YES 11.759 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
  ((listToFM :: (Ord a, Ord c) => [((c,a),b)]  ->  FiniteMap (c,a) b) :: (Ord a, Ord c) => [((c,a),b)]  ->  FiniteMap (c,a) b)

module FiniteMap where
  import qualified Maybe
import qualified Prelude

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


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

  addListToFM :: Ord b => FiniteMap b a  ->  [(b,a)]  ->  FiniteMap b a
addListToFM fm key_elt_pairs addListToFM_C (\old new ->new) fm key_elt_pairs

  addListToFM_C :: Ord b => (a  ->  a  ->  a ->  FiniteMap b a  ->  [(b,a)]  ->  FiniteMap b a
addListToFM_C combiner fm key_elt_pairs 
foldl add fm key_elt_pairs where 
add fmap (key,eltaddToFM_C combiner fmap key elt

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

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

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

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

  listToFM :: Ord a => [(a,b)]  ->  FiniteMap a b
listToFM addListToFM emptyFM

  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



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
addListToFM0 old new = new



↳ HASKELL
  ↳ LR
HASKELL
      ↳ CR

mainModule FiniteMap
  ((listToFM :: (Ord b, Ord c) => [((b,c),a)]  ->  FiniteMap (b,c) a) :: (Ord c, Ord b) => [((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

  addListToFM :: Ord b => FiniteMap b a  ->  [(b,a)]  ->  FiniteMap b a
addListToFM fm key_elt_pairs addListToFM_C addListToFM0 fm key_elt_pairs

  
addListToFM0 old new new

  addListToFM_C :: Ord b => (a  ->  a  ->  a ->  FiniteMap b a  ->  [(b,a)]  ->  FiniteMap b a
addListToFM_C combiner fm key_elt_pairs 
foldl add fm key_elt_pairs where 
add fmap (key,eltaddToFM_C combiner fmap 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 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 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

  listToFM :: Ord b => [(b,a)]  ->  FiniteMap b a
listToFM addListToFM emptyFM

  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 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



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

module FiniteMap where
  import qualified Maybe
import qualified Prelude

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


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

  addListToFM :: Ord b => FiniteMap b a  ->  [(b,a)]  ->  FiniteMap b a
addListToFM fm key_elt_pairs addListToFM_C addListToFM0 fm key_elt_pairs

  
addListToFM0 old new new

  addListToFM_C :: Ord b => (a  ->  a  ->  a ->  FiniteMap b a  ->  [(b,a)]  ->  FiniteMap b a
addListToFM_C combiner fm key_elt_pairs 
foldl add fm key_elt_pairs where 
add fmap (key,eltaddToFM_C combiner fmap 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 a b  ->  [(a,b)]
fmToList fm foldFM fmToList0 [] fm

  
fmToList0 key elt rest (key,elt: rest

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

  listToFM :: Ord b => [(b,a)]  ->  FiniteMap b a
listToFM addListToFM emptyFM

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

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude



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
  ((listToFM :: (Ord a, Ord b) => [((a,b),c)]  ->  FiniteMap (a,b) c) :: (Ord b, Ord a) => [((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 a b) where 
   
(==) fm_1 fm_2 sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2

  addListToFM :: Ord a => FiniteMap a b  ->  [(a,b)]  ->  FiniteMap a b
addListToFM fm key_elt_pairs addListToFM_C addListToFM0 fm key_elt_pairs

  
addListToFM0 old new new

  addListToFM_C :: Ord a => (b  ->  b  ->  b ->  FiniteMap a b  ->  [(a,b)]  ->  FiniteMap a b
addListToFM_C combiner fm key_elt_pairs 
foldl add fm key_elt_pairs where 
add fmap (key,eltaddToFM_C combiner fmap key elt

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

  emptyFM :: FiniteMap 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 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 :: (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

  listToFM :: Ord a => [(a,b)]  ->  FiniteMap a b
listToFM addListToFM emptyFM

  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 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



Replaced joker patterns by fresh variables and removed binding patterns.

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

mainModule FiniteMap
  ((listToFM :: (Ord a, Ord b) => [((b,a),c)]  ->  FiniteMap (b,a) c) :: (Ord a, Ord b) => [((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

  addListToFM :: Ord b => FiniteMap b a  ->  [(b,a)]  ->  FiniteMap b a
addListToFM fm key_elt_pairs addListToFM_C addListToFM0 fm key_elt_pairs

  
addListToFM0 old new new

  addListToFM_C :: Ord b => (a  ->  a  ->  a ->  FiniteMap b a  ->  [(b,a)]  ->  FiniteMap b a
addListToFM_C combiner fm key_elt_pairs 
foldl add fm key_elt_pairs where 
add fmap (key,eltaddToFM_C combiner fmap 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 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  ->  a  ->  c  ->  c ->  c  ->  FiniteMap b a  ->  c
foldFM k z EmptyFM z
foldFM k z (Branch key elt wy fm_l fm_rfoldFM k (k key elt (foldFM k z fm_r)) fm_l

  listToFM :: Ord a => [(a,b)]  ->  FiniteMap a b
listToFM addListToFM emptyFM

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

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

  sIZE_RATIO :: Int
sIZE_RATIO 5

  sizeFM :: FiniteMap b a  ->  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



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)

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

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

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

The following Function with conditions
mkBalBranch0 fm_L fm_R (Branch zx zy zz fm_rl fm_rr)
 | sizeFM fm_rl < 2 * sizeFM fm_rr
 = single_L fm_L fm_R
 | otherwise
 = double_L fm_L fm_R

is transformed to
mkBalBranch0 fm_L fm_R (Branch zx zy zz fm_rl fm_rr) = mkBalBranch02 fm_L fm_R (Branch zx zy zz fm_rl fm_rr)

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

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

mkBalBranch02 fm_L fm_R (Branch zx zy zz fm_rl fm_rr) = mkBalBranch01 fm_L fm_R zx zy zz fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr)

The following Function with conditions
mkBalBranch key elt fm_L fm_R
 | size_l + size_r < 2
 = mkBranch 1 key elt fm_L fm_R
 | size_r > sIZE_RATIO * size_l
 = mkBalBranch0 fm_L fm_R fm_R
 | size_l > sIZE_RATIO * size_r
 = mkBalBranch1 fm_L fm_R fm_L
 | otherwise
 = mkBranch 2 key elt fm_L fm_R
where 
double_L fm_l (Branch key_r elt_r zv (Branch key_rl elt_rl zw fm_rll fm_rlrfm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 key elt fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr)
double_R (Branch key_l elt_l yw fm_ll (Branch key_lr elt_lr yx fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 key elt fm_lrr fm_r)
mkBalBranch0 fm_L fm_R (Branch zx zy zz fm_rl fm_rr)
 | sizeFM fm_rl < 2 * sizeFM fm_rr
 = single_L fm_L fm_R
 | otherwise
 = double_L fm_L fm_R
mkBalBranch1 fm_L fm_R (Branch yy yz zu fm_ll fm_lr)
 | sizeFM fm_lr < 2 * sizeFM fm_ll
 = single_R fm_L fm_R
 | otherwise
 = double_R fm_L fm_R
single_L fm_l (Branch key_r elt_r vuu fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rlfm_rr
single_R (Branch key_l elt_l yv fm_ll fm_lrfm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r)
size_l  = sizeFM fm_L
size_r  = sizeFM fm_R

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

mkBalBranch6 key elt fm_L fm_R = 
mkBalBranch5 key elt fm_L fm_R (size_l + size_r < 2)
where 
double_L fm_l (Branch key_r elt_r zv (Branch key_rl elt_rl zw fm_rll fm_rlrfm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 key elt fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr)
double_R (Branch key_l elt_l yw fm_ll (Branch key_lr elt_lr yx fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 key elt fm_lrr fm_r)
mkBalBranch0 fm_L fm_R (Branch zx zy zz fm_rl fm_rr) = mkBalBranch02 fm_L fm_R (Branch zx zy zz fm_rl fm_rr)
mkBalBranch00 fm_L fm_R zx zy zz fm_rl fm_rr True = double_L fm_L fm_R
mkBalBranch01 fm_L fm_R zx zy zz fm_rl fm_rr True = single_L fm_L fm_R
mkBalBranch01 fm_L fm_R zx zy zz fm_rl fm_rr False = mkBalBranch00 fm_L fm_R zx zy zz fm_rl fm_rr otherwise
mkBalBranch02 fm_L fm_R (Branch zx zy zz fm_rl fm_rr) = mkBalBranch01 fm_L fm_R zx zy zz fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr)
mkBalBranch1 fm_L fm_R (Branch yy yz zu fm_ll fm_lr) = mkBalBranch12 fm_L fm_R (Branch yy yz zu fm_ll fm_lr)
mkBalBranch10 fm_L fm_R yy yz zu fm_ll fm_lr True = double_R fm_L fm_R
mkBalBranch11 fm_L fm_R yy yz zu fm_ll fm_lr True = single_R fm_L fm_R
mkBalBranch11 fm_L fm_R yy yz zu fm_ll fm_lr False = mkBalBranch10 fm_L fm_R yy yz zu fm_ll fm_lr otherwise
mkBalBranch12 fm_L fm_R (Branch yy yz zu fm_ll fm_lr) = mkBalBranch11 fm_L fm_R yy yz zu fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll)
mkBalBranch2 key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R
mkBalBranch3 key elt fm_L fm_R True = mkBalBranch1 fm_L fm_R fm_L
mkBalBranch3 key elt fm_L fm_R False = mkBalBranch2 key elt fm_L fm_R otherwise
mkBalBranch4 key elt fm_L fm_R True = mkBalBranch0 fm_L fm_R fm_R
mkBalBranch4 key elt fm_L fm_R False = mkBalBranch3 key elt fm_L fm_R (size_l > sIZE_RATIO * size_r)
mkBalBranch5 key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R
mkBalBranch5 key elt fm_L fm_R False = mkBalBranch4 key elt fm_L fm_R (size_r > sIZE_RATIO * size_l)
single_L fm_l (Branch key_r elt_r vuu fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rlfm_rr
single_R (Branch key_l elt_l yv fm_ll fm_lrfm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r)
size_l  = sizeFM fm_L
size_r  = sizeFM fm_R

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

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

addToFM_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

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

compare0 x y True = GT

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

compare3 x y = compare2 x y (x == y)

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

is transformed to
gcd' x 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

absReal0 x True = `negate` x

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

absReal2 x = absReal1 x (x >= 0)

The following Function with conditions
undefined 
 | False
 = undefined

is transformed to
undefined  = undefined1

undefined0 True = undefined

undefined1  = undefined0 False

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

is transformed to
reduce x y = reduce2 x y

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



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

mainModule FiniteMap
  ((listToFM :: (Ord b, Ord a) => [((a,b),c)]  ->  FiniteMap (a,b) c) :: (Ord a, Ord b) => [((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

  addListToFM :: Ord b => FiniteMap b a  ->  [(b,a)]  ->  FiniteMap b a
addListToFM fm key_elt_pairs addListToFM_C addListToFM0 fm key_elt_pairs

  
addListToFM0 old new new

  addListToFM_C :: Ord b => (a  ->  a  ->  a ->  FiniteMap b a  ->  [(b,a)]  ->  FiniteMap b a
addListToFM_C combiner fm key_elt_pairs 
foldl add fm key_elt_pairs where 
add fmap (key,eltaddToFM_C combiner fmap key elt

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

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

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

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

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

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

  emptyFM :: FiniteMap a b
emptyFM EmptyFM

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

  listToFM :: Ord b => [(b,a)]  ->  FiniteMap b a
listToFM addListToFM emptyFM

  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 vw vx vy vz
let 
biggest_left_key fst (findMax fm_l)
in biggest_left_key < key
left_size sizeFM fm_l
right_ok right_ok0 fm_r key fm_r
right_ok0 fm_r key EmptyFM True
right_ok0 fm_r key (Branch right_key wu wv ww wx
let 
smallest_right_key fst (findMin fm_r)
in key < smallest_right_key
right_size sizeFM fm_r
unbox :: Int  ->  Int
unbox x x

  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 vw vx vy vz) = 
let 
biggest_left_key  = fst (findMax fm_l)
in biggest_left_key < key
left_size  = sizeFM fm_l
right_ok  = right_ok0 fm_r key fm_r
right_ok0 fm_r key EmptyFM = True
right_ok0 fm_r key (Branch right_key wu wv ww wx) = 
let 
smallest_right_key  = fst (findMin fm_r)
in key < smallest_right_key
right_size  = sizeFM fm_r
unbox x = x

are unpacked to the following functions on top level
mkBranchBalance_ok wxw wxx wxy = True

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

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

mkBranchUnbox wxw wxx wxy x = x

mkBranchRight_size wxw wxx wxy = sizeFM wxw

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

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

mkBranchLeft_size wxw wxx wxy = sizeFM wxy

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

are unpacked to the following functions on top level
mkBranchResult wxz wyu wyv wyw = Branch wxz wyu (mkBranchUnbox wyv wxz wyw (1 + mkBranchLeft_size wyv wxz wyw + mkBranchRight_size wyv wxz wyw)) 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
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)

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)

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

mkBalBranch6Size_l wyx wyy wyz wzu = sizeFM wyx

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)

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

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

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

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

mkBalBranch6Size_r wyx wyy wyz wzu = sizeFM wzu

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)

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)

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

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)

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
foldl add fm key_elt_pairs
where 
add fmap (key,elt) = addToFM_C combiner fmap key elt

are unpacked to the following functions on top level
addListToFM_CAdd wzv fmap (key,elt) = addToFM_C wzv fmap key elt

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
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 wzx = fst (findMin wzx)

The bindings of the following Let/Where expression
reduce1 x y (y == 0)
where 
d  = gcd x y
reduce0 x y True = x `quot` d :% (y `quot` d)
reduce1 x y True = error []
reduce1 x y False = reduce0 x y otherwise

are unpacked to the following functions on top level
reduce2Reduce0 wzy wzz x y True = x `quot` reduce2D wzy wzz :% (y `quot` reduce2D wzy wzz)

reduce2D wzy wzz = gcd wzy wzz

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

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

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

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

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



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

mainModule FiniteMap
  ((listToFM :: (Ord a, Ord b) => [((a,b),c)]  ->  FiniteMap (a,b) c) :: (Ord a, Ord b) => [((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 a b) where 
   
(==) fm_1 fm_2 sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2

  addListToFM :: Ord b => FiniteMap b a  ->  [(b,a)]  ->  FiniteMap b a
addListToFM fm key_elt_pairs addListToFM_C addListToFM0 fm key_elt_pairs

  
addListToFM0 old new new

  addListToFM_C :: Ord a => (b  ->  b  ->  b ->  FiniteMap a b  ->  [(a,b)]  ->  FiniteMap a b
addListToFM_C combiner fm key_elt_pairs foldl (addListToFM_CAdd combiner) fm key_elt_pairs

  
addListToFM_CAdd wzv fmap (key,eltaddToFM_C wzv fmap key elt

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

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

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

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

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

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

  emptyFM :: FiniteMap b a
emptyFM EmptyFM

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

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

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

  listToFM :: Ord a => [(a,b)]  ->  FiniteMap a b
listToFM addListToFM emptyFM

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

  
mkBalBranch6 key elt fm_L fm_R mkBalBranch6MkBalBranch5 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 vw vx vy vzmkBranchLeft_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 wu wv ww wxkey < mkBranchRight_ok0Smallest_right_key fm_r

  
mkBranchRight_ok0Smallest_right_key wzx fst (findMin wzx)

  
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 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



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

module FiniteMap where
  import qualified Maybe
import qualified Prelude

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


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

  addListToFM :: Ord b => FiniteMap b a  ->  [(b,a)]  ->  FiniteMap b a
addListToFM fm key_elt_pairs addListToFM_C addListToFM0 fm key_elt_pairs

  
addListToFM0 old new new

  addListToFM_C :: Ord b => (a  ->  a  ->  a ->  FiniteMap b a  ->  [(b,a)]  ->  FiniteMap b a
addListToFM_C combiner fm key_elt_pairs foldl (addListToFM_CAdd combiner) fm key_elt_pairs

  
addListToFM_CAdd wzv fmap (key,eltaddToFM_C wzv fmap key elt

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

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

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

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

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

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

  emptyFM :: FiniteMap b a
emptyFM EmptyFM

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

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

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

  
fmToList0 key elt rest (key,elt: rest

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

  listToFM :: Ord b => [(b,a)]  ->  FiniteMap b a
listToFM addListToFM emptyFM

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

  
mkBalBranch6 key elt fm_L fm_R mkBalBranch6MkBalBranch5 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 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 vw vx vy vzmkBranchLeft_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 wu wv ww wxkey < mkBranchRight_ok0Smallest_right_key fm_r

  
mkBranchRight_ok0Smallest_right_key wzx fst (findMin wzx)

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude



Haskell To QDPs


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

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

new_primEqNat(Succ(xuu31100000), Succ(xuu60000)) → new_primEqNat(xuu31100000, xuu60000)

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

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



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

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

new_primCmpNat(Succ(xuu49000), Succ(xuu51000)) → new_primCmpNat(xuu49000, xuu51000)

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

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



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

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

new_primMinusNat(Succ(xuu41200), Succ(xuu9200)) → new_primMinusNat(xuu41200, xuu9200)

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

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



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

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

new_primPlusNat(Succ(xuu41200), Succ(xuu9200)) → new_primPlusNat(xuu41200, xuu9200)

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

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



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

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

new_primMulNat(Succ(xuu311000100), Succ(xuu600100)) → new_primMulNat(xuu311000100, Succ(xuu600100))

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

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



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

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

new_esEs1(@2(xuu3110000, xuu3110001), @2(xuu6000, xuu6001), app(ty_Maybe, df), de) → new_esEs0(xuu3110000, xuu6000, df)
new_esEs2(@3(xuu3110000, xuu3110001, xuu3110002), @3(xuu6000, xuu6001, xuu6002), app(app(app(ty_@3, gg), gh), ha), gb, gc) → new_esEs2(xuu3110000, xuu6000, gg, gh, ha)
new_esEs0(Just(xuu3110000), Just(xuu6000), app(app(app(ty_@3, cf), cg), da)) → new_esEs2(xuu3110000, xuu6000, cf, cg, da)
new_esEs3(Right(xuu3110000), Right(xuu6000), bda, app(ty_[], bdb)) → new_esEs(xuu3110000, xuu6000, bdb)
new_esEs2(@3(xuu3110000, xuu3110001, xuu3110002), @3(xuu6000, xuu6001, xuu6002), hd, gb, app(ty_[], baf)) → new_esEs(xuu3110002, xuu6002, baf)
new_esEs2(@3(xuu3110000, xuu3110001, xuu3110002), @3(xuu6000, xuu6001, xuu6002), hd, app(app(ty_Either, bad), bae), gc) → new_esEs3(xuu3110001, xuu6001, bad, bae)
new_esEs0(Just(xuu3110000), Just(xuu6000), app(app(ty_Either, db), dc)) → new_esEs3(xuu3110000, xuu6000, db, dc)
new_esEs2(@3(xuu3110000, xuu3110001, xuu3110002), @3(xuu6000, xuu6001, xuu6002), hd, gb, app(app(ty_@2, bah), bba)) → new_esEs1(xuu3110002, xuu6002, bah, bba)
new_esEs(:(xuu3110000, xuu3110001), :(xuu6000, xuu6001), app(app(app(ty_@3, bd), be), bf)) → new_esEs2(xuu3110000, xuu6000, bd, be, bf)
new_esEs1(@2(xuu3110000, xuu3110001), @2(xuu6000, xuu6001), ef, app(app(app(ty_@3, fc), fd), ff)) → new_esEs2(xuu3110001, xuu6001, fc, fd, ff)
new_esEs2(@3(xuu3110000, xuu3110001, xuu3110002), @3(xuu6000, xuu6001, xuu6002), app(ty_[], ga), gb, gc) → new_esEs(xuu3110000, xuu6000, ga)
new_esEs2(@3(xuu3110000, xuu3110001, xuu3110002), @3(xuu6000, xuu6001, xuu6002), hd, app(ty_Maybe, hf), gc) → new_esEs0(xuu3110001, xuu6001, hf)
new_esEs3(Right(xuu3110000), Right(xuu6000), bda, app(app(ty_Either, bea), beb)) → new_esEs3(xuu3110000, xuu6000, bea, beb)
new_esEs0(Just(xuu3110000), Just(xuu6000), app(ty_Maybe, cc)) → new_esEs0(xuu3110000, xuu6000, cc)
new_esEs0(Just(xuu3110000), Just(xuu6000), app(ty_[], cb)) → new_esEs(xuu3110000, xuu6000, cb)
new_esEs3(Left(xuu3110000), Left(xuu6000), app(ty_[], bbg), bbh) → new_esEs(xuu3110000, xuu6000, bbg)
new_esEs3(Left(xuu3110000), Left(xuu6000), app(app(ty_Either, bcg), bch), bbh) → new_esEs3(xuu3110000, xuu6000, bcg, bch)
new_esEs2(@3(xuu3110000, xuu3110001, xuu3110002), @3(xuu6000, xuu6001, xuu6002), hd, gb, app(ty_Maybe, bag)) → new_esEs0(xuu3110002, xuu6002, bag)
new_esEs1(@2(xuu3110000, xuu3110001), @2(xuu6000, xuu6001), ef, app(ty_[], eg)) → new_esEs(xuu3110001, xuu6001, eg)
new_esEs2(@3(xuu3110000, xuu3110001, xuu3110002), @3(xuu6000, xuu6001, xuu6002), app(ty_Maybe, gd), gb, gc) → new_esEs0(xuu3110000, xuu6000, gd)
new_esEs1(@2(xuu3110000, xuu3110001), @2(xuu6000, xuu6001), app(ty_[], dd), de) → new_esEs(xuu3110000, xuu6000, dd)
new_esEs(:(xuu3110000, xuu3110001), :(xuu6000, xuu6001), app(ty_Maybe, ba)) → new_esEs0(xuu3110000, xuu6000, ba)
new_esEs1(@2(xuu3110000, xuu3110001), @2(xuu6000, xuu6001), ef, app(app(ty_Either, fg), fh)) → new_esEs3(xuu3110001, xuu6001, fg, fh)
new_esEs2(@3(xuu3110000, xuu3110001, xuu3110002), @3(xuu6000, xuu6001, xuu6002), app(app(ty_@2, ge), gf), gb, gc) → new_esEs1(xuu3110000, xuu6000, ge, gf)
new_esEs1(@2(xuu3110000, xuu3110001), @2(xuu6000, xuu6001), ef, app(app(ty_@2, fa), fb)) → new_esEs1(xuu3110001, xuu6001, fa, fb)
new_esEs(:(xuu3110000, xuu3110001), :(xuu6000, xuu6001), app(app(ty_@2, bb), bc)) → new_esEs1(xuu3110000, xuu6000, bb, bc)
new_esEs(:(xuu3110000, xuu3110001), :(xuu6000, xuu6001), ca) → new_esEs(xuu3110001, xuu6001, ca)
new_esEs(:(xuu3110000, xuu3110001), :(xuu6000, xuu6001), app(app(ty_Either, bg), bh)) → new_esEs3(xuu3110000, xuu6000, bg, bh)
new_esEs2(@3(xuu3110000, xuu3110001, xuu3110002), @3(xuu6000, xuu6001, xuu6002), app(app(ty_Either, hb), hc), gb, gc) → new_esEs3(xuu3110000, xuu6000, hb, hc)
new_esEs2(@3(xuu3110000, xuu3110001, xuu3110002), @3(xuu6000, xuu6001, xuu6002), hd, app(app(ty_@2, hg), hh), gc) → new_esEs1(xuu3110001, xuu6001, hg, hh)
new_esEs3(Left(xuu3110000), Left(xuu6000), app(app(ty_@2, bcb), bcc), bbh) → new_esEs1(xuu3110000, xuu6000, bcb, bcc)
new_esEs2(@3(xuu3110000, xuu3110001, xuu3110002), @3(xuu6000, xuu6001, xuu6002), hd, app(app(app(ty_@3, baa), bab), bac), gc) → new_esEs2(xuu3110001, xuu6001, baa, bab, bac)
new_esEs1(@2(xuu3110000, xuu3110001), @2(xuu6000, xuu6001), app(app(ty_@2, dg), dh), de) → new_esEs1(xuu3110000, xuu6000, dg, dh)
new_esEs2(@3(xuu3110000, xuu3110001, xuu3110002), @3(xuu6000, xuu6001, xuu6002), hd, app(ty_[], he), gc) → new_esEs(xuu3110001, xuu6001, he)
new_esEs3(Right(xuu3110000), Right(xuu6000), bda, app(app(app(ty_@3, bdf), bdg), bdh)) → new_esEs2(xuu3110000, xuu6000, bdf, bdg, bdh)
new_esEs1(@2(xuu3110000, xuu3110001), @2(xuu6000, xuu6001), app(app(ty_Either, ed), ee), de) → new_esEs3(xuu3110000, xuu6000, ed, ee)
new_esEs3(Left(xuu3110000), Left(xuu6000), app(app(app(ty_@3, bcd), bce), bcf), bbh) → new_esEs2(xuu3110000, xuu6000, bcd, bce, bcf)
new_esEs2(@3(xuu3110000, xuu3110001, xuu3110002), @3(xuu6000, xuu6001, xuu6002), hd, gb, app(app(ty_Either, bbe), bbf)) → new_esEs3(xuu3110002, xuu6002, bbe, bbf)
new_esEs3(Right(xuu3110000), Right(xuu6000), bda, app(app(ty_@2, bdd), bde)) → new_esEs1(xuu3110000, xuu6000, bdd, bde)
new_esEs1(@2(xuu3110000, xuu3110001), @2(xuu6000, xuu6001), ef, app(ty_Maybe, eh)) → new_esEs0(xuu3110001, xuu6001, eh)
new_esEs3(Left(xuu3110000), Left(xuu6000), app(ty_Maybe, bca), bbh) → new_esEs0(xuu3110000, xuu6000, bca)
new_esEs3(Right(xuu3110000), Right(xuu6000), bda, app(ty_Maybe, bdc)) → new_esEs0(xuu3110000, xuu6000, bdc)
new_esEs0(Just(xuu3110000), Just(xuu6000), app(app(ty_@2, cd), ce)) → new_esEs1(xuu3110000, xuu6000, cd, ce)
new_esEs(:(xuu3110000, xuu3110001), :(xuu6000, xuu6001), app(ty_[], h)) → new_esEs(xuu3110000, xuu6000, h)
new_esEs2(@3(xuu3110000, xuu3110001, xuu3110002), @3(xuu6000, xuu6001, xuu6002), hd, gb, app(app(app(ty_@3, bbb), bbc), bbd)) → new_esEs2(xuu3110002, xuu6002, bbb, bbc, bbd)
new_esEs1(@2(xuu3110000, xuu3110001), @2(xuu6000, xuu6001), app(app(app(ty_@3, ea), eb), ec), de) → new_esEs2(xuu3110000, xuu6000, ea, eb, ec)

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

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



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

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

new_compare2(@2(xuu490, @2(xuu4910, xuu4911)), @2(xuu510, @2(xuu5110, xuu5111)), False, dg, app(app(ty_@2, cb), app(app(app(ty_@3, db), dc), dd))) → new_ltEs3(xuu4911, xuu5111, db, dc, dd)
new_compare2(@2(xuu490, xuu491), @2(xuu510, xuu511), False, dg, app(ty_[], dh)) → new_compare0(xuu491, xuu511, dh)
new_compare2(@2(xuu490, Left(xuu4910)), @2(xuu510, Left(xuu5110)), False, dg, app(app(ty_Either, app(ty_Maybe, fg)), fd)) → new_ltEs1(xuu4910, xuu5110, fg)
new_ltEs(@2(xuu4910, xuu4911), @2(xuu5110, xuu5111), app(ty_[], bc), bb) → new_lt0(xuu4910, xuu5110, bc)
new_ltEs3(@3(xuu4910, xuu4911, xuu4912), @3(xuu5110, xuu5111, xuu5112), bbb, app(app(ty_Either, bbg), bbh), bab) → new_lt2(xuu4911, xuu5111, bbg, bbh)
new_compare2(@2(xuu490, Left(xuu4910)), @2(xuu510, Left(xuu5110)), False, dg, app(app(ty_Either, app(app(ty_@2, fb), fc)), fd)) → new_ltEs(xuu4910, xuu5110, fb, fc)
new_compare3(xuu490, xuu510, bdg) → new_compare20(xuu490, xuu510, new_esEs5(xuu490, xuu510, bdg), bdg)
new_compare0(:(xuu4900, xuu4901), :(xuu5100, xuu5101), bdf) → new_compare0(xuu4901, xuu5101, bdf)
new_ltEs2(Left(xuu4910), Left(xuu5110), app(app(ty_Either, fh), ga), fd) → new_ltEs2(xuu4910, xuu5110, fh, ga)
new_compare2(@2(xuu490, Right(xuu4910)), @2(xuu510, Right(xuu5110)), False, dg, app(app(ty_Either, ge), app(app(ty_@2, gf), gg))) → new_ltEs(xuu4910, xuu5110, gf, gg)
new_compare2(@2(xuu490, @3(xuu4910, xuu4911, xuu4912)), @2(xuu510, @3(xuu5110, xuu5111, xuu5112)), False, dg, app(app(app(ty_@3, bbb), app(app(app(ty_@3, bca), bcb), bcc)), bab)) → new_lt3(xuu4911, xuu5111, bca, bcb, bcc)
new_ltEs3(@3(xuu4910, xuu4911, xuu4912), @3(xuu5110, xuu5111, xuu5112), bbb, app(ty_[], bbe), bab) → new_lt0(xuu4911, xuu5111, bbe)
new_compare2(@2(xuu490, @2(xuu4910, xuu4911)), @2(xuu510, @2(xuu5110, xuu5111)), False, dg, app(app(ty_@2, app(app(ty_@2, h), ba)), bb)) → new_lt(xuu4910, xuu5110, h, ba)
new_ltEs(@2(xuu4910, xuu4911), @2(xuu5110, xuu5111), app(app(app(ty_@3, bg), bh), ca), bb) → new_lt3(xuu4910, xuu5110, bg, bh, ca)
new_ltEs3(@3(xuu4910, xuu4911, xuu4912), @3(xuu5110, xuu5111, xuu5112), app(app(ty_@2, hg), hh), baa, bab) → new_lt(xuu4910, xuu5110, hg, hh)
new_compare(xuu490, xuu510, de, df) → new_compare2(xuu490, xuu510, new_esEs4(xuu490, xuu510, de, df), de, df)
new_ltEs(@2(xuu4910, xuu4911), @2(xuu5110, xuu5111), cb, app(ty_[], ce)) → new_ltEs0(xuu4911, xuu5111, ce)
new_compare22(xuu490, xuu510, False, beb, bec, bed) → new_ltEs3(xuu490, xuu510, beb, bec, bed)
new_compare2(@2(xuu490, @3(xuu4910, xuu4911, xuu4912)), @2(xuu510, @3(xuu5110, xuu5111, xuu5112)), False, dg, app(app(app(ty_@3, bbb), baa), app(app(ty_Either, bch), bda))) → new_ltEs2(xuu4912, xuu5112, bch, bda)
new_compare2(@2(xuu490, @3(xuu4910, xuu4911, xuu4912)), @2(xuu510, @3(xuu5110, xuu5111, xuu5112)), False, dg, app(app(app(ty_@3, bbb), baa), app(ty_[], bcf))) → new_ltEs0(xuu4912, xuu5112, bcf)
new_compare2(@2(xuu490, @2(xuu4910, xuu4911)), @2(xuu510, @2(xuu5110, xuu5111)), False, dg, app(app(ty_@2, cb), app(app(ty_@2, cc), cd))) → new_ltEs(xuu4911, xuu5111, cc, cd)
new_compare2(@2(xuu490, @2(xuu4910, xuu4911)), @2(xuu510, @2(xuu5110, xuu5111)), False, dg, app(app(ty_@2, cb), app(app(ty_Either, cg), da))) → new_ltEs2(xuu4911, xuu5111, cg, da)
new_compare20(xuu490, xuu510, False, bdg) → new_ltEs1(xuu490, xuu510, bdg)
new_compare2(@2(xuu490, Just(xuu4910)), @2(xuu510, Just(xuu5110)), False, dg, app(ty_Maybe, app(ty_[], ec))) → new_ltEs0(xuu4910, xuu5110, ec)
new_ltEs1(Just(xuu4910), Just(xuu5110), app(app(app(ty_@3, eg), eh), fa)) → new_ltEs3(xuu4910, xuu5110, eg, eh, fa)
new_ltEs3(@3(xuu4910, xuu4911, xuu4912), @3(xuu5110, xuu5111, xuu5112), bbb, baa, app(ty_Maybe, bcg)) → new_ltEs1(xuu4912, xuu5112, bcg)
new_ltEs(@2(xuu4910, xuu4911), @2(xuu5110, xuu5111), app(ty_Maybe, bd), bb) → new_lt1(xuu4910, xuu5110, bd)
new_compare2(@2(:(xuu4900, xuu4901), xuu491), @2(:(xuu5100, xuu5101), xuu511), False, app(ty_[], bdf), bde) → new_compare0(xuu4901, xuu5101, bdf)
new_compare2(@2(xuu490, @3(xuu4910, xuu4911, xuu4912)), @2(xuu510, @3(xuu5110, xuu5111, xuu5112)), False, dg, app(app(app(ty_@3, bbb), app(ty_[], bbe)), bab)) → new_lt0(xuu4911, xuu5111, bbe)
new_compare2(@2(xuu490, Right(xuu4910)), @2(xuu510, Right(xuu5110)), False, dg, app(app(ty_Either, ge), app(ty_[], gh))) → new_ltEs0(xuu4910, xuu5110, gh)
new_primCompAux(xuu4900, xuu5100, xuu130, app(app(ty_@2, bee), bef)) → new_compare(xuu4900, xuu5100, bee, bef)
new_lt0(:(xuu4900, xuu4901), :(xuu5100, xuu5101), bdf) → new_primCompAux(xuu4900, xuu5100, new_compare1(xuu4901, xuu5101, bdf), bdf)
new_ltEs3(@3(xuu4910, xuu4911, xuu4912), @3(xuu5110, xuu5111, xuu5112), app(app(ty_Either, bae), baf), baa, bab) → new_lt2(xuu4910, xuu5110, bae, baf)
new_compare2(@2(:(xuu4900, xuu4901), xuu491), @2(:(xuu5100, xuu5101), xuu511), False, app(ty_[], bdf), bde) → new_primCompAux(xuu4900, xuu5100, new_compare1(xuu4901, xuu5101, bdf), bdf)
new_compare2(@2(xuu490, @2(xuu4910, xuu4911)), @2(xuu510, @2(xuu5110, xuu5111)), False, dg, app(app(ty_@2, app(ty_[], bc)), bb)) → new_lt0(xuu4910, xuu5110, bc)
new_ltEs2(Left(xuu4910), Left(xuu5110), app(ty_Maybe, fg), fd) → new_ltEs1(xuu4910, xuu5110, fg)
new_compare2(@2(xuu490, @3(xuu4910, xuu4911, xuu4912)), @2(xuu510, @3(xuu5110, xuu5111, xuu5112)), False, dg, app(app(app(ty_@3, bbb), baa), app(app(ty_@2, bcd), bce))) → new_ltEs(xuu4912, xuu5112, bcd, bce)
new_compare21(xuu490, xuu510, False, bdh, bea) → new_ltEs2(xuu490, xuu510, bdh, bea)
new_compare2(@2(xuu490, xuu491), @2(xuu510, xuu511), False, app(ty_Maybe, bdg), bde) → new_compare20(xuu490, xuu510, new_esEs5(xuu490, xuu510, bdg), bdg)
new_ltEs2(Right(xuu4910), Right(xuu5110), ge, app(ty_[], gh)) → new_ltEs0(xuu4910, xuu5110, gh)
new_ltEs3(@3(xuu4910, xuu4911, xuu4912), @3(xuu5110, xuu5111, xuu5112), bbb, baa, app(app(ty_@2, bcd), bce)) → new_ltEs(xuu4912, xuu5112, bcd, bce)
new_compare2(@2(xuu490, @3(xuu4910, xuu4911, xuu4912)), @2(xuu510, @3(xuu5110, xuu5111, xuu5112)), False, dg, app(app(app(ty_@3, app(ty_[], bac)), baa), bab)) → new_lt0(xuu4910, xuu5110, bac)
new_ltEs0(xuu491, xuu511, dh) → new_compare0(xuu491, xuu511, dh)
new_ltEs1(Just(xuu4910), Just(xuu5110), app(ty_[], ec)) → new_ltEs0(xuu4910, xuu5110, ec)
new_ltEs3(@3(xuu4910, xuu4911, xuu4912), @3(xuu5110, xuu5111, xuu5112), bbb, app(ty_Maybe, bbf), bab) → new_lt1(xuu4911, xuu5111, bbf)
new_primCompAux(xuu4900, xuu5100, xuu130, app(app(app(ty_@3, bfc), bfd), bfe)) → new_compare5(xuu4900, xuu5100, bfc, bfd, bfe)
new_compare2(@2(xuu490, @2(xuu4910, xuu4911)), @2(xuu510, @2(xuu5110, xuu5111)), False, dg, app(app(ty_@2, app(app(app(ty_@3, bg), bh), ca)), bb)) → new_lt3(xuu4910, xuu5110, bg, bh, ca)
new_ltEs3(@3(xuu4910, xuu4911, xuu4912), @3(xuu5110, xuu5111, xuu5112), app(ty_Maybe, bad), baa, bab) → new_lt1(xuu4910, xuu5110, bad)
new_compare2(@2(xuu490, @3(xuu4910, xuu4911, xuu4912)), @2(xuu510, @3(xuu5110, xuu5111, xuu5112)), False, dg, app(app(app(ty_@3, app(app(app(ty_@3, bag), bah), bba)), baa), bab)) → new_lt3(xuu4910, xuu5110, bag, bah, bba)
new_compare2(@2(xuu490, Right(xuu4910)), @2(xuu510, Right(xuu5110)), False, dg, app(app(ty_Either, ge), app(app(app(ty_@3, hd), he), hf))) → new_ltEs3(xuu4910, xuu5110, hd, he, hf)
new_ltEs(@2(xuu4910, xuu4911), @2(xuu5110, xuu5111), app(app(ty_Either, be), bf), bb) → new_lt2(xuu4910, xuu5110, be, bf)
new_ltEs(@2(xuu4910, xuu4911), @2(xuu5110, xuu5111), cb, app(ty_Maybe, cf)) → new_ltEs1(xuu4911, xuu5111, cf)
new_ltEs(@2(xuu4910, xuu4911), @2(xuu5110, xuu5111), cb, app(app(ty_@2, cc), cd)) → new_ltEs(xuu4911, xuu5111, cc, cd)
new_ltEs1(Just(xuu4910), Just(xuu5110), app(app(ty_Either, ee), ef)) → new_ltEs2(xuu4910, xuu5110, ee, ef)
new_ltEs2(Right(xuu4910), Right(xuu5110), ge, app(app(ty_@2, gf), gg)) → new_ltEs(xuu4910, xuu5110, gf, gg)
new_compare2(@2(xuu490, @2(xuu4910, xuu4911)), @2(xuu510, @2(xuu5110, xuu5111)), False, dg, app(app(ty_@2, app(app(ty_Either, be), bf)), bb)) → new_lt2(xuu4910, xuu5110, be, bf)
new_ltEs3(@3(xuu4910, xuu4911, xuu4912), @3(xuu5110, xuu5111, xuu5112), bbb, app(app(app(ty_@3, bca), bcb), bcc), bab) → new_lt3(xuu4911, xuu5111, bca, bcb, bcc)
new_compare0(:(xuu4900, xuu4901), :(xuu5100, xuu5101), bdf) → new_primCompAux(xuu4900, xuu5100, new_compare1(xuu4901, xuu5101, bdf), bdf)
new_ltEs1(Just(xuu4910), Just(xuu5110), app(app(ty_@2, ea), eb)) → new_ltEs(xuu4910, xuu5110, ea, eb)
new_compare2(@2(xuu490, Left(xuu4910)), @2(xuu510, Left(xuu5110)), False, dg, app(app(ty_Either, app(app(app(ty_@3, gb), gc), gd)), fd)) → new_ltEs3(xuu4910, xuu5110, gb, gc, gd)
new_ltEs2(Right(xuu4910), Right(xuu5110), ge, app(app(app(ty_@3, hd), he), hf)) → new_ltEs3(xuu4910, xuu5110, hd, he, hf)
new_compare4(xuu490, xuu510, bdh, bea) → new_compare21(xuu490, xuu510, new_esEs6(xuu490, xuu510, bdh, bea), bdh, bea)
new_compare2(@2(xuu490, Just(xuu4910)), @2(xuu510, Just(xuu5110)), False, dg, app(ty_Maybe, app(app(app(ty_@3, eg), eh), fa))) → new_ltEs3(xuu4910, xuu5110, eg, eh, fa)
new_compare2(@2(xuu490, Left(xuu4910)), @2(xuu510, Left(xuu5110)), False, dg, app(app(ty_Either, app(ty_[], ff)), fd)) → new_ltEs0(xuu4910, xuu5110, ff)
new_ltEs2(Left(xuu4910), Left(xuu5110), app(ty_[], ff), fd) → new_ltEs0(xuu4910, xuu5110, ff)
new_compare2(@2(xuu490, @3(xuu4910, xuu4911, xuu4912)), @2(xuu510, @3(xuu5110, xuu5111, xuu5112)), False, dg, app(app(app(ty_@3, app(ty_Maybe, bad)), baa), bab)) → new_lt1(xuu4910, xuu5110, bad)
new_lt(xuu490, xuu510, de, df) → new_compare2(xuu490, xuu510, new_esEs4(xuu490, xuu510, de, df), de, df)
new_compare2(@2(xuu490, @3(xuu4910, xuu4911, xuu4912)), @2(xuu510, @3(xuu5110, xuu5111, xuu5112)), False, dg, app(app(app(ty_@3, bbb), app(app(ty_Either, bbg), bbh)), bab)) → new_lt2(xuu4911, xuu5111, bbg, bbh)
new_ltEs2(Left(xuu4910), Left(xuu5110), app(app(app(ty_@3, gb), gc), gd), fd) → new_ltEs3(xuu4910, xuu5110, gb, gc, gd)
new_compare5(xuu490, xuu510, beb, bec, bed) → new_compare22(xuu490, xuu510, new_esEs7(xuu490, xuu510, beb, bec, bed), beb, bec, bed)
new_compare2(@2(xuu490, Right(xuu4910)), @2(xuu510, Right(xuu5110)), False, dg, app(app(ty_Either, ge), app(app(ty_Either, hb), hc))) → new_ltEs2(xuu4910, xuu5110, hb, hc)
new_ltEs1(Just(xuu4910), Just(xuu5110), app(ty_Maybe, ed)) → new_ltEs1(xuu4910, xuu5110, ed)
new_compare2(@2(xuu490, Just(xuu4910)), @2(xuu510, Just(xuu5110)), False, dg, app(ty_Maybe, app(app(ty_Either, ee), ef))) → new_ltEs2(xuu4910, xuu5110, ee, ef)
new_ltEs(@2(xuu4910, xuu4911), @2(xuu5110, xuu5111), cb, app(app(ty_Either, cg), da)) → new_ltEs2(xuu4911, xuu5111, cg, da)
new_ltEs3(@3(xuu4910, xuu4911, xuu4912), @3(xuu5110, xuu5111, xuu5112), app(ty_[], bac), baa, bab) → new_lt0(xuu4910, xuu5110, bac)
new_compare2(@2(xuu490, Just(xuu4910)), @2(xuu510, Just(xuu5110)), False, dg, app(ty_Maybe, app(app(ty_@2, ea), eb))) → new_ltEs(xuu4910, xuu5110, ea, eb)
new_compare2(@2(xuu490, @3(xuu4910, xuu4911, xuu4912)), @2(xuu510, @3(xuu5110, xuu5111, xuu5112)), False, dg, app(app(app(ty_@3, bbb), baa), app(app(app(ty_@3, bdb), bdc), bdd))) → new_ltEs3(xuu4912, xuu5112, bdb, bdc, bdd)
new_ltEs(@2(xuu4910, xuu4911), @2(xuu5110, xuu5111), app(app(ty_@2, h), ba), bb) → new_lt(xuu4910, xuu5110, h, ba)
new_ltEs2(Left(xuu4910), Left(xuu5110), app(app(ty_@2, fb), fc), fd) → new_ltEs(xuu4910, xuu5110, fb, fc)
new_lt3(xuu490, xuu510, beb, bec, bed) → new_compare22(xuu490, xuu510, new_esEs7(xuu490, xuu510, beb, bec, bed), beb, bec, bed)
new_primCompAux(xuu4900, xuu5100, xuu130, app(ty_[], beg)) → new_compare0(xuu4900, xuu5100, beg)
new_compare2(@2(xuu490, @3(xuu4910, xuu4911, xuu4912)), @2(xuu510, @3(xuu5110, xuu5111, xuu5112)), False, dg, app(app(app(ty_@3, bbb), baa), app(ty_Maybe, bcg))) → new_ltEs1(xuu4912, xuu5112, bcg)
new_compare2(@2(xuu490, xuu491), @2(xuu510, xuu511), False, app(app(ty_@2, de), df), bde) → new_compare2(xuu490, xuu510, new_esEs4(xuu490, xuu510, de, df), de, df)
new_lt1(xuu490, xuu510, bdg) → new_compare20(xuu490, xuu510, new_esEs5(xuu490, xuu510, bdg), bdg)
new_compare2(@2(xuu490, @2(xuu4910, xuu4911)), @2(xuu510, @2(xuu5110, xuu5111)), False, dg, app(app(ty_@2, cb), app(ty_[], ce))) → new_ltEs0(xuu4911, xuu5111, ce)
new_primCompAux(xuu4900, xuu5100, xuu130, app(app(ty_Either, bfa), bfb)) → new_compare4(xuu4900, xuu5100, bfa, bfb)
new_ltEs(@2(xuu4910, xuu4911), @2(xuu5110, xuu5111), cb, app(app(app(ty_@3, db), dc), dd)) → new_ltEs3(xuu4911, xuu5111, db, dc, dd)
new_ltEs2(Right(xuu4910), Right(xuu5110), ge, app(app(ty_Either, hb), hc)) → new_ltEs2(xuu4910, xuu5110, hb, hc)
new_compare2(@2(xuu490, Right(xuu4910)), @2(xuu510, Right(xuu5110)), False, dg, app(app(ty_Either, ge), app(ty_Maybe, ha))) → new_ltEs1(xuu4910, xuu5110, ha)
new_compare2(@2(xuu490, xuu491), @2(xuu510, xuu511), False, app(app(ty_Either, bdh), bea), bde) → new_compare21(xuu490, xuu510, new_esEs6(xuu490, xuu510, bdh, bea), bdh, bea)
new_ltEs3(@3(xuu4910, xuu4911, xuu4912), @3(xuu5110, xuu5111, xuu5112), bbb, baa, app(ty_[], bcf)) → new_ltEs0(xuu4912, xuu5112, bcf)
new_ltEs3(@3(xuu4910, xuu4911, xuu4912), @3(xuu5110, xuu5111, xuu5112), bbb, app(app(ty_@2, bbc), bbd), bab) → new_lt(xuu4911, xuu5111, bbc, bbd)
new_ltEs3(@3(xuu4910, xuu4911, xuu4912), @3(xuu5110, xuu5111, xuu5112), bbb, baa, app(app(app(ty_@3, bdb), bdc), bdd)) → new_ltEs3(xuu4912, xuu5112, bdb, bdc, bdd)
new_compare2(@2(xuu490, @3(xuu4910, xuu4911, xuu4912)), @2(xuu510, @3(xuu5110, xuu5111, xuu5112)), False, dg, app(app(app(ty_@3, bbb), app(ty_Maybe, bbf)), bab)) → new_lt1(xuu4911, xuu5111, bbf)
new_lt2(xuu490, xuu510, bdh, bea) → new_compare21(xuu490, xuu510, new_esEs6(xuu490, xuu510, bdh, bea), bdh, bea)
new_ltEs3(@3(xuu4910, xuu4911, xuu4912), @3(xuu5110, xuu5111, xuu5112), app(app(app(ty_@3, bag), bah), bba), baa, bab) → new_lt3(xuu4910, xuu5110, bag, bah, bba)
new_compare2(@2(xuu490, Just(xuu4910)), @2(xuu510, Just(xuu5110)), False, dg, app(ty_Maybe, app(ty_Maybe, ed))) → new_ltEs1(xuu4910, xuu5110, ed)
new_compare2(@2(xuu490, @3(xuu4910, xuu4911, xuu4912)), @2(xuu510, @3(xuu5110, xuu5111, xuu5112)), False, dg, app(app(app(ty_@3, app(app(ty_Either, bae), baf)), baa), bab)) → new_lt2(xuu4910, xuu5110, bae, baf)
new_compare2(@2(xuu490, Left(xuu4910)), @2(xuu510, Left(xuu5110)), False, dg, app(app(ty_Either, app(app(ty_Either, fh), ga)), fd)) → new_ltEs2(xuu4910, xuu5110, fh, ga)
new_compare2(@2(xuu490, @3(xuu4910, xuu4911, xuu4912)), @2(xuu510, @3(xuu5110, xuu5111, xuu5112)), False, dg, app(app(app(ty_@3, bbb), app(app(ty_@2, bbc), bbd)), bab)) → new_lt(xuu4911, xuu5111, bbc, bbd)
new_compare2(@2(xuu490, @3(xuu4910, xuu4911, xuu4912)), @2(xuu510, @3(xuu5110, xuu5111, xuu5112)), False, dg, app(app(app(ty_@3, app(app(ty_@2, hg), hh)), baa), bab)) → new_lt(xuu4910, xuu5110, hg, hh)
new_compare2(@2(xuu490, xuu491), @2(xuu510, xuu511), False, app(app(app(ty_@3, beb), bec), bed), bde) → new_compare22(xuu490, xuu510, new_esEs7(xuu490, xuu510, beb, bec, bed), beb, bec, bed)
new_compare2(@2(xuu490, @2(xuu4910, xuu4911)), @2(xuu510, @2(xuu5110, xuu5111)), False, dg, app(app(ty_@2, app(ty_Maybe, bd)), bb)) → new_lt1(xuu4910, xuu5110, bd)
new_ltEs3(@3(xuu4910, xuu4911, xuu4912), @3(xuu5110, xuu5111, xuu5112), bbb, baa, app(app(ty_Either, bch), bda)) → new_ltEs2(xuu4912, xuu5112, bch, bda)
new_compare2(@2(xuu490, @2(xuu4910, xuu4911)), @2(xuu510, @2(xuu5110, xuu5111)), False, dg, app(app(ty_@2, cb), app(ty_Maybe, cf))) → new_ltEs1(xuu4911, xuu5111, cf)
new_ltEs2(Right(xuu4910), Right(xuu5110), ge, app(ty_Maybe, ha)) → new_ltEs1(xuu4910, xuu5110, ha)
new_primCompAux(xuu4900, xuu5100, xuu130, app(ty_Maybe, beh)) → new_compare3(xuu4900, xuu5100, beh)
new_lt0(:(xuu4900, xuu4901), :(xuu5100, xuu5101), bdf) → new_compare0(xuu4901, xuu5101, bdf)

The TRS R consists of the following rules:

new_lt10(xuu490, xuu510) → new_esEs8(new_compare18(xuu490, xuu510), LT)
new_primCmpNat0(xuu4900, Succ(xuu5100)) → new_primCmpNat2(xuu4900, xuu5100)
new_compare19(xuu490, xuu510, beb, bec, bed) → new_compare26(xuu490, xuu510, new_esEs7(xuu490, xuu510, beb, bec, bed), beb, bec, bed)
new_lt19(xuu4910, xuu5110, app(ty_Maybe, bd)) → new_lt15(xuu4910, xuu5110, bd)
new_lt19(xuu4910, xuu5110, ty_Double) → new_lt7(xuu4910, xuu5110)
new_esEs21(xuu3110001, xuu6001, ty_Float) → new_esEs14(xuu3110001, xuu6001)
new_esEs5(Just(xuu3110000), Just(xuu6000), ty_Ordering) → new_esEs8(xuu3110000, xuu6000)
new_esEs13(False, True) → False
new_esEs13(True, False) → False
new_esEs23(xuu4910, xuu5110, app(app(ty_@2, h), ba)) → new_esEs4(xuu4910, xuu5110, h, ba)
new_esEs28(xuu3110000, xuu6000, ty_Float) → new_esEs14(xuu3110000, xuu6000)
new_compare6(xuu490, xuu510, bdh, bea) → new_compare28(xuu490, xuu510, new_esEs6(xuu490, xuu510, bdh, bea), bdh, bea)
new_lt21(xuu4911, xuu5111, ty_Ordering) → new_lt14(xuu4911, xuu5111)
new_compare29(xuu4900, xuu5100, ty_Double) → new_compare8(xuu4900, xuu5100)
new_esEs20(xuu3110000, xuu6000, ty_Double) → new_esEs12(xuu3110000, xuu6000)
new_ltEs15(Left(xuu4910), Left(xuu5110), ty_Ordering, fd) → new_ltEs13(xuu4910, xuu5110)
new_lt19(xuu4910, xuu5110, ty_Ordering) → new_lt14(xuu4910, xuu5110)
new_esEs21(xuu3110001, xuu6001, ty_@0) → new_esEs17(xuu3110001, xuu6001)
new_lt21(xuu4911, xuu5111, ty_@0) → new_lt17(xuu4911, xuu5111)
new_primMulNat0(Zero, Zero) → Zero
new_ltEs15(Left(xuu4910), Left(xuu5110), app(ty_Maybe, fg), fd) → new_ltEs14(xuu4910, xuu5110, fg)
new_esEs6(Left(xuu3110000), Left(xuu6000), app(ty_[], bga), bfh) → new_esEs11(xuu3110000, xuu6000, bga)
new_esEs5(Just(xuu3110000), Just(xuu6000), app(ty_Ratio, dad)) → new_esEs16(xuu3110000, xuu6000, dad)
new_esEs6(Left(xuu3110000), Left(xuu6000), app(app(app(ty_@3, bge), bgf), bgg), bfh) → new_esEs7(xuu3110000, xuu6000, bge, bgf, bgg)
new_compare29(xuu4900, xuu5100, ty_Float) → new_compare16(xuu4900, xuu5100)
new_esEs20(xuu3110000, xuu6000, app(ty_Ratio, cdg)) → new_esEs16(xuu3110000, xuu6000, cdg)
new_esEs6(Left(xuu3110000), Left(xuu6000), app(ty_Ratio, bgh), bfh) → new_esEs16(xuu3110000, xuu6000, bgh)
new_ltEs15(Right(xuu4910), Right(xuu5110), ge, ty_Integer) → new_ltEs10(xuu4910, xuu5110)
new_esEs18(xuu490, xuu510, ty_Double) → new_esEs12(xuu490, xuu510)
new_ltEs15(Right(xuu4910), Right(xuu5110), ge, ty_Ordering) → new_ltEs13(xuu4910, xuu5110)
new_ltEs4(xuu491, xuu511, ty_Ordering) → new_ltEs13(xuu491, xuu511)
new_lt20(xuu4910, xuu5110, app(app(app(ty_@3, bag), bah), bba)) → new_lt18(xuu4910, xuu5110, bag, bah, bba)
new_esEs22(xuu3110002, xuu6002, ty_@0) → new_esEs17(xuu3110002, xuu6002)
new_compare10(xuu105, xuu106, xuu107, xuu108, True, bff, bfg) → LT
new_esEs28(xuu3110000, xuu6000, ty_Int) → new_esEs15(xuu3110000, xuu6000)
new_lt20(xuu4910, xuu5110, app(app(ty_@2, hg), hh)) → new_lt11(xuu4910, xuu5110, hg, hh)
new_compare1([], :(xuu5100, xuu5101), bdf) → LT
new_esEs19(xuu3110000, xuu6000, app(app(app(ty_@3, cbg), cbh), cca)) → new_esEs7(xuu3110000, xuu6000, cbg, cbh, cca)
new_lt21(xuu4911, xuu5111, app(ty_Ratio, chb)) → new_lt8(xuu4911, xuu5111, chb)
new_ltEs15(Right(xuu4910), Right(xuu5110), ge, app(ty_[], gh)) → new_ltEs11(xuu4910, xuu5110, gh)
new_esEs21(xuu3110001, xuu6001, ty_Int) → new_esEs15(xuu3110001, xuu6001)
new_ltEs13(LT, EQ) → True
new_ltEs15(Left(xuu4910), Left(xuu5110), ty_Int, fd) → new_ltEs7(xuu4910, xuu5110)
new_lt16(xuu490, xuu510) → new_esEs8(new_compare16(xuu490, xuu510), LT)
new_esEs11([], [], cbb) → True
new_esEs21(xuu3110001, xuu6001, app(app(app(ty_@3, cef), ceg), ceh)) → new_esEs7(xuu3110001, xuu6001, cef, ceg, ceh)
new_esEs5(Just(xuu3110000), Just(xuu6000), ty_Float) → new_esEs14(xuu3110000, xuu6000)
new_esEs5(Just(xuu3110000), Just(xuu6000), app(ty_Maybe, chf)) → new_esEs5(xuu3110000, xuu6000, chf)
new_esEs20(xuu3110000, xuu6000, ty_Char) → new_esEs10(xuu3110000, xuu6000)
new_esEs22(xuu3110002, xuu6002, ty_Integer) → new_esEs9(xuu3110002, xuu6002)
new_esEs6(Left(xuu3110000), Left(xuu6000), ty_Float, bfh) → new_esEs14(xuu3110000, xuu6000)
new_esEs21(xuu3110001, xuu6001, app(app(ty_Either, cfb), cfc)) → new_esEs6(xuu3110001, xuu6001, cfb, cfc)
new_esEs29(xuu3110001, xuu6001, app(app(app(ty_@3, ddb), ddc), ddd)) → new_esEs7(xuu3110001, xuu6001, ddb, ddc, ddd)
new_lt20(xuu4910, xuu5110, app(ty_Maybe, bad)) → new_lt15(xuu4910, xuu5110, bad)
new_lt20(xuu4910, xuu5110, app(ty_[], bac)) → new_lt13(xuu4910, xuu5110, bac)
new_ltEs4(xuu491, xuu511, ty_Double) → new_ltEs5(xuu491, xuu511)
new_compare15(xuu490, xuu510, False) → GT
new_esEs23(xuu4910, xuu5110, ty_Bool) → new_esEs13(xuu4910, xuu5110)
new_esEs17(@0, @0) → True
new_ltEs19(xuu4911, xuu5111, ty_Float) → new_ltEs16(xuu4911, xuu5111)
new_lt20(xuu4910, xuu5110, ty_Double) → new_lt7(xuu4910, xuu5110)
new_pePe(False, xuu129) → xuu129
new_compare29(xuu4900, xuu5100, app(ty_Maybe, beh)) → new_compare31(xuu4900, xuu5100, beh)
new_ltEs6(xuu491, xuu511, cag) → new_fsEs(new_compare30(xuu491, xuu511, cag))
new_esEs5(Just(xuu3110000), Just(xuu6000), ty_Bool) → new_esEs13(xuu3110000, xuu6000)
new_esEs6(Left(xuu3110000), Left(xuu6000), app(app(ty_@2, bgc), bgd), bfh) → new_esEs4(xuu3110000, xuu6000, bgc, bgd)
new_ltEs12(True, False) → False
new_esEs23(xuu4910, xuu5110, ty_Float) → new_esEs14(xuu4910, xuu5110)
new_lt6(xuu490, xuu510, ty_Double) → new_lt7(xuu490, xuu510)
new_esEs15(xuu311000, xuu600) → new_primEqInt(xuu311000, xuu600)
new_ltEs14(Just(xuu4910), Just(xuu5110), app(app(ty_@2, ea), eb)) → new_ltEs9(xuu4910, xuu5110, ea, eb)
new_compare29(xuu4900, xuu5100, app(app(ty_@2, bee), bef)) → new_compare12(xuu4900, xuu5100, bee, bef)
new_esEs29(xuu3110001, xuu6001, ty_@0) → new_esEs17(xuu3110001, xuu6001)
new_ltEs14(Just(xuu4910), Just(xuu5110), app(ty_Maybe, ed)) → new_ltEs14(xuu4910, xuu5110, ed)
new_ltEs19(xuu4911, xuu5111, app(ty_[], ce)) → new_ltEs11(xuu4911, xuu5111, ce)
new_ltEs15(Right(xuu4910), Right(xuu5110), ge, ty_Char) → new_ltEs8(xuu4910, xuu5110)
new_esEs22(xuu3110002, xuu6002, app(app(ty_@2, cff), cfg)) → new_esEs4(xuu3110002, xuu6002, cff, cfg)
new_compare15(xuu490, xuu510, True) → LT
new_esEs19(xuu3110000, xuu6000, ty_Float) → new_esEs14(xuu3110000, xuu6000)
new_ltEs20(xuu4912, xuu5112, ty_Double) → new_ltEs5(xuu4912, xuu5112)
new_compare9(xuu86, xuu85) → new_primCmpInt(xuu86, xuu85)
new_ltEs13(EQ, GT) → True
new_esEs22(xuu3110002, xuu6002, ty_Ordering) → new_esEs8(xuu3110002, xuu6002)
new_ltEs15(Right(xuu4910), Right(xuu5110), ge, ty_@0) → new_ltEs17(xuu4910, xuu5110)
new_lt21(xuu4911, xuu5111, ty_Char) → new_lt10(xuu4911, xuu5111)
new_esEs28(xuu3110000, xuu6000, app(ty_Ratio, dcc)) → new_esEs16(xuu3110000, xuu6000, dcc)
new_lt21(xuu4911, xuu5111, app(app(ty_Either, bbg), bbh)) → new_lt4(xuu4911, xuu5111, bbg, bbh)
new_ltEs14(Just(xuu4910), Just(xuu5110), ty_Int) → new_ltEs7(xuu4910, xuu5110)
new_esEs29(xuu3110001, xuu6001, app(ty_[], dcf)) → new_esEs11(xuu3110001, xuu6001, dcf)
new_esEs29(xuu3110001, xuu6001, app(app(ty_@2, dch), dda)) → new_esEs4(xuu3110001, xuu6001, dch, dda)
new_ltEs19(xuu4911, xuu5111, ty_Int) → new_ltEs7(xuu4911, xuu5111)
new_esEs18(xuu490, xuu510, app(app(ty_Either, bdh), bea)) → new_esEs6(xuu490, xuu510, bdh, bea)
new_esEs23(xuu4910, xuu5110, app(app(app(ty_@3, bg), bh), ca)) → new_esEs7(xuu4910, xuu5110, bg, bh, ca)
new_ltEs15(Left(xuu4910), Left(xuu5110), ty_Float, fd) → new_ltEs16(xuu4910, xuu5110)
new_lt6(xuu490, xuu510, app(app(ty_@2, de), df)) → new_lt11(xuu490, xuu510, de, df)
new_primCmpInt(Neg(Succ(xuu4900)), Neg(xuu510)) → new_primCmpNat1(xuu510, xuu4900)
new_primCompAux0(xuu4900, xuu5100, xuu130, bdf) → new_primCompAux00(xuu130, new_compare29(xuu4900, xuu5100, bdf))
new_esEs27(xuu4911, xuu5111, app(app(app(ty_@3, bca), bcb), bcc)) → new_esEs7(xuu4911, xuu5111, bca, bcb, bcc)
new_lt6(xuu490, xuu510, app(ty_[], bdf)) → new_lt13(xuu490, xuu510, bdf)
new_esEs26(xuu4910, xuu5110, ty_Double) → new_esEs12(xuu4910, xuu5110)
new_compare29(xuu4900, xuu5100, app(ty_[], beg)) → new_compare1(xuu4900, xuu5100, beg)
new_ltEs14(Just(xuu4910), Nothing, cah) → False
new_ltEs14(Just(xuu4910), Just(xuu5110), ty_Bool) → new_ltEs12(xuu4910, xuu5110)
new_esEs6(Right(xuu3110000), Left(xuu6000), bhc, bfh) → False
new_esEs6(Left(xuu3110000), Right(xuu6000), bhc, bfh) → False
new_esEs8(LT, LT) → True
new_compare29(xuu4900, xuu5100, app(app(app(ty_@3, bfc), bfd), bfe)) → new_compare19(xuu4900, xuu5100, bfc, bfd, bfe)
new_lt6(xuu490, xuu510, app(app(ty_Either, bdh), bea)) → new_lt4(xuu490, xuu510, bdh, bea)
new_esEs28(xuu3110000, xuu6000, app(ty_[], dbd)) → new_esEs11(xuu3110000, xuu6000, dbd)
new_ltEs4(xuu491, xuu511, ty_Float) → new_ltEs16(xuu491, xuu511)
new_esEs29(xuu3110001, xuu6001, ty_Char) → new_esEs10(xuu3110001, xuu6001)
new_esEs29(xuu3110001, xuu6001, ty_Bool) → new_esEs13(xuu3110001, xuu6001)
new_esEs18(xuu490, xuu510, app(ty_Ratio, caf)) → new_esEs16(xuu490, xuu510, caf)
new_lt19(xuu4910, xuu5110, app(app(ty_@2, h), ba)) → new_lt11(xuu4910, xuu5110, h, ba)
new_pePe(True, xuu129) → True
new_compare14(xuu490, xuu510, False, bdh, bea) → GT
new_primEqNat0(Zero, Zero) → True
new_ltEs19(xuu4911, xuu5111, app(ty_Maybe, cf)) → new_ltEs14(xuu4911, xuu5111, cf)
new_ltEs12(False, False) → True
new_esEs23(xuu4910, xuu5110, app(app(ty_Either, be), bf)) → new_esEs6(xuu4910, xuu5110, be, bf)
new_esEs5(Just(xuu3110000), Just(xuu6000), ty_@0) → new_esEs17(xuu3110000, xuu6000)
new_esEs5(Just(xuu3110000), Just(xuu6000), app(app(ty_@2, chg), chh)) → new_esEs4(xuu3110000, xuu6000, chg, chh)
new_esEs23(xuu4910, xuu5110, ty_Integer) → new_esEs9(xuu4910, xuu5110)
new_lt20(xuu4910, xuu5110, app(ty_Ratio, cha)) → new_lt8(xuu4910, xuu5110, cha)
new_compare12(xuu490, xuu510, de, df) → new_compare23(xuu490, xuu510, new_esEs4(xuu490, xuu510, de, df), de, df)
new_esEs20(xuu3110000, xuu6000, ty_Bool) → new_esEs13(xuu3110000, xuu6000)
new_esEs6(Right(xuu3110000), Right(xuu6000), bhc, app(app(ty_Either, cad), cae)) → new_esEs6(xuu3110000, xuu6000, cad, cae)
new_lt11(xuu490, xuu510, de, df) → new_esEs8(new_compare12(xuu490, xuu510, de, df), LT)
new_esEs25(xuu3110001, xuu6001, ty_Int) → new_esEs15(xuu3110001, xuu6001)
new_lt6(xuu490, xuu510, ty_Int) → new_lt9(xuu490, xuu510)
new_esEs18(xuu490, xuu510, ty_Char) → new_esEs10(xuu490, xuu510)
new_lt6(xuu490, xuu510, ty_Char) → new_lt10(xuu490, xuu510)
new_ltEs20(xuu4912, xuu5112, app(app(ty_@2, bcd), bce)) → new_ltEs9(xuu4912, xuu5112, bcd, bce)
new_sr(xuu3110001, xuu6001) → new_primMulInt(xuu3110001, xuu6001)
new_esEs28(xuu3110000, xuu6000, app(app(ty_Either, dcd), dce)) → new_esEs6(xuu3110000, xuu6000, dcd, dce)
new_lt13(xuu490, xuu510, bdf) → new_esEs8(new_compare1(xuu490, xuu510, bdf), LT)
new_compare10(xuu105, xuu106, xuu107, xuu108, False, bff, bfg) → GT
new_esEs26(xuu4910, xuu5110, ty_Ordering) → new_esEs8(xuu4910, xuu5110)
new_primCmpInt(Neg(Zero), Neg(Succ(xuu5100))) → new_primCmpNat0(xuu5100, Zero)
new_esEs8(GT, GT) → True
new_esEs20(xuu3110000, xuu6000, ty_Integer) → new_esEs9(xuu3110000, xuu6000)
new_primPlusNat0(Succ(xuu960), xuu600100) → Succ(Succ(new_primPlusNat1(xuu960, xuu600100)))
new_esEs27(xuu4911, xuu5111, ty_Char) → new_esEs10(xuu4911, xuu5111)
new_primCmpInt(Pos(Zero), Pos(Succ(xuu5100))) → new_primCmpNat1(Zero, xuu5100)
new_lt20(xuu4910, xuu5110, ty_Ordering) → new_lt14(xuu4910, xuu5110)
new_esEs20(xuu3110000, xuu6000, app(app(app(ty_@3, cdd), cde), cdf)) → new_esEs7(xuu3110000, xuu6000, cdd, cde, cdf)
new_ltEs19(xuu4911, xuu5111, ty_Bool) → new_ltEs12(xuu4911, xuu5111)
new_esEs8(LT, GT) → False
new_esEs8(GT, LT) → False
new_ltEs11(xuu491, xuu511, dh) → new_fsEs(new_compare1(xuu491, xuu511, dh))
new_ltEs20(xuu4912, xuu5112, ty_Float) → new_ltEs16(xuu4912, xuu5112)
new_lt21(xuu4911, xuu5111, app(app(app(ty_@3, bca), bcb), bcc)) → new_lt18(xuu4911, xuu5111, bca, bcb, bcc)
new_ltEs15(Left(xuu4910), Left(xuu5110), ty_@0, fd) → new_ltEs17(xuu4910, xuu5110)
new_esEs5(Just(xuu3110000), Just(xuu6000), ty_Double) → new_esEs12(xuu3110000, xuu6000)
new_esEs6(Left(xuu3110000), Left(xuu6000), ty_Int, bfh) → new_esEs15(xuu3110000, xuu6000)
new_compare28(xuu490, xuu510, False, bdh, bea) → new_compare14(xuu490, xuu510, new_ltEs15(xuu490, xuu510, bdh, bea), bdh, bea)
new_compare25(xuu490, xuu510, True) → EQ
new_primEqInt(Neg(Succ(xuu31100000)), Neg(Succ(xuu60000))) → new_primEqNat0(xuu31100000, xuu60000)
new_ltEs15(Left(xuu4910), Left(xuu5110), ty_Double, fd) → new_ltEs5(xuu4910, xuu5110)
new_esEs20(xuu3110000, xuu6000, ty_Ordering) → new_esEs8(xuu3110000, xuu6000)
new_esEs23(xuu4910, xuu5110, ty_Int) → new_esEs15(xuu4910, xuu5110)
new_esEs6(Right(xuu3110000), Right(xuu6000), bhc, app(app(app(ty_@3, bhh), caa), cab)) → new_esEs7(xuu3110000, xuu6000, bhh, caa, cab)
new_ltEs19(xuu4911, xuu5111, ty_Double) → new_ltEs5(xuu4911, xuu5111)
new_esEs23(xuu4910, xuu5110, ty_Ordering) → new_esEs8(xuu4910, xuu5110)
new_esEs27(xuu4911, xuu5111, ty_Bool) → new_esEs13(xuu4911, xuu5111)
new_ltEs14(Just(xuu4910), Just(xuu5110), ty_Ordering) → new_ltEs13(xuu4910, xuu5110)
new_primPlusNat1(Succ(xuu41200), Zero) → Succ(xuu41200)
new_primPlusNat1(Zero, Succ(xuu9200)) → Succ(xuu9200)
new_ltEs20(xuu4912, xuu5112, ty_Bool) → new_ltEs12(xuu4912, xuu5112)
new_esEs28(xuu3110000, xuu6000, ty_@0) → new_esEs17(xuu3110000, xuu6000)
new_esEs22(xuu3110002, xuu6002, ty_Int) → new_esEs15(xuu3110002, xuu6002)
new_esEs26(xuu4910, xuu5110, app(app(app(ty_@3, bag), bah), bba)) → new_esEs7(xuu4910, xuu5110, bag, bah, bba)
new_esEs20(xuu3110000, xuu6000, ty_Int) → new_esEs15(xuu3110000, xuu6000)
new_ltEs13(LT, GT) → True
new_primCmpNat1(Zero, xuu4900) → LT
new_lt20(xuu4910, xuu5110, app(app(ty_Either, bae), baf)) → new_lt4(xuu4910, xuu5110, bae, baf)
new_esEs6(Left(xuu3110000), Left(xuu6000), ty_Integer, bfh) → new_esEs9(xuu3110000, xuu6000)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_compare11(xuu105, xuu106, xuu107, xuu108, False, xuu110, bff, bfg) → new_compare10(xuu105, xuu106, xuu107, xuu108, xuu110, bff, bfg)
new_lt19(xuu4910, xuu5110, ty_Integer) → new_lt12(xuu4910, xuu5110)
new_lt6(xuu490, xuu510, app(ty_Ratio, caf)) → new_lt8(xuu490, xuu510, caf)
new_primEqInt(Neg(Succ(xuu31100000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(xuu60000))) → False
new_esEs8(EQ, EQ) → True
new_lt6(xuu490, xuu510, ty_Float) → new_lt16(xuu490, xuu510)
new_compare111(xuu490, xuu510, True, bdg) → LT
new_esEs24(xuu3110000, xuu6000, ty_Integer) → new_esEs9(xuu3110000, xuu6000)
new_ltEs15(Right(xuu4910), Right(xuu5110), ge, app(app(ty_@2, gf), gg)) → new_ltEs9(xuu4910, xuu5110, gf, gg)
new_esEs6(Left(xuu3110000), Left(xuu6000), ty_Char, bfh) → new_esEs10(xuu3110000, xuu6000)
new_esEs20(xuu3110000, xuu6000, ty_@0) → new_esEs17(xuu3110000, xuu6000)
new_lt21(xuu4911, xuu5111, ty_Float) → new_lt16(xuu4911, xuu5111)
new_ltEs7(xuu491, xuu511) → new_fsEs(new_compare9(xuu491, xuu511))
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_ltEs15(Left(xuu4910), Left(xuu5110), ty_Char, fd) → new_ltEs8(xuu4910, xuu5110)
new_ltEs16(xuu491, xuu511) → new_fsEs(new_compare16(xuu491, xuu511))
new_compare29(xuu4900, xuu5100, ty_Integer) → new_compare17(xuu4900, xuu5100)
new_ltEs15(Right(xuu4910), Right(xuu5110), ge, ty_Double) → new_ltEs5(xuu4910, xuu5110)
new_esEs9(Integer(xuu3110000), Integer(xuu6000)) → new_primEqInt(xuu3110000, xuu6000)
new_esEs11(:(xuu3110000, xuu3110001), :(xuu6000, xuu6001), cbb) → new_asAs(new_esEs19(xuu3110000, xuu6000, cbb), new_esEs11(xuu3110001, xuu6001, cbb))
new_ltEs13(GT, LT) → False
new_ltEs15(Right(xuu4910), Right(xuu5110), ge, ty_Int) → new_ltEs7(xuu4910, xuu5110)
new_primEqInt(Pos(Succ(xuu31100000)), Pos(Succ(xuu60000))) → new_primEqNat0(xuu31100000, xuu60000)
new_ltEs14(Just(xuu4910), Just(xuu5110), app(ty_Ratio, dag)) → new_ltEs6(xuu4910, xuu5110, dag)
new_esEs22(xuu3110002, xuu6002, ty_Bool) → new_esEs13(xuu3110002, xuu6002)
new_ltEs13(EQ, EQ) → True
new_esEs29(xuu3110001, xuu6001, app(ty_Maybe, dcg)) → new_esEs5(xuu3110001, xuu6001, dcg)
new_esEs19(xuu3110000, xuu6000, app(app(ty_Either, ccc), ccd)) → new_esEs6(xuu3110000, xuu6000, ccc, ccd)
new_esEs5(Just(xuu3110000), Just(xuu6000), ty_Char) → new_esEs10(xuu3110000, xuu6000)
new_lt14(xuu490, xuu510) → new_esEs8(new_compare13(xuu490, xuu510), LT)
new_primEqNat0(Succ(xuu31100000), Succ(xuu60000)) → new_primEqNat0(xuu31100000, xuu60000)
new_ltEs4(xuu491, xuu511, app(app(ty_@2, cb), bb)) → new_ltEs9(xuu491, xuu511, cb, bb)
new_esEs27(xuu4911, xuu5111, ty_Ordering) → new_esEs8(xuu4911, xuu5111)
new_lt5(xuu490, xuu510) → new_esEs8(new_compare7(xuu490, xuu510), LT)
new_esEs26(xuu4910, xuu5110, app(ty_[], bac)) → new_esEs11(xuu4910, xuu5110, bac)
new_primCompAux00(xuu134, LT) → LT
new_lt19(xuu4910, xuu5110, app(ty_[], bc)) → new_lt13(xuu4910, xuu5110, bc)
new_ltEs19(xuu4911, xuu5111, app(app(app(ty_@3, db), dc), dd)) → new_ltEs18(xuu4911, xuu5111, db, dc, dd)
new_esEs26(xuu4910, xuu5110, app(app(ty_@2, hg), hh)) → new_esEs4(xuu4910, xuu5110, hg, hh)
new_esEs6(Right(xuu3110000), Right(xuu6000), bhc, app(ty_Maybe, bhe)) → new_esEs5(xuu3110000, xuu6000, bhe)
new_lt15(xuu490, xuu510, bdg) → new_esEs8(new_compare31(xuu490, xuu510, bdg), LT)
new_esEs28(xuu3110000, xuu6000, ty_Ordering) → new_esEs8(xuu3110000, xuu6000)
new_compare1(:(xuu4900, xuu4901), :(xuu5100, xuu5101), bdf) → new_primCompAux0(xuu4900, xuu5100, new_compare1(xuu4901, xuu5101, bdf), bdf)
new_esEs8(LT, EQ) → False
new_esEs8(EQ, LT) → False
new_primEqInt(Pos(Succ(xuu31100000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(xuu60000))) → False
new_compare11(xuu105, xuu106, xuu107, xuu108, True, xuu110, bff, bfg) → new_compare10(xuu105, xuu106, xuu107, xuu108, True, bff, bfg)
new_esEs23(xuu4910, xuu5110, ty_@0) → new_esEs17(xuu4910, xuu5110)
new_esEs6(Left(xuu3110000), Left(xuu6000), ty_@0, bfh) → new_esEs17(xuu3110000, xuu6000)
new_compare29(xuu4900, xuu5100, app(ty_Ratio, cba)) → new_compare30(xuu4900, xuu5100, cba)
new_esEs19(xuu3110000, xuu6000, ty_Integer) → new_esEs9(xuu3110000, xuu6000)
new_compare25(xuu490, xuu510, False) → new_compare15(xuu490, xuu510, new_ltEs12(xuu490, xuu510))
new_lt20(xuu4910, xuu5110, ty_Bool) → new_lt5(xuu4910, xuu5110)
new_primCmpInt(Neg(Zero), Pos(Succ(xuu5100))) → LT
new_ltEs20(xuu4912, xuu5112, ty_Integer) → new_ltEs10(xuu4912, xuu5112)
new_ltEs10(xuu491, xuu511) → new_fsEs(new_compare17(xuu491, xuu511))
new_esEs18(xuu490, xuu510, app(app(app(ty_@3, beb), bec), bed)) → new_esEs7(xuu490, xuu510, beb, bec, bed)
new_ltEs15(Left(xuu4910), Left(xuu5110), app(ty_[], ff), fd) → new_ltEs11(xuu4910, xuu5110, ff)
new_esEs27(xuu4911, xuu5111, ty_Integer) → new_esEs9(xuu4911, xuu5111)
new_esEs28(xuu3110000, xuu6000, ty_Double) → new_esEs12(xuu3110000, xuu6000)
new_sr0(Integer(xuu51000), Integer(xuu49010)) → Integer(new_primMulInt(xuu51000, xuu49010))
new_primPlusNat1(Succ(xuu41200), Succ(xuu9200)) → Succ(Succ(new_primPlusNat1(xuu41200, xuu9200)))
new_lt21(xuu4911, xuu5111, app(app(ty_@2, bbc), bbd)) → new_lt11(xuu4911, xuu5111, bbc, bbd)
new_lt6(xuu490, xuu510, app(app(app(ty_@3, beb), bec), bed)) → new_lt18(xuu490, xuu510, beb, bec, bed)
new_compare28(xuu490, xuu510, True, bdh, bea) → EQ
new_primEqInt(Pos(Succ(xuu31100000)), Neg(xuu6000)) → False
new_primEqInt(Neg(Succ(xuu31100000)), Pos(xuu6000)) → False
new_compare210(xuu490, xuu510, True, bdg) → EQ
new_compare29(xuu4900, xuu5100, app(app(ty_Either, bfa), bfb)) → new_compare6(xuu4900, xuu5100, bfa, bfb)
new_esEs27(xuu4911, xuu5111, app(ty_Maybe, bbf)) → new_esEs5(xuu4911, xuu5111, bbf)
new_compare210(xuu490, xuu510, False, bdg) → new_compare111(xuu490, xuu510, new_ltEs14(xuu490, xuu510, bdg), bdg)
new_compare13(xuu490, xuu510) → new_compare24(xuu490, xuu510, new_esEs8(xuu490, xuu510))
new_ltEs4(xuu491, xuu511, ty_Char) → new_ltEs8(xuu491, xuu511)
new_lt19(xuu4910, xuu5110, ty_Bool) → new_lt5(xuu4910, xuu5110)
new_esEs18(xuu490, xuu510, app(app(ty_@2, de), df)) → new_esEs4(xuu490, xuu510, de, df)
new_esEs27(xuu4911, xuu5111, ty_Double) → new_esEs12(xuu4911, xuu5111)
new_esEs18(xuu490, xuu510, ty_Bool) → new_esEs13(xuu490, xuu510)
new_esEs11(:(xuu3110000, xuu3110001), [], cbb) → False
new_esEs11([], :(xuu6000, xuu6001), cbb) → False
new_esEs26(xuu4910, xuu5110, app(ty_Ratio, cha)) → new_esEs16(xuu4910, xuu5110, cha)
new_esEs12(Double(xuu3110000, xuu3110001), Double(xuu6000, xuu6001)) → new_esEs15(new_sr(xuu3110000, xuu6000), new_sr(xuu3110001, xuu6001))
new_primCmpNat2(Zero, Succ(xuu51000)) → LT
new_esEs22(xuu3110002, xuu6002, ty_Float) → new_esEs14(xuu3110002, xuu6002)
new_esEs10(Char(xuu3110000), Char(xuu6000)) → new_primEqNat0(xuu3110000, xuu6000)
new_primEqInt(Pos(Zero), Neg(Succ(xuu60000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(xuu60000))) → False
new_ltEs19(xuu4911, xuu5111, app(app(ty_@2, cc), cd)) → new_ltEs9(xuu4911, xuu5111, cc, cd)
new_esEs22(xuu3110002, xuu6002, app(ty_[], cfd)) → new_esEs11(xuu3110002, xuu6002, cfd)
new_primCompAux00(xuu134, EQ) → xuu134
new_esEs28(xuu3110000, xuu6000, ty_Char) → new_esEs10(xuu3110000, xuu6000)
new_compare24(xuu490, xuu510, True) → EQ
new_ltEs15(Right(xuu4910), Right(xuu5110), ge, app(ty_Ratio, dba)) → new_ltEs6(xuu4910, xuu5110, dba)
new_esEs23(xuu4910, xuu5110, ty_Char) → new_esEs10(xuu4910, xuu5110)
new_ltEs13(GT, EQ) → False
new_ltEs13(EQ, LT) → False
new_ltEs4(xuu491, xuu511, ty_Bool) → new_ltEs12(xuu491, xuu511)
new_esEs8(EQ, GT) → False
new_esEs8(GT, EQ) → False
new_esEs29(xuu3110001, xuu6001, ty_Double) → new_esEs12(xuu3110001, xuu6001)
new_compare24(xuu490, xuu510, False) → new_compare110(xuu490, xuu510, new_ltEs13(xuu490, xuu510))
new_ltEs4(xuu491, xuu511, app(ty_Maybe, cah)) → new_ltEs14(xuu491, xuu511, cah)
new_lt21(xuu4911, xuu5111, app(ty_[], bbe)) → new_lt13(xuu4911, xuu5111, bbe)
new_esEs27(xuu4911, xuu5111, app(ty_Ratio, chb)) → new_esEs16(xuu4911, xuu5111, chb)
new_ltEs14(Nothing, Just(xuu5110), cah) → True
new_ltEs14(Just(xuu4910), Just(xuu5110), ty_Integer) → new_ltEs10(xuu4910, xuu5110)
new_lt21(xuu4911, xuu5111, ty_Integer) → new_lt12(xuu4911, xuu5111)
new_ltEs19(xuu4911, xuu5111, ty_Char) → new_ltEs8(xuu4911, xuu5111)
new_lt6(xuu490, xuu510, ty_Bool) → new_lt5(xuu490, xuu510)
new_not(False) → True
new_lt21(xuu4911, xuu5111, app(ty_Maybe, bbf)) → new_lt15(xuu4911, xuu5111, bbf)
new_esEs6(Left(xuu3110000), Left(xuu6000), app(app(ty_Either, bha), bhb), bfh) → new_esEs6(xuu3110000, xuu6000, bha, bhb)
new_lt19(xuu4910, xuu5110, ty_Char) → new_lt10(xuu4910, xuu5110)
new_ltEs20(xuu4912, xuu5112, ty_Ordering) → new_ltEs13(xuu4912, xuu5112)
new_primPlusNat0(Zero, xuu600100) → Succ(xuu600100)
new_ltEs14(Just(xuu4910), Just(xuu5110), ty_@0) → new_ltEs17(xuu4910, xuu5110)
new_esEs19(xuu3110000, xuu6000, ty_Double) → new_esEs12(xuu3110000, xuu6000)
new_esEs20(xuu3110000, xuu6000, ty_Float) → new_esEs14(xuu3110000, xuu6000)
new_esEs20(xuu3110000, xuu6000, app(ty_[], cch)) → new_esEs11(xuu3110000, xuu6000, cch)
new_ltEs14(Just(xuu4910), Just(xuu5110), app(app(ty_Either, ee), ef)) → new_ltEs15(xuu4910, xuu5110, ee, ef)
new_ltEs15(Left(xuu4910), Left(xuu5110), ty_Integer, fd) → new_ltEs10(xuu4910, xuu5110)
new_ltEs19(xuu4911, xuu5111, app(app(ty_Either, cg), da)) → new_ltEs15(xuu4911, xuu5111, cg, da)
new_esEs6(Left(xuu3110000), Left(xuu6000), ty_Bool, bfh) → new_esEs13(xuu3110000, xuu6000)
new_esEs29(xuu3110001, xuu6001, ty_Int) → new_esEs15(xuu3110001, xuu6001)
new_esEs27(xuu4911, xuu5111, app(app(ty_Either, bbg), bbh)) → new_esEs6(xuu4911, xuu5111, bbg, bbh)
new_lt7(xuu490, xuu510) → new_esEs8(new_compare8(xuu490, xuu510), LT)
new_esEs6(Right(xuu3110000), Right(xuu6000), bhc, app(ty_[], bhd)) → new_esEs11(xuu3110000, xuu6000, bhd)
new_esEs24(xuu3110000, xuu6000, ty_Int) → new_esEs15(xuu3110000, xuu6000)
new_lt6(xuu490, xuu510, ty_@0) → new_lt17(xuu490, xuu510)
new_ltEs4(xuu491, xuu511, ty_@0) → new_ltEs17(xuu491, xuu511)
new_ltEs20(xuu4912, xuu5112, ty_@0) → new_ltEs17(xuu4912, xuu5112)
new_esEs22(xuu3110002, xuu6002, app(app(app(ty_@3, cfh), cga), cgb)) → new_esEs7(xuu3110002, xuu6002, cfh, cga, cgb)
new_primCmpInt(Pos(Succ(xuu4900)), Neg(xuu510)) → GT
new_esEs26(xuu4910, xuu5110, ty_@0) → new_esEs17(xuu4910, xuu5110)
new_lt18(xuu490, xuu510, beb, bec, bed) → new_esEs8(new_compare19(xuu490, xuu510, beb, bec, bed), LT)
new_esEs29(xuu3110001, xuu6001, ty_Integer) → new_esEs9(xuu3110001, xuu6001)
new_esEs5(Just(xuu3110000), Just(xuu6000), ty_Int) → new_esEs15(xuu3110000, xuu6000)
new_lt19(xuu4910, xuu5110, ty_Float) → new_lt16(xuu4910, xuu5110)
new_primMulInt(Pos(xuu31100010), Pos(xuu60010)) → Pos(new_primMulNat0(xuu31100010, xuu60010))
new_ltEs4(xuu491, xuu511, app(app(ty_Either, ge), fd)) → new_ltEs15(xuu491, xuu511, ge, fd)
new_esEs21(xuu3110001, xuu6001, app(app(ty_@2, ced), cee)) → new_esEs4(xuu3110001, xuu6001, ced, cee)
new_esEs6(Right(xuu3110000), Right(xuu6000), bhc, ty_Bool) → new_esEs13(xuu3110000, xuu6000)
new_esEs28(xuu3110000, xuu6000, app(app(app(ty_@3, dbh), dca), dcb)) → new_esEs7(xuu3110000, xuu6000, dbh, dca, dcb)
new_esEs19(xuu3110000, xuu6000, ty_Bool) → new_esEs13(xuu3110000, xuu6000)
new_esEs7(@3(xuu3110000, xuu3110001, xuu3110002), @3(xuu6000, xuu6001, xuu6002), cce, ccf, ccg) → new_asAs(new_esEs20(xuu3110000, xuu6000, cce), new_asAs(new_esEs21(xuu3110001, xuu6001, ccf), new_esEs22(xuu3110002, xuu6002, ccg)))
new_primMulInt(Neg(xuu31100010), Neg(xuu60010)) → Pos(new_primMulNat0(xuu31100010, xuu60010))
new_primCmpNat2(Zero, Zero) → EQ
new_ltEs19(xuu4911, xuu5111, app(ty_Ratio, cgg)) → new_ltEs6(xuu4911, xuu5111, cgg)
new_esEs21(xuu3110001, xuu6001, ty_Char) → new_esEs10(xuu3110001, xuu6001)
new_compare110(xuu490, xuu510, True) → LT
new_ltEs19(xuu4911, xuu5111, ty_Integer) → new_ltEs10(xuu4911, xuu5111)
new_primEqNat0(Zero, Succ(xuu60000)) → False
new_primEqNat0(Succ(xuu31100000), Zero) → False
new_esEs6(Right(xuu3110000), Right(xuu6000), bhc, ty_Double) → new_esEs12(xuu3110000, xuu6000)
new_lt20(xuu4910, xuu5110, ty_@0) → new_lt17(xuu4910, xuu5110)
new_compare110(xuu490, xuu510, False) → GT
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_ltEs20(xuu4912, xuu5112, ty_Int) → new_ltEs7(xuu4912, xuu5112)
new_lt9(xuu490, xuu510) → new_esEs8(new_compare9(xuu490, xuu510), LT)
new_compare30(:%(xuu4900, xuu4901), :%(xuu5100, xuu5101), ty_Integer) → new_compare17(new_sr0(xuu4900, xuu5101), new_sr0(xuu5100, xuu4901))
new_esEs6(Right(xuu3110000), Right(xuu6000), bhc, ty_Float) → new_esEs14(xuu3110000, xuu6000)
new_primCmpNat2(Succ(xuu49000), Succ(xuu51000)) → new_primCmpNat2(xuu49000, xuu51000)
new_primCmpInt(Pos(Succ(xuu4900)), Pos(xuu510)) → new_primCmpNat0(xuu4900, xuu510)
new_esEs20(xuu3110000, xuu6000, app(app(ty_Either, cdh), cea)) → new_esEs6(xuu3110000, xuu6000, cdh, cea)
new_compare31(xuu490, xuu510, bdg) → new_compare210(xuu490, xuu510, new_esEs5(xuu490, xuu510, bdg), bdg)
new_ltEs14(Just(xuu4910), Just(xuu5110), ty_Double) → new_ltEs5(xuu4910, xuu5110)
new_primCmpNat0(xuu4900, Zero) → GT
new_esEs19(xuu3110000, xuu6000, app(ty_Maybe, cbd)) → new_esEs5(xuu3110000, xuu6000, cbd)
new_esEs18(xuu490, xuu510, ty_@0) → new_esEs17(xuu490, xuu510)
new_esEs29(xuu3110001, xuu6001, app(app(ty_Either, ddf), ddg)) → new_esEs6(xuu3110001, xuu6001, ddf, ddg)
new_ltEs19(xuu4911, xuu5111, ty_@0) → new_ltEs17(xuu4911, xuu5111)
new_esEs26(xuu4910, xuu5110, app(ty_Maybe, bad)) → new_esEs5(xuu4910, xuu5110, bad)
new_compare112(xuu490, xuu510, True, beb, bec, bed) → LT
new_compare23(xuu49, xuu51, True, dg, bde) → EQ
new_primCmpInt(Pos(Zero), Neg(Succ(xuu5100))) → GT
new_esEs18(xuu490, xuu510, ty_Float) → new_esEs14(xuu490, xuu510)
new_lt17(xuu490, xuu510) → new_esEs8(new_compare27(xuu490, xuu510), LT)
new_esEs6(Left(xuu3110000), Left(xuu6000), ty_Ordering, bfh) → new_esEs8(xuu3110000, xuu6000)
new_ltEs20(xuu4912, xuu5112, ty_Char) → new_ltEs8(xuu4912, xuu5112)
new_lt20(xuu4910, xuu5110, ty_Float) → new_lt16(xuu4910, xuu5110)
new_ltEs4(xuu491, xuu511, app(app(app(ty_@3, bbb), baa), bab)) → new_ltEs18(xuu491, xuu511, bbb, baa, bab)
new_compare26(xuu490, xuu510, False, beb, bec, bed) → new_compare112(xuu490, xuu510, new_ltEs18(xuu490, xuu510, beb, bec, bed), beb, bec, bed)
new_esEs27(xuu4911, xuu5111, ty_@0) → new_esEs17(xuu4911, xuu5111)
new_esEs6(Right(xuu3110000), Right(xuu6000), bhc, app(app(ty_@2, bhf), bhg)) → new_esEs4(xuu3110000, xuu6000, bhf, bhg)
new_compare29(xuu4900, xuu5100, ty_Ordering) → new_compare13(xuu4900, xuu5100)
new_esEs23(xuu4910, xuu5110, app(ty_[], bc)) → new_esEs11(xuu4910, xuu5110, bc)
new_ltEs20(xuu4912, xuu5112, app(ty_Maybe, bcg)) → new_ltEs14(xuu4912, xuu5112, bcg)
new_lt8(xuu490, xuu510, caf) → new_esEs8(new_compare30(xuu490, xuu510, caf), LT)
new_esEs6(Right(xuu3110000), Right(xuu6000), bhc, ty_Integer) → new_esEs9(xuu3110000, xuu6000)
new_ltEs15(Right(xuu4910), Right(xuu5110), ge, ty_Float) → new_ltEs16(xuu4910, xuu5110)
new_lt19(xuu4910, xuu5110, app(app(ty_Either, be), bf)) → new_lt4(xuu4910, xuu5110, be, bf)
new_esEs23(xuu4910, xuu5110, app(ty_Ratio, cgf)) → new_esEs16(xuu4910, xuu5110, cgf)
new_esEs22(xuu3110002, xuu6002, app(ty_Ratio, cgc)) → new_esEs16(xuu3110002, xuu6002, cgc)
new_ltEs14(Just(xuu4910), Just(xuu5110), app(ty_[], ec)) → new_ltEs11(xuu4910, xuu5110, ec)
new_esEs4(@2(xuu3110000, xuu3110001), @2(xuu6000, xuu6001), dbb, dbc) → new_asAs(new_esEs28(xuu3110000, xuu6000, dbb), new_esEs29(xuu3110001, xuu6001, dbc))
new_esEs18(xuu490, xuu510, app(ty_[], bdf)) → new_esEs11(xuu490, xuu510, bdf)
new_lt20(xuu4910, xuu5110, ty_Char) → new_lt10(xuu4910, xuu5110)
new_ltEs20(xuu4912, xuu5112, app(app(ty_Either, bch), bda)) → new_ltEs15(xuu4912, xuu5112, bch, bda)
new_esEs28(xuu3110000, xuu6000, ty_Integer) → new_esEs9(xuu3110000, xuu6000)
new_esEs19(xuu3110000, xuu6000, app(ty_Ratio, ccb)) → new_esEs16(xuu3110000, xuu6000, ccb)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_ltEs15(Right(xuu4910), Right(xuu5110), ge, app(ty_Maybe, ha)) → new_ltEs14(xuu4910, xuu5110, ha)
new_ltEs4(xuu491, xuu511, ty_Integer) → new_ltEs10(xuu491, xuu511)
new_esEs6(Left(xuu3110000), Left(xuu6000), ty_Double, bfh) → new_esEs12(xuu3110000, xuu6000)
new_compare29(xuu4900, xuu5100, ty_Int) → new_compare9(xuu4900, xuu5100)
new_esEs20(xuu3110000, xuu6000, app(ty_Maybe, cda)) → new_esEs5(xuu3110000, xuu6000, cda)
new_ltEs13(GT, GT) → True
new_ltEs4(xuu491, xuu511, app(ty_Ratio, cag)) → new_ltEs6(xuu491, xuu511, cag)
new_esEs28(xuu3110000, xuu6000, app(app(ty_@2, dbf), dbg)) → new_esEs4(xuu3110000, xuu6000, dbf, dbg)
new_asAs(False, xuu59) → False
new_esEs22(xuu3110002, xuu6002, ty_Double) → new_esEs12(xuu3110002, xuu6002)
new_lt6(xuu490, xuu510, ty_Integer) → new_lt12(xuu490, xuu510)
new_primMulInt(Neg(xuu31100010), Pos(xuu60010)) → Neg(new_primMulNat0(xuu31100010, xuu60010))
new_primMulInt(Pos(xuu31100010), Neg(xuu60010)) → Neg(new_primMulNat0(xuu31100010, xuu60010))
new_ltEs20(xuu4912, xuu5112, app(ty_[], bcf)) → new_ltEs11(xuu4912, xuu5112, bcf)
new_compare23(@2(xuu490, xuu491), @2(xuu510, xuu511), False, dg, bde) → new_compare11(xuu490, xuu491, xuu510, xuu511, new_lt6(xuu490, xuu510, dg), new_asAs(new_esEs18(xuu490, xuu510, dg), new_ltEs4(xuu491, xuu511, bde)), dg, bde)
new_primMulNat0(Succ(xuu311000100), Zero) → Zero
new_primMulNat0(Zero, Succ(xuu600100)) → Zero
new_ltEs14(Just(xuu4910), Just(xuu5110), ty_Float) → new_ltEs16(xuu4910, xuu5110)
new_compare29(xuu4900, xuu5100, ty_Char) → new_compare18(xuu4900, xuu5100)
new_esEs21(xuu3110001, xuu6001, ty_Ordering) → new_esEs8(xuu3110001, xuu6001)
new_esEs21(xuu3110001, xuu6001, ty_Bool) → new_esEs13(xuu3110001, xuu6001)
new_lt6(xuu490, xuu510, ty_Ordering) → new_lt14(xuu490, xuu510)
new_compare17(Integer(xuu4900), Integer(xuu5100)) → new_primCmpInt(xuu4900, xuu5100)
new_esEs5(Just(xuu3110000), Just(xuu6000), app(ty_[], che)) → new_esEs11(xuu3110000, xuu6000, che)
new_esEs19(xuu3110000, xuu6000, app(ty_[], cbc)) → new_esEs11(xuu3110000, xuu6000, cbc)
new_esEs5(Just(xuu3110000), Just(xuu6000), ty_Integer) → new_esEs9(xuu3110000, xuu6000)
new_esEs6(Right(xuu3110000), Right(xuu6000), bhc, app(ty_Ratio, cac)) → new_esEs16(xuu3110000, xuu6000, cac)
new_ltEs8(xuu491, xuu511) → new_fsEs(new_compare18(xuu491, xuu511))
new_lt19(xuu4910, xuu5110, app(app(app(ty_@3, bg), bh), ca)) → new_lt18(xuu4910, xuu5110, bg, bh, ca)
new_lt21(xuu4911, xuu5111, ty_Int) → new_lt9(xuu4911, xuu5111)
new_esEs18(xuu490, xuu510, app(ty_Maybe, bdg)) → new_esEs5(xuu490, xuu510, bdg)
new_primCmpNat1(Succ(xuu5100), xuu4900) → new_primCmpNat2(xuu5100, xuu4900)
new_esEs22(xuu3110002, xuu6002, ty_Char) → new_esEs10(xuu3110002, xuu6002)
new_ltEs12(True, True) → True
new_primCmpNat2(Succ(xuu49000), Zero) → GT
new_esEs18(xuu490, xuu510, ty_Ordering) → new_esEs8(xuu490, xuu510)
new_esEs29(xuu3110001, xuu6001, app(ty_Ratio, dde)) → new_esEs16(xuu3110001, xuu6001, dde)
new_esEs13(False, False) → True
new_esEs21(xuu3110001, xuu6001, ty_Integer) → new_esEs9(xuu3110001, xuu6001)
new_ltEs20(xuu4912, xuu5112, app(app(app(ty_@3, bdb), bdc), bdd)) → new_ltEs18(xuu4912, xuu5112, bdb, bdc, bdd)
new_esEs23(xuu4910, xuu5110, app(ty_Maybe, bd)) → new_esEs5(xuu4910, xuu5110, bd)
new_esEs29(xuu3110001, xuu6001, ty_Float) → new_esEs14(xuu3110001, xuu6001)
new_esEs16(:%(xuu3110000, xuu3110001), :%(xuu6000, xuu6001), cgh) → new_asAs(new_esEs24(xuu3110000, xuu6000, cgh), new_esEs25(xuu3110001, xuu6001, cgh))
new_esEs6(Right(xuu3110000), Right(xuu6000), bhc, ty_Char) → new_esEs10(xuu3110000, xuu6000)
new_esEs6(Left(xuu3110000), Left(xuu6000), app(ty_Maybe, bgb), bfh) → new_esEs5(xuu3110000, xuu6000, bgb)
new_esEs26(xuu4910, xuu5110, ty_Integer) → new_esEs9(xuu4910, xuu5110)
new_ltEs12(False, True) → True
new_esEs20(xuu3110000, xuu6000, app(app(ty_@2, cdb), cdc)) → new_esEs4(xuu3110000, xuu6000, cdb, cdc)
new_compare29(xuu4900, xuu5100, ty_@0) → new_compare27(xuu4900, xuu5100)
new_compare112(xuu490, xuu510, False, beb, bec, bed) → GT
new_compare30(:%(xuu4900, xuu4901), :%(xuu5100, xuu5101), ty_Int) → new_compare9(new_sr(xuu4900, xuu5101), new_sr(xuu5100, xuu4901))
new_ltEs15(Right(xuu4910), Right(xuu5110), ge, ty_Bool) → new_ltEs12(xuu4910, xuu5110)
new_compare111(xuu490, xuu510, False, bdg) → GT
new_esEs21(xuu3110001, xuu6001, app(ty_Ratio, cfa)) → new_esEs16(xuu3110001, xuu6001, cfa)
new_esEs5(Just(xuu3110000), Nothing, chd) → False
new_esEs5(Nothing, Just(xuu6000), chd) → False
new_esEs18(xuu490, xuu510, ty_Int) → new_esEs15(xuu490, xuu510)
new_lt19(xuu4910, xuu5110, ty_@0) → new_lt17(xuu4910, xuu5110)
new_compare16(Float(xuu4900, xuu4901), Float(xuu5100, xuu5101)) → new_compare9(new_sr(xuu4900, xuu5100), new_sr(xuu4901, xuu5101))
new_lt19(xuu4910, xuu5110, ty_Int) → new_lt9(xuu4910, xuu5110)
new_esEs6(Right(xuu3110000), Right(xuu6000), bhc, ty_@0) → new_esEs17(xuu3110000, xuu6000)
new_esEs27(xuu4911, xuu5111, app(app(ty_@2, bbc), bbd)) → new_esEs4(xuu4911, xuu5111, bbc, bbd)
new_lt21(xuu4911, xuu5111, ty_Bool) → new_lt5(xuu4911, xuu5111)
new_esEs27(xuu4911, xuu5111, app(ty_[], bbe)) → new_esEs11(xuu4911, xuu5111, bbe)
new_esEs27(xuu4911, xuu5111, ty_Int) → new_esEs15(xuu4911, xuu5111)
new_compare8(Double(xuu4900, xuu4901), Double(xuu5100, xuu5101)) → new_compare9(new_sr(xuu4900, xuu5100), new_sr(xuu4901, xuu5101))
new_esEs5(Just(xuu3110000), Just(xuu6000), app(app(ty_Either, dae), daf)) → new_esEs6(xuu3110000, xuu6000, dae, daf)
new_lt20(xuu4910, xuu5110, ty_Integer) → new_lt12(xuu4910, xuu5110)
new_ltEs18(@3(xuu4910, xuu4911, xuu4912), @3(xuu5110, xuu5111, xuu5112), bbb, baa, bab) → new_pePe(new_lt20(xuu4910, xuu5110, bbb), new_asAs(new_esEs26(xuu4910, xuu5110, bbb), new_pePe(new_lt21(xuu4911, xuu5111, baa), new_asAs(new_esEs27(xuu4911, xuu5111, baa), new_ltEs20(xuu4912, xuu5112, bab)))))
new_esEs5(Nothing, Nothing, chd) → True
new_ltEs20(xuu4912, xuu5112, app(ty_Ratio, chc)) → new_ltEs6(xuu4912, xuu5112, chc)
new_esEs26(xuu4910, xuu5110, ty_Char) → new_esEs10(xuu4910, xuu5110)
new_esEs22(xuu3110002, xuu6002, app(app(ty_Either, cgd), cge)) → new_esEs6(xuu3110002, xuu6002, cgd, cge)
new_esEs28(xuu3110000, xuu6000, app(ty_Maybe, dbe)) → new_esEs5(xuu3110000, xuu6000, dbe)
new_lt12(xuu490, xuu510) → new_esEs8(new_compare17(xuu490, xuu510), LT)
new_esEs5(Just(xuu3110000), Just(xuu6000), app(app(app(ty_@3, daa), dab), dac)) → new_esEs7(xuu3110000, xuu6000, daa, dab, dac)
new_esEs28(xuu3110000, xuu6000, ty_Bool) → new_esEs13(xuu3110000, xuu6000)
new_esEs21(xuu3110001, xuu6001, ty_Double) → new_esEs12(xuu3110001, xuu6001)
new_compare14(xuu490, xuu510, True, bdh, bea) → LT
new_ltEs14(Just(xuu4910), Just(xuu5110), ty_Char) → new_ltEs8(xuu4910, xuu5110)
new_esEs21(xuu3110001, xuu6001, app(ty_[], ceb)) → new_esEs11(xuu3110001, xuu6001, ceb)
new_ltEs15(Left(xuu4910), Left(xuu5110), app(ty_Ratio, dah), fd) → new_ltEs6(xuu4910, xuu5110, dah)
new_ltEs15(Right(xuu4910), Right(xuu5110), ge, app(app(ty_Either, hb), hc)) → new_ltEs15(xuu4910, xuu5110, hb, hc)
new_compare29(xuu4900, xuu5100, ty_Bool) → new_compare7(xuu4900, xuu5100)
new_ltEs13(LT, LT) → True
new_esEs23(xuu4910, xuu5110, ty_Double) → new_esEs12(xuu4910, xuu5110)
new_compare7(xuu490, xuu510) → new_compare25(xuu490, xuu510, new_esEs13(xuu490, xuu510))
new_esEs22(xuu3110002, xuu6002, app(ty_Maybe, cfe)) → new_esEs5(xuu3110002, xuu6002, cfe)
new_compare26(xuu490, xuu510, True, beb, bec, bed) → EQ
new_esEs21(xuu3110001, xuu6001, app(ty_Maybe, cec)) → new_esEs5(xuu3110001, xuu6001, cec)
new_lt4(xuu490, xuu510, bdh, bea) → new_esEs8(new_compare6(xuu490, xuu510, bdh, bea), LT)
new_esEs26(xuu4910, xuu5110, app(app(ty_Either, bae), baf)) → new_esEs6(xuu4910, xuu5110, bae, baf)
new_primPlusNat1(Zero, Zero) → Zero
new_esEs14(Float(xuu3110000, xuu3110001), Float(xuu6000, xuu6001)) → new_esEs15(new_sr(xuu3110000, xuu6000), new_sr(xuu3110001, xuu6001))
new_ltEs14(Nothing, Nothing, cah) → True
new_esEs19(xuu3110000, xuu6000, ty_@0) → new_esEs17(xuu3110000, xuu6000)
new_asAs(True, xuu59) → xuu59
new_esEs26(xuu4910, xuu5110, ty_Float) → new_esEs14(xuu4910, xuu5110)
new_compare27(@0, @0) → EQ
new_ltEs4(xuu491, xuu511, app(ty_[], dh)) → new_ltEs11(xuu491, xuu511, dh)
new_primMulNat0(Succ(xuu311000100), Succ(xuu600100)) → new_primPlusNat0(new_primMulNat0(xuu311000100, Succ(xuu600100)), xuu600100)
new_esEs13(True, True) → True
new_ltEs14(Just(xuu4910), Just(xuu5110), app(app(app(ty_@3, eg), eh), fa)) → new_ltEs18(xuu4910, xuu5110, eg, eh, fa)
new_compare1(:(xuu4900, xuu4901), [], bdf) → GT
new_esEs19(xuu3110000, xuu6000, ty_Char) → new_esEs10(xuu3110000, xuu6000)
new_fsEs(xuu117) → new_not(new_esEs8(xuu117, GT))
new_ltEs15(Left(xuu4910), Left(xuu5110), ty_Bool, fd) → new_ltEs12(xuu4910, xuu5110)
new_lt6(xuu490, xuu510, app(ty_Maybe, bdg)) → new_lt15(xuu490, xuu510, bdg)
new_esEs18(xuu490, xuu510, ty_Integer) → new_esEs9(xuu490, xuu510)
new_esEs19(xuu3110000, xuu6000, ty_Int) → new_esEs15(xuu3110000, xuu6000)
new_lt20(xuu4910, xuu5110, ty_Int) → new_lt9(xuu4910, xuu5110)
new_esEs19(xuu3110000, xuu6000, ty_Ordering) → new_esEs8(xuu3110000, xuu6000)
new_esEs27(xuu4911, xuu5111, ty_Float) → new_esEs14(xuu4911, xuu5111)
new_ltEs15(Left(xuu4910), Left(xuu5110), app(app(ty_Either, fh), ga), fd) → new_ltEs15(xuu4910, xuu5110, fh, ga)
new_ltEs15(Left(xuu4910), Right(xuu5110), ge, fd) → True
new_lt19(xuu4910, xuu5110, app(ty_Ratio, cgf)) → new_lt8(xuu4910, xuu5110, cgf)
new_ltEs17(xuu491, xuu511) → new_fsEs(new_compare27(xuu491, xuu511))
new_esEs26(xuu4910, xuu5110, ty_Int) → new_esEs15(xuu4910, xuu5110)
new_ltEs4(xuu491, xuu511, ty_Int) → new_ltEs7(xuu491, xuu511)
new_ltEs9(@2(xuu4910, xuu4911), @2(xuu5110, xuu5111), cb, bb) → new_pePe(new_lt19(xuu4910, xuu5110, cb), new_asAs(new_esEs23(xuu4910, xuu5110, cb), new_ltEs19(xuu4911, xuu5111, bb)))
new_ltEs15(Left(xuu4910), Left(xuu5110), app(app(ty_@2, fb), fc), fd) → new_ltEs9(xuu4910, xuu5110, fb, fc)
new_primCompAux00(xuu134, GT) → GT
new_compare18(Char(xuu4900), Char(xuu5100)) → new_primCmpNat2(xuu4900, xuu5100)
new_ltEs15(Right(xuu4910), Right(xuu5110), ge, app(app(app(ty_@3, hd), he), hf)) → new_ltEs18(xuu4910, xuu5110, hd, he, hf)
new_ltEs15(Left(xuu4910), Left(xuu5110), app(app(app(ty_@3, gb), gc), gd), fd) → new_ltEs18(xuu4910, xuu5110, gb, gc, gd)
new_esEs26(xuu4910, xuu5110, ty_Bool) → new_esEs13(xuu4910, xuu5110)
new_esEs6(Right(xuu3110000), Right(xuu6000), bhc, ty_Ordering) → new_esEs8(xuu3110000, xuu6000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs29(xuu3110001, xuu6001, ty_Ordering) → new_esEs8(xuu3110001, xuu6001)
new_esEs19(xuu3110000, xuu6000, app(app(ty_@2, cbe), cbf)) → new_esEs4(xuu3110000, xuu6000, cbe, cbf)
new_ltEs15(Right(xuu4910), Left(xuu5110), ge, fd) → False
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_ltEs5(xuu491, xuu511) → new_fsEs(new_compare8(xuu491, xuu511))
new_esEs6(Right(xuu3110000), Right(xuu6000), bhc, ty_Int) → new_esEs15(xuu3110000, xuu6000)
new_primCmpInt(Neg(Succ(xuu4900)), Pos(xuu510)) → LT
new_lt21(xuu4911, xuu5111, ty_Double) → new_lt7(xuu4911, xuu5111)
new_ltEs19(xuu4911, xuu5111, ty_Ordering) → new_ltEs13(xuu4911, xuu5111)
new_not(True) → False
new_esEs25(xuu3110001, xuu6001, ty_Integer) → new_esEs9(xuu3110001, xuu6001)
new_compare1([], [], bdf) → EQ

The set Q consists of the following terms:

new_compare29(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs4(x0, x1, app(ty_Ratio, x2))
new_ltEs15(Right(x0), Right(x1), x2, ty_Integer)
new_primCmpNat2(Succ(x0), Succ(x1))
new_esEs18(x0, x1, ty_Int)
new_lt21(x0, x1, ty_Int)
new_esEs29(x0, x1, ty_Ordering)
new_compare29(x0, x1, ty_Bool)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_lt4(x0, x1, x2, x3)
new_lt21(x0, x1, ty_Float)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs18(x0, x1, app(ty_Ratio, x2))
new_esEs18(x0, x1, ty_Double)
new_primEqNat0(Zero, Succ(x0))
new_ltEs17(x0, x1)
new_esEs28(x0, x1, app(ty_[], x2))
new_ltEs15(Right(x0), Right(x1), x2, ty_Bool)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_lt6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare29(x0, x1, app(ty_Ratio, x2))
new_compare1(:(x0, x1), [], x2)
new_lt21(x0, x1, app(ty_[], x2))
new_esEs6(Left(x0), Left(x1), ty_Double, x2)
new_esEs6(Right(x0), Left(x1), x2, x3)
new_esEs6(Left(x0), Right(x1), x2, x3)
new_ltEs14(Just(x0), Just(x1), ty_Integer)
new_ltEs20(x0, x1, ty_Float)
new_ltEs15(Right(x0), Right(x1), x2, ty_Double)
new_ltEs10(x0, x1)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs18(x0, x1, ty_Ordering)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_compare26(x0, x1, False, x2, x3, x4)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, ty_Double)
new_compare29(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_@0)
new_esEs22(x0, x1, ty_Char)
new_esEs28(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, ty_Bool)
new_compare30(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs27(x0, x1, ty_Char)
new_ltEs18(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs5(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs14(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs19(x0, x1, ty_Char)
new_esEs12(Double(x0, x1), Double(x2, x3))
new_ltEs15(Right(x0), Right(x1), x2, ty_Float)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(GT, GT)
new_lt6(x0, x1, app(ty_[], x2))
new_lt9(x0, x1)
new_primCmpNat0(x0, Zero)
new_esEs27(x0, x1, ty_Ordering)
new_lt21(x0, x1, ty_Char)
new_esEs6(Left(x0), Left(x1), ty_Int, x2)
new_esEs5(Just(x0), Nothing, x1)
new_esEs8(LT, LT)
new_compare14(x0, x1, True, x2, x3)
new_ltEs4(x0, x1, ty_Integer)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_esEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs5(Just(x0), Just(x1), ty_Ordering)
new_ltEs15(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs14(Just(x0), Just(x1), ty_Ordering)
new_ltEs14(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_lt6(x0, x1, ty_Ordering)
new_lt6(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_Double)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs11(x0, x1, x2)
new_lt8(x0, x1, x2)
new_ltEs15(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_compare29(x0, x1, app(ty_[], x2))
new_compare25(x0, x1, False)
new_esEs27(x0, x1, app(ty_[], x2))
new_compare112(x0, x1, True, x2, x3, x4)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs16(:%(x0, x1), :%(x2, x3), x4)
new_ltEs4(x0, x1, app(app(ty_Either, x2), x3))
new_compare18(Char(x0), Char(x1))
new_esEs18(x0, x1, ty_Bool)
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_asAs(True, x0)
new_compare17(Integer(x0), Integer(x1))
new_esEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, ty_Double)
new_esEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Left(x0), Left(x1), ty_@0, x2)
new_ltEs15(Left(x0), Left(x1), app(ty_[], x2), x3)
new_pePe(True, x0)
new_lt19(x0, x1, ty_@0)
new_primEqNat0(Zero, Zero)
new_esEs18(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs15(Left(x0), Left(x1), ty_Char, x2)
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs25(x0, x1, ty_Int)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, ty_Int)
new_esEs11([], :(x0, x1), x2)
new_esEs5(Just(x0), Just(x1), ty_Char)
new_compare1(:(x0, x1), :(x2, x3), x4)
new_ltEs13(EQ, EQ)
new_esEs5(Nothing, Just(x0), x1)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare29(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Char)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_compare9(x0, x1)
new_esEs26(x0, x1, ty_Ordering)
new_esEs19(x0, x1, ty_Ordering)
new_ltEs15(Right(x0), Right(x1), x2, ty_Int)
new_esEs13(False, False)
new_primMulNat0(Zero, Zero)
new_esEs23(x0, x1, ty_Bool)
new_esEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Double)
new_esEs19(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_compare29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs18(x0, x1, ty_@0)
new_esEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs14(Just(x0), Just(x1), app(ty_[], x2))
new_lt6(x0, x1, ty_Bool)
new_compare29(x0, x1, ty_@0)
new_lt20(x0, x1, ty_Float)
new_ltEs13(LT, EQ)
new_ltEs13(EQ, LT)
new_lt5(x0, x1)
new_lt20(x0, x1, ty_Integer)
new_primCmpNat2(Zero, Succ(x0))
new_esEs18(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Int)
new_esEs5(Just(x0), Just(x1), ty_Double)
new_ltEs15(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs29(x0, x1, ty_Int)
new_lt6(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs8(x0, x1)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primMulNat0(Zero, Succ(x0))
new_compare28(x0, x1, True, x2, x3)
new_esEs5(Nothing, Nothing, x0)
new_compare26(x0, x1, True, x2, x3, x4)
new_ltEs15(Right(x0), Right(x1), x2, ty_Char)
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, ty_Char)
new_ltEs14(Just(x0), Just(x1), ty_Double)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_compare10(x0, x1, x2, x3, True, x4, x5)
new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs14(Just(x0), Just(x1), ty_Bool)
new_lt19(x0, x1, app(ty_[], x2))
new_asAs(False, x0)
new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs26(x0, x1, ty_Integer)
new_esEs20(x0, x1, app(ty_[], x2))
new_ltEs12(False, False)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_lt17(x0, x1)
new_esEs6(Right(x0), Right(x1), x2, ty_Int)
new_lt19(x0, x1, ty_Double)
new_esEs19(x0, x1, ty_Int)
new_lt18(x0, x1, x2, x3, x4)
new_esEs21(x0, x1, ty_Ordering)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs4(x0, x1, app(ty_[], x2))
new_compare1([], :(x0, x1), x2)
new_primCompAux00(x0, LT)
new_esEs21(x0, x1, ty_Integer)
new_esEs6(Right(x0), Right(x1), x2, ty_@0)
new_esEs22(x0, x1, ty_Bool)
new_ltEs4(x0, x1, ty_Double)
new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs25(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_Float)
new_esEs5(Just(x0), Just(x1), ty_Bool)
new_ltEs15(Right(x0), Right(x1), x2, ty_@0)
new_primPlusNat1(Zero, Zero)
new_esEs22(x0, x1, ty_Float)
new_primCmpNat2(Zero, Zero)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpNat1(Zero, x0)
new_ltEs14(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs6(Left(x0), Left(x1), ty_Integer, x2)
new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_compare29(x0, x1, ty_Float)
new_esEs29(x0, x1, ty_Double)
new_lt16(x0, x1)
new_ltEs15(Left(x0), Left(x1), ty_Double, x2)
new_esEs15(x0, x1)
new_primCompAux00(x0, EQ)
new_esEs5(Just(x0), Just(x1), ty_Int)
new_ltEs4(x0, x1, ty_Char)
new_esEs14(Float(x0, x1), Float(x2, x3))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs23(x0, x1, ty_Float)
new_ltEs4(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, ty_Bool)
new_ltEs19(x0, x1, ty_@0)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_ltEs5(x0, x1)
new_esEs22(x0, x1, ty_Ordering)
new_lt20(x0, x1, ty_Int)
new_primPlusNat1(Zero, Succ(x0))
new_esEs17(@0, @0)
new_compare29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, app(ty_[], x2))
new_lt10(x0, x1)
new_ltEs15(Right(x0), Right(x1), x2, app(ty_[], x3))
new_pePe(False, x0)
new_primCmpNat2(Succ(x0), Zero)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_ltEs6(x0, x1, x2)
new_primCmpNat1(Succ(x0), x1)
new_esEs28(x0, x1, ty_Char)
new_ltEs4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs13(EQ, GT)
new_ltEs13(GT, EQ)
new_esEs24(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_Float)
new_lt21(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs14(Just(x0), Just(x1), ty_Char)
new_esEs6(Left(x0), Left(x1), ty_Bool, x2)
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs19(x0, x1, ty_@0)
new_lt21(x0, x1, app(ty_Ratio, x2))
new_lt7(x0, x1)
new_esEs19(x0, x1, ty_Double)
new_ltEs15(Left(x0), Left(x1), ty_Integer, x2)
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs15(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs23(x0, x1, ty_Integer)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_ltEs15(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_compare15(x0, x1, True)
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_Float)
new_esEs20(x0, x1, ty_Int)
new_lt20(x0, x1, ty_@0)
new_compare28(x0, x1, False, x2, x3)
new_esEs26(x0, x1, ty_@0)
new_ltEs13(LT, GT)
new_ltEs13(GT, LT)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_compare14(x0, x1, False, x2, x3)
new_esEs26(x0, x1, ty_Float)
new_sr(x0, x1)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs14(Nothing, Just(x0), x1)
new_esEs18(x0, x1, ty_Integer)
new_ltEs20(x0, x1, ty_Char)
new_compare23(@2(x0, x1), @2(x2, x3), False, x4, x5)
new_esEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Right(x0), Right(x1), x2, ty_Float)
new_compare7(x0, x1)
new_esEs22(x0, x1, ty_@0)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_esEs11(:(x0, x1), [], x2)
new_esEs18(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_primPlusNat0(Zero, x0)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Neg(Zero), Neg(Zero))
new_compare19(x0, x1, x2, x3, x4)
new_compare112(x0, x1, False, x2, x3, x4)
new_compare210(x0, x1, False, x2)
new_ltEs15(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Bool)
new_esEs19(x0, x1, ty_Bool)
new_lt6(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Float)
new_ltEs7(x0, x1)
new_compare6(x0, x1, x2, x3)
new_primCmpNat0(x0, Succ(x1))
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_compare12(x0, x1, x2, x3)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs29(x0, x1, ty_Char)
new_lt6(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_Bool)
new_ltEs15(Left(x0), Left(x1), ty_Float, x2)
new_lt21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1, ty_Float)
new_lt21(x0, x1, ty_Ordering)
new_compare23(x0, x1, True, x2, x3)
new_esEs6(Right(x0), Right(x1), x2, ty_Integer)
new_esEs21(x0, x1, ty_Float)
new_esEs20(x0, x1, ty_Ordering)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, ty_Double)
new_compare31(x0, x1, x2)
new_ltEs15(Right(x0), Left(x1), x2, x3)
new_ltEs15(Left(x0), Right(x1), x2, x3)
new_lt6(x0, x1, ty_Float)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(GT, EQ)
new_esEs8(EQ, GT)
new_ltEs14(Just(x0), Just(x1), ty_@0)
new_esEs26(x0, x1, ty_Int)
new_ltEs12(False, True)
new_ltEs15(Left(x0), Left(x1), ty_@0, x2)
new_ltEs12(True, False)
new_ltEs15(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs6(Right(x0), Right(x1), x2, ty_Double)
new_esEs22(x0, x1, ty_Int)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_ltEs4(x0, x1, ty_Float)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Left(x0), Left(x1), ty_Char, x2)
new_ltEs19(x0, x1, app(ty_[], x2))
new_primEqNat0(Succ(x0), Zero)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_compare210(x0, x1, True, x2)
new_ltEs15(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs16(x0, x1)
new_esEs18(x0, x1, ty_Float)
new_ltEs14(Just(x0), Just(x1), ty_Float)
new_lt20(x0, x1, app(ty_[], x2))
new_primMulInt(Pos(x0), Pos(x1))
new_ltEs15(Left(x0), Left(x1), ty_Int, x2)
new_compare15(x0, x1, False)
new_compare25(x0, x1, True)
new_compare29(x0, x1, ty_Char)
new_ltEs13(LT, LT)
new_esEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_lt21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_lt21(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, ty_Integer)
new_ltEs4(x0, x1, ty_Ordering)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare111(x0, x1, False, x2)
new_ltEs15(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt19(x0, x1, ty_Ordering)
new_lt15(x0, x1, x2)
new_esEs28(x0, x1, ty_@0)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_Integer)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Char)
new_esEs11([], [], x0)
new_lt20(x0, x1, ty_Ordering)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs29(x0, x1, ty_Float)
new_lt6(x0, x1, ty_Int)
new_ltEs15(Left(x0), Left(x1), ty_Bool, x2)
new_lt13(x0, x1, x2)
new_compare29(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_Int)
new_lt21(x0, x1, ty_@0)
new_ltEs13(GT, GT)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs13(False, True)
new_esEs13(True, False)
new_esEs22(x0, x1, ty_Integer)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_compare8(Double(x0, x1), Double(x2, x3))
new_lt21(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_@0)
new_esEs23(x0, x1, ty_@0)
new_esEs18(x0, x1, ty_Char)
new_compare110(x0, x1, True)
new_ltEs14(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_compare29(x0, x1, app(ty_Maybe, x2))
new_compare13(x0, x1)
new_compare11(x0, x1, x2, x3, True, x4, x5, x6)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, ty_Double)
new_ltEs14(Just(x0), Just(x1), app(ty_Maybe, x2))
new_compare111(x0, x1, True, x2)
new_esEs5(Just(x0), Just(x1), ty_@0)
new_ltEs4(x0, x1, app(ty_Maybe, x2))
new_not(True)
new_esEs28(x0, x1, ty_Int)
new_esEs28(x0, x1, ty_Bool)
new_esEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, ty_Double)
new_compare24(x0, x1, False)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs13(True, True)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_ltEs14(Nothing, Nothing, x0)
new_lt14(x0, x1)
new_esEs29(x0, x1, ty_@0)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, ty_Bool)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_not(False)
new_compare110(x0, x1, False)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_ltEs4(x0, x1, ty_Bool)
new_lt6(x0, x1, ty_@0)
new_ltEs9(@2(x0, x1), @2(x2, x3), x4, x5)
new_compare30(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs11(:(x0, x1), :(x2, x3), x4)
new_esEs5(Just(x0), Just(x1), ty_Float)
new_ltEs12(True, True)
new_esEs23(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_@0)
new_esEs22(x0, x1, ty_Double)
new_compare24(x0, x1, True)
new_lt6(x0, x1, ty_Char)
new_ltEs4(x0, x1, ty_@0)
new_esEs6(Right(x0), Right(x1), x2, ty_Bool)
new_esEs9(Integer(x0), Integer(x1))
new_ltEs19(x0, x1, ty_Bool)
new_esEs19(x0, x1, ty_Float)
new_esEs27(x0, x1, ty_Double)
new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_lt11(x0, x1, x2, x3)
new_esEs20(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_Ordering)
new_esEs27(x0, x1, ty_Bool)
new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_lt19(x0, x1, ty_Bool)
new_ltEs14(Just(x0), Just(x1), ty_Int)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_compare16(Float(x0, x1), Float(x2, x3))
new_compare29(x0, x1, ty_Double)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Just(x0), Just(x1), ty_Integer)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_lt21(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_@0)
new_ltEs20(x0, x1, ty_Integer)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_lt6(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_lt12(x0, x1)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_fsEs(x0)
new_compare27(@0, @0)
new_esEs6(Right(x0), Right(x1), x2, ty_Char)
new_esEs19(x0, x1, ty_Integer)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primCompAux00(x0, GT)
new_esEs26(x0, x1, ty_Char)
new_sr0(Integer(x0), Integer(x1))
new_esEs21(x0, x1, ty_Bool)
new_primMulNat0(Succ(x0), Zero)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs10(Char(x0), Char(x1))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs21(x0, x1, ty_Char)
new_primPlusNat1(Succ(x0), Zero)
new_ltEs19(x0, x1, ty_Integer)
new_primEqInt(Pos(Zero), Pos(Zero))
new_primMulNat0(Succ(x0), Succ(x1))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_primEqNat0(Succ(x0), Succ(x1))
new_primCompAux0(x0, x1, x2, x3)
new_esEs23(x0, x1, ty_Int)
new_lt19(x0, x1, ty_Int)
new_esEs18(x0, x1, app(ty_[], x2))
new_lt21(x0, x1, ty_Double)
new_esEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs23(x0, x1, ty_Ordering)
new_compare11(x0, x1, x2, x3, False, x4, x5, x6)
new_ltEs15(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt6(x0, x1, app(ty_Maybe, x2))
new_compare1([], [], x0)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs15(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs29(x0, x1, ty_Integer)
new_primPlusNat0(Succ(x0), x1)
new_esEs6(Left(x0), Left(x1), ty_Float, x2)
new_ltEs15(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_compare10(x0, x1, x2, x3, False, x4, x5)
new_ltEs4(x0, x1, ty_Int)
new_esEs28(x0, x1, ty_Integer)
new_ltEs14(Just(x0), Nothing, x1)
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Double)
new_esEs21(x0, x1, ty_Int)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))

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

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



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

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

new_addToFM_C(Branch(@2(xuu600, xuu601), xuu61, xuu62, xuu63, xuu64), @2(xuu311000, xuu311001), xuu31101, bc, bd, be) → new_addToFM_C2(xuu600, xuu601, xuu61, xuu62, xuu63, xuu64, xuu311000, xuu311001, xuu31101, new_esEs30(xuu311000, xuu311001, xuu600, xuu601, new_esEs31(xuu311000, xuu600, bc), bc, bd), bc, bd, be)
new_addToFM_C2(xuu19, xuu20, xuu21, xuu22, xuu23, xuu24, xuu25, xuu26, xuu27, False, h, ba, bb) → new_addToFM_C1(xuu19, xuu20, xuu21, xuu22, xuu23, xuu24, xuu25, xuu26, xuu27, new_esEs8(new_compare23(@2(xuu25, xuu26), @2(xuu19, xuu20), new_esEs4(@2(xuu25, xuu26), @2(xuu19, xuu20), h, ba), h, ba), GT), h, ba, bb)
new_addToFM_C2(xuu19, xuu20, xuu21, xuu22, xuu23, xuu24, xuu25, xuu26, xuu27, True, h, ba, bb) → new_addToFM_C(xuu23, @2(xuu25, xuu26), xuu27, h, ba, bb)
new_addToFM_C1(xuu19, xuu20, xuu21, xuu22, xuu23, xuu24, xuu25, xuu26, xuu27, True, h, ba, bb) → new_addToFM_C(xuu24, @2(xuu25, xuu26), xuu27, h, ba, bb)

The TRS R consists of the following rules:

new_lt10(xuu490, xuu510) → new_esEs8(new_compare18(xuu490, xuu510), LT)
new_primCmpNat0(xuu4900, Succ(xuu5100)) → new_primCmpNat2(xuu4900, xuu5100)
new_compare19(xuu490, xuu510, ga, gb, gc) → new_compare26(xuu490, xuu510, new_esEs7(xuu490, xuu510, ga, gb, gc), ga, gb, gc)
new_lt19(xuu4910, xuu5110, app(ty_Maybe, bhd)) → new_lt15(xuu4910, xuu5110, bhd)
new_lt19(xuu4910, xuu5110, ty_Double) → new_lt7(xuu4910, xuu5110)
new_esEs21(xuu3110001, xuu6001, ty_Float) → new_esEs14(xuu3110001, xuu6001)
new_esEs13(False, True) → False
new_esEs13(True, False) → False
new_esEs5(Just(xuu3110000), Just(xuu6000), ty_Ordering) → new_esEs8(xuu3110000, xuu6000)
new_esEs31(xuu311000, xuu600, ty_Ordering) → new_esEs8(xuu311000, xuu600)
new_esEs23(xuu4910, xuu5110, app(app(ty_@2, bha), bhb)) → new_esEs4(xuu4910, xuu5110, bha, bhb)
new_esEs28(xuu3110000, xuu6000, ty_Float) → new_esEs14(xuu3110000, xuu6000)
new_compare6(xuu490, xuu510, bf, bg) → new_compare28(xuu490, xuu510, new_esEs6(xuu490, xuu510, bf, bg), bf, bg)
new_lt21(xuu4911, xuu5111, ty_Ordering) → new_lt14(xuu4911, xuu5111)
new_compare29(xuu4900, xuu5100, ty_Double) → new_compare8(xuu4900, xuu5100)
new_esEs20(xuu3110000, xuu6000, ty_Double) → new_esEs12(xuu3110000, xuu6000)
new_esEs31(xuu311000, xuu600, ty_@0) → new_esEs17(xuu311000, xuu600)
new_ltEs15(Left(xuu4910), Left(xuu5110), ty_Ordering, hb) → new_ltEs13(xuu4910, xuu5110)
new_lt19(xuu4910, xuu5110, ty_Ordering) → new_lt14(xuu4910, xuu5110)
new_esEs21(xuu3110001, xuu6001, ty_@0) → new_esEs17(xuu3110001, xuu6001)
new_lt21(xuu4911, xuu5111, ty_@0) → new_lt17(xuu4911, xuu5111)
new_primMulNat0(Zero, Zero) → Zero
new_ltEs15(Left(xuu4910), Left(xuu5110), app(ty_Maybe, dbf), hb) → new_ltEs14(xuu4910, xuu5110, dbf)
new_esEs6(Left(xuu3110000), Left(xuu6000), app(ty_[], cc), cb) → new_esEs11(xuu3110000, xuu6000, cc)
new_esEs5(Just(xuu3110000), Just(xuu6000), app(ty_Ratio, cga)) → new_esEs16(xuu3110000, xuu6000, cga)
new_esEs6(Left(xuu3110000), Left(xuu6000), app(app(app(ty_@3, cg), da), db), cb) → new_esEs7(xuu3110000, xuu6000, cg, da, db)
new_compare29(xuu4900, xuu5100, ty_Float) → new_compare16(xuu4900, xuu5100)
new_esEs20(xuu3110000, xuu6000, app(ty_Ratio, bea)) → new_esEs16(xuu3110000, xuu6000, bea)
new_esEs6(Left(xuu3110000), Left(xuu6000), app(ty_Ratio, dc), cb) → new_esEs16(xuu3110000, xuu6000, dc)
new_ltEs15(Right(xuu4910), Right(xuu5110), ha, ty_Integer) → new_ltEs10(xuu4910, xuu5110)
new_esEs18(xuu490, xuu510, ty_Double) → new_esEs12(xuu490, xuu510)
new_ltEs15(Right(xuu4910), Right(xuu5110), ha, ty_Ordering) → new_ltEs13(xuu4910, xuu5110)
new_ltEs4(xuu491, xuu511, ty_Ordering) → new_ltEs13(xuu491, xuu511)
new_lt20(xuu4910, xuu5110, app(app(app(ty_@3, ccc), ccd), cce)) → new_lt18(xuu4910, xuu5110, ccc, ccd, cce)
new_esEs22(xuu3110002, xuu6002, ty_@0) → new_esEs17(xuu3110002, xuu6002)
new_compare10(xuu105, xuu106, xuu107, xuu108, True, bh, ca) → LT
new_esEs28(xuu3110000, xuu6000, ty_Int) → new_esEs15(xuu3110000, xuu6000)
new_lt20(xuu4910, xuu5110, app(app(ty_@2, cbe), cbf)) → new_lt11(xuu4910, xuu5110, cbe, cbf)
new_compare1([], :(xuu5100, xuu5101), fg) → LT
new_esEs32(xuu37, xuu39, ty_Bool) → new_esEs13(xuu37, xuu39)
new_esEs19(xuu3110000, xuu6000, app(app(app(ty_@3, bcd), bce), bcf)) → new_esEs7(xuu3110000, xuu6000, bcd, bce, bcf)
new_lt21(xuu4911, xuu5111, app(ty_Ratio, ccf)) → new_lt8(xuu4911, xuu5111, ccf)
new_ltEs15(Right(xuu4910), Right(xuu5110), ha, app(ty_[], dcg)) → new_ltEs11(xuu4910, xuu5110, dcg)
new_esEs21(xuu3110001, xuu6001, ty_Int) → new_esEs15(xuu3110001, xuu6001)
new_ltEs13(LT, EQ) → True
new_ltEs15(Left(xuu4910), Left(xuu5110), ty_Int, hb) → new_ltEs7(xuu4910, xuu5110)
new_lt16(xuu490, xuu510) → new_esEs8(new_compare16(xuu490, xuu510), LT)
new_esEs11([], [], hf) → True
new_esEs32(xuu37, xuu39, app(app(ty_@2, dab), dac)) → new_esEs4(xuu37, xuu39, dab, dac)
new_esEs21(xuu3110001, xuu6001, app(app(app(ty_@3, beh), bfa), bfb)) → new_esEs7(xuu3110001, xuu6001, beh, bfa, bfb)
new_esEs5(Just(xuu3110000), Just(xuu6000), app(ty_Maybe, cfc)) → new_esEs5(xuu3110000, xuu6000, cfc)
new_esEs5(Just(xuu3110000), Just(xuu6000), ty_Float) → new_esEs14(xuu3110000, xuu6000)
new_esEs20(xuu3110000, xuu6000, ty_Char) → new_esEs10(xuu3110000, xuu6000)
new_esEs22(xuu3110002, xuu6002, ty_Integer) → new_esEs9(xuu3110002, xuu6002)
new_esEs6(Left(xuu3110000), Left(xuu6000), ty_Float, cb) → new_esEs14(xuu3110000, xuu6000)
new_esEs21(xuu3110001, xuu6001, app(app(ty_Either, bfd), bfe)) → new_esEs6(xuu3110001, xuu6001, bfd, bfe)
new_esEs29(xuu3110001, xuu6001, app(app(app(ty_@3, dfd), dfe), dff)) → new_esEs7(xuu3110001, xuu6001, dfd, dfe, dff)
new_lt20(xuu4910, xuu5110, app(ty_Maybe, cbh)) → new_lt15(xuu4910, xuu5110, cbh)
new_lt20(xuu4910, xuu5110, app(ty_[], cbg)) → new_lt13(xuu4910, xuu5110, cbg)
new_ltEs4(xuu491, xuu511, ty_Double) → new_ltEs5(xuu491, xuu511)
new_compare15(xuu490, xuu510, False) → GT
new_esEs23(xuu4910, xuu5110, ty_Bool) → new_esEs13(xuu4910, xuu5110)
new_esEs17(@0, @0) → True
new_ltEs19(xuu4911, xuu5111, ty_Float) → new_ltEs16(xuu4911, xuu5111)
new_lt20(xuu4910, xuu5110, ty_Double) → new_lt7(xuu4910, xuu5110)
new_pePe(False, xuu129) → xuu129
new_compare29(xuu4900, xuu5100, app(ty_Maybe, bbb)) → new_compare31(xuu4900, xuu5100, bbb)
new_ltEs6(xuu491, xuu511, gd) → new_fsEs(new_compare30(xuu491, xuu511, gd))
new_esEs5(Just(xuu3110000), Just(xuu6000), ty_Bool) → new_esEs13(xuu3110000, xuu6000)
new_esEs6(Left(xuu3110000), Left(xuu6000), app(app(ty_@2, ce), cf), cb) → new_esEs4(xuu3110000, xuu6000, ce, cf)
new_ltEs12(True, False) → False
new_esEs23(xuu4910, xuu5110, ty_Float) → new_esEs14(xuu4910, xuu5110)
new_lt6(xuu490, xuu510, ty_Double) → new_lt7(xuu490, xuu510)
new_esEs15(xuu311000, xuu600) → new_primEqInt(xuu311000, xuu600)
new_ltEs14(Just(xuu4910), Just(xuu5110), app(app(ty_@2, cge), cgf)) → new_ltEs9(xuu4910, xuu5110, cge, cgf)
new_compare29(xuu4900, xuu5100, app(app(ty_@2, bag), bah)) → new_compare12(xuu4900, xuu5100, bag, bah)
new_esEs29(xuu3110001, xuu6001, ty_@0) → new_esEs17(xuu3110001, xuu6001)
new_ltEs14(Just(xuu4910), Just(xuu5110), app(ty_Maybe, cgh)) → new_ltEs14(xuu4910, xuu5110, cgh)
new_ltEs19(xuu4911, xuu5111, app(ty_[], cae)) → new_ltEs11(xuu4911, xuu5111, cae)
new_ltEs15(Right(xuu4910), Right(xuu5110), ha, ty_Char) → new_ltEs8(xuu4910, xuu5110)
new_esEs22(xuu3110002, xuu6002, app(app(ty_@2, bfh), bga)) → new_esEs4(xuu3110002, xuu6002, bfh, bga)
new_compare15(xuu490, xuu510, True) → LT
new_esEs19(xuu3110000, xuu6000, ty_Float) → new_esEs14(xuu3110000, xuu6000)
new_ltEs20(xuu4912, xuu5112, ty_Double) → new_ltEs5(xuu4912, xuu5112)
new_compare9(xuu86, xuu85) → new_primCmpInt(xuu86, xuu85)
new_ltEs13(EQ, GT) → True
new_esEs22(xuu3110002, xuu6002, ty_Ordering) → new_esEs8(xuu3110002, xuu6002)
new_ltEs15(Right(xuu4910), Right(xuu5110), ha, ty_@0) → new_ltEs17(xuu4910, xuu5110)
new_lt21(xuu4911, xuu5111, ty_Char) → new_lt10(xuu4911, xuu5111)
new_esEs28(xuu3110000, xuu6000, app(ty_Ratio, dee)) → new_esEs16(xuu3110000, xuu6000, dee)
new_lt21(xuu4911, xuu5111, app(app(ty_Either, cdc), cdd)) → new_lt4(xuu4911, xuu5111, cdc, cdd)
new_ltEs14(Just(xuu4910), Just(xuu5110), ty_Int) → new_ltEs7(xuu4910, xuu5110)
new_esEs29(xuu3110001, xuu6001, app(ty_[], deh)) → new_esEs11(xuu3110001, xuu6001, deh)
new_esEs29(xuu3110001, xuu6001, app(app(ty_@2, dfb), dfc)) → new_esEs4(xuu3110001, xuu6001, dfb, dfc)
new_esEs31(xuu311000, xuu600, ty_Char) → new_esEs10(xuu311000, xuu600)
new_ltEs19(xuu4911, xuu5111, ty_Int) → new_ltEs7(xuu4911, xuu5111)
new_esEs18(xuu490, xuu510, app(app(ty_Either, bf), bg)) → new_esEs6(xuu490, xuu510, bf, bg)
new_esEs23(xuu4910, xuu5110, app(app(app(ty_@3, bhg), bhh), caa)) → new_esEs7(xuu4910, xuu5110, bhg, bhh, caa)
new_ltEs15(Left(xuu4910), Left(xuu5110), ty_Float, hb) → new_ltEs16(xuu4910, xuu5110)
new_lt6(xuu490, xuu510, app(app(ty_@2, fd), ff)) → new_lt11(xuu490, xuu510, fd, ff)
new_primCmpInt(Neg(Succ(xuu4900)), Neg(xuu510)) → new_primCmpNat1(xuu510, xuu4900)
new_primCompAux0(xuu4900, xuu5100, xuu130, fg) → new_primCompAux00(xuu130, new_compare29(xuu4900, xuu5100, fg))
new_esEs27(xuu4911, xuu5111, app(app(app(ty_@3, cde), cdf), cdg)) → new_esEs7(xuu4911, xuu5111, cde, cdf, cdg)
new_lt6(xuu490, xuu510, app(ty_[], fg)) → new_lt13(xuu490, xuu510, fg)
new_esEs26(xuu4910, xuu5110, ty_Double) → new_esEs12(xuu4910, xuu5110)
new_compare29(xuu4900, xuu5100, app(ty_[], bba)) → new_compare1(xuu4900, xuu5100, bba)
new_esEs31(xuu311000, xuu600, app(app(ty_@2, hh), baa)) → new_esEs4(xuu311000, xuu600, hh, baa)
new_ltEs14(Just(xuu4910), Nothing, gh) → False
new_ltEs14(Just(xuu4910), Just(xuu5110), ty_Bool) → new_ltEs12(xuu4910, xuu5110)
new_esEs6(Right(xuu3110000), Left(xuu6000), df, cb) → False
new_esEs6(Left(xuu3110000), Right(xuu6000), df, cb) → False
new_esEs31(xuu311000, xuu600, ty_Int) → new_esEs15(xuu311000, xuu600)
new_esEs8(LT, LT) → True
new_esEs31(xuu311000, xuu600, app(ty_Maybe, hg)) → new_esEs5(xuu311000, xuu600, hg)
new_compare29(xuu4900, xuu5100, app(app(app(ty_@3, bbe), bbf), bbg)) → new_compare19(xuu4900, xuu5100, bbe, bbf, bbg)
new_lt6(xuu490, xuu510, app(app(ty_Either, bf), bg)) → new_lt4(xuu490, xuu510, bf, bg)
new_esEs28(xuu3110000, xuu6000, app(ty_[], ddf)) → new_esEs11(xuu3110000, xuu6000, ddf)
new_ltEs4(xuu491, xuu511, ty_Float) → new_ltEs16(xuu491, xuu511)
new_esEs29(xuu3110001, xuu6001, ty_Char) → new_esEs10(xuu3110001, xuu6001)
new_esEs29(xuu3110001, xuu6001, ty_Bool) → new_esEs13(xuu3110001, xuu6001)
new_esEs18(xuu490, xuu510, app(ty_Ratio, fc)) → new_esEs16(xuu490, xuu510, fc)
new_lt19(xuu4910, xuu5110, app(app(ty_@2, bha), bhb)) → new_lt11(xuu4910, xuu5110, bha, bhb)
new_pePe(True, xuu129) → True
new_compare14(xuu490, xuu510, False, bf, bg) → GT
new_primEqNat0(Zero, Zero) → True
new_ltEs19(xuu4911, xuu5111, app(ty_Maybe, caf)) → new_ltEs14(xuu4911, xuu5111, caf)
new_ltEs12(False, False) → True
new_esEs23(xuu4910, xuu5110, app(app(ty_Either, bhe), bhf)) → new_esEs6(xuu4910, xuu5110, bhe, bhf)
new_esEs5(Just(xuu3110000), Just(xuu6000), ty_@0) → new_esEs17(xuu3110000, xuu6000)
new_esEs5(Just(xuu3110000), Just(xuu6000), app(app(ty_@2, cfd), cfe)) → new_esEs4(xuu3110000, xuu6000, cfd, cfe)
new_esEs23(xuu4910, xuu5110, ty_Integer) → new_esEs9(xuu4910, xuu5110)
new_lt20(xuu4910, xuu5110, app(ty_Ratio, cbd)) → new_lt8(xuu4910, xuu5110, cbd)
new_compare12(xuu490, xuu510, fd, ff) → new_compare23(xuu490, xuu510, new_esEs4(xuu490, xuu510, fd, ff), fd, ff)
new_esEs20(xuu3110000, xuu6000, ty_Bool) → new_esEs13(xuu3110000, xuu6000)
new_esEs6(Right(xuu3110000), Right(xuu6000), df, app(app(ty_Either, eg), eh)) → new_esEs6(xuu3110000, xuu6000, eg, eh)
new_lt11(xuu490, xuu510, fd, ff) → new_esEs8(new_compare12(xuu490, xuu510, fd, ff), LT)
new_esEs25(xuu3110001, xuu6001, ty_Int) → new_esEs15(xuu3110001, xuu6001)
new_lt6(xuu490, xuu510, ty_Int) → new_lt9(xuu490, xuu510)
new_esEs18(xuu490, xuu510, ty_Char) → new_esEs10(xuu490, xuu510)
new_lt6(xuu490, xuu510, ty_Char) → new_lt10(xuu490, xuu510)
new_ltEs20(xuu4912, xuu5112, app(app(ty_@2, cea), ceb)) → new_ltEs9(xuu4912, xuu5112, cea, ceb)
new_sr(xuu3110001, xuu6001) → new_primMulInt(xuu3110001, xuu6001)
new_esEs28(xuu3110000, xuu6000, app(app(ty_Either, def), deg)) → new_esEs6(xuu3110000, xuu6000, def, deg)
new_lt13(xuu490, xuu510, fg) → new_esEs8(new_compare1(xuu490, xuu510, fg), LT)
new_compare10(xuu105, xuu106, xuu107, xuu108, False, bh, ca) → GT
new_esEs26(xuu4910, xuu5110, ty_Ordering) → new_esEs8(xuu4910, xuu5110)
new_primCmpInt(Neg(Zero), Neg(Succ(xuu5100))) → new_primCmpNat0(xuu5100, Zero)
new_esEs31(xuu311000, xuu600, app(app(app(ty_@3, bab), bac), bad)) → new_esEs7(xuu311000, xuu600, bab, bac, bad)
new_esEs8(GT, GT) → True
new_esEs20(xuu3110000, xuu6000, ty_Integer) → new_esEs9(xuu3110000, xuu6000)
new_primPlusNat0(Succ(xuu960), xuu600100) → Succ(Succ(new_primPlusNat1(xuu960, xuu600100)))
new_esEs27(xuu4911, xuu5111, ty_Char) → new_esEs10(xuu4911, xuu5111)
new_esEs30(xuu36, xuu37, xuu38, xuu39, False, chf, chg) → new_esEs8(new_compare23(@2(xuu36, xuu37), @2(xuu38, xuu39), False, chf, chg), LT)
new_primCmpInt(Pos(Zero), Pos(Succ(xuu5100))) → new_primCmpNat1(Zero, xuu5100)
new_lt20(xuu4910, xuu5110, ty_Ordering) → new_lt14(xuu4910, xuu5110)
new_esEs20(xuu3110000, xuu6000, app(app(app(ty_@3, bdf), bdg), bdh)) → new_esEs7(xuu3110000, xuu6000, bdf, bdg, bdh)
new_ltEs19(xuu4911, xuu5111, ty_Bool) → new_ltEs12(xuu4911, xuu5111)
new_esEs8(LT, GT) → False
new_esEs8(GT, LT) → False
new_ltEs11(xuu491, xuu511, gg) → new_fsEs(new_compare1(xuu491, xuu511, gg))
new_ltEs20(xuu4912, xuu5112, ty_Float) → new_ltEs16(xuu4912, xuu5112)
new_lt21(xuu4911, xuu5111, app(app(app(ty_@3, cde), cdf), cdg)) → new_lt18(xuu4911, xuu5111, cde, cdf, cdg)
new_ltEs15(Left(xuu4910), Left(xuu5110), ty_@0, hb) → new_ltEs17(xuu4910, xuu5110)
new_esEs5(Just(xuu3110000), Just(xuu6000), ty_Double) → new_esEs12(xuu3110000, xuu6000)
new_esEs6(Left(xuu3110000), Left(xuu6000), ty_Int, cb) → new_esEs15(xuu3110000, xuu6000)
new_compare28(xuu490, xuu510, False, bf, bg) → new_compare14(xuu490, xuu510, new_ltEs15(xuu490, xuu510, bf, bg), bf, bg)
new_compare25(xuu490, xuu510, True) → EQ
new_primEqInt(Neg(Succ(xuu31100000)), Neg(Succ(xuu60000))) → new_primEqNat0(xuu31100000, xuu60000)
new_ltEs15(Left(xuu4910), Left(xuu5110), ty_Double, hb) → new_ltEs5(xuu4910, xuu5110)
new_esEs20(xuu3110000, xuu6000, ty_Ordering) → new_esEs8(xuu3110000, xuu6000)
new_esEs23(xuu4910, xuu5110, ty_Int) → new_esEs15(xuu4910, xuu5110)
new_esEs6(Right(xuu3110000), Right(xuu6000), df, app(app(app(ty_@3, ec), ed), ee)) → new_esEs7(xuu3110000, xuu6000, ec, ed, ee)
new_ltEs19(xuu4911, xuu5111, ty_Double) → new_ltEs5(xuu4911, xuu5111)
new_esEs23(xuu4910, xuu5110, ty_Ordering) → new_esEs8(xuu4910, xuu5110)
new_esEs27(xuu4911, xuu5111, ty_Bool) → new_esEs13(xuu4911, xuu5111)
new_ltEs14(Just(xuu4910), Just(xuu5110), ty_Ordering) → new_ltEs13(xuu4910, xuu5110)
new_primPlusNat1(Succ(xuu41200), Zero) → Succ(xuu41200)
new_primPlusNat1(Zero, Succ(xuu9200)) → Succ(xuu9200)
new_ltEs20(xuu4912, xuu5112, ty_Bool) → new_ltEs12(xuu4912, xuu5112)
new_esEs28(xuu3110000, xuu6000, ty_@0) → new_esEs17(xuu3110000, xuu6000)
new_esEs22(xuu3110002, xuu6002, ty_Int) → new_esEs15(xuu3110002, xuu6002)
new_esEs26(xuu4910, xuu5110, app(app(app(ty_@3, ccc), ccd), cce)) → new_esEs7(xuu4910, xuu5110, ccc, ccd, cce)
new_esEs20(xuu3110000, xuu6000, ty_Int) → new_esEs15(xuu3110000, xuu6000)
new_ltEs13(LT, GT) → True
new_primCmpNat1(Zero, xuu4900) → LT
new_lt20(xuu4910, xuu5110, app(app(ty_Either, cca), ccb)) → new_lt4(xuu4910, xuu5110, cca, ccb)
new_esEs6(Left(xuu3110000), Left(xuu6000), ty_Integer, cb) → new_esEs9(xuu3110000, xuu6000)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_compare11(xuu105, xuu106, xuu107, xuu108, False, xuu110, bh, ca) → new_compare10(xuu105, xuu106, xuu107, xuu108, xuu110, bh, ca)
new_lt19(xuu4910, xuu5110, ty_Integer) → new_lt12(xuu4910, xuu5110)
new_lt6(xuu490, xuu510, app(ty_Ratio, fc)) → new_lt8(xuu490, xuu510, fc)
new_esEs32(xuu37, xuu39, ty_Float) → new_esEs14(xuu37, xuu39)
new_primEqInt(Neg(Succ(xuu31100000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(xuu60000))) → False
new_esEs8(EQ, EQ) → True
new_lt6(xuu490, xuu510, ty_Float) → new_lt16(xuu490, xuu510)
new_compare111(xuu490, xuu510, True, fh) → LT
new_esEs24(xuu3110000, xuu6000, ty_Integer) → new_esEs9(xuu3110000, xuu6000)
new_ltEs15(Right(xuu4910), Right(xuu5110), ha, app(app(ty_@2, dce), dcf)) → new_ltEs9(xuu4910, xuu5110, dce, dcf)
new_esEs20(xuu3110000, xuu6000, ty_@0) → new_esEs17(xuu3110000, xuu6000)
new_esEs6(Left(xuu3110000), Left(xuu6000), ty_Char, cb) → new_esEs10(xuu3110000, xuu6000)
new_lt21(xuu4911, xuu5111, ty_Float) → new_lt16(xuu4911, xuu5111)
new_ltEs7(xuu491, xuu511) → new_fsEs(new_compare9(xuu491, xuu511))
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_ltEs15(Left(xuu4910), Left(xuu5110), ty_Char, hb) → new_ltEs8(xuu4910, xuu5110)
new_ltEs16(xuu491, xuu511) → new_fsEs(new_compare16(xuu491, xuu511))
new_compare29(xuu4900, xuu5100, ty_Integer) → new_compare17(xuu4900, xuu5100)
new_ltEs15(Right(xuu4910), Right(xuu5110), ha, ty_Double) → new_ltEs5(xuu4910, xuu5110)
new_esEs9(Integer(xuu3110000), Integer(xuu6000)) → new_primEqInt(xuu3110000, xuu6000)
new_esEs11(:(xuu3110000, xuu3110001), :(xuu6000, xuu6001), hf) → new_asAs(new_esEs19(xuu3110000, xuu6000, hf), new_esEs11(xuu3110001, xuu6001, hf))
new_ltEs13(GT, LT) → False
new_ltEs15(Right(xuu4910), Right(xuu5110), ha, ty_Int) → new_ltEs7(xuu4910, xuu5110)
new_primEqInt(Pos(Succ(xuu31100000)), Pos(Succ(xuu60000))) → new_primEqNat0(xuu31100000, xuu60000)
new_ltEs14(Just(xuu4910), Just(xuu5110), app(ty_Ratio, cgd)) → new_ltEs6(xuu4910, xuu5110, cgd)
new_esEs22(xuu3110002, xuu6002, ty_Bool) → new_esEs13(xuu3110002, xuu6002)
new_ltEs13(EQ, EQ) → True
new_esEs29(xuu3110001, xuu6001, app(ty_Maybe, dfa)) → new_esEs5(xuu3110001, xuu6001, dfa)
new_esEs19(xuu3110000, xuu6000, app(app(ty_Either, bch), bda)) → new_esEs6(xuu3110000, xuu6000, bch, bda)
new_esEs5(Just(xuu3110000), Just(xuu6000), ty_Char) → new_esEs10(xuu3110000, xuu6000)
new_lt14(xuu490, xuu510) → new_esEs8(new_compare13(xuu490, xuu510), LT)
new_primEqNat0(Succ(xuu31100000), Succ(xuu60000)) → new_primEqNat0(xuu31100000, xuu60000)
new_ltEs4(xuu491, xuu511, app(app(ty_@2, ge), gf)) → new_ltEs9(xuu491, xuu511, ge, gf)
new_esEs27(xuu4911, xuu5111, ty_Ordering) → new_esEs8(xuu4911, xuu5111)
new_lt5(xuu490, xuu510) → new_esEs8(new_compare7(xuu490, xuu510), LT)
new_esEs26(xuu4910, xuu5110, app(ty_[], cbg)) → new_esEs11(xuu4910, xuu5110, cbg)
new_primCompAux00(xuu134, LT) → LT
new_lt19(xuu4910, xuu5110, app(ty_[], bhc)) → new_lt13(xuu4910, xuu5110, bhc)
new_ltEs19(xuu4911, xuu5111, app(app(app(ty_@3, cba), cbb), cbc)) → new_ltEs18(xuu4911, xuu5111, cba, cbb, cbc)
new_esEs26(xuu4910, xuu5110, app(app(ty_@2, cbe), cbf)) → new_esEs4(xuu4910, xuu5110, cbe, cbf)
new_esEs6(Right(xuu3110000), Right(xuu6000), df, app(ty_Maybe, dh)) → new_esEs5(xuu3110000, xuu6000, dh)
new_lt15(xuu490, xuu510, fh) → new_esEs8(new_compare31(xuu490, xuu510, fh), LT)
new_esEs28(xuu3110000, xuu6000, ty_Ordering) → new_esEs8(xuu3110000, xuu6000)
new_compare1(:(xuu4900, xuu4901), :(xuu5100, xuu5101), fg) → new_primCompAux0(xuu4900, xuu5100, new_compare1(xuu4901, xuu5101, fg), fg)
new_esEs8(LT, EQ) → False
new_esEs8(EQ, LT) → False
new_primEqInt(Pos(Succ(xuu31100000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(xuu60000))) → False
new_compare11(xuu105, xuu106, xuu107, xuu108, True, xuu110, bh, ca) → new_compare10(xuu105, xuu106, xuu107, xuu108, True, bh, ca)
new_esEs23(xuu4910, xuu5110, ty_@0) → new_esEs17(xuu4910, xuu5110)
new_esEs6(Left(xuu3110000), Left(xuu6000), ty_@0, cb) → new_esEs17(xuu3110000, xuu6000)
new_compare29(xuu4900, xuu5100, app(ty_Ratio, baf)) → new_compare30(xuu4900, xuu5100, baf)
new_esEs19(xuu3110000, xuu6000, ty_Integer) → new_esEs9(xuu3110000, xuu6000)
new_compare25(xuu490, xuu510, False) → new_compare15(xuu490, xuu510, new_ltEs12(xuu490, xuu510))
new_lt20(xuu4910, xuu5110, ty_Bool) → new_lt5(xuu4910, xuu5110)
new_esEs31(xuu311000, xuu600, app(ty_Ratio, bae)) → new_esEs16(xuu311000, xuu600, bae)
new_primCmpInt(Neg(Zero), Pos(Succ(xuu5100))) → LT
new_ltEs20(xuu4912, xuu5112, ty_Integer) → new_ltEs10(xuu4912, xuu5112)
new_ltEs10(xuu491, xuu511) → new_fsEs(new_compare17(xuu491, xuu511))
new_esEs18(xuu490, xuu510, app(app(app(ty_@3, ga), gb), gc)) → new_esEs7(xuu490, xuu510, ga, gb, gc)
new_ltEs15(Left(xuu4910), Left(xuu5110), app(ty_[], dbe), hb) → new_ltEs11(xuu4910, xuu5110, dbe)
new_esEs27(xuu4911, xuu5111, ty_Integer) → new_esEs9(xuu4911, xuu5111)
new_esEs28(xuu3110000, xuu6000, ty_Double) → new_esEs12(xuu3110000, xuu6000)
new_sr0(Integer(xuu51000), Integer(xuu49010)) → Integer(new_primMulInt(xuu51000, xuu49010))
new_esEs32(xuu37, xuu39, ty_@0) → new_esEs17(xuu37, xuu39)
new_primPlusNat1(Succ(xuu41200), Succ(xuu9200)) → Succ(Succ(new_primPlusNat1(xuu41200, xuu9200)))
new_lt21(xuu4911, xuu5111, app(app(ty_@2, ccg), cch)) → new_lt11(xuu4911, xuu5111, ccg, cch)
new_lt6(xuu490, xuu510, app(app(app(ty_@3, ga), gb), gc)) → new_lt18(xuu490, xuu510, ga, gb, gc)
new_compare28(xuu490, xuu510, True, bf, bg) → EQ
new_esEs32(xuu37, xuu39, app(ty_Maybe, daa)) → new_esEs5(xuu37, xuu39, daa)
new_primEqInt(Pos(Succ(xuu31100000)), Neg(xuu6000)) → False
new_primEqInt(Neg(Succ(xuu31100000)), Pos(xuu6000)) → False
new_compare210(xuu490, xuu510, True, fh) → EQ
new_compare29(xuu4900, xuu5100, app(app(ty_Either, bbc), bbd)) → new_compare6(xuu4900, xuu5100, bbc, bbd)
new_esEs27(xuu4911, xuu5111, app(ty_Maybe, cdb)) → new_esEs5(xuu4911, xuu5111, cdb)
new_compare210(xuu490, xuu510, False, fh) → new_compare111(xuu490, xuu510, new_ltEs14(xuu490, xuu510, fh), fh)
new_compare13(xuu490, xuu510) → new_compare24(xuu490, xuu510, new_esEs8(xuu490, xuu510))
new_ltEs4(xuu491, xuu511, ty_Char) → new_ltEs8(xuu491, xuu511)
new_lt19(xuu4910, xuu5110, ty_Bool) → new_lt5(xuu4910, xuu5110)
new_esEs18(xuu490, xuu510, app(app(ty_@2, fd), ff)) → new_esEs4(xuu490, xuu510, fd, ff)
new_esEs27(xuu4911, xuu5111, ty_Double) → new_esEs12(xuu4911, xuu5111)
new_esEs18(xuu490, xuu510, ty_Bool) → new_esEs13(xuu490, xuu510)
new_esEs11(:(xuu3110000, xuu3110001), [], hf) → False
new_esEs11([], :(xuu6000, xuu6001), hf) → False
new_esEs26(xuu4910, xuu5110, app(ty_Ratio, cbd)) → new_esEs16(xuu4910, xuu5110, cbd)
new_esEs12(Double(xuu3110000, xuu3110001), Double(xuu6000, xuu6001)) → new_esEs15(new_sr(xuu3110000, xuu6000), new_sr(xuu3110001, xuu6001))
new_primCmpNat2(Zero, Succ(xuu51000)) → LT
new_esEs22(xuu3110002, xuu6002, ty_Float) → new_esEs14(xuu3110002, xuu6002)
new_esEs10(Char(xuu3110000), Char(xuu6000)) → new_primEqNat0(xuu3110000, xuu6000)
new_primEqInt(Pos(Zero), Neg(Succ(xuu60000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(xuu60000))) → False
new_ltEs19(xuu4911, xuu5111, app(app(ty_@2, cac), cad)) → new_ltEs9(xuu4911, xuu5111, cac, cad)
new_esEs22(xuu3110002, xuu6002, app(ty_[], bff)) → new_esEs11(xuu3110002, xuu6002, bff)
new_primCompAux00(xuu134, EQ) → xuu134
new_esEs28(xuu3110000, xuu6000, ty_Char) → new_esEs10(xuu3110000, xuu6000)
new_compare24(xuu490, xuu510, True) → EQ
new_ltEs15(Right(xuu4910), Right(xuu5110), ha, app(ty_Ratio, dcd)) → new_ltEs6(xuu4910, xuu5110, dcd)
new_esEs23(xuu4910, xuu5110, ty_Char) → new_esEs10(xuu4910, xuu5110)
new_ltEs13(GT, EQ) → False
new_ltEs13(EQ, LT) → False
new_ltEs4(xuu491, xuu511, ty_Bool) → new_ltEs12(xuu491, xuu511)
new_esEs8(EQ, GT) → False
new_esEs8(GT, EQ) → False
new_esEs29(xuu3110001, xuu6001, ty_Double) → new_esEs12(xuu3110001, xuu6001)
new_compare24(xuu490, xuu510, False) → new_compare110(xuu490, xuu510, new_ltEs13(xuu490, xuu510))
new_ltEs4(xuu491, xuu511, app(ty_Maybe, gh)) → new_ltEs14(xuu491, xuu511, gh)
new_lt21(xuu4911, xuu5111, app(ty_[], cda)) → new_lt13(xuu4911, xuu5111, cda)
new_esEs27(xuu4911, xuu5111, app(ty_Ratio, ccf)) → new_esEs16(xuu4911, xuu5111, ccf)
new_ltEs14(Nothing, Just(xuu5110), gh) → True
new_ltEs14(Just(xuu4910), Just(xuu5110), ty_Integer) → new_ltEs10(xuu4910, xuu5110)
new_lt21(xuu4911, xuu5111, ty_Integer) → new_lt12(xuu4911, xuu5111)
new_ltEs19(xuu4911, xuu5111, ty_Char) → new_ltEs8(xuu4911, xuu5111)
new_lt6(xuu490, xuu510, ty_Bool) → new_lt5(xuu490, xuu510)
new_not(False) → True
new_lt21(xuu4911, xuu5111, app(ty_Maybe, cdb)) → new_lt15(xuu4911, xuu5111, cdb)
new_esEs6(Left(xuu3110000), Left(xuu6000), app(app(ty_Either, dd), de), cb) → new_esEs6(xuu3110000, xuu6000, dd, de)
new_lt19(xuu4910, xuu5110, ty_Char) → new_lt10(xuu4910, xuu5110)
new_ltEs20(xuu4912, xuu5112, ty_Ordering) → new_ltEs13(xuu4912, xuu5112)
new_primPlusNat0(Zero, xuu600100) → Succ(xuu600100)
new_ltEs14(Just(xuu4910), Just(xuu5110), ty_@0) → new_ltEs17(xuu4910, xuu5110)
new_esEs32(xuu37, xuu39, ty_Ordering) → new_esEs8(xuu37, xuu39)
new_esEs19(xuu3110000, xuu6000, ty_Double) → new_esEs12(xuu3110000, xuu6000)
new_esEs20(xuu3110000, xuu6000, ty_Float) → new_esEs14(xuu3110000, xuu6000)
new_esEs20(xuu3110000, xuu6000, app(ty_[], bdb)) → new_esEs11(xuu3110000, xuu6000, bdb)
new_ltEs14(Just(xuu4910), Just(xuu5110), app(app(ty_Either, cha), chb)) → new_ltEs15(xuu4910, xuu5110, cha, chb)
new_ltEs15(Left(xuu4910), Left(xuu5110), ty_Integer, hb) → new_ltEs10(xuu4910, xuu5110)
new_esEs31(xuu311000, xuu600, ty_Integer) → new_esEs9(xuu311000, xuu600)
new_ltEs19(xuu4911, xuu5111, app(app(ty_Either, cag), cah)) → new_ltEs15(xuu4911, xuu5111, cag, cah)
new_esEs6(Left(xuu3110000), Left(xuu6000), ty_Bool, cb) → new_esEs13(xuu3110000, xuu6000)
new_esEs29(xuu3110001, xuu6001, ty_Int) → new_esEs15(xuu3110001, xuu6001)
new_esEs27(xuu4911, xuu5111, app(app(ty_Either, cdc), cdd)) → new_esEs6(xuu4911, xuu5111, cdc, cdd)
new_lt7(xuu490, xuu510) → new_esEs8(new_compare8(xuu490, xuu510), LT)
new_esEs6(Right(xuu3110000), Right(xuu6000), df, app(ty_[], dg)) → new_esEs11(xuu3110000, xuu6000, dg)
new_esEs24(xuu3110000, xuu6000, ty_Int) → new_esEs15(xuu3110000, xuu6000)
new_lt6(xuu490, xuu510, ty_@0) → new_lt17(xuu490, xuu510)
new_ltEs4(xuu491, xuu511, ty_@0) → new_ltEs17(xuu491, xuu511)
new_ltEs20(xuu4912, xuu5112, ty_@0) → new_ltEs17(xuu4912, xuu5112)
new_esEs22(xuu3110002, xuu6002, app(app(app(ty_@3, bgb), bgc), bgd)) → new_esEs7(xuu3110002, xuu6002, bgb, bgc, bgd)
new_primCmpInt(Pos(Succ(xuu4900)), Neg(xuu510)) → GT
new_esEs26(xuu4910, xuu5110, ty_@0) → new_esEs17(xuu4910, xuu5110)
new_lt18(xuu490, xuu510, ga, gb, gc) → new_esEs8(new_compare19(xuu490, xuu510, ga, gb, gc), LT)
new_esEs29(xuu3110001, xuu6001, ty_Integer) → new_esEs9(xuu3110001, xuu6001)
new_esEs5(Just(xuu3110000), Just(xuu6000), ty_Int) → new_esEs15(xuu3110000, xuu6000)
new_lt19(xuu4910, xuu5110, ty_Float) → new_lt16(xuu4910, xuu5110)
new_primMulInt(Pos(xuu31100010), Pos(xuu60010)) → Pos(new_primMulNat0(xuu31100010, xuu60010))
new_ltEs4(xuu491, xuu511, app(app(ty_Either, ha), hb)) → new_ltEs15(xuu491, xuu511, ha, hb)
new_esEs21(xuu3110001, xuu6001, app(app(ty_@2, bef), beg)) → new_esEs4(xuu3110001, xuu6001, bef, beg)
new_esEs6(Right(xuu3110000), Right(xuu6000), df, ty_Bool) → new_esEs13(xuu3110000, xuu6000)
new_esEs28(xuu3110000, xuu6000, app(app(app(ty_@3, deb), dec), ded)) → new_esEs7(xuu3110000, xuu6000, deb, dec, ded)
new_esEs19(xuu3110000, xuu6000, ty_Bool) → new_esEs13(xuu3110000, xuu6000)
new_esEs7(@3(xuu3110000, xuu3110001, xuu3110002), @3(xuu6000, xuu6001, xuu6002), bab, bac, bad) → new_asAs(new_esEs20(xuu3110000, xuu6000, bab), new_asAs(new_esEs21(xuu3110001, xuu6001, bac), new_esEs22(xuu3110002, xuu6002, bad)))
new_esEs31(xuu311000, xuu600, ty_Float) → new_esEs14(xuu311000, xuu600)
new_primMulInt(Neg(xuu31100010), Neg(xuu60010)) → Pos(new_primMulNat0(xuu31100010, xuu60010))
new_primCmpNat2(Zero, Zero) → EQ
new_ltEs19(xuu4911, xuu5111, app(ty_Ratio, cab)) → new_ltEs6(xuu4911, xuu5111, cab)
new_esEs21(xuu3110001, xuu6001, ty_Char) → new_esEs10(xuu3110001, xuu6001)
new_compare110(xuu490, xuu510, True) → LT
new_ltEs19(xuu4911, xuu5111, ty_Integer) → new_ltEs10(xuu4911, xuu5111)
new_primEqNat0(Zero, Succ(xuu60000)) → False
new_primEqNat0(Succ(xuu31100000), Zero) → False
new_esEs6(Right(xuu3110000), Right(xuu6000), df, ty_Double) → new_esEs12(xuu3110000, xuu6000)
new_lt20(xuu4910, xuu5110, ty_@0) → new_lt17(xuu4910, xuu5110)
new_compare110(xuu490, xuu510, False) → GT
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_ltEs20(xuu4912, xuu5112, ty_Int) → new_ltEs7(xuu4912, xuu5112)
new_lt9(xuu490, xuu510) → new_esEs8(new_compare9(xuu490, xuu510), LT)
new_compare30(:%(xuu4900, xuu4901), :%(xuu5100, xuu5101), ty_Integer) → new_compare17(new_sr0(xuu4900, xuu5101), new_sr0(xuu5100, xuu4901))
new_esEs6(Right(xuu3110000), Right(xuu6000), df, ty_Float) → new_esEs14(xuu3110000, xuu6000)
new_primCmpNat2(Succ(xuu49000), Succ(xuu51000)) → new_primCmpNat2(xuu49000, xuu51000)
new_primCmpInt(Pos(Succ(xuu4900)), Pos(xuu510)) → new_primCmpNat0(xuu4900, xuu510)
new_esEs32(xuu37, xuu39, ty_Integer) → new_esEs9(xuu37, xuu39)
new_esEs20(xuu3110000, xuu6000, app(app(ty_Either, beb), bec)) → new_esEs6(xuu3110000, xuu6000, beb, bec)
new_compare31(xuu490, xuu510, fh) → new_compare210(xuu490, xuu510, new_esEs5(xuu490, xuu510, fh), fh)
new_ltEs14(Just(xuu4910), Just(xuu5110), ty_Double) → new_ltEs5(xuu4910, xuu5110)
new_primCmpNat0(xuu4900, Zero) → GT
new_esEs19(xuu3110000, xuu6000, app(ty_Maybe, bca)) → new_esEs5(xuu3110000, xuu6000, bca)
new_esEs18(xuu490, xuu510, ty_@0) → new_esEs17(xuu490, xuu510)
new_esEs29(xuu3110001, xuu6001, app(app(ty_Either, dfh), dga)) → new_esEs6(xuu3110001, xuu6001, dfh, dga)
new_ltEs19(xuu4911, xuu5111, ty_@0) → new_ltEs17(xuu4911, xuu5111)
new_esEs26(xuu4910, xuu5110, app(ty_Maybe, cbh)) → new_esEs5(xuu4910, xuu5110, cbh)
new_esEs32(xuu37, xuu39, ty_Char) → new_esEs10(xuu37, xuu39)
new_compare112(xuu490, xuu510, True, ga, gb, gc) → LT
new_compare23(xuu49, xuu51, True, fa, fb) → EQ
new_primCmpInt(Pos(Zero), Neg(Succ(xuu5100))) → GT
new_esEs18(xuu490, xuu510, ty_Float) → new_esEs14(xuu490, xuu510)
new_lt17(xuu490, xuu510) → new_esEs8(new_compare27(xuu490, xuu510), LT)
new_esEs32(xuu37, xuu39, ty_Int) → new_esEs15(xuu37, xuu39)
new_esEs6(Left(xuu3110000), Left(xuu6000), ty_Ordering, cb) → new_esEs8(xuu3110000, xuu6000)
new_ltEs20(xuu4912, xuu5112, ty_Char) → new_ltEs8(xuu4912, xuu5112)
new_lt20(xuu4910, xuu5110, ty_Float) → new_lt16(xuu4910, xuu5110)
new_ltEs4(xuu491, xuu511, app(app(app(ty_@3, hc), hd), he)) → new_ltEs18(xuu491, xuu511, hc, hd, he)
new_compare26(xuu490, xuu510, False, ga, gb, gc) → new_compare112(xuu490, xuu510, new_ltEs18(xuu490, xuu510, ga, gb, gc), ga, gb, gc)
new_esEs27(xuu4911, xuu5111, ty_@0) → new_esEs17(xuu4911, xuu5111)
new_esEs6(Right(xuu3110000), Right(xuu6000), df, app(app(ty_@2, ea), eb)) → new_esEs4(xuu3110000, xuu6000, ea, eb)
new_compare29(xuu4900, xuu5100, ty_Ordering) → new_compare13(xuu4900, xuu5100)
new_esEs23(xuu4910, xuu5110, app(ty_[], bhc)) → new_esEs11(xuu4910, xuu5110, bhc)
new_ltEs20(xuu4912, xuu5112, app(ty_Maybe, ced)) → new_ltEs14(xuu4912, xuu5112, ced)
new_esEs32(xuu37, xuu39, app(ty_[], chh)) → new_esEs11(xuu37, xuu39, chh)
new_lt8(xuu490, xuu510, fc) → new_esEs8(new_compare30(xuu490, xuu510, fc), LT)
new_esEs6(Right(xuu3110000), Right(xuu6000), df, ty_Integer) → new_esEs9(xuu3110000, xuu6000)
new_esEs31(xuu311000, xuu600, ty_Double) → new_esEs12(xuu311000, xuu600)
new_ltEs15(Right(xuu4910), Right(xuu5110), ha, ty_Float) → new_ltEs16(xuu4910, xuu5110)
new_lt19(xuu4910, xuu5110, app(app(ty_Either, bhe), bhf)) → new_lt4(xuu4910, xuu5110, bhe, bhf)
new_esEs23(xuu4910, xuu5110, app(ty_Ratio, bgh)) → new_esEs16(xuu4910, xuu5110, bgh)
new_esEs22(xuu3110002, xuu6002, app(ty_Ratio, bge)) → new_esEs16(xuu3110002, xuu6002, bge)
new_ltEs14(Just(xuu4910), Just(xuu5110), app(ty_[], cgg)) → new_ltEs11(xuu4910, xuu5110, cgg)
new_esEs4(@2(xuu3110000, xuu3110001), @2(xuu6000, xuu6001), hh, baa) → new_asAs(new_esEs28(xuu3110000, xuu6000, hh), new_esEs29(xuu3110001, xuu6001, baa))
new_esEs18(xuu490, xuu510, app(ty_[], fg)) → new_esEs11(xuu490, xuu510, fg)
new_lt20(xuu4910, xuu5110, ty_Char) → new_lt10(xuu4910, xuu5110)
new_ltEs20(xuu4912, xuu5112, app(app(ty_Either, cee), cef)) → new_ltEs15(xuu4912, xuu5112, cee, cef)
new_esEs28(xuu3110000, xuu6000, ty_Integer) → new_esEs9(xuu3110000, xuu6000)
new_esEs19(xuu3110000, xuu6000, app(ty_Ratio, bcg)) → new_esEs16(xuu3110000, xuu6000, bcg)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_ltEs15(Right(xuu4910), Right(xuu5110), ha, app(ty_Maybe, dch)) → new_ltEs14(xuu4910, xuu5110, dch)
new_ltEs4(xuu491, xuu511, ty_Integer) → new_ltEs10(xuu491, xuu511)
new_esEs6(Left(xuu3110000), Left(xuu6000), ty_Double, cb) → new_esEs12(xuu3110000, xuu6000)
new_compare29(xuu4900, xuu5100, ty_Int) → new_compare9(xuu4900, xuu5100)
new_esEs20(xuu3110000, xuu6000, app(ty_Maybe, bdc)) → new_esEs5(xuu3110000, xuu6000, bdc)
new_ltEs13(GT, GT) → True
new_ltEs4(xuu491, xuu511, app(ty_Ratio, gd)) → new_ltEs6(xuu491, xuu511, gd)
new_esEs28(xuu3110000, xuu6000, app(app(ty_@2, ddh), dea)) → new_esEs4(xuu3110000, xuu6000, ddh, dea)
new_asAs(False, xuu59) → False
new_esEs22(xuu3110002, xuu6002, ty_Double) → new_esEs12(xuu3110002, xuu6002)
new_lt6(xuu490, xuu510, ty_Integer) → new_lt12(xuu490, xuu510)
new_primMulInt(Neg(xuu31100010), Pos(xuu60010)) → Neg(new_primMulNat0(xuu31100010, xuu60010))
new_primMulInt(Pos(xuu31100010), Neg(xuu60010)) → Neg(new_primMulNat0(xuu31100010, xuu60010))
new_ltEs20(xuu4912, xuu5112, app(ty_[], cec)) → new_ltEs11(xuu4912, xuu5112, cec)
new_compare23(@2(xuu490, xuu491), @2(xuu510, xuu511), False, fa, fb) → new_compare11(xuu490, xuu491, xuu510, xuu511, new_lt6(xuu490, xuu510, fa), new_asAs(new_esEs18(xuu490, xuu510, fa), new_ltEs4(xuu491, xuu511, fb)), fa, fb)
new_primMulNat0(Succ(xuu311000100), Zero) → Zero
new_primMulNat0(Zero, Succ(xuu600100)) → Zero
new_ltEs14(Just(xuu4910), Just(xuu5110), ty_Float) → new_ltEs16(xuu4910, xuu5110)
new_compare29(xuu4900, xuu5100, ty_Char) → new_compare18(xuu4900, xuu5100)
new_esEs32(xuu37, xuu39, app(app(app(ty_@3, dad), dae), daf)) → new_esEs7(xuu37, xuu39, dad, dae, daf)
new_esEs21(xuu3110001, xuu6001, ty_Ordering) → new_esEs8(xuu3110001, xuu6001)
new_esEs32(xuu37, xuu39, app(ty_Ratio, dag)) → new_esEs16(xuu37, xuu39, dag)
new_esEs21(xuu3110001, xuu6001, ty_Bool) → new_esEs13(xuu3110001, xuu6001)
new_lt6(xuu490, xuu510, ty_Ordering) → new_lt14(xuu490, xuu510)
new_compare17(Integer(xuu4900), Integer(xuu5100)) → new_primCmpInt(xuu4900, xuu5100)
new_esEs19(xuu3110000, xuu6000, app(ty_[], bbh)) → new_esEs11(xuu3110000, xuu6000, bbh)
new_esEs5(Just(xuu3110000), Just(xuu6000), app(ty_[], cfb)) → new_esEs11(xuu3110000, xuu6000, cfb)
new_esEs5(Just(xuu3110000), Just(xuu6000), ty_Integer) → new_esEs9(xuu3110000, xuu6000)
new_esEs6(Right(xuu3110000), Right(xuu6000), df, app(ty_Ratio, ef)) → new_esEs16(xuu3110000, xuu6000, ef)
new_ltEs8(xuu491, xuu511) → new_fsEs(new_compare18(xuu491, xuu511))
new_lt19(xuu4910, xuu5110, app(app(app(ty_@3, bhg), bhh), caa)) → new_lt18(xuu4910, xuu5110, bhg, bhh, caa)
new_lt21(xuu4911, xuu5111, ty_Int) → new_lt9(xuu4911, xuu5111)
new_esEs18(xuu490, xuu510, app(ty_Maybe, fh)) → new_esEs5(xuu490, xuu510, fh)
new_primCmpNat1(Succ(xuu5100), xuu4900) → new_primCmpNat2(xuu5100, xuu4900)
new_esEs22(xuu3110002, xuu6002, ty_Char) → new_esEs10(xuu3110002, xuu6002)
new_ltEs12(True, True) → True
new_primCmpNat2(Succ(xuu49000), Zero) → GT
new_esEs18(xuu490, xuu510, ty_Ordering) → new_esEs8(xuu490, xuu510)
new_esEs29(xuu3110001, xuu6001, app(ty_Ratio, dfg)) → new_esEs16(xuu3110001, xuu6001, dfg)
new_esEs13(False, False) → True
new_esEs21(xuu3110001, xuu6001, ty_Integer) → new_esEs9(xuu3110001, xuu6001)
new_ltEs20(xuu4912, xuu5112, app(app(app(ty_@3, ceg), ceh), cfa)) → new_ltEs18(xuu4912, xuu5112, ceg, ceh, cfa)
new_esEs23(xuu4910, xuu5110, app(ty_Maybe, bhd)) → new_esEs5(xuu4910, xuu5110, bhd)
new_esEs29(xuu3110001, xuu6001, ty_Float) → new_esEs14(xuu3110001, xuu6001)
new_esEs16(:%(xuu3110000, xuu3110001), :%(xuu6000, xuu6001), bae) → new_asAs(new_esEs24(xuu3110000, xuu6000, bae), new_esEs25(xuu3110001, xuu6001, bae))
new_esEs6(Right(xuu3110000), Right(xuu6000), df, ty_Char) → new_esEs10(xuu3110000, xuu6000)
new_esEs6(Left(xuu3110000), Left(xuu6000), app(ty_Maybe, cd), cb) → new_esEs5(xuu3110000, xuu6000, cd)
new_esEs26(xuu4910, xuu5110, ty_Integer) → new_esEs9(xuu4910, xuu5110)
new_ltEs12(False, True) → True
new_esEs20(xuu3110000, xuu6000, app(app(ty_@2, bdd), bde)) → new_esEs4(xuu3110000, xuu6000, bdd, bde)
new_compare29(xuu4900, xuu5100, ty_@0) → new_compare27(xuu4900, xuu5100)
new_compare112(xuu490, xuu510, False, ga, gb, gc) → GT
new_compare30(:%(xuu4900, xuu4901), :%(xuu5100, xuu5101), ty_Int) → new_compare9(new_sr(xuu4900, xuu5101), new_sr(xuu5100, xuu4901))
new_ltEs15(Right(xuu4910), Right(xuu5110), ha, ty_Bool) → new_ltEs12(xuu4910, xuu5110)
new_compare111(xuu490, xuu510, False, fh) → GT
new_esEs21(xuu3110001, xuu6001, app(ty_Ratio, bfc)) → new_esEs16(xuu3110001, xuu6001, bfc)
new_esEs18(xuu490, xuu510, ty_Int) → new_esEs15(xuu490, xuu510)
new_esEs5(Nothing, Just(xuu6000), hg) → False
new_esEs5(Just(xuu3110000), Nothing, hg) → False
new_esEs30(xuu36, xuu37, xuu38, xuu39, True, chf, chg) → new_esEs8(new_compare23(@2(xuu36, xuu37), @2(xuu38, xuu39), new_esEs32(xuu37, xuu39, chg), chf, chg), LT)
new_lt19(xuu4910, xuu5110, ty_@0) → new_lt17(xuu4910, xuu5110)
new_esEs31(xuu311000, xuu600, app(app(ty_Either, df), cb)) → new_esEs6(xuu311000, xuu600, df, cb)
new_compare16(Float(xuu4900, xuu4901), Float(xuu5100, xuu5101)) → new_compare9(new_sr(xuu4900, xuu5100), new_sr(xuu4901, xuu5101))
new_lt19(xuu4910, xuu5110, ty_Int) → new_lt9(xuu4910, xuu5110)
new_esEs6(Right(xuu3110000), Right(xuu6000), df, ty_@0) → new_esEs17(xuu3110000, xuu6000)
new_esEs27(xuu4911, xuu5111, app(app(ty_@2, ccg), cch)) → new_esEs4(xuu4911, xuu5111, ccg, cch)
new_lt21(xuu4911, xuu5111, ty_Bool) → new_lt5(xuu4911, xuu5111)
new_esEs27(xuu4911, xuu5111, app(ty_[], cda)) → new_esEs11(xuu4911, xuu5111, cda)
new_esEs27(xuu4911, xuu5111, ty_Int) → new_esEs15(xuu4911, xuu5111)
new_compare8(Double(xuu4900, xuu4901), Double(xuu5100, xuu5101)) → new_compare9(new_sr(xuu4900, xuu5100), new_sr(xuu4901, xuu5101))
new_esEs5(Just(xuu3110000), Just(xuu6000), app(app(ty_Either, cgb), cgc)) → new_esEs6(xuu3110000, xuu6000, cgb, cgc)
new_lt20(xuu4910, xuu5110, ty_Integer) → new_lt12(xuu4910, xuu5110)
new_esEs32(xuu37, xuu39, app(app(ty_Either, dah), dba)) → new_esEs6(xuu37, xuu39, dah, dba)
new_ltEs18(@3(xuu4910, xuu4911, xuu4912), @3(xuu5110, xuu5111, xuu5112), hc, hd, he) → new_pePe(new_lt20(xuu4910, xuu5110, hc), new_asAs(new_esEs26(xuu4910, xuu5110, hc), new_pePe(new_lt21(xuu4911, xuu5111, hd), new_asAs(new_esEs27(xuu4911, xuu5111, hd), new_ltEs20(xuu4912, xuu5112, he)))))
new_ltEs20(xuu4912, xuu5112, app(ty_Ratio, cdh)) → new_ltEs6(xuu4912, xuu5112, cdh)
new_esEs5(Nothing, Nothing, hg) → True
new_esEs26(xuu4910, xuu5110, ty_Char) → new_esEs10(xuu4910, xuu5110)
new_esEs22(xuu3110002, xuu6002, app(app(ty_Either, bgf), bgg)) → new_esEs6(xuu3110002, xuu6002, bgf, bgg)
new_esEs28(xuu3110000, xuu6000, app(ty_Maybe, ddg)) → new_esEs5(xuu3110000, xuu6000, ddg)
new_lt12(xuu490, xuu510) → new_esEs8(new_compare17(xuu490, xuu510), LT)
new_esEs5(Just(xuu3110000), Just(xuu6000), app(app(app(ty_@3, cff), cfg), cfh)) → new_esEs7(xuu3110000, xuu6000, cff, cfg, cfh)
new_esEs28(xuu3110000, xuu6000, ty_Bool) → new_esEs13(xuu3110000, xuu6000)
new_esEs21(xuu3110001, xuu6001, ty_Double) → new_esEs12(xuu3110001, xuu6001)
new_compare14(xuu490, xuu510, True, bf, bg) → LT
new_ltEs14(Just(xuu4910), Just(xuu5110), ty_Char) → new_ltEs8(xuu4910, xuu5110)
new_esEs21(xuu3110001, xuu6001, app(ty_[], bed)) → new_esEs11(xuu3110001, xuu6001, bed)
new_ltEs15(Left(xuu4910), Left(xuu5110), app(ty_Ratio, dbb), hb) → new_ltEs6(xuu4910, xuu5110, dbb)
new_ltEs15(Right(xuu4910), Right(xuu5110), ha, app(app(ty_Either, dda), ddb)) → new_ltEs15(xuu4910, xuu5110, dda, ddb)
new_compare29(xuu4900, xuu5100, ty_Bool) → new_compare7(xuu4900, xuu5100)
new_ltEs13(LT, LT) → True
new_esEs23(xuu4910, xuu5110, ty_Double) → new_esEs12(xuu4910, xuu5110)
new_compare7(xuu490, xuu510) → new_compare25(xuu490, xuu510, new_esEs13(xuu490, xuu510))
new_esEs22(xuu3110002, xuu6002, app(ty_Maybe, bfg)) → new_esEs5(xuu3110002, xuu6002, bfg)
new_compare26(xuu490, xuu510, True, ga, gb, gc) → EQ
new_esEs21(xuu3110001, xuu6001, app(ty_Maybe, bee)) → new_esEs5(xuu3110001, xuu6001, bee)
new_lt4(xuu490, xuu510, bf, bg) → new_esEs8(new_compare6(xuu490, xuu510, bf, bg), LT)
new_esEs26(xuu4910, xuu5110, app(app(ty_Either, cca), ccb)) → new_esEs6(xuu4910, xuu5110, cca, ccb)
new_primPlusNat1(Zero, Zero) → Zero
new_esEs14(Float(xuu3110000, xuu3110001), Float(xuu6000, xuu6001)) → new_esEs15(new_sr(xuu3110000, xuu6000), new_sr(xuu3110001, xuu6001))
new_ltEs14(Nothing, Nothing, gh) → True
new_esEs31(xuu311000, xuu600, ty_Bool) → new_esEs13(xuu311000, xuu600)
new_esEs19(xuu3110000, xuu6000, ty_@0) → new_esEs17(xuu3110000, xuu6000)
new_asAs(True, xuu59) → xuu59
new_esEs26(xuu4910, xuu5110, ty_Float) → new_esEs14(xuu4910, xuu5110)
new_compare27(@0, @0) → EQ
new_ltEs4(xuu491, xuu511, app(ty_[], gg)) → new_ltEs11(xuu491, xuu511, gg)
new_primMulNat0(Succ(xuu311000100), Succ(xuu600100)) → new_primPlusNat0(new_primMulNat0(xuu311000100, Succ(xuu600100)), xuu600100)
new_esEs13(True, True) → True
new_ltEs14(Just(xuu4910), Just(xuu5110), app(app(app(ty_@3, chc), chd), che)) → new_ltEs18(xuu4910, xuu5110, chc, chd, che)
new_compare1(:(xuu4900, xuu4901), [], fg) → GT
new_esEs19(xuu3110000, xuu6000, ty_Char) → new_esEs10(xuu3110000, xuu6000)
new_fsEs(xuu117) → new_not(new_esEs8(xuu117, GT))
new_ltEs15(Left(xuu4910), Left(xuu5110), ty_Bool, hb) → new_ltEs12(xuu4910, xuu5110)
new_lt6(xuu490, xuu510, app(ty_Maybe, fh)) → new_lt15(xuu490, xuu510, fh)
new_esEs18(xuu490, xuu510, ty_Integer) → new_esEs9(xuu490, xuu510)
new_esEs19(xuu3110000, xuu6000, ty_Int) → new_esEs15(xuu3110000, xuu6000)
new_lt20(xuu4910, xuu5110, ty_Int) → new_lt9(xuu4910, xuu5110)
new_esEs19(xuu3110000, xuu6000, ty_Ordering) → new_esEs8(xuu3110000, xuu6000)
new_esEs27(xuu4911, xuu5111, ty_Float) → new_esEs14(xuu4911, xuu5111)
new_ltEs15(Left(xuu4910), Left(xuu5110), app(app(ty_Either, dbg), dbh), hb) → new_ltEs15(xuu4910, xuu5110, dbg, dbh)
new_ltEs15(Left(xuu4910), Right(xuu5110), ha, hb) → True
new_esEs32(xuu37, xuu39, ty_Double) → new_esEs12(xuu37, xuu39)
new_lt19(xuu4910, xuu5110, app(ty_Ratio, bgh)) → new_lt8(xuu4910, xuu5110, bgh)
new_ltEs17(xuu491, xuu511) → new_fsEs(new_compare27(xuu491, xuu511))
new_esEs26(xuu4910, xuu5110, ty_Int) → new_esEs15(xuu4910, xuu5110)
new_ltEs4(xuu491, xuu511, ty_Int) → new_ltEs7(xuu491, xuu511)
new_ltEs9(@2(xuu4910, xuu4911), @2(xuu5110, xuu5111), ge, gf) → new_pePe(new_lt19(xuu4910, xuu5110, ge), new_asAs(new_esEs23(xuu4910, xuu5110, ge), new_ltEs19(xuu4911, xuu5111, gf)))
new_ltEs15(Left(xuu4910), Left(xuu5110), app(app(ty_@2, dbc), dbd), hb) → new_ltEs9(xuu4910, xuu5110, dbc, dbd)
new_primCompAux00(xuu134, GT) → GT
new_compare18(Char(xuu4900), Char(xuu5100)) → new_primCmpNat2(xuu4900, xuu5100)
new_ltEs15(Right(xuu4910), Right(xuu5110), ha, app(app(app(ty_@3, ddc), ddd), dde)) → new_ltEs18(xuu4910, xuu5110, ddc, ddd, dde)
new_ltEs15(Left(xuu4910), Left(xuu5110), app(app(app(ty_@3, dca), dcb), dcc), hb) → new_ltEs18(xuu4910, xuu5110, dca, dcb, dcc)
new_esEs26(xuu4910, xuu5110, ty_Bool) → new_esEs13(xuu4910, xuu5110)
new_esEs6(Right(xuu3110000), Right(xuu6000), df, ty_Ordering) → new_esEs8(xuu3110000, xuu6000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs29(xuu3110001, xuu6001, ty_Ordering) → new_esEs8(xuu3110001, xuu6001)
new_esEs19(xuu3110000, xuu6000, app(app(ty_@2, bcb), bcc)) → new_esEs4(xuu3110000, xuu6000, bcb, bcc)
new_ltEs15(Right(xuu4910), Left(xuu5110), ha, hb) → False
new_esEs31(xuu311000, xuu600, app(ty_[], hf)) → new_esEs11(xuu311000, xuu600, hf)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_ltEs5(xuu491, xuu511) → new_fsEs(new_compare8(xuu491, xuu511))
new_esEs6(Right(xuu3110000), Right(xuu6000), df, ty_Int) → new_esEs15(xuu3110000, xuu6000)
new_primCmpInt(Neg(Succ(xuu4900)), Pos(xuu510)) → LT
new_lt21(xuu4911, xuu5111, ty_Double) → new_lt7(xuu4911, xuu5111)
new_ltEs19(xuu4911, xuu5111, ty_Ordering) → new_ltEs13(xuu4911, xuu5111)
new_not(True) → False
new_esEs25(xuu3110001, xuu6001, ty_Integer) → new_esEs9(xuu3110001, xuu6001)
new_compare1([], [], fg) → EQ

The set Q consists of the following terms:

new_esEs32(x0, x1, ty_Integer)
new_esEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_primCmpNat2(Succ(x0), Succ(x1))
new_lt6(x0, x1, app(app(ty_Either, x2), x3))
new_esEs18(x0, x1, ty_Int)
new_lt21(x0, x1, ty_Int)
new_lt6(x0, x1, app(ty_[], x2))
new_ltEs15(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs29(x0, x1, ty_Ordering)
new_compare29(x0, x1, ty_Bool)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_lt21(x0, x1, ty_Float)
new_ltEs4(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs18(x0, x1, ty_Double)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_primEqNat0(Zero, Succ(x0))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_ltEs17(x0, x1)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs6(Left(x0), Left(x1), ty_Integer, x2)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_ltEs15(Left(x0), Left(x1), ty_Bool, x2)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_esEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, app(ty_[], x2))
new_ltEs15(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs14(Just(x0), Just(x1), ty_Integer)
new_ltEs20(x0, x1, ty_Float)
new_esEs5(Nothing, Nothing, x0)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs10(x0, x1)
new_esEs5(Just(x0), Just(x1), app(ty_[], x2))
new_esEs31(x0, x1, ty_@0)
new_esEs31(x0, x1, ty_Integer)
new_esEs18(x0, x1, ty_Ordering)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs23(x0, x1, ty_Double)
new_compare29(x0, x1, ty_Int)
new_ltEs15(Right(x0), Right(x1), x2, ty_Float)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_@0)
new_esEs22(x0, x1, ty_Char)
new_esEs28(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, ty_Bool)
new_compare30(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs6(Left(x0), Left(x1), ty_Double, x2)
new_esEs27(x0, x1, ty_Char)
new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs19(x0, x1, ty_Char)
new_esEs12(Double(x0, x1), Double(x2, x3))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs18(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare28(x0, x1, False, x2, x3)
new_compare210(x0, x1, False, x2)
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs8(GT, GT)
new_lt8(x0, x1, x2)
new_lt9(x0, x1)
new_esEs32(x0, x1, app(ty_Ratio, x2))
new_primCmpNat0(x0, Zero)
new_ltEs15(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, ty_Ordering)
new_lt21(x0, x1, ty_Char)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs15(Right(x0), Right(x1), x2, ty_Int)
new_esEs20(x0, x1, app(ty_[], x2))
new_compare14(x0, x1, False, x2, x3)
new_esEs8(LT, LT)
new_ltEs15(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs4(x0, x1, ty_Integer)
new_esEs5(Just(x0), Just(x1), ty_Ordering)
new_esEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs14(Just(x0), Just(x1), ty_Ordering)
new_ltEs15(Left(x0), Left(x1), ty_Char, x2)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_lt6(x0, x1, ty_Ordering)
new_lt6(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_Double)
new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_compare25(x0, x1, False)
new_compare31(x0, x1, x2)
new_compare18(Char(x0), Char(x1))
new_esEs18(x0, x1, ty_Bool)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_lt13(x0, x1, x2)
new_esEs11(:(x0, x1), :(x2, x3), x4)
new_esEs31(x0, x1, ty_Bool)
new_asAs(True, x0)
new_compare17(Integer(x0), Integer(x1))
new_primCompAux0(x0, x1, x2, x3)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Double)
new_esEs32(x0, x1, app(app(ty_Either, x2), x3))
new_lt21(x0, x1, app(ty_Maybe, x2))
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs6(Right(x0), Right(x1), x2, ty_Int)
new_esEs28(x0, x1, app(ty_[], x2))
new_ltEs11(x0, x1, x2)
new_pePe(True, x0)
new_lt19(x0, x1, ty_@0)
new_primEqNat0(Zero, Zero)
new_esEs25(x0, x1, ty_Int)
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_Int)
new_esEs5(Just(x0), Just(x1), ty_Char)
new_compare11(x0, x1, x2, x3, True, x4, x5, x6)
new_ltEs15(Left(x0), Left(x1), ty_Int, x2)
new_esEs6(Right(x0), Right(x1), x2, ty_Bool)
new_compare11(x0, x1, x2, x3, False, x4, x5, x6)
new_ltEs13(EQ, EQ)
new_compare29(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Char)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_compare9(x0, x1)
new_esEs26(x0, x1, ty_Ordering)
new_esEs19(x0, x1, ty_Ordering)
new_esEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs13(False, False)
new_primMulNat0(Zero, Zero)
new_esEs23(x0, x1, ty_Bool)
new_lt20(x0, x1, ty_Double)
new_esEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs32(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_compare23(@2(x0, x1), @2(x2, x3), False, x4, x5)
new_esEs6(Left(x0), Left(x1), ty_Bool, x2)
new_ltEs15(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs18(x0, x1, ty_@0)
new_esEs6(Left(x0), Left(x1), ty_Int, x2)
new_ltEs19(x0, x1, app(ty_[], x2))
new_lt6(x0, x1, ty_Bool)
new_ltEs15(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_compare29(x0, x1, ty_@0)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, ty_Float)
new_esEs26(x0, x1, app(ty_[], x2))
new_ltEs13(LT, EQ)
new_ltEs13(EQ, LT)
new_lt5(x0, x1)
new_lt20(x0, x1, ty_Integer)
new_primCmpNat2(Zero, Succ(x0))
new_ltEs14(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs11([], :(x0, x1), x2)
new_ltEs19(x0, x1, ty_Int)
new_esEs5(Just(x0), Just(x1), ty_Double)
new_compare111(x0, x1, True, x2)
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs29(x0, x1, ty_Int)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs8(x0, x1)
new_esEs6(Right(x0), Right(x1), x2, ty_@0)
new_primMulNat0(Zero, Succ(x0))
new_ltEs15(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs15(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs19(x0, x1, ty_Char)
new_ltEs14(Just(x0), Just(x1), ty_Double)
new_compare29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(Just(x0), Just(x1), ty_Bool)
new_esEs31(x0, x1, app(app(ty_Either, x2), x3))
new_compare112(x0, x1, False, x2, x3, x4)
new_ltEs15(Right(x0), Right(x1), x2, ty_Integer)
new_asAs(False, x0)
new_esEs26(x0, x1, ty_Integer)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs12(False, False)
new_lt17(x0, x1)
new_esEs18(x0, x1, app(app(ty_@2, x2), x3))
new_lt21(x0, x1, app(ty_[], x2))
new_lt19(x0, x1, ty_Double)
new_esEs19(x0, x1, ty_Int)
new_lt6(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, ty_Ordering)
new_esEs30(x0, x1, x2, x3, True, x4, x5)
new_ltEs15(Right(x0), Right(x1), x2, ty_Char)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_primCompAux00(x0, LT)
new_esEs21(x0, x1, ty_Integer)
new_esEs5(Just(x0), Nothing, x1)
new_esEs22(x0, x1, ty_Bool)
new_ltEs4(x0, x1, ty_Double)
new_ltEs15(Right(x0), Right(x1), x2, ty_@0)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_compare26(x0, x1, False, x2, x3, x4)
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Integer)
new_ltEs14(Just(x0), Just(x1), app(ty_Maybe, x2))
new_compare112(x0, x1, True, x2, x3, x4)
new_esEs20(x0, x1, ty_Float)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Just(x0), Just(x1), ty_Bool)
new_esEs31(x0, x1, ty_Float)
new_primPlusNat1(Zero, Zero)
new_ltEs15(Left(x0), Left(x1), ty_Double, x2)
new_ltEs15(Left(x0), Left(x1), ty_Integer, x2)
new_esEs22(x0, x1, ty_Float)
new_primCmpNat2(Zero, Zero)
new_esEs18(x0, x1, app(ty_Maybe, x2))
new_primCmpNat1(Zero, x0)
new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_compare29(x0, x1, ty_Float)
new_esEs31(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, ty_Double)
new_ltEs15(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt16(x0, x1)
new_esEs27(x0, x1, app(ty_[], x2))
new_compare6(x0, x1, x2, x3)
new_esEs6(Right(x0), Right(x1), x2, ty_Double)
new_esEs15(x0, x1)
new_primCompAux00(x0, EQ)
new_esEs5(Just(x0), Just(x1), ty_Int)
new_ltEs4(x0, x1, ty_Char)
new_esEs14(Float(x0, x1), Float(x2, x3))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs23(x0, x1, ty_Float)
new_esEs26(x0, x1, ty_Bool)
new_ltEs19(x0, x1, ty_@0)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_ltEs5(x0, x1)
new_esEs22(x0, x1, ty_Ordering)
new_esEs32(x0, x1, ty_Bool)
new_lt20(x0, x1, ty_Int)
new_primPlusNat1(Zero, Succ(x0))
new_esEs17(@0, @0)
new_esEs31(x0, x1, app(ty_Ratio, x2))
new_ltEs15(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs32(x0, x1, ty_Char)
new_lt10(x0, x1)
new_esEs19(x0, x1, app(ty_[], x2))
new_pePe(False, x0)
new_esEs16(:%(x0, x1), :%(x2, x3), x4)
new_primCmpNat2(Succ(x0), Zero)
new_compare23(x0, x1, True, x2, x3)
new_primCmpNat1(Succ(x0), x1)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, ty_Char)
new_ltEs4(x0, x1, app(ty_[], x2))
new_ltEs13(EQ, GT)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_ltEs13(GT, EQ)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, ty_Float)
new_esEs24(x0, x1, ty_Integer)
new_ltEs14(Just(x0), Just(x1), ty_Char)
new_lt21(x0, x1, app(ty_Ratio, x2))
new_esEs32(x0, x1, app(ty_[], x2))
new_ltEs15(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs19(x0, x1, ty_@0)
new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_lt7(x0, x1)
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs19(x0, x1, ty_Double)
new_ltEs15(Right(x0), Right(x1), x2, ty_Double)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, ty_Integer)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_esEs31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_compare15(x0, x1, True)
new_compare29(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_Float)
new_ltEs15(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs20(x0, x1, ty_Int)
new_lt20(x0, x1, ty_@0)
new_esEs26(x0, x1, ty_@0)
new_ltEs13(LT, GT)
new_ltEs13(GT, LT)
new_ltEs18(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs31(x0, x1, ty_Char)
new_ltEs4(x0, x1, app(app(ty_@2, x2), x3))
new_compare26(x0, x1, True, x2, x3, x4)
new_esEs26(x0, x1, ty_Float)
new_sr(x0, x1)
new_esEs18(x0, x1, ty_Integer)
new_ltEs20(x0, x1, ty_Char)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_compare7(x0, x1)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, ty_@0)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs15(Left(x0), Left(x1), ty_Float, x2)
new_primPlusNat0(Zero, x0)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_compare29(x0, x1, app(ty_Maybe, x2))
new_esEs6(Left(x0), Left(x1), ty_Char, x2)
new_lt20(x0, x1, ty_Bool)
new_esEs19(x0, x1, ty_Bool)
new_compare1([], [], x0)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_lt6(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Float)
new_ltEs14(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs7(x0, x1)
new_primCmpNat0(x0, Succ(x1))
new_ltEs15(Right(x0), Right(x1), x2, ty_Bool)
new_compare1(:(x0, x1), :(x2, x3), x4)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare28(x0, x1, True, x2, x3)
new_esEs32(x0, x1, ty_Float)
new_esEs29(x0, x1, ty_Char)
new_esEs20(x0, x1, ty_Bool)
new_compare111(x0, x1, False, x2)
new_lt19(x0, x1, ty_Float)
new_lt21(x0, x1, ty_Ordering)
new_esEs6(Right(x0), Right(x1), x2, ty_Float)
new_compare19(x0, x1, x2, x3, x4)
new_esEs21(x0, x1, ty_Float)
new_esEs5(Nothing, Just(x0), x1)
new_ltEs15(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs20(x0, x1, ty_Ordering)
new_compare10(x0, x1, x2, x3, False, x4, x5)
new_esEs26(x0, x1, ty_Double)
new_lt6(x0, x1, ty_Float)
new_esEs30(x0, x1, x2, x3, False, x4, x5)
new_lt19(x0, x1, app(ty_[], x2))
new_esEs8(GT, EQ)
new_esEs8(EQ, GT)
new_ltEs14(Just(x0), Just(x1), ty_@0)
new_esEs26(x0, x1, ty_Int)
new_ltEs12(False, True)
new_ltEs12(True, False)
new_ltEs15(Right(x0), Left(x1), x2, x3)
new_ltEs15(Left(x0), Right(x1), x2, x3)
new_lt21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, ty_Int)
new_primMulInt(Neg(x0), Neg(x1))
new_compare210(x0, x1, True, x2)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_ltEs4(x0, x1, ty_Float)
new_ltEs14(Just(x0), Just(x1), app(ty_[], x2))
new_primEqNat0(Succ(x0), Zero)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs16(x0, x1)
new_ltEs4(x0, x1, app(app(ty_Either, x2), x3))
new_esEs18(x0, x1, ty_Float)
new_ltEs14(Just(x0), Just(x1), ty_Float)
new_esEs31(x0, x1, app(ty_Maybe, x2))
new_primMulInt(Pos(x0), Pos(x1))
new_compare15(x0, x1, False)
new_compare25(x0, x1, True)
new_lt15(x0, x1, x2)
new_compare29(x0, x1, ty_Char)
new_ltEs13(LT, LT)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs6(Left(x0), Left(x1), ty_Float, x2)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, ty_Integer)
new_ltEs4(x0, x1, ty_Ordering)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs6(Right(x0), Right(x1), x2, ty_Integer)
new_compare1(:(x0, x1), [], x2)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1, ty_Ordering)
new_esEs6(Right(x0), Right(x1), x2, ty_Char)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, ty_@0)
new_esEs20(x0, x1, ty_Integer)
new_lt20(x0, x1, ty_Char)
new_lt20(x0, x1, ty_Ordering)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs29(x0, x1, ty_Float)
new_esEs32(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_lt6(x0, x1, ty_Int)
new_compare29(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_Int)
new_lt21(x0, x1, ty_@0)
new_ltEs13(GT, GT)
new_compare12(x0, x1, x2, x3)
new_esEs13(False, True)
new_esEs13(True, False)
new_esEs22(x0, x1, ty_Integer)
new_compare8(Double(x0, x1), Double(x2, x3))
new_lt21(x0, x1, ty_Integer)
new_compare29(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, ty_@0)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_compare1([], :(x0, x1), x2)
new_esEs23(x0, x1, ty_@0)
new_esEs32(x0, x1, ty_Double)
new_esEs18(x0, x1, ty_Char)
new_compare110(x0, x1, True)
new_compare14(x0, x1, True, x2, x3)
new_compare13(x0, x1)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Double)
new_esEs5(Just(x0), Just(x1), ty_@0)
new_not(True)
new_esEs28(x0, x1, ty_Int)
new_esEs28(x0, x1, ty_Bool)
new_esEs28(x0, x1, ty_Double)
new_compare24(x0, x1, False)
new_esEs13(True, True)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs31(x0, x1, app(app(ty_@2, x2), x3))
new_lt6(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_lt14(x0, x1)
new_ltEs14(Nothing, Nothing, x0)
new_esEs29(x0, x1, ty_@0)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs29(x0, x1, ty_Bool)
new_ltEs9(@2(x0, x1), @2(x2, x3), x4, x5)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_not(False)
new_esEs11(:(x0, x1), [], x2)
new_compare110(x0, x1, False)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs31(x0, x1, ty_Int)
new_ltEs4(x0, x1, ty_Bool)
new_lt6(x0, x1, ty_@0)
new_compare30(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs6(Right(x0), Left(x1), x2, x3)
new_esEs6(Left(x0), Right(x1), x2, x3)
new_ltEs15(Left(x0), Left(x1), ty_@0, x2)
new_esEs5(Just(x0), Just(x1), ty_Float)
new_lt4(x0, x1, x2, x3)
new_esEs32(x0, x1, ty_@0)
new_ltEs12(True, True)
new_esEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs23(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_@0)
new_esEs22(x0, x1, ty_Double)
new_compare24(x0, x1, True)
new_lt6(x0, x1, ty_Char)
new_ltEs4(x0, x1, ty_@0)
new_ltEs4(x0, x1, app(ty_Maybe, x2))
new_esEs9(Integer(x0), Integer(x1))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, ty_Bool)
new_esEs19(x0, x1, ty_Float)
new_esEs27(x0, x1, ty_Double)
new_ltEs6(x0, x1, x2)
new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_esEs20(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_Ordering)
new_esEs27(x0, x1, ty_Bool)
new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt19(x0, x1, ty_Bool)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs32(x0, x1, ty_Int)
new_ltEs14(Just(x0), Just(x1), ty_Int)
new_compare16(Float(x0, x1), Float(x2, x3))
new_esEs11([], [], x0)
new_compare29(x0, x1, ty_Double)
new_esEs32(x0, x1, ty_Ordering)
new_esEs5(Just(x0), Just(x1), ty_Integer)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare29(x0, x1, app(app(ty_@2, x2), x3))
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_lt21(x0, x1, ty_Bool)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, ty_@0)
new_ltEs20(x0, x1, ty_Integer)
new_lt12(x0, x1)
new_fsEs(x0)
new_compare27(@0, @0)
new_esEs19(x0, x1, ty_Integer)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_ltEs15(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_primCompAux00(x0, GT)
new_esEs26(x0, x1, ty_Char)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_sr0(Integer(x0), Integer(x1))
new_esEs21(x0, x1, ty_Bool)
new_primMulNat0(Succ(x0), Zero)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs10(Char(x0), Char(x1))
new_ltEs14(Just(x0), Nothing, x1)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs21(x0, x1, ty_Char)
new_primPlusNat1(Succ(x0), Zero)
new_ltEs19(x0, x1, ty_Integer)
new_primEqInt(Pos(Zero), Pos(Zero))
new_primMulNat0(Succ(x0), Succ(x1))
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs31(x0, x1, ty_Ordering)
new_compare29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Int)
new_lt11(x0, x1, x2, x3)
new_compare10(x0, x1, x2, x3, True, x4, x5)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_lt19(x0, x1, ty_Int)
new_lt6(x0, x1, app(ty_Ratio, x2))
new_lt21(x0, x1, ty_Double)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, ty_Ordering)
new_lt21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, app(ty_[], x2))
new_lt6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt18(x0, x1, x2, x3, x4)
new_esEs29(x0, x1, ty_Integer)
new_esEs31(x0, x1, ty_Double)
new_primPlusNat0(Succ(x0), x1)
new_esEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs6(Left(x0), Left(x1), ty_@0, x2)
new_ltEs14(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs18(x0, x1, app(ty_[], x2))
new_ltEs4(x0, x1, ty_Int)
new_esEs18(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(Nothing, Just(x0), x1)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs28(x0, x1, ty_Integer)
new_esEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Double)
new_esEs21(x0, x1, ty_Int)

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

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



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

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

new_foldl(xuu6, :(xuu3110, xuu3111), h, ba, bb) → new_foldl(new_addListToFM_CAdd(xuu6, xuu3110, h, ba, bb), xuu3111, h, ba, bb)

The TRS R consists of the following rules:

new_primCmpNat0(xuu4900, Succ(xuu5100)) → new_primCmpNat2(xuu4900, xuu5100)
new_lt10(xuu490, xuu510) → new_esEs8(new_compare18(xuu490, xuu510), LT)
new_compare19(xuu490, xuu510, cg, da, db) → new_compare26(xuu490, xuu510, new_esEs7(xuu490, xuu510, cg, da, db), cg, da, db)
new_mkBranch0(xuu142, xuu143, xuu144, xuu145, xuu146, xuu147, xuu148, xuu149, xuu150, be, bf, bg) → new_mkBranchResult0(xuu142, xuu143, xuu145, xuu146, xuu147, xuu148, xuu149, xuu150, xuu144, be, bf, bg)
new_lt19(xuu4910, xuu5110, ty_Double) → new_lt7(xuu4910, xuu5110)
new_lt19(xuu4910, xuu5110, app(ty_Maybe, cfa)) → new_lt15(xuu4910, xuu5110, cfa)
new_esEs21(xuu3110001, xuu6001, ty_Float) → new_esEs14(xuu3110001, xuu6001)
new_esEs13(True, False) → False
new_esEs13(False, True) → False
new_esEs5(Just(xuu3110000), Just(xuu6000), ty_Ordering) → new_esEs8(xuu3110000, xuu6000)
new_esEs31(xuu311000, xuu600, ty_Ordering) → new_esEs8(xuu311000, xuu600)
new_esEs23(xuu4910, xuu5110, app(app(ty_@2, cef), ceg)) → new_esEs4(xuu4910, xuu5110, cef, ceg)
new_esEs28(xuu3110000, xuu6000, ty_Float) → new_esEs14(xuu3110000, xuu6000)
new_compare6(xuu490, xuu510, bc, bd) → new_compare28(xuu490, xuu510, new_esEs6(xuu490, xuu510, bc, bd), bc, bd)
new_lt21(xuu4911, xuu5111, ty_Ordering) → new_lt14(xuu4911, xuu5111)
new_compare29(xuu4900, xuu5100, ty_Double) → new_compare8(xuu4900, xuu5100)
new_esEs20(xuu3110000, xuu6000, ty_Double) → new_esEs12(xuu3110000, xuu6000)
new_esEs31(xuu311000, xuu600, ty_@0) → new_esEs17(xuu311000, xuu600)
new_ltEs15(Left(xuu4910), Left(xuu5110), ty_Ordering, ea) → new_ltEs13(xuu4910, xuu5110)
new_lt19(xuu4910, xuu5110, ty_Ordering) → new_lt14(xuu4910, xuu5110)
new_esEs21(xuu3110001, xuu6001, ty_@0) → new_esEs17(xuu3110001, xuu6001)
new_primMulNat0(Zero, Zero) → Zero
new_lt21(xuu4911, xuu5111, ty_@0) → new_lt17(xuu4911, xuu5111)
new_ltEs15(Left(xuu4910), Left(xuu5110), app(ty_Maybe, dcg), ea) → new_ltEs14(xuu4910, xuu5110, dcg)
new_esEs6(Left(xuu3110000), Left(xuu6000), app(ty_[], bfg), bff) → new_esEs11(xuu3110000, xuu6000, bfg)
new_esEs5(Just(xuu3110000), Just(xuu6000), app(ty_Ratio, dad)) → new_esEs16(xuu3110000, xuu6000, dad)
new_esEs6(Left(xuu3110000), Left(xuu6000), app(app(app(ty_@3, bgc), bgd), bge), bff) → new_esEs7(xuu3110000, xuu6000, bgc, bgd, bge)
new_compare29(xuu4900, xuu5100, ty_Float) → new_compare16(xuu4900, xuu5100)
new_esEs20(xuu3110000, xuu6000, app(ty_Ratio, cbf)) → new_esEs16(xuu3110000, xuu6000, cbf)
new_esEs6(Left(xuu3110000), Left(xuu6000), app(ty_Ratio, bgf), bff) → new_esEs16(xuu3110000, xuu6000, bgf)
new_ltEs15(Right(xuu4910), Right(xuu5110), dh, ty_Integer) → new_ltEs10(xuu4910, xuu5110)
new_esEs18(xuu490, xuu510, ty_Double) → new_esEs12(xuu490, xuu510)
new_ltEs15(Right(xuu4910), Right(xuu5110), dh, ty_Ordering) → new_ltEs13(xuu4910, xuu5110)
new_ltEs4(xuu491, xuu511, ty_Ordering) → new_ltEs13(xuu491, xuu511)
new_lt20(xuu4910, xuu5110, app(app(app(ty_@3, bbb), bbc), bbd)) → new_lt18(xuu4910, xuu5110, bbb, bbc, bbd)
new_esEs22(xuu3110002, xuu6002, ty_@0) → new_esEs17(xuu3110002, xuu6002)
new_compare10(xuu105, xuu106, xuu107, xuu108, True, ee, ef) → LT
new_esEs28(xuu3110000, xuu6000, ty_Int) → new_esEs15(xuu3110000, xuu6000)
new_lt20(xuu4910, xuu5110, app(app(ty_@2, bad), bae)) → new_lt11(xuu4910, xuu5110, bad, bae)
new_mkBranchResult1(xuu160, xuu161, xuu163, xuu162, hh, baa, bab) → Branch(xuu160, xuu161, new_mkBranchUnbox(xuu163, xuu160, xuu162, new_ps(xuu163, xuu160, xuu162, xuu162, hh, baa, bab), hh, baa, bab), xuu162, xuu163)
new_compare1([], :(xuu5100, xuu5101), ce) → LT
new_esEs32(xuu37, xuu39, ty_Bool) → new_esEs13(xuu37, xuu39)
new_esEs19(xuu3110000, xuu6000, app(app(app(ty_@3, fd), ff), fg)) → new_esEs7(xuu3110000, xuu6000, fd, ff, fg)
new_lt21(xuu4911, xuu5111, app(ty_Ratio, bbe)) → new_lt8(xuu4911, xuu5111, bbe)
new_ltEs15(Right(xuu4910), Right(xuu5110), dh, app(ty_[], ddh)) → new_ltEs11(xuu4910, xuu5110, ddh)
new_mkBranch4(xuu160, xuu161, xuu162, xuu163, hh, baa, bab) → new_mkBranchResult1(xuu160, xuu161, xuu163, xuu162, hh, baa, bab)
new_esEs21(xuu3110001, xuu6001, ty_Int) → new_esEs15(xuu3110001, xuu6001)
new_ltEs13(LT, EQ) → True
new_ltEs15(Left(xuu4910), Left(xuu5110), ty_Int, ea) → new_ltEs7(xuu4910, xuu5110)
new_lt16(xuu490, xuu510) → new_esEs8(new_compare16(xuu490, xuu510), LT)
new_mkBranch(xuu145, xuu146, xuu147, xuu148, xuu149, xuu150, be, bf, bg) → new_mkBranchResult(xuu146, xuu147, xuu148, xuu150, xuu149, be, bf, bg)
new_esEs11([], [], eg) → True
new_esEs32(xuu37, xuu39, app(app(ty_@2, dbc), dbd)) → new_esEs4(xuu37, xuu39, dbc, dbd)
new_esEs21(xuu3110001, xuu6001, app(app(app(ty_@3, cce), ccf), ccg)) → new_esEs7(xuu3110001, xuu6001, cce, ccf, ccg)
new_esEs5(Just(xuu3110000), Just(xuu6000), app(ty_Maybe, chf)) → new_esEs5(xuu3110000, xuu6000, chf)
new_esEs5(Just(xuu3110000), Just(xuu6000), ty_Float) → new_esEs14(xuu3110000, xuu6000)
new_esEs20(xuu3110000, xuu6000, ty_Char) → new_esEs10(xuu3110000, xuu6000)
new_esEs22(xuu3110002, xuu6002, ty_Integer) → new_esEs9(xuu3110002, xuu6002)
new_esEs6(Left(xuu3110000), Left(xuu6000), ty_Float, bff) → new_esEs14(xuu3110000, xuu6000)
new_esEs21(xuu3110001, xuu6001, app(app(ty_Either, cda), cdb)) → new_esEs6(xuu3110001, xuu6001, cda, cdb)
new_esEs29(xuu3110001, xuu6001, app(app(app(ty_@3, dge), dgf), dgg)) → new_esEs7(xuu3110001, xuu6001, dge, dgf, dgg)
new_lt20(xuu4910, xuu5110, app(ty_Maybe, bag)) → new_lt15(xuu4910, xuu5110, bag)
new_lt20(xuu4910, xuu5110, app(ty_[], baf)) → new_lt13(xuu4910, xuu5110, baf)
new_mkBranch1(xuu194, xuu195, xuu196, xuu197, xuu198, xuu199, xuu200, xuu201, xuu202, xuu203, xuu204, xuu205, xuu206, xuu207, bea, beb, bec) → new_mkBranchResult0(xuu195, xuu196, xuu202, xuu203, xuu204, xuu205, xuu206, xuu207, new_mkBranch2(xuu197, xuu198, xuu199, xuu200, xuu201, bea, beb, bec), bea, beb, bec)
new_ltEs4(xuu491, xuu511, ty_Double) → new_ltEs5(xuu491, xuu511)
new_compare15(xuu490, xuu510, False) → GT
new_esEs23(xuu4910, xuu5110, ty_Bool) → new_esEs13(xuu4910, xuu5110)
new_esEs17(@0, @0) → True
new_ltEs19(xuu4911, xuu5111, ty_Float) → new_ltEs16(xuu4911, xuu5111)
new_lt20(xuu4910, xuu5110, ty_Double) → new_lt7(xuu4910, xuu5110)
new_pePe(False, xuu129) → xuu129
new_compare29(xuu4900, xuu5100, app(ty_Maybe, gg)) → new_compare31(xuu4900, xuu5100, gg)
new_ltEs6(xuu491, xuu511, dc) → new_fsEs(new_compare30(xuu491, xuu511, dc))
new_esEs5(Just(xuu3110000), Just(xuu6000), ty_Bool) → new_esEs13(xuu3110000, xuu6000)
new_esEs6(Left(xuu3110000), Left(xuu6000), app(app(ty_@2, bga), bgb), bff) → new_esEs4(xuu3110000, xuu6000, bga, bgb)
new_ltEs12(True, False) → False
new_lt6(xuu490, xuu510, ty_Double) → new_lt7(xuu490, xuu510)
new_esEs23(xuu4910, xuu5110, ty_Float) → new_esEs14(xuu4910, xuu5110)
new_ltEs14(Just(xuu4910), Just(xuu5110), app(app(ty_@2, bee), bef)) → new_ltEs9(xuu4910, xuu5110, bee, bef)
new_esEs15(xuu311000, xuu600) → new_primEqInt(xuu311000, xuu600)
new_compare29(xuu4900, xuu5100, app(app(ty_@2, gd), ge)) → new_compare12(xuu4900, xuu5100, gd, ge)
new_esEs29(xuu3110001, xuu6001, ty_@0) → new_esEs17(xuu3110001, xuu6001)
new_ltEs14(Just(xuu4910), Just(xuu5110), app(ty_Maybe, beh)) → new_ltEs14(xuu4910, xuu5110, beh)
new_ltEs19(xuu4911, xuu5111, app(ty_[], cgb)) → new_ltEs11(xuu4911, xuu5111, cgb)
new_mkBalBranch6MkBalBranch3(xuu41, xuu19, xuu20, xuu21, xuu24, False, he, hf, hg) → new_mkBranchResult(xuu19, xuu20, xuu21, xuu24, xuu41, he, hf, hg)
new_ltEs15(Right(xuu4910), Right(xuu5110), dh, ty_Char) → new_ltEs8(xuu4910, xuu5110)
new_esEs22(xuu3110002, xuu6002, app(app(ty_@2, cde), cdf)) → new_esEs4(xuu3110002, xuu6002, cde, cdf)
new_compare15(xuu490, xuu510, True) → LT
new_esEs19(xuu3110000, xuu6000, ty_Float) → new_esEs14(xuu3110000, xuu6000)
new_compare9(xuu86, xuu85) → new_primCmpInt(xuu86, xuu85)
new_ltEs20(xuu4912, xuu5112, ty_Double) → new_ltEs5(xuu4912, xuu5112)
new_ltEs13(EQ, GT) → True
new_esEs22(xuu3110002, xuu6002, ty_Ordering) → new_esEs8(xuu3110002, xuu6002)
new_ltEs15(Right(xuu4910), Right(xuu5110), dh, ty_@0) → new_ltEs17(xuu4910, xuu5110)
new_lt21(xuu4911, xuu5111, ty_Char) → new_lt10(xuu4911, xuu5111)
new_esEs28(xuu3110000, xuu6000, app(ty_Ratio, dff)) → new_esEs16(xuu3110000, xuu6000, dff)
new_lt21(xuu4911, xuu5111, app(app(ty_Either, bcb), bcc)) → new_lt4(xuu4911, xuu5111, bcb, bcc)
new_ltEs14(Just(xuu4910), Just(xuu5110), ty_Int) → new_ltEs7(xuu4910, xuu5110)
new_esEs29(xuu3110001, xuu6001, app(ty_[], dga)) → new_esEs11(xuu3110001, xuu6001, dga)
new_esEs29(xuu3110001, xuu6001, app(app(ty_@2, dgc), dgd)) → new_esEs4(xuu3110001, xuu6001, dgc, dgd)
new_esEs31(xuu311000, xuu600, ty_Char) → new_esEs10(xuu311000, xuu600)
new_ltEs19(xuu4911, xuu5111, ty_Int) → new_ltEs7(xuu4911, xuu5111)
new_esEs18(xuu490, xuu510, app(app(ty_Either, bc), bd)) → new_esEs6(xuu490, xuu510, bc, bd)
new_esEs23(xuu4910, xuu5110, app(app(app(ty_@3, cfd), cfe), cff)) → new_esEs7(xuu4910, xuu5110, cfd, cfe, cff)
new_ltEs15(Left(xuu4910), Left(xuu5110), ty_Float, ea) → new_ltEs16(xuu4910, xuu5110)
new_primCmpInt(Neg(Succ(xuu4900)), Neg(xuu510)) → new_primCmpNat1(xuu510, xuu4900)
new_lt6(xuu490, xuu510, app(app(ty_@2, cc), cd)) → new_lt11(xuu490, xuu510, cc, cd)
new_primCompAux0(xuu4900, xuu5100, xuu130, ce) → new_primCompAux00(xuu130, new_compare29(xuu4900, xuu5100, ce))
new_esEs27(xuu4911, xuu5111, app(app(app(ty_@3, bcd), bce), bcf)) → new_esEs7(xuu4911, xuu5111, bcd, bce, bcf)
new_lt6(xuu490, xuu510, app(ty_[], ce)) → new_lt13(xuu490, xuu510, ce)
new_compare29(xuu4900, xuu5100, app(ty_[], gf)) → new_compare1(xuu4900, xuu5100, gf)
new_esEs26(xuu4910, xuu5110, ty_Double) → new_esEs12(xuu4910, xuu5110)
new_mkBalBranch6Size_r(xuu41, xuu19, xuu20, xuu21, xuu24, he, hf, hg) → new_sizeFM(xuu24, he, hf, hg)
new_esEs31(xuu311000, xuu600, app(app(ty_@2, chc), chd)) → new_esEs4(xuu311000, xuu600, chc, chd)
new_ltEs14(Just(xuu4910), Just(xuu5110), ty_Bool) → new_ltEs12(xuu4910, xuu5110)
new_ltEs14(Just(xuu4910), Nothing, dg) → False
new_esEs6(Right(xuu3110000), Left(xuu6000), bha, bff) → False
new_esEs6(Left(xuu3110000), Right(xuu6000), bha, bff) → False
new_esEs8(LT, LT) → True
new_esEs31(xuu311000, xuu600, ty_Int) → new_esEs15(xuu311000, xuu600)
new_esEs31(xuu311000, xuu600, app(ty_Maybe, chb)) → new_esEs5(xuu311000, xuu600, chb)
new_compare29(xuu4900, xuu5100, app(app(app(ty_@3, hb), hc), hd)) → new_compare19(xuu4900, xuu5100, hb, hc, hd)
new_lt6(xuu490, xuu510, app(app(ty_Either, bc), bd)) → new_lt4(xuu490, xuu510, bc, bd)
new_esEs28(xuu3110000, xuu6000, app(ty_[], deg)) → new_esEs11(xuu3110000, xuu6000, deg)
new_ltEs4(xuu491, xuu511, ty_Float) → new_ltEs16(xuu491, xuu511)
new_esEs29(xuu3110001, xuu6001, ty_Char) → new_esEs10(xuu3110001, xuu6001)
new_esEs29(xuu3110001, xuu6001, ty_Bool) → new_esEs13(xuu3110001, xuu6001)
new_esEs18(xuu490, xuu510, app(ty_Ratio, cb)) → new_esEs16(xuu490, xuu510, cb)
new_lt19(xuu4910, xuu5110, app(app(ty_@2, cef), ceg)) → new_lt11(xuu4910, xuu5110, cef, ceg)
new_pePe(True, xuu129) → True
new_compare14(xuu490, xuu510, False, bc, bd) → GT
new_primEqNat0(Zero, Zero) → True
new_ltEs19(xuu4911, xuu5111, app(ty_Maybe, cgc)) → new_ltEs14(xuu4911, xuu5111, cgc)
new_ltEs12(False, False) → True
new_esEs23(xuu4910, xuu5110, app(app(ty_Either, cfb), cfc)) → new_esEs6(xuu4910, xuu5110, cfb, cfc)
new_esEs5(Just(xuu3110000), Just(xuu6000), ty_@0) → new_esEs17(xuu3110000, xuu6000)
new_esEs5(Just(xuu3110000), Just(xuu6000), app(app(ty_@2, chg), chh)) → new_esEs4(xuu3110000, xuu6000, chg, chh)
new_esEs23(xuu4910, xuu5110, ty_Integer) → new_esEs9(xuu4910, xuu5110)
new_compare12(xuu490, xuu510, cc, cd) → new_compare23(xuu490, xuu510, new_esEs4(xuu490, xuu510, cc, cd), cc, cd)
new_lt20(xuu4910, xuu5110, app(ty_Ratio, bac)) → new_lt8(xuu4910, xuu5110, bac)
new_esEs20(xuu3110000, xuu6000, ty_Bool) → new_esEs13(xuu3110000, xuu6000)
new_esEs6(Right(xuu3110000), Right(xuu6000), bha, app(app(ty_Either, cab), cac)) → new_esEs6(xuu3110000, xuu6000, cab, cac)
new_lt11(xuu490, xuu510, cc, cd) → new_esEs8(new_compare12(xuu490, xuu510, cc, cd), LT)
new_esEs25(xuu3110001, xuu6001, ty_Int) → new_esEs15(xuu3110001, xuu6001)
new_lt6(xuu490, xuu510, ty_Int) → new_lt9(xuu490, xuu510)
new_mkBranch2(xuu197, xuu198, xuu199, xuu200, xuu201, bea, beb, bec) → new_mkBranchResult1(xuu198, xuu199, xuu201, xuu200, bea, beb, bec)
new_esEs18(xuu490, xuu510, ty_Char) → new_esEs10(xuu490, xuu510)
new_lt6(xuu490, xuu510, ty_Char) → new_lt10(xuu490, xuu510)
new_ltEs20(xuu4912, xuu5112, app(app(ty_@2, bch), bda)) → new_ltEs9(xuu4912, xuu5112, bch, bda)
new_sr(xuu3110001, xuu6001) → new_primMulInt(xuu3110001, xuu6001)
new_esEs28(xuu3110000, xuu6000, app(app(ty_Either, dfg), dfh)) → new_esEs6(xuu3110000, xuu6000, dfg, dfh)
new_lt13(xuu490, xuu510, ce) → new_esEs8(new_compare1(xuu490, xuu510, ce), LT)
new_compare10(xuu105, xuu106, xuu107, xuu108, False, ee, ef) → GT
new_primPlusInt(Neg(xuu4120), Neg(xuu920)) → Neg(new_primPlusNat1(xuu4120, xuu920))
new_primCmpInt(Neg(Zero), Neg(Succ(xuu5100))) → new_primCmpNat0(xuu5100, Zero)
new_esEs26(xuu4910, xuu5110, ty_Ordering) → new_esEs8(xuu4910, xuu5110)
new_esEs31(xuu311000, xuu600, app(app(app(ty_@3, cad), cae), caf)) → new_esEs7(xuu311000, xuu600, cad, cae, caf)
new_addToFM_C10(xuu19, xuu20, xuu21, xuu22, xuu23, xuu24, xuu25, xuu26, xuu27, True, he, hf, hg) → new_mkBalBranch(xuu19, xuu20, xuu21, xuu23, new_addToFM_C0(xuu24, @2(xuu25, xuu26), xuu27, he, hf, hg), he, hf, hg)
new_esEs8(GT, GT) → True
new_esEs20(xuu3110000, xuu6000, ty_Integer) → new_esEs9(xuu3110000, xuu6000)
new_primPlusNat0(Succ(xuu960), xuu600100) → Succ(Succ(new_primPlusNat1(xuu960, xuu600100)))
new_esEs27(xuu4911, xuu5111, ty_Char) → new_esEs10(xuu4911, xuu5111)
new_esEs30(xuu36, xuu37, xuu38, xuu39, False, dag, dah) → new_esEs8(new_compare23(@2(xuu36, xuu37), @2(xuu38, xuu39), False, dag, dah), LT)
new_primCmpInt(Pos(Zero), Pos(Succ(xuu5100))) → new_primCmpNat1(Zero, xuu5100)
new_lt20(xuu4910, xuu5110, ty_Ordering) → new_lt14(xuu4910, xuu5110)
new_esEs20(xuu3110000, xuu6000, app(app(app(ty_@3, cbc), cbd), cbe)) → new_esEs7(xuu3110000, xuu6000, cbc, cbd, cbe)
new_ltEs19(xuu4911, xuu5111, ty_Bool) → new_ltEs12(xuu4911, xuu5111)
new_esEs8(GT, LT) → False
new_esEs8(LT, GT) → False
new_ltEs11(xuu491, xuu511, df) → new_fsEs(new_compare1(xuu491, xuu511, df))
new_addToFM_C0(EmptyFM, xuu31100, xuu31101, h, ba, bb) → Branch(xuu31100, xuu31101, Pos(Succ(Zero)), new_emptyFM(h, ba, bb), new_emptyFM(h, ba, bb))
new_ltEs20(xuu4912, xuu5112, ty_Float) → new_ltEs16(xuu4912, xuu5112)
new_lt21(xuu4911, xuu5111, app(app(app(ty_@3, bcd), bce), bcf)) → new_lt18(xuu4911, xuu5111, bcd, bce, bcf)
new_ltEs15(Left(xuu4910), Left(xuu5110), ty_@0, ea) → new_ltEs17(xuu4910, xuu5110)
new_esEs5(Just(xuu3110000), Just(xuu6000), ty_Double) → new_esEs12(xuu3110000, xuu6000)
new_esEs6(Left(xuu3110000), Left(xuu6000), ty_Int, bff) → new_esEs15(xuu3110000, xuu6000)
new_compare28(xuu490, xuu510, False, bc, bd) → new_compare14(xuu490, xuu510, new_ltEs15(xuu490, xuu510, bc, bd), bc, bd)
new_compare25(xuu490, xuu510, True) → EQ
new_primEqInt(Neg(Succ(xuu31100000)), Neg(Succ(xuu60000))) → new_primEqNat0(xuu31100000, xuu60000)
new_mkBranchResult(xuu19, xuu20, xuu21, xuu24, xuu41, he, hf, hg) → Branch(@2(xuu19, xuu20), xuu21, new_mkBranchUnbox(xuu24, @2(xuu19, xuu20), xuu41, new_ps(xuu24, @2(xuu19, xuu20), xuu41, xuu41, he, hf, hg), he, hf, hg), xuu41, xuu24)
new_mkBranchResult0(xuu142, xuu143, xuu145, xuu146, xuu147, xuu148, xuu149, xuu150, xuu144, be, bf, bg) → Branch(xuu142, xuu143, new_mkBranchUnbox(new_mkBranch(xuu145, xuu146, xuu147, xuu148, xuu149, xuu150, be, bf, bg), xuu142, xuu144, new_ps(new_mkBranch2(xuu145, @2(xuu146, xuu147), xuu148, xuu149, xuu150, be, bf, bg), xuu142, xuu144, xuu144, be, bf, bg), be, bf, bg), xuu144, new_mkBranch(xuu145, xuu146, xuu147, xuu148, xuu149, xuu150, be, bf, bg))
new_ltEs15(Left(xuu4910), Left(xuu5110), ty_Double, ea) → new_ltEs5(xuu4910, xuu5110)
new_esEs20(xuu3110000, xuu6000, ty_Ordering) → new_esEs8(xuu3110000, xuu6000)
new_esEs6(Right(xuu3110000), Right(xuu6000), bha, app(app(app(ty_@3, bhf), bhg), bhh)) → new_esEs7(xuu3110000, xuu6000, bhf, bhg, bhh)
new_esEs23(xuu4910, xuu5110, ty_Int) → new_esEs15(xuu4910, xuu5110)
new_esEs23(xuu4910, xuu5110, ty_Ordering) → new_esEs8(xuu4910, xuu5110)
new_ltEs19(xuu4911, xuu5111, ty_Double) → new_ltEs5(xuu4911, xuu5111)
new_esEs27(xuu4911, xuu5111, ty_Bool) → new_esEs13(xuu4911, xuu5111)
new_ltEs14(Just(xuu4910), Just(xuu5110), ty_Ordering) → new_ltEs13(xuu4910, xuu5110)
new_primPlusNat1(Zero, Succ(xuu9200)) → Succ(xuu9200)
new_primPlusNat1(Succ(xuu41200), Zero) → Succ(xuu41200)
new_ltEs20(xuu4912, xuu5112, ty_Bool) → new_ltEs12(xuu4912, xuu5112)
new_esEs28(xuu3110000, xuu6000, ty_@0) → new_esEs17(xuu3110000, xuu6000)
new_esEs22(xuu3110002, xuu6002, ty_Int) → new_esEs15(xuu3110002, xuu6002)
new_esEs26(xuu4910, xuu5110, app(app(app(ty_@3, bbb), bbc), bbd)) → new_esEs7(xuu4910, xuu5110, bbb, bbc, bbd)
new_esEs20(xuu3110000, xuu6000, ty_Int) → new_esEs15(xuu3110000, xuu6000)
new_ltEs13(LT, GT) → True
new_primCmpNat1(Zero, xuu4900) → LT
new_esEs6(Left(xuu3110000), Left(xuu6000), ty_Integer, bff) → new_esEs9(xuu3110000, xuu6000)
new_lt20(xuu4910, xuu5110, app(app(ty_Either, bah), bba)) → new_lt4(xuu4910, xuu5110, bah, bba)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_mkBalBranch6MkBalBranch4(xuu41, xuu19, xuu20, xuu21, Branch(xuu240, xuu241, xuu242, xuu243, xuu244), True, he, hf, hg) → new_mkBalBranch6MkBalBranch01(xuu41, xuu19, xuu20, xuu21, xuu240, xuu241, xuu242, xuu243, xuu244, new_lt9(new_sizeFM(xuu243, he, hf, hg), new_sr(Pos(Succ(Succ(Zero))), new_sizeFM(xuu244, he, hf, hg))), he, hf, hg)
new_compare11(xuu105, xuu106, xuu107, xuu108, False, xuu110, ee, ef) → new_compare10(xuu105, xuu106, xuu107, xuu108, xuu110, ee, ef)
new_lt6(xuu490, xuu510, app(ty_Ratio, cb)) → new_lt8(xuu490, xuu510, cb)
new_lt19(xuu4910, xuu5110, ty_Integer) → new_lt12(xuu4910, xuu5110)
new_esEs32(xuu37, xuu39, ty_Float) → new_esEs14(xuu37, xuu39)
new_primEqInt(Neg(Succ(xuu31100000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(xuu60000))) → False
new_esEs8(EQ, EQ) → True
new_lt6(xuu490, xuu510, ty_Float) → new_lt16(xuu490, xuu510)
new_compare111(xuu490, xuu510, True, cf) → LT
new_esEs24(xuu3110000, xuu6000, ty_Integer) → new_esEs9(xuu3110000, xuu6000)
new_ltEs15(Right(xuu4910), Right(xuu5110), dh, app(app(ty_@2, ddf), ddg)) → new_ltEs9(xuu4910, xuu5110, ddf, ddg)
new_esEs20(xuu3110000, xuu6000, ty_@0) → new_esEs17(xuu3110000, xuu6000)
new_esEs6(Left(xuu3110000), Left(xuu6000), ty_Char, bff) → new_esEs10(xuu3110000, xuu6000)
new_lt21(xuu4911, xuu5111, ty_Float) → new_lt16(xuu4911, xuu5111)
new_ltEs7(xuu491, xuu511) → new_fsEs(new_compare9(xuu491, xuu511))
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_ltEs15(Left(xuu4910), Left(xuu5110), ty_Char, ea) → new_ltEs8(xuu4910, xuu5110)
new_ltEs16(xuu491, xuu511) → new_fsEs(new_compare16(xuu491, xuu511))
new_compare29(xuu4900, xuu5100, ty_Integer) → new_compare17(xuu4900, xuu5100)
new_ltEs15(Right(xuu4910), Right(xuu5110), dh, ty_Double) → new_ltEs5(xuu4910, xuu5110)
new_primMinusNat0(Succ(xuu41200), Zero) → Pos(Succ(xuu41200))
new_esEs9(Integer(xuu3110000), Integer(xuu6000)) → new_primEqInt(xuu3110000, xuu6000)
new_esEs11(:(xuu3110000, xuu3110001), :(xuu6000, xuu6001), eg) → new_asAs(new_esEs19(xuu3110000, xuu6000, eg), new_esEs11(xuu3110001, xuu6001, eg))
new_addToFM_C20(xuu19, xuu20, xuu21, xuu22, xuu23, xuu24, xuu25, xuu26, xuu27, False, he, hf, hg) → new_addToFM_C10(xuu19, xuu20, xuu21, xuu22, xuu23, xuu24, xuu25, xuu26, xuu27, new_esEs8(new_compare23(@2(xuu25, xuu26), @2(xuu19, xuu20), new_esEs4(@2(xuu25, xuu26), @2(xuu19, xuu20), he, hf), he, hf), GT), he, hf, hg)
new_ltEs13(GT, LT) → False
new_ltEs15(Right(xuu4910), Right(xuu5110), dh, ty_Int) → new_ltEs7(xuu4910, xuu5110)
new_primEqInt(Pos(Succ(xuu31100000)), Pos(Succ(xuu60000))) → new_primEqNat0(xuu31100000, xuu60000)
new_ltEs14(Just(xuu4910), Just(xuu5110), app(ty_Ratio, bed)) → new_ltEs6(xuu4910, xuu5110, bed)
new_esEs22(xuu3110002, xuu6002, ty_Bool) → new_esEs13(xuu3110002, xuu6002)
new_ltEs13(EQ, EQ) → True
new_esEs29(xuu3110001, xuu6001, app(ty_Maybe, dgb)) → new_esEs5(xuu3110001, xuu6001, dgb)
new_mkBalBranch6MkBalBranch01(xuu41, xuu19, xuu20, xuu21, xuu240, xuu241, xuu242, EmptyFM, xuu244, False, he, hf, hg) → error([])
new_esEs19(xuu3110000, xuu6000, app(app(ty_Either, ga), gb)) → new_esEs6(xuu3110000, xuu6000, ga, gb)
new_addToFM_C20(xuu19, xuu20, xuu21, xuu22, xuu23, xuu24, xuu25, xuu26, xuu27, True, he, hf, hg) → new_mkBalBranch(xuu19, xuu20, xuu21, new_addToFM_C0(xuu23, @2(xuu25, xuu26), xuu27, he, hf, hg), xuu24, he, hf, hg)
new_esEs5(Just(xuu3110000), Just(xuu6000), ty_Char) → new_esEs10(xuu3110000, xuu6000)
new_lt14(xuu490, xuu510) → new_esEs8(new_compare13(xuu490, xuu510), LT)
new_primEqNat0(Succ(xuu31100000), Succ(xuu60000)) → new_primEqNat0(xuu31100000, xuu60000)
new_ltEs4(xuu491, xuu511, app(app(ty_@2, dd), de)) → new_ltEs9(xuu491, xuu511, dd, de)
new_esEs27(xuu4911, xuu5111, ty_Ordering) → new_esEs8(xuu4911, xuu5111)
new_lt5(xuu490, xuu510) → new_esEs8(new_compare7(xuu490, xuu510), LT)
new_primCompAux00(xuu134, LT) → LT
new_esEs26(xuu4910, xuu5110, app(ty_[], baf)) → new_esEs11(xuu4910, xuu5110, baf)
new_lt19(xuu4910, xuu5110, app(ty_[], ceh)) → new_lt13(xuu4910, xuu5110, ceh)
new_ltEs19(xuu4911, xuu5111, app(app(app(ty_@3, cgf), cgg), cgh)) → new_ltEs18(xuu4911, xuu5111, cgf, cgg, cgh)
new_esEs26(xuu4910, xuu5110, app(app(ty_@2, bad), bae)) → new_esEs4(xuu4910, xuu5110, bad, bae)
new_esEs6(Right(xuu3110000), Right(xuu6000), bha, app(ty_Maybe, bhc)) → new_esEs5(xuu3110000, xuu6000, bhc)
new_lt15(xuu490, xuu510, cf) → new_esEs8(new_compare31(xuu490, xuu510, cf), LT)
new_esEs28(xuu3110000, xuu6000, ty_Ordering) → new_esEs8(xuu3110000, xuu6000)
new_compare1(:(xuu4900, xuu4901), :(xuu5100, xuu5101), ce) → new_primCompAux0(xuu4900, xuu5100, new_compare1(xuu4901, xuu5101, ce), ce)
new_esEs8(EQ, LT) → False
new_esEs8(LT, EQ) → False
new_primEqInt(Pos(Succ(xuu31100000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(xuu60000))) → False
new_compare11(xuu105, xuu106, xuu107, xuu108, True, xuu110, ee, ef) → new_compare10(xuu105, xuu106, xuu107, xuu108, True, ee, ef)
new_esEs23(xuu4910, xuu5110, ty_@0) → new_esEs17(xuu4910, xuu5110)
new_esEs6(Left(xuu3110000), Left(xuu6000), ty_@0, bff) → new_esEs17(xuu3110000, xuu6000)
new_esEs19(xuu3110000, xuu6000, ty_Integer) → new_esEs9(xuu3110000, xuu6000)
new_compare29(xuu4900, xuu5100, app(ty_Ratio, gc)) → new_compare30(xuu4900, xuu5100, gc)
new_compare25(xuu490, xuu510, False) → new_compare15(xuu490, xuu510, new_ltEs12(xuu490, xuu510))
new_lt20(xuu4910, xuu5110, ty_Bool) → new_lt5(xuu4910, xuu5110)
new_esEs31(xuu311000, xuu600, app(ty_Ratio, cha)) → new_esEs16(xuu311000, xuu600, cha)
new_primCmpInt(Neg(Zero), Pos(Succ(xuu5100))) → LT
new_ltEs20(xuu4912, xuu5112, ty_Integer) → new_ltEs10(xuu4912, xuu5112)
new_ltEs10(xuu491, xuu511) → new_fsEs(new_compare17(xuu491, xuu511))
new_esEs18(xuu490, xuu510, app(app(app(ty_@3, cg), da), db)) → new_esEs7(xuu490, xuu510, cg, da, db)
new_ltEs15(Left(xuu4910), Left(xuu5110), app(ty_[], dcf), ea) → new_ltEs11(xuu4910, xuu5110, dcf)
new_esEs27(xuu4911, xuu5111, ty_Integer) → new_esEs9(xuu4911, xuu5111)
new_esEs28(xuu3110000, xuu6000, ty_Double) → new_esEs12(xuu3110000, xuu6000)
new_sr0(Integer(xuu51000), Integer(xuu49010)) → Integer(new_primMulInt(xuu51000, xuu49010))
new_esEs32(xuu37, xuu39, ty_@0) → new_esEs17(xuu37, xuu39)
new_primPlusNat1(Succ(xuu41200), Succ(xuu9200)) → Succ(Succ(new_primPlusNat1(xuu41200, xuu9200)))
new_compare28(xuu490, xuu510, True, bc, bd) → EQ
new_lt6(xuu490, xuu510, app(app(app(ty_@3, cg), da), db)) → new_lt18(xuu490, xuu510, cg, da, db)
new_lt21(xuu4911, xuu5111, app(app(ty_@2, bbf), bbg)) → new_lt11(xuu4911, xuu5111, bbf, bbg)
new_esEs32(xuu37, xuu39, app(ty_Maybe, dbb)) → new_esEs5(xuu37, xuu39, dbb)
new_primEqInt(Pos(Succ(xuu31100000)), Neg(xuu6000)) → False
new_primEqInt(Neg(Succ(xuu31100000)), Pos(xuu6000)) → False
new_compare210(xuu490, xuu510, True, cf) → EQ
new_compare29(xuu4900, xuu5100, app(app(ty_Either, gh), ha)) → new_compare6(xuu4900, xuu5100, gh, ha)
new_esEs27(xuu4911, xuu5111, app(ty_Maybe, bca)) → new_esEs5(xuu4911, xuu5111, bca)
new_compare210(xuu490, xuu510, False, cf) → new_compare111(xuu490, xuu510, new_ltEs14(xuu490, xuu510, cf), cf)
new_compare13(xuu490, xuu510) → new_compare24(xuu490, xuu510, new_esEs8(xuu490, xuu510))
new_ltEs4(xuu491, xuu511, ty_Char) → new_ltEs8(xuu491, xuu511)
new_esEs18(xuu490, xuu510, app(app(ty_@2, cc), cd)) → new_esEs4(xuu490, xuu510, cc, cd)
new_lt19(xuu4910, xuu5110, ty_Bool) → new_lt5(xuu4910, xuu5110)
new_primPlusInt(Neg(xuu4120), Pos(xuu920)) → new_primMinusNat0(xuu920, xuu4120)
new_primPlusInt(Pos(xuu4120), Neg(xuu920)) → new_primMinusNat0(xuu4120, xuu920)
new_esEs27(xuu4911, xuu5111, ty_Double) → new_esEs12(xuu4911, xuu5111)
new_esEs11([], :(xuu6000, xuu6001), eg) → False
new_esEs11(:(xuu3110000, xuu3110001), [], eg) → False
new_esEs18(xuu490, xuu510, ty_Bool) → new_esEs13(xuu490, xuu510)
new_esEs26(xuu4910, xuu5110, app(ty_Ratio, bac)) → new_esEs16(xuu4910, xuu5110, bac)
new_esEs12(Double(xuu3110000, xuu3110001), Double(xuu6000, xuu6001)) → new_esEs15(new_sr(xuu3110000, xuu6000), new_sr(xuu3110001, xuu6001))
new_primCmpNat2(Zero, Succ(xuu51000)) → LT
new_esEs22(xuu3110002, xuu6002, ty_Float) → new_esEs14(xuu3110002, xuu6002)
new_esEs10(Char(xuu3110000), Char(xuu6000)) → new_primEqNat0(xuu3110000, xuu6000)
new_primEqInt(Pos(Zero), Neg(Succ(xuu60000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(xuu60000))) → False
new_ltEs19(xuu4911, xuu5111, app(app(ty_@2, cfh), cga)) → new_ltEs9(xuu4911, xuu5111, cfh, cga)
new_esEs22(xuu3110002, xuu6002, app(ty_[], cdc)) → new_esEs11(xuu3110002, xuu6002, cdc)
new_primCompAux00(xuu134, EQ) → xuu134
new_esEs28(xuu3110000, xuu6000, ty_Char) → new_esEs10(xuu3110000, xuu6000)
new_gt(xuu86, xuu85) → new_esEs8(new_compare9(xuu86, xuu85), GT)
new_compare24(xuu490, xuu510, True) → EQ
new_ltEs15(Right(xuu4910), Right(xuu5110), dh, app(ty_Ratio, dde)) → new_ltEs6(xuu4910, xuu5110, dde)
new_esEs23(xuu4910, xuu5110, ty_Char) → new_esEs10(xuu4910, xuu5110)
new_ltEs13(GT, EQ) → False
new_ltEs13(EQ, LT) → False
new_ltEs4(xuu491, xuu511, ty_Bool) → new_ltEs12(xuu491, xuu511)
new_esEs8(GT, EQ) → False
new_esEs8(EQ, GT) → False
new_esEs29(xuu3110001, xuu6001, ty_Double) → new_esEs12(xuu3110001, xuu6001)
new_ltEs4(xuu491, xuu511, app(ty_Maybe, dg)) → new_ltEs14(xuu491, xuu511, dg)
new_compare24(xuu490, xuu510, False) → new_compare110(xuu490, xuu510, new_ltEs13(xuu490, xuu510))
new_lt21(xuu4911, xuu5111, app(ty_[], bbh)) → new_lt13(xuu4911, xuu5111, bbh)
new_esEs27(xuu4911, xuu5111, app(ty_Ratio, bbe)) → new_esEs16(xuu4911, xuu5111, bbe)
new_ltEs14(Nothing, Just(xuu5110), dg) → True
new_ltEs14(Just(xuu4910), Just(xuu5110), ty_Integer) → new_ltEs10(xuu4910, xuu5110)
new_lt21(xuu4911, xuu5111, ty_Integer) → new_lt12(xuu4911, xuu5111)
new_ltEs19(xuu4911, xuu5111, ty_Char) → new_ltEs8(xuu4911, xuu5111)
new_lt6(xuu490, xuu510, ty_Bool) → new_lt5(xuu490, xuu510)
new_not(False) → True
new_lt21(xuu4911, xuu5111, app(ty_Maybe, bca)) → new_lt15(xuu4911, xuu5111, bca)
new_esEs6(Left(xuu3110000), Left(xuu6000), app(app(ty_Either, bgg), bgh), bff) → new_esEs6(xuu3110000, xuu6000, bgg, bgh)
new_lt19(xuu4910, xuu5110, ty_Char) → new_lt10(xuu4910, xuu5110)
new_primPlusNat0(Zero, xuu600100) → Succ(xuu600100)
new_ltEs20(xuu4912, xuu5112, ty_Ordering) → new_ltEs13(xuu4912, xuu5112)
new_mkBalBranch6MkBalBranch3(EmptyFM, xuu19, xuu20, xuu21, xuu24, True, he, hf, hg) → error([])
new_ltEs14(Just(xuu4910), Just(xuu5110), ty_@0) → new_ltEs17(xuu4910, xuu5110)
new_esEs32(xuu37, xuu39, ty_Ordering) → new_esEs8(xuu37, xuu39)
new_esEs19(xuu3110000, xuu6000, ty_Double) → new_esEs12(xuu3110000, xuu6000)
new_esEs20(xuu3110000, xuu6000, ty_Float) → new_esEs14(xuu3110000, xuu6000)
new_sizeFM(Branch(xuu240, xuu241, xuu242, xuu243, xuu244), he, hf, hg) → xuu242
new_esEs20(xuu3110000, xuu6000, app(ty_[], cag)) → new_esEs11(xuu3110000, xuu6000, cag)
new_ltEs14(Just(xuu4910), Just(xuu5110), app(app(ty_Either, bfa), bfb)) → new_ltEs15(xuu4910, xuu5110, bfa, bfb)
new_ltEs15(Left(xuu4910), Left(xuu5110), ty_Integer, ea) → new_ltEs10(xuu4910, xuu5110)
new_esEs31(xuu311000, xuu600, ty_Integer) → new_esEs9(xuu311000, xuu600)
new_ltEs19(xuu4911, xuu5111, app(app(ty_Either, cgd), cge)) → new_ltEs15(xuu4911, xuu5111, cgd, cge)
new_esEs6(Left(xuu3110000), Left(xuu6000), ty_Bool, bff) → new_esEs13(xuu3110000, xuu6000)
new_esEs29(xuu3110001, xuu6001, ty_Int) → new_esEs15(xuu3110001, xuu6001)
new_esEs27(xuu4911, xuu5111, app(app(ty_Either, bcb), bcc)) → new_esEs6(xuu4911, xuu5111, bcb, bcc)
new_lt7(xuu490, xuu510) → new_esEs8(new_compare8(xuu490, xuu510), LT)
new_esEs6(Right(xuu3110000), Right(xuu6000), bha, app(ty_[], bhb)) → new_esEs11(xuu3110000, xuu6000, bhb)
new_lt6(xuu490, xuu510, ty_@0) → new_lt17(xuu490, xuu510)
new_esEs24(xuu3110000, xuu6000, ty_Int) → new_esEs15(xuu3110000, xuu6000)
new_ltEs4(xuu491, xuu511, ty_@0) → new_ltEs17(xuu491, xuu511)
new_mkBranch3(xuu152, xuu153, xuu154, xuu155, xuu156, xuu157, xuu158, xuu159, xuu160, xuu161, xuu162, xuu163, hh, baa, bab) → Branch(xuu153, xuu154, new_mkBranchUnbox(new_mkBranch4(xuu160, xuu161, xuu162, xuu163, hh, baa, bab), xuu153, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Zero))))), xuu155, xuu156, xuu157, xuu158, xuu159, hh, baa, bab), new_ps(new_mkBranch2(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))), xuu160, xuu161, xuu162, xuu163, hh, baa, bab), xuu153, new_mkBranch2(Succ(Succ(Succ(Succ(Succ(Zero))))), @2(xuu155, xuu156), xuu157, xuu158, xuu159, hh, baa, bab), new_mkBranch2(Succ(Succ(Succ(Succ(Succ(Zero))))), @2(xuu155, xuu156), xuu157, xuu158, xuu159, hh, baa, bab), hh, baa, bab), hh, baa, bab), new_mkBranch(Succ(Succ(Succ(Succ(Succ(Zero))))), xuu155, xuu156, xuu157, xuu158, xuu159, hh, baa, bab), new_mkBranch4(xuu160, xuu161, xuu162, xuu163, hh, baa, bab))
new_ltEs20(xuu4912, xuu5112, ty_@0) → new_ltEs17(xuu4912, xuu5112)
new_primCmpInt(Pos(Succ(xuu4900)), Neg(xuu510)) → GT
new_esEs22(xuu3110002, xuu6002, app(app(app(ty_@3, cdg), cdh), cea)) → new_esEs7(xuu3110002, xuu6002, cdg, cdh, cea)
new_esEs26(xuu4910, xuu5110, ty_@0) → new_esEs17(xuu4910, xuu5110)
new_lt18(xuu490, xuu510, cg, da, db) → new_esEs8(new_compare19(xuu490, xuu510, cg, da, db), LT)
new_esEs29(xuu3110001, xuu6001, ty_Integer) → new_esEs9(xuu3110001, xuu6001)
new_esEs5(Just(xuu3110000), Just(xuu6000), ty_Int) → new_esEs15(xuu3110000, xuu6000)
new_primMulInt(Pos(xuu31100010), Pos(xuu60010)) → Pos(new_primMulNat0(xuu31100010, xuu60010))
new_ltEs4(xuu491, xuu511, app(app(ty_Either, dh), ea)) → new_ltEs15(xuu491, xuu511, dh, ea)
new_lt19(xuu4910, xuu5110, ty_Float) → new_lt16(xuu4910, xuu5110)
new_esEs21(xuu3110001, xuu6001, app(app(ty_@2, ccc), ccd)) → new_esEs4(xuu3110001, xuu6001, ccc, ccd)
new_mkBalBranch6MkBalBranch01(xuu41, xuu19, xuu20, xuu21, xuu240, xuu241, xuu242, xuu243, xuu244, True, he, hf, hg) → Branch(xuu240, xuu241, new_mkBranchUnbox(xuu244, xuu240, new_mkBranch(Succ(Succ(Succ(Zero))), xuu19, xuu20, xuu21, xuu41, xuu243, he, hf, hg), new_ps(xuu244, xuu240, new_mkBranch(Succ(Succ(Succ(Zero))), xuu19, xuu20, xuu21, xuu41, xuu243, he, hf, hg), new_mkBranch(Succ(Succ(Succ(Zero))), xuu19, xuu20, xuu21, xuu41, xuu243, he, hf, hg), he, hf, hg), he, hf, hg), new_mkBranch5(xuu19, xuu20, xuu21, xuu41, xuu243, he, hf, hg), xuu244)
new_esEs6(Right(xuu3110000), Right(xuu6000), bha, ty_Bool) → new_esEs13(xuu3110000, xuu6000)
new_esEs28(xuu3110000, xuu6000, app(app(app(ty_@3, dfc), dfd), dfe)) → new_esEs7(xuu3110000, xuu6000, dfc, dfd, dfe)
new_esEs7(@3(xuu3110000, xuu3110001, xuu3110002), @3(xuu6000, xuu6001, xuu6002), cad, cae, caf) → new_asAs(new_esEs20(xuu3110000, xuu6000, cad), new_asAs(new_esEs21(xuu3110001, xuu6001, cae), new_esEs22(xuu3110002, xuu6002, caf)))
new_esEs19(xuu3110000, xuu6000, ty_Bool) → new_esEs13(xuu3110000, xuu6000)
new_esEs31(xuu311000, xuu600, ty_Float) → new_esEs14(xuu311000, xuu600)
new_mkBalBranch6MkBalBranch11(xuu410, xuu411, xuu412, xuu413, EmptyFM, xuu19, xuu20, xuu21, xuu24, False, he, hf, hg) → error([])
new_primMulInt(Neg(xuu31100010), Neg(xuu60010)) → Pos(new_primMulNat0(xuu31100010, xuu60010))
new_esEs21(xuu3110001, xuu6001, ty_Char) → new_esEs10(xuu3110001, xuu6001)
new_primCmpNat2(Zero, Zero) → EQ
new_ltEs19(xuu4911, xuu5111, app(ty_Ratio, cfg)) → new_ltEs6(xuu4911, xuu5111, cfg)
new_compare110(xuu490, xuu510, True) → LT
new_ltEs19(xuu4911, xuu5111, ty_Integer) → new_ltEs10(xuu4911, xuu5111)
new_ps(xuu244, xuu240, xuu220, xuu219, he, hf, hg) → new_primPlusInt(new_primPlusInt(Pos(Succ(Zero)), new_sizeFM(xuu220, he, hf, hg)), new_sizeFM(xuu244, he, hf, hg))
new_primEqNat0(Zero, Succ(xuu60000)) → False
new_primEqNat0(Succ(xuu31100000), Zero) → False
new_esEs6(Right(xuu3110000), Right(xuu6000), bha, ty_Double) → new_esEs12(xuu3110000, xuu6000)
new_lt20(xuu4910, xuu5110, ty_@0) → new_lt17(xuu4910, xuu5110)
new_compare110(xuu490, xuu510, False) → GT
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_ltEs20(xuu4912, xuu5112, ty_Int) → new_ltEs7(xuu4912, xuu5112)
new_lt9(xuu490, xuu510) → new_esEs8(new_compare9(xuu490, xuu510), LT)
new_esEs6(Right(xuu3110000), Right(xuu6000), bha, ty_Float) → new_esEs14(xuu3110000, xuu6000)
new_compare30(:%(xuu4900, xuu4901), :%(xuu5100, xuu5101), ty_Integer) → new_compare17(new_sr0(xuu4900, xuu5101), new_sr0(xuu5100, xuu4901))
new_primCmpInt(Pos(Succ(xuu4900)), Pos(xuu510)) → new_primCmpNat0(xuu4900, xuu510)
new_primCmpNat2(Succ(xuu49000), Succ(xuu51000)) → new_primCmpNat2(xuu49000, xuu51000)
new_mkBranch5(xuu19, xuu20, xuu21, xuu41, xuu243, he, hf, hg) → new_mkBranchResult(xuu19, xuu20, xuu21, xuu243, xuu41, he, hf, hg)
new_esEs32(xuu37, xuu39, ty_Integer) → new_esEs9(xuu37, xuu39)
new_esEs20(xuu3110000, xuu6000, app(app(ty_Either, cbg), cbh)) → new_esEs6(xuu3110000, xuu6000, cbg, cbh)
new_compare31(xuu490, xuu510, cf) → new_compare210(xuu490, xuu510, new_esEs5(xuu490, xuu510, cf), cf)
new_ltEs14(Just(xuu4910), Just(xuu5110), ty_Double) → new_ltEs5(xuu4910, xuu5110)
new_primCmpNat0(xuu4900, Zero) → GT
new_esEs19(xuu3110000, xuu6000, app(ty_Maybe, fa)) → new_esEs5(xuu3110000, xuu6000, fa)
new_esEs18(xuu490, xuu510, ty_@0) → new_esEs17(xuu490, xuu510)
new_esEs29(xuu3110001, xuu6001, app(app(ty_Either, dha), dhb)) → new_esEs6(xuu3110001, xuu6001, dha, dhb)
new_ltEs19(xuu4911, xuu5111, ty_@0) → new_ltEs17(xuu4911, xuu5111)
new_esEs26(xuu4910, xuu5110, app(ty_Maybe, bag)) → new_esEs5(xuu4910, xuu5110, bag)
new_esEs32(xuu37, xuu39, ty_Char) → new_esEs10(xuu37, xuu39)
new_primMinusNat0(Zero, Zero) → Pos(Zero)
new_compare112(xuu490, xuu510, True, cg, da, db) → LT
new_compare23(xuu49, xuu51, True, bh, ca) → EQ
new_primCmpInt(Pos(Zero), Neg(Succ(xuu5100))) → GT
new_lt17(xuu490, xuu510) → new_esEs8(new_compare27(xuu490, xuu510), LT)
new_esEs18(xuu490, xuu510, ty_Float) → new_esEs14(xuu490, xuu510)
new_esEs32(xuu37, xuu39, ty_Int) → new_esEs15(xuu37, xuu39)
new_esEs6(Left(xuu3110000), Left(xuu6000), ty_Ordering, bff) → new_esEs8(xuu3110000, xuu6000)
new_ltEs20(xuu4912, xuu5112, ty_Char) → new_ltEs8(xuu4912, xuu5112)
new_mkBalBranch6Size_l(xuu41, xuu19, xuu20, xuu21, xuu24, he, hf, hg) → new_sizeFM(xuu41, he, hf, hg)
new_lt20(xuu4910, xuu5110, ty_Float) → new_lt16(xuu4910, xuu5110)
new_ltEs4(xuu491, xuu511, app(app(app(ty_@3, eb), ec), ed)) → new_ltEs18(xuu491, xuu511, eb, ec, ed)
new_compare26(xuu490, xuu510, False, cg, da, db) → new_compare112(xuu490, xuu510, new_ltEs18(xuu490, xuu510, cg, da, db), cg, da, db)
new_esEs6(Right(xuu3110000), Right(xuu6000), bha, app(app(ty_@2, bhd), bhe)) → new_esEs4(xuu3110000, xuu6000, bhd, bhe)
new_esEs27(xuu4911, xuu5111, ty_@0) → new_esEs17(xuu4911, xuu5111)
new_sIZE_RATIOPos(Succ(Succ(Succ(Succ(Succ(Zero))))))
new_compare29(xuu4900, xuu5100, ty_Ordering) → new_compare13(xuu4900, xuu5100)
new_esEs23(xuu4910, xuu5110, app(ty_[], ceh)) → new_esEs11(xuu4910, xuu5110, ceh)
new_ltEs20(xuu4912, xuu5112, app(ty_Maybe, bdc)) → new_ltEs14(xuu4912, xuu5112, bdc)
new_esEs32(xuu37, xuu39, app(ty_[], dba)) → new_esEs11(xuu37, xuu39, dba)
new_lt8(xuu490, xuu510, cb) → new_esEs8(new_compare30(xuu490, xuu510, cb), LT)
new_emptyFM(h, ba, bb) → EmptyFM
new_esEs6(Right(xuu3110000), Right(xuu6000), bha, ty_Integer) → new_esEs9(xuu3110000, xuu6000)
new_esEs31(xuu311000, xuu600, ty_Double) → new_esEs12(xuu311000, xuu600)
new_ltEs15(Right(xuu4910), Right(xuu5110), dh, ty_Float) → new_ltEs16(xuu4910, xuu5110)
new_lt19(xuu4910, xuu5110, app(app(ty_Either, cfb), cfc)) → new_lt4(xuu4910, xuu5110, cfb, cfc)
new_esEs23(xuu4910, xuu5110, app(ty_Ratio, cee)) → new_esEs16(xuu4910, xuu5110, cee)
new_ltEs14(Just(xuu4910), Just(xuu5110), app(ty_[], beg)) → new_ltEs11(xuu4910, xuu5110, beg)
new_esEs22(xuu3110002, xuu6002, app(ty_Ratio, ceb)) → new_esEs16(xuu3110002, xuu6002, ceb)
new_esEs4(@2(xuu3110000, xuu3110001), @2(xuu6000, xuu6001), chc, chd) → new_asAs(new_esEs28(xuu3110000, xuu6000, chc), new_esEs29(xuu3110001, xuu6001, chd))
new_esEs18(xuu490, xuu510, app(ty_[], ce)) → new_esEs11(xuu490, xuu510, ce)
new_lt20(xuu4910, xuu5110, ty_Char) → new_lt10(xuu4910, xuu5110)
new_ltEs20(xuu4912, xuu5112, app(app(ty_Either, bdd), bde)) → new_ltEs15(xuu4912, xuu5112, bdd, bde)
new_primPlusInt(Pos(xuu4120), Pos(xuu920)) → Pos(new_primPlusNat1(xuu4120, xuu920))
new_esEs28(xuu3110000, xuu6000, ty_Integer) → new_esEs9(xuu3110000, xuu6000)
new_esEs19(xuu3110000, xuu6000, app(ty_Ratio, fh)) → new_esEs16(xuu3110000, xuu6000, fh)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_ltEs15(Right(xuu4910), Right(xuu5110), dh, app(ty_Maybe, dea)) → new_ltEs14(xuu4910, xuu5110, dea)
new_ltEs4(xuu491, xuu511, ty_Integer) → new_ltEs10(xuu491, xuu511)
new_esEs6(Left(xuu3110000), Left(xuu6000), ty_Double, bff) → new_esEs12(xuu3110000, xuu6000)
new_compare29(xuu4900, xuu5100, ty_Int) → new_compare9(xuu4900, xuu5100)
new_esEs20(xuu3110000, xuu6000, app(ty_Maybe, cah)) → new_esEs5(xuu3110000, xuu6000, cah)
new_ltEs13(GT, GT) → True
new_ltEs4(xuu491, xuu511, app(ty_Ratio, dc)) → new_ltEs6(xuu491, xuu511, dc)
new_esEs28(xuu3110000, xuu6000, app(app(ty_@2, dfa), dfb)) → new_esEs4(xuu3110000, xuu6000, dfa, dfb)
new_asAs(False, xuu59) → False
new_esEs22(xuu3110002, xuu6002, ty_Double) → new_esEs12(xuu3110002, xuu6002)
new_lt6(xuu490, xuu510, ty_Integer) → new_lt12(xuu490, xuu510)
new_primMulInt(Neg(xuu31100010), Pos(xuu60010)) → Neg(new_primMulNat0(xuu31100010, xuu60010))
new_primMulInt(Pos(xuu31100010), Neg(xuu60010)) → Neg(new_primMulNat0(xuu31100010, xuu60010))
new_ltEs20(xuu4912, xuu5112, app(ty_[], bdb)) → new_ltEs11(xuu4912, xuu5112, bdb)
new_compare23(@2(xuu490, xuu491), @2(xuu510, xuu511), False, bh, ca) → new_compare11(xuu490, xuu491, xuu510, xuu511, new_lt6(xuu490, xuu510, bh), new_asAs(new_esEs18(xuu490, xuu510, bh), new_ltEs4(xuu491, xuu511, ca)), bh, ca)
new_primMulNat0(Zero, Succ(xuu600100)) → Zero
new_primMulNat0(Succ(xuu311000100), Zero) → Zero
new_ltEs14(Just(xuu4910), Just(xuu5110), ty_Float) → new_ltEs16(xuu4910, xuu5110)
new_compare29(xuu4900, xuu5100, ty_Char) → new_compare18(xuu4900, xuu5100)
new_mkBalBranch6MkBalBranch5(xuu41, xuu19, xuu20, xuu21, xuu24, True, he, hf, hg) → new_mkBranchResult(xuu19, xuu20, xuu21, xuu24, xuu41, he, hf, hg)
new_esEs32(xuu37, xuu39, app(app(app(ty_@3, dbe), dbf), dbg)) → new_esEs7(xuu37, xuu39, dbe, dbf, dbg)
new_esEs21(xuu3110001, xuu6001, ty_Ordering) → new_esEs8(xuu3110001, xuu6001)
new_esEs32(xuu37, xuu39, app(ty_Ratio, dbh)) → new_esEs16(xuu37, xuu39, dbh)
new_esEs21(xuu3110001, xuu6001, ty_Bool) → new_esEs13(xuu3110001, xuu6001)
new_lt6(xuu490, xuu510, ty_Ordering) → new_lt14(xuu490, xuu510)
new_compare17(Integer(xuu4900), Integer(xuu5100)) → new_primCmpInt(xuu4900, xuu5100)
new_esEs19(xuu3110000, xuu6000, app(ty_[], eh)) → new_esEs11(xuu3110000, xuu6000, eh)
new_esEs5(Just(xuu3110000), Just(xuu6000), app(ty_[], che)) → new_esEs11(xuu3110000, xuu6000, che)
new_esEs5(Just(xuu3110000), Just(xuu6000), ty_Integer) → new_esEs9(xuu3110000, xuu6000)
new_esEs6(Right(xuu3110000), Right(xuu6000), bha, app(ty_Ratio, caa)) → new_esEs16(xuu3110000, xuu6000, caa)
new_ltEs8(xuu491, xuu511) → new_fsEs(new_compare18(xuu491, xuu511))
new_lt19(xuu4910, xuu5110, app(app(app(ty_@3, cfd), cfe), cff)) → new_lt18(xuu4910, xuu5110, cfd, cfe, cff)
new_lt21(xuu4911, xuu5111, ty_Int) → new_lt9(xuu4911, xuu5111)
new_esEs18(xuu490, xuu510, app(ty_Maybe, cf)) → new_esEs5(xuu490, xuu510, cf)
new_primCmpNat1(Succ(xuu5100), xuu4900) → new_primCmpNat2(xuu5100, xuu4900)
new_esEs22(xuu3110002, xuu6002, ty_Char) → new_esEs10(xuu3110002, xuu6002)
new_ltEs12(True, True) → True
new_mkBalBranch6MkBalBranch4(xuu41, xuu19, xuu20, xuu21, xuu24, False, he, hf, hg) → new_mkBalBranch6MkBalBranch3(xuu41, xuu19, xuu20, xuu21, xuu24, new_gt(new_mkBalBranch6Size_l(xuu41, xuu19, xuu20, xuu21, xuu24, he, hf, hg), new_sr(new_sIZE_RATIO, new_mkBalBranch6Size_r(xuu41, xuu19, xuu20, xuu21, xuu24, he, hf, hg))), he, hf, hg)
new_primCmpNat2(Succ(xuu49000), Zero) → GT
new_addToFM_C0(Branch(@2(xuu600, xuu601), xuu61, xuu62, xuu63, xuu64), @2(xuu311000, xuu311001), xuu31101, h, ba, bb) → new_addToFM_C20(xuu600, xuu601, xuu61, xuu62, xuu63, xuu64, xuu311000, xuu311001, xuu31101, new_esEs30(xuu311000, xuu311001, xuu600, xuu601, new_esEs31(xuu311000, xuu600, h), h, ba), h, ba, bb)
new_esEs18(xuu490, xuu510, ty_Ordering) → new_esEs8(xuu490, xuu510)
new_primCmpInt0(EmptyFM, xuu19, xuu20, xuu21, xuu24, he, hf, hg) → new_primCmpInt(new_primPlusInt(Pos(Zero), new_mkBalBranch6Size_r(EmptyFM, xuu19, xuu20, xuu21, xuu24, he, hf, hg)), Pos(Succ(Succ(Zero))))
new_esEs29(xuu3110001, xuu6001, app(ty_Ratio, dgh)) → new_esEs16(xuu3110001, xuu6001, dgh)
new_esEs13(False, False) → True
new_esEs21(xuu3110001, xuu6001, ty_Integer) → new_esEs9(xuu3110001, xuu6001)
new_ltEs20(xuu4912, xuu5112, app(app(app(ty_@3, bdf), bdg), bdh)) → new_ltEs18(xuu4912, xuu5112, bdf, bdg, bdh)
new_esEs23(xuu4910, xuu5110, app(ty_Maybe, cfa)) → new_esEs5(xuu4910, xuu5110, cfa)
new_esEs29(xuu3110001, xuu6001, ty_Float) → new_esEs14(xuu3110001, xuu6001)
new_esEs6(Right(xuu3110000), Right(xuu6000), bha, ty_Char) → new_esEs10(xuu3110000, xuu6000)
new_esEs16(:%(xuu3110000, xuu3110001), :%(xuu6000, xuu6001), cha) → new_asAs(new_esEs24(xuu3110000, xuu6000, cha), new_esEs25(xuu3110001, xuu6001, cha))
new_esEs6(Left(xuu3110000), Left(xuu6000), app(ty_Maybe, bfh), bff) → new_esEs5(xuu3110000, xuu6000, bfh)
new_esEs26(xuu4910, xuu5110, ty_Integer) → new_esEs9(xuu4910, xuu5110)
new_ltEs12(False, True) → True
new_esEs20(xuu3110000, xuu6000, app(app(ty_@2, cba), cbb)) → new_esEs4(xuu3110000, xuu6000, cba, cbb)
new_compare29(xuu4900, xuu5100, ty_@0) → new_compare27(xuu4900, xuu5100)
new_compare112(xuu490, xuu510, False, cg, da, db) → GT
new_compare30(:%(xuu4900, xuu4901), :%(xuu5100, xuu5101), ty_Int) → new_compare9(new_sr(xuu4900, xuu5101), new_sr(xuu5100, xuu4901))
new_compare111(xuu490, xuu510, False, cf) → GT
new_ltEs15(Right(xuu4910), Right(xuu5110), dh, ty_Bool) → new_ltEs12(xuu4910, xuu5110)
new_esEs21(xuu3110001, xuu6001, app(ty_Ratio, cch)) → new_esEs16(xuu3110001, xuu6001, cch)
new_addToFM_C10(xuu19, xuu20, xuu21, xuu22, xuu23, xuu24, xuu25, xuu26, xuu27, False, he, hf, hg) → Branch(@2(xuu25, xuu26), xuu27, xuu22, xuu23, xuu24)
new_esEs18(xuu490, xuu510, ty_Int) → new_esEs15(xuu490, xuu510)
new_esEs5(Nothing, Just(xuu6000), chb) → False
new_esEs5(Just(xuu3110000), Nothing, chb) → False
new_esEs30(xuu36, xuu37, xuu38, xuu39, True, dag, dah) → new_esEs8(new_compare23(@2(xuu36, xuu37), @2(xuu38, xuu39), new_esEs32(xuu37, xuu39, dah), dag, dah), LT)
new_lt19(xuu4910, xuu5110, ty_@0) → new_lt17(xuu4910, xuu5110)
new_primMinusNat0(Zero, Succ(xuu9200)) → Neg(Succ(xuu9200))
new_compare16(Float(xuu4900, xuu4901), Float(xuu5100, xuu5101)) → new_compare9(new_sr(xuu4900, xuu5100), new_sr(xuu4901, xuu5101))
new_esEs31(xuu311000, xuu600, app(app(ty_Either, bha), bff)) → new_esEs6(xuu311000, xuu600, bha, bff)
new_lt19(xuu4910, xuu5110, ty_Int) → new_lt9(xuu4910, xuu5110)
new_esEs6(Right(xuu3110000), Right(xuu6000), bha, ty_@0) → new_esEs17(xuu3110000, xuu6000)
new_esEs27(xuu4911, xuu5111, app(app(ty_@2, bbf), bbg)) → new_esEs4(xuu4911, xuu5111, bbf, bbg)
new_lt21(xuu4911, xuu5111, ty_Bool) → new_lt5(xuu4911, xuu5111)
new_esEs27(xuu4911, xuu5111, app(ty_[], bbh)) → new_esEs11(xuu4911, xuu5111, bbh)
new_esEs27(xuu4911, xuu5111, ty_Int) → new_esEs15(xuu4911, xuu5111)
new_mkBalBranch6MkBalBranch5(xuu41, xuu19, xuu20, xuu21, xuu24, False, he, hf, hg) → new_mkBalBranch6MkBalBranch4(xuu41, xuu19, xuu20, xuu21, xuu24, new_gt(new_mkBalBranch6Size_r(xuu41, xuu19, xuu20, xuu21, xuu24, he, hf, hg), new_sr(new_sIZE_RATIO, new_mkBalBranch6Size_l(xuu41, xuu19, xuu20, xuu21, xuu24, he, hf, hg))), he, hf, hg)
new_sizeFM(EmptyFM, he, hf, hg) → Pos(Zero)
new_addListToFM_CAdd(xuu6, @2(xuu31100, xuu31101), h, ba, bb) → new_addToFM_C0(xuu6, xuu31100, xuu31101, h, ba, bb)
new_compare8(Double(xuu4900, xuu4901), Double(xuu5100, xuu5101)) → new_compare9(new_sr(xuu4900, xuu5100), new_sr(xuu4901, xuu5101))
new_esEs5(Just(xuu3110000), Just(xuu6000), app(app(ty_Either, dae), daf)) → new_esEs6(xuu3110000, xuu6000, dae, daf)
new_lt20(xuu4910, xuu5110, ty_Integer) → new_lt12(xuu4910, xuu5110)
new_esEs32(xuu37, xuu39, app(app(ty_Either, dca), dcb)) → new_esEs6(xuu37, xuu39, dca, dcb)
new_ltEs18(@3(xuu4910, xuu4911, xuu4912), @3(xuu5110, xuu5111, xuu5112), eb, ec, ed) → new_pePe(new_lt20(xuu4910, xuu5110, eb), new_asAs(new_esEs26(xuu4910, xuu5110, eb), new_pePe(new_lt21(xuu4911, xuu5111, ec), new_asAs(new_esEs27(xuu4911, xuu5111, ec), new_ltEs20(xuu4912, xuu5112, ed)))))
new_ltEs20(xuu4912, xuu5112, app(ty_Ratio, bcg)) → new_ltEs6(xuu4912, xuu5112, bcg)
new_esEs5(Nothing, Nothing, chb) → True
new_esEs26(xuu4910, xuu5110, ty_Char) → new_esEs10(xuu4910, xuu5110)
new_esEs22(xuu3110002, xuu6002, app(app(ty_Either, cec), ced)) → new_esEs6(xuu3110002, xuu6002, cec, ced)
new_esEs28(xuu3110000, xuu6000, app(ty_Maybe, deh)) → new_esEs5(xuu3110000, xuu6000, deh)
new_lt12(xuu490, xuu510) → new_esEs8(new_compare17(xuu490, xuu510), LT)
new_esEs5(Just(xuu3110000), Just(xuu6000), app(app(app(ty_@3, daa), dab), dac)) → new_esEs7(xuu3110000, xuu6000, daa, dab, dac)
new_esEs28(xuu3110000, xuu6000, ty_Bool) → new_esEs13(xuu3110000, xuu6000)
new_esEs21(xuu3110001, xuu6001, ty_Double) → new_esEs12(xuu3110001, xuu6001)
new_compare14(xuu490, xuu510, True, bc, bd) → LT
new_ltEs14(Just(xuu4910), Just(xuu5110), ty_Char) → new_ltEs8(xuu4910, xuu5110)
new_esEs21(xuu3110001, xuu6001, app(ty_[], cca)) → new_esEs11(xuu3110001, xuu6001, cca)
new_ltEs15(Left(xuu4910), Left(xuu5110), app(ty_Ratio, dcc), ea) → new_ltEs6(xuu4910, xuu5110, dcc)
new_ltEs15(Right(xuu4910), Right(xuu5110), dh, app(app(ty_Either, deb), dec)) → new_ltEs15(xuu4910, xuu5110, deb, dec)
new_compare29(xuu4900, xuu5100, ty_Bool) → new_compare7(xuu4900, xuu5100)
new_ltEs13(LT, LT) → True
new_esEs23(xuu4910, xuu5110, ty_Double) → new_esEs12(xuu4910, xuu5110)
new_compare7(xuu490, xuu510) → new_compare25(xuu490, xuu510, new_esEs13(xuu490, xuu510))
new_compare26(xuu490, xuu510, True, cg, da, db) → EQ
new_esEs22(xuu3110002, xuu6002, app(ty_Maybe, cdd)) → new_esEs5(xuu3110002, xuu6002, cdd)
new_esEs21(xuu3110001, xuu6001, app(ty_Maybe, ccb)) → new_esEs5(xuu3110001, xuu6001, ccb)
new_lt4(xuu490, xuu510, bc, bd) → new_esEs8(new_compare6(xuu490, xuu510, bc, bd), LT)
new_esEs26(xuu4910, xuu5110, app(app(ty_Either, bah), bba)) → new_esEs6(xuu4910, xuu5110, bah, bba)
new_primPlusNat1(Zero, Zero) → Zero
new_ltEs14(Nothing, Nothing, dg) → True
new_esEs14(Float(xuu3110000, xuu3110001), Float(xuu6000, xuu6001)) → new_esEs15(new_sr(xuu3110000, xuu6000), new_sr(xuu3110001, xuu6001))
new_esEs19(xuu3110000, xuu6000, ty_@0) → new_esEs17(xuu3110000, xuu6000)
new_esEs31(xuu311000, xuu600, ty_Bool) → new_esEs13(xuu311000, xuu600)
new_asAs(True, xuu59) → xuu59
new_esEs26(xuu4910, xuu5110, ty_Float) → new_esEs14(xuu4910, xuu5110)
new_compare27(@0, @0) → EQ
new_primMulNat0(Succ(xuu311000100), Succ(xuu600100)) → new_primPlusNat0(new_primMulNat0(xuu311000100, Succ(xuu600100)), xuu600100)
new_ltEs4(xuu491, xuu511, app(ty_[], df)) → new_ltEs11(xuu491, xuu511, df)
new_esEs13(True, True) → True
new_mkBranchUnbox(xuu218, xuu142, xuu144, xuu208, be, bf, bg) → xuu208
new_primCmpInt0(Branch(xuu410, xuu411, xuu412, xuu413, xuu414), xuu19, xuu20, xuu21, xuu24, he, hf, hg) → new_primCmpInt(new_primPlusInt(xuu412, new_mkBalBranch6Size_r(Branch(xuu410, xuu411, xuu412, xuu413, xuu414), xuu19, xuu20, xuu21, xuu24, he, hf, hg)), Pos(Succ(Succ(Zero))))
new_ltEs14(Just(xuu4910), Just(xuu5110), app(app(app(ty_@3, bfc), bfd), bfe)) → new_ltEs18(xuu4910, xuu5110, bfc, bfd, bfe)
new_mkBalBranch6MkBalBranch3(Branch(xuu410, xuu411, xuu412, xuu413, xuu414), xuu19, xuu20, xuu21, xuu24, True, he, hf, hg) → new_mkBalBranch6MkBalBranch11(xuu410, xuu411, xuu412, xuu413, xuu414, xuu19, xuu20, xuu21, xuu24, new_lt9(new_sizeFM(xuu414, he, hf, hg), new_sr(Pos(Succ(Succ(Zero))), new_sizeFM(xuu413, he, hf, hg))), he, hf, hg)
new_compare1(:(xuu4900, xuu4901), [], ce) → GT
new_mkBalBranch6MkBalBranch4(xuu41, xuu19, xuu20, xuu21, EmptyFM, True, he, hf, hg) → error([])
new_esEs19(xuu3110000, xuu6000, ty_Char) → new_esEs10(xuu3110000, xuu6000)
new_fsEs(xuu117) → new_not(new_esEs8(xuu117, GT))
new_ltEs15(Left(xuu4910), Left(xuu5110), ty_Bool, ea) → new_ltEs12(xuu4910, xuu5110)
new_lt6(xuu490, xuu510, app(ty_Maybe, cf)) → new_lt15(xuu490, xuu510, cf)
new_esEs18(xuu490, xuu510, ty_Integer) → new_esEs9(xuu490, xuu510)
new_esEs19(xuu3110000, xuu6000, ty_Int) → new_esEs15(xuu3110000, xuu6000)
new_esEs19(xuu3110000, xuu6000, ty_Ordering) → new_esEs8(xuu3110000, xuu6000)
new_lt20(xuu4910, xuu5110, ty_Int) → new_lt9(xuu4910, xuu5110)
new_esEs27(xuu4911, xuu5111, ty_Float) → new_esEs14(xuu4911, xuu5111)
new_ltEs15(Left(xuu4910), Left(xuu5110), app(app(ty_Either, dch), dda), ea) → new_ltEs15(xuu4910, xuu5110, dch, dda)
new_ltEs15(Left(xuu4910), Right(xuu5110), dh, ea) → True
new_esEs32(xuu37, xuu39, ty_Double) → new_esEs12(xuu37, xuu39)
new_lt19(xuu4910, xuu5110, app(ty_Ratio, cee)) → new_lt8(xuu4910, xuu5110, cee)
new_mkBalBranch(xuu19, xuu20, xuu21, xuu41, xuu24, he, hf, hg) → new_mkBalBranch6MkBalBranch5(xuu41, xuu19, xuu20, xuu21, xuu24, new_esEs8(new_primCmpInt0(xuu41, xuu19, xuu20, xuu21, xuu24, he, hf, hg), LT), he, hf, hg)
new_mkBalBranch6MkBalBranch01(xuu41, xuu19, xuu20, xuu21, xuu240, xuu241, xuu242, Branch(xuu2430, xuu2431, xuu2432, xuu2433, xuu2434), xuu244, False, he, hf, hg) → new_mkBranch3(Succ(Succ(Succ(Succ(Zero)))), xuu2430, xuu2431, xuu19, xuu20, xuu21, xuu41, xuu2433, xuu240, xuu241, xuu2434, xuu244, he, hf, hg)
new_ltEs17(xuu491, xuu511) → new_fsEs(new_compare27(xuu491, xuu511))
new_esEs26(xuu4910, xuu5110, ty_Int) → new_esEs15(xuu4910, xuu5110)
new_ltEs4(xuu491, xuu511, ty_Int) → new_ltEs7(xuu491, xuu511)
new_ltEs9(@2(xuu4910, xuu4911), @2(xuu5110, xuu5111), dd, de) → new_pePe(new_lt19(xuu4910, xuu5110, dd), new_asAs(new_esEs23(xuu4910, xuu5110, dd), new_ltEs19(xuu4911, xuu5111, de)))
new_primCompAux00(xuu134, GT) → GT
new_ltEs15(Left(xuu4910), Left(xuu5110), app(app(ty_@2, dcd), dce), ea) → new_ltEs9(xuu4910, xuu5110, dcd, dce)
new_compare18(Char(xuu4900), Char(xuu5100)) → new_primCmpNat2(xuu4900, xuu5100)
new_mkBalBranch6MkBalBranch11(xuu410, xuu411, xuu412, xuu413, xuu414, xuu19, xuu20, xuu21, xuu24, True, he, hf, hg) → new_mkBranch0(xuu410, xuu411, xuu413, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), xuu19, xuu20, xuu21, xuu414, xuu24, he, hf, hg)
new_ltEs15(Right(xuu4910), Right(xuu5110), dh, app(app(app(ty_@3, ded), dee), def)) → new_ltEs18(xuu4910, xuu5110, ded, dee, def)
new_ltEs15(Left(xuu4910), Left(xuu5110), app(app(app(ty_@3, ddb), ddc), ddd), ea) → new_ltEs18(xuu4910, xuu5110, ddb, ddc, ddd)
new_esEs6(Right(xuu3110000), Right(xuu6000), bha, ty_Ordering) → new_esEs8(xuu3110000, xuu6000)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs26(xuu4910, xuu5110, ty_Bool) → new_esEs13(xuu4910, xuu5110)
new_esEs29(xuu3110001, xuu6001, ty_Ordering) → new_esEs8(xuu3110001, xuu6001)
new_mkBalBranch6MkBalBranch11(xuu410, xuu411, xuu412, xuu413, Branch(xuu4140, xuu4141, xuu4142, xuu4143, xuu4144), xuu19, xuu20, xuu21, xuu24, False, he, hf, hg) → new_mkBranch1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))), xuu4140, xuu4141, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), xuu410, xuu411, xuu413, xuu4143, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), xuu19, xuu20, xuu21, xuu4144, xuu24, he, hf, hg)
new_esEs19(xuu3110000, xuu6000, app(app(ty_@2, fb), fc)) → new_esEs4(xuu3110000, xuu6000, fb, fc)
new_ltEs15(Right(xuu4910), Left(xuu5110), dh, ea) → False
new_esEs31(xuu311000, xuu600, app(ty_[], eg)) → new_esEs11(xuu311000, xuu600, eg)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_esEs6(Right(xuu3110000), Right(xuu6000), bha, ty_Int) → new_esEs15(xuu3110000, xuu6000)
new_primCmpInt(Neg(Succ(xuu4900)), Pos(xuu510)) → LT
new_ltEs5(xuu491, xuu511) → new_fsEs(new_compare8(xuu491, xuu511))
new_lt21(xuu4911, xuu5111, ty_Double) → new_lt7(xuu4911, xuu5111)
new_not(True) → False
new_ltEs19(xuu4911, xuu5111, ty_Ordering) → new_ltEs13(xuu4911, xuu5111)
new_primMinusNat0(Succ(xuu41200), Succ(xuu9200)) → new_primMinusNat0(xuu41200, xuu9200)
new_esEs25(xuu3110001, xuu6001, ty_Integer) → new_esEs9(xuu3110001, xuu6001)
new_compare1([], [], ce) → EQ

The set Q consists of the following terms:

new_esEs31(x0, x1, app(app(ty_@2, x2), x3))
new_esEs31(x0, x1, app(app(ty_Either, x2), x3))
new_esEs32(x0, x1, ty_Integer)
new_compare14(x0, x1, True, x2, x3)
new_primCmpNat2(Succ(x0), Succ(x1))
new_ltEs4(x0, x1, app(app(ty_Either, x2), x3))
new_esEs18(x0, x1, ty_Int)
new_lt21(x0, x1, ty_Int)
new_esEs29(x0, x1, ty_Ordering)
new_compare29(x0, x1, ty_Bool)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_lt21(x0, x1, ty_Float)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_ltEs15(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs18(x0, x1, ty_Double)
new_primEqNat0(Zero, Succ(x0))
new_esEs11([], [], x0)
new_mkBranch4(x0, x1, x2, x3, x4, x5, x6)
new_primMinusNat0(Zero, Zero)
new_ltEs15(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs17(x0, x1)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_ltEs14(Just(x0), Just(x1), ty_Integer)
new_mkBranchResult(x0, x1, x2, x3, x4, x5, x6, x7)
new_ltEs20(x0, x1, ty_Float)
new_esEs5(Nothing, Just(x0), x1)
new_esEs6(Right(x0), Right(x1), x2, ty_Float)
new_ltEs10(x0, x1)
new_esEs31(x0, x1, ty_@0)
new_ltEs15(Right(x0), Right(x1), x2, ty_Bool)
new_esEs31(x0, x1, ty_Integer)
new_esEs18(x0, x1, ty_Ordering)
new_addToFM_C10(x0, x1, x2, x3, x4, x5, x6, x7, x8, False, x9, x10, x11)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs23(x0, x1, ty_Double)
new_compare29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_mkBranch0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_compare29(x0, x1, ty_Int)
new_primPlusInt(Pos(x0), Neg(x1))
new_primPlusInt(Neg(x0), Pos(x1))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_mkBalBranch6MkBalBranch01(x0, x1, x2, x3, x4, x5, x6, Branch(x7, x8, x9, x10, x11), x12, False, x13, x14, x15)
new_esEs27(x0, x1, ty_@0)
new_esEs22(x0, x1, ty_Char)
new_esEs28(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, ty_Bool)
new_compare30(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs27(x0, x1, ty_Char)
new_esEs5(Just(x0), Just(x1), app(ty_[], x2))
new_esEs19(x0, x1, ty_Char)
new_esEs12(Double(x0, x1), Double(x2, x3))
new_ltEs14(Nothing, Just(x0), x1)
new_ltEs19(x0, x1, ty_Ordering)
new_compare11(x0, x1, x2, x3, False, x4, x5, x6)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_lt6(x0, x1, app(ty_Ratio, x2))
new_lt6(x0, x1, app(app(ty_Either, x2), x3))
new_compare29(x0, x1, app(ty_[], x2))
new_esEs8(GT, GT)
new_esEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_mkBalBranch6MkBalBranch01(x0, x1, x2, x3, x4, x5, x6, EmptyFM, x7, False, x8, x9, x10)
new_lt9(x0, x1)
new_primMinusNat0(Succ(x0), Succ(x1))
new_lt19(x0, x1, app(ty_[], x2))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_primPlusInt(Neg(x0), Neg(x1))
new_compare19(x0, x1, x2, x3, x4)
new_primCmpNat0(x0, Zero)
new_esEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs27(x0, x1, ty_Ordering)
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt21(x0, x1, ty_Char)
new_esEs32(x0, x1, app(app(ty_Either, x2), x3))
new_compare11(x0, x1, x2, x3, True, x4, x5, x6)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_ltEs15(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs18(x0, x1, app(ty_Ratio, x2))
new_ltEs4(x0, x1, app(ty_[], x2))
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs8(LT, LT)
new_ltEs15(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs4(x0, x1, ty_Integer)
new_esEs31(x0, x1, app(ty_Ratio, x2))
new_esEs5(Just(x0), Just(x1), ty_Ordering)
new_ltEs14(Just(x0), Just(x1), ty_Ordering)
new_compare10(x0, x1, x2, x3, True, x4, x5)
new_lt6(x0, x1, ty_Ordering)
new_lt6(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_Double)
new_ltEs14(Just(x0), Just(x1), app(ty_Maybe, x2))
new_compare23(@2(x0, x1), @2(x2, x3), False, x4, x5)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_ltEs15(Left(x0), Left(x1), ty_Int, x2)
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare25(x0, x1, False)
new_compare18(Char(x0), Char(x1))
new_esEs18(x0, x1, ty_Bool)
new_esEs6(Right(x0), Right(x1), x2, ty_Char)
new_lt21(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs6(Right(x0), Right(x1), x2, ty_@0)
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_esEs31(x0, x1, ty_Bool)
new_asAs(True, x0)
new_compare17(Integer(x0), Integer(x1))
new_esEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs20(x0, x1, ty_Double)
new_esEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs30(x0, x1, x2, x3, False, x4, x5)
new_esEs31(x0, x1, app(ty_Maybe, x2))
new_pePe(True, x0)
new_compare28(x0, x1, False, x2, x3)
new_lt21(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1, ty_@0)
new_primEqNat0(Zero, Zero)
new_esEs25(x0, x1, ty_Int)
new_esEs27(x0, x1, ty_Int)
new_ltEs6(x0, x1, x2)
new_compare6(x0, x1, x2, x3)
new_lt15(x0, x1, x2)
new_addToFM_C10(x0, x1, x2, x3, x4, x5, x6, x7, x8, True, x9, x10, x11)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs5(Just(x0), Just(x1), ty_Char)
new_ltEs13(EQ, EQ)
new_esEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_compare29(x0, x1, ty_Ordering)
new_ltEs15(Right(x0), Right(x1), x2, ty_Ordering)
new_lt19(x0, x1, ty_Char)
new_ltEs14(Just(x0), Nothing, x1)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_lt19(x0, x1, app(ty_Ratio, x2))
new_compare9(x0, x1)
new_esEs26(x0, x1, ty_Ordering)
new_esEs19(x0, x1, ty_Ordering)
new_lt21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs13(False, False)
new_primMulNat0(Zero, Zero)
new_esEs23(x0, x1, ty_Bool)
new_esEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Double)
new_compare1([], [], x0)
new_esEs27(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_primCmpInt0(EmptyFM, x0, x1, x2, x3, x4, x5, x6)
new_mkBalBranch6MkBalBranch11(x0, x1, x2, x3, EmptyFM, x4, x5, x6, x7, False, x8, x9, x10)
new_primMinusNat0(Zero, Succ(x0))
new_addToFM_C20(x0, x1, x2, x3, x4, x5, x6, x7, x8, False, x9, x10, x11)
new_esEs18(x0, x1, ty_@0)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt6(x0, x1, ty_Bool)
new_compare29(x0, x1, ty_@0)
new_lt20(x0, x1, ty_Float)
new_sIZE_RATIO
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs15(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs13(LT, EQ)
new_ltEs13(EQ, LT)
new_lt5(x0, x1)
new_lt20(x0, x1, ty_Integer)
new_esEs18(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpNat2(Zero, Succ(x0))
new_compare210(x0, x1, True, x2)
new_esEs6(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs19(x0, x1, ty_Int)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_ltEs15(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs5(Just(x0), Just(x1), ty_Double)
new_esEs32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, ty_Int)
new_compare10(x0, x1, x2, x3, False, x4, x5)
new_mkBranch3(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_ltEs8(x0, x1)
new_primMulNat0(Zero, Succ(x0))
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_lt21(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, ty_Char)
new_lt6(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs14(Just(x0), Just(x1), ty_Double)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(Just(x0), Just(x1), ty_Bool)
new_ltEs15(Left(x0), Left(x1), ty_Char, x2)
new_addListToFM_CAdd(x0, @2(x1, x2), x3, x4, x5)
new_mkBalBranch6MkBalBranch4(x0, x1, x2, x3, Branch(x4, x5, x6, x7, x8), True, x9, x10, x11)
new_esEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_asAs(False, x0)
new_esEs26(x0, x1, ty_Integer)
new_ltEs15(Right(x0), Right(x1), x2, ty_Int)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Right(x0), Left(x1), x2, x3)
new_esEs6(Left(x0), Right(x1), x2, x3)
new_esEs6(Right(x0), Right(x1), x2, ty_Double)
new_ltEs15(Left(x0), Left(x1), ty_@0, x2)
new_ltEs12(False, False)
new_esEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_lt17(x0, x1)
new_ltEs14(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs18(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs20(x0, x1, app(ty_[], x2))
new_lt19(x0, x1, ty_Double)
new_esEs11(:(x0, x1), [], x2)
new_compare31(x0, x1, x2)
new_esEs19(x0, x1, ty_Int)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, ty_Ordering)
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_mkBranch1(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16)
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_primCompAux00(x0, LT)
new_esEs21(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Bool)
new_ltEs4(x0, x1, ty_Double)
new_mkBranchResult1(x0, x1, x2, x3, x4, x5, x6)
new_esEs25(x0, x1, ty_Integer)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, ty_Float)
new_esEs5(Just(x0), Just(x1), ty_Bool)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs31(x0, x1, ty_Float)
new_primPlusNat1(Zero, Zero)
new_compare14(x0, x1, False, x2, x3)
new_esEs22(x0, x1, ty_Float)
new_primCmpNat2(Zero, Zero)
new_primCmpNat1(Zero, x0)
new_primCompAux0(x0, x1, x2, x3)
new_mkBalBranch6MkBalBranch11(x0, x1, x2, x3, Branch(x4, x5, x6, x7, x8), x9, x10, x11, x12, False, x13, x14, x15)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_mkBalBranch(x0, x1, x2, x3, x4, x5, x6, x7)
new_compare29(x0, x1, ty_Float)
new_esEs29(x0, x1, ty_Double)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_lt16(x0, x1)
new_ltEs15(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs15(x0, x1)
new_primCompAux00(x0, EQ)
new_esEs5(Just(x0), Just(x1), ty_Int)
new_ltEs4(x0, x1, ty_Char)
new_ltEs15(Right(x0), Right(x1), x2, ty_Float)
new_esEs14(Float(x0, x1), Float(x2, x3))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs23(x0, x1, ty_Float)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6, x7)
new_esEs26(x0, x1, ty_Bool)
new_ltEs19(x0, x1, ty_@0)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_ltEs5(x0, x1)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Ordering)
new_esEs32(x0, x1, ty_Bool)
new_lt20(x0, x1, ty_Int)
new_primPlusNat1(Zero, Succ(x0))
new_esEs17(@0, @0)
new_esEs18(x0, x1, app(ty_Maybe, x2))
new_mkBalBranch6MkBalBranch5(x0, x1, x2, x3, x4, True, x5, x6, x7)
new_compare26(x0, x1, False, x2, x3, x4)
new_esEs32(x0, x1, ty_Char)
new_compare26(x0, x1, True, x2, x3, x4)
new_mkBranchResult0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_lt10(x0, x1)
new_pePe(False, x0)
new_esEs6(Right(x0), Right(x1), x2, ty_Int)
new_primCmpNat2(Succ(x0), Zero)
new_lt18(x0, x1, x2, x3, x4)
new_primCmpNat1(Succ(x0), x1)
new_esEs16(:%(x0, x1), :%(x2, x3), x4)
new_esEs28(x0, x1, ty_Char)
new_ltEs15(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs13(EQ, GT)
new_ltEs13(GT, EQ)
new_ltEs19(x0, x1, ty_Float)
new_esEs24(x0, x1, ty_Integer)
new_primMinusNat0(Succ(x0), Zero)
new_ltEs14(Just(x0), Just(x1), ty_Char)
new_mkBranch(x0, x1, x2, x3, x4, x5, x6, x7, x8)
new_esEs19(x0, x1, ty_@0)
new_lt7(x0, x1)
new_esEs19(x0, x1, ty_Double)
new_ltEs9(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs23(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(ty_[], x2))
new_mkBranch2(x0, x1, x2, x3, x4, x5, x6, x7)
new_ltEs4(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primPlusInt(Pos(x0), Pos(x1))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_compare15(x0, x1, True)
new_esEs28(x0, x1, ty_Float)
new_esEs6(Left(x0), Left(x1), ty_@0, x2)
new_esEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs20(x0, x1, ty_Int)
new_lt20(x0, x1, ty_@0)
new_ltEs14(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare112(x0, x1, False, x2, x3, x4)
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, ty_@0)
new_ltEs13(LT, GT)
new_ltEs13(GT, LT)
new_esEs31(x0, x1, ty_Char)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Float)
new_sr(x0, x1)
new_esEs18(x0, x1, ty_Integer)
new_ltEs20(x0, x1, ty_Char)
new_esEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare7(x0, x1)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, ty_@0)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_esEs6(Left(x0), Left(x1), ty_Bool, x2)
new_compare28(x0, x1, True, x2, x3)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_compare29(x0, x1, app(app(ty_@2, x2), x3))
new_primPlusNat0(Zero, x0)
new_esEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs14(Just(x0), Just(x1), app(ty_[], x2))
new_primEqInt(Neg(Zero), Neg(Zero))
new_emptyFM(x0, x1, x2)
new_compare1(:(x0, x1), [], x2)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs15(Right(x0), Right(x1), x2, ty_Double)
new_ltEs20(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Bool)
new_compare29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs19(x0, x1, ty_Bool)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs11(:(x0, x1), :(x2, x3), x4)
new_lt6(x0, x1, ty_Double)
new_ltEs15(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs27(x0, x1, ty_Float)
new_compare111(x0, x1, False, x2)
new_ltEs7(x0, x1)
new_primCmpNat0(x0, Succ(x1))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs32(x0, x1, ty_Float)
new_esEs29(x0, x1, ty_Char)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs20(x0, x1, ty_Bool)
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs15(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_lt6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs19(x0, x1, app(ty_[], x2))
new_ltEs15(Right(x0), Left(x1), x2, x3)
new_ltEs15(Left(x0), Right(x1), x2, x3)
new_lt19(x0, x1, ty_Float)
new_lt21(x0, x1, ty_Ordering)
new_ltEs14(Nothing, Nothing, x0)
new_ltEs15(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_sizeFM(EmptyFM, x0, x1, x2)
new_esEs21(x0, x1, ty_Float)
new_esEs20(x0, x1, ty_Ordering)
new_esEs26(x0, x1, ty_Double)
new_compare112(x0, x1, True, x2, x3, x4)
new_mkBalBranch6MkBalBranch01(x0, x1, x2, x3, x4, x5, x6, x7, x8, True, x9, x10, x11)
new_lt6(x0, x1, ty_Float)
new_compare23(x0, x1, True, x2, x3)
new_esEs32(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_ltEs14(Just(x0), Just(x1), ty_@0)
new_esEs26(x0, x1, ty_Int)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare29(x0, x1, app(ty_Maybe, x2))
new_ltEs12(False, True)
new_ltEs12(True, False)
new_lt11(x0, x1, x2, x3)
new_esEs22(x0, x1, ty_Int)
new_primMulInt(Neg(x0), Neg(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_ltEs4(x0, x1, ty_Float)
new_primEqNat0(Succ(x0), Zero)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs16(x0, x1)
new_esEs18(x0, x1, ty_Float)
new_ltEs14(Just(x0), Just(x1), ty_Float)
new_esEs5(Nothing, Nothing, x0)
new_ltEs15(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_primMulInt(Pos(x0), Pos(x1))
new_mkBalBranch6MkBalBranch3(EmptyFM, x0, x1, x2, x3, True, x4, x5, x6)
new_addToFM_C0(EmptyFM, x0, x1, x2, x3, x4)
new_esEs6(Left(x0), Left(x1), ty_Float, x2)
new_compare15(x0, x1, False)
new_esEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_compare25(x0, x1, True)
new_ltEs15(Left(x0), Left(x1), ty_Double, x2)
new_compare29(x0, x1, ty_Char)
new_addToFM_C20(x0, x1, x2, x3, x4, x5, x6, x7, x8, True, x9, x10, x11)
new_ltEs13(LT, LT)
new_esEs28(x0, x1, app(ty_[], x2))
new_ltEs11(x0, x1, x2)
new_compare1([], :(x0, x1), x2)
new_esEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs18(x0, x1, app(ty_[], x2))
new_lt13(x0, x1, x2)
new_esEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs4(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Integer)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_mkBalBranch6Size_r(x0, x1, x2, x3, x4, x5, x6, x7)
new_esEs6(Left(x0), Left(x1), ty_Integer, x2)
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_esEs31(x0, x1, app(ty_[], x2))
new_lt19(x0, x1, ty_Ordering)
new_esEs28(x0, x1, ty_@0)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs20(x0, x1, ty_Integer)
new_lt20(x0, x1, ty_Char)
new_esEs11([], :(x0, x1), x2)
new_lt20(x0, x1, ty_Ordering)
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_lt6(x0, x1, app(ty_Maybe, x2))
new_esEs29(x0, x1, ty_Float)
new_lt6(x0, x1, ty_Int)
new_ltEs15(Right(x0), Right(x1), x2, ty_Char)
new_mkBalBranch6Size_l(x0, x1, x2, x3, x4, x5, x6, x7)
new_compare29(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_Int)
new_lt21(x0, x1, ty_@0)
new_ltEs13(GT, GT)
new_esEs13(True, False)
new_esEs13(False, True)
new_esEs22(x0, x1, ty_Integer)
new_compare8(Double(x0, x1), Double(x2, x3))
new_lt21(x0, x1, ty_Integer)
new_ltEs15(Left(x0), Left(x1), ty_Float, x2)
new_esEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs6(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs15(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs20(x0, x1, ty_@0)
new_esEs23(x0, x1, ty_@0)
new_esEs32(x0, x1, ty_Double)
new_esEs6(Left(x0), Left(x1), ty_Int, x2)
new_esEs18(x0, x1, ty_Char)
new_compare110(x0, x1, True)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_addToFM_C0(Branch(@2(x0, x1), x2, x3, x4, x5), @2(x6, x7), x8, x9, x10, x11)
new_compare13(x0, x1)
new_esEs21(x0, x1, ty_Double)
new_esEs5(Just(x0), Just(x1), ty_@0)
new_ltEs15(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_not(True)
new_esEs28(x0, x1, ty_Int)
new_esEs28(x0, x1, ty_Bool)
new_esEs28(x0, x1, ty_Double)
new_mkBalBranch6MkBalBranch3(Branch(x0, x1, x2, x3, x4), x5, x6, x7, x8, True, x9, x10, x11)
new_lt6(x0, x1, app(ty_[], x2))
new_compare24(x0, x1, False)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs13(True, True)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs15(Left(x0), Left(x1), ty_Bool, x2)
new_lt14(x0, x1)
new_esEs5(Just(x0), Nothing, x1)
new_esEs29(x0, x1, ty_@0)
new_compare12(x0, x1, x2, x3)
new_esEs29(x0, x1, ty_Bool)
new_lt21(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_not(False)
new_compare110(x0, x1, False)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs31(x0, x1, ty_Int)
new_ltEs4(x0, x1, ty_Bool)
new_esEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_lt6(x0, x1, ty_@0)
new_mkBalBranch6MkBalBranch5(x0, x1, x2, x3, x4, False, x5, x6, x7)
new_primCmpInt0(Branch(x0, x1, x2, x3, x4), x5, x6, x7, x8, x9, x10, x11)
new_compare30(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs5(Just(x0), Just(x1), ty_Float)
new_esEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs6(Left(x0), Left(x1), ty_Char, x2)
new_mkBalBranch6MkBalBranch4(x0, x1, x2, x3, EmptyFM, True, x4, x5, x6)
new_esEs32(x0, x1, ty_@0)
new_ltEs12(True, True)
new_esEs23(x0, x1, ty_Char)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_@0)
new_esEs22(x0, x1, ty_Double)
new_ltEs4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, app(ty_[], x2))
new_compare24(x0, x1, True)
new_lt6(x0, x1, ty_Char)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs4(x0, x1, ty_@0)
new_esEs32(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs9(Integer(x0), Integer(x1))
new_ltEs19(x0, x1, ty_Bool)
new_esEs19(x0, x1, ty_Float)
new_esEs27(x0, x1, ty_Double)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_esEs20(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_Ordering)
new_esEs27(x0, x1, ty_Bool)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs30(x0, x1, x2, x3, True, x4, x5)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1, ty_Bool)
new_esEs6(Left(x0), Left(x1), ty_Double, x2)
new_esEs32(x0, x1, ty_Int)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(Just(x0), Just(x1), ty_Int)
new_compare16(Float(x0, x1), Float(x2, x3))
new_compare29(x0, x1, ty_Double)
new_ltEs14(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs32(x0, x1, app(app(ty_@2, x2), x3))
new_esEs32(x0, x1, ty_Ordering)
new_esEs5(Just(x0), Just(x1), ty_Integer)
new_mkBranch5(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkBalBranch6MkBalBranch3(x0, x1, x2, x3, x4, False, x5, x6, x7)
new_lt21(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_@0)
new_ltEs20(x0, x1, ty_Integer)
new_lt12(x0, x1)
new_fsEs(x0)
new_compare27(@0, @0)
new_esEs19(x0, x1, ty_Integer)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs18(x0, x1, app(app(ty_Either, x2), x3))
new_primCompAux00(x0, GT)
new_esEs26(x0, x1, ty_Char)
new_sr0(Integer(x0), Integer(x1))
new_esEs21(x0, x1, ty_Bool)
new_primMulNat0(Succ(x0), Zero)
new_ltEs15(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs10(Char(x0), Char(x1))
new_compare1(:(x0, x1), :(x2, x3), x4)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs21(x0, x1, ty_Char)
new_lt4(x0, x1, x2, x3)
new_compare29(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare111(x0, x1, True, x2)
new_ltEs4(x0, x1, app(ty_Ratio, x2))
new_primPlusNat1(Succ(x0), Zero)
new_ltEs19(x0, x1, ty_Integer)
new_esEs32(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Zero), Pos(Zero))
new_primMulNat0(Succ(x0), Succ(x1))
new_mkBalBranch6MkBalBranch4(x0, x1, x2, x3, x4, False, x5, x6, x7)
new_primEqNat0(Succ(x0), Succ(x1))
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs31(x0, x1, ty_Ordering)
new_mkBalBranch6MkBalBranch11(x0, x1, x2, x3, x4, x5, x6, x7, x8, True, x9, x10, x11)
new_lt21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, ty_Int)
new_ltEs14(Just(x0), Just(x1), app(ty_Ratio, x2))
new_mkBranchUnbox(x0, x1, x2, x3, x4, x5, x6)
new_lt19(x0, x1, ty_Int)
new_compare210(x0, x1, False, x2)
new_lt21(x0, x1, ty_Double)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, ty_Ordering)
new_ltEs15(Right(x0), Right(x1), x2, ty_@0)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_esEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_gt(x0, x1)
new_esEs29(x0, x1, ty_Integer)
new_esEs31(x0, x1, ty_Double)
new_primPlusNat0(Succ(x0), x1)
new_ps(x0, x1, x2, x3, x4, x5, x6)
new_lt8(x0, x1, x2)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs4(x0, x1, ty_Int)
new_esEs28(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_Double)
new_esEs21(x0, x1, ty_Int)

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: