YES 9.467 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
  ((addToFM :: Ord b => FiniteMap (Maybe b) a  ->  Maybe b  ->  a  ->  FiniteMap (Maybe b) a) :: Ord b => FiniteMap (Maybe b) a  ->  Maybe b  ->  a  ->  FiniteMap (Maybe b) a)

module FiniteMap where
  import qualified Maybe
import qualified Prelude

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


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

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

  emptyFM :: FiniteMap a b
emptyFM EmptyFM

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

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

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

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

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

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

  sIZE_RATIO :: Int
sIZE_RATIO 5

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude



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

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

The following Lambda expression
\oldnewnew

is transformed to
addToFM0 old new = new



↳ HASKELL
  ↳ LR
HASKELL
      ↳ CR

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

  emptyFM :: FiniteMap b a
emptyFM EmptyFM

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

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

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

  
fmToList0 key elt rest (key,elt: rest

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

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

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

  sIZE_RATIO :: Int
sIZE_RATIO 5

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude



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

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

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

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

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

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

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

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

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

module FiniteMap where
  import qualified Maybe
import qualified Prelude

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


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

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

  
addToFM0 old new new

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

  emptyFM :: FiniteMap a b
emptyFM EmptyFM

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

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

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

  
fmToList0 key elt rest (key,elt: rest

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

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

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

  sIZE_RATIO :: Int
sIZE_RATIO 5

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude



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

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

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

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



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

mainModule FiniteMap
  ((addToFM :: Ord b => FiniteMap (Maybe b) a  ->  Maybe b  ->  a  ->  FiniteMap (Maybe b) a) :: Ord b => FiniteMap (Maybe b) a  ->  Maybe b  ->  a  ->  FiniteMap (Maybe b) a)

module FiniteMap where
  import qualified Maybe
import qualified Prelude

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


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

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

  
addToFM0 old new new

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

  emptyFM :: FiniteMap b a
emptyFM EmptyFM

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

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

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

  
fmToList0 key elt rest (key,elt: rest

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

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

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

  sIZE_RATIO :: Int
sIZE_RATIO 5

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude



Replaced joker patterns by fresh variables and removed binding patterns.

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

mainModule FiniteMap
  ((addToFM :: Ord a => FiniteMap (Maybe a) b  ->  Maybe a  ->  b  ->  FiniteMap (Maybe a) b) :: Ord a => FiniteMap (Maybe a) b  ->  Maybe a  ->  b  ->  FiniteMap (Maybe a) b)

module FiniteMap where
  import qualified Maybe
import qualified Prelude

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


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

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

  
addToFM0 old new new

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

  emptyFM :: FiniteMap b a
emptyFM EmptyFM

  findMax :: FiniteMap b a  ->  (b,a)
findMax (Branch key elt vuv vuw EmptyFM(key,elt)
findMax (Branch key elt vux vuy fm_rfindMax fm_r

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

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

  
fmToList0 key elt rest (key,elt: rest

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

  mkBalBranch :: Ord b => b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a
mkBalBranch key elt fm_L fm_R 
 | size_l + size_r < 2 = 
mkBranch 1 key elt fm_L fm_R
 | size_r > sIZE_RATIO * size_l = 
mkBalBranch0 fm_L fm_R fm_R
 | size_l > sIZE_RATIO * size_r = 
mkBalBranch1 fm_L fm_R fm_L
 | otherwise = 
mkBranch 2 key elt fm_L fm_R where 
double_L fm_l (Branch key_r elt_r zv (Branch key_rl elt_rl zw fm_rll fm_rlr) fm_rrmkBranch 5 key_rl elt_rl (mkBranch 6 key elt fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr)
double_R (Branch key_l elt_l yw fm_ll (Branch key_lr elt_lr yx 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 zx zy zz 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 yy yz zu 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 vuu fm_rl fm_rrmkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr
single_R (Branch key_l elt_l yv fm_ll fm_lrfm_r mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r)
size_l sizeFM fm_L
size_r sizeFM fm_R

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

  sIZE_RATIO :: Int
sIZE_RATIO 5

  sizeFM :: FiniteMap b a  ->  Int
sizeFM EmptyFM 0
sizeFM (Branch xx xy size xz yusize

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude



Cond Reductions:
The following Function with conditions
mkBalBranch1 fm_L fm_R (Branch yy yz zu 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 yy yz zu fm_ll fm_lr) = mkBalBranch12 fm_L fm_R (Branch yy yz zu fm_ll fm_lr)

mkBalBranch10 fm_L fm_R yy yz zu fm_ll fm_lr True = double_R fm_L fm_R

mkBalBranch11 fm_L fm_R yy yz zu fm_ll fm_lr True = single_R fm_L fm_R
mkBalBranch11 fm_L fm_R yy yz zu fm_ll fm_lr False = mkBalBranch10 fm_L fm_R yy yz zu fm_ll fm_lr otherwise

mkBalBranch12 fm_L fm_R (Branch yy yz zu fm_ll fm_lr) = mkBalBranch11 fm_L fm_R yy yz zu fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll)

The following Function with conditions
mkBalBranch0 fm_L fm_R (Branch zx zy zz 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 zx zy zz fm_rl fm_rr) = mkBalBranch02 fm_L fm_R (Branch zx zy zz fm_rl fm_rr)

mkBalBranch01 fm_L fm_R zx zy zz fm_rl fm_rr True = single_L fm_L fm_R
mkBalBranch01 fm_L fm_R zx zy zz fm_rl fm_rr False = mkBalBranch00 fm_L fm_R zx zy zz fm_rl fm_rr otherwise

mkBalBranch00 fm_L fm_R zx zy zz fm_rl fm_rr True = double_L fm_L fm_R

mkBalBranch02 fm_L fm_R (Branch zx zy zz fm_rl fm_rr) = mkBalBranch01 fm_L fm_R zx zy zz 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 zv (Branch key_rl elt_rl zw fm_rll fm_rlrfm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 key elt fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr)
double_R (Branch key_l elt_l yw fm_ll (Branch key_lr elt_lr yx 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 zx zy zz 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 yy yz zu 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 vuu fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rlfm_rr
single_R (Branch key_l elt_l yv fm_ll fm_lrfm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r)
size_l  = sizeFM fm_L
size_r  = sizeFM fm_R

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

mkBalBranch6 key elt fm_L fm_R = 
mkBalBranch5 key elt fm_L fm_R (size_l + size_r < 2)
where 
double_L fm_l (Branch key_r elt_r zv (Branch key_rl elt_rl zw fm_rll fm_rlrfm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 key elt fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr)
double_R (Branch key_l elt_l yw fm_ll (Branch key_lr elt_lr yx 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 zx zy zz fm_rl fm_rr) = mkBalBranch02 fm_L fm_R (Branch zx zy zz fm_rl fm_rr)
mkBalBranch00 fm_L fm_R zx zy zz fm_rl fm_rr True = double_L fm_L fm_R
mkBalBranch01 fm_L fm_R zx zy zz fm_rl fm_rr True = single_L fm_L fm_R
mkBalBranch01 fm_L fm_R zx zy zz fm_rl fm_rr False = mkBalBranch00 fm_L fm_R zx zy zz fm_rl fm_rr otherwise
mkBalBranch02 fm_L fm_R (Branch zx zy zz fm_rl fm_rr) = mkBalBranch01 fm_L fm_R zx zy zz fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr)
mkBalBranch1 fm_L fm_R (Branch yy yz zu fm_ll fm_lr) = mkBalBranch12 fm_L fm_R (Branch yy yz zu fm_ll fm_lr)
mkBalBranch10 fm_L fm_R yy yz zu fm_ll fm_lr True = double_R fm_L fm_R
mkBalBranch11 fm_L fm_R yy yz zu fm_ll fm_lr True = single_R fm_L fm_R
mkBalBranch11 fm_L fm_R yy yz zu fm_ll fm_lr False = mkBalBranch10 fm_L fm_R yy yz zu fm_ll fm_lr otherwise
mkBalBranch12 fm_L fm_R (Branch yy yz zu fm_ll fm_lr) = mkBalBranch11 fm_L fm_R yy yz zu 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 vuu fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rlfm_rr
single_R (Branch key_l elt_l yv fm_ll fm_lrfm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r)
size_l  = sizeFM fm_L
size_r  = sizeFM fm_R

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

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

addToFM_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_eltsize 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_eltfm_r
addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt False = addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt (new_key > key)

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

addToFM_C4 combiner EmptyFM key elt = unitFM key elt
addToFM_C4 wuu wuv wuw wux = addToFM_C3 wuu wuv wuw wux

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

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

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

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 wuy = gcd'2 x wuy
gcd' x y = gcd'0 x y

gcd'0 x y = gcd' y (x `rem` y)

gcd'1 True x wuy = x
gcd'1 wuz wvu wvv = gcd'0 wvu wvv

gcd'2 x wuy = gcd'1 (wuy == 0) x wuy
gcd'2 wvw wvx = gcd'0 wvw wvx

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 wvy wvz = gcd3 wvy wvz
gcd x y = gcd0 x y

gcd0 x y = 
gcd' (abs x) (abs y)
where 
gcd' x wuy = gcd'2 x wuy
gcd' x y = gcd'0 x y
gcd'0 x y = gcd' y (x `rem` y)
gcd'1 True x wuy = x
gcd'1 wuz wvu wvv = gcd'0 wvu wvv
gcd'2 x wuy = gcd'1 (wuy == 0) x wuy
gcd'2 wvw wvx = gcd'0 wvw wvx

gcd1 True wvy wvz = error []
gcd1 wwu wwv www = gcd0 wwv www

gcd2 True wvy wvz = gcd1 (wvz == 0) wvy wvz
gcd2 wwx wwy wwz = gcd0 wwy wwz

gcd3 wvy wvz = gcd2 (wvy == 0) wvy wvz
gcd3 wxu wxv = gcd0 wxu wxv

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

is transformed to
absReal x = absReal2 x

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

absReal0 x True = `negate` x

absReal2 x = absReal1 x (x >= 0)

The following Function with conditions
undefined 
 | False
 = undefined

is transformed to
undefined  = undefined1

undefined0 True = undefined

undefined1  = undefined0 False

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

is transformed to
reduce x y = reduce2 x y

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



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

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

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

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

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

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

  
addToFM_C4 combiner EmptyFM key elt unitFM key elt
addToFM_C4 wuu wuv wuw wux addToFM_C3 wuu wuv wuw wux

  emptyFM :: FiniteMap b a
emptyFM EmptyFM

  findMax :: FiniteMap b a  ->  (b,a)
findMax (Branch key elt vuv vuw EmptyFM(key,elt)
findMax (Branch key elt vux vuy fm_rfindMax fm_r

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

  fmToList :: FiniteMap 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 vw fm_l fm_rfoldFM k (k key elt (foldFM k z fm_r)) fm_l

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

  
mkBalBranch6 key elt fm_L fm_R 
mkBalBranch5 key elt fm_L fm_R (size_l + size_r < 2) where 
double_L fm_l (Branch key_r elt_r zv (Branch key_rl elt_rl zw fm_rll fm_rlr) fm_rrmkBranch 5 key_rl elt_rl (mkBranch 6 key elt fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr)
double_R (Branch key_l elt_l yw fm_ll (Branch key_lr elt_lr yx 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 zx zy zz fm_rl fm_rrmkBalBranch02 fm_L fm_R (Branch zx zy zz fm_rl fm_rr)
mkBalBranch00 fm_L fm_R zx zy zz fm_rl fm_rr True double_L fm_L fm_R
mkBalBranch01 fm_L fm_R zx zy zz fm_rl fm_rr True single_L fm_L fm_R
mkBalBranch01 fm_L fm_R zx zy zz fm_rl fm_rr False mkBalBranch00 fm_L fm_R zx zy zz fm_rl fm_rr otherwise
mkBalBranch02 fm_L fm_R (Branch zx zy zz fm_rl fm_rrmkBalBranch01 fm_L fm_R zx zy zz fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr)
mkBalBranch1 fm_L fm_R (Branch yy yz zu fm_ll fm_lrmkBalBranch12 fm_L fm_R (Branch yy yz zu fm_ll fm_lr)
mkBalBranch10 fm_L fm_R yy yz zu fm_ll fm_lr True double_R fm_L fm_R
mkBalBranch11 fm_L fm_R yy yz zu fm_ll fm_lr True single_R fm_L fm_R
mkBalBranch11 fm_L fm_R yy yz zu fm_ll fm_lr False mkBalBranch10 fm_L fm_R yy yz zu fm_ll fm_lr otherwise
mkBalBranch12 fm_L fm_R (Branch yy yz zu fm_ll fm_lrmkBalBranch11 fm_L fm_R yy yz zu 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 vuu fm_rl fm_rrmkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr
single_R (Branch key_l elt_l yv fm_ll fm_lrfm_r mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r)
size_l sizeFM fm_L
size_r sizeFM fm_R

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

  sIZE_RATIO :: Int
sIZE_RATIO 5

  sizeFM :: FiniteMap b a  ->  Int
sizeFM EmptyFM 0
sizeFM (Branch xx xy size xz yusize

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude



Let/Where Reductions:
The bindings of the following Let/Where expression
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 vx vy vz wu) = 
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 wv ww wx wy) = 
let 
smallest_right_key  = fst (findMin fm_r)
in key < smallest_right_key
right_size  = sizeFM fm_r
unbox x = x

are unpacked to the following functions on top level
mkBranchLeft_ok wxw wxx wxy = mkBranchLeft_ok0 wxw wxx wxy wxw wxx wxw

mkBranchLeft_ok0 wxw wxx wxy fm_l key EmptyFM = True
mkBranchLeft_ok0 wxw wxx wxy fm_l key (Branch left_key vx vy vz wu) = mkBranchLeft_ok0Biggest_left_key fm_l < key

mkBranchBalance_ok wxw wxx wxy = True

mkBranchLeft_size wxw wxx wxy = sizeFM wxw

mkBranchUnbox wxw wxx wxy x = x

mkBranchRight_ok0 wxw wxx wxy fm_r key EmptyFM = True
mkBranchRight_ok0 wxw wxx wxy fm_r key (Branch right_key wv ww wx wy) = key < mkBranchRight_ok0Smallest_right_key fm_r

mkBranchRight_ok wxw wxx wxy = mkBranchRight_ok0 wxw wxx wxy wxy wxx wxy

mkBranchRight_size wxw wxx wxy = sizeFM wxy

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 wxz wyu wyv wyw = Branch wxz wyu (mkBranchUnbox wyv wxz wyw (1 + mkBranchLeft_size wyv wxz wyw + mkBranchRight_size wyv wxz wyw)) wyv wyw

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 zv (Branch key_rl elt_rl zw fm_rll fm_rlrfm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 key elt fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr)
double_R (Branch key_l elt_l yw fm_ll (Branch key_lr elt_lr yx 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 zx zy zz fm_rl fm_rr) = mkBalBranch02 fm_L fm_R (Branch zx zy zz fm_rl fm_rr)
mkBalBranch00 fm_L fm_R zx zy zz fm_rl fm_rr True = double_L fm_L fm_R
mkBalBranch01 fm_L fm_R zx zy zz fm_rl fm_rr True = single_L fm_L fm_R
mkBalBranch01 fm_L fm_R zx zy zz fm_rl fm_rr False = mkBalBranch00 fm_L fm_R zx zy zz fm_rl fm_rr otherwise
mkBalBranch02 fm_L fm_R (Branch zx zy zz fm_rl fm_rr) = mkBalBranch01 fm_L fm_R zx zy zz fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr)
mkBalBranch1 fm_L fm_R (Branch yy yz zu fm_ll fm_lr) = mkBalBranch12 fm_L fm_R (Branch yy yz zu fm_ll fm_lr)
mkBalBranch10 fm_L fm_R yy yz zu fm_ll fm_lr True = double_R fm_L fm_R
mkBalBranch11 fm_L fm_R yy yz zu fm_ll fm_lr True = single_R fm_L fm_R
mkBalBranch11 fm_L fm_R yy yz zu fm_ll fm_lr False = mkBalBranch10 fm_L fm_R yy yz zu fm_ll fm_lr otherwise
mkBalBranch12 fm_L fm_R (Branch yy yz zu fm_ll fm_lr) = mkBalBranch11 fm_L fm_R yy yz zu 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 vuu fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rlfm_rr
single_R (Branch key_l elt_l yv fm_ll fm_lrfm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r)
size_l  = sizeFM fm_L
size_r  = sizeFM fm_R

are unpacked to the following functions on top level
mkBalBranch6MkBalBranch1 wyx wyy wyz wzu fm_L fm_R (Branch yy yz zu fm_ll fm_lr) = mkBalBranch6MkBalBranch12 wyx wyy wyz wzu fm_L fm_R (Branch yy yz zu fm_ll fm_lr)

mkBalBranch6MkBalBranch3 wyx wyy wyz wzu key elt fm_L fm_R True = mkBalBranch6MkBalBranch1 wyx wyy wyz wzu fm_L fm_R fm_L
mkBalBranch6MkBalBranch3 wyx wyy wyz wzu key elt fm_L fm_R False = mkBalBranch6MkBalBranch2 wyx wyy wyz wzu key elt fm_L fm_R otherwise

mkBalBranch6MkBalBranch12 wyx wyy wyz wzu fm_L fm_R (Branch yy yz zu fm_ll fm_lr) = mkBalBranch6MkBalBranch11 wyx wyy wyz wzu fm_L fm_R yy yz zu fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll)

mkBalBranch6MkBalBranch02 wyx wyy wyz wzu fm_L fm_R (Branch zx zy zz fm_rl fm_rr) = mkBalBranch6MkBalBranch01 wyx wyy wyz wzu fm_L fm_R zx zy zz fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr)

mkBalBranch6Single_L wyx wyy wyz wzu fm_l (Branch key_r elt_r vuu fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 wyx wyy fm_l fm_rlfm_rr

mkBalBranch6MkBalBranch10 wyx wyy wyz wzu fm_L fm_R yy yz zu fm_ll fm_lr True = mkBalBranch6Double_R wyx wyy wyz wzu fm_L fm_R

mkBalBranch6MkBalBranch0 wyx wyy wyz wzu fm_L fm_R (Branch zx zy zz fm_rl fm_rr) = mkBalBranch6MkBalBranch02 wyx wyy wyz wzu fm_L fm_R (Branch zx zy zz fm_rl fm_rr)

mkBalBranch6MkBalBranch4 wyx wyy wyz wzu key elt fm_L fm_R True = mkBalBranch6MkBalBranch0 wyx wyy wyz wzu fm_L fm_R fm_R
mkBalBranch6MkBalBranch4 wyx wyy wyz wzu key elt fm_L fm_R False = mkBalBranch6MkBalBranch3 wyx wyy wyz wzu key elt fm_L fm_R (mkBalBranch6Size_l wyx wyy wyz wzu > sIZE_RATIO * mkBalBranch6Size_r wyx wyy wyz wzu)

mkBalBranch6Size_l wyx wyy wyz wzu = sizeFM wyz

mkBalBranch6MkBalBranch11 wyx wyy wyz wzu fm_L fm_R yy yz zu fm_ll fm_lr True = mkBalBranch6Single_R wyx wyy wyz wzu fm_L fm_R
mkBalBranch6MkBalBranch11 wyx wyy wyz wzu fm_L fm_R yy yz zu fm_ll fm_lr False = mkBalBranch6MkBalBranch10 wyx wyy wyz wzu fm_L fm_R yy yz zu fm_ll fm_lr otherwise

mkBalBranch6MkBalBranch2 wyx wyy wyz wzu key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R

mkBalBranch6Double_L wyx wyy wyz wzu fm_l (Branch key_r elt_r zv (Branch key_rl elt_rl zw fm_rll fm_rlrfm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 wyx wyy fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr)

mkBalBranch6MkBalBranch5 wyx wyy wyz wzu key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R
mkBalBranch6MkBalBranch5 wyx wyy wyz wzu key elt fm_L fm_R False = mkBalBranch6MkBalBranch4 wyx wyy wyz wzu key elt fm_L fm_R (mkBalBranch6Size_r wyx wyy wyz wzu > sIZE_RATIO * mkBalBranch6Size_l wyx wyy wyz wzu)

mkBalBranch6MkBalBranch01 wyx wyy wyz wzu fm_L fm_R zx zy zz fm_rl fm_rr True = mkBalBranch6Single_L wyx wyy wyz wzu fm_L fm_R
mkBalBranch6MkBalBranch01 wyx wyy wyz wzu fm_L fm_R zx zy zz fm_rl fm_rr False = mkBalBranch6MkBalBranch00 wyx wyy wyz wzu fm_L fm_R zx zy zz fm_rl fm_rr otherwise

mkBalBranch6Double_R wyx wyy wyz wzu (Branch key_l elt_l yw fm_ll (Branch key_lr elt_lr yx fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 wyx wyy fm_lrr fm_r)

mkBalBranch6Single_R wyx wyy wyz wzu (Branch key_l elt_l yv fm_ll fm_lrfm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 wyx wyy fm_lr fm_r)

mkBalBranch6MkBalBranch00 wyx wyy wyz wzu fm_L fm_R zx zy zz fm_rl fm_rr True = mkBalBranch6Double_L wyx wyy wyz wzu fm_L fm_R

mkBalBranch6Size_r wyx wyy wyz wzu = sizeFM wzu

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 wzv = fst (findMax wzv)

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 wzw = fst (findMin wzw)

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 wzx wzy x y True = error []
reduce2Reduce1 wzx wzy x y False = reduce2Reduce0 wzx wzy x y otherwise

reduce2D wzx wzy = gcd wzx wzy

reduce2Reduce0 wzx wzy x y True = x `quot` reduce2D wzx wzy :% (y `quot` reduce2D wzx wzy)

The bindings of the following Let/Where expression
gcd' (abs x) (abs y)
where 
gcd' x wuy = gcd'2 x wuy
gcd' x y = gcd'0 x y
gcd'0 x y = gcd' y (x `rem` y)
gcd'1 True x wuy = x
gcd'1 wuz wvu wvv = gcd'0 wvu wvv
gcd'2 x wuy = gcd'1 (wuy == 0) x wuy
gcd'2 wvw wvx = gcd'0 wvw wvx

are unpacked to the following functions on top level
gcd0Gcd'0 x y = gcd0Gcd' y (x `rem` y)

gcd0Gcd'1 True x wuy = x
gcd0Gcd'1 wuz wvu wvv = gcd0Gcd'0 wvu wvv

gcd0Gcd'2 x wuy = gcd0Gcd'1 (wuy == 0) x wuy
gcd0Gcd'2 wvw wvx = gcd0Gcd'0 wvw wvx

gcd0Gcd' x wuy = gcd0Gcd'2 x wuy
gcd0Gcd' x y = gcd0Gcd'0 x y



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

mainModule FiniteMap
  ((addToFM :: Ord b => FiniteMap (Maybe b) a  ->  Maybe b  ->  a  ->  FiniteMap (Maybe b) a) :: Ord b => FiniteMap (Maybe b) a  ->  Maybe b  ->  a  ->  FiniteMap (Maybe b) a)

module FiniteMap where
  import qualified Maybe
import qualified Prelude

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


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

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

  
addToFM0 old new new

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

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

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

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

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

  
addToFM_C4 combiner EmptyFM key elt unitFM key elt
addToFM_C4 wuu wuv wuw wux addToFM_C3 wuu wuv wuw wux

  emptyFM :: FiniteMap a b
emptyFM EmptyFM

  findMax :: FiniteMap b a  ->  (b,a)
findMax (Branch key elt vuv vuw EmptyFM(key,elt)
findMax (Branch key elt vux vuy fm_rfindMax fm_r

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

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

  
fmToList0 key elt rest (key,elt: rest

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

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

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

  
mkBalBranch6Double_L wyx wyy wyz wzu fm_l (Branch key_r elt_r zv (Branch key_rl elt_rl zw fm_rll fm_rlr) fm_rrmkBranch 5 key_rl elt_rl (mkBranch 6 wyx wyy fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr)

  
mkBalBranch6Double_R wyx wyy wyz wzu (Branch key_l elt_l yw fm_ll (Branch key_lr elt_lr yx fm_lrl fm_lrr)) fm_r mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 wyx wyy fm_lrr fm_r)

  
mkBalBranch6MkBalBranch0 wyx wyy wyz wzu fm_L fm_R (Branch zx zy zz fm_rl fm_rrmkBalBranch6MkBalBranch02 wyx wyy wyz wzu fm_L fm_R (Branch zx zy zz fm_rl fm_rr)

  
mkBalBranch6MkBalBranch00 wyx wyy wyz wzu fm_L fm_R zx zy zz fm_rl fm_rr True mkBalBranch6Double_L wyx wyy wyz wzu fm_L fm_R

  
mkBalBranch6MkBalBranch01 wyx wyy wyz wzu fm_L fm_R zx zy zz fm_rl fm_rr True mkBalBranch6Single_L wyx wyy wyz wzu fm_L fm_R
mkBalBranch6MkBalBranch01 wyx wyy wyz wzu fm_L fm_R zx zy zz fm_rl fm_rr False mkBalBranch6MkBalBranch00 wyx wyy wyz wzu fm_L fm_R zx zy zz fm_rl fm_rr otherwise

  
mkBalBranch6MkBalBranch02 wyx wyy wyz wzu fm_L fm_R (Branch zx zy zz fm_rl fm_rrmkBalBranch6MkBalBranch01 wyx wyy wyz wzu fm_L fm_R zx zy zz fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr)

  
mkBalBranch6MkBalBranch1 wyx wyy wyz wzu fm_L fm_R (Branch yy yz zu fm_ll fm_lrmkBalBranch6MkBalBranch12 wyx wyy wyz wzu fm_L fm_R (Branch yy yz zu fm_ll fm_lr)

  
mkBalBranch6MkBalBranch10 wyx wyy wyz wzu fm_L fm_R yy yz zu fm_ll fm_lr True mkBalBranch6Double_R wyx wyy wyz wzu fm_L fm_R

  
mkBalBranch6MkBalBranch11 wyx wyy wyz wzu fm_L fm_R yy yz zu fm_ll fm_lr True mkBalBranch6Single_R wyx wyy wyz wzu fm_L fm_R
mkBalBranch6MkBalBranch11 wyx wyy wyz wzu fm_L fm_R yy yz zu fm_ll fm_lr False mkBalBranch6MkBalBranch10 wyx wyy wyz wzu fm_L fm_R yy yz zu fm_ll fm_lr otherwise

  
mkBalBranch6MkBalBranch12 wyx wyy wyz wzu fm_L fm_R (Branch yy yz zu fm_ll fm_lrmkBalBranch6MkBalBranch11 wyx wyy wyz wzu fm_L fm_R yy yz zu fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll)

  
mkBalBranch6MkBalBranch2 wyx wyy wyz wzu key elt fm_L fm_R True mkBranch 2 key elt fm_L fm_R

  
mkBalBranch6MkBalBranch3 wyx wyy wyz wzu key elt fm_L fm_R True mkBalBranch6MkBalBranch1 wyx wyy wyz wzu fm_L fm_R fm_L
mkBalBranch6MkBalBranch3 wyx wyy wyz wzu key elt fm_L fm_R False mkBalBranch6MkBalBranch2 wyx wyy wyz wzu key elt fm_L fm_R otherwise

  
mkBalBranch6MkBalBranch4 wyx wyy wyz wzu key elt fm_L fm_R True mkBalBranch6MkBalBranch0 wyx wyy wyz wzu fm_L fm_R fm_R
mkBalBranch6MkBalBranch4 wyx wyy wyz wzu key elt fm_L fm_R False mkBalBranch6MkBalBranch3 wyx wyy wyz wzu key elt fm_L fm_R (mkBalBranch6Size_l wyx wyy wyz wzu > sIZE_RATIO * mkBalBranch6Size_r wyx wyy wyz wzu)

  
mkBalBranch6MkBalBranch5 wyx wyy wyz wzu key elt fm_L fm_R True mkBranch 1 key elt fm_L fm_R
mkBalBranch6MkBalBranch5 wyx wyy wyz wzu key elt fm_L fm_R False mkBalBranch6MkBalBranch4 wyx wyy wyz wzu key elt fm_L fm_R (mkBalBranch6Size_r wyx wyy wyz wzu > sIZE_RATIO * mkBalBranch6Size_l wyx wyy wyz wzu)

  
mkBalBranch6Single_L wyx wyy wyz wzu fm_l (Branch key_r elt_r vuu fm_rl fm_rrmkBranch 3 key_r elt_r (mkBranch 4 wyx wyy fm_l fm_rl) fm_rr

  
mkBalBranch6Single_R wyx wyy wyz wzu (Branch key_l elt_l yv fm_ll fm_lrfm_r mkBranch 8 key_l elt_l fm_ll (mkBranch 9 wyx wyy fm_lr fm_r)

  
mkBalBranch6Size_l wyx wyy wyz wzu sizeFM wyz

  
mkBalBranch6Size_r wyx wyy wyz wzu sizeFM wzu

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

  
mkBranchBalance_ok wxw wxx wxy True

  
mkBranchLeft_ok wxw wxx wxy mkBranchLeft_ok0 wxw wxx wxy wxw wxx wxw

  
mkBranchLeft_ok0 wxw wxx wxy fm_l key EmptyFM True
mkBranchLeft_ok0 wxw wxx wxy fm_l key (Branch left_key vx vy vz wumkBranchLeft_ok0Biggest_left_key fm_l < key

  
mkBranchLeft_ok0Biggest_left_key wzv fst (findMax wzv)

  
mkBranchLeft_size wxw wxx wxy sizeFM wxw

  
mkBranchResult wxz wyu wyv wyw Branch wxz wyu (mkBranchUnbox wyv wxz wyw (1 + mkBranchLeft_size wyv wxz wyw + mkBranchRight_size wyv wxz wyw)) wyv wyw

  
mkBranchRight_ok wxw wxx wxy mkBranchRight_ok0 wxw wxx wxy wxy wxx wxy

  
mkBranchRight_ok0 wxw wxx wxy fm_r key EmptyFM True
mkBranchRight_ok0 wxw wxx wxy fm_r key (Branch right_key wv ww wx wykey < mkBranchRight_ok0Smallest_right_key fm_r

  
mkBranchRight_ok0Smallest_right_key wzw fst (findMin wzw)

  
mkBranchRight_size wxw wxx wxy sizeFM wxy

  mkBranchUnbox :: Ord a =>  ->  (FiniteMap a b) ( ->  a ( ->  (FiniteMap a b) (Int  ->  Int)))
mkBranchUnbox wxw wxx wxy x x

  sIZE_RATIO :: Int
sIZE_RATIO 5

  sizeFM :: FiniteMap a b  ->  Int
sizeFM EmptyFM 0
sizeFM (Branch xx xy size xz yusize

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude



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

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

mainModule FiniteMap
  (addToFM :: Ord a => FiniteMap (Maybe a) b  ->  Maybe a  ->  b  ->  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 b => FiniteMap b a  ->  b  ->  a  ->  FiniteMap b a
addToFM fm key elt addToFM_C addToFM0 fm key elt

  
addToFM0 old new new

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

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

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

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

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

  
addToFM_C4 combiner EmptyFM key elt unitFM key elt
addToFM_C4 wuu wuv wuw wux addToFM_C3 wuu wuv wuw wux

  emptyFM :: FiniteMap b a
emptyFM EmptyFM

  findMax :: FiniteMap a b  ->  (a,b)
findMax (Branch key elt vuv vuw EmptyFM(key,elt)
findMax (Branch key elt vux vuy fm_rfindMax fm_r

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

  fmToList :: FiniteMap 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 vw fm_l fm_rfoldFM k (k key elt (foldFM k z fm_r)) fm_l

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

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

  
mkBalBranch6Double_L wyx wyy wyz wzu fm_l (Branch key_r elt_r zv (Branch key_rl elt_rl zw fm_rll fm_rlr) fm_rrmkBranch (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) key_rl elt_rl (mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))) wyx wyy fm_l fm_rll) (mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) key_r elt_r fm_rlr fm_rr)

  
mkBalBranch6Double_R wyx wyy wyz wzu (Branch key_l elt_l yw fm_ll (Branch key_lr elt_lr yx 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))))))))))))) wyx wyy fm_lrr fm_r)

  
mkBalBranch6MkBalBranch0 wyx wyy wyz wzu fm_L fm_R (Branch zx zy zz fm_rl fm_rrmkBalBranch6MkBalBranch02 wyx wyy wyz wzu fm_L fm_R (Branch zx zy zz fm_rl fm_rr)

  
mkBalBranch6MkBalBranch00 wyx wyy wyz wzu fm_L fm_R zx zy zz fm_rl fm_rr True mkBalBranch6Double_L wyx wyy wyz wzu fm_L fm_R

  
mkBalBranch6MkBalBranch01 wyx wyy wyz wzu fm_L fm_R zx zy zz fm_rl fm_rr True mkBalBranch6Single_L wyx wyy wyz wzu fm_L fm_R
mkBalBranch6MkBalBranch01 wyx wyy wyz wzu fm_L fm_R zx zy zz fm_rl fm_rr False mkBalBranch6MkBalBranch00 wyx wyy wyz wzu fm_L fm_R zx zy zz fm_rl fm_rr otherwise

  
mkBalBranch6MkBalBranch02 wyx wyy wyz wzu fm_L fm_R (Branch zx zy zz fm_rl fm_rrmkBalBranch6MkBalBranch01 wyx wyy wyz wzu fm_L fm_R zx zy zz fm_rl fm_rr (sizeFM fm_rl < Pos (Succ (Succ Zero)) * sizeFM fm_rr)

  
mkBalBranch6MkBalBranch1 wyx wyy wyz wzu fm_L fm_R (Branch yy yz zu fm_ll fm_lrmkBalBranch6MkBalBranch12 wyx wyy wyz wzu fm_L fm_R (Branch yy yz zu fm_ll fm_lr)

  
mkBalBranch6MkBalBranch10 wyx wyy wyz wzu fm_L fm_R yy yz zu fm_ll fm_lr True mkBalBranch6Double_R wyx wyy wyz wzu fm_L fm_R

  
mkBalBranch6MkBalBranch11 wyx wyy wyz wzu fm_L fm_R yy yz zu fm_ll fm_lr True mkBalBranch6Single_R wyx wyy wyz wzu fm_L fm_R
mkBalBranch6MkBalBranch11 wyx wyy wyz wzu fm_L fm_R yy yz zu fm_ll fm_lr False mkBalBranch6MkBalBranch10 wyx wyy wyz wzu fm_L fm_R yy yz zu fm_ll fm_lr otherwise

  
mkBalBranch6MkBalBranch12 wyx wyy wyz wzu fm_L fm_R (Branch yy yz zu fm_ll fm_lrmkBalBranch6MkBalBranch11 wyx wyy wyz wzu fm_L fm_R yy yz zu fm_ll fm_lr (sizeFM fm_lr < Pos (Succ (Succ Zero)) * sizeFM fm_ll)

  
mkBalBranch6MkBalBranch2 wyx wyy wyz wzu key elt fm_L fm_R True mkBranch (Pos (Succ (Succ Zero))) key elt fm_L fm_R

  
mkBalBranch6MkBalBranch3 wyx wyy wyz wzu key elt fm_L fm_R True mkBalBranch6MkBalBranch1 wyx wyy wyz wzu fm_L fm_R fm_L
mkBalBranch6MkBalBranch3 wyx wyy wyz wzu key elt fm_L fm_R False mkBalBranch6MkBalBranch2 wyx wyy wyz wzu key elt fm_L fm_R otherwise

  
mkBalBranch6MkBalBranch4 wyx wyy wyz wzu key elt fm_L fm_R True mkBalBranch6MkBalBranch0 wyx wyy wyz wzu fm_L fm_R fm_R
mkBalBranch6MkBalBranch4 wyx wyy wyz wzu key elt fm_L fm_R False mkBalBranch6MkBalBranch3 wyx wyy wyz wzu key elt fm_L fm_R (mkBalBranch6Size_l wyx wyy wyz wzu > sIZE_RATIO * mkBalBranch6Size_r wyx wyy wyz wzu)

  
mkBalBranch6MkBalBranch5 wyx wyy wyz wzu key elt fm_L fm_R True mkBranch (Pos (Succ Zero)) key elt fm_L fm_R
mkBalBranch6MkBalBranch5 wyx wyy wyz wzu key elt fm_L fm_R False mkBalBranch6MkBalBranch4 wyx wyy wyz wzu key elt fm_L fm_R (mkBalBranch6Size_r wyx wyy wyz wzu > sIZE_RATIO * mkBalBranch6Size_l wyx wyy wyz wzu)

  
mkBalBranch6Single_L wyx wyy wyz wzu fm_l (Branch key_r elt_r vuu fm_rl fm_rrmkBranch (Pos (Succ (Succ (Succ Zero)))) key_r elt_r (mkBranch (Pos (Succ (Succ (Succ (Succ Zero))))) wyx wyy fm_l fm_rl) fm_rr

  
mkBalBranch6Single_R wyx wyy wyz wzu (Branch key_l elt_l yv fm_ll fm_lrfm_r mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))) key_l elt_l fm_ll (mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))) wyx wyy fm_lr fm_r)

  
mkBalBranch6Size_l wyx wyy wyz wzu sizeFM wyz

  
mkBalBranch6Size_r wyx wyy wyz wzu sizeFM wzu

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

  
mkBranchBalance_ok wxw wxx wxy True

  
mkBranchLeft_ok wxw wxx wxy mkBranchLeft_ok0 wxw wxx wxy wxw wxx wxw

  
mkBranchLeft_ok0 wxw wxx wxy fm_l key EmptyFM True
mkBranchLeft_ok0 wxw wxx wxy fm_l key (Branch left_key vx vy vz wumkBranchLeft_ok0Biggest_left_key fm_l < key

  
mkBranchLeft_ok0Biggest_left_key wzv fst (findMax wzv)

  
mkBranchLeft_size wxw wxx wxy sizeFM wxw

  
mkBranchResult wxz wyu wyv wyw Branch wxz wyu (mkBranchUnbox wyv wxz wyw (Pos (Succ Zero+ mkBranchLeft_size wyv wxz wyw + mkBranchRight_size wyv wxz wyw)) wyv wyw

  
mkBranchRight_ok wxw wxx wxy mkBranchRight_ok0 wxw wxx wxy wxy wxx wxy

  
mkBranchRight_ok0 wxw wxx wxy fm_r key EmptyFM True
mkBranchRight_ok0 wxw wxx wxy fm_r key (Branch right_key wv ww wx wykey < mkBranchRight_ok0Smallest_right_key fm_r

  
mkBranchRight_ok0Smallest_right_key wzw fst (findMin wzw)

  
mkBranchRight_size wxw wxx wxy sizeFM wxy

  mkBranchUnbox :: Ord a =>  ->  (FiniteMap a b) ( ->  a ( ->  (FiniteMap a b) (Int  ->  Int)))
mkBranchUnbox wxw wxx wxy x x

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

  sizeFM :: FiniteMap b a  ->  Int
sizeFM EmptyFM Pos Zero
sizeFM (Branch xx xy size xz yusize

  unitFM :: a  ->  b  ->  FiniteMap a b
unitFM key elt Branch key elt (Pos (Succ Zero)) emptyFM emptyFM


module Maybe where
  import qualified FiniteMap
import qualified Prelude



Haskell To QDPs


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

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

new_primEqNat(Succ(wzz4000), Succ(wzz30000)) → new_primEqNat(wzz4000, wzz30000)

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

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

new_primCmpNat(Succ(wzz31000), Succ(wzz32000)) → new_primCmpNat(wzz31000, wzz32000)

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

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

new_primMinusNat(Succ(wzz26200), Succ(wzz8700)) → new_primMinusNat(wzz26200, wzz8700)

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

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

new_primPlusNat(Succ(wzz26200), Succ(wzz8700)) → new_primPlusNat(wzz26200, wzz8700)

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

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

new_primMulNat(Succ(wzz40100), Succ(wzz300100)) → new_primMulNat(wzz40100, Succ(wzz300100))

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

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

new_esEs1(@2(wzz400, wzz401), @2(wzz3000, wzz3001), gb, app(ty_Maybe, hc)) → new_esEs3(wzz401, wzz3001, hc)
new_esEs2(@3(wzz400, wzz401, wzz402), @3(wzz3000, wzz3001, wzz3002), app(app(app(ty_@3, bac), bad), bae), hf, hg) → new_esEs2(wzz400, wzz3000, bac, bad, bae)
new_esEs1(@2(wzz400, wzz401), @2(wzz3000, wzz3001), app(app(ty_Either, eg), eh), fa) → new_esEs(wzz400, wzz3000, eg, eh)
new_esEs2(@3(wzz400, wzz401, wzz402), @3(wzz3000, wzz3001, wzz3002), bag, hf, app(ty_[], bcc)) → new_esEs0(wzz402, wzz3002, bcc)
new_esEs0(:(wzz400, wzz401), :(wzz3000, wzz3001), app(ty_Maybe, ee)) → new_esEs3(wzz400, wzz3000, ee)
new_esEs2(@3(wzz400, wzz401, wzz402), @3(wzz3000, wzz3001, wzz3002), app(app(ty_Either, hd), he), hf, hg) → new_esEs(wzz400, wzz3000, hd, he)
new_esEs3(Just(wzz400), Just(wzz3000), app(app(ty_@2, bde), bdf)) → new_esEs1(wzz400, wzz3000, bde, bdf)
new_esEs2(@3(wzz400, wzz401, wzz402), @3(wzz3000, wzz3001, wzz3002), bag, app(ty_Maybe, bbh), hg) → new_esEs3(wzz401, wzz3001, bbh)
new_esEs(Left(wzz400), Left(wzz3000), app(app(ty_@2, bd), be), bb) → new_esEs1(wzz400, wzz3000, bd, be)
new_esEs2(@3(wzz400, wzz401, wzz402), @3(wzz3000, wzz3001, wzz3002), bag, hf, app(app(ty_@2, bcd), bce)) → new_esEs1(wzz402, wzz3002, bcd, bce)
new_esEs(Right(wzz400), Right(wzz3000), cb, app(ty_Maybe, dd)) → new_esEs3(wzz400, wzz3000, dd)
new_esEs1(@2(wzz400, wzz401), @2(wzz3000, wzz3001), app(ty_[], fb), fa) → new_esEs0(wzz400, wzz3000, fb)
new_esEs0(:(wzz400, wzz401), :(wzz3000, wzz3001), app(app(app(ty_@3, eb), ec), ed)) → new_esEs2(wzz400, wzz3000, eb, ec, ed)
new_esEs1(@2(wzz400, wzz401), @2(wzz3000, wzz3001), gb, app(app(app(ty_@3, gh), ha), hb)) → new_esEs2(wzz401, wzz3001, gh, ha, hb)
new_esEs2(@3(wzz400, wzz401, wzz402), @3(wzz3000, wzz3001, wzz3002), bag, hf, app(ty_Maybe, bda)) → new_esEs3(wzz402, wzz3002, bda)
new_esEs1(@2(wzz400, wzz401), @2(wzz3000, wzz3001), app(ty_Maybe, ga), fa) → new_esEs3(wzz400, wzz3000, ga)
new_esEs3(Just(wzz400), Just(wzz3000), app(ty_[], bdd)) → new_esEs0(wzz400, wzz3000, bdd)
new_esEs1(@2(wzz400, wzz401), @2(wzz3000, wzz3001), gb, app(ty_[], ge)) → new_esEs0(wzz401, wzz3001, ge)
new_esEs2(@3(wzz400, wzz401, wzz402), @3(wzz3000, wzz3001, wzz3002), bag, app(app(ty_Either, bah), bba), hg) → new_esEs(wzz401, wzz3001, bah, bba)
new_esEs2(@3(wzz400, wzz401, wzz402), @3(wzz3000, wzz3001, wzz3002), app(app(ty_@2, baa), bab), hf, hg) → new_esEs1(wzz400, wzz3000, baa, bab)
new_esEs1(@2(wzz400, wzz401), @2(wzz3000, wzz3001), gb, app(app(ty_@2, gf), gg)) → new_esEs1(wzz401, wzz3001, gf, gg)
new_esEs2(@3(wzz400, wzz401, wzz402), @3(wzz3000, wzz3001, wzz3002), bag, hf, app(app(ty_Either, bca), bcb)) → new_esEs(wzz402, wzz3002, bca, bcb)
new_esEs(Right(wzz400), Right(wzz3000), cb, app(app(ty_Either, cc), cd)) → new_esEs(wzz400, wzz3000, cc, cd)
new_esEs2(@3(wzz400, wzz401, wzz402), @3(wzz3000, wzz3001, wzz3002), bag, app(app(ty_@2, bbc), bbd), hg) → new_esEs1(wzz401, wzz3001, bbc, bbd)
new_esEs0(:(wzz400, wzz401), :(wzz3000, wzz3001), app(app(ty_@2, dh), ea)) → new_esEs1(wzz400, wzz3000, dh, ea)
new_esEs2(@3(wzz400, wzz401, wzz402), @3(wzz3000, wzz3001, wzz3002), bag, app(app(app(ty_@3, bbe), bbf), bbg), hg) → new_esEs2(wzz401, wzz3001, bbe, bbf, bbg)
new_esEs1(@2(wzz400, wzz401), @2(wzz3000, wzz3001), app(app(ty_@2, fc), fd), fa) → new_esEs1(wzz400, wzz3000, fc, fd)
new_esEs3(Just(wzz400), Just(wzz3000), app(app(app(ty_@3, bdg), bdh), bea)) → new_esEs2(wzz400, wzz3000, bdg, bdh, bea)
new_esEs3(Just(wzz400), Just(wzz3000), app(ty_Maybe, beb)) → new_esEs3(wzz400, wzz3000, beb)
new_esEs2(@3(wzz400, wzz401, wzz402), @3(wzz3000, wzz3001, wzz3002), app(ty_Maybe, baf), hf, hg) → new_esEs3(wzz400, wzz3000, baf)
new_esEs(Left(wzz400), Left(wzz3000), app(ty_Maybe, ca), bb) → new_esEs3(wzz400, wzz3000, ca)
new_esEs3(Just(wzz400), Just(wzz3000), app(app(ty_Either, bdb), bdc)) → new_esEs(wzz400, wzz3000, bdb, bdc)
new_esEs(Right(wzz400), Right(wzz3000), cb, app(app(ty_@2, cf), cg)) → new_esEs1(wzz400, wzz3000, cf, cg)
new_esEs0(:(wzz400, wzz401), :(wzz3000, wzz3001), app(app(ty_Either, de), df)) → new_esEs(wzz400, wzz3000, de, df)
new_esEs(Left(wzz400), Left(wzz3000), app(ty_[], bc), bb) → new_esEs0(wzz400, wzz3000, bc)
new_esEs(Left(wzz400), Left(wzz3000), app(app(app(ty_@3, bf), bg), bh), bb) → new_esEs2(wzz400, wzz3000, bf, bg, bh)
new_esEs(Right(wzz400), Right(wzz3000), cb, app(app(app(ty_@3, da), db), dc)) → new_esEs2(wzz400, wzz3000, da, db, dc)
new_esEs0(:(wzz400, wzz401), :(wzz3000, wzz3001), app(ty_[], dg)) → new_esEs0(wzz400, wzz3000, dg)
new_esEs2(@3(wzz400, wzz401, wzz402), @3(wzz3000, wzz3001, wzz3002), app(ty_[], hh), hf, hg) → new_esEs0(wzz400, wzz3000, hh)
new_esEs2(@3(wzz400, wzz401, wzz402), @3(wzz3000, wzz3001, wzz3002), bag, app(ty_[], bbb), hg) → new_esEs0(wzz401, wzz3001, bbb)
new_esEs(Right(wzz400), Right(wzz3000), cb, app(ty_[], ce)) → new_esEs0(wzz400, wzz3000, ce)
new_esEs1(@2(wzz400, wzz401), @2(wzz3000, wzz3001), gb, app(app(ty_Either, gc), gd)) → new_esEs(wzz401, wzz3001, gc, gd)
new_esEs0(:(wzz400, wzz401), :(wzz3000, wzz3001), ef) → new_esEs0(wzz401, wzz3001, ef)
new_esEs(Left(wzz400), Left(wzz3000), app(app(ty_Either, h), ba), bb) → new_esEs(wzz400, wzz3000, h, ba)
new_esEs2(@3(wzz400, wzz401, wzz402), @3(wzz3000, wzz3001, wzz3002), bag, hf, app(app(app(ty_@3, bcf), bcg), bch)) → new_esEs2(wzz402, wzz3002, bcf, bcg, bch)
new_esEs1(@2(wzz400, wzz401), @2(wzz3000, wzz3001), app(app(app(ty_@3, ff), fg), fh), fa) → new_esEs2(wzz400, wzz3000, ff, fg, fh)

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

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

new_compare21(Just(Just(wzz31000)), Just(Just(wzz32000)), False, app(ty_Maybe, app(ty_[], fa))) → new_ltEs(wzz31000, wzz32000, fa)
new_compare21(Just(Just(wzz31000)), Just(Just(wzz32000)), False, app(ty_Maybe, app(app(ty_Either, fb), fc))) → new_ltEs0(wzz31000, wzz32000, fb, fc)
new_compare21(Just(@3(wzz31000, wzz31001, wzz31002)), Just(@3(wzz32000, wzz32001, wzz32002)), False, app(app(app(ty_@3, bbh), app(app(ty_Either, bcb), bcc)), bag)) → new_lt0(wzz31001, wzz32001, bcb, bcc)
new_ltEs0(Left(wzz31000), Left(wzz32000), app(app(app(ty_@3, dd), de), df), ce) → new_ltEs3(wzz31000, wzz32000, dd, de, df)
new_ltEs3(@3(wzz31000, wzz31001, wzz31002), @3(wzz32000, wzz32001, wzz32002), bbh, app(ty_[], bca), bag) → new_lt(wzz31001, wzz32001, bca)
new_compare21(Just(Just(wzz31000)), Just(Just(wzz32000)), False, app(ty_Maybe, app(ty_Maybe, fd))) → new_ltEs1(wzz31000, wzz32000, fd)
new_compare21(Just(Right(wzz31000)), Just(Right(wzz32000)), False, app(app(ty_Either, dg), app(ty_[], dh))) → new_ltEs(wzz31000, wzz32000, dh)
new_compare0(:(wzz31000, wzz31001), :(wzz32000, wzz32001), h) → new_compare0(wzz31001, wzz32001, h)
new_compare21(Just(Just(wzz31000)), Just(Just(wzz32000)), False, app(ty_Maybe, app(app(ty_@2, ff), fg))) → new_ltEs2(wzz31000, wzz32000, ff, fg)
new_compare21(Just(@3(wzz31000, wzz31001, wzz31002)), Just(@3(wzz32000, wzz32001, wzz32002)), False, app(app(app(ty_@3, app(ty_[], bae)), baf), bag)) → new_lt(wzz31000, wzz32000, bae)
new_compare21(Just(@2(wzz31000, wzz31001)), Just(@2(wzz32000, wzz32001)), False, app(app(ty_@2, hc), app(ty_[], hd))) → new_ltEs(wzz31001, wzz32001, hd)
new_compare21(Just(@3(wzz31000, wzz31001, wzz31002)), Just(@3(wzz32000, wzz32001, wzz32002)), False, app(app(app(ty_@3, bbh), baf), app(app(app(ty_@3, bdh), bea), beb))) → new_ltEs3(wzz31002, wzz32002, bdh, bea, beb)
new_compare3(wzz31000, wzz32000, gf, gg) → new_compare22(wzz31000, wzz32000, new_esEs6(wzz31000, wzz32000, gf, gg), gf, gg)
new_compare21(Just(@3(wzz31000, wzz31001, wzz31002)), Just(@3(wzz32000, wzz32001, wzz32002)), False, app(app(app(ty_@3, bbh), app(app(ty_@2, bce), bcf)), bag)) → new_lt2(wzz31001, wzz32001, bce, bcf)
new_compare21(Just(@3(wzz31000, wzz31001, wzz31002)), Just(@3(wzz32000, wzz32001, wzz32002)), False, app(app(app(ty_@3, bbh), app(app(app(ty_@3, bcg), bch), bda)), bag)) → new_lt3(wzz31001, wzz32001, bcg, bch, bda)
new_ltEs1(Just(wzz31000), Just(wzz32000), app(app(ty_Either, fb), fc)) → new_ltEs0(wzz31000, wzz32000, fb, fc)
new_ltEs3(@3(wzz31000, wzz31001, wzz31002), @3(wzz32000, wzz32001, wzz32002), bbh, baf, app(app(ty_Either, bdc), bdd)) → new_ltEs0(wzz31002, wzz32002, bdc, bdd)
new_lt1(wzz31000, wzz32000, ge) → new_compare21(wzz31000, wzz32000, new_esEs5(wzz31000, wzz32000, ge), ge)
new_ltEs1(Just(wzz31000), Just(wzz32000), app(app(app(ty_@3, fh), ga), gb)) → new_ltEs3(wzz31000, wzz32000, fh, ga, gb)
new_ltEs3(@3(wzz31000, wzz31001, wzz31002), @3(wzz32000, wzz32001, wzz32002), app(app(ty_@2, bbc), bbd), baf, bag) → new_lt2(wzz31000, wzz32000, bbc, bbd)
new_ltEs3(@3(wzz31000, wzz31001, wzz31002), @3(wzz32000, wzz32001, wzz32002), bbh, baf, app(ty_Maybe, bde)) → new_ltEs1(wzz31002, wzz32002, bde)
new_compare21(Just(Left(wzz31000)), Just(Left(wzz32000)), False, app(app(ty_Either, app(ty_[], cd)), ce)) → new_ltEs(wzz31000, wzz32000, cd)
new_compare21(Just(@2(wzz31000, wzz31001)), Just(@2(wzz32000, wzz32001)), False, app(app(ty_@2, hc), app(app(ty_@2, hh), baa))) → new_ltEs2(wzz31001, wzz32001, hh, baa)
new_ltEs1(Just(wzz31000), Just(wzz32000), app(ty_[], fa)) → new_ltEs(wzz31000, wzz32000, fa)
new_primCompAux(wzz31000, wzz32000, wzz151, app(ty_Maybe, bd)) → new_compare2(wzz31000, wzz32000, bd)
new_compare21(Just(Right(wzz31000)), Just(Right(wzz32000)), False, app(app(ty_Either, dg), app(app(ty_Either, ea), eb))) → new_ltEs0(wzz31000, wzz32000, ea, eb)
new_ltEs2(@2(wzz31000, wzz31001), @2(wzz32000, wzz32001), app(ty_[], gc), gd) → new_compare0(wzz31000, wzz32000, gc)
new_compare21(Just(@2(wzz31000, wzz31001)), Just(@2(wzz32000, wzz32001)), False, app(app(ty_@2, app(ty_Maybe, ge)), gd)) → new_compare21(wzz31000, wzz32000, new_esEs5(wzz31000, wzz32000, ge), ge)
new_ltEs3(@3(wzz31000, wzz31001, wzz31002), @3(wzz32000, wzz32001, wzz32002), bbh, baf, app(app(ty_@2, bdf), bdg)) → new_ltEs2(wzz31002, wzz32002, bdf, bdg)
new_lt0(wzz31000, wzz32000, cb, cc) → new_compare20(wzz31000, wzz32000, new_esEs4(wzz31000, wzz32000, cb, cc), cb, cc)
new_ltEs2(@2(wzz31000, wzz31001), @2(wzz32000, wzz32001), app(app(app(ty_@3, gh), ha), hb), gd) → new_compare23(wzz31000, wzz32000, new_esEs7(wzz31000, wzz32000, gh, ha, hb), gh, ha, hb)
new_compare21(Just(:(wzz31000, wzz31001)), Just(:(wzz32000, wzz32001)), False, app(ty_[], h)) → new_primCompAux(wzz31000, wzz32000, new_compare(wzz31001, wzz32001, h), h)
new_ltEs0(Right(wzz31000), Right(wzz32000), dg, app(ty_[], dh)) → new_ltEs(wzz31000, wzz32000, dh)
new_ltEs0(Right(wzz31000), Right(wzz32000), dg, app(app(ty_Either, ea), eb)) → new_ltEs0(wzz31000, wzz32000, ea, eb)
new_ltEs2(@2(wzz31000, wzz31001), @2(wzz32000, wzz32001), hc, app(ty_Maybe, hg)) → new_ltEs1(wzz31001, wzz32001, hg)
new_compare21(Just(@3(wzz31000, wzz31001, wzz31002)), Just(@3(wzz32000, wzz32001, wzz32002)), False, app(app(app(ty_@3, bbh), baf), app(ty_Maybe, bde))) → new_ltEs1(wzz31002, wzz32002, bde)
new_ltEs3(@3(wzz31000, wzz31001, wzz31002), @3(wzz32000, wzz32001, wzz32002), bbh, app(ty_Maybe, bcd), bag) → new_lt1(wzz31001, wzz32001, bcd)
new_compare21(Just(Left(wzz31000)), Just(Left(wzz32000)), False, app(app(ty_Either, app(app(ty_Either, cf), cg)), ce)) → new_ltEs0(wzz31000, wzz32000, cf, cg)
new_ltEs0(Left(wzz31000), Left(wzz32000), app(app(ty_@2, db), dc), ce) → new_ltEs2(wzz31000, wzz32000, db, dc)
new_ltEs3(@3(wzz31000, wzz31001, wzz31002), @3(wzz32000, wzz32001, wzz32002), app(ty_Maybe, bbb), baf, bag) → new_lt1(wzz31000, wzz32000, bbb)
new_compare21(Just(@3(wzz31000, wzz31001, wzz31002)), Just(@3(wzz32000, wzz32001, wzz32002)), False, app(app(app(ty_@3, bbh), baf), app(ty_[], bdb))) → new_ltEs(wzz31002, wzz32002, bdb)
new_compare21(Just(Right(wzz31000)), Just(Right(wzz32000)), False, app(app(ty_Either, dg), app(app(ty_@2, ed), ee))) → new_ltEs2(wzz31000, wzz32000, ed, ee)
new_ltEs2(@2(wzz31000, wzz31001), @2(wzz32000, wzz32001), hc, app(ty_[], hd)) → new_ltEs(wzz31001, wzz32001, hd)
new_compare21(Just(Right(wzz31000)), Just(Right(wzz32000)), False, app(app(ty_Either, dg), app(app(app(ty_@3, ef), eg), eh))) → new_ltEs3(wzz31000, wzz32000, ef, eg, eh)
new_ltEs0(Right(wzz31000), Right(wzz32000), dg, app(app(ty_@2, ed), ee)) → new_ltEs2(wzz31000, wzz32000, ed, ee)
new_compare21(Just(@3(wzz31000, wzz31001, wzz31002)), Just(@3(wzz32000, wzz32001, wzz32002)), False, app(app(app(ty_@3, app(app(app(ty_@3, bbe), bbf), bbg)), baf), bag)) → new_lt3(wzz31000, wzz32000, bbe, bbf, bbg)
new_ltEs3(@3(wzz31000, wzz31001, wzz31002), @3(wzz32000, wzz32001, wzz32002), bbh, app(app(app(ty_@3, bcg), bch), bda), bag) → new_lt3(wzz31001, wzz32001, bcg, bch, bda)
new_compare21(Just(@2(wzz31000, wzz31001)), Just(@2(wzz32000, wzz32001)), False, app(app(ty_@2, app(app(ty_Either, cb), cc)), gd)) → new_compare20(wzz31000, wzz32000, new_esEs4(wzz31000, wzz32000, cb, cc), cb, cc)
new_ltEs2(@2(wzz31000, wzz31001), @2(wzz32000, wzz32001), hc, app(app(ty_Either, he), hf)) → new_ltEs0(wzz31001, wzz32001, he, hf)
new_compare21(Just(Left(wzz31000)), Just(Left(wzz32000)), False, app(app(ty_Either, app(app(app(ty_@3, dd), de), df)), ce)) → new_ltEs3(wzz31000, wzz32000, dd, de, df)
new_compare21(Just(@2(wzz31000, wzz31001)), Just(@2(wzz32000, wzz32001)), False, app(app(ty_@2, app(ty_[], gc)), gd)) → new_compare0(wzz31000, wzz32000, gc)
new_compare4(wzz31000, wzz32000, gh, ha, hb) → new_compare23(wzz31000, wzz32000, new_esEs7(wzz31000, wzz32000, gh, ha, hb), gh, ha, hb)
new_compare1(wzz31000, wzz32000, cb, cc) → new_compare20(wzz31000, wzz32000, new_esEs4(wzz31000, wzz32000, cb, cc), cb, cc)
new_ltEs3(@3(wzz31000, wzz31001, wzz31002), @3(wzz32000, wzz32001, wzz32002), app(app(ty_Either, bah), bba), baf, bag) → new_lt0(wzz31000, wzz32000, bah, bba)
new_ltEs2(@2(wzz31000, wzz31001), @2(wzz32000, wzz32001), app(app(ty_Either, cb), cc), gd) → new_compare20(wzz31000, wzz32000, new_esEs4(wzz31000, wzz32000, cb, cc), cb, cc)
new_compare23(wzz31000, wzz32000, False, gh, ha, hb) → new_ltEs3(wzz31000, wzz32000, gh, ha, hb)
new_compare21(Just(@2(wzz31000, wzz31001)), Just(@2(wzz32000, wzz32001)), False, app(app(ty_@2, app(app(app(ty_@3, gh), ha), hb)), gd)) → new_compare23(wzz31000, wzz32000, new_esEs7(wzz31000, wzz32000, gh, ha, hb), gh, ha, hb)
new_ltEs2(@2(wzz31000, wzz31001), @2(wzz32000, wzz32001), app(ty_Maybe, ge), gd) → new_compare21(wzz31000, wzz32000, new_esEs5(wzz31000, wzz32000, ge), ge)
new_compare0(:(wzz31000, wzz31001), :(wzz32000, wzz32001), h) → new_primCompAux(wzz31000, wzz32000, new_compare(wzz31001, wzz32001, h), h)
new_ltEs0(Right(wzz31000), Right(wzz32000), dg, app(app(app(ty_@3, ef), eg), eh)) → new_ltEs3(wzz31000, wzz32000, ef, eg, eh)
new_lt3(wzz31000, wzz32000, gh, ha, hb) → new_compare23(wzz31000, wzz32000, new_esEs7(wzz31000, wzz32000, gh, ha, hb), gh, ha, hb)
new_ltEs2(@2(wzz31000, wzz31001), @2(wzz32000, wzz32001), hc, app(app(app(ty_@3, bab), bac), bad)) → new_ltEs3(wzz31001, wzz32001, bab, bac, bad)
new_ltEs3(@3(wzz31000, wzz31001, wzz31002), @3(wzz32000, wzz32001, wzz32002), app(ty_[], bae), baf, bag) → new_lt(wzz31000, wzz32000, bae)
new_primCompAux(wzz31000, wzz32000, wzz151, app(app(ty_@2, be), bf)) → new_compare3(wzz31000, wzz32000, be, bf)
new_ltEs3(@3(wzz31000, wzz31001, wzz31002), @3(wzz32000, wzz32001, wzz32002), bbh, baf, app(ty_[], bdb)) → new_ltEs(wzz31002, wzz32002, bdb)
new_ltEs1(Just(wzz31000), Just(wzz32000), app(ty_Maybe, fd)) → new_ltEs1(wzz31000, wzz32000, fd)
new_compare21(Just(@3(wzz31000, wzz31001, wzz31002)), Just(@3(wzz32000, wzz32001, wzz32002)), False, app(app(app(ty_@3, bbh), app(ty_[], bca)), bag)) → new_lt(wzz31001, wzz32001, bca)
new_compare21(Just(@2(wzz31000, wzz31001)), Just(@2(wzz32000, wzz32001)), False, app(app(ty_@2, app(app(ty_@2, gf), gg)), gd)) → new_compare22(wzz31000, wzz32000, new_esEs6(wzz31000, wzz32000, gf, gg), gf, gg)
new_ltEs0(Left(wzz31000), Left(wzz32000), app(app(ty_Either, cf), cg), ce) → new_ltEs0(wzz31000, wzz32000, cf, cg)
new_compare21(Just(Left(wzz31000)), Just(Left(wzz32000)), False, app(app(ty_Either, app(app(ty_@2, db), dc)), ce)) → new_ltEs2(wzz31000, wzz32000, db, dc)
new_compare21(Just(@3(wzz31000, wzz31001, wzz31002)), Just(@3(wzz32000, wzz32001, wzz32002)), False, app(app(app(ty_@3, app(ty_Maybe, bbb)), baf), bag)) → new_lt1(wzz31000, wzz32000, bbb)
new_ltEs(:(wzz31000, wzz31001), :(wzz32000, wzz32001), h) → new_primCompAux(wzz31000, wzz32000, new_compare(wzz31001, wzz32001, h), h)
new_compare21(Just(Right(wzz31000)), Just(Right(wzz32000)), False, app(app(ty_Either, dg), app(ty_Maybe, ec))) → new_ltEs1(wzz31000, wzz32000, ec)
new_primCompAux(wzz31000, wzz32000, wzz151, app(ty_[], ba)) → new_compare0(wzz31000, wzz32000, ba)
new_ltEs0(Left(wzz31000), Left(wzz32000), app(ty_[], cd), ce) → new_ltEs(wzz31000, wzz32000, cd)
new_compare21(Just(@2(wzz31000, wzz31001)), Just(@2(wzz32000, wzz32001)), False, app(app(ty_@2, hc), app(app(app(ty_@3, bab), bac), bad))) → new_ltEs3(wzz31001, wzz32001, bab, bac, bad)
new_compare20(wzz31000, wzz32000, False, cb, cc) → new_ltEs0(wzz31000, wzz32000, cb, cc)
new_primCompAux(wzz31000, wzz32000, wzz151, app(app(ty_Either, bb), bc)) → new_compare1(wzz31000, wzz32000, bb, bc)
new_ltEs3(@3(wzz31000, wzz31001, wzz31002), @3(wzz32000, wzz32001, wzz32002), bbh, app(app(ty_@2, bce), bcf), bag) → new_lt2(wzz31001, wzz32001, bce, bcf)
new_compare21(Just(Left(wzz31000)), Just(Left(wzz32000)), False, app(app(ty_Either, app(ty_Maybe, da)), ce)) → new_ltEs1(wzz31000, wzz32000, da)
new_compare21(Just(@3(wzz31000, wzz31001, wzz31002)), Just(@3(wzz32000, wzz32001, wzz32002)), False, app(app(app(ty_@3, bbh), baf), app(app(ty_Either, bdc), bdd))) → new_ltEs0(wzz31002, wzz32002, bdc, bdd)
new_ltEs1(Just(wzz31000), Just(wzz32000), app(app(ty_@2, ff), fg)) → new_ltEs2(wzz31000, wzz32000, ff, fg)
new_compare21(Just(@3(wzz31000, wzz31001, wzz31002)), Just(@3(wzz32000, wzz32001, wzz32002)), False, app(app(app(ty_@3, bbh), app(ty_Maybe, bcd)), bag)) → new_lt1(wzz31001, wzz32001, bcd)
new_compare21(Just(@2(wzz31000, wzz31001)), Just(@2(wzz32000, wzz32001)), False, app(app(ty_@2, hc), app(app(ty_Either, he), hf))) → new_ltEs0(wzz31001, wzz32001, he, hf)
new_compare21(Just(Just(wzz31000)), Just(Just(wzz32000)), False, app(ty_Maybe, app(app(app(ty_@3, fh), ga), gb))) → new_ltEs3(wzz31000, wzz32000, fh, ga, gb)
new_ltEs3(@3(wzz31000, wzz31001, wzz31002), @3(wzz32000, wzz32001, wzz32002), bbh, baf, app(app(app(ty_@3, bdh), bea), beb)) → new_ltEs3(wzz31002, wzz32002, bdh, bea, beb)
new_compare21(Just(@2(wzz31000, wzz31001)), Just(@2(wzz32000, wzz32001)), False, app(app(ty_@2, hc), app(ty_Maybe, hg))) → new_ltEs1(wzz31001, wzz32001, hg)
new_ltEs2(@2(wzz31000, wzz31001), @2(wzz32000, wzz32001), hc, app(app(ty_@2, hh), baa)) → new_ltEs2(wzz31001, wzz32001, hh, baa)
new_ltEs(:(wzz31000, wzz31001), :(wzz32000, wzz32001), h) → new_compare0(wzz31001, wzz32001, h)
new_ltEs3(@3(wzz31000, wzz31001, wzz31002), @3(wzz32000, wzz32001, wzz32002), app(app(app(ty_@3, bbe), bbf), bbg), baf, bag) → new_lt3(wzz31000, wzz32000, bbe, bbf, bbg)
new_ltEs2(@2(wzz31000, wzz31001), @2(wzz32000, wzz32001), app(app(ty_@2, gf), gg), gd) → new_compare22(wzz31000, wzz32000, new_esEs6(wzz31000, wzz32000, gf, gg), gf, gg)
new_compare21(Just(@3(wzz31000, wzz31001, wzz31002)), Just(@3(wzz32000, wzz32001, wzz32002)), False, app(app(app(ty_@3, bbh), baf), app(app(ty_@2, bdf), bdg))) → new_ltEs2(wzz31002, wzz32002, bdf, bdg)
new_lt(wzz31000, wzz32000, gc) → new_compare0(wzz31000, wzz32000, gc)
new_ltEs3(@3(wzz31000, wzz31001, wzz31002), @3(wzz32000, wzz32001, wzz32002), bbh, app(app(ty_Either, bcb), bcc), bag) → new_lt0(wzz31001, wzz32001, bcb, bcc)
new_compare21(Just(@3(wzz31000, wzz31001, wzz31002)), Just(@3(wzz32000, wzz32001, wzz32002)), False, app(app(app(ty_@3, app(app(ty_@2, bbc), bbd)), baf), bag)) → new_lt2(wzz31000, wzz32000, bbc, bbd)
new_compare21(Just(@3(wzz31000, wzz31001, wzz31002)), Just(@3(wzz32000, wzz32001, wzz32002)), False, app(app(app(ty_@3, app(app(ty_Either, bah), bba)), baf), bag)) → new_lt0(wzz31000, wzz32000, bah, bba)
new_lt2(wzz31000, wzz32000, gf, gg) → new_compare22(wzz31000, wzz32000, new_esEs6(wzz31000, wzz32000, gf, gg), gf, gg)
new_compare2(wzz31000, wzz32000, ge) → new_compare21(wzz31000, wzz32000, new_esEs5(wzz31000, wzz32000, ge), ge)
new_compare22(wzz31000, wzz32000, False, gf, gg) → new_ltEs2(wzz31000, wzz32000, gf, gg)
new_ltEs0(Right(wzz31000), Right(wzz32000), dg, app(ty_Maybe, ec)) → new_ltEs1(wzz31000, wzz32000, ec)
new_primCompAux(wzz31000, wzz32000, wzz151, app(app(app(ty_@3, bg), bh), ca)) → new_compare4(wzz31000, wzz32000, bg, bh, ca)
new_ltEs0(Left(wzz31000), Left(wzz32000), app(ty_Maybe, da), ce) → new_ltEs1(wzz31000, wzz32000, da)
new_compare21(Just(:(wzz31000, wzz31001)), Just(:(wzz32000, wzz32001)), False, app(ty_[], h)) → new_compare0(wzz31001, wzz32001, h)

The TRS R consists of the following rules:

new_ltEs19(wzz3100, wzz3200, app(app(ty_@2, hc), gd)) → new_ltEs5(wzz3100, wzz3200, hc, gd)
new_ltEs20(wzz31001, wzz32001, ty_Bool) → new_ltEs4(wzz31001, wzz32001)
new_ltEs20(wzz31001, wzz32001, ty_Int) → new_ltEs9(wzz31001, wzz32001)
new_esEs21(wzz400, wzz3000, app(app(ty_@2, cbc), cbd)) → new_esEs6(wzz400, wzz3000, cbc, cbd)
new_lt20(wzz31000, wzz32000, ty_Int) → new_lt16(wzz31000, wzz32000)
new_esEs18(Char(wzz400), Char(wzz3000)) → new_primEqNat0(wzz400, wzz3000)
new_primCmpNat2(Zero, wzz3100) → LT
new_esEs14(wzz402, wzz3002, ty_Float) → new_esEs19(wzz402, wzz3002)
new_esEs25(wzz400, wzz3000, app(ty_[], cgd)) → new_esEs16(wzz400, wzz3000, cgd)
new_compare8(Integer(wzz31000), Integer(wzz32000)) → new_primCmpInt(wzz31000, wzz32000)
new_esEs25(wzz400, wzz3000, ty_Bool) → new_esEs15(wzz400, wzz3000)
new_esEs23(wzz31001, wzz32001, ty_Ordering) → new_esEs11(wzz31001, wzz32001)
new_esEs13(wzz401, wzz3001, ty_Double) → new_esEs8(wzz401, wzz3001)
new_ltEs14(Right(wzz31000), Right(wzz32000), dg, ty_Ordering) → new_ltEs10(wzz31000, wzz32000)
new_esEs27(wzz400, wzz3000, ty_Integer) → new_esEs20(wzz400, wzz3000)
new_compare110(wzz31000, wzz32000, True, cb, cc) → LT
new_ltEs20(wzz31001, wzz32001, ty_Ordering) → new_ltEs10(wzz31001, wzz32001)
new_primCmpNat1(Zero, Succ(wzz32000)) → LT
new_compare([], :(wzz32000, wzz32001), h) → LT
new_esEs22(wzz31000, wzz32000, ty_Float) → new_esEs19(wzz31000, wzz32000)
new_esEs13(wzz401, wzz3001, ty_Char) → new_esEs18(wzz401, wzz3001)
new_lt12(wzz31000, wzz32000, app(app(ty_Either, bah), bba)) → new_lt9(wzz31000, wzz32000, bah, bba)
new_ltEs15(Just(wzz31000), Just(wzz32000), app(ty_[], fa)) → new_ltEs13(wzz31000, wzz32000, fa)
new_ltEs15(Just(wzz31000), Just(wzz32000), app(ty_Ratio, daf)) → new_ltEs6(wzz31000, wzz32000, daf)
new_esEs4(Right(wzz400), Right(wzz3000), cee, app(ty_Maybe, cfg)) → new_esEs5(wzz400, wzz3000, cfg)
new_compare30(wzz31000, wzz32000) → new_compare25(wzz31000, wzz32000, new_esEs15(wzz31000, wzz32000))
new_esEs11(EQ, EQ) → True
new_ltEs14(Left(wzz31000), Left(wzz32000), ty_Bool, ce) → new_ltEs4(wzz31000, wzz32000)
new_ltEs20(wzz31001, wzz32001, ty_Double) → new_ltEs7(wzz31001, wzz32001)
new_esEs13(wzz401, wzz3001, ty_Integer) → new_esEs20(wzz401, wzz3001)
new_esEs23(wzz31001, wzz32001, ty_Float) → new_esEs19(wzz31001, wzz32001)
new_esEs26(wzz401, wzz3001, ty_Integer) → new_esEs20(wzz401, wzz3001)
new_esEs14(wzz402, wzz3002, ty_Ordering) → new_esEs11(wzz402, wzz3002)
new_compare17(Float(wzz31000, wzz31001), Float(wzz32000, wzz32001)) → new_compare14(new_sr(wzz31000, wzz32000), new_sr(wzz31001, wzz32001))
new_primMulNat0(Zero, Zero) → Zero
new_compare(:(wzz31000, wzz31001), [], h) → GT
new_esEs26(wzz401, wzz3001, app(ty_[], chf)) → new_esEs16(wzz401, wzz3001, chf)
new_esEs5(Just(wzz400), Just(wzz3000), ty_Int) → new_esEs9(wzz400, wzz3000)
new_ltEs14(Right(wzz31000), Right(wzz32000), dg, app(ty_[], dh)) → new_ltEs13(wzz31000, wzz32000, dh)
new_compare31(wzz31000, wzz32000, app(app(ty_@2, be), bf)) → new_compare6(wzz31000, wzz32000, be, bf)
new_esEs12(wzz400, wzz3000, ty_Bool) → new_esEs15(wzz400, wzz3000)
new_ltEs15(Nothing, Just(wzz32000), ccf) → True
new_esEs25(wzz400, wzz3000, ty_Double) → new_esEs8(wzz400, wzz3000)
new_esEs4(Right(wzz400), Right(wzz3000), cee, ty_Int) → new_esEs9(wzz400, wzz3000)
new_ltEs19(wzz3100, wzz3200, app(ty_Maybe, ccf)) → new_ltEs15(wzz3100, wzz3200, ccf)
new_esEs4(Left(wzz400), Left(wzz3000), app(ty_Ratio, cdf), cdd) → new_esEs17(wzz400, wzz3000, cdf)
new_lt20(wzz31000, wzz32000, app(app(ty_@2, gf), gg)) → new_lt8(wzz31000, wzz32000, gf, gg)
new_ltEs15(Just(wzz31000), Just(wzz32000), ty_Bool) → new_ltEs4(wzz31000, wzz32000)
new_esEs20(Integer(wzz400), Integer(wzz3000)) → new_primEqInt(wzz400, wzz3000)
new_esEs25(wzz400, wzz3000, ty_Ordering) → new_esEs11(wzz400, wzz3000)
new_lt12(wzz31000, wzz32000, ty_Integer) → new_lt6(wzz31000, wzz32000)
new_esEs5(Just(wzz400), Just(wzz3000), ty_Bool) → new_esEs15(wzz400, wzz3000)
new_lt20(wzz31000, wzz32000, ty_Double) → new_lt14(wzz31000, wzz32000)
new_ltEs20(wzz31001, wzz32001, app(app(app(ty_@3, bab), bac), bad)) → new_ltEs11(wzz31001, wzz32001, bab, bac, bad)
new_compare18(Double(wzz31000, wzz31001), Double(wzz32000, wzz32001)) → new_compare14(new_sr(wzz31000, wzz32000), new_sr(wzz31001, wzz32001))
new_esEs4(Right(wzz400), Right(wzz3000), cee, app(app(app(ty_@3, cfd), cfe), cff)) → new_esEs7(wzz400, wzz3000, cfd, cfe, cff)
new_esEs4(Left(wzz400), Left(wzz3000), app(app(ty_@2, cdg), cdh), cdd) → new_esEs6(wzz400, wzz3000, cdg, cdh)
new_esEs26(wzz401, wzz3001, ty_Double) → new_esEs8(wzz401, wzz3001)
new_ltEs19(wzz3100, wzz3200, ty_Ordering) → new_ltEs10(wzz3100, wzz3200)
new_ltEs19(wzz3100, wzz3200, ty_Bool) → new_ltEs4(wzz3100, wzz3200)
new_esEs13(wzz401, wzz3001, app(ty_Ratio, bgc)) → new_esEs17(wzz401, wzz3001, bgc)
new_esEs21(wzz400, wzz3000, app(app(app(ty_@3, cbe), cbf), cbg)) → new_esEs7(wzz400, wzz3000, cbe, cbf, cbg)
new_primCmpNat1(Succ(wzz31000), Succ(wzz32000)) → new_primCmpNat1(wzz31000, wzz32000)
new_compare28(wzz31000, wzz32000, ge) → new_compare29(wzz31000, wzz32000, new_esEs5(wzz31000, wzz32000, ge), ge)
new_esEs5(Just(wzz400), Just(wzz3000), app(ty_Maybe, dca)) → new_esEs5(wzz400, wzz3000, dca)
new_ltEs14(Right(wzz31000), Right(wzz32000), dg, ty_Bool) → new_ltEs4(wzz31000, wzz32000)
new_ltEs4(False, True) → True
new_ltEs10(EQ, GT) → True
new_esEs4(Right(wzz400), Right(wzz3000), cee, ty_Integer) → new_esEs20(wzz400, wzz3000)
new_compare19(Char(wzz31000), Char(wzz32000)) → new_primCmpNat1(wzz31000, wzz32000)
new_ltEs15(Just(wzz31000), Just(wzz32000), ty_@0) → new_ltEs17(wzz31000, wzz32000)
new_ltEs15(Just(wzz31000), Just(wzz32000), ty_Double) → new_ltEs7(wzz31000, wzz32000)
new_ltEs14(Left(wzz31000), Left(wzz32000), ty_Float, ce) → new_ltEs16(wzz31000, wzz32000)
new_lt20(wzz31000, wzz32000, app(ty_Maybe, ge)) → new_lt15(wzz31000, wzz32000, ge)
new_lt16(wzz310, wzz320) → new_esEs11(new_compare14(wzz310, wzz320), LT)
new_ltEs15(Just(wzz31000), Just(wzz32000), ty_Integer) → new_ltEs18(wzz31000, wzz32000)
new_compare26(wzz31000, wzz32000, False, cb, cc) → new_compare110(wzz31000, wzz32000, new_ltEs14(wzz31000, wzz32000, cb, cc), cb, cc)
new_lt20(wzz31000, wzz32000, ty_Float) → new_lt17(wzz31000, wzz32000)
new_esEs4(Left(wzz400), Left(wzz3000), ty_Double, cdd) → new_esEs8(wzz400, wzz3000)
new_esEs14(wzz402, wzz3002, app(ty_Ratio, bhe)) → new_esEs17(wzz402, wzz3002, bhe)
new_ltEs19(wzz3100, wzz3200, ty_Float) → new_ltEs16(wzz3100, wzz3200)
new_esEs26(wzz401, wzz3001, ty_Ordering) → new_esEs11(wzz401, wzz3001)
new_ltEs4(True, True) → True
new_pePe(False, wzz150) → wzz150
new_esEs25(wzz400, wzz3000, app(app(ty_Either, cgb), cgc)) → new_esEs4(wzz400, wzz3000, cgb, cgc)
new_esEs15(False, True) → False
new_esEs15(True, False) → False
new_lt20(wzz31000, wzz32000, ty_Bool) → new_lt11(wzz31000, wzz32000)
new_ltEs14(Right(wzz31000), Right(wzz32000), dg, ty_Float) → new_ltEs16(wzz31000, wzz32000)
new_esEs22(wzz31000, wzz32000, app(app(ty_Either, bah), bba)) → new_esEs4(wzz31000, wzz32000, bah, bba)
new_lt13(wzz31001, wzz32001, ty_Double) → new_lt14(wzz31001, wzz32001)
new_esEs23(wzz31001, wzz32001, ty_Double) → new_esEs8(wzz31001, wzz32001)
new_esEs17(:%(wzz400, wzz401), :%(wzz3000, wzz3001), dcb) → new_asAs(new_esEs27(wzz400, wzz3000, dcb), new_esEs28(wzz401, wzz3001, dcb))
new_esEs26(wzz401, wzz3001, app(ty_Ratio, chg)) → new_esEs17(wzz401, wzz3001, chg)
new_esEs13(wzz401, wzz3001, ty_Ordering) → new_esEs11(wzz401, wzz3001)
new_compare31(wzz31000, wzz32000, ty_@0) → new_compare13(wzz31000, wzz32000)
new_ltEs12(wzz31002, wzz32002, app(ty_Ratio, ccd)) → new_ltEs6(wzz31002, wzz32002, ccd)
new_ltEs20(wzz31001, wzz32001, app(ty_[], hd)) → new_ltEs13(wzz31001, wzz32001, hd)
new_esEs14(wzz402, wzz3002, app(app(ty_@2, bhf), bhg)) → new_esEs6(wzz402, wzz3002, bhf, bhg)
new_compare111(wzz31000, wzz32000, False) → GT
new_compare111(wzz31000, wzz32000, True) → LT
new_compare31(wzz31000, wzz32000, ty_Int) → new_compare14(wzz31000, wzz32000)
new_ltEs5(@2(wzz31000, wzz31001), @2(wzz32000, wzz32001), hc, gd) → new_pePe(new_lt20(wzz31000, wzz32000, hc), new_asAs(new_esEs24(wzz31000, wzz32000, hc), new_ltEs20(wzz31001, wzz32001, gd)))
new_esEs12(wzz400, wzz3000, app(ty_[], beh)) → new_esEs16(wzz400, wzz3000, beh)
new_ltEs15(Just(wzz31000), Just(wzz32000), app(ty_Maybe, fd)) → new_ltEs15(wzz31000, wzz32000, fd)
new_ltEs12(wzz31002, wzz32002, app(app(ty_Either, bdc), bdd)) → new_ltEs14(wzz31002, wzz32002, bdc, bdd)
new_esEs22(wzz31000, wzz32000, ty_Integer) → new_esEs20(wzz31000, wzz32000)
new_esEs23(wzz31001, wzz32001, app(app(app(ty_@3, bcg), bch), bda)) → new_esEs7(wzz31001, wzz32001, bcg, bch, bda)
new_esEs23(wzz31001, wzz32001, ty_Integer) → new_esEs20(wzz31001, wzz32001)
new_esEs25(wzz400, wzz3000, app(app(ty_@2, cgf), cgg)) → new_esEs6(wzz400, wzz3000, cgf, cgg)
new_esEs11(GT, GT) → True
new_esEs23(wzz31001, wzz32001, ty_Char) → new_esEs18(wzz31001, wzz32001)
new_esEs24(wzz31000, wzz32000, app(app(ty_@2, gf), gg)) → new_esEs6(wzz31000, wzz32000, gf, gg)
new_pePe(True, wzz150) → True
new_primEqNat0(Zero, Zero) → True
new_ltEs19(wzz3100, wzz3200, ty_Integer) → new_ltEs18(wzz3100, wzz3200)
new_esEs13(wzz401, wzz3001, app(ty_Maybe, bha)) → new_esEs5(wzz401, wzz3001, bha)
new_primMulNat0(Succ(wzz40100), Succ(wzz300100)) → new_primPlusNat1(new_primMulNat0(wzz40100, Succ(wzz300100)), wzz300100)
new_lt12(wzz31000, wzz32000, ty_Char) → new_lt18(wzz31000, wzz32000)
new_ltEs12(wzz31002, wzz32002, ty_@0) → new_ltEs17(wzz31002, wzz32002)
new_compare29(Nothing, Just(wzz3200), False, cce) → LT
new_compare31(wzz31000, wzz32000, ty_Bool) → new_compare30(wzz31000, wzz32000)
new_ltEs14(Right(wzz31000), Right(wzz32000), dg, app(ty_Maybe, ec)) → new_ltEs15(wzz31000, wzz32000, ec)
new_esEs26(wzz401, wzz3001, ty_Bool) → new_esEs15(wzz401, wzz3001)
new_esEs24(wzz31000, wzz32000, app(ty_Ratio, cad)) → new_esEs17(wzz31000, wzz32000, cad)
new_esEs13(wzz401, wzz3001, ty_@0) → new_esEs10(wzz401, wzz3001)
new_compare110(wzz31000, wzz32000, False, cb, cc) → GT
new_compare(:(wzz31000, wzz31001), :(wzz32000, wzz32001), h) → new_primCompAux1(wzz31000, wzz32000, new_compare(wzz31001, wzz32001, h), h)
new_sr(wzz401, wzz3001) → new_primMulInt(wzz401, wzz3001)
new_ltEs15(Just(wzz31000), Just(wzz32000), ty_Char) → new_ltEs8(wzz31000, wzz32000)
new_compare210(wzz31000, wzz32000, False, gh, ha, hb) → new_compare12(wzz31000, wzz32000, new_ltEs11(wzz31000, wzz32000, gh, ha, hb), gh, ha, hb)
new_compare12(wzz31000, wzz32000, True, gh, ha, hb) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_esEs5(Just(wzz400), Just(wzz3000), ty_Char) → new_esEs18(wzz400, wzz3000)
new_ltEs12(wzz31002, wzz32002, app(app(ty_@2, bdf), bdg)) → new_ltEs5(wzz31002, wzz32002, bdf, bdg)
new_lt4(wzz31000, wzz32000) → new_esEs11(new_compare5(wzz31000, wzz32000), LT)
new_esEs4(Left(wzz400), Left(wzz3000), ty_Int, cdd) → new_esEs9(wzz400, wzz3000)
new_esEs13(wzz401, wzz3001, ty_Int) → new_esEs9(wzz401, wzz3001)
new_primCmpInt(Neg(Zero), Neg(Succ(wzz3200))) → new_primCmpNat0(wzz3200, Zero)
new_esEs25(wzz400, wzz3000, ty_@0) → new_esEs10(wzz400, wzz3000)
new_compare7(wzz31000, wzz32000, gh, ha, hb) → new_compare210(wzz31000, wzz32000, new_esEs7(wzz31000, wzz32000, gh, ha, hb), gh, ha, hb)
new_lt13(wzz31001, wzz32001, ty_Ordering) → new_lt4(wzz31001, wzz32001)
new_esEs19(Float(wzz400, wzz401), Float(wzz3000, wzz3001)) → new_esEs9(new_sr(wzz400, wzz3000), new_sr(wzz401, wzz3001))
new_ltEs20(wzz31001, wzz32001, ty_Float) → new_ltEs16(wzz31001, wzz32001)
new_ltEs15(Just(wzz31000), Just(wzz32000), ty_Int) → new_ltEs9(wzz31000, wzz32000)
new_primCmpNat1(Succ(wzz31000), Zero) → GT
new_esEs4(Right(wzz400), Right(wzz3000), cee, app(app(ty_Either, cef), ceg)) → new_esEs4(wzz400, wzz3000, cef, ceg)
new_ltEs12(wzz31002, wzz32002, ty_Ordering) → new_ltEs10(wzz31002, wzz32002)
new_primEqInt(Neg(Succ(wzz4000)), Neg(Succ(wzz30000))) → new_primEqNat0(wzz4000, wzz30000)
new_compare25(wzz31000, wzz32000, True) → EQ
new_esEs15(True, True) → True
new_lt13(wzz31001, wzz32001, app(ty_[], bca)) → new_lt10(wzz31001, wzz32001, bca)
new_ltEs15(Just(wzz31000), Just(wzz32000), ty_Float) → new_ltEs16(wzz31000, wzz32000)
new_compare16(wzz118, wzz119, True, cca) → LT
new_esEs4(Left(wzz400), Left(wzz3000), app(app(ty_Either, cdb), cdc), cdd) → new_esEs4(wzz400, wzz3000, cdb, cdc)
new_compare31(wzz31000, wzz32000, app(app(ty_Either, bb), bc)) → new_compare15(wzz31000, wzz32000, bb, bc)
new_esEs24(wzz31000, wzz32000, ty_Integer) → new_esEs20(wzz31000, wzz32000)
new_lt12(wzz31000, wzz32000, app(ty_Ratio, ccb)) → new_lt7(wzz31000, wzz32000, ccb)
new_ltEs14(Right(wzz31000), Right(wzz32000), dg, ty_@0) → new_ltEs17(wzz31000, wzz32000)
new_esEs4(Right(wzz400), Right(wzz3000), cee, ty_Ordering) → new_esEs11(wzz400, wzz3000)
new_lt14(wzz31000, wzz32000) → new_esEs11(new_compare18(wzz31000, wzz32000), LT)
new_esEs26(wzz401, wzz3001, app(app(app(ty_@3, dab), dac), dad)) → new_esEs7(wzz401, wzz3001, dab, dac, dad)
new_ltEs14(Right(wzz31000), Left(wzz32000), dg, ce) → False
new_esEs25(wzz400, wzz3000, ty_Char) → new_esEs18(wzz400, wzz3000)
new_compare29(Just(wzz3100), Nothing, False, cce) → GT
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_ltEs12(wzz31002, wzz32002, app(ty_[], bdb)) → new_ltEs13(wzz31002, wzz32002, bdb)
new_esEs21(wzz400, wzz3000, ty_Double) → new_esEs8(wzz400, wzz3000)
new_ltEs11(@3(wzz31000, wzz31001, wzz31002), @3(wzz32000, wzz32001, wzz32002), bbh, baf, bag) → new_pePe(new_lt12(wzz31000, wzz32000, bbh), new_asAs(new_esEs22(wzz31000, wzz32000, bbh), new_pePe(new_lt13(wzz31001, wzz32001, baf), new_asAs(new_esEs23(wzz31001, wzz32001, baf), new_ltEs12(wzz31002, wzz32002, bag)))))
new_compare15(wzz31000, wzz32000, cb, cc) → new_compare26(wzz31000, wzz32000, new_esEs4(wzz31000, wzz32000, cb, cc), cb, cc)
new_esEs4(Left(wzz400), Left(wzz3000), ty_Char, cdd) → new_esEs18(wzz400, wzz3000)
new_primEqInt(Neg(Zero), Neg(Succ(wzz30000))) → False
new_primEqInt(Neg(Succ(wzz4000)), Neg(Zero)) → False
new_esEs4(Right(wzz400), Right(wzz3000), cee, app(ty_[], ceh)) → new_esEs16(wzz400, wzz3000, ceh)
new_primCompAux0(wzz165, GT) → GT
new_compare26(wzz31000, wzz32000, True, cb, cc) → EQ
new_ltEs9(wzz3100, wzz3200) → new_fsEs(new_compare14(wzz3100, wzz3200))
new_esEs4(Right(wzz400), Right(wzz3000), cee, ty_Double) → new_esEs8(wzz400, wzz3000)
new_esEs21(wzz400, wzz3000, app(app(ty_Either, cag), cah)) → new_esEs4(wzz400, wzz3000, cag, cah)
new_compare24(wzz31000, wzz32000, True, gf, gg) → EQ
new_ltEs15(Just(wzz31000), Just(wzz32000), app(app(app(ty_@3, fh), ga), gb)) → new_ltEs11(wzz31000, wzz32000, fh, ga, gb)
new_ltEs12(wzz31002, wzz32002, ty_Bool) → new_ltEs4(wzz31002, wzz32002)
new_esEs4(Right(wzz400), Right(wzz3000), cee, ty_Bool) → new_esEs15(wzz400, wzz3000)
new_compare([], [], h) → EQ
new_compare14(wzz31, wzz32) → new_primCmpInt(wzz31, wzz32)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_esEs21(wzz400, wzz3000, app(ty_Ratio, cbb)) → new_esEs17(wzz400, wzz3000, cbb)
new_esEs5(Just(wzz400), Just(wzz3000), ty_@0) → new_esEs10(wzz400, wzz3000)
new_ltEs20(wzz31001, wzz32001, app(app(ty_@2, hh), baa)) → new_ltEs5(wzz31001, wzz32001, hh, baa)
new_ltEs19(wzz3100, wzz3200, ty_Double) → new_ltEs7(wzz3100, wzz3200)
new_ltEs14(Left(wzz31000), Left(wzz32000), ty_Int, ce) → new_ltEs9(wzz31000, wzz32000)
new_esEs4(Left(wzz400), Left(wzz3000), ty_Float, cdd) → new_esEs19(wzz400, wzz3000)
new_esEs22(wzz31000, wzz32000, ty_Double) → new_esEs8(wzz31000, wzz32000)
new_primEqInt(Pos(Succ(wzz4000)), Pos(Succ(wzz30000))) → new_primEqNat0(wzz4000, wzz30000)
new_compare5(wzz31000, wzz32000) → new_compare27(wzz31000, wzz32000, new_esEs11(wzz31000, wzz32000))
new_lt9(wzz31000, wzz32000, cb, cc) → new_esEs11(new_compare15(wzz31000, wzz32000, cb, cc), LT)
new_esEs25(wzz400, wzz3000, app(ty_Maybe, chc)) → new_esEs5(wzz400, wzz3000, chc)
new_ltEs12(wzz31002, wzz32002, app(ty_Maybe, bde)) → new_ltEs15(wzz31002, wzz32002, bde)
new_esEs12(wzz400, wzz3000, ty_Double) → new_esEs8(wzz400, wzz3000)
new_esEs16(:(wzz400, wzz401), :(wzz3000, wzz3001), caf) → new_asAs(new_esEs21(wzz400, wzz3000, caf), new_esEs16(wzz401, wzz3001, caf))
new_esEs25(wzz400, wzz3000, ty_Int) → new_esEs9(wzz400, wzz3000)
new_lt13(wzz31001, wzz32001, app(app(ty_Either, bcb), bcc)) → new_lt9(wzz31001, wzz32001, bcb, bcc)
new_ltEs10(GT, EQ) → False
new_primEqNat0(Succ(wzz4000), Succ(wzz30000)) → new_primEqNat0(wzz4000, wzz30000)
new_esEs12(wzz400, wzz3000, ty_@0) → new_esEs10(wzz400, wzz3000)
new_compare31(wzz31000, wzz32000, ty_Float) → new_compare17(wzz31000, wzz32000)
new_lt13(wzz31001, wzz32001, ty_Integer) → new_lt6(wzz31001, wzz32001)
new_esEs4(Left(wzz400), Left(wzz3000), app(app(app(ty_@3, cea), ceb), cec), cdd) → new_esEs7(wzz400, wzz3000, cea, ceb, cec)
new_esEs14(wzz402, wzz3002, app(ty_Maybe, cac)) → new_esEs5(wzz402, wzz3002, cac)
new_lt12(wzz31000, wzz32000, ty_Ordering) → new_lt4(wzz31000, wzz32000)
new_esEs21(wzz400, wzz3000, ty_Float) → new_esEs19(wzz400, wzz3000)
new_compare16(wzz118, wzz119, False, cca) → GT
new_ltEs14(Left(wzz31000), Left(wzz32000), ty_Ordering, ce) → new_ltEs10(wzz31000, wzz32000)
new_esEs23(wzz31001, wzz32001, ty_Bool) → new_esEs15(wzz31001, wzz32001)
new_esEs12(wzz400, wzz3000, app(app(ty_Either, bef), beg)) → new_esEs4(wzz400, wzz3000, bef, beg)
new_lt13(wzz31001, wzz32001, ty_Int) → new_lt16(wzz31001, wzz32001)
new_primEqInt(Pos(Zero), Pos(Succ(wzz30000))) → False
new_primEqInt(Pos(Succ(wzz4000)), Pos(Zero)) → False
new_esEs25(wzz400, wzz3000, ty_Integer) → new_esEs20(wzz400, wzz3000)
new_esEs22(wzz31000, wzz32000, ty_Ordering) → new_esEs11(wzz31000, wzz32000)
new_esEs21(wzz400, wzz3000, ty_Bool) → new_esEs15(wzz400, wzz3000)
new_lt20(wzz31000, wzz32000, ty_Char) → new_lt18(wzz31000, wzz32000)
new_esEs12(wzz400, wzz3000, app(app(app(ty_@3, bfd), bfe), bff)) → new_esEs7(wzz400, wzz3000, bfd, bfe, bff)
new_primPlusNat0(Succ(wzz26200), Zero) → Succ(wzz26200)
new_primPlusNat0(Zero, Succ(wzz8700)) → Succ(wzz8700)
new_lt13(wzz31001, wzz32001, ty_@0) → new_lt19(wzz31001, wzz32001)
new_esEs24(wzz31000, wzz32000, ty_@0) → new_esEs10(wzz31000, wzz32000)
new_esEs28(wzz401, wzz3001, ty_Integer) → new_esEs20(wzz401, wzz3001)
new_esEs4(Right(wzz400), Right(wzz3000), cee, ty_@0) → new_esEs10(wzz400, wzz3000)
new_ltEs14(Left(wzz31000), Left(wzz32000), ty_Char, ce) → new_ltEs8(wzz31000, wzz32000)
new_ltEs10(LT, EQ) → True
new_primCmpInt(Neg(Zero), Pos(Succ(wzz3200))) → LT
new_ltEs15(Just(wzz31000), Just(wzz32000), ty_Ordering) → new_ltEs10(wzz31000, wzz32000)
new_esEs4(Left(wzz400), Left(wzz3000), ty_Ordering, cdd) → new_esEs11(wzz400, wzz3000)
new_compare11(wzz31000, wzz32000, True, gf, gg) → LT
new_compare210(wzz31000, wzz32000, True, gh, ha, hb) → EQ
new_compare31(wzz31000, wzz32000, app(ty_Ratio, dcc)) → new_compare9(wzz31000, wzz32000, dcc)
new_sr0(Integer(wzz310000), Integer(wzz320010)) → Integer(new_primMulInt(wzz310000, wzz320010))
new_primEqInt(Neg(Succ(wzz4000)), Pos(wzz3000)) → False
new_primEqInt(Pos(Succ(wzz4000)), Neg(wzz3000)) → False
new_compare25(wzz31000, wzz32000, False) → new_compare10(wzz31000, wzz32000, new_ltEs4(wzz31000, wzz32000))
new_esEs13(wzz401, wzz3001, ty_Bool) → new_esEs15(wzz401, wzz3001)
new_ltEs7(wzz3100, wzz3200) → new_fsEs(new_compare18(wzz3100, wzz3200))
new_ltEs14(Left(wzz31000), Left(wzz32000), app(ty_[], cd), ce) → new_ltEs13(wzz31000, wzz32000, cd)
new_ltEs10(GT, GT) → True
new_esEs14(wzz402, wzz3002, app(ty_[], bhd)) → new_esEs16(wzz402, wzz3002, bhd)
new_esEs22(wzz31000, wzz32000, app(app(ty_@2, bbc), bbd)) → new_esEs6(wzz31000, wzz32000, bbc, bbd)
new_ltEs20(wzz31001, wzz32001, ty_Integer) → new_ltEs18(wzz31001, wzz32001)
new_esEs26(wzz401, wzz3001, ty_Int) → new_esEs9(wzz401, wzz3001)
new_ltEs20(wzz31001, wzz32001, app(ty_Maybe, hg)) → new_ltEs15(wzz31001, wzz32001, hg)
new_lt13(wzz31001, wzz32001, app(ty_Ratio, ccc)) → new_lt7(wzz31001, wzz32001, ccc)
new_esEs24(wzz31000, wzz32000, ty_Ordering) → new_esEs11(wzz31000, wzz32000)
new_primEqInt(Neg(Zero), Pos(Succ(wzz30000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(wzz30000))) → False
new_primCmpNat2(Succ(wzz3200), wzz3100) → new_primCmpNat1(wzz3200, wzz3100)
new_ltEs14(Right(wzz31000), Right(wzz32000), dg, ty_Double) → new_ltEs7(wzz31000, wzz32000)
new_lt12(wzz31000, wzz32000, app(ty_[], bae)) → new_lt10(wzz31000, wzz32000, bae)
new_esEs21(wzz400, wzz3000, ty_Ordering) → new_esEs11(wzz400, wzz3000)
new_lt20(wzz31000, wzz32000, ty_Ordering) → new_lt4(wzz31000, wzz32000)
new_lt8(wzz31000, wzz32000, gf, gg) → new_esEs11(new_compare6(wzz31000, wzz32000, gf, gg), LT)
new_esEs14(wzz402, wzz3002, ty_Double) → new_esEs8(wzz402, wzz3002)
new_esEs5(Just(wzz400), Just(wzz3000), ty_Ordering) → new_esEs11(wzz400, wzz3000)
new_compare31(wzz31000, wzz32000, ty_Ordering) → new_compare5(wzz31000, wzz32000)
new_lt20(wzz31000, wzz32000, ty_Integer) → new_lt6(wzz31000, wzz32000)
new_esEs21(wzz400, wzz3000, ty_Char) → new_esEs18(wzz400, wzz3000)
new_primCompAux0(wzz165, LT) → LT
new_ltEs19(wzz3100, wzz3200, ty_Char) → new_ltEs8(wzz3100, wzz3200)
new_lt13(wzz31001, wzz32001, ty_Bool) → new_lt11(wzz31001, wzz32001)
new_ltEs14(Right(wzz31000), Right(wzz32000), dg, ty_Integer) → new_ltEs18(wzz31000, wzz32000)
new_not(False) → True
new_esEs24(wzz31000, wzz32000, ty_Float) → new_esEs19(wzz31000, wzz32000)
new_esEs4(Right(wzz400), Right(wzz3000), cee, app(ty_Ratio, cfa)) → new_esEs17(wzz400, wzz3000, cfa)
new_esEs23(wzz31001, wzz32001, app(app(ty_@2, bce), bcf)) → new_esEs6(wzz31001, wzz32001, bce, bcf)
new_compare12(wzz31000, wzz32000, False, gh, ha, hb) → GT
new_esEs12(wzz400, wzz3000, ty_Integer) → new_esEs20(wzz400, wzz3000)
new_esEs11(LT, GT) → False
new_esEs11(GT, LT) → False
new_compare31(wzz31000, wzz32000, app(ty_Maybe, bd)) → new_compare28(wzz31000, wzz32000, bd)
new_ltEs14(Right(wzz31000), Right(wzz32000), dg, app(ty_Ratio, cda)) → new_ltEs6(wzz31000, wzz32000, cda)
new_compare27(wzz31000, wzz32000, False) → new_compare111(wzz31000, wzz32000, new_ltEs10(wzz31000, wzz32000))
new_lt20(wzz31000, wzz32000, app(ty_[], gc)) → new_lt10(wzz31000, wzz32000, gc)
new_esEs13(wzz401, wzz3001, app(ty_[], bgb)) → new_esEs16(wzz401, wzz3001, bgb)
new_esEs12(wzz400, wzz3000, ty_Float) → new_esEs19(wzz400, wzz3000)
new_esEs11(LT, EQ) → False
new_esEs11(EQ, LT) → False
new_esEs24(wzz31000, wzz32000, app(ty_Maybe, ge)) → new_esEs5(wzz31000, wzz32000, ge)
new_esEs4(Right(wzz400), Right(wzz3000), cee, app(app(ty_@2, cfb), cfc)) → new_esEs6(wzz400, wzz3000, cfb, cfc)
new_esEs23(wzz31001, wzz32001, ty_@0) → new_esEs10(wzz31001, wzz32001)
new_esEs14(wzz402, wzz3002, ty_Char) → new_esEs18(wzz402, wzz3002)
new_esEs14(wzz402, wzz3002, ty_@0) → new_esEs10(wzz402, wzz3002)
new_lt12(wzz31000, wzz32000, ty_Double) → new_lt14(wzz31000, wzz32000)
new_ltEs20(wzz31001, wzz32001, ty_@0) → new_ltEs17(wzz31001, wzz32001)
new_compare11(wzz31000, wzz32000, False, gf, gg) → GT
new_ltEs17(wzz3100, wzz3200) → new_fsEs(new_compare13(wzz3100, wzz3200))
new_esEs22(wzz31000, wzz32000, app(app(app(ty_@3, bbe), bbf), bbg)) → new_esEs7(wzz31000, wzz32000, bbe, bbf, bbg)
new_esEs13(wzz401, wzz3001, app(app(ty_Either, bfh), bga)) → new_esEs4(wzz401, wzz3001, bfh, bga)
new_primCmpInt(Pos(Succ(wzz3100)), Neg(wzz320)) → GT
new_esEs22(wzz31000, wzz32000, ty_Char) → new_esEs18(wzz31000, wzz32000)
new_ltEs19(wzz3100, wzz3200, ty_Int) → new_ltEs9(wzz3100, wzz3200)
new_lt12(wzz31000, wzz32000, app(app(app(ty_@3, bbe), bbf), bbg)) → new_lt5(wzz31000, wzz32000, bbe, bbf, bbg)
new_ltEs18(wzz3100, wzz3200) → new_fsEs(new_compare8(wzz3100, wzz3200))
new_esEs22(wzz31000, wzz32000, app(ty_[], bae)) → new_esEs16(wzz31000, wzz32000, bae)
new_esEs14(wzz402, wzz3002, app(app(ty_Either, bhb), bhc)) → new_esEs4(wzz402, wzz3002, bhb, bhc)
new_primMulInt(Pos(wzz4010), Pos(wzz30010)) → Pos(new_primMulNat0(wzz4010, wzz30010))
new_esEs26(wzz401, wzz3001, ty_@0) → new_esEs10(wzz401, wzz3001)
new_esEs4(Left(wzz400), Left(wzz3000), ty_Bool, cdd) → new_esEs15(wzz400, wzz3000)
new_esEs23(wzz31001, wzz32001, app(app(ty_Either, bcb), bcc)) → new_esEs4(wzz31001, wzz32001, bcb, bcc)
new_esEs14(wzz402, wzz3002, ty_Bool) → new_esEs15(wzz402, wzz3002)
new_primMulInt(Neg(wzz4010), Neg(wzz30010)) → Pos(new_primMulNat0(wzz4010, wzz30010))
new_ltEs19(wzz3100, wzz3200, app(ty_Ratio, cae)) → new_ltEs6(wzz3100, wzz3200, cae)
new_lt6(wzz31000, wzz32000) → new_esEs11(new_compare8(wzz31000, wzz32000), LT)
new_esEs24(wzz31000, wzz32000, ty_Bool) → new_esEs15(wzz31000, wzz32000)
new_primEqNat0(Zero, Succ(wzz30000)) → False
new_primEqNat0(Succ(wzz4000), Zero) → False
new_esEs21(wzz400, wzz3000, ty_@0) → new_esEs10(wzz400, wzz3000)
new_esEs21(wzz400, wzz3000, ty_Int) → new_esEs9(wzz400, wzz3000)
new_primPlusNat0(Zero, Zero) → Zero
new_esEs25(wzz400, wzz3000, app(ty_Ratio, cge)) → new_esEs17(wzz400, wzz3000, cge)
new_lt12(wzz31000, wzz32000, ty_Bool) → new_lt11(wzz31000, wzz32000)
new_compare31(wzz31000, wzz32000, ty_Integer) → new_compare8(wzz31000, wzz32000)
new_lt12(wzz31000, wzz32000, ty_Int) → new_lt16(wzz31000, wzz32000)
new_ltEs14(Left(wzz31000), Left(wzz32000), app(app(ty_@2, db), dc), ce) → new_ltEs5(wzz31000, wzz32000, db, dc)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_compare9(:%(wzz31000, wzz31001), :%(wzz32000, wzz32001), ty_Integer) → new_compare8(new_sr0(wzz31000, wzz32001), new_sr0(wzz32000, wzz31001))
new_esEs24(wzz31000, wzz32000, app(app(ty_Either, cb), cc)) → new_esEs4(wzz31000, wzz32000, cb, cc)
new_compare31(wzz31000, wzz32000, ty_Double) → new_compare18(wzz31000, wzz32000)
new_esEs5(Just(wzz400), Just(wzz3000), ty_Float) → new_esEs19(wzz400, wzz3000)
new_primCmpInt(Pos(Succ(wzz3100)), Pos(wzz320)) → new_primCmpNat0(wzz3100, wzz320)
new_ltEs13(wzz3100, wzz3200, h) → new_fsEs(new_compare(wzz3100, wzz3200, h))
new_ltEs12(wzz31002, wzz32002, app(app(app(ty_@3, bdh), bea), beb)) → new_ltEs11(wzz31002, wzz32002, bdh, bea, beb)
new_fsEs(wzz135) → new_not(new_esEs11(wzz135, GT))
new_esEs22(wzz31000, wzz32000, ty_Int) → new_esEs9(wzz31000, wzz32000)
new_ltEs15(Just(wzz31000), Nothing, ccf) → False
new_esEs16([], :(wzz3000, wzz3001), caf) → False
new_esEs16(:(wzz400, wzz401), [], caf) → False
new_primCmpNat0(wzz3100, Zero) → GT
new_esEs5(Just(wzz400), Just(wzz3000), ty_Integer) → new_esEs20(wzz400, wzz3000)
new_ltEs4(True, False) → False
new_esEs12(wzz400, wzz3000, ty_Int) → new_esEs9(wzz400, wzz3000)
new_ltEs19(wzz3100, wzz3200, ty_@0) → new_ltEs17(wzz3100, wzz3200)
new_lt13(wzz31001, wzz32001, ty_Char) → new_lt18(wzz31001, wzz32001)
new_esEs26(wzz401, wzz3001, app(ty_Maybe, dae)) → new_esEs5(wzz401, wzz3001, dae)
new_esEs22(wzz31000, wzz32000, ty_@0) → new_esEs10(wzz31000, wzz32000)
new_lt13(wzz31001, wzz32001, app(ty_Maybe, bcd)) → new_lt15(wzz31001, wzz32001, bcd)
new_ltEs15(Just(wzz31000), Just(wzz32000), app(app(ty_@2, ff), fg)) → new_ltEs5(wzz31000, wzz32000, ff, fg)
new_ltEs14(Right(wzz31000), Right(wzz32000), dg, app(app(ty_@2, ed), ee)) → new_ltEs5(wzz31000, wzz32000, ed, ee)
new_esEs24(wzz31000, wzz32000, ty_Int) → new_esEs9(wzz31000, wzz32000)
new_ltEs12(wzz31002, wzz32002, ty_Integer) → new_ltEs18(wzz31002, wzz32002)
new_esEs23(wzz31001, wzz32001, app(ty_Ratio, ccc)) → new_esEs17(wzz31001, wzz32001, ccc)
new_primCmpInt(Pos(Zero), Neg(Succ(wzz3200))) → GT
new_ltEs20(wzz31001, wzz32001, ty_Char) → new_ltEs8(wzz31001, wzz32001)
new_lt5(wzz31000, wzz32000, gh, ha, hb) → new_esEs11(new_compare7(wzz31000, wzz32000, gh, ha, hb), LT)
new_esEs12(wzz400, wzz3000, ty_Char) → new_esEs18(wzz400, wzz3000)
new_compare31(wzz31000, wzz32000, app(ty_[], ba)) → new_compare(wzz31000, wzz32000, ba)
new_esEs27(wzz400, wzz3000, ty_Int) → new_esEs9(wzz400, wzz3000)
new_esEs13(wzz401, wzz3001, app(app(ty_@2, bgd), bge)) → new_esEs6(wzz401, wzz3001, bgd, bge)
new_ltEs12(wzz31002, wzz32002, ty_Double) → new_ltEs7(wzz31002, wzz32002)
new_ltEs16(wzz3100, wzz3200) → new_fsEs(new_compare17(wzz3100, wzz3200))
new_compare29(Nothing, Nothing, False, cce) → LT
new_esEs4(Left(wzz400), Left(wzz3000), ty_Integer, cdd) → new_esEs20(wzz400, wzz3000)
new_ltEs14(Left(wzz31000), Left(wzz32000), ty_Integer, ce) → new_ltEs18(wzz31000, wzz32000)
new_esEs10(@0, @0) → True
new_esEs24(wzz31000, wzz32000, app(app(app(ty_@3, gh), ha), hb)) → new_esEs7(wzz31000, wzz32000, gh, ha, hb)
new_compare29(wzz310, wzz320, True, cce) → EQ
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_lt10(wzz31000, wzz32000, gc) → new_esEs11(new_compare(wzz31000, wzz32000, gc), LT)
new_esEs13(wzz401, wzz3001, ty_Float) → new_esEs19(wzz401, wzz3001)
new_primCompAux1(wzz31000, wzz32000, wzz151, h) → new_primCompAux0(wzz151, new_compare31(wzz31000, wzz32000, h))
new_esEs5(Just(wzz400), Just(wzz3000), app(ty_[], dbb)) → new_esEs16(wzz400, wzz3000, dbb)
new_ltEs14(Left(wzz31000), Right(wzz32000), dg, ce) → True
new_ltEs6(wzz3100, wzz3200, cae) → new_fsEs(new_compare9(wzz3100, wzz3200, cae))
new_esEs12(wzz400, wzz3000, ty_Ordering) → new_esEs11(wzz400, wzz3000)
new_ltEs20(wzz31001, wzz32001, app(app(ty_Either, he), hf)) → new_ltEs14(wzz31001, wzz32001, he, hf)
new_asAs(False, wzz125) → False
new_esEs4(Left(wzz400), Left(wzz3000), ty_@0, cdd) → new_esEs10(wzz400, wzz3000)
new_ltEs19(wzz3100, wzz3200, app(app(ty_Either, dg), ce)) → new_ltEs14(wzz3100, wzz3200, dg, ce)
new_primMulInt(Pos(wzz4010), Neg(wzz30010)) → Neg(new_primMulNat0(wzz4010, wzz30010))
new_primMulInt(Neg(wzz4010), Pos(wzz30010)) → Neg(new_primMulNat0(wzz4010, wzz30010))
new_esEs7(@3(wzz400, wzz401, wzz402), @3(wzz3000, wzz3001, wzz3002), bec, bed, bee) → new_asAs(new_esEs12(wzz400, wzz3000, bec), new_asAs(new_esEs13(wzz401, wzz3001, bed), new_esEs14(wzz402, wzz3002, bee)))
new_ltEs10(LT, GT) → True
new_lt20(wzz31000, wzz32000, ty_@0) → new_lt19(wzz31000, wzz32000)
new_primCmpInt(Neg(Succ(wzz3100)), Neg(wzz320)) → new_primCmpNat2(wzz320, wzz3100)
new_primMulNat0(Zero, Succ(wzz300100)) → Zero
new_primMulNat0(Succ(wzz40100), Zero) → Zero
new_esEs14(wzz402, wzz3002, app(app(app(ty_@3, bhh), caa), cab)) → new_esEs7(wzz402, wzz3002, bhh, caa, cab)
new_ltEs14(Left(wzz31000), Left(wzz32000), app(ty_Ratio, cch), ce) → new_ltEs6(wzz31000, wzz32000, cch)
new_ltEs12(wzz31002, wzz32002, ty_Char) → new_ltEs8(wzz31002, wzz32002)
new_compare6(wzz31000, wzz32000, gf, gg) → new_compare24(wzz31000, wzz32000, new_esEs6(wzz31000, wzz32000, gf, gg), gf, gg)
new_lt13(wzz31001, wzz32001, ty_Float) → new_lt17(wzz31001, wzz32001)
new_lt17(wzz31000, wzz32000) → new_esEs11(new_compare17(wzz31000, wzz32000), LT)
new_ltEs14(Left(wzz31000), Left(wzz32000), app(ty_Maybe, da), ce) → new_ltEs15(wzz31000, wzz32000, da)
new_esEs24(wzz31000, wzz32000, app(ty_[], gc)) → new_esEs16(wzz31000, wzz32000, gc)
new_esEs23(wzz31001, wzz32001, ty_Int) → new_esEs9(wzz31001, wzz32001)
new_esEs5(Just(wzz400), Just(wzz3000), app(app(ty_@2, dbd), dbe)) → new_esEs6(wzz400, wzz3000, dbd, dbe)
new_ltEs14(Right(wzz31000), Right(wzz32000), dg, app(app(app(ty_@3, ef), eg), eh)) → new_ltEs11(wzz31000, wzz32000, ef, eg, eh)
new_ltEs14(Right(wzz31000), Right(wzz32000), dg, app(app(ty_Either, ea), eb)) → new_ltEs14(wzz31000, wzz32000, ea, eb)
new_esEs4(Left(wzz400), Left(wzz3000), app(ty_Maybe, ced), cdd) → new_esEs5(wzz400, wzz3000, ced)
new_compare13(@0, @0) → EQ
new_ltEs14(Left(wzz31000), Left(wzz32000), app(app(app(ty_@3, dd), de), df), ce) → new_ltEs11(wzz31000, wzz32000, dd, de, df)
new_ltEs14(Left(wzz31000), Left(wzz32000), ty_Double, ce) → new_ltEs7(wzz31000, wzz32000)
new_esEs23(wzz31001, wzz32001, app(ty_Maybe, bcd)) → new_esEs5(wzz31001, wzz32001, bcd)
new_ltEs4(False, False) → True
new_primCmpInt(Pos(Zero), Pos(Succ(wzz3200))) → new_primCmpNat2(Zero, wzz3200)
new_ltEs10(EQ, EQ) → True
new_compare27(wzz31000, wzz32000, True) → EQ
new_ltEs10(LT, LT) → True
new_ltEs15(Nothing, Nothing, ccf) → True
new_ltEs14(Right(wzz31000), Right(wzz32000), dg, ty_Char) → new_ltEs8(wzz31000, wzz32000)
new_esEs5(Nothing, Just(wzz3000), dag) → False
new_esEs5(Just(wzz400), Nothing, dag) → False
new_esEs22(wzz31000, wzz32000, ty_Bool) → new_esEs15(wzz31000, wzz32000)
new_esEs4(Right(wzz400), Right(wzz3000), cee, ty_Char) → new_esEs18(wzz400, wzz3000)
new_ltEs14(Right(wzz31000), Right(wzz32000), dg, ty_Int) → new_ltEs9(wzz31000, wzz32000)
new_ltEs14(Left(wzz31000), Left(wzz32000), app(app(ty_Either, cf), cg), ce) → new_ltEs14(wzz31000, wzz32000, cf, cg)
new_esEs25(wzz400, wzz3000, app(app(app(ty_@3, cgh), cha), chb)) → new_esEs7(wzz400, wzz3000, cgh, cha, chb)
new_compare31(wzz31000, wzz32000, ty_Char) → new_compare19(wzz31000, wzz32000)
new_esEs24(wzz31000, wzz32000, ty_Double) → new_esEs8(wzz31000, wzz32000)
new_esEs25(wzz400, wzz3000, ty_Float) → new_esEs19(wzz400, wzz3000)
new_lt7(wzz31000, wzz32000, cad) → new_esEs11(new_compare9(wzz31000, wzz32000, cad), LT)
new_compare31(wzz31000, wzz32000, app(app(app(ty_@3, bg), bh), ca)) → new_compare7(wzz31000, wzz32000, bg, bh, ca)
new_ltEs19(wzz3100, wzz3200, app(app(app(ty_@3, bbh), baf), bag)) → new_ltEs11(wzz3100, wzz3200, bbh, baf, bag)
new_esEs16([], [], caf) → True
new_ltEs12(wzz31002, wzz32002, ty_Float) → new_ltEs16(wzz31002, wzz32002)
new_lt11(wzz31000, wzz32000) → new_esEs11(new_compare30(wzz31000, wzz32000), LT)
new_esEs8(Double(wzz400, wzz401), Double(wzz3000, wzz3001)) → new_esEs9(new_sr(wzz400, wzz3000), new_sr(wzz401, wzz3001))
new_lt13(wzz31001, wzz32001, app(app(app(ty_@3, bcg), bch), bda)) → new_lt5(wzz31001, wzz32001, bcg, bch, bda)
new_compare29(Just(wzz3100), Just(wzz3200), False, cce) → new_compare16(wzz3100, wzz3200, new_ltEs19(wzz3100, wzz3200, cce), cce)
new_esEs14(wzz402, wzz3002, ty_Int) → new_esEs9(wzz402, wzz3002)
new_lt12(wzz31000, wzz32000, app(app(ty_@2, bbc), bbd)) → new_lt8(wzz31000, wzz32000, bbc, bbd)
new_esEs12(wzz400, wzz3000, app(ty_Ratio, bfa)) → new_esEs17(wzz400, wzz3000, bfa)
new_ltEs20(wzz31001, wzz32001, app(ty_Ratio, ccg)) → new_ltEs6(wzz31001, wzz32001, ccg)
new_esEs5(Nothing, Nothing, dag) → True
new_esEs4(Left(wzz400), Left(wzz3000), app(ty_[], cde), cdd) → new_esEs16(wzz400, wzz3000, cde)
new_esEs26(wzz401, wzz3001, ty_Float) → new_esEs19(wzz401, wzz3001)
new_esEs5(Just(wzz400), Just(wzz3000), app(app(app(ty_@3, dbf), dbg), dbh)) → new_esEs7(wzz400, wzz3000, dbf, dbg, dbh)
new_esEs28(wzz401, wzz3001, ty_Int) → new_esEs9(wzz401, wzz3001)
new_ltEs10(EQ, LT) → False
new_esEs5(Just(wzz400), Just(wzz3000), app(ty_Ratio, dbc)) → new_esEs17(wzz400, wzz3000, dbc)
new_lt15(wzz31000, wzz32000, ge) → new_esEs11(new_compare28(wzz31000, wzz32000, ge), LT)
new_esEs22(wzz31000, wzz32000, app(ty_Ratio, ccb)) → new_esEs17(wzz31000, wzz32000, ccb)
new_esEs26(wzz401, wzz3001, ty_Char) → new_esEs18(wzz401, wzz3001)
new_lt18(wzz31000, wzz32000) → new_esEs11(new_compare19(wzz31000, wzz32000), LT)
new_lt12(wzz31000, wzz32000, ty_Float) → new_lt17(wzz31000, wzz32000)
new_ltEs10(GT, LT) → False
new_lt20(wzz31000, wzz32000, app(app(app(ty_@3, gh), ha), hb)) → new_lt5(wzz31000, wzz32000, gh, ha, hb)
new_esEs4(Right(wzz400), Right(wzz3000), cee, ty_Float) → new_esEs19(wzz400, wzz3000)
new_primPlusNat0(Succ(wzz26200), Succ(wzz8700)) → Succ(Succ(new_primPlusNat0(wzz26200, wzz8700)))
new_esEs22(wzz31000, wzz32000, app(ty_Maybe, bbb)) → new_esEs5(wzz31000, wzz32000, bbb)
new_esEs23(wzz31001, wzz32001, app(ty_[], bca)) → new_esEs16(wzz31001, wzz32001, bca)
new_esEs21(wzz400, wzz3000, app(ty_Maybe, cbh)) → new_esEs5(wzz400, wzz3000, cbh)
new_esEs26(wzz401, wzz3001, app(app(ty_Either, chd), che)) → new_esEs4(wzz401, wzz3001, chd, che)
new_esEs21(wzz400, wzz3000, ty_Integer) → new_esEs20(wzz400, wzz3000)
new_asAs(True, wzz125) → wzz125
new_esEs4(Right(wzz400), Left(wzz3000), cee, cdd) → False
new_esEs4(Left(wzz400), Right(wzz3000), cee, cdd) → False
new_ltEs8(wzz3100, wzz3200) → new_fsEs(new_compare19(wzz3100, wzz3200))
new_esEs11(LT, LT) → True
new_primPlusNat1(wzz97, wzz300100) → new_primPlusNat0(wzz97, Succ(wzz300100))
new_esEs14(wzz402, wzz3002, ty_Integer) → new_esEs20(wzz402, wzz3002)
new_esEs5(Just(wzz400), Just(wzz3000), ty_Double) → new_esEs8(wzz400, wzz3000)
new_compare24(wzz31000, wzz32000, False, gf, gg) → new_compare11(wzz31000, wzz32000, new_ltEs5(wzz31000, wzz32000, gf, gg), gf, gg)
new_esEs26(wzz401, wzz3001, app(app(ty_@2, chh), daa)) → new_esEs6(wzz401, wzz3001, chh, daa)
new_lt13(wzz31001, wzz32001, app(app(ty_@2, bce), bcf)) → new_lt8(wzz31001, wzz32001, bce, bcf)
new_ltEs12(wzz31002, wzz32002, ty_Int) → new_ltEs9(wzz31002, wzz32002)
new_compare10(wzz31000, wzz32000, True) → LT
new_esEs9(wzz40, wzz300) → new_primEqInt(wzz40, wzz300)
new_esEs11(EQ, GT) → False
new_esEs11(GT, EQ) → False
new_lt20(wzz31000, wzz32000, app(ty_Ratio, cad)) → new_lt7(wzz31000, wzz32000, cad)
new_lt19(wzz31000, wzz32000) → new_esEs11(new_compare13(wzz31000, wzz32000), LT)
new_compare10(wzz31000, wzz32000, False) → GT
new_esEs6(@2(wzz400, wzz401), @2(wzz3000, wzz3001), cfh, cga) → new_asAs(new_esEs25(wzz400, wzz3000, cfh), new_esEs26(wzz401, wzz3001, cga))
new_esEs13(wzz401, wzz3001, app(app(app(ty_@3, bgf), bgg), bgh)) → new_esEs7(wzz401, wzz3001, bgf, bgg, bgh)
new_esEs21(wzz400, wzz3000, app(ty_[], cba)) → new_esEs16(wzz400, wzz3000, cba)
new_esEs5(Just(wzz400), Just(wzz3000), app(app(ty_Either, dah), dba)) → new_esEs4(wzz400, wzz3000, dah, dba)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCompAux0(wzz165, EQ) → wzz165
new_esEs24(wzz31000, wzz32000, ty_Char) → new_esEs18(wzz31000, wzz32000)
new_lt12(wzz31000, wzz32000, ty_@0) → new_lt19(wzz31000, wzz32000)
new_ltEs19(wzz3100, wzz3200, app(ty_[], h)) → new_ltEs13(wzz3100, wzz3200, h)
new_lt12(wzz31000, wzz32000, app(ty_Maybe, bbb)) → new_lt15(wzz31000, wzz32000, bbb)
new_ltEs14(Left(wzz31000), Left(wzz32000), ty_@0, ce) → new_ltEs17(wzz31000, wzz32000)
new_compare9(:%(wzz31000, wzz31001), :%(wzz32000, wzz32001), ty_Int) → new_compare14(new_sr(wzz31000, wzz32001), new_sr(wzz32000, wzz31001))
new_ltEs15(Just(wzz31000), Just(wzz32000), app(app(ty_Either, fb), fc)) → new_ltEs14(wzz31000, wzz32000, fb, fc)
new_esEs12(wzz400, wzz3000, app(ty_Maybe, bfg)) → new_esEs5(wzz400, wzz3000, bfg)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primCmpNat0(wzz3100, Succ(wzz3200)) → new_primCmpNat1(wzz3100, wzz3200)
new_lt20(wzz31000, wzz32000, app(app(ty_Either, cb), cc)) → new_lt9(wzz31000, wzz32000, cb, cc)
new_esEs12(wzz400, wzz3000, app(app(ty_@2, bfb), bfc)) → new_esEs6(wzz400, wzz3000, bfb, bfc)
new_primCmpInt(Neg(Succ(wzz3100)), Pos(wzz320)) → LT
new_not(True) → False
new_esEs15(False, False) → True

The set Q consists of the following terms:

new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_compare31(x0, x1, ty_Int)
new_compare10(x0, x1, True)
new_compare31(x0, x1, ty_@0)
new_ltEs15(Just(x0), Just(x1), ty_@0)
new_primCmpNat2(Succ(x0), x1)
new_esEs25(x0, x1, ty_Float)
new_lt13(x0, x1, ty_Float)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Nothing, Just(x0), x1)
new_compare30(x0, x1)
new_ltEs14(Left(x0), Left(x1), ty_Int, x2)
new_esEs12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpNat1(Succ(x0), Succ(x1))
new_ltEs14(Right(x0), Right(x1), x2, ty_Bool)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs26(x0, x1, ty_Bool)
new_pePe(False, x0)
new_esEs24(x0, x1, ty_@0)
new_lt7(x0, x1, x2)
new_esEs12(x0, x1, app(ty_Ratio, x2))
new_esEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_lt20(x0, x1, ty_Char)
new_esEs23(x0, x1, app(ty_[], x2))
new_lt13(x0, x1, ty_Double)
new_esEs16(:(x0, x1), [], x2)
new_esEs13(x0, x1, ty_Double)
new_compare17(Float(x0, x1), Float(x2, x3))
new_ltEs15(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_lt13(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Just(x0), Just(x1), ty_Int)
new_esEs15(True, True)
new_esEs13(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Just(x0), Just(x1), ty_Bool)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs18(Char(x0), Char(x1))
new_compare14(x0, x1)
new_esEs12(x0, x1, ty_Char)
new_ltEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs10(LT, LT)
new_compare31(x0, x1, ty_Float)
new_esEs5(Just(x0), Nothing, x1)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs14(Right(x0), Left(x1), x2, x3)
new_ltEs14(Left(x0), Right(x1), x2, x3)
new_ltEs12(x0, x1, ty_@0)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_ltEs20(x0, x1, ty_@0)
new_esEs22(x0, x1, ty_Bool)
new_ltEs14(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_lt8(x0, x1, x2, x3)
new_lt15(x0, x1, x2)
new_sr(x0, x1)
new_lt20(x0, x1, ty_Bool)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_lt5(x0, x1, x2, x3, x4)
new_primCompAux0(x0, LT)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs15(False, False)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, ty_Double)
new_esEs21(x0, x1, ty_Bool)
new_compare110(x0, x1, False, x2, x3)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs20(Integer(x0), Integer(x1))
new_ltEs12(x0, x1, ty_Double)
new_esEs22(x0, x1, ty_Double)
new_compare([], :(x0, x1), x2)
new_compare210(x0, x1, True, x2, x3, x4)
new_esEs5(Just(x0), Just(x1), ty_Double)
new_esEs23(x0, x1, ty_Integer)
new_esEs14(x0, x1, ty_@0)
new_compare31(x0, x1, app(ty_Ratio, x2))
new_compare31(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Ordering)
new_compare31(x0, x1, app(ty_Maybe, x2))
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs23(x0, x1, ty_Int)
new_compare31(x0, x1, app(app(ty_@2, x2), x3))
new_primEqNat0(Succ(x0), Zero)
new_ltEs15(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs22(x0, x1, ty_Int)
new_ltEs12(x0, x1, ty_Integer)
new_ltEs12(x0, x1, app(ty_Maybe, x2))
new_esEs13(x0, x1, app(ty_Ratio, x2))
new_ltEs20(x0, x1, ty_Bool)
new_compare16(x0, x1, True, x2)
new_ltEs19(x0, x1, ty_@0)
new_compare29(Just(x0), Nothing, False, x1)
new_primCmpNat1(Zero, Zero)
new_primCompAux1(x0, x1, x2, x3)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs4(Left(x0), Left(x1), ty_Bool, x2)
new_compare9(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs23(x0, x1, ty_@0)
new_ltEs7(x0, x1)
new_esEs11(EQ, GT)
new_esEs11(GT, EQ)
new_fsEs(x0)
new_esEs5(Just(x0), Just(x1), ty_@0)
new_primPlusNat0(Succ(x0), Zero)
new_lt12(x0, x1, ty_Bool)
new_esEs4(Right(x0), Right(x1), x2, ty_Bool)
new_lt13(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Ordering)
new_ltEs14(Left(x0), Left(x1), ty_Float, x2)
new_primEqNat0(Zero, Zero)
new_esEs16(:(x0, x1), :(x2, x3), x4)
new_ltEs14(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_primCompAux0(x0, EQ)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs15(Just(x0), Just(x1), ty_Bool)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(True, True)
new_esEs21(x0, x1, ty_Int)
new_ltEs6(x0, x1, x2)
new_ltEs12(x0, x1, ty_Ordering)
new_primMulNat0(Succ(x0), Zero)
new_esEs23(x0, x1, ty_Float)
new_compare31(x0, x1, ty_Integer)
new_lt13(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs12(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, ty_Ordering)
new_compare29(Nothing, Just(x0), False, x1)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs16([], :(x0, x1), x2)
new_compare8(Integer(x0), Integer(x1))
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_compare24(x0, x1, True, x2, x3)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare(:(x0, x1), :(x2, x3), x4)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_compare29(x0, x1, True, x2)
new_ltEs12(x0, x1, ty_Int)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare28(x0, x1, x2)
new_lt17(x0, x1)
new_lt13(x0, x1, ty_Integer)
new_compare6(x0, x1, x2, x3)
new_ltEs10(EQ, LT)
new_ltEs10(LT, EQ)
new_esEs12(x0, x1, ty_Integer)
new_lt11(x0, x1)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_ltEs15(Just(x0), Just(x1), ty_Integer)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_lt9(x0, x1, x2, x3)
new_lt20(x0, x1, ty_@0)
new_ltEs14(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs15(Just(x0), Just(x1), app(ty_[], x2))
new_primEqNat0(Zero, Succ(x0))
new_esEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs19(x0, x1, ty_Char)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_esEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, ty_Float)
new_esEs21(x0, x1, ty_Double)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs13(x0, x1, ty_Integer)
new_ltEs12(x0, x1, ty_Bool)
new_esEs11(GT, LT)
new_esEs11(LT, GT)
new_compare25(x0, x1, True)
new_lt12(x0, x1, ty_Int)
new_esEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_primCmpNat2(Zero, x0)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_lt14(x0, x1)
new_ltEs15(Just(x0), Just(x1), ty_Double)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_asAs(False, x0)
new_ltEs4(False, False)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, ty_Bool)
new_ltEs19(x0, x1, ty_Double)
new_ltEs14(Left(x0), Left(x1), ty_Ordering, x2)
new_compare27(x0, x1, False)
new_compare31(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Float)
new_ltEs15(Just(x0), Just(x1), ty_Ordering)
new_ltEs14(Right(x0), Right(x1), x2, ty_Float)
new_esEs14(x0, x1, app(ty_Maybe, x2))
new_compare7(x0, x1, x2, x3, x4)
new_lt20(x0, x1, ty_Ordering)
new_lt12(x0, x1, ty_Float)
new_esEs4(Left(x0), Left(x1), ty_Integer, x2)
new_compare26(x0, x1, True, x2, x3)
new_ltEs14(Right(x0), Right(x1), x2, ty_@0)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs13(x0, x1, x2)
new_compare210(x0, x1, False, x2, x3, x4)
new_esEs12(x0, x1, ty_Float)
new_esEs4(Right(x0), Left(x1), x2, x3)
new_esEs4(Left(x0), Right(x1), x2, x3)
new_esEs28(x0, x1, ty_Int)
new_esEs12(x0, x1, app(ty_Maybe, x2))
new_lt12(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, ty_Integer)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs26(x0, x1, ty_Int)
new_asAs(True, x0)
new_ltEs12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_compare([], [], x0)
new_esEs11(LT, LT)
new_compare11(x0, x1, True, x2, x3)
new_ltEs15(Just(x0), Just(x1), ty_Int)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs23(x0, x1, ty_Bool)
new_lt19(x0, x1)
new_esEs23(x0, x1, ty_Char)
new_compare31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs12(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_primPlusNat0(Zero, Zero)
new_lt12(x0, x1, ty_Char)
new_ltEs15(Nothing, Nothing, x0)
new_esEs26(x0, x1, ty_@0)
new_lt12(x0, x1, ty_Integer)
new_lt20(x0, x1, ty_Integer)
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_primPlusNat0(Succ(x0), Succ(x1))
new_esEs13(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs14(x0, x1, app(app(ty_@2, x2), x3))
new_esEs14(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Ordering)
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs4(Right(x0), Right(x1), x2, ty_Double)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs24(x0, x1, ty_Double)
new_esEs23(x0, x1, ty_Double)
new_esEs25(x0, x1, ty_Double)
new_esEs24(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_Double)
new_compare110(x0, x1, True, x2, x3)
new_compare19(Char(x0), Char(x1))
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs21(x0, x1, ty_Char)
new_compare(:(x0, x1), [], x2)
new_esEs14(x0, x1, ty_Ordering)
new_ltEs9(x0, x1)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Right(x0), Right(x1), x2, ty_Char)
new_ltEs20(x0, x1, ty_Int)
new_lt6(x0, x1)
new_ltEs17(x0, x1)
new_ltEs10(GT, LT)
new_ltEs10(LT, GT)
new_ltEs14(Right(x0), Right(x1), x2, ty_Double)
new_lt12(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_primPlusNat0(Zero, Succ(x0))
new_esEs14(x0, x1, ty_Bool)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(@0, @0)
new_lt13(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, ty_Ordering)
new_esEs14(x0, x1, ty_Char)
new_compare12(x0, x1, True, x2, x3, x4)
new_compare31(x0, x1, ty_Double)
new_ltEs16(x0, x1)
new_compare111(x0, x1, True)
new_lt12(x0, x1, ty_Double)
new_esEs9(x0, x1)
new_esEs5(Just(x0), Just(x1), ty_Ordering)
new_esEs13(x0, x1, ty_Bool)
new_esEs13(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_Float)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_ltEs14(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_esEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs16([], [], x0)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs15(Just(x0), Just(x1), ty_Char)
new_ltEs14(Left(x0), Left(x1), ty_Bool, x2)
new_esEs14(x0, x1, app(app(ty_Either, x2), x3))
new_compare13(@0, @0)
new_esEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Char)
new_esEs11(EQ, LT)
new_esEs11(LT, EQ)
new_esEs12(x0, x1, ty_Ordering)
new_esEs13(x0, x1, ty_Int)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_ltEs11(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs15(True, False)
new_esEs15(False, True)
new_sr0(Integer(x0), Integer(x1))
new_ltEs15(Just(x0), Nothing, x1)
new_lt13(x0, x1, ty_Bool)
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs14(Left(x0), Left(x1), ty_Char, x2)
new_primMulInt(Neg(x0), Neg(x1))
new_lt12(x0, x1, app(app(ty_@2, x2), x3))
new_esEs19(Float(x0, x1), Float(x2, x3))
new_lt13(x0, x1, app(app(ty_Either, x2), x3))
new_esEs13(x0, x1, ty_Float)
new_lt16(x0, x1)
new_esEs27(x0, x1, ty_Int)
new_lt18(x0, x1)
new_esEs14(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Right(x0), Right(x1), x2, ty_@0)
new_compare11(x0, x1, False, x2, x3)
new_ltEs14(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs24(x0, x1, ty_Bool)
new_esEs4(Left(x0), Left(x1), ty_Float, x2)
new_esEs12(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, ty_@0)
new_ltEs14(Right(x0), Right(x1), x2, ty_Int)
new_compare18(Double(x0, x1), Double(x2, x3))
new_primCmpNat1(Succ(x0), Zero)
new_ltEs12(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_lt13(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Integer)
new_primCompAux0(x0, GT)
new_lt13(x0, x1, ty_Ordering)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare29(Nothing, Nothing, False, x0)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Left(x0), Left(x1), ty_Double, x2)
new_esEs24(x0, x1, ty_Int)
new_esEs22(x0, x1, ty_@0)
new_primMulNat0(Zero, Succ(x0))
new_lt12(x0, x1, ty_Ordering)
new_esEs5(Just(x0), Just(x1), ty_Integer)
new_esEs5(Just(x0), Just(x1), ty_Char)
new_compare31(x0, x1, app(ty_[], x2))
new_esEs13(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(Double(x0, x1), Double(x2, x3))
new_esEs22(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Ordering)
new_ltEs14(Right(x0), Right(x1), x2, ty_Char)
new_esEs14(x0, x1, app(ty_Ratio, x2))
new_lt13(x0, x1, app(ty_Ratio, x2))
new_ltEs4(False, True)
new_ltEs4(True, False)
new_ltEs14(Left(x0), Left(x1), ty_@0, x2)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs26(x0, x1, ty_Float)
new_lt10(x0, x1, x2)
new_lt4(x0, x1)
new_esEs12(x0, x1, ty_Bool)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs12(x0, x1, ty_Int)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs14(x0, x1, ty_Int)
new_primPlusNat1(x0, x1)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, ty_Ordering)
new_ltEs18(x0, x1)
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs4(Right(x0), Right(x1), x2, ty_Int)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs12(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs14(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs14(Left(x0), Left(x1), ty_Double, x2)
new_esEs4(Left(x0), Left(x1), ty_Int, x2)
new_compare111(x0, x1, False)
new_ltEs20(x0, x1, app(ty_[], x2))
new_lt12(x0, x1, app(ty_Maybe, x2))
new_esEs13(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs10(GT, GT)
new_esEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs25(x0, x1, ty_Integer)
new_lt20(x0, x1, ty_Float)
new_ltEs15(Just(x0), Just(x1), ty_Float)
new_esEs4(Left(x0), Left(x1), ty_Char, x2)
new_esEs11(GT, GT)
new_esEs14(x0, x1, app(ty_[], x2))
new_ltEs15(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs15(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_ltEs20(x0, x1, ty_Integer)
new_primCmpNat0(x0, Zero)
new_not(True)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs25(x0, x1, ty_Char)
new_esEs22(x0, x1, ty_Float)
new_compare9(:%(x0, x1), :%(x2, x3), ty_Integer)
new_compare15(x0, x1, x2, x3)
new_esEs12(x0, x1, ty_Double)
new_esEs26(x0, x1, ty_Integer)
new_lt12(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, ty_Float)
new_lt20(x0, x1, ty_Double)
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_not(False)
new_ltEs14(Right(x0), Right(x1), x2, ty_Integer)
new_esEs26(x0, x1, ty_Char)
new_primCmpNat1(Zero, Succ(x0))
new_ltEs10(EQ, GT)
new_ltEs10(GT, EQ)
new_ltEs14(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs20(x0, x1, ty_Char)
new_lt13(x0, x1, ty_Char)
new_compare27(x0, x1, True)
new_esEs4(Left(x0), Left(x1), ty_@0, x2)
new_compare31(x0, x1, ty_Char)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_primCmpNat0(x0, Succ(x1))
new_esEs14(x0, x1, ty_Double)
new_ltEs12(x0, x1, ty_Char)
new_ltEs15(Nothing, Just(x0), x1)
new_esEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs14(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs4(Right(x0), Right(x1), x2, ty_Float)
new_ltEs12(x0, x1, ty_Float)
new_esEs21(x0, x1, ty_@0)
new_ltEs15(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs8(x0, x1)
new_ltEs19(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Int)
new_compare31(x0, x1, ty_Bool)
new_esEs13(x0, x1, ty_@0)
new_compare24(x0, x1, False, x2, x3)
new_compare16(x0, x1, False, x2)
new_compare12(x0, x1, False, x2, x3, x4)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs5(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs19(x0, x1, ty_Integer)
new_esEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt20(x0, x1, ty_Int)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs19(x0, x1, ty_Int)
new_esEs14(x0, x1, ty_Float)
new_esEs12(x0, x1, ty_@0)
new_lt12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, ty_Integer)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs13(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs11(EQ, EQ)
new_esEs13(x0, x1, app(ty_Maybe, x2))
new_esEs12(x0, x1, app(ty_[], x2))
new_ltEs12(x0, x1, app(ty_[], x2))
new_compare25(x0, x1, False)
new_esEs4(Right(x0), Right(x1), x2, ty_Integer)
new_esEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_compare29(Just(x0), Just(x1), False, x2)
new_esEs22(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Nothing, Nothing, x0)
new_compare10(x0, x1, False)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_pePe(True, x0)
new_ltEs14(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs27(x0, x1, ty_Integer)
new_esEs5(Just(x0), Just(x1), ty_Float)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_compare5(x0, x1)
new_lt20(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, ty_Ordering)
new_lt13(x0, x1, ty_@0)
new_compare26(x0, x1, False, x2, x3)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs17(:%(x0, x1), :%(x2, x3), x4)
new_ltEs10(EQ, EQ)
new_lt12(x0, x1, ty_@0)

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

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



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

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

new_addToFM_C1(wzz31, wzz32, wzz33, wzz34, wzz5, True, h, ba) → new_addToFM_C(wzz34, Nothing, wzz5, h, ba)
new_addToFM_C21(wzz15, wzz16, wzz17, wzz18, wzz19, wzz20, wzz21, True, bb, bc) → new_addToFM_C(wzz18, Just(wzz20), wzz21, bb, bc)
new_addToFM_C2(wzz300, wzz31, wzz32, wzz33, wzz34, wzz5, True, h, ba) → new_addToFM_C(wzz33, Nothing, wzz5, h, ba)
new_addToFM_C(Branch(Nothing, wzz31, wzz32, wzz33, wzz34), Nothing, wzz5, h, ba) → new_addToFM_C1(wzz31, wzz32, wzz33, wzz34, wzz5, new_esEs11(new_compare29(Nothing, Nothing, True, h), GT), h, ba)
new_addToFM_C21(wzz15, wzz16, wzz17, wzz18, wzz19, wzz20, wzz21, False, bb, bc) → new_addToFM_C12(wzz15, wzz16, wzz17, wzz18, wzz19, wzz20, wzz21, new_esEs11(new_compare29(Just(wzz20), Just(wzz15), new_esEs30(wzz20, wzz15, bb), bb), GT), bb, bc)
new_addToFM_C20(wzz31, wzz32, wzz33, wzz34, wzz40, wzz5, True, h, ba) → new_addToFM_C(wzz33, Just(wzz40), wzz5, h, ba)
new_addToFM_C20(wzz31, wzz32, wzz33, wzz34, wzz40, wzz5, False, h, ba) → new_addToFM_C11(wzz31, wzz32, wzz33, wzz34, wzz40, wzz5, new_esEs11(new_compare29(Just(wzz40), Nothing, False, h), GT), h, ba)
new_addToFM_C11(wzz31, wzz32, wzz33, wzz34, wzz40, wzz5, True, h, ba) → new_addToFM_C(wzz34, Just(wzz40), wzz5, h, ba)
new_addToFM_C2(wzz300, wzz31, wzz32, wzz33, wzz34, wzz5, False, h, ba) → new_addToFM_C10(wzz300, wzz31, wzz32, wzz33, wzz34, wzz5, new_esEs11(new_compare29(Nothing, Just(wzz300), False, h), GT), h, ba)
new_addToFM_C(Branch(Just(wzz300), wzz31, wzz32, wzz33, wzz34), Just(wzz40), wzz5, h, ba) → new_addToFM_C21(wzz300, wzz31, wzz32, wzz33, wzz34, wzz40, wzz5, new_esEs11(new_compare29(Just(wzz40), Just(wzz300), new_esEs29(wzz40, wzz300, h), h), LT), h, ba)
new_addToFM_C(Branch(Just(wzz300), wzz31, wzz32, wzz33, wzz34), Nothing, wzz5, h, ba) → new_addToFM_C2(wzz300, wzz31, wzz32, wzz33, wzz34, wzz5, new_esEs11(new_compare29(Nothing, Just(wzz300), False, h), LT), h, ba)
new_addToFM_C(Branch(Nothing, wzz31, wzz32, wzz33, wzz34), Just(wzz40), wzz5, h, ba) → new_addToFM_C20(wzz31, wzz32, wzz33, wzz34, wzz40, wzz5, new_esEs11(new_compare29(Just(wzz40), Nothing, False, h), LT), h, ba)
new_addToFM_C10(wzz300, wzz31, wzz32, wzz33, wzz34, wzz5, True, h, ba) → new_addToFM_C(wzz34, Nothing, wzz5, h, ba)
new_addToFM_C12(wzz15, wzz16, wzz17, wzz18, wzz19, wzz20, wzz21, True, bb, bc) → new_addToFM_C(wzz19, Just(wzz20), wzz21, bb, bc)

The TRS R consists of the following rules:

new_ltEs19(wzz3100, wzz3200, app(app(ty_@2, bfd), bfe)) → new_ltEs5(wzz3100, wzz3200, bfd, bfe)
new_ltEs20(wzz31001, wzz32001, ty_Bool) → new_ltEs4(wzz31001, wzz32001)
new_ltEs20(wzz31001, wzz32001, ty_Int) → new_ltEs9(wzz31001, wzz32001)
new_esEs21(wzz400, wzz3000, app(app(ty_@2, hg), hh)) → new_esEs6(wzz400, wzz3000, hg, hh)
new_lt20(wzz31000, wzz32000, ty_Int) → new_lt16(wzz31000, wzz32000)
new_esEs18(Char(wzz400), Char(wzz3000)) → new_primEqNat0(wzz400, wzz3000)
new_primCmpNat2(Zero, wzz3100) → LT
new_esEs14(wzz402, wzz3002, ty_Float) → new_esEs19(wzz402, wzz3002)
new_esEs25(wzz400, wzz3000, app(ty_[], cgb)) → new_esEs16(wzz400, wzz3000, cgb)
new_compare8(Integer(wzz31000), Integer(wzz32000)) → new_primCmpInt(wzz31000, wzz32000)
new_esEs25(wzz400, wzz3000, ty_Bool) → new_esEs15(wzz400, wzz3000)
new_esEs23(wzz31001, wzz32001, ty_Ordering) → new_esEs11(wzz31001, wzz32001)
new_esEs13(wzz401, wzz3001, ty_Double) → new_esEs8(wzz401, wzz3001)
new_ltEs14(Right(wzz31000), Right(wzz32000), bfa, ty_Ordering) → new_ltEs10(wzz31000, wzz32000)
new_esEs27(wzz400, wzz3000, ty_Integer) → new_esEs20(wzz400, wzz3000)
new_compare110(wzz31000, wzz32000, True, gg, gh) → LT
new_ltEs20(wzz31001, wzz32001, ty_Ordering) → new_ltEs10(wzz31001, wzz32001)
new_primCmpNat1(Zero, Succ(wzz32000)) → LT
new_compare([], :(wzz32000, wzz32001), gd) → LT
new_esEs22(wzz31000, wzz32000, ty_Float) → new_esEs19(wzz31000, wzz32000)
new_esEs13(wzz401, wzz3001, ty_Char) → new_esEs18(wzz401, wzz3001)
new_lt12(wzz31000, wzz32000, app(app(ty_Either, bbd), bbe)) → new_lt9(wzz31000, wzz32000, bbd, bbe)
new_ltEs15(Just(wzz31000), Just(wzz32000), app(ty_[], dae)) → new_ltEs13(wzz31000, wzz32000, dae)
new_esEs29(wzz40, wzz300, ty_Int) → new_esEs9(wzz40, wzz300)
new_ltEs15(Just(wzz31000), Just(wzz32000), app(ty_Ratio, dad)) → new_ltEs6(wzz31000, wzz32000, dad)
new_esEs4(Right(wzz400), Right(wzz3000), ccg, app(ty_Maybe, cea)) → new_esEs5(wzz400, wzz3000, cea)
new_compare30(wzz31000, wzz32000) → new_compare25(wzz31000, wzz32000, new_esEs15(wzz31000, wzz32000))
new_esEs11(EQ, EQ) → True
new_ltEs14(Left(wzz31000), Left(wzz32000), ty_Bool, bfb) → new_ltEs4(wzz31000, wzz32000)
new_ltEs20(wzz31001, wzz32001, ty_Double) → new_ltEs7(wzz31001, wzz32001)
new_esEs13(wzz401, wzz3001, ty_Integer) → new_esEs20(wzz401, wzz3001)
new_esEs23(wzz31001, wzz32001, ty_Float) → new_esEs19(wzz31001, wzz32001)
new_esEs26(wzz401, wzz3001, ty_Integer) → new_esEs20(wzz401, wzz3001)
new_esEs14(wzz402, wzz3002, ty_Ordering) → new_esEs11(wzz402, wzz3002)
new_compare17(Float(wzz31000, wzz31001), Float(wzz32000, wzz32001)) → new_compare14(new_sr(wzz31000, wzz32000), new_sr(wzz31001, wzz32001))
new_primMulNat0(Zero, Zero) → Zero
new_compare(:(wzz31000, wzz31001), [], gd) → GT
new_esEs26(wzz401, wzz3001, app(ty_[], chd)) → new_esEs16(wzz401, wzz3001, chd)
new_esEs5(Just(wzz400), Just(wzz3000), ty_Int) → new_esEs9(wzz400, wzz3000)
new_ltEs14(Right(wzz31000), Right(wzz32000), bfa, app(ty_[], cac)) → new_ltEs13(wzz31000, wzz32000, cac)
new_compare31(wzz31000, wzz32000, app(app(ty_@2, dde), ddf)) → new_compare6(wzz31000, wzz32000, dde, ddf)
new_esEs12(wzz400, wzz3000, ty_Bool) → new_esEs15(wzz400, wzz3000)
new_ltEs15(Nothing, Just(wzz32000), bfc) → True
new_esEs25(wzz400, wzz3000, ty_Double) → new_esEs8(wzz400, wzz3000)
new_esEs4(Right(wzz400), Right(wzz3000), ccg, ty_Int) → new_esEs9(wzz400, wzz3000)
new_ltEs19(wzz3100, wzz3200, app(ty_Maybe, bfc)) → new_ltEs15(wzz3100, wzz3200, bfc)
new_esEs4(Left(wzz400), Left(wzz3000), app(ty_Ratio, cbh), cbf) → new_esEs17(wzz400, wzz3000, cbh)
new_lt20(wzz31000, wzz32000, app(app(ty_@2, bd), be)) → new_lt8(wzz31000, wzz32000, bd, be)
new_ltEs15(Just(wzz31000), Just(wzz32000), ty_Bool) → new_ltEs4(wzz31000, wzz32000)
new_esEs20(Integer(wzz400), Integer(wzz3000)) → new_primEqInt(wzz400, wzz3000)
new_esEs25(wzz400, wzz3000, ty_Ordering) → new_esEs11(wzz400, wzz3000)
new_lt12(wzz31000, wzz32000, ty_Integer) → new_lt6(wzz31000, wzz32000)
new_esEs29(wzz40, wzz300, app(app(ty_Either, ccg), cbf)) → new_esEs4(wzz40, wzz300, ccg, cbf)
new_esEs5(Just(wzz400), Just(wzz3000), ty_Bool) → new_esEs15(wzz400, wzz3000)
new_lt20(wzz31000, wzz32000, ty_Double) → new_lt14(wzz31000, wzz32000)
new_ltEs20(wzz31001, wzz32001, app(app(app(ty_@3, bge), bgf), bgg)) → new_ltEs11(wzz31001, wzz32001, bge, bgf, bgg)
new_compare18(Double(wzz31000, wzz31001), Double(wzz32000, wzz32001)) → new_compare14(new_sr(wzz31000, wzz32000), new_sr(wzz31001, wzz32001))
new_esEs4(Right(wzz400), Right(wzz3000), ccg, app(app(app(ty_@3, cdf), cdg), cdh)) → new_esEs7(wzz400, wzz3000, cdf, cdg, cdh)
new_esEs30(wzz20, wzz15, ty_Int) → new_esEs9(wzz20, wzz15)
new_esEs4(Left(wzz400), Left(wzz3000), app(app(ty_@2, cca), ccb), cbf) → new_esEs6(wzz400, wzz3000, cca, ccb)
new_esEs26(wzz401, wzz3001, ty_Double) → new_esEs8(wzz401, wzz3001)
new_ltEs19(wzz3100, wzz3200, ty_Ordering) → new_ltEs10(wzz3100, wzz3200)
new_ltEs19(wzz3100, wzz3200, ty_Bool) → new_ltEs4(wzz3100, wzz3200)
new_esEs13(wzz401, wzz3001, app(ty_Ratio, eb)) → new_esEs17(wzz401, wzz3001, eb)
new_esEs21(wzz400, wzz3000, app(app(app(ty_@3, baa), bab), bac)) → new_esEs7(wzz400, wzz3000, baa, bab, bac)
new_primCmpNat1(Succ(wzz31000), Succ(wzz32000)) → new_primCmpNat1(wzz31000, wzz32000)
new_compare28(wzz31000, wzz32000, bae) → new_compare29(wzz31000, wzz32000, new_esEs5(wzz31000, wzz32000, bae), bae)
new_esEs5(Just(wzz400), Just(wzz3000), app(ty_Maybe, dcg)) → new_esEs5(wzz400, wzz3000, dcg)
new_ltEs14(Right(wzz31000), Right(wzz32000), bfa, ty_Bool) → new_ltEs4(wzz31000, wzz32000)
new_ltEs4(False, True) → True
new_ltEs10(EQ, GT) → True
new_esEs4(Right(wzz400), Right(wzz3000), ccg, ty_Integer) → new_esEs20(wzz400, wzz3000)
new_compare19(Char(wzz31000), Char(wzz32000)) → new_primCmpNat1(wzz31000, wzz32000)
new_esEs30(wzz20, wzz15, ty_Float) → new_esEs19(wzz20, wzz15)
new_ltEs15(Just(wzz31000), Just(wzz32000), ty_@0) → new_ltEs17(wzz31000, wzz32000)
new_esEs29(wzz40, wzz300, app(app(app(ty_@3, ca), cb), cc)) → new_esEs7(wzz40, wzz300, ca, cb, cc)
new_ltEs15(Just(wzz31000), Just(wzz32000), ty_Double) → new_ltEs7(wzz31000, wzz32000)
new_ltEs14(Left(wzz31000), Left(wzz32000), ty_Float, bfb) → new_ltEs16(wzz31000, wzz32000)
new_lt20(wzz31000, wzz32000, app(ty_Maybe, bae)) → new_lt15(wzz31000, wzz32000, bae)
new_lt16(wzz310, wzz320) → new_esEs11(new_compare14(wzz310, wzz320), LT)
new_ltEs15(Just(wzz31000), Just(wzz32000), ty_Integer) → new_ltEs18(wzz31000, wzz32000)
new_compare26(wzz31000, wzz32000, False, gg, gh) → new_compare110(wzz31000, wzz32000, new_ltEs14(wzz31000, wzz32000, gg, gh), gg, gh)
new_lt20(wzz31000, wzz32000, ty_Float) → new_lt17(wzz31000, wzz32000)
new_esEs4(Left(wzz400), Left(wzz3000), ty_Double, cbf) → new_esEs8(wzz400, wzz3000)
new_esEs14(wzz402, wzz3002, app(ty_Ratio, fd)) → new_esEs17(wzz402, wzz3002, fd)
new_ltEs19(wzz3100, wzz3200, ty_Float) → new_ltEs16(wzz3100, wzz3200)
new_esEs26(wzz401, wzz3001, ty_Ordering) → new_esEs11(wzz401, wzz3001)
new_ltEs4(True, True) → True
new_pePe(False, wzz150) → wzz150
new_esEs25(wzz400, wzz3000, app(app(ty_Either, cfh), cga)) → new_esEs4(wzz400, wzz3000, cfh, cga)
new_esEs15(False, True) → False
new_esEs15(True, False) → False
new_lt20(wzz31000, wzz32000, ty_Bool) → new_lt11(wzz31000, wzz32000)
new_ltEs14(Right(wzz31000), Right(wzz32000), bfa, ty_Float) → new_ltEs16(wzz31000, wzz32000)
new_esEs22(wzz31000, wzz32000, app(app(ty_Either, bbd), bbe)) → new_esEs4(wzz31000, wzz32000, bbd, bbe)
new_lt13(wzz31001, wzz32001, ty_Double) → new_lt14(wzz31001, wzz32001)
new_esEs29(wzz40, wzz300, ty_Char) → new_esEs18(wzz40, wzz300)
new_esEs23(wzz31001, wzz32001, ty_Double) → new_esEs8(wzz31001, wzz32001)
new_esEs17(:%(wzz400, wzz401), :%(wzz3000, wzz3001), ceb) → new_asAs(new_esEs27(wzz400, wzz3000, ceb), new_esEs28(wzz401, wzz3001, ceb))
new_esEs26(wzz401, wzz3001, app(ty_Ratio, che)) → new_esEs17(wzz401, wzz3001, che)
new_esEs13(wzz401, wzz3001, ty_Ordering) → new_esEs11(wzz401, wzz3001)
new_esEs30(wzz20, wzz15, ty_Bool) → new_esEs15(wzz20, wzz15)
new_compare31(wzz31000, wzz32000, ty_@0) → new_compare13(wzz31000, wzz32000)
new_ltEs12(wzz31002, wzz32002, app(ty_Ratio, bdf)) → new_ltEs6(wzz31002, wzz32002, bdf)
new_ltEs20(wzz31001, wzz32001, app(ty_[], bfg)) → new_ltEs13(wzz31001, wzz32001, bfg)
new_esEs14(wzz402, wzz3002, app(app(ty_@2, ff), fg)) → new_esEs6(wzz402, wzz3002, ff, fg)
new_compare111(wzz31000, wzz32000, False) → GT
new_compare111(wzz31000, wzz32000, True) → LT
new_compare31(wzz31000, wzz32000, ty_Int) → new_compare14(wzz31000, wzz32000)
new_ltEs5(@2(wzz31000, wzz31001), @2(wzz32000, wzz32001), bfd, bfe) → new_pePe(new_lt20(wzz31000, wzz32000, bfd), new_asAs(new_esEs24(wzz31000, wzz32000, bfd), new_ltEs20(wzz31001, wzz32001, bfe)))
new_esEs12(wzz400, wzz3000, app(ty_[], cf)) → new_esEs16(wzz400, wzz3000, cf)
new_ltEs15(Just(wzz31000), Just(wzz32000), app(ty_Maybe, dah)) → new_ltEs15(wzz31000, wzz32000, dah)
new_ltEs12(wzz31002, wzz32002, app(app(ty_Either, bdh), bea)) → new_ltEs14(wzz31002, wzz32002, bdh, bea)
new_esEs22(wzz31000, wzz32000, ty_Integer) → new_esEs20(wzz31000, wzz32000)
new_esEs23(wzz31001, wzz32001, app(app(app(ty_@3, bdc), bdd), bde)) → new_esEs7(wzz31001, wzz32001, bdc, bdd, bde)
new_esEs23(wzz31001, wzz32001, ty_Integer) → new_esEs20(wzz31001, wzz32001)
new_esEs25(wzz400, wzz3000, app(app(ty_@2, cgd), cge)) → new_esEs6(wzz400, wzz3000, cgd, cge)
new_esEs11(GT, GT) → True
new_esEs23(wzz31001, wzz32001, ty_Char) → new_esEs18(wzz31001, wzz32001)
new_esEs29(wzz40, wzz300, ty_Ordering) → new_esEs11(wzz40, wzz300)
new_esEs24(wzz31000, wzz32000, app(app(ty_@2, bd), be)) → new_esEs6(wzz31000, wzz32000, bd, be)
new_pePe(True, wzz150) → True
new_primEqNat0(Zero, Zero) → True
new_ltEs19(wzz3100, wzz3200, ty_Integer) → new_ltEs18(wzz3100, wzz3200)
new_esEs13(wzz401, wzz3001, app(ty_Maybe, eh)) → new_esEs5(wzz401, wzz3001, eh)
new_primMulNat0(Succ(wzz40100), Succ(wzz300100)) → new_primPlusNat1(new_primMulNat0(wzz40100, Succ(wzz300100)), wzz300100)
new_lt12(wzz31000, wzz32000, ty_Char) → new_lt18(wzz31000, wzz32000)
new_ltEs12(wzz31002, wzz32002, ty_@0) → new_ltEs17(wzz31002, wzz32002)
new_compare29(Nothing, Just(wzz3200), False, beh) → LT
new_compare31(wzz31000, wzz32000, ty_Bool) → new_compare30(wzz31000, wzz32000)
new_ltEs14(Right(wzz31000), Right(wzz32000), bfa, app(ty_Maybe, caf)) → new_ltEs15(wzz31000, wzz32000, caf)
new_esEs26(wzz401, wzz3001, ty_Bool) → new_esEs15(wzz401, wzz3001)
new_esEs24(wzz31000, wzz32000, app(ty_Ratio, ge)) → new_esEs17(wzz31000, wzz32000, ge)
new_esEs13(wzz401, wzz3001, ty_@0) → new_esEs10(wzz401, wzz3001)
new_compare110(wzz31000, wzz32000, False, gg, gh) → GT
new_compare(:(wzz31000, wzz31001), :(wzz32000, wzz32001), gd) → new_primCompAux1(wzz31000, wzz32000, new_compare(wzz31001, wzz32001, gd), gd)
new_sr(wzz401, wzz3001) → new_primMulInt(wzz401, wzz3001)
new_ltEs15(Just(wzz31000), Just(wzz32000), ty_Char) → new_ltEs8(wzz31000, wzz32000)
new_compare210(wzz31000, wzz32000, False, bf, bg, bh) → new_compare12(wzz31000, wzz32000, new_ltEs11(wzz31000, wzz32000, bf, bg, bh), bf, bg, bh)
new_compare12(wzz31000, wzz32000, True, bf, bg, bh) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_esEs5(Just(wzz400), Just(wzz3000), ty_Char) → new_esEs18(wzz400, wzz3000)
new_ltEs12(wzz31002, wzz32002, app(app(ty_@2, bec), bed)) → new_ltEs5(wzz31002, wzz32002, bec, bed)
new_lt4(wzz31000, wzz32000) → new_esEs11(new_compare5(wzz31000, wzz32000), LT)
new_esEs4(Left(wzz400), Left(wzz3000), ty_Int, cbf) → new_esEs9(wzz400, wzz3000)
new_esEs13(wzz401, wzz3001, ty_Int) → new_esEs9(wzz401, wzz3001)
new_primCmpInt(Neg(Zero), Neg(Succ(wzz3200))) → new_primCmpNat0(wzz3200, Zero)
new_esEs25(wzz400, wzz3000, ty_@0) → new_esEs10(wzz400, wzz3000)
new_compare7(wzz31000, wzz32000, bf, bg, bh) → new_compare210(wzz31000, wzz32000, new_esEs7(wzz31000, wzz32000, bf, bg, bh), bf, bg, bh)
new_lt13(wzz31001, wzz32001, ty_Ordering) → new_lt4(wzz31001, wzz32001)
new_esEs19(Float(wzz400, wzz401), Float(wzz3000, wzz3001)) → new_esEs9(new_sr(wzz400, wzz3000), new_sr(wzz401, wzz3001))
new_ltEs20(wzz31001, wzz32001, ty_Float) → new_ltEs16(wzz31001, wzz32001)
new_ltEs15(Just(wzz31000), Just(wzz32000), ty_Int) → new_ltEs9(wzz31000, wzz32000)
new_primCmpNat1(Succ(wzz31000), Zero) → GT
new_esEs4(Right(wzz400), Right(wzz3000), ccg, app(app(ty_Either, cch), cda)) → new_esEs4(wzz400, wzz3000, cch, cda)
new_ltEs12(wzz31002, wzz32002, ty_Ordering) → new_ltEs10(wzz31002, wzz32002)
new_primEqInt(Neg(Succ(wzz4000)), Neg(Succ(wzz30000))) → new_primEqNat0(wzz4000, wzz30000)
new_compare25(wzz31000, wzz32000, True) → EQ
new_esEs15(True, True) → True
new_lt13(wzz31001, wzz32001, app(ty_[], bce)) → new_lt10(wzz31001, wzz32001, bce)
new_ltEs15(Just(wzz31000), Just(wzz32000), ty_Float) → new_ltEs16(wzz31000, wzz32000)
new_compare16(wzz118, wzz119, True, ha) → LT
new_esEs4(Left(wzz400), Left(wzz3000), app(app(ty_Either, cbd), cbe), cbf) → new_esEs4(wzz400, wzz3000, cbd, cbe)
new_compare31(wzz31000, wzz32000, app(app(ty_Either, ddb), ddc)) → new_compare15(wzz31000, wzz32000, ddb, ddc)
new_esEs24(wzz31000, wzz32000, ty_Integer) → new_esEs20(wzz31000, wzz32000)
new_lt12(wzz31000, wzz32000, app(ty_Ratio, bbb)) → new_lt7(wzz31000, wzz32000, bbb)
new_ltEs14(Right(wzz31000), Right(wzz32000), bfa, ty_@0) → new_ltEs17(wzz31000, wzz32000)
new_esEs4(Right(wzz400), Right(wzz3000), ccg, ty_Ordering) → new_esEs11(wzz400, wzz3000)
new_lt14(wzz31000, wzz32000) → new_esEs11(new_compare18(wzz31000, wzz32000), LT)
new_esEs26(wzz401, wzz3001, app(app(app(ty_@3, chh), daa), dab)) → new_esEs7(wzz401, wzz3001, chh, daa, dab)
new_ltEs14(Right(wzz31000), Left(wzz32000), bfa, bfb) → False
new_esEs25(wzz400, wzz3000, ty_Char) → new_esEs18(wzz400, wzz3000)
new_compare29(Just(wzz3100), Nothing, False, beh) → GT
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_ltEs12(wzz31002, wzz32002, app(ty_[], bdg)) → new_ltEs13(wzz31002, wzz32002, bdg)
new_esEs21(wzz400, wzz3000, ty_Double) → new_esEs8(wzz400, wzz3000)
new_ltEs11(@3(wzz31000, wzz31001, wzz31002), @3(wzz32000, wzz32001, wzz32002), bag, bah, bba) → new_pePe(new_lt12(wzz31000, wzz32000, bag), new_asAs(new_esEs22(wzz31000, wzz32000, bag), new_pePe(new_lt13(wzz31001, wzz32001, bah), new_asAs(new_esEs23(wzz31001, wzz32001, bah), new_ltEs12(wzz31002, wzz32002, bba)))))
new_compare15(wzz31000, wzz32000, gg, gh) → new_compare26(wzz31000, wzz32000, new_esEs4(wzz31000, wzz32000, gg, gh), gg, gh)
new_esEs4(Left(wzz400), Left(wzz3000), ty_Char, cbf) → new_esEs18(wzz400, wzz3000)
new_esEs30(wzz20, wzz15, app(app(app(ty_@3, cfd), cfe), cff)) → new_esEs7(wzz20, wzz15, cfd, cfe, cff)
new_primEqInt(Neg(Zero), Neg(Succ(wzz30000))) → False
new_primEqInt(Neg(Succ(wzz4000)), Neg(Zero)) → False
new_esEs4(Right(wzz400), Right(wzz3000), ccg, app(ty_[], cdb)) → new_esEs16(wzz400, wzz3000, cdb)
new_primCompAux0(wzz165, GT) → GT
new_compare26(wzz31000, wzz32000, True, gg, gh) → EQ
new_ltEs9(wzz3100, wzz3200) → new_fsEs(new_compare14(wzz3100, wzz3200))
new_esEs4(Right(wzz400), Right(wzz3000), ccg, ty_Double) → new_esEs8(wzz400, wzz3000)
new_compare24(wzz31000, wzz32000, True, bd, be) → EQ
new_esEs21(wzz400, wzz3000, app(app(ty_Either, hc), hd)) → new_esEs4(wzz400, wzz3000, hc, hd)
new_ltEs15(Just(wzz31000), Just(wzz32000), app(app(app(ty_@3, dbc), dbd), dbe)) → new_ltEs11(wzz31000, wzz32000, dbc, dbd, dbe)
new_esEs29(wzz40, wzz300, app(ty_[], hb)) → new_esEs16(wzz40, wzz300, hb)
new_ltEs12(wzz31002, wzz32002, ty_Bool) → new_ltEs4(wzz31002, wzz32002)
new_esEs4(Right(wzz400), Right(wzz3000), ccg, ty_Bool) → new_esEs15(wzz400, wzz3000)
new_compare([], [], gd) → EQ
new_compare14(wzz31, wzz32) → new_primCmpInt(wzz31, wzz32)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_esEs21(wzz400, wzz3000, app(ty_Ratio, hf)) → new_esEs17(wzz400, wzz3000, hf)
new_esEs5(Just(wzz400), Just(wzz3000), ty_@0) → new_esEs10(wzz400, wzz3000)
new_ltEs20(wzz31001, wzz32001, app(app(ty_@2, bgc), bgd)) → new_ltEs5(wzz31001, wzz32001, bgc, bgd)
new_ltEs19(wzz3100, wzz3200, ty_Double) → new_ltEs7(wzz3100, wzz3200)
new_ltEs14(Left(wzz31000), Left(wzz32000), ty_Int, bfb) → new_ltEs9(wzz31000, wzz32000)
new_esEs4(Left(wzz400), Left(wzz3000), ty_Float, cbf) → new_esEs19(wzz400, wzz3000)
new_esEs22(wzz31000, wzz32000, ty_Double) → new_esEs8(wzz31000, wzz32000)
new_primEqInt(Pos(Succ(wzz4000)), Pos(Succ(wzz30000))) → new_primEqNat0(wzz4000, wzz30000)
new_compare5(wzz31000, wzz32000) → new_compare27(wzz31000, wzz32000, new_esEs11(wzz31000, wzz32000))
new_lt9(wzz31000, wzz32000, gg, gh) → new_esEs11(new_compare15(wzz31000, wzz32000, gg, gh), LT)
new_esEs25(wzz400, wzz3000, app(ty_Maybe, cha)) → new_esEs5(wzz400, wzz3000, cha)
new_ltEs12(wzz31002, wzz32002, app(ty_Maybe, beb)) → new_ltEs15(wzz31002, wzz32002, beb)
new_esEs12(wzz400, wzz3000, ty_Double) → new_esEs8(wzz400, wzz3000)
new_esEs29(wzz40, wzz300, app(ty_Maybe, cee)) → new_esEs5(wzz40, wzz300, cee)
new_esEs30(wzz20, wzz15, ty_Integer) → new_esEs20(wzz20, wzz15)
new_esEs16(:(wzz400, wzz401), :(wzz3000, wzz3001), hb) → new_asAs(new_esEs21(wzz400, wzz3000, hb), new_esEs16(wzz401, wzz3001, hb))
new_esEs29(wzz40, wzz300, ty_Double) → new_esEs8(wzz40, wzz300)
new_esEs25(wzz400, wzz3000, ty_Int) → new_esEs9(wzz400, wzz3000)
new_lt13(wzz31001, wzz32001, app(app(ty_Either, bcf), bcg)) → new_lt9(wzz31001, wzz32001, bcf, bcg)
new_ltEs10(GT, EQ) → False
new_primEqNat0(Succ(wzz4000), Succ(wzz30000)) → new_primEqNat0(wzz4000, wzz30000)
new_esEs12(wzz400, wzz3000, ty_@0) → new_esEs10(wzz400, wzz3000)
new_compare31(wzz31000, wzz32000, ty_Float) → new_compare17(wzz31000, wzz32000)
new_lt13(wzz31001, wzz32001, ty_Integer) → new_lt6(wzz31001, wzz32001)
new_esEs4(Left(wzz400), Left(wzz3000), app(app(app(ty_@3, ccc), ccd), cce), cbf) → new_esEs7(wzz400, wzz3000, ccc, ccd, cce)
new_esEs14(wzz402, wzz3002, app(ty_Maybe, gc)) → new_esEs5(wzz402, wzz3002, gc)
new_lt12(wzz31000, wzz32000, ty_Ordering) → new_lt4(wzz31000, wzz32000)
new_compare16(wzz118, wzz119, False, ha) → GT
new_esEs21(wzz400, wzz3000, ty_Float) → new_esEs19(wzz400, wzz3000)
new_ltEs14(Left(wzz31000), Left(wzz32000), ty_Ordering, bfb) → new_ltEs10(wzz31000, wzz32000)
new_esEs23(wzz31001, wzz32001, ty_Bool) → new_esEs15(wzz31001, wzz32001)
new_esEs12(wzz400, wzz3000, app(app(ty_Either, cd), ce)) → new_esEs4(wzz400, wzz3000, cd, ce)
new_lt13(wzz31001, wzz32001, ty_Int) → new_lt16(wzz31001, wzz32001)
new_primEqInt(Pos(Zero), Pos(Succ(wzz30000))) → False
new_primEqInt(Pos(Succ(wzz4000)), Pos(Zero)) → False
new_esEs25(wzz400, wzz3000, ty_Integer) → new_esEs20(wzz400, wzz3000)
new_esEs22(wzz31000, wzz32000, ty_Ordering) → new_esEs11(wzz31000, wzz32000)
new_esEs21(wzz400, wzz3000, ty_Bool) → new_esEs15(wzz400, wzz3000)
new_lt20(wzz31000, wzz32000, ty_Char) → new_lt18(wzz31000, wzz32000)
new_esEs12(wzz400, wzz3000, app(app(app(ty_@3, dc), dd), de)) → new_esEs7(wzz400, wzz3000, dc, dd, de)
new_primPlusNat0(Succ(wzz26200), Zero) → Succ(wzz26200)
new_primPlusNat0(Zero, Succ(wzz8700)) → Succ(wzz8700)
new_lt13(wzz31001, wzz32001, ty_@0) → new_lt19(wzz31001, wzz32001)
new_esEs24(wzz31000, wzz32000, ty_@0) → new_esEs10(wzz31000, wzz32000)
new_esEs30(wzz20, wzz15, ty_Double) → new_esEs8(wzz20, wzz15)
new_esEs28(wzz401, wzz3001, ty_Integer) → new_esEs20(wzz401, wzz3001)
new_esEs4(Right(wzz400), Right(wzz3000), ccg, ty_@0) → new_esEs10(wzz400, wzz3000)
new_ltEs14(Left(wzz31000), Left(wzz32000), ty_Char, bfb) → new_ltEs8(wzz31000, wzz32000)
new_ltEs10(LT, EQ) → True
new_primCmpInt(Neg(Zero), Pos(Succ(wzz3200))) → LT
new_ltEs15(Just(wzz31000), Just(wzz32000), ty_Ordering) → new_ltEs10(wzz31000, wzz32000)
new_esEs4(Left(wzz400), Left(wzz3000), ty_Ordering, cbf) → new_esEs11(wzz400, wzz3000)
new_compare11(wzz31000, wzz32000, True, bd, be) → LT
new_compare210(wzz31000, wzz32000, True, bf, bg, bh) → EQ
new_compare31(wzz31000, wzz32000, app(ty_Ratio, dch)) → new_compare9(wzz31000, wzz32000, dch)
new_sr0(Integer(wzz310000), Integer(wzz320010)) → Integer(new_primMulInt(wzz310000, wzz320010))
new_primEqInt(Neg(Succ(wzz4000)), Pos(wzz3000)) → False
new_primEqInt(Pos(Succ(wzz4000)), Neg(wzz3000)) → False
new_compare25(wzz31000, wzz32000, False) → new_compare10(wzz31000, wzz32000, new_ltEs4(wzz31000, wzz32000))
new_esEs13(wzz401, wzz3001, ty_Bool) → new_esEs15(wzz401, wzz3001)
new_ltEs7(wzz3100, wzz3200) → new_fsEs(new_compare18(wzz3100, wzz3200))
new_ltEs14(Left(wzz31000), Left(wzz32000), app(ty_[], bha), bfb) → new_ltEs13(wzz31000, wzz32000, bha)
new_ltEs10(GT, GT) → True
new_esEs14(wzz402, wzz3002, app(ty_[], fc)) → new_esEs16(wzz402, wzz3002, fc)
new_esEs22(wzz31000, wzz32000, app(app(ty_@2, bbg), bbh)) → new_esEs6(wzz31000, wzz32000, bbg, bbh)
new_ltEs20(wzz31001, wzz32001, ty_Integer) → new_ltEs18(wzz31001, wzz32001)
new_esEs26(wzz401, wzz3001, ty_Int) → new_esEs9(wzz401, wzz3001)
new_ltEs20(wzz31001, wzz32001, app(ty_Maybe, bgb)) → new_ltEs15(wzz31001, wzz32001, bgb)
new_lt13(wzz31001, wzz32001, app(ty_Ratio, bcd)) → new_lt7(wzz31001, wzz32001, bcd)
new_esEs24(wzz31000, wzz32000, ty_Ordering) → new_esEs11(wzz31000, wzz32000)
new_primEqInt(Neg(Zero), Pos(Succ(wzz30000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(wzz30000))) → False
new_primCmpNat2(Succ(wzz3200), wzz3100) → new_primCmpNat1(wzz3200, wzz3100)
new_ltEs14(Right(wzz31000), Right(wzz32000), bfa, ty_Double) → new_ltEs7(wzz31000, wzz32000)
new_esEs30(wzz20, wzz15, app(ty_Ratio, cfa)) → new_esEs17(wzz20, wzz15, cfa)
new_lt12(wzz31000, wzz32000, app(ty_[], bbc)) → new_lt10(wzz31000, wzz32000, bbc)
new_esEs21(wzz400, wzz3000, ty_Ordering) → new_esEs11(wzz400, wzz3000)
new_lt20(wzz31000, wzz32000, ty_Ordering) → new_lt4(wzz31000, wzz32000)
new_lt8(wzz31000, wzz32000, bd, be) → new_esEs11(new_compare6(wzz31000, wzz32000, bd, be), LT)
new_esEs14(wzz402, wzz3002, ty_Double) → new_esEs8(wzz402, wzz3002)
new_esEs5(Just(wzz400), Just(wzz3000), ty_Ordering) → new_esEs11(wzz400, wzz3000)
new_compare31(wzz31000, wzz32000, ty_Ordering) → new_compare5(wzz31000, wzz32000)
new_lt20(wzz31000, wzz32000, ty_Integer) → new_lt6(wzz31000, wzz32000)
new_esEs21(wzz400, wzz3000, ty_Char) → new_esEs18(wzz400, wzz3000)
new_primCompAux0(wzz165, LT) → LT
new_esEs30(wzz20, wzz15, ty_@0) → new_esEs10(wzz20, wzz15)
new_ltEs19(wzz3100, wzz3200, ty_Char) → new_ltEs8(wzz3100, wzz3200)
new_lt13(wzz31001, wzz32001, ty_Bool) → new_lt11(wzz31001, wzz32001)
new_ltEs14(Right(wzz31000), Right(wzz32000), bfa, ty_Integer) → new_ltEs18(wzz31000, wzz32000)
new_not(False) → True
new_esEs24(wzz31000, wzz32000, ty_Float) → new_esEs19(wzz31000, wzz32000)
new_esEs4(Right(wzz400), Right(wzz3000), ccg, app(ty_Ratio, cdc)) → new_esEs17(wzz400, wzz3000, cdc)
new_esEs23(wzz31001, wzz32001, app(app(ty_@2, bda), bdb)) → new_esEs6(wzz31001, wzz32001, bda, bdb)
new_compare12(wzz31000, wzz32000, False, bf, bg, bh) → GT
new_esEs12(wzz400, wzz3000, ty_Integer) → new_esEs20(wzz400, wzz3000)
new_esEs11(LT, GT) → False
new_esEs11(GT, LT) → False
new_esEs30(wzz20, wzz15, app(app(ty_Either, cef), ceg)) → new_esEs4(wzz20, wzz15, cef, ceg)
new_compare31(wzz31000, wzz32000, app(ty_Maybe, ddd)) → new_compare28(wzz31000, wzz32000, ddd)
new_ltEs14(Right(wzz31000), Right(wzz32000), bfa, app(ty_Ratio, cab)) → new_ltEs6(wzz31000, wzz32000, cab)
new_compare27(wzz31000, wzz32000, False) → new_compare111(wzz31000, wzz32000, new_ltEs10(wzz31000, wzz32000))
new_lt20(wzz31000, wzz32000, app(ty_[], baf)) → new_lt10(wzz31000, wzz32000, baf)
new_esEs13(wzz401, wzz3001, app(ty_[], ea)) → new_esEs16(wzz401, wzz3001, ea)
new_esEs12(wzz400, wzz3000, ty_Float) → new_esEs19(wzz400, wzz3000)
new_esEs11(LT, EQ) → False
new_esEs11(EQ, LT) → False
new_esEs24(wzz31000, wzz32000, app(ty_Maybe, bae)) → new_esEs5(wzz31000, wzz32000, bae)
new_esEs4(Right(wzz400), Right(wzz3000), ccg, app(app(ty_@2, cdd), cde)) → new_esEs6(wzz400, wzz3000, cdd, cde)
new_esEs23(wzz31001, wzz32001, ty_@0) → new_esEs10(wzz31001, wzz32001)
new_esEs14(wzz402, wzz3002, ty_Char) → new_esEs18(wzz402, wzz3002)
new_esEs14(wzz402, wzz3002, ty_@0) → new_esEs10(wzz402, wzz3002)
new_lt12(wzz31000, wzz32000, ty_Double) → new_lt14(wzz31000, wzz32000)
new_ltEs20(wzz31001, wzz32001, ty_@0) → new_ltEs17(wzz31001, wzz32001)
new_compare11(wzz31000, wzz32000, False, bd, be) → GT
new_ltEs17(wzz3100, wzz3200) → new_fsEs(new_compare13(wzz3100, wzz3200))
new_esEs22(wzz31000, wzz32000, app(app(app(ty_@3, bca), bcb), bcc)) → new_esEs7(wzz31000, wzz32000, bca, bcb, bcc)
new_esEs13(wzz401, wzz3001, app(app(ty_Either, dg), dh)) → new_esEs4(wzz401, wzz3001, dg, dh)
new_primCmpInt(Pos(Succ(wzz3100)), Neg(wzz320)) → GT
new_esEs22(wzz31000, wzz32000, ty_Char) → new_esEs18(wzz31000, wzz32000)
new_ltEs19(wzz3100, wzz3200, ty_Int) → new_ltEs9(wzz3100, wzz3200)
new_lt12(wzz31000, wzz32000, app(app(app(ty_@3, bca), bcb), bcc)) → new_lt5(wzz31000, wzz32000, bca, bcb, bcc)
new_ltEs18(wzz3100, wzz3200) → new_fsEs(new_compare8(wzz3100, wzz3200))
new_esEs22(wzz31000, wzz32000, app(ty_[], bbc)) → new_esEs16(wzz31000, wzz32000, bbc)
new_esEs14(wzz402, wzz3002, app(app(ty_Either, fa), fb)) → new_esEs4(wzz402, wzz3002, fa, fb)
new_primMulInt(Pos(wzz4010), Pos(wzz30010)) → Pos(new_primMulNat0(wzz4010, wzz30010))
new_esEs26(wzz401, wzz3001, ty_@0) → new_esEs10(wzz401, wzz3001)
new_esEs4(Left(wzz400), Left(wzz3000), ty_Bool, cbf) → new_esEs15(wzz400, wzz3000)
new_esEs30(wzz20, wzz15, ty_Ordering) → new_esEs11(wzz20, wzz15)
new_esEs23(wzz31001, wzz32001, app(app(ty_Either, bcf), bcg)) → new_esEs4(wzz31001, wzz32001, bcf, bcg)
new_esEs14(wzz402, wzz3002, ty_Bool) → new_esEs15(wzz402, wzz3002)
new_primMulInt(Neg(wzz4010), Neg(wzz30010)) → Pos(new_primMulNat0(wzz4010, wzz30010))
new_ltEs19(wzz3100, wzz3200, app(ty_Ratio, gf)) → new_ltEs6(wzz3100, wzz3200, gf)
new_lt6(wzz31000, wzz32000) → new_esEs11(new_compare8(wzz31000, wzz32000), LT)
new_esEs24(wzz31000, wzz32000, ty_Bool) → new_esEs15(wzz31000, wzz32000)
new_esEs29(wzz40, wzz300, app(app(ty_@2, cec), ced)) → new_esEs6(wzz40, wzz300, cec, ced)
new_primEqNat0(Zero, Succ(wzz30000)) → False
new_primEqNat0(Succ(wzz4000), Zero) → False
new_esEs29(wzz40, wzz300, app(ty_Ratio, ceb)) → new_esEs17(wzz40, wzz300, ceb)
new_esEs21(wzz400, wzz3000, ty_@0) → new_esEs10(wzz400, wzz3000)
new_esEs21(wzz400, wzz3000, ty_Int) → new_esEs9(wzz400, wzz3000)
new_primPlusNat0(Zero, Zero) → Zero
new_esEs25(wzz400, wzz3000, app(ty_Ratio, cgc)) → new_esEs17(wzz400, wzz3000, cgc)
new_lt12(wzz31000, wzz32000, ty_Bool) → new_lt11(wzz31000, wzz32000)
new_compare31(wzz31000, wzz32000, ty_Integer) → new_compare8(wzz31000, wzz32000)
new_lt12(wzz31000, wzz32000, ty_Int) → new_lt16(wzz31000, wzz32000)
new_ltEs14(Left(wzz31000), Left(wzz32000), app(app(ty_@2, bhe), bhf), bfb) → new_ltEs5(wzz31000, wzz32000, bhe, bhf)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_compare9(:%(wzz31000, wzz31001), :%(wzz32000, wzz32001), ty_Integer) → new_compare8(new_sr0(wzz31000, wzz32001), new_sr0(wzz32000, wzz31001))
new_esEs24(wzz31000, wzz32000, app(app(ty_Either, gg), gh)) → new_esEs4(wzz31000, wzz32000, gg, gh)
new_compare31(wzz31000, wzz32000, ty_Double) → new_compare18(wzz31000, wzz32000)
new_esEs5(Just(wzz400), Just(wzz3000), ty_Float) → new_esEs19(wzz400, wzz3000)
new_primCmpInt(Pos(Succ(wzz3100)), Pos(wzz320)) → new_primCmpNat0(wzz3100, wzz320)
new_ltEs13(wzz3100, wzz3200, gd) → new_fsEs(new_compare(wzz3100, wzz3200, gd))
new_ltEs12(wzz31002, wzz32002, app(app(app(ty_@3, bee), bef), beg)) → new_ltEs11(wzz31002, wzz32002, bee, bef, beg)
new_fsEs(wzz135) → new_not(new_esEs11(wzz135, GT))
new_esEs29(wzz40, wzz300, ty_Integer) → new_esEs20(wzz40, wzz300)
new_esEs22(wzz31000, wzz32000, ty_Int) → new_esEs9(wzz31000, wzz32000)
new_ltEs15(Just(wzz31000), Nothing, bfc) → False
new_esEs16([], :(wzz3000, wzz3001), hb) → False
new_esEs16(:(wzz400, wzz401), [], hb) → False
new_primCmpNat0(wzz3100, Zero) → GT
new_esEs5(Just(wzz400), Just(wzz3000), ty_Integer) → new_esEs20(wzz400, wzz3000)
new_ltEs4(True, False) → False
new_esEs12(wzz400, wzz3000, ty_Int) → new_esEs9(wzz400, wzz3000)
new_ltEs19(wzz3100, wzz3200, ty_@0) → new_ltEs17(wzz3100, wzz3200)
new_lt13(wzz31001, wzz32001, ty_Char) → new_lt18(wzz31001, wzz32001)
new_esEs26(wzz401, wzz3001, app(ty_Maybe, dac)) → new_esEs5(wzz401, wzz3001, dac)
new_esEs22(wzz31000, wzz32000, ty_@0) → new_esEs10(wzz31000, wzz32000)
new_lt13(wzz31001, wzz32001, app(ty_Maybe, bch)) → new_lt15(wzz31001, wzz32001, bch)
new_ltEs15(Just(wzz31000), Just(wzz32000), app(app(ty_@2, dba), dbb)) → new_ltEs5(wzz31000, wzz32000, dba, dbb)
new_ltEs14(Right(wzz31000), Right(wzz32000), bfa, app(app(ty_@2, cag), cah)) → new_ltEs5(wzz31000, wzz32000, cag, cah)
new_esEs24(wzz31000, wzz32000, ty_Int) → new_esEs9(wzz31000, wzz32000)
new_ltEs12(wzz31002, wzz32002, ty_Integer) → new_ltEs18(wzz31002, wzz32002)
new_esEs23(wzz31001, wzz32001, app(ty_Ratio, bcd)) → new_esEs17(wzz31001, wzz32001, bcd)
new_primCmpInt(Pos(Zero), Neg(Succ(wzz3200))) → GT
new_esEs30(wzz20, wzz15, ty_Char) → new_esEs18(wzz20, wzz15)
new_ltEs20(wzz31001, wzz32001, ty_Char) → new_ltEs8(wzz31001, wzz32001)
new_lt5(wzz31000, wzz32000, bf, bg, bh) → new_esEs11(new_compare7(wzz31000, wzz32000, bf, bg, bh), LT)
new_esEs12(wzz400, wzz3000, ty_Char) → new_esEs18(wzz400, wzz3000)
new_compare31(wzz31000, wzz32000, app(ty_[], dda)) → new_compare(wzz31000, wzz32000, dda)
new_esEs27(wzz400, wzz3000, ty_Int) → new_esEs9(wzz400, wzz3000)
new_esEs13(wzz401, wzz3001, app(app(ty_@2, ec), ed)) → new_esEs6(wzz401, wzz3001, ec, ed)
new_ltEs12(wzz31002, wzz32002, ty_Double) → new_ltEs7(wzz31002, wzz32002)
new_ltEs16(wzz3100, wzz3200) → new_fsEs(new_compare17(wzz3100, wzz3200))
new_esEs30(wzz20, wzz15, app(ty_[], ceh)) → new_esEs16(wzz20, wzz15, ceh)
new_compare29(Nothing, Nothing, False, beh) → LT
new_esEs4(Left(wzz400), Left(wzz3000), ty_Integer, cbf) → new_esEs20(wzz400, wzz3000)
new_ltEs14(Left(wzz31000), Left(wzz32000), ty_Integer, bfb) → new_ltEs18(wzz31000, wzz32000)
new_esEs10(@0, @0) → True
new_esEs24(wzz31000, wzz32000, app(app(app(ty_@3, bf), bg), bh)) → new_esEs7(wzz31000, wzz32000, bf, bg, bh)
new_compare29(wzz310, wzz320, True, beh) → EQ
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_lt10(wzz31000, wzz32000, baf) → new_esEs11(new_compare(wzz31000, wzz32000, baf), LT)
new_esEs13(wzz401, wzz3001, ty_Float) → new_esEs19(wzz401, wzz3001)
new_primCompAux1(wzz31000, wzz32000, wzz151, gd) → new_primCompAux0(wzz151, new_compare31(wzz31000, wzz32000, gd))
new_esEs5(Just(wzz400), Just(wzz3000), app(ty_[], dbh)) → new_esEs16(wzz400, wzz3000, dbh)
new_ltEs14(Left(wzz31000), Right(wzz32000), bfa, bfb) → True
new_ltEs6(wzz3100, wzz3200, gf) → new_fsEs(new_compare9(wzz3100, wzz3200, gf))
new_esEs12(wzz400, wzz3000, ty_Ordering) → new_esEs11(wzz400, wzz3000)
new_esEs29(wzz40, wzz300, ty_Bool) → new_esEs15(wzz40, wzz300)
new_ltEs20(wzz31001, wzz32001, app(app(ty_Either, bfh), bga)) → new_ltEs14(wzz31001, wzz32001, bfh, bga)
new_asAs(False, wzz125) → False
new_esEs4(Left(wzz400), Left(wzz3000), ty_@0, cbf) → new_esEs10(wzz400, wzz3000)
new_ltEs19(wzz3100, wzz3200, app(app(ty_Either, bfa), bfb)) → new_ltEs14(wzz3100, wzz3200, bfa, bfb)
new_primMulInt(Pos(wzz4010), Neg(wzz30010)) → Neg(new_primMulNat0(wzz4010, wzz30010))
new_primMulInt(Neg(wzz4010), Pos(wzz30010)) → Neg(new_primMulNat0(wzz4010, wzz30010))
new_esEs7(@3(wzz400, wzz401, wzz402), @3(wzz3000, wzz3001, wzz3002), ca, cb, cc) → new_asAs(new_esEs12(wzz400, wzz3000, ca), new_asAs(new_esEs13(wzz401, wzz3001, cb), new_esEs14(wzz402, wzz3002, cc)))
new_ltEs10(LT, GT) → True
new_lt20(wzz31000, wzz32000, ty_@0) → new_lt19(wzz31000, wzz32000)
new_primCmpInt(Neg(Succ(wzz3100)), Neg(wzz320)) → new_primCmpNat2(wzz320, wzz3100)
new_primMulNat0(Zero, Succ(wzz300100)) → Zero
new_primMulNat0(Succ(wzz40100), Zero) → Zero
new_esEs14(wzz402, wzz3002, app(app(app(ty_@3, fh), ga), gb)) → new_esEs7(wzz402, wzz3002, fh, ga, gb)
new_ltEs14(Left(wzz31000), Left(wzz32000), app(ty_Ratio, bgh), bfb) → new_ltEs6(wzz31000, wzz32000, bgh)
new_ltEs12(wzz31002, wzz32002, ty_Char) → new_ltEs8(wzz31002, wzz32002)
new_compare6(wzz31000, wzz32000, bd, be) → new_compare24(wzz31000, wzz32000, new_esEs6(wzz31000, wzz32000, bd, be), bd, be)
new_lt13(wzz31001, wzz32001, ty_Float) → new_lt17(wzz31001, wzz32001)
new_lt17(wzz31000, wzz32000) → new_esEs11(new_compare17(wzz31000, wzz32000), LT)
new_ltEs14(Left(wzz31000), Left(wzz32000), app(ty_Maybe, bhd), bfb) → new_ltEs15(wzz31000, wzz32000, bhd)
new_esEs24(wzz31000, wzz32000, app(ty_[], baf)) → new_esEs16(wzz31000, wzz32000, baf)
new_esEs23(wzz31001, wzz32001, ty_Int) → new_esEs9(wzz31001, wzz32001)
new_esEs5(Just(wzz400), Just(wzz3000), app(app(ty_@2, dcb), dcc)) → new_esEs6(wzz400, wzz3000, dcb, dcc)
new_ltEs14(Right(wzz31000), Right(wzz32000), bfa, app(app(app(ty_@3, cba), cbb), cbc)) → new_ltEs11(wzz31000, wzz32000, cba, cbb, cbc)
new_ltEs14(Right(wzz31000), Right(wzz32000), bfa, app(app(ty_Either, cad), cae)) → new_ltEs14(wzz31000, wzz32000, cad, cae)
new_esEs4(Left(wzz400), Left(wzz3000), app(ty_Maybe, ccf), cbf) → new_esEs5(wzz400, wzz3000, ccf)
new_compare13(@0, @0) → EQ
new_ltEs14(Left(wzz31000), Left(wzz32000), app(app(app(ty_@3, bhg), bhh), caa), bfb) → new_ltEs11(wzz31000, wzz32000, bhg, bhh, caa)
new_ltEs14(Left(wzz31000), Left(wzz32000), ty_Double, bfb) → new_ltEs7(wzz31000, wzz32000)
new_esEs23(wzz31001, wzz32001, app(ty_Maybe, bch)) → new_esEs5(wzz31001, wzz32001, bch)
new_ltEs4(False, False) → True
new_primCmpInt(Pos(Zero), Pos(Succ(wzz3200))) → new_primCmpNat2(Zero, wzz3200)
new_ltEs10(EQ, EQ) → True
new_compare27(wzz31000, wzz32000, True) → EQ
new_ltEs10(LT, LT) → True
new_ltEs15(Nothing, Nothing, bfc) → True
new_ltEs14(Right(wzz31000), Right(wzz32000), bfa, ty_Char) → new_ltEs8(wzz31000, wzz32000)
new_esEs5(Nothing, Just(wzz3000), cee) → False
new_esEs5(Just(wzz400), Nothing, cee) → False
new_esEs22(wzz31000, wzz32000, ty_Bool) → new_esEs15(wzz31000, wzz32000)
new_esEs4(Right(wzz400), Right(wzz3000), ccg, ty_Char) → new_esEs18(wzz400, wzz3000)
new_ltEs14(Right(wzz31000), Right(wzz32000), bfa, ty_Int) → new_ltEs9(wzz31000, wzz32000)
new_ltEs14(Left(wzz31000), Left(wzz32000), app(app(ty_Either, bhb), bhc), bfb) → new_ltEs14(wzz31000, wzz32000, bhb, bhc)
new_esEs29(wzz40, wzz300, ty_Float) → new_esEs19(wzz40, wzz300)
new_esEs25(wzz400, wzz3000, app(app(app(ty_@3, cgf), cgg), cgh)) → new_esEs7(wzz400, wzz3000, cgf, cgg, cgh)
new_compare31(wzz31000, wzz32000, ty_Char) → new_compare19(wzz31000, wzz32000)
new_esEs24(wzz31000, wzz32000, ty_Double) → new_esEs8(wzz31000, wzz32000)
new_esEs25(wzz400, wzz3000, ty_Float) → new_esEs19(wzz400, wzz3000)
new_lt7(wzz31000, wzz32000, ge) → new_esEs11(new_compare9(wzz31000, wzz32000, ge), LT)
new_compare31(wzz31000, wzz32000, app(app(app(ty_@3, ddg), ddh), dea)) → new_compare7(wzz31000, wzz32000, ddg, ddh, dea)
new_ltEs19(wzz3100, wzz3200, app(app(app(ty_@3, bag), bah), bba)) → new_ltEs11(wzz3100, wzz3200, bag, bah, bba)
new_esEs16([], [], hb) → True
new_lt11(wzz31000, wzz32000) → new_esEs11(new_compare30(wzz31000, wzz32000), LT)
new_ltEs12(wzz31002, wzz32002, ty_Float) → new_ltEs16(wzz31002, wzz32002)
new_esEs30(wzz20, wzz15, app(app(ty_@2, cfb), cfc)) → new_esEs6(wzz20, wzz15, cfb, cfc)
new_esEs8(Double(wzz400, wzz401), Double(wzz3000, wzz3001)) → new_esEs9(new_sr(wzz400, wzz3000), new_sr(wzz401, wzz3001))
new_lt13(wzz31001, wzz32001, app(app(app(ty_@3, bdc), bdd), bde)) → new_lt5(wzz31001, wzz32001, bdc, bdd, bde)
new_compare29(Just(wzz3100), Just(wzz3200), False, beh) → new_compare16(wzz3100, wzz3200, new_ltEs19(wzz3100, wzz3200, beh), beh)
new_esEs14(wzz402, wzz3002, ty_Int) → new_esEs9(wzz402, wzz3002)
new_lt12(wzz31000, wzz32000, app(app(ty_@2, bbg), bbh)) → new_lt8(wzz31000, wzz32000, bbg, bbh)
new_esEs12(wzz400, wzz3000, app(ty_Ratio, cg)) → new_esEs17(wzz400, wzz3000, cg)
new_ltEs20(wzz31001, wzz32001, app(ty_Ratio, bff)) → new_ltEs6(wzz31001, wzz32001, bff)
new_esEs5(Nothing, Nothing, cee) → True
new_esEs4(Left(wzz400), Left(wzz3000), app(ty_[], cbg), cbf) → new_esEs16(wzz400, wzz3000, cbg)
new_esEs26(wzz401, wzz3001, ty_Float) → new_esEs19(wzz401, wzz3001)
new_esEs5(Just(wzz400), Just(wzz3000), app(app(app(ty_@3, dcd), dce), dcf)) → new_esEs7(wzz400, wzz3000, dcd, dce, dcf)
new_esEs28(wzz401, wzz3001, ty_Int) → new_esEs9(wzz401, wzz3001)
new_ltEs10(EQ, LT) → False
new_esEs5(Just(wzz400), Just(wzz3000), app(ty_Ratio, dca)) → new_esEs17(wzz400, wzz3000, dca)
new_lt15(wzz31000, wzz32000, bae) → new_esEs11(new_compare28(wzz31000, wzz32000, bae), LT)
new_esEs22(wzz31000, wzz32000, app(ty_Ratio, bbb)) → new_esEs17(wzz31000, wzz32000, bbb)
new_esEs26(wzz401, wzz3001, ty_Char) → new_esEs18(wzz401, wzz3001)
new_lt18(wzz31000, wzz32000) → new_esEs11(new_compare19(wzz31000, wzz32000), LT)
new_lt12(wzz31000, wzz32000, ty_Float) → new_lt17(wzz31000, wzz32000)
new_ltEs10(GT, LT) → False
new_lt20(wzz31000, wzz32000, app(app(app(ty_@3, bf), bg), bh)) → new_lt5(wzz31000, wzz32000, bf, bg, bh)
new_esEs4(Right(wzz400), Right(wzz3000), ccg, ty_Float) → new_esEs19(wzz400, wzz3000)
new_primPlusNat0(Succ(wzz26200), Succ(wzz8700)) → Succ(Succ(new_primPlusNat0(wzz26200, wzz8700)))
new_esEs22(wzz31000, wzz32000, app(ty_Maybe, bbf)) → new_esEs5(wzz31000, wzz32000, bbf)
new_esEs23(wzz31001, wzz32001, app(ty_[], bce)) → new_esEs16(wzz31001, wzz32001, bce)
new_esEs21(wzz400, wzz3000, app(ty_Maybe, bad)) → new_esEs5(wzz400, wzz3000, bad)
new_esEs29(wzz40, wzz300, ty_@0) → new_esEs10(wzz40, wzz300)
new_esEs26(wzz401, wzz3001, app(app(ty_Either, chb), chc)) → new_esEs4(wzz401, wzz3001, chb, chc)
new_esEs21(wzz400, wzz3000, ty_Integer) → new_esEs20(wzz400, wzz3000)
new_asAs(True, wzz125) → wzz125
new_esEs4(Right(wzz400), Left(wzz3000), ccg, cbf) → False
new_esEs4(Left(wzz400), Right(wzz3000), ccg, cbf) → False
new_ltEs8(wzz3100, wzz3200) → new_fsEs(new_compare19(wzz3100, wzz3200))
new_esEs30(wzz20, wzz15, app(ty_Maybe, cfg)) → new_esEs5(wzz20, wzz15, cfg)
new_esEs11(LT, LT) → True
new_primPlusNat1(wzz97, wzz300100) → new_primPlusNat0(wzz97, Succ(wzz300100))
new_esEs14(wzz402, wzz3002, ty_Integer) → new_esEs20(wzz402, wzz3002)
new_esEs5(Just(wzz400), Just(wzz3000), ty_Double) → new_esEs8(wzz400, wzz3000)
new_compare24(wzz31000, wzz32000, False, bd, be) → new_compare11(wzz31000, wzz32000, new_ltEs5(wzz31000, wzz32000, bd, be), bd, be)
new_esEs26(wzz401, wzz3001, app(app(ty_@2, chf), chg)) → new_esEs6(wzz401, wzz3001, chf, chg)
new_lt13(wzz31001, wzz32001, app(app(ty_@2, bda), bdb)) → new_lt8(wzz31001, wzz32001, bda, bdb)
new_ltEs12(wzz31002, wzz32002, ty_Int) → new_ltEs9(wzz31002, wzz32002)
new_compare10(wzz31000, wzz32000, True) → LT
new_esEs9(wzz40, wzz300) → new_primEqInt(wzz40, wzz300)
new_esEs11(EQ, GT) → False
new_esEs11(GT, EQ) → False
new_lt20(wzz31000, wzz32000, app(ty_Ratio, ge)) → new_lt7(wzz31000, wzz32000, ge)
new_lt19(wzz31000, wzz32000) → new_esEs11(new_compare13(wzz31000, wzz32000), LT)
new_compare10(wzz31000, wzz32000, False) → GT
new_esEs6(@2(wzz400, wzz401), @2(wzz3000, wzz3001), cec, ced) → new_asAs(new_esEs25(wzz400, wzz3000, cec), new_esEs26(wzz401, wzz3001, ced))
new_esEs13(wzz401, wzz3001, app(app(app(ty_@3, ee), ef), eg)) → new_esEs7(wzz401, wzz3001, ee, ef, eg)
new_esEs21(wzz400, wzz3000, app(ty_[], he)) → new_esEs16(wzz400, wzz3000, he)
new_esEs5(Just(wzz400), Just(wzz3000), app(app(ty_Either, dbf), dbg)) → new_esEs4(wzz400, wzz3000, dbf, dbg)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCompAux0(wzz165, EQ) → wzz165
new_esEs24(wzz31000, wzz32000, ty_Char) → new_esEs18(wzz31000, wzz32000)
new_lt12(wzz31000, wzz32000, ty_@0) → new_lt19(wzz31000, wzz32000)
new_ltEs19(wzz3100, wzz3200, app(ty_[], gd)) → new_ltEs13(wzz3100, wzz3200, gd)
new_lt12(wzz31000, wzz32000, app(ty_Maybe, bbf)) → new_lt15(wzz31000, wzz32000, bbf)
new_ltEs14(Left(wzz31000), Left(wzz32000), ty_@0, bfb) → new_ltEs17(wzz31000, wzz32000)
new_compare9(:%(wzz31000, wzz31001), :%(wzz32000, wzz32001), ty_Int) → new_compare14(new_sr(wzz31000, wzz32001), new_sr(wzz32000, wzz31001))
new_ltEs15(Just(wzz31000), Just(wzz32000), app(app(ty_Either, daf), dag)) → new_ltEs14(wzz31000, wzz32000, daf, dag)
new_esEs12(wzz400, wzz3000, app(ty_Maybe, df)) → new_esEs5(wzz400, wzz3000, df)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primCmpNat0(wzz3100, Succ(wzz3200)) → new_primCmpNat1(wzz3100, wzz3200)
new_lt20(wzz31000, wzz32000, app(app(ty_Either, gg), gh)) → new_lt9(wzz31000, wzz32000, gg, gh)
new_esEs12(wzz400, wzz3000, app(app(ty_@2, da), db)) → new_esEs6(wzz400, wzz3000, da, db)
new_primCmpInt(Neg(Succ(wzz3100)), Pos(wzz320)) → LT
new_not(True) → False
new_esEs15(False, False) → True

The set Q consists of the following terms:

new_compare210(x0, x1, False, x2, x3, x4)
new_compare31(x0, x1, ty_Int)
new_esEs4(Right(x0), Right(x1), x2, ty_Integer)
new_compare10(x0, x1, True)
new_compare31(x0, x1, ty_@0)
new_ltEs15(Just(x0), Just(x1), ty_@0)
new_esEs29(x0, x1, ty_Float)
new_primCmpNat2(Succ(x0), x1)
new_lt12(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Float)
new_lt5(x0, x1, x2, x3, x4)
new_lt13(x0, x1, ty_Float)
new_esEs13(x0, x1, app(app(ty_Either, x2), x3))
new_compare30(x0, x1)
new_primCmpNat1(Succ(x0), Succ(x1))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs26(x0, x1, ty_Bool)
new_esEs4(Right(x0), Right(x1), x2, ty_Float)
new_pePe(False, x0)
new_esEs24(x0, x1, ty_@0)
new_lt20(x0, x1, ty_Char)
new_ltEs14(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_lt13(x0, x1, ty_Double)
new_esEs13(x0, x1, ty_Double)
new_compare17(Float(x0, x1), Float(x2, x3))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Just(x0), Just(x1), ty_Int)
new_esEs15(True, True)
new_esEs13(x0, x1, ty_Ordering)
new_esEs5(Just(x0), Just(x1), ty_Bool)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs18(Char(x0), Char(x1))
new_compare14(x0, x1)
new_esEs12(x0, x1, ty_Char)
new_ltEs10(LT, LT)
new_compare31(x0, x1, ty_Float)
new_esEs4(Right(x0), Right(x1), x2, ty_Bool)
new_compare31(x0, x1, app(ty_[], x2))
new_ltEs12(x0, x1, ty_@0)
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Nothing, Just(x0), x1)
new_ltEs20(x0, x1, ty_@0)
new_esEs22(x0, x1, ty_Bool)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_sr(x0, x1)
new_esEs29(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Bool)
new_compare29(Nothing, Nothing, False, x0)
new_primCompAux0(x0, LT)
new_ltEs14(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs15(False, False)
new_lt10(x0, x1, x2)
new_ltEs14(Left(x0), Left(x1), ty_Float, x2)
new_esEs26(x0, x1, ty_Double)
new_esEs21(x0, x1, ty_Bool)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs20(Integer(x0), Integer(x1))
new_ltEs12(x0, x1, ty_Double)
new_ltEs14(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Double)
new_esEs12(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_Double)
new_ltEs14(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_compare12(x0, x1, True, x2, x3, x4)
new_esEs5(Just(x0), Just(x1), ty_Double)
new_lt13(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare110(x0, x1, True, x2, x3)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, ty_Integer)
new_esEs14(x0, x1, app(app(ty_Either, x2), x3))
new_esEs14(x0, x1, app(ty_Ratio, x2))
new_esEs14(x0, x1, ty_@0)
new_compare31(x0, x1, ty_Ordering)
new_compare210(x0, x1, True, x2, x3, x4)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs30(x0, x1, ty_Integer)
new_ltEs15(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Int)
new_lt13(x0, x1, app(ty_Ratio, x2))
new_primEqNat0(Succ(x0), Zero)
new_esEs22(x0, x1, ty_Int)
new_ltEs12(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Bool)
new_esEs4(Right(x0), Right(x1), x2, ty_@0)
new_ltEs19(x0, x1, ty_@0)
new_esEs16([], [], x0)
new_ltEs12(x0, x1, app(ty_Ratio, x2))
new_lt13(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpNat1(Zero, Zero)
new_compare(:(x0, x1), :(x2, x3), x4)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_primMulNat0(Succ(x0), Succ(x1))
new_compare9(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs23(x0, x1, ty_@0)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_lt12(x0, x1, app(ty_Ratio, x2))
new_ltEs7(x0, x1)
new_esEs11(EQ, GT)
new_esEs11(GT, EQ)
new_ltEs14(Left(x0), Left(x1), ty_Int, x2)
new_ltEs12(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_fsEs(x0)
new_esEs5(Just(x0), Just(x1), ty_@0)
new_primPlusNat0(Succ(x0), Zero)
new_lt12(x0, x1, ty_Bool)
new_compare12(x0, x1, False, x2, x3, x4)
new_esEs25(x0, x1, ty_Ordering)
new_esEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_compare11(x0, x1, False, x2, x3)
new_primEqNat0(Zero, Zero)
new_esEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs5(Nothing, Nothing, x0)
new_compare7(x0, x1, x2, x3, x4)
new_lt12(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Left(x0), Left(x1), app(ty_[], x2), x3)
new_primCompAux0(x0, EQ)
new_ltEs15(Just(x0), Just(x1), ty_Bool)
new_esEs25(x0, x1, app(ty_[], x2))
new_ltEs4(True, True)
new_esEs21(x0, x1, ty_Int)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs12(x0, x1, ty_Ordering)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_primMulNat0(Succ(x0), Zero)
new_esEs23(x0, x1, ty_Float)
new_compare31(x0, x1, ty_Integer)
new_compare31(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_Ordering)
new_compare8(Integer(x0), Integer(x1))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs22(x0, x1, app(ty_[], x2))
new_ltEs12(x0, x1, ty_Int)
new_lt17(x0, x1)
new_compare26(x0, x1, True, x2, x3)
new_ltEs14(Right(x0), Right(x1), x2, ty_Integer)
new_lt13(x0, x1, ty_Integer)
new_ltEs10(EQ, LT)
new_ltEs10(LT, EQ)
new_esEs12(x0, x1, ty_Integer)
new_esEs12(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_Int)
new_lt11(x0, x1)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_ltEs15(Just(x0), Just(x1), ty_Integer)
new_lt13(x0, x1, app(ty_[], x2))
new_esEs4(Left(x0), Left(x1), ty_@0, x2)
new_lt20(x0, x1, ty_@0)
new_ltEs14(Left(x0), Left(x1), ty_Char, x2)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_primEqNat0(Zero, Succ(x0))
new_lt13(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, ty_Char)
new_esEs30(x0, x1, ty_Ordering)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Float)
new_esEs21(x0, x1, ty_Double)
new_lt13(x0, x1, app(ty_Maybe, x2))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs13(x0, x1, ty_Integer)
new_ltEs12(x0, x1, ty_Bool)
new_esEs11(GT, LT)
new_esEs11(LT, GT)
new_ltEs14(Left(x0), Left(x1), ty_Integer, x2)
new_compare25(x0, x1, True)
new_esEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_lt12(x0, x1, ty_Int)
new_primCmpNat2(Zero, x0)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_lt14(x0, x1)
new_ltEs15(Just(x0), Just(x1), ty_Double)
new_asAs(False, x0)
new_ltEs4(False, False)
new_esEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Bool)
new_esEs5(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs19(x0, x1, ty_Double)
new_compare27(x0, x1, False)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, ty_@0)
new_esEs21(x0, x1, ty_Float)
new_compare28(x0, x1, x2)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs15(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs15(Just(x0), Just(x1), ty_Ordering)
new_lt20(x0, x1, ty_Ordering)
new_lt12(x0, x1, ty_Float)
new_esEs4(Right(x0), Left(x1), x2, x3)
new_esEs4(Left(x0), Right(x1), x2, x3)
new_esEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs12(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Int)
new_esEs28(x0, x1, ty_Integer)
new_compare16(x0, x1, True, x2)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs26(x0, x1, ty_Int)
new_asAs(True, x0)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs11(LT, LT)
new_compare26(x0, x1, False, x2, x3)
new_ltEs15(Just(x0), Just(x1), ty_Int)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_Bool)
new_lt19(x0, x1)
new_esEs23(x0, x1, ty_Char)
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_primPlusNat0(Zero, Zero)
new_ltEs12(x0, x1, app(ty_[], x2))
new_lt12(x0, x1, ty_Char)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_compare31(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_@0)
new_lt12(x0, x1, ty_Integer)
new_lt20(x0, x1, ty_Integer)
new_esEs24(x0, x1, app(ty_[], x2))
new_primPlusNat0(Succ(x0), Succ(x1))
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_lt12(x0, x1, app(app(ty_Either, x2), x3))
new_esEs14(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Ordering)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs30(x0, x1, ty_Float)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs24(x0, x1, ty_Double)
new_esEs23(x0, x1, ty_Double)
new_esEs25(x0, x1, ty_Double)
new_esEs24(x0, x1, ty_Char)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_ltEs20(x0, x1, ty_Double)
new_compare19(Char(x0), Char(x1))
new_esEs21(x0, x1, ty_Char)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs14(x0, x1, ty_Ordering)
new_ltEs14(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs9(x0, x1)
new_compare([], :(x0, x1), x2)
new_ltEs15(Just(x0), Nothing, x1)
new_ltEs20(x0, x1, ty_Int)
new_lt6(x0, x1)
new_compare29(Just(x0), Nothing, False, x1)
new_esEs30(x0, x1, ty_Double)
new_ltEs17(x0, x1)
new_esEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_compare24(x0, x1, False, x2, x3)
new_ltEs10(GT, LT)
new_ltEs10(LT, GT)
new_primPlusNat0(Zero, Succ(x0))
new_esEs14(x0, x1, ty_Bool)
new_esEs30(x0, x1, ty_Bool)
new_esEs10(@0, @0)
new_esEs24(x0, x1, ty_Ordering)
new_esEs14(x0, x1, ty_Char)
new_esEs30(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, app(ty_[], x2))
new_compare31(x0, x1, ty_Double)
new_ltEs16(x0, x1)
new_ltEs11(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_compare111(x0, x1, True)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_lt12(x0, x1, ty_Double)
new_esEs9(x0, x1)
new_esEs5(Just(x0), Just(x1), ty_Ordering)
new_esEs5(Just(x0), Nothing, x1)
new_lt9(x0, x1, x2, x3)
new_esEs13(x0, x1, ty_Bool)
new_esEs29(x0, x1, ty_Ordering)
new_esEs13(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_Float)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_ltEs14(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs15(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs15(Just(x0), Just(x1), ty_Char)
new_compare13(@0, @0)
new_esEs16([], :(x0, x1), x2)
new_ltEs15(Nothing, Just(x0), x1)
new_esEs22(x0, x1, ty_Char)
new_esEs11(EQ, LT)
new_esEs11(LT, EQ)
new_esEs12(x0, x1, app(ty_[], x2))
new_compare11(x0, x1, True, x2, x3)
new_esEs12(x0, x1, ty_Ordering)
new_compare6(x0, x1, x2, x3)
new_esEs13(x0, x1, ty_Int)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs15(True, False)
new_esEs15(False, True)
new_sr0(Integer(x0), Integer(x1))
new_esEs4(Left(x0), Left(x1), ty_Integer, x2)
new_esEs29(x0, x1, ty_Double)
new_esEs17(:%(x0, x1), :%(x2, x3), x4)
new_lt13(x0, x1, ty_Bool)
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs30(x0, x1, ty_Int)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs14(Left(x0), Left(x1), ty_Bool, x2)
new_compare31(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, ty_Bool)
new_esEs19(Float(x0, x1), Float(x2, x3))
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs14(Right(x0), Right(x1), x2, ty_@0)
new_esEs13(x0, x1, ty_Float)
new_lt16(x0, x1)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Int)
new_lt18(x0, x1)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs16(:(x0, x1), :(x2, x3), x4)
new_esEs24(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_@0)
new_esEs16(:(x0, x1), [], x2)
new_lt7(x0, x1, x2)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_compare18(Double(x0, x1), Double(x2, x3))
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_primCmpNat1(Succ(x0), Zero)
new_esEs13(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt13(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Integer)
new_primCompAux0(x0, GT)
new_esEs4(Left(x0), Left(x1), ty_Int, x2)
new_lt13(x0, x1, ty_Ordering)
new_ltEs12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare(:(x0, x1), [], x2)
new_lt12(x0, x1, app(ty_[], x2))
new_ltEs14(Left(x0), Left(x1), ty_Double, x2)
new_esEs30(x0, x1, ty_@0)
new_ltEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, ty_Int)
new_esEs22(x0, x1, ty_@0)
new_primMulNat0(Zero, Succ(x0))
new_lt12(x0, x1, ty_Ordering)
new_esEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Just(x0), Just(x1), ty_Integer)
new_esEs5(Just(x0), Just(x1), ty_Char)
new_esEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs12(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(Double(x0, x1), Double(x2, x3))
new_esEs4(Left(x0), Left(x1), ty_Char, x2)
new_esEs22(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Ordering)
new_esEs12(x0, x1, app(ty_Maybe, x2))
new_compare29(Nothing, Just(x0), False, x1)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs4(False, True)
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_ltEs4(True, False)
new_esEs14(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs26(x0, x1, ty_Float)
new_lt4(x0, x1)
new_compare([], [], x0)
new_esEs12(x0, x1, ty_Bool)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs12(x0, x1, ty_Int)
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs14(x0, x1, ty_Int)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_primPlusNat1(x0, x1)
new_esEs21(x0, x1, ty_Ordering)
new_ltEs18(x0, x1)
new_ltEs15(Nothing, Nothing, x0)
new_esEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs29(x0, x1, ty_Integer)
new_esEs12(x0, x1, app(ty_Ratio, x2))
new_compare111(x0, x1, False)
new_ltEs12(x0, x1, app(ty_Maybe, x2))
new_compare31(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs6(x0, x1, x2)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs10(GT, GT)
new_esEs25(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs13(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Float)
new_esEs29(x0, x1, ty_Char)
new_ltEs15(Just(x0), Just(x1), ty_Float)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs30(x0, x1, ty_Char)
new_esEs11(GT, GT)
new_ltEs14(Right(x0), Right(x1), x2, ty_Char)
new_compare16(x0, x1, False, x2)
new_primEqNat0(Succ(x0), Succ(x1))
new_ltEs20(x0, x1, ty_Integer)
new_primCmpNat0(x0, Zero)
new_lt20(x0, x1, app(ty_[], x2))
new_lt12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_not(True)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_compare29(x0, x1, True, x2)
new_esEs12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, ty_Char)
new_esEs22(x0, x1, ty_Float)
new_esEs4(Right(x0), Right(x1), x2, ty_Char)
new_compare9(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs12(x0, x1, ty_Double)
new_esEs4(Left(x0), Left(x1), ty_Double, x2)
new_esEs26(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_Float)
new_lt20(x0, x1, ty_Double)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_not(False)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs14(x0, x1, app(ty_Maybe, x2))
new_ltEs13(x0, x1, x2)
new_esEs26(x0, x1, ty_Char)
new_primCompAux1(x0, x1, x2, x3)
new_primCmpNat1(Zero, Succ(x0))
new_compare110(x0, x1, False, x2, x3)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs10(EQ, GT)
new_ltEs10(GT, EQ)
new_ltEs20(x0, x1, ty_Char)
new_lt13(x0, x1, ty_Char)
new_ltEs14(Left(x0), Left(x1), ty_@0, x2)
new_esEs23(x0, x1, app(ty_[], x2))
new_compare27(x0, x1, True)
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_compare31(x0, x1, ty_Char)
new_compare29(Just(x0), Just(x1), False, x2)
new_esEs4(Right(x0), Right(x1), x2, ty_Int)
new_compare15(x0, x1, x2, x3)
new_primCmpNat0(x0, Succ(x1))
new_esEs14(x0, x1, ty_Double)
new_ltEs12(x0, x1, ty_Char)
new_compare24(x0, x1, True, x2, x3)
new_lt8(x0, x1, x2, x3)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(Right(x0), Right(x1), x2, ty_Float)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_ltEs12(x0, x1, ty_Float)
new_esEs21(x0, x1, ty_@0)
new_esEs13(x0, x1, app(ty_Maybe, x2))
new_esEs4(Left(x0), Left(x1), ty_Float, x2)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_ltEs15(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs8(x0, x1)
new_ltEs19(x0, x1, ty_Bool)
new_esEs29(x0, x1, ty_Int)
new_esEs13(x0, x1, app(ty_[], x2))
new_esEs25(x0, x1, ty_Int)
new_compare31(x0, x1, ty_Bool)
new_esEs13(x0, x1, ty_@0)
new_ltEs15(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_compare31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs14(x0, x1, app(app(ty_@2, x2), x3))
new_esEs14(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Integer)
new_lt20(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_Int)
new_esEs14(x0, x1, ty_Float)
new_esEs12(x0, x1, ty_@0)
new_esEs24(x0, x1, ty_Integer)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_primEqInt(Pos(Zero), Pos(Zero))
new_ltEs14(Left(x0), Right(x1), x2, x3)
new_ltEs14(Right(x0), Left(x1), x2, x3)
new_esEs11(EQ, EQ)
new_lt15(x0, x1, x2)
new_esEs13(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_compare25(x0, x1, False)
new_ltEs15(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs14(Right(x0), Right(x1), x2, ty_Bool)
new_esEs4(Right(x0), Right(x1), x2, ty_Double)
new_compare10(x0, x1, False)
new_pePe(True, x0)
new_esEs27(x0, x1, ty_Integer)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Just(x0), Just(x1), ty_Float)
new_compare5(x0, x1)
new_ltEs20(x0, x1, ty_Ordering)
new_lt13(x0, x1, ty_@0)
new_esEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs21(x0, x1, app(ty_[], x2))
new_ltEs10(EQ, EQ)
new_lt12(x0, x1, ty_@0)

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

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

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

new_addToFM_C21(wzz15, wzz16, wzz17, wzz18, wzz19, wzz20, wzz21, True, bb, bc) → new_addToFM_C(wzz18, Just(wzz20), wzz21, bb, bc)
new_addToFM_C11(wzz31, wzz32, wzz33, wzz34, wzz40, wzz5, True, h, ba) → new_addToFM_C(wzz34, Just(wzz40), wzz5, h, ba)
new_addToFM_C21(wzz15, wzz16, wzz17, wzz18, wzz19, wzz20, wzz21, False, bb, bc) → new_addToFM_C12(wzz15, wzz16, wzz17, wzz18, wzz19, wzz20, wzz21, new_esEs11(new_compare29(Just(wzz20), Just(wzz15), new_esEs30(wzz20, wzz15, bb), bb), GT), bb, bc)
new_addToFM_C(Branch(Just(wzz300), wzz31, wzz32, wzz33, wzz34), Just(wzz40), wzz5, h, ba) → new_addToFM_C21(wzz300, wzz31, wzz32, wzz33, wzz34, wzz40, wzz5, new_esEs11(new_compare29(Just(wzz40), Just(wzz300), new_esEs29(wzz40, wzz300, h), h), LT), h, ba)
new_addToFM_C(Branch(Nothing, wzz31, wzz32, wzz33, wzz34), Just(wzz40), wzz5, h, ba) → new_addToFM_C20(wzz31, wzz32, wzz33, wzz34, wzz40, wzz5, new_esEs11(new_compare29(Just(wzz40), Nothing, False, h), LT), h, ba)
new_addToFM_C12(wzz15, wzz16, wzz17, wzz18, wzz19, wzz20, wzz21, True, bb, bc) → new_addToFM_C(wzz19, Just(wzz20), wzz21, bb, bc)
new_addToFM_C20(wzz31, wzz32, wzz33, wzz34, wzz40, wzz5, True, h, ba) → new_addToFM_C(wzz33, Just(wzz40), wzz5, h, ba)
new_addToFM_C20(wzz31, wzz32, wzz33, wzz34, wzz40, wzz5, False, h, ba) → new_addToFM_C11(wzz31, wzz32, wzz33, wzz34, wzz40, wzz5, new_esEs11(new_compare29(Just(wzz40), Nothing, False, h), GT), h, ba)

The TRS R consists of the following rules:

new_ltEs19(wzz3100, wzz3200, app(app(ty_@2, bfd), bfe)) → new_ltEs5(wzz3100, wzz3200, bfd, bfe)
new_ltEs20(wzz31001, wzz32001, ty_Bool) → new_ltEs4(wzz31001, wzz32001)
new_ltEs20(wzz31001, wzz32001, ty_Int) → new_ltEs9(wzz31001, wzz32001)
new_esEs21(wzz400, wzz3000, app(app(ty_@2, hg), hh)) → new_esEs6(wzz400, wzz3000, hg, hh)
new_lt20(wzz31000, wzz32000, ty_Int) → new_lt16(wzz31000, wzz32000)
new_esEs18(Char(wzz400), Char(wzz3000)) → new_primEqNat0(wzz400, wzz3000)
new_primCmpNat2(Zero, wzz3100) → LT
new_esEs14(wzz402, wzz3002, ty_Float) → new_esEs19(wzz402, wzz3002)
new_esEs25(wzz400, wzz3000, app(ty_[], cgb)) → new_esEs16(wzz400, wzz3000, cgb)
new_compare8(Integer(wzz31000), Integer(wzz32000)) → new_primCmpInt(wzz31000, wzz32000)
new_esEs25(wzz400, wzz3000, ty_Bool) → new_esEs15(wzz400, wzz3000)
new_esEs23(wzz31001, wzz32001, ty_Ordering) → new_esEs11(wzz31001, wzz32001)
new_esEs13(wzz401, wzz3001, ty_Double) → new_esEs8(wzz401, wzz3001)
new_ltEs14(Right(wzz31000), Right(wzz32000), bfa, ty_Ordering) → new_ltEs10(wzz31000, wzz32000)
new_esEs27(wzz400, wzz3000, ty_Integer) → new_esEs20(wzz400, wzz3000)
new_compare110(wzz31000, wzz32000, True, gg, gh) → LT
new_ltEs20(wzz31001, wzz32001, ty_Ordering) → new_ltEs10(wzz31001, wzz32001)
new_primCmpNat1(Zero, Succ(wzz32000)) → LT
new_compare([], :(wzz32000, wzz32001), gd) → LT
new_esEs22(wzz31000, wzz32000, ty_Float) → new_esEs19(wzz31000, wzz32000)
new_esEs13(wzz401, wzz3001, ty_Char) → new_esEs18(wzz401, wzz3001)
new_lt12(wzz31000, wzz32000, app(app(ty_Either, bbd), bbe)) → new_lt9(wzz31000, wzz32000, bbd, bbe)
new_ltEs15(Just(wzz31000), Just(wzz32000), app(ty_[], dae)) → new_ltEs13(wzz31000, wzz32000, dae)
new_esEs29(wzz40, wzz300, ty_Int) → new_esEs9(wzz40, wzz300)
new_ltEs15(Just(wzz31000), Just(wzz32000), app(ty_Ratio, dad)) → new_ltEs6(wzz31000, wzz32000, dad)
new_esEs4(Right(wzz400), Right(wzz3000), ccg, app(ty_Maybe, cea)) → new_esEs5(wzz400, wzz3000, cea)
new_compare30(wzz31000, wzz32000) → new_compare25(wzz31000, wzz32000, new_esEs15(wzz31000, wzz32000))
new_esEs11(EQ, EQ) → True
new_ltEs14(Left(wzz31000), Left(wzz32000), ty_Bool, bfb) → new_ltEs4(wzz31000, wzz32000)
new_ltEs20(wzz31001, wzz32001, ty_Double) → new_ltEs7(wzz31001, wzz32001)
new_esEs13(wzz401, wzz3001, ty_Integer) → new_esEs20(wzz401, wzz3001)
new_esEs23(wzz31001, wzz32001, ty_Float) → new_esEs19(wzz31001, wzz32001)
new_esEs26(wzz401, wzz3001, ty_Integer) → new_esEs20(wzz401, wzz3001)
new_esEs14(wzz402, wzz3002, ty_Ordering) → new_esEs11(wzz402, wzz3002)
new_compare17(Float(wzz31000, wzz31001), Float(wzz32000, wzz32001)) → new_compare14(new_sr(wzz31000, wzz32000), new_sr(wzz31001, wzz32001))
new_primMulNat0(Zero, Zero) → Zero
new_compare(:(wzz31000, wzz31001), [], gd) → GT
new_esEs26(wzz401, wzz3001, app(ty_[], chd)) → new_esEs16(wzz401, wzz3001, chd)
new_esEs5(Just(wzz400), Just(wzz3000), ty_Int) → new_esEs9(wzz400, wzz3000)
new_ltEs14(Right(wzz31000), Right(wzz32000), bfa, app(ty_[], cac)) → new_ltEs13(wzz31000, wzz32000, cac)
new_compare31(wzz31000, wzz32000, app(app(ty_@2, dde), ddf)) → new_compare6(wzz31000, wzz32000, dde, ddf)
new_esEs12(wzz400, wzz3000, ty_Bool) → new_esEs15(wzz400, wzz3000)
new_ltEs15(Nothing, Just(wzz32000), bfc) → True
new_esEs25(wzz400, wzz3000, ty_Double) → new_esEs8(wzz400, wzz3000)
new_esEs4(Right(wzz400), Right(wzz3000), ccg, ty_Int) → new_esEs9(wzz400, wzz3000)
new_ltEs19(wzz3100, wzz3200, app(ty_Maybe, bfc)) → new_ltEs15(wzz3100, wzz3200, bfc)
new_esEs4(Left(wzz400), Left(wzz3000), app(ty_Ratio, cbh), cbf) → new_esEs17(wzz400, wzz3000, cbh)
new_lt20(wzz31000, wzz32000, app(app(ty_@2, bd), be)) → new_lt8(wzz31000, wzz32000, bd, be)
new_ltEs15(Just(wzz31000), Just(wzz32000), ty_Bool) → new_ltEs4(wzz31000, wzz32000)
new_esEs20(Integer(wzz400), Integer(wzz3000)) → new_primEqInt(wzz400, wzz3000)
new_esEs25(wzz400, wzz3000, ty_Ordering) → new_esEs11(wzz400, wzz3000)
new_lt12(wzz31000, wzz32000, ty_Integer) → new_lt6(wzz31000, wzz32000)
new_esEs29(wzz40, wzz300, app(app(ty_Either, ccg), cbf)) → new_esEs4(wzz40, wzz300, ccg, cbf)
new_esEs5(Just(wzz400), Just(wzz3000), ty_Bool) → new_esEs15(wzz400, wzz3000)
new_lt20(wzz31000, wzz32000, ty_Double) → new_lt14(wzz31000, wzz32000)
new_ltEs20(wzz31001, wzz32001, app(app(app(ty_@3, bge), bgf), bgg)) → new_ltEs11(wzz31001, wzz32001, bge, bgf, bgg)
new_compare18(Double(wzz31000, wzz31001), Double(wzz32000, wzz32001)) → new_compare14(new_sr(wzz31000, wzz32000), new_sr(wzz31001, wzz32001))
new_esEs4(Right(wzz400), Right(wzz3000), ccg, app(app(app(ty_@3, cdf), cdg), cdh)) → new_esEs7(wzz400, wzz3000, cdf, cdg, cdh)
new_esEs30(wzz20, wzz15, ty_Int) → new_esEs9(wzz20, wzz15)
new_esEs4(Left(wzz400), Left(wzz3000), app(app(ty_@2, cca), ccb), cbf) → new_esEs6(wzz400, wzz3000, cca, ccb)
new_esEs26(wzz401, wzz3001, ty_Double) → new_esEs8(wzz401, wzz3001)
new_ltEs19(wzz3100, wzz3200, ty_Ordering) → new_ltEs10(wzz3100, wzz3200)
new_ltEs19(wzz3100, wzz3200, ty_Bool) → new_ltEs4(wzz3100, wzz3200)
new_esEs13(wzz401, wzz3001, app(ty_Ratio, eb)) → new_esEs17(wzz401, wzz3001, eb)
new_esEs21(wzz400, wzz3000, app(app(app(ty_@3, baa), bab), bac)) → new_esEs7(wzz400, wzz3000, baa, bab, bac)
new_primCmpNat1(Succ(wzz31000), Succ(wzz32000)) → new_primCmpNat1(wzz31000, wzz32000)
new_compare28(wzz31000, wzz32000, bae) → new_compare29(wzz31000, wzz32000, new_esEs5(wzz31000, wzz32000, bae), bae)
new_esEs5(Just(wzz400), Just(wzz3000), app(ty_Maybe, dcg)) → new_esEs5(wzz400, wzz3000, dcg)
new_ltEs14(Right(wzz31000), Right(wzz32000), bfa, ty_Bool) → new_ltEs4(wzz31000, wzz32000)
new_ltEs4(False, True) → True
new_ltEs10(EQ, GT) → True
new_esEs4(Right(wzz400), Right(wzz3000), ccg, ty_Integer) → new_esEs20(wzz400, wzz3000)
new_compare19(Char(wzz31000), Char(wzz32000)) → new_primCmpNat1(wzz31000, wzz32000)
new_esEs30(wzz20, wzz15, ty_Float) → new_esEs19(wzz20, wzz15)
new_ltEs15(Just(wzz31000), Just(wzz32000), ty_@0) → new_ltEs17(wzz31000, wzz32000)
new_esEs29(wzz40, wzz300, app(app(app(ty_@3, ca), cb), cc)) → new_esEs7(wzz40, wzz300, ca, cb, cc)
new_ltEs15(Just(wzz31000), Just(wzz32000), ty_Double) → new_ltEs7(wzz31000, wzz32000)
new_ltEs14(Left(wzz31000), Left(wzz32000), ty_Float, bfb) → new_ltEs16(wzz31000, wzz32000)
new_lt20(wzz31000, wzz32000, app(ty_Maybe, bae)) → new_lt15(wzz31000, wzz32000, bae)
new_lt16(wzz310, wzz320) → new_esEs11(new_compare14(wzz310, wzz320), LT)
new_ltEs15(Just(wzz31000), Just(wzz32000), ty_Integer) → new_ltEs18(wzz31000, wzz32000)
new_compare26(wzz31000, wzz32000, False, gg, gh) → new_compare110(wzz31000, wzz32000, new_ltEs14(wzz31000, wzz32000, gg, gh), gg, gh)
new_lt20(wzz31000, wzz32000, ty_Float) → new_lt17(wzz31000, wzz32000)
new_esEs4(Left(wzz400), Left(wzz3000), ty_Double, cbf) → new_esEs8(wzz400, wzz3000)
new_esEs14(wzz402, wzz3002, app(ty_Ratio, fd)) → new_esEs17(wzz402, wzz3002, fd)
new_ltEs19(wzz3100, wzz3200, ty_Float) → new_ltEs16(wzz3100, wzz3200)
new_esEs26(wzz401, wzz3001, ty_Ordering) → new_esEs11(wzz401, wzz3001)
new_ltEs4(True, True) → True
new_pePe(False, wzz150) → wzz150
new_esEs25(wzz400, wzz3000, app(app(ty_Either, cfh), cga)) → new_esEs4(wzz400, wzz3000, cfh, cga)
new_esEs15(False, True) → False
new_esEs15(True, False) → False
new_lt20(wzz31000, wzz32000, ty_Bool) → new_lt11(wzz31000, wzz32000)
new_ltEs14(Right(wzz31000), Right(wzz32000), bfa, ty_Float) → new_ltEs16(wzz31000, wzz32000)
new_esEs22(wzz31000, wzz32000, app(app(ty_Either, bbd), bbe)) → new_esEs4(wzz31000, wzz32000, bbd, bbe)
new_lt13(wzz31001, wzz32001, ty_Double) → new_lt14(wzz31001, wzz32001)
new_esEs29(wzz40, wzz300, ty_Char) → new_esEs18(wzz40, wzz300)
new_esEs23(wzz31001, wzz32001, ty_Double) → new_esEs8(wzz31001, wzz32001)
new_esEs17(:%(wzz400, wzz401), :%(wzz3000, wzz3001), ceb) → new_asAs(new_esEs27(wzz400, wzz3000, ceb), new_esEs28(wzz401, wzz3001, ceb))
new_esEs26(wzz401, wzz3001, app(ty_Ratio, che)) → new_esEs17(wzz401, wzz3001, che)
new_esEs13(wzz401, wzz3001, ty_Ordering) → new_esEs11(wzz401, wzz3001)
new_esEs30(wzz20, wzz15, ty_Bool) → new_esEs15(wzz20, wzz15)
new_compare31(wzz31000, wzz32000, ty_@0) → new_compare13(wzz31000, wzz32000)
new_ltEs12(wzz31002, wzz32002, app(ty_Ratio, bdf)) → new_ltEs6(wzz31002, wzz32002, bdf)
new_ltEs20(wzz31001, wzz32001, app(ty_[], bfg)) → new_ltEs13(wzz31001, wzz32001, bfg)
new_esEs14(wzz402, wzz3002, app(app(ty_@2, ff), fg)) → new_esEs6(wzz402, wzz3002, ff, fg)
new_compare111(wzz31000, wzz32000, False) → GT
new_compare111(wzz31000, wzz32000, True) → LT
new_compare31(wzz31000, wzz32000, ty_Int) → new_compare14(wzz31000, wzz32000)
new_ltEs5(@2(wzz31000, wzz31001), @2(wzz32000, wzz32001), bfd, bfe) → new_pePe(new_lt20(wzz31000, wzz32000, bfd), new_asAs(new_esEs24(wzz31000, wzz32000, bfd), new_ltEs20(wzz31001, wzz32001, bfe)))
new_esEs12(wzz400, wzz3000, app(ty_[], cf)) → new_esEs16(wzz400, wzz3000, cf)
new_ltEs15(Just(wzz31000), Just(wzz32000), app(ty_Maybe, dah)) → new_ltEs15(wzz31000, wzz32000, dah)
new_ltEs12(wzz31002, wzz32002, app(app(ty_Either, bdh), bea)) → new_ltEs14(wzz31002, wzz32002, bdh, bea)
new_esEs22(wzz31000, wzz32000, ty_Integer) → new_esEs20(wzz31000, wzz32000)
new_esEs23(wzz31001, wzz32001, app(app(app(ty_@3, bdc), bdd), bde)) → new_esEs7(wzz31001, wzz32001, bdc, bdd, bde)
new_esEs23(wzz31001, wzz32001, ty_Integer) → new_esEs20(wzz31001, wzz32001)
new_esEs25(wzz400, wzz3000, app(app(ty_@2, cgd), cge)) → new_esEs6(wzz400, wzz3000, cgd, cge)
new_esEs11(GT, GT) → True
new_esEs23(wzz31001, wzz32001, ty_Char) → new_esEs18(wzz31001, wzz32001)
new_esEs29(wzz40, wzz300, ty_Ordering) → new_esEs11(wzz40, wzz300)
new_esEs24(wzz31000, wzz32000, app(app(ty_@2, bd), be)) → new_esEs6(wzz31000, wzz32000, bd, be)
new_pePe(True, wzz150) → True
new_primEqNat0(Zero, Zero) → True
new_ltEs19(wzz3100, wzz3200, ty_Integer) → new_ltEs18(wzz3100, wzz3200)
new_esEs13(wzz401, wzz3001, app(ty_Maybe, eh)) → new_esEs5(wzz401, wzz3001, eh)
new_primMulNat0(Succ(wzz40100), Succ(wzz300100)) → new_primPlusNat1(new_primMulNat0(wzz40100, Succ(wzz300100)), wzz300100)
new_lt12(wzz31000, wzz32000, ty_Char) → new_lt18(wzz31000, wzz32000)
new_ltEs12(wzz31002, wzz32002, ty_@0) → new_ltEs17(wzz31002, wzz32002)
new_compare29(Nothing, Just(wzz3200), False, beh) → LT
new_compare31(wzz31000, wzz32000, ty_Bool) → new_compare30(wzz31000, wzz32000)
new_ltEs14(Right(wzz31000), Right(wzz32000), bfa, app(ty_Maybe, caf)) → new_ltEs15(wzz31000, wzz32000, caf)
new_esEs26(wzz401, wzz3001, ty_Bool) → new_esEs15(wzz401, wzz3001)
new_esEs24(wzz31000, wzz32000, app(ty_Ratio, ge)) → new_esEs17(wzz31000, wzz32000, ge)
new_esEs13(wzz401, wzz3001, ty_@0) → new_esEs10(wzz401, wzz3001)
new_compare110(wzz31000, wzz32000, False, gg, gh) → GT
new_compare(:(wzz31000, wzz31001), :(wzz32000, wzz32001), gd) → new_primCompAux1(wzz31000, wzz32000, new_compare(wzz31001, wzz32001, gd), gd)
new_sr(wzz401, wzz3001) → new_primMulInt(wzz401, wzz3001)
new_ltEs15(Just(wzz31000), Just(wzz32000), ty_Char) → new_ltEs8(wzz31000, wzz32000)
new_compare210(wzz31000, wzz32000, False, bf, bg, bh) → new_compare12(wzz31000, wzz32000, new_ltEs11(wzz31000, wzz32000, bf, bg, bh), bf, bg, bh)
new_compare12(wzz31000, wzz32000, True, bf, bg, bh) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_esEs5(Just(wzz400), Just(wzz3000), ty_Char) → new_esEs18(wzz400, wzz3000)
new_ltEs12(wzz31002, wzz32002, app(app(ty_@2, bec), bed)) → new_ltEs5(wzz31002, wzz32002, bec, bed)
new_lt4(wzz31000, wzz32000) → new_esEs11(new_compare5(wzz31000, wzz32000), LT)
new_esEs4(Left(wzz400), Left(wzz3000), ty_Int, cbf) → new_esEs9(wzz400, wzz3000)
new_esEs13(wzz401, wzz3001, ty_Int) → new_esEs9(wzz401, wzz3001)
new_primCmpInt(Neg(Zero), Neg(Succ(wzz3200))) → new_primCmpNat0(wzz3200, Zero)
new_esEs25(wzz400, wzz3000, ty_@0) → new_esEs10(wzz400, wzz3000)
new_compare7(wzz31000, wzz32000, bf, bg, bh) → new_compare210(wzz31000, wzz32000, new_esEs7(wzz31000, wzz32000, bf, bg, bh), bf, bg, bh)
new_lt13(wzz31001, wzz32001, ty_Ordering) → new_lt4(wzz31001, wzz32001)
new_esEs19(Float(wzz400, wzz401), Float(wzz3000, wzz3001)) → new_esEs9(new_sr(wzz400, wzz3000), new_sr(wzz401, wzz3001))
new_ltEs20(wzz31001, wzz32001, ty_Float) → new_ltEs16(wzz31001, wzz32001)
new_ltEs15(Just(wzz31000), Just(wzz32000), ty_Int) → new_ltEs9(wzz31000, wzz32000)
new_primCmpNat1(Succ(wzz31000), Zero) → GT
new_esEs4(Right(wzz400), Right(wzz3000), ccg, app(app(ty_Either, cch), cda)) → new_esEs4(wzz400, wzz3000, cch, cda)
new_ltEs12(wzz31002, wzz32002, ty_Ordering) → new_ltEs10(wzz31002, wzz32002)
new_primEqInt(Neg(Succ(wzz4000)), Neg(Succ(wzz30000))) → new_primEqNat0(wzz4000, wzz30000)
new_compare25(wzz31000, wzz32000, True) → EQ
new_esEs15(True, True) → True
new_lt13(wzz31001, wzz32001, app(ty_[], bce)) → new_lt10(wzz31001, wzz32001, bce)
new_ltEs15(Just(wzz31000), Just(wzz32000), ty_Float) → new_ltEs16(wzz31000, wzz32000)
new_compare16(wzz118, wzz119, True, ha) → LT
new_esEs4(Left(wzz400), Left(wzz3000), app(app(ty_Either, cbd), cbe), cbf) → new_esEs4(wzz400, wzz3000, cbd, cbe)
new_compare31(wzz31000, wzz32000, app(app(ty_Either, ddb), ddc)) → new_compare15(wzz31000, wzz32000, ddb, ddc)
new_esEs24(wzz31000, wzz32000, ty_Integer) → new_esEs20(wzz31000, wzz32000)
new_lt12(wzz31000, wzz32000, app(ty_Ratio, bbb)) → new_lt7(wzz31000, wzz32000, bbb)
new_ltEs14(Right(wzz31000), Right(wzz32000), bfa, ty_@0) → new_ltEs17(wzz31000, wzz32000)
new_esEs4(Right(wzz400), Right(wzz3000), ccg, ty_Ordering) → new_esEs11(wzz400, wzz3000)
new_lt14(wzz31000, wzz32000) → new_esEs11(new_compare18(wzz31000, wzz32000), LT)
new_esEs26(wzz401, wzz3001, app(app(app(ty_@3, chh), daa), dab)) → new_esEs7(wzz401, wzz3001, chh, daa, dab)
new_ltEs14(Right(wzz31000), Left(wzz32000), bfa, bfb) → False
new_esEs25(wzz400, wzz3000, ty_Char) → new_esEs18(wzz400, wzz3000)
new_compare29(Just(wzz3100), Nothing, False, beh) → GT
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_ltEs12(wzz31002, wzz32002, app(ty_[], bdg)) → new_ltEs13(wzz31002, wzz32002, bdg)
new_esEs21(wzz400, wzz3000, ty_Double) → new_esEs8(wzz400, wzz3000)
new_ltEs11(@3(wzz31000, wzz31001, wzz31002), @3(wzz32000, wzz32001, wzz32002), bag, bah, bba) → new_pePe(new_lt12(wzz31000, wzz32000, bag), new_asAs(new_esEs22(wzz31000, wzz32000, bag), new_pePe(new_lt13(wzz31001, wzz32001, bah), new_asAs(new_esEs23(wzz31001, wzz32001, bah), new_ltEs12(wzz31002, wzz32002, bba)))))
new_compare15(wzz31000, wzz32000, gg, gh) → new_compare26(wzz31000, wzz32000, new_esEs4(wzz31000, wzz32000, gg, gh), gg, gh)
new_esEs4(Left(wzz400), Left(wzz3000), ty_Char, cbf) → new_esEs18(wzz400, wzz3000)
new_esEs30(wzz20, wzz15, app(app(app(ty_@3, cfd), cfe), cff)) → new_esEs7(wzz20, wzz15, cfd, cfe, cff)
new_primEqInt(Neg(Zero), Neg(Succ(wzz30000))) → False
new_primEqInt(Neg(Succ(wzz4000)), Neg(Zero)) → False
new_esEs4(Right(wzz400), Right(wzz3000), ccg, app(ty_[], cdb)) → new_esEs16(wzz400, wzz3000, cdb)
new_primCompAux0(wzz165, GT) → GT
new_compare26(wzz31000, wzz32000, True, gg, gh) → EQ
new_ltEs9(wzz3100, wzz3200) → new_fsEs(new_compare14(wzz3100, wzz3200))
new_esEs4(Right(wzz400), Right(wzz3000), ccg, ty_Double) → new_esEs8(wzz400, wzz3000)
new_compare24(wzz31000, wzz32000, True, bd, be) → EQ
new_esEs21(wzz400, wzz3000, app(app(ty_Either, hc), hd)) → new_esEs4(wzz400, wzz3000, hc, hd)
new_ltEs15(Just(wzz31000), Just(wzz32000), app(app(app(ty_@3, dbc), dbd), dbe)) → new_ltEs11(wzz31000, wzz32000, dbc, dbd, dbe)
new_esEs29(wzz40, wzz300, app(ty_[], hb)) → new_esEs16(wzz40, wzz300, hb)
new_ltEs12(wzz31002, wzz32002, ty_Bool) → new_ltEs4(wzz31002, wzz32002)
new_esEs4(Right(wzz400), Right(wzz3000), ccg, ty_Bool) → new_esEs15(wzz400, wzz3000)
new_compare([], [], gd) → EQ
new_compare14(wzz31, wzz32) → new_primCmpInt(wzz31, wzz32)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_esEs21(wzz400, wzz3000, app(ty_Ratio, hf)) → new_esEs17(wzz400, wzz3000, hf)
new_esEs5(Just(wzz400), Just(wzz3000), ty_@0) → new_esEs10(wzz400, wzz3000)
new_ltEs20(wzz31001, wzz32001, app(app(ty_@2, bgc), bgd)) → new_ltEs5(wzz31001, wzz32001, bgc, bgd)
new_ltEs19(wzz3100, wzz3200, ty_Double) → new_ltEs7(wzz3100, wzz3200)
new_ltEs14(Left(wzz31000), Left(wzz32000), ty_Int, bfb) → new_ltEs9(wzz31000, wzz32000)
new_esEs4(Left(wzz400), Left(wzz3000), ty_Float, cbf) → new_esEs19(wzz400, wzz3000)
new_esEs22(wzz31000, wzz32000, ty_Double) → new_esEs8(wzz31000, wzz32000)
new_primEqInt(Pos(Succ(wzz4000)), Pos(Succ(wzz30000))) → new_primEqNat0(wzz4000, wzz30000)
new_compare5(wzz31000, wzz32000) → new_compare27(wzz31000, wzz32000, new_esEs11(wzz31000, wzz32000))
new_lt9(wzz31000, wzz32000, gg, gh) → new_esEs11(new_compare15(wzz31000, wzz32000, gg, gh), LT)
new_esEs25(wzz400, wzz3000, app(ty_Maybe, cha)) → new_esEs5(wzz400, wzz3000, cha)
new_ltEs12(wzz31002, wzz32002, app(ty_Maybe, beb)) → new_ltEs15(wzz31002, wzz32002, beb)
new_esEs12(wzz400, wzz3000, ty_Double) → new_esEs8(wzz400, wzz3000)
new_esEs29(wzz40, wzz300, app(ty_Maybe, cee)) → new_esEs5(wzz40, wzz300, cee)
new_esEs30(wzz20, wzz15, ty_Integer) → new_esEs20(wzz20, wzz15)
new_esEs16(:(wzz400, wzz401), :(wzz3000, wzz3001), hb) → new_asAs(new_esEs21(wzz400, wzz3000, hb), new_esEs16(wzz401, wzz3001, hb))
new_esEs29(wzz40, wzz300, ty_Double) → new_esEs8(wzz40, wzz300)
new_esEs25(wzz400, wzz3000, ty_Int) → new_esEs9(wzz400, wzz3000)
new_lt13(wzz31001, wzz32001, app(app(ty_Either, bcf), bcg)) → new_lt9(wzz31001, wzz32001, bcf, bcg)
new_ltEs10(GT, EQ) → False
new_primEqNat0(Succ(wzz4000), Succ(wzz30000)) → new_primEqNat0(wzz4000, wzz30000)
new_esEs12(wzz400, wzz3000, ty_@0) → new_esEs10(wzz400, wzz3000)
new_compare31(wzz31000, wzz32000, ty_Float) → new_compare17(wzz31000, wzz32000)
new_lt13(wzz31001, wzz32001, ty_Integer) → new_lt6(wzz31001, wzz32001)
new_esEs4(Left(wzz400), Left(wzz3000), app(app(app(ty_@3, ccc), ccd), cce), cbf) → new_esEs7(wzz400, wzz3000, ccc, ccd, cce)
new_esEs14(wzz402, wzz3002, app(ty_Maybe, gc)) → new_esEs5(wzz402, wzz3002, gc)
new_lt12(wzz31000, wzz32000, ty_Ordering) → new_lt4(wzz31000, wzz32000)
new_compare16(wzz118, wzz119, False, ha) → GT
new_esEs21(wzz400, wzz3000, ty_Float) → new_esEs19(wzz400, wzz3000)
new_ltEs14(Left(wzz31000), Left(wzz32000), ty_Ordering, bfb) → new_ltEs10(wzz31000, wzz32000)
new_esEs23(wzz31001, wzz32001, ty_Bool) → new_esEs15(wzz31001, wzz32001)
new_esEs12(wzz400, wzz3000, app(app(ty_Either, cd), ce)) → new_esEs4(wzz400, wzz3000, cd, ce)
new_lt13(wzz31001, wzz32001, ty_Int) → new_lt16(wzz31001, wzz32001)
new_primEqInt(Pos(Zero), Pos(Succ(wzz30000))) → False
new_primEqInt(Pos(Succ(wzz4000)), Pos(Zero)) → False
new_esEs25(wzz400, wzz3000, ty_Integer) → new_esEs20(wzz400, wzz3000)
new_esEs22(wzz31000, wzz32000, ty_Ordering) → new_esEs11(wzz31000, wzz32000)
new_esEs21(wzz400, wzz3000, ty_Bool) → new_esEs15(wzz400, wzz3000)
new_lt20(wzz31000, wzz32000, ty_Char) → new_lt18(wzz31000, wzz32000)
new_esEs12(wzz400, wzz3000, app(app(app(ty_@3, dc), dd), de)) → new_esEs7(wzz400, wzz3000, dc, dd, de)
new_primPlusNat0(Succ(wzz26200), Zero) → Succ(wzz26200)
new_primPlusNat0(Zero, Succ(wzz8700)) → Succ(wzz8700)
new_lt13(wzz31001, wzz32001, ty_@0) → new_lt19(wzz31001, wzz32001)
new_esEs24(wzz31000, wzz32000, ty_@0) → new_esEs10(wzz31000, wzz32000)
new_esEs30(wzz20, wzz15, ty_Double) → new_esEs8(wzz20, wzz15)
new_esEs28(wzz401, wzz3001, ty_Integer) → new_esEs20(wzz401, wzz3001)
new_esEs4(Right(wzz400), Right(wzz3000), ccg, ty_@0) → new_esEs10(wzz400, wzz3000)
new_ltEs14(Left(wzz31000), Left(wzz32000), ty_Char, bfb) → new_ltEs8(wzz31000, wzz32000)
new_ltEs10(LT, EQ) → True
new_primCmpInt(Neg(Zero), Pos(Succ(wzz3200))) → LT
new_ltEs15(Just(wzz31000), Just(wzz32000), ty_Ordering) → new_ltEs10(wzz31000, wzz32000)
new_esEs4(Left(wzz400), Left(wzz3000), ty_Ordering, cbf) → new_esEs11(wzz400, wzz3000)
new_compare11(wzz31000, wzz32000, True, bd, be) → LT
new_compare210(wzz31000, wzz32000, True, bf, bg, bh) → EQ
new_compare31(wzz31000, wzz32000, app(ty_Ratio, dch)) → new_compare9(wzz31000, wzz32000, dch)
new_sr0(Integer(wzz310000), Integer(wzz320010)) → Integer(new_primMulInt(wzz310000, wzz320010))
new_primEqInt(Neg(Succ(wzz4000)), Pos(wzz3000)) → False
new_primEqInt(Pos(Succ(wzz4000)), Neg(wzz3000)) → False
new_compare25(wzz31000, wzz32000, False) → new_compare10(wzz31000, wzz32000, new_ltEs4(wzz31000, wzz32000))
new_esEs13(wzz401, wzz3001, ty_Bool) → new_esEs15(wzz401, wzz3001)
new_ltEs7(wzz3100, wzz3200) → new_fsEs(new_compare18(wzz3100, wzz3200))
new_ltEs14(Left(wzz31000), Left(wzz32000), app(ty_[], bha), bfb) → new_ltEs13(wzz31000, wzz32000, bha)
new_ltEs10(GT, GT) → True
new_esEs14(wzz402, wzz3002, app(ty_[], fc)) → new_esEs16(wzz402, wzz3002, fc)
new_esEs22(wzz31000, wzz32000, app(app(ty_@2, bbg), bbh)) → new_esEs6(wzz31000, wzz32000, bbg, bbh)
new_ltEs20(wzz31001, wzz32001, ty_Integer) → new_ltEs18(wzz31001, wzz32001)
new_esEs26(wzz401, wzz3001, ty_Int) → new_esEs9(wzz401, wzz3001)
new_ltEs20(wzz31001, wzz32001, app(ty_Maybe, bgb)) → new_ltEs15(wzz31001, wzz32001, bgb)
new_lt13(wzz31001, wzz32001, app(ty_Ratio, bcd)) → new_lt7(wzz31001, wzz32001, bcd)
new_esEs24(wzz31000, wzz32000, ty_Ordering) → new_esEs11(wzz31000, wzz32000)
new_primEqInt(Neg(Zero), Pos(Succ(wzz30000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(wzz30000))) → False
new_primCmpNat2(Succ(wzz3200), wzz3100) → new_primCmpNat1(wzz3200, wzz3100)
new_ltEs14(Right(wzz31000), Right(wzz32000), bfa, ty_Double) → new_ltEs7(wzz31000, wzz32000)
new_esEs30(wzz20, wzz15, app(ty_Ratio, cfa)) → new_esEs17(wzz20, wzz15, cfa)
new_lt12(wzz31000, wzz32000, app(ty_[], bbc)) → new_lt10(wzz31000, wzz32000, bbc)
new_esEs21(wzz400, wzz3000, ty_Ordering) → new_esEs11(wzz400, wzz3000)
new_lt20(wzz31000, wzz32000, ty_Ordering) → new_lt4(wzz31000, wzz32000)
new_lt8(wzz31000, wzz32000, bd, be) → new_esEs11(new_compare6(wzz31000, wzz32000, bd, be), LT)
new_esEs14(wzz402, wzz3002, ty_Double) → new_esEs8(wzz402, wzz3002)
new_esEs5(Just(wzz400), Just(wzz3000), ty_Ordering) → new_esEs11(wzz400, wzz3000)
new_compare31(wzz31000, wzz32000, ty_Ordering) → new_compare5(wzz31000, wzz32000)
new_lt20(wzz31000, wzz32000, ty_Integer) → new_lt6(wzz31000, wzz32000)
new_esEs21(wzz400, wzz3000, ty_Char) → new_esEs18(wzz400, wzz3000)
new_primCompAux0(wzz165, LT) → LT
new_esEs30(wzz20, wzz15, ty_@0) → new_esEs10(wzz20, wzz15)
new_ltEs19(wzz3100, wzz3200, ty_Char) → new_ltEs8(wzz3100, wzz3200)
new_lt13(wzz31001, wzz32001, ty_Bool) → new_lt11(wzz31001, wzz32001)
new_ltEs14(Right(wzz31000), Right(wzz32000), bfa, ty_Integer) → new_ltEs18(wzz31000, wzz32000)
new_not(False) → True
new_esEs24(wzz31000, wzz32000, ty_Float) → new_esEs19(wzz31000, wzz32000)
new_esEs4(Right(wzz400), Right(wzz3000), ccg, app(ty_Ratio, cdc)) → new_esEs17(wzz400, wzz3000, cdc)
new_esEs23(wzz31001, wzz32001, app(app(ty_@2, bda), bdb)) → new_esEs6(wzz31001, wzz32001, bda, bdb)
new_compare12(wzz31000, wzz32000, False, bf, bg, bh) → GT
new_esEs12(wzz400, wzz3000, ty_Integer) → new_esEs20(wzz400, wzz3000)
new_esEs11(LT, GT) → False
new_esEs11(GT, LT) → False
new_esEs30(wzz20, wzz15, app(app(ty_Either, cef), ceg)) → new_esEs4(wzz20, wzz15, cef, ceg)
new_compare31(wzz31000, wzz32000, app(ty_Maybe, ddd)) → new_compare28(wzz31000, wzz32000, ddd)
new_ltEs14(Right(wzz31000), Right(wzz32000), bfa, app(ty_Ratio, cab)) → new_ltEs6(wzz31000, wzz32000, cab)
new_compare27(wzz31000, wzz32000, False) → new_compare111(wzz31000, wzz32000, new_ltEs10(wzz31000, wzz32000))
new_lt20(wzz31000, wzz32000, app(ty_[], baf)) → new_lt10(wzz31000, wzz32000, baf)
new_esEs13(wzz401, wzz3001, app(ty_[], ea)) → new_esEs16(wzz401, wzz3001, ea)
new_esEs12(wzz400, wzz3000, ty_Float) → new_esEs19(wzz400, wzz3000)
new_esEs11(LT, EQ) → False
new_esEs11(EQ, LT) → False
new_esEs24(wzz31000, wzz32000, app(ty_Maybe, bae)) → new_esEs5(wzz31000, wzz32000, bae)
new_esEs4(Right(wzz400), Right(wzz3000), ccg, app(app(ty_@2, cdd), cde)) → new_esEs6(wzz400, wzz3000, cdd, cde)
new_esEs23(wzz31001, wzz32001, ty_@0) → new_esEs10(wzz31001, wzz32001)
new_esEs14(wzz402, wzz3002, ty_Char) → new_esEs18(wzz402, wzz3002)
new_esEs14(wzz402, wzz3002, ty_@0) → new_esEs10(wzz402, wzz3002)
new_lt12(wzz31000, wzz32000, ty_Double) → new_lt14(wzz31000, wzz32000)
new_ltEs20(wzz31001, wzz32001, ty_@0) → new_ltEs17(wzz31001, wzz32001)
new_compare11(wzz31000, wzz32000, False, bd, be) → GT
new_ltEs17(wzz3100, wzz3200) → new_fsEs(new_compare13(wzz3100, wzz3200))
new_esEs22(wzz31000, wzz32000, app(app(app(ty_@3, bca), bcb), bcc)) → new_esEs7(wzz31000, wzz32000, bca, bcb, bcc)
new_esEs13(wzz401, wzz3001, app(app(ty_Either, dg), dh)) → new_esEs4(wzz401, wzz3001, dg, dh)
new_primCmpInt(Pos(Succ(wzz3100)), Neg(wzz320)) → GT
new_esEs22(wzz31000, wzz32000, ty_Char) → new_esEs18(wzz31000, wzz32000)
new_ltEs19(wzz3100, wzz3200, ty_Int) → new_ltEs9(wzz3100, wzz3200)
new_lt12(wzz31000, wzz32000, app(app(app(ty_@3, bca), bcb), bcc)) → new_lt5(wzz31000, wzz32000, bca, bcb, bcc)
new_ltEs18(wzz3100, wzz3200) → new_fsEs(new_compare8(wzz3100, wzz3200))
new_esEs22(wzz31000, wzz32000, app(ty_[], bbc)) → new_esEs16(wzz31000, wzz32000, bbc)
new_esEs14(wzz402, wzz3002, app(app(ty_Either, fa), fb)) → new_esEs4(wzz402, wzz3002, fa, fb)
new_primMulInt(Pos(wzz4010), Pos(wzz30010)) → Pos(new_primMulNat0(wzz4010, wzz30010))
new_esEs26(wzz401, wzz3001, ty_@0) → new_esEs10(wzz401, wzz3001)
new_esEs4(Left(wzz400), Left(wzz3000), ty_Bool, cbf) → new_esEs15(wzz400, wzz3000)
new_esEs30(wzz20, wzz15, ty_Ordering) → new_esEs11(wzz20, wzz15)
new_esEs23(wzz31001, wzz32001, app(app(ty_Either, bcf), bcg)) → new_esEs4(wzz31001, wzz32001, bcf, bcg)
new_esEs14(wzz402, wzz3002, ty_Bool) → new_esEs15(wzz402, wzz3002)
new_primMulInt(Neg(wzz4010), Neg(wzz30010)) → Pos(new_primMulNat0(wzz4010, wzz30010))
new_ltEs19(wzz3100, wzz3200, app(ty_Ratio, gf)) → new_ltEs6(wzz3100, wzz3200, gf)
new_lt6(wzz31000, wzz32000) → new_esEs11(new_compare8(wzz31000, wzz32000), LT)
new_esEs24(wzz31000, wzz32000, ty_Bool) → new_esEs15(wzz31000, wzz32000)
new_esEs29(wzz40, wzz300, app(app(ty_@2, cec), ced)) → new_esEs6(wzz40, wzz300, cec, ced)
new_primEqNat0(Zero, Succ(wzz30000)) → False
new_primEqNat0(Succ(wzz4000), Zero) → False
new_esEs29(wzz40, wzz300, app(ty_Ratio, ceb)) → new_esEs17(wzz40, wzz300, ceb)
new_esEs21(wzz400, wzz3000, ty_@0) → new_esEs10(wzz400, wzz3000)
new_esEs21(wzz400, wzz3000, ty_Int) → new_esEs9(wzz400, wzz3000)
new_primPlusNat0(Zero, Zero) → Zero
new_esEs25(wzz400, wzz3000, app(ty_Ratio, cgc)) → new_esEs17(wzz400, wzz3000, cgc)
new_lt12(wzz31000, wzz32000, ty_Bool) → new_lt11(wzz31000, wzz32000)
new_compare31(wzz31000, wzz32000, ty_Integer) → new_compare8(wzz31000, wzz32000)
new_lt12(wzz31000, wzz32000, ty_Int) → new_lt16(wzz31000, wzz32000)
new_ltEs14(Left(wzz31000), Left(wzz32000), app(app(ty_@2, bhe), bhf), bfb) → new_ltEs5(wzz31000, wzz32000, bhe, bhf)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_compare9(:%(wzz31000, wzz31001), :%(wzz32000, wzz32001), ty_Integer) → new_compare8(new_sr0(wzz31000, wzz32001), new_sr0(wzz32000, wzz31001))
new_esEs24(wzz31000, wzz32000, app(app(ty_Either, gg), gh)) → new_esEs4(wzz31000, wzz32000, gg, gh)
new_compare31(wzz31000, wzz32000, ty_Double) → new_compare18(wzz31000, wzz32000)
new_esEs5(Just(wzz400), Just(wzz3000), ty_Float) → new_esEs19(wzz400, wzz3000)
new_primCmpInt(Pos(Succ(wzz3100)), Pos(wzz320)) → new_primCmpNat0(wzz3100, wzz320)
new_ltEs13(wzz3100, wzz3200, gd) → new_fsEs(new_compare(wzz3100, wzz3200, gd))
new_ltEs12(wzz31002, wzz32002, app(app(app(ty_@3, bee), bef), beg)) → new_ltEs11(wzz31002, wzz32002, bee, bef, beg)
new_fsEs(wzz135) → new_not(new_esEs11(wzz135, GT))
new_esEs29(wzz40, wzz300, ty_Integer) → new_esEs20(wzz40, wzz300)
new_esEs22(wzz31000, wzz32000, ty_Int) → new_esEs9(wzz31000, wzz32000)
new_ltEs15(Just(wzz31000), Nothing, bfc) → False
new_esEs16([], :(wzz3000, wzz3001), hb) → False
new_esEs16(:(wzz400, wzz401), [], hb) → False
new_primCmpNat0(wzz3100, Zero) → GT
new_esEs5(Just(wzz400), Just(wzz3000), ty_Integer) → new_esEs20(wzz400, wzz3000)
new_ltEs4(True, False) → False
new_esEs12(wzz400, wzz3000, ty_Int) → new_esEs9(wzz400, wzz3000)
new_ltEs19(wzz3100, wzz3200, ty_@0) → new_ltEs17(wzz3100, wzz3200)
new_lt13(wzz31001, wzz32001, ty_Char) → new_lt18(wzz31001, wzz32001)
new_esEs26(wzz401, wzz3001, app(ty_Maybe, dac)) → new_esEs5(wzz401, wzz3001, dac)
new_esEs22(wzz31000, wzz32000, ty_@0) → new_esEs10(wzz31000, wzz32000)
new_lt13(wzz31001, wzz32001, app(ty_Maybe, bch)) → new_lt15(wzz31001, wzz32001, bch)
new_ltEs15(Just(wzz31000), Just(wzz32000), app(app(ty_@2, dba), dbb)) → new_ltEs5(wzz31000, wzz32000, dba, dbb)
new_ltEs14(Right(wzz31000), Right(wzz32000), bfa, app(app(ty_@2, cag), cah)) → new_ltEs5(wzz31000, wzz32000, cag, cah)
new_esEs24(wzz31000, wzz32000, ty_Int) → new_esEs9(wzz31000, wzz32000)
new_ltEs12(wzz31002, wzz32002, ty_Integer) → new_ltEs18(wzz31002, wzz32002)
new_esEs23(wzz31001, wzz32001, app(ty_Ratio, bcd)) → new_esEs17(wzz31001, wzz32001, bcd)
new_primCmpInt(Pos(Zero), Neg(Succ(wzz3200))) → GT
new_esEs30(wzz20, wzz15, ty_Char) → new_esEs18(wzz20, wzz15)
new_ltEs20(wzz31001, wzz32001, ty_Char) → new_ltEs8(wzz31001, wzz32001)
new_lt5(wzz31000, wzz32000, bf, bg, bh) → new_esEs11(new_compare7(wzz31000, wzz32000, bf, bg, bh), LT)
new_esEs12(wzz400, wzz3000, ty_Char) → new_esEs18(wzz400, wzz3000)
new_compare31(wzz31000, wzz32000, app(ty_[], dda)) → new_compare(wzz31000, wzz32000, dda)
new_esEs27(wzz400, wzz3000, ty_Int) → new_esEs9(wzz400, wzz3000)
new_esEs13(wzz401, wzz3001, app(app(ty_@2, ec), ed)) → new_esEs6(wzz401, wzz3001, ec, ed)
new_ltEs12(wzz31002, wzz32002, ty_Double) → new_ltEs7(wzz31002, wzz32002)
new_ltEs16(wzz3100, wzz3200) → new_fsEs(new_compare17(wzz3100, wzz3200))
new_esEs30(wzz20, wzz15, app(ty_[], ceh)) → new_esEs16(wzz20, wzz15, ceh)
new_compare29(Nothing, Nothing, False, beh) → LT
new_esEs4(Left(wzz400), Left(wzz3000), ty_Integer, cbf) → new_esEs20(wzz400, wzz3000)
new_ltEs14(Left(wzz31000), Left(wzz32000), ty_Integer, bfb) → new_ltEs18(wzz31000, wzz32000)
new_esEs10(@0, @0) → True
new_esEs24(wzz31000, wzz32000, app(app(app(ty_@3, bf), bg), bh)) → new_esEs7(wzz31000, wzz32000, bf, bg, bh)
new_compare29(wzz310, wzz320, True, beh) → EQ
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_lt10(wzz31000, wzz32000, baf) → new_esEs11(new_compare(wzz31000, wzz32000, baf), LT)
new_esEs13(wzz401, wzz3001, ty_Float) → new_esEs19(wzz401, wzz3001)
new_primCompAux1(wzz31000, wzz32000, wzz151, gd) → new_primCompAux0(wzz151, new_compare31(wzz31000, wzz32000, gd))
new_esEs5(Just(wzz400), Just(wzz3000), app(ty_[], dbh)) → new_esEs16(wzz400, wzz3000, dbh)
new_ltEs14(Left(wzz31000), Right(wzz32000), bfa, bfb) → True
new_ltEs6(wzz3100, wzz3200, gf) → new_fsEs(new_compare9(wzz3100, wzz3200, gf))
new_esEs12(wzz400, wzz3000, ty_Ordering) → new_esEs11(wzz400, wzz3000)
new_esEs29(wzz40, wzz300, ty_Bool) → new_esEs15(wzz40, wzz300)
new_ltEs20(wzz31001, wzz32001, app(app(ty_Either, bfh), bga)) → new_ltEs14(wzz31001, wzz32001, bfh, bga)
new_asAs(False, wzz125) → False
new_esEs4(Left(wzz400), Left(wzz3000), ty_@0, cbf) → new_esEs10(wzz400, wzz3000)
new_ltEs19(wzz3100, wzz3200, app(app(ty_Either, bfa), bfb)) → new_ltEs14(wzz3100, wzz3200, bfa, bfb)
new_primMulInt(Pos(wzz4010), Neg(wzz30010)) → Neg(new_primMulNat0(wzz4010, wzz30010))
new_primMulInt(Neg(wzz4010), Pos(wzz30010)) → Neg(new_primMulNat0(wzz4010, wzz30010))
new_esEs7(@3(wzz400, wzz401, wzz402), @3(wzz3000, wzz3001, wzz3002), ca, cb, cc) → new_asAs(new_esEs12(wzz400, wzz3000, ca), new_asAs(new_esEs13(wzz401, wzz3001, cb), new_esEs14(wzz402, wzz3002, cc)))
new_ltEs10(LT, GT) → True
new_lt20(wzz31000, wzz32000, ty_@0) → new_lt19(wzz31000, wzz32000)
new_primCmpInt(Neg(Succ(wzz3100)), Neg(wzz320)) → new_primCmpNat2(wzz320, wzz3100)
new_primMulNat0(Zero, Succ(wzz300100)) → Zero
new_primMulNat0(Succ(wzz40100), Zero) → Zero
new_esEs14(wzz402, wzz3002, app(app(app(ty_@3, fh), ga), gb)) → new_esEs7(wzz402, wzz3002, fh, ga, gb)
new_ltEs14(Left(wzz31000), Left(wzz32000), app(ty_Ratio, bgh), bfb) → new_ltEs6(wzz31000, wzz32000, bgh)
new_ltEs12(wzz31002, wzz32002, ty_Char) → new_ltEs8(wzz31002, wzz32002)
new_compare6(wzz31000, wzz32000, bd, be) → new_compare24(wzz31000, wzz32000, new_esEs6(wzz31000, wzz32000, bd, be), bd, be)
new_lt13(wzz31001, wzz32001, ty_Float) → new_lt17(wzz31001, wzz32001)
new_lt17(wzz31000, wzz32000) → new_esEs11(new_compare17(wzz31000, wzz32000), LT)
new_ltEs14(Left(wzz31000), Left(wzz32000), app(ty_Maybe, bhd), bfb) → new_ltEs15(wzz31000, wzz32000, bhd)
new_esEs24(wzz31000, wzz32000, app(ty_[], baf)) → new_esEs16(wzz31000, wzz32000, baf)
new_esEs23(wzz31001, wzz32001, ty_Int) → new_esEs9(wzz31001, wzz32001)
new_esEs5(Just(wzz400), Just(wzz3000), app(app(ty_@2, dcb), dcc)) → new_esEs6(wzz400, wzz3000, dcb, dcc)
new_ltEs14(Right(wzz31000), Right(wzz32000), bfa, app(app(app(ty_@3, cba), cbb), cbc)) → new_ltEs11(wzz31000, wzz32000, cba, cbb, cbc)
new_ltEs14(Right(wzz31000), Right(wzz32000), bfa, app(app(ty_Either, cad), cae)) → new_ltEs14(wzz31000, wzz32000, cad, cae)
new_esEs4(Left(wzz400), Left(wzz3000), app(ty_Maybe, ccf), cbf) → new_esEs5(wzz400, wzz3000, ccf)
new_compare13(@0, @0) → EQ
new_ltEs14(Left(wzz31000), Left(wzz32000), app(app(app(ty_@3, bhg), bhh), caa), bfb) → new_ltEs11(wzz31000, wzz32000, bhg, bhh, caa)
new_ltEs14(Left(wzz31000), Left(wzz32000), ty_Double, bfb) → new_ltEs7(wzz31000, wzz32000)
new_esEs23(wzz31001, wzz32001, app(ty_Maybe, bch)) → new_esEs5(wzz31001, wzz32001, bch)
new_ltEs4(False, False) → True
new_primCmpInt(Pos(Zero), Pos(Succ(wzz3200))) → new_primCmpNat2(Zero, wzz3200)
new_ltEs10(EQ, EQ) → True
new_compare27(wzz31000, wzz32000, True) → EQ
new_ltEs10(LT, LT) → True
new_ltEs15(Nothing, Nothing, bfc) → True
new_ltEs14(Right(wzz31000), Right(wzz32000), bfa, ty_Char) → new_ltEs8(wzz31000, wzz32000)
new_esEs5(Nothing, Just(wzz3000), cee) → False
new_esEs5(Just(wzz400), Nothing, cee) → False
new_esEs22(wzz31000, wzz32000, ty_Bool) → new_esEs15(wzz31000, wzz32000)
new_esEs4(Right(wzz400), Right(wzz3000), ccg, ty_Char) → new_esEs18(wzz400, wzz3000)
new_ltEs14(Right(wzz31000), Right(wzz32000), bfa, ty_Int) → new_ltEs9(wzz31000, wzz32000)
new_ltEs14(Left(wzz31000), Left(wzz32000), app(app(ty_Either, bhb), bhc), bfb) → new_ltEs14(wzz31000, wzz32000, bhb, bhc)
new_esEs29(wzz40, wzz300, ty_Float) → new_esEs19(wzz40, wzz300)
new_esEs25(wzz400, wzz3000, app(app(app(ty_@3, cgf), cgg), cgh)) → new_esEs7(wzz400, wzz3000, cgf, cgg, cgh)
new_compare31(wzz31000, wzz32000, ty_Char) → new_compare19(wzz31000, wzz32000)
new_esEs24(wzz31000, wzz32000, ty_Double) → new_esEs8(wzz31000, wzz32000)
new_esEs25(wzz400, wzz3000, ty_Float) → new_esEs19(wzz400, wzz3000)
new_lt7(wzz31000, wzz32000, ge) → new_esEs11(new_compare9(wzz31000, wzz32000, ge), LT)
new_compare31(wzz31000, wzz32000, app(app(app(ty_@3, ddg), ddh), dea)) → new_compare7(wzz31000, wzz32000, ddg, ddh, dea)
new_ltEs19(wzz3100, wzz3200, app(app(app(ty_@3, bag), bah), bba)) → new_ltEs11(wzz3100, wzz3200, bag, bah, bba)
new_esEs16([], [], hb) → True
new_lt11(wzz31000, wzz32000) → new_esEs11(new_compare30(wzz31000, wzz32000), LT)
new_ltEs12(wzz31002, wzz32002, ty_Float) → new_ltEs16(wzz31002, wzz32002)
new_esEs30(wzz20, wzz15, app(app(ty_@2, cfb), cfc)) → new_esEs6(wzz20, wzz15, cfb, cfc)
new_esEs8(Double(wzz400, wzz401), Double(wzz3000, wzz3001)) → new_esEs9(new_sr(wzz400, wzz3000), new_sr(wzz401, wzz3001))
new_lt13(wzz31001, wzz32001, app(app(app(ty_@3, bdc), bdd), bde)) → new_lt5(wzz31001, wzz32001, bdc, bdd, bde)
new_compare29(Just(wzz3100), Just(wzz3200), False, beh) → new_compare16(wzz3100, wzz3200, new_ltEs19(wzz3100, wzz3200, beh), beh)
new_esEs14(wzz402, wzz3002, ty_Int) → new_esEs9(wzz402, wzz3002)
new_lt12(wzz31000, wzz32000, app(app(ty_@2, bbg), bbh)) → new_lt8(wzz31000, wzz32000, bbg, bbh)
new_esEs12(wzz400, wzz3000, app(ty_Ratio, cg)) → new_esEs17(wzz400, wzz3000, cg)
new_ltEs20(wzz31001, wzz32001, app(ty_Ratio, bff)) → new_ltEs6(wzz31001, wzz32001, bff)
new_esEs5(Nothing, Nothing, cee) → True
new_esEs4(Left(wzz400), Left(wzz3000), app(ty_[], cbg), cbf) → new_esEs16(wzz400, wzz3000, cbg)
new_esEs26(wzz401, wzz3001, ty_Float) → new_esEs19(wzz401, wzz3001)
new_esEs5(Just(wzz400), Just(wzz3000), app(app(app(ty_@3, dcd), dce), dcf)) → new_esEs7(wzz400, wzz3000, dcd, dce, dcf)
new_esEs28(wzz401, wzz3001, ty_Int) → new_esEs9(wzz401, wzz3001)
new_ltEs10(EQ, LT) → False
new_esEs5(Just(wzz400), Just(wzz3000), app(ty_Ratio, dca)) → new_esEs17(wzz400, wzz3000, dca)
new_lt15(wzz31000, wzz32000, bae) → new_esEs11(new_compare28(wzz31000, wzz32000, bae), LT)
new_esEs22(wzz31000, wzz32000, app(ty_Ratio, bbb)) → new_esEs17(wzz31000, wzz32000, bbb)
new_esEs26(wzz401, wzz3001, ty_Char) → new_esEs18(wzz401, wzz3001)
new_lt18(wzz31000, wzz32000) → new_esEs11(new_compare19(wzz31000, wzz32000), LT)
new_lt12(wzz31000, wzz32000, ty_Float) → new_lt17(wzz31000, wzz32000)
new_ltEs10(GT, LT) → False
new_lt20(wzz31000, wzz32000, app(app(app(ty_@3, bf), bg), bh)) → new_lt5(wzz31000, wzz32000, bf, bg, bh)
new_esEs4(Right(wzz400), Right(wzz3000), ccg, ty_Float) → new_esEs19(wzz400, wzz3000)
new_primPlusNat0(Succ(wzz26200), Succ(wzz8700)) → Succ(Succ(new_primPlusNat0(wzz26200, wzz8700)))
new_esEs22(wzz31000, wzz32000, app(ty_Maybe, bbf)) → new_esEs5(wzz31000, wzz32000, bbf)
new_esEs23(wzz31001, wzz32001, app(ty_[], bce)) → new_esEs16(wzz31001, wzz32001, bce)
new_esEs21(wzz400, wzz3000, app(ty_Maybe, bad)) → new_esEs5(wzz400, wzz3000, bad)
new_esEs29(wzz40, wzz300, ty_@0) → new_esEs10(wzz40, wzz300)
new_esEs26(wzz401, wzz3001, app(app(ty_Either, chb), chc)) → new_esEs4(wzz401, wzz3001, chb, chc)
new_esEs21(wzz400, wzz3000, ty_Integer) → new_esEs20(wzz400, wzz3000)
new_asAs(True, wzz125) → wzz125
new_esEs4(Right(wzz400), Left(wzz3000), ccg, cbf) → False
new_esEs4(Left(wzz400), Right(wzz3000), ccg, cbf) → False
new_ltEs8(wzz3100, wzz3200) → new_fsEs(new_compare19(wzz3100, wzz3200))
new_esEs30(wzz20, wzz15, app(ty_Maybe, cfg)) → new_esEs5(wzz20, wzz15, cfg)
new_esEs11(LT, LT) → True
new_primPlusNat1(wzz97, wzz300100) → new_primPlusNat0(wzz97, Succ(wzz300100))
new_esEs14(wzz402, wzz3002, ty_Integer) → new_esEs20(wzz402, wzz3002)
new_esEs5(Just(wzz400), Just(wzz3000), ty_Double) → new_esEs8(wzz400, wzz3000)
new_compare24(wzz31000, wzz32000, False, bd, be) → new_compare11(wzz31000, wzz32000, new_ltEs5(wzz31000, wzz32000, bd, be), bd, be)
new_esEs26(wzz401, wzz3001, app(app(ty_@2, chf), chg)) → new_esEs6(wzz401, wzz3001, chf, chg)
new_lt13(wzz31001, wzz32001, app(app(ty_@2, bda), bdb)) → new_lt8(wzz31001, wzz32001, bda, bdb)
new_ltEs12(wzz31002, wzz32002, ty_Int) → new_ltEs9(wzz31002, wzz32002)
new_compare10(wzz31000, wzz32000, True) → LT
new_esEs9(wzz40, wzz300) → new_primEqInt(wzz40, wzz300)
new_esEs11(EQ, GT) → False
new_esEs11(GT, EQ) → False
new_lt20(wzz31000, wzz32000, app(ty_Ratio, ge)) → new_lt7(wzz31000, wzz32000, ge)
new_lt19(wzz31000, wzz32000) → new_esEs11(new_compare13(wzz31000, wzz32000), LT)
new_compare10(wzz31000, wzz32000, False) → GT
new_esEs6(@2(wzz400, wzz401), @2(wzz3000, wzz3001), cec, ced) → new_asAs(new_esEs25(wzz400, wzz3000, cec), new_esEs26(wzz401, wzz3001, ced))
new_esEs13(wzz401, wzz3001, app(app(app(ty_@3, ee), ef), eg)) → new_esEs7(wzz401, wzz3001, ee, ef, eg)
new_esEs21(wzz400, wzz3000, app(ty_[], he)) → new_esEs16(wzz400, wzz3000, he)
new_esEs5(Just(wzz400), Just(wzz3000), app(app(ty_Either, dbf), dbg)) → new_esEs4(wzz400, wzz3000, dbf, dbg)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCompAux0(wzz165, EQ) → wzz165
new_esEs24(wzz31000, wzz32000, ty_Char) → new_esEs18(wzz31000, wzz32000)
new_lt12(wzz31000, wzz32000, ty_@0) → new_lt19(wzz31000, wzz32000)
new_ltEs19(wzz3100, wzz3200, app(ty_[], gd)) → new_ltEs13(wzz3100, wzz3200, gd)
new_lt12(wzz31000, wzz32000, app(ty_Maybe, bbf)) → new_lt15(wzz31000, wzz32000, bbf)
new_ltEs14(Left(wzz31000), Left(wzz32000), ty_@0, bfb) → new_ltEs17(wzz31000, wzz32000)
new_compare9(:%(wzz31000, wzz31001), :%(wzz32000, wzz32001), ty_Int) → new_compare14(new_sr(wzz31000, wzz32001), new_sr(wzz32000, wzz31001))
new_ltEs15(Just(wzz31000), Just(wzz32000), app(app(ty_Either, daf), dag)) → new_ltEs14(wzz31000, wzz32000, daf, dag)
new_esEs12(wzz400, wzz3000, app(ty_Maybe, df)) → new_esEs5(wzz400, wzz3000, df)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primCmpNat0(wzz3100, Succ(wzz3200)) → new_primCmpNat1(wzz3100, wzz3200)
new_lt20(wzz31000, wzz32000, app(app(ty_Either, gg), gh)) → new_lt9(wzz31000, wzz32000, gg, gh)
new_esEs12(wzz400, wzz3000, app(app(ty_@2, da), db)) → new_esEs6(wzz400, wzz3000, da, db)
new_primCmpInt(Neg(Succ(wzz3100)), Pos(wzz320)) → LT
new_not(True) → False
new_esEs15(False, False) → True

The set Q consists of the following terms:

new_compare210(x0, x1, False, x2, x3, x4)
new_compare31(x0, x1, ty_Int)
new_esEs4(Right(x0), Right(x1), x2, ty_Integer)
new_compare10(x0, x1, True)
new_compare31(x0, x1, ty_@0)
new_ltEs15(Just(x0), Just(x1), ty_@0)
new_esEs29(x0, x1, ty_Float)
new_primCmpNat2(Succ(x0), x1)
new_lt12(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Float)
new_lt5(x0, x1, x2, x3, x4)
new_lt13(x0, x1, ty_Float)
new_esEs13(x0, x1, app(app(ty_Either, x2), x3))
new_compare30(x0, x1)
new_primCmpNat1(Succ(x0), Succ(x1))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs26(x0, x1, ty_Bool)
new_esEs4(Right(x0), Right(x1), x2, ty_Float)
new_pePe(False, x0)
new_esEs24(x0, x1, ty_@0)
new_lt20(x0, x1, ty_Char)
new_ltEs14(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_lt13(x0, x1, ty_Double)
new_esEs13(x0, x1, ty_Double)
new_compare17(Float(x0, x1), Float(x2, x3))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Just(x0), Just(x1), ty_Int)
new_esEs15(True, True)
new_esEs13(x0, x1, ty_Ordering)
new_esEs5(Just(x0), Just(x1), ty_Bool)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs18(Char(x0), Char(x1))
new_compare14(x0, x1)
new_esEs12(x0, x1, ty_Char)
new_ltEs10(LT, LT)
new_compare31(x0, x1, ty_Float)
new_esEs4(Right(x0), Right(x1), x2, ty_Bool)
new_compare31(x0, x1, app(ty_[], x2))
new_ltEs12(x0, x1, ty_@0)
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Nothing, Just(x0), x1)
new_ltEs20(x0, x1, ty_@0)
new_esEs22(x0, x1, ty_Bool)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_sr(x0, x1)
new_esEs29(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Bool)
new_compare29(Nothing, Nothing, False, x0)
new_primCompAux0(x0, LT)
new_ltEs14(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs15(False, False)
new_lt10(x0, x1, x2)
new_ltEs14(Left(x0), Left(x1), ty_Float, x2)
new_esEs26(x0, x1, ty_Double)
new_esEs21(x0, x1, ty_Bool)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs20(Integer(x0), Integer(x1))
new_ltEs12(x0, x1, ty_Double)
new_ltEs14(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Double)
new_esEs12(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_Double)
new_ltEs14(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_compare12(x0, x1, True, x2, x3, x4)
new_esEs5(Just(x0), Just(x1), ty_Double)
new_lt13(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare110(x0, x1, True, x2, x3)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, ty_Integer)
new_esEs14(x0, x1, app(app(ty_Either, x2), x3))
new_esEs14(x0, x1, app(ty_Ratio, x2))
new_esEs14(x0, x1, ty_@0)
new_compare31(x0, x1, ty_Ordering)
new_compare210(x0, x1, True, x2, x3, x4)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs30(x0, x1, ty_Integer)
new_ltEs15(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Int)
new_lt13(x0, x1, app(ty_Ratio, x2))
new_primEqNat0(Succ(x0), Zero)
new_esEs22(x0, x1, ty_Int)
new_ltEs12(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Bool)
new_esEs4(Right(x0), Right(x1), x2, ty_@0)
new_ltEs19(x0, x1, ty_@0)
new_esEs16([], [], x0)
new_ltEs12(x0, x1, app(ty_Ratio, x2))
new_lt13(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpNat1(Zero, Zero)
new_compare(:(x0, x1), :(x2, x3), x4)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_primMulNat0(Succ(x0), Succ(x1))
new_compare9(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs23(x0, x1, ty_@0)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_lt12(x0, x1, app(ty_Ratio, x2))
new_ltEs7(x0, x1)
new_esEs11(EQ, GT)
new_esEs11(GT, EQ)
new_ltEs14(Left(x0), Left(x1), ty_Int, x2)
new_ltEs12(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_fsEs(x0)
new_esEs5(Just(x0), Just(x1), ty_@0)
new_primPlusNat0(Succ(x0), Zero)
new_lt12(x0, x1, ty_Bool)
new_compare12(x0, x1, False, x2, x3, x4)
new_esEs25(x0, x1, ty_Ordering)
new_esEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_compare11(x0, x1, False, x2, x3)
new_primEqNat0(Zero, Zero)
new_esEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs5(Nothing, Nothing, x0)
new_compare7(x0, x1, x2, x3, x4)
new_lt12(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Left(x0), Left(x1), app(ty_[], x2), x3)
new_primCompAux0(x0, EQ)
new_ltEs15(Just(x0), Just(x1), ty_Bool)
new_esEs25(x0, x1, app(ty_[], x2))
new_ltEs4(True, True)
new_esEs21(x0, x1, ty_Int)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs12(x0, x1, ty_Ordering)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_primMulNat0(Succ(x0), Zero)
new_esEs23(x0, x1, ty_Float)
new_compare31(x0, x1, ty_Integer)
new_compare31(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_Ordering)
new_compare8(Integer(x0), Integer(x1))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs22(x0, x1, app(ty_[], x2))
new_ltEs12(x0, x1, ty_Int)
new_lt17(x0, x1)
new_compare26(x0, x1, True, x2, x3)
new_ltEs14(Right(x0), Right(x1), x2, ty_Integer)
new_lt13(x0, x1, ty_Integer)
new_ltEs10(EQ, LT)
new_ltEs10(LT, EQ)
new_esEs12(x0, x1, ty_Integer)
new_esEs12(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_Int)
new_lt11(x0, x1)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_ltEs15(Just(x0), Just(x1), ty_Integer)
new_lt13(x0, x1, app(ty_[], x2))
new_esEs4(Left(x0), Left(x1), ty_@0, x2)
new_lt20(x0, x1, ty_@0)
new_ltEs14(Left(x0), Left(x1), ty_Char, x2)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_primEqNat0(Zero, Succ(x0))
new_lt13(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, ty_Char)
new_esEs30(x0, x1, ty_Ordering)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Float)
new_esEs21(x0, x1, ty_Double)
new_lt13(x0, x1, app(ty_Maybe, x2))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs13(x0, x1, ty_Integer)
new_ltEs12(x0, x1, ty_Bool)
new_esEs11(GT, LT)
new_esEs11(LT, GT)
new_ltEs14(Left(x0), Left(x1), ty_Integer, x2)
new_compare25(x0, x1, True)
new_esEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_lt12(x0, x1, ty_Int)
new_primCmpNat2(Zero, x0)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_lt14(x0, x1)
new_ltEs15(Just(x0), Just(x1), ty_Double)
new_asAs(False, x0)
new_ltEs4(False, False)
new_esEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Bool)
new_esEs5(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs19(x0, x1, ty_Double)
new_compare27(x0, x1, False)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, ty_@0)
new_esEs21(x0, x1, ty_Float)
new_compare28(x0, x1, x2)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs15(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs15(Just(x0), Just(x1), ty_Ordering)
new_lt20(x0, x1, ty_Ordering)
new_lt12(x0, x1, ty_Float)
new_esEs4(Right(x0), Left(x1), x2, x3)
new_esEs4(Left(x0), Right(x1), x2, x3)
new_esEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs12(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Int)
new_esEs28(x0, x1, ty_Integer)
new_compare16(x0, x1, True, x2)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs26(x0, x1, ty_Int)
new_asAs(True, x0)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs11(LT, LT)
new_compare26(x0, x1, False, x2, x3)
new_ltEs15(Just(x0), Just(x1), ty_Int)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_Bool)
new_lt19(x0, x1)
new_esEs23(x0, x1, ty_Char)
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_primPlusNat0(Zero, Zero)
new_ltEs12(x0, x1, app(ty_[], x2))
new_lt12(x0, x1, ty_Char)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_compare31(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_@0)
new_lt12(x0, x1, ty_Integer)
new_lt20(x0, x1, ty_Integer)
new_esEs24(x0, x1, app(ty_[], x2))
new_primPlusNat0(Succ(x0), Succ(x1))
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_lt12(x0, x1, app(app(ty_Either, x2), x3))
new_esEs14(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Ordering)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs30(x0, x1, ty_Float)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs24(x0, x1, ty_Double)
new_esEs23(x0, x1, ty_Double)
new_esEs25(x0, x1, ty_Double)
new_esEs24(x0, x1, ty_Char)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_ltEs20(x0, x1, ty_Double)
new_compare19(Char(x0), Char(x1))
new_esEs21(x0, x1, ty_Char)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs14(x0, x1, ty_Ordering)
new_ltEs14(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs9(x0, x1)
new_compare([], :(x0, x1), x2)
new_ltEs15(Just(x0), Nothing, x1)
new_ltEs20(x0, x1, ty_Int)
new_lt6(x0, x1)
new_compare29(Just(x0), Nothing, False, x1)
new_esEs30(x0, x1, ty_Double)
new_ltEs17(x0, x1)
new_esEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_compare24(x0, x1, False, x2, x3)
new_ltEs10(GT, LT)
new_ltEs10(LT, GT)
new_primPlusNat0(Zero, Succ(x0))
new_esEs14(x0, x1, ty_Bool)
new_esEs30(x0, x1, ty_Bool)
new_esEs10(@0, @0)
new_esEs24(x0, x1, ty_Ordering)
new_esEs14(x0, x1, ty_Char)
new_esEs30(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, app(ty_[], x2))
new_compare31(x0, x1, ty_Double)
new_ltEs16(x0, x1)
new_ltEs11(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_compare111(x0, x1, True)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_lt12(x0, x1, ty_Double)
new_esEs9(x0, x1)
new_esEs5(Just(x0), Just(x1), ty_Ordering)
new_esEs5(Just(x0), Nothing, x1)
new_lt9(x0, x1, x2, x3)
new_esEs13(x0, x1, ty_Bool)
new_esEs29(x0, x1, ty_Ordering)
new_esEs13(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_Float)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_ltEs14(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs15(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs15(Just(x0), Just(x1), ty_Char)
new_compare13(@0, @0)
new_esEs16([], :(x0, x1), x2)
new_ltEs15(Nothing, Just(x0), x1)
new_esEs22(x0, x1, ty_Char)
new_esEs11(EQ, LT)
new_esEs11(LT, EQ)
new_esEs12(x0, x1, app(ty_[], x2))
new_compare11(x0, x1, True, x2, x3)
new_esEs12(x0, x1, ty_Ordering)
new_compare6(x0, x1, x2, x3)
new_esEs13(x0, x1, ty_Int)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs15(True, False)
new_esEs15(False, True)
new_sr0(Integer(x0), Integer(x1))
new_esEs4(Left(x0), Left(x1), ty_Integer, x2)
new_esEs29(x0, x1, ty_Double)
new_esEs17(:%(x0, x1), :%(x2, x3), x4)
new_lt13(x0, x1, ty_Bool)
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs30(x0, x1, ty_Int)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs14(Left(x0), Left(x1), ty_Bool, x2)
new_compare31(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, ty_Bool)
new_esEs19(Float(x0, x1), Float(x2, x3))
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs14(Right(x0), Right(x1), x2, ty_@0)
new_esEs13(x0, x1, ty_Float)
new_lt16(x0, x1)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Int)
new_lt18(x0, x1)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs16(:(x0, x1), :(x2, x3), x4)
new_esEs24(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_@0)
new_esEs16(:(x0, x1), [], x2)
new_lt7(x0, x1, x2)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_compare18(Double(x0, x1), Double(x2, x3))
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_primCmpNat1(Succ(x0), Zero)
new_esEs13(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt13(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Integer)
new_primCompAux0(x0, GT)
new_esEs4(Left(x0), Left(x1), ty_Int, x2)
new_lt13(x0, x1, ty_Ordering)
new_ltEs12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare(:(x0, x1), [], x2)
new_lt12(x0, x1, app(ty_[], x2))
new_ltEs14(Left(x0), Left(x1), ty_Double, x2)
new_esEs30(x0, x1, ty_@0)
new_ltEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, ty_Int)
new_esEs22(x0, x1, ty_@0)
new_primMulNat0(Zero, Succ(x0))
new_lt12(x0, x1, ty_Ordering)
new_esEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Just(x0), Just(x1), ty_Integer)
new_esEs5(Just(x0), Just(x1), ty_Char)
new_esEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs12(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(Double(x0, x1), Double(x2, x3))
new_esEs4(Left(x0), Left(x1), ty_Char, x2)
new_esEs22(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Ordering)
new_esEs12(x0, x1, app(ty_Maybe, x2))
new_compare29(Nothing, Just(x0), False, x1)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs4(False, True)
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_ltEs4(True, False)
new_esEs14(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs26(x0, x1, ty_Float)
new_lt4(x0, x1)
new_compare([], [], x0)
new_esEs12(x0, x1, ty_Bool)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs12(x0, x1, ty_Int)
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs14(x0, x1, ty_Int)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_primPlusNat1(x0, x1)
new_esEs21(x0, x1, ty_Ordering)
new_ltEs18(x0, x1)
new_ltEs15(Nothing, Nothing, x0)
new_esEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs29(x0, x1, ty_Integer)
new_esEs12(x0, x1, app(ty_Ratio, x2))
new_compare111(x0, x1, False)
new_ltEs12(x0, x1, app(ty_Maybe, x2))
new_compare31(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs6(x0, x1, x2)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs10(GT, GT)
new_esEs25(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs13(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Float)
new_esEs29(x0, x1, ty_Char)
new_ltEs15(Just(x0), Just(x1), ty_Float)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs30(x0, x1, ty_Char)
new_esEs11(GT, GT)
new_ltEs14(Right(x0), Right(x1), x2, ty_Char)
new_compare16(x0, x1, False, x2)
new_primEqNat0(Succ(x0), Succ(x1))
new_ltEs20(x0, x1, ty_Integer)
new_primCmpNat0(x0, Zero)
new_lt20(x0, x1, app(ty_[], x2))
new_lt12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_not(True)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_compare29(x0, x1, True, x2)
new_esEs12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, ty_Char)
new_esEs22(x0, x1, ty_Float)
new_esEs4(Right(x0), Right(x1), x2, ty_Char)
new_compare9(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs12(x0, x1, ty_Double)
new_esEs4(Left(x0), Left(x1), ty_Double, x2)
new_esEs26(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_Float)
new_lt20(x0, x1, ty_Double)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_not(False)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs14(x0, x1, app(ty_Maybe, x2))
new_ltEs13(x0, x1, x2)
new_esEs26(x0, x1, ty_Char)
new_primCompAux1(x0, x1, x2, x3)
new_primCmpNat1(Zero, Succ(x0))
new_compare110(x0, x1, False, x2, x3)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs10(EQ, GT)
new_ltEs10(GT, EQ)
new_ltEs20(x0, x1, ty_Char)
new_lt13(x0, x1, ty_Char)
new_ltEs14(Left(x0), Left(x1), ty_@0, x2)
new_esEs23(x0, x1, app(ty_[], x2))
new_compare27(x0, x1, True)
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_compare31(x0, x1, ty_Char)
new_compare29(Just(x0), Just(x1), False, x2)
new_esEs4(Right(x0), Right(x1), x2, ty_Int)
new_compare15(x0, x1, x2, x3)
new_primCmpNat0(x0, Succ(x1))
new_esEs14(x0, x1, ty_Double)
new_ltEs12(x0, x1, ty_Char)
new_compare24(x0, x1, True, x2, x3)
new_lt8(x0, x1, x2, x3)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(Right(x0), Right(x1), x2, ty_Float)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_ltEs12(x0, x1, ty_Float)
new_esEs21(x0, x1, ty_@0)
new_esEs13(x0, x1, app(ty_Maybe, x2))
new_esEs4(Left(x0), Left(x1), ty_Float, x2)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_ltEs15(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs8(x0, x1)
new_ltEs19(x0, x1, ty_Bool)
new_esEs29(x0, x1, ty_Int)
new_esEs13(x0, x1, app(ty_[], x2))
new_esEs25(x0, x1, ty_Int)
new_compare31(x0, x1, ty_Bool)
new_esEs13(x0, x1, ty_@0)
new_ltEs15(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_compare31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs14(x0, x1, app(app(ty_@2, x2), x3))
new_esEs14(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Integer)
new_lt20(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_Int)
new_esEs14(x0, x1, ty_Float)
new_esEs12(x0, x1, ty_@0)
new_esEs24(x0, x1, ty_Integer)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_primEqInt(Pos(Zero), Pos(Zero))
new_ltEs14(Left(x0), Right(x1), x2, x3)
new_ltEs14(Right(x0), Left(x1), x2, x3)
new_esEs11(EQ, EQ)
new_lt15(x0, x1, x2)
new_esEs13(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_compare25(x0, x1, False)
new_ltEs15(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs14(Right(x0), Right(x1), x2, ty_Bool)
new_esEs4(Right(x0), Right(x1), x2, ty_Double)
new_compare10(x0, x1, False)
new_pePe(True, x0)
new_esEs27(x0, x1, ty_Integer)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Just(x0), Just(x1), ty_Float)
new_compare5(x0, x1)
new_ltEs20(x0, x1, ty_Ordering)
new_lt13(x0, x1, ty_@0)
new_esEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs21(x0, x1, app(ty_[], x2))
new_ltEs10(EQ, EQ)
new_lt12(x0, x1, ty_@0)

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

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



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

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

new_addToFM_C1(wzz31, wzz32, wzz33, wzz34, wzz5, True, h, ba) → new_addToFM_C(wzz34, Nothing, wzz5, h, ba)
new_addToFM_C2(wzz300, wzz31, wzz32, wzz33, wzz34, wzz5, True, h, ba) → new_addToFM_C(wzz33, Nothing, wzz5, h, ba)
new_addToFM_C(Branch(Nothing, wzz31, wzz32, wzz33, wzz34), Nothing, wzz5, h, ba) → new_addToFM_C1(wzz31, wzz32, wzz33, wzz34, wzz5, new_esEs11(new_compare29(Nothing, Nothing, True, h), GT), h, ba)
new_addToFM_C2(wzz300, wzz31, wzz32, wzz33, wzz34, wzz5, False, h, ba) → new_addToFM_C10(wzz300, wzz31, wzz32, wzz33, wzz34, wzz5, new_esEs11(new_compare29(Nothing, Just(wzz300), False, h), GT), h, ba)
new_addToFM_C10(wzz300, wzz31, wzz32, wzz33, wzz34, wzz5, True, h, ba) → new_addToFM_C(wzz34, Nothing, wzz5, h, ba)
new_addToFM_C(Branch(Just(wzz300), wzz31, wzz32, wzz33, wzz34), Nothing, wzz5, h, ba) → new_addToFM_C2(wzz300, wzz31, wzz32, wzz33, wzz34, wzz5, new_esEs11(new_compare29(Nothing, Just(wzz300), False, h), LT), h, ba)

The TRS R consists of the following rules:

new_ltEs19(wzz3100, wzz3200, app(app(ty_@2, bfd), bfe)) → new_ltEs5(wzz3100, wzz3200, bfd, bfe)
new_ltEs20(wzz31001, wzz32001, ty_Bool) → new_ltEs4(wzz31001, wzz32001)
new_ltEs20(wzz31001, wzz32001, ty_Int) → new_ltEs9(wzz31001, wzz32001)
new_esEs21(wzz400, wzz3000, app(app(ty_@2, hg), hh)) → new_esEs6(wzz400, wzz3000, hg, hh)
new_lt20(wzz31000, wzz32000, ty_Int) → new_lt16(wzz31000, wzz32000)
new_esEs18(Char(wzz400), Char(wzz3000)) → new_primEqNat0(wzz400, wzz3000)
new_primCmpNat2(Zero, wzz3100) → LT
new_esEs14(wzz402, wzz3002, ty_Float) → new_esEs19(wzz402, wzz3002)
new_esEs25(wzz400, wzz3000, app(ty_[], cgb)) → new_esEs16(wzz400, wzz3000, cgb)
new_compare8(Integer(wzz31000), Integer(wzz32000)) → new_primCmpInt(wzz31000, wzz32000)
new_esEs25(wzz400, wzz3000, ty_Bool) → new_esEs15(wzz400, wzz3000)
new_esEs23(wzz31001, wzz32001, ty_Ordering) → new_esEs11(wzz31001, wzz32001)
new_esEs13(wzz401, wzz3001, ty_Double) → new_esEs8(wzz401, wzz3001)
new_ltEs14(Right(wzz31000), Right(wzz32000), bfa, ty_Ordering) → new_ltEs10(wzz31000, wzz32000)
new_esEs27(wzz400, wzz3000, ty_Integer) → new_esEs20(wzz400, wzz3000)
new_compare110(wzz31000, wzz32000, True, gg, gh) → LT
new_ltEs20(wzz31001, wzz32001, ty_Ordering) → new_ltEs10(wzz31001, wzz32001)
new_primCmpNat1(Zero, Succ(wzz32000)) → LT
new_compare([], :(wzz32000, wzz32001), gd) → LT
new_esEs22(wzz31000, wzz32000, ty_Float) → new_esEs19(wzz31000, wzz32000)
new_esEs13(wzz401, wzz3001, ty_Char) → new_esEs18(wzz401, wzz3001)
new_lt12(wzz31000, wzz32000, app(app(ty_Either, bbd), bbe)) → new_lt9(wzz31000, wzz32000, bbd, bbe)
new_ltEs15(Just(wzz31000), Just(wzz32000), app(ty_[], dae)) → new_ltEs13(wzz31000, wzz32000, dae)
new_esEs29(wzz40, wzz300, ty_Int) → new_esEs9(wzz40, wzz300)
new_ltEs15(Just(wzz31000), Just(wzz32000), app(ty_Ratio, dad)) → new_ltEs6(wzz31000, wzz32000, dad)
new_esEs4(Right(wzz400), Right(wzz3000), ccg, app(ty_Maybe, cea)) → new_esEs5(wzz400, wzz3000, cea)
new_compare30(wzz31000, wzz32000) → new_compare25(wzz31000, wzz32000, new_esEs15(wzz31000, wzz32000))
new_esEs11(EQ, EQ) → True
new_ltEs14(Left(wzz31000), Left(wzz32000), ty_Bool, bfb) → new_ltEs4(wzz31000, wzz32000)
new_ltEs20(wzz31001, wzz32001, ty_Double) → new_ltEs7(wzz31001, wzz32001)
new_esEs13(wzz401, wzz3001, ty_Integer) → new_esEs20(wzz401, wzz3001)
new_esEs23(wzz31001, wzz32001, ty_Float) → new_esEs19(wzz31001, wzz32001)
new_esEs26(wzz401, wzz3001, ty_Integer) → new_esEs20(wzz401, wzz3001)
new_esEs14(wzz402, wzz3002, ty_Ordering) → new_esEs11(wzz402, wzz3002)
new_compare17(Float(wzz31000, wzz31001), Float(wzz32000, wzz32001)) → new_compare14(new_sr(wzz31000, wzz32000), new_sr(wzz31001, wzz32001))
new_primMulNat0(Zero, Zero) → Zero
new_compare(:(wzz31000, wzz31001), [], gd) → GT
new_esEs26(wzz401, wzz3001, app(ty_[], chd)) → new_esEs16(wzz401, wzz3001, chd)
new_esEs5(Just(wzz400), Just(wzz3000), ty_Int) → new_esEs9(wzz400, wzz3000)
new_ltEs14(Right(wzz31000), Right(wzz32000), bfa, app(ty_[], cac)) → new_ltEs13(wzz31000, wzz32000, cac)
new_compare31(wzz31000, wzz32000, app(app(ty_@2, dde), ddf)) → new_compare6(wzz31000, wzz32000, dde, ddf)
new_esEs12(wzz400, wzz3000, ty_Bool) → new_esEs15(wzz400, wzz3000)
new_ltEs15(Nothing, Just(wzz32000), bfc) → True
new_esEs25(wzz400, wzz3000, ty_Double) → new_esEs8(wzz400, wzz3000)
new_esEs4(Right(wzz400), Right(wzz3000), ccg, ty_Int) → new_esEs9(wzz400, wzz3000)
new_ltEs19(wzz3100, wzz3200, app(ty_Maybe, bfc)) → new_ltEs15(wzz3100, wzz3200, bfc)
new_esEs4(Left(wzz400), Left(wzz3000), app(ty_Ratio, cbh), cbf) → new_esEs17(wzz400, wzz3000, cbh)
new_lt20(wzz31000, wzz32000, app(app(ty_@2, bd), be)) → new_lt8(wzz31000, wzz32000, bd, be)
new_ltEs15(Just(wzz31000), Just(wzz32000), ty_Bool) → new_ltEs4(wzz31000, wzz32000)
new_esEs20(Integer(wzz400), Integer(wzz3000)) → new_primEqInt(wzz400, wzz3000)
new_esEs25(wzz400, wzz3000, ty_Ordering) → new_esEs11(wzz400, wzz3000)
new_lt12(wzz31000, wzz32000, ty_Integer) → new_lt6(wzz31000, wzz32000)
new_esEs29(wzz40, wzz300, app(app(ty_Either, ccg), cbf)) → new_esEs4(wzz40, wzz300, ccg, cbf)
new_esEs5(Just(wzz400), Just(wzz3000), ty_Bool) → new_esEs15(wzz400, wzz3000)
new_lt20(wzz31000, wzz32000, ty_Double) → new_lt14(wzz31000, wzz32000)
new_ltEs20(wzz31001, wzz32001, app(app(app(ty_@3, bge), bgf), bgg)) → new_ltEs11(wzz31001, wzz32001, bge, bgf, bgg)
new_compare18(Double(wzz31000, wzz31001), Double(wzz32000, wzz32001)) → new_compare14(new_sr(wzz31000, wzz32000), new_sr(wzz31001, wzz32001))
new_esEs4(Right(wzz400), Right(wzz3000), ccg, app(app(app(ty_@3, cdf), cdg), cdh)) → new_esEs7(wzz400, wzz3000, cdf, cdg, cdh)
new_esEs30(wzz20, wzz15, ty_Int) → new_esEs9(wzz20, wzz15)
new_esEs4(Left(wzz400), Left(wzz3000), app(app(ty_@2, cca), ccb), cbf) → new_esEs6(wzz400, wzz3000, cca, ccb)
new_esEs26(wzz401, wzz3001, ty_Double) → new_esEs8(wzz401, wzz3001)
new_ltEs19(wzz3100, wzz3200, ty_Ordering) → new_ltEs10(wzz3100, wzz3200)
new_ltEs19(wzz3100, wzz3200, ty_Bool) → new_ltEs4(wzz3100, wzz3200)
new_esEs13(wzz401, wzz3001, app(ty_Ratio, eb)) → new_esEs17(wzz401, wzz3001, eb)
new_esEs21(wzz400, wzz3000, app(app(app(ty_@3, baa), bab), bac)) → new_esEs7(wzz400, wzz3000, baa, bab, bac)
new_primCmpNat1(Succ(wzz31000), Succ(wzz32000)) → new_primCmpNat1(wzz31000, wzz32000)
new_compare28(wzz31000, wzz32000, bae) → new_compare29(wzz31000, wzz32000, new_esEs5(wzz31000, wzz32000, bae), bae)
new_esEs5(Just(wzz400), Just(wzz3000), app(ty_Maybe, dcg)) → new_esEs5(wzz400, wzz3000, dcg)
new_ltEs14(Right(wzz31000), Right(wzz32000), bfa, ty_Bool) → new_ltEs4(wzz31000, wzz32000)
new_ltEs4(False, True) → True
new_ltEs10(EQ, GT) → True
new_esEs4(Right(wzz400), Right(wzz3000), ccg, ty_Integer) → new_esEs20(wzz400, wzz3000)
new_compare19(Char(wzz31000), Char(wzz32000)) → new_primCmpNat1(wzz31000, wzz32000)
new_esEs30(wzz20, wzz15, ty_Float) → new_esEs19(wzz20, wzz15)
new_ltEs15(Just(wzz31000), Just(wzz32000), ty_@0) → new_ltEs17(wzz31000, wzz32000)
new_esEs29(wzz40, wzz300, app(app(app(ty_@3, ca), cb), cc)) → new_esEs7(wzz40, wzz300, ca, cb, cc)
new_ltEs15(Just(wzz31000), Just(wzz32000), ty_Double) → new_ltEs7(wzz31000, wzz32000)
new_ltEs14(Left(wzz31000), Left(wzz32000), ty_Float, bfb) → new_ltEs16(wzz31000, wzz32000)
new_lt20(wzz31000, wzz32000, app(ty_Maybe, bae)) → new_lt15(wzz31000, wzz32000, bae)
new_lt16(wzz310, wzz320) → new_esEs11(new_compare14(wzz310, wzz320), LT)
new_ltEs15(Just(wzz31000), Just(wzz32000), ty_Integer) → new_ltEs18(wzz31000, wzz32000)
new_compare26(wzz31000, wzz32000, False, gg, gh) → new_compare110(wzz31000, wzz32000, new_ltEs14(wzz31000, wzz32000, gg, gh), gg, gh)
new_lt20(wzz31000, wzz32000, ty_Float) → new_lt17(wzz31000, wzz32000)
new_esEs4(Left(wzz400), Left(wzz3000), ty_Double, cbf) → new_esEs8(wzz400, wzz3000)
new_esEs14(wzz402, wzz3002, app(ty_Ratio, fd)) → new_esEs17(wzz402, wzz3002, fd)
new_ltEs19(wzz3100, wzz3200, ty_Float) → new_ltEs16(wzz3100, wzz3200)
new_esEs26(wzz401, wzz3001, ty_Ordering) → new_esEs11(wzz401, wzz3001)
new_ltEs4(True, True) → True
new_pePe(False, wzz150) → wzz150
new_esEs25(wzz400, wzz3000, app(app(ty_Either, cfh), cga)) → new_esEs4(wzz400, wzz3000, cfh, cga)
new_esEs15(False, True) → False
new_esEs15(True, False) → False
new_lt20(wzz31000, wzz32000, ty_Bool) → new_lt11(wzz31000, wzz32000)
new_ltEs14(Right(wzz31000), Right(wzz32000), bfa, ty_Float) → new_ltEs16(wzz31000, wzz32000)
new_esEs22(wzz31000, wzz32000, app(app(ty_Either, bbd), bbe)) → new_esEs4(wzz31000, wzz32000, bbd, bbe)
new_lt13(wzz31001, wzz32001, ty_Double) → new_lt14(wzz31001, wzz32001)
new_esEs29(wzz40, wzz300, ty_Char) → new_esEs18(wzz40, wzz300)
new_esEs23(wzz31001, wzz32001, ty_Double) → new_esEs8(wzz31001, wzz32001)
new_esEs17(:%(wzz400, wzz401), :%(wzz3000, wzz3001), ceb) → new_asAs(new_esEs27(wzz400, wzz3000, ceb), new_esEs28(wzz401, wzz3001, ceb))
new_esEs26(wzz401, wzz3001, app(ty_Ratio, che)) → new_esEs17(wzz401, wzz3001, che)
new_esEs13(wzz401, wzz3001, ty_Ordering) → new_esEs11(wzz401, wzz3001)
new_esEs30(wzz20, wzz15, ty_Bool) → new_esEs15(wzz20, wzz15)
new_compare31(wzz31000, wzz32000, ty_@0) → new_compare13(wzz31000, wzz32000)
new_ltEs12(wzz31002, wzz32002, app(ty_Ratio, bdf)) → new_ltEs6(wzz31002, wzz32002, bdf)
new_ltEs20(wzz31001, wzz32001, app(ty_[], bfg)) → new_ltEs13(wzz31001, wzz32001, bfg)
new_esEs14(wzz402, wzz3002, app(app(ty_@2, ff), fg)) → new_esEs6(wzz402, wzz3002, ff, fg)
new_compare111(wzz31000, wzz32000, False) → GT
new_compare111(wzz31000, wzz32000, True) → LT
new_compare31(wzz31000, wzz32000, ty_Int) → new_compare14(wzz31000, wzz32000)
new_ltEs5(@2(wzz31000, wzz31001), @2(wzz32000, wzz32001), bfd, bfe) → new_pePe(new_lt20(wzz31000, wzz32000, bfd), new_asAs(new_esEs24(wzz31000, wzz32000, bfd), new_ltEs20(wzz31001, wzz32001, bfe)))
new_esEs12(wzz400, wzz3000, app(ty_[], cf)) → new_esEs16(wzz400, wzz3000, cf)
new_ltEs15(Just(wzz31000), Just(wzz32000), app(ty_Maybe, dah)) → new_ltEs15(wzz31000, wzz32000, dah)
new_ltEs12(wzz31002, wzz32002, app(app(ty_Either, bdh), bea)) → new_ltEs14(wzz31002, wzz32002, bdh, bea)
new_esEs22(wzz31000, wzz32000, ty_Integer) → new_esEs20(wzz31000, wzz32000)
new_esEs23(wzz31001, wzz32001, app(app(app(ty_@3, bdc), bdd), bde)) → new_esEs7(wzz31001, wzz32001, bdc, bdd, bde)
new_esEs23(wzz31001, wzz32001, ty_Integer) → new_esEs20(wzz31001, wzz32001)
new_esEs25(wzz400, wzz3000, app(app(ty_@2, cgd), cge)) → new_esEs6(wzz400, wzz3000, cgd, cge)
new_esEs11(GT, GT) → True
new_esEs23(wzz31001, wzz32001, ty_Char) → new_esEs18(wzz31001, wzz32001)
new_esEs29(wzz40, wzz300, ty_Ordering) → new_esEs11(wzz40, wzz300)
new_esEs24(wzz31000, wzz32000, app(app(ty_@2, bd), be)) → new_esEs6(wzz31000, wzz32000, bd, be)
new_pePe(True, wzz150) → True
new_primEqNat0(Zero, Zero) → True
new_ltEs19(wzz3100, wzz3200, ty_Integer) → new_ltEs18(wzz3100, wzz3200)
new_esEs13(wzz401, wzz3001, app(ty_Maybe, eh)) → new_esEs5(wzz401, wzz3001, eh)
new_primMulNat0(Succ(wzz40100), Succ(wzz300100)) → new_primPlusNat1(new_primMulNat0(wzz40100, Succ(wzz300100)), wzz300100)
new_lt12(wzz31000, wzz32000, ty_Char) → new_lt18(wzz31000, wzz32000)
new_ltEs12(wzz31002, wzz32002, ty_@0) → new_ltEs17(wzz31002, wzz32002)
new_compare29(Nothing, Just(wzz3200), False, beh) → LT
new_compare31(wzz31000, wzz32000, ty_Bool) → new_compare30(wzz31000, wzz32000)
new_ltEs14(Right(wzz31000), Right(wzz32000), bfa, app(ty_Maybe, caf)) → new_ltEs15(wzz31000, wzz32000, caf)
new_esEs26(wzz401, wzz3001, ty_Bool) → new_esEs15(wzz401, wzz3001)
new_esEs24(wzz31000, wzz32000, app(ty_Ratio, ge)) → new_esEs17(wzz31000, wzz32000, ge)
new_esEs13(wzz401, wzz3001, ty_@0) → new_esEs10(wzz401, wzz3001)
new_compare110(wzz31000, wzz32000, False, gg, gh) → GT
new_compare(:(wzz31000, wzz31001), :(wzz32000, wzz32001), gd) → new_primCompAux1(wzz31000, wzz32000, new_compare(wzz31001, wzz32001, gd), gd)
new_sr(wzz401, wzz3001) → new_primMulInt(wzz401, wzz3001)
new_ltEs15(Just(wzz31000), Just(wzz32000), ty_Char) → new_ltEs8(wzz31000, wzz32000)
new_compare210(wzz31000, wzz32000, False, bf, bg, bh) → new_compare12(wzz31000, wzz32000, new_ltEs11(wzz31000, wzz32000, bf, bg, bh), bf, bg, bh)
new_compare12(wzz31000, wzz32000, True, bf, bg, bh) → LT
new_primCmpNat1(Zero, Zero) → EQ
new_esEs5(Just(wzz400), Just(wzz3000), ty_Char) → new_esEs18(wzz400, wzz3000)
new_ltEs12(wzz31002, wzz32002, app(app(ty_@2, bec), bed)) → new_ltEs5(wzz31002, wzz32002, bec, bed)
new_lt4(wzz31000, wzz32000) → new_esEs11(new_compare5(wzz31000, wzz32000), LT)
new_esEs4(Left(wzz400), Left(wzz3000), ty_Int, cbf) → new_esEs9(wzz400, wzz3000)
new_esEs13(wzz401, wzz3001, ty_Int) → new_esEs9(wzz401, wzz3001)
new_primCmpInt(Neg(Zero), Neg(Succ(wzz3200))) → new_primCmpNat0(wzz3200, Zero)
new_esEs25(wzz400, wzz3000, ty_@0) → new_esEs10(wzz400, wzz3000)
new_compare7(wzz31000, wzz32000, bf, bg, bh) → new_compare210(wzz31000, wzz32000, new_esEs7(wzz31000, wzz32000, bf, bg, bh), bf, bg, bh)
new_lt13(wzz31001, wzz32001, ty_Ordering) → new_lt4(wzz31001, wzz32001)
new_esEs19(Float(wzz400, wzz401), Float(wzz3000, wzz3001)) → new_esEs9(new_sr(wzz400, wzz3000), new_sr(wzz401, wzz3001))
new_ltEs20(wzz31001, wzz32001, ty_Float) → new_ltEs16(wzz31001, wzz32001)
new_ltEs15(Just(wzz31000), Just(wzz32000), ty_Int) → new_ltEs9(wzz31000, wzz32000)
new_primCmpNat1(Succ(wzz31000), Zero) → GT
new_esEs4(Right(wzz400), Right(wzz3000), ccg, app(app(ty_Either, cch), cda)) → new_esEs4(wzz400, wzz3000, cch, cda)
new_ltEs12(wzz31002, wzz32002, ty_Ordering) → new_ltEs10(wzz31002, wzz32002)
new_primEqInt(Neg(Succ(wzz4000)), Neg(Succ(wzz30000))) → new_primEqNat0(wzz4000, wzz30000)
new_compare25(wzz31000, wzz32000, True) → EQ
new_esEs15(True, True) → True
new_lt13(wzz31001, wzz32001, app(ty_[], bce)) → new_lt10(wzz31001, wzz32001, bce)
new_ltEs15(Just(wzz31000), Just(wzz32000), ty_Float) → new_ltEs16(wzz31000, wzz32000)
new_compare16(wzz118, wzz119, True, ha) → LT
new_esEs4(Left(wzz400), Left(wzz3000), app(app(ty_Either, cbd), cbe), cbf) → new_esEs4(wzz400, wzz3000, cbd, cbe)
new_compare31(wzz31000, wzz32000, app(app(ty_Either, ddb), ddc)) → new_compare15(wzz31000, wzz32000, ddb, ddc)
new_esEs24(wzz31000, wzz32000, ty_Integer) → new_esEs20(wzz31000, wzz32000)
new_lt12(wzz31000, wzz32000, app(ty_Ratio, bbb)) → new_lt7(wzz31000, wzz32000, bbb)
new_ltEs14(Right(wzz31000), Right(wzz32000), bfa, ty_@0) → new_ltEs17(wzz31000, wzz32000)
new_esEs4(Right(wzz400), Right(wzz3000), ccg, ty_Ordering) → new_esEs11(wzz400, wzz3000)
new_lt14(wzz31000, wzz32000) → new_esEs11(new_compare18(wzz31000, wzz32000), LT)
new_esEs26(wzz401, wzz3001, app(app(app(ty_@3, chh), daa), dab)) → new_esEs7(wzz401, wzz3001, chh, daa, dab)
new_ltEs14(Right(wzz31000), Left(wzz32000), bfa, bfb) → False
new_esEs25(wzz400, wzz3000, ty_Char) → new_esEs18(wzz400, wzz3000)
new_compare29(Just(wzz3100), Nothing, False, beh) → GT
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_ltEs12(wzz31002, wzz32002, app(ty_[], bdg)) → new_ltEs13(wzz31002, wzz32002, bdg)
new_esEs21(wzz400, wzz3000, ty_Double) → new_esEs8(wzz400, wzz3000)
new_ltEs11(@3(wzz31000, wzz31001, wzz31002), @3(wzz32000, wzz32001, wzz32002), bag, bah, bba) → new_pePe(new_lt12(wzz31000, wzz32000, bag), new_asAs(new_esEs22(wzz31000, wzz32000, bag), new_pePe(new_lt13(wzz31001, wzz32001, bah), new_asAs(new_esEs23(wzz31001, wzz32001, bah), new_ltEs12(wzz31002, wzz32002, bba)))))
new_compare15(wzz31000, wzz32000, gg, gh) → new_compare26(wzz31000, wzz32000, new_esEs4(wzz31000, wzz32000, gg, gh), gg, gh)
new_esEs4(Left(wzz400), Left(wzz3000), ty_Char, cbf) → new_esEs18(wzz400, wzz3000)
new_esEs30(wzz20, wzz15, app(app(app(ty_@3, cfd), cfe), cff)) → new_esEs7(wzz20, wzz15, cfd, cfe, cff)
new_primEqInt(Neg(Zero), Neg(Succ(wzz30000))) → False
new_primEqInt(Neg(Succ(wzz4000)), Neg(Zero)) → False
new_esEs4(Right(wzz400), Right(wzz3000), ccg, app(ty_[], cdb)) → new_esEs16(wzz400, wzz3000, cdb)
new_primCompAux0(wzz165, GT) → GT
new_compare26(wzz31000, wzz32000, True, gg, gh) → EQ
new_ltEs9(wzz3100, wzz3200) → new_fsEs(new_compare14(wzz3100, wzz3200))
new_esEs4(Right(wzz400), Right(wzz3000), ccg, ty_Double) → new_esEs8(wzz400, wzz3000)
new_compare24(wzz31000, wzz32000, True, bd, be) → EQ
new_esEs21(wzz400, wzz3000, app(app(ty_Either, hc), hd)) → new_esEs4(wzz400, wzz3000, hc, hd)
new_ltEs15(Just(wzz31000), Just(wzz32000), app(app(app(ty_@3, dbc), dbd), dbe)) → new_ltEs11(wzz31000, wzz32000, dbc, dbd, dbe)
new_esEs29(wzz40, wzz300, app(ty_[], hb)) → new_esEs16(wzz40, wzz300, hb)
new_ltEs12(wzz31002, wzz32002, ty_Bool) → new_ltEs4(wzz31002, wzz32002)
new_esEs4(Right(wzz400), Right(wzz3000), ccg, ty_Bool) → new_esEs15(wzz400, wzz3000)
new_compare([], [], gd) → EQ
new_compare14(wzz31, wzz32) → new_primCmpInt(wzz31, wzz32)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_esEs21(wzz400, wzz3000, app(ty_Ratio, hf)) → new_esEs17(wzz400, wzz3000, hf)
new_esEs5(Just(wzz400), Just(wzz3000), ty_@0) → new_esEs10(wzz400, wzz3000)
new_ltEs20(wzz31001, wzz32001, app(app(ty_@2, bgc), bgd)) → new_ltEs5(wzz31001, wzz32001, bgc, bgd)
new_ltEs19(wzz3100, wzz3200, ty_Double) → new_ltEs7(wzz3100, wzz3200)
new_ltEs14(Left(wzz31000), Left(wzz32000), ty_Int, bfb) → new_ltEs9(wzz31000, wzz32000)
new_esEs4(Left(wzz400), Left(wzz3000), ty_Float, cbf) → new_esEs19(wzz400, wzz3000)
new_esEs22(wzz31000, wzz32000, ty_Double) → new_esEs8(wzz31000, wzz32000)
new_primEqInt(Pos(Succ(wzz4000)), Pos(Succ(wzz30000))) → new_primEqNat0(wzz4000, wzz30000)
new_compare5(wzz31000, wzz32000) → new_compare27(wzz31000, wzz32000, new_esEs11(wzz31000, wzz32000))
new_lt9(wzz31000, wzz32000, gg, gh) → new_esEs11(new_compare15(wzz31000, wzz32000, gg, gh), LT)
new_esEs25(wzz400, wzz3000, app(ty_Maybe, cha)) → new_esEs5(wzz400, wzz3000, cha)
new_ltEs12(wzz31002, wzz32002, app(ty_Maybe, beb)) → new_ltEs15(wzz31002, wzz32002, beb)
new_esEs12(wzz400, wzz3000, ty_Double) → new_esEs8(wzz400, wzz3000)
new_esEs29(wzz40, wzz300, app(ty_Maybe, cee)) → new_esEs5(wzz40, wzz300, cee)
new_esEs30(wzz20, wzz15, ty_Integer) → new_esEs20(wzz20, wzz15)
new_esEs16(:(wzz400, wzz401), :(wzz3000, wzz3001), hb) → new_asAs(new_esEs21(wzz400, wzz3000, hb), new_esEs16(wzz401, wzz3001, hb))
new_esEs29(wzz40, wzz300, ty_Double) → new_esEs8(wzz40, wzz300)
new_esEs25(wzz400, wzz3000, ty_Int) → new_esEs9(wzz400, wzz3000)
new_lt13(wzz31001, wzz32001, app(app(ty_Either, bcf), bcg)) → new_lt9(wzz31001, wzz32001, bcf, bcg)
new_ltEs10(GT, EQ) → False
new_primEqNat0(Succ(wzz4000), Succ(wzz30000)) → new_primEqNat0(wzz4000, wzz30000)
new_esEs12(wzz400, wzz3000, ty_@0) → new_esEs10(wzz400, wzz3000)
new_compare31(wzz31000, wzz32000, ty_Float) → new_compare17(wzz31000, wzz32000)
new_lt13(wzz31001, wzz32001, ty_Integer) → new_lt6(wzz31001, wzz32001)
new_esEs4(Left(wzz400), Left(wzz3000), app(app(app(ty_@3, ccc), ccd), cce), cbf) → new_esEs7(wzz400, wzz3000, ccc, ccd, cce)
new_esEs14(wzz402, wzz3002, app(ty_Maybe, gc)) → new_esEs5(wzz402, wzz3002, gc)
new_lt12(wzz31000, wzz32000, ty_Ordering) → new_lt4(wzz31000, wzz32000)
new_compare16(wzz118, wzz119, False, ha) → GT
new_esEs21(wzz400, wzz3000, ty_Float) → new_esEs19(wzz400, wzz3000)
new_ltEs14(Left(wzz31000), Left(wzz32000), ty_Ordering, bfb) → new_ltEs10(wzz31000, wzz32000)
new_esEs23(wzz31001, wzz32001, ty_Bool) → new_esEs15(wzz31001, wzz32001)
new_esEs12(wzz400, wzz3000, app(app(ty_Either, cd), ce)) → new_esEs4(wzz400, wzz3000, cd, ce)
new_lt13(wzz31001, wzz32001, ty_Int) → new_lt16(wzz31001, wzz32001)
new_primEqInt(Pos(Zero), Pos(Succ(wzz30000))) → False
new_primEqInt(Pos(Succ(wzz4000)), Pos(Zero)) → False
new_esEs25(wzz400, wzz3000, ty_Integer) → new_esEs20(wzz400, wzz3000)
new_esEs22(wzz31000, wzz32000, ty_Ordering) → new_esEs11(wzz31000, wzz32000)
new_esEs21(wzz400, wzz3000, ty_Bool) → new_esEs15(wzz400, wzz3000)
new_lt20(wzz31000, wzz32000, ty_Char) → new_lt18(wzz31000, wzz32000)
new_esEs12(wzz400, wzz3000, app(app(app(ty_@3, dc), dd), de)) → new_esEs7(wzz400, wzz3000, dc, dd, de)
new_primPlusNat0(Succ(wzz26200), Zero) → Succ(wzz26200)
new_primPlusNat0(Zero, Succ(wzz8700)) → Succ(wzz8700)
new_lt13(wzz31001, wzz32001, ty_@0) → new_lt19(wzz31001, wzz32001)
new_esEs24(wzz31000, wzz32000, ty_@0) → new_esEs10(wzz31000, wzz32000)
new_esEs30(wzz20, wzz15, ty_Double) → new_esEs8(wzz20, wzz15)
new_esEs28(wzz401, wzz3001, ty_Integer) → new_esEs20(wzz401, wzz3001)
new_esEs4(Right(wzz400), Right(wzz3000), ccg, ty_@0) → new_esEs10(wzz400, wzz3000)
new_ltEs14(Left(wzz31000), Left(wzz32000), ty_Char, bfb) → new_ltEs8(wzz31000, wzz32000)
new_ltEs10(LT, EQ) → True
new_primCmpInt(Neg(Zero), Pos(Succ(wzz3200))) → LT
new_ltEs15(Just(wzz31000), Just(wzz32000), ty_Ordering) → new_ltEs10(wzz31000, wzz32000)
new_esEs4(Left(wzz400), Left(wzz3000), ty_Ordering, cbf) → new_esEs11(wzz400, wzz3000)
new_compare11(wzz31000, wzz32000, True, bd, be) → LT
new_compare210(wzz31000, wzz32000, True, bf, bg, bh) → EQ
new_compare31(wzz31000, wzz32000, app(ty_Ratio, dch)) → new_compare9(wzz31000, wzz32000, dch)
new_sr0(Integer(wzz310000), Integer(wzz320010)) → Integer(new_primMulInt(wzz310000, wzz320010))
new_primEqInt(Neg(Succ(wzz4000)), Pos(wzz3000)) → False
new_primEqInt(Pos(Succ(wzz4000)), Neg(wzz3000)) → False
new_compare25(wzz31000, wzz32000, False) → new_compare10(wzz31000, wzz32000, new_ltEs4(wzz31000, wzz32000))
new_esEs13(wzz401, wzz3001, ty_Bool) → new_esEs15(wzz401, wzz3001)
new_ltEs7(wzz3100, wzz3200) → new_fsEs(new_compare18(wzz3100, wzz3200))
new_ltEs14(Left(wzz31000), Left(wzz32000), app(ty_[], bha), bfb) → new_ltEs13(wzz31000, wzz32000, bha)
new_ltEs10(GT, GT) → True
new_esEs14(wzz402, wzz3002, app(ty_[], fc)) → new_esEs16(wzz402, wzz3002, fc)
new_esEs22(wzz31000, wzz32000, app(app(ty_@2, bbg), bbh)) → new_esEs6(wzz31000, wzz32000, bbg, bbh)
new_ltEs20(wzz31001, wzz32001, ty_Integer) → new_ltEs18(wzz31001, wzz32001)
new_esEs26(wzz401, wzz3001, ty_Int) → new_esEs9(wzz401, wzz3001)
new_ltEs20(wzz31001, wzz32001, app(ty_Maybe, bgb)) → new_ltEs15(wzz31001, wzz32001, bgb)
new_lt13(wzz31001, wzz32001, app(ty_Ratio, bcd)) → new_lt7(wzz31001, wzz32001, bcd)
new_esEs24(wzz31000, wzz32000, ty_Ordering) → new_esEs11(wzz31000, wzz32000)
new_primEqInt(Neg(Zero), Pos(Succ(wzz30000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(wzz30000))) → False
new_primCmpNat2(Succ(wzz3200), wzz3100) → new_primCmpNat1(wzz3200, wzz3100)
new_ltEs14(Right(wzz31000), Right(wzz32000), bfa, ty_Double) → new_ltEs7(wzz31000, wzz32000)
new_esEs30(wzz20, wzz15, app(ty_Ratio, cfa)) → new_esEs17(wzz20, wzz15, cfa)
new_lt12(wzz31000, wzz32000, app(ty_[], bbc)) → new_lt10(wzz31000, wzz32000, bbc)
new_esEs21(wzz400, wzz3000, ty_Ordering) → new_esEs11(wzz400, wzz3000)
new_lt20(wzz31000, wzz32000, ty_Ordering) → new_lt4(wzz31000, wzz32000)
new_lt8(wzz31000, wzz32000, bd, be) → new_esEs11(new_compare6(wzz31000, wzz32000, bd, be), LT)
new_esEs14(wzz402, wzz3002, ty_Double) → new_esEs8(wzz402, wzz3002)
new_esEs5(Just(wzz400), Just(wzz3000), ty_Ordering) → new_esEs11(wzz400, wzz3000)
new_compare31(wzz31000, wzz32000, ty_Ordering) → new_compare5(wzz31000, wzz32000)
new_lt20(wzz31000, wzz32000, ty_Integer) → new_lt6(wzz31000, wzz32000)
new_esEs21(wzz400, wzz3000, ty_Char) → new_esEs18(wzz400, wzz3000)
new_primCompAux0(wzz165, LT) → LT
new_esEs30(wzz20, wzz15, ty_@0) → new_esEs10(wzz20, wzz15)
new_ltEs19(wzz3100, wzz3200, ty_Char) → new_ltEs8(wzz3100, wzz3200)
new_lt13(wzz31001, wzz32001, ty_Bool) → new_lt11(wzz31001, wzz32001)
new_ltEs14(Right(wzz31000), Right(wzz32000), bfa, ty_Integer) → new_ltEs18(wzz31000, wzz32000)
new_not(False) → True
new_esEs24(wzz31000, wzz32000, ty_Float) → new_esEs19(wzz31000, wzz32000)
new_esEs4(Right(wzz400), Right(wzz3000), ccg, app(ty_Ratio, cdc)) → new_esEs17(wzz400, wzz3000, cdc)
new_esEs23(wzz31001, wzz32001, app(app(ty_@2, bda), bdb)) → new_esEs6(wzz31001, wzz32001, bda, bdb)
new_compare12(wzz31000, wzz32000, False, bf, bg, bh) → GT
new_esEs12(wzz400, wzz3000, ty_Integer) → new_esEs20(wzz400, wzz3000)
new_esEs11(LT, GT) → False
new_esEs11(GT, LT) → False
new_esEs30(wzz20, wzz15, app(app(ty_Either, cef), ceg)) → new_esEs4(wzz20, wzz15, cef, ceg)
new_compare31(wzz31000, wzz32000, app(ty_Maybe, ddd)) → new_compare28(wzz31000, wzz32000, ddd)
new_ltEs14(Right(wzz31000), Right(wzz32000), bfa, app(ty_Ratio, cab)) → new_ltEs6(wzz31000, wzz32000, cab)
new_compare27(wzz31000, wzz32000, False) → new_compare111(wzz31000, wzz32000, new_ltEs10(wzz31000, wzz32000))
new_lt20(wzz31000, wzz32000, app(ty_[], baf)) → new_lt10(wzz31000, wzz32000, baf)
new_esEs13(wzz401, wzz3001, app(ty_[], ea)) → new_esEs16(wzz401, wzz3001, ea)
new_esEs12(wzz400, wzz3000, ty_Float) → new_esEs19(wzz400, wzz3000)
new_esEs11(LT, EQ) → False
new_esEs11(EQ, LT) → False
new_esEs24(wzz31000, wzz32000, app(ty_Maybe, bae)) → new_esEs5(wzz31000, wzz32000, bae)
new_esEs4(Right(wzz400), Right(wzz3000), ccg, app(app(ty_@2, cdd), cde)) → new_esEs6(wzz400, wzz3000, cdd, cde)
new_esEs23(wzz31001, wzz32001, ty_@0) → new_esEs10(wzz31001, wzz32001)
new_esEs14(wzz402, wzz3002, ty_Char) → new_esEs18(wzz402, wzz3002)
new_esEs14(wzz402, wzz3002, ty_@0) → new_esEs10(wzz402, wzz3002)
new_lt12(wzz31000, wzz32000, ty_Double) → new_lt14(wzz31000, wzz32000)
new_ltEs20(wzz31001, wzz32001, ty_@0) → new_ltEs17(wzz31001, wzz32001)
new_compare11(wzz31000, wzz32000, False, bd, be) → GT
new_ltEs17(wzz3100, wzz3200) → new_fsEs(new_compare13(wzz3100, wzz3200))
new_esEs22(wzz31000, wzz32000, app(app(app(ty_@3, bca), bcb), bcc)) → new_esEs7(wzz31000, wzz32000, bca, bcb, bcc)
new_esEs13(wzz401, wzz3001, app(app(ty_Either, dg), dh)) → new_esEs4(wzz401, wzz3001, dg, dh)
new_primCmpInt(Pos(Succ(wzz3100)), Neg(wzz320)) → GT
new_esEs22(wzz31000, wzz32000, ty_Char) → new_esEs18(wzz31000, wzz32000)
new_ltEs19(wzz3100, wzz3200, ty_Int) → new_ltEs9(wzz3100, wzz3200)
new_lt12(wzz31000, wzz32000, app(app(app(ty_@3, bca), bcb), bcc)) → new_lt5(wzz31000, wzz32000, bca, bcb, bcc)
new_ltEs18(wzz3100, wzz3200) → new_fsEs(new_compare8(wzz3100, wzz3200))
new_esEs22(wzz31000, wzz32000, app(ty_[], bbc)) → new_esEs16(wzz31000, wzz32000, bbc)
new_esEs14(wzz402, wzz3002, app(app(ty_Either, fa), fb)) → new_esEs4(wzz402, wzz3002, fa, fb)
new_primMulInt(Pos(wzz4010), Pos(wzz30010)) → Pos(new_primMulNat0(wzz4010, wzz30010))
new_esEs26(wzz401, wzz3001, ty_@0) → new_esEs10(wzz401, wzz3001)
new_esEs4(Left(wzz400), Left(wzz3000), ty_Bool, cbf) → new_esEs15(wzz400, wzz3000)
new_esEs30(wzz20, wzz15, ty_Ordering) → new_esEs11(wzz20, wzz15)
new_esEs23(wzz31001, wzz32001, app(app(ty_Either, bcf), bcg)) → new_esEs4(wzz31001, wzz32001, bcf, bcg)
new_esEs14(wzz402, wzz3002, ty_Bool) → new_esEs15(wzz402, wzz3002)
new_primMulInt(Neg(wzz4010), Neg(wzz30010)) → Pos(new_primMulNat0(wzz4010, wzz30010))
new_ltEs19(wzz3100, wzz3200, app(ty_Ratio, gf)) → new_ltEs6(wzz3100, wzz3200, gf)
new_lt6(wzz31000, wzz32000) → new_esEs11(new_compare8(wzz31000, wzz32000), LT)
new_esEs24(wzz31000, wzz32000, ty_Bool) → new_esEs15(wzz31000, wzz32000)
new_esEs29(wzz40, wzz300, app(app(ty_@2, cec), ced)) → new_esEs6(wzz40, wzz300, cec, ced)
new_primEqNat0(Zero, Succ(wzz30000)) → False
new_primEqNat0(Succ(wzz4000), Zero) → False
new_esEs29(wzz40, wzz300, app(ty_Ratio, ceb)) → new_esEs17(wzz40, wzz300, ceb)
new_esEs21(wzz400, wzz3000, ty_@0) → new_esEs10(wzz400, wzz3000)
new_esEs21(wzz400, wzz3000, ty_Int) → new_esEs9(wzz400, wzz3000)
new_primPlusNat0(Zero, Zero) → Zero
new_esEs25(wzz400, wzz3000, app(ty_Ratio, cgc)) → new_esEs17(wzz400, wzz3000, cgc)
new_lt12(wzz31000, wzz32000, ty_Bool) → new_lt11(wzz31000, wzz32000)
new_compare31(wzz31000, wzz32000, ty_Integer) → new_compare8(wzz31000, wzz32000)
new_lt12(wzz31000, wzz32000, ty_Int) → new_lt16(wzz31000, wzz32000)
new_ltEs14(Left(wzz31000), Left(wzz32000), app(app(ty_@2, bhe), bhf), bfb) → new_ltEs5(wzz31000, wzz32000, bhe, bhf)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_compare9(:%(wzz31000, wzz31001), :%(wzz32000, wzz32001), ty_Integer) → new_compare8(new_sr0(wzz31000, wzz32001), new_sr0(wzz32000, wzz31001))
new_esEs24(wzz31000, wzz32000, app(app(ty_Either, gg), gh)) → new_esEs4(wzz31000, wzz32000, gg, gh)
new_compare31(wzz31000, wzz32000, ty_Double) → new_compare18(wzz31000, wzz32000)
new_esEs5(Just(wzz400), Just(wzz3000), ty_Float) → new_esEs19(wzz400, wzz3000)
new_primCmpInt(Pos(Succ(wzz3100)), Pos(wzz320)) → new_primCmpNat0(wzz3100, wzz320)
new_ltEs13(wzz3100, wzz3200, gd) → new_fsEs(new_compare(wzz3100, wzz3200, gd))
new_ltEs12(wzz31002, wzz32002, app(app(app(ty_@3, bee), bef), beg)) → new_ltEs11(wzz31002, wzz32002, bee, bef, beg)
new_fsEs(wzz135) → new_not(new_esEs11(wzz135, GT))
new_esEs29(wzz40, wzz300, ty_Integer) → new_esEs20(wzz40, wzz300)
new_esEs22(wzz31000, wzz32000, ty_Int) → new_esEs9(wzz31000, wzz32000)
new_ltEs15(Just(wzz31000), Nothing, bfc) → False
new_esEs16([], :(wzz3000, wzz3001), hb) → False
new_esEs16(:(wzz400, wzz401), [], hb) → False
new_primCmpNat0(wzz3100, Zero) → GT
new_esEs5(Just(wzz400), Just(wzz3000), ty_Integer) → new_esEs20(wzz400, wzz3000)
new_ltEs4(True, False) → False
new_esEs12(wzz400, wzz3000, ty_Int) → new_esEs9(wzz400, wzz3000)
new_ltEs19(wzz3100, wzz3200, ty_@0) → new_ltEs17(wzz3100, wzz3200)
new_lt13(wzz31001, wzz32001, ty_Char) → new_lt18(wzz31001, wzz32001)
new_esEs26(wzz401, wzz3001, app(ty_Maybe, dac)) → new_esEs5(wzz401, wzz3001, dac)
new_esEs22(wzz31000, wzz32000, ty_@0) → new_esEs10(wzz31000, wzz32000)
new_lt13(wzz31001, wzz32001, app(ty_Maybe, bch)) → new_lt15(wzz31001, wzz32001, bch)
new_ltEs15(Just(wzz31000), Just(wzz32000), app(app(ty_@2, dba), dbb)) → new_ltEs5(wzz31000, wzz32000, dba, dbb)
new_ltEs14(Right(wzz31000), Right(wzz32000), bfa, app(app(ty_@2, cag), cah)) → new_ltEs5(wzz31000, wzz32000, cag, cah)
new_esEs24(wzz31000, wzz32000, ty_Int) → new_esEs9(wzz31000, wzz32000)
new_ltEs12(wzz31002, wzz32002, ty_Integer) → new_ltEs18(wzz31002, wzz32002)
new_esEs23(wzz31001, wzz32001, app(ty_Ratio, bcd)) → new_esEs17(wzz31001, wzz32001, bcd)
new_primCmpInt(Pos(Zero), Neg(Succ(wzz3200))) → GT
new_esEs30(wzz20, wzz15, ty_Char) → new_esEs18(wzz20, wzz15)
new_ltEs20(wzz31001, wzz32001, ty_Char) → new_ltEs8(wzz31001, wzz32001)
new_lt5(wzz31000, wzz32000, bf, bg, bh) → new_esEs11(new_compare7(wzz31000, wzz32000, bf, bg, bh), LT)
new_esEs12(wzz400, wzz3000, ty_Char) → new_esEs18(wzz400, wzz3000)
new_compare31(wzz31000, wzz32000, app(ty_[], dda)) → new_compare(wzz31000, wzz32000, dda)
new_esEs27(wzz400, wzz3000, ty_Int) → new_esEs9(wzz400, wzz3000)
new_esEs13(wzz401, wzz3001, app(app(ty_@2, ec), ed)) → new_esEs6(wzz401, wzz3001, ec, ed)
new_ltEs12(wzz31002, wzz32002, ty_Double) → new_ltEs7(wzz31002, wzz32002)
new_ltEs16(wzz3100, wzz3200) → new_fsEs(new_compare17(wzz3100, wzz3200))
new_esEs30(wzz20, wzz15, app(ty_[], ceh)) → new_esEs16(wzz20, wzz15, ceh)
new_compare29(Nothing, Nothing, False, beh) → LT
new_esEs4(Left(wzz400), Left(wzz3000), ty_Integer, cbf) → new_esEs20(wzz400, wzz3000)
new_ltEs14(Left(wzz31000), Left(wzz32000), ty_Integer, bfb) → new_ltEs18(wzz31000, wzz32000)
new_esEs10(@0, @0) → True
new_esEs24(wzz31000, wzz32000, app(app(app(ty_@3, bf), bg), bh)) → new_esEs7(wzz31000, wzz32000, bf, bg, bh)
new_compare29(wzz310, wzz320, True, beh) → EQ
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_lt10(wzz31000, wzz32000, baf) → new_esEs11(new_compare(wzz31000, wzz32000, baf), LT)
new_esEs13(wzz401, wzz3001, ty_Float) → new_esEs19(wzz401, wzz3001)
new_primCompAux1(wzz31000, wzz32000, wzz151, gd) → new_primCompAux0(wzz151, new_compare31(wzz31000, wzz32000, gd))
new_esEs5(Just(wzz400), Just(wzz3000), app(ty_[], dbh)) → new_esEs16(wzz400, wzz3000, dbh)
new_ltEs14(Left(wzz31000), Right(wzz32000), bfa, bfb) → True
new_ltEs6(wzz3100, wzz3200, gf) → new_fsEs(new_compare9(wzz3100, wzz3200, gf))
new_esEs12(wzz400, wzz3000, ty_Ordering) → new_esEs11(wzz400, wzz3000)
new_esEs29(wzz40, wzz300, ty_Bool) → new_esEs15(wzz40, wzz300)
new_ltEs20(wzz31001, wzz32001, app(app(ty_Either, bfh), bga)) → new_ltEs14(wzz31001, wzz32001, bfh, bga)
new_asAs(False, wzz125) → False
new_esEs4(Left(wzz400), Left(wzz3000), ty_@0, cbf) → new_esEs10(wzz400, wzz3000)
new_ltEs19(wzz3100, wzz3200, app(app(ty_Either, bfa), bfb)) → new_ltEs14(wzz3100, wzz3200, bfa, bfb)
new_primMulInt(Pos(wzz4010), Neg(wzz30010)) → Neg(new_primMulNat0(wzz4010, wzz30010))
new_primMulInt(Neg(wzz4010), Pos(wzz30010)) → Neg(new_primMulNat0(wzz4010, wzz30010))
new_esEs7(@3(wzz400, wzz401, wzz402), @3(wzz3000, wzz3001, wzz3002), ca, cb, cc) → new_asAs(new_esEs12(wzz400, wzz3000, ca), new_asAs(new_esEs13(wzz401, wzz3001, cb), new_esEs14(wzz402, wzz3002, cc)))
new_ltEs10(LT, GT) → True
new_lt20(wzz31000, wzz32000, ty_@0) → new_lt19(wzz31000, wzz32000)
new_primCmpInt(Neg(Succ(wzz3100)), Neg(wzz320)) → new_primCmpNat2(wzz320, wzz3100)
new_primMulNat0(Zero, Succ(wzz300100)) → Zero
new_primMulNat0(Succ(wzz40100), Zero) → Zero
new_esEs14(wzz402, wzz3002, app(app(app(ty_@3, fh), ga), gb)) → new_esEs7(wzz402, wzz3002, fh, ga, gb)
new_ltEs14(Left(wzz31000), Left(wzz32000), app(ty_Ratio, bgh), bfb) → new_ltEs6(wzz31000, wzz32000, bgh)
new_ltEs12(wzz31002, wzz32002, ty_Char) → new_ltEs8(wzz31002, wzz32002)
new_compare6(wzz31000, wzz32000, bd, be) → new_compare24(wzz31000, wzz32000, new_esEs6(wzz31000, wzz32000, bd, be), bd, be)
new_lt13(wzz31001, wzz32001, ty_Float) → new_lt17(wzz31001, wzz32001)
new_lt17(wzz31000, wzz32000) → new_esEs11(new_compare17(wzz31000, wzz32000), LT)
new_ltEs14(Left(wzz31000), Left(wzz32000), app(ty_Maybe, bhd), bfb) → new_ltEs15(wzz31000, wzz32000, bhd)
new_esEs24(wzz31000, wzz32000, app(ty_[], baf)) → new_esEs16(wzz31000, wzz32000, baf)
new_esEs23(wzz31001, wzz32001, ty_Int) → new_esEs9(wzz31001, wzz32001)
new_esEs5(Just(wzz400), Just(wzz3000), app(app(ty_@2, dcb), dcc)) → new_esEs6(wzz400, wzz3000, dcb, dcc)
new_ltEs14(Right(wzz31000), Right(wzz32000), bfa, app(app(app(ty_@3, cba), cbb), cbc)) → new_ltEs11(wzz31000, wzz32000, cba, cbb, cbc)
new_ltEs14(Right(wzz31000), Right(wzz32000), bfa, app(app(ty_Either, cad), cae)) → new_ltEs14(wzz31000, wzz32000, cad, cae)
new_esEs4(Left(wzz400), Left(wzz3000), app(ty_Maybe, ccf), cbf) → new_esEs5(wzz400, wzz3000, ccf)
new_compare13(@0, @0) → EQ
new_ltEs14(Left(wzz31000), Left(wzz32000), app(app(app(ty_@3, bhg), bhh), caa), bfb) → new_ltEs11(wzz31000, wzz32000, bhg, bhh, caa)
new_ltEs14(Left(wzz31000), Left(wzz32000), ty_Double, bfb) → new_ltEs7(wzz31000, wzz32000)
new_esEs23(wzz31001, wzz32001, app(ty_Maybe, bch)) → new_esEs5(wzz31001, wzz32001, bch)
new_ltEs4(False, False) → True
new_primCmpInt(Pos(Zero), Pos(Succ(wzz3200))) → new_primCmpNat2(Zero, wzz3200)
new_ltEs10(EQ, EQ) → True
new_compare27(wzz31000, wzz32000, True) → EQ
new_ltEs10(LT, LT) → True
new_ltEs15(Nothing, Nothing, bfc) → True
new_ltEs14(Right(wzz31000), Right(wzz32000), bfa, ty_Char) → new_ltEs8(wzz31000, wzz32000)
new_esEs5(Nothing, Just(wzz3000), cee) → False
new_esEs5(Just(wzz400), Nothing, cee) → False
new_esEs22(wzz31000, wzz32000, ty_Bool) → new_esEs15(wzz31000, wzz32000)
new_esEs4(Right(wzz400), Right(wzz3000), ccg, ty_Char) → new_esEs18(wzz400, wzz3000)
new_ltEs14(Right(wzz31000), Right(wzz32000), bfa, ty_Int) → new_ltEs9(wzz31000, wzz32000)
new_ltEs14(Left(wzz31000), Left(wzz32000), app(app(ty_Either, bhb), bhc), bfb) → new_ltEs14(wzz31000, wzz32000, bhb, bhc)
new_esEs29(wzz40, wzz300, ty_Float) → new_esEs19(wzz40, wzz300)
new_esEs25(wzz400, wzz3000, app(app(app(ty_@3, cgf), cgg), cgh)) → new_esEs7(wzz400, wzz3000, cgf, cgg, cgh)
new_compare31(wzz31000, wzz32000, ty_Char) → new_compare19(wzz31000, wzz32000)
new_esEs24(wzz31000, wzz32000, ty_Double) → new_esEs8(wzz31000, wzz32000)
new_esEs25(wzz400, wzz3000, ty_Float) → new_esEs19(wzz400, wzz3000)
new_lt7(wzz31000, wzz32000, ge) → new_esEs11(new_compare9(wzz31000, wzz32000, ge), LT)
new_compare31(wzz31000, wzz32000, app(app(app(ty_@3, ddg), ddh), dea)) → new_compare7(wzz31000, wzz32000, ddg, ddh, dea)
new_ltEs19(wzz3100, wzz3200, app(app(app(ty_@3, bag), bah), bba)) → new_ltEs11(wzz3100, wzz3200, bag, bah, bba)
new_esEs16([], [], hb) → True
new_lt11(wzz31000, wzz32000) → new_esEs11(new_compare30(wzz31000, wzz32000), LT)
new_ltEs12(wzz31002, wzz32002, ty_Float) → new_ltEs16(wzz31002, wzz32002)
new_esEs30(wzz20, wzz15, app(app(ty_@2, cfb), cfc)) → new_esEs6(wzz20, wzz15, cfb, cfc)
new_esEs8(Double(wzz400, wzz401), Double(wzz3000, wzz3001)) → new_esEs9(new_sr(wzz400, wzz3000), new_sr(wzz401, wzz3001))
new_lt13(wzz31001, wzz32001, app(app(app(ty_@3, bdc), bdd), bde)) → new_lt5(wzz31001, wzz32001, bdc, bdd, bde)
new_compare29(Just(wzz3100), Just(wzz3200), False, beh) → new_compare16(wzz3100, wzz3200, new_ltEs19(wzz3100, wzz3200, beh), beh)
new_esEs14(wzz402, wzz3002, ty_Int) → new_esEs9(wzz402, wzz3002)
new_lt12(wzz31000, wzz32000, app(app(ty_@2, bbg), bbh)) → new_lt8(wzz31000, wzz32000, bbg, bbh)
new_esEs12(wzz400, wzz3000, app(ty_Ratio, cg)) → new_esEs17(wzz400, wzz3000, cg)
new_ltEs20(wzz31001, wzz32001, app(ty_Ratio, bff)) → new_ltEs6(wzz31001, wzz32001, bff)
new_esEs5(Nothing, Nothing, cee) → True
new_esEs4(Left(wzz400), Left(wzz3000), app(ty_[], cbg), cbf) → new_esEs16(wzz400, wzz3000, cbg)
new_esEs26(wzz401, wzz3001, ty_Float) → new_esEs19(wzz401, wzz3001)
new_esEs5(Just(wzz400), Just(wzz3000), app(app(app(ty_@3, dcd), dce), dcf)) → new_esEs7(wzz400, wzz3000, dcd, dce, dcf)
new_esEs28(wzz401, wzz3001, ty_Int) → new_esEs9(wzz401, wzz3001)
new_ltEs10(EQ, LT) → False
new_esEs5(Just(wzz400), Just(wzz3000), app(ty_Ratio, dca)) → new_esEs17(wzz400, wzz3000, dca)
new_lt15(wzz31000, wzz32000, bae) → new_esEs11(new_compare28(wzz31000, wzz32000, bae), LT)
new_esEs22(wzz31000, wzz32000, app(ty_Ratio, bbb)) → new_esEs17(wzz31000, wzz32000, bbb)
new_esEs26(wzz401, wzz3001, ty_Char) → new_esEs18(wzz401, wzz3001)
new_lt18(wzz31000, wzz32000) → new_esEs11(new_compare19(wzz31000, wzz32000), LT)
new_lt12(wzz31000, wzz32000, ty_Float) → new_lt17(wzz31000, wzz32000)
new_ltEs10(GT, LT) → False
new_lt20(wzz31000, wzz32000, app(app(app(ty_@3, bf), bg), bh)) → new_lt5(wzz31000, wzz32000, bf, bg, bh)
new_esEs4(Right(wzz400), Right(wzz3000), ccg, ty_Float) → new_esEs19(wzz400, wzz3000)
new_primPlusNat0(Succ(wzz26200), Succ(wzz8700)) → Succ(Succ(new_primPlusNat0(wzz26200, wzz8700)))
new_esEs22(wzz31000, wzz32000, app(ty_Maybe, bbf)) → new_esEs5(wzz31000, wzz32000, bbf)
new_esEs23(wzz31001, wzz32001, app(ty_[], bce)) → new_esEs16(wzz31001, wzz32001, bce)
new_esEs21(wzz400, wzz3000, app(ty_Maybe, bad)) → new_esEs5(wzz400, wzz3000, bad)
new_esEs29(wzz40, wzz300, ty_@0) → new_esEs10(wzz40, wzz300)
new_esEs26(wzz401, wzz3001, app(app(ty_Either, chb), chc)) → new_esEs4(wzz401, wzz3001, chb, chc)
new_esEs21(wzz400, wzz3000, ty_Integer) → new_esEs20(wzz400, wzz3000)
new_asAs(True, wzz125) → wzz125
new_esEs4(Right(wzz400), Left(wzz3000), ccg, cbf) → False
new_esEs4(Left(wzz400), Right(wzz3000), ccg, cbf) → False
new_ltEs8(wzz3100, wzz3200) → new_fsEs(new_compare19(wzz3100, wzz3200))
new_esEs30(wzz20, wzz15, app(ty_Maybe, cfg)) → new_esEs5(wzz20, wzz15, cfg)
new_esEs11(LT, LT) → True
new_primPlusNat1(wzz97, wzz300100) → new_primPlusNat0(wzz97, Succ(wzz300100))
new_esEs14(wzz402, wzz3002, ty_Integer) → new_esEs20(wzz402, wzz3002)
new_esEs5(Just(wzz400), Just(wzz3000), ty_Double) → new_esEs8(wzz400, wzz3000)
new_compare24(wzz31000, wzz32000, False, bd, be) → new_compare11(wzz31000, wzz32000, new_ltEs5(wzz31000, wzz32000, bd, be), bd, be)
new_esEs26(wzz401, wzz3001, app(app(ty_@2, chf), chg)) → new_esEs6(wzz401, wzz3001, chf, chg)
new_lt13(wzz31001, wzz32001, app(app(ty_@2, bda), bdb)) → new_lt8(wzz31001, wzz32001, bda, bdb)
new_ltEs12(wzz31002, wzz32002, ty_Int) → new_ltEs9(wzz31002, wzz32002)
new_compare10(wzz31000, wzz32000, True) → LT
new_esEs9(wzz40, wzz300) → new_primEqInt(wzz40, wzz300)
new_esEs11(EQ, GT) → False
new_esEs11(GT, EQ) → False
new_lt20(wzz31000, wzz32000, app(ty_Ratio, ge)) → new_lt7(wzz31000, wzz32000, ge)
new_lt19(wzz31000, wzz32000) → new_esEs11(new_compare13(wzz31000, wzz32000), LT)
new_compare10(wzz31000, wzz32000, False) → GT
new_esEs6(@2(wzz400, wzz401), @2(wzz3000, wzz3001), cec, ced) → new_asAs(new_esEs25(wzz400, wzz3000, cec), new_esEs26(wzz401, wzz3001, ced))
new_esEs13(wzz401, wzz3001, app(app(app(ty_@3, ee), ef), eg)) → new_esEs7(wzz401, wzz3001, ee, ef, eg)
new_esEs21(wzz400, wzz3000, app(ty_[], he)) → new_esEs16(wzz400, wzz3000, he)
new_esEs5(Just(wzz400), Just(wzz3000), app(app(ty_Either, dbf), dbg)) → new_esEs4(wzz400, wzz3000, dbf, dbg)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCompAux0(wzz165, EQ) → wzz165
new_esEs24(wzz31000, wzz32000, ty_Char) → new_esEs18(wzz31000, wzz32000)
new_lt12(wzz31000, wzz32000, ty_@0) → new_lt19(wzz31000, wzz32000)
new_ltEs19(wzz3100, wzz3200, app(ty_[], gd)) → new_ltEs13(wzz3100, wzz3200, gd)
new_lt12(wzz31000, wzz32000, app(ty_Maybe, bbf)) → new_lt15(wzz31000, wzz32000, bbf)
new_ltEs14(Left(wzz31000), Left(wzz32000), ty_@0, bfb) → new_ltEs17(wzz31000, wzz32000)
new_compare9(:%(wzz31000, wzz31001), :%(wzz32000, wzz32001), ty_Int) → new_compare14(new_sr(wzz31000, wzz32001), new_sr(wzz32000, wzz31001))
new_ltEs15(Just(wzz31000), Just(wzz32000), app(app(ty_Either, daf), dag)) → new_ltEs14(wzz31000, wzz32000, daf, dag)
new_esEs12(wzz400, wzz3000, app(ty_Maybe, df)) → new_esEs5(wzz400, wzz3000, df)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primCmpNat0(wzz3100, Succ(wzz3200)) → new_primCmpNat1(wzz3100, wzz3200)
new_lt20(wzz31000, wzz32000, app(app(ty_Either, gg), gh)) → new_lt9(wzz31000, wzz32000, gg, gh)
new_esEs12(wzz400, wzz3000, app(app(ty_@2, da), db)) → new_esEs6(wzz400, wzz3000, da, db)
new_primCmpInt(Neg(Succ(wzz3100)), Pos(wzz320)) → LT
new_not(True) → False
new_esEs15(False, False) → True

The set Q consists of the following terms:

new_compare210(x0, x1, False, x2, x3, x4)
new_compare31(x0, x1, ty_Int)
new_esEs4(Right(x0), Right(x1), x2, ty_Integer)
new_compare10(x0, x1, True)
new_compare31(x0, x1, ty_@0)
new_ltEs15(Just(x0), Just(x1), ty_@0)
new_esEs29(x0, x1, ty_Float)
new_primCmpNat2(Succ(x0), x1)
new_lt12(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Float)
new_lt5(x0, x1, x2, x3, x4)
new_lt13(x0, x1, ty_Float)
new_esEs13(x0, x1, app(app(ty_Either, x2), x3))
new_compare30(x0, x1)
new_primCmpNat1(Succ(x0), Succ(x1))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs26(x0, x1, ty_Bool)
new_esEs4(Right(x0), Right(x1), x2, ty_Float)
new_pePe(False, x0)
new_esEs24(x0, x1, ty_@0)
new_lt20(x0, x1, ty_Char)
new_ltEs14(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_lt13(x0, x1, ty_Double)
new_esEs13(x0, x1, ty_Double)
new_compare17(Float(x0, x1), Float(x2, x3))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Just(x0), Just(x1), ty_Int)
new_esEs15(True, True)
new_esEs13(x0, x1, ty_Ordering)
new_esEs5(Just(x0), Just(x1), ty_Bool)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs18(Char(x0), Char(x1))
new_compare14(x0, x1)
new_esEs12(x0, x1, ty_Char)
new_ltEs10(LT, LT)
new_compare31(x0, x1, ty_Float)
new_esEs4(Right(x0), Right(x1), x2, ty_Bool)
new_compare31(x0, x1, app(ty_[], x2))
new_ltEs12(x0, x1, ty_@0)
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Nothing, Just(x0), x1)
new_ltEs20(x0, x1, ty_@0)
new_esEs22(x0, x1, ty_Bool)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_sr(x0, x1)
new_esEs29(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Bool)
new_compare29(Nothing, Nothing, False, x0)
new_primCompAux0(x0, LT)
new_ltEs14(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs15(False, False)
new_lt10(x0, x1, x2)
new_ltEs14(Left(x0), Left(x1), ty_Float, x2)
new_esEs26(x0, x1, ty_Double)
new_esEs21(x0, x1, ty_Bool)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs20(Integer(x0), Integer(x1))
new_ltEs12(x0, x1, ty_Double)
new_ltEs14(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Double)
new_esEs12(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_Double)
new_ltEs14(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_compare12(x0, x1, True, x2, x3, x4)
new_esEs5(Just(x0), Just(x1), ty_Double)
new_lt13(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare110(x0, x1, True, x2, x3)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, ty_Integer)
new_esEs14(x0, x1, app(app(ty_Either, x2), x3))
new_esEs14(x0, x1, app(ty_Ratio, x2))
new_esEs14(x0, x1, ty_@0)
new_compare31(x0, x1, ty_Ordering)
new_compare210(x0, x1, True, x2, x3, x4)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs30(x0, x1, ty_Integer)
new_ltEs15(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Int)
new_lt13(x0, x1, app(ty_Ratio, x2))
new_primEqNat0(Succ(x0), Zero)
new_esEs22(x0, x1, ty_Int)
new_ltEs12(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Bool)
new_esEs4(Right(x0), Right(x1), x2, ty_@0)
new_ltEs19(x0, x1, ty_@0)
new_esEs16([], [], x0)
new_ltEs12(x0, x1, app(ty_Ratio, x2))
new_lt13(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpNat1(Zero, Zero)
new_compare(:(x0, x1), :(x2, x3), x4)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_primMulNat0(Succ(x0), Succ(x1))
new_compare9(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs23(x0, x1, ty_@0)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_lt12(x0, x1, app(ty_Ratio, x2))
new_ltEs7(x0, x1)
new_esEs11(EQ, GT)
new_esEs11(GT, EQ)
new_ltEs14(Left(x0), Left(x1), ty_Int, x2)
new_ltEs12(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_fsEs(x0)
new_esEs5(Just(x0), Just(x1), ty_@0)
new_primPlusNat0(Succ(x0), Zero)
new_lt12(x0, x1, ty_Bool)
new_compare12(x0, x1, False, x2, x3, x4)
new_esEs25(x0, x1, ty_Ordering)
new_esEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_compare11(x0, x1, False, x2, x3)
new_primEqNat0(Zero, Zero)
new_esEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs5(Nothing, Nothing, x0)
new_compare7(x0, x1, x2, x3, x4)
new_lt12(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Left(x0), Left(x1), app(ty_[], x2), x3)
new_primCompAux0(x0, EQ)
new_ltEs15(Just(x0), Just(x1), ty_Bool)
new_esEs25(x0, x1, app(ty_[], x2))
new_ltEs4(True, True)
new_esEs21(x0, x1, ty_Int)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs12(x0, x1, ty_Ordering)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_primMulNat0(Succ(x0), Zero)
new_esEs23(x0, x1, ty_Float)
new_compare31(x0, x1, ty_Integer)
new_compare31(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_Ordering)
new_compare8(Integer(x0), Integer(x1))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs22(x0, x1, app(ty_[], x2))
new_ltEs12(x0, x1, ty_Int)
new_lt17(x0, x1)
new_compare26(x0, x1, True, x2, x3)
new_ltEs14(Right(x0), Right(x1), x2, ty_Integer)
new_lt13(x0, x1, ty_Integer)
new_ltEs10(EQ, LT)
new_ltEs10(LT, EQ)
new_esEs12(x0, x1, ty_Integer)
new_esEs12(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_Int)
new_lt11(x0, x1)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_ltEs15(Just(x0), Just(x1), ty_Integer)
new_lt13(x0, x1, app(ty_[], x2))
new_esEs4(Left(x0), Left(x1), ty_@0, x2)
new_lt20(x0, x1, ty_@0)
new_ltEs14(Left(x0), Left(x1), ty_Char, x2)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_primEqNat0(Zero, Succ(x0))
new_lt13(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, ty_Char)
new_esEs30(x0, x1, ty_Ordering)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Float)
new_esEs21(x0, x1, ty_Double)
new_lt13(x0, x1, app(ty_Maybe, x2))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs13(x0, x1, ty_Integer)
new_ltEs12(x0, x1, ty_Bool)
new_esEs11(GT, LT)
new_esEs11(LT, GT)
new_ltEs14(Left(x0), Left(x1), ty_Integer, x2)
new_compare25(x0, x1, True)
new_esEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_lt12(x0, x1, ty_Int)
new_primCmpNat2(Zero, x0)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_lt14(x0, x1)
new_ltEs15(Just(x0), Just(x1), ty_Double)
new_asAs(False, x0)
new_ltEs4(False, False)
new_esEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Bool)
new_esEs5(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs19(x0, x1, ty_Double)
new_compare27(x0, x1, False)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, ty_@0)
new_esEs21(x0, x1, ty_Float)
new_compare28(x0, x1, x2)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs15(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs15(Just(x0), Just(x1), ty_Ordering)
new_lt20(x0, x1, ty_Ordering)
new_lt12(x0, x1, ty_Float)
new_esEs4(Right(x0), Left(x1), x2, x3)
new_esEs4(Left(x0), Right(x1), x2, x3)
new_esEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs12(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Int)
new_esEs28(x0, x1, ty_Integer)
new_compare16(x0, x1, True, x2)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs26(x0, x1, ty_Int)
new_asAs(True, x0)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs11(LT, LT)
new_compare26(x0, x1, False, x2, x3)
new_ltEs15(Just(x0), Just(x1), ty_Int)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_Bool)
new_lt19(x0, x1)
new_esEs23(x0, x1, ty_Char)
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_primPlusNat0(Zero, Zero)
new_ltEs12(x0, x1, app(ty_[], x2))
new_lt12(x0, x1, ty_Char)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_compare31(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_@0)
new_lt12(x0, x1, ty_Integer)
new_lt20(x0, x1, ty_Integer)
new_esEs24(x0, x1, app(ty_[], x2))
new_primPlusNat0(Succ(x0), Succ(x1))
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_lt12(x0, x1, app(app(ty_Either, x2), x3))
new_esEs14(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Ordering)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs30(x0, x1, ty_Float)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs24(x0, x1, ty_Double)
new_esEs23(x0, x1, ty_Double)
new_esEs25(x0, x1, ty_Double)
new_esEs24(x0, x1, ty_Char)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_ltEs20(x0, x1, ty_Double)
new_compare19(Char(x0), Char(x1))
new_esEs21(x0, x1, ty_Char)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs14(x0, x1, ty_Ordering)
new_ltEs14(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs9(x0, x1)
new_compare([], :(x0, x1), x2)
new_ltEs15(Just(x0), Nothing, x1)
new_ltEs20(x0, x1, ty_Int)
new_lt6(x0, x1)
new_compare29(Just(x0), Nothing, False, x1)
new_esEs30(x0, x1, ty_Double)
new_ltEs17(x0, x1)
new_esEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_compare24(x0, x1, False, x2, x3)
new_ltEs10(GT, LT)
new_ltEs10(LT, GT)
new_primPlusNat0(Zero, Succ(x0))
new_esEs14(x0, x1, ty_Bool)
new_esEs30(x0, x1, ty_Bool)
new_esEs10(@0, @0)
new_esEs24(x0, x1, ty_Ordering)
new_esEs14(x0, x1, ty_Char)
new_esEs30(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, app(ty_[], x2))
new_compare31(x0, x1, ty_Double)
new_ltEs16(x0, x1)
new_ltEs11(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_compare111(x0, x1, True)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_lt12(x0, x1, ty_Double)
new_esEs9(x0, x1)
new_esEs5(Just(x0), Just(x1), ty_Ordering)
new_esEs5(Just(x0), Nothing, x1)
new_lt9(x0, x1, x2, x3)
new_esEs13(x0, x1, ty_Bool)
new_esEs29(x0, x1, ty_Ordering)
new_esEs13(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_Float)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_ltEs14(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs15(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs15(Just(x0), Just(x1), ty_Char)
new_compare13(@0, @0)
new_esEs16([], :(x0, x1), x2)
new_ltEs15(Nothing, Just(x0), x1)
new_esEs22(x0, x1, ty_Char)
new_esEs11(EQ, LT)
new_esEs11(LT, EQ)
new_esEs12(x0, x1, app(ty_[], x2))
new_compare11(x0, x1, True, x2, x3)
new_esEs12(x0, x1, ty_Ordering)
new_compare6(x0, x1, x2, x3)
new_esEs13(x0, x1, ty_Int)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs15(True, False)
new_esEs15(False, True)
new_sr0(Integer(x0), Integer(x1))
new_esEs4(Left(x0), Left(x1), ty_Integer, x2)
new_esEs29(x0, x1, ty_Double)
new_esEs17(:%(x0, x1), :%(x2, x3), x4)
new_lt13(x0, x1, ty_Bool)
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs30(x0, x1, ty_Int)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs14(Left(x0), Left(x1), ty_Bool, x2)
new_compare31(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, ty_Bool)
new_esEs19(Float(x0, x1), Float(x2, x3))
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs14(Right(x0), Right(x1), x2, ty_@0)
new_esEs13(x0, x1, ty_Float)
new_lt16(x0, x1)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Int)
new_lt18(x0, x1)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs16(:(x0, x1), :(x2, x3), x4)
new_esEs24(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_@0)
new_esEs16(:(x0, x1), [], x2)
new_lt7(x0, x1, x2)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_compare18(Double(x0, x1), Double(x2, x3))
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_primCmpNat1(Succ(x0), Zero)
new_esEs13(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt13(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Integer)
new_primCompAux0(x0, GT)
new_esEs4(Left(x0), Left(x1), ty_Int, x2)
new_lt13(x0, x1, ty_Ordering)
new_ltEs12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare(:(x0, x1), [], x2)
new_lt12(x0, x1, app(ty_[], x2))
new_ltEs14(Left(x0), Left(x1), ty_Double, x2)
new_esEs30(x0, x1, ty_@0)
new_ltEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, ty_Int)
new_esEs22(x0, x1, ty_@0)
new_primMulNat0(Zero, Succ(x0))
new_lt12(x0, x1, ty_Ordering)
new_esEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Just(x0), Just(x1), ty_Integer)
new_esEs5(Just(x0), Just(x1), ty_Char)
new_esEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs12(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(Double(x0, x1), Double(x2, x3))
new_esEs4(Left(x0), Left(x1), ty_Char, x2)
new_esEs22(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Ordering)
new_esEs12(x0, x1, app(ty_Maybe, x2))
new_compare29(Nothing, Just(x0), False, x1)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs4(False, True)
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_ltEs4(True, False)
new_esEs14(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs26(x0, x1, ty_Float)
new_lt4(x0, x1)
new_compare([], [], x0)
new_esEs12(x0, x1, ty_Bool)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs12(x0, x1, ty_Int)
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs14(x0, x1, ty_Int)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_primPlusNat1(x0, x1)
new_esEs21(x0, x1, ty_Ordering)
new_ltEs18(x0, x1)
new_ltEs15(Nothing, Nothing, x0)
new_esEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs29(x0, x1, ty_Integer)
new_esEs12(x0, x1, app(ty_Ratio, x2))
new_compare111(x0, x1, False)
new_ltEs12(x0, x1, app(ty_Maybe, x2))
new_compare31(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs6(x0, x1, x2)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs10(GT, GT)
new_esEs25(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs13(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Float)
new_esEs29(x0, x1, ty_Char)
new_ltEs15(Just(x0), Just(x1), ty_Float)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs30(x0, x1, ty_Char)
new_esEs11(GT, GT)
new_ltEs14(Right(x0), Right(x1), x2, ty_Char)
new_compare16(x0, x1, False, x2)
new_primEqNat0(Succ(x0), Succ(x1))
new_ltEs20(x0, x1, ty_Integer)
new_primCmpNat0(x0, Zero)
new_lt20(x0, x1, app(ty_[], x2))
new_lt12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_not(True)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_compare29(x0, x1, True, x2)
new_esEs12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, ty_Char)
new_esEs22(x0, x1, ty_Float)
new_esEs4(Right(x0), Right(x1), x2, ty_Char)
new_compare9(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs12(x0, x1, ty_Double)
new_esEs4(Left(x0), Left(x1), ty_Double, x2)
new_esEs26(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_Float)
new_lt20(x0, x1, ty_Double)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_not(False)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs14(x0, x1, app(ty_Maybe, x2))
new_ltEs13(x0, x1, x2)
new_esEs26(x0, x1, ty_Char)
new_primCompAux1(x0, x1, x2, x3)
new_primCmpNat1(Zero, Succ(x0))
new_compare110(x0, x1, False, x2, x3)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs10(EQ, GT)
new_ltEs10(GT, EQ)
new_ltEs20(x0, x1, ty_Char)
new_lt13(x0, x1, ty_Char)
new_ltEs14(Left(x0), Left(x1), ty_@0, x2)
new_esEs23(x0, x1, app(ty_[], x2))
new_compare27(x0, x1, True)
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_compare31(x0, x1, ty_Char)
new_compare29(Just(x0), Just(x1), False, x2)
new_esEs4(Right(x0), Right(x1), x2, ty_Int)
new_compare15(x0, x1, x2, x3)
new_primCmpNat0(x0, Succ(x1))
new_esEs14(x0, x1, ty_Double)
new_ltEs12(x0, x1, ty_Char)
new_compare24(x0, x1, True, x2, x3)
new_lt8(x0, x1, x2, x3)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(Right(x0), Right(x1), x2, ty_Float)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_ltEs12(x0, x1, ty_Float)
new_esEs21(x0, x1, ty_@0)
new_esEs13(x0, x1, app(ty_Maybe, x2))
new_esEs4(Left(x0), Left(x1), ty_Float, x2)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_ltEs15(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs8(x0, x1)
new_ltEs19(x0, x1, ty_Bool)
new_esEs29(x0, x1, ty_Int)
new_esEs13(x0, x1, app(ty_[], x2))
new_esEs25(x0, x1, ty_Int)
new_compare31(x0, x1, ty_Bool)
new_esEs13(x0, x1, ty_@0)
new_ltEs15(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_compare31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs14(x0, x1, app(app(ty_@2, x2), x3))
new_esEs14(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Integer)
new_lt20(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_Int)
new_esEs14(x0, x1, ty_Float)
new_esEs12(x0, x1, ty_@0)
new_esEs24(x0, x1, ty_Integer)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_primEqInt(Pos(Zero), Pos(Zero))
new_ltEs14(Left(x0), Right(x1), x2, x3)
new_ltEs14(Right(x0), Left(x1), x2, x3)
new_esEs11(EQ, EQ)
new_lt15(x0, x1, x2)
new_esEs13(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_compare25(x0, x1, False)
new_ltEs15(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs14(Right(x0), Right(x1), x2, ty_Bool)
new_esEs4(Right(x0), Right(x1), x2, ty_Double)
new_compare10(x0, x1, False)
new_pePe(True, x0)
new_esEs27(x0, x1, ty_Integer)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Just(x0), Just(x1), ty_Float)
new_compare5(x0, x1)
new_ltEs20(x0, x1, ty_Ordering)
new_lt13(x0, x1, ty_@0)
new_esEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs21(x0, x1, app(ty_[], x2))
new_ltEs10(EQ, EQ)
new_lt12(x0, x1, ty_@0)

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

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

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

new_addToFM_C1(wzz31, wzz32, wzz33, wzz34, wzz5, True, h, ba) → new_addToFM_C(wzz34, Nothing, wzz5, h, ba)
new_addToFM_C2(wzz300, wzz31, wzz32, wzz33, wzz34, wzz5, True, h, ba) → new_addToFM_C(wzz33, Nothing, wzz5, h, ba)
new_addToFM_C(Branch(Nothing, wzz31, wzz32, wzz33, wzz34), Nothing, wzz5, h, ba) → new_addToFM_C1(wzz31, wzz32, wzz33, wzz34, wzz5, new_esEs11(new_compare29(Nothing, Nothing, True, h), GT), h, ba)
new_addToFM_C2(wzz300, wzz31, wzz32, wzz33, wzz34, wzz5, False, h, ba) → new_addToFM_C10(wzz300, wzz31, wzz32, wzz33, wzz34, wzz5, new_esEs11(new_compare29(Nothing, Just(wzz300), False, h), GT), h, ba)
new_addToFM_C10(wzz300, wzz31, wzz32, wzz33, wzz34, wzz5, True, h, ba) → new_addToFM_C(wzz34, Nothing, wzz5, h, ba)
new_addToFM_C(Branch(Just(wzz300), wzz31, wzz32, wzz33, wzz34), Nothing, wzz5, h, ba) → new_addToFM_C2(wzz300, wzz31, wzz32, wzz33, wzz34, wzz5, new_esEs11(new_compare29(Nothing, Just(wzz300), False, h), LT), h, ba)

The TRS R consists of the following rules:

new_compare29(Nothing, Just(wzz3200), False, beh) → LT
new_esEs11(GT, LT) → False
new_esEs11(EQ, LT) → False
new_esEs11(LT, LT) → True
new_compare29(wzz310, wzz320, True, beh) → EQ
new_esEs11(GT, GT) → True
new_esEs11(LT, GT) → False
new_esEs11(EQ, GT) → False

The set Q consists of the following terms:

new_compare210(x0, x1, False, x2, x3, x4)
new_compare31(x0, x1, ty_Int)
new_esEs4(Right(x0), Right(x1), x2, ty_Integer)
new_compare10(x0, x1, True)
new_compare31(x0, x1, ty_@0)
new_ltEs15(Just(x0), Just(x1), ty_@0)
new_esEs29(x0, x1, ty_Float)
new_primCmpNat2(Succ(x0), x1)
new_lt12(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Float)
new_lt5(x0, x1, x2, x3, x4)
new_lt13(x0, x1, ty_Float)
new_esEs13(x0, x1, app(app(ty_Either, x2), x3))
new_compare30(x0, x1)
new_primCmpNat1(Succ(x0), Succ(x1))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs26(x0, x1, ty_Bool)
new_esEs4(Right(x0), Right(x1), x2, ty_Float)
new_pePe(False, x0)
new_esEs24(x0, x1, ty_@0)
new_lt20(x0, x1, ty_Char)
new_ltEs14(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_lt13(x0, x1, ty_Double)
new_esEs13(x0, x1, ty_Double)
new_compare17(Float(x0, x1), Float(x2, x3))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Just(x0), Just(x1), ty_Int)
new_esEs15(True, True)
new_esEs13(x0, x1, ty_Ordering)
new_esEs5(Just(x0), Just(x1), ty_Bool)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs18(Char(x0), Char(x1))
new_compare14(x0, x1)
new_esEs12(x0, x1, ty_Char)
new_ltEs10(LT, LT)
new_compare31(x0, x1, ty_Float)
new_esEs4(Right(x0), Right(x1), x2, ty_Bool)
new_compare31(x0, x1, app(ty_[], x2))
new_ltEs12(x0, x1, ty_@0)
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Nothing, Just(x0), x1)
new_ltEs20(x0, x1, ty_@0)
new_esEs22(x0, x1, ty_Bool)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_sr(x0, x1)
new_esEs29(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Bool)
new_compare29(Nothing, Nothing, False, x0)
new_primCompAux0(x0, LT)
new_ltEs14(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs15(False, False)
new_lt10(x0, x1, x2)
new_ltEs14(Left(x0), Left(x1), ty_Float, x2)
new_esEs26(x0, x1, ty_Double)
new_esEs21(x0, x1, ty_Bool)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs20(Integer(x0), Integer(x1))
new_ltEs12(x0, x1, ty_Double)
new_ltEs14(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Double)
new_esEs12(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_Double)
new_ltEs14(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_compare12(x0, x1, True, x2, x3, x4)
new_esEs5(Just(x0), Just(x1), ty_Double)
new_lt13(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare110(x0, x1, True, x2, x3)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, ty_Integer)
new_esEs14(x0, x1, app(app(ty_Either, x2), x3))
new_esEs14(x0, x1, app(ty_Ratio, x2))
new_esEs14(x0, x1, ty_@0)
new_compare31(x0, x1, ty_Ordering)
new_compare210(x0, x1, True, x2, x3, x4)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs30(x0, x1, ty_Integer)
new_ltEs15(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Int)
new_lt13(x0, x1, app(ty_Ratio, x2))
new_primEqNat0(Succ(x0), Zero)
new_esEs22(x0, x1, ty_Int)
new_ltEs12(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Bool)
new_esEs4(Right(x0), Right(x1), x2, ty_@0)
new_ltEs19(x0, x1, ty_@0)
new_esEs16([], [], x0)
new_ltEs12(x0, x1, app(ty_Ratio, x2))
new_lt13(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpNat1(Zero, Zero)
new_compare(:(x0, x1), :(x2, x3), x4)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_primMulNat0(Succ(x0), Succ(x1))
new_compare9(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs23(x0, x1, ty_@0)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_lt12(x0, x1, app(ty_Ratio, x2))
new_ltEs7(x0, x1)
new_esEs11(EQ, GT)
new_esEs11(GT, EQ)
new_ltEs14(Left(x0), Left(x1), ty_Int, x2)
new_ltEs12(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_fsEs(x0)
new_esEs5(Just(x0), Just(x1), ty_@0)
new_primPlusNat0(Succ(x0), Zero)
new_lt12(x0, x1, ty_Bool)
new_compare12(x0, x1, False, x2, x3, x4)
new_esEs25(x0, x1, ty_Ordering)
new_esEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_compare11(x0, x1, False, x2, x3)
new_primEqNat0(Zero, Zero)
new_esEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs5(Nothing, Nothing, x0)
new_compare7(x0, x1, x2, x3, x4)
new_lt12(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Left(x0), Left(x1), app(ty_[], x2), x3)
new_primCompAux0(x0, EQ)
new_ltEs15(Just(x0), Just(x1), ty_Bool)
new_esEs25(x0, x1, app(ty_[], x2))
new_ltEs4(True, True)
new_esEs21(x0, x1, ty_Int)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs12(x0, x1, ty_Ordering)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_primMulNat0(Succ(x0), Zero)
new_esEs23(x0, x1, ty_Float)
new_compare31(x0, x1, ty_Integer)
new_compare31(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_Ordering)
new_compare8(Integer(x0), Integer(x1))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs22(x0, x1, app(ty_[], x2))
new_ltEs12(x0, x1, ty_Int)
new_lt17(x0, x1)
new_compare26(x0, x1, True, x2, x3)
new_ltEs14(Right(x0), Right(x1), x2, ty_Integer)
new_lt13(x0, x1, ty_Integer)
new_ltEs10(EQ, LT)
new_ltEs10(LT, EQ)
new_esEs12(x0, x1, ty_Integer)
new_esEs12(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_Int)
new_lt11(x0, x1)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_ltEs15(Just(x0), Just(x1), ty_Integer)
new_lt13(x0, x1, app(ty_[], x2))
new_esEs4(Left(x0), Left(x1), ty_@0, x2)
new_lt20(x0, x1, ty_@0)
new_ltEs14(Left(x0), Left(x1), ty_Char, x2)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_primEqNat0(Zero, Succ(x0))
new_lt13(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, ty_Char)
new_esEs30(x0, x1, ty_Ordering)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Float)
new_esEs21(x0, x1, ty_Double)
new_lt13(x0, x1, app(ty_Maybe, x2))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs13(x0, x1, ty_Integer)
new_ltEs12(x0, x1, ty_Bool)
new_esEs11(GT, LT)
new_esEs11(LT, GT)
new_ltEs14(Left(x0), Left(x1), ty_Integer, x2)
new_compare25(x0, x1, True)
new_esEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_lt12(x0, x1, ty_Int)
new_primCmpNat2(Zero, x0)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_lt14(x0, x1)
new_ltEs15(Just(x0), Just(x1), ty_Double)
new_asAs(False, x0)
new_ltEs4(False, False)
new_esEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Bool)
new_esEs5(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs19(x0, x1, ty_Double)
new_compare27(x0, x1, False)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, ty_@0)
new_esEs21(x0, x1, ty_Float)
new_compare28(x0, x1, x2)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs15(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs15(Just(x0), Just(x1), ty_Ordering)
new_lt20(x0, x1, ty_Ordering)
new_lt12(x0, x1, ty_Float)
new_esEs4(Right(x0), Left(x1), x2, x3)
new_esEs4(Left(x0), Right(x1), x2, x3)
new_esEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs12(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Int)
new_esEs28(x0, x1, ty_Integer)
new_compare16(x0, x1, True, x2)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs26(x0, x1, ty_Int)
new_asAs(True, x0)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs11(LT, LT)
new_compare26(x0, x1, False, x2, x3)
new_ltEs15(Just(x0), Just(x1), ty_Int)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_Bool)
new_lt19(x0, x1)
new_esEs23(x0, x1, ty_Char)
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_primPlusNat0(Zero, Zero)
new_ltEs12(x0, x1, app(ty_[], x2))
new_lt12(x0, x1, ty_Char)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_compare31(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_@0)
new_lt12(x0, x1, ty_Integer)
new_lt20(x0, x1, ty_Integer)
new_esEs24(x0, x1, app(ty_[], x2))
new_primPlusNat0(Succ(x0), Succ(x1))
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_lt12(x0, x1, app(app(ty_Either, x2), x3))
new_esEs14(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Ordering)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs30(x0, x1, ty_Float)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs24(x0, x1, ty_Double)
new_esEs23(x0, x1, ty_Double)
new_esEs25(x0, x1, ty_Double)
new_esEs24(x0, x1, ty_Char)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_ltEs20(x0, x1, ty_Double)
new_compare19(Char(x0), Char(x1))
new_esEs21(x0, x1, ty_Char)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs14(x0, x1, ty_Ordering)
new_ltEs14(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs9(x0, x1)
new_compare([], :(x0, x1), x2)
new_ltEs15(Just(x0), Nothing, x1)
new_ltEs20(x0, x1, ty_Int)
new_lt6(x0, x1)
new_compare29(Just(x0), Nothing, False, x1)
new_esEs30(x0, x1, ty_Double)
new_ltEs17(x0, x1)
new_esEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_compare24(x0, x1, False, x2, x3)
new_ltEs10(GT, LT)
new_ltEs10(LT, GT)
new_primPlusNat0(Zero, Succ(x0))
new_esEs14(x0, x1, ty_Bool)
new_esEs30(x0, x1, ty_Bool)
new_esEs10(@0, @0)
new_esEs24(x0, x1, ty_Ordering)
new_esEs14(x0, x1, ty_Char)
new_esEs30(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, app(ty_[], x2))
new_compare31(x0, x1, ty_Double)
new_ltEs16(x0, x1)
new_ltEs11(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_compare111(x0, x1, True)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_lt12(x0, x1, ty_Double)
new_esEs9(x0, x1)
new_esEs5(Just(x0), Just(x1), ty_Ordering)
new_esEs5(Just(x0), Nothing, x1)
new_lt9(x0, x1, x2, x3)
new_esEs13(x0, x1, ty_Bool)
new_esEs29(x0, x1, ty_Ordering)
new_esEs13(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_Float)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_ltEs14(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs15(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs15(Just(x0), Just(x1), ty_Char)
new_compare13(@0, @0)
new_esEs16([], :(x0, x1), x2)
new_ltEs15(Nothing, Just(x0), x1)
new_esEs22(x0, x1, ty_Char)
new_esEs11(EQ, LT)
new_esEs11(LT, EQ)
new_esEs12(x0, x1, app(ty_[], x2))
new_compare11(x0, x1, True, x2, x3)
new_esEs12(x0, x1, ty_Ordering)
new_compare6(x0, x1, x2, x3)
new_esEs13(x0, x1, ty_Int)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs15(True, False)
new_esEs15(False, True)
new_sr0(Integer(x0), Integer(x1))
new_esEs4(Left(x0), Left(x1), ty_Integer, x2)
new_esEs29(x0, x1, ty_Double)
new_esEs17(:%(x0, x1), :%(x2, x3), x4)
new_lt13(x0, x1, ty_Bool)
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs30(x0, x1, ty_Int)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs14(Left(x0), Left(x1), ty_Bool, x2)
new_compare31(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, ty_Bool)
new_esEs19(Float(x0, x1), Float(x2, x3))
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs14(Right(x0), Right(x1), x2, ty_@0)
new_esEs13(x0, x1, ty_Float)
new_lt16(x0, x1)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Int)
new_lt18(x0, x1)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs16(:(x0, x1), :(x2, x3), x4)
new_esEs24(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_@0)
new_esEs16(:(x0, x1), [], x2)
new_lt7(x0, x1, x2)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_compare18(Double(x0, x1), Double(x2, x3))
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_primCmpNat1(Succ(x0), Zero)
new_esEs13(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt13(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Integer)
new_primCompAux0(x0, GT)
new_esEs4(Left(x0), Left(x1), ty_Int, x2)
new_lt13(x0, x1, ty_Ordering)
new_ltEs12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare(:(x0, x1), [], x2)
new_lt12(x0, x1, app(ty_[], x2))
new_ltEs14(Left(x0), Left(x1), ty_Double, x2)
new_esEs30(x0, x1, ty_@0)
new_ltEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, ty_Int)
new_esEs22(x0, x1, ty_@0)
new_primMulNat0(Zero, Succ(x0))
new_lt12(x0, x1, ty_Ordering)
new_esEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Just(x0), Just(x1), ty_Integer)
new_esEs5(Just(x0), Just(x1), ty_Char)
new_esEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs12(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(Double(x0, x1), Double(x2, x3))
new_esEs4(Left(x0), Left(x1), ty_Char, x2)
new_esEs22(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Ordering)
new_esEs12(x0, x1, app(ty_Maybe, x2))
new_compare29(Nothing, Just(x0), False, x1)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs4(False, True)
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_ltEs4(True, False)
new_esEs14(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs26(x0, x1, ty_Float)
new_lt4(x0, x1)
new_compare([], [], x0)
new_esEs12(x0, x1, ty_Bool)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs12(x0, x1, ty_Int)
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs14(x0, x1, ty_Int)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_primPlusNat1(x0, x1)
new_esEs21(x0, x1, ty_Ordering)
new_ltEs18(x0, x1)
new_ltEs15(Nothing, Nothing, x0)
new_esEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs29(x0, x1, ty_Integer)
new_esEs12(x0, x1, app(ty_Ratio, x2))
new_compare111(x0, x1, False)
new_ltEs12(x0, x1, app(ty_Maybe, x2))
new_compare31(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs6(x0, x1, x2)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs10(GT, GT)
new_esEs25(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs13(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Float)
new_esEs29(x0, x1, ty_Char)
new_ltEs15(Just(x0), Just(x1), ty_Float)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs30(x0, x1, ty_Char)
new_esEs11(GT, GT)
new_ltEs14(Right(x0), Right(x1), x2, ty_Char)
new_compare16(x0, x1, False, x2)
new_primEqNat0(Succ(x0), Succ(x1))
new_ltEs20(x0, x1, ty_Integer)
new_primCmpNat0(x0, Zero)
new_lt20(x0, x1, app(ty_[], x2))
new_lt12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_not(True)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_compare29(x0, x1, True, x2)
new_esEs12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, ty_Char)
new_esEs22(x0, x1, ty_Float)
new_esEs4(Right(x0), Right(x1), x2, ty_Char)
new_compare9(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs12(x0, x1, ty_Double)
new_esEs4(Left(x0), Left(x1), ty_Double, x2)
new_esEs26(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_Float)
new_lt20(x0, x1, ty_Double)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_not(False)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs14(x0, x1, app(ty_Maybe, x2))
new_ltEs13(x0, x1, x2)
new_esEs26(x0, x1, ty_Char)
new_primCompAux1(x0, x1, x2, x3)
new_primCmpNat1(Zero, Succ(x0))
new_compare110(x0, x1, False, x2, x3)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs10(EQ, GT)
new_ltEs10(GT, EQ)
new_ltEs20(x0, x1, ty_Char)
new_lt13(x0, x1, ty_Char)
new_ltEs14(Left(x0), Left(x1), ty_@0, x2)
new_esEs23(x0, x1, app(ty_[], x2))
new_compare27(x0, x1, True)
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_compare31(x0, x1, ty_Char)
new_compare29(Just(x0), Just(x1), False, x2)
new_esEs4(Right(x0), Right(x1), x2, ty_Int)
new_compare15(x0, x1, x2, x3)
new_primCmpNat0(x0, Succ(x1))
new_esEs14(x0, x1, ty_Double)
new_ltEs12(x0, x1, ty_Char)
new_compare24(x0, x1, True, x2, x3)
new_lt8(x0, x1, x2, x3)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(Right(x0), Right(x1), x2, ty_Float)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_ltEs12(x0, x1, ty_Float)
new_esEs21(x0, x1, ty_@0)
new_esEs13(x0, x1, app(ty_Maybe, x2))
new_esEs4(Left(x0), Left(x1), ty_Float, x2)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_ltEs15(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs8(x0, x1)
new_ltEs19(x0, x1, ty_Bool)
new_esEs29(x0, x1, ty_Int)
new_esEs13(x0, x1, app(ty_[], x2))
new_esEs25(x0, x1, ty_Int)
new_compare31(x0, x1, ty_Bool)
new_esEs13(x0, x1, ty_@0)
new_ltEs15(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_compare31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs14(x0, x1, app(app(ty_@2, x2), x3))
new_esEs14(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Integer)
new_lt20(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_Int)
new_esEs14(x0, x1, ty_Float)
new_esEs12(x0, x1, ty_@0)
new_esEs24(x0, x1, ty_Integer)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_primEqInt(Pos(Zero), Pos(Zero))
new_ltEs14(Left(x0), Right(x1), x2, x3)
new_ltEs14(Right(x0), Left(x1), x2, x3)
new_esEs11(EQ, EQ)
new_lt15(x0, x1, x2)
new_esEs13(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_compare25(x0, x1, False)
new_ltEs15(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs14(Right(x0), Right(x1), x2, ty_Bool)
new_esEs4(Right(x0), Right(x1), x2, ty_Double)
new_compare10(x0, x1, False)
new_pePe(True, x0)
new_esEs27(x0, x1, ty_Integer)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Just(x0), Just(x1), ty_Float)
new_compare5(x0, x1)
new_ltEs20(x0, x1, ty_Ordering)
new_lt13(x0, x1, ty_@0)
new_esEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs21(x0, x1, app(ty_[], x2))
new_ltEs10(EQ, EQ)
new_lt12(x0, x1, ty_@0)

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_compare210(x0, x1, False, x2, x3, x4)
new_compare31(x0, x1, ty_Int)
new_esEs4(Right(x0), Right(x1), x2, ty_Integer)
new_compare10(x0, x1, True)
new_compare31(x0, x1, ty_@0)
new_ltEs15(Just(x0), Just(x1), ty_@0)
new_esEs29(x0, x1, ty_Float)
new_primCmpNat2(Succ(x0), x1)
new_lt12(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Float)
new_lt5(x0, x1, x2, x3, x4)
new_lt13(x0, x1, ty_Float)
new_esEs13(x0, x1, app(app(ty_Either, x2), x3))
new_compare30(x0, x1)
new_primCmpNat1(Succ(x0), Succ(x1))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs26(x0, x1, ty_Bool)
new_esEs4(Right(x0), Right(x1), x2, ty_Float)
new_pePe(False, x0)
new_esEs24(x0, x1, ty_@0)
new_lt20(x0, x1, ty_Char)
new_ltEs14(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_lt13(x0, x1, ty_Double)
new_esEs13(x0, x1, ty_Double)
new_compare17(Float(x0, x1), Float(x2, x3))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Just(x0), Just(x1), ty_Int)
new_esEs15(True, True)
new_esEs13(x0, x1, ty_Ordering)
new_esEs5(Just(x0), Just(x1), ty_Bool)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs18(Char(x0), Char(x1))
new_compare14(x0, x1)
new_esEs12(x0, x1, ty_Char)
new_ltEs10(LT, LT)
new_compare31(x0, x1, ty_Float)
new_esEs4(Right(x0), Right(x1), x2, ty_Bool)
new_compare31(x0, x1, app(ty_[], x2))
new_ltEs12(x0, x1, ty_@0)
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Nothing, Just(x0), x1)
new_ltEs20(x0, x1, ty_@0)
new_esEs22(x0, x1, ty_Bool)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_sr(x0, x1)
new_esEs29(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Bool)
new_primCompAux0(x0, LT)
new_ltEs14(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs15(False, False)
new_lt10(x0, x1, x2)
new_ltEs14(Left(x0), Left(x1), ty_Float, x2)
new_esEs26(x0, x1, ty_Double)
new_esEs21(x0, x1, ty_Bool)
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs20(Integer(x0), Integer(x1))
new_ltEs12(x0, x1, ty_Double)
new_ltEs14(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Double)
new_esEs12(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_Double)
new_ltEs14(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_compare12(x0, x1, True, x2, x3, x4)
new_esEs5(Just(x0), Just(x1), ty_Double)
new_lt13(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare110(x0, x1, True, x2, x3)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, ty_Integer)
new_esEs14(x0, x1, app(app(ty_Either, x2), x3))
new_esEs14(x0, x1, app(ty_Ratio, x2))
new_esEs14(x0, x1, ty_@0)
new_compare31(x0, x1, ty_Ordering)
new_compare210(x0, x1, True, x2, x3, x4)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs30(x0, x1, ty_Integer)
new_ltEs15(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Int)
new_lt13(x0, x1, app(ty_Ratio, x2))
new_primEqNat0(Succ(x0), Zero)
new_esEs22(x0, x1, ty_Int)
new_ltEs12(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Bool)
new_esEs4(Right(x0), Right(x1), x2, ty_@0)
new_ltEs19(x0, x1, ty_@0)
new_esEs16([], [], x0)
new_ltEs12(x0, x1, app(ty_Ratio, x2))
new_lt13(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpNat1(Zero, Zero)
new_compare(:(x0, x1), :(x2, x3), x4)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_primMulNat0(Succ(x0), Succ(x1))
new_compare9(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs23(x0, x1, ty_@0)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_lt12(x0, x1, app(ty_Ratio, x2))
new_ltEs7(x0, x1)
new_ltEs14(Left(x0), Left(x1), ty_Int, x2)
new_ltEs12(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_fsEs(x0)
new_esEs5(Just(x0), Just(x1), ty_@0)
new_primPlusNat0(Succ(x0), Zero)
new_lt12(x0, x1, ty_Bool)
new_compare12(x0, x1, False, x2, x3, x4)
new_esEs25(x0, x1, ty_Ordering)
new_esEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_compare11(x0, x1, False, x2, x3)
new_primEqNat0(Zero, Zero)
new_esEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs5(Nothing, Nothing, x0)
new_compare7(x0, x1, x2, x3, x4)
new_lt12(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Left(x0), Left(x1), app(ty_[], x2), x3)
new_primCompAux0(x0, EQ)
new_ltEs15(Just(x0), Just(x1), ty_Bool)
new_esEs25(x0, x1, app(ty_[], x2))
new_ltEs4(True, True)
new_esEs21(x0, x1, ty_Int)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs12(x0, x1, ty_Ordering)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_primMulNat0(Succ(x0), Zero)
new_esEs23(x0, x1, ty_Float)
new_compare31(x0, x1, ty_Integer)
new_compare31(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_Ordering)
new_compare8(Integer(x0), Integer(x1))
new_primMulInt(Pos(x0), Pos(x1))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primMulNat0(Zero, Zero)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs22(x0, x1, app(ty_[], x2))
new_ltEs12(x0, x1, ty_Int)
new_lt17(x0, x1)
new_compare26(x0, x1, True, x2, x3)
new_ltEs14(Right(x0), Right(x1), x2, ty_Integer)
new_lt13(x0, x1, ty_Integer)
new_ltEs10(EQ, LT)
new_ltEs10(LT, EQ)
new_esEs12(x0, x1, ty_Integer)
new_esEs12(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_Int)
new_lt11(x0, x1)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_ltEs15(Just(x0), Just(x1), ty_Integer)
new_lt13(x0, x1, app(ty_[], x2))
new_esEs4(Left(x0), Left(x1), ty_@0, x2)
new_lt20(x0, x1, ty_@0)
new_ltEs14(Left(x0), Left(x1), ty_Char, x2)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_primEqNat0(Zero, Succ(x0))
new_lt13(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, ty_Char)
new_esEs30(x0, x1, ty_Ordering)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Float)
new_esEs21(x0, x1, ty_Double)
new_lt13(x0, x1, app(ty_Maybe, x2))
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs13(x0, x1, ty_Integer)
new_ltEs12(x0, x1, ty_Bool)
new_ltEs14(Left(x0), Left(x1), ty_Integer, x2)
new_compare25(x0, x1, True)
new_esEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_lt12(x0, x1, ty_Int)
new_primCmpNat2(Zero, x0)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_lt14(x0, x1)
new_ltEs15(Just(x0), Just(x1), ty_Double)
new_asAs(False, x0)
new_ltEs4(False, False)
new_esEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Bool)
new_esEs5(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs19(x0, x1, ty_Double)
new_compare27(x0, x1, False)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, ty_@0)
new_esEs21(x0, x1, ty_Float)
new_compare28(x0, x1, x2)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs15(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs15(Just(x0), Just(x1), ty_Ordering)
new_lt20(x0, x1, ty_Ordering)
new_lt12(x0, x1, ty_Float)
new_esEs4(Right(x0), Left(x1), x2, x3)
new_esEs4(Left(x0), Right(x1), x2, x3)
new_esEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs12(x0, x1, ty_Float)
new_esEs28(x0, x1, ty_Int)
new_esEs28(x0, x1, ty_Integer)
new_compare16(x0, x1, True, x2)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs26(x0, x1, ty_Int)
new_asAs(True, x0)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_compare26(x0, x1, False, x2, x3)
new_ltEs15(Just(x0), Just(x1), ty_Int)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_Bool)
new_lt19(x0, x1)
new_esEs23(x0, x1, ty_Char)
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_primPlusNat0(Zero, Zero)
new_ltEs12(x0, x1, app(ty_[], x2))
new_lt12(x0, x1, ty_Char)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_compare31(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_@0)
new_lt12(x0, x1, ty_Integer)
new_lt20(x0, x1, ty_Integer)
new_esEs24(x0, x1, app(ty_[], x2))
new_primPlusNat0(Succ(x0), Succ(x1))
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_lt12(x0, x1, app(app(ty_Either, x2), x3))
new_esEs14(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Ordering)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs30(x0, x1, ty_Float)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs24(x0, x1, ty_Double)
new_esEs23(x0, x1, ty_Double)
new_esEs25(x0, x1, ty_Double)
new_esEs24(x0, x1, ty_Char)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_ltEs20(x0, x1, ty_Double)
new_compare19(Char(x0), Char(x1))
new_esEs21(x0, x1, ty_Char)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs14(x0, x1, ty_Ordering)
new_ltEs14(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs9(x0, x1)
new_compare([], :(x0, x1), x2)
new_ltEs15(Just(x0), Nothing, x1)
new_ltEs20(x0, x1, ty_Int)
new_lt6(x0, x1)
new_esEs30(x0, x1, ty_Double)
new_ltEs17(x0, x1)
new_esEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_compare24(x0, x1, False, x2, x3)
new_ltEs10(GT, LT)
new_ltEs10(LT, GT)
new_primPlusNat0(Zero, Succ(x0))
new_esEs14(x0, x1, ty_Bool)
new_esEs30(x0, x1, ty_Bool)
new_esEs10(@0, @0)
new_esEs24(x0, x1, ty_Ordering)
new_esEs14(x0, x1, ty_Char)
new_esEs30(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, app(ty_[], x2))
new_compare31(x0, x1, ty_Double)
new_ltEs16(x0, x1)
new_ltEs11(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_compare111(x0, x1, True)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_lt12(x0, x1, ty_Double)
new_esEs9(x0, x1)
new_esEs5(Just(x0), Just(x1), ty_Ordering)
new_esEs5(Just(x0), Nothing, x1)
new_lt9(x0, x1, x2, x3)
new_esEs13(x0, x1, ty_Bool)
new_esEs29(x0, x1, ty_Ordering)
new_esEs13(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_Float)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_ltEs14(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs15(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs15(Just(x0), Just(x1), ty_Char)
new_compare13(@0, @0)
new_esEs16([], :(x0, x1), x2)
new_ltEs15(Nothing, Just(x0), x1)
new_esEs22(x0, x1, ty_Char)
new_esEs12(x0, x1, app(ty_[], x2))
new_compare11(x0, x1, True, x2, x3)
new_esEs12(x0, x1, ty_Ordering)
new_compare6(x0, x1, x2, x3)
new_esEs13(x0, x1, ty_Int)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs15(True, False)
new_esEs15(False, True)
new_sr0(Integer(x0), Integer(x1))
new_esEs4(Left(x0), Left(x1), ty_Integer, x2)
new_esEs29(x0, x1, ty_Double)
new_esEs17(:%(x0, x1), :%(x2, x3), x4)
new_lt13(x0, x1, ty_Bool)
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs30(x0, x1, ty_Int)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs14(Left(x0), Left(x1), ty_Bool, x2)
new_compare31(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, ty_Bool)
new_esEs19(Float(x0, x1), Float(x2, x3))
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs14(Right(x0), Right(x1), x2, ty_@0)
new_esEs13(x0, x1, ty_Float)
new_lt16(x0, x1)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Int)
new_lt18(x0, x1)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs16(:(x0, x1), :(x2, x3), x4)
new_esEs24(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_@0)
new_esEs16(:(x0, x1), [], x2)
new_lt7(x0, x1, x2)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_compare18(Double(x0, x1), Double(x2, x3))
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_primCmpNat1(Succ(x0), Zero)
new_esEs13(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt13(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Integer)
new_primCompAux0(x0, GT)
new_esEs4(Left(x0), Left(x1), ty_Int, x2)
new_lt13(x0, x1, ty_Ordering)
new_ltEs12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare(:(x0, x1), [], x2)
new_lt12(x0, x1, app(ty_[], x2))
new_ltEs14(Left(x0), Left(x1), ty_Double, x2)
new_esEs30(x0, x1, ty_@0)
new_ltEs5(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, ty_Int)
new_esEs22(x0, x1, ty_@0)
new_primMulNat0(Zero, Succ(x0))
new_lt12(x0, x1, ty_Ordering)
new_esEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Just(x0), Just(x1), ty_Integer)
new_esEs5(Just(x0), Just(x1), ty_Char)
new_esEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs12(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs8(Double(x0, x1), Double(x2, x3))
new_esEs4(Left(x0), Left(x1), ty_Char, x2)
new_esEs22(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Ordering)
new_esEs12(x0, x1, app(ty_Maybe, x2))
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs4(False, True)
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_ltEs4(True, False)
new_esEs14(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs26(x0, x1, ty_Float)
new_lt4(x0, x1)
new_compare([], [], x0)
new_esEs12(x0, x1, ty_Bool)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs12(x0, x1, ty_Int)
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs14(x0, x1, ty_Int)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_primPlusNat1(x0, x1)
new_esEs21(x0, x1, ty_Ordering)
new_ltEs18(x0, x1)
new_ltEs15(Nothing, Nothing, x0)
new_esEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs29(x0, x1, ty_Integer)
new_esEs12(x0, x1, app(ty_Ratio, x2))
new_compare111(x0, x1, False)
new_ltEs12(x0, x1, app(ty_Maybe, x2))
new_compare31(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs6(x0, x1, x2)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs10(GT, GT)
new_esEs25(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs13(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Float)
new_esEs29(x0, x1, ty_Char)
new_ltEs15(Just(x0), Just(x1), ty_Float)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs30(x0, x1, ty_Char)
new_ltEs14(Right(x0), Right(x1), x2, ty_Char)
new_compare16(x0, x1, False, x2)
new_primEqNat0(Succ(x0), Succ(x1))
new_ltEs20(x0, x1, ty_Integer)
new_primCmpNat0(x0, Zero)
new_lt20(x0, x1, app(ty_[], x2))
new_lt12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_not(True)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, ty_Char)
new_esEs22(x0, x1, ty_Float)
new_esEs4(Right(x0), Right(x1), x2, ty_Char)
new_compare9(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs12(x0, x1, ty_Double)
new_esEs4(Left(x0), Left(x1), ty_Double, x2)
new_esEs26(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_Float)
new_lt20(x0, x1, ty_Double)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_not(False)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs14(x0, x1, app(ty_Maybe, x2))
new_ltEs13(x0, x1, x2)
new_esEs26(x0, x1, ty_Char)
new_primCompAux1(x0, x1, x2, x3)
new_primCmpNat1(Zero, Succ(x0))
new_compare110(x0, x1, False, x2, x3)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs10(EQ, GT)
new_ltEs10(GT, EQ)
new_ltEs20(x0, x1, ty_Char)
new_lt13(x0, x1, ty_Char)
new_ltEs14(Left(x0), Left(x1), ty_@0, x2)
new_esEs23(x0, x1, app(ty_[], x2))
new_compare27(x0, x1, True)
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_compare31(x0, x1, ty_Char)
new_esEs4(Right(x0), Right(x1), x2, ty_Int)
new_compare15(x0, x1, x2, x3)
new_primCmpNat0(x0, Succ(x1))
new_esEs14(x0, x1, ty_Double)
new_ltEs12(x0, x1, ty_Char)
new_compare24(x0, x1, True, x2, x3)
new_lt8(x0, x1, x2, x3)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(Right(x0), Right(x1), x2, ty_Float)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_ltEs12(x0, x1, ty_Float)
new_esEs21(x0, x1, ty_@0)
new_esEs13(x0, x1, app(ty_Maybe, x2))
new_esEs4(Left(x0), Left(x1), ty_Float, x2)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_ltEs15(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs8(x0, x1)
new_ltEs19(x0, x1, ty_Bool)
new_esEs29(x0, x1, ty_Int)
new_esEs13(x0, x1, app(ty_[], x2))
new_esEs25(x0, x1, ty_Int)
new_compare31(x0, x1, ty_Bool)
new_esEs13(x0, x1, ty_@0)
new_ltEs15(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_compare31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs14(x0, x1, app(app(ty_@2, x2), x3))
new_esEs14(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Integer)
new_lt20(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_Int)
new_esEs14(x0, x1, ty_Float)
new_esEs12(x0, x1, ty_@0)
new_esEs24(x0, x1, ty_Integer)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_primEqInt(Pos(Zero), Pos(Zero))
new_ltEs14(Left(x0), Right(x1), x2, x3)
new_ltEs14(Right(x0), Left(x1), x2, x3)
new_lt15(x0, x1, x2)
new_esEs13(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_compare25(x0, x1, False)
new_ltEs15(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs14(Right(x0), Right(x1), x2, ty_Bool)
new_esEs4(Right(x0), Right(x1), x2, ty_Double)
new_compare10(x0, x1, False)
new_pePe(True, x0)
new_esEs27(x0, x1, ty_Integer)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Just(x0), Just(x1), ty_Float)
new_compare5(x0, x1)
new_ltEs20(x0, x1, ty_Ordering)
new_lt13(x0, x1, ty_@0)
new_esEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs21(x0, x1, app(ty_[], x2))
new_ltEs10(EQ, EQ)
new_lt12(x0, x1, ty_@0)



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

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

new_addToFM_C1(wzz31, wzz32, wzz33, wzz34, wzz5, True, h, ba) → new_addToFM_C(wzz34, Nothing, wzz5, h, ba)
new_addToFM_C2(wzz300, wzz31, wzz32, wzz33, wzz34, wzz5, True, h, ba) → new_addToFM_C(wzz33, Nothing, wzz5, h, ba)
new_addToFM_C(Branch(Nothing, wzz31, wzz32, wzz33, wzz34), Nothing, wzz5, h, ba) → new_addToFM_C1(wzz31, wzz32, wzz33, wzz34, wzz5, new_esEs11(new_compare29(Nothing, Nothing, True, h), GT), h, ba)
new_addToFM_C2(wzz300, wzz31, wzz32, wzz33, wzz34, wzz5, False, h, ba) → new_addToFM_C10(wzz300, wzz31, wzz32, wzz33, wzz34, wzz5, new_esEs11(new_compare29(Nothing, Just(wzz300), False, h), GT), h, ba)
new_addToFM_C(Branch(Just(wzz300), wzz31, wzz32, wzz33, wzz34), Nothing, wzz5, h, ba) → new_addToFM_C2(wzz300, wzz31, wzz32, wzz33, wzz34, wzz5, new_esEs11(new_compare29(Nothing, Just(wzz300), False, h), LT), h, ba)
new_addToFM_C10(wzz300, wzz31, wzz32, wzz33, wzz34, wzz5, True, h, ba) → new_addToFM_C(wzz34, Nothing, wzz5, h, ba)

The TRS R consists of the following rules:

new_compare29(Nothing, Just(wzz3200), False, beh) → LT
new_esEs11(GT, LT) → False
new_esEs11(EQ, LT) → False
new_esEs11(LT, LT) → True
new_compare29(wzz310, wzz320, True, beh) → EQ
new_esEs11(GT, GT) → True
new_esEs11(LT, GT) → False
new_esEs11(EQ, GT) → False

The set Q consists of the following terms:

new_compare29(Nothing, Nothing, False, x0)
new_esEs11(EQ, GT)
new_esEs11(GT, EQ)
new_esEs11(GT, LT)
new_esEs11(LT, GT)
new_esEs11(LT, LT)
new_compare29(Just(x0), Nothing, False, x1)
new_esEs11(EQ, LT)
new_esEs11(LT, EQ)
new_compare29(Nothing, Just(x0), False, x1)
new_esEs11(GT, GT)
new_compare29(x0, x1, True, x2)
new_compare29(Just(x0), Just(x1), False, x2)
new_esEs11(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: