YES 9.954 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 c, Ord a) => FiniteMap (a,c) b  ->  (a,c ->  b  ->  FiniteMap (a,c) b) :: (Ord c, Ord a) => FiniteMap (a,c) b  ->  (a,c ->  b  ->  FiniteMap (a,c) b)

module FiniteMap where
  import qualified Maybe
import qualified Prelude

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


  instance (Eq a, Eq b) => Eq (FiniteMap 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 (\old new ->new) fm key elt

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

  emptyFM :: FiniteMap b a
emptyFM EmptyFM

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

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

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

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

  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



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

module FiniteMap where
  import qualified Maybe
import qualified Prelude

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


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

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

  
addToFM0 old new new

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

  emptyFM :: FiniteMap b a
emptyFM EmptyFM

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

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

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

  
fmToList0 key elt rest (key,elt: rest

  foldFM :: (b  ->  c  ->  a  ->  a ->  a  ->  FiniteMap b c  ->  a
foldFM k z EmptyFM z
foldFM k z (Branch key elt _ fm_l fm_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 :: b  ->  a  ->  FiniteMap b a
unitFM key elt Branch key elt 1 emptyFM emptyFM


module Maybe where
  import qualified FiniteMap
import qualified Prelude



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

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

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

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

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

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

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

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

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

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



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
HASKELL
          ↳ IFR

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

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

  
fmToList0 key elt rest (key,elt: rest

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

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

module FiniteMap where
  import qualified Maybe
import qualified Prelude

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


  instance (Eq a, Eq b) => Eq (FiniteMap 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 a b
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 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 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 c, Ord b) => FiniteMap (b,c) a  ->  (b,c ->  a  ->  FiniteMap (b,c) a) :: (Ord c, Ord b) => FiniteMap (b,c) a  ->  (b,c ->  a  ->  FiniteMap (b,c) a)

module FiniteMap where
  import qualified Maybe
import qualified Prelude

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


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

  addToFM :: Ord 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 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 
 | 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 b => Int  ->  b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a
mkBranch which key elt fm_l fm_r 
let 
result Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r
in result
 where 
balance_ok True
left_ok left_ok0 fm_l key fm_l
left_ok0 fm_l key EmptyFM True
left_ok0 fm_l key (Branch left_key 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 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



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)

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)

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_C0 combiner key elt size fm_l fm_r new_key new_elt True = Branch new_key (combiner elt new_eltsize fm_l fm_r

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

addToFM_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)

compare0 x y True = GT

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

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 c, Ord b) => FiniteMap (b,c) a  ->  (b,c ->  a  ->  FiniteMap (b,c) a) :: (Ord c, Ord b) => FiniteMap (b,c) a  ->  (b,c ->  a  ->  FiniteMap (b,c) 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 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 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 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 b => Int  ->  b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a
mkBranch which key elt fm_l fm_r 
let 
result Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r
in result
 where 
balance_ok True
left_ok left_ok0 fm_l key fm_l
left_ok0 fm_l key EmptyFM True
left_ok0 fm_l key (Branch left_key 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 a b  ->  Int
sizeFM EmptyFM 0
sizeFM (Branch xx xy size xz yusize

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude



Let/Where Reductions:
The bindings of the following Let/Where expression
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
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

mkBranchBalance_ok wxw wxx wxy = True

mkBranchRight_ok wxw wxx wxy = mkBranchRight_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

mkBranchLeft_size wxw wxx wxy = sizeFM wxy

mkBranchRight_size wxw wxx wxy = sizeFM wxw

mkBranchLeft_ok wxw wxx wxy = mkBranchLeft_ok0 wxw wxx wxy wxy wxx wxy

mkBranchUnbox wxw wxx wxy x = x

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)) wyw wyv

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
mkBalBranch6Size_l wyx wyy wyz wzu = sizeFM wyx

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

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 wyy wyz 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

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 wyy wyz fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr)

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)

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)

mkBalBranch6Size_r wyx wyy wyz wzu = sizeFM wzu

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

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

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)

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 wyy wyz fm_lrr fm_r)

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)

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)

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

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 wyy wyz fm_lr fm_r)

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 wzv = fst (findMin wzv)

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 wzw = fst (findMax 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' x wuy = gcd0Gcd'2 x wuy
gcd0Gcd' x y = gcd0Gcd'0 x y

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

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

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



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

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

module FiniteMap where
  import qualified Maybe
import qualified Prelude

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


  instance (Eq a, Eq b) => Eq (FiniteMap 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 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 :: (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 mkBalBranch6 key elt fm_L fm_R

  
mkBalBranch6 key elt fm_L fm_R mkBalBranch6MkBalBranch5 fm_L key elt fm_R key elt fm_L fm_R (mkBalBranch6Size_l fm_L key elt fm_R + mkBalBranch6Size_r fm_L key elt 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 wyy wyz 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 wyy wyz 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 wyy wyz 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 wyy wyz fm_lr fm_r)

  
mkBalBranch6Size_l wyx wyy wyz wzu sizeFM wyx

  
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_r fm_l

  
mkBranchBalance_ok wxw wxx wxy True

  
mkBranchLeft_ok wxw wxx wxy mkBranchLeft_ok0 wxw wxx wxy wxy wxx wxy

  
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 wzw fst (findMax wzw)

  
mkBranchLeft_size wxw wxx wxy sizeFM wxy

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

  
mkBranchRight_ok wxw wxx wxy mkBranchRight_ok0 wxw wxx wxy wxw wxx wxw

  
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 wzv fst (findMin wzv)

  
mkBranchRight_size wxw wxx wxy sizeFM wxw

  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 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



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 c, Ord b) => FiniteMap (b,c) a  ->  (b,c ->  a  ->  FiniteMap (b,c) a)

module FiniteMap where
  import qualified Maybe
import qualified Prelude

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


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

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

  
addToFM0 old new new

  addToFM_C :: Ord a => (b  ->  b  ->  b ->  FiniteMap a b  ->  a  ->  b  ->  FiniteMap a b
addToFM_C combiner EmptyFM key elt addToFM_C4 combiner EmptyFM key elt
addToFM_C combiner (Branch key elt size fm_l fm_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 b a  ->  (b,a)
findMin (Branch key elt wz EmptyFM xu(key,elt)
findMin (Branch key elt xv fm_l xwfindMin fm_l

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

  
fmToList0 key elt rest (key,elt: rest

  foldFM :: (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 fm_L key elt fm_R key elt fm_L fm_R (mkBalBranch6Size_l fm_L key elt fm_R + mkBalBranch6Size_r fm_L key elt 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))))))) wyy wyz 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))))))))))))) wyy wyz 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))))) wyy wyz 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)))))))))) wyy wyz fm_lr fm_r)

  
mkBalBranch6Size_l wyx wyy wyz wzu sizeFM wyx

  
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_r fm_l

  
mkBranchBalance_ok wxw wxx wxy True

  
mkBranchLeft_ok wxw wxx wxy mkBranchLeft_ok0 wxw wxx wxy wxy wxx wxy

  
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 wzw fst (findMax wzw)

  
mkBranchLeft_size wxw wxx wxy sizeFM wxy

  
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)) wyw wyv

  
mkBranchRight_ok wxw wxx wxy mkBranchRight_ok0 wxw wxx wxy wxw wxx wxw

  
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 wzv fst (findMin wzv)

  
mkBranchRight_size wxw wxx wxy sizeFM wxw

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude



Haskell To QDPs


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

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(wzz47000), Succ(wzz49000)) → new_primCmpNat(wzz47000, wzz49000)

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(wzz39200), Succ(wzz10100)) → new_primMinusNat(wzz39200, wzz10100)

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(wzz39200), Succ(wzz10100)) → new_primPlusNat(wzz39200, wzz10100)

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(wzz40000), Succ(wzz300000)) → new_primMulNat(wzz40000, Succ(wzz300000))

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

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_ltEs0(@3(wzz4710, wzz4711, wzz4712), @3(wzz4910, wzz4911, wzz4912), fb, app(ty_Maybe, gd), eb) → new_lt3(wzz4711, wzz4911, gd)
new_ltEs1(@2(wzz4710, wzz4711), @2(wzz4910, wzz4911), bbf, app(app(ty_@2, bcd), bce)) → new_ltEs1(wzz4711, wzz4911, bcd, bce)
new_lt3(wzz470, wzz490, bed) → new_compare22(wzz470, wzz490, new_esEs7(wzz470, wzz490, bed), bed)
new_compare21(@2(wzz470, @3(wzz4710, wzz4711, wzz4712)), @2(wzz490, @3(wzz4910, wzz4911, wzz4912)), False, bac, app(app(app(ty_@3, fb), ea), app(app(ty_@2, hb), hc))) → new_ltEs1(wzz4712, wzz4912, hb, hc)
new_compare3(:(wzz4700, wzz4701), :(wzz4900, wzz4901), bec) → new_compare3(wzz4701, wzz4901, bec)
new_compare21(@2(wzz470, @3(wzz4710, wzz4711, wzz4712)), @2(wzz490, @3(wzz4910, wzz4911, wzz4912)), False, bac, app(app(app(ty_@3, fb), ea), app(ty_[], hd))) → new_ltEs2(wzz4712, wzz4912, hd)
new_ltEs(Right(wzz4710), Right(wzz4910), cd, app(app(ty_Either, ce), cf)) → new_ltEs(wzz4710, wzz4910, ce, cf)
new_ltEs3(Just(wzz4710), Just(wzz4910), app(app(app(ty_@3, bdc), bdd), bde)) → new_ltEs0(wzz4710, wzz4910, bdc, bdd, bde)
new_compare21(@2(wzz470, @2(wzz4710, wzz4711)), @2(wzz490, @2(wzz4910, wzz4911)), False, bac, app(app(ty_@2, bbf), app(ty_Maybe, bcg))) → new_ltEs3(wzz4711, wzz4911, bcg)
new_ltEs3(Just(wzz4710), Just(wzz4910), app(app(ty_Either, bda), bdb)) → new_ltEs(wzz4710, wzz4910, bda, bdb)
new_compare(wzz470, wzz490, h, ba) → new_compare2(wzz470, wzz490, new_esEs4(wzz470, wzz490, h, ba), h, ba)
new_compare3(:(wzz4700, wzz4701), :(wzz4900, wzz4901), bec) → new_primCompAux(wzz4700, wzz4900, new_compare4(wzz4701, wzz4901, bec), bec)
new_compare21(@2(wzz470, @3(wzz4710, wzz4711, wzz4712)), @2(wzz490, @3(wzz4910, wzz4911, wzz4912)), False, bac, app(app(app(ty_@3, fb), app(ty_Maybe, gd)), eb)) → new_lt3(wzz4711, wzz4911, gd)
new_compare21(@2(wzz470, @3(wzz4710, wzz4711, wzz4712)), @2(wzz490, @3(wzz4910, wzz4911, wzz4912)), False, bac, app(app(app(ty_@3, app(app(ty_Either, dg), dh)), ea), eb)) → new_lt(wzz4710, wzz4910, dg, dh)
new_ltEs0(@3(wzz4710, wzz4711, wzz4712), @3(wzz4910, wzz4911, wzz4912), app(app(ty_@2, ef), eg), ea, eb) → new_lt1(wzz4710, wzz4910, ef, eg)
new_compare21(@2(wzz470, @3(wzz4710, wzz4711, wzz4712)), @2(wzz490, @3(wzz4910, wzz4911, wzz4912)), False, bac, app(app(app(ty_@3, fb), ea), app(app(app(ty_@3, gg), gh), ha))) → new_ltEs0(wzz4712, wzz4912, gg, gh, ha)
new_compare21(@2(wzz470, @2(wzz4710, wzz4711)), @2(wzz490, @2(wzz4910, wzz4911)), False, bac, app(app(ty_@2, app(app(ty_@2, bbb), bbc)), baf)) → new_lt1(wzz4710, wzz4910, bbb, bbc)
new_ltEs(Left(wzz4710), Left(wzz4910), app(ty_Maybe, cc), bd) → new_ltEs3(wzz4710, wzz4910, cc)
new_ltEs0(@3(wzz4710, wzz4711, wzz4712), @3(wzz4910, wzz4911, wzz4912), fb, app(ty_[], gc), eb) → new_lt2(wzz4711, wzz4911, gc)
new_compare21(@2(wzz470, @3(wzz4710, wzz4711, wzz4712)), @2(wzz490, @3(wzz4910, wzz4911, wzz4912)), False, bac, app(app(app(ty_@3, app(ty_Maybe, fa)), ea), eb)) → new_lt3(wzz4710, wzz4910, fa)
new_compare21(@2(wzz470, @2(wzz4710, wzz4711)), @2(wzz490, @2(wzz4910, wzz4911)), False, bac, app(app(ty_@2, app(ty_Maybe, bbe)), baf)) → new_lt3(wzz4710, wzz4910, bbe)
new_ltEs1(@2(wzz4710, wzz4711), @2(wzz4910, wzz4911), bbf, app(ty_Maybe, bcg)) → new_ltEs3(wzz4711, wzz4911, bcg)
new_ltEs0(@3(wzz4710, wzz4711, wzz4712), @3(wzz4910, wzz4911, wzz4912), app(ty_[], eh), ea, eb) → new_lt2(wzz4710, wzz4910, eh)
new_ltEs0(@3(wzz4710, wzz4711, wzz4712), @3(wzz4910, wzz4911, wzz4912), fb, ea, app(ty_Maybe, he)) → new_ltEs3(wzz4712, wzz4912, he)
new_ltEs(Left(wzz4710), Left(wzz4910), app(app(ty_@2, bh), ca), bd) → new_ltEs1(wzz4710, wzz4910, bh, ca)
new_lt0(wzz470, wzz490, hf, hg, hh) → new_compare20(wzz470, wzz490, new_esEs5(wzz470, wzz490, hf, hg, hh), hf, hg, hh)
new_compare21(@2(wzz470, Left(wzz4710)), @2(wzz490, Left(wzz4910)), False, bac, app(app(ty_Either, app(ty_[], cb)), bd)) → new_ltEs2(wzz4710, wzz4910, cb)
new_compare21(@2(wzz470, wzz471), @2(wzz490, wzz491), False, app(ty_Maybe, bed), beb) → new_compare22(wzz470, wzz490, new_esEs7(wzz470, wzz490, bed), bed)
new_lt1(wzz470, wzz490, baa, bab) → new_compare21(wzz470, wzz490, new_esEs6(wzz470, wzz490, baa, bab), baa, bab)
new_compare0(wzz470, wzz490, hf, hg, hh) → new_compare20(wzz470, wzz490, new_esEs5(wzz470, wzz490, hf, hg, hh), hf, hg, hh)
new_compare21(@2(wzz470, Right(wzz4710)), @2(wzz490, Right(wzz4910)), False, bac, app(app(ty_Either, cd), app(app(ty_Either, ce), cf))) → new_ltEs(wzz4710, wzz4910, ce, cf)
new_ltEs1(@2(wzz4710, wzz4711), @2(wzz4910, wzz4911), app(ty_[], bbd), baf) → new_lt2(wzz4710, wzz4910, bbd)
new_compare21(@2(wzz470, @2(wzz4710, wzz4711)), @2(wzz490, @2(wzz4910, wzz4911)), False, bac, app(app(ty_@2, app(app(ty_Either, bad), bae)), baf)) → new_lt(wzz4710, wzz4910, bad, bae)
new_ltEs0(@3(wzz4710, wzz4711, wzz4712), @3(wzz4910, wzz4911, wzz4912), fb, app(app(ty_Either, fc), fd), eb) → new_lt(wzz4711, wzz4911, fc, fd)
new_compare21(@2(wzz470, Left(wzz4710)), @2(wzz490, Left(wzz4910)), False, bac, app(app(ty_Either, app(app(app(ty_@3, be), bf), bg)), bd)) → new_ltEs0(wzz4710, wzz4910, be, bf, bg)
new_ltEs0(@3(wzz4710, wzz4711, wzz4712), @3(wzz4910, wzz4911, wzz4912), fb, ea, app(app(app(ty_@3, gg), gh), ha)) → new_ltEs0(wzz4712, wzz4912, gg, gh, ha)
new_ltEs0(@3(wzz4710, wzz4711, wzz4712), @3(wzz4910, wzz4911, wzz4912), fb, app(app(ty_@2, ga), gb), eb) → new_lt1(wzz4711, wzz4911, ga, gb)
new_ltEs(Right(wzz4710), Right(wzz4910), cd, app(ty_Maybe, df)) → new_ltEs3(wzz4710, wzz4910, df)
new_compare21(@2(wzz470, @3(wzz4710, wzz4711, wzz4712)), @2(wzz490, @3(wzz4910, wzz4911, wzz4912)), False, bac, app(app(app(ty_@3, app(ty_[], eh)), ea), eb)) → new_lt2(wzz4710, wzz4910, eh)
new_compare21(@2(:(wzz4700, wzz4701), wzz471), @2(:(wzz4900, wzz4901), wzz491), False, app(ty_[], bec), beb) → new_primCompAux(wzz4700, wzz4900, new_compare4(wzz4701, wzz4901, bec), bec)
new_compare21(@2(wzz470, @3(wzz4710, wzz4711, wzz4712)), @2(wzz490, @3(wzz4910, wzz4911, wzz4912)), False, bac, app(app(app(ty_@3, fb), app(ty_[], gc)), eb)) → new_lt2(wzz4711, wzz4911, gc)
new_lt2(:(wzz4700, wzz4701), :(wzz4900, wzz4901), bec) → new_primCompAux(wzz4700, wzz4900, new_compare4(wzz4701, wzz4901, bec), bec)
new_primCompAux(wzz4700, wzz4900, wzz140, app(ty_[], bfd)) → new_compare3(wzz4700, wzz4900, bfd)
new_primCompAux(wzz4700, wzz4900, wzz140, app(app(ty_Either, bee), bef)) → new_compare(wzz4700, wzz4900, bee, bef)
new_ltEs0(@3(wzz4710, wzz4711, wzz4712), @3(wzz4910, wzz4911, wzz4912), fb, ea, app(app(ty_@2, hb), hc)) → new_ltEs1(wzz4712, wzz4912, hb, hc)
new_compare21(@2(wzz470, Left(wzz4710)), @2(wzz490, Left(wzz4910)), False, bac, app(app(ty_Either, app(app(ty_Either, bb), bc)), bd)) → new_ltEs(wzz4710, wzz4910, bb, bc)
new_ltEs(Left(wzz4710), Left(wzz4910), app(app(app(ty_@3, be), bf), bg), bd) → new_ltEs0(wzz4710, wzz4910, be, bf, bg)
new_ltEs(Left(wzz4710), Left(wzz4910), app(ty_[], cb), bd) → new_ltEs2(wzz4710, wzz4910, cb)
new_compare20(wzz470, wzz490, False, hf, hg, hh) → new_ltEs0(wzz470, wzz490, hf, hg, hh)
new_compare21(@2(wzz470, Left(wzz4710)), @2(wzz490, Left(wzz4910)), False, bac, app(app(ty_Either, app(app(ty_@2, bh), ca)), bd)) → new_ltEs1(wzz4710, wzz4910, bh, ca)
new_ltEs(Right(wzz4710), Right(wzz4910), cd, app(ty_[], de)) → new_ltEs2(wzz4710, wzz4910, de)
new_primCompAux(wzz4700, wzz4900, wzz140, app(app(ty_@2, bfb), bfc)) → new_compare1(wzz4700, wzz4900, bfb, bfc)
new_compare21(@2(wzz470, @2(wzz4710, wzz4711)), @2(wzz490, @2(wzz4910, wzz4911)), False, bac, app(app(ty_@2, bbf), app(ty_[], bcf))) → new_ltEs2(wzz4711, wzz4911, bcf)
new_ltEs3(Just(wzz4710), Just(wzz4910), app(ty_Maybe, bea)) → new_ltEs3(wzz4710, wzz4910, bea)
new_compare21(@2(wzz470, @3(wzz4710, wzz4711, wzz4712)), @2(wzz490, @3(wzz4910, wzz4911, wzz4912)), False, bac, app(app(app(ty_@3, fb), app(app(ty_Either, fc), fd)), eb)) → new_lt(wzz4711, wzz4911, fc, fd)
new_compare21(@2(wzz470, @3(wzz4710, wzz4711, wzz4712)), @2(wzz490, @3(wzz4910, wzz4911, wzz4912)), False, bac, app(app(app(ty_@3, fb), ea), app(app(ty_Either, ge), gf))) → new_ltEs(wzz4712, wzz4912, ge, gf)
new_compare21(@2(wzz470, Right(wzz4710)), @2(wzz490, Right(wzz4910)), False, bac, app(app(ty_Either, cd), app(ty_[], de))) → new_ltEs2(wzz4710, wzz4910, de)
new_lt(wzz470, wzz490, h, ba) → new_compare2(wzz470, wzz490, new_esEs4(wzz470, wzz490, h, ba), h, ba)
new_compare21(@2(wzz470, @2(wzz4710, wzz4711)), @2(wzz490, @2(wzz4910, wzz4911)), False, bac, app(app(ty_@2, bbf), app(app(ty_@2, bcd), bce))) → new_ltEs1(wzz4711, wzz4911, bcd, bce)
new_compare21(@2(wzz470, @2(wzz4710, wzz4711)), @2(wzz490, @2(wzz4910, wzz4911)), False, bac, app(app(ty_@2, app(ty_[], bbd)), baf)) → new_lt2(wzz4710, wzz4910, bbd)
new_compare2(wzz470, wzz490, False, h, ba) → new_ltEs(wzz470, wzz490, h, ba)
new_ltEs(Left(wzz4710), Left(wzz4910), app(app(ty_Either, bb), bc), bd) → new_ltEs(wzz4710, wzz4910, bb, bc)
new_lt2(:(wzz4700, wzz4701), :(wzz4900, wzz4901), bec) → new_compare3(wzz4701, wzz4901, bec)
new_ltEs0(@3(wzz4710, wzz4711, wzz4712), @3(wzz4910, wzz4911, wzz4912), app(app(app(ty_@3, ec), ed), ee), ea, eb) → new_lt0(wzz4710, wzz4910, ec, ed, ee)
new_ltEs1(@2(wzz4710, wzz4711), @2(wzz4910, wzz4911), bbf, app(app(app(ty_@3, bca), bcb), bcc)) → new_ltEs0(wzz4711, wzz4911, bca, bcb, bcc)
new_compare21(@2(wzz470, @3(wzz4710, wzz4711, wzz4712)), @2(wzz490, @3(wzz4910, wzz4911, wzz4912)), False, bac, app(app(app(ty_@3, fb), app(app(ty_@2, ga), gb)), eb)) → new_lt1(wzz4711, wzz4911, ga, gb)
new_compare21(@2(wzz470, Just(wzz4710)), @2(wzz490, Just(wzz4910)), False, bac, app(ty_Maybe, app(app(ty_Either, bda), bdb))) → new_ltEs(wzz4710, wzz4910, bda, bdb)
new_primCompAux(wzz4700, wzz4900, wzz140, app(app(app(ty_@3, beg), beh), bfa)) → new_compare0(wzz4700, wzz4900, beg, beh, bfa)
new_ltEs1(@2(wzz4710, wzz4711), @2(wzz4910, wzz4911), app(ty_Maybe, bbe), baf) → new_lt3(wzz4710, wzz4910, bbe)
new_compare21(@2(wzz470, Right(wzz4710)), @2(wzz490, Right(wzz4910)), False, bac, app(app(ty_Either, cd), app(app(app(ty_@3, cg), da), db))) → new_ltEs0(wzz4710, wzz4910, cg, da, db)
new_compare21(@2(:(wzz4700, wzz4701), wzz471), @2(:(wzz4900, wzz4901), wzz491), False, app(ty_[], bec), beb) → new_compare3(wzz4701, wzz4901, bec)
new_compare21(@2(wzz470, @3(wzz4710, wzz4711, wzz4712)), @2(wzz490, @3(wzz4910, wzz4911, wzz4912)), False, bac, app(app(app(ty_@3, app(app(ty_@2, ef), eg)), ea), eb)) → new_lt1(wzz4710, wzz4910, ef, eg)
new_ltEs0(@3(wzz4710, wzz4711, wzz4712), @3(wzz4910, wzz4911, wzz4912), app(ty_Maybe, fa), ea, eb) → new_lt3(wzz4710, wzz4910, fa)
new_compare21(@2(wzz470, Just(wzz4710)), @2(wzz490, Just(wzz4910)), False, bac, app(ty_Maybe, app(ty_[], bdh))) → new_ltEs2(wzz4710, wzz4910, bdh)
new_compare5(wzz470, wzz490, bed) → new_compare22(wzz470, wzz490, new_esEs7(wzz470, wzz490, bed), bed)
new_compare22(wzz470, wzz490, False, bed) → new_ltEs3(wzz470, wzz490, bed)
new_ltEs1(@2(wzz4710, wzz4711), @2(wzz4910, wzz4911), app(app(ty_Either, bad), bae), baf) → new_lt(wzz4710, wzz4910, bad, bae)
new_ltEs3(Just(wzz4710), Just(wzz4910), app(ty_[], bdh)) → new_ltEs2(wzz4710, wzz4910, bdh)
new_ltEs1(@2(wzz4710, wzz4711), @2(wzz4910, wzz4911), bbf, app(ty_[], bcf)) → new_ltEs2(wzz4711, wzz4911, bcf)
new_compare21(@2(wzz470, @2(wzz4710, wzz4711)), @2(wzz490, @2(wzz4910, wzz4911)), False, bac, app(app(ty_@2, app(app(app(ty_@3, bag), bah), bba)), baf)) → new_lt0(wzz4710, wzz4910, bag, bah, bba)
new_compare21(@2(wzz470, Right(wzz4710)), @2(wzz490, Right(wzz4910)), False, bac, app(app(ty_Either, cd), app(app(ty_@2, dc), dd))) → new_ltEs1(wzz4710, wzz4910, dc, dd)
new_ltEs3(Just(wzz4710), Just(wzz4910), app(app(ty_@2, bdf), bdg)) → new_ltEs1(wzz4710, wzz4910, bdf, bdg)
new_compare21(@2(wzz470, @2(wzz4710, wzz4711)), @2(wzz490, @2(wzz4910, wzz4911)), False, bac, app(app(ty_@2, bbf), app(app(app(ty_@3, bca), bcb), bcc))) → new_ltEs0(wzz4711, wzz4911, bca, bcb, bcc)
new_ltEs2(wzz471, wzz491, bch) → new_compare3(wzz471, wzz491, bch)
new_ltEs0(@3(wzz4710, wzz4711, wzz4712), @3(wzz4910, wzz4911, wzz4912), fb, app(app(app(ty_@3, ff), fg), fh), eb) → new_lt0(wzz4711, wzz4911, ff, fg, fh)
new_compare1(wzz470, wzz490, baa, bab) → new_compare21(wzz470, wzz490, new_esEs6(wzz470, wzz490, baa, bab), baa, bab)
new_compare21(@2(wzz470, Just(wzz4710)), @2(wzz490, Just(wzz4910)), False, bac, app(ty_Maybe, app(ty_Maybe, bea))) → new_ltEs3(wzz4710, wzz4910, bea)
new_compare21(@2(wzz470, @3(wzz4710, wzz4711, wzz4712)), @2(wzz490, @3(wzz4910, wzz4911, wzz4912)), False, bac, app(app(app(ty_@3, fb), ea), app(ty_Maybe, he))) → new_ltEs3(wzz4712, wzz4912, he)
new_ltEs1(@2(wzz4710, wzz4711), @2(wzz4910, wzz4911), app(app(ty_@2, bbb), bbc), baf) → new_lt1(wzz4710, wzz4910, bbb, bbc)
new_ltEs1(@2(wzz4710, wzz4711), @2(wzz4910, wzz4911), bbf, app(app(ty_Either, bbg), bbh)) → new_ltEs(wzz4711, wzz4911, bbg, bbh)
new_compare21(@2(wzz470, Right(wzz4710)), @2(wzz490, Right(wzz4910)), False, bac, app(app(ty_Either, cd), app(ty_Maybe, df))) → new_ltEs3(wzz4710, wzz4910, df)
new_compare21(@2(wzz470, @2(wzz4710, wzz4711)), @2(wzz490, @2(wzz4910, wzz4911)), False, bac, app(app(ty_@2, bbf), app(app(ty_Either, bbg), bbh))) → new_ltEs(wzz4711, wzz4911, bbg, bbh)
new_ltEs0(@3(wzz4710, wzz4711, wzz4712), @3(wzz4910, wzz4911, wzz4912), fb, ea, app(ty_[], hd)) → new_ltEs2(wzz4712, wzz4912, hd)
new_compare21(@2(wzz470, wzz471), @2(wzz490, wzz491), False, app(app(ty_@2, baa), bab), beb) → new_compare21(wzz470, wzz490, new_esEs6(wzz470, wzz490, baa, bab), baa, bab)
new_compare21(@2(wzz470, wzz471), @2(wzz490, wzz491), False, app(app(app(ty_@3, hf), hg), hh), beb) → new_compare20(wzz470, wzz490, new_esEs5(wzz470, wzz490, hf, hg, hh), hf, hg, hh)
new_ltEs(Right(wzz4710), Right(wzz4910), cd, app(app(ty_@2, dc), dd)) → new_ltEs1(wzz4710, wzz4910, dc, dd)
new_ltEs1(@2(wzz4710, wzz4711), @2(wzz4910, wzz4911), app(app(app(ty_@3, bag), bah), bba), baf) → new_lt0(wzz4710, wzz4910, bag, bah, bba)
new_ltEs0(@3(wzz4710, wzz4711, wzz4712), @3(wzz4910, wzz4911, wzz4912), fb, ea, app(app(ty_Either, ge), gf)) → new_ltEs(wzz4712, wzz4912, ge, gf)
new_primCompAux(wzz4700, wzz4900, wzz140, app(ty_Maybe, bfe)) → new_compare5(wzz4700, wzz4900, bfe)
new_compare21(@2(wzz470, Just(wzz4710)), @2(wzz490, Just(wzz4910)), False, bac, app(ty_Maybe, app(app(app(ty_@3, bdc), bdd), bde))) → new_ltEs0(wzz4710, wzz4910, bdc, bdd, bde)
new_compare21(@2(wzz470, wzz471), @2(wzz490, wzz491), False, bac, app(ty_[], bch)) → new_compare3(wzz471, wzz491, bch)
new_compare21(@2(wzz470, @3(wzz4710, wzz4711, wzz4712)), @2(wzz490, @3(wzz4910, wzz4911, wzz4912)), False, bac, app(app(app(ty_@3, app(app(app(ty_@3, ec), ed), ee)), ea), eb)) → new_lt0(wzz4710, wzz4910, ec, ed, ee)
new_ltEs(Right(wzz4710), Right(wzz4910), cd, app(app(app(ty_@3, cg), da), db)) → new_ltEs0(wzz4710, wzz4910, cg, da, db)
new_compare21(@2(wzz470, Just(wzz4710)), @2(wzz490, Just(wzz4910)), False, bac, app(ty_Maybe, app(app(ty_@2, bdf), bdg))) → new_ltEs1(wzz4710, wzz4910, bdf, bdg)
new_compare21(@2(wzz470, wzz471), @2(wzz490, wzz491), False, app(app(ty_Either, h), ba), beb) → new_compare2(wzz470, wzz490, new_esEs4(wzz470, wzz490, h, ba), h, ba)
new_compare21(@2(wzz470, Left(wzz4710)), @2(wzz490, Left(wzz4910)), False, bac, app(app(ty_Either, app(ty_Maybe, cc)), bd)) → new_ltEs3(wzz4710, wzz4910, cc)
new_ltEs0(@3(wzz4710, wzz4711, wzz4712), @3(wzz4910, wzz4911, wzz4912), app(app(ty_Either, dg), dh), ea, eb) → new_lt(wzz4710, wzz4910, dg, dh)
new_compare21(@2(wzz470, @3(wzz4710, wzz4711, wzz4712)), @2(wzz490, @3(wzz4910, wzz4911, wzz4912)), False, bac, app(app(app(ty_@3, fb), app(app(app(ty_@3, ff), fg), fh)), eb)) → new_lt0(wzz4711, wzz4911, ff, fg, fh)

The TRS R consists of the following rules:

new_esEs7(Just(wzz400), Just(wzz3000), app(ty_Maybe, dde)) → new_esEs7(wzz400, wzz3000, dde)
new_esEs4(Right(wzz400), Right(wzz3000), ceb, ty_Ordering) → new_esEs8(wzz400, wzz3000)
new_esEs20(wzz401, wzz3001, app(ty_Maybe, cah)) → new_esEs7(wzz401, wzz3001, cah)
new_lt21(wzz4710, wzz4910, ty_Float) → new_lt13(wzz4710, wzz4910)
new_esEs4(Left(wzz400), Left(wzz3000), app(ty_[], cea), ccg) → new_esEs9(wzz400, wzz3000, cea)
new_esEs21(wzz400, wzz3000, app(app(ty_@2, cbc), cbd)) → new_esEs6(wzz400, wzz3000, cbc, cbd)
new_lt6(wzz470, wzz490, app(app(app(ty_@3, hf), hg), hh)) → new_lt7(wzz470, wzz490, hf, hg, hh)
new_ltEs5(Right(wzz4710), Right(wzz4910), cd, app(ty_[], de)) → new_ltEs4(wzz4710, wzz4910, de)
new_esEs23(wzz4710, wzz4910, app(ty_[], eh)) → new_esEs9(wzz4710, wzz4910, eh)
new_esEs5(@3(wzz400, wzz401, wzz402), @3(wzz3000, wzz3001, wzz3002), cga, cgb, cgc) → new_asAs(new_esEs26(wzz400, wzz3000, cga), new_asAs(new_esEs25(wzz401, wzz3001, cgb), new_esEs24(wzz402, wzz3002, cgc)))
new_primCmpNat2(wzz4700, Succ(wzz4900)) → new_primCmpNat0(wzz4700, wzz4900)
new_compare116(wzz470, wzz490, False) → GT
new_ltEs16(Just(wzz4710), Just(wzz4910), app(app(ty_Either, bda), bdb)) → new_ltEs5(wzz4710, wzz4910, bda, bdb)
new_esEs24(wzz402, wzz3002, app(app(app(ty_@3, cgf), cgg), cgh)) → new_esEs5(wzz402, wzz3002, cgf, cgg, cgh)
new_ltEs5(Right(wzz4710), Right(wzz4910), cd, ty_Float) → new_ltEs12(wzz4710, wzz4910)
new_esEs4(Right(wzz400), Right(wzz3000), ceb, ty_Char) → new_esEs11(wzz400, wzz3000)
new_esEs20(wzz401, wzz3001, ty_Bool) → new_esEs12(wzz401, wzz3001)
new_lt21(wzz4710, wzz4910, ty_Char) → new_lt5(wzz4710, wzz4910)
new_ltEs7(LT, EQ) → True
new_esEs26(wzz400, wzz3000, ty_Double) → new_esEs14(wzz400, wzz3000)
new_ltEs5(Right(wzz4710), Right(wzz4910), cd, ty_Int) → new_ltEs8(wzz4710, wzz4910)
new_esEs27(wzz4710, wzz4910, app(ty_Maybe, bbe)) → new_esEs7(wzz4710, wzz4910, bbe)
new_ltEs5(Right(wzz4710), Right(wzz4910), cd, ty_Bool) → new_ltEs14(wzz4710, wzz4910)
new_ltEs19(wzz4712, wzz4912, ty_Double) → new_ltEs11(wzz4712, wzz4912)
new_esEs23(wzz4710, wzz4910, ty_Float) → new_esEs17(wzz4710, wzz4910)
new_esEs26(wzz400, wzz3000, ty_Float) → new_esEs17(wzz400, wzz3000)
new_lt21(wzz4710, wzz4910, ty_@0) → new_lt17(wzz4710, wzz4910)
new_primMulNat0(Zero, Zero) → Zero
new_esEs10(wzz400, wzz3000, ty_@0) → new_esEs13(wzz400, wzz3000)
new_lt21(wzz4710, wzz4910, ty_Double) → new_lt12(wzz4710, wzz4910)
new_ltEs5(Right(wzz4710), Right(wzz4910), cd, app(ty_Maybe, df)) → new_ltEs16(wzz4710, wzz4910, df)
new_ltEs20(wzz4711, wzz4911, ty_@0) → new_ltEs15(wzz4711, wzz4911)
new_esEs24(wzz402, wzz3002, ty_@0) → new_esEs13(wzz402, wzz3002)
new_ltEs16(Just(wzz4710), Just(wzz4910), app(ty_[], bdh)) → new_ltEs4(wzz4710, wzz4910, bdh)
new_ltEs18(wzz471, wzz491, ty_Int) → new_ltEs8(wzz471, wzz491)
new_ltEs20(wzz4711, wzz4911, ty_Float) → new_ltEs12(wzz4711, wzz4911)
new_esEs12(True, True) → True
new_ltEs5(Left(wzz4710), Left(wzz4910), ty_@0, bd) → new_ltEs15(wzz4710, wzz4910)
new_esEs20(wzz401, wzz3001, app(ty_Ratio, cba)) → new_esEs16(wzz401, wzz3001, cba)
new_ltEs16(Just(wzz4710), Just(wzz4910), ty_Int) → new_ltEs8(wzz4710, wzz4910)
new_esEs23(wzz4710, wzz4910, ty_Bool) → new_esEs12(wzz4710, wzz4910)
new_esEs24(wzz402, wzz3002, ty_Integer) → new_esEs15(wzz402, wzz3002)
new_ltEs18(wzz471, wzz491, ty_Char) → new_ltEs17(wzz471, wzz491)
new_ltEs14(False, True) → True
new_ltEs19(wzz4712, wzz4912, ty_Integer) → new_ltEs9(wzz4712, wzz4912)
new_compare9(wzz4700, wzz4900, app(app(ty_@2, bfb), bfc)) → new_compare6(wzz4700, wzz4900, bfb, bfc)
new_compare9(wzz4700, wzz4900, ty_Double) → new_compare15(wzz4700, wzz4900)
new_lt21(wzz4710, wzz4910, app(ty_[], bbd)) → new_lt16(wzz4710, wzz4910, bbd)
new_esEs20(wzz401, wzz3001, app(app(ty_Either, caf), cag)) → new_esEs4(wzz401, wzz3001, caf, cag)
new_esEs23(wzz4710, wzz4910, ty_@0) → new_esEs13(wzz4710, wzz4910)
new_compare18(@0, @0) → EQ
new_esEs4(Left(wzz400), Left(wzz3000), app(app(ty_@2, cch), cda), ccg) → new_esEs6(wzz400, wzz3000, cch, cda)
new_ltEs5(Left(wzz4710), Left(wzz4910), app(app(ty_@2, bh), ca), bd) → new_ltEs13(wzz4710, wzz4910, bh, ca)
new_ltEs6(@3(wzz4710, wzz4711, wzz4712), @3(wzz4910, wzz4911, wzz4912), fb, ea, eb) → new_pePe(new_lt19(wzz4710, wzz4910, fb), new_asAs(new_esEs23(wzz4710, wzz4910, fb), new_pePe(new_lt20(wzz4711, wzz4911, ea), new_asAs(new_esEs22(wzz4711, wzz4911, ea), new_ltEs19(wzz4712, wzz4912, eb)))))
new_ltEs5(Left(wzz4710), Right(wzz4910), cd, bd) → True
new_lt19(wzz4710, wzz4910, ty_Float) → new_lt13(wzz4710, wzz4910)
new_lt19(wzz4710, wzz4910, ty_Ordering) → new_lt8(wzz4710, wzz4910)
new_esEs7(Just(wzz400), Just(wzz3000), app(app(ty_@2, dcf), dcg)) → new_esEs6(wzz400, wzz3000, dcf, dcg)
new_lt18(wzz470, wzz490, bed) → new_esEs8(new_compare19(wzz470, wzz490, bed), LT)
new_esEs15(Integer(wzz400), Integer(wzz3000)) → new_primEqInt(wzz400, wzz3000)
new_compare110(wzz114, wzz115, wzz116, wzz117, True, wzz119, cce, ccf) → new_compare111(wzz114, wzz115, wzz116, wzz117, True, cce, ccf)
new_ltEs18(wzz471, wzz491, ty_Ordering) → new_ltEs7(wzz471, wzz491)
new_ltEs5(Right(wzz4710), Right(wzz4910), cd, app(app(ty_Either, ce), cf)) → new_ltEs5(wzz4710, wzz4910, ce, cf)
new_esEs25(wzz401, wzz3001, ty_Double) → new_esEs14(wzz401, wzz3001)
new_lt8(wzz470, wzz490) → new_esEs8(new_compare11(wzz470, wzz490), LT)
new_esEs19(wzz470, wzz490, app(app(app(ty_@3, hf), hg), hh)) → new_esEs5(wzz470, wzz490, hf, hg, hh)
new_ltEs5(Left(wzz4710), Left(wzz4910), ty_Ordering, bd) → new_ltEs7(wzz4710, wzz4910)
new_esEs20(wzz401, wzz3001, app(app(ty_@2, caa), cab)) → new_esEs6(wzz401, wzz3001, caa, cab)
new_esEs6(@2(wzz400, wzz401), @2(wzz3000, wzz3001), bhg, bhh) → new_asAs(new_esEs21(wzz400, wzz3000, bhg), new_esEs20(wzz401, wzz3001, bhh))
new_esEs27(wzz4710, wzz4910, ty_Double) → new_esEs14(wzz4710, wzz4910)
new_esEs29(wzz400, wzz3000, ty_Integer) → new_esEs15(wzz400, wzz3000)
new_ltEs5(Right(wzz4710), Left(wzz4910), cd, bd) → False
new_esEs7(Just(wzz400), Just(wzz3000), app(ty_[], ddg)) → new_esEs9(wzz400, wzz3000, ddg)
new_esEs4(Left(wzz400), Left(wzz3000), ty_Ordering, ccg) → new_esEs8(wzz400, wzz3000)
new_compare23(@2(wzz470, wzz471), @2(wzz490, wzz491), False, bac, beb) → new_compare110(wzz470, wzz471, wzz490, wzz491, new_lt6(wzz470, wzz490, bac), new_asAs(new_esEs19(wzz470, wzz490, bac), new_ltEs18(wzz471, wzz491, beb)), bac, beb)
new_esEs28(wzz401, wzz3001, ty_Int) → new_esEs18(wzz401, wzz3001)
new_pePe(False, wzz139) → wzz139
new_esEs25(wzz401, wzz3001, app(app(ty_Either, dac), dad)) → new_esEs4(wzz401, wzz3001, dac, dad)
new_esEs27(wzz4710, wzz4910, ty_Int) → new_esEs18(wzz4710, wzz4910)
new_esEs25(wzz401, wzz3001, ty_Char) → new_esEs11(wzz401, wzz3001)
new_esEs10(wzz400, wzz3000, ty_Bool) → new_esEs12(wzz400, wzz3000)
new_esEs22(wzz4711, wzz4911, app(app(ty_Either, fc), fd)) → new_esEs4(wzz4711, wzz4911, fc, fd)
new_esEs4(Right(wzz400), Right(wzz3000), ceb, app(ty_Ratio, cfc)) → new_esEs16(wzz400, wzz3000, cfc)
new_compare9(wzz4700, wzz4900, ty_Float) → new_compare16(wzz4700, wzz4900)
new_esEs29(wzz400, wzz3000, ty_Int) → new_esEs18(wzz400, wzz3000)
new_esEs27(wzz4710, wzz4910, ty_Float) → new_esEs17(wzz4710, wzz4910)
new_lt19(wzz4710, wzz4910, app(ty_[], eh)) → new_lt16(wzz4710, wzz4910, eh)
new_esEs4(Left(wzz400), Left(wzz3000), ty_@0, ccg) → new_esEs13(wzz400, wzz3000)
new_esEs26(wzz400, wzz3000, ty_@0) → new_esEs13(wzz400, wzz3000)
new_esEs10(wzz400, wzz3000, app(ty_Maybe, bgg)) → new_esEs7(wzz400, wzz3000, bgg)
new_lt20(wzz4711, wzz4911, ty_Double) → new_lt12(wzz4711, wzz4911)
new_esEs24(wzz402, wzz3002, app(ty_Maybe, chc)) → new_esEs7(wzz402, wzz3002, chc)
new_ltEs5(Left(wzz4710), Left(wzz4910), app(ty_[], cb), bd) → new_ltEs4(wzz4710, wzz4910, cb)
new_esEs26(wzz400, wzz3000, ty_Bool) → new_esEs12(wzz400, wzz3000)
new_ltEs5(Left(wzz4710), Left(wzz4910), ty_Float, bd) → new_ltEs12(wzz4710, wzz4910)
new_esEs23(wzz4710, wzz4910, app(ty_Maybe, fa)) → new_esEs7(wzz4710, wzz4910, fa)
new_esEs4(Left(wzz400), Left(wzz3000), app(ty_Ratio, cdh), ccg) → new_esEs16(wzz400, wzz3000, cdh)
new_lt20(wzz4711, wzz4911, app(app(ty_@2, ga), gb)) → new_lt14(wzz4711, wzz4911, ga, gb)
new_esEs10(wzz400, wzz3000, app(app(app(ty_@3, bgb), bgc), bgd)) → new_esEs5(wzz400, wzz3000, bgb, bgc, bgd)
new_ltEs16(Just(wzz4710), Just(wzz4910), ty_Double) → new_ltEs11(wzz4710, wzz4910)
new_esEs22(wzz4711, wzz4911, ty_Ordering) → new_esEs8(wzz4711, wzz4911)
new_esEs21(wzz400, wzz3000, ty_Int) → new_esEs18(wzz400, wzz3000)
new_compare9(wzz4700, wzz4900, app(ty_Ratio, bff)) → new_compare14(wzz4700, wzz4900, bff)
new_esEs4(Right(wzz400), Right(wzz3000), ceb, ty_Integer) → new_esEs15(wzz400, wzz3000)
new_ltEs7(GT, GT) → True
new_compare14(:%(wzz4700, wzz4701), :%(wzz4900, wzz4901), ty_Int) → new_compare12(new_sr(wzz4700, wzz4901), new_sr(wzz4900, wzz4701))
new_esEs18(wzz40, wzz300) → new_primEqInt(wzz40, wzz300)
new_lt21(wzz4710, wzz4910, app(app(ty_Either, bad), bae)) → new_lt4(wzz4710, wzz4910, bad, bae)
new_esEs10(wzz400, wzz3000, app(app(ty_@2, bfh), bga)) → new_esEs6(wzz400, wzz3000, bfh, bga)
new_ltEs19(wzz4712, wzz4912, ty_Int) → new_ltEs8(wzz4712, wzz4912)
new_esEs23(wzz4710, wzz4910, ty_Double) → new_esEs14(wzz4710, wzz4910)
new_primCmpNat0(Zero, Succ(wzz49000)) → LT
new_primCmpInt(Neg(Succ(wzz4700)), Neg(wzz490)) → new_primCmpNat1(wzz490, wzz4700)
new_ltEs16(Just(wzz4710), Just(wzz4910), app(ty_Ratio, cfh)) → new_ltEs10(wzz4710, wzz4910, cfh)
new_ltEs20(wzz4711, wzz4911, ty_Bool) → new_ltEs14(wzz4711, wzz4911)
new_esEs25(wzz401, wzz3001, app(app(ty_@2, chf), chg)) → new_esEs6(wzz401, wzz3001, chf, chg)
new_ltEs12(wzz471, wzz491) → new_fsEs(new_compare16(wzz471, wzz491))
new_esEs8(LT, LT) → True
new_lt6(wzz470, wzz490, ty_Ordering) → new_lt8(wzz470, wzz490)
new_esEs19(wzz470, wzz490, ty_Float) → new_esEs17(wzz470, wzz490)
new_ltEs16(Nothing, Nothing, bhe) → True
new_compare9(wzz4700, wzz4900, ty_Char) → new_compare8(wzz4700, wzz4900)
new_lt6(wzz470, wzz490, app(app(ty_Either, h), ba)) → new_lt4(wzz470, wzz490, h, ba)
new_esEs19(wzz470, wzz490, ty_Bool) → new_esEs12(wzz470, wzz490)
new_esEs7(Just(wzz400), Just(wzz3000), ty_Double) → new_esEs14(wzz400, wzz3000)
new_esEs25(wzz401, wzz3001, ty_Ordering) → new_esEs8(wzz401, wzz3001)
new_esEs10(wzz400, wzz3000, app(app(ty_Either, bge), bgf)) → new_esEs4(wzz400, wzz3000, bge, bgf)
new_esEs19(wzz470, wzz490, app(ty_Maybe, bed)) → new_esEs7(wzz470, wzz490, bed)
new_esEs24(wzz402, wzz3002, app(ty_[], che)) → new_esEs9(wzz402, wzz3002, che)
new_lt21(wzz4710, wzz4910, ty_Bool) → new_lt15(wzz4710, wzz4910)
new_esEs24(wzz402, wzz3002, app(app(ty_@2, cgd), cge)) → new_esEs6(wzz402, wzz3002, cgd, cge)
new_esEs22(wzz4711, wzz4911, ty_Int) → new_esEs18(wzz4711, wzz4911)
new_pePe(True, wzz139) → True
new_primEqNat0(Zero, Zero) → True
new_lt6(wzz470, wzz490, ty_Bool) → new_lt15(wzz470, wzz490)
new_compare26(wzz470, wzz490, True) → EQ
new_esEs7(Just(wzz400), Just(wzz3000), ty_Float) → new_esEs17(wzz400, wzz3000)
new_lt21(wzz4710, wzz4910, app(ty_Maybe, bbe)) → new_lt18(wzz4710, wzz4910, bbe)
new_compare9(wzz4700, wzz4900, ty_Bool) → new_compare17(wzz4700, wzz4900)
new_lt7(wzz470, wzz490, hf, hg, hh) → new_esEs8(new_compare10(wzz470, wzz490, hf, hg, hh), LT)
new_ltEs5(Right(wzz4710), Right(wzz4910), cd, app(app(app(ty_@3, cg), da), db)) → new_ltEs6(wzz4710, wzz4910, cg, da, db)
new_ltEs19(wzz4712, wzz4912, app(ty_[], hd)) → new_ltEs4(wzz4712, wzz4912, hd)
new_esEs7(Just(wzz400), Just(wzz3000), ty_@0) → new_esEs13(wzz400, wzz3000)
new_lt6(wzz470, wzz490, ty_Int) → new_lt9(wzz470, wzz490)
new_sr(wzz400, wzz3000) → new_primMulInt(wzz400, wzz3000)
new_esEs4(Right(wzz400), Right(wzz3000), ceb, ty_@0) → new_esEs13(wzz400, wzz3000)
new_ltEs16(Just(wzz4710), Just(wzz4910), ty_@0) → new_ltEs15(wzz4710, wzz4910)
new_esEs26(wzz400, wzz3000, ty_Ordering) → new_esEs8(wzz400, wzz3000)
new_esEs8(GT, GT) → True
new_compare24(wzz470, wzz490, False) → new_compare113(wzz470, wzz490, new_ltEs14(wzz470, wzz490))
new_primPlusNat0(Succ(wzz1050), wzz300000) → Succ(Succ(new_primPlusNat1(wzz1050, wzz300000)))
new_compare4([], [], bec) → EQ
new_esEs22(wzz4711, wzz4911, app(ty_[], gc)) → new_esEs9(wzz4711, wzz4911, gc)
new_lt19(wzz4710, wzz4910, app(ty_Ratio, cfe)) → new_lt11(wzz4710, wzz4910, cfe)
new_primCmpInt(Pos(Zero), Pos(Succ(wzz4900))) → new_primCmpNat1(Zero, wzz4900)
new_esEs12(False, False) → True
new_lt6(wzz470, wzz490, ty_Double) → new_lt12(wzz470, wzz490)
new_esEs8(GT, LT) → False
new_esEs8(LT, GT) → False
new_ltEs18(wzz471, wzz491, app(app(ty_Either, cd), bd)) → new_ltEs5(wzz471, wzz491, cd, bd)
new_compare110(wzz114, wzz115, wzz116, wzz117, False, wzz119, cce, ccf) → new_compare111(wzz114, wzz115, wzz116, wzz117, wzz119, cce, ccf)
new_esEs10(wzz400, wzz3000, ty_Char) → new_esEs11(wzz400, wzz3000)
new_lt21(wzz4710, wzz4910, ty_Ordering) → new_lt8(wzz4710, wzz4910)
new_esEs4(Right(wzz400), Right(wzz3000), ceb, app(app(ty_Either, ceh), cfa)) → new_esEs4(wzz400, wzz3000, ceh, cfa)
new_ltEs16(Nothing, Just(wzz4910), bhe) → True
new_primEqInt(Neg(Succ(wzz4000)), Neg(Succ(wzz30000))) → new_primEqNat0(wzz4000, wzz30000)
new_lt20(wzz4711, wzz4911, app(ty_Ratio, cff)) → new_lt11(wzz4711, wzz4911, cff)
new_ltEs18(wzz471, wzz491, app(ty_Ratio, bhd)) → new_ltEs10(wzz471, wzz491, bhd)
new_esEs20(wzz401, wzz3001, ty_Ordering) → new_esEs8(wzz401, wzz3001)
new_esEs23(wzz4710, wzz4910, ty_Ordering) → new_esEs8(wzz4710, wzz4910)
new_esEs4(Left(wzz400), Left(wzz3000), app(app(ty_Either, cde), cdf), ccg) → new_esEs4(wzz400, wzz3000, cde, cdf)
new_esEs4(Left(wzz400), Left(wzz3000), app(app(app(ty_@3, cdb), cdc), cdd), ccg) → new_esEs5(wzz400, wzz3000, cdb, cdc, cdd)
new_esEs7(Just(wzz400), Just(wzz3000), ty_Int) → new_esEs18(wzz400, wzz3000)
new_primPlusNat1(Succ(wzz39200), Zero) → Succ(wzz39200)
new_primPlusNat1(Zero, Succ(wzz10100)) → Succ(wzz10100)
new_ltEs13(@2(wzz4710, wzz4711), @2(wzz4910, wzz4911), bbf, baf) → new_pePe(new_lt21(wzz4710, wzz4910, bbf), new_asAs(new_esEs27(wzz4710, wzz4910, bbf), new_ltEs20(wzz4711, wzz4911, baf)))
new_lt19(wzz4710, wzz4910, ty_Integer) → new_lt10(wzz4710, wzz4910)
new_ltEs9(wzz471, wzz491) → new_fsEs(new_compare13(wzz471, wzz491))
new_primCmpNat1(Zero, wzz4700) → LT
new_lt20(wzz4711, wzz4911, app(app(ty_Either, fc), fd)) → new_lt4(wzz4711, wzz4911, fc, fd)
new_compare111(wzz114, wzz115, wzz116, wzz117, True, cce, ccf) → LT
new_esEs25(wzz401, wzz3001, ty_Int) → new_esEs18(wzz401, wzz3001)
new_esEs21(wzz400, wzz3000, ty_Double) → new_esEs14(wzz400, wzz3000)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_ltEs16(Just(wzz4710), Just(wzz4910), app(ty_Maybe, bea)) → new_ltEs16(wzz4710, wzz4910, bea)
new_lt20(wzz4711, wzz4911, app(ty_Maybe, gd)) → new_lt18(wzz4711, wzz4911, gd)
new_ltEs5(Right(wzz4710), Right(wzz4910), cd, ty_Double) → new_ltEs11(wzz4710, wzz4910)
new_esEs4(Left(wzz400), Left(wzz3000), ty_Bool, ccg) → new_esEs12(wzz400, wzz3000)
new_esEs7(Just(wzz400), Just(wzz3000), ty_Ordering) → new_esEs8(wzz400, wzz3000)
new_esEs23(wzz4710, wzz4910, ty_Char) → new_esEs11(wzz4710, wzz4910)
new_lt6(wzz470, wzz490, app(ty_Ratio, bhf)) → new_lt11(wzz470, wzz490, bhf)
new_ltEs7(EQ, EQ) → True
new_ltEs10(wzz471, wzz491, bhd) → new_fsEs(new_compare14(wzz471, wzz491, bhd))
new_compare112(wzz470, wzz490, False, h, ba) → GT
new_ltEs20(wzz4711, wzz4911, app(ty_[], bcf)) → new_ltEs4(wzz4711, wzz4911, bcf)
new_primEqInt(Neg(Succ(wzz4000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(wzz30000))) → False
new_ltEs5(Left(wzz4710), Left(wzz4910), app(ty_Ratio, bhb), bd) → new_ltEs10(wzz4710, wzz4910, bhb)
new_esEs8(EQ, EQ) → True
new_ltEs4(wzz471, wzz491, bch) → new_fsEs(new_compare4(wzz471, wzz491, bch))
new_esEs4(Left(wzz400), Left(wzz3000), ty_Float, ccg) → new_esEs17(wzz400, wzz3000)
new_compare26(wzz470, wzz490, False) → new_compare116(wzz470, wzz490, new_ltEs7(wzz470, wzz490))
new_lt20(wzz4711, wzz4911, ty_Ordering) → new_lt8(wzz4711, wzz4911)
new_esEs21(wzz400, wzz3000, app(app(ty_Either, cbh), cca)) → new_esEs4(wzz400, wzz3000, cbh, cca)
new_esEs22(wzz4711, wzz4911, app(app(app(ty_@3, ff), fg), fh)) → new_esEs5(wzz4711, wzz4911, ff, fg, fh)
new_ltEs19(wzz4712, wzz4912, ty_Char) → new_ltEs17(wzz4712, wzz4912)
new_esEs21(wzz400, wzz3000, ty_Float) → new_esEs17(wzz400, wzz3000)
new_esEs4(Left(wzz400), Left(wzz3000), ty_Char, ccg) → new_esEs11(wzz400, wzz3000)
new_ltEs19(wzz4712, wzz4912, app(ty_Maybe, he)) → new_ltEs16(wzz4712, wzz4912, he)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_ltEs7(GT, LT) → False
new_primCmpNat1(Succ(wzz4900), wzz4700) → new_primCmpNat0(wzz4900, wzz4700)
new_lt5(wzz470, wzz490) → new_esEs8(new_compare8(wzz470, wzz490), LT)
new_primCmpNat0(Succ(wzz47000), Succ(wzz49000)) → new_primCmpNat0(wzz47000, wzz49000)
new_ltEs7(GT, EQ) → False
new_esEs19(wzz470, wzz490, ty_Char) → new_esEs11(wzz470, wzz490)
new_ltEs20(wzz4711, wzz4911, app(ty_Maybe, bcg)) → new_ltEs16(wzz4711, wzz4911, bcg)
new_primEqInt(Pos(Succ(wzz4000)), Pos(Succ(wzz30000))) → new_primEqNat0(wzz4000, wzz30000)
new_compare9(wzz4700, wzz4900, ty_Int) → new_compare12(wzz4700, wzz4900)
new_ltEs16(Just(wzz4710), Just(wzz4910), ty_Integer) → new_ltEs9(wzz4710, wzz4910)
new_ltEs5(Left(wzz4710), Left(wzz4910), app(app(ty_Either, bb), bc), bd) → new_ltEs5(wzz4710, wzz4910, bb, bc)
new_esEs24(wzz402, wzz3002, app(ty_Ratio, chd)) → new_esEs16(wzz402, wzz3002, chd)
new_ltEs19(wzz4712, wzz4912, ty_Bool) → new_ltEs14(wzz4712, wzz4912)
new_lt21(wzz4710, wzz4910, ty_Integer) → new_lt10(wzz4710, wzz4910)
new_ltEs5(Right(wzz4710), Right(wzz4910), cd, ty_Ordering) → new_ltEs7(wzz4710, wzz4910)
new_esEs26(wzz400, wzz3000, ty_Integer) → new_esEs15(wzz400, wzz3000)
new_esEs24(wzz402, wzz3002, ty_Int) → new_esEs18(wzz402, wzz3002)
new_ltEs19(wzz4712, wzz4912, app(ty_Ratio, cfg)) → new_ltEs10(wzz4712, wzz4912, cfg)
new_ltEs5(Left(wzz4710), Left(wzz4910), app(app(app(ty_@3, be), bf), bg), bd) → new_ltEs6(wzz4710, wzz4910, be, bf, bg)
new_primEqNat0(Succ(wzz4000), Succ(wzz30000)) → new_primEqNat0(wzz4000, wzz30000)
new_lt6(wzz470, wzz490, app(app(ty_@2, baa), bab)) → new_lt14(wzz470, wzz490, baa, bab)
new_esEs27(wzz4710, wzz4910, ty_Ordering) → new_esEs8(wzz4710, wzz4910)
new_ltEs14(False, False) → True
new_compare9(wzz4700, wzz4900, app(ty_Maybe, bfe)) → new_compare19(wzz4700, wzz4900, bfe)
new_esEs19(wzz470, wzz490, app(app(ty_@2, baa), bab)) → new_esEs6(wzz470, wzz490, baa, bab)
new_lt13(wzz470, wzz490) → new_esEs8(new_compare16(wzz470, wzz490), LT)
new_compare15(Double(wzz4700, wzz4701), Double(wzz4900, wzz4901)) → new_compare12(new_sr(wzz4700, wzz4900), new_sr(wzz4701, wzz4901))
new_esEs20(wzz401, wzz3001, ty_Double) → new_esEs14(wzz401, wzz3001)
new_esEs22(wzz4711, wzz4911, ty_Bool) → new_esEs12(wzz4711, wzz4911)
new_esEs10(wzz400, wzz3000, app(ty_Ratio, bgh)) → new_esEs16(wzz400, wzz3000, bgh)
new_primCompAux00(wzz148, LT) → LT
new_lt11(wzz470, wzz490, bhf) → new_esEs8(new_compare14(wzz470, wzz490, bhf), LT)
new_compare27(wzz470, wzz490, False, bed) → new_compare114(wzz470, wzz490, new_ltEs16(wzz470, wzz490, bed), bed)
new_esEs24(wzz402, wzz3002, ty_Ordering) → new_esEs8(wzz402, wzz3002)
new_esEs27(wzz4710, wzz4910, app(app(app(ty_@3, bag), bah), bba)) → new_esEs5(wzz4710, wzz4910, bag, bah, bba)
new_esEs10(wzz400, wzz3000, app(ty_[], bha)) → new_esEs9(wzz400, wzz3000, bha)
new_compare115(wzz470, wzz490, True, hf, hg, hh) → LT
new_ltEs17(wzz471, wzz491) → new_fsEs(new_compare8(wzz471, wzz491))
new_ltEs18(wzz471, wzz491, ty_Double) → new_ltEs11(wzz471, wzz491)
new_esEs7(Nothing, Nothing, dce) → True
new_esEs8(EQ, LT) → False
new_esEs8(LT, EQ) → False
new_primEqInt(Pos(Succ(wzz4000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(wzz30000))) → False
new_compare9(wzz4700, wzz4900, ty_Ordering) → new_compare11(wzz4700, wzz4900)
new_ltEs8(wzz471, wzz491) → new_fsEs(new_compare12(wzz471, wzz491))
new_esEs25(wzz401, wzz3001, ty_Float) → new_esEs17(wzz401, wzz3001)
new_primCmpNat0(Zero, Zero) → EQ
new_compare6(wzz470, wzz490, baa, bab) → new_compare23(wzz470, wzz490, new_esEs6(wzz470, wzz490, baa, bab), baa, bab)
new_lt6(wzz470, wzz490, ty_Integer) → new_lt10(wzz470, wzz490)
new_primCmpNat0(Succ(wzz47000), Zero) → GT
new_esEs4(Right(wzz400), Right(wzz3000), ceb, app(app(app(ty_@3, cee), cef), ceg)) → new_esEs5(wzz400, wzz3000, cee, cef, ceg)
new_esEs21(wzz400, wzz3000, ty_@0) → new_esEs13(wzz400, wzz3000)
new_esEs19(wzz470, wzz490, ty_@0) → new_esEs13(wzz470, wzz490)
new_primCmpInt(Neg(Zero), Pos(Succ(wzz4900))) → LT
new_sr0(Integer(wzz49000), Integer(wzz47010)) → Integer(new_primMulInt(wzz49000, wzz47010))
new_primPlusNat1(Succ(wzz39200), Succ(wzz10100)) → Succ(Succ(new_primPlusNat1(wzz39200, wzz10100)))
new_esEs7(Just(wzz400), Just(wzz3000), ty_Integer) → new_esEs15(wzz400, wzz3000)
new_primEqInt(Pos(Succ(wzz4000)), Neg(wzz3000)) → False
new_primEqInt(Neg(Succ(wzz4000)), Pos(wzz3000)) → False
new_esEs7(Nothing, Just(wzz3000), dce) → False
new_esEs7(Just(wzz400), Nothing, dce) → False
new_compare14(:%(wzz4700, wzz4701), :%(wzz4900, wzz4901), ty_Integer) → new_compare13(new_sr0(wzz4700, wzz4901), new_sr0(wzz4900, wzz4701))
new_esEs25(wzz401, wzz3001, ty_@0) → new_esEs13(wzz401, wzz3001)
new_ltEs16(Just(wzz4710), Just(wzz4910), ty_Ordering) → new_ltEs7(wzz4710, wzz4910)
new_ltEs18(wzz471, wzz491, app(ty_Maybe, bhe)) → new_ltEs16(wzz471, wzz491, bhe)
new_ltEs19(wzz4712, wzz4912, ty_@0) → new_ltEs15(wzz4712, wzz4912)
new_esEs26(wzz400, wzz3000, app(ty_Ratio, dbh)) → new_esEs16(wzz400, wzz3000, dbh)
new_esEs22(wzz4711, wzz4911, app(app(ty_@2, ga), gb)) → new_esEs6(wzz4711, wzz4911, ga, gb)
new_compare12(wzz47, wzz49) → new_primCmpInt(wzz47, wzz49)
new_esEs9([], [], bfg) → True
new_compare9(wzz4700, wzz4900, ty_@0) → new_compare18(wzz4700, wzz4900)
new_ltEs7(EQ, GT) → True
new_primEqInt(Pos(Zero), Neg(Succ(wzz30000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(wzz30000))) → False
new_ltEs16(Just(wzz4710), Just(wzz4910), ty_Bool) → new_ltEs14(wzz4710, wzz4910)
new_esEs13(@0, @0) → True
new_esEs21(wzz400, wzz3000, ty_Integer) → new_esEs15(wzz400, wzz3000)
new_esEs21(wzz400, wzz3000, ty_Char) → new_esEs11(wzz400, wzz3000)
new_primCompAux00(wzz148, EQ) → wzz148
new_esEs4(Right(wzz400), Right(wzz3000), ceb, ty_Double) → new_esEs14(wzz400, wzz3000)
new_compare24(wzz470, wzz490, True) → EQ
new_ltEs5(Right(wzz4710), Right(wzz4910), cd, ty_Char) → new_ltEs17(wzz4710, wzz4910)
new_lt6(wzz470, wzz490, app(ty_[], bec)) → new_lt16(wzz470, wzz490, bec)
new_esEs23(wzz4710, wzz4910, ty_Int) → new_esEs18(wzz4710, wzz4910)
new_esEs4(Left(wzz400), Left(wzz3000), ty_Integer, ccg) → new_esEs15(wzz400, wzz3000)
new_esEs8(GT, EQ) → False
new_esEs8(EQ, GT) → False
new_ltEs18(wzz471, wzz491, ty_@0) → new_ltEs15(wzz471, wzz491)
new_esEs26(wzz400, wzz3000, ty_Char) → new_esEs11(wzz400, wzz3000)
new_esEs27(wzz4710, wzz4910, app(ty_Ratio, dcb)) → new_esEs16(wzz4710, wzz4910, dcb)
new_ltEs16(Just(wzz4710), Nothing, bhe) → False
new_lt19(wzz4710, wzz4910, app(ty_Maybe, fa)) → new_lt18(wzz4710, wzz4910, fa)
new_ltEs19(wzz4712, wzz4912, app(app(ty_@2, hb), hc)) → new_ltEs13(wzz4712, wzz4912, hb, hc)
new_ltEs5(Left(wzz4710), Left(wzz4910), ty_Bool, bd) → new_ltEs14(wzz4710, wzz4910)
new_compare113(wzz470, wzz490, True) → LT
new_ltEs20(wzz4711, wzz4911, app(app(app(ty_@3, bca), bcb), bcc)) → new_ltEs6(wzz4711, wzz4911, bca, bcb, bcc)
new_not(False) → True
new_primCompAux0(wzz4700, wzz4900, wzz140, bec) → new_primCompAux00(wzz140, new_compare9(wzz4700, wzz4900, bec))
new_lt20(wzz4711, wzz4911, ty_Bool) → new_lt15(wzz4711, wzz4911)
new_ltEs20(wzz4711, wzz4911, app(ty_Ratio, dcc)) → new_ltEs10(wzz4711, wzz4911, dcc)
new_ltEs5(Right(wzz4710), Right(wzz4910), cd, ty_Integer) → new_ltEs9(wzz4710, wzz4910)
new_compare7(wzz470, wzz490, h, ba) → new_compare25(wzz470, wzz490, new_esEs4(wzz470, wzz490, h, ba), h, ba)
new_primPlusNat0(Zero, wzz300000) → Succ(wzz300000)
new_esEs26(wzz400, wzz3000, app(ty_[], dca)) → new_esEs9(wzz400, wzz3000, dca)
new_esEs23(wzz4710, wzz4910, app(app(ty_@2, ef), eg)) → new_esEs6(wzz4710, wzz4910, ef, eg)
new_compare17(wzz470, wzz490) → new_compare24(wzz470, wzz490, new_esEs12(wzz470, wzz490))
new_compare113(wzz470, wzz490, False) → GT
new_ltEs18(wzz471, wzz491, app(app(app(ty_@3, fb), ea), eb)) → new_ltEs6(wzz471, wzz491, fb, ea, eb)
new_esEs25(wzz401, wzz3001, ty_Integer) → new_esEs15(wzz401, wzz3001)
new_esEs4(Left(wzz400), Left(wzz3000), ty_Double, ccg) → new_esEs14(wzz400, wzz3000)
new_esEs25(wzz401, wzz3001, app(ty_Ratio, daf)) → new_esEs16(wzz401, wzz3001, daf)
new_esEs26(wzz400, wzz3000, ty_Int) → new_esEs18(wzz400, wzz3000)
new_esEs24(wzz402, wzz3002, ty_Float) → new_esEs17(wzz402, wzz3002)
new_ltEs19(wzz4712, wzz4912, app(app(app(ty_@3, gg), gh), ha)) → new_ltEs6(wzz4712, wzz4912, gg, gh, ha)
new_ltEs5(Left(wzz4710), Left(wzz4910), app(ty_Maybe, cc), bd) → new_ltEs16(wzz4710, wzz4910, cc)
new_lt20(wzz4711, wzz4911, app(app(app(ty_@3, ff), fg), fh)) → new_lt7(wzz4711, wzz4911, ff, fg, fh)
new_esEs19(wzz470, wzz490, ty_Int) → new_esEs18(wzz470, wzz490)
new_esEs4(Right(wzz400), Right(wzz3000), ceb, app(app(ty_@2, cec), ced)) → new_esEs6(wzz400, wzz3000, cec, ced)
new_esEs4(Right(wzz400), Right(wzz3000), ceb, ty_Int) → new_esEs18(wzz400, wzz3000)
new_esEs7(Just(wzz400), Just(wzz3000), ty_Bool) → new_esEs12(wzz400, wzz3000)
new_esEs20(wzz401, wzz3001, ty_Int) → new_esEs18(wzz401, wzz3001)
new_lt6(wzz470, wzz490, ty_@0) → new_lt17(wzz470, wzz490)
new_esEs10(wzz400, wzz3000, ty_Int) → new_esEs18(wzz400, wzz3000)
new_esEs20(wzz401, wzz3001, app(app(app(ty_@3, cac), cad), cae)) → new_esEs5(wzz401, wzz3001, cac, cad, cae)
new_primCmpInt(Pos(Succ(wzz4700)), Neg(wzz490)) → GT
new_esEs22(wzz4711, wzz4911, ty_Char) → new_esEs11(wzz4711, wzz4911)
new_compare10(wzz470, wzz490, hf, hg, hh) → new_compare28(wzz470, wzz490, new_esEs5(wzz470, wzz490, hf, hg, hh), hf, hg, hh)
new_lt21(wzz4710, wzz4910, app(app(ty_@2, bbb), bbc)) → new_lt14(wzz4710, wzz4910, bbb, bbc)
new_esEs4(Left(wzz400), Left(wzz3000), ty_Int, ccg) → new_esEs18(wzz400, wzz3000)
new_esEs21(wzz400, wzz3000, app(app(app(ty_@3, cbe), cbf), cbg)) → new_esEs5(wzz400, wzz3000, cbe, cbf, cbg)
new_esEs21(wzz400, wzz3000, app(ty_Maybe, ccb)) → new_esEs7(wzz400, wzz3000, ccb)
new_compare115(wzz470, wzz490, False, hf, hg, hh) → GT
new_lt20(wzz4711, wzz4911, ty_Integer) → new_lt10(wzz4711, wzz4911)
new_primMulInt(Pos(wzz4000), Pos(wzz30000)) → Pos(new_primMulNat0(wzz4000, wzz30000))
new_lt19(wzz4710, wzz4910, app(app(ty_@2, ef), eg)) → new_lt14(wzz4710, wzz4910, ef, eg)
new_esEs23(wzz4710, wzz4910, app(app(ty_Either, dg), dh)) → new_esEs4(wzz4710, wzz4910, dg, dh)
new_esEs20(wzz401, wzz3001, ty_Char) → new_esEs11(wzz401, wzz3001)
new_esEs4(Left(wzz400), Left(wzz3000), app(ty_Maybe, cdg), ccg) → new_esEs7(wzz400, wzz3000, cdg)
new_primMulInt(Neg(wzz4000), Neg(wzz30000)) → Pos(new_primMulNat0(wzz4000, wzz30000))
new_esEs27(wzz4710, wzz4910, app(app(ty_@2, bbb), bbc)) → new_esEs6(wzz4710, wzz4910, bbb, bbc)
new_esEs10(wzz400, wzz3000, ty_Integer) → new_esEs15(wzz400, wzz3000)
new_lt6(wzz470, wzz490, app(ty_Maybe, bed)) → new_lt18(wzz470, wzz490, bed)
new_esEs20(wzz401, wzz3001, ty_Integer) → new_esEs15(wzz401, wzz3001)
new_ltEs19(wzz4712, wzz4912, app(app(ty_Either, ge), gf)) → new_ltEs5(wzz4712, wzz4912, ge, gf)
new_primEqNat0(Succ(wzz4000), Zero) → False
new_primEqNat0(Zero, Succ(wzz30000)) → False
new_esEs22(wzz4711, wzz4911, ty_Float) → new_esEs17(wzz4711, wzz4911)
new_esEs4(Right(wzz400), Right(wzz3000), ceb, app(ty_[], cfd)) → new_esEs9(wzz400, wzz3000, cfd)
new_compare25(wzz470, wzz490, True, h, ba) → EQ
new_lt20(wzz4711, wzz4911, ty_@0) → new_lt17(wzz4711, wzz4911)
new_ltEs14(True, True) → True
new_esEs22(wzz4711, wzz4911, ty_Double) → new_esEs14(wzz4711, wzz4911)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs24(wzz402, wzz3002, app(app(ty_Either, cha), chb)) → new_esEs4(wzz402, wzz3002, cha, chb)
new_ltEs16(Just(wzz4710), Just(wzz4910), app(app(app(ty_@3, bdc), bdd), bde)) → new_ltEs6(wzz4710, wzz4910, bdc, bdd, bde)
new_esEs27(wzz4710, wzz4910, app(app(ty_Either, bad), bae)) → new_esEs4(wzz4710, wzz4910, bad, bae)
new_ltEs11(wzz471, wzz491) → new_fsEs(new_compare15(wzz471, wzz491))
new_compare4(:(wzz4700, wzz4701), [], bec) → GT
new_compare28(wzz470, wzz490, True, hf, hg, hh) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(wzz4900))) → new_primCmpNat2(wzz4900, Zero)
new_esEs19(wzz470, wzz490, app(ty_[], bec)) → new_esEs9(wzz470, wzz490, bec)
new_lt14(wzz470, wzz490, baa, bab) → new_esEs8(new_compare6(wzz470, wzz490, baa, bab), LT)
new_compare23(wzz47, wzz49, True, bac, beb) → EQ
new_primCmpInt(Pos(Zero), Neg(Succ(wzz4900))) → GT
new_lt9(wzz470, wzz490) → new_esEs8(new_compare12(wzz470, wzz490), LT)
new_compare25(wzz470, wzz490, False, h, ba) → new_compare112(wzz470, wzz490, new_ltEs5(wzz470, wzz490, h, ba), h, ba)
new_compare4([], :(wzz4900, wzz4901), bec) → LT
new_compare114(wzz470, wzz490, True, bed) → LT
new_ltEs18(wzz471, wzz491, ty_Float) → new_ltEs12(wzz471, wzz491)
new_ltEs18(wzz471, wzz491, ty_Integer) → new_ltEs9(wzz471, wzz491)
new_esEs19(wzz470, wzz490, ty_Double) → new_esEs14(wzz470, wzz490)
new_ltEs16(Just(wzz4710), Just(wzz4910), ty_Float) → new_ltEs12(wzz4710, wzz4910)
new_esEs27(wzz4710, wzz4910, app(ty_[], bbd)) → new_esEs9(wzz4710, wzz4910, bbd)
new_esEs25(wzz401, wzz3001, app(ty_[], dag)) → new_esEs9(wzz401, wzz3001, dag)
new_esEs11(Char(wzz400), Char(wzz3000)) → new_primEqNat0(wzz400, wzz3000)
new_compare9(wzz4700, wzz4900, app(app(app(ty_@3, beg), beh), bfa)) → new_compare10(wzz4700, wzz4900, beg, beh, bfa)
new_lt19(wzz4710, wzz4910, app(app(ty_Either, dg), dh)) → new_lt4(wzz4710, wzz4910, dg, dh)
new_esEs25(wzz401, wzz3001, app(ty_Maybe, dae)) → new_esEs7(wzz401, wzz3001, dae)
new_esEs7(Just(wzz400), Just(wzz3000), app(app(app(ty_@3, dch), dda), ddb)) → new_esEs5(wzz400, wzz3000, dch, dda, ddb)
new_esEs23(wzz4710, wzz4910, app(ty_Ratio, cfe)) → new_esEs16(wzz4710, wzz4910, cfe)
new_esEs22(wzz4711, wzz4911, app(ty_Ratio, cff)) → new_esEs16(wzz4711, wzz4911, cff)
new_lt20(wzz4711, wzz4911, app(ty_[], gc)) → new_lt16(wzz4711, wzz4911, gc)
new_ltEs5(Right(wzz4710), Right(wzz4910), cd, app(app(ty_@2, dc), dd)) → new_ltEs13(wzz4710, wzz4910, dc, dd)
new_ltEs5(Left(wzz4710), Left(wzz4910), ty_Integer, bd) → new_ltEs9(wzz4710, wzz4910)
new_esEs19(wzz470, wzz490, app(ty_Ratio, bhf)) → new_esEs16(wzz470, wzz490, bhf)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs25(wzz401, wzz3001, ty_Bool) → new_esEs12(wzz401, wzz3001)
new_ltEs16(Just(wzz4710), Just(wzz4910), app(app(ty_@2, bdf), bdg)) → new_ltEs13(wzz4710, wzz4910, bdf, bdg)
new_esEs24(wzz402, wzz3002, ty_Char) → new_esEs11(wzz402, wzz3002)
new_compare11(wzz470, wzz490) → new_compare26(wzz470, wzz490, new_esEs8(wzz470, wzz490))
new_asAs(False, wzz64) → False
new_primMulInt(Pos(wzz4000), Neg(wzz30000)) → Neg(new_primMulNat0(wzz4000, wzz30000))
new_primMulInt(Neg(wzz4000), Pos(wzz30000)) → Neg(new_primMulNat0(wzz4000, wzz30000))
new_esEs4(Right(wzz400), Right(wzz3000), ceb, ty_Bool) → new_esEs12(wzz400, wzz3000)
new_primMulNat0(Succ(wzz40000), Zero) → Zero
new_primMulNat0(Zero, Succ(wzz300000)) → Zero
new_ltEs5(Left(wzz4710), Left(wzz4910), ty_Char, bd) → new_ltEs17(wzz4710, wzz4910)
new_esEs21(wzz400, wzz3000, ty_Ordering) → new_esEs8(wzz400, wzz3000)
new_compare4(:(wzz4700, wzz4701), :(wzz4900, wzz4901), bec) → new_primCompAux0(wzz4700, wzz4900, new_compare4(wzz4701, wzz4901, bec), bec)
new_primCmpNat2(wzz4700, Zero) → GT
new_compare9(wzz4700, wzz4900, ty_Integer) → new_compare13(wzz4700, wzz4900)
new_ltEs20(wzz4711, wzz4911, ty_Double) → new_ltEs11(wzz4711, wzz4911)
new_ltEs18(wzz471, wzz491, app(ty_[], bch)) → new_ltEs4(wzz471, wzz491, bch)
new_compare16(Float(wzz4700, wzz4701), Float(wzz4900, wzz4901)) → new_compare12(new_sr(wzz4700, wzz4900), new_sr(wzz4701, wzz4901))
new_esEs26(wzz400, wzz3000, app(ty_Maybe, dbg)) → new_esEs7(wzz400, wzz3000, dbg)
new_esEs14(Double(wzz400, wzz401), Double(wzz3000, wzz3001)) → new_esEs18(new_sr(wzz400, wzz3000), new_sr(wzz401, wzz3001))
new_lt15(wzz470, wzz490) → new_esEs8(new_compare17(wzz470, wzz490), LT)
new_lt21(wzz4710, wzz4910, ty_Int) → new_lt9(wzz4710, wzz4910)
new_esEs9(:(wzz400, wzz401), :(wzz3000, wzz3001), bfg) → new_asAs(new_esEs10(wzz400, wzz3000, bfg), new_esEs9(wzz401, wzz3001, bfg))
new_ltEs16(Just(wzz4710), Just(wzz4910), ty_Char) → new_ltEs17(wzz4710, wzz4910)
new_esEs27(wzz4710, wzz4910, ty_@0) → new_esEs13(wzz4710, wzz4910)
new_ltEs5(Right(wzz4710), Right(wzz4910), cd, app(ty_Ratio, bhc)) → new_ltEs10(wzz4710, wzz4910, bhc)
new_ltEs18(wzz471, wzz491, ty_Bool) → new_ltEs14(wzz471, wzz491)
new_lt12(wzz470, wzz490) → new_esEs8(new_compare15(wzz470, wzz490), LT)
new_esEs28(wzz401, wzz3001, ty_Integer) → new_esEs15(wzz401, wzz3001)
new_esEs4(Right(wzz400), Right(wzz3000), ceb, app(ty_Maybe, cfb)) → new_esEs7(wzz400, wzz3000, cfb)
new_lt20(wzz4711, wzz4911, ty_Float) → new_lt13(wzz4711, wzz4911)
new_compare111(wzz114, wzz115, wzz116, wzz117, False, cce, ccf) → GT
new_esEs24(wzz402, wzz3002, ty_Bool) → new_esEs12(wzz402, wzz3002)
new_ltEs18(wzz471, wzz491, app(app(ty_@2, bbf), baf)) → new_ltEs13(wzz471, wzz491, bbf, baf)
new_esEs23(wzz4710, wzz4910, ty_Integer) → new_esEs15(wzz4710, wzz4910)
new_compare9(wzz4700, wzz4900, app(ty_[], bfd)) → new_compare4(wzz4700, wzz4900, bfd)
new_lt10(wzz470, wzz490) → new_esEs8(new_compare13(wzz470, wzz490), LT)
new_lt19(wzz4710, wzz4910, ty_Bool) → new_lt15(wzz4710, wzz4910)
new_esEs7(Just(wzz400), Just(wzz3000), app(app(ty_Either, ddc), ddd)) → new_esEs4(wzz400, wzz3000, ddc, ddd)
new_esEs21(wzz400, wzz3000, app(ty_Ratio, ccc)) → new_esEs16(wzz400, wzz3000, ccc)
new_lt4(wzz470, wzz490, h, ba) → new_esEs8(new_compare7(wzz470, wzz490, h, ba), LT)
new_esEs12(False, True) → False
new_esEs12(True, False) → False
new_lt21(wzz4710, wzz4910, app(ty_Ratio, dcb)) → new_lt11(wzz4710, wzz4910, dcb)
new_lt19(wzz4710, wzz4910, ty_@0) → new_lt17(wzz4710, wzz4910)
new_esEs27(wzz4710, wzz4910, ty_Bool) → new_esEs12(wzz4710, wzz4910)
new_lt20(wzz4711, wzz4911, ty_Char) → new_lt5(wzz4711, wzz4911)
new_lt19(wzz4710, wzz4910, app(app(app(ty_@3, ec), ed), ee)) → new_lt7(wzz4710, wzz4910, ec, ed, ee)
new_lt19(wzz4710, wzz4910, ty_Int) → new_lt9(wzz4710, wzz4910)
new_esEs7(Just(wzz400), Just(wzz3000), app(ty_Ratio, ddf)) → new_esEs16(wzz400, wzz3000, ddf)
new_esEs20(wzz401, wzz3001, ty_Float) → new_esEs17(wzz401, wzz3001)
new_esEs9(:(wzz400, wzz401), [], bfg) → False
new_esEs9([], :(wzz3000, wzz3001), bfg) → False
new_esEs10(wzz400, wzz3000, ty_Float) → new_esEs17(wzz400, wzz3000)
new_ltEs14(True, False) → False
new_compare13(Integer(wzz4700), Integer(wzz4900)) → new_primCmpInt(wzz4700, wzz4900)
new_ltEs5(Left(wzz4710), Left(wzz4910), ty_Int, bd) → new_ltEs8(wzz4710, wzz4910)
new_esEs25(wzz401, wzz3001, app(app(app(ty_@3, chh), daa), dab)) → new_esEs5(wzz401, wzz3001, chh, daa, dab)
new_lt17(wzz470, wzz490) → new_esEs8(new_compare18(wzz470, wzz490), LT)
new_lt19(wzz4710, wzz4910, ty_Double) → new_lt12(wzz4710, wzz4910)
new_esEs17(Float(wzz400, wzz401), Float(wzz3000, wzz3001)) → new_esEs18(new_sr(wzz400, wzz3000), new_sr(wzz401, wzz3001))
new_compare27(wzz470, wzz490, True, bed) → EQ
new_lt6(wzz470, wzz490, ty_Float) → new_lt13(wzz470, wzz490)
new_ltEs7(EQ, LT) → False
new_compare114(wzz470, wzz490, False, bed) → GT
new_ltEs7(LT, LT) → True
new_compare19(wzz470, wzz490, bed) → new_compare27(wzz470, wzz490, new_esEs7(wzz470, wzz490, bed), bed)
new_lt19(wzz4710, wzz4910, ty_Char) → new_lt5(wzz4710, wzz4910)
new_compare28(wzz470, wzz490, False, hf, hg, hh) → new_compare115(wzz470, wzz490, new_ltEs6(wzz470, wzz490, hf, hg, hh), hf, hg, hh)
new_esEs10(wzz400, wzz3000, ty_Ordering) → new_esEs8(wzz400, wzz3000)
new_esEs22(wzz4711, wzz4911, ty_@0) → new_esEs13(wzz4711, wzz4911)
new_esEs22(wzz4711, wzz4911, ty_Integer) → new_esEs15(wzz4711, wzz4911)
new_lt16(wzz470, wzz490, bec) → new_esEs8(new_compare4(wzz470, wzz490, bec), LT)
new_ltEs5(Right(wzz4710), Right(wzz4910), cd, ty_@0) → new_ltEs15(wzz4710, wzz4910)
new_primPlusNat1(Zero, Zero) → Zero
new_esEs19(wzz470, wzz490, ty_Integer) → new_esEs15(wzz470, wzz490)
new_esEs26(wzz400, wzz3000, app(app(ty_Either, dbe), dbf)) → new_esEs4(wzz400, wzz3000, dbe, dbf)
new_asAs(True, wzz64) → wzz64
new_esEs19(wzz470, wzz490, app(app(ty_Either, h), ba)) → new_esEs4(wzz470, wzz490, h, ba)
new_ltEs7(LT, GT) → True
new_compare112(wzz470, wzz490, True, h, ba) → LT
new_esEs26(wzz400, wzz3000, app(app(app(ty_@3, dbb), dbc), dbd)) → new_esEs5(wzz400, wzz3000, dbb, dbc, dbd)
new_primMulNat0(Succ(wzz40000), Succ(wzz300000)) → new_primPlusNat0(new_primMulNat0(wzz40000, Succ(wzz300000)), wzz300000)
new_esEs4(Right(wzz400), Left(wzz3000), ceb, ccg) → False
new_esEs4(Left(wzz400), Right(wzz3000), ceb, ccg) → False
new_ltEs19(wzz4712, wzz4912, ty_Float) → new_ltEs12(wzz4712, wzz4912)
new_fsEs(wzz126) → new_not(new_esEs8(wzz126, GT))
new_esEs26(wzz400, wzz3000, app(app(ty_@2, dah), dba)) → new_esEs6(wzz400, wzz3000, dah, dba)
new_esEs23(wzz4710, wzz4910, app(app(app(ty_@3, ec), ed), ee)) → new_esEs5(wzz4710, wzz4910, ec, ed, ee)
new_ltEs19(wzz4712, wzz4912, ty_Ordering) → new_ltEs7(wzz4712, wzz4912)
new_lt20(wzz4711, wzz4911, ty_Int) → new_lt9(wzz4711, wzz4911)
new_esEs19(wzz470, wzz490, ty_Ordering) → new_esEs8(wzz470, wzz490)
new_ltEs20(wzz4711, wzz4911, ty_Int) → new_ltEs8(wzz4711, wzz4911)
new_ltEs20(wzz4711, wzz4911, app(app(ty_@2, bcd), bce)) → new_ltEs13(wzz4711, wzz4911, bcd, bce)
new_lt6(wzz470, wzz490, ty_Char) → new_lt5(wzz470, wzz490)
new_esEs27(wzz4710, wzz4910, ty_Char) → new_esEs11(wzz4710, wzz4910)
new_esEs16(:%(wzz400, wzz401), :%(wzz3000, wzz3001), dcd) → new_asAs(new_esEs29(wzz400, wzz3000, dcd), new_esEs28(wzz401, wzz3001, dcd))
new_esEs21(wzz400, wzz3000, ty_Bool) → new_esEs12(wzz400, wzz3000)
new_esEs7(Just(wzz400), Just(wzz3000), ty_Char) → new_esEs11(wzz400, wzz3000)
new_primCompAux00(wzz148, GT) → GT
new_ltEs20(wzz4711, wzz4911, ty_Ordering) → new_ltEs7(wzz4711, wzz4911)
new_ltEs20(wzz4711, wzz4911, ty_Integer) → new_ltEs9(wzz4711, wzz4911)
new_compare116(wzz470, wzz490, True) → LT
new_compare8(Char(wzz4700), Char(wzz4900)) → new_primCmpNat0(wzz4700, wzz4900)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_ltEs15(wzz471, wzz491) → new_fsEs(new_compare18(wzz471, wzz491))
new_esEs20(wzz401, wzz3001, ty_@0) → new_esEs13(wzz401, wzz3001)
new_esEs4(Right(wzz400), Right(wzz3000), ceb, ty_Float) → new_esEs17(wzz400, wzz3000)
new_ltEs20(wzz4711, wzz4911, app(app(ty_Either, bbg), bbh)) → new_ltEs5(wzz4711, wzz4911, bbg, bbh)
new_esEs21(wzz400, wzz3000, app(ty_[], ccd)) → new_esEs9(wzz400, wzz3000, ccd)
new_esEs20(wzz401, wzz3001, app(ty_[], cbb)) → new_esEs9(wzz401, wzz3001, cbb)
new_compare9(wzz4700, wzz4900, app(app(ty_Either, bee), bef)) → new_compare7(wzz4700, wzz4900, bee, bef)
new_primCmpInt(Pos(Succ(wzz4700)), Pos(wzz490)) → new_primCmpNat2(wzz4700, wzz490)
new_ltEs20(wzz4711, wzz4911, ty_Char) → new_ltEs17(wzz4711, wzz4911)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_esEs22(wzz4711, wzz4911, app(ty_Maybe, gd)) → new_esEs7(wzz4711, wzz4911, gd)
new_ltEs5(Left(wzz4710), Left(wzz4910), ty_Double, bd) → new_ltEs11(wzz4710, wzz4910)
new_esEs27(wzz4710, wzz4910, ty_Integer) → new_esEs15(wzz4710, wzz4910)
new_lt21(wzz4710, wzz4910, app(app(app(ty_@3, bag), bah), bba)) → new_lt7(wzz4710, wzz4910, bag, bah, bba)
new_primCmpInt(Neg(Succ(wzz4700)), Pos(wzz490)) → LT
new_esEs10(wzz400, wzz3000, ty_Double) → new_esEs14(wzz400, wzz3000)
new_esEs24(wzz402, wzz3002, ty_Double) → new_esEs14(wzz402, wzz3002)
new_not(True) → False

The set Q consists of the following terms:

new_lt21(x0, x1, app(ty_[], x2))
new_compare15(Double(x0, x1), Double(x2, x3))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, app(ty_[], x2))
new_compare9(x0, x1, ty_Integer)
new_esEs13(@0, @0)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_lt6(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, ty_Bool)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs16(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs4(Left(x0), Left(x1), ty_@0, x2)
new_ltEs19(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_Double)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs20(x0, x1, ty_@0)
new_esEs10(x0, x1, ty_Char)
new_ltEs12(x0, x1)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs22(x0, x1, ty_@0)
new_esEs25(x0, x1, app(ty_[], x2))
new_ltEs16(Just(x0), Just(x1), ty_Char)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_ltEs10(x0, x1, x2)
new_esEs12(False, False)
new_lt7(x0, x1, x2, x3, x4)
new_ltEs4(x0, x1, x2)
new_ltEs9(x0, x1)
new_lt19(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs25(x0, x1, ty_Char)
new_ltEs16(Just(x0), Just(x1), ty_Ordering)
new_ltEs5(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_pePe(True, x0)
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_lt21(x0, x1, app(ty_Maybe, x2))
new_ltEs7(EQ, EQ)
new_esEs26(x0, x1, ty_Char)
new_esEs25(x0, x1, ty_@0)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Bool)
new_ltEs17(x0, x1)
new_esEs4(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs5(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs14(True, False)
new_ltEs20(x0, x1, ty_Bool)
new_ltEs14(False, True)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs5(Left(x0), Left(x1), ty_Char, x2)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs27(x0, x1, ty_Integer)
new_ltEs16(Just(x0), Nothing, x1)
new_esEs21(x0, x1, ty_Bool)
new_esEs8(GT, GT)
new_ltEs18(x0, x1, ty_Double)
new_esEs7(Just(x0), Just(x1), ty_Int)
new_ltEs19(x0, x1, ty_Integer)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, app(ty_[], x2))
new_fsEs(x0)
new_ltEs7(EQ, LT)
new_ltEs7(LT, EQ)
new_lt20(x0, x1, ty_Integer)
new_sr0(Integer(x0), Integer(x1))
new_esEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_primCompAux0(x0, x1, x2, x3)
new_asAs(False, x0)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_primCompAux00(x0, LT)
new_compare114(x0, x1, False, x2)
new_esEs8(LT, LT)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs5(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_compare113(x0, x1, False)
new_compare113(x0, x1, True)
new_esEs19(x0, x1, ty_Integer)
new_compare9(x0, x1, app(ty_Ratio, x2))
new_ltEs5(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs8(x0, x1)
new_primEqNat0(Succ(x0), Zero)
new_esEs20(x0, x1, ty_Integer)
new_esEs10(x0, x1, ty_@0)
new_ltEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs7(LT, LT)
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_ltEs5(Left(x0), Right(x1), x2, x3)
new_ltEs5(Right(x0), Left(x1), x2, x3)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs19(x0, x1, ty_Bool)
new_lt21(x0, x1, ty_Ordering)
new_esEs4(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs16(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_compare16(Float(x0, x1), Float(x2, x3))
new_esEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs5(Left(x0), Left(x1), ty_Float, x2)
new_esEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs25(x0, x1, ty_Double)
new_esEs23(x0, x1, app(ty_[], x2))
new_compare18(@0, @0)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_ltEs5(Left(x0), Left(x1), ty_Int, x2)
new_ltEs19(x0, x1, ty_Bool)
new_ltEs5(Right(x0), Right(x1), x2, ty_Float)
new_lt6(x0, x1, ty_@0)
new_lt5(x0, x1)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs7(Nothing, Nothing, x0)
new_pePe(False, x0)
new_esEs19(x0, x1, ty_Char)
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_ltEs19(x0, x1, ty_Char)
new_primEqNat0(Zero, Zero)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs10(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_Float)
new_ltEs16(Just(x0), Just(x1), app(ty_[], x2))
new_compare112(x0, x1, False, x2, x3)
new_ltEs11(x0, x1)
new_esEs21(x0, x1, ty_Int)
new_ltEs15(x0, x1)
new_esEs16(:%(x0, x1), :%(x2, x3), x4)
new_lt6(x0, x1, ty_Char)
new_ltEs5(Right(x0), Right(x1), x2, ty_Int)
new_lt6(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_lt9(x0, x1)
new_compare9(x0, x1, ty_Bool)
new_primMulNat0(Zero, Zero)
new_lt20(x0, x1, ty_Int)
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs4(Right(x0), Right(x1), x2, ty_Double)
new_esEs19(x0, x1, ty_Ordering)
new_ltEs5(Left(x0), Left(x1), ty_Ordering, x2)
new_sr(x0, x1)
new_ltEs5(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_compare115(x0, x1, False, x2, x3, x4)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_primEqNat0(Zero, Succ(x0))
new_compare8(Char(x0), Char(x1))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs9([], :(x0, x1), x2)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, ty_Int)
new_primCmpNat2(x0, Zero)
new_esEs21(x0, x1, ty_Double)
new_esEs24(x0, x1, ty_Integer)
new_primMulNat0(Succ(x0), Zero)
new_lt6(x0, x1, ty_Double)
new_compare26(x0, x1, True)
new_esEs23(x0, x1, ty_Char)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_ltEs5(Right(x0), Right(x1), x2, ty_Char)
new_ltEs18(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, ty_Integer)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, app(ty_[], x2))
new_lt15(x0, x1)
new_ltEs20(x0, x1, ty_@0)
new_compare9(x0, x1, ty_Ordering)
new_esEs7(Just(x0), Just(x1), ty_Double)
new_compare14(:%(x0, x1), :%(x2, x3), ty_Int)
new_lt21(x0, x1, ty_@0)
new_esEs10(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_ltEs20(x0, x1, ty_Double)
new_esEs21(x0, x1, ty_Float)
new_compare111(x0, x1, x2, x3, False, x4, x5)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_lt6(x0, x1, app(ty_Ratio, x2))
new_lt6(x0, x1, app(app(ty_Either, x2), x3))
new_lt21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, ty_Float)
new_esEs27(x0, x1, ty_Int)
new_esEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_compare26(x0, x1, False)
new_compare27(x0, x1, True, x2)
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare9(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, ty_Char)
new_ltEs16(Nothing, Just(x0), x1)
new_esEs28(x0, x1, ty_Int)
new_primPlusNat0(Zero, x0)
new_esEs28(x0, x1, ty_Integer)
new_lt20(x0, x1, ty_Double)
new_compare9(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, app(ty_[], x2))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs4(Right(x0), Left(x1), x2, x3)
new_esEs4(Left(x0), Right(x1), x2, x3)
new_esEs23(x0, x1, ty_Ordering)
new_lt10(x0, x1)
new_ltEs5(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_compare24(x0, x1, True)
new_esEs23(x0, x1, ty_Double)
new_esEs24(x0, x1, ty_Double)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs20(x0, x1, ty_Float)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_primPlusNat1(Zero, Zero)
new_compare115(x0, x1, True, x2, x3, x4)
new_lt19(x0, x1, ty_@0)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs7(Nothing, Just(x0), x1)
new_ltEs16(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs18(x0, x1, ty_Char)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Int)
new_esEs4(Right(x0), Right(x1), x2, ty_Bool)
new_esEs21(x0, x1, ty_Char)
new_ltEs5(Right(x0), Right(x1), x2, ty_@0)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_compare7(x0, x1, x2, x3)
new_esEs10(x0, x1, app(ty_Ratio, x2))
new_lt21(x0, x1, app(ty_Ratio, x2))
new_esEs10(x0, x1, app(ty_Maybe, x2))
new_esEs20(x0, x1, ty_Int)
new_lt6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primPlusNat0(Succ(x0), x1)
new_compare19(x0, x1, x2)
new_ltEs20(x0, x1, ty_Char)
new_esEs27(x0, x1, ty_Double)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(x0, x1, ty_Bool)
new_primCmpNat0(Zero, Succ(x0))
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs12(True, True)
new_compare25(x0, x1, False, x2, x3)
new_lt16(x0, x1, x2)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, ty_Int)
new_lt21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs5(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_esEs7(Just(x0), Nothing, x1)
new_compare4([], :(x0, x1), x2)
new_ltEs16(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs5(Right(x0), Right(x1), x2, ty_Double)
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_compare9(x0, x1, app(app(ty_@2, x2), x3))
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs18(x0, x1, ty_Int)
new_esEs10(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Bool)
new_ltEs16(Just(x0), Just(x1), ty_Double)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, ty_Char)
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Bool)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_compare4(:(x0, x1), [], x2)
new_esEs26(x0, x1, ty_Bool)
new_primCompAux00(x0, GT)
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_lt18(x0, x1, x2)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_esEs19(x0, x1, ty_Float)
new_esEs26(x0, x1, ty_Ordering)
new_esEs26(x0, x1, ty_Integer)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt21(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Neg(Zero), Neg(Zero))
new_compare9(x0, x1, ty_Float)
new_primCmpNat0(Succ(x0), Succ(x1))
new_esEs4(Left(x0), Left(x1), ty_Integer, x2)
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs18(x0, x1, ty_Integer)
new_esEs9(:(x0, x1), :(x2, x3), x4)
new_lt11(x0, x1, x2)
new_lt12(x0, x1)
new_asAs(True, x0)
new_ltEs5(Left(x0), Left(x1), ty_Integer, x2)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs4(Left(x0), Left(x1), ty_Double, x2)
new_ltEs20(x0, x1, ty_Float)
new_esEs27(x0, x1, ty_Ordering)
new_esEs24(x0, x1, ty_@0)
new_compare9(x0, x1, ty_Char)
new_compare6(x0, x1, x2, x3)
new_lt19(x0, x1, ty_Float)
new_esEs9([], [], x0)
new_lt20(x0, x1, ty_Char)
new_esEs27(x0, x1, ty_@0)
new_primPlusNat1(Succ(x0), Zero)
new_ltEs16(Just(x0), Just(x1), ty_Int)
new_compare12(x0, x1)
new_compare23(x0, x1, True, x2, x3)
new_esEs27(x0, x1, ty_Bool)
new_esEs18(x0, x1)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, ty_@0)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, ty_Integer)
new_esEs19(x0, x1, ty_Int)
new_esEs14(Double(x0, x1), Double(x2, x3))
new_esEs26(x0, x1, ty_Float)
new_lt21(x0, x1, ty_Char)
new_esEs4(Left(x0), Left(x1), ty_Int, x2)
new_lt20(x0, x1, ty_@0)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_ltEs16(Just(x0), Just(x1), ty_Float)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare14(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs5(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_esEs4(Left(x0), Left(x1), ty_Float, x2)
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_ltEs16(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, ty_Int)
new_compare9(x0, x1, ty_Double)
new_compare116(x0, x1, True)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs4(Right(x0), Right(x1), x2, ty_@0)
new_lt6(x0, x1, ty_Bool)
new_esEs4(Right(x0), Right(x1), x2, ty_Char)
new_primPlusNat1(Zero, Succ(x0))
new_ltEs18(x0, x1, ty_Float)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_compare17(x0, x1)
new_primCmpNat0(Zero, Zero)
new_esEs24(x0, x1, ty_Float)
new_compare27(x0, x1, False, x2)
new_compare114(x0, x1, True, x2)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, ty_Float)
new_compare28(x0, x1, True, x2, x3, x4)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_ltEs5(Left(x0), Left(x1), ty_@0, x2)
new_esEs24(x0, x1, ty_Ordering)
new_compare110(x0, x1, x2, x3, False, x4, x5, x6)
new_esEs10(x0, x1, ty_Double)
new_compare112(x0, x1, True, x2, x3)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_lt19(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, ty_Char)
new_compare116(x0, x1, False)
new_lt19(x0, x1, ty_Bool)
new_esEs29(x0, x1, ty_Int)
new_compare28(x0, x1, False, x2, x3, x4)
new_esEs21(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs9(:(x0, x1), [], x2)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs29(x0, x1, ty_Integer)
new_compare9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_lt4(x0, x1, x2, x3)
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_compare23(@2(x0, x1), @2(x2, x3), False, x4, x5)
new_esEs10(x0, x1, ty_Integer)
new_esEs12(False, True)
new_esEs12(True, False)
new_ltEs5(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs4(Right(x0), Right(x1), x2, ty_Int)
new_esEs10(x0, x1, app(ty_[], x2))
new_lt6(x0, x1, app(ty_Maybe, x2))
new_ltEs7(LT, GT)
new_compare4([], [], x0)
new_ltEs5(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs18(x0, x1, ty_Ordering)
new_ltEs7(GT, LT)
new_ltEs14(True, True)
new_ltEs14(False, False)
new_esEs19(x0, x1, ty_Double)
new_lt13(x0, x1)
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Just(x0), Just(x1), ty_Float)
new_primPlusNat1(Succ(x0), Succ(x1))
new_compare9(x0, x1, ty_@0)
new_ltEs18(x0, x1, ty_@0)
new_esEs17(Float(x0, x1), Float(x2, x3))
new_primEqNat0(Succ(x0), Succ(x1))
new_compare9(x0, x1, ty_Int)
new_esEs4(Left(x0), Left(x1), ty_Char, x2)
new_primCmpNat0(Succ(x0), Zero)
new_lt6(x0, x1, ty_Integer)
new_not(True)
new_esEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_compare24(x0, x1, False)
new_esEs22(x0, x1, ty_Double)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_ltEs16(Just(x0), Just(x1), ty_Bool)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_not(False)
new_lt21(x0, x1, ty_Float)
new_esEs19(x0, x1, ty_@0)
new_esEs24(x0, x1, ty_Int)
new_lt17(x0, x1)
new_ltEs5(Left(x0), Left(x1), ty_Double, x2)
new_lt21(x0, x1, ty_Integer)
new_compare4(:(x0, x1), :(x2, x3), x4)
new_esEs11(Char(x0), Char(x1))
new_lt6(x0, x1, ty_Int)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1, ty_Double)
new_compare111(x0, x1, x2, x3, True, x4, x5)
new_lt6(x0, x1, ty_Ordering)
new_ltEs5(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs4(Right(x0), Right(x1), x2, ty_Float)
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs7(Just(x0), Just(x1), ty_@0)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Just(x0), Just(x1), ty_Char)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_lt21(x0, x1, ty_Double)
new_ltEs20(x0, x1, ty_Ordering)
new_lt21(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_@0)
new_ltEs16(Just(x0), Just(x1), ty_@0)
new_esEs21(x0, x1, ty_@0)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Ordering)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_ltEs5(Right(x0), Right(x1), x2, ty_Bool)
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_compare11(x0, x1)
new_primCmpNat1(Succ(x0), x1)
new_esEs10(x0, x1, ty_Float)
new_lt21(x0, x1, ty_Bool)
new_primMulNat0(Zero, Succ(x0))
new_ltEs16(Nothing, Nothing, x0)
new_esEs10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, ty_@0)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_Bool)
new_ltEs5(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs20(x0, x1, ty_Double)
new_compare25(x0, x1, True, x2, x3)
new_esEs20(x0, x1, ty_Bool)
new_lt8(x0, x1)
new_lt20(x0, x1, ty_Float)
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs19(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, ty_Integer)
new_primCompAux00(x0, EQ)
new_esEs22(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Integer)
new_compare10(x0, x1, x2, x3, x4)
new_esEs20(x0, x1, ty_Char)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare13(Integer(x0), Integer(x1))
new_esEs26(x0, x1, ty_Int)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_ltEs13(@2(x0, x1), @2(x2, x3), x4, x5)
new_compare9(x0, x1, app(ty_[], x2))
new_primEqInt(Pos(Zero), Pos(Zero))
new_primCmpNat2(x0, Succ(x1))
new_esEs15(Integer(x0), Integer(x1))
new_esEs19(x0, x1, app(ty_[], x2))
new_lt19(x0, x1, ty_Char)
new_esEs20(x0, x1, ty_Ordering)
new_lt14(x0, x1, x2, x3)
new_ltEs16(Just(x0), Just(x1), ty_Integer)
new_ltEs5(Right(x0), Right(x1), x2, ty_Integer)
new_lt6(x0, x1, ty_Float)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs26(x0, x1, ty_Double)
new_esEs22(x0, x1, ty_Float)
new_ltEs5(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs25(x0, x1, ty_Int)
new_esEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs10(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs7(GT, EQ)
new_ltEs7(EQ, GT)
new_primMulInt(Pos(x0), Pos(x1))
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs10(x0, x1, ty_Ordering)
new_ltEs7(GT, GT)
new_compare110(x0, x1, x2, x3, True, x4, x5, x6)
new_primCmpNat1(Zero, x0)
new_ltEs5(Left(x0), Left(x1), ty_Bool, x2)
new_esEs22(x0, x1, ty_Integer)

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

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



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

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

new_addToFM_C(Branch(@2(wzz300, wzz301), wzz31, wzz32, wzz33, wzz34), @2(wzz40, wzz41), wzz5, bc, bd, be) → new_addToFM_C2(wzz300, wzz301, wzz31, wzz32, wzz33, wzz34, wzz40, wzz41, wzz5, new_esEs30(wzz40, wzz41, wzz300, wzz301, new_esEs31(wzz40, wzz300, bc), bc, bd), bc, bd, be)
new_addToFM_C2(wzz17, wzz18, wzz19, wzz20, wzz21, wzz22, wzz23, wzz24, wzz25, False, h, ba, bb) → new_addToFM_C1(wzz17, wzz18, wzz19, wzz20, wzz21, wzz22, wzz23, wzz24, wzz25, new_esEs8(new_compare23(@2(wzz23, wzz24), @2(wzz17, wzz18), new_esEs6(@2(wzz23, wzz24), @2(wzz17, wzz18), h, ba), h, ba), GT), h, ba, bb)
new_addToFM_C2(wzz17, wzz18, wzz19, wzz20, wzz21, wzz22, wzz23, wzz24, wzz25, True, h, ba, bb) → new_addToFM_C(wzz21, @2(wzz23, wzz24), wzz25, h, ba, bb)
new_addToFM_C1(wzz17, wzz18, wzz19, wzz20, wzz21, wzz22, wzz23, wzz24, wzz25, True, h, ba, bb) → new_addToFM_C(wzz22, @2(wzz23, wzz24), wzz25, h, ba, bb)

The TRS R consists of the following rules:

new_esEs7(Just(wzz400), Just(wzz3000), app(ty_Maybe, dfg)) → new_esEs7(wzz400, wzz3000, dfg)
new_esEs4(Right(wzz400), Right(wzz3000), bcd, ty_Ordering) → new_esEs8(wzz400, wzz3000)
new_esEs20(wzz401, wzz3001, app(ty_Maybe, bdg)) → new_esEs7(wzz401, wzz3001, bdg)
new_esEs32(wzz35, wzz37, ty_Float) → new_esEs17(wzz35, wzz37)
new_lt21(wzz4710, wzz4910, ty_Float) → new_lt13(wzz4710, wzz4910)
new_esEs4(Left(wzz400), Left(wzz3000), app(ty_[], cac), bce) → new_esEs9(wzz400, wzz3000, cac)
new_esEs21(wzz400, wzz3000, app(app(ty_@2, beb), bec)) → new_esEs6(wzz400, wzz3000, beb, bec)
new_lt6(wzz470, wzz490, app(app(app(ty_@3, bbb), bbc), bbd)) → new_lt7(wzz470, wzz490, bbb, bbc, bbd)
new_ltEs5(Right(wzz4710), Right(wzz4910), fb, app(ty_[], gd)) → new_ltEs4(wzz4710, wzz4910, gd)
new_esEs23(wzz4710, wzz4910, app(ty_[], ccf)) → new_esEs9(wzz4710, wzz4910, ccf)
new_esEs5(@3(wzz400, wzz401, wzz402), @3(wzz3000, wzz3001, wzz3002), bca, bcb, bcc) → new_asAs(new_esEs26(wzz400, wzz3000, bca), new_asAs(new_esEs25(wzz401, wzz3001, bcb), new_esEs24(wzz402, wzz3002, bcc)))
new_primCmpNat2(wzz4700, Succ(wzz4900)) → new_primCmpNat0(wzz4700, wzz4900)
new_compare116(wzz470, wzz490, False) → GT
new_ltEs16(Just(wzz4710), Just(wzz4910), app(app(ty_Either, cfd), cfe)) → new_ltEs5(wzz4710, wzz4910, cfd, cfe)
new_esEs24(wzz402, wzz3002, app(app(app(ty_@3, cgh), cha), chb)) → new_esEs5(wzz402, wzz3002, cgh, cha, chb)
new_ltEs5(Right(wzz4710), Right(wzz4910), fb, ty_Float) → new_ltEs12(wzz4710, wzz4910)
new_esEs4(Right(wzz400), Right(wzz3000), bcd, ty_Char) → new_esEs11(wzz400, wzz3000)
new_esEs20(wzz401, wzz3001, ty_Bool) → new_esEs12(wzz401, wzz3001)
new_esEs31(wzz40, wzz300, ty_Ordering) → new_esEs8(wzz40, wzz300)
new_lt21(wzz4710, wzz4910, ty_Char) → new_lt5(wzz4710, wzz4910)
new_ltEs7(LT, EQ) → True
new_esEs26(wzz400, wzz3000, ty_Double) → new_esEs14(wzz400, wzz3000)
new_ltEs5(Right(wzz4710), Right(wzz4910), fb, ty_Int) → new_ltEs8(wzz4710, wzz4910)
new_esEs27(wzz4710, wzz4910, app(ty_Maybe, dde)) → new_esEs7(wzz4710, wzz4910, dde)
new_ltEs5(Right(wzz4710), Right(wzz4910), fb, ty_Bool) → new_ltEs14(wzz4710, wzz4910)
new_ltEs19(wzz4712, wzz4912, ty_Double) → new_ltEs11(wzz4712, wzz4912)
new_esEs31(wzz40, wzz300, app(app(app(ty_@3, bca), bcb), bcc)) → new_esEs5(wzz40, wzz300, bca, bcb, bcc)
new_esEs23(wzz4710, wzz4910, ty_Float) → new_esEs17(wzz4710, wzz4910)
new_esEs26(wzz400, wzz3000, ty_Float) → new_esEs17(wzz400, wzz3000)
new_lt21(wzz4710, wzz4910, ty_@0) → new_lt17(wzz4710, wzz4910)
new_primMulNat0(Zero, Zero) → Zero
new_esEs10(wzz400, wzz3000, ty_@0) → new_esEs13(wzz400, wzz3000)
new_ltEs5(Right(wzz4710), Right(wzz4910), fb, app(ty_Maybe, ge)) → new_ltEs16(wzz4710, wzz4910, ge)
new_lt21(wzz4710, wzz4910, ty_Double) → new_lt12(wzz4710, wzz4910)
new_ltEs20(wzz4711, wzz4911, ty_@0) → new_ltEs15(wzz4711, wzz4911)
new_esEs24(wzz402, wzz3002, ty_@0) → new_esEs13(wzz402, wzz3002)
new_ltEs16(Just(wzz4710), Just(wzz4910), app(ty_[], cgd)) → new_ltEs4(wzz4710, wzz4910, cgd)
new_ltEs18(wzz471, wzz491, ty_Int) → new_ltEs8(wzz471, wzz491)
new_ltEs20(wzz4711, wzz4911, ty_Float) → new_ltEs12(wzz4711, wzz4911)
new_esEs12(True, True) → True
new_ltEs5(Left(wzz4710), Left(wzz4910), ty_@0, ea) → new_ltEs15(wzz4710, wzz4910)
new_esEs20(wzz401, wzz3001, app(ty_Ratio, bdh)) → new_esEs16(wzz401, wzz3001, bdh)
new_esEs32(wzz35, wzz37, ty_Integer) → new_esEs15(wzz35, wzz37)
new_ltEs16(Just(wzz4710), Just(wzz4910), ty_Int) → new_ltEs8(wzz4710, wzz4910)
new_esEs23(wzz4710, wzz4910, ty_Bool) → new_esEs12(wzz4710, wzz4910)
new_esEs24(wzz402, wzz3002, ty_Integer) → new_esEs15(wzz402, wzz3002)
new_ltEs18(wzz471, wzz491, ty_Char) → new_ltEs17(wzz471, wzz491)
new_ltEs14(False, True) → True
new_ltEs19(wzz4712, wzz4912, ty_Integer) → new_ltEs9(wzz4712, wzz4912)
new_compare9(wzz4700, wzz4900, app(app(ty_@2, dc), dd)) → new_compare6(wzz4700, wzz4900, dc, dd)
new_esEs31(wzz40, wzz300, app(ty_[], gf)) → new_esEs9(wzz40, wzz300, gf)
new_compare9(wzz4700, wzz4900, ty_Double) → new_compare15(wzz4700, wzz4900)
new_lt21(wzz4710, wzz4910, app(ty_[], ddd)) → new_lt16(wzz4710, wzz4910, ddd)
new_esEs20(wzz401, wzz3001, app(app(ty_Either, bde), bdf)) → new_esEs4(wzz401, wzz3001, bde, bdf)
new_esEs23(wzz4710, wzz4910, ty_@0) → new_esEs13(wzz4710, wzz4910)
new_compare18(@0, @0) → EQ
new_esEs4(Left(wzz400), Left(wzz3000), app(app(ty_@2, bhb), bhc), bce) → new_esEs6(wzz400, wzz3000, bhb, bhc)
new_ltEs5(Left(wzz4710), Left(wzz4910), app(app(ty_@2, ef), eg), ea) → new_ltEs13(wzz4710, wzz4910, ef, eg)
new_ltEs6(@3(wzz4710, wzz4711, wzz4712), @3(wzz4910, wzz4911, wzz4912), bac, bad, bae) → new_pePe(new_lt19(wzz4710, wzz4910, bac), new_asAs(new_esEs23(wzz4710, wzz4910, bac), new_pePe(new_lt20(wzz4711, wzz4911, bad), new_asAs(new_esEs22(wzz4711, wzz4911, bad), new_ltEs19(wzz4712, wzz4912, bae)))))
new_ltEs5(Left(wzz4710), Right(wzz4910), fb, ea) → True
new_lt19(wzz4710, wzz4910, ty_Float) → new_lt13(wzz4710, wzz4910)
new_lt19(wzz4710, wzz4910, ty_Ordering) → new_lt8(wzz4710, wzz4910)
new_esEs7(Just(wzz400), Just(wzz3000), app(app(ty_@2, deh), dfa)) → new_esEs6(wzz400, wzz3000, deh, dfa)
new_lt18(wzz470, wzz490, bbf) → new_esEs8(new_compare19(wzz470, wzz490, bbf), LT)
new_esEs32(wzz35, wzz37, ty_@0) → new_esEs13(wzz35, wzz37)
new_esEs15(Integer(wzz400), Integer(wzz3000)) → new_primEqInt(wzz400, wzz3000)
new_compare110(wzz114, wzz115, wzz116, wzz117, True, wzz119, bgh, bha) → new_compare111(wzz114, wzz115, wzz116, wzz117, True, bgh, bha)
new_ltEs18(wzz471, wzz491, ty_Ordering) → new_ltEs7(wzz471, wzz491)
new_ltEs5(Right(wzz4710), Right(wzz4910), fb, app(app(ty_Either, fc), fd)) → new_ltEs5(wzz4710, wzz4910, fc, fd)
new_esEs25(wzz401, wzz3001, ty_Double) → new_esEs14(wzz401, wzz3001)
new_lt8(wzz470, wzz490) → new_esEs8(new_compare11(wzz470, wzz490), LT)
new_esEs19(wzz470, wzz490, app(app(app(ty_@3, bbb), bbc), bbd)) → new_esEs5(wzz470, wzz490, bbb, bbc, bbd)
new_ltEs5(Left(wzz4710), Left(wzz4910), ty_Ordering, ea) → new_ltEs7(wzz4710, wzz4910)
new_esEs20(wzz401, wzz3001, app(app(ty_@2, bch), bda)) → new_esEs6(wzz401, wzz3001, bch, bda)
new_esEs6(@2(wzz400, wzz401), @2(wzz3000, wzz3001), bbg, bbh) → new_asAs(new_esEs21(wzz400, wzz3000, bbg), new_esEs20(wzz401, wzz3001, bbh))
new_esEs27(wzz4710, wzz4910, ty_Double) → new_esEs14(wzz4710, wzz4910)
new_esEs31(wzz40, wzz300, ty_Int) → new_esEs18(wzz40, wzz300)
new_esEs29(wzz400, wzz3000, ty_Integer) → new_esEs15(wzz400, wzz3000)
new_ltEs5(Right(wzz4710), Left(wzz4910), fb, ea) → False
new_esEs7(Just(wzz400), Just(wzz3000), app(ty_[], dga)) → new_esEs9(wzz400, wzz3000, dga)
new_esEs4(Left(wzz400), Left(wzz3000), ty_Ordering, bce) → new_esEs8(wzz400, wzz3000)
new_compare23(@2(wzz470, wzz471), @2(wzz490, wzz491), False, baa, bab) → new_compare110(wzz470, wzz471, wzz490, wzz491, new_lt6(wzz470, wzz490, baa), new_asAs(new_esEs19(wzz470, wzz490, baa), new_ltEs18(wzz471, wzz491, bab)), baa, bab)
new_esEs32(wzz35, wzz37, app(app(ty_@2, bff), bfg)) → new_esEs6(wzz35, wzz37, bff, bfg)
new_esEs28(wzz401, wzz3001, ty_Int) → new_esEs18(wzz401, wzz3001)
new_pePe(False, wzz139) → wzz139
new_esEs25(wzz401, wzz3001, app(app(ty_Either, dae), daf)) → new_esEs4(wzz401, wzz3001, dae, daf)
new_esEs27(wzz4710, wzz4910, ty_Int) → new_esEs18(wzz4710, wzz4910)
new_esEs25(wzz401, wzz3001, ty_Char) → new_esEs11(wzz401, wzz3001)
new_esEs10(wzz400, wzz3000, ty_Bool) → new_esEs12(wzz400, wzz3000)
new_esEs22(wzz4711, wzz4911, app(app(ty_Either, cch), cda)) → new_esEs4(wzz4711, wzz4911, cch, cda)
new_esEs4(Right(wzz400), Right(wzz3000), bcd, app(ty_Ratio, cbd)) → new_esEs16(wzz400, wzz3000, cbd)
new_compare9(wzz4700, wzz4900, ty_Float) → new_compare16(wzz4700, wzz4900)
new_esEs31(wzz40, wzz300, ty_Float) → new_esEs17(wzz40, wzz300)
new_esEs29(wzz400, wzz3000, ty_Int) → new_esEs18(wzz400, wzz3000)
new_esEs27(wzz4710, wzz4910, ty_Float) → new_esEs17(wzz4710, wzz4910)
new_lt19(wzz4710, wzz4910, app(ty_[], ccf)) → new_lt16(wzz4710, wzz4910, ccf)
new_esEs4(Left(wzz400), Left(wzz3000), ty_@0, bce) → new_esEs13(wzz400, wzz3000)
new_esEs26(wzz400, wzz3000, ty_@0) → new_esEs13(wzz400, wzz3000)
new_esEs10(wzz400, wzz3000, app(ty_Maybe, hf)) → new_esEs7(wzz400, wzz3000, hf)
new_lt20(wzz4711, wzz4911, ty_Double) → new_lt12(wzz4711, wzz4911)
new_esEs32(wzz35, wzz37, app(ty_Maybe, bge)) → new_esEs7(wzz35, wzz37, bge)
new_esEs24(wzz402, wzz3002, app(ty_Maybe, che)) → new_esEs7(wzz402, wzz3002, che)
new_ltEs5(Left(wzz4710), Left(wzz4910), app(ty_[], eh), ea) → new_ltEs4(wzz4710, wzz4910, eh)
new_esEs26(wzz400, wzz3000, ty_Bool) → new_esEs12(wzz400, wzz3000)
new_ltEs5(Left(wzz4710), Left(wzz4910), ty_Float, ea) → new_ltEs12(wzz4710, wzz4910)
new_esEs23(wzz4710, wzz4910, app(ty_Maybe, ccg)) → new_esEs7(wzz4710, wzz4910, ccg)
new_esEs4(Left(wzz400), Left(wzz3000), app(ty_Ratio, cab), bce) → new_esEs16(wzz400, wzz3000, cab)
new_lt20(wzz4711, wzz4911, app(app(ty_@2, cdf), cdg)) → new_lt14(wzz4711, wzz4911, cdf, cdg)
new_esEs10(wzz400, wzz3000, app(app(app(ty_@3, ha), hb), hc)) → new_esEs5(wzz400, wzz3000, ha, hb, hc)
new_ltEs16(Just(wzz4710), Just(wzz4910), ty_Double) → new_ltEs11(wzz4710, wzz4910)
new_esEs22(wzz4711, wzz4911, ty_Ordering) → new_esEs8(wzz4711, wzz4911)
new_esEs21(wzz400, wzz3000, ty_Int) → new_esEs18(wzz400, wzz3000)
new_compare9(wzz4700, wzz4900, app(ty_Ratio, db)) → new_compare14(wzz4700, wzz4900, db)
new_esEs4(Right(wzz400), Right(wzz3000), bcd, ty_Integer) → new_esEs15(wzz400, wzz3000)
new_ltEs7(GT, GT) → True
new_compare14(:%(wzz4700, wzz4701), :%(wzz4900, wzz4901), ty_Int) → new_compare12(new_sr(wzz4700, wzz4901), new_sr(wzz4900, wzz4701))
new_esEs18(wzz40, wzz300) → new_primEqInt(wzz40, wzz300)
new_lt21(wzz4710, wzz4910, app(app(ty_Either, dcd), dce)) → new_lt4(wzz4710, wzz4910, dcd, dce)
new_esEs10(wzz400, wzz3000, app(app(ty_@2, gg), gh)) → new_esEs6(wzz400, wzz3000, gg, gh)
new_ltEs19(wzz4712, wzz4912, ty_Int) → new_ltEs8(wzz4712, wzz4912)
new_esEs23(wzz4710, wzz4910, ty_Double) → new_esEs14(wzz4710, wzz4910)
new_primCmpNat0(Zero, Succ(wzz49000)) → LT
new_primCmpInt(Neg(Succ(wzz4700)), Neg(wzz490)) → new_primCmpNat1(wzz490, wzz4700)
new_ltEs16(Just(wzz4710), Just(wzz4910), app(ty_Ratio, cga)) → new_ltEs10(wzz4710, wzz4910, cga)
new_ltEs20(wzz4711, wzz4911, ty_Bool) → new_ltEs14(wzz4711, wzz4911)
new_esEs25(wzz401, wzz3001, app(app(ty_@2, chh), daa)) → new_esEs6(wzz401, wzz3001, chh, daa)
new_ltEs12(wzz471, wzz491) → new_fsEs(new_compare16(wzz471, wzz491))
new_esEs8(LT, LT) → True
new_lt6(wzz470, wzz490, ty_Ordering) → new_lt8(wzz470, wzz490)
new_esEs19(wzz470, wzz490, ty_Float) → new_esEs17(wzz470, wzz490)
new_ltEs16(Nothing, Nothing, bba) → True
new_compare9(wzz4700, wzz4900, ty_Char) → new_compare8(wzz4700, wzz4900)
new_lt6(wzz470, wzz490, app(app(ty_Either, ca), cb)) → new_lt4(wzz470, wzz490, ca, cb)
new_esEs19(wzz470, wzz490, ty_Bool) → new_esEs12(wzz470, wzz490)
new_esEs7(Just(wzz400), Just(wzz3000), ty_Double) → new_esEs14(wzz400, wzz3000)
new_esEs25(wzz401, wzz3001, ty_Ordering) → new_esEs8(wzz401, wzz3001)
new_esEs10(wzz400, wzz3000, app(app(ty_Either, hd), he)) → new_esEs4(wzz400, wzz3000, hd, he)
new_esEs19(wzz470, wzz490, app(ty_Maybe, bbf)) → new_esEs7(wzz470, wzz490, bbf)
new_esEs24(wzz402, wzz3002, app(ty_[], chg)) → new_esEs9(wzz402, wzz3002, chg)
new_lt21(wzz4710, wzz4910, ty_Bool) → new_lt15(wzz4710, wzz4910)
new_esEs24(wzz402, wzz3002, app(app(ty_@2, cgf), cgg)) → new_esEs6(wzz402, wzz3002, cgf, cgg)
new_esEs22(wzz4711, wzz4911, ty_Int) → new_esEs18(wzz4711, wzz4911)
new_pePe(True, wzz139) → True
new_primEqNat0(Zero, Zero) → True
new_lt6(wzz470, wzz490, ty_Bool) → new_lt15(wzz470, wzz490)
new_esEs32(wzz35, wzz37, ty_Double) → new_esEs14(wzz35, wzz37)
new_compare26(wzz470, wzz490, True) → EQ
new_esEs7(Just(wzz400), Just(wzz3000), ty_Float) → new_esEs17(wzz400, wzz3000)
new_lt21(wzz4710, wzz4910, app(ty_Maybe, dde)) → new_lt18(wzz4710, wzz4910, dde)
new_compare9(wzz4700, wzz4900, ty_Bool) → new_compare17(wzz4700, wzz4900)
new_lt7(wzz470, wzz490, bbb, bbc, bbd) → new_esEs8(new_compare10(wzz470, wzz490, bbb, bbc, bbd), LT)
new_ltEs5(Right(wzz4710), Right(wzz4910), fb, app(app(app(ty_@3, ff), fg), fh)) → new_ltEs6(wzz4710, wzz4910, ff, fg, fh)
new_ltEs19(wzz4712, wzz4912, app(ty_[], cfb)) → new_ltEs4(wzz4712, wzz4912, cfb)
new_esEs32(wzz35, wzz37, ty_Bool) → new_esEs12(wzz35, wzz37)
new_esEs7(Just(wzz400), Just(wzz3000), ty_@0) → new_esEs13(wzz400, wzz3000)
new_lt6(wzz470, wzz490, ty_Int) → new_lt9(wzz470, wzz490)
new_sr(wzz400, wzz3000) → new_primMulInt(wzz400, wzz3000)
new_esEs4(Right(wzz400), Right(wzz3000), bcd, ty_@0) → new_esEs13(wzz400, wzz3000)
new_ltEs16(Just(wzz4710), Just(wzz4910), ty_@0) → new_ltEs15(wzz4710, wzz4910)
new_esEs26(wzz400, wzz3000, ty_Ordering) → new_esEs8(wzz400, wzz3000)
new_esEs8(GT, GT) → True
new_compare24(wzz470, wzz490, False) → new_compare113(wzz470, wzz490, new_ltEs14(wzz470, wzz490))
new_primPlusNat0(Succ(wzz1050), wzz300000) → Succ(Succ(new_primPlusNat1(wzz1050, wzz300000)))
new_compare4([], [], cc) → EQ
new_esEs22(wzz4711, wzz4911, app(ty_[], cdh)) → new_esEs9(wzz4711, wzz4911, cdh)
new_esEs30(wzz34, wzz35, wzz36, wzz37, False, bfd, bfe) → new_esEs8(new_compare23(@2(wzz34, wzz35), @2(wzz36, wzz37), False, bfd, bfe), LT)
new_lt19(wzz4710, wzz4910, app(ty_Ratio, ccc)) → new_lt11(wzz4710, wzz4910, ccc)
new_primCmpInt(Pos(Zero), Pos(Succ(wzz4900))) → new_primCmpNat1(Zero, wzz4900)
new_esEs12(False, False) → True
new_lt6(wzz470, wzz490, ty_Double) → new_lt12(wzz470, wzz490)
new_esEs8(GT, LT) → False
new_esEs8(LT, GT) → False
new_ltEs18(wzz471, wzz491, app(app(ty_Either, fb), ea)) → new_ltEs5(wzz471, wzz491, fb, ea)
new_compare110(wzz114, wzz115, wzz116, wzz117, False, wzz119, bgh, bha) → new_compare111(wzz114, wzz115, wzz116, wzz117, wzz119, bgh, bha)
new_esEs10(wzz400, wzz3000, ty_Char) → new_esEs11(wzz400, wzz3000)
new_lt21(wzz4710, wzz4910, ty_Ordering) → new_lt8(wzz4710, wzz4910)
new_esEs4(Right(wzz400), Right(wzz3000), bcd, app(app(ty_Either, cba), cbb)) → new_esEs4(wzz400, wzz3000, cba, cbb)
new_ltEs16(Nothing, Just(wzz4910), bba) → True
new_primEqInt(Neg(Succ(wzz4000)), Neg(Succ(wzz30000))) → new_primEqNat0(wzz4000, wzz30000)
new_lt20(wzz4711, wzz4911, app(ty_Ratio, cde)) → new_lt11(wzz4711, wzz4911, cde)
new_ltEs18(wzz471, wzz491, app(ty_Ratio, baf)) → new_ltEs10(wzz471, wzz491, baf)
new_esEs20(wzz401, wzz3001, ty_Ordering) → new_esEs8(wzz401, wzz3001)
new_esEs23(wzz4710, wzz4910, ty_Ordering) → new_esEs8(wzz4710, wzz4910)
new_esEs31(wzz40, wzz300, app(app(ty_Either, bcd), bce)) → new_esEs4(wzz40, wzz300, bcd, bce)
new_esEs4(Left(wzz400), Left(wzz3000), app(app(ty_Either, bhg), bhh), bce) → new_esEs4(wzz400, wzz3000, bhg, bhh)
new_esEs4(Left(wzz400), Left(wzz3000), app(app(app(ty_@3, bhd), bhe), bhf), bce) → new_esEs5(wzz400, wzz3000, bhd, bhe, bhf)
new_esEs7(Just(wzz400), Just(wzz3000), ty_Int) → new_esEs18(wzz400, wzz3000)
new_primPlusNat1(Succ(wzz39200), Zero) → Succ(wzz39200)
new_primPlusNat1(Zero, Succ(wzz10100)) → Succ(wzz10100)
new_lt19(wzz4710, wzz4910, ty_Integer) → new_lt10(wzz4710, wzz4910)
new_ltEs13(@2(wzz4710, wzz4711), @2(wzz4910, wzz4911), bag, bah) → new_pePe(new_lt21(wzz4710, wzz4910, bag), new_asAs(new_esEs27(wzz4710, wzz4910, bag), new_ltEs20(wzz4711, wzz4911, bah)))
new_ltEs9(wzz471, wzz491) → new_fsEs(new_compare13(wzz471, wzz491))
new_primCmpNat1(Zero, wzz4700) → LT
new_lt20(wzz4711, wzz4911, app(app(ty_Either, cch), cda)) → new_lt4(wzz4711, wzz4911, cch, cda)
new_compare111(wzz114, wzz115, wzz116, wzz117, True, bgh, bha) → LT
new_esEs21(wzz400, wzz3000, ty_Double) → new_esEs14(wzz400, wzz3000)
new_esEs25(wzz401, wzz3001, ty_Int) → new_esEs18(wzz401, wzz3001)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_ltEs16(Just(wzz4710), Just(wzz4910), app(ty_Maybe, cge)) → new_ltEs16(wzz4710, wzz4910, cge)
new_lt20(wzz4711, wzz4911, app(ty_Maybe, cea)) → new_lt18(wzz4711, wzz4911, cea)
new_ltEs5(Right(wzz4710), Right(wzz4910), fb, ty_Double) → new_ltEs11(wzz4710, wzz4910)
new_esEs4(Left(wzz400), Left(wzz3000), ty_Bool, bce) → new_esEs12(wzz400, wzz3000)
new_esEs7(Just(wzz400), Just(wzz3000), ty_Ordering) → new_esEs8(wzz400, wzz3000)
new_esEs23(wzz4710, wzz4910, ty_Char) → new_esEs11(wzz4710, wzz4910)
new_lt6(wzz470, wzz490, app(ty_Ratio, bbe)) → new_lt11(wzz470, wzz490, bbe)
new_ltEs7(EQ, EQ) → True
new_esEs32(wzz35, wzz37, app(app(app(ty_@3, bfh), bga), bgb)) → new_esEs5(wzz35, wzz37, bfh, bga, bgb)
new_ltEs10(wzz471, wzz491, baf) → new_fsEs(new_compare14(wzz471, wzz491, baf))
new_compare112(wzz470, wzz490, False, ca, cb) → GT
new_ltEs20(wzz4711, wzz4911, app(ty_[], def)) → new_ltEs4(wzz4711, wzz4911, def)
new_primEqInt(Neg(Succ(wzz4000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(wzz30000))) → False
new_ltEs5(Left(wzz4710), Left(wzz4910), app(ty_Ratio, ee), ea) → new_ltEs10(wzz4710, wzz4910, ee)
new_esEs8(EQ, EQ) → True
new_ltEs4(wzz471, wzz491, bh) → new_fsEs(new_compare4(wzz471, wzz491, bh))
new_esEs4(Left(wzz400), Left(wzz3000), ty_Float, bce) → new_esEs17(wzz400, wzz3000)
new_compare26(wzz470, wzz490, False) → new_compare116(wzz470, wzz490, new_ltEs7(wzz470, wzz490))
new_lt20(wzz4711, wzz4911, ty_Ordering) → new_lt8(wzz4711, wzz4911)
new_esEs21(wzz400, wzz3000, app(app(ty_Either, beg), beh)) → new_esEs4(wzz400, wzz3000, beg, beh)
new_esEs22(wzz4711, wzz4911, app(app(app(ty_@3, cdb), cdc), cdd)) → new_esEs5(wzz4711, wzz4911, cdb, cdc, cdd)
new_ltEs19(wzz4712, wzz4912, ty_Char) → new_ltEs17(wzz4712, wzz4912)
new_esEs4(Left(wzz400), Left(wzz3000), ty_Char, bce) → new_esEs11(wzz400, wzz3000)
new_esEs21(wzz400, wzz3000, ty_Float) → new_esEs17(wzz400, wzz3000)
new_ltEs19(wzz4712, wzz4912, app(ty_Maybe, cfc)) → new_ltEs16(wzz4712, wzz4912, cfc)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_ltEs7(GT, LT) → False
new_primCmpNat1(Succ(wzz4900), wzz4700) → new_primCmpNat0(wzz4900, wzz4700)
new_lt5(wzz470, wzz490) → new_esEs8(new_compare8(wzz470, wzz490), LT)
new_primCmpNat0(Succ(wzz47000), Succ(wzz49000)) → new_primCmpNat0(wzz47000, wzz49000)
new_ltEs7(GT, EQ) → False
new_esEs19(wzz470, wzz490, ty_Char) → new_esEs11(wzz470, wzz490)
new_ltEs20(wzz4711, wzz4911, app(ty_Maybe, deg)) → new_ltEs16(wzz4711, wzz4911, deg)
new_primEqInt(Pos(Succ(wzz4000)), Pos(Succ(wzz30000))) → new_primEqNat0(wzz4000, wzz30000)
new_compare9(wzz4700, wzz4900, ty_Int) → new_compare12(wzz4700, wzz4900)
new_ltEs16(Just(wzz4710), Just(wzz4910), ty_Integer) → new_ltEs9(wzz4710, wzz4910)
new_ltEs5(Left(wzz4710), Left(wzz4910), app(app(ty_Either, dg), dh), ea) → new_ltEs5(wzz4710, wzz4910, dg, dh)
new_esEs24(wzz402, wzz3002, app(ty_Ratio, chf)) → new_esEs16(wzz402, wzz3002, chf)
new_ltEs19(wzz4712, wzz4912, ty_Bool) → new_ltEs14(wzz4712, wzz4912)
new_lt21(wzz4710, wzz4910, ty_Integer) → new_lt10(wzz4710, wzz4910)
new_ltEs5(Right(wzz4710), Right(wzz4910), fb, ty_Ordering) → new_ltEs7(wzz4710, wzz4910)
new_esEs26(wzz400, wzz3000, ty_Integer) → new_esEs15(wzz400, wzz3000)
new_esEs24(wzz402, wzz3002, ty_Int) → new_esEs18(wzz402, wzz3002)
new_ltEs19(wzz4712, wzz4912, app(ty_Ratio, ceg)) → new_ltEs10(wzz4712, wzz4912, ceg)
new_ltEs5(Left(wzz4710), Left(wzz4910), app(app(app(ty_@3, eb), ec), ed), ea) → new_ltEs6(wzz4710, wzz4910, eb, ec, ed)
new_primEqNat0(Succ(wzz4000), Succ(wzz30000)) → new_primEqNat0(wzz4000, wzz30000)
new_lt6(wzz470, wzz490, app(app(ty_@2, bf), bg)) → new_lt14(wzz470, wzz490, bf, bg)
new_esEs27(wzz4710, wzz4910, ty_Ordering) → new_esEs8(wzz4710, wzz4910)
new_ltEs14(False, False) → True
new_compare9(wzz4700, wzz4900, app(ty_Maybe, df)) → new_compare19(wzz4700, wzz4900, df)
new_esEs19(wzz470, wzz490, app(app(ty_@2, bf), bg)) → new_esEs6(wzz470, wzz490, bf, bg)
new_lt13(wzz470, wzz490) → new_esEs8(new_compare16(wzz470, wzz490), LT)
new_compare15(Double(wzz4700, wzz4701), Double(wzz4900, wzz4901)) → new_compare12(new_sr(wzz4700, wzz4900), new_sr(wzz4701, wzz4901))
new_esEs20(wzz401, wzz3001, ty_Double) → new_esEs14(wzz401, wzz3001)
new_esEs22(wzz4711, wzz4911, ty_Bool) → new_esEs12(wzz4711, wzz4911)
new_esEs10(wzz400, wzz3000, app(ty_Ratio, hg)) → new_esEs16(wzz400, wzz3000, hg)
new_primCompAux00(wzz148, LT) → LT
new_lt11(wzz470, wzz490, bbe) → new_esEs8(new_compare14(wzz470, wzz490, bbe), LT)
new_compare27(wzz470, wzz490, False, bbf) → new_compare114(wzz470, wzz490, new_ltEs16(wzz470, wzz490, bbf), bbf)
new_esEs24(wzz402, wzz3002, ty_Ordering) → new_esEs8(wzz402, wzz3002)
new_esEs27(wzz4710, wzz4910, app(app(app(ty_@3, dcf), dcg), dch)) → new_esEs5(wzz4710, wzz4910, dcf, dcg, dch)
new_esEs10(wzz400, wzz3000, app(ty_[], hh)) → new_esEs9(wzz400, wzz3000, hh)
new_compare115(wzz470, wzz490, True, bbb, bbc, bbd) → LT
new_ltEs17(wzz471, wzz491) → new_fsEs(new_compare8(wzz471, wzz491))
new_ltEs18(wzz471, wzz491, ty_Double) → new_ltEs11(wzz471, wzz491)
new_esEs7(Nothing, Nothing, bcf) → True
new_esEs8(EQ, LT) → False
new_esEs8(LT, EQ) → False
new_primEqInt(Pos(Succ(wzz4000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(wzz30000))) → False
new_compare9(wzz4700, wzz4900, ty_Ordering) → new_compare11(wzz4700, wzz4900)
new_ltEs8(wzz471, wzz491) → new_fsEs(new_compare12(wzz471, wzz491))
new_esEs25(wzz401, wzz3001, ty_Float) → new_esEs17(wzz401, wzz3001)
new_primCmpNat0(Zero, Zero) → EQ
new_compare6(wzz470, wzz490, bf, bg) → new_compare23(wzz470, wzz490, new_esEs6(wzz470, wzz490, bf, bg), bf, bg)
new_lt6(wzz470, wzz490, ty_Integer) → new_lt10(wzz470, wzz490)
new_primCmpNat0(Succ(wzz47000), Zero) → GT
new_esEs4(Right(wzz400), Right(wzz3000), bcd, app(app(app(ty_@3, caf), cag), cah)) → new_esEs5(wzz400, wzz3000, caf, cag, cah)
new_esEs31(wzz40, wzz300, app(ty_Ratio, bcg)) → new_esEs16(wzz40, wzz300, bcg)
new_esEs21(wzz400, wzz3000, ty_@0) → new_esEs13(wzz400, wzz3000)
new_esEs19(wzz470, wzz490, ty_@0) → new_esEs13(wzz470, wzz490)
new_primCmpInt(Neg(Zero), Pos(Succ(wzz4900))) → LT
new_sr0(Integer(wzz49000), Integer(wzz47010)) → Integer(new_primMulInt(wzz49000, wzz47010))
new_primPlusNat1(Succ(wzz39200), Succ(wzz10100)) → Succ(Succ(new_primPlusNat1(wzz39200, wzz10100)))
new_esEs7(Just(wzz400), Just(wzz3000), ty_Integer) → new_esEs15(wzz400, wzz3000)
new_primEqInt(Pos(Succ(wzz4000)), Neg(wzz3000)) → False
new_primEqInt(Neg(Succ(wzz4000)), Pos(wzz3000)) → False
new_esEs7(Nothing, Just(wzz3000), bcf) → False
new_esEs7(Just(wzz400), Nothing, bcf) → False
new_compare14(:%(wzz4700, wzz4701), :%(wzz4900, wzz4901), ty_Integer) → new_compare13(new_sr0(wzz4700, wzz4901), new_sr0(wzz4900, wzz4701))
new_esEs25(wzz401, wzz3001, ty_@0) → new_esEs13(wzz401, wzz3001)
new_ltEs16(Just(wzz4710), Just(wzz4910), ty_Ordering) → new_ltEs7(wzz4710, wzz4910)
new_ltEs18(wzz471, wzz491, app(ty_Maybe, bba)) → new_ltEs16(wzz471, wzz491, bba)
new_ltEs19(wzz4712, wzz4912, ty_@0) → new_ltEs15(wzz4712, wzz4912)
new_esEs26(wzz400, wzz3000, app(ty_Ratio, dcb)) → new_esEs16(wzz400, wzz3000, dcb)
new_esEs22(wzz4711, wzz4911, app(app(ty_@2, cdf), cdg)) → new_esEs6(wzz4711, wzz4911, cdf, cdg)
new_compare12(wzz47, wzz49) → new_primCmpInt(wzz47, wzz49)
new_esEs9([], [], gf) → True
new_compare9(wzz4700, wzz4900, ty_@0) → new_compare18(wzz4700, wzz4900)
new_ltEs7(EQ, GT) → True
new_primEqInt(Pos(Zero), Neg(Succ(wzz30000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(wzz30000))) → False
new_ltEs16(Just(wzz4710), Just(wzz4910), ty_Bool) → new_ltEs14(wzz4710, wzz4910)
new_esEs13(@0, @0) → True
new_esEs21(wzz400, wzz3000, ty_Integer) → new_esEs15(wzz400, wzz3000)
new_esEs31(wzz40, wzz300, ty_Integer) → new_esEs15(wzz40, wzz300)
new_primCompAux00(wzz148, EQ) → wzz148
new_esEs21(wzz400, wzz3000, ty_Char) → new_esEs11(wzz400, wzz3000)
new_esEs4(Right(wzz400), Right(wzz3000), bcd, ty_Double) → new_esEs14(wzz400, wzz3000)
new_compare24(wzz470, wzz490, True) → EQ
new_ltEs5(Right(wzz4710), Right(wzz4910), fb, ty_Char) → new_ltEs17(wzz4710, wzz4910)
new_lt6(wzz470, wzz490, app(ty_[], cc)) → new_lt16(wzz470, wzz490, cc)
new_esEs23(wzz4710, wzz4910, ty_Int) → new_esEs18(wzz4710, wzz4910)
new_esEs4(Left(wzz400), Left(wzz3000), ty_Integer, bce) → new_esEs15(wzz400, wzz3000)
new_esEs8(GT, EQ) → False
new_esEs8(EQ, GT) → False
new_ltEs18(wzz471, wzz491, ty_@0) → new_ltEs15(wzz471, wzz491)
new_esEs26(wzz400, wzz3000, ty_Char) → new_esEs11(wzz400, wzz3000)
new_esEs27(wzz4710, wzz4910, app(ty_Ratio, dda)) → new_esEs16(wzz4710, wzz4910, dda)
new_ltEs16(Just(wzz4710), Nothing, bba) → False
new_lt19(wzz4710, wzz4910, app(ty_Maybe, ccg)) → new_lt18(wzz4710, wzz4910, ccg)
new_ltEs19(wzz4712, wzz4912, app(app(ty_@2, ceh), cfa)) → new_ltEs13(wzz4712, wzz4912, ceh, cfa)
new_ltEs5(Left(wzz4710), Left(wzz4910), ty_Bool, ea) → new_ltEs14(wzz4710, wzz4910)
new_compare113(wzz470, wzz490, True) → LT
new_ltEs20(wzz4711, wzz4911, app(app(app(ty_@3, ddh), dea), deb)) → new_ltEs6(wzz4711, wzz4911, ddh, dea, deb)
new_not(False) → True
new_primCompAux0(wzz4700, wzz4900, wzz140, cc) → new_primCompAux00(wzz140, new_compare9(wzz4700, wzz4900, cc))
new_lt20(wzz4711, wzz4911, ty_Bool) → new_lt15(wzz4711, wzz4911)
new_esEs32(wzz35, wzz37, app(ty_[], bgg)) → new_esEs9(wzz35, wzz37, bgg)
new_ltEs20(wzz4711, wzz4911, app(ty_Ratio, dec)) → new_ltEs10(wzz4711, wzz4911, dec)
new_ltEs5(Right(wzz4710), Right(wzz4910), fb, ty_Integer) → new_ltEs9(wzz4710, wzz4910)
new_compare7(wzz470, wzz490, ca, cb) → new_compare25(wzz470, wzz490, new_esEs4(wzz470, wzz490, ca, cb), ca, cb)
new_primPlusNat0(Zero, wzz300000) → Succ(wzz300000)
new_esEs26(wzz400, wzz3000, app(ty_[], dcc)) → new_esEs9(wzz400, wzz3000, dcc)
new_esEs23(wzz4710, wzz4910, app(app(ty_@2, ccd), cce)) → new_esEs6(wzz4710, wzz4910, ccd, cce)
new_compare17(wzz470, wzz490) → new_compare24(wzz470, wzz490, new_esEs12(wzz470, wzz490))
new_compare113(wzz470, wzz490, False) → GT
new_ltEs18(wzz471, wzz491, app(app(app(ty_@3, bac), bad), bae)) → new_ltEs6(wzz471, wzz491, bac, bad, bae)
new_esEs25(wzz401, wzz3001, ty_Integer) → new_esEs15(wzz401, wzz3001)
new_esEs4(Left(wzz400), Left(wzz3000), ty_Double, bce) → new_esEs14(wzz400, wzz3000)
new_esEs32(wzz35, wzz37, ty_Ordering) → new_esEs8(wzz35, wzz37)
new_esEs25(wzz401, wzz3001, app(ty_Ratio, dah)) → new_esEs16(wzz401, wzz3001, dah)
new_esEs26(wzz400, wzz3000, ty_Int) → new_esEs18(wzz400, wzz3000)
new_esEs24(wzz402, wzz3002, ty_Float) → new_esEs17(wzz402, wzz3002)
new_ltEs19(wzz4712, wzz4912, app(app(app(ty_@3, ced), cee), cef)) → new_ltEs6(wzz4712, wzz4912, ced, cee, cef)
new_ltEs5(Left(wzz4710), Left(wzz4910), app(ty_Maybe, fa), ea) → new_ltEs16(wzz4710, wzz4910, fa)
new_lt20(wzz4711, wzz4911, app(app(app(ty_@3, cdb), cdc), cdd)) → new_lt7(wzz4711, wzz4911, cdb, cdc, cdd)
new_esEs19(wzz470, wzz490, ty_Int) → new_esEs18(wzz470, wzz490)
new_esEs4(Right(wzz400), Right(wzz3000), bcd, app(app(ty_@2, cad), cae)) → new_esEs6(wzz400, wzz3000, cad, cae)
new_esEs4(Right(wzz400), Right(wzz3000), bcd, ty_Int) → new_esEs18(wzz400, wzz3000)
new_esEs7(Just(wzz400), Just(wzz3000), ty_Bool) → new_esEs12(wzz400, wzz3000)
new_esEs20(wzz401, wzz3001, ty_Int) → new_esEs18(wzz401, wzz3001)
new_lt6(wzz470, wzz490, ty_@0) → new_lt17(wzz470, wzz490)
new_esEs10(wzz400, wzz3000, ty_Int) → new_esEs18(wzz400, wzz3000)
new_esEs20(wzz401, wzz3001, app(app(app(ty_@3, bdb), bdc), bdd)) → new_esEs5(wzz401, wzz3001, bdb, bdc, bdd)
new_primCmpInt(Pos(Succ(wzz4700)), Neg(wzz490)) → GT
new_esEs22(wzz4711, wzz4911, ty_Char) → new_esEs11(wzz4711, wzz4911)
new_compare10(wzz470, wzz490, bbb, bbc, bbd) → new_compare28(wzz470, wzz490, new_esEs5(wzz470, wzz490, bbb, bbc, bbd), bbb, bbc, bbd)
new_esEs4(Left(wzz400), Left(wzz3000), ty_Int, bce) → new_esEs18(wzz400, wzz3000)
new_lt21(wzz4710, wzz4910, app(app(ty_@2, ddb), ddc)) → new_lt14(wzz4710, wzz4910, ddb, ddc)
new_esEs21(wzz400, wzz3000, app(app(app(ty_@3, bed), bee), bef)) → new_esEs5(wzz400, wzz3000, bed, bee, bef)
new_esEs21(wzz400, wzz3000, app(ty_Maybe, bfa)) → new_esEs7(wzz400, wzz3000, bfa)
new_compare115(wzz470, wzz490, False, bbb, bbc, bbd) → GT
new_lt20(wzz4711, wzz4911, ty_Integer) → new_lt10(wzz4711, wzz4911)
new_primMulInt(Pos(wzz4000), Pos(wzz30000)) → Pos(new_primMulNat0(wzz4000, wzz30000))
new_lt19(wzz4710, wzz4910, app(app(ty_@2, ccd), cce)) → new_lt14(wzz4710, wzz4910, ccd, cce)
new_esEs23(wzz4710, wzz4910, app(app(ty_Either, cbf), cbg)) → new_esEs4(wzz4710, wzz4910, cbf, cbg)
new_esEs20(wzz401, wzz3001, ty_Char) → new_esEs11(wzz401, wzz3001)
new_esEs4(Left(wzz400), Left(wzz3000), app(ty_Maybe, caa), bce) → new_esEs7(wzz400, wzz3000, caa)
new_primMulInt(Neg(wzz4000), Neg(wzz30000)) → Pos(new_primMulNat0(wzz4000, wzz30000))
new_esEs27(wzz4710, wzz4910, app(app(ty_@2, ddb), ddc)) → new_esEs6(wzz4710, wzz4910, ddb, ddc)
new_esEs10(wzz400, wzz3000, ty_Integer) → new_esEs15(wzz400, wzz3000)
new_lt6(wzz470, wzz490, app(ty_Maybe, bbf)) → new_lt18(wzz470, wzz490, bbf)
new_esEs20(wzz401, wzz3001, ty_Integer) → new_esEs15(wzz401, wzz3001)
new_ltEs19(wzz4712, wzz4912, app(app(ty_Either, ceb), cec)) → new_ltEs5(wzz4712, wzz4912, ceb, cec)
new_primEqNat0(Zero, Succ(wzz30000)) → False
new_primEqNat0(Succ(wzz4000), Zero) → False
new_esEs22(wzz4711, wzz4911, ty_Float) → new_esEs17(wzz4711, wzz4911)
new_esEs4(Right(wzz400), Right(wzz3000), bcd, app(ty_[], cbe)) → new_esEs9(wzz400, wzz3000, cbe)
new_compare25(wzz470, wzz490, True, ca, cb) → EQ
new_lt20(wzz4711, wzz4911, ty_@0) → new_lt17(wzz4711, wzz4911)
new_ltEs14(True, True) → True
new_esEs22(wzz4711, wzz4911, ty_Double) → new_esEs14(wzz4711, wzz4911)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs24(wzz402, wzz3002, app(app(ty_Either, chc), chd)) → new_esEs4(wzz402, wzz3002, chc, chd)
new_ltEs16(Just(wzz4710), Just(wzz4910), app(app(app(ty_@3, cff), cfg), cfh)) → new_ltEs6(wzz4710, wzz4910, cff, cfg, cfh)
new_esEs27(wzz4710, wzz4910, app(app(ty_Either, dcd), dce)) → new_esEs4(wzz4710, wzz4910, dcd, dce)
new_ltEs11(wzz471, wzz491) → new_fsEs(new_compare15(wzz471, wzz491))
new_compare4(:(wzz4700, wzz4701), [], cc) → GT
new_compare28(wzz470, wzz490, True, bbb, bbc, bbd) → EQ
new_primCmpInt(Neg(Zero), Neg(Succ(wzz4900))) → new_primCmpNat2(wzz4900, Zero)
new_esEs19(wzz470, wzz490, app(ty_[], cc)) → new_esEs9(wzz470, wzz490, cc)
new_lt14(wzz470, wzz490, bf, bg) → new_esEs8(new_compare6(wzz470, wzz490, bf, bg), LT)
new_compare23(wzz47, wzz49, True, baa, bab) → EQ
new_primCmpInt(Pos(Zero), Neg(Succ(wzz4900))) → GT
new_lt9(wzz470, wzz490) → new_esEs8(new_compare12(wzz470, wzz490), LT)
new_compare25(wzz470, wzz490, False, ca, cb) → new_compare112(wzz470, wzz490, new_ltEs5(wzz470, wzz490, ca, cb), ca, cb)
new_compare4([], :(wzz4900, wzz4901), cc) → LT
new_ltEs18(wzz471, wzz491, ty_Float) → new_ltEs12(wzz471, wzz491)
new_ltEs18(wzz471, wzz491, ty_Integer) → new_ltEs9(wzz471, wzz491)
new_compare114(wzz470, wzz490, True, bbf) → LT
new_esEs19(wzz470, wzz490, ty_Double) → new_esEs14(wzz470, wzz490)
new_ltEs16(Just(wzz4710), Just(wzz4910), ty_Float) → new_ltEs12(wzz4710, wzz4910)
new_esEs27(wzz4710, wzz4910, app(ty_[], ddd)) → new_esEs9(wzz4710, wzz4910, ddd)
new_esEs25(wzz401, wzz3001, app(ty_[], dba)) → new_esEs9(wzz401, wzz3001, dba)
new_esEs11(Char(wzz400), Char(wzz3000)) → new_primEqNat0(wzz400, wzz3000)
new_compare9(wzz4700, wzz4900, app(app(app(ty_@3, cf), cg), da)) → new_compare10(wzz4700, wzz4900, cf, cg, da)
new_lt19(wzz4710, wzz4910, app(app(ty_Either, cbf), cbg)) → new_lt4(wzz4710, wzz4910, cbf, cbg)
new_esEs25(wzz401, wzz3001, app(ty_Maybe, dag)) → new_esEs7(wzz401, wzz3001, dag)
new_esEs7(Just(wzz400), Just(wzz3000), app(app(app(ty_@3, dfb), dfc), dfd)) → new_esEs5(wzz400, wzz3000, dfb, dfc, dfd)
new_esEs23(wzz4710, wzz4910, app(ty_Ratio, ccc)) → new_esEs16(wzz4710, wzz4910, ccc)
new_esEs22(wzz4711, wzz4911, app(ty_Ratio, cde)) → new_esEs16(wzz4711, wzz4911, cde)
new_lt20(wzz4711, wzz4911, app(ty_[], cdh)) → new_lt16(wzz4711, wzz4911, cdh)
new_ltEs5(Right(wzz4710), Right(wzz4910), fb, app(app(ty_@2, gb), gc)) → new_ltEs13(wzz4710, wzz4910, gb, gc)
new_ltEs5(Left(wzz4710), Left(wzz4910), ty_Integer, ea) → new_ltEs9(wzz4710, wzz4910)
new_esEs19(wzz470, wzz490, app(ty_Ratio, bbe)) → new_esEs16(wzz470, wzz490, bbe)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs25(wzz401, wzz3001, ty_Bool) → new_esEs12(wzz401, wzz3001)
new_ltEs16(Just(wzz4710), Just(wzz4910), app(app(ty_@2, cgb), cgc)) → new_ltEs13(wzz4710, wzz4910, cgb, cgc)
new_esEs24(wzz402, wzz3002, ty_Char) → new_esEs11(wzz402, wzz3002)
new_compare11(wzz470, wzz490) → new_compare26(wzz470, wzz490, new_esEs8(wzz470, wzz490))
new_asAs(False, wzz64) → False
new_primMulInt(Pos(wzz4000), Neg(wzz30000)) → Neg(new_primMulNat0(wzz4000, wzz30000))
new_primMulInt(Neg(wzz4000), Pos(wzz30000)) → Neg(new_primMulNat0(wzz4000, wzz30000))
new_esEs4(Right(wzz400), Right(wzz3000), bcd, ty_Bool) → new_esEs12(wzz400, wzz3000)
new_primMulNat0(Succ(wzz40000), Zero) → Zero
new_primMulNat0(Zero, Succ(wzz300000)) → Zero
new_ltEs5(Left(wzz4710), Left(wzz4910), ty_Char, ea) → new_ltEs17(wzz4710, wzz4910)
new_esEs21(wzz400, wzz3000, ty_Ordering) → new_esEs8(wzz400, wzz3000)
new_esEs32(wzz35, wzz37, app(ty_Ratio, bgf)) → new_esEs16(wzz35, wzz37, bgf)
new_compare4(:(wzz4700, wzz4701), :(wzz4900, wzz4901), cc) → new_primCompAux0(wzz4700, wzz4900, new_compare4(wzz4701, wzz4901, cc), cc)
new_primCmpNat2(wzz4700, Zero) → GT
new_compare9(wzz4700, wzz4900, ty_Integer) → new_compare13(wzz4700, wzz4900)
new_ltEs20(wzz4711, wzz4911, ty_Double) → new_ltEs11(wzz4711, wzz4911)
new_ltEs18(wzz471, wzz491, app(ty_[], bh)) → new_ltEs4(wzz471, wzz491, bh)
new_compare16(Float(wzz4700, wzz4701), Float(wzz4900, wzz4901)) → new_compare12(new_sr(wzz4700, wzz4900), new_sr(wzz4701, wzz4901))
new_esEs14(Double(wzz400, wzz401), Double(wzz3000, wzz3001)) → new_esEs18(new_sr(wzz400, wzz3000), new_sr(wzz401, wzz3001))
new_esEs26(wzz400, wzz3000, app(ty_Maybe, dca)) → new_esEs7(wzz400, wzz3000, dca)
new_esEs31(wzz40, wzz300, ty_@0) → new_esEs13(wzz40, wzz300)
new_lt15(wzz470, wzz490) → new_esEs8(new_compare17(wzz470, wzz490), LT)
new_esEs9(:(wzz400, wzz401), :(wzz3000, wzz3001), gf) → new_asAs(new_esEs10(wzz400, wzz3000, gf), new_esEs9(wzz401, wzz3001, gf))
new_lt21(wzz4710, wzz4910, ty_Int) → new_lt9(wzz4710, wzz4910)
new_ltEs16(Just(wzz4710), Just(wzz4910), ty_Char) → new_ltEs17(wzz4710, wzz4910)
new_esEs27(wzz4710, wzz4910, ty_@0) → new_esEs13(wzz4710, wzz4910)
new_ltEs5(Right(wzz4710), Right(wzz4910), fb, app(ty_Ratio, ga)) → new_ltEs10(wzz4710, wzz4910, ga)
new_lt12(wzz470, wzz490) → new_esEs8(new_compare15(wzz470, wzz490), LT)
new_ltEs18(wzz471, wzz491, ty_Bool) → new_ltEs14(wzz471, wzz491)
new_esEs28(wzz401, wzz3001, ty_Integer) → new_esEs15(wzz401, wzz3001)
new_esEs4(Right(wzz400), Right(wzz3000), bcd, app(ty_Maybe, cbc)) → new_esEs7(wzz400, wzz3000, cbc)
new_lt20(wzz4711, wzz4911, ty_Float) → new_lt13(wzz4711, wzz4911)
new_compare111(wzz114, wzz115, wzz116, wzz117, False, bgh, bha) → GT
new_esEs24(wzz402, wzz3002, ty_Bool) → new_esEs12(wzz402, wzz3002)
new_ltEs18(wzz471, wzz491, app(app(ty_@2, bag), bah)) → new_ltEs13(wzz471, wzz491, bag, bah)
new_esEs23(wzz4710, wzz4910, ty_Integer) → new_esEs15(wzz4710, wzz4910)
new_compare9(wzz4700, wzz4900, app(ty_[], de)) → new_compare4(wzz4700, wzz4900, de)
new_lt10(wzz470, wzz490) → new_esEs8(new_compare13(wzz470, wzz490), LT)
new_lt19(wzz4710, wzz4910, ty_Bool) → new_lt15(wzz4710, wzz4910)
new_esEs7(Just(wzz400), Just(wzz3000), app(app(ty_Either, dfe), dff)) → new_esEs4(wzz400, wzz3000, dfe, dff)
new_esEs21(wzz400, wzz3000, app(ty_Ratio, bfb)) → new_esEs16(wzz400, wzz3000, bfb)
new_lt4(wzz470, wzz490, ca, cb) → new_esEs8(new_compare7(wzz470, wzz490, ca, cb), LT)
new_esEs12(False, True) → False
new_esEs12(True, False) → False
new_esEs30(wzz34, wzz35, wzz36, wzz37, True, bfd, bfe) → new_esEs8(new_compare23(@2(wzz34, wzz35), @2(wzz36, wzz37), new_esEs32(wzz35, wzz37, bfe), bfd, bfe), LT)
new_lt21(wzz4710, wzz4910, app(ty_Ratio, dda)) → new_lt11(wzz4710, wzz4910, dda)
new_lt19(wzz4710, wzz4910, ty_@0) → new_lt17(wzz4710, wzz4910)
new_esEs27(wzz4710, wzz4910, ty_Bool) → new_esEs12(wzz4710, wzz4910)
new_lt20(wzz4711, wzz4911, ty_Char) → new_lt5(wzz4711, wzz4911)
new_lt19(wzz4710, wzz4910, app(app(app(ty_@3, cbh), cca), ccb)) → new_lt7(wzz4710, wzz4910, cbh, cca, ccb)
new_lt19(wzz4710, wzz4910, ty_Int) → new_lt9(wzz4710, wzz4910)
new_esEs7(Just(wzz400), Just(wzz3000), app(ty_Ratio, dfh)) → new_esEs16(wzz400, wzz3000, dfh)
new_esEs31(wzz40, wzz300, ty_Char) → new_esEs11(wzz40, wzz300)
new_esEs20(wzz401, wzz3001, ty_Float) → new_esEs17(wzz401, wzz3001)
new_esEs9([], :(wzz3000, wzz3001), gf) → False
new_esEs9(:(wzz400, wzz401), [], gf) → False
new_esEs10(wzz400, wzz3000, ty_Float) → new_esEs17(wzz400, wzz3000)
new_esEs32(wzz35, wzz37, app(app(ty_Either, bgc), bgd)) → new_esEs4(wzz35, wzz37, bgc, bgd)
new_ltEs14(True, False) → False
new_esEs32(wzz35, wzz37, ty_Char) → new_esEs11(wzz35, wzz37)
new_compare13(Integer(wzz4700), Integer(wzz4900)) → new_primCmpInt(wzz4700, wzz4900)
new_ltEs5(Left(wzz4710), Left(wzz4910), ty_Int, ea) → new_ltEs8(wzz4710, wzz4910)
new_esEs25(wzz401, wzz3001, app(app(app(ty_@3, dab), dac), dad)) → new_esEs5(wzz401, wzz3001, dab, dac, dad)
new_lt17(wzz470, wzz490) → new_esEs8(new_compare18(wzz470, wzz490), LT)
new_lt19(wzz4710, wzz4910, ty_Double) → new_lt12(wzz4710, wzz4910)
new_esEs17(Float(wzz400, wzz401), Float(wzz3000, wzz3001)) → new_esEs18(new_sr(wzz400, wzz3000), new_sr(wzz401, wzz3001))
new_compare27(wzz470, wzz490, True, bbf) → EQ
new_lt6(wzz470, wzz490, ty_Float) → new_lt13(wzz470, wzz490)
new_ltEs7(EQ, LT) → False
new_compare114(wzz470, wzz490, False, bbf) → GT
new_ltEs7(LT, LT) → True
new_compare19(wzz470, wzz490, bbf) → new_compare27(wzz470, wzz490, new_esEs7(wzz470, wzz490, bbf), bbf)
new_lt19(wzz4710, wzz4910, ty_Char) → new_lt5(wzz4710, wzz4910)
new_compare28(wzz470, wzz490, False, bbb, bbc, bbd) → new_compare115(wzz470, wzz490, new_ltEs6(wzz470, wzz490, bbb, bbc, bbd), bbb, bbc, bbd)
new_esEs10(wzz400, wzz3000, ty_Ordering) → new_esEs8(wzz400, wzz3000)
new_esEs22(wzz4711, wzz4911, ty_@0) → new_esEs13(wzz4711, wzz4911)
new_esEs22(wzz4711, wzz4911, ty_Integer) → new_esEs15(wzz4711, wzz4911)
new_lt16(wzz470, wzz490, cc) → new_esEs8(new_compare4(wzz470, wzz490, cc), LT)
new_ltEs5(Right(wzz4710), Right(wzz4910), fb, ty_@0) → new_ltEs15(wzz4710, wzz4910)
new_primPlusNat1(Zero, Zero) → Zero
new_esEs19(wzz470, wzz490, ty_Integer) → new_esEs15(wzz470, wzz490)
new_esEs31(wzz40, wzz300, ty_Double) → new_esEs14(wzz40, wzz300)
new_esEs26(wzz400, wzz3000, app(app(ty_Either, dbg), dbh)) → new_esEs4(wzz400, wzz3000, dbg, dbh)
new_asAs(True, wzz64) → wzz64
new_compare112(wzz470, wzz490, True, ca, cb) → LT
new_esEs19(wzz470, wzz490, app(app(ty_Either, ca), cb)) → new_esEs4(wzz470, wzz490, ca, cb)
new_ltEs7(LT, GT) → True
new_esEs26(wzz400, wzz3000, app(app(app(ty_@3, dbd), dbe), dbf)) → new_esEs5(wzz400, wzz3000, dbd, dbe, dbf)
new_primMulNat0(Succ(wzz40000), Succ(wzz300000)) → new_primPlusNat0(new_primMulNat0(wzz40000, Succ(wzz300000)), wzz300000)
new_esEs4(Right(wzz400), Left(wzz3000), bcd, bce) → False
new_esEs4(Left(wzz400), Right(wzz3000), bcd, bce) → False
new_esEs31(wzz40, wzz300, app(ty_Maybe, bcf)) → new_esEs7(wzz40, wzz300, bcf)
new_ltEs19(wzz4712, wzz4912, ty_Float) → new_ltEs12(wzz4712, wzz4912)
new_esEs31(wzz40, wzz300, ty_Bool) → new_esEs12(wzz40, wzz300)
new_esEs32(wzz35, wzz37, ty_Int) → new_esEs18(wzz35, wzz37)
new_fsEs(wzz126) → new_not(new_esEs8(wzz126, GT))
new_esEs26(wzz400, wzz3000, app(app(ty_@2, dbb), dbc)) → new_esEs6(wzz400, wzz3000, dbb, dbc)
new_esEs23(wzz4710, wzz4910, app(app(app(ty_@3, cbh), cca), ccb)) → new_esEs5(wzz4710, wzz4910, cbh, cca, ccb)
new_ltEs19(wzz4712, wzz4912, ty_Ordering) → new_ltEs7(wzz4712, wzz4912)
new_lt20(wzz4711, wzz4911, ty_Int) → new_lt9(wzz4711, wzz4911)
new_esEs19(wzz470, wzz490, ty_Ordering) → new_esEs8(wzz470, wzz490)
new_ltEs20(wzz4711, wzz4911, ty_Int) → new_ltEs8(wzz4711, wzz4911)
new_ltEs20(wzz4711, wzz4911, app(app(ty_@2, ded), dee)) → new_ltEs13(wzz4711, wzz4911, ded, dee)
new_lt6(wzz470, wzz490, ty_Char) → new_lt5(wzz470, wzz490)
new_esEs27(wzz4710, wzz4910, ty_Char) → new_esEs11(wzz4710, wzz4910)
new_esEs16(:%(wzz400, wzz401), :%(wzz3000, wzz3001), bcg) → new_asAs(new_esEs29(wzz400, wzz3000, bcg), new_esEs28(wzz401, wzz3001, bcg))
new_esEs21(wzz400, wzz3000, ty_Bool) → new_esEs12(wzz400, wzz3000)
new_esEs7(Just(wzz400), Just(wzz3000), ty_Char) → new_esEs11(wzz400, wzz3000)
new_primCompAux00(wzz148, GT) → GT
new_ltEs20(wzz4711, wzz4911, ty_Ordering) → new_ltEs7(wzz4711, wzz4911)
new_ltEs20(wzz4711, wzz4911, ty_Integer) → new_ltEs9(wzz4711, wzz4911)
new_compare116(wzz470, wzz490, True) → LT
new_compare8(Char(wzz4700), Char(wzz4900)) → new_primCmpNat0(wzz4700, wzz4900)
new_esEs31(wzz40, wzz300, app(app(ty_@2, bbg), bbh)) → new_esEs6(wzz40, wzz300, bbg, bbh)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_ltEs15(wzz471, wzz491) → new_fsEs(new_compare18(wzz471, wzz491))
new_esEs20(wzz401, wzz3001, ty_@0) → new_esEs13(wzz401, wzz3001)
new_esEs4(Right(wzz400), Right(wzz3000), bcd, ty_Float) → new_esEs17(wzz400, wzz3000)
new_ltEs20(wzz4711, wzz4911, app(app(ty_Either, ddf), ddg)) → new_ltEs5(wzz4711, wzz4911, ddf, ddg)
new_esEs21(wzz400, wzz3000, app(ty_[], bfc)) → new_esEs9(wzz400, wzz3000, bfc)
new_esEs20(wzz401, wzz3001, app(ty_[], bea)) → new_esEs9(wzz401, wzz3001, bea)
new_compare9(wzz4700, wzz4900, app(app(ty_Either, cd), ce)) → new_compare7(wzz4700, wzz4900, cd, ce)
new_primCmpInt(Pos(Succ(wzz4700)), Pos(wzz490)) → new_primCmpNat2(wzz4700, wzz490)
new_ltEs20(wzz4711, wzz4911, ty_Char) → new_ltEs17(wzz4711, wzz4911)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_esEs22(wzz4711, wzz4911, app(ty_Maybe, cea)) → new_esEs7(wzz4711, wzz4911, cea)
new_ltEs5(Left(wzz4710), Left(wzz4910), ty_Double, ea) → new_ltEs11(wzz4710, wzz4910)
new_esEs27(wzz4710, wzz4910, ty_Integer) → new_esEs15(wzz4710, wzz4910)
new_lt21(wzz4710, wzz4910, app(app(app(ty_@3, dcf), dcg), dch)) → new_lt7(wzz4710, wzz4910, dcf, dcg, dch)
new_primCmpInt(Neg(Succ(wzz4700)), Pos(wzz490)) → LT
new_esEs10(wzz400, wzz3000, ty_Double) → new_esEs14(wzz400, wzz3000)
new_esEs24(wzz402, wzz3002, ty_Double) → new_esEs14(wzz402, wzz3002)
new_not(True) → False

The set Q consists of the following terms:

new_compare15(Double(x0, x1), Double(x2, x3))
new_compare9(x0, x1, ty_Integer)
new_esEs13(@0, @0)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs31(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, ty_Bool)
new_lt21(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, ty_Int)
new_ltEs5(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs19(x0, x1, ty_Double)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs20(x0, x1, ty_@0)
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(x0, x1, ty_Char)
new_lt6(x0, x1, app(ty_Maybe, x2))
new_compare25(x0, x1, True, x2, x3)
new_ltEs12(x0, x1)
new_esEs31(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs22(x0, x1, ty_@0)
new_ltEs16(Just(x0), Just(x1), ty_Char)
new_esEs4(Right(x0), Right(x1), x2, ty_Bool)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs32(x0, x1, app(app(ty_@2, x2), x3))
new_esEs12(False, False)
new_compare115(x0, x1, False, x2, x3, x4)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_ltEs9(x0, x1)
new_lt19(x0, x1, ty_Ordering)
new_esEs31(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, ty_Ordering)
new_ltEs5(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs25(x0, x1, ty_Char)
new_ltEs16(Just(x0), Just(x1), ty_Ordering)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_pePe(True, x0)
new_ltEs5(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs5(Right(x0), Right(x1), x2, ty_Bool)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs16(Nothing, Just(x0), x1)
new_esEs4(Left(x0), Left(x1), ty_Integer, x2)
new_compare112(x0, x1, True, x2, x3)
new_ltEs7(EQ, EQ)
new_esEs26(x0, x1, ty_Char)
new_esEs25(x0, x1, ty_@0)
new_esEs24(x0, x1, ty_Bool)
new_ltEs17(x0, x1)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_compare4([], [], x0)
new_esEs32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs14(True, False)
new_ltEs20(x0, x1, ty_Bool)
new_ltEs14(False, True)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_Bool)
new_esEs8(GT, GT)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs18(x0, x1, ty_Double)
new_esEs7(Just(x0), Just(x1), ty_Int)
new_ltEs19(x0, x1, ty_Integer)
new_fsEs(x0)
new_ltEs7(EQ, LT)
new_ltEs7(LT, EQ)
new_lt20(x0, x1, ty_Integer)
new_sr0(Integer(x0), Integer(x1))
new_lt11(x0, x1, x2)
new_esEs4(Left(x0), Left(x1), ty_Double, x2)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_compare114(x0, x1, False, x2)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_compare25(x0, x1, False, x2, x3)
new_asAs(False, x0)
new_primCompAux00(x0, LT)
new_esEs8(LT, LT)
new_esEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_compare113(x0, x1, False)
new_compare113(x0, x1, True)
new_esEs19(x0, x1, ty_Integer)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs13(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs8(x0, x1)
new_primEqNat0(Succ(x0), Zero)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs32(x0, x1, app(ty_[], x2))
new_compare7(x0, x1, x2, x3)
new_esEs20(x0, x1, ty_Integer)
new_esEs10(x0, x1, ty_@0)
new_ltEs7(LT, LT)
new_esEs30(x0, x1, x2, x3, True, x4, x5)
new_ltEs5(Right(x0), Right(x1), x2, ty_Char)
new_esEs32(x0, x1, ty_Float)
new_esEs19(x0, x1, ty_Bool)
new_lt21(x0, x1, ty_Ordering)
new_ltEs5(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs31(x0, x1, ty_Int)
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_ltEs16(Just(x0), Nothing, x1)
new_compare16(Float(x0, x1), Float(x2, x3))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Double)
new_compare18(@0, @0)
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs5(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs19(x0, x1, ty_Bool)
new_esEs27(x0, x1, app(ty_[], x2))
new_lt6(x0, x1, ty_@0)
new_ltEs16(Just(x0), Just(x1), app(ty_Maybe, x2))
new_lt5(x0, x1)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_pePe(False, x0)
new_esEs19(x0, x1, ty_Char)
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_ltEs19(x0, x1, ty_Char)
new_esEs23(x0, x1, app(ty_[], x2))
new_primEqNat0(Zero, Zero)
new_esEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs5(Right(x0), Right(x1), x2, ty_@0)
new_esEs10(x0, x1, ty_Int)
new_esEs4(Left(x0), Left(x1), ty_Float, x2)
new_lt6(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs5(Left(x0), Left(x1), ty_Char, x2)
new_esEs19(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, ty_Float)
new_ltEs11(x0, x1)
new_esEs21(x0, x1, ty_Int)
new_compare28(x0, x1, False, x2, x3, x4)
new_esEs30(x0, x1, x2, x3, False, x4, x5)
new_ltEs15(x0, x1)
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt6(x0, x1, ty_Char)
new_lt6(x0, x1, app(ty_Ratio, x2))
new_ltEs5(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_lt9(x0, x1)
new_compare9(x0, x1, ty_Bool)
new_primMulNat0(Zero, Zero)
new_lt20(x0, x1, ty_Int)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_esEs10(x0, x1, app(ty_[], x2))
new_esEs19(x0, x1, ty_Ordering)
new_ltEs5(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs5(Left(x0), Left(x1), ty_Ordering, x2)
new_sr(x0, x1)
new_esEs24(x0, x1, app(ty_[], x2))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Right(x0), Left(x1), x2, x3)
new_esEs4(Left(x0), Right(x1), x2, x3)
new_primEqNat0(Zero, Succ(x0))
new_compare8(Char(x0), Char(x1))
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_lt19(x0, x1, ty_Int)
new_primCmpNat2(x0, Zero)
new_esEs24(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_Double)
new_primMulNat0(Succ(x0), Zero)
new_compare9(x0, x1, app(ty_Maybe, x2))
new_compare9(x0, x1, app(app(ty_Either, x2), x3))
new_lt21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt6(x0, x1, ty_Double)
new_compare26(x0, x1, True)
new_lt19(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, ty_Char)
new_ltEs5(Right(x0), Right(x1), x2, ty_Ordering)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_ltEs20(x0, x1, ty_Integer)
new_lt15(x0, x1)
new_ltEs20(x0, x1, ty_@0)
new_compare9(x0, x1, ty_Ordering)
new_ltEs5(Left(x0), Left(x1), ty_Bool, x2)
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs7(Just(x0), Just(x1), ty_Double)
new_compare14(:%(x0, x1), :%(x2, x3), ty_Int)
new_lt21(x0, x1, ty_@0)
new_lt20(x0, x1, app(ty_[], x2))
new_ltEs5(Left(x0), Left(x1), ty_Int, x2)
new_compare110(x0, x1, x2, x3, True, x4, x5, x6)
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_ltEs20(x0, x1, ty_Double)
new_esEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs32(x0, x1, ty_Int)
new_esEs21(x0, x1, ty_Float)
new_esEs32(x0, x1, app(ty_Maybe, x2))
new_esEs4(Left(x0), Left(x1), ty_Char, x2)
new_esEs27(x0, x1, ty_Float)
new_esEs27(x0, x1, ty_Int)
new_compare26(x0, x1, False)
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_compare4(:(x0, x1), [], x2)
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs24(x0, x1, ty_Char)
new_esEs28(x0, x1, ty_Int)
new_primPlusNat0(Zero, x0)
new_esEs28(x0, x1, ty_Integer)
new_lt20(x0, x1, ty_Double)
new_lt6(x0, x1, app(ty_[], x2))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs23(x0, x1, ty_Ordering)
new_lt10(x0, x1)
new_compare24(x0, x1, True)
new_esEs23(x0, x1, ty_Double)
new_lt21(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Double)
new_esEs20(x0, x1, ty_Float)
new_lt7(x0, x1, x2, x3, x4)
new_compare23(x0, x1, True, x2, x3)
new_primPlusNat1(Zero, Zero)
new_compare110(x0, x1, x2, x3, False, x4, x5, x6)
new_ltEs16(Nothing, Nothing, x0)
new_lt19(x0, x1, ty_@0)
new_lt14(x0, x1, x2, x3)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_ltEs16(Just(x0), Just(x1), app(ty_[], x2))
new_esEs10(x0, x1, app(ty_Ratio, x2))
new_esEs9([], [], x0)
new_esEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_compare28(x0, x1, True, x2, x3, x4)
new_compare112(x0, x1, False, x2, x3)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_ltEs18(x0, x1, ty_Char)
new_esEs9([], :(x0, x1), x2)
new_esEs4(Right(x0), Right(x1), x2, ty_Char)
new_esEs25(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Int)
new_esEs32(x0, x1, ty_@0)
new_esEs21(x0, x1, ty_Char)
new_esEs20(x0, x1, ty_Int)
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs9(:(x0, x1), :(x2, x3), x4)
new_ltEs16(Just(x0), Just(x1), app(ty_Ratio, x2))
new_primPlusNat0(Succ(x0), x1)
new_compare114(x0, x1, True, x2)
new_ltEs20(x0, x1, ty_Char)
new_esEs27(x0, x1, ty_Double)
new_esEs31(x0, x1, ty_Integer)
new_lt4(x0, x1, x2, x3)
new_esEs32(x0, x1, app(ty_Ratio, x2))
new_ltEs18(x0, x1, ty_Bool)
new_primCmpNat0(Zero, Succ(x0))
new_esEs12(True, True)
new_esEs32(x0, x1, ty_Integer)
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs31(x0, x1, ty_Double)
new_esEs31(x0, x1, ty_Ordering)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_Int)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_ltEs10(x0, x1, x2)
new_compare9(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Just(x0), Nothing, x1)
new_ltEs18(x0, x1, ty_Int)
new_esEs10(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Bool)
new_ltEs16(Just(x0), Just(x1), ty_Double)
new_esEs27(x0, x1, ty_Char)
new_lt20(x0, x1, ty_Bool)
new_esEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_compare23(@2(x0, x1), @2(x2, x3), False, x4, x5)
new_esEs7(Nothing, Nothing, x0)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_Bool)
new_esEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_primCompAux00(x0, GT)
new_compare111(x0, x1, x2, x3, False, x4, x5)
new_esEs4(Left(x0), Left(x1), ty_Int, x2)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_esEs19(x0, x1, ty_Float)
new_esEs26(x0, x1, ty_Ordering)
new_esEs26(x0, x1, ty_Integer)
new_esEs32(x0, x1, ty_Bool)
new_esEs10(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs5(Right(x0), Right(x1), x2, ty_Int)
new_primEqInt(Neg(Zero), Neg(Zero))
new_compare9(x0, x1, ty_Float)
new_primCmpNat0(Succ(x0), Succ(x1))
new_ltEs5(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs16(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, ty_Integer)
new_esEs31(x0, x1, ty_@0)
new_esEs9(:(x0, x1), [], x2)
new_lt12(x0, x1)
new_ltEs5(Right(x0), Right(x1), x2, ty_Double)
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_asAs(True, x0)
new_esEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_compare111(x0, x1, x2, x3, True, x4, x5)
new_ltEs20(x0, x1, ty_Float)
new_esEs27(x0, x1, ty_Ordering)
new_esEs24(x0, x1, ty_@0)
new_compare9(x0, x1, ty_Char)
new_lt19(x0, x1, ty_Float)
new_lt20(x0, x1, ty_Char)
new_esEs27(x0, x1, ty_@0)
new_primPlusNat1(Succ(x0), Zero)
new_ltEs16(Just(x0), Just(x1), ty_Int)
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_compare12(x0, x1)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, ty_Bool)
new_esEs18(x0, x1)
new_ltEs19(x0, x1, ty_@0)
new_esEs7(Nothing, Just(x0), x1)
new_esEs21(x0, x1, ty_Integer)
new_ltEs5(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs5(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs31(x0, x1, ty_Float)
new_esEs19(x0, x1, ty_Int)
new_esEs14(Double(x0, x1), Double(x2, x3))
new_esEs26(x0, x1, ty_Float)
new_lt21(x0, x1, ty_Char)
new_lt20(x0, x1, ty_@0)
new_ltEs5(Right(x0), Right(x1), x2, ty_Float)
new_ltEs16(Just(x0), Just(x1), ty_Float)
new_compare14(:%(x0, x1), :%(x2, x3), ty_Integer)
new_compare19(x0, x1, x2)
new_ltEs5(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_compare9(x0, x1, app(ty_Ratio, x2))
new_primCompAux0(x0, x1, x2, x3)
new_ltEs20(x0, x1, ty_Int)
new_compare9(x0, x1, ty_Double)
new_ltEs16(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare116(x0, x1, True)
new_esEs10(x0, x1, app(app(ty_Either, x2), x3))
new_lt6(x0, x1, ty_Bool)
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_primPlusNat1(Zero, Succ(x0))
new_ltEs18(x0, x1, ty_Float)
new_compare17(x0, x1)
new_primCmpNat0(Zero, Zero)
new_esEs4(Right(x0), Right(x1), x2, ty_@0)
new_esEs24(x0, x1, ty_Float)
new_ltEs5(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_compare115(x0, x1, True, x2, x3, x4)
new_esEs25(x0, x1, ty_Float)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_compare4([], :(x0, x1), x2)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_primMulInt(Neg(x0), Neg(x1))
new_esEs4(Left(x0), Left(x1), ty_Bool, x2)
new_esEs24(x0, x1, ty_Ordering)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs10(x0, x1, ty_Double)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_compare10(x0, x1, x2, x3, x4)
new_esEs22(x0, x1, ty_Char)
new_compare4(:(x0, x1), :(x2, x3), x4)
new_compare116(x0, x1, False)
new_lt19(x0, x1, ty_Bool)
new_esEs29(x0, x1, ty_Int)
new_esEs31(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Ordering)
new_ltEs5(Left(x0), Left(x1), ty_Float, x2)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs10(x0, x1, app(app(ty_@2, x2), x3))
new_compare27(x0, x1, False, x2)
new_esEs29(x0, x1, ty_Integer)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(x0, x1, ty_Integer)
new_esEs12(False, True)
new_esEs12(True, False)
new_esEs32(x0, x1, ty_Ordering)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs16(:%(x0, x1), :%(x2, x3), x4)
new_lt21(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs7(LT, GT)
new_ltEs18(x0, x1, ty_Ordering)
new_ltEs7(GT, LT)
new_ltEs14(True, True)
new_ltEs14(False, False)
new_esEs19(x0, x1, ty_Double)
new_compare9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt21(x0, x1, app(ty_Maybe, x2))
new_lt13(x0, x1)
new_esEs7(Just(x0), Just(x1), ty_Float)
new_primPlusNat1(Succ(x0), Succ(x1))
new_compare9(x0, x1, ty_@0)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, ty_@0)
new_esEs17(Float(x0, x1), Float(x2, x3))
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_primEqNat0(Succ(x0), Succ(x1))
new_compare9(x0, x1, ty_Int)
new_primCmpNat0(Succ(x0), Zero)
new_lt6(x0, x1, ty_Integer)
new_not(True)
new_esEs31(x0, x1, ty_Bool)
new_ltEs4(x0, x1, x2)
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, app(ty_[], x2))
new_compare24(x0, x1, False)
new_esEs31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt6(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs31(x0, x1, app(app(ty_Either, x2), x3))
new_lt18(x0, x1, x2)
new_esEs31(x0, x1, app(ty_[], x2))
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs22(x0, x1, ty_Double)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_ltEs18(x0, x1, app(ty_[], x2))
new_ltEs16(Just(x0), Just(x1), ty_Bool)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_not(False)
new_lt21(x0, x1, ty_Float)
new_esEs19(x0, x1, ty_@0)
new_ltEs5(Left(x0), Left(x1), ty_Double, x2)
new_esEs24(x0, x1, ty_Int)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_lt17(x0, x1)
new_lt21(x0, x1, ty_Integer)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs11(Char(x0), Char(x1))
new_lt6(x0, x1, ty_Int)
new_lt16(x0, x1, x2)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1, ty_Double)
new_lt6(x0, x1, ty_Ordering)
new_esEs32(x0, x1, ty_Double)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_lt21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Just(x0), Just(x1), ty_@0)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Just(x0), Just(x1), ty_Char)
new_lt21(x0, x1, ty_Double)
new_ltEs5(Left(x0), Right(x1), x2, x3)
new_ltEs5(Right(x0), Left(x1), x2, x3)
new_ltEs20(x0, x1, ty_Ordering)
new_lt21(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_@0)
new_ltEs16(Just(x0), Just(x1), ty_@0)
new_esEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs21(x0, x1, ty_@0)
new_lt20(x0, x1, ty_Ordering)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare11(x0, x1)
new_primCmpNat1(Succ(x0), x1)
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(x0, x1, ty_Float)
new_lt21(x0, x1, ty_Bool)
new_primMulNat0(Zero, Succ(x0))
new_ltEs16(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_compare9(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, ty_@0)
new_esEs10(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_Bool)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs32(x0, x1, ty_Char)
new_esEs20(x0, x1, ty_Double)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_Bool)
new_lt8(x0, x1)
new_ltEs5(Left(x0), Left(x1), ty_@0, x2)
new_lt20(x0, x1, ty_Float)
new_compare6(x0, x1, x2, x3)
new_compare27(x0, x1, True, x2)
new_ltEs19(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Ordering)
new_esEs4(Right(x0), Right(x1), x2, ty_Int)
new_lt19(x0, x1, ty_Integer)
new_primCompAux00(x0, EQ)
new_esEs22(x0, x1, ty_Ordering)
new_esEs23(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_Char)
new_esEs4(Right(x0), Right(x1), x2, ty_Double)
new_esEs4(Right(x0), Right(x1), x2, ty_Float)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_compare13(Integer(x0), Integer(x1))
new_esEs4(Left(x0), Left(x1), ty_@0, x2)
new_esEs26(x0, x1, ty_Int)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs20(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Pos(Zero), Pos(Zero))
new_primCmpNat2(x0, Succ(x1))
new_esEs15(Integer(x0), Integer(x1))
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1, ty_Char)
new_esEs20(x0, x1, ty_Ordering)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_ltEs16(Just(x0), Just(x1), ty_Integer)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt6(x0, x1, ty_Float)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs5(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs26(x0, x1, ty_Double)
new_esEs22(x0, x1, ty_Float)
new_esEs25(x0, x1, ty_Int)
new_ltEs5(Left(x0), Left(x1), ty_Integer, x2)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs7(GT, EQ)
new_ltEs7(EQ, GT)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs10(x0, x1, ty_Ordering)
new_ltEs7(GT, GT)
new_lt6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs32(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_primCmpNat1(Zero, x0)
new_esEs22(x0, x1, ty_Integer)

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

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