, app(app(app(ty_@3, cfh), cga), cgb)) → new_ltEs16(zzz500002, zzz4300002, cfh, cga, cgb)
new_compare112(zzz500000, zzz4300000, False) → GT
new_ltEs10(EQ, LT) → False
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Float) → new_esEs13(zzz5000, zzz4000)
new_esEs14(False, False) → True
new_esEs7(Just(zzz5000), Just(zzz4000), app(app(ty_@2, db), dc)) → new_esEs5(zzz5000, zzz4000, db, dc)
new_lt20(zzz500001, zzz4300001, ty_Char) → new_lt12(zzz500001, zzz4300001)
new_lt9(zzz500000, zzz4300000) → new_esEs8(new_compare6(zzz500000, zzz4300000), LT)
new_ltEs10(GT, LT) → False
new_esEs18(zzz5001, zzz4001, ty_Bool) → new_esEs14(zzz5001, zzz4001)
new_esEs22(zzz5000, zzz4000, ty_Integer) → new_esEs15(zzz5000, zzz4000)
new_primPlusNat1(Zero, Zero) → Zero
new_compare30(zzz500000, zzz4300000, app(app(app(ty_@3, cae), caf), cag)) → new_compare13(zzz500000, zzz4300000, cae, caf, cag)
new_esEs19(zzz5000, zzz4000, ty_Integer) → new_esEs15(zzz5000, zzz4000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(ty_[], bff), bfa) → new_esEs12(zzz5000, zzz4000, bff)
new_esEs26(zzz5002, zzz4002, app(app(ty_Either, cgg), cgh)) → new_esEs4(zzz5002, zzz4002, cgg, cgh)
new_asAs(True, zzz207) → zzz207
new_esEs28(zzz5000, zzz4000, app(ty_[], dbg)) → new_esEs12(zzz5000, zzz4000, dbg)
new_esEs27(zzz5001, zzz4001, app(ty_[], dae)) → new_esEs12(zzz5001, zzz4001, dae)
new_esEs19(zzz5000, zzz4000, app(app(ty_Either, fg), fh)) → new_esEs4(zzz5000, zzz4000, fg, fh)
new_ltEs4(Just(zzz500000), Nothing, bb) → False
new_esEs20(zzz5000, zzz4000, ty_Double) → new_esEs9(zzz5000, zzz4000)
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_ltEs4(Just(zzz500000), Just(zzz4300000), app(ty_[], cd)) → new_ltEs17(zzz500000, zzz4300000, cd)
new_esEs4(Right(zzz5000), Left(zzz4000), bgd, bfa) → False
new_esEs4(Left(zzz5000), Right(zzz4000), bgd, bfa) → False
new_ltEs19(zzz500001, zzz4300001, ty_Float) → new_ltEs12(zzz500001, zzz4300001)
new_ltEs20(zzz500002, zzz4300002, app(ty_Maybe, cff)) → new_ltEs4(zzz500002, zzz4300002, cff)
new_esEs4(Left(zzz5000), Left(zzz4000), app(app(app(ty_@3, bfg), bfh), bga), bfa) → new_esEs6(zzz5000, zzz4000, bfg, bfh, bga)
new_ltEs19(zzz500001, zzz4300001, ty_Char) → new_ltEs5(zzz500001, zzz4300001)
new_fsEs(zzz210) → new_not(new_esEs8(zzz210, GT))
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Double, bbe) → new_ltEs8(zzz500000, zzz4300000)
new_esEs19(zzz5000, zzz4000, ty_@0) → new_esEs10(zzz5000, zzz4000)
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Bool) → new_esEs14(zzz5000, zzz4000)
new_esEs24(zzz500001, zzz4300001, ty_Float) → new_esEs13(zzz500001, zzz4300001)
new_ltEs11(zzz50000, zzz430000) → new_fsEs(new_compare11(zzz50000, zzz430000))
new_lt20(zzz500001, zzz4300001, ty_Int) → new_lt14(zzz500001, zzz4300001)
new_esEs4(Right(zzz5000), Right(zzz4000), bgd, ty_Float) → new_esEs13(zzz5000, zzz4000)
new_esEs19(zzz5000, zzz4000, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_ltEs20(zzz500002, zzz4300002, app(app(ty_@2, cfd), cfe)) → new_ltEs13(zzz500002, zzz4300002, cfd, cfe)
new_esEs30(Nothing, h) → True
new_esEs27(zzz5001, zzz4001, ty_Char) → new_esEs11(zzz5001, zzz4001)
new_ltEs20(zzz500002, zzz4300002, ty_Int) → new_ltEs6(zzz500002, zzz4300002)
new_compare110(zzz500000, zzz4300000, False, hc, hd, he) → GT
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Char) → new_ltEs5(zzz500000, zzz4300000)
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Char) → new_esEs11(zzz5000, zzz4000)
new_primCompAux00(zzz225, GT) → GT
new_ltEs20(zzz500002, zzz4300002, ty_Integer) → new_ltEs9(zzz500002, zzz4300002)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, app(ty_Maybe, bde)) → new_ltEs4(zzz500000, zzz4300000, bde)
new_lt19(zzz500000, zzz4300000, ty_Int) → new_lt14(zzz500000, zzz4300000)
new_ltEs4(Just(zzz500000), Just(zzz4300000), app(app(app(ty_@3, ca), cb), cc)) → new_ltEs16(zzz500000, zzz4300000, ca, cb, cc)
new_ltEs18(zzz50000, zzz430000, ty_Ordering) → new_ltEs10(zzz50000, zzz430000)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Integer) → new_ltEs9(zzz500000, zzz4300000)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_compare30(zzz500000, zzz4300000, ty_Ordering) → new_compare6(zzz500000, zzz4300000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, ty_Float) → new_ltEs12(zzz500000, zzz4300000)
new_esEs27(zzz5001, zzz4001, ty_Integer) → new_esEs15(zzz5001, zzz4001)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_ltEs7(Right(zzz500000), Right(zzz4300000), bch, ty_Int) → new_ltEs6(zzz500000, zzz4300000)
new_not(True) → False

The set Q consists of the following terms:

new_ltEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_compare23(x0, x1, True)
new_lt11(x0, x1, x2)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_lt14(x0, x1)
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs18(x0, x1, app(app(ty_@2, x2), x3))
new_asAs(True, x0)
new_compare29(Nothing, Nothing, False, x0)
new_compare19(x0, x1, True)
new_esEs26(x0, x1, ty_@0)
new_ltEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, app(ty_[], x2))
new_ltEs18(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_Ordering)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_lt13(x0, x1, app(ty_Ratio, x2))
new_esEs18(x0, x1, ty_Int)
new_primPlusNat1(Zero, Succ(x0))
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare29(Nothing, Just(x0), False, x1)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_compare30(x0, x1, ty_@0)
new_lt20(x0, x1, ty_Ordering)
new_esEs9(Double(x0, x1), Double(x2, x3))
new_ltEs7(Right(x0), Right(x1), x2, ty_@0)
new_primCompAux0(x0, x1, x2, x3)
new_primMulNat0(Succ(x0), Zero)
new_lt19(x0, x1, ty_Double)
new_primMulInt(Neg(x0), Neg(x1))
new_lt19(x0, x1, ty_Integer)
new_esEs30(Just(x0), x1)
new_esEs24(x0, x1, ty_@0)
new_primPlusNat1(Succ(x0), Zero)
new_esEs21(x0, x1, ty_Int)
new_compare4(:(x0, x1), :(x2, x3), x4)
new_esEs4(Right(x0), Right(x1), x2, ty_Integer)
new_esEs4(Left(x0), Left(x1), ty_Double, x2)
new_ltEs10(LT, LT)
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs23(x0, x1, ty_Bool)
new_primPlusNat1(Succ(x0), Succ(x1))
new_compare30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, ty_Int)
new_esEs18(x0, x1, ty_Char)
new_esEs24(x0, x1, ty_Char)
new_ltEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(True, False)
new_ltEs14(False, True)
new_esEs25(x0, x1, ty_Double)
new_pePe(False, x0)
new_esEs19(x0, x1, ty_Char)
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Char)
new_compare27(x0, x1, True, x2, x3)
new_esEs7(Just(x0), Just(x1), ty_Double)
new_esEs8(GT, GT)
new_esEs23(x0, x1, ty_@0)
new_compare4([], :(x0, x1), x2)
new_lt9(x0, x1)
new_lt19(x0, x1, ty_Ordering)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs11(Char(x0), Char(x1))
new_esEs7(Nothing, Just(x0), x1)
new_esEs4(Right(x0), Right(x1), x2, ty_Bool)
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs8(LT, LT)
new_sr0(x0, x1)
new_compare6(x0, x1)
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_compare30(x0, x1, ty_Double)
new_esEs7(Just(x0), Just(x1), ty_Char)
new_esEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs18(x0, x1, app(ty_[], x2))
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare19(x0, x1, False)
new_ltEs4(Nothing, Nothing, x0)
new_compare110(x0, x1, False, x2, x3, x4)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs26(x0, x1, ty_Double)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs4(Right(x0), Right(x1), x2, ty_Float)
new_lt16(x0, x1, x2, x3)
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_compare111(x0, x1, False, x2)
new_compare4([], [], x0)
new_ltEs7(Left(x0), Left(x1), ty_Char, x2)
new_ltEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs17(x0, x1)
new_ltEs19(x0, x1, ty_Char)
new_esEs4(Left(x0), Left(x1), ty_Float, x2)
new_esEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs14(True, True)
new_compare26(x0, x1, True)
new_lt20(x0, x1, ty_Char)
new_compare112(x0, x1, False)
new_esEs18(x0, x1, ty_Bool)
new_esEs20(x0, x1, ty_Float)
new_primEqNat0(Zero, Zero)
new_ltEs4(Just(x0), Just(x1), ty_Double)
new_compare30(x0, x1, ty_Char)
new_lt20(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_ltEs7(Right(x0), Right(x1), x2, ty_Char)
new_esEs20(x0, x1, ty_Int)
new_lt13(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Double)
new_lt19(x0, x1, ty_Bool)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, ty_@0)
new_esEs12([], :(x0, x1), x2)
new_esEs28(x0, x1, ty_Integer)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_compare17(x0, x1)
new_ltEs17(x0, x1, x2)
new_primPlusNat0(Zero, x0)
new_ltEs20(x0, x1, ty_Int)
new_compare13(x0, x1, x2, x3, x4)
new_primMulNat0(Zero, Zero)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpNat0(Succ(x0), Zero)
new_compare16(Float(x0, x1), Float(x2, x3))
new_ltEs20(x0, x1, ty_Integer)
new_compare30(x0, x1, ty_Ordering)
new_ltEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs26(x0, x1, ty_Integer)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs10(EQ, LT)
new_ltEs10(LT, EQ)
new_lt4(x0, x1)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_ltEs7(Left(x0), Left(x1), ty_@0, x2)
new_lt13(x0, x1, app(app(ty_@2, x2), x3))
new_esEs19(x0, x1, ty_Bool)
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs28(x0, x1, ty_@0)
new_primMulNat0(Succ(x0), Succ(x1))
new_lt7(x0, x1)
new_esEs23(x0, x1, ty_Float)
new_ltEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Int)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs19(x0, x1, ty_Double)
new_compare113(x0, x1, False, x2, x3)
new_ltEs18(x0, x1, ty_@0)
new_compare15(x0, x1, True, x2, x3)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs4(Right(x0), Right(x1), x2, ty_@0)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Char)
new_esEs24(x0, x1, ty_Int)
new_compare9(Integer(x0), Integer(x1))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, ty_Ordering)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_ltEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_compare4(:(x0, x1), [], x2)
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_esEs24(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_Char)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_compare25(x0, x1, False, x2, x3)
new_esEs20(x0, x1, ty_Ordering)
new_esEs30(Nothing, x0)
new_esEs12(:(x0, x1), :(x2, x3), x4)
new_compare30(x0, x1, app(ty_[], x2))
new_fsEs(x0)
new_lt8(x0, x1, x2, x3, x4)
new_ltEs11(x0, x1)
new_esEs23(x0, x1, ty_Double)
new_lt13(x0, x1, ty_@0)
new_gt1(x0, x1)
new_ltEs7(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Just(x0), Just(x1), ty_Int)
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_compare26(x0, x1, False)
new_ltEs18(x0, x1, ty_Double)
new_ltEs7(Right(x0), Left(x1), x2, x3)
new_ltEs7(Left(x0), Right(x1), x2, x3)
new_ltEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs25(x0, x1, ty_Bool)
new_lt17(x0, x1, x2)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primPlusNat1(Zero, Zero)
new_esEs28(x0, x1, ty_Float)
new_ltEs7(Right(x0), Right(x1), x2, ty_Int)
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_lt12(x0, x1)
new_compare7(:%(x0, x1), :%(x2, x3), ty_Int)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_ltEs4(Just(x0), Just(x1), ty_Int)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_compare11(@0, @0)
new_primMulNat0(Zero, Succ(x0))
new_esEs26(x0, x1, ty_Bool)
new_asAs(False, x0)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs12(:(x0, x1), [], x2)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs4(Just(x0), Just(x1), ty_Bool)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1, app(ty_[], x2))
new_ltEs8(x0, x1)
new_ltEs18(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Float)
new_esEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_Double)
new_ltEs19(x0, x1, ty_Ordering)
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(Just(x0), Just(x1), ty_Ordering)
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs18(x0, x1, ty_Double)
new_ltEs10(GT, LT)
new_ltEs10(LT, GT)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs28(x0, x1, ty_Double)
new_esEs10(@0, @0)
new_compare14(Double(x0, x1), Double(x2, x3))
new_compare24(x0, x1, True, x2, x3, x4)
new_compare30(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_Integer)
new_compare30(x0, x1, app(ty_Maybe, x2))
new_ltEs18(x0, x1, ty_Float)
new_ltEs15(x0, x1, x2)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_compare8(x0, x1)
new_lt13(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs20(x0, x1, ty_Char)
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs7(Right(x0), Right(x1), x2, ty_Integer)
new_compare30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Integer)
new_pePe(True, x0)
new_compare29(Just(x0), Just(x1), False, x2)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_Float)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_esEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCompAux00(x0, EQ)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1, ty_Float)
new_primEqNat0(Succ(x0), Zero)
new_ltEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_compare30(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_Int)
new_compare27(x0, x1, False, x2, x3)
new_esEs18(x0, x1, ty_Ordering)
new_esEs25(x0, x1, ty_Int)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs18(x0, x1, app(ty_Ratio, x2))
new_esEs7(Nothing, Nothing, x0)
new_ltEs4(Just(x0), Just(x1), ty_@0)
new_esEs19(x0, x1, app(ty_[], x2))
new_compare23(x0, x1, False)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_ltEs4(Just(x0), Nothing, x1)
new_esEs8(EQ, EQ)
new_compare112(x0, x1, True)
new_esEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs19(x0, x1, ty_Double)
new_esEs13(Float(x0, x1), Float(x2, x3))
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs4(Right(x0), Right(x1), x2, ty_Double)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_lt13(x0, x1, ty_Char)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, ty_Char)
new_esEs15(Integer(x0), Integer(x1))
new_ltEs12(x0, x1)
new_lt20(x0, x1, ty_@0)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_@0)
new_esEs14(True, False)
new_esEs14(False, True)
new_ltEs4(Just(x0), Just(x1), ty_Float)
new_ltEs7(Right(x0), Right(x1), x2, ty_Float)
new_esEs18(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs6(x0, x1)
new_esEs22(x0, x1, ty_Int)
new_esEs20(x0, x1, ty_Double)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare110(x0, x1, True, x2, x3, x4)
new_ltEs9(x0, x1)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs19(x0, x1, ty_@0)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Ordering)
new_esEs27(x0, x1, ty_Integer)
new_esEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs16(:%(x0, x1), :%(x2, x3), x4)
new_lt20(x0, x1, ty_Float)
new_compare25(x0, x1, True, x2, x3)
new_compare30(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Integer)
new_primCmpNat0(Succ(x0), Succ(x1))
new_lt19(x0, x1, ty_Char)
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_esEs20(x0, x1, ty_Integer)
new_esEs28(x0, x1, ty_Ordering)
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_esEs21(x0, x1, ty_Integer)
new_compare28(x0, x1, x2)
new_ltEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_ltEs7(Right(x0), Right(x1), x2, ty_Double)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Bool)
new_primPlusNat0(Succ(x0), x1)
new_esEs20(x0, x1, ty_@0)
new_ltEs13(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs18(x0, x1, ty_Integer)
new_esEs4(Left(x0), Left(x1), ty_Int, x2)
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Just(x0), Just(x1), ty_Float)
new_compare18(x0, x1, x2, x3)
new_esEs19(x0, x1, ty_Float)
new_ltEs20(x0, x1, ty_Bool)
new_primCmpNat0(Zero, Zero)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs4(Left(x0), Left(x1), ty_Integer, x2)
new_esEs19(x0, x1, ty_Ordering)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_lt13(x0, x1, app(ty_Maybe, x2))
new_lt13(x0, x1, ty_Bool)
new_lt18(x0, x1, x2)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, ty_Float)
new_ltEs7(Left(x0), Left(x1), ty_Double, x2)
new_ltEs16(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs12([], [], x0)
new_lt10(x0, x1)
new_compare7(:%(x0, x1), :%(x2, x3), ty_Integer)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_compare113(x0, x1, True, x2, x3)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs20(x0, x1, app(ty_[], x2))
new_ltEs7(Left(x0), Left(x1), ty_Bool, x2)
new_esEs4(Left(x0), Left(x1), ty_Char, x2)
new_esEs25(x0, x1, ty_Ordering)
new_esEs27(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_Float)
new_ltEs7(Left(x0), Left(x1), ty_Float, x2)
new_lt5(x0, x1, x2, x3)
new_compare29(Just(x0), Nothing, False, x1)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs10(GT, GT)
new_esEs4(Right(x0), Right(x1), x2, ty_Int)
new_ltEs14(True, True)
new_ltEs14(False, False)
new_esEs24(x0, x1, ty_Ordering)
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_lt19(x0, x1, ty_@0)
new_esEs18(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Char)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs7(Left(x0), Left(x1), ty_Int, x2)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_not(True)
new_esEs19(x0, x1, ty_Int)
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Just(x0), Just(x1), ty_@0)
new_compare30(x0, x1, ty_Integer)
new_ltEs5(x0, x1)
new_ltEs20(x0, x1, ty_Double)
new_esEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(Just(x0), Just(x1), ty_Integer)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_not(False)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_Integer)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_ltEs4(Just(x0), Just(x1), app(ty_[], x2))
new_primCompAux00(x0, LT)
new_esEs4(Left(x0), Left(x1), ty_@0, x2)
new_lt6(x0, x1)
new_ltEs10(EQ, GT)
new_ltEs10(GT, EQ)
new_esEs4(Right(x0), Left(x1), x2, x3)
new_esEs4(Left(x0), Right(x1), x2, x3)
new_ltEs19(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_Int)
new_esEs25(x0, x1, ty_Float)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_ltEs18(x0, x1, ty_Char)
new_esEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs19(x0, x1, ty_Integer)
new_esEs18(x0, x1, app(ty_[], x2))
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_sr(Integer(x0), Integer(x1))
new_esEs27(x0, x1, ty_Char)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs20(x0, x1, ty_Bool)
new_ltEs4(Just(x0), Just(x1), ty_Char)
new_ltEs4(Nothing, Just(x0), x1)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs18(x0, x1, ty_@0)
new_esEs24(x0, x1, app(ty_[], x2))
new_ltEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_lt13(x0, x1, ty_Double)
new_esEs18(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_lt13(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, ty_Bool)
new_lt13(x0, x1, ty_Ordering)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare12(x0, x1, x2, x3)
new_compare30(x0, x1, app(app(ty_Either, x2), x3))
new_compare15(x0, x1, False, x2, x3)
new_ltEs18(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Ordering)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_compare30(x0, x1, ty_Float)
new_compare111(x0, x1, True, x2)
new_lt13(x0, x1, ty_Integer)
new_esEs14(False, False)
new_primEqInt(Pos(Zero), Pos(Zero))
new_compare10(Char(x0), Char(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs24(x0, x1, ty_Integer)
new_esEs4(Right(x0), Right(x1), x2, ty_Char)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Double)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_ltEs20(x0, x1, ty_Float)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_lt13(x0, x1, ty_Int)
new_compare29(x0, x1, True, x2)
new_lt13(x0, x1, ty_Float)
new_lt20(x0, x1, ty_Integer)
new_primCmpNat0(Zero, Succ(x0))
new_ltEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs23(x0, x1, ty_Int)
new_primCompAux00(x0, GT)
new_ltEs20(x0, x1, ty_@0)
new_lt15(x0, x1)
new_ltEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primEqNat0(Zero, Succ(x0))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs7(Left(x0), Left(x1), ty_Integer, x2)
new_esEs27(x0, x1, ty_Bool)
new_ltEs19(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_@0)
new_compare24(x0, x1, False, x2, x3, x4)
new_compare32(x0, x1)
new_esEs7(Just(x0), Nothing, x1)
new_esEs18(x0, x1, ty_Integer)
new_ltEs10(EQ, EQ)

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_intersectFM_C(zzz3, Branch(Just(zzz400), zzz41, zzz42, zzz43, zzz44), Branch(Nothing, zzz51, zzz52, zzz53, zzz54), be, bf, bg, bh) → new_intersectFM_C2IntersectFM_C12(zzz400, zzz41, zzz42, zzz43, zzz44, zzz3, zzz51, zzz52, zzz53, zzz54, Just(zzz400), zzz41, zzz42, zzz43, zzz44, new_esEs8(new_compare29(Nothing, Just(zzz400), False, be), LT), be, bf, bg, bh, bh)
new_intersectFM_C2IntersectFM_C12(zzz245, zzz246, zzz247, zzz248, zzz249, zzz250, zzz251, zzz252, zzz253, zzz254, zzz255, zzz256, zzz257, EmptyFM, zzz259, True, ca, cb, cc, cd, ce) → new_intersectFM_C(zzz250, new_intersectFM_C2Gts0(zzz245, zzz246, zzz247, zzz248, zzz249, ca, cd), zzz254, ca, cb, cc, cd)
new_intersectFM_C2IntersectFM_C17(zzz261, zzz262, zzz263, zzz264, zzz265, zzz266, zzz267, zzz268, zzz269, zzz270, zzz271, zzz272, zzz273, zzz274, zzz275, False, cf, cg, da, db, dc) → new_intersectFM_C(zzz266, new_intersectFM_C2Gts1(zzz261, zzz262, zzz263, zzz264, zzz265, cf, db), zzz270, cf, cg, da, db)
new_intersectFM_C2IntersectFM_C16(zzz245, zzz246, zzz247, zzz248, zzz249, zzz250, zzz251, zzz252, zzz253, zzz254, EmptyFM, ca, cb, cc, cd, ce) → new_intersectFM_C(zzz250, new_intersectFM_C2Gts0(zzz245, zzz246, zzz247, zzz248, zzz249, ca, cd), zzz254, ca, cb, cc, cd)
new_intersectFM_C2IntersectFM_C13(zzz261, zzz262, zzz263, zzz264, zzz265, zzz266, zzz267, zzz268, zzz269, zzz270, zzz271, zzz272, zzz273, Branch(zzz2740, zzz2741, zzz2742, zzz2743, zzz2744), zzz275, True, cf, cg, da, db, dc) → new_intersectFM_C2IntersectFM_C13(zzz261, zzz262, zzz263, zzz264, zzz265, zzz266, zzz267, zzz268, zzz269, zzz270, zzz2740, zzz2741, zzz2742, zzz2743, zzz2744, new_lt11(Just(zzz265), zzz2740, cf), cf, cg, da, db, dc)
new_intersectFM_C2IntersectFM_C13(zzz261, zzz262, zzz263, zzz264, zzz265, zzz266, zzz267, zzz268, zzz269, zzz270, zzz271, zzz272, zzz273, zzz274, zzz275, False, cf, cg, da, db, dc) → new_intersectFM_C2IntersectFM_C17(zzz261, zzz262, zzz263, zzz264, zzz265, zzz266, zzz267, zzz268, zzz269, zzz270, zzz271, zzz272, zzz273, zzz274, zzz275, new_gt0(zzz265, zzz271, cf), cf, cg, da, db, dc)
new_intersectFM_C2IntersectFM_C19(zzz279, zzz280, zzz281, zzz282, zzz283, zzz284, zzz285, zzz286, zzz287, zzz288, zzz289, zzz290, zzz291, zzz292, zzz293, zzz294, True, dd, de, df, dg, dh) → new_intersectFM_C2IntersectFM_C110(zzz279, zzz280, zzz281, zzz282, zzz283, zzz284, zzz285, zzz286, zzz287, zzz288, zzz289, zzz294, dd, de, df, dg, dh)
new_intersectFM_C2IntersectFM_C13(zzz261, zzz262, zzz263, zzz264, zzz265, zzz266, zzz267, zzz268, zzz269, zzz270, zzz271, zzz272, zzz273, EmptyFM, zzz275, True, cf, cg, da, db, dc) → new_intersectFM_C(zzz266, new_intersectFM_C2Lts1(zzz261, zzz262, zzz263, zzz264, zzz265, cf, db), zzz269, cf, cg, da, db)
new_intersectFM_C2IntersectFM_C16(zzz245, zzz246, zzz247, zzz248, zzz249, zzz250, zzz251, zzz252, zzz253, zzz254, EmptyFM, ca, cb, cc, cd, ce) → new_intersectFM_C(zzz250, new_intersectFM_C2Lts0(zzz245, zzz246, zzz247, zzz248, zzz249, ca, cd), zzz253, ca, cb, cc, cd)
new_intersectFM_C2IntersectFM_C12(zzz245, zzz246, zzz247, zzz248, zzz249, zzz250, zzz251, zzz252, zzz253, zzz254, zzz255, zzz256, zzz257, Branch(zzz2580, zzz2581, zzz2582, zzz2583, zzz2584), zzz259, True, ca, cb, cc, cd, ce) → new_intersectFM_C2IntersectFM_C12(zzz245, zzz246, zzz247, zzz248, zzz249, zzz250, zzz251, zzz252, zzz253, zzz254, zzz2580, zzz2581, zzz2582, zzz2583, zzz2584, new_lt11(Nothing, zzz2580, ca), ca, cb, cc, cd, ce)
new_intersectFM_C2IntersectFM_C110(zzz279, zzz280, zzz281, zzz282, zzz283, zzz284, zzz285, zzz286, zzz287, zzz288, zzz289, EmptyFM, dd, de, df, dg, dh) → new_intersectFM_C(zzz285, new_intersectFM_C2Lts2(zzz279, zzz280, zzz281, zzz282, zzz283, zzz284, dd, dg), zzz288, dd, de, df, dg)
new_intersectFM_C2IntersectFM_C110(zzz279, zzz280, zzz281, zzz282, zzz283, zzz284, zzz285, zzz286, zzz287, zzz288, zzz289, Branch(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934), dd, de, df, dg, dh) → new_intersectFM_C2IntersectFM_C14(zzz279, zzz280, zzz281, zzz282, zzz283, zzz284, zzz285, zzz286, zzz287, zzz288, zzz289, zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, new_lt11(Just(zzz284), zzz2930, dd), dd, de, df, dg, dh)
new_intersectFM_C2IntersectFM_C18(zzz261, zzz262, zzz263, zzz264, zzz265, zzz266, zzz267, zzz268, zzz269, zzz270, EmptyFM, cf, cg, da, db, dc) → new_intersectFM_C(zzz266, new_intersectFM_C2Gts1(zzz261, zzz262, zzz263, zzz264, zzz265, cf, db), zzz270, cf, cg, da, db)
new_intersectFM_C(zzz3, Branch(Nothing, zzz41, zzz42, zzz43, zzz44), Branch(Just(zzz500), zzz51, zzz52, zzz53, zzz54), be, bf, bg, bh) → new_intersectFM_C2IntersectFM_C13(zzz41, zzz42, zzz43, zzz44, zzz500, zzz3, zzz51, zzz52, zzz53, zzz54, Nothing, zzz41, zzz42, zzz43, zzz44, new_esEs8(new_compare29(Just(zzz500), Nothing, False, be), LT), be, bf, bg, bh, bh)
new_intersectFM_C2IntersectFM_C1(zzz381, zzz382, zzz383, zzz384, zzz385, zzz386, zzz387, zzz388, zzz389, zzz390, zzz391, zzz392, EmptyFM, zzz394, True, h, ba, bb, bc, bd) → new_intersectFM_C(zzz385, new_intersectFM_C2Gts(zzz381, zzz382, zzz383, zzz384, h, bc), zzz389, h, ba, bb, bc)
new_intersectFM_C2IntersectFM_C15(zzz245, zzz246, zzz247, zzz248, zzz249, zzz250, zzz251, zzz252, zzz253, zzz254, zzz255, zzz256, zzz257, zzz258, zzz259, False, ca, cb, cc, cd, ce) → new_intersectFM_C(zzz250, new_intersectFM_C2Lts0(zzz245, zzz246, zzz247, zzz248, zzz249, ca, cd), zzz253, ca, cb, cc, cd)
new_intersectFM_C2IntersectFM_C14(zzz279, zzz280, zzz281, zzz282, zzz283, zzz284, zzz285, zzz286, zzz287, zzz288, zzz289, zzz290, zzz291, zzz292, zzz293, zzz294, False, dd, de, df, dg, dh) → new_intersectFM_C2IntersectFM_C19(zzz279, zzz280, zzz281, zzz282, zzz283, zzz284, zzz285, zzz286, zzz287, zzz288, zzz289, zzz290, zzz291, zzz292, zzz293, zzz294, new_gt0(zzz284, zzz290, dd), dd, de, df, dg, dh)
new_intersectFM_C2IntersectFM_C10(zzz381, zzz382, zzz383, zzz384, zzz385, zzz386, zzz387, zzz388, zzz389, zzz390, zzz391, zzz392, zzz393, zzz394, False, h, ba, bb, bc, bd) → new_intersectFM_C(zzz385, new_intersectFM_C2Gts(zzz381, zzz382, zzz383, zzz384, h, bc), zzz389, h, ba, bb, bc)
new_intersectFM_C2IntersectFM_C1(zzz381, zzz382, zzz383, zzz384, zzz385, zzz386, zzz387, zzz388, zzz389, zzz390, zzz391, zzz392, EmptyFM, zzz394, True, h, ba, bb, bc, bd) → new_intersectFM_C(zzz385, new_intersectFM_C2Lts(zzz381, zzz382, zzz383, zzz384, h, bc), zzz388, h, ba, bb, bc)
new_intersectFM_C2IntersectFM_C11(zzz381, zzz382, zzz383, zzz384, zzz385, zzz386, zzz387, zzz388, zzz389, EmptyFM, h, ba, bb, bc, bd) → new_intersectFM_C(zzz385, new_intersectFM_C2Lts(zzz381, zzz382, zzz383, zzz384, h, bc), zzz388, h, ba, bb, bc)
new_intersectFM_C2IntersectFM_C15(zzz245, zzz246, zzz247, zzz248, zzz249, zzz250, zzz251, zzz252, zzz253, zzz254, zzz255, zzz256, zzz257, zzz258, zzz259, True, ca, cb, cc, cd, ce) → new_intersectFM_C2IntersectFM_C16(zzz245, zzz246, zzz247, zzz248, zzz249, zzz250, zzz251, zzz252, zzz253, zzz254, zzz259, ca, cb, cc, cd, ce)
new_intersectFM_C2IntersectFM_C13(zzz261, zzz262, zzz263, zzz264, zzz265, zzz266, zzz267, zzz268, zzz269, zzz270, zzz271, zzz272, zzz273, EmptyFM, zzz275, True, cf, cg, da, db, dc) → new_intersectFM_C(zzz266, new_intersectFM_C2Gts1(zzz261, zzz262, zzz263, zzz264, zzz265, cf, db), zzz270, cf, cg, da, db)
new_intersectFM_C2IntersectFM_C19(zzz279, zzz280, zzz281, zzz282, zzz283, zzz284, zzz285, zzz286, zzz287, zzz288, zzz289, zzz290, zzz291, zzz292, zzz293, zzz294, False, dd, de, df, dg, dh) → new_intersectFM_C(zzz285, new_intersectFM_C2Lts2(zzz279, zzz280, zzz281, zzz282, zzz283, zzz284, dd, dg), zzz288, dd, de, df, dg)
new_intersectFM_C2IntersectFM_C14(zzz279, zzz280, zzz281, zzz282, zzz283, zzz284, zzz285, zzz286, zzz287, zzz288, zzz289, zzz290, zzz291, zzz292, EmptyFM, zzz294, True, dd, de, df, dg, dh) → new_intersectFM_C(zzz285, new_intersectFM_C2Gts2(zzz279, zzz280, zzz281, zzz282, zzz283, zzz284, dd, dg), zzz289, dd, de, df, dg)
new_intersectFM_C2IntersectFM_C17(zzz261, zzz262, zzz263, zzz264, zzz265, zzz266, zzz267, zzz268, zzz269, zzz270, zzz271, zzz272, zzz273, zzz274, zzz275, False, cf, cg, da, db, dc) → new_intersectFM_C(zzz266, new_intersectFM_C2Lts1(zzz261, zzz262, zzz263, zzz264, zzz265, cf, db), zzz269, cf, cg, da, db)
new_intersectFM_C2IntersectFM_C110(zzz279, zzz280, zzz281, zzz282, zzz283, zzz284, zzz285, zzz286, zzz287, zzz288, zzz289, EmptyFM, dd, de, df, dg, dh) → new_intersectFM_C(zzz285, new_intersectFM_C2Gts2(zzz279, zzz280, zzz281, zzz282, zzz283, zzz284, dd, dg), zzz289, dd, de, df, dg)
new_intersectFM_C2IntersectFM_C17(zzz261, zzz262, zzz263, zzz264, zzz265, zzz266, zzz267, zzz268, zzz269, zzz270, zzz271, zzz272, zzz273, zzz274, zzz275, True, cf, cg, da, db, dc) → new_intersectFM_C2IntersectFM_C18(zzz261, zzz262, zzz263, zzz264, zzz265, zzz266, zzz267, zzz268, zzz269, zzz270, zzz275, cf, cg, da, db, dc)
new_intersectFM_C2IntersectFM_C19(zzz279, zzz280, zzz281, zzz282, zzz283, zzz284, zzz285, zzz286, zzz287, zzz288, zzz289, zzz290, zzz291, zzz292, zzz293, zzz294, False, dd, de, df, dg, dh) → new_intersectFM_C(zzz285, new_intersectFM_C2Gts2(zzz279, zzz280, zzz281, zzz282, zzz283, zzz284, dd, dg), zzz289, dd, de, df, dg)
new_intersectFM_C2IntersectFM_C11(zzz381, zzz382, zzz383, zzz384, zzz385, zzz386, zzz387, zzz388, zzz389, Branch(zzz3930, zzz3931, zzz3932, zzz3933, zzz3934), h, ba, bb, bc, bd) → new_intersectFM_C2IntersectFM_C1(zzz381, zzz382, zzz383, zzz384, zzz385, zzz386, zzz387, zzz388, zzz389, zzz3930, zzz3931, zzz3932, zzz3933, zzz3934, new_lt11(Nothing, zzz3930, h), h, ba, bb, bc, bd)
new_intersectFM_C(zzz3, Branch(Nothing, zzz41, zzz42, zzz43, zzz44), Branch(Nothing, zzz51, zzz52, zzz53, zzz54), be, bf, bg, bh) → new_intersectFM_C2IntersectFM_C1(zzz41, zzz42, zzz43, zzz44, zzz3, zzz51, zzz52, zzz53, zzz54, Nothing, zzz41, zzz42, zzz43, zzz44, new_esEs8(new_compare29(Nothing, Nothing, True, be), LT), be, bf, bg, bh, bh)
new_intersectFM_C2IntersectFM_C18(zzz261, zzz262, zzz263, zzz264, zzz265, zzz266, zzz267, zzz268, zzz269, zzz270, Branch(zzz2740, zzz2741, zzz2742, zzz2743, zzz2744), cf, cg, da, db, dc) → new_intersectFM_C2IntersectFM_C13(zzz261, zzz262, zzz263, zzz264, zzz265, zzz266, zzz267, zzz268, zzz269, zzz270, zzz2740, zzz2741, zzz2742, zzz2743, zzz2744, new_lt11(Just(zzz265), zzz2740, cf), cf, cg, da, db, dc)
new_intersectFM_C2IntersectFM_C1(zzz381, zzz382, zzz383, zzz384, zzz385, zzz386, zzz387, zzz388, zzz389, zzz390, zzz391, zzz392, zzz393, zzz394, False, h, ba, bb, bc, bd) → new_intersectFM_C2IntersectFM_C10(zzz381, zzz382, zzz383, zzz384, zzz385, zzz386, zzz387, zzz388, zzz389, zzz390, zzz391, zzz392, zzz393, zzz394, new_gt(Nothing, zzz390, h), h, ba, bb, bc, bd)
new_intersectFM_C2IntersectFM_C10(zzz381, zzz382, zzz383, zzz384, zzz385, zzz386, zzz387, zzz388, zzz389, zzz390, zzz391, zzz392, zzz393, zzz394, True, h, ba, bb, bc, bd) → new_intersectFM_C2IntersectFM_C11(zzz381, zzz382, zzz383, zzz384, zzz385, zzz386, zzz387, zzz388, zzz389, zzz394, h, ba, bb, bc, bd)
new_intersectFM_C(zzz3, Branch(Just(zzz400), zzz41, zzz42, zzz43, zzz44), Branch(Just(zzz500), zzz51, zzz52, zzz53, zzz54), be, bf, bg, bh) → new_intersectFM_C2IntersectFM_C14(zzz400, zzz41, zzz42, zzz43, zzz44, zzz500, zzz3, zzz51, zzz52, zzz53, zzz54, Just(zzz400), zzz41, zzz42, zzz43, zzz44, new_esEs8(new_compare29(Just(zzz500), Just(zzz400), new_esEs31(zzz500, zzz400, be), be), LT), be, bf, bg, bh, bh)
new_intersectFM_C2IntersectFM_C14(zzz279, zzz280, zzz281, zzz282, zzz283, zzz284, zzz285, zzz286, zzz287, zzz288, zzz289, zzz290, zzz291, zzz292, EmptyFM, zzz294, True, dd, de, df, dg, dh) → new_intersectFM_C(zzz285, new_intersectFM_C2Lts2(zzz279, zzz280, zzz281, zzz282, zzz283, zzz284, dd, dg), zzz288, dd, de, df, dg)
new_intersectFM_C2IntersectFM_C10(zzz381, zzz382, zzz383, zzz384, zzz385, zzz386, zzz387, zzz388, zzz389, zzz390, zzz391, zzz392, zzz393, zzz394, False, h, ba, bb, bc, bd) → new_intersectFM_C(zzz385, new_intersectFM_C2Lts(zzz381, zzz382, zzz383, zzz384, h, bc), zzz388, h, ba, bb, bc)
new_intersectFM_C2IntersectFM_C11(zzz381, zzz382, zzz383, zzz384, zzz385, zzz386, zzz387, zzz388, zzz389, EmptyFM, h, ba, bb, bc, bd) → new_intersectFM_C(zzz385, new_intersectFM_C2Gts(zzz381, zzz382, zzz383, zzz384, h, bc), zzz389, h, ba, bb, bc)
new_intersectFM_C2IntersectFM_C1(zzz381, zzz382, zzz383, zzz384, zzz385, zzz386, zzz387, zzz388, zzz389, zzz390, zzz391, zzz392, Branch(zzz3930, zzz3931, zzz3932, zzz3933, zzz3934), zzz394, True, h, ba, bb, bc, bd) → new_intersectFM_C2IntersectFM_C1(zzz381, zzz382, zzz383, zzz384, zzz385, zzz386, zzz387, zzz388, zzz389, zzz3930, zzz3931, zzz3932, zzz3933, zzz3934, new_lt11(Nothing, zzz3930, h), h, ba, bb, bc, bd)
new_intersectFM_C2IntersectFM_C16(zzz245, zzz246, zzz247, zzz248, zzz249, zzz250, zzz251, zzz252, zzz253, zzz254, Branch(zzz2580, zzz2581, zzz2582, zzz2583, zzz2584), ca, cb, cc, cd, ce) → new_intersectFM_C2IntersectFM_C12(zzz245, zzz246, zzz247, zzz248, zzz249, zzz250, zzz251, zzz252, zzz253, zzz254, zzz2580, zzz2581, zzz2582, zzz2583, zzz2584, new_lt11(Nothing, zzz2580, ca), ca, cb, cc, cd, ce)
new_intersectFM_C2IntersectFM_C14(zzz279, zzz280, zzz281, zzz282, zzz283, zzz284, zzz285, zzz286, zzz287, zzz288, zzz289, zzz290, zzz291, zzz292, Branch(zzz2930, zzz2931, zzz2932, zzz2933, zzz2934), zzz294, True, dd, de, df, dg, dh) → new_intersectFM_C2IntersectFM_C14(zzz279, zzz280, zzz281, zzz282, zzz283, zzz284, zzz285, zzz286, zzz287, zzz288, zzz289, zzz2930, zzz2931, zzz2932, zzz2933, zzz2934, new_lt11(Just(zzz284), zzz2930, dd), dd, de, df, dg, dh)
new_intersectFM_C2IntersectFM_C12(zzz245, zzz246, zzz247, zzz248, zzz249, zzz250, zzz251, zzz252, zzz253, zzz254, zzz255, zzz256, zzz257, EmptyFM, zzz259, True, ca, cb, cc, cd, ce) → new_intersectFM_C(zzz250, new_intersectFM_C2Lts0(zzz245, zzz246, zzz247, zzz248, zzz249, ca, cd), zzz253, ca, cb, cc, cd)
new_intersectFM_C2IntersectFM_C12(zzz245, zzz246, zzz247, zzz248, zzz249, zzz250, zzz251, zzz252, zzz253, zzz254, zzz255, zzz256, zzz257, zzz258, zzz259, False, ca, cb, cc, cd, ce) → new_intersectFM_C2IntersectFM_C15(zzz245, zzz246, zzz247, zzz248, zzz249, zzz250, zzz251, zzz252, zzz253, zzz254, zzz255, zzz256, zzz257, zzz258, zzz259, new_gt1(zzz255, ca), ca, cb, cc, cd, ce)
new_intersectFM_C2IntersectFM_C18(zzz261, zzz262, zzz263, zzz264, zzz265, zzz266, zzz267, zzz268, zzz269, zzz270, EmptyFM, cf, cg, da, db, dc) → new_intersectFM_C(zzz266, new_intersectFM_C2Lts1(zzz261, zzz262, zzz263, zzz264, zzz265, cf, db), zzz269, cf, cg, da, db)
new_intersectFM_C2IntersectFM_C15(zzz245, zzz246, zzz247, zzz248, zzz249, zzz250, zzz251, zzz252, zzz253, zzz254, zzz255, zzz256, zzz257, zzz258, zzz259, False, ca, cb, cc, cd, ce) → new_intersectFM_C(zzz250, new_intersectFM_C2Gts0(zzz245, zzz246, zzz247, zzz248, zzz249, ca, cd), zzz254, ca, cb, cc, cd)

The TRS R consists of the following rules:

new_lt19(zzz500000, zzz4300000, ty_Float) → new_lt6(zzz500000, zzz4300000)
new_splitLT3(EmptyFM, be, bh) → new_emptyFM(be, bh)
new_ltEs18(zzz50000, zzz430000, app(ty_Ratio, dcf)) → new_ltEs15(zzz50000, zzz430000, dcf)
new_esEs7(Just(zzz5000), Just(zzz4000), app(ty_Maybe, fc)) → new_esEs7(zzz5000, zzz4000, fc)
new_esEs4(Right(zzz5000), Right(zzz4000), ge, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_esEs20(zzz5000, zzz4000, app(ty_Maybe, chd)) → new_esEs7(zzz5000, zzz4000, chd)
new_esEs12(:(zzz5000, zzz5001), :(zzz4000, zzz4001), ha) → new_asAs(new_esEs20(zzz5000, zzz4000, ha), new_esEs12(zzz5001, zzz4001, ha))
new_esEs7(Just(zzz5000), Just(zzz4000), app(ty_[], eg)) → new_esEs12(zzz5000, zzz4000, eg)
new_ltEs7(Right(zzz500000), Right(zzz4300000), dba, ty_Ordering) → new_ltEs10(zzz500000, zzz4300000)
new_lt19(zzz500000, zzz4300000, app(app(app(ty_@3, bdh), bea), beb)) → new_lt8(zzz500000, zzz4300000, bdh, bea, beb)
new_ltEs18(zzz50000, zzz430000, app(app(app(ty_@3, bcg), bch), bda)) → new_ltEs16(zzz50000, zzz430000, bcg, bch, bda)
new_lt20(zzz500001, zzz4300001, app(ty_[], bfe)) → new_lt18(zzz500001, zzz4300001, bfe)
new_compare15(zzz500000, zzz4300000, True, fh, ga) → LT
new_esEs4(Right(zzz5000), Right(zzz4000), ge, ty_Char) → new_esEs11(zzz5000, zzz4000)
new_esEs31(zzz500, zzz400, ty_Ordering) → new_esEs8(zzz500, zzz400)
new_esEs31(zzz500, zzz400, app(ty_[], ha)) → new_esEs12(zzz500, zzz400, ha)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Bool, gf) → new_esEs14(zzz5000, zzz4000)
new_ltEs20(zzz500002, zzz4300002, ty_Ordering) → new_ltEs10(zzz500002, zzz4300002)
new_ltEs18(zzz50000, zzz430000, app(ty_Maybe, ccf)) → new_ltEs4(zzz50000, zzz430000, ccf)
new_esEs4(Right(zzz5000), Right(zzz4000), ge, app(app(app(ty_@3, bbg), bbh), bca)) → new_esEs6(zzz5000, zzz4000, bbg, bbh, bca)
new_splitGT22(zzz2640, zzz2641, zzz2642, zzz2643, zzz2644, zzz265, True, cf, db) → new_splitGT4(zzz2644, zzz265, cf, db)
new_lt13(zzz500000, zzz4300000, app(app(app(ty_@3, gb), gc), gd)) → new_lt8(zzz500000, zzz4300000, gb, gc, gd)
new_compare32(zzz430, be) → new_compare29(Nothing, zzz430, new_esEs30(zzz430, be), be)
new_lt15(zzz500000, zzz4300000) → new_esEs8(new_compare14(zzz500000, zzz4300000), LT)
new_lt20(zzz500001, zzz4300001, app(app(app(ty_@3, bfb), bfc), bfd)) → new_lt8(zzz500001, zzz4300001, bfb, bfc, bfd)
new_esEs27(zzz5001, zzz4001, app(ty_Maybe, cbb)) → new_esEs7(zzz5001, zzz4001, cbb)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Ordering) → new_ltEs10(zzz500000, zzz4300000)
new_esEs23(zzz500000, zzz4300000, ty_Bool) → new_esEs14(zzz500000, zzz4300000)
new_compare27(zzz500000, zzz4300000, False, ff, fg) → new_compare113(zzz500000, zzz4300000, new_ltEs7(zzz500000, zzz4300000, ff, fg), ff, fg)
new_addToFM_C20(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz440, zzz441, False, be, bh) → new_addToFM_C10(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz440, zzz441, new_gt(zzz440, zzz4440, be), be, bh)
new_lt19(zzz500000, zzz4300000, ty_Double) → new_lt15(zzz500000, zzz4300000)
new_sizeFM0(Branch(zzz7640, zzz7641, zzz7642, zzz7643, zzz7644), be, bf) → zzz7642
new_ltEs7(Left(zzz500000), Left(zzz4300000), app(ty_Maybe, dac), chf) → new_ltEs4(zzz500000, zzz4300000, dac)
new_ltEs7(Right(zzz500000), Right(zzz4300000), dba, ty_@0) → new_ltEs11(zzz500000, zzz4300000)
new_ltEs20(zzz500002, zzz4300002, app(ty_Ratio, bgc)) → new_ltEs15(zzz500002, zzz4300002, bgc)
new_esEs26(zzz5002, zzz4002, ty_Float) → new_esEs13(zzz5002, zzz4002)
new_lt13(zzz500000, zzz4300000, app(ty_[], deb)) → new_lt18(zzz500000, zzz4300000, deb)
new_ltEs7(Left(zzz500000), Right(zzz4300000), dba, chf) → True
new_primMulNat0(Zero, Zero) → Zero
new_esEs29(zzz500, Just(zzz4300), ty_Integer) → new_esEs15(zzz500, zzz4300)
new_esEs19(zzz5000, zzz4000, ty_Int) → new_esEs17(zzz5000, zzz4000)
new_sr(Integer(zzz43000000), Integer(zzz5000010)) → Integer(new_primMulInt(zzz43000000, zzz5000010))
new_ltEs20(zzz500002, zzz4300002, ty_Float) → new_ltEs12(zzz500002, zzz4300002)
new_esEs29(zzz500, Just(zzz4300), ty_Double) → new_esEs9(zzz500, zzz4300)
new_mkVBalBranch0(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), be, bh) → new_mkVBalBranch3MkVBalBranch20(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_lt14(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, be, bh)), new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, be, bh)), be, bh)
new_ltEs20(zzz500002, zzz4300002, ty_@0) → new_ltEs11(zzz500002, zzz4300002)
new_esEs20(zzz5000, zzz4000, app(ty_Ratio, che)) → new_esEs16(zzz5000, zzz4000, che)
new_esEs18(zzz5001, zzz4001, ty_Double) → new_esEs9(zzz5001, zzz4001)
new_lt20(zzz500001, zzz4300001, ty_Float) → new_lt6(zzz500001, zzz4300001)
new_esEs23(zzz500000, zzz4300000, ty_Double) → new_esEs9(zzz500000, zzz4300000)
new_esEs4(Right(zzz5000), Right(zzz4000), ge, app(ty_[], bbf)) → new_esEs12(zzz5000, zzz4000, bbf)
new_intersectFM_C2Gts(zzz381, zzz382, zzz383, zzz384, h, bc) → new_splitGT3(Branch(Nothing, zzz381, zzz382, zzz383, zzz384), h, bc)
new_esEs24(zzz500001, zzz4300001, ty_Integer) → new_esEs15(zzz500001, zzz4300001)
new_ltEs14(False, True) → True
new_ltEs19(zzz500001, zzz4300001, ty_Integer) → new_ltEs9(zzz500001, zzz4300001)
new_esEs29(zzz500, Just(zzz4300), ty_Char) → new_esEs11(zzz500, zzz4300)
new_splitLT4(EmptyFM, zzz265, cf, db) → new_emptyFM(cf, db)
new_ltEs4(Just(zzz500000), Just(zzz4300000), app(app(ty_@2, cda), cdb)) → new_ltEs13(zzz500000, zzz4300000, cda, cdb)
new_esEs20(zzz5000, zzz4000, app(app(ty_Either, cgd), cge)) → new_esEs4(zzz5000, zzz4000, cgd, cge)
new_esEs12([], [], ha) → True
new_primPlusInt1(Branch(zzz1540, zzz1541, Neg(zzz15420), zzz1543, zzz1544), zzz760, zzz761, zzz764, be, bf) → new_primPlusInt0(zzz15420, new_sizeFM0(zzz764, be, bf))
new_esEs31(zzz500, zzz400, ty_@0) → new_esEs10(zzz500, zzz400)
new_ltEs19(zzz500001, zzz4300001, ty_Ordering) → new_ltEs10(zzz500001, zzz4300001)
new_esEs24(zzz500001, zzz4300001, app(app(ty_@2, bef), beg)) → new_esEs5(zzz500001, zzz4300001, bef, beg)
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Ordering, chf) → new_ltEs10(zzz500000, zzz4300000)
new_lt12(zzz500000, zzz4300000) → new_esEs8(new_compare10(zzz500000, zzz4300000), LT)
new_ltEs7(Right(zzz500000), Right(zzz4300000), dba, app(ty_Ratio, dbg)) → new_ltEs15(zzz500000, zzz4300000, dbg)
new_esEs15(Integer(zzz5000), Integer(zzz4000)) → new_primEqInt(zzz5000, zzz4000)
new_ltEs10(EQ, GT) → True
new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, be, bh) → new_sizeFM(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, be, bh)
new_esEs21(zzz5001, zzz4001, ty_Int) → new_esEs17(zzz5001, zzz4001)
new_ltEs19(zzz500001, zzz4300001, app(ty_Maybe, deg)) → new_ltEs4(zzz500001, zzz4300001, deg)
new_ltEs7(Left(zzz500000), Left(zzz4300000), app(app(app(ty_@3, dae), daf), dag), chf) → new_ltEs16(zzz500000, zzz4300000, dae, daf, dag)
new_lt13(zzz500000, zzz4300000, ty_Char) → new_lt12(zzz500000, zzz4300000)
new_splitLT22(zzz430, zzz431, zzz432, zzz433, zzz434, True, be, bh) → new_splitLT3(zzz433, be, bh)
new_esEs24(zzz500001, zzz4300001, app(ty_[], bfe)) → new_esEs12(zzz500001, zzz4300001, bfe)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Ordering, gf) → new_esEs8(zzz5000, zzz4000)
new_esEs25(zzz500000, zzz4300000, ty_Double) → new_esEs9(zzz500000, zzz4300000)
new_esEs25(zzz500000, zzz4300000, ty_Float) → new_esEs13(zzz500000, zzz4300000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), dba, app(ty_[], dcc)) → new_ltEs17(zzz500000, zzz4300000, dcc)
new_pePe(False, zzz218) → zzz218
new_lt14(zzz5000, zzz43000) → new_esEs8(new_compare8(zzz5000, zzz43000), LT)
new_esEs25(zzz500000, zzz4300000, app(app(ty_Either, bdb), bdc)) → new_esEs4(zzz500000, zzz4300000, bdb, bdc)
new_esEs25(zzz500000, zzz4300000, ty_Char) → new_esEs11(zzz500000, zzz4300000)
new_esEs12(:(zzz5000, zzz5001), [], ha) → False
new_esEs12([], :(zzz4000, zzz4001), ha) → False
new_esEs25(zzz500000, zzz4300000, ty_Bool) → new_esEs14(zzz500000, zzz4300000)
new_lt19(zzz500000, zzz4300000, ty_Ordering) → new_lt9(zzz500000, zzz4300000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), dba, app(app(ty_@2, dbd), dbe)) → new_ltEs13(zzz500000, zzz4300000, dbd, dbe)
new_esEs4(Right(zzz5000), Right(zzz4000), ge, app(ty_Ratio, bcc)) → new_esEs16(zzz5000, zzz4000, bcc)
new_compare23(zzz500000, zzz4300000, True) → EQ
new_esEs29(zzz500, Just(zzz4300), app(ty_[], ha)) → new_esEs12(zzz500, zzz4300, ha)
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Float, chf) → new_ltEs12(zzz500000, zzz4300000)
new_esEs24(zzz500001, zzz4300001, app(ty_Maybe, beh)) → new_esEs7(zzz500001, zzz4300001, beh)
new_lt19(zzz500000, zzz4300000, app(ty_Ratio, bdg)) → new_lt17(zzz500000, zzz4300000, bdg)
new_ltEs4(Nothing, Just(zzz4300000), ccf) → True
new_intersectFM_C2Lts0(zzz245, zzz246, zzz247, zzz248, zzz249, ca, cd) → new_splitLT22(Just(zzz245), zzz246, zzz247, zzz248, zzz249, new_lt11(Nothing, Just(zzz245), ca), ca, cd)
new_compare30(zzz500000, zzz4300000, ty_Integer) → new_compare9(zzz500000, zzz4300000)
new_esEs23(zzz500000, zzz4300000, app(ty_Maybe, dea)) → new_esEs7(zzz500000, zzz4300000, dea)
new_esEs4(Left(zzz5000), Left(zzz4000), app(ty_Ratio, bba), gf) → new_esEs16(zzz5000, zzz4000, bba)
new_ltEs7(Right(zzz500000), Right(zzz4300000), dba, ty_Char) → new_ltEs5(zzz500000, zzz4300000)
new_compare13(zzz500000, zzz4300000, gb, gc, gd) → new_compare24(zzz500000, zzz4300000, new_esEs6(zzz500000, zzz4300000, gb, gc, gd), gb, gc, gd)
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Succ(zzz430000))) → new_primCmpNat0(zzz430000, zzz50000)
new_lt4(zzz500000, zzz4300000) → new_esEs8(new_compare11(zzz500000, zzz4300000), LT)
new_esEs28(zzz5000, zzz4000, app(ty_Ratio, cce)) → new_esEs16(zzz5000, zzz4000, cce)
new_esEs4(Right(zzz5000), Right(zzz4000), ge, ty_Integer) → new_esEs15(zzz5000, zzz4000)
new_esEs20(zzz5000, zzz4000, app(app(ty_@2, cgf), cgg)) → new_esEs5(zzz5000, zzz4000, cgf, cgg)
new_compare30(zzz500000, zzz4300000, app(ty_Ratio, ddd)) → new_compare7(zzz500000, zzz4300000, ddd)
new_compare19(zzz500000, zzz4300000, True) → LT
new_compare6(zzz500000, zzz4300000) → new_compare23(zzz500000, zzz4300000, new_esEs8(zzz500000, zzz4300000))
new_mkBalBranch6MkBalBranch5(zzz760, zzz761, zzz764, zzz154, False, be, bf) → new_mkBalBranch6MkBalBranch4(zzz760, zzz761, zzz764, zzz154, new_gt2(new_mkBalBranch6Size_r(zzz760, zzz761, zzz764, zzz154, be, bf), new_sr0(new_sIZE_RATIO, new_mkBalBranch6Size_l(zzz760, zzz761, zzz764, zzz154, be, bf))), be, bf)
new_ltEs18(zzz50000, zzz430000, ty_@0) → new_ltEs11(zzz50000, zzz430000)
new_addToFM_C20(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz440, zzz441, True, be, bh) → new_mkBalBranch(zzz4440, zzz4441, new_addToFM_C0(zzz4443, zzz440, zzz441, be, bh), zzz4444, be, bh)
new_primCmpNat0(Zero, Succ(zzz43000000)) → LT
new_ltEs19(zzz500001, zzz4300001, app(ty_Ratio, deh)) → new_ltEs15(zzz500001, zzz4300001, deh)
new_addToFM(zzz444, zzz440, zzz441, be, bh) → new_addToFM_C0(zzz444, zzz440, zzz441, be, bh)
new_ltEs20(zzz500002, zzz4300002, ty_Bool) → new_ltEs14(zzz500002, zzz4300002)
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Int) → new_esEs17(zzz5000, zzz4000)
new_mkBalBranch(zzz760, zzz761, zzz154, zzz764, be, bf) → new_mkBalBranch6MkBalBranch5(zzz760, zzz761, zzz764, zzz154, new_lt14(new_primPlusInt1(zzz154, zzz760, zzz761, zzz764, be, bf), Pos(Succ(Succ(Zero)))), be, bf)
new_intersectFM_C2Gts2(zzz279, zzz280, zzz281, zzz282, zzz283, zzz284, dd, dg) → new_splitGT22(Just(zzz279), zzz280, zzz281, zzz282, zzz283, zzz284, new_gt0(zzz284, Just(zzz279), dd), dd, dg)
new_esEs27(zzz5001, zzz4001, ty_@0) → new_esEs10(zzz5001, zzz4001)
new_esEs8(LT, LT) → True
new_ltEs12(zzz50000, zzz430000) → new_fsEs(new_compare16(zzz50000, zzz430000))
new_lt19(zzz500000, zzz4300000, app(app(ty_@2, bdd), bde)) → new_lt16(zzz500000, zzz4300000, bdd, bde)
new_esEs25(zzz500000, zzz4300000, ty_Ordering) → new_esEs8(zzz500000, zzz4300000)
new_esEs19(zzz5000, zzz4000, app(ty_Maybe, hg)) → new_esEs7(zzz5000, zzz4000, hg)
new_esEs20(zzz5000, zzz4000, app(app(app(ty_@3, cha), chb), chc)) → new_esEs6(zzz5000, zzz4000, cha, chb, chc)
new_esEs18(zzz5001, zzz4001, app(ty_Ratio, cfb)) → new_esEs16(zzz5001, zzz4001, cfb)
new_mkVBalBranch0(zzz440, zzz441, EmptyFM, zzz444, be, bh) → new_addToFM(zzz444, zzz440, zzz441, be, bh)
new_pePe(True, zzz218) → True
new_primEqNat0(Zero, Zero) → True
new_compare26(zzz500000, zzz4300000, True) → EQ
new_lt20(zzz500001, zzz4300001, app(app(ty_Either, bed), bee)) → new_lt5(zzz500001, zzz4300001, bed, bee)
new_mkBalBranch6MkBalBranch11(zzz760, zzz761, zzz764, zzz1540, zzz1541, zzz1542, zzz1543, Branch(zzz15440, zzz15441, zzz15442, zzz15443, zzz15444), False, be, bf) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))), zzz15440, zzz15441, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), zzz1540, zzz1541, zzz1543, zzz15443, app(ty_Maybe, be), bf), new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), zzz760, zzz761, zzz15444, zzz764, app(ty_Maybe, be), bf), app(ty_Maybe, be), bf)
new_esEs13(Float(zzz5000, zzz5001), Float(zzz4000, zzz4001)) → new_esEs17(new_sr0(zzz5000, zzz4000), new_sr0(zzz5001, zzz4001))
new_lt20(zzz500001, zzz4300001, ty_Bool) → new_lt7(zzz500001, zzz4300001)
new_esEs19(zzz5000, zzz4000, app(ty_[], cfg)) → new_esEs12(zzz5000, zzz4000, cfg)
new_compare29(Nothing, Just(zzz430000), False, hg) → LT
new_esEs19(zzz5000, zzz4000, ty_Float) → new_esEs13(zzz5000, zzz4000)
new_compare30(zzz500000, zzz4300000, app(ty_Maybe, ddc)) → new_compare28(zzz500000, zzz4300000, ddc)
new_esEs18(zzz5001, zzz4001, app(app(ty_@2, cec), ced)) → new_esEs5(zzz5001, zzz4001, cec, ced)
new_esEs25(zzz500000, zzz4300000, ty_Int) → new_esEs17(zzz500000, zzz4300000)
new_esEs26(zzz5002, zzz4002, ty_Ordering) → new_esEs8(zzz5002, zzz4002)
new_esEs9(Double(zzz5000, zzz5001), Double(zzz4000, zzz4001)) → new_esEs17(new_sr0(zzz5000, zzz4000), new_sr0(zzz5001, zzz4001))
new_esEs8(GT, GT) → True
new_esEs18(zzz5001, zzz4001, app(app(app(ty_@3, cef), ceg), ceh)) → new_esEs6(zzz5001, zzz4001, cef, ceg, ceh)
new_lt20(zzz500001, zzz4300001, app(ty_Maybe, beh)) → new_lt11(zzz500001, zzz4300001, beh)
new_esEs25(zzz500000, zzz4300000, ty_@0) → new_esEs10(zzz500000, zzz4300000)
new_compare4([], [], ea) → EQ
new_primPlusNat0(Succ(zzz2210), zzz400000) → Succ(Succ(new_primPlusNat1(zzz2210, zzz400000)))
new_esEs4(Left(zzz5000), Left(zzz4000), app(app(ty_@2, bab), bac), gf) → new_esEs5(zzz5000, zzz4000, bab, bac)
new_lt19(zzz500000, zzz4300000, ty_@0) → new_lt4(zzz500000, zzz4300000)
new_esEs26(zzz5002, zzz4002, app(app(app(ty_@3, bhe), bhf), bhg)) → new_esEs6(zzz5002, zzz4002, bhe, bhf, bhg)
new_ltEs7(Right(zzz500000), Right(zzz4300000), dba, ty_Integer) → new_ltEs9(zzz500000, zzz4300000)
new_compare18(zzz500000, zzz4300000, fh, ga) → new_compare25(zzz500000, zzz4300000, new_esEs5(zzz500000, zzz4300000, fh, ga), fh, ga)
new_ltEs17(zzz50000, zzz430000, ea) → new_fsEs(new_compare4(zzz50000, zzz430000, ea))
new_esEs8(GT, LT) → False
new_esEs8(LT, GT) → False
new_compare30(zzz500000, zzz4300000, app(ty_[], ddh)) → new_compare4(zzz500000, zzz4300000, ddh)
new_compare30(zzz500000, zzz4300000, ty_Double) → new_compare14(zzz500000, zzz4300000)
new_ltEs13(@2(zzz500000, zzz500001), @2(zzz4300000, zzz4300001), dcd, dce) → new_pePe(new_lt13(zzz500000, zzz4300000, dcd), new_asAs(new_esEs23(zzz500000, zzz4300000, dcd), new_ltEs19(zzz500001, zzz4300001, dce)))
new_esEs25(zzz500000, zzz4300000, app(ty_[], bec)) → new_esEs12(zzz500000, zzz4300000, bec)
new_esEs4(Right(zzz5000), Right(zzz4000), ge, app(app(ty_Either, bbb), bbc)) → new_esEs4(zzz5000, zzz4000, bbb, bbc)
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Int, chf) → new_ltEs6(zzz500000, zzz4300000)
new_compare24(zzz500000, zzz4300000, True, gb, gc, gd) → EQ
new_lt20(zzz500001, zzz4300001, ty_Ordering) → new_lt9(zzz500001, zzz4300001)
new_primEqInt(Neg(Succ(zzz50000)), Neg(Succ(zzz40000))) → new_primEqNat0(zzz50000, zzz40000)
new_esEs20(zzz5000, zzz4000, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_compare113(zzz500000, zzz4300000, True, ff, fg) → LT
new_primPlusInt0(zzz15420, Pos(zzz4420)) → new_primMinusNat0(zzz4420, zzz15420)
new_esEs31(zzz500, zzz400, app(app(ty_Either, ge), gf)) → new_esEs4(zzz500, zzz400, ge, gf)
new_esEs23(zzz500000, zzz4300000, ty_Ordering) → new_esEs8(zzz500000, zzz4300000)
new_sizeFM1(Branch(zzz5560, zzz5561, zzz5562, zzz5563, zzz5564), bce, bcf) → zzz5562
new_esEs4(Left(zzz5000), Left(zzz4000), app(app(ty_Either, hh), baa), gf) → new_esEs4(zzz5000, zzz4000, hh, baa)
new_ltEs18(zzz50000, zzz430000, app(app(ty_Either, dba), chf)) → new_ltEs7(zzz50000, zzz430000, dba, chf)
new_esEs24(zzz500001, zzz4300001, ty_Bool) → new_esEs14(zzz500001, zzz4300001)
new_primPlusNat1(Succ(zzz22100), Zero) → Succ(zzz22100)
new_primPlusNat1(Zero, Succ(zzz4000000)) → Succ(zzz4000000)
new_lt19(zzz500000, zzz4300000, ty_Bool) → new_lt7(zzz500000, zzz4300000)
new_lt19(zzz500000, zzz4300000, ty_Integer) → new_lt10(zzz500000, zzz4300000)
new_ltEs4(Nothing, Nothing, ccf) → True
new_lt13(zzz500000, zzz4300000, ty_Float) → new_lt6(zzz500000, zzz4300000)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_@0) → new_ltEs11(zzz500000, zzz4300000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Char, chf) → new_ltEs5(zzz500000, zzz4300000)
new_lt13(zzz500000, zzz4300000, ty_Int) → new_lt14(zzz500000, zzz4300000)
new_splitGT12(zzz2640, zzz2641, zzz2642, zzz2643, zzz2644, zzz265, True, cf, db) → new_mkVBalBranch0(zzz2640, zzz2641, new_splitGT4(zzz2643, zzz265, cf, db), zzz2644, cf, db)
new_lt6(zzz500000, zzz4300000) → new_esEs8(new_compare16(zzz500000, zzz4300000), LT)
new_compare29(Just(zzz50000), Nothing, False, hg) → GT
new_esEs31(zzz500, zzz400, app(app(app(ty_@3, hb), hc), hd)) → new_esEs6(zzz500, zzz400, hb, hc, hd)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_ltEs7(Right(zzz500000), Left(zzz4300000), dba, chf) → False
new_splitLT11(zzz430, zzz431, zzz432, zzz433, zzz434, True, be, bh) → new_mkVBalBranch0(zzz430, zzz431, zzz433, new_splitLT3(zzz434, be, bh), be, bh)
new_esEs24(zzz500001, zzz4300001, app(app(app(ty_@3, bfb), bfc), bfd)) → new_esEs6(zzz500001, zzz4300001, bfb, bfc, bfd)
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_mkBalBranch6MkBalBranch5(zzz760, zzz761, zzz764, zzz154, True, be, bf) → new_mkBranch(Zero, zzz760, zzz761, zzz154, zzz764, app(ty_Maybe, be), bf)
new_esEs23(zzz500000, zzz4300000, ty_Char) → new_esEs11(zzz500000, zzz4300000)
new_lt13(zzz500000, zzz4300000, ty_Bool) → new_lt7(zzz500000, zzz4300000)
new_esEs19(zzz5000, zzz4000, ty_Bool) → new_esEs14(zzz5000, zzz4000)
new_esEs20(zzz5000, zzz4000, ty_Float) → new_esEs13(zzz5000, zzz4000)
new_compare14(Double(zzz500000, zzz500001), Double(zzz4300000, zzz4300001)) → new_compare8(new_sr0(zzz500000, zzz4300000), new_sr0(zzz500001, zzz4300001))
new_compare12(zzz500000, zzz4300000, ff, fg) → new_compare27(zzz500000, zzz4300000, new_esEs4(zzz500000, zzz4300000, ff, fg), ff, fg)
new_compare8(zzz500, zzz4300) → new_primCmpInt(zzz500, zzz4300)
new_primEqInt(Neg(Zero), Neg(Succ(zzz40000))) → False
new_primEqInt(Neg(Succ(zzz50000)), Neg(Zero)) → False
new_lt19(zzz500000, zzz4300000, ty_Char) → new_lt12(zzz500000, zzz4300000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), dba, app(app(app(ty_@3, dbh), dca), dcb)) → new_ltEs16(zzz500000, zzz4300000, dbh, dca, dcb)
new_compare17(zzz500000, zzz4300000) → new_compare26(zzz500000, zzz4300000, new_esEs14(zzz500000, zzz4300000))
new_esEs8(EQ, EQ) → True
new_lt13(zzz500000, zzz4300000, ty_Double) → new_lt15(zzz500000, zzz4300000)
new_compare111(zzz200, zzz201, True, hf) → LT
new_esEs20(zzz5000, zzz4000, ty_@0) → new_esEs10(zzz5000, zzz4000)
new_splitGT21(zzz440, zzz441, zzz442, zzz443, zzz444, False, be, bh) → new_splitGT11(zzz440, zzz441, zzz442, zzz443, zzz444, new_lt11(Nothing, zzz440, be), be, bh)
new_mkBalBranch6MkBalBranch4(zzz760, zzz761, zzz764, zzz154, False, be, bf) → new_mkBalBranch6MkBalBranch3(zzz760, zzz761, zzz764, zzz154, new_gt2(new_mkBalBranch6Size_l(zzz760, zzz761, zzz764, zzz154, be, bf), new_sr0(new_sIZE_RATIO, new_mkBalBranch6Size_r(zzz760, zzz761, zzz764, zzz154, be, bf))), be, bf)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Char, gf) → new_esEs11(zzz5000, zzz4000)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primPlusInt1(EmptyFM, zzz760, zzz761, zzz764, be, bf) → new_primPlusInt(Zero, new_mkBalBranch6Size_r(zzz760, zzz761, zzz764, EmptyFM, be, bf))
new_primMinusNat0(Succ(zzz154200), Zero) → Pos(Succ(zzz154200))
new_primCmpNat0(Succ(zzz5000000), Succ(zzz43000000)) → new_primCmpNat0(zzz5000000, zzz43000000)
new_ltEs19(zzz500001, zzz4300001, ty_@0) → new_ltEs11(zzz500001, zzz4300001)
new_esEs18(zzz5001, zzz4001, ty_Char) → new_esEs11(zzz5001, zzz4001)
new_compare112(zzz500000, zzz4300000, True) → LT
new_esEs19(zzz5000, zzz4000, ty_Char) → new_esEs11(zzz5000, zzz4000)
new_compare30(zzz500000, zzz4300000, app(app(ty_Either, dcg), dch)) → new_compare12(zzz500000, zzz4300000, dcg, dch)
new_primEqInt(Pos(Succ(zzz50000)), Pos(Succ(zzz40000))) → new_primEqNat0(zzz50000, zzz40000)
new_ltEs18(zzz50000, zzz430000, ty_Double) → new_ltEs8(zzz50000, zzz430000)
new_mkVBalBranch3MkVBalBranch20(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, False, be, bh) → new_mkVBalBranch3MkVBalBranch10(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, new_lt14(new_sr0(new_sIZE_RATIO, new_mkVBalBranch3Size_r(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, be, bh)), new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, be, bh)), be, bh)
new_compare27(zzz500000, zzz4300000, True, ff, fg) → EQ
new_lt10(zzz500000, zzz4300000) → new_esEs8(new_compare9(zzz500000, zzz4300000), LT)
new_esEs24(zzz500001, zzz4300001, app(ty_Ratio, bfa)) → new_esEs16(zzz500001, zzz4300001, bfa)
new_ltEs19(zzz500001, zzz4300001, ty_Bool) → new_ltEs14(zzz500001, zzz4300001)
new_esEs14(False, True) → False
new_esEs14(True, False) → False
new_ltEs4(Just(zzz500000), Just(zzz4300000), app(app(ty_Either, ccg), cch)) → new_ltEs7(zzz500000, zzz4300000, ccg, cch)
new_esEs23(zzz500000, zzz4300000, app(ty_[], deb)) → new_esEs12(zzz500000, zzz4300000, deb)
new_esEs29(zzz500, Just(zzz4300), app(ty_Maybe, eb)) → new_esEs7(zzz500, zzz4300, eb)
new_esEs26(zzz5002, zzz4002, ty_Integer) → new_esEs15(zzz5002, zzz4002)
new_mkBalBranch6MkBalBranch11(zzz760, zzz761, zzz764, zzz1540, zzz1541, zzz1542, zzz1543, zzz1544, True, be, bf) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), zzz1540, zzz1541, zzz1543, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), zzz760, zzz761, zzz1544, zzz764, app(ty_Maybe, be), bf), app(ty_Maybe, be), bf)
new_splitLT12(zzz2630, zzz2631, zzz2632, zzz2633, zzz2634, zzz265, True, cf, db) → new_mkVBalBranch0(zzz2630, zzz2631, zzz2633, new_splitLT4(zzz2634, zzz265, cf, db), cf, db)
new_ltEs10(GT, EQ) → False
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Double) → new_ltEs8(zzz500000, zzz4300000)
new_esEs24(zzz500001, zzz4300001, ty_Int) → new_esEs17(zzz500001, zzz4300001)
new_lt17(zzz500000, zzz4300000, bcd) → new_esEs8(new_compare7(zzz500000, zzz4300000, bcd), LT)
new_primEqNat0(Succ(zzz50000), Succ(zzz40000)) → new_primEqNat0(zzz50000, zzz40000)
new_ltEs20(zzz500002, zzz4300002, app(ty_[], bgg)) → new_ltEs17(zzz500002, zzz4300002, bgg)
new_splitLT22(zzz430, zzz431, zzz432, zzz433, zzz434, False, be, bh) → new_splitLT11(zzz430, zzz431, zzz432, zzz433, zzz434, new_gt1(zzz430, be), be, bh)
new_esEs27(zzz5001, zzz4001, ty_Ordering) → new_esEs8(zzz5001, zzz4001)
new_ltEs14(False, False) → True
new_compare11(@0, @0) → EQ
new_esEs19(zzz5000, zzz4000, app(app(app(ty_@3, cfh), cga), cgb)) → new_esEs6(zzz5000, zzz4000, cfh, cga, cgb)
new_lt7(zzz500000, zzz4300000) → new_esEs8(new_compare17(zzz500000, zzz4300000), LT)
new_ltEs9(zzz50000, zzz430000) → new_fsEs(new_compare9(zzz50000, zzz430000))
new_ltEs20(zzz500002, zzz4300002, ty_Char) → new_ltEs5(zzz500002, zzz4300002)
new_esEs29(zzz500, Nothing, be) → False
new_compare113(zzz500000, zzz4300000, False, ff, fg) → GT
new_ltEs7(Right(zzz500000), Right(zzz4300000), dba, ty_Bool) → new_ltEs14(zzz500000, zzz4300000)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Int) → new_ltEs6(zzz500000, zzz4300000)
new_splitGT4(EmptyFM, zzz265, cf, db) → new_emptyFM(cf, db)
new_primCompAux00(zzz225, LT) → LT
new_splitLT3(Branch(zzz4330, zzz4331, zzz4332, zzz4333, zzz4334), be, bh) → new_splitLT22(zzz4330, zzz4331, zzz4332, zzz4333, zzz4334, new_lt11(Nothing, zzz4330, be), be, bh)
new_lt20(zzz500001, zzz4300001, ty_@0) → new_lt4(zzz500001, zzz4300001)
new_compare7(:%(zzz500000, zzz500001), :%(zzz4300000, zzz4300001), ty_Int) → new_compare8(new_sr0(zzz500000, zzz4300001), new_sr0(zzz4300000, zzz500001))
new_ltEs19(zzz500001, zzz4300001, app(app(ty_Either, dec), ded)) → new_ltEs7(zzz500001, zzz4300001, dec, ded)
new_ltEs19(zzz500001, zzz4300001, app(ty_[], dfd)) → new_ltEs17(zzz500001, zzz4300001, dfd)
new_esEs24(zzz500001, zzz4300001, ty_Ordering) → new_esEs8(zzz500001, zzz4300001)
new_primPlusInt2(Neg(zzz6060), zzz557, zzz554, zzz556, bce, bcf) → new_primPlusInt0(zzz6060, new_sizeFM1(zzz557, bce, bcf))
new_ltEs8(zzz50000, zzz430000) → new_fsEs(new_compare14(zzz50000, zzz430000))
new_esEs28(zzz5000, zzz4000, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_esEs7(Nothing, Nothing, eb) → True
new_sizeFM(zzz760, zzz761, zzz762, zzz763, zzz764, be, bf) → zzz762
new_esEs8(EQ, LT) → False
new_esEs8(LT, EQ) → False
new_esEs18(zzz5001, zzz4001, app(ty_Maybe, cfa)) → new_esEs7(zzz5001, zzz4001, cfa)
new_primEqInt(Pos(Succ(zzz50000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(zzz40000))) → False
new_lt20(zzz500001, zzz4300001, app(ty_Ratio, bfa)) → new_lt17(zzz500001, zzz4300001, bfa)
new_compare30(zzz500000, zzz4300000, ty_Int) → new_compare8(zzz500000, zzz4300000)
new_mkBalBranch6MkBalBranch01(zzz760, zzz761, zzz7640, zzz7641, zzz7642, Branch(zzz76430, zzz76431, zzz76432, zzz76433, zzz76434), zzz7644, zzz154, False, be, bf) → new_mkBranch(Succ(Succ(Succ(Succ(Zero)))), zzz76430, zzz76431, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Zero))))), zzz760, zzz761, zzz154, zzz76433, app(ty_Maybe, be), bf), new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz7640, zzz7641, zzz76434, zzz7644, app(ty_Maybe, be), bf), app(ty_Maybe, be), bf)
new_compare24(zzz500000, zzz4300000, False, gb, gc, gd) → new_compare110(zzz500000, zzz4300000, new_ltEs16(zzz500000, zzz4300000, gb, gc, gd), gb, gc, gd)
new_esEs31(zzz500, zzz400, app(app(ty_@2, gg), gh)) → new_esEs5(zzz500, zzz400, gg, gh)
new_esEs24(zzz500001, zzz4300001, ty_@0) → new_esEs10(zzz500001, zzz4300001)
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(zzz5000000), Zero) → GT
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Integer, chf) → new_ltEs9(zzz500000, zzz4300000)
new_esEs23(zzz500000, zzz4300000, app(app(ty_@2, fh), ga)) → new_esEs5(zzz500000, zzz4300000, fh, ga)
new_esEs31(zzz500, zzz400, app(ty_Ratio, he)) → new_esEs16(zzz500, zzz400, he)
new_esEs4(Right(zzz5000), Right(zzz4000), ge, ty_@0) → new_esEs10(zzz5000, zzz4000)
new_ltEs10(LT, EQ) → True
new_primCmpInt(Neg(Zero), Pos(Succ(zzz430000))) → LT
new_compare19(zzz500000, zzz4300000, False) → GT
new_esEs27(zzz5001, zzz4001, ty_Double) → new_esEs9(zzz5001, zzz4001)
new_splitGT11(zzz440, zzz441, zzz442, zzz443, zzz444, True, be, bh) → new_mkVBalBranch0(zzz440, zzz441, new_splitGT3(zzz443, be, bh), zzz444, be, bh)
new_ltEs15(zzz50000, zzz430000, dcf) → new_fsEs(new_compare7(zzz50000, zzz430000, dcf))
new_esEs23(zzz500000, zzz4300000, ty_Float) → new_esEs13(zzz500000, zzz4300000)
new_primPlusNat1(Succ(zzz22100), Succ(zzz4000000)) → Succ(Succ(new_primPlusNat1(zzz22100, zzz4000000)))
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Integer) → new_esEs15(zzz5000, zzz4000)
new_primEqInt(Neg(Succ(zzz50000)), Pos(zzz4000)) → False
new_primEqInt(Pos(Succ(zzz50000)), Neg(zzz4000)) → False
new_compare29(Just(zzz50000), Just(zzz430000), False, hg) → new_compare111(zzz50000, zzz430000, new_ltEs18(zzz50000, zzz430000, hg), hg)
new_esEs7(Nothing, Just(zzz4000), eb) → False
new_esEs7(Just(zzz5000), Nothing, eb) → False
new_lt13(zzz500000, zzz4300000, app(ty_Ratio, bcd)) → new_lt17(zzz500000, zzz4300000, bcd)
new_esEs18(zzz5001, zzz4001, app(ty_[], cee)) → new_esEs12(zzz5001, zzz4001, cee)
new_esEs28(zzz5000, zzz4000, ty_Char) → new_esEs11(zzz5000, zzz4000)
new_mkBalBranch6MkBalBranch3(zzz760, zzz761, zzz764, EmptyFM, True, be, bf) → error([])
new_ltEs10(GT, GT) → True
new_esEs26(zzz5002, zzz4002, app(ty_Ratio, caa)) → new_esEs16(zzz5002, zzz4002, caa)
new_esEs26(zzz5002, zzz4002, ty_Int) → new_esEs17(zzz5002, zzz4002)
new_mkVBalBranch3MkVBalBranch10(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, True, be, bh) → new_mkBalBranch(zzz3540, zzz3541, zzz3543, new_mkVBalBranch0(zzz440, zzz441, zzz3544, Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), be, bh), be, bh)
new_splitGT12(zzz2640, zzz2641, zzz2642, zzz2643, zzz2644, zzz265, False, cf, db) → zzz2644
new_esEs4(Right(zzz5000), Right(zzz4000), ge, ty_Bool) → new_esEs14(zzz5000, zzz4000)
new_primCmpInt(Neg(Succ(zzz50000)), Neg(Zero)) → LT
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_@0, chf) → new_ltEs11(zzz500000, zzz4300000)
new_primEqInt(Neg(Zero), Pos(Succ(zzz40000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(zzz40000))) → False
new_esEs20(zzz5000, zzz4000, app(ty_[], cgh)) → new_esEs12(zzz5000, zzz4000, cgh)
new_ltEs6(zzz50000, zzz430000) → new_fsEs(new_compare8(zzz50000, zzz430000))
new_esEs21(zzz5001, zzz4001, ty_Integer) → new_esEs15(zzz5001, zzz4001)
new_esEs31(zzz500, zzz400, ty_Integer) → new_esEs15(zzz500, zzz400)
new_primCompAux00(zzz225, EQ) → zzz225
new_primCmpInt(Pos(Zero), Pos(Succ(zzz430000))) → new_primCmpNat0(Zero, Succ(zzz430000))
new_compare30(zzz500000, zzz4300000, app(app(ty_@2, dda), ddb)) → new_compare18(zzz500000, zzz4300000, dda, ddb)
new_gt(zzz440, zzz4440, be) → new_esEs8(new_compare28(zzz440, zzz4440, be), GT)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Double, gf) → new_esEs9(zzz5000, zzz4000)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Integer, gf) → new_esEs15(zzz5000, zzz4000)
new_esEs18(zzz5001, zzz4001, ty_Int) → new_esEs17(zzz5001, zzz4001)
new_lt16(zzz500000, zzz4300000, fh, ga) → new_esEs8(new_compare18(zzz500000, zzz4300000, fh, ga), LT)
new_esEs8(GT, EQ) → False
new_esEs8(EQ, GT) → False
new_splitLT21(zzz2630, zzz2631, zzz2632, zzz2633, zzz2634, zzz265, True, cf, db) → new_splitLT4(zzz2633, zzz265, cf, db)
new_esEs29(zzz500, Just(zzz4300), app(app(ty_@2, gg), gh)) → new_esEs5(zzz500, zzz4300, gg, gh)
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Double) → new_esEs9(zzz5000, zzz4000)
new_emptyFM(be, bf) → EmptyFM
new_esEs27(zzz5001, zzz4001, app(ty_Ratio, cbc)) → new_esEs16(zzz5001, zzz4001, cbc)
new_esEs26(zzz5002, zzz4002, ty_Char) → new_esEs11(zzz5002, zzz4002)
new_esEs26(zzz5002, zzz4002, app(app(ty_@2, bhb), bhc)) → new_esEs5(zzz5002, zzz4002, bhb, bhc)
new_esEs29(zzz500, Just(zzz4300), ty_Bool) → new_esEs14(zzz500, zzz4300)
new_ltEs19(zzz500001, zzz4300001, app(app(ty_@2, dee), def)) → new_ltEs13(zzz500001, zzz4300001, dee, def)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Bool) → new_ltEs14(zzz500000, zzz4300000)
new_not(False) → True
new_esEs24(zzz500001, zzz4300001, ty_Double) → new_esEs9(zzz500001, zzz4300001)
new_primPlusNat0(Zero, zzz400000) → Succ(zzz400000)
new_ltEs5(zzz50000, zzz430000) → new_fsEs(new_compare10(zzz50000, zzz430000))
new_splitGT4(Branch(zzz26440, zzz26441, zzz26442, zzz26443, zzz26444), zzz265, cf, db) → new_splitGT22(zzz26440, zzz26441, zzz26442, zzz26443, zzz26444, zzz265, new_gt(Just(zzz265), zzz26440, cf), cf, db)
new_mkVBalBranch3Size_l(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, be, bh) → new_sizeFM(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, be, bh)
new_esEs25(zzz500000, zzz4300000, ty_Integer) → new_esEs15(zzz500000, zzz4300000)
new_esEs26(zzz5002, zzz4002, ty_Bool) → new_esEs14(zzz5002, zzz4002)
new_esEs25(zzz500000, zzz4300000, app(ty_Ratio, bdg)) → new_esEs16(zzz500000, zzz4300000, bdg)
new_ltEs19(zzz500001, zzz4300001, ty_Int) → new_ltEs6(zzz500001, zzz4300001)
new_splitGT3(EmptyFM, be, bh) → new_emptyFM(be, bh)
new_esEs4(Right(zzz5000), Right(zzz4000), ge, ty_Int) → new_esEs17(zzz5000, zzz4000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Bool, chf) → new_ltEs14(zzz500000, zzz4300000)
new_esEs28(zzz5000, zzz4000, app(app(ty_@2, cbf), cbg)) → new_esEs5(zzz5000, zzz4000, cbf, cbg)
new_primPlusInt1(Branch(zzz1540, zzz1541, Pos(zzz15420), zzz1543, zzz1544), zzz760, zzz761, zzz764, be, bf) → new_primPlusInt(zzz15420, new_sizeFM0(zzz764, be, bf))
new_mkBalBranch6MkBalBranch3(zzz760, zzz761, zzz764, zzz154, False, be, bf) → new_mkBranch(Succ(Zero), zzz760, zzz761, zzz154, zzz764, app(ty_Maybe, be), bf)
new_compare30(zzz500000, zzz4300000, ty_@0) → new_compare11(zzz500000, zzz4300000)
new_esEs23(zzz500000, zzz4300000, ty_@0) → new_esEs10(zzz500000, zzz4300000)
new_esEs18(zzz5001, zzz4001, app(app(ty_Either, cea), ceb)) → new_esEs4(zzz5001, zzz4001, cea, ceb)
new_lt18(zzz500000, zzz4300000, deb) → new_esEs8(new_compare4(zzz500000, zzz4300000, deb), LT)
new_ltEs18(zzz50000, zzz430000, ty_Int) → new_ltEs6(zzz50000, zzz430000)
new_intersectFM_C2Lts1(zzz261, zzz262, zzz263, zzz264, zzz265, cf, db) → new_splitLT21(Nothing, zzz261, zzz262, zzz263, zzz264, zzz265, new_lt11(Just(zzz265), Nothing, cf), cf, db)
new_esEs22(zzz5000, zzz4000, ty_Int) → new_esEs17(zzz5000, zzz4000)
new_esEs6(@3(zzz5000, zzz5001, zzz5002), @3(zzz4000, zzz4001, zzz4002), hb, hc, hd) → new_asAs(new_esEs28(zzz5000, zzz4000, hb), new_asAs(new_esEs27(zzz5001, zzz4001, hc), new_esEs26(zzz5002, zzz4002, hd)))
new_primCmpInt(Pos(Succ(zzz50000)), Neg(zzz43000)) → GT
new_esEs28(zzz5000, zzz4000, app(ty_Maybe, ccd)) → new_esEs7(zzz5000, zzz4000, ccd)
new_esEs28(zzz5000, zzz4000, ty_Double) → new_esEs9(zzz5000, zzz4000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), dba, ty_Double) → new_ltEs8(zzz500000, zzz4300000)
new_lt20(zzz500001, zzz4300001, ty_Double) → new_lt15(zzz500001, zzz4300001)
new_esEs26(zzz5002, zzz4002, ty_@0) → new_esEs10(zzz5002, zzz4002)
new_lt20(zzz500001, zzz4300001, ty_Integer) → new_lt10(zzz500001, zzz4300001)
new_primMulInt(Pos(zzz50000), Pos(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_esEs18(zzz5001, zzz4001, ty_Float) → new_esEs13(zzz5001, zzz4001)
new_compare25(zzz500000, zzz4300000, False, fh, ga) → new_compare15(zzz500000, zzz4300000, new_ltEs13(zzz500000, zzz4300000, fh, ga), fh, ga)
new_esEs23(zzz500000, zzz4300000, app(app(ty_Either, ff), fg)) → new_esEs4(zzz500000, zzz4300000, ff, fg)
new_esEs20(zzz5000, zzz4000, ty_Char) → new_esEs11(zzz5000, zzz4000)
new_esEs4(Left(zzz5000), Left(zzz4000), app(ty_Maybe, bah), gf) → new_esEs7(zzz5000, zzz4000, bah)
new_lt19(zzz500000, zzz4300000, app(ty_Maybe, bdf)) → new_lt11(zzz500000, zzz4300000, bdf)
new_mkVBalBranch3MkVBalBranch20(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, True, be, bh) → new_mkBalBranch(zzz4440, zzz4441, new_mkVBalBranch0(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), zzz4443, be, bh), zzz4444, be, bh)
new_primMulInt(Neg(zzz50000), Neg(zzz40000)) → Pos(new_primMulNat0(zzz50000, zzz40000))
new_esEs20(zzz5000, zzz4000, ty_Integer) → new_esEs15(zzz5000, zzz4000)
new_primEqNat0(Zero, Succ(zzz40000)) → False
new_primEqNat0(Succ(zzz50000), Zero) → False
new_esEs18(zzz5001, zzz4001, ty_Integer) → new_esEs15(zzz5001, zzz4001)
new_esEs17(zzz500, zzz400) → new_primEqInt(zzz500, zzz400)
new_lt5(zzz500000, zzz4300000, ff, fg) → new_esEs8(new_compare12(zzz500000, zzz4300000, ff, fg), LT)
new_mkVBalBranch0(zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), EmptyFM, be, bh) → new_addToFM(Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), zzz440, zzz441, be, bh)
new_compare25(zzz500000, zzz4300000, True, fh, ga) → EQ
new_esEs20(zzz5000, zzz4000, ty_Bool) → new_esEs14(zzz5000, zzz4000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), app(app(ty_Either, chg), chh), chf) → new_ltEs7(zzz500000, zzz4300000, chg, chh)
new_ltEs14(True, True) → True
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs28(zzz5000, zzz4000, app(app(app(ty_@3, cca), ccb), ccc)) → new_esEs6(zzz5000, zzz4000, cca, ccb, ccc)
new_esEs24(zzz500001, zzz4300001, app(app(ty_Either, bed), bee)) → new_esEs4(zzz500001, zzz4300001, bed, bee)
new_compare30(zzz500000, zzz4300000, ty_Bool) → new_compare17(zzz500000, zzz4300000)
new_esEs27(zzz5001, zzz4001, app(app(ty_Either, cab), cac)) → new_esEs4(zzz5001, zzz4001, cab, cac)
new_splitGT22(zzz2640, zzz2641, zzz2642, zzz2643, zzz2644, zzz265, False, cf, db) → new_splitGT12(zzz2640, zzz2641, zzz2642, zzz2643, zzz2644, zzz265, new_lt11(Just(zzz265), zzz2640, cf), cf, db)
new_esEs27(zzz5001, zzz4001, app(app(app(ty_@3, cag), cah), cba)) → new_esEs6(zzz5001, zzz4001, cag, cah, cba)
new_compare4(:(zzz500000, zzz500001), [], ea) → GT
new_ltEs18(zzz50000, zzz430000, app(ty_[], ea)) → new_ltEs17(zzz50000, zzz430000, ea)
new_esEs27(zzz5001, zzz4001, app(app(ty_@2, cad), cae)) → new_esEs5(zzz5001, zzz4001, cad, cae)
new_mkVBalBranch3MkVBalBranch10(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz3540, zzz3541, zzz3542, zzz3543, zzz3544, zzz440, zzz441, False, be, bh) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), zzz440, zzz441, Branch(zzz3540, zzz3541, zzz3542, zzz3543, zzz3544), Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), app(ty_Maybe, be), bh)
new_esEs27(zzz5001, zzz4001, ty_Int) → new_esEs17(zzz5001, zzz4001)
new_sizeFM0(EmptyFM, be, bf) → Pos(Zero)
new_mkBalBranch6MkBalBranch4(zzz760, zzz761, Branch(zzz7640, zzz7641, zzz7642, zzz7643, zzz7644), zzz154, True, be, bf) → new_mkBalBranch6MkBalBranch01(zzz760, zzz761, zzz7640, zzz7641, zzz7642, zzz7643, zzz7644, zzz154, new_lt14(new_sizeFM0(zzz7643, be, bf), new_sr0(Pos(Succ(Succ(Zero))), new_sizeFM0(zzz7644, be, bf))), be, bf)
new_esEs23(zzz500000, zzz4300000, ty_Int) → new_esEs17(zzz500000, zzz4300000)
new_lt13(zzz500000, zzz4300000, ty_@0) → new_lt4(zzz500000, zzz4300000)
new_compare30(zzz500000, zzz4300000, ty_Char) → new_compare10(zzz500000, zzz4300000)
new_primMinusNat0(Zero, Zero) → Pos(Zero)
new_esEs29(zzz500, Just(zzz4300), ty_@0) → new_esEs10(zzz500, zzz4300)
new_primCmpInt(Neg(Zero), Neg(Succ(zzz430000))) → new_primCmpNat0(Succ(zzz430000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(zzz430000))) → GT
new_splitGT11(zzz440, zzz441, zzz442, zzz443, zzz444, False, be, bh) → zzz444
new_compare4([], :(zzz4300000, zzz4300001), ea) → LT
new_primPlusInt(zzz15420, Pos(zzz4400)) → Pos(new_primPlusNat1(zzz15420, zzz4400))
new_sr0(zzz5000, zzz4000) → new_primMulInt(zzz5000, zzz4000)
new_compare15(zzz500000, zzz4300000, False, fh, ga) → GT
new_lt19(zzz500000, zzz4300000, app(ty_[], bec)) → new_lt18(zzz500000, zzz4300000, bec)
new_sIZE_RATIO → Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_ltEs18(zzz50000, zzz430000, ty_Integer) → new_ltEs9(zzz50000, zzz430000)
new_ltEs18(zzz50000, zzz430000, ty_Float) → new_ltEs12(zzz50000, zzz430000)
new_ltEs19(zzz500001, zzz4300001, ty_Double) → new_ltEs8(zzz500001, zzz4300001)
new_mkBalBranch6MkBalBranch4(zzz760, zzz761, EmptyFM, zzz154, True, be, bf) → error([])
new_compare30(zzz500000, zzz4300000, ty_Float) → new_compare16(zzz500000, zzz4300000)
new_primPlusInt2(Pos(zzz6060), zzz557, zzz554, zzz556, bce, bcf) → new_primPlusInt(zzz6060, new_sizeFM1(zzz557, bce, bcf))
new_ltEs7(Left(zzz500000), Left(zzz4300000), app(ty_[], dah), chf) → new_ltEs17(zzz500000, zzz4300000, dah)
new_esEs11(Char(zzz5000), Char(zzz4000)) → new_primEqNat0(zzz5000, zzz4000)
new_esEs25(zzz500000, zzz4300000, app(ty_Maybe, bdf)) → new_esEs7(zzz500000, zzz4300000, bdf)
new_esEs7(Just(zzz5000), Just(zzz4000), app(app(app(ty_@3, eh), fa), fb)) → new_esEs6(zzz5000, zzz4000, eh, fa, fb)
new_compare29(Nothing, Nothing, False, hg) → LT
new_primPlusInt(zzz15420, Neg(zzz4400)) → new_primMinusNat0(zzz15420, zzz4400)
new_esEs31(zzz500, zzz400, ty_Int) → new_esEs17(zzz500, zzz400)
new_lt13(zzz500000, zzz4300000, app(app(ty_Either, ff), fg)) → new_lt5(zzz500000, zzz4300000, ff, fg)
new_esEs23(zzz500000, zzz4300000, app(ty_Ratio, bcd)) → new_esEs16(zzz500000, zzz4300000, bcd)
new_esEs16(:%(zzz5000, zzz5001), :%(zzz4000, zzz4001), he) → new_asAs(new_esEs22(zzz5000, zzz4000, he), new_esEs21(zzz5001, zzz4001, he))
new_ltEs4(Just(zzz500000), Just(zzz4300000), app(ty_Maybe, cdc)) → new_ltEs4(zzz500000, zzz4300000, cdc)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Float) → new_ltEs12(zzz500000, zzz4300000)
new_esEs19(zzz5000, zzz4000, app(app(ty_@2, cfe), cff)) → new_esEs5(zzz5000, zzz4000, cfe, cff)
new_primCompAux0(zzz500000, zzz4300000, zzz220, ea) → new_primCompAux00(zzz220, new_compare30(zzz500000, zzz4300000, ea))
new_esEs19(zzz5000, zzz4000, app(ty_Ratio, cgc)) → new_esEs16(zzz5000, zzz4000, cgc)
new_esEs10(@0, @0) → True
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_compare29(zzz5000, zzz43000, True, hg) → EQ
new_esEs27(zzz5001, zzz4001, ty_Float) → new_esEs13(zzz5001, zzz4001)
new_gt2(zzz438, zzz437) → new_esEs8(new_compare8(zzz438, zzz437), GT)
new_lt13(zzz500000, zzz4300000, ty_Integer) → new_lt10(zzz500000, zzz4300000)
new_esEs4(Right(zzz5000), Right(zzz4000), ge, app(app(ty_@2, bbd), bbe)) → new_esEs5(zzz5000, zzz4000, bbd, bbe)
new_compare28(zzz5000, zzz43000, hg) → new_compare29(zzz5000, zzz43000, new_esEs7(zzz5000, zzz43000, hg), hg)
new_esEs24(zzz500001, zzz4300001, ty_Char) → new_esEs11(zzz500001, zzz4300001)
new_esEs28(zzz5000, zzz4000, ty_@0) → new_esEs10(zzz5000, zzz4000)
new_ltEs7(Right(zzz500000), Right(zzz4300000), dba, app(app(ty_Either, dbb), dbc)) → new_ltEs7(zzz500000, zzz4300000, dbb, dbc)
new_esEs28(zzz5000, zzz4000, ty_Int) → new_esEs17(zzz5000, zzz4000)
new_compare7(:%(zzz500000, zzz500001), :%(zzz4300000, zzz4300001), ty_Integer) → new_compare9(new_sr(zzz500000, zzz4300001), new_sr(zzz4300000, zzz500001))
new_compare9(Integer(zzz500000), Integer(zzz4300000)) → new_primCmpInt(zzz500000, zzz4300000)
new_compare23(zzz500000, zzz4300000, False) → new_compare112(zzz500000, zzz4300000, new_ltEs10(zzz500000, zzz4300000))
new_asAs(False, zzz207) → False
new_addToFM_C0(Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), zzz440, zzz441, be, bh) → new_addToFM_C20(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz440, zzz441, new_lt11(zzz440, zzz4440, be), be, bh)
new_esEs29(zzz500, Just(zzz4300), ty_Float) → new_esEs13(zzz500, zzz4300)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_@0, gf) → new_esEs10(zzz5000, zzz4000)
new_primMulInt(Pos(zzz50000), Neg(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_primMulInt(Neg(zzz50000), Pos(zzz40000)) → Neg(new_primMulNat0(zzz50000, zzz40000))
new_esEs26(zzz5002, zzz4002, ty_Double) → new_esEs9(zzz5002, zzz4002)
new_sizeFM1(EmptyFM, bce, bcf) → Pos(Zero)
new_ltEs10(LT, GT) → True
new_primMulNat0(Succ(zzz500000), Zero) → Zero
new_primMulNat0(Zero, Succ(zzz400000)) → Zero
new_ltEs4(Just(zzz500000), Just(zzz4300000), app(ty_Ratio, cdd)) → new_ltEs15(zzz500000, zzz4300000, cdd)
new_lt8(zzz500000, zzz4300000, gb, gc, gd) → new_esEs8(new_compare13(zzz500000, zzz4300000, gb, gc, gd), LT)
new_lt11(zzz5000, zzz43000, hg) → new_esEs8(new_compare28(zzz5000, zzz43000, hg), LT)
new_esEs23(zzz500000, zzz4300000, app(app(app(ty_@3, gb), gc), gd)) → new_esEs6(zzz500000, zzz4300000, gb, gc, gd)
new_esEs26(zzz5002, zzz4002, app(ty_[], bhd)) → new_esEs12(zzz5002, zzz4002, bhd)
new_esEs29(zzz500, Just(zzz4300), ty_Int) → new_esEs17(zzz500, zzz4300)
new_compare4(:(zzz500000, zzz500001), :(zzz4300000, zzz4300001), ea) → new_primCompAux0(zzz500000, zzz4300000, new_compare4(zzz500001, zzz4300001, ea), ea)
new_esEs31(zzz500, zzz400, ty_Double) → new_esEs9(zzz500, zzz400)
new_compare16(Float(zzz500000, zzz500001), Float(zzz4300000, zzz4300001)) → new_compare8(new_sr0(zzz500000, zzz4300000), new_sr0(zzz500001, zzz4300001))
new_esEs26(zzz5002, zzz4002, app(ty_Maybe, bhh)) → new_esEs7(zzz5002, zzz4002, bhh)
new_esEs28(zzz5000, zzz4000, ty_Bool) → new_esEs14(zzz5000, zzz4000)
new_compare110(zzz500000, zzz4300000, True, gb, gc, gd) → LT
new_lt19(zzz500000, zzz4300000, app(app(ty_Either, bdb), bdc)) → new_lt5(zzz500000, zzz4300000, bdb, bdc)
new_mkBalBranch6MkBalBranch3(zzz760, zzz761, zzz764, Branch(zzz1540, zzz1541, zzz1542, zzz1543, zzz1544), True, be, bf) → new_mkBalBranch6MkBalBranch11(zzz760, zzz761, zzz764, zzz1540, zzz1541, zzz1542, zzz1543, zzz1544, new_lt14(new_sizeFM0(zzz1544, be, bf), new_sr0(Pos(Succ(Succ(Zero))), new_sizeFM0(zzz1543, be, bf))), be, bf)
new_ltEs18(zzz50000, zzz430000, ty_Bool) → new_ltEs14(zzz50000, zzz430000)
new_esEs28(zzz5000, zzz4000, ty_Integer) → new_esEs15(zzz5000, zzz4000)
new_esEs18(zzz5001, zzz4001, ty_Ordering) → new_esEs8(zzz5001, zzz4001)
new_esEs19(zzz5000, zzz4000, ty_Double) → new_esEs9(zzz5000, zzz4000)
new_esEs5(@2(zzz5000, zzz5001), @2(zzz4000, zzz4001), gg, gh) → new_asAs(new_esEs19(zzz5000, zzz4000, gg), new_esEs18(zzz5001, zzz4001, gh))
new_esEs28(zzz5000, zzz4000, app(app(ty_Either, cbd), cbe)) → new_esEs4(zzz5000, zzz4000, cbd, cbe)
new_lt20(zzz500001, zzz4300001, app(app(ty_@2, bef), beg)) → new_lt16(zzz500001, zzz4300001, bef, beg)
new_compare26(zzz500000, zzz4300000, False) → new_compare19(zzz500000, zzz4300000, new_ltEs14(zzz500000, zzz4300000))
new_splitLT11(zzz430, zzz431, zzz432, zzz433, zzz434, False, be, bh) → zzz433
new_esEs4(Right(zzz5000), Right(zzz4000), ge, app(ty_Maybe, bcb)) → new_esEs7(zzz5000, zzz4000, bcb)
new_esEs7(Just(zzz5000), Just(zzz4000), ty_@0) → new_esEs10(zzz5000, zzz4000)
new_esEs28(zzz5000, zzz4000, ty_Float) → new_esEs13(zzz5000, zzz4000)
new_ltEs18(zzz50000, zzz430000, ty_Char) → new_ltEs5(zzz50000, zzz430000)
new_lt13(zzz500000, zzz4300000, ty_Ordering) → new_lt9(zzz500000, zzz4300000)
new_esEs25(zzz500000, zzz4300000, app(app(app(ty_@3, bdh), bea), beb)) → new_esEs6(zzz500000, zzz4300000, bdh, bea, beb)
new_ltEs10(EQ, EQ) → True
new_mkBalBranch6MkBalBranch01(zzz760, zzz761, zzz7640, zzz7641, zzz7642, EmptyFM, zzz7644, zzz154, False, be, bf) → error([])
new_ltEs18(zzz50000, zzz430000, app(app(ty_@2, dcd), dce)) → new_ltEs13(zzz50000, zzz430000, dcd, dce)
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Int, gf) → new_esEs17(zzz5000, zzz4000)
new_esEs23(zzz500000, zzz4300000, ty_Integer) → new_esEs15(zzz500000, zzz4300000)
new_intersectFM_C2Lts(zzz381, zzz382, zzz383, zzz384, h, bc) → new_splitLT3(Branch(Nothing, zzz381, zzz382, zzz383, zzz384), h, bc)
new_ltEs10(LT, LT) → True
new_esEs14(True, True) → True
new_compare111(zzz200, zzz201, False, hf) → GT
new_esEs27(zzz5001, zzz4001, ty_Bool) → new_esEs14(zzz5001, zzz4001)
new_esEs7(Just(zzz5000), Just(zzz4000), app(app(ty_Either, ec), ed)) → new_esEs4(zzz5000, zzz4000, ec, ed)
new_compare10(Char(zzz500000), Char(zzz4300000)) → new_primCmpNat0(zzz500000, zzz4300000)
new_primMinusNat0(Zero, Succ(zzz44000)) → Neg(Succ(zzz44000))
new_esEs30(Just(zzz4300), be) → False
new_esEs4(Left(zzz5000), Left(zzz4000), ty_Float, gf) → new_esEs13(zzz5000, zzz4000)
new_mkBalBranch6MkBalBranch01(zzz760, zzz761, zzz7640, zzz7641, zzz7642, zzz7643, zzz7644, zzz154, True, be, bf) → new_mkBranch(Succ(Succ(Zero)), zzz7640, zzz7641, new_mkBranch(Succ(Succ(Succ(Zero))), zzz760, zzz761, zzz154, zzz7643, app(ty_Maybe, be), bf), zzz7644, app(ty_Maybe, be), bf)
new_lt13(zzz500000, zzz4300000, app(app(ty_@2, fh), ga)) → new_lt16(zzz500000, zzz4300000, fh, ga)
new_esEs7(Just(zzz5000), Just(zzz4000), app(ty_Ratio, fd)) → new_esEs16(zzz5000, zzz4000, fd)
new_ltEs7(Left(zzz500000), Left(zzz4300000), app(app(ty_@2, daa), dab), chf) → new_ltEs13(zzz500000, zzz4300000, daa, dab)
new_lt13(zzz500000, zzz4300000, app(ty_Maybe, dea)) → new_lt11(zzz500000, zzz4300000, dea)
new_ltEs20(zzz500002, zzz4300002, app(app(ty_Either, bff), bfg)) → new_ltEs7(zzz500002, zzz4300002, bff, bfg)
new_esEs31(zzz500, zzz400, ty_Char) → new_esEs11(zzz500, zzz400)
new_esEs18(zzz5001, zzz4001, ty_@0) → new_esEs10(zzz5001, zzz4001)
new_ltEs16(@3(zzz500000, zzz500001, zzz500002), @3(zzz4300000, zzz4300001, zzz4300002), bcg, bch, bda) → new_pePe(new_lt19(zzz500000, zzz4300000, bcg), new_asAs(new_esEs25(zzz500000, zzz4300000, bcg), new_pePe(new_lt20(zzz500001, zzz4300001, bch), new_asAs(new_esEs24(zzz500001, zzz4300001, bch), new_ltEs20(zzz500002, zzz4300002, bda)))))
new_ltEs14(True, False) → False
new_esEs4(Right(zzz5000), Right(zzz4000), ge, ty_Double) → new_esEs9(zzz5000, zzz4000)
new_intersectFM_C2Gts1(zzz261, zzz262, zzz263, zzz264, zzz265, cf, db) → new_splitGT22(Nothing, zzz261, zzz262, zzz263, zzz264, zzz265, new_gt0(zzz265, Nothing, cf), cf, db)
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Zero)) → GT
new_esEs20(zzz5000, zzz4000, ty_Int) → new_esEs17(zzz5000, zzz4000)
new_primCmpInt(Pos(Succ(zzz50000)), Pos(Succ(zzz430000))) → new_primCmpNat0(zzz50000, zzz430000)
new_esEs25(zzz500000, zzz4300000, app(app(ty_@2, bdd), bde)) → new_esEs5(zzz500000, zzz4300000, bdd, bde)
new_esEs31(zzz500, zzz400, ty_Float) → new_esEs13(zzz500, zzz400)
new_ltEs20(zzz500002, zzz4300002, ty_Double) → new_ltEs8(zzz500002, zzz4300002)
new_gt1(zzz430, be) → new_esEs8(new_compare32(zzz430, be), GT)
new_ltEs7(Left(zzz500000), Left(zzz4300000), app(ty_Ratio, dad), chf) → new_ltEs15(zzz500000, zzz4300000, dad)
new_ltEs20(zzz500002, zzz4300002, app(app(app(ty_@3, bgd), bge), bgf)) → new_ltEs16(zzz500002, zzz4300002, bgd, bge, bgf)
new_ltEs19(zzz500001, zzz4300001, app(app(app(ty_@3, dfa), dfb), dfc)) → new_ltEs16(zzz500001, zzz4300001, dfa, dfb, dfc)
new_compare112(zzz500000, zzz4300000, False) → GT
new_esEs29(zzz500, Just(zzz4300), app(app(app(ty_@3, hb), hc), hd)) → new_esEs6(zzz500, zzz4300, hb, hc, hd)
new_ltEs10(EQ, LT) → False
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Float) → new_esEs13(zzz5000, zzz4000)
new_esEs14(False, False) → True
new_intersectFM_C2Lts2(zzz279, zzz280, zzz281, zzz282, zzz283, zzz284, dd, dg) → new_splitLT21(Just(zzz279), zzz280, zzz281, zzz282, zzz283, zzz284, new_lt11(Just(zzz284), Just(zzz279), dd), dd, dg)
new_esEs7(Just(zzz5000), Just(zzz4000), app(app(ty_@2, ee), ef)) → new_esEs5(zzz5000, zzz4000, ee, ef)
new_lt20(zzz500001, zzz4300001, ty_Char) → new_lt12(zzz500001, zzz4300001)
new_intersectFM_C2Gts0(zzz245, zzz246, zzz247, zzz248, zzz249, ca, cd) → new_splitGT21(Just(zzz245), zzz246, zzz247, zzz248, zzz249, new_gt1(Just(zzz245), ca), ca, cd)
new_mkBalBranch6MkBalBranch11(zzz760, zzz761, zzz764, zzz1540, zzz1541, zzz1542, zzz1543, EmptyFM, False, be, bf) → error([])
new_esEs29(zzz500, Just(zzz4300), app(app(ty_Either, ge), gf)) → new_esEs4(zzz500, zzz4300, ge, gf)
new_splitGT21(zzz440, zzz441, zzz442, zzz443, zzz444, True, be, bh) → new_splitGT3(zzz444, be, bh)
new_lt9(zzz500000, zzz4300000) → new_esEs8(new_compare6(zzz500000, zzz4300000), LT)
new_ltEs10(GT, LT) → False
new_esEs18(zzz5001, zzz4001, ty_Bool) → new_esEs14(zzz5001, zzz4001)
new_mkBranch(zzz553, zzz554, zzz555, zzz556, zzz557, bce, bcf) → Branch(zzz554, zzz555, new_primPlusInt2(new_primPlusInt(Succ(Zero), new_sizeFM1(zzz556, bce, bcf)), zzz557, zzz554, zzz556, bce, bcf), zzz556, zzz557)
new_esEs22(zzz5000, zzz4000, ty_Integer) → new_esEs15(zzz5000, zzz4000)
new_primPlusNat1(Zero, Zero) → Zero
new_addToFM_C0(EmptyFM, zzz440, zzz441, be, bh) → Branch(zzz440, zzz441, Pos(Succ(Zero)), new_emptyFM(be, bh), new_emptyFM(be, bh))
new_mkBalBranch6Size_l(zzz760, zzz761, zzz764, zzz154, be, bf) → new_sizeFM0(zzz154, be, bf)
new_esEs19(zzz5000, zzz4000, ty_Integer) → new_esEs15(zzz5000, zzz4000)
new_compare30(zzz500000, zzz4300000, app(app(app(ty_@3, dde), ddf), ddg)) → new_compare13(zzz500000, zzz4300000, dde, ddf, ddg)
new_esEs4(Left(zzz5000), Left(zzz4000), app(ty_[], bad), gf) → new_esEs12(zzz5000, zzz4000, bad)
new_esEs26(zzz5002, zzz4002, app(app(ty_Either, bgh), bha)) → new_esEs4(zzz5002, zzz4002, bgh, bha)
new_asAs(True, zzz207) → zzz207
new_esEs28(zzz5000, zzz4000, app(ty_[], cbh)) → new_esEs12(zzz5000, zzz4000, cbh)
new_esEs27(zzz5001, zzz4001, app(ty_[], caf)) → new_esEs12(zzz5001, zzz4001, caf)
new_esEs19(zzz5000, zzz4000, app(app(ty_Either, cfc), cfd)) → new_esEs4(zzz5000, zzz4000, cfc, cfd)
new_ltEs4(Just(zzz500000), Nothing, ccf) → False
new_esEs20(zzz5000, zzz4000, ty_Double) → new_esEs9(zzz5000, zzz4000)
new_primMulNat0(Succ(zzz500000), Succ(zzz400000)) → new_primPlusNat0(new_primMulNat0(zzz500000, Succ(zzz400000)), zzz400000)
new_ltEs4(Just(zzz500000), Just(zzz4300000), app(ty_[], cdh)) → new_ltEs17(zzz500000, zzz4300000, cdh)
new_esEs4(Left(zzz5000), Right(zzz4000), ge, gf) → False
new_esEs4(Right(zzz5000), Left(zzz4000), ge, gf) → False
new_esEs29(zzz500, Just(zzz4300), ty_Ordering) → new_esEs8(zzz500, zzz4300)
new_esEs31(zzz500, zzz400, app(ty_Maybe, eb)) → new_esEs7(zzz500, zzz400, eb)
new_ltEs19(zzz500001, zzz4300001, ty_Float) → new_ltEs12(zzz500001, zzz4300001)
new_ltEs20(zzz500002, zzz4300002, app(ty_Maybe, bgb)) → new_ltEs4(zzz500002, zzz4300002, bgb)
new_primPlusInt0(zzz15420, Neg(zzz4420)) → Neg(new_primPlusNat1(zzz15420, zzz4420))
new_esEs4(Left(zzz5000), Left(zzz4000), app(app(app(ty_@3, bae), baf), bag), gf) → new_esEs6(zzz5000, zzz4000, bae, baf, bag)
new_fsEs(zzz210) → new_not(new_esEs8(zzz210, GT))
new_ltEs19(zzz500001, zzz4300001, ty_Char) → new_ltEs5(zzz500001, zzz4300001)
new_esEs19(zzz5000, zzz4000, ty_@0) → new_esEs10(zzz5000, zzz4000)
new_splitGT3(Branch(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444), be, bh) → new_splitGT21(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, new_gt1(zzz4440, be), be, bh)
new_esEs24(zzz500001, zzz4300001, ty_Float) → new_esEs13(zzz500001, zzz4300001)
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Bool) → new_esEs14(zzz5000, zzz4000)
new_ltEs7(Left(zzz500000), Left(zzz4300000), ty_Double, chf) → new_ltEs8(zzz500000, zzz4300000)
new_ltEs11(zzz50000, zzz430000) → new_fsEs(new_compare11(zzz50000, zzz430000))
new_lt20(zzz500001, zzz4300001, ty_Int) → new_lt14(zzz500001, zzz4300001)
new_esEs19(zzz5000, zzz4000, ty_Ordering) → new_esEs8(zzz5000, zzz4000)
new_esEs4(Right(zzz5000), Right(zzz4000), ge, ty_Float) → new_esEs13(zzz5000, zzz4000)
new_ltEs20(zzz500002, zzz4300002, app(app(ty_@2, bfh), bga)) → new_ltEs13(zzz500002, zzz4300002, bfh, bga)
new_esEs30(Nothing, be) → True
new_esEs31(zzz500, zzz400, ty_Bool) → new_esEs14(zzz500, zzz400)
new_addToFM_C10(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz440, zzz441, False, be, bh) → Branch(zzz440, zzz441, zzz4442, zzz4443, zzz4444)
new_esEs27(zzz5001, zzz4001, ty_Char) → new_esEs11(zzz5001, zzz4001)
new_ltEs20(zzz500002, zzz4300002, ty_Int) → new_ltEs6(zzz500002, zzz4300002)
new_splitLT4(Branch(zzz26330, zzz26331, zzz26332, zzz26333, zzz26334), zzz265, cf, db) → new_splitLT21(zzz26330, zzz26331, zzz26332, zzz26333, zzz26334, zzz265, new_lt11(Just(zzz265), zzz26330, cf), cf, db)
new_compare110(zzz500000, zzz4300000, False, gb, gc, gd) → GT
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Char) → new_ltEs5(zzz500000, zzz4300000)
new_esEs7(Just(zzz5000), Just(zzz4000), ty_Char) → new_esEs11(zzz5000, zzz4000)
new_splitLT12(zzz2630, zzz2631, zzz2632, zzz2633, zzz2634, zzz265, False, cf, db) → zzz2633
new_ltEs20(zzz500002, zzz4300002, ty_Integer) → new_ltEs9(zzz500002, zzz4300002)
new_addToFM_C10(zzz4440, zzz4441, zzz4442, zzz4443, zzz4444, zzz440, zzz441, True, be, bh) → new_mkBalBranch(zzz4440, zzz4441, zzz4443, new_addToFM_C0(zzz4444, zzz440, zzz441, be, bh), be, bh)
new_primCompAux00(zzz225, GT) → GT
new_mkBalBranch6Size_r(zzz760, zzz761, zzz764, zzz154, be, bf) → new_sizeFM0(zzz764, be, bf)
new_compare31(zzz500, zzz430, be) → new_compare29(Just(zzz500), zzz430, new_esEs29(zzz500, zzz430, be), be)
new_gt0(zzz500, zzz430, be) → new_esEs8(new_compare31(zzz500, zzz430, be), GT)
new_esEs29(zzz500, Just(zzz4300), app(ty_Ratio, he)) → new_esEs16(zzz500, zzz4300, he)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_ltEs7(Right(zzz500000), Right(zzz4300000), dba, app(ty_Maybe, dbf)) → new_ltEs4(zzz500000, zzz4300000, dbf)
new_lt19(zzz500000, zzz4300000, ty_Int) → new_lt14(zzz500000, zzz4300000)
new_ltEs4(Just(zzz500000), Just(zzz4300000), app(app(app(ty_@3, cde), cdf), cdg)) → new_ltEs16(zzz500000, zzz4300000, cde, cdf, cdg)
new_ltEs18(zzz50000, zzz430000, ty_Ordering) → new_ltEs10(zzz50000, zzz430000)
new_splitLT21(zzz2630, zzz2631, zzz2632, zzz2633, zzz2634, zzz265, False, cf, db) → new_splitLT12(zzz2630, zzz2631, zzz2632, zzz2633, zzz2634, zzz265, new_gt0(zzz265, zzz2630, cf), cf, db)
new_ltEs4(Just(zzz500000), Just(zzz4300000), ty_Integer) → new_ltEs9(zzz500000, zzz4300000)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_esEs27(zzz5001, zzz4001, ty_Integer) → new_esEs15(zzz5001, zzz4001)
new_ltEs7(Right(zzz500000), Right(zzz4300000), dba, ty_Float) → new_ltEs12(zzz500000, zzz4300000)
new_compare30(zzz500000, zzz4300000, ty_Ordering) → new_compare6(zzz500000, zzz4300000)
new_primCmpInt(Neg(Succ(zzz50000)), Pos(zzz43000)) → LT
new_ltEs7(Right(zzz500000), Right(zzz4300000), dba, ty_Int) → new_ltEs6(zzz500000, zzz4300000)
new_not(True) → False
new_primMinusNat0(Succ(zzz154200), Succ(zzz44000)) → new_primMinusNat0(zzz154200, zzz44000)

The set Q consists of the following terms:

new_compare23(x0, x1, True)
new_ltEs7(Right(x0), Right(x1), x2, ty_Float)
new_mkVBalBranch3MkVBalBranch10(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, False, x12, x13)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_lt14(x0, x1)
new_splitLT3(EmptyFM, x0, x1)
new_esEs31(x0, x1, ty_@0)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_asAs(True, x0)
new_mkBalBranch6MkBalBranch11(x0, x1, x2, x3, x4, x5, x6, x7, True, x8, x9)
new_compare19(x0, x1, True)
new_primMinusNat0(Zero, Zero)
new_esEs26(x0, x1, ty_@0)
new_ltEs4(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_Ordering)
new_mkVBalBranch3MkVBalBranch20(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, True, x12, x13)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs18(x0, x1, ty_Int)
new_compare31(x0, x1, x2)
new_primPlusNat1(Zero, Succ(x0))
new_compare30(x0, x1, app(ty_Ratio, x2))
new_compare30(x0, x1, ty_@0)
new_lt20(x0, x1, ty_Ordering)
new_esEs9(Double(x0, x1), Double(x2, x3))
new_primMulNat0(Succ(x0), Zero)
new_ltEs7(Right(x0), Right(x1), x2, ty_Integer)
new_lt19(x0, x1, ty_Double)
new_ltEs4(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primMulInt(Neg(x0), Neg(x1))
new_lt19(x0, x1, ty_Integer)
new_lt13(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, ty_@0)
new_esEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_primPlusNat1(Succ(x0), Zero)
new_esEs21(x0, x1, ty_Int)
new_compare29(Nothing, Just(x0), False, x1)
new_ltEs10(LT, LT)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, Just(x1), app(app(ty_Either, x2), x3))
new_esEs12([], :(x0, x1), x2)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_lt11(x0, x1, x2)
new_esEs23(x0, x1, ty_Bool)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_primPlusNat1(Succ(x0), Succ(x1))
new_mkBalBranch6MkBalBranch4(x0, x1, EmptyFM, x2, True, x3, x4)
new_esEs27(x0, x1, ty_Int)
new_esEs18(x0, x1, ty_Char)
new_esEs29(x0, Just(x1), ty_Bool)
new_esEs24(x0, x1, ty_Char)
new_ltEs14(True, False)
new_ltEs14(False, True)
new_esEs25(x0, x1, ty_Double)
new_mkBalBranch6MkBalBranch01(x0, x1, x2, x3, x4, x5, x6, x7, True, x8, x9)
new_gt1(x0, x1)
new_pePe(False, x0)
new_splitGT4(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs19(x0, x1, ty_Char)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, ty_Char)
new_esEs7(Just(x0), Just(x1), ty_Double)
new_esEs8(GT, GT)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, ty_@0)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_lt9(x0, x1)
new_lt19(x0, x1, ty_Ordering)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_esEs11(Char(x0), Char(x1))
new_esEs25(x0, x1, app(ty_[], x2))
new_mkBalBranch6MkBalBranch4(x0, x1, Branch(x2, x3, x4, x5, x6), x7, True, x8, x9)
new_esEs29(x0, Just(x1), ty_Integer)
new_sr0(x0, x1)
new_esEs8(LT, LT)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs31(x0, x1, ty_Bool)
new_compare6(x0, x1)
new_sizeFM1(EmptyFM, x0, x1)
new_compare30(x0, x1, ty_Double)
new_mkBalBranch6MkBalBranch5(x0, x1, x2, x3, False, x4, x5)
new_esEs7(Just(x0), Just(x1), ty_Char)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_compare15(x0, x1, False, x2, x3)
new_sizeFM1(Branch(x0, x1, x2, x3, x4), x5, x6)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_compare19(x0, x1, False)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs26(x0, x1, ty_Double)
new_esEs29(x0, Just(x1), ty_@0)
new_compare29(x0, x1, True, x2)
new_compare4(:(x0, x1), :(x2, x3), x4)
new_ltEs16(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_compare28(x0, x1, x2)
new_esEs29(x0, Just(x1), app(ty_[], x2))
new_compare25(x0, x1, False, x2, x3)
new_primPlusInt2(Pos(x0), x1, x2, x3, x4, x5)
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_splitGT12(x0, x1, x2, x3, x4, x5, False, x6, x7)
new_splitGT21(x0, x1, x2, x3, x4, True, x5, x6)
new_esEs17(x0, x1)
new_ltEs19(x0, x1, ty_Char)
new_esEs14(True, True)
new_compare26(x0, x1, True)
new_esEs18(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Char)
new_mkVBalBranch0(x0, x1, EmptyFM, x2, x3, x4)
new_ltEs7(Right(x0), Left(x1), x2, x3)
new_compare29(Just(x0), Nothing, False, x1)
new_ltEs7(Left(x0), Right(x1), x2, x3)
new_splitGT12(x0, x1, x2, x3, x4, x5, True, x6, x7)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_compare4([], :(x0, x1), x2)
new_compare112(x0, x1, False)
new_esEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs18(x0, x1, ty_Bool)
new_esEs18(x0, x1, app(ty_[], x2))
new_primEqNat0(Zero, Zero)
new_esEs20(x0, x1, ty_Float)
new_ltEs4(Just(x0), Just(x1), ty_Double)
new_esEs24(x0, x1, app(ty_[], x2))
new_compare30(x0, x1, ty_Char)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs20(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Double)
new_lt19(x0, x1, ty_Bool)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt18(x0, x1, x2)
new_mkBalBranch6MkBalBranch01(x0, x1, x2, x3, x4, Branch(x5, x6, x7, x8, x9), x10, x11, False, x12, x13)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_splitLT22(x0, x1, x2, x3, x4, True, x5, x6)
new_mkBalBranch6MkBalBranch3(x0, x1, x2, Branch(x3, x4, x5, x6, x7), True, x8, x9)
new_esEs25(x0, x1, ty_@0)
new_esEs18(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, ty_Integer)
new_compare17(x0, x1)
new_ltEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs18(x0, x1, app(ty_[], x2))
new_primPlusNat0(Zero, x0)
new_ltEs20(x0, x1, ty_Int)
new_primPlusInt1(EmptyFM, x0, x1, x2, x3, x4)
new_lt5(x0, x1, x2, x3)
new_primMulNat0(Zero, Zero)
new_compare25(x0, x1, True, x2, x3)
new_primCmpNat0(Succ(x0), Zero)
new_esEs4(Left(x0), Left(x1), ty_Integer, x2)
new_compare16(Float(x0, x1), Float(x2, x3))
new_ltEs20(x0, x1, ty_Integer)
new_compare30(x0, x1, ty_Ordering)
new_gt(x0, x1, x2)
new_splitLT22(x0, x1, x2, x3, x4, False, x5, x6)
new_esEs26(x0, x1, ty_Integer)
new_ltEs10(EQ, LT)
new_ltEs10(LT, EQ)
new_lt4(x0, x1)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_sizeFM0(EmptyFM, x0, x1)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_compare113(x0, x1, True, x2, x3)
new_compare4([], [], x0)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs19(x0, x1, ty_Bool)
new_mkBalBranch6MkBalBranch01(x0, x1, x2, x3, x4, EmptyFM, x5, x6, False, x7, x8)
new_esEs28(x0, x1, ty_@0)
new_primMulNat0(Succ(x0), Succ(x1))
new_intersectFM_C2Lts0(x0, x1, x2, x3, x4, x5, x6)
new_lt7(x0, x1)
new_esEs23(x0, x1, ty_Float)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Int)
new_sIZE_RATIO
new_ltEs19(x0, x1, ty_Double)
new_esEs29(x0, Just(x1), app(ty_Maybe, x2))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(x0, x1, ty_@0)
new_esEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs4(Left(x0), Right(x1), x2, x3)
new_esEs4(Right(x0), Left(x1), x2, x3)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_splitGT3(Branch(x0, x1, x2, x3, x4), x5, x6)
new_esEs23(x0, x1, ty_Char)
new_splitGT4(EmptyFM, x0, x1, x2)
new_compare9(Integer(x0), Integer(x1))
new_esEs24(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_Ordering)
new_ltEs4(Nothing, Just(x0), x1)
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_primPlusInt0(x0, Pos(x1))
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_Char)
new_esEs31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_mkBalBranch6Size_l(x0, x1, x2, x3, x4, x5)
new_splitLT21(x0, x1, x2, x3, x4, x5, True, x6, x7)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_Ordering)
new_esEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_addToFM_C0(Branch(x0, x1, x2, x3, x4), x5, x6, x7, x8)
new_fsEs(x0)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_compare30(x0, x1, app(ty_[], x2))
new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6)
new_ltEs11(x0, x1)
new_splitLT11(x0, x1, x2, x3, x4, True, x5, x6)
new_esEs23(x0, x1, ty_Double)
new_mkBalBranch6MkBalBranch3(x0, x1, x2, EmptyFM, True, x3, x4)
new_primMinusNat0(Succ(x0), Succ(x1))
new_lt13(x0, x1, ty_@0)
new_esEs16(:%(x0, x1), :%(x2, x3), x4)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs7(Right(x0), Right(x1), x2, ty_Int)
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs7(Just(x0), Nothing, x1)
new_emptyFM(x0, x1)
new_compare24(x0, x1, False, x2, x3, x4)
new_esEs7(Just(x0), Just(x1), ty_Int)
new_esEs4(Right(x0), Right(x1), x2, ty_Double)
new_intersectFM_C2Lts1(x0, x1, x2, x3, x4, x5, x6)
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_lt13(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpInt(Neg(Succ(x0)), Neg(Zero))
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_compare26(x0, x1, False)
new_esEs29(x0, Just(x1), ty_Char)
new_ltEs4(Nothing, Nothing, x0)
new_ltEs18(x0, x1, ty_Double)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs25(x0, x1, ty_Bool)
new_ltEs19(x0, x1, app(ty_[], x2))
new_primPlusNat1(Zero, Zero)
new_ltEs13(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs28(x0, x1, ty_Float)
new_primPlusInt1(Branch(x0, x1, Pos(x2), x3, x4), x5, x6, x7, x8, x9)
new_esEs29(x0, Just(x1), ty_Ordering)
new_lt12(x0, x1)
new_ltEs7(Left(x0), Left(x1), ty_Double, x2)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_splitGT21(x0, x1, x2, x3, x4, False, x5, x6)
new_compare7(:%(x0, x1), :%(x2, x3), ty_Int)
new_ltEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_mkVBalBranch0(x0, x1, Branch(x2, x3, x4, x5, x6), EmptyFM, x7, x8)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs4(Just(x0), Nothing, x1)
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_addToFM(x0, x1, x2, x3, x4)
new_ltEs4(Just(x0), Just(x1), ty_Int)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_compare11(@0, @0)
new_primMulNat0(Zero, Succ(x0))
new_asAs(False, x0)
new_esEs26(x0, x1, ty_Bool)
new_primPlusInt(x0, Neg(x1))
new_ltEs4(Just(x0), Just(x1), ty_Bool)
new_ltEs8(x0, x1)
new_ltEs18(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Float)
new_esEs27(x0, x1, ty_Double)
new_esEs26(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, ty_Ordering)
new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_splitLT4(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_intersectFM_C2Gts0(x0, x1, x2, x3, x4, x5, x6)
new_ltEs7(Right(x0), Right(x1), x2, ty_Bool)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs4(Just(x0), Just(x1), ty_Ordering)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs7(Left(x0), Left(x1), ty_Integer, x2)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs18(x0, x1, ty_Double)
new_gt0(x0, x1, x2)
new_ltEs10(GT, LT)
new_ltEs10(LT, GT)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs28(x0, x1, ty_Double)
new_ltEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs10(@0, @0)
new_esEs4(Left(x0), Left(x1), ty_Double, x2)
new_lt13(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare14(Double(x0, x1), Double(x2, x3))
new_compare30(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_Integer)
new_ltEs18(x0, x1, ty_Float)
new_splitLT12(x0, x1, x2, x3, x4, x5, True, x6, x7)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_mkBalBranch6MkBalBranch5(x0, x1, x2, x3, True, x4, x5)
new_compare8(x0, x1)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs20(x0, x1, ty_Char)
new_mkBalBranch6Size_r(x0, x1, x2, x3, x4, x5)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_compare4(:(x0, x1), [], x2)
new_ltEs19(x0, x1, ty_Integer)
new_mkBalBranch6MkBalBranch3(x0, x1, x2, x3, False, x4, x5)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_pePe(True, x0)
new_esEs27(x0, x1, ty_Float)
new_mkVBalBranch3MkVBalBranch10(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, True, x12, x13)
new_ltEs7(Left(x0), Left(x1), ty_Bool, x2)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_splitGT3(EmptyFM, x0, x1)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_primCompAux00(x0, EQ)
new_lt19(x0, x1, ty_Float)
new_primEqNat0(Succ(x0), Zero)
new_ltEs17(x0, x1, x2)
new_ltEs20(x0, x1, app(ty_[], x2))
new_intersectFM_C2Gts(x0, x1, x2, x3, x4, x5)
new_intersectFM_C2Gts1(x0, x1, x2, x3, x4, x5, x6)
new_esEs28(x0, x1, ty_Int)
new_esEs4(Right(x0), Right(x1), x2, ty_Bool)
new_esEs20(x0, x1, app(ty_[], x2))
new_esEs31(x0, x1, ty_Int)
new_primPlusInt1(Branch(x0, x1, Neg(x2), x3, x4), x5, x6, x7, x8, x9)
new_esEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs18(x0, x1, ty_Ordering)
new_esEs25(x0, x1, ty_Int)
new_mkBalBranch6MkBalBranch11(x0, x1, x2, x3, x4, x5, x6, EmptyFM, False, x7, x8)
new_compare29(Nothing, Nothing, False, x0)
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs4(Left(x0), Left(x1), ty_Char, x2)
new_ltEs4(Just(x0), Just(x1), ty_@0)
new_compare23(x0, x1, False)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare112(x0, x1, True)
new_esEs19(x0, x1, ty_Double)
new_esEs13(Float(x0, x1), Float(x2, x3))
new_esEs29(x0, Just(x1), ty_Double)
new_esEs4(Right(x0), Right(x1), x2, ty_@0)
new_mkVBalBranch0(x0, x1, Branch(x2, x3, x4, x5, x6), Branch(x7, x8, x9, x10, x11), x12, x13)
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs7(Right(x0), Right(x1), x2, ty_Double)
new_ltEs4(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_lt13(x0, x1, ty_Char)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_ltEs20(x0, x1, ty_Char)
new_esEs15(Integer(x0), Integer(x1))
new_ltEs12(x0, x1)
new_ltEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_lt20(x0, x1, ty_@0)
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, ty_@0)
new_compare111(x0, x1, False, x2)
new_lt13(x0, x1, app(ty_Ratio, x2))
new_ltEs4(Just(x0), Just(x1), ty_Float)
new_esEs14(True, False)
new_esEs14(False, True)
new_ltEs6(x0, x1)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, ty_Int)
new_compare30(x0, x1, app(ty_Maybe, x2))
new_esEs20(x0, x1, ty_Double)
new_mkBalBranch(x0, x1, x2, x3, x4, x5)
new_compare24(x0, x1, True, x2, x3, x4)
new_ltEs9(x0, x1)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs31(x0, x1, ty_Integer)
new_esEs31(x0, x1, ty_Float)
new_esEs19(x0, x1, ty_@0)
new_compare30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Ordering)
new_esEs27(x0, x1, ty_Integer)
new_ltEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_compare110(x0, x1, True, x2, x3, x4)
new_esEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs29(x0, Just(x1), ty_Float)
new_lt20(x0, x1, ty_Float)
new_esEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_compare30(x0, x1, ty_Bool)
new_esEs29(x0, Just(x1), app(ty_Ratio, x2))
new_esEs22(x0, x1, ty_Integer)
new_lt19(x0, x1, ty_Char)
new_primCmpNat0(Succ(x0), Succ(x1))
new_splitLT3(Branch(x0, x1, x2, x3, x4), x5, x6)
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_esEs4(Left(x0), Left(x1), ty_Bool, x2)
new_esEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs20(x0, x1, ty_Integer)
new_esEs28(x0, x1, ty_Ordering)
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_esEs21(x0, x1, ty_Integer)
new_mkVBalBranch3MkVBalBranch20(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, False, x12, x13)
new_esEs31(x0, x1, app(ty_Maybe, x2))
new_esEs4(Left(x0), Left(x1), ty_@0, x2)
new_primMinusNat0(Zero, Succ(x0))
new_esEs4(Right(x0), Right(x1), x2, ty_Int)
new_esEs4(Left(x0), Left(x1), ty_Int, x2)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs12(:(x0, x1), [], x2)
new_mkBalBranch6MkBalBranch4(x0, x1, x2, x3, False, x4, x5)
new_lt20(x0, x1, ty_Bool)
new_esEs31(x0, x1, app(ty_Ratio, x2))
new_primPlusNat0(Succ(x0), x1)
new_esEs20(x0, x1, ty_@0)
new_esEs4(Right(x0), Right(x1), x2, ty_Integer)
new_esEs4(Left(x0), Left(x1), ty_Float, x2)
new_ltEs18(x0, x1, ty_Integer)
new_lt13(x0, x1, app(ty_[], x2))
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Just(x0), Just(x1), ty_Float)
new_compare15(x0, x1, True, x2, x3)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_esEs19(x0, x1, ty_Float)
new_ltEs20(x0, x1, ty_Bool)
new_primCmpNat0(Zero, Zero)
new_esEs31(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs7(Right(x0), Right(x1), x2, ty_@0)
new_compare111(x0, x1, True, x2)
new_esEs19(x0, x1, ty_Ordering)
new_splitGT11(x0, x1, x2, x3, x4, True, x5, x6)
new_primCompAux0(x0, x1, x2, x3)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_lt13(x0, x1, ty_Bool)
new_splitLT12(x0, x1, x2, x3, x4, x5, False, x6, x7)
new_ltEs19(x0, x1, ty_Float)
new_esEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs15(x0, x1, x2)
new_lt10(x0, x1)
new_esEs7(Nothing, Just(x0), x1)
new_compare12(x0, x1, x2, x3)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_compare7(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_esEs29(x0, Just(x1), app(app(ty_@2, x2), x3))
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_lt19(x0, x1, app(ty_[], x2))
new_primPlusInt2(Neg(x0), x1, x2, x3, x4, x5)
new_addToFM_C20(x0, x1, x2, x3, x4, x5, x6, False, x7, x8)
new_esEs12([], [], x0)
new_splitGT11(x0, x1, x2, x3, x4, False, x5, x6)
new_esEs25(x0, x1, ty_Ordering)
new_primPlusInt(x0, Pos(x1))
new_esEs18(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Float)
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt8(x0, x1, x2, x3, x4)
new_esEs4(Right(x0), Right(x1), x2, ty_Float)
new_ltEs10(GT, GT)
new_ltEs4(Just(x0), Just(x1), app(ty_[], x2))
new_lt13(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_ltEs14(True, True)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(False, False)
new_esEs24(x0, x1, ty_Ordering)
new_primCmpInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_lt19(x0, x1, ty_@0)
new_esEs18(x0, x1, ty_Float)
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_intersectFM_C2Lts2(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkBranch(x0, x1, x2, x3, x4, x5, x6)
new_esEs28(x0, x1, ty_Char)
new_esEs7(Nothing, Nothing, x0)
new_esEs31(x0, x1, app(app(ty_@2, x2), x3))
new_primPlusInt0(x0, Neg(x1))
new_not(True)
new_gt2(x0, x1)
new_esEs19(x0, x1, ty_Int)
new_esEs30(Just(x0), x1)
new_esEs7(Just(x0), Just(x1), ty_@0)
new_esEs29(x0, Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare30(x0, x1, ty_Integer)
new_compare27(x0, x1, True, x2, x3)
new_ltEs5(x0, x1)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_ltEs20(x0, x1, ty_Double)
new_esEs4(Right(x0), Right(x1), x2, ty_Char)
new_ltEs4(Just(x0), Just(x1), ty_Integer)
new_ltEs7(Left(x0), Left(x1), ty_@0, x2)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_not(False)
new_splitGT22(x0, x1, x2, x3, x4, x5, False, x6, x7)
new_compare13(x0, x1, x2, x3, x4)
new_esEs25(x0, x1, ty_Integer)
new_compare32(x0, x1)
new_lt17(x0, x1, x2)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primCompAux00(x0, LT)
new_lt6(x0, x1)
new_ltEs10(EQ, GT)
new_ltEs10(GT, EQ)
new_compare110(x0, x1, False, x2, x3, x4)
new_ltEs19(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_Int)
new_addToFM_C0(EmptyFM, x0, x1, x2, x3)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, ty_Float)
new_compare18(x0, x1, x2, x3)
new_esEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs31(x0, x1, ty_Ordering)
new_sizeFM(x0, x1, x2, x3, x4, x5, x6)
new_ltEs7(Left(x0), Left(x1), ty_Int, x2)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_ltEs4(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs18(x0, x1, ty_Char)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_esEs19(x0, x1, ty_Integer)
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_addToFM_C10(x0, x1, x2, x3, x4, x5, x6, False, x7, x8)
new_compare29(Just(x0), Just(x1), False, x2)
new_ltEs4(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_lt16(x0, x1, x2, x3)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(Zero))
new_sr(Integer(x0), Integer(x1))
new_esEs30(Nothing, x0)
new_esEs27(x0, x1, ty_Char)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, ty_Bool)
new_primMulInt(Pos(x0), Pos(x1))
new_ltEs4(Just(x0), Just(x1), ty_Char)
new_primMinusNat0(Succ(x0), Zero)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_addToFM_C20(x0, x1, x2, x3, x4, x5, x6, True, x7, x8)
new_esEs18(x0, x1, ty_@0)
new_ltEs7(Right(x0), Right(x1), x2, ty_Char)
new_lt13(x0, x1, ty_Double)
new_splitLT11(x0, x1, x2, x3, x4, False, x5, x6)
new_ltEs7(Left(x0), Left(x1), ty_Char, x2)
new_compare30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, ty_Bool)
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_mkBalBranch6MkBalBranch11(x0, x1, x2, x3, x4, x5, x6, Branch(x7, x8, x9, x10, x11), False, x12, x13)
new_lt13(x0, x1, ty_Ordering)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_compare113(x0, x1, False, x2, x3)
new_esEs12(:(x0, x1), :(x2, x3), x4)
new_esEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, app(ty_[], x2))
new_splitLT4(EmptyFM, x0, x1, x2)
new_ltEs18(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Ordering)
new_compare30(x0, x1, ty_Float)
new_esEs31(x0, x1, ty_Double)
new_lt13(x0, x1, ty_Integer)
new_intersectFM_C2Gts2(x0, x1, x2, x3, x4, x5, x6, x7)
new_addToFM_C10(x0, x1, x2, x3, x4, x5, x6, True, x7, x8)
new_esEs14(False, False)
new_primEqInt(Pos(Zero), Pos(Zero))
new_ltEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_compare10(Char(x0), Char(x1))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs24(x0, x1, ty_Integer)
new_lt20(x0, x1, ty_Double)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_intersectFM_C2Lts(x0, x1, x2, x3, x4, x5)
new_ltEs20(x0, x1, ty_Float)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_lt13(x0, x1, ty_Int)
new_ltEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_lt13(x0, x1, ty_Float)
new_lt20(x0, x1, ty_Integer)
new_primCmpNat0(Zero, Succ(x0))
new_esEs23(x0, x1, ty_Int)
new_primCompAux00(x0, GT)
new_compare27(x0, x1, False, x2, x3)
new_ltEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs23(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, ty_@0)
new_esEs29(x0, Nothing, x1)
new_lt15(x0, x1)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, Just(x1), ty_Int)
new_primEqNat0(Zero, Succ(x0))
new_ltEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs19(x0, x1, app(ty_[], x2))
new_splitGT22(x0, x1, x2, x3, x4, x5, True, x6, x7)
new_esEs27(x0, x1, ty_Bool)
new_esEs18(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, ty_Int)
new_ltEs7(Left(x0), Left(x1), ty_Float, x2)
new_ltEs19(x0, x1, ty_@0)
new_esEs31(x0, x1, ty_Char)
new_esEs18(x0, x1, ty_Integer)
new_splitLT21(x0, x1, x2, x3, x4, x5, False, x6, x7)
new_esEs31(x0, x1, app(ty_[], x2))
new_ltEs10(EQ, EQ)

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: