YES 9.254 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
  ((addListToFM_C :: (Ord b, Ord c) => (a  ->  a  ->  a ->  FiniteMap (c,b) a  ->  [((c,b),a)]  ->  FiniteMap (c,b) a) :: (Ord b, Ord c) => (a  ->  a  ->  a ->  FiniteMap (c,b) a  ->  [((c,b),a)]  ->  FiniteMap (c,b) a)

module FiniteMap where
  import qualified Maybe
import qualified Prelude

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


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

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

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

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

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude



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

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



↳ HASKELL
  ↳ LR
HASKELL
      ↳ CR

mainModule FiniteMap
  ((addListToFM_C :: (Ord b, Ord a) => (c  ->  c  ->  c ->  FiniteMap (a,b) c  ->  [((a,b),c)]  ->  FiniteMap (a,b) c) :: (Ord b, Ord a) => (c  ->  c  ->  c ->  FiniteMap (a,b) c  ->  [((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_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 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 b a  ->  (b,a)
findMax (Branch key elt _ _ EmptyFM(key,elt)
findMax (Branch key elt _ _ fm_rfindMax fm_r

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

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

  
fmToList0 key elt rest (key,elt: rest

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

  mkBalBranch :: Ord a => a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b
mkBalBranch key elt fm_L fm_R 
 | size_l + size_r < 2 = 
mkBranch 1 key elt fm_L fm_R
 | size_r > sIZE_RATIO * size_l = 
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 :: a  ->  b  ->  FiniteMap a b
unitFM key elt Branch key elt 1 emptyFM emptyFM


module Maybe where
  import qualified FiniteMap
import qualified Prelude



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

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

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

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

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

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

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

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

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

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



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
HASKELL
          ↳ IFR

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

module FiniteMap where
  import qualified Maybe
import qualified Prelude

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


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

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

  
fmToList0 key elt rest (key,elt: rest

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

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

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

  sIZE_RATIO :: Int
sIZE_RATIO 5

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude



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

module FiniteMap where
  import qualified Maybe
import qualified Prelude

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


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

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

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

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

  sIZE_RATIO :: Int
sIZE_RATIO 5

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude



Replaced joker patterns by fresh variables and removed binding patterns.

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

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

module FiniteMap where
  import qualified Maybe
import qualified Prelude

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


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

  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 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 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 vw fm_l fm_rfoldFM k (k key elt (foldFM k z fm_r)) fm_l

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

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

  sIZE_RATIO :: Int
sIZE_RATIO 5

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

  unitFM :: 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)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

is transformed to
compare x y = compare3 x y

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

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

compare0 x y True = GT

compare3 x y = compare2 x y (x == y)

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

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

gcd'0 x y = gcd' y (x `rem` y)

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

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

The following Function with conditions
gcd 0 0 = error []
gcd x y = 
gcd' (abs x) (abs y)
where 
gcd' x 0 = x
gcd' x y = gcd' y (x `rem` y)

is transformed to
gcd wvy wvz = gcd3 wvy wvz
gcd x y = gcd0 x y

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

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

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

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

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

is transformed to
absReal x = absReal2 x

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

absReal0 x True = `negate` x

absReal2 x = absReal1 x (x >= 0)

The following Function with conditions
undefined 
 | False
 = undefined

is transformed to
undefined  = undefined1

undefined0 True = undefined

undefined1  = undefined0 False

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

is transformed to
reduce x y = reduce2 x y

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



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

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

module FiniteMap where
  import qualified Maybe
import qualified Prelude

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


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

  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 addToFM_C4 combiner EmptyFM key elt
addToFM_C combiner (Branch key elt size fm_l fm_rnew_key new_elt addToFM_C3 combiner (Branch key elt size fm_l fm_r) new_key new_elt

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

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

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

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

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

  emptyFM :: FiniteMap b a
emptyFM EmptyFM

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

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

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

  
fmToList0 key elt rest (key,elt: rest

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

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

  
mkBalBranch6 key elt fm_L fm_R 
mkBalBranch5 key elt fm_L fm_R (size_l + size_r < 2) where 
double_L fm_l (Branch key_r elt_r zv (Branch key_rl elt_rl zw fm_rll fm_rlr) fm_rrmkBranch 5 key_rl elt_rl (mkBranch 6 key elt fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr)
double_R (Branch key_l elt_l yw fm_ll (Branch key_lr elt_lr yx fm_lrl fm_lrr)) fm_r mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 key elt fm_lrr fm_r)
mkBalBranch0 fm_L fm_R (Branch zx zy zz fm_rl fm_rrmkBalBranch02 fm_L fm_R (Branch zx zy zz fm_rl fm_rr)
mkBalBranch00 fm_L fm_R zx zy zz fm_rl fm_rr True double_L fm_L fm_R
mkBalBranch01 fm_L fm_R zx zy zz fm_rl fm_rr True single_L fm_L fm_R
mkBalBranch01 fm_L fm_R zx zy zz fm_rl fm_rr False mkBalBranch00 fm_L fm_R zx zy zz fm_rl fm_rr otherwise
mkBalBranch02 fm_L fm_R (Branch zx zy zz fm_rl fm_rrmkBalBranch01 fm_L fm_R zx zy zz fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr)
mkBalBranch1 fm_L fm_R (Branch yy yz zu fm_ll fm_lrmkBalBranch12 fm_L fm_R (Branch yy yz zu fm_ll fm_lr)
mkBalBranch10 fm_L fm_R yy yz zu fm_ll fm_lr True double_R fm_L fm_R
mkBalBranch11 fm_L fm_R yy yz zu fm_ll fm_lr True single_R fm_L fm_R
mkBalBranch11 fm_L fm_R yy yz zu fm_ll fm_lr False mkBalBranch10 fm_L fm_R yy yz zu fm_ll fm_lr otherwise
mkBalBranch12 fm_L fm_R (Branch yy yz zu fm_ll fm_lrmkBalBranch11 fm_L fm_R yy yz zu fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll)
mkBalBranch2 key elt fm_L fm_R True mkBranch 2 key elt fm_L fm_R
mkBalBranch3 key elt fm_L fm_R True mkBalBranch1 fm_L fm_R fm_L
mkBalBranch3 key elt fm_L fm_R False mkBalBranch2 key elt fm_L fm_R otherwise
mkBalBranch4 key elt fm_L fm_R True mkBalBranch0 fm_L fm_R fm_R
mkBalBranch4 key elt fm_L fm_R False mkBalBranch3 key elt fm_L fm_R (size_l > sIZE_RATIO * size_r)
mkBalBranch5 key elt fm_L fm_R True mkBranch 1 key elt fm_L fm_R
mkBalBranch5 key elt fm_L fm_R False mkBalBranch4 key elt fm_L fm_R (size_r > sIZE_RATIO * size_l)
single_L fm_l (Branch key_r elt_r vuu fm_rl fm_rrmkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr
single_R (Branch key_l elt_l yv fm_ll fm_lrfm_r mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r)
size_l sizeFM fm_L
size_r sizeFM fm_R

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

  sIZE_RATIO :: Int
sIZE_RATIO 5

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude



Let/Where Reductions:
The bindings of the following Let/Where expression
let 
result  = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r
in result
where 
balance_ok  = True
left_ok  = left_ok0 fm_l key fm_l
left_ok0 fm_l key EmptyFM = True
left_ok0 fm_l key (Branch left_key vx vy vz wu) = 
let 
biggest_left_key  = fst (findMax fm_l)
in biggest_left_key < key
left_size  = sizeFM fm_l
right_ok  = right_ok0 fm_r key fm_r
right_ok0 fm_r key EmptyFM = True
right_ok0 fm_r key (Branch right_key wv ww wx wy) = 
let 
smallest_right_key  = fst (findMin fm_r)
in key < smallest_right_key
right_size  = sizeFM fm_r
unbox x = x

are unpacked to the following functions on top level
mkBranchUnbox wxw wxx wxy x = x

mkBranchLeft_size wxw wxx wxy = sizeFM wxw

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

mkBranchRight_size wxw wxx wxy = sizeFM wxy

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 vx vy vz wu) = mkBranchLeft_ok0Biggest_left_key fm_l < key

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

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

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

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

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

are unpacked to the following functions on top level
mkBalBranch6Single_R wyx wyy wyz wzu (Branch key_l elt_l yv fm_ll fm_lrfm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 wyx wyy fm_lr fm_r)

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

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)

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)

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)

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

mkBalBranch6Size_r wyx wyy wyz wzu = sizeFM wyz

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)

mkBalBranch6Size_l wyx wyy wyz wzu = sizeFM wzu

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

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)

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

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

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

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

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

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

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)

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

reduce2D wzy wzz = gcd wzy wzz

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

are unpacked to the following functions on top level
gcd0Gcd' x wuy = gcd0Gcd'2 x wuy
gcd0Gcd' x y = gcd0Gcd'0 x y

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

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

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

module FiniteMap where
  import qualified Maybe
import qualified Prelude

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


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

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

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

  
fmToList0 key elt rest (key,elt: rest

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

  
mkBalBranch6Size_l wyx wyy wyz wzu sizeFM wzu

  
mkBalBranch6Size_r wyx wyy wyz wzu sizeFM wyz

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

  
mkBranchBalance_ok wxw wxx wxy True

  
mkBranchLeft_ok wxw wxx wxy mkBranchLeft_ok0 wxw wxx wxy wxw wxx wxw

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

  
mkBranchLeft_ok0Biggest_left_key wzw fst (findMax wzw)

  
mkBranchLeft_size wxw wxx wxy sizeFM wxw

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

  
mkBranchRight_ok wxw wxx wxy mkBranchRight_ok0 wxw wxx wxy wxy wxx wxy

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

  
mkBranchRight_ok0Smallest_right_key wzx fst (findMin wzx)

  
mkBranchRight_size wxw wxx wxy sizeFM wxy

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

  sIZE_RATIO :: Int
sIZE_RATIO 5

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

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

module FiniteMap where
  import qualified Maybe
import qualified Prelude

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


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

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

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

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

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

  
mkBalBranch6Double_R wyx wyy wyz wzu (Branch key_l elt_l yw fm_ll (Branch key_lr elt_lr yx fm_lrl fm_lrr)) fm_r mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))) key_lr elt_lr (mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))) key_l elt_l fm_ll fm_lrl) (mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))) wyx wyy fm_lrr fm_r)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

  
mkBalBranch6Size_l wyx wyy wyz wzu sizeFM wzu

  
mkBalBranch6Size_r wyx wyy wyz wzu sizeFM wyz

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

  
mkBranchBalance_ok wxw wxx wxy True

  
mkBranchLeft_ok wxw wxx wxy mkBranchLeft_ok0 wxw wxx wxy wxw wxx wxw

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

  
mkBranchLeft_ok0Biggest_left_key wzw fst (findMax wzw)

  
mkBranchLeft_size wxw wxx wxy sizeFM wxw

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

  
mkBranchRight_ok wxw wxx wxy mkBranchRight_ok0 wxw wxx wxy wxy wxx wxy

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

  
mkBranchRight_ok0Smallest_right_key wzx fst (findMin wzx)

  
mkBranchRight_size wxw wxx wxy sizeFM wxy

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

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

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude



Haskell To QDPs


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

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

new_primEqNat(Succ(xuu500000), Succ(xuu40000)) → new_primEqNat(xuu500000, xuu40000)

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(xuu9700)) → new_primMinusNat(xuu41200, xuu9700)

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(xuu9700)) → new_primPlusNat(xuu41200, xuu9700)

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(xuu5000000), Succ(xuu400000)) → new_primMulNat(xuu5000000, Succ(xuu400000))

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_esEs3(Just(xuu50000), Just(xuu4000), app(app(ty_@2, bdd), bde)) → new_esEs0(xuu50000, xuu4000, bdd, bde)
new_esEs0(@2(xuu50000, xuu50001), @2(xuu4000, xuu4001), app(app(app(ty_@3, ff), fg), fh), fa) → new_esEs2(xuu50000, xuu4000, ff, fg, fh)
new_esEs2(@3(xuu50000, xuu50001, xuu50002), @3(xuu4000, xuu4001, xuu4002), app(app(app(ty_@3, bcf), bcg), bch), he, bba) → new_esEs2(xuu50000, xuu4000, bcf, bcg, bch)
new_esEs2(@3(xuu50000, xuu50001, xuu50002), @3(xuu4000, xuu4001, xuu4002), hd, app(app(ty_@2, bbb), bbc), bba) → new_esEs0(xuu50001, xuu4001, bbb, bbc)
new_esEs2(@3(xuu50000, xuu50001, xuu50002), @3(xuu4000, xuu4001, xuu4002), app(app(ty_Either, bca), bcb), he, bba) → new_esEs(xuu50000, xuu4000, bca, bcb)
new_esEs0(@2(xuu50000, xuu50001), @2(xuu4000, xuu4001), de, app(app(app(ty_@3, ec), ed), ee)) → new_esEs2(xuu50001, xuu4001, ec, ed, ee)
new_esEs2(@3(xuu50000, xuu50001, xuu50002), @3(xuu4000, xuu4001, xuu4002), hd, app(ty_Maybe, bbh), bba) → new_esEs3(xuu50001, xuu4001, bbh)
new_esEs2(@3(xuu50000, xuu50001, xuu50002), @3(xuu4000, xuu4001, xuu4002), hd, he, app(app(ty_@2, hh), baa)) → new_esEs0(xuu50002, xuu4002, hh, baa)
new_esEs(Right(xuu50000), Right(xuu4000), cb, app(ty_Maybe, dd)) → new_esEs3(xuu50000, xuu4000, dd)
new_esEs(Right(xuu50000), Right(xuu4000), cb, app(ty_[], cg)) → new_esEs1(xuu50000, xuu4000, cg)
new_esEs2(@3(xuu50000, xuu50001, xuu50002), @3(xuu4000, xuu4001, xuu4002), hd, he, app(ty_Maybe, baf)) → new_esEs3(xuu50002, xuu4002, baf)
new_esEs1(:(xuu50000, xuu50001), :(xuu4000, xuu4001), gb) → new_esEs1(xuu50001, xuu4001, gb)
new_esEs2(@3(xuu50000, xuu50001, xuu50002), @3(xuu4000, xuu4001, xuu4002), app(app(ty_@2, bcc), bcd), he, bba) → new_esEs0(xuu50000, xuu4000, bcc, bcd)
new_esEs2(@3(xuu50000, xuu50001, xuu50002), @3(xuu4000, xuu4001, xuu4002), hd, app(ty_[], bbd), bba) → new_esEs1(xuu50001, xuu4001, bbd)
new_esEs0(@2(xuu50000, xuu50001), @2(xuu4000, xuu4001), app(ty_[], fd), fa) → new_esEs1(xuu50000, xuu4000, fd)
new_esEs1(:(xuu50000, xuu50001), :(xuu4000, xuu4001), app(ty_[], gg)) → new_esEs1(xuu50000, xuu4000, gg)
new_esEs(Right(xuu50000), Right(xuu4000), cb, app(app(ty_@2, ce), cf)) → new_esEs0(xuu50000, xuu4000, ce, cf)
new_esEs0(@2(xuu50000, xuu50001), @2(xuu4000, xuu4001), app(app(ty_Either, eg), eh), fa) → new_esEs(xuu50000, xuu4000, eg, eh)
new_esEs0(@2(xuu50000, xuu50001), @2(xuu4000, xuu4001), de, app(app(ty_Either, df), dg)) → new_esEs(xuu50001, xuu4001, df, dg)
new_esEs2(@3(xuu50000, xuu50001, xuu50002), @3(xuu4000, xuu4001, xuu4002), hd, app(app(ty_Either, bag), bah), bba) → new_esEs(xuu50001, xuu4001, bag, bah)
new_esEs2(@3(xuu50000, xuu50001, xuu50002), @3(xuu4000, xuu4001, xuu4002), hd, he, app(app(ty_Either, hf), hg)) → new_esEs(xuu50002, xuu4002, hf, hg)
new_esEs(Right(xuu50000), Right(xuu4000), cb, app(app(ty_Either, cc), cd)) → new_esEs(xuu50000, xuu4000, cc, cd)
new_esEs0(@2(xuu50000, xuu50001), @2(xuu4000, xuu4001), de, app(ty_Maybe, ef)) → new_esEs3(xuu50001, xuu4001, ef)
new_esEs(Left(xuu50000), Left(xuu4000), app(app(ty_@2, bc), bd), bb) → new_esEs0(xuu50000, xuu4000, bc, bd)
new_esEs0(@2(xuu50000, xuu50001), @2(xuu4000, xuu4001), app(ty_Maybe, ga), fa) → new_esEs3(xuu50000, xuu4000, ga)
new_esEs2(@3(xuu50000, xuu50001, xuu50002), @3(xuu4000, xuu4001, xuu4002), hd, app(app(app(ty_@3, bbe), bbf), bbg), bba) → new_esEs2(xuu50001, xuu4001, bbe, bbf, bbg)
new_esEs3(Just(xuu50000), Just(xuu4000), app(app(app(ty_@3, bdg), bdh), bea)) → new_esEs2(xuu50000, xuu4000, bdg, bdh, bea)
new_esEs3(Just(xuu50000), Just(xuu4000), app(ty_Maybe, beb)) → new_esEs3(xuu50000, xuu4000, beb)
new_esEs2(@3(xuu50000, xuu50001, xuu50002), @3(xuu4000, xuu4001, xuu4002), app(ty_Maybe, bda), he, bba) → new_esEs3(xuu50000, xuu4000, bda)
new_esEs(Left(xuu50000), Left(xuu4000), app(ty_Maybe, ca), bb) → new_esEs3(xuu50000, xuu4000, ca)
new_esEs3(Just(xuu50000), Just(xuu4000), app(app(ty_Either, bdb), bdc)) → new_esEs(xuu50000, xuu4000, bdb, bdc)
new_esEs0(@2(xuu50000, xuu50001), @2(xuu4000, xuu4001), app(app(ty_@2, fb), fc), fa) → new_esEs0(xuu50000, xuu4000, fb, fc)
new_esEs2(@3(xuu50000, xuu50001, xuu50002), @3(xuu4000, xuu4001, xuu4002), hd, he, app(ty_[], bab)) → new_esEs1(xuu50002, xuu4002, bab)
new_esEs(Left(xuu50000), Left(xuu4000), app(ty_[], be), bb) → new_esEs1(xuu50000, xuu4000, be)
new_esEs(Left(xuu50000), Left(xuu4000), app(app(app(ty_@3, bf), bg), bh), bb) → new_esEs2(xuu50000, xuu4000, bf, bg, bh)
new_esEs(Right(xuu50000), Right(xuu4000), cb, app(app(app(ty_@3, da), db), dc)) → new_esEs2(xuu50000, xuu4000, da, db, dc)
new_esEs3(Just(xuu50000), Just(xuu4000), app(ty_[], bdf)) → new_esEs1(xuu50000, xuu4000, bdf)
new_esEs0(@2(xuu50000, xuu50001), @2(xuu4000, xuu4001), de, app(ty_[], eb)) → new_esEs1(xuu50001, xuu4001, eb)
new_esEs2(@3(xuu50000, xuu50001, xuu50002), @3(xuu4000, xuu4001, xuu4002), app(ty_[], bce), he, bba) → new_esEs1(xuu50000, xuu4000, bce)
new_esEs1(:(xuu50000, xuu50001), :(xuu4000, xuu4001), app(app(app(ty_@3, gh), ha), hb)) → new_esEs2(xuu50000, xuu4000, gh, ha, hb)
new_esEs0(@2(xuu50000, xuu50001), @2(xuu4000, xuu4001), de, app(app(ty_@2, dh), ea)) → new_esEs0(xuu50001, xuu4001, dh, ea)
new_esEs1(:(xuu50000, xuu50001), :(xuu4000, xuu4001), app(app(ty_Either, gc), gd)) → new_esEs(xuu50000, xuu4000, gc, gd)
new_esEs1(:(xuu50000, xuu50001), :(xuu4000, xuu4001), app(ty_Maybe, hc)) → new_esEs3(xuu50000, xuu4000, hc)
new_esEs1(:(xuu50000, xuu50001), :(xuu4000, xuu4001), app(app(ty_@2, ge), gf)) → new_esEs0(xuu50000, xuu4000, ge, gf)
new_esEs(Left(xuu50000), Left(xuu4000), app(app(ty_Either, h), ba), bb) → new_esEs(xuu50000, xuu4000, h, ba)
new_esEs2(@3(xuu50000, xuu50001, xuu50002), @3(xuu4000, xuu4001, xuu4002), hd, he, app(app(app(ty_@3, bac), bad), bae)) → new_esEs2(xuu50002, xuu4002, bac, bad, bae)

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

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



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

The TRS R consists of the following rules:

new_esEs25(xuu4911, xuu5111, app(ty_[], hb)) → new_esEs14(xuu4911, xuu5111, hb)
new_compare112(xuu490, xuu510, True, bg) → LT
new_ltEs20(xuu4912, xuu5112, ty_Char) → new_ltEs18(xuu4912, xuu5112)
new_compare27(xuu490, xuu510) → new_compare24(xuu490, xuu510, new_esEs8(xuu490, xuu510))
new_esEs7(Left(xuu50000), Left(xuu4000), app(app(ty_Either, cdg), cdh), cea) → new_esEs7(xuu50000, xuu4000, cdg, cdh)
new_primCmpNat2(Zero, xuu4900) → LT
new_lt19(xuu4910, xuu5110, ty_Int) → new_lt18(xuu4910, xuu5110)
new_lt21(xuu4911, xuu5111, app(ty_Maybe, hc)) → new_lt8(xuu4911, xuu5111, hc)
new_lt19(xuu4910, xuu5110, ty_Double) → new_lt7(xuu4910, xuu5110)
new_ltEs11(LT, GT) → True
new_ltEs14(Left(xuu4910), Left(xuu5110), ty_Double, bcc) → new_ltEs16(xuu4910, xuu5110)
new_compare110(xuu490, xuu510, True, bh, ca) → LT
new_esEs27(xuu50001, xuu4001, app(ty_Ratio, dbb)) → new_esEs18(xuu50001, xuu4001, dbb)
new_primCmpNat1(Zero, Succ(xuu51000)) → LT
new_compare([], :(xuu5100, xuu5101), bf) → LT
new_lt21(xuu4911, xuu5111, ty_Ordering) → new_lt14(xuu4911, xuu5111)
new_compare23(@2(xuu490, xuu491), @2(xuu510, xuu511), False, cb, bb) → new_compare14(xuu490, xuu491, xuu510, xuu511, new_lt9(xuu490, xuu510, cb), new_asAs(new_esEs12(xuu490, xuu510, cb), new_ltEs6(xuu491, xuu511, bb)), cb, bb)
new_ltEs15(xuu491, xuu511) → new_fsEs(new_compare19(xuu491, xuu511))
new_lt19(xuu4910, xuu5110, app(app(ty_@2, cc), cd)) → new_lt10(xuu4910, xuu5110, cc, cd)
new_lt19(xuu4910, xuu5110, ty_Ordering) → new_lt14(xuu4910, xuu5110)
new_esEs12(xuu490, xuu510, ty_Char) → new_esEs11(xuu490, xuu510)
new_esEs26(xuu4910, xuu5110, ty_Float) → new_esEs13(xuu4910, xuu5110)
new_esEs21(xuu50000, xuu4000, ty_@0) → new_esEs17(xuu50000, xuu4000)
new_lt21(xuu4911, xuu5111, ty_@0) → new_lt17(xuu4911, xuu5111)
new_primMulNat0(Zero, Zero) → Zero
new_esEs19(xuu50002, xuu4002, app(ty_Ratio, bhe)) → new_esEs18(xuu50002, xuu4002, bhe)
new_esEs7(Left(xuu50000), Left(xuu4000), app(app(app(ty_@3, cee), cef), ceg), cea) → new_esEs5(xuu50000, xuu4000, cee, cef, ceg)
new_ltEs20(xuu4912, xuu5112, ty_@0) → new_ltEs15(xuu4912, xuu5112)
new_compare(:(xuu4900, xuu4901), [], bf) → GT
new_sr(Integer(xuu51000), Integer(xuu49010)) → Integer(new_primMulInt(xuu51000, xuu49010))
new_ltEs6(xuu491, xuu511, app(app(ty_Either, bdc), bcc)) → new_ltEs14(xuu491, xuu511, bdc, bcc)
new_esEs25(xuu4911, xuu5111, app(app(ty_@2, ge), gf)) → new_esEs4(xuu4911, xuu5111, ge, gf)
new_compare30(xuu4900, xuu5100, app(ty_Maybe, bfc)) → new_compare13(xuu4900, xuu5100, bfc)
new_esEs28(xuu50000, xuu4000, ty_Bool) → new_esEs16(xuu50000, xuu4000)
new_lt19(xuu4910, xuu5110, ty_Bool) → new_lt4(xuu4910, xuu5110)
new_esEs7(Right(xuu50000), Right(xuu4000), cfb, ty_Ordering) → new_esEs8(xuu50000, xuu4000)
new_esEs22(xuu4910, xuu5110, ty_@0) → new_esEs17(xuu4910, xuu5110)
new_lt14(xuu490, xuu510) → new_esEs8(new_compare27(xuu490, xuu510), LT)
new_lt20(xuu4910, xuu5110, ty_Int) → new_lt18(xuu4910, xuu5110)
new_esEs24(xuu50000, xuu4000, ty_Integer) → new_esEs15(xuu50000, xuu4000)
new_esEs19(xuu50002, xuu4002, ty_Int) → new_esEs10(xuu50002, xuu4002)
new_compare30(xuu4900, xuu5100, app(ty_Ratio, chf)) → new_compare6(xuu4900, xuu5100, chf)
new_esEs25(xuu4911, xuu5111, app(ty_Ratio, chc)) → new_esEs18(xuu4911, xuu5111, chc)
new_ltEs5(xuu491, xuu511, bag) → new_fsEs(new_compare(xuu491, xuu511, bag))
new_ltEs10(Just(xuu4910), Just(xuu5110), ty_Int) → new_ltEs17(xuu4910, xuu5110)
new_ltEs10(Just(xuu4910), Just(xuu5110), ty_@0) → new_ltEs15(xuu4910, xuu5110)
new_ltEs10(Just(xuu4910), Just(xuu5110), ty_Integer) → new_ltEs12(xuu4910, xuu5110)
new_compare13(xuu490, xuu510, bg) → new_compare29(xuu490, xuu510, new_esEs6(xuu490, xuu510, bg), bg)
new_lt17(xuu490, xuu510) → new_esEs8(new_compare19(xuu490, xuu510), LT)
new_esEs7(Right(xuu50000), Right(xuu4000), cfb, app(app(app(ty_@3, cfh), cga), cgb)) → new_esEs5(xuu50000, xuu4000, cfh, cga, cgb)
new_esEs19(xuu50002, xuu4002, app(ty_[], bgh)) → new_esEs14(xuu50002, xuu4002, bgh)
new_ltEs6(xuu491, xuu511, app(ty_[], bag)) → new_ltEs5(xuu491, xuu511, bag)
new_esEs22(xuu4910, xuu5110, app(ty_Maybe, dc)) → new_esEs6(xuu4910, xuu5110, dc)
new_primCmpNat1(Succ(xuu49000), Succ(xuu51000)) → new_primCmpNat1(xuu49000, xuu51000)
new_esEs27(xuu50001, xuu4001, app(ty_Maybe, dba)) → new_esEs6(xuu50001, xuu4001, dba)
new_ltEs13(True, False) → False
new_esEs29(xuu50000, xuu4000, ty_Char) → new_esEs11(xuu50000, xuu4000)
new_esEs15(Integer(xuu50000), Integer(xuu4000)) → new_primEqInt(xuu50000, xuu4000)
new_lt20(xuu4910, xuu5110, ty_Float) → new_lt12(xuu4910, xuu5110)
new_lt9(xuu490, xuu510, app(app(app(ty_@3, bc), bd), be)) → new_lt11(xuu490, xuu510, bc, bd, be)
new_lt20(xuu4910, xuu5110, app(ty_[], fh)) → new_lt13(xuu4910, xuu5110, fh)
new_esEs19(xuu50002, xuu4002, app(app(app(ty_@3, bha), bhb), bhc)) → new_esEs5(xuu50002, xuu4002, bha, bhb, bhc)
new_compare15(xuu490, xuu510, False) → GT
new_esEs22(xuu4910, xuu5110, app(ty_[], db)) → new_esEs14(xuu4910, xuu5110, db)
new_esEs28(xuu50000, xuu4000, app(app(app(ty_@3, dbh), dca), dcb)) → new_esEs5(xuu50000, xuu4000, dbh, dca, dcb)
new_esEs22(xuu4910, xuu5110, app(ty_Ratio, cge)) → new_esEs18(xuu4910, xuu5110, cge)
new_esEs22(xuu4910, xuu5110, app(app(ty_Either, dd), de)) → new_esEs7(xuu4910, xuu5110, dd, de)
new_esEs29(xuu50000, xuu4000, ty_Integer) → new_esEs15(xuu50000, xuu4000)
new_ltEs19(xuu4911, xuu5111, ty_Char) → new_ltEs18(xuu4911, xuu5111)
new_esEs25(xuu4911, xuu5111, ty_Double) → new_esEs9(xuu4911, xuu5111)
new_esEs17(@0, @0) → True
new_esEs25(xuu4911, xuu5111, ty_Float) → new_esEs13(xuu4911, xuu5111)
new_esEs7(Right(xuu50000), Right(xuu4000), cfb, app(ty_Maybe, cgc)) → new_esEs6(xuu50000, xuu4000, cgc)
new_lt20(xuu4910, xuu5110, ty_Double) → new_lt7(xuu4910, xuu5110)
new_lt20(xuu4910, xuu5110, ty_Bool) → new_lt4(xuu4910, xuu5110)
new_pePe(False, xuu135) → xuu135
new_esEs14([], [], dce) → True
new_esEs7(Left(xuu50000), Right(xuu4000), cfb, cea) → False
new_esEs7(Right(xuu50000), Left(xuu4000), cfb, cea) → False
new_esEs25(xuu4911, xuu5111, ty_Char) → new_esEs11(xuu4911, xuu5111)
new_ltEs20(xuu4912, xuu5112, app(ty_[], bac)) → new_ltEs5(xuu4912, xuu5112, bac)
new_esEs5(@3(xuu50000, xuu50001, xuu50002), @3(xuu4000, xuu4001, xuu4002), bga, bgb, bgc) → new_asAs(new_esEs21(xuu50000, xuu4000, bga), new_asAs(new_esEs20(xuu50001, xuu4001, bgb), new_esEs19(xuu50002, xuu4002, bgc)))
new_esEs29(xuu50000, xuu4000, app(ty_[], ddb)) → new_esEs14(xuu50000, xuu4000, ddb)
new_esEs27(xuu50001, xuu4001, app(app(ty_Either, daa), dab)) → new_esEs7(xuu50001, xuu4001, daa, dab)
new_ltEs14(Left(xuu4910), Left(xuu5110), ty_@0, bcc) → new_ltEs15(xuu4910, xuu5110)
new_esEs29(xuu50000, xuu4000, ty_@0) → new_esEs17(xuu50000, xuu4000)
new_esEs19(xuu50002, xuu4002, app(ty_Maybe, bhd)) → new_esEs6(xuu50002, xuu4002, bhd)
new_ltEs14(Right(xuu4910), Right(xuu5110), bdc, app(app(app(ty_@3, bdf), bdg), bdh)) → new_ltEs8(xuu4910, xuu5110, bdf, bdg, bdh)
new_esEs22(xuu4910, xuu5110, app(app(ty_@2, cc), cd)) → new_esEs4(xuu4910, xuu5110, cc, cd)
new_compare15(xuu490, xuu510, True) → LT
new_compare25(xuu490, xuu510, False, bh, ca) → new_compare110(xuu490, xuu510, new_ltEs14(xuu490, xuu510, bh, ca), bh, ca)
new_lt15(xuu490, xuu510) → new_esEs8(new_compare7(xuu490, xuu510), LT)
new_ltEs6(xuu491, xuu511, app(app(ty_@2, df), ce)) → new_ltEs7(xuu491, xuu511, df, ce)
new_esEs12(xuu490, xuu510, ty_Double) → new_esEs9(xuu490, xuu510)
new_ltEs20(xuu4912, xuu5112, ty_Integer) → new_ltEs12(xuu4912, xuu5112)
new_esEs22(xuu4910, xuu5110, ty_Ordering) → new_esEs8(xuu4910, xuu5110)
new_lt9(xuu490, xuu510, app(ty_[], bf)) → new_lt13(xuu490, xuu510, bf)
new_esEs19(xuu50002, xuu4002, app(app(ty_Either, bgd), bge)) → new_esEs7(xuu50002, xuu4002, bgd, bge)
new_esEs7(Left(xuu50000), Left(xuu4000), ty_Double, cea) → new_esEs9(xuu50000, xuu4000)
new_compare9(xuu490, xuu510) → new_compare26(xuu490, xuu510, new_esEs16(xuu490, xuu510))
new_esEs7(Right(xuu50000), Right(xuu4000), cfb, ty_Double) → new_esEs9(xuu50000, xuu4000)
new_ltEs14(Left(xuu4910), Left(xuu5110), ty_Ordering, bcc) → new_ltEs11(xuu4910, xuu5110)
new_esEs7(Left(xuu50000), Left(xuu4000), ty_Bool, cea) → new_esEs16(xuu50000, xuu4000)
new_esEs29(xuu50000, xuu4000, app(app(ty_@2, dch), dda)) → new_esEs4(xuu50000, xuu4000, dch, dda)
new_esEs20(xuu50001, xuu4001, ty_Bool) → new_esEs16(xuu50001, xuu4001)
new_lt9(xuu490, xuu510, app(app(ty_@2, h), ba)) → new_lt10(xuu490, xuu510, h, ba)
new_esEs6(Just(xuu50000), Just(xuu4000), app(app(app(ty_@3, cdb), cdc), cdd)) → new_esEs5(xuu50000, xuu4000, cdb, cdc, cdd)
new_esEs12(xuu490, xuu510, ty_@0) → new_esEs17(xuu490, xuu510)
new_lt6(xuu490, xuu510) → new_esEs8(new_compare10(xuu490, xuu510), LT)
new_ltEs20(xuu4912, xuu5112, app(app(ty_@2, hf), hg)) → new_ltEs7(xuu4912, xuu5112, hf, hg)
new_esEs25(xuu4911, xuu5111, ty_Bool) → new_esEs16(xuu4911, xuu5111)
new_ltEs10(Just(xuu4910), Just(xuu5110), app(ty_Ratio, che)) → new_ltEs4(xuu4910, xuu5110, che)
new_esEs8(LT, LT) → True
new_ltEs13(False, True) → True
new_ltEs18(xuu491, xuu511) → new_fsEs(new_compare10(xuu491, xuu511))
new_lt18(xuu490, xuu510) → new_esEs8(new_compare8(xuu490, xuu510), LT)
new_esEs25(xuu4911, xuu5111, ty_Ordering) → new_esEs8(xuu4911, xuu5111)
new_esEs7(Left(xuu50000), Left(xuu4000), ty_Float, cea) → new_esEs13(xuu50000, xuu4000)
new_compare30(xuu4900, xuu5100, app(app(ty_@2, bee), bef)) → new_compare12(xuu4900, xuu5100, bee, bef)
new_ltEs14(Right(xuu4910), Right(xuu5110), bdc, ty_@0) → new_ltEs15(xuu4910, xuu5110)
new_lt9(xuu490, xuu510, app(app(ty_Either, bh), ca)) → new_lt16(xuu490, xuu510, bh, ca)
new_ltEs10(Just(xuu4910), Just(xuu5110), app(ty_Maybe, bbf)) → new_ltEs10(xuu4910, xuu5110, bbf)
new_ltEs4(xuu491, xuu511, bfg) → new_fsEs(new_compare6(xuu491, xuu511, bfg))
new_pePe(True, xuu135) → True
new_primEqNat0(Zero, Zero) → True
new_compare26(xuu490, xuu510, True) → EQ
new_esEs29(xuu50000, xuu4000, app(ty_Maybe, ddf)) → new_esEs6(xuu50000, xuu4000, ddf)
new_lt21(xuu4911, xuu5111, app(app(ty_Either, hd), he)) → new_lt16(xuu4911, xuu5111, hd, he)
new_esEs26(xuu4910, xuu5110, app(ty_Maybe, ga)) → new_esEs6(xuu4910, xuu5110, ga)
new_primMulNat0(Succ(xuu5000000), Succ(xuu400000)) → new_primPlusNat1(new_primMulNat0(xuu5000000, Succ(xuu400000)), xuu400000)
new_lt20(xuu4910, xuu5110, app(app(ty_@2, eh), fa)) → new_lt10(xuu4910, xuu5110, eh, fa)
new_compare12(xuu490, xuu510, h, ba) → new_compare23(xuu490, xuu510, new_esEs4(xuu490, xuu510, h, ba), h, ba)
new_esEs4(@2(xuu50000, xuu50001), @2(xuu4000, xuu4001), chg, chh) → new_asAs(new_esEs28(xuu50000, xuu4000, chg), new_esEs27(xuu50001, xuu4001, chh))
new_ltEs10(Just(xuu4910), Just(xuu5110), app(app(ty_Either, bbg), bbh)) → new_ltEs14(xuu4910, xuu5110, bbg, bbh)
new_esEs7(Left(xuu50000), Left(xuu4000), ty_Ordering, cea) → new_esEs8(xuu50000, xuu4000)
new_esEs19(xuu50002, xuu4002, ty_Float) → new_esEs13(xuu50002, xuu4002)
new_compare110(xuu490, xuu510, False, bh, ca) → GT
new_ltEs14(Right(xuu4910), Right(xuu5110), bdc, app(ty_[], bea)) → new_ltEs5(xuu4910, xuu5110, bea)
new_ltEs14(Right(xuu4910), Right(xuu5110), bdc, ty_Int) → new_ltEs17(xuu4910, xuu5110)
new_esEs26(xuu4910, xuu5110, ty_Bool) → new_esEs16(xuu4910, xuu5110)
new_lt19(xuu4910, xuu5110, app(ty_Maybe, dc)) → new_lt8(xuu4910, xuu5110, dc)
new_primCmpNat1(Zero, Zero) → EQ
new_esEs6(Just(xuu50000), Just(xuu4000), ty_@0) → new_esEs17(xuu50000, xuu4000)
new_esEs6(Just(xuu50000), Just(xuu4000), ty_Bool) → new_esEs16(xuu50000, xuu4000)
new_lt7(xuu490, xuu510) → new_esEs8(new_compare11(xuu490, xuu510), LT)
new_ltEs10(Just(xuu4910), Just(xuu5110), ty_Float) → new_ltEs9(xuu4910, xuu5110)
new_esEs22(xuu4910, xuu5110, ty_Double) → new_esEs9(xuu4910, xuu5110)
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_esEs7(Left(xuu50000), Left(xuu4000), ty_Int, cea) → new_esEs10(xuu50000, xuu4000)
new_lt20(xuu4910, xuu5110, ty_Ordering) → new_lt14(xuu4910, xuu5110)
new_lt19(xuu4910, xuu5110, app(app(app(ty_@3, cf), cg), da)) → new_lt11(xuu4910, xuu5110, cf, cg, da)
new_compare29(xuu490, xuu510, False, bg) → new_compare112(xuu490, xuu510, new_ltEs10(xuu490, xuu510, bg), bg)
new_esEs7(Right(xuu50000), Right(xuu4000), cfb, app(app(ty_Either, cfc), cfd)) → new_esEs7(xuu50000, xuu4000, cfc, cfd)
new_esEs8(GT, LT) → False
new_esEs8(LT, GT) → False
new_primCmpNat1(Succ(xuu49000), Zero) → GT
new_lt21(xuu4911, xuu5111, app(app(app(ty_@3, gg), gh), ha)) → new_lt11(xuu4911, xuu5111, gg, gh, ha)
new_ltEs14(Right(xuu4910), Right(xuu5110), bdc, app(app(ty_@2, bdd), bde)) → new_ltEs7(xuu4910, xuu5110, bdd, bde)
new_ltEs14(Left(xuu4910), Left(xuu5110), ty_Bool, bcc) → new_ltEs13(xuu4910, xuu5110)
new_primEqInt(Neg(Succ(xuu500000)), Neg(Succ(xuu40000))) → new_primEqNat0(xuu500000, xuu40000)
new_compare30(xuu4900, xuu5100, ty_Float) → new_compare18(xuu4900, xuu5100)
new_ltEs20(xuu4912, xuu5112, app(ty_Ratio, chd)) → new_ltEs4(xuu4912, xuu5112, chd)
new_lt21(xuu4911, xuu5111, app(app(ty_@2, ge), gf)) → new_lt10(xuu4911, xuu5111, ge, gf)
new_esEs20(xuu50001, xuu4001, ty_Ordering) → new_esEs8(xuu50001, xuu4001)
new_esEs7(Left(xuu50000), Left(xuu4000), ty_Char, cea) → new_esEs11(xuu50000, xuu4000)
new_lt20(xuu4910, xuu5110, ty_Char) → new_lt6(xuu4910, xuu5110)
new_ltEs16(xuu491, xuu511) → new_fsEs(new_compare11(xuu491, xuu511))
new_ltEs6(xuu491, xuu511, ty_Char) → new_ltEs18(xuu491, xuu511)
new_esEs28(xuu50000, xuu4000, ty_@0) → new_esEs17(xuu50000, xuu4000)
new_ltEs14(Right(xuu4910), Left(xuu5110), bdc, bcc) → False
new_esEs16(False, True) → False
new_esEs16(True, False) → False
new_esEs7(Right(xuu50000), Right(xuu4000), cfb, ty_Float) → new_esEs13(xuu50000, xuu4000)
new_esEs14(:(xuu50000, xuu50001), [], dce) → False
new_esEs14([], :(xuu4000, xuu4001), dce) → False
new_compare111(xuu110, xuu111, xuu112, xuu113, True, cgh, cha) → LT
new_ltEs19(xuu4911, xuu5111, ty_Float) → new_ltEs9(xuu4911, xuu5111)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs7(Left(xuu50000), Left(xuu4000), ty_Integer, cea) → new_esEs15(xuu50000, xuu4000)
new_esEs20(xuu50001, xuu4001, ty_Float) → new_esEs13(xuu50001, xuu4001)
new_lt19(xuu4910, xuu5110, ty_Integer) → new_lt15(xuu4910, xuu5110)
new_esEs6(Just(xuu50000), Just(xuu4000), ty_Float) → new_esEs13(xuu50000, xuu4000)
new_esEs26(xuu4910, xuu5110, app(ty_[], fh)) → new_esEs14(xuu4910, xuu5110, fh)
new_compare8(xuu92, xuu91) → new_primCmpInt(xuu92, xuu91)
new_primEqInt(Neg(Zero), Neg(Succ(xuu40000))) → False
new_primEqInt(Neg(Succ(xuu500000)), Neg(Zero)) → False
new_esEs8(EQ, EQ) → True
new_primPlusNat1(Zero, xuu400000) → Succ(xuu400000)
new_esEs22(xuu4910, xuu5110, ty_Float) → new_esEs13(xuu4910, xuu5110)
new_esEs28(xuu50000, xuu4000, app(ty_[], dbg)) → new_esEs14(xuu50000, xuu4000, dbg)
new_esEs20(xuu50001, xuu4001, ty_@0) → new_esEs17(xuu50001, xuu4001)
new_esEs22(xuu4910, xuu5110, app(app(app(ty_@3, cf), cg), da)) → new_esEs5(xuu4910, xuu5110, cf, cg, da)
new_compare([], [], bf) → EQ
new_esEs26(xuu4910, xuu5110, app(app(ty_Either, gb), gc)) → new_esEs7(xuu4910, xuu5110, gb, gc)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_ltEs19(xuu4911, xuu5111, ty_Bool) → new_ltEs13(xuu4911, xuu5111)
new_esEs29(xuu50000, xuu4000, ty_Bool) → new_esEs16(xuu50000, xuu4000)
new_esEs25(xuu4911, xuu5111, ty_@0) → new_esEs17(xuu4911, xuu5111)
new_esEs29(xuu50000, xuu4000, ty_Float) → new_esEs13(xuu50000, xuu4000)
new_ltEs19(xuu4911, xuu5111, app(ty_Ratio, cgf)) → new_ltEs4(xuu4911, xuu5111, cgf)
new_lt19(xuu4910, xuu5110, app(app(ty_Either, dd), de)) → new_lt16(xuu4910, xuu5110, dd, de)
new_esEs6(Nothing, Nothing, ccd) → True
new_compare113(xuu490, xuu510, False, bc, bd, be) → GT
new_compare18(Float(xuu4900, xuu4901), Float(xuu5100, xuu5101)) → new_compare8(new_sr0(xuu4900, xuu5100), new_sr0(xuu4901, xuu5101))
new_esEs19(xuu50002, xuu4002, ty_Char) → new_esEs11(xuu50002, xuu4002)
new_lt21(xuu4911, xuu5111, app(ty_Ratio, chc)) → new_lt5(xuu4911, xuu5111, chc)
new_primEqInt(Pos(Succ(xuu500000)), Pos(Succ(xuu40000))) → new_primEqNat0(xuu500000, xuu40000)
new_esEs12(xuu490, xuu510, app(app(app(ty_@3, bc), bd), be)) → new_esEs5(xuu490, xuu510, bc, bd, be)
new_ltEs8(@3(xuu4910, xuu4911, xuu4912), @3(xuu5110, xuu5111, xuu5112), gd, fb, fc) → new_pePe(new_lt20(xuu4910, xuu5110, gd), new_asAs(new_esEs26(xuu4910, xuu5110, gd), new_pePe(new_lt21(xuu4911, xuu5111, fb), new_asAs(new_esEs25(xuu4911, xuu5111, fb), new_ltEs20(xuu4912, xuu5112, fc)))))
new_esEs21(xuu50000, xuu4000, app(ty_Maybe, cbh)) → new_esEs6(xuu50000, xuu4000, cbh)
new_esEs20(xuu50001, xuu4001, ty_Int) → new_esEs10(xuu50001, xuu4001)
new_esEs26(xuu4910, xuu5110, ty_Integer) → new_esEs15(xuu4910, xuu5110)
new_lt12(xuu490, xuu510) → new_esEs8(new_compare18(xuu490, xuu510), LT)
new_esEs6(Nothing, Just(xuu4000), ccd) → False
new_esEs6(Just(xuu50000), Nothing, ccd) → False
new_primEqNat0(Succ(xuu500000), Succ(xuu40000)) → new_primEqNat0(xuu500000, xuu40000)
new_ltEs14(Left(xuu4910), Left(xuu5110), app(ty_Maybe, bch), bcc) → new_ltEs10(xuu4910, xuu5110, bch)
new_lt9(xuu490, xuu510, ty_Integer) → new_lt15(xuu490, xuu510)
new_lt5(xuu490, xuu510, bff) → new_esEs8(new_compare6(xuu490, xuu510, bff), LT)
new_esEs27(xuu50001, xuu4001, ty_Ordering) → new_esEs8(xuu50001, xuu4001)
new_esEs12(xuu490, xuu510, ty_Float) → new_esEs13(xuu490, xuu510)
new_esEs21(xuu50000, xuu4000, app(ty_[], cbd)) → new_esEs14(xuu50000, xuu4000, cbd)
new_lt21(xuu4911, xuu5111, ty_Char) → new_lt6(xuu4911, xuu5111)
new_ltEs14(Left(xuu4910), Left(xuu5110), ty_Int, bcc) → new_ltEs17(xuu4910, xuu5110)
new_esEs29(xuu50000, xuu4000, ty_Double) → new_esEs9(xuu50000, xuu4000)
new_ltEs14(Right(xuu4910), Right(xuu5110), bdc, app(ty_Ratio, ccc)) → new_ltEs4(xuu4910, xuu5110, ccc)
new_esEs29(xuu50000, xuu4000, ty_Int) → new_esEs10(xuu50000, xuu4000)
new_primCompAux00(xuu140, LT) → LT
new_esEs22(xuu4910, xuu5110, ty_Bool) → new_esEs16(xuu4910, xuu5110)
new_lt19(xuu4910, xuu5110, app(ty_[], db)) → new_lt13(xuu4910, xuu5110, db)
new_ltEs6(xuu491, xuu511, app(ty_Ratio, bfg)) → new_ltEs4(xuu491, xuu511, bfg)
new_esEs26(xuu4910, xuu5110, app(app(ty_@2, eh), fa)) → new_esEs4(xuu4910, xuu5110, eh, fa)
new_esEs27(xuu50001, xuu4001, app(app(app(ty_@3, daf), dag), dah)) → new_esEs5(xuu50001, xuu4001, daf, dag, dah)
new_ltEs19(xuu4911, xuu5111, ty_Int) → new_ltEs17(xuu4911, xuu5111)
new_lt9(xuu490, xuu510, ty_Float) → new_lt12(xuu490, xuu510)
new_esEs12(xuu490, xuu510, app(ty_Ratio, bff)) → new_esEs18(xuu490, xuu510, bff)
new_esEs6(Just(xuu50000), Just(xuu4000), ty_Int) → new_esEs10(xuu50000, xuu4000)
new_ltEs17(xuu491, xuu511) → new_fsEs(new_compare8(xuu491, xuu511))
new_esEs7(Left(xuu50000), Left(xuu4000), app(ty_Ratio, cfa), cea) → new_esEs18(xuu50000, xuu4000, cfa)
new_esEs28(xuu50000, xuu4000, ty_Ordering) → new_esEs8(xuu50000, xuu4000)
new_lt20(xuu4910, xuu5110, app(ty_Ratio, chb)) → new_lt5(xuu4910, xuu5110, chb)
new_esEs8(EQ, LT) → False
new_esEs8(LT, EQ) → False
new_primEqInt(Pos(Zero), Pos(Succ(xuu40000))) → False
new_primEqInt(Pos(Succ(xuu500000)), Pos(Zero)) → False
new_lt9(xuu490, xuu510, app(ty_Maybe, bg)) → new_lt8(xuu490, xuu510, bg)
new_compare30(xuu4900, xuu5100, ty_Int) → new_compare8(xuu4900, xuu5100)
new_compare19(@0, @0) → EQ
new_primPlusNat0(Succ(xuu41200), Zero) → Succ(xuu41200)
new_primPlusNat0(Zero, Succ(xuu9700)) → Succ(xuu9700)
new_esEs7(Right(xuu50000), Right(xuu4000), cfb, ty_Int) → new_esEs10(xuu50000, xuu4000)
new_compare30(xuu4900, xuu5100, ty_Integer) → new_compare7(xuu4900, xuu5100)
new_ltEs11(GT, EQ) → False
new_primCmpInt(Neg(Zero), Pos(Succ(xuu5100))) → LT
new_compare24(xuu490, xuu510, False) → new_compare15(xuu490, xuu510, new_ltEs11(xuu490, xuu510))
new_compare210(xuu490, xuu510, True, bc, bd, be) → EQ
new_esEs27(xuu50001, xuu4001, ty_Double) → new_esEs9(xuu50001, xuu4001)
new_ltEs7(@2(xuu4910, xuu4911), @2(xuu5110, xuu5111), df, ce) → new_pePe(new_lt19(xuu4910, xuu5110, df), new_asAs(new_esEs22(xuu4910, xuu5110, df), new_ltEs19(xuu4911, xuu5111, ce)))
new_ltEs6(xuu491, xuu511, ty_Int) → new_ltEs17(xuu491, xuu511)
new_compare30(xuu4900, xuu5100, app(ty_[], bfb)) → new_compare(xuu4900, xuu5100, bfb)
new_esEs29(xuu50000, xuu4000, app(ty_Ratio, ddg)) → new_esEs18(xuu50000, xuu4000, ddg)
new_primEqInt(Neg(Succ(xuu500000)), Pos(xuu4000)) → False
new_primEqInt(Pos(Succ(xuu500000)), Neg(xuu4000)) → False
new_ltEs19(xuu4911, xuu5111, ty_Double) → new_ltEs16(xuu4911, xuu5111)
new_ltEs9(xuu491, xuu511) → new_fsEs(new_compare18(xuu491, xuu511))
new_esEs25(xuu4911, xuu5111, ty_Int) → new_esEs10(xuu4911, xuu5111)
new_compare11(Double(xuu4900, xuu4901), Double(xuu5100, xuu5101)) → new_compare8(new_sr0(xuu4900, xuu5100), new_sr0(xuu4901, xuu5101))
new_compare(:(xuu4900, xuu4901), :(xuu5100, xuu5101), bf) → new_primCompAux0(xuu4900, xuu5100, new_compare(xuu4901, xuu5101, bf), bf)
new_compare10(Char(xuu4900), Char(xuu5100)) → new_primCmpNat1(xuu4900, xuu5100)
new_esEs28(xuu50000, xuu4000, ty_Char) → new_esEs11(xuu50000, xuu4000)
new_ltEs19(xuu4911, xuu5111, ty_@0) → new_ltEs15(xuu4911, xuu5111)
new_ltEs14(Left(xuu4910), Left(xuu5110), app(app(ty_@2, bca), bcb), bcc) → new_ltEs7(xuu4910, xuu5110, bca, bcb)
new_ltEs14(Left(xuu4910), Left(xuu5110), app(app(app(ty_@3, bcd), bce), bcf), bcc) → new_ltEs8(xuu4910, xuu5110, bcd, bce, bcf)
new_esEs6(Just(xuu50000), Just(xuu4000), ty_Char) → new_esEs11(xuu50000, xuu4000)
new_compare28(xuu490, xuu510, bc, bd, be) → new_compare210(xuu490, xuu510, new_esEs5(xuu490, xuu510, bc, bd, be), bc, bd, be)
new_lt16(xuu490, xuu510, bh, ca) → new_esEs8(new_compare16(xuu490, xuu510, bh, ca), LT)
new_ltEs10(Just(xuu4910), Just(xuu5110), app(app(app(ty_@3, bbb), bbc), bbd)) → new_ltEs8(xuu4910, xuu5110, bbb, bbc, bbd)
new_esEs28(xuu50000, xuu4000, app(ty_Maybe, dcc)) → new_esEs6(xuu50000, xuu4000, dcc)
new_ltEs11(GT, LT) → False
new_primEqInt(Neg(Zero), Pos(Succ(xuu40000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(xuu40000))) → False
new_esEs26(xuu4910, xuu5110, ty_Int) → new_esEs10(xuu4910, xuu5110)
new_primCmpNat2(Succ(xuu5100), xuu4900) → new_primCmpNat1(xuu5100, xuu4900)
new_esEs21(xuu50000, xuu4000, ty_Integer) → new_esEs15(xuu50000, xuu4000)
new_esEs21(xuu50000, xuu4000, ty_Char) → new_esEs11(xuu50000, xuu4000)
new_primCompAux00(xuu140, EQ) → xuu140
new_esEs28(xuu50000, xuu4000, app(app(ty_Either, dbc), dbd)) → new_esEs7(xuu50000, xuu4000, dbc, dbd)
new_compare24(xuu490, xuu510, True) → EQ
new_ltEs14(Right(xuu4910), Right(xuu5110), bdc, app(ty_Maybe, beb)) → new_ltEs10(xuu4910, xuu5110, beb)
new_ltEs6(xuu491, xuu511, ty_Integer) → new_ltEs12(xuu491, xuu511)
new_ltEs14(Left(xuu4910), Left(xuu5110), ty_Float, bcc) → new_ltEs9(xuu4910, xuu5110)
new_esEs8(GT, EQ) → False
new_esEs8(EQ, GT) → False
new_ltEs11(LT, EQ) → True
new_ltEs14(Left(xuu4910), Left(xuu5110), app(ty_[], bcg), bcc) → new_ltEs5(xuu4910, xuu5110, bcg)
new_lt21(xuu4911, xuu5111, app(ty_[], hb)) → new_lt13(xuu4911, xuu5111, hb)
new_ltEs14(Left(xuu4910), Left(xuu5110), ty_Char, bcc) → new_ltEs18(xuu4910, xuu5110)
new_esEs26(xuu4910, xuu5110, ty_Char) → new_esEs11(xuu4910, xuu5110)
new_ltEs11(LT, LT) → True
new_compare14(xuu110, xuu111, xuu112, xuu113, True, xuu115, cgh, cha) → new_compare111(xuu110, xuu111, xuu112, xuu113, True, cgh, cha)
new_ltEs10(Nothing, Nothing, bfh) → True
new_not(False) → True
new_ltEs6(xuu491, xuu511, app(ty_Maybe, bfh)) → new_ltEs10(xuu491, xuu511, bfh)
new_esEs21(xuu50000, xuu4000, ty_Bool) → new_esEs16(xuu50000, xuu4000)
new_esEs7(Left(xuu50000), Left(xuu4000), app(ty_Maybe, ceh), cea) → new_esEs6(xuu50000, xuu4000, ceh)
new_lt21(xuu4911, xuu5111, ty_Bool) → new_lt4(xuu4911, xuu5111)
new_esEs26(xuu4910, xuu5110, app(ty_Ratio, chb)) → new_esEs18(xuu4910, xuu5110, chb)
new_esEs25(xuu4911, xuu5111, ty_Integer) → new_esEs15(xuu4911, xuu5111)
new_lt9(xuu490, xuu510, ty_Int) → new_lt18(xuu490, xuu510)
new_compare30(xuu4900, xuu5100, ty_Double) → new_compare11(xuu4900, xuu5100)
new_compare17(xuu490, xuu510, True) → LT
new_lt20(xuu4910, xuu5110, app(app(ty_Either, gb), gc)) → new_lt16(xuu4910, xuu5110, gb, gc)
new_compare30(xuu4900, xuu5100, app(app(app(ty_@3, beg), beh), bfa)) → new_compare28(xuu4900, xuu5100, beg, beh, bfa)
new_ltEs6(xuu491, xuu511, ty_Float) → new_ltEs9(xuu491, xuu511)
new_ltEs11(GT, GT) → True
new_ltEs14(Right(xuu4910), Right(xuu5110), bdc, ty_Char) → new_ltEs18(xuu4910, xuu5110)
new_ltEs20(xuu4912, xuu5112, app(app(app(ty_@3, hh), baa), bab)) → new_ltEs8(xuu4912, xuu5112, hh, baa, bab)
new_lt19(xuu4910, xuu5110, ty_Char) → new_lt6(xuu4910, xuu5110)
new_esEs20(xuu50001, xuu4001, app(app(app(ty_@3, cac), cad), cae)) → new_esEs5(xuu50001, xuu4001, cac, cad, cae)
new_ltEs19(xuu4911, xuu5111, ty_Integer) → new_ltEs12(xuu4911, xuu5111)
new_primCmpInt(Pos(Succ(xuu4900)), Neg(xuu510)) → GT
new_esEs22(xuu4910, xuu5110, ty_Char) → new_esEs11(xuu4910, xuu5110)
new_esEs21(xuu50000, xuu4000, app(app(app(ty_@3, cbe), cbf), cbg)) → new_esEs5(xuu50000, xuu4000, cbe, cbf, cbg)
new_esEs28(xuu50000, xuu4000, ty_Double) → new_esEs9(xuu50000, xuu4000)
new_esEs26(xuu4910, xuu5110, ty_@0) → new_esEs17(xuu4910, xuu5110)
new_primMulInt(Pos(xuu500000), Pos(xuu40000)) → Pos(new_primMulNat0(xuu500000, xuu40000))
new_esEs21(xuu50000, xuu4000, app(app(ty_@2, cbb), cbc)) → new_esEs4(xuu50000, xuu4000, cbb, cbc)
new_ltEs14(Right(xuu4910), Right(xuu5110), bdc, ty_Float) → new_ltEs9(xuu4910, xuu5110)
new_compare30(xuu4900, xuu5100, app(app(ty_Either, bfd), bfe)) → new_compare16(xuu4900, xuu5100, bfd, bfe)
new_esEs22(xuu4910, xuu5110, ty_Int) → new_esEs10(xuu4910, xuu5110)
new_esEs20(xuu50001, xuu4001, ty_Char) → new_esEs11(xuu50001, xuu4001)
new_esEs9(Double(xuu50000, xuu50001), Double(xuu4000, xuu4001)) → new_esEs10(new_sr0(xuu50000, xuu4000), new_sr0(xuu50001, xuu4001))
new_esEs6(Just(xuu50000), Just(xuu4000), app(ty_[], cda)) → new_esEs14(xuu50000, xuu4000, cda)
new_primMulInt(Neg(xuu500000), Neg(xuu40000)) → Pos(new_primMulNat0(xuu500000, xuu40000))
new_esEs20(xuu50001, xuu4001, ty_Integer) → new_esEs15(xuu50001, xuu4001)
new_esEs7(Right(xuu50000), Right(xuu4000), cfb, app(app(ty_@2, cfe), cff)) → new_esEs4(xuu50000, xuu4000, cfe, cff)
new_lt20(xuu4910, xuu5110, app(app(app(ty_@3, fd), ff), fg)) → new_lt11(xuu4910, xuu5110, fd, ff, fg)
new_primEqNat0(Zero, Succ(xuu40000)) → False
new_primEqNat0(Succ(xuu500000), Zero) → False
new_primPlusNat0(Zero, Zero) → Zero
new_compare30(xuu4900, xuu5100, ty_Bool) → new_compare9(xuu4900, xuu5100)
new_compare25(xuu490, xuu510, True, bh, ca) → EQ
new_esEs25(xuu4911, xuu5111, app(ty_Maybe, hc)) → new_esEs6(xuu4911, xuu5111, hc)
new_lt20(xuu4910, xuu5110, ty_@0) → new_lt17(xuu4910, xuu5110)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_ltEs12(xuu491, xuu511) → new_fsEs(new_compare7(xuu491, xuu511))
new_compare113(xuu490, xuu510, True, bc, bd, be) → LT
new_ltEs14(Right(xuu4910), Right(xuu5110), bdc, ty_Double) → new_ltEs16(xuu4910, xuu5110)
new_primCmpInt(Pos(Succ(xuu4900)), Pos(xuu510)) → new_primCmpNat0(xuu4900, xuu510)
new_lt19(xuu4910, xuu5110, app(ty_Ratio, cge)) → new_lt5(xuu4910, xuu5110, cge)
new_ltEs19(xuu4911, xuu5111, app(app(app(ty_@3, ea), eb), ec)) → new_ltEs8(xuu4911, xuu5111, ea, eb, ec)
new_ltEs19(xuu4911, xuu5111, ty_Ordering) → new_ltEs11(xuu4911, xuu5111)
new_primCmpNat0(xuu4900, Zero) → GT
new_lt4(xuu490, xuu510) → new_esEs8(new_compare9(xuu490, xuu510), LT)
new_compare26(xuu490, xuu510, False) → new_compare17(xuu490, xuu510, new_ltEs13(xuu490, xuu510))
new_ltEs20(xuu4912, xuu5112, ty_Int) → new_ltEs17(xuu4912, xuu5112)
new_esEs21(xuu50000, xuu4000, app(app(ty_Either, cah), cba)) → new_esEs7(xuu50000, xuu4000, cah, cba)
new_ltEs10(Just(xuu4910), Just(xuu5110), app(ty_[], bbe)) → new_ltEs5(xuu4910, xuu5110, bbe)
new_esEs12(xuu490, xuu510, ty_Bool) → new_esEs16(xuu490, xuu510)
new_primPlusNat1(Succ(xuu1010), xuu400000) → Succ(Succ(new_primPlusNat0(xuu1010, xuu400000)))
new_compare30(xuu4900, xuu5100, ty_Char) → new_compare10(xuu4900, xuu5100)
new_lt21(xuu4911, xuu5111, ty_Integer) → new_lt15(xuu4911, xuu5111)
new_esEs27(xuu50001, xuu4001, ty_Bool) → new_esEs16(xuu50001, xuu4001)
new_esEs29(xuu50000, xuu4000, app(app(app(ty_@3, ddc), ddd), dde)) → new_esEs5(xuu50000, xuu4000, ddc, ddd, dde)
new_ltEs14(Left(xuu4910), Left(xuu5110), app(ty_Ratio, ccb), bcc) → new_ltEs4(xuu4910, xuu5110, ccb)
new_esEs7(Right(xuu50000), Right(xuu4000), cfb, app(ty_[], cfg)) → new_esEs14(xuu50000, xuu4000, cfg)
new_esEs16(True, True) → True
new_compare23(xuu49, xuu51, True, cb, bb) → EQ
new_primCmpInt(Pos(Zero), Neg(Succ(xuu5100))) → GT
new_esEs7(Left(xuu50000), Left(xuu4000), app(app(ty_@2, ceb), cec), cea) → new_esEs4(xuu50000, xuu4000, ceb, cec)
new_ltEs6(xuu491, xuu511, app(app(app(ty_@3, gd), fb), fc)) → new_ltEs8(xuu491, xuu511, gd, fb, fc)
new_ltEs10(Just(xuu4910), Nothing, bfh) → False
new_esEs7(Right(xuu50000), Right(xuu4000), cfb, ty_Bool) → new_esEs16(xuu50000, xuu4000)
new_sr0(xuu50000, xuu4000) → new_primMulInt(xuu50000, xuu4000)
new_esEs27(xuu50001, xuu4001, ty_@0) → new_esEs17(xuu50001, xuu4001)
new_ltEs20(xuu4912, xuu5112, ty_Ordering) → new_ltEs11(xuu4912, xuu5112)
new_esEs20(xuu50001, xuu4001, app(ty_Ratio, cag)) → new_esEs18(xuu50001, xuu4001, cag)
new_lt9(xuu490, xuu510, ty_Ordering) → new_lt14(xuu490, xuu510)
new_esEs12(xuu490, xuu510, app(app(ty_Either, bh), ca)) → new_esEs7(xuu490, xuu510, bh, ca)
new_esEs11(Char(xuu50000), Char(xuu4000)) → new_primEqNat0(xuu50000, xuu4000)
new_ltEs10(Nothing, Just(xuu5110), bfh) → True
new_ltEs11(EQ, EQ) → True
new_esEs20(xuu50001, xuu4001, app(app(ty_Either, bhf), bhg)) → new_esEs7(xuu50001, xuu4001, bhf, bhg)
new_compare14(xuu110, xuu111, xuu112, xuu113, False, xuu115, cgh, cha) → new_compare111(xuu110, xuu111, xuu112, xuu113, xuu115, cgh, cha)
new_esEs21(xuu50000, xuu4000, ty_Double) → new_esEs9(xuu50000, xuu4000)
new_esEs21(xuu50000, xuu4000, ty_Float) → new_esEs13(xuu50000, xuu4000)
new_primCompAux0(xuu4900, xuu5100, xuu130, bf) → new_primCompAux00(xuu130, new_compare30(xuu4900, xuu5100, bf))
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_compare29(xuu490, xuu510, True, bg) → EQ
new_esEs27(xuu50001, xuu4001, ty_Float) → new_esEs13(xuu50001, xuu4001)
new_esEs20(xuu50001, xuu4001, app(ty_Maybe, caf)) → new_esEs6(xuu50001, xuu4001, caf)
new_ltEs14(Left(xuu4910), Right(xuu5110), bdc, bcc) → True
new_lt9(xuu490, xuu510, ty_Bool) → new_lt4(xuu490, xuu510)
new_esEs24(xuu50000, xuu4000, ty_Int) → new_esEs10(xuu50000, xuu4000)
new_esEs6(Just(xuu50000), Just(xuu4000), ty_Integer) → new_esEs15(xuu50000, xuu4000)
new_esEs28(xuu50000, xuu4000, app(app(ty_@2, dbe), dbf)) → new_esEs4(xuu50000, xuu4000, dbe, dbf)
new_lt9(xuu490, xuu510, ty_Char) → new_lt6(xuu490, xuu510)
new_ltEs20(xuu4912, xuu5112, app(app(ty_Either, bae), baf)) → new_ltEs14(xuu4912, xuu5112, bae, baf)
new_asAs(False, xuu66) → False
new_ltEs19(xuu4911, xuu5111, app(app(ty_@2, dg), dh)) → new_ltEs7(xuu4911, xuu5111, dg, dh)
new_ltEs20(xuu4912, xuu5112, ty_Double) → new_ltEs16(xuu4912, xuu5112)
new_esEs18(:%(xuu50000, xuu50001), :%(xuu4000, xuu4001), cgg) → new_asAs(new_esEs24(xuu50000, xuu4000, cgg), new_esEs23(xuu50001, xuu4001, cgg))
new_primMulInt(Neg(xuu500000), Pos(xuu40000)) → Neg(new_primMulNat0(xuu500000, xuu40000))
new_primMulInt(Pos(xuu500000), Neg(xuu40000)) → Neg(new_primMulNat0(xuu500000, xuu40000))
new_ltEs19(xuu4911, xuu5111, app(app(ty_Either, ef), eg)) → new_ltEs14(xuu4911, xuu5111, ef, eg)
new_esEs26(xuu4910, xuu5110, ty_Double) → new_esEs9(xuu4910, xuu5110)
new_primCmpInt(Neg(Succ(xuu4900)), Neg(xuu510)) → new_primCmpNat2(xuu510, xuu4900)
new_primMulNat0(Zero, Succ(xuu400000)) → Zero
new_primMulNat0(Succ(xuu5000000), Zero) → Zero
new_lt19(xuu4910, xuu5110, ty_Float) → new_lt12(xuu4910, xuu5110)
new_lt8(xuu490, xuu510, bg) → new_esEs8(new_compare13(xuu490, xuu510, bg), LT)
new_esEs7(Right(xuu50000), Right(xuu4000), cfb, ty_Integer) → new_esEs15(xuu50000, xuu4000)
new_lt11(xuu490, xuu510, bc, bd, be) → new_esEs8(new_compare28(xuu490, xuu510, bc, bd, be), LT)
new_esEs6(Just(xuu50000), Just(xuu4000), app(ty_Maybe, cde)) → new_esEs6(xuu50000, xuu4000, cde)
new_esEs6(Just(xuu50000), Just(xuu4000), ty_Double) → new_esEs9(xuu50000, xuu4000)
new_lt13(xuu490, xuu510, bf) → new_esEs8(new_compare(xuu490, xuu510, bf), LT)
new_esEs21(xuu50000, xuu4000, ty_Ordering) → new_esEs8(xuu50000, xuu4000)
new_ltEs11(EQ, LT) → False
new_ltEs6(xuu491, xuu511, ty_@0) → new_ltEs15(xuu491, xuu511)
new_ltEs10(Just(xuu4910), Just(xuu5110), ty_Bool) → new_ltEs13(xuu4910, xuu5110)
new_esEs6(Just(xuu50000), Just(xuu4000), app(app(ty_@2, ccg), cch)) → new_esEs4(xuu50000, xuu4000, ccg, cch)
new_ltEs20(xuu4912, xuu5112, ty_Bool) → new_ltEs13(xuu4912, xuu5112)
new_ltEs14(Right(xuu4910), Right(xuu5110), bdc, app(app(ty_Either, bec), bed)) → new_ltEs14(xuu4910, xuu5110, bec, bed)
new_esEs28(xuu50000, xuu4000, ty_Integer) → new_esEs15(xuu50000, xuu4000)
new_lt9(xuu490, xuu510, ty_@0) → new_lt17(xuu490, xuu510)
new_esEs19(xuu50002, xuu4002, ty_Double) → new_esEs9(xuu50002, xuu4002)
new_ltEs14(Right(xuu4910), Right(xuu5110), bdc, ty_Bool) → new_ltEs13(xuu4910, xuu5110)
new_ltEs6(xuu491, xuu511, ty_Bool) → new_ltEs13(xuu491, xuu511)
new_esEs28(xuu50000, xuu4000, ty_Float) → new_esEs13(xuu50000, xuu4000)
new_primCmpInt(Pos(Zero), Pos(Succ(xuu5100))) → new_primCmpNat2(Zero, xuu5100)
new_ltEs14(Right(xuu4910), Right(xuu5110), bdc, ty_Ordering) → new_ltEs11(xuu4910, xuu5110)
new_compare16(xuu490, xuu510, bh, ca) → new_compare25(xuu490, xuu510, new_esEs7(xuu490, xuu510, bh, ca), bh, ca)
new_esEs7(Right(xuu50000), Right(xuu4000), cfb, ty_Char) → new_esEs11(xuu50000, xuu4000)
new_compare111(xuu110, xuu111, xuu112, xuu113, False, cgh, cha) → GT
new_esEs23(xuu50001, xuu4001, ty_Integer) → new_esEs15(xuu50001, xuu4001)
new_esEs20(xuu50001, xuu4001, app(app(ty_@2, bhh), caa)) → new_esEs4(xuu50001, xuu4001, bhh, caa)
new_esEs16(False, False) → True
new_lt19(xuu4910, xuu5110, ty_@0) → new_lt17(xuu4910, xuu5110)
new_ltEs14(Left(xuu4910), Left(xuu5110), app(app(ty_Either, bda), bdb), bcc) → new_ltEs14(xuu4910, xuu5110, bda, bdb)
new_esEs12(xuu490, xuu510, ty_Int) → new_esEs10(xuu490, xuu510)
new_ltEs13(True, True) → True
new_compare6(:%(xuu4900, xuu4901), :%(xuu5100, xuu5101), ty_Integer) → new_compare7(new_sr(xuu4900, xuu5101), new_sr(xuu5100, xuu4901))
new_ltEs13(False, False) → True
new_esEs27(xuu50001, xuu4001, app(app(ty_@2, dac), dad)) → new_esEs4(xuu50001, xuu4001, dac, dad)
new_ltEs6(xuu491, xuu511, ty_Ordering) → new_ltEs11(xuu491, xuu511)
new_ltEs10(Just(xuu4910), Just(xuu5110), ty_Ordering) → new_ltEs11(xuu4910, xuu5110)
new_esEs7(Left(xuu50000), Left(xuu4000), ty_@0, cea) → new_esEs17(xuu50000, xuu4000)
new_ltEs19(xuu4911, xuu5111, app(ty_Maybe, ee)) → new_ltEs10(xuu4911, xuu5111, ee)
new_ltEs10(Just(xuu4910), Just(xuu5110), ty_Char) → new_ltEs18(xuu4910, xuu5110)
new_compare7(Integer(xuu4900), Integer(xuu5100)) → new_primCmpInt(xuu4900, xuu5100)
new_compare30(xuu4900, xuu5100, ty_Ordering) → new_compare27(xuu4900, xuu5100)
new_lt20(xuu4910, xuu5110, ty_Integer) → new_lt15(xuu4910, xuu5110)
new_esEs25(xuu4911, xuu5111, app(app(app(ty_@3, gg), gh), ha)) → new_esEs5(xuu4911, xuu5111, gg, gh, ha)
new_esEs6(Just(xuu50000), Just(xuu4000), ty_Ordering) → new_esEs8(xuu50000, xuu4000)
new_ltEs6(xuu491, xuu511, ty_Double) → new_ltEs16(xuu491, xuu511)
new_esEs29(xuu50000, xuu4000, app(app(ty_Either, dcf), dcg)) → new_esEs7(xuu50000, xuu4000, dcf, dcg)
new_lt21(xuu4911, xuu5111, ty_Float) → new_lt12(xuu4911, xuu5111)
new_compare112(xuu490, xuu510, False, bg) → GT
new_esEs28(xuu50000, xuu4000, ty_Int) → new_esEs10(xuu50000, xuu4000)
new_primPlusNat0(Succ(xuu41200), Succ(xuu9700)) → Succ(Succ(new_primPlusNat0(xuu41200, xuu9700)))
new_lt20(xuu4910, xuu5110, app(ty_Maybe, ga)) → new_lt8(xuu4910, xuu5110, ga)
new_esEs22(xuu4910, xuu5110, ty_Integer) → new_esEs15(xuu4910, xuu5110)
new_compare30(xuu4900, xuu5100, ty_@0) → new_compare19(xuu4900, xuu5100)
new_esEs7(Right(xuu50000), Right(xuu4000), cfb, ty_@0) → new_esEs17(xuu50000, xuu4000)
new_esEs12(xuu490, xuu510, ty_Ordering) → new_esEs8(xuu490, xuu510)
new_esEs19(xuu50002, xuu4002, ty_@0) → new_esEs17(xuu50002, xuu4002)
new_esEs27(xuu50001, xuu4001, app(ty_[], dae)) → new_esEs14(xuu50001, xuu4001, dae)
new_esEs19(xuu50002, xuu4002, ty_Integer) → new_esEs15(xuu50002, xuu4002)
new_ltEs14(Right(xuu4910), Right(xuu5110), bdc, ty_Integer) → new_ltEs12(xuu4910, xuu5110)
new_esEs12(xuu490, xuu510, app(ty_[], bf)) → new_esEs14(xuu490, xuu510, bf)
new_lt10(xuu490, xuu510, h, ba) → new_esEs8(new_compare12(xuu490, xuu510, h, ba), LT)
new_asAs(True, xuu66) → xuu66
new_esEs12(xuu490, xuu510, ty_Integer) → new_esEs15(xuu490, xuu510)
new_esEs20(xuu50001, xuu4001, ty_Double) → new_esEs9(xuu50001, xuu4001)
new_esEs26(xuu4910, xuu5110, app(app(app(ty_@3, fd), ff), fg)) → new_esEs5(xuu4910, xuu5110, fd, ff, fg)
new_esEs7(Right(xuu50000), Right(xuu4000), cfb, app(ty_Ratio, cgd)) → new_esEs18(xuu50000, xuu4000, cgd)
new_esEs6(Just(xuu50000), Just(xuu4000), app(app(ty_Either, cce), ccf)) → new_esEs7(xuu50000, xuu4000, cce, ccf)
new_esEs27(xuu50001, xuu4001, ty_Int) → new_esEs10(xuu50001, xuu4001)
new_lt9(xuu490, xuu510, ty_Double) → new_lt7(xuu490, xuu510)
new_esEs28(xuu50000, xuu4000, app(ty_Ratio, dcd)) → new_esEs18(xuu50000, xuu4000, dcd)
new_esEs23(xuu50001, xuu4001, ty_Int) → new_esEs10(xuu50001, xuu4001)
new_ltEs10(Just(xuu4910), Just(xuu5110), app(app(ty_@2, bah), bba)) → new_ltEs7(xuu4910, xuu5110, bah, bba)
new_compare17(xuu490, xuu510, False) → GT
new_esEs21(xuu50000, xuu4000, ty_Int) → new_esEs10(xuu50000, xuu4000)
new_fsEs(xuu122) → new_not(new_esEs8(xuu122, GT))
new_ltEs20(xuu4912, xuu5112, ty_Float) → new_ltEs9(xuu4912, xuu5112)
new_esEs19(xuu50002, xuu4002, ty_Ordering) → new_esEs8(xuu50002, xuu4002)
new_compare210(xuu490, xuu510, False, bc, bd, be) → new_compare113(xuu490, xuu510, new_ltEs8(xuu490, xuu510, bc, bd, be), bc, bd, be)
new_ltEs10(Just(xuu4910), Just(xuu5110), ty_Double) → new_ltEs16(xuu4910, xuu5110)
new_esEs20(xuu50001, xuu4001, app(ty_[], cab)) → new_esEs14(xuu50001, xuu4001, cab)
new_ltEs20(xuu4912, xuu5112, app(ty_Maybe, bad)) → new_ltEs10(xuu4912, xuu5112, bad)
new_esEs13(Float(xuu50000, xuu50001), Float(xuu4000, xuu4001)) → new_esEs10(new_sr0(xuu50000, xuu4000), new_sr0(xuu50001, xuu4001))
new_lt9(xuu490, xuu510, app(ty_Ratio, bff)) → new_lt5(xuu490, xuu510, bff)
new_ltEs14(Left(xuu4910), Left(xuu5110), ty_Integer, bcc) → new_ltEs12(xuu4910, xuu5110)
new_esEs12(xuu490, xuu510, app(ty_Maybe, bg)) → new_esEs6(xuu490, xuu510, bg)
new_esEs27(xuu50001, xuu4001, ty_Char) → new_esEs11(xuu50001, xuu4001)
new_ltEs19(xuu4911, xuu5111, app(ty_[], ed)) → new_ltEs5(xuu4911, xuu5111, ed)
new_lt21(xuu4911, xuu5111, ty_Int) → new_lt18(xuu4911, xuu5111)
new_esEs10(xuu5000, xuu400) → new_primEqInt(xuu5000, xuu400)
new_primCompAux00(xuu140, GT) → GT
new_esEs25(xuu4911, xuu5111, app(app(ty_Either, hd), he)) → new_esEs7(xuu4911, xuu5111, hd, he)
new_esEs19(xuu50002, xuu4002, ty_Bool) → new_esEs16(xuu50002, xuu4002)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs29(xuu50000, xuu4000, ty_Ordering) → new_esEs8(xuu50000, xuu4000)
new_ltEs11(EQ, GT) → True
new_esEs19(xuu50002, xuu4002, app(app(ty_@2, bgf), bgg)) → new_esEs4(xuu50002, xuu4002, bgf, bgg)
new_esEs12(xuu490, xuu510, app(app(ty_@2, h), ba)) → new_esEs4(xuu490, xuu510, h, ba)
new_esEs7(Left(xuu50000), Left(xuu4000), app(ty_[], ced), cea) → new_esEs14(xuu50000, xuu4000, ced)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primCmpNat0(xuu4900, Succ(xuu5100)) → new_primCmpNat1(xuu4900, xuu5100)
new_esEs27(xuu50001, xuu4001, ty_Integer) → new_esEs15(xuu50001, xuu4001)
new_esEs21(xuu50000, xuu4000, app(ty_Ratio, cca)) → new_esEs18(xuu50000, xuu4000, cca)
new_primCmpInt(Neg(Succ(xuu4900)), Pos(xuu510)) → LT
new_lt21(xuu4911, xuu5111, ty_Double) → new_lt7(xuu4911, xuu5111)
new_not(True) → False
new_compare6(:%(xuu4900, xuu4901), :%(xuu5100, xuu5101), ty_Int) → new_compare8(new_sr0(xuu4900, xuu5101), new_sr0(xuu5100, xuu4901))
new_esEs14(:(xuu50000, xuu50001), :(xuu4000, xuu4001), dce) → new_asAs(new_esEs29(xuu50000, xuu4000, dce), new_esEs14(xuu50001, xuu4001, dce))
new_esEs6(Just(xuu50000), Just(xuu4000), app(ty_Ratio, cdf)) → new_esEs18(xuu50000, xuu4000, cdf)

The set Q consists of the following terms:

new_compare26(x0, x1, True)
new_esEs12(x0, x1, ty_Ordering)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt21(x0, x1, ty_Int)
new_lt21(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs11(EQ, GT)
new_ltEs11(GT, EQ)
new_esEs28(x0, x1, ty_Int)
new_esEs22(x0, x1, ty_Double)
new_lt21(x0, x1, ty_Float)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs28(x0, x1, ty_Ordering)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(Left(x0), Left(x1), ty_Double, x2)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_ltEs17(x0, x1)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Just(x0), Nothing, x1)
new_esEs6(Nothing, Just(x0), x1)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs29(x0, x1, app(ty_[], x2))
new_ltEs14(Right(x0), Right(x1), x2, ty_Bool)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs11(EQ, EQ)
new_compare29(x0, x1, False, x2)
new_compare18(Float(x0, x1), Float(x2, x3))
new_ltEs20(x0, x1, ty_Float)
new_ltEs14(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs20(x0, x1, ty_Float)
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs12(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpNat1(Zero, Succ(x0))
new_esEs22(x0, x1, ty_Bool)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_compare30(x0, x1, ty_Char)
new_ltEs14(Left(x0), Left(x1), ty_Bool, x2)
new_esEs27(x0, x1, ty_Char)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, ty_Char)
new_compare8(x0, x1)
new_ltEs10(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, ty_Bool)
new_lt9(x0, x1, ty_Int)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_primMulInt(Pos(x0), Pos(x1))
new_lt19(x0, x1, app(ty_[], x2))
new_ltEs10(Nothing, Nothing, x0)
new_ltEs19(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_compare113(x0, x1, False, x2, x3, x4)
new_ltEs10(Just(x0), Just(x1), ty_Char)
new_esEs6(Just(x0), Just(x1), ty_Ordering)
new_esEs6(Just(x0), Just(x1), ty_Float)
new_esEs8(GT, GT)
new_fsEs(x0)
new_ltEs6(x0, x1, ty_@0)
new_primCompAux00(x0, LT)
new_primCmpNat1(Succ(x0), Zero)
new_compare11(Double(x0, x1), Double(x2, x3))
new_compare30(x0, x1, app(ty_[], x2))
new_primCmpNat0(x0, Zero)
new_lt21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1, app(ty_Ratio, x2))
new_lt10(x0, x1, x2, x3)
new_compare25(x0, x1, False, x2, x3)
new_ltEs14(Right(x0), Right(x1), x2, ty_Ordering)
new_lt21(x0, x1, ty_Char)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs19(x0, x1, ty_Int)
new_esEs6(Just(x0), Just(x1), ty_Char)
new_esEs21(x0, x1, ty_Int)
new_esEs8(LT, LT)
new_compare30(x0, x1, ty_Float)
new_esEs19(x0, x1, app(ty_[], x2))
new_ltEs10(Just(x0), Just(x1), app(ty_[], x2))
new_compare30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs29(x0, x1, ty_Double)
new_compare9(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs10(Just(x0), Just(x1), ty_@0)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_ltEs7(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs16(False, True)
new_esEs16(True, False)
new_esEs25(x0, x1, app(ty_[], x2))
new_ltEs6(x0, x1, ty_Float)
new_lt9(x0, x1, ty_Bool)
new_esEs28(x0, x1, ty_Integer)
new_ltEs14(Left(x0), Right(x1), x2, x3)
new_ltEs14(Right(x0), Left(x1), x2, x3)
new_primCmpNat1(Zero, Zero)
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_ltEs11(LT, GT)
new_compare210(x0, x1, True, x2, x3, x4)
new_ltEs11(GT, LT)
new_ltEs14(Right(x0), Right(x1), x2, ty_Integer)
new_esEs16(True, True)
new_ltEs14(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs14(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs20(x0, x1, ty_Double)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, ty_Int)
new_esEs20(x0, x1, ty_Char)
new_esEs19(x0, x1, ty_Double)
new_esEs7(Right(x0), Right(x1), x2, ty_Int)
new_compare13(x0, x1, x2)
new_lt9(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1, ty_@0)
new_primEqNat0(Zero, Zero)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_compare30(x0, x1, ty_Double)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs7(Left(x0), Left(x1), ty_Char, x2)
new_esEs29(x0, x1, ty_Int)
new_lt19(x0, x1, ty_Char)
new_compare(:(x0, x1), :(x2, x3), x4)
new_esEs28(x0, x1, ty_Double)
new_esEs22(x0, x1, ty_@0)
new_esEs22(x0, x1, ty_Float)
new_esEs26(x0, x1, ty_Ordering)
new_ltEs14(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_primMulNat0(Zero, Zero)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt20(x0, x1, ty_Double)
new_esEs21(x0, x1, ty_Ordering)
new_esEs20(x0, x1, ty_Bool)
new_lt21(x0, x1, app(ty_Maybe, x2))
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_compare27(x0, x1)
new_esEs29(x0, x1, ty_Ordering)
new_esEs21(x0, x1, app(ty_[], x2))
new_compare17(x0, x1, False)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_lt4(x0, x1)
new_esEs7(Left(x0), Left(x1), ty_Int, x2)
new_esEs27(x0, x1, ty_Integer)
new_esEs6(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs10(Just(x0), Just(x1), ty_Float)
new_ltEs6(x0, x1, app(ty_Ratio, x2))
new_esEs7(Right(x0), Right(x1), x2, ty_@0)
new_esEs25(x0, x1, ty_Int)
new_esEs26(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Float)
new_lt20(x0, x1, ty_Integer)
new_esEs27(x0, x1, ty_Float)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Int)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs19(x0, x1, ty_Ordering)
new_ltEs10(Just(x0), Just(x1), ty_Integer)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs6(Just(x0), Just(x1), ty_Double)
new_lt9(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Char)
new_ltEs14(Right(x0), Right(x1), x2, ty_@0)
new_ltEs6(x0, x1, ty_Int)
new_compare113(x0, x1, True, x2, x3, x4)
new_esEs12(x0, x1, ty_Bool)
new_lt13(x0, x1, x2)
new_esEs12(x0, x1, ty_Char)
new_compare26(x0, x1, False)
new_compare210(x0, x1, False, x2, x3, x4)
new_esEs26(x0, x1, ty_Integer)
new_lt6(x0, x1)
new_ltEs8(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs12(x0, x1, ty_@0)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs14([], [], x0)
new_lt17(x0, x1)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_primCompAux00(x0, EQ)
new_compare23(@2(x0, x1), @2(x2, x3), False, x4, x5)
new_lt19(x0, x1, ty_Double)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, ty_Char)
new_esEs20(x0, x1, ty_@0)
new_ltEs6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(Left(x0), Left(x1), ty_Ordering, x2)
new_primMulNat0(Succ(x0), Zero)
new_compare14(x0, x1, x2, x3, True, x4, x5, x6)
new_esEs7(Left(x0), Left(x1), ty_Bool, x2)
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs13(True, True)
new_esEs21(x0, x1, ty_Double)
new_esEs22(x0, x1, ty_Int)
new_esEs12(x0, x1, app(ty_[], x2))
new_esEs19(x0, x1, ty_@0)
new_primPlusNat0(Zero, Zero)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs6(Just(x0), Just(x1), ty_Bool)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_[], x3))
new_compare30(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_ltEs13(False, False)
new_asAs(False, x0)
new_esEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs12(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_Ordering)
new_primEqNat0(Succ(x0), Zero)
new_ltEs19(x0, x1, ty_@0)
new_esEs22(x0, x1, ty_Integer)
new_esEs6(Just(x0), Just(x1), ty_Integer)
new_esEs12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Right(x0), Right(x1), x2, ty_Char)
new_lt21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs29(x0, x1, ty_Float)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs6(Just(x0), Just(x1), ty_Int)
new_lt20(x0, x1, ty_Int)
new_esEs17(@0, @0)
new_ltEs13(False, True)
new_ltEs13(True, False)
new_esEs25(x0, x1, ty_Double)
new_ltEs6(x0, x1, app(app(ty_@2, x2), x3))
new_lt9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_lt9(x0, x1, ty_Float)
new_esEs21(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_compare30(x0, x1, ty_Bool)
new_lt9(x0, x1, app(app(ty_Either, x2), x3))
new_esEs14([], :(x0, x1), x2)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs15(x0, x1)
new_lt9(x0, x1, app(ty_[], x2))
new_esEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_Int)
new_ltEs19(x0, x1, ty_Float)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, ty_@0)
new_esEs20(x0, x1, ty_Integer)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_Bool)
new_compare112(x0, x1, False, x2)
new_compare112(x0, x1, True, x2)
new_esEs23(x0, x1, ty_Int)
new_lt7(x0, x1)
new_esEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, ty_Float)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_compare15(x0, x1, True)
new_ltEs10(Just(x0), Just(x1), ty_Int)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs12(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_@0)
new_esEs26(x0, x1, ty_@0)
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, ty_Float)
new_compare30(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, ty_Integer)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs20(x0, x1, ty_Char)
new_lt16(x0, x1, x2, x3)
new_sr0(x0, x1)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_esEs29(x0, x1, ty_Integer)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs7(Right(x0), Right(x1), x2, ty_Double)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_compare17(x0, x1, True)
new_ltEs10(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs25(x0, x1, ty_Ordering)
new_primPlusNat0(Succ(x0), Succ(x1))
new_compare6(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Zero), Neg(Zero))
new_ltEs18(x0, x1)
new_esEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs7(Left(x0), Left(x1), ty_@0, x2)
new_lt20(x0, x1, ty_Bool)
new_ltEs14(Right(x0), Right(x1), x2, ty_Float)
new_esEs6(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs14(Right(x0), Right(x1), x2, ty_Char)
new_esEs22(x0, x1, ty_Char)
new_esEs29(x0, x1, ty_Char)
new_esEs20(x0, x1, app(ty_[], x2))
new_esEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpNat0(x0, Succ(x1))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, app(ty_[], x2))
new_primCmpNat1(Succ(x0), Succ(x1))
new_esEs28(x0, x1, app(ty_[], x2))
new_ltEs10(Just(x0), Nothing, x1)
new_ltEs10(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs28(x0, x1, ty_Bool)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, app(ty_[], x2))
new_compare10(Char(x0), Char(x1))
new_compare30(x0, x1, ty_@0)
new_lt19(x0, x1, ty_Float)
new_lt20(x0, x1, app(ty_[], x2))
new_esEs13(Float(x0, x1), Float(x2, x3))
new_lt21(x0, x1, ty_Ordering)
new_esEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_lt9(x0, x1, ty_Double)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs12(x0, x1)
new_esEs26(x0, x1, ty_Double)
new_lt9(x0, x1, ty_Char)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_primPlusNat0(Zero, Succ(x0))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs11(LT, LT)
new_esEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs10(Just(x0), Just(x1), ty_Ordering)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_esEs25(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Int)
new_ltEs6(x0, x1, app(ty_Maybe, x2))
new_ltEs11(EQ, LT)
new_ltEs11(LT, EQ)
new_esEs20(x0, x1, ty_Ordering)
new_ltEs6(x0, x1, app(ty_[], x2))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs19(x0, x1, ty_Char)
new_ltEs6(x0, x1, ty_Double)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, ty_Integer)
new_ltEs16(x0, x1)
new_ltEs10(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_ltEs14(Left(x0), Left(x1), ty_Char, x2)
new_primPlusNat0(Succ(x0), Zero)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_ltEs4(x0, x1, x2)
new_compare15(x0, x1, False)
new_primCmpNat2(Zero, x0)
new_compare(:(x0, x1), [], x2)
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs6(Nothing, Nothing, x0)
new_esEs6(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt19(x0, x1, ty_Integer)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs7(Left(x0), Left(x1), ty_Float, x2)
new_ltEs6(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, ty_Bool)
new_lt19(x0, x1, ty_Ordering)
new_pePe(False, x0)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs14(Left(x0), Left(x1), ty_Int, x2)
new_esEs6(Just(x0), Just(x1), app(ty_Ratio, x2))
new_lt20(x0, x1, ty_Char)
new_esEs29(x0, x1, ty_@0)
new_esEs25(x0, x1, ty_Bool)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_compare111(x0, x1, x2, x3, True, x4, x5)
new_esEs20(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Ordering)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_esEs25(x0, x1, ty_Integer)
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_compare([], :(x0, x1), x2)
new_esEs16(False, False)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Int)
new_lt21(x0, x1, ty_@0)
new_esEs15(Integer(x0), Integer(x1))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, ty_Int)
new_esEs9(Double(x0, x1), Double(x2, x3))
new_primEqNat0(Zero, Succ(x0))
new_lt5(x0, x1, x2)
new_lt21(x0, x1, ty_Integer)
new_lt9(x0, x1, ty_@0)
new_sr(Integer(x0), Integer(x1))
new_compare([], [], x0)
new_compare16(x0, x1, x2, x3)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, ty_Ordering)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_lt8(x0, x1, x2)
new_esEs14(:(x0, x1), :(x2, x3), x4)
new_esEs10(x0, x1)
new_not(True)
new_ltEs9(x0, x1)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_compare24(x0, x1, False)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs12(x0, x1, ty_Float)
new_lt14(x0, x1)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs25(x0, x1, ty_@0)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_not(False)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs14(:(x0, x1), [], x2)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs12(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_compare7(Integer(x0), Integer(x1))
new_compare29(x0, x1, True, x2)
new_primCmpNat2(Succ(x0), x1)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primPlusNat1(Succ(x0), x1)
new_esEs7(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs20(x0, x1, ty_@0)
new_primPlusNat1(Zero, x0)
new_lt21(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_Float)
new_compare24(x0, x1, True)
new_compare30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare30(x0, x1, ty_Int)
new_compare111(x0, x1, x2, x3, False, x4, x5)
new_pePe(True, x0)
new_esEs25(x0, x1, ty_Float)
new_compare28(x0, x1, x2, x3, x4)
new_lt18(x0, x1)
new_ltEs5(x0, x1, x2)
new_esEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs19(x0, x1, ty_Bool)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_compare19(@0, @0)
new_ltEs20(x0, x1, ty_Ordering)
new_esEs11(Char(x0), Char(x1))
new_ltEs6(x0, x1, ty_Ordering)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_lt19(x0, x1, ty_Bool)
new_ltEs14(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_lt9(x0, x1, ty_Ordering)
new_compare30(x0, x1, ty_Ordering)
new_primCompAux0(x0, x1, x2, x3)
new_esEs20(x0, x1, ty_Int)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_primMulNat0(Zero, Succ(x0))
new_esEs18(:%(x0, x1), :%(x2, x3), x4)
new_lt21(x0, x1, ty_Bool)
new_esEs6(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs6(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_Integer)
new_ltEs6(x0, x1, ty_Bool)
new_lt12(x0, x1)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, ty_Float)
new_esEs27(x0, x1, ty_Double)
new_esEs26(x0, x1, ty_Char)
new_lt9(x0, x1, ty_Integer)
new_esEs6(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_lt21(x0, x1, app(ty_[], x2))
new_esEs19(x0, x1, ty_Float)
new_asAs(True, x0)
new_ltEs19(x0, x1, ty_Integer)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs12(x0, x1, ty_Int)
new_esEs19(x0, x1, ty_Integer)
new_compare110(x0, x1, True, x2, x3)
new_esEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_primCompAux00(x0, GT)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_compare25(x0, x1, True, x2, x3)
new_lt9(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, ty_Bool)
new_esEs7(Left(x0), Left(x1), ty_Integer, x2)
new_compare12(x0, x1, x2, x3)
new_ltEs10(Just(x0), Just(x1), ty_Double)
new_esEs28(x0, x1, ty_@0)
new_esEs6(Just(x0), Just(x1), ty_@0)
new_ltEs10(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs14(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_compare23(x0, x1, True, x2, x3)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs12(x0, x1, ty_Double)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, ty_Int)
new_ltEs6(x0, x1, ty_Integer)
new_lt21(x0, x1, ty_Double)
new_esEs12(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs14(Left(x0), Left(x1), ty_Float, x2)
new_esEs19(x0, x1, ty_Bool)
new_ltEs14(Left(x0), Left(x1), ty_@0, x2)
new_esEs29(x0, x1, ty_Bool)
new_compare30(x0, x1, ty_Integer)
new_ltEs10(Nothing, Just(x0), x1)
new_esEs7(Left(x0), Left(x1), ty_Double, x2)
new_compare14(x0, x1, x2, x3, False, x4, x5, x6)
new_lt11(x0, x1, x2, x3, x4)
new_esEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs7(Right(x0), Left(x1), x2, x3)
new_esEs7(Left(x0), Right(x1), x2, x3)
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs10(Just(x0), Just(x1), ty_Bool)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_compare30(x0, x1, app(ty_Ratio, x2))
new_lt15(x0, x1)
new_compare6(:%(x0, x1), :%(x2, x3), ty_Integer)
new_compare110(x0, x1, False, x2, x3)
new_esEs21(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_Double)
new_ltEs11(GT, GT)
new_ltEs14(Right(x0), Right(x1), x2, ty_Double)

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_C2(xuu18, xuu19, xuu20, xuu21, xuu22, xuu23, xuu24, xuu25, xuu26, xuu27, False, h, ba, bb) → new_addToFM_C1(xuu18, 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(xuu18, xuu19, xuu20, xuu21, xuu22, xuu23, xuu24, xuu25, xuu26, xuu27, True, h, ba, bb) → new_addToFM_C(xuu18, xuu23, @2(xuu25, xuu26), xuu27, h, ba, bb)
new_addToFM_C1(xuu18, xuu19, xuu20, xuu21, xuu22, xuu23, xuu24, xuu25, xuu26, xuu27, True, h, ba, bb) → new_addToFM_C(xuu18, xuu24, @2(xuu25, xuu26), xuu27, h, ba, bb)
new_addToFM_C(xuu3, Branch(@2(xuu400, xuu401), xuu41, xuu42, xuu43, xuu44), @2(xuu5000, xuu5001), xuu501, bc, bd, be) → new_addToFM_C2(xuu3, xuu400, xuu401, xuu41, xuu42, xuu43, xuu44, xuu5000, xuu5001, xuu501, new_esEs30(xuu5000, xuu5001, xuu400, xuu401, new_esEs31(xuu5000, xuu400, bc), bc, bd), bc, bd, be)

The TRS R consists of the following rules:

new_esEs25(xuu4911, xuu5111, app(ty_[], cga)) → new_esEs14(xuu4911, xuu5111, cga)
new_compare112(xuu490, xuu510, True, ca) → LT
new_compare27(xuu490, xuu510) → new_compare24(xuu490, xuu510, new_esEs8(xuu490, xuu510))
new_ltEs20(xuu4912, xuu5112, ty_Char) → new_ltEs18(xuu4912, xuu5112)
new_esEs7(Left(xuu50000), Left(xuu4000), app(app(ty_Either, bgb), bgc), bgd) → new_esEs7(xuu50000, xuu4000, bgb, bgc)
new_primCmpNat2(Zero, xuu4900) → LT
new_lt19(xuu4910, xuu5110, ty_Int) → new_lt18(xuu4910, xuu5110)
new_lt21(xuu4911, xuu5111, app(ty_Maybe, cgb)) → new_lt8(xuu4911, xuu5111, cgb)
new_lt19(xuu4910, xuu5110, ty_Double) → new_lt7(xuu4910, xuu5110)
new_ltEs11(LT, GT) → True
new_ltEs14(Left(xuu4910), Left(xuu5110), ty_Double, ed) → new_ltEs16(xuu4910, xuu5110)
new_esEs31(xuu5000, xuu400, ty_Ordering) → new_esEs8(xuu5000, xuu400)
new_compare110(xuu490, xuu510, True, dc, dd) → LT
new_esEs27(xuu50001, xuu4001, app(ty_Ratio, dde)) → new_esEs18(xuu50001, xuu4001, dde)
new_primCmpNat1(Zero, Succ(xuu51000)) → LT
new_compare([], :(xuu5100, xuu5101), db) → LT
new_lt21(xuu4911, xuu5111, ty_Ordering) → new_lt14(xuu4911, xuu5111)
new_compare23(@2(xuu490, xuu491), @2(xuu510, xuu511), False, cd, ce) → new_compare14(xuu490, xuu491, xuu510, xuu511, new_lt9(xuu490, xuu510, cd), new_asAs(new_esEs12(xuu490, xuu510, cd), new_ltEs6(xuu491, xuu511, ce)), cd, ce)
new_ltEs15(xuu491, xuu511) → new_fsEs(new_compare19(xuu491, xuu511))
new_lt19(xuu4910, xuu5110, app(app(ty_@2, cah), cba)) → new_lt10(xuu4910, xuu5110, cah, cba)
new_esEs31(xuu5000, xuu400, app(ty_[], cdf)) → new_esEs14(xuu5000, xuu400, cdf)
new_esEs31(xuu5000, xuu400, app(app(app(ty_@3, ee), ef), eg)) → new_esEs5(xuu5000, xuu400, ee, ef, eg)
new_esEs31(xuu5000, xuu400, ty_@0) → new_esEs17(xuu5000, xuu400)
new_lt19(xuu4910, xuu5110, ty_Ordering) → new_lt14(xuu4910, xuu5110)
new_esEs12(xuu490, xuu510, ty_Char) → new_esEs11(xuu490, xuu510)
new_esEs26(xuu4910, xuu5110, ty_Float) → new_esEs13(xuu4910, xuu5110)
new_esEs21(xuu50000, xuu4000, ty_@0) → new_esEs17(xuu50000, xuu4000)
new_primMulNat0(Zero, Zero) → Zero
new_esEs19(xuu50002, xuu4002, app(ty_Ratio, gb)) → new_esEs18(xuu50002, xuu4002, gb)
new_lt21(xuu4911, xuu5111, ty_@0) → new_lt17(xuu4911, xuu5111)
new_esEs7(Left(xuu50000), Left(xuu4000), app(app(app(ty_@3, bgh), bha), bhb), bgd) → new_esEs5(xuu50000, xuu4000, bgh, bha, bhb)
new_compare(:(xuu4900, xuu4901), [], db) → GT
new_ltEs20(xuu4912, xuu5112, ty_@0) → new_ltEs15(xuu4912, xuu5112)
new_sr(Integer(xuu51000), Integer(xuu49010)) → Integer(new_primMulInt(xuu51000, xuu49010))
new_ltEs6(xuu491, xuu511, app(app(ty_Either, ec), ed)) → new_ltEs14(xuu491, xuu511, ec, ed)
new_esEs25(xuu4911, xuu5111, app(app(ty_@2, cfd), cfe)) → new_esEs4(xuu4911, xuu5111, cfd, cfe)
new_esEs32(xuu37, xuu39, ty_Integer) → new_esEs15(xuu37, xuu39)
new_compare30(xuu4900, xuu5100, app(ty_Maybe, dbh)) → new_compare13(xuu4900, xuu5100, dbh)
new_esEs28(xuu50000, xuu4000, ty_Bool) → new_esEs16(xuu50000, xuu4000)
new_esEs31(xuu5000, xuu400, ty_Bool) → new_esEs16(xuu5000, xuu400)
new_lt19(xuu4910, xuu5110, ty_Bool) → new_lt4(xuu4910, xuu5110)
new_esEs7(Right(xuu50000), Right(xuu4000), bhe, ty_Ordering) → new_esEs8(xuu50000, xuu4000)
new_esEs22(xuu4910, xuu5110, ty_@0) → new_esEs17(xuu4910, xuu5110)
new_lt14(xuu490, xuu510) → new_esEs8(new_compare27(xuu490, xuu510), LT)
new_lt20(xuu4910, xuu5110, ty_Int) → new_lt18(xuu4910, xuu5110)
new_esEs24(xuu50000, xuu4000, ty_Integer) → new_esEs15(xuu50000, xuu4000)
new_esEs19(xuu50002, xuu4002, ty_Int) → new_esEs10(xuu50002, xuu4002)
new_compare30(xuu4900, xuu5100, app(ty_Ratio, dcc)) → new_compare6(xuu4900, xuu5100, dcc)
new_esEs25(xuu4911, xuu5111, app(ty_Ratio, cge)) → new_esEs18(xuu4911, xuu5111, cge)
new_ltEs5(xuu491, xuu511, bh) → new_fsEs(new_compare(xuu491, xuu511, bh))
new_ltEs10(Just(xuu4910), Just(xuu5110), ty_Int) → new_ltEs17(xuu4910, xuu5110)
new_ltEs10(Just(xuu4910), Just(xuu5110), ty_@0) → new_ltEs15(xuu4910, xuu5110)
new_ltEs10(Just(xuu4910), Just(xuu5110), ty_Integer) → new_ltEs12(xuu4910, xuu5110)
new_compare13(xuu490, xuu510, ca) → new_compare29(xuu490, xuu510, new_esEs6(xuu490, xuu510, ca), ca)
new_lt17(xuu490, xuu510) → new_esEs8(new_compare19(xuu490, xuu510), LT)
new_esEs7(Right(xuu50000), Right(xuu4000), bhe, app(app(app(ty_@3, cac), cad), cae)) → new_esEs5(xuu50000, xuu4000, cac, cad, cae)
new_esEs19(xuu50002, xuu4002, app(ty_[], fd)) → new_esEs14(xuu50002, xuu4002, fd)
new_esEs32(xuu37, xuu39, app(app(ty_@2, bbc), bbd)) → new_esEs4(xuu37, xuu39, bbc, bbd)
new_ltEs6(xuu491, xuu511, app(ty_[], bh)) → new_ltEs5(xuu491, xuu511, bh)
new_esEs22(xuu4910, xuu5110, app(ty_Maybe, cbf)) → new_esEs6(xuu4910, xuu5110, cbf)
new_primCmpNat1(Succ(xuu49000), Succ(xuu51000)) → new_primCmpNat1(xuu49000, xuu51000)
new_esEs27(xuu50001, xuu4001, app(ty_Maybe, ddd)) → new_esEs6(xuu50001, xuu4001, ddd)
new_ltEs13(True, False) → False
new_esEs29(xuu50000, xuu4000, ty_Char) → new_esEs11(xuu50000, xuu4000)
new_esEs15(Integer(xuu50000), Integer(xuu4000)) → new_primEqInt(xuu50000, xuu4000)
new_lt20(xuu4910, xuu5110, ty_Float) → new_lt12(xuu4910, xuu5110)
new_lt9(xuu490, xuu510, app(app(app(ty_@3, cf), cg), da)) → new_lt11(xuu490, xuu510, cf, cg, da)
new_lt20(xuu4910, xuu5110, app(ty_[], ceg)) → new_lt13(xuu4910, xuu5110, ceg)
new_esEs19(xuu50002, xuu4002, app(app(app(ty_@3, ff), fg), fh)) → new_esEs5(xuu50002, xuu4002, ff, fg, fh)
new_compare15(xuu490, xuu510, False) → GT
new_esEs22(xuu4910, xuu5110, app(ty_[], cbe)) → new_esEs14(xuu4910, xuu5110, cbe)
new_esEs28(xuu50000, xuu4000, app(app(app(ty_@3, dec), ded), dee)) → new_esEs5(xuu50000, xuu4000, dec, ded, dee)
new_esEs22(xuu4910, xuu5110, app(ty_Ratio, cca)) → new_esEs18(xuu4910, xuu5110, cca)
new_esEs22(xuu4910, xuu5110, app(app(ty_Either, cbg), cbh)) → new_esEs7(xuu4910, xuu5110, cbg, cbh)
new_esEs29(xuu50000, xuu4000, ty_Integer) → new_esEs15(xuu50000, xuu4000)
new_ltEs19(xuu4911, xuu5111, ty_Char) → new_ltEs18(xuu4911, xuu5111)
new_esEs25(xuu4911, xuu5111, ty_Double) → new_esEs9(xuu4911, xuu5111)
new_esEs17(@0, @0) → True
new_esEs25(xuu4911, xuu5111, ty_Float) → new_esEs13(xuu4911, xuu5111)
new_esEs7(Right(xuu50000), Right(xuu4000), bhe, app(ty_Maybe, caf)) → new_esEs6(xuu50000, xuu4000, caf)
new_lt20(xuu4910, xuu5110, ty_Double) → new_lt7(xuu4910, xuu5110)
new_lt20(xuu4910, xuu5110, ty_Bool) → new_lt4(xuu4910, xuu5110)
new_esEs32(xuu37, xuu39, app(ty_[], bbe)) → new_esEs14(xuu37, xuu39, bbe)
new_pePe(False, xuu135) → xuu135
new_esEs14([], [], cdf) → True
new_esEs7(Right(xuu50000), Left(xuu4000), bhe, bgd) → False
new_esEs7(Left(xuu50000), Right(xuu4000), bhe, bgd) → False
new_esEs25(xuu4911, xuu5111, ty_Char) → new_esEs11(xuu4911, xuu5111)
new_ltEs20(xuu4912, xuu5112, app(ty_[], chc)) → new_ltEs5(xuu4912, xuu5112, chc)
new_esEs5(@3(xuu50000, xuu50001, xuu50002), @3(xuu4000, xuu4001, xuu4002), ee, ef, eg) → new_asAs(new_esEs21(xuu50000, xuu4000, ee), new_asAs(new_esEs20(xuu50001, xuu4001, ef), new_esEs19(xuu50002, xuu4002, eg)))
new_esEs29(xuu50000, xuu4000, app(ty_[], dfd)) → new_esEs14(xuu50000, xuu4000, dfd)
new_esEs27(xuu50001, xuu4001, app(app(ty_Either, dcd), dce)) → new_esEs7(xuu50001, xuu4001, dcd, dce)
new_ltEs14(Left(xuu4910), Left(xuu5110), ty_@0, ed) → new_ltEs15(xuu4910, xuu5110)
new_esEs29(xuu50000, xuu4000, ty_@0) → new_esEs17(xuu50000, xuu4000)
new_esEs19(xuu50002, xuu4002, app(ty_Maybe, ga)) → new_esEs6(xuu50002, xuu4002, ga)
new_ltEs14(Right(xuu4910), Right(xuu5110), ec, app(app(app(ty_@3, bdg), bdh), bea)) → new_ltEs8(xuu4910, xuu5110, bdg, bdh, bea)
new_esEs22(xuu4910, xuu5110, app(app(ty_@2, cah), cba)) → new_esEs4(xuu4910, xuu5110, cah, cba)
new_compare15(xuu490, xuu510, True) → LT
new_compare25(xuu490, xuu510, False, dc, dd) → new_compare110(xuu490, xuu510, new_ltEs14(xuu490, xuu510, dc, dd), dc, dd)
new_lt15(xuu490, xuu510) → new_esEs8(new_compare7(xuu490, xuu510), LT)
new_ltEs6(xuu491, xuu511, app(app(ty_@2, de), df)) → new_ltEs7(xuu491, xuu511, de, df)
new_esEs12(xuu490, xuu510, ty_Double) → new_esEs9(xuu490, xuu510)
new_esEs22(xuu4910, xuu5110, ty_Ordering) → new_esEs8(xuu4910, xuu5110)
new_lt9(xuu490, xuu510, app(ty_[], db)) → new_lt13(xuu490, xuu510, db)
new_ltEs20(xuu4912, xuu5112, ty_Integer) → new_ltEs12(xuu4912, xuu5112)
new_esEs7(Left(xuu50000), Left(xuu4000), ty_Double, bgd) → new_esEs9(xuu50000, xuu4000)
new_esEs19(xuu50002, xuu4002, app(app(ty_Either, eh), fa)) → new_esEs7(xuu50002, xuu4002, eh, fa)
new_compare9(xuu490, xuu510) → new_compare26(xuu490, xuu510, new_esEs16(xuu490, xuu510))
new_esEs7(Right(xuu50000), Right(xuu4000), bhe, ty_Double) → new_esEs9(xuu50000, xuu4000)
new_ltEs14(Left(xuu4910), Left(xuu5110), ty_Ordering, ed) → new_ltEs11(xuu4910, xuu5110)
new_esEs7(Left(xuu50000), Left(xuu4000), ty_Bool, bgd) → new_esEs16(xuu50000, xuu4000)
new_esEs29(xuu50000, xuu4000, app(app(ty_@2, dfb), dfc)) → new_esEs4(xuu50000, xuu4000, dfb, dfc)
new_esEs20(xuu50001, xuu4001, ty_Bool) → new_esEs16(xuu50001, xuu4001)
new_lt9(xuu490, xuu510, app(app(ty_@2, cb), cc)) → new_lt10(xuu490, xuu510, cb, cc)
new_esEs6(Just(xuu50000), Just(xuu4000), app(app(app(ty_@3, bfe), bff), bfg)) → new_esEs5(xuu50000, xuu4000, bfe, bff, bfg)
new_esEs12(xuu490, xuu510, ty_@0) → new_esEs17(xuu490, xuu510)
new_lt6(xuu490, xuu510) → new_esEs8(new_compare10(xuu490, xuu510), LT)
new_ltEs20(xuu4912, xuu5112, app(app(ty_@2, cgf), cgg)) → new_ltEs7(xuu4912, xuu5112, cgf, cgg)
new_esEs31(xuu5000, xuu400, app(app(ty_@2, cdd), cde)) → new_esEs4(xuu5000, xuu400, cdd, cde)
new_esEs25(xuu4911, xuu5111, ty_Bool) → new_esEs16(xuu4911, xuu5111)
new_ltEs10(Just(xuu4910), Just(xuu5110), app(ty_Ratio, dba)) → new_ltEs4(xuu4910, xuu5110, dba)
new_esEs8(LT, LT) → True
new_ltEs13(False, True) → True
new_ltEs18(xuu491, xuu511) → new_fsEs(new_compare10(xuu491, xuu511))
new_lt18(xuu490, xuu510) → new_esEs8(new_compare8(xuu490, xuu510), LT)
new_esEs25(xuu4911, xuu5111, ty_Ordering) → new_esEs8(xuu4911, xuu5111)
new_esEs7(Left(xuu50000), Left(xuu4000), ty_Float, bgd) → new_esEs13(xuu50000, xuu4000)
new_compare30(xuu4900, xuu5100, app(app(ty_@2, dbb), dbc)) → new_compare12(xuu4900, xuu5100, dbb, dbc)
new_ltEs14(Right(xuu4910), Right(xuu5110), ec, ty_@0) → new_ltEs15(xuu4910, xuu5110)
new_lt9(xuu490, xuu510, app(app(ty_Either, dc), dd)) → new_lt16(xuu490, xuu510, dc, dd)
new_ltEs10(Just(xuu4910), Just(xuu5110), app(ty_Maybe, daf)) → new_ltEs10(xuu4910, xuu5110, daf)
new_ltEs4(xuu491, xuu511, bg) → new_fsEs(new_compare6(xuu491, xuu511, bg))
new_pePe(True, xuu135) → True
new_primEqNat0(Zero, Zero) → True
new_compare26(xuu490, xuu510, True) → EQ
new_esEs29(xuu50000, xuu4000, app(ty_Maybe, dfh)) → new_esEs6(xuu50000, xuu4000, dfh)
new_lt21(xuu4911, xuu5111, app(app(ty_Either, cgc), cgd)) → new_lt16(xuu4911, xuu5111, cgc, cgd)
new_esEs26(xuu4910, xuu5110, app(ty_Maybe, ceh)) → new_esEs6(xuu4910, xuu5110, ceh)
new_primMulNat0(Succ(xuu5000000), Succ(xuu400000)) → new_primPlusNat1(new_primMulNat0(xuu5000000, Succ(xuu400000)), xuu400000)
new_lt20(xuu4910, xuu5110, app(app(ty_@2, ceb), cec)) → new_lt10(xuu4910, xuu5110, ceb, cec)
new_compare12(xuu490, xuu510, cb, cc) → new_compare23(xuu490, xuu510, new_esEs4(xuu490, xuu510, cb, cc), cb, cc)
new_esEs4(@2(xuu50000, xuu50001), @2(xuu4000, xuu4001), cdd, cde) → new_asAs(new_esEs28(xuu50000, xuu4000, cdd), new_esEs27(xuu50001, xuu4001, cde))
new_ltEs10(Just(xuu4910), Just(xuu5110), app(app(ty_Either, dag), dah)) → new_ltEs14(xuu4910, xuu5110, dag, dah)
new_esEs7(Left(xuu50000), Left(xuu4000), ty_Ordering, bgd) → new_esEs8(xuu50000, xuu4000)
new_esEs19(xuu50002, xuu4002, ty_Float) → new_esEs13(xuu50002, xuu4002)
new_compare110(xuu490, xuu510, False, dc, dd) → GT
new_ltEs14(Right(xuu4910), Right(xuu5110), ec, app(ty_[], beb)) → new_ltEs5(xuu4910, xuu5110, beb)
new_ltEs14(Right(xuu4910), Right(xuu5110), ec, ty_Int) → new_ltEs17(xuu4910, xuu5110)
new_esEs26(xuu4910, xuu5110, ty_Bool) → new_esEs16(xuu4910, xuu5110)
new_lt19(xuu4910, xuu5110, app(ty_Maybe, cbf)) → new_lt8(xuu4910, xuu5110, cbf)
new_primCmpNat1(Zero, Zero) → EQ
new_esEs6(Just(xuu50000), Just(xuu4000), ty_@0) → new_esEs17(xuu50000, xuu4000)
new_esEs6(Just(xuu50000), Just(xuu4000), ty_Bool) → new_esEs16(xuu50000, xuu4000)
new_lt7(xuu490, xuu510) → new_esEs8(new_compare11(xuu490, xuu510), LT)
new_ltEs10(Just(xuu4910), Just(xuu5110), ty_Float) → new_ltEs9(xuu4910, xuu5110)
new_esEs22(xuu4910, xuu5110, ty_Double) → new_esEs9(xuu4910, xuu5110)
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_esEs30(xuu36, xuu37, xuu38, xuu39, False, bag, bah) → new_esEs8(new_compare23(@2(xuu36, xuu37), @2(xuu38, xuu39), False, bag, bah), LT)
new_esEs7(Left(xuu50000), Left(xuu4000), ty_Int, bgd) → new_esEs10(xuu50000, xuu4000)
new_lt20(xuu4910, xuu5110, ty_Ordering) → new_lt14(xuu4910, xuu5110)
new_lt19(xuu4910, xuu5110, app(app(app(ty_@3, cbb), cbc), cbd)) → new_lt11(xuu4910, xuu5110, cbb, cbc, cbd)
new_compare29(xuu490, xuu510, False, ca) → new_compare112(xuu490, xuu510, new_ltEs10(xuu490, xuu510, ca), ca)
new_esEs31(xuu5000, xuu400, app(app(ty_Either, bhe), bgd)) → new_esEs7(xuu5000, xuu400, bhe, bgd)
new_esEs7(Right(xuu50000), Right(xuu4000), bhe, app(app(ty_Either, bhf), bhg)) → new_esEs7(xuu50000, xuu4000, bhf, bhg)
new_esEs8(GT, LT) → False
new_esEs8(LT, GT) → False
new_primCmpNat1(Succ(xuu49000), Zero) → GT
new_lt21(xuu4911, xuu5111, app(app(app(ty_@3, cff), cfg), cfh)) → new_lt11(xuu4911, xuu5111, cff, cfg, cfh)
new_ltEs14(Right(xuu4910), Right(xuu5110), ec, app(app(ty_@2, bde), bdf)) → new_ltEs7(xuu4910, xuu5110, bde, bdf)
new_ltEs14(Left(xuu4910), Left(xuu5110), ty_Bool, ed) → new_ltEs13(xuu4910, xuu5110)
new_primEqInt(Neg(Succ(xuu500000)), Neg(Succ(xuu40000))) → new_primEqNat0(xuu500000, xuu40000)
new_compare30(xuu4900, xuu5100, ty_Float) → new_compare18(xuu4900, xuu5100)
new_ltEs20(xuu4912, xuu5112, app(ty_Ratio, chg)) → new_ltEs4(xuu4912, xuu5112, chg)
new_lt21(xuu4911, xuu5111, app(app(ty_@2, cfd), cfe)) → new_lt10(xuu4911, xuu5111, cfd, cfe)
new_esEs20(xuu50001, xuu4001, ty_Ordering) → new_esEs8(xuu50001, xuu4001)
new_esEs7(Left(xuu50000), Left(xuu4000), ty_Char, bgd) → new_esEs11(xuu50000, xuu4000)
new_esEs31(xuu5000, xuu400, ty_Int) → new_esEs10(xuu5000, xuu400)
new_lt20(xuu4910, xuu5110, ty_Char) → new_lt6(xuu4910, xuu5110)
new_ltEs16(xuu491, xuu511) → new_fsEs(new_compare11(xuu491, xuu511))
new_ltEs6(xuu491, xuu511, ty_Char) → new_ltEs18(xuu491, xuu511)
new_esEs28(xuu50000, xuu4000, ty_@0) → new_esEs17(xuu50000, xuu4000)
new_esEs32(xuu37, xuu39, ty_Double) → new_esEs9(xuu37, xuu39)
new_ltEs14(Right(xuu4910), Left(xuu5110), ec, ed) → False
new_esEs16(False, True) → False
new_esEs16(True, False) → False
new_esEs7(Right(xuu50000), Right(xuu4000), bhe, ty_Float) → new_esEs13(xuu50000, xuu4000)
new_esEs14(:(xuu50000, xuu50001), [], cdf) → False
new_esEs14([], :(xuu4000, xuu4001), cdf) → False
new_compare111(xuu110, xuu111, xuu112, xuu113, True, cdh, cea) → LT
new_ltEs19(xuu4911, xuu5111, ty_Float) → new_ltEs9(xuu4911, xuu5111)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs7(Left(xuu50000), Left(xuu4000), ty_Integer, bgd) → new_esEs15(xuu50000, xuu4000)
new_esEs20(xuu50001, xuu4001, ty_Float) → new_esEs13(xuu50001, xuu4001)
new_esEs32(xuu37, xuu39, app(app(app(ty_@3, bbf), bbg), bbh)) → new_esEs5(xuu37, xuu39, bbf, bbg, bbh)
new_lt19(xuu4910, xuu5110, ty_Integer) → new_lt15(xuu4910, xuu5110)
new_esEs6(Just(xuu50000), Just(xuu4000), ty_Float) → new_esEs13(xuu50000, xuu4000)
new_esEs26(xuu4910, xuu5110, app(ty_[], ceg)) → new_esEs14(xuu4910, xuu5110, ceg)
new_compare8(xuu92, xuu91) → new_primCmpInt(xuu92, xuu91)
new_primEqInt(Neg(Zero), Neg(Succ(xuu40000))) → False
new_primEqInt(Neg(Succ(xuu500000)), Neg(Zero)) → False
new_esEs8(EQ, EQ) → True
new_primPlusNat1(Zero, xuu400000) → Succ(xuu400000)
new_esEs31(xuu5000, xuu400, app(ty_Ratio, cdg)) → new_esEs18(xuu5000, xuu400, cdg)
new_esEs22(xuu4910, xuu5110, ty_Float) → new_esEs13(xuu4910, xuu5110)
new_esEs28(xuu50000, xuu4000, app(ty_[], deb)) → new_esEs14(xuu50000, xuu4000, deb)
new_esEs20(xuu50001, xuu4001, ty_@0) → new_esEs17(xuu50001, xuu4001)
new_esEs22(xuu4910, xuu5110, app(app(app(ty_@3, cbb), cbc), cbd)) → new_esEs5(xuu4910, xuu5110, cbb, cbc, cbd)
new_compare([], [], db) → EQ
new_esEs26(xuu4910, xuu5110, app(app(ty_Either, cfa), cfb)) → new_esEs7(xuu4910, xuu5110, cfa, cfb)
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_ltEs19(xuu4911, xuu5111, ty_Bool) → new_ltEs13(xuu4911, xuu5111)
new_esEs29(xuu50000, xuu4000, ty_Bool) → new_esEs16(xuu50000, xuu4000)
new_esEs25(xuu4911, xuu5111, ty_@0) → new_esEs17(xuu4911, xuu5111)
new_esEs29(xuu50000, xuu4000, ty_Float) → new_esEs13(xuu50000, xuu4000)
new_ltEs19(xuu4911, xuu5111, app(ty_Ratio, cdc)) → new_ltEs4(xuu4911, xuu5111, cdc)
new_lt19(xuu4910, xuu5110, app(app(ty_Either, cbg), cbh)) → new_lt16(xuu4910, xuu5110, cbg, cbh)
new_esEs6(Nothing, Nothing, beg) → True
new_compare113(xuu490, xuu510, False, cf, cg, da) → GT
new_compare18(Float(xuu4900, xuu4901), Float(xuu5100, xuu5101)) → new_compare8(new_sr0(xuu4900, xuu5100), new_sr0(xuu4901, xuu5101))
new_esEs19(xuu50002, xuu4002, ty_Char) → new_esEs11(xuu50002, xuu4002)
new_lt21(xuu4911, xuu5111, app(ty_Ratio, cge)) → new_lt5(xuu4911, xuu5111, cge)
new_primEqInt(Pos(Succ(xuu500000)), Pos(Succ(xuu40000))) → new_primEqNat0(xuu500000, xuu40000)
new_esEs12(xuu490, xuu510, app(app(app(ty_@3, cf), cg), da)) → new_esEs5(xuu490, xuu510, cf, cg, da)
new_ltEs8(@3(xuu4910, xuu4911, xuu4912), @3(xuu5110, xuu5111, xuu5112), dg, dh, ea) → new_pePe(new_lt20(xuu4910, xuu5110, dg), new_asAs(new_esEs26(xuu4910, xuu5110, dg), new_pePe(new_lt21(xuu4911, xuu5111, dh), new_asAs(new_esEs25(xuu4911, xuu5111, dh), new_ltEs20(xuu4912, xuu5112, ea)))))
new_esEs21(xuu50000, xuu4000, app(ty_Maybe, bae)) → new_esEs6(xuu50000, xuu4000, bae)
new_esEs32(xuu37, xuu39, app(app(ty_Either, bba), bbb)) → new_esEs7(xuu37, xuu39, bba, bbb)
new_esEs20(xuu50001, xuu4001, ty_Int) → new_esEs10(xuu50001, xuu4001)
new_esEs26(xuu4910, xuu5110, ty_Integer) → new_esEs15(xuu4910, xuu5110)
new_lt12(xuu490, xuu510) → new_esEs8(new_compare18(xuu490, xuu510), LT)
new_esEs6(Nothing, Just(xuu4000), beg) → False
new_esEs6(Just(xuu50000), Nothing, beg) → False
new_primEqNat0(Succ(xuu500000), Succ(xuu40000)) → new_primEqNat0(xuu500000, xuu40000)
new_ltEs14(Left(xuu4910), Left(xuu5110), app(ty_Maybe, bda), ed) → new_ltEs10(xuu4910, xuu5110, bda)
new_lt9(xuu490, xuu510, ty_Integer) → new_lt15(xuu490, xuu510)
new_lt5(xuu490, xuu510, bf) → new_esEs8(new_compare6(xuu490, xuu510, bf), LT)
new_esEs27(xuu50001, xuu4001, ty_Ordering) → new_esEs8(xuu50001, xuu4001)
new_esEs12(xuu490, xuu510, ty_Float) → new_esEs13(xuu490, xuu510)
new_esEs21(xuu50000, xuu4000, app(ty_[], baa)) → new_esEs14(xuu50000, xuu4000, baa)
new_ltEs14(Left(xuu4910), Left(xuu5110), ty_Int, ed) → new_ltEs17(xuu4910, xuu5110)
new_lt21(xuu4911, xuu5111, ty_Char) → new_lt6(xuu4911, xuu5111)
new_esEs29(xuu50000, xuu4000, ty_Double) → new_esEs9(xuu50000, xuu4000)
new_ltEs14(Right(xuu4910), Right(xuu5110), ec, app(ty_Ratio, bef)) → new_ltEs4(xuu4910, xuu5110, bef)
new_esEs29(xuu50000, xuu4000, ty_Int) → new_esEs10(xuu50000, xuu4000)
new_primCompAux00(xuu140, LT) → LT
new_esEs22(xuu4910, xuu5110, ty_Bool) → new_esEs16(xuu4910, xuu5110)
new_lt19(xuu4910, xuu5110, app(ty_[], cbe)) → new_lt13(xuu4910, xuu5110, cbe)
new_ltEs6(xuu491, xuu511, app(ty_Ratio, bg)) → new_ltEs4(xuu491, xuu511, bg)
new_esEs26(xuu4910, xuu5110, app(app(ty_@2, ceb), cec)) → new_esEs4(xuu4910, xuu5110, ceb, cec)
new_esEs27(xuu50001, xuu4001, app(app(app(ty_@3, dda), ddb), ddc)) → new_esEs5(xuu50001, xuu4001, dda, ddb, ddc)
new_ltEs19(xuu4911, xuu5111, ty_Int) → new_ltEs17(xuu4911, xuu5111)
new_lt9(xuu490, xuu510, ty_Float) → new_lt12(xuu490, xuu510)
new_esEs12(xuu490, xuu510, app(ty_Ratio, bf)) → new_esEs18(xuu490, xuu510, bf)
new_esEs6(Just(xuu50000), Just(xuu4000), ty_Int) → new_esEs10(xuu50000, xuu4000)
new_ltEs17(xuu491, xuu511) → new_fsEs(new_compare8(xuu491, xuu511))
new_esEs7(Left(xuu50000), Left(xuu4000), app(ty_Ratio, bhd), bgd) → new_esEs18(xuu50000, xuu4000, bhd)
new_esEs28(xuu50000, xuu4000, ty_Ordering) → new_esEs8(xuu50000, xuu4000)
new_lt20(xuu4910, xuu5110, app(ty_Ratio, cfc)) → new_lt5(xuu4910, xuu5110, cfc)
new_esEs8(EQ, LT) → False
new_esEs8(LT, EQ) → False
new_primEqInt(Pos(Zero), Pos(Succ(xuu40000))) → False
new_primEqInt(Pos(Succ(xuu500000)), Pos(Zero)) → False
new_lt9(xuu490, xuu510, app(ty_Maybe, ca)) → new_lt8(xuu490, xuu510, ca)
new_compare30(xuu4900, xuu5100, ty_Int) → new_compare8(xuu4900, xuu5100)
new_compare19(@0, @0) → EQ
new_primPlusNat0(Succ(xuu41200), Zero) → Succ(xuu41200)
new_primPlusNat0(Zero, Succ(xuu9700)) → Succ(xuu9700)
new_esEs7(Right(xuu50000), Right(xuu4000), bhe, ty_Int) → new_esEs10(xuu50000, xuu4000)
new_compare30(xuu4900, xuu5100, ty_Integer) → new_compare7(xuu4900, xuu5100)
new_ltEs11(GT, EQ) → False
new_esEs32(xuu37, xuu39, app(ty_Maybe, bca)) → new_esEs6(xuu37, xuu39, bca)
new_primCmpInt(Neg(Zero), Pos(Succ(xuu5100))) → LT
new_compare24(xuu490, xuu510, False) → new_compare15(xuu490, xuu510, new_ltEs11(xuu490, xuu510))
new_compare210(xuu490, xuu510, True, cf, cg, da) → EQ
new_esEs27(xuu50001, xuu4001, ty_Double) → new_esEs9(xuu50001, xuu4001)
new_ltEs7(@2(xuu4910, xuu4911), @2(xuu5110, xuu5111), de, df) → new_pePe(new_lt19(xuu4910, xuu5110, de), new_asAs(new_esEs22(xuu4910, xuu5110, de), new_ltEs19(xuu4911, xuu5111, df)))
new_esEs32(xuu37, xuu39, ty_@0) → new_esEs17(xuu37, xuu39)
new_ltEs6(xuu491, xuu511, ty_Int) → new_ltEs17(xuu491, xuu511)
new_compare30(xuu4900, xuu5100, app(ty_[], dbg)) → new_compare(xuu4900, xuu5100, dbg)
new_esEs29(xuu50000, xuu4000, app(ty_Ratio, dga)) → new_esEs18(xuu50000, xuu4000, dga)
new_primEqInt(Neg(Succ(xuu500000)), Pos(xuu4000)) → False
new_primEqInt(Pos(Succ(xuu500000)), Neg(xuu4000)) → False
new_ltEs19(xuu4911, xuu5111, ty_Double) → new_ltEs16(xuu4911, xuu5111)
new_ltEs9(xuu491, xuu511) → new_fsEs(new_compare18(xuu491, xuu511))
new_esEs25(xuu4911, xuu5111, ty_Int) → new_esEs10(xuu4911, xuu5111)
new_compare11(Double(xuu4900, xuu4901), Double(xuu5100, xuu5101)) → new_compare8(new_sr0(xuu4900, xuu5100), new_sr0(xuu4901, xuu5101))
new_compare(:(xuu4900, xuu4901), :(xuu5100, xuu5101), db) → new_primCompAux0(xuu4900, xuu5100, new_compare(xuu4901, xuu5101, db), db)
new_compare10(Char(xuu4900), Char(xuu5100)) → new_primCmpNat1(xuu4900, xuu5100)
new_esEs28(xuu50000, xuu4000, ty_Char) → new_esEs11(xuu50000, xuu4000)
new_ltEs19(xuu4911, xuu5111, ty_@0) → new_ltEs15(xuu4911, xuu5111)
new_ltEs14(Left(xuu4910), Left(xuu5110), app(app(ty_@2, bcc), bcd), ed) → new_ltEs7(xuu4910, xuu5110, bcc, bcd)
new_ltEs14(Left(xuu4910), Left(xuu5110), app(app(app(ty_@3, bce), bcf), bcg), ed) → new_ltEs8(xuu4910, xuu5110, bce, bcf, bcg)
new_esEs6(Just(xuu50000), Just(xuu4000), ty_Char) → new_esEs11(xuu50000, xuu4000)
new_compare28(xuu490, xuu510, cf, cg, da) → new_compare210(xuu490, xuu510, new_esEs5(xuu490, xuu510, cf, cg, da), cf, cg, da)
new_lt16(xuu490, xuu510, dc, dd) → new_esEs8(new_compare16(xuu490, xuu510, dc, dd), LT)
new_ltEs10(Just(xuu4910), Just(xuu5110), app(app(app(ty_@3, dab), dac), dad)) → new_ltEs8(xuu4910, xuu5110, dab, dac, dad)
new_esEs28(xuu50000, xuu4000, app(ty_Maybe, def)) → new_esEs6(xuu50000, xuu4000, def)
new_ltEs11(GT, LT) → False
new_primEqInt(Neg(Zero), Pos(Succ(xuu40000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(xuu40000))) → False
new_esEs26(xuu4910, xuu5110, ty_Int) → new_esEs10(xuu4910, xuu5110)
new_primCmpNat2(Succ(xuu5100), xuu4900) → new_primCmpNat1(xuu5100, xuu4900)
new_esEs21(xuu50000, xuu4000, ty_Integer) → new_esEs15(xuu50000, xuu4000)
new_esEs31(xuu5000, xuu400, ty_Integer) → new_esEs15(xuu5000, xuu400)
new_esEs21(xuu50000, xuu4000, ty_Char) → new_esEs11(xuu50000, xuu4000)
new_primCompAux00(xuu140, EQ) → xuu140
new_esEs28(xuu50000, xuu4000, app(app(ty_Either, ddf), ddg)) → new_esEs7(xuu50000, xuu4000, ddf, ddg)
new_compare24(xuu490, xuu510, True) → EQ
new_ltEs14(Right(xuu4910), Right(xuu5110), ec, app(ty_Maybe, bec)) → new_ltEs10(xuu4910, xuu5110, bec)
new_ltEs6(xuu491, xuu511, ty_Integer) → new_ltEs12(xuu491, xuu511)
new_ltEs14(Left(xuu4910), Left(xuu5110), ty_Float, ed) → new_ltEs9(xuu4910, xuu5110)
new_esEs8(GT, EQ) → False
new_esEs8(EQ, GT) → False
new_ltEs11(LT, EQ) → True
new_ltEs14(Left(xuu4910), Left(xuu5110), app(ty_[], bch), ed) → new_ltEs5(xuu4910, xuu5110, bch)
new_lt21(xuu4911, xuu5111, app(ty_[], cga)) → new_lt13(xuu4911, xuu5111, cga)
new_ltEs14(Left(xuu4910), Left(xuu5110), ty_Char, ed) → new_ltEs18(xuu4910, xuu5110)
new_esEs26(xuu4910, xuu5110, ty_Char) → new_esEs11(xuu4910, xuu5110)
new_ltEs11(LT, LT) → True
new_compare14(xuu110, xuu111, xuu112, xuu113, True, xuu115, cdh, cea) → new_compare111(xuu110, xuu111, xuu112, xuu113, True, cdh, cea)
new_ltEs10(Nothing, Nothing, eb) → True
new_not(False) → True
new_ltEs6(xuu491, xuu511, app(ty_Maybe, eb)) → new_ltEs10(xuu491, xuu511, eb)
new_esEs21(xuu50000, xuu4000, ty_Bool) → new_esEs16(xuu50000, xuu4000)
new_esEs7(Left(xuu50000), Left(xuu4000), app(ty_Maybe, bhc), bgd) → new_esEs6(xuu50000, xuu4000, bhc)
new_lt21(xuu4911, xuu5111, ty_Bool) → new_lt4(xuu4911, xuu5111)
new_esEs26(xuu4910, xuu5110, app(ty_Ratio, cfc)) → new_esEs18(xuu4910, xuu5110, cfc)
new_esEs25(xuu4911, xuu5111, ty_Integer) → new_esEs15(xuu4911, xuu5111)
new_lt9(xuu490, xuu510, ty_Int) → new_lt18(xuu490, xuu510)
new_esEs32(xuu37, xuu39, ty_Ordering) → new_esEs8(xuu37, xuu39)
new_compare30(xuu4900, xuu5100, ty_Double) → new_compare11(xuu4900, xuu5100)
new_compare17(xuu490, xuu510, True) → LT
new_lt20(xuu4910, xuu5110, app(app(ty_Either, cfa), cfb)) → new_lt16(xuu4910, xuu5110, cfa, cfb)
new_compare30(xuu4900, xuu5100, app(app(app(ty_@3, dbd), dbe), dbf)) → new_compare28(xuu4900, xuu5100, dbd, dbe, dbf)
new_ltEs6(xuu491, xuu511, ty_Float) → new_ltEs9(xuu491, xuu511)
new_ltEs11(GT, GT) → True
new_ltEs14(Right(xuu4910), Right(xuu5110), ec, ty_Char) → new_ltEs18(xuu4910, xuu5110)
new_ltEs20(xuu4912, xuu5112, app(app(app(ty_@3, cgh), cha), chb)) → new_ltEs8(xuu4912, xuu5112, cgh, cha, chb)
new_lt19(xuu4910, xuu5110, ty_Char) → new_lt6(xuu4910, xuu5110)
new_esEs20(xuu50001, xuu4001, app(app(app(ty_@3, gh), ha), hb)) → new_esEs5(xuu50001, xuu4001, gh, ha, hb)
new_ltEs19(xuu4911, xuu5111, ty_Integer) → new_ltEs12(xuu4911, xuu5111)
new_primCmpInt(Pos(Succ(xuu4900)), Neg(xuu510)) → GT
new_esEs22(xuu4910, xuu5110, ty_Char) → new_esEs11(xuu4910, xuu5110)
new_esEs21(xuu50000, xuu4000, app(app(app(ty_@3, bab), bac), bad)) → new_esEs5(xuu50000, xuu4000, bab, bac, bad)
new_esEs28(xuu50000, xuu4000, ty_Double) → new_esEs9(xuu50000, xuu4000)
new_esEs26(xuu4910, xuu5110, ty_@0) → new_esEs17(xuu4910, xuu5110)
new_primMulInt(Pos(xuu500000), Pos(xuu40000)) → Pos(new_primMulNat0(xuu500000, xuu40000))
new_esEs21(xuu50000, xuu4000, app(app(ty_@2, hg), hh)) → new_esEs4(xuu50000, xuu4000, hg, hh)
new_ltEs14(Right(xuu4910), Right(xuu5110), ec, ty_Float) → new_ltEs9(xuu4910, xuu5110)
new_compare30(xuu4900, xuu5100, app(app(ty_Either, dca), dcb)) → new_compare16(xuu4900, xuu5100, dca, dcb)
new_esEs22(xuu4910, xuu5110, ty_Int) → new_esEs10(xuu4910, xuu5110)
new_esEs20(xuu50001, xuu4001, ty_Char) → new_esEs11(xuu50001, xuu4001)
new_esEs9(Double(xuu50000, xuu50001), Double(xuu4000, xuu4001)) → new_esEs10(new_sr0(xuu50000, xuu4000), new_sr0(xuu50001, xuu4001))
new_esEs6(Just(xuu50000), Just(xuu4000), app(ty_[], bfd)) → new_esEs14(xuu50000, xuu4000, bfd)
new_primMulInt(Neg(xuu500000), Neg(xuu40000)) → Pos(new_primMulNat0(xuu500000, xuu40000))
new_esEs7(Right(xuu50000), Right(xuu4000), bhe, app(app(ty_@2, bhh), caa)) → new_esEs4(xuu50000, xuu4000, bhh, caa)
new_esEs20(xuu50001, xuu4001, ty_Integer) → new_esEs15(xuu50001, xuu4001)
new_lt20(xuu4910, xuu5110, app(app(app(ty_@3, ced), cee), cef)) → new_lt11(xuu4910, xuu5110, ced, cee, cef)
new_primEqNat0(Zero, Succ(xuu40000)) → False
new_primEqNat0(Succ(xuu500000), Zero) → False
new_primPlusNat0(Zero, Zero) → Zero
new_compare30(xuu4900, xuu5100, ty_Bool) → new_compare9(xuu4900, xuu5100)
new_compare25(xuu490, xuu510, True, dc, dd) → EQ
new_lt20(xuu4910, xuu5110, ty_@0) → new_lt17(xuu4910, xuu5110)
new_esEs25(xuu4911, xuu5111, app(ty_Maybe, cgb)) → new_esEs6(xuu4911, xuu5111, cgb)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_ltEs12(xuu491, xuu511) → new_fsEs(new_compare7(xuu491, xuu511))
new_compare113(xuu490, xuu510, True, cf, cg, da) → LT
new_ltEs14(Right(xuu4910), Right(xuu5110), ec, ty_Double) → new_ltEs16(xuu4910, xuu5110)
new_primCmpInt(Pos(Succ(xuu4900)), Pos(xuu510)) → new_primCmpNat0(xuu4900, xuu510)
new_lt19(xuu4910, xuu5110, app(ty_Ratio, cca)) → new_lt5(xuu4910, xuu5110, cca)
new_ltEs19(xuu4911, xuu5111, app(app(app(ty_@3, ccd), cce), ccf)) → new_ltEs8(xuu4911, xuu5111, ccd, cce, ccf)
new_ltEs19(xuu4911, xuu5111, ty_Ordering) → new_ltEs11(xuu4911, xuu5111)
new_primCmpNat0(xuu4900, Zero) → GT
new_lt4(xuu490, xuu510) → new_esEs8(new_compare9(xuu490, xuu510), LT)
new_compare26(xuu490, xuu510, False) → new_compare17(xuu490, xuu510, new_ltEs13(xuu490, xuu510))
new_esEs21(xuu50000, xuu4000, app(app(ty_Either, he), hf)) → new_esEs7(xuu50000, xuu4000, he, hf)
new_ltEs20(xuu4912, xuu5112, ty_Int) → new_ltEs17(xuu4912, xuu5112)
new_ltEs10(Just(xuu4910), Just(xuu5110), app(ty_[], dae)) → new_ltEs5(xuu4910, xuu5110, dae)
new_esEs12(xuu490, xuu510, ty_Bool) → new_esEs16(xuu490, xuu510)
new_primPlusNat1(Succ(xuu1010), xuu400000) → Succ(Succ(new_primPlusNat0(xuu1010, xuu400000)))
new_compare30(xuu4900, xuu5100, ty_Char) → new_compare10(xuu4900, xuu5100)
new_lt21(xuu4911, xuu5111, ty_Integer) → new_lt15(xuu4911, xuu5111)
new_esEs27(xuu50001, xuu4001, ty_Bool) → new_esEs16(xuu50001, xuu4001)
new_esEs29(xuu50000, xuu4000, app(app(app(ty_@3, dfe), dff), dfg)) → new_esEs5(xuu50000, xuu4000, dfe, dff, dfg)
new_ltEs14(Left(xuu4910), Left(xuu5110), app(ty_Ratio, bdd), ed) → new_ltEs4(xuu4910, xuu5110, bdd)
new_esEs7(Right(xuu50000), Right(xuu4000), bhe, app(ty_[], cab)) → new_esEs14(xuu50000, xuu4000, cab)
new_esEs16(True, True) → True
new_compare23(xuu49, xuu51, True, cd, ce) → EQ
new_primCmpInt(Pos(Zero), Neg(Succ(xuu5100))) → GT
new_esEs7(Left(xuu50000), Left(xuu4000), app(app(ty_@2, bge), bgf), bgd) → new_esEs4(xuu50000, xuu4000, bge, bgf)
new_esEs32(xuu37, xuu39, ty_Float) → new_esEs13(xuu37, xuu39)
new_ltEs6(xuu491, xuu511, app(app(app(ty_@3, dg), dh), ea)) → new_ltEs8(xuu491, xuu511, dg, dh, ea)
new_ltEs10(Just(xuu4910), Nothing, eb) → False
new_esEs7(Right(xuu50000), Right(xuu4000), bhe, ty_Bool) → new_esEs16(xuu50000, xuu4000)
new_sr0(xuu50000, xuu4000) → new_primMulInt(xuu50000, xuu4000)
new_esEs27(xuu50001, xuu4001, ty_@0) → new_esEs17(xuu50001, xuu4001)
new_ltEs20(xuu4912, xuu5112, ty_Ordering) → new_ltEs11(xuu4912, xuu5112)
new_esEs32(xuu37, xuu39, ty_Bool) → new_esEs16(xuu37, xuu39)
new_esEs20(xuu50001, xuu4001, app(ty_Ratio, hd)) → new_esEs18(xuu50001, xuu4001, hd)
new_lt9(xuu490, xuu510, ty_Ordering) → new_lt14(xuu490, xuu510)
new_esEs12(xuu490, xuu510, app(app(ty_Either, dc), dd)) → new_esEs7(xuu490, xuu510, dc, dd)
new_esEs11(Char(xuu50000), Char(xuu4000)) → new_primEqNat0(xuu50000, xuu4000)
new_ltEs10(Nothing, Just(xuu5110), eb) → True
new_ltEs11(EQ, EQ) → True
new_esEs20(xuu50001, xuu4001, app(app(ty_Either, gc), gd)) → new_esEs7(xuu50001, xuu4001, gc, gd)
new_compare14(xuu110, xuu111, xuu112, xuu113, False, xuu115, cdh, cea) → new_compare111(xuu110, xuu111, xuu112, xuu113, xuu115, cdh, cea)
new_esEs21(xuu50000, xuu4000, ty_Double) → new_esEs9(xuu50000, xuu4000)
new_esEs21(xuu50000, xuu4000, ty_Float) → new_esEs13(xuu50000, xuu4000)
new_primCompAux0(xuu4900, xuu5100, xuu130, db) → new_primCompAux00(xuu130, new_compare30(xuu4900, xuu5100, db))
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_compare29(xuu490, xuu510, True, ca) → EQ
new_esEs27(xuu50001, xuu4001, ty_Float) → new_esEs13(xuu50001, xuu4001)
new_esEs20(xuu50001, xuu4001, app(ty_Maybe, hc)) → new_esEs6(xuu50001, xuu4001, hc)
new_ltEs14(Left(xuu4910), Right(xuu5110), ec, ed) → True
new_lt9(xuu490, xuu510, ty_Bool) → new_lt4(xuu490, xuu510)
new_esEs24(xuu50000, xuu4000, ty_Int) → new_esEs10(xuu50000, xuu4000)
new_esEs6(Just(xuu50000), Just(xuu4000), ty_Integer) → new_esEs15(xuu50000, xuu4000)
new_esEs28(xuu50000, xuu4000, app(app(ty_@2, ddh), dea)) → new_esEs4(xuu50000, xuu4000, ddh, dea)
new_lt9(xuu490, xuu510, ty_Char) → new_lt6(xuu490, xuu510)
new_asAs(False, xuu66) → False
new_ltEs19(xuu4911, xuu5111, app(app(ty_@2, ccb), ccc)) → new_ltEs7(xuu4911, xuu5111, ccb, ccc)
new_ltEs20(xuu4912, xuu5112, app(app(ty_Either, che), chf)) → new_ltEs14(xuu4912, xuu5112, che, chf)
new_esEs18(:%(xuu50000, xuu50001), :%(xuu4000, xuu4001), cdg) → new_asAs(new_esEs24(xuu50000, xuu4000, cdg), new_esEs23(xuu50001, xuu4001, cdg))
new_ltEs20(xuu4912, xuu5112, ty_Double) → new_ltEs16(xuu4912, xuu5112)
new_primMulInt(Neg(xuu500000), Pos(xuu40000)) → Neg(new_primMulNat0(xuu500000, xuu40000))
new_primMulInt(Pos(xuu500000), Neg(xuu40000)) → Neg(new_primMulNat0(xuu500000, xuu40000))
new_ltEs19(xuu4911, xuu5111, app(app(ty_Either, cda), cdb)) → new_ltEs14(xuu4911, xuu5111, cda, cdb)
new_esEs26(xuu4910, xuu5110, ty_Double) → new_esEs9(xuu4910, xuu5110)
new_primCmpInt(Neg(Succ(xuu4900)), Neg(xuu510)) → new_primCmpNat2(xuu510, xuu4900)
new_primMulNat0(Zero, Succ(xuu400000)) → Zero
new_primMulNat0(Succ(xuu5000000), Zero) → Zero
new_lt19(xuu4910, xuu5110, ty_Float) → new_lt12(xuu4910, xuu5110)
new_lt8(xuu490, xuu510, ca) → new_esEs8(new_compare13(xuu490, xuu510, ca), LT)
new_esEs7(Right(xuu50000), Right(xuu4000), bhe, ty_Integer) → new_esEs15(xuu50000, xuu4000)
new_lt11(xuu490, xuu510, cf, cg, da) → new_esEs8(new_compare28(xuu490, xuu510, cf, cg, da), LT)
new_esEs6(Just(xuu50000), Just(xuu4000), app(ty_Maybe, bfh)) → new_esEs6(xuu50000, xuu4000, bfh)
new_esEs6(Just(xuu50000), Just(xuu4000), ty_Double) → new_esEs9(xuu50000, xuu4000)
new_lt13(xuu490, xuu510, db) → new_esEs8(new_compare(xuu490, xuu510, db), LT)
new_esEs21(xuu50000, xuu4000, ty_Ordering) → new_esEs8(xuu50000, xuu4000)
new_ltEs11(EQ, LT) → False
new_esEs31(xuu5000, xuu400, ty_Double) → new_esEs9(xuu5000, xuu400)
new_ltEs6(xuu491, xuu511, ty_@0) → new_ltEs15(xuu491, xuu511)
new_esEs32(xuu37, xuu39, ty_Int) → new_esEs10(xuu37, xuu39)
new_ltEs10(Just(xuu4910), Just(xuu5110), ty_Bool) → new_ltEs13(xuu4910, xuu5110)
new_esEs6(Just(xuu50000), Just(xuu4000), app(app(ty_@2, bfb), bfc)) → new_esEs4(xuu50000, xuu4000, bfb, bfc)
new_ltEs20(xuu4912, xuu5112, ty_Bool) → new_ltEs13(xuu4912, xuu5112)
new_ltEs14(Right(xuu4910), Right(xuu5110), ec, app(app(ty_Either, bed), bee)) → new_ltEs14(xuu4910, xuu5110, bed, bee)
new_esEs28(xuu50000, xuu4000, ty_Integer) → new_esEs15(xuu50000, xuu4000)
new_lt9(xuu490, xuu510, ty_@0) → new_lt17(xuu490, xuu510)
new_esEs19(xuu50002, xuu4002, ty_Double) → new_esEs9(xuu50002, xuu4002)
new_ltEs14(Right(xuu4910), Right(xuu5110), ec, ty_Bool) → new_ltEs13(xuu4910, xuu5110)
new_ltEs6(xuu491, xuu511, ty_Bool) → new_ltEs13(xuu491, xuu511)
new_esEs28(xuu50000, xuu4000, ty_Float) → new_esEs13(xuu50000, xuu4000)
new_primCmpInt(Pos(Zero), Pos(Succ(xuu5100))) → new_primCmpNat2(Zero, xuu5100)
new_ltEs14(Right(xuu4910), Right(xuu5110), ec, ty_Ordering) → new_ltEs11(xuu4910, xuu5110)
new_esEs7(Right(xuu50000), Right(xuu4000), bhe, ty_Char) → new_esEs11(xuu50000, xuu4000)
new_compare16(xuu490, xuu510, dc, dd) → new_compare25(xuu490, xuu510, new_esEs7(xuu490, xuu510, dc, dd), dc, dd)
new_compare111(xuu110, xuu111, xuu112, xuu113, False, cdh, cea) → GT
new_esEs23(xuu50001, xuu4001, ty_Integer) → new_esEs15(xuu50001, xuu4001)
new_esEs20(xuu50001, xuu4001, app(app(ty_@2, ge), gf)) → new_esEs4(xuu50001, xuu4001, ge, gf)
new_esEs30(xuu36, xuu37, xuu38, xuu39, True, bag, bah) → new_esEs8(new_compare23(@2(xuu36, xuu37), @2(xuu38, xuu39), new_esEs32(xuu37, xuu39, bah), bag, bah), LT)
new_esEs16(False, False) → True
new_lt19(xuu4910, xuu5110, ty_@0) → new_lt17(xuu4910, xuu5110)
new_ltEs14(Left(xuu4910), Left(xuu5110), app(app(ty_Either, bdb), bdc), ed) → new_ltEs14(xuu4910, xuu5110, bdb, bdc)
new_esEs12(xuu490, xuu510, ty_Int) → new_esEs10(xuu490, xuu510)
new_ltEs13(True, True) → True
new_esEs31(xuu5000, xuu400, ty_Char) → new_esEs11(xuu5000, xuu400)
new_compare6(:%(xuu4900, xuu4901), :%(xuu5100, xuu5101), ty_Integer) → new_compare7(new_sr(xuu4900, xuu5101), new_sr(xuu5100, xuu4901))
new_ltEs13(False, False) → True
new_esEs27(xuu50001, xuu4001, app(app(ty_@2, dcf), dcg)) → new_esEs4(xuu50001, xuu4001, dcf, dcg)
new_ltEs6(xuu491, xuu511, ty_Ordering) → new_ltEs11(xuu491, xuu511)
new_ltEs10(Just(xuu4910), Just(xuu5110), ty_Ordering) → new_ltEs11(xuu4910, xuu5110)
new_esEs32(xuu37, xuu39, ty_Char) → new_esEs11(xuu37, xuu39)
new_esEs31(xuu5000, xuu400, ty_Float) → new_esEs13(xuu5000, xuu400)
new_esEs7(Left(xuu50000), Left(xuu4000), ty_@0, bgd) → new_esEs17(xuu50000, xuu4000)
new_ltEs19(xuu4911, xuu5111, app(ty_Maybe, cch)) → new_ltEs10(xuu4911, xuu5111, cch)
new_ltEs10(Just(xuu4910), Just(xuu5110), ty_Char) → new_ltEs18(xuu4910, xuu5110)
new_compare7(Integer(xuu4900), Integer(xuu5100)) → new_primCmpInt(xuu4900, xuu5100)
new_compare30(xuu4900, xuu5100, ty_Ordering) → new_compare27(xuu4900, xuu5100)
new_lt20(xuu4910, xuu5110, ty_Integer) → new_lt15(xuu4910, xuu5110)
new_esEs25(xuu4911, xuu5111, app(app(app(ty_@3, cff), cfg), cfh)) → new_esEs5(xuu4911, xuu5111, cff, cfg, cfh)
new_esEs6(Just(xuu50000), Just(xuu4000), ty_Ordering) → new_esEs8(xuu50000, xuu4000)
new_ltEs6(xuu491, xuu511, ty_Double) → new_ltEs16(xuu491, xuu511)
new_esEs32(xuu37, xuu39, app(ty_Ratio, bcb)) → new_esEs18(xuu37, xuu39, bcb)
new_esEs29(xuu50000, xuu4000, app(app(ty_Either, deh), dfa)) → new_esEs7(xuu50000, xuu4000, deh, dfa)
new_lt21(xuu4911, xuu5111, ty_Float) → new_lt12(xuu4911, xuu5111)
new_compare112(xuu490, xuu510, False, ca) → GT
new_esEs28(xuu50000, xuu4000, ty_Int) → new_esEs10(xuu50000, xuu4000)
new_primPlusNat0(Succ(xuu41200), Succ(xuu9700)) → Succ(Succ(new_primPlusNat0(xuu41200, xuu9700)))
new_lt20(xuu4910, xuu5110, app(ty_Maybe, ceh)) → new_lt8(xuu4910, xuu5110, ceh)
new_esEs22(xuu4910, xuu5110, ty_Integer) → new_esEs15(xuu4910, xuu5110)
new_compare30(xuu4900, xuu5100, ty_@0) → new_compare19(xuu4900, xuu5100)
new_esEs7(Right(xuu50000), Right(xuu4000), bhe, ty_@0) → new_esEs17(xuu50000, xuu4000)
new_esEs12(xuu490, xuu510, ty_Ordering) → new_esEs8(xuu490, xuu510)
new_esEs19(xuu50002, xuu4002, ty_@0) → new_esEs17(xuu50002, xuu4002)
new_esEs27(xuu50001, xuu4001, app(ty_[], dch)) → new_esEs14(xuu50001, xuu4001, dch)
new_esEs19(xuu50002, xuu4002, ty_Integer) → new_esEs15(xuu50002, xuu4002)
new_ltEs14(Right(xuu4910), Right(xuu5110), ec, ty_Integer) → new_ltEs12(xuu4910, xuu5110)
new_esEs12(xuu490, xuu510, app(ty_[], db)) → new_esEs14(xuu490, xuu510, db)
new_lt10(xuu490, xuu510, cb, cc) → new_esEs8(new_compare12(xuu490, xuu510, cb, cc), LT)
new_asAs(True, xuu66) → xuu66
new_esEs12(xuu490, xuu510, ty_Integer) → new_esEs15(xuu490, xuu510)
new_esEs20(xuu50001, xuu4001, ty_Double) → new_esEs9(xuu50001, xuu4001)
new_esEs26(xuu4910, xuu5110, app(app(app(ty_@3, ced), cee), cef)) → new_esEs5(xuu4910, xuu5110, ced, cee, cef)
new_esEs7(Right(xuu50000), Right(xuu4000), bhe, app(ty_Ratio, cag)) → new_esEs18(xuu50000, xuu4000, cag)
new_esEs6(Just(xuu50000), Just(xuu4000), app(app(ty_Either, beh), bfa)) → new_esEs7(xuu50000, xuu4000, beh, bfa)
new_esEs27(xuu50001, xuu4001, ty_Int) → new_esEs10(xuu50001, xuu4001)
new_lt9(xuu490, xuu510, ty_Double) → new_lt7(xuu490, xuu510)
new_esEs28(xuu50000, xuu4000, app(ty_Ratio, deg)) → new_esEs18(xuu50000, xuu4000, deg)
new_esEs23(xuu50001, xuu4001, ty_Int) → new_esEs10(xuu50001, xuu4001)
new_ltEs10(Just(xuu4910), Just(xuu5110), app(app(ty_@2, chh), daa)) → new_ltEs7(xuu4910, xuu5110, chh, daa)
new_compare17(xuu490, xuu510, False) → GT
new_esEs21(xuu50000, xuu4000, ty_Int) → new_esEs10(xuu50000, xuu4000)
new_fsEs(xuu122) → new_not(new_esEs8(xuu122, GT))
new_ltEs20(xuu4912, xuu5112, ty_Float) → new_ltEs9(xuu4912, xuu5112)
new_esEs19(xuu50002, xuu4002, ty_Ordering) → new_esEs8(xuu50002, xuu4002)
new_compare210(xuu490, xuu510, False, cf, cg, da) → new_compare113(xuu490, xuu510, new_ltEs8(xuu490, xuu510, cf, cg, da), cf, cg, da)
new_ltEs10(Just(xuu4910), Just(xuu5110), ty_Double) → new_ltEs16(xuu4910, xuu5110)
new_esEs20(xuu50001, xuu4001, app(ty_[], gg)) → new_esEs14(xuu50001, xuu4001, gg)
new_esEs13(Float(xuu50000, xuu50001), Float(xuu4000, xuu4001)) → new_esEs10(new_sr0(xuu50000, xuu4000), new_sr0(xuu50001, xuu4001))
new_ltEs20(xuu4912, xuu5112, app(ty_Maybe, chd)) → new_ltEs10(xuu4912, xuu5112, chd)
new_lt9(xuu490, xuu510, app(ty_Ratio, bf)) → new_lt5(xuu490, xuu510, bf)
new_ltEs14(Left(xuu4910), Left(xuu5110), ty_Integer, ed) → new_ltEs12(xuu4910, xuu5110)
new_esEs12(xuu490, xuu510, app(ty_Maybe, ca)) → new_esEs6(xuu490, xuu510, ca)
new_esEs27(xuu50001, xuu4001, ty_Char) → new_esEs11(xuu50001, xuu4001)
new_ltEs19(xuu4911, xuu5111, app(ty_[], ccg)) → new_ltEs5(xuu4911, xuu5111, ccg)
new_lt21(xuu4911, xuu5111, ty_Int) → new_lt18(xuu4911, xuu5111)
new_esEs10(xuu5000, xuu400) → new_primEqInt(xuu5000, xuu400)
new_primCompAux00(xuu140, GT) → GT
new_esEs25(xuu4911, xuu5111, app(app(ty_Either, cgc), cgd)) → new_esEs7(xuu4911, xuu5111, cgc, cgd)
new_esEs19(xuu50002, xuu4002, ty_Bool) → new_esEs16(xuu50002, xuu4002)
new_esEs31(xuu5000, xuu400, app(ty_Maybe, beg)) → new_esEs6(xuu5000, xuu400, beg)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs29(xuu50000, xuu4000, ty_Ordering) → new_esEs8(xuu50000, xuu4000)
new_ltEs11(EQ, GT) → True
new_esEs19(xuu50002, xuu4002, app(app(ty_@2, fb), fc)) → new_esEs4(xuu50002, xuu4002, fb, fc)
new_esEs12(xuu490, xuu510, app(app(ty_@2, cb), cc)) → new_esEs4(xuu490, xuu510, cb, cc)
new_esEs7(Left(xuu50000), Left(xuu4000), app(ty_[], bgg), bgd) → new_esEs14(xuu50000, xuu4000, bgg)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primCmpNat0(xuu4900, Succ(xuu5100)) → new_primCmpNat1(xuu4900, xuu5100)
new_esEs27(xuu50001, xuu4001, ty_Integer) → new_esEs15(xuu50001, xuu4001)
new_esEs21(xuu50000, xuu4000, app(ty_Ratio, baf)) → new_esEs18(xuu50000, xuu4000, baf)
new_primCmpInt(Neg(Succ(xuu4900)), Pos(xuu510)) → LT
new_lt21(xuu4911, xuu5111, ty_Double) → new_lt7(xuu4911, xuu5111)
new_not(True) → False
new_compare6(:%(xuu4900, xuu4901), :%(xuu5100, xuu5101), ty_Int) → new_compare8(new_sr0(xuu4900, xuu5101), new_sr0(xuu5100, xuu4901))
new_esEs14(:(xuu50000, xuu50001), :(xuu4000, xuu4001), cdf) → new_asAs(new_esEs29(xuu50000, xuu4000, cdf), new_esEs14(xuu50001, xuu4001, cdf))
new_esEs6(Just(xuu50000), Just(xuu4000), app(ty_Ratio, bga)) → new_esEs18(xuu50000, xuu4000, bga)

The set Q consists of the following terms:

new_compare26(x0, x1, True)
new_esEs14([], [], x0)
new_esEs32(x0, x1, ty_Integer)
new_esEs12(x0, x1, ty_Ordering)
new_lt21(x0, x1, ty_Int)
new_ltEs11(EQ, GT)
new_lt19(x0, x1, app(ty_[], x2))
new_ltEs11(GT, EQ)
new_esEs28(x0, x1, ty_Int)
new_esEs22(x0, x1, ty_Double)
new_lt21(x0, x1, ty_Float)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs28(x0, x1, ty_Ordering)
new_ltEs14(Right(x0), Right(x1), x2, ty_@0)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_esEs31(x0, x1, ty_Float)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs17(x0, x1)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs14(Right(x0), Right(x1), x2, ty_Char)
new_ltEs11(EQ, EQ)
new_compare18(Float(x0, x1), Float(x2, x3))
new_ltEs20(x0, x1, ty_Float)
new_lt5(x0, x1, x2)
new_esEs20(x0, x1, ty_Float)
new_esEs7(Right(x0), Right(x1), x2, ty_Int)
new_ltEs10(Just(x0), Just(x1), app(ty_[], x2))
new_primCmpNat1(Zero, Succ(x0))
new_esEs22(x0, x1, ty_Bool)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare30(x0, x1, ty_Char)
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Char)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, app(ty_[], x2))
new_lt21(x0, x1, app(ty_Ratio, x2))
new_esEs6(Nothing, Nothing, x0)
new_compare8(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, ty_Double)
new_esEs31(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, ty_Bool)
new_esEs7(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt9(x0, x1, ty_Int)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs18(:%(x0, x1), :%(x2, x3), x4)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_lt8(x0, x1, x2)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs19(x0, x1, ty_Ordering)
new_lt21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt9(x0, x1, app(ty_[], x2))
new_lt9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs10(Just(x0), Just(x1), ty_Char)
new_esEs6(Just(x0), Just(x1), ty_Ordering)
new_esEs6(Just(x0), Just(x1), ty_Float)
new_esEs8(GT, GT)
new_fsEs(x0)
new_ltEs6(x0, x1, ty_@0)
new_primCompAux00(x0, LT)
new_primCmpNat1(Succ(x0), Zero)
new_compare11(Double(x0, x1), Double(x2, x3))
new_primCmpNat0(x0, Zero)
new_lt10(x0, x1, x2, x3)
new_lt21(x0, x1, ty_Char)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs19(x0, x1, ty_Int)
new_esEs6(Just(x0), Just(x1), ty_Char)
new_ltEs14(Right(x0), Right(x1), x2, ty_Int)
new_ltEs10(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs14(Left(x0), Left(x1), ty_@0, x2)
new_compare14(x0, x1, x2, x3, False, x4, x5, x6)
new_esEs7(Left(x0), Left(x1), ty_Char, x2)
new_esEs21(x0, x1, ty_Int)
new_esEs8(LT, LT)
new_esEs29(x0, x1, app(ty_[], x2))
new_compare30(x0, x1, ty_Float)
new_ltEs7(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs14(Right(x0), Right(x1), x2, ty_Bool)
new_esEs7(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs29(x0, x1, ty_Double)
new_compare9(x0, x1)
new_esEs6(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs10(Just(x0), Just(x1), ty_@0)
new_compare110(x0, x1, True, x2, x3)
new_esEs16(False, True)
new_esEs16(True, False)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs6(x0, x1, ty_Float)
new_lt9(x0, x1, ty_Bool)
new_esEs28(x0, x1, ty_Integer)
new_primCmpNat1(Zero, Zero)
new_esEs31(x0, x1, ty_Int)
new_compare112(x0, x1, True, x2)
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_ltEs11(LT, GT)
new_ltEs11(GT, LT)
new_esEs16(True, True)
new_ltEs20(x0, x1, ty_Double)
new_ltEs14(Left(x0), Right(x1), x2, x3)
new_ltEs14(Right(x0), Left(x1), x2, x3)
new_compare([], :(x0, x1), x2)
new_esEs27(x0, x1, ty_Int)
new_esEs20(x0, x1, ty_Char)
new_esEs19(x0, x1, ty_Double)
new_ltEs8(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs14([], :(x0, x1), x2)
new_ltEs10(Nothing, Just(x0), x1)
new_esEs14(:(x0, x1), [], x2)
new_lt19(x0, x1, ty_@0)
new_primEqNat0(Zero, Zero)
new_ltEs14(Left(x0), Left(x1), ty_Integer, x2)
new_compare16(x0, x1, x2, x3)
new_compare30(x0, x1, ty_Double)
new_esEs5(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs29(x0, x1, ty_Int)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt19(x0, x1, ty_Char)
new_esEs32(x0, x1, app(ty_[], x2))
new_ltEs14(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, ty_Double)
new_esEs22(x0, x1, ty_@0)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs12(x0, x1, app(app(ty_Either, x2), x3))
new_lt21(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_Ordering)
new_esEs22(x0, x1, ty_Float)
new_primMulNat0(Zero, Zero)
new_esEs6(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Double)
new_esEs30(x0, x1, x2, x3, True, x4, x5)
new_esEs21(x0, x1, ty_Ordering)
new_ltEs6(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_Bool)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Right(x0), Right(x1), x2, ty_Bool)
new_compare27(x0, x1)
new_esEs29(x0, x1, ty_Ordering)
new_compare17(x0, x1, False)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs20(x0, x1, app(ty_[], x2))
new_lt4(x0, x1)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs31(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, ty_Integer)
new_ltEs10(Just(x0), Just(x1), ty_Float)
new_ltEs4(x0, x1, x2)
new_esEs4(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs25(x0, x1, ty_Int)
new_ltEs19(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Float)
new_lt20(x0, x1, ty_Integer)
new_esEs27(x0, x1, ty_Float)
new_ltEs14(Left(x0), Left(x1), ty_Bool, x2)
new_esEs31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, ty_Int)
new_ltEs14(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs14(Left(x0), Left(x1), ty_Ordering, x2)
new_compare113(x0, x1, False, x2, x3, x4)
new_esEs19(x0, x1, ty_Ordering)
new_ltEs10(Just(x0), Just(x1), ty_Integer)
new_esEs7(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs10(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs6(Just(x0), Just(x1), ty_Double)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, ty_Char)
new_ltEs6(x0, x1, ty_Int)
new_ltEs14(Left(x0), Left(x1), ty_Char, x2)
new_compare111(x0, x1, x2, x3, False, x4, x5)
new_esEs12(x0, x1, ty_Bool)
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs12(x0, x1, ty_Char)
new_compare26(x0, x1, False)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Integer)
new_lt6(x0, x1)
new_primCompAux0(x0, x1, x2, x3)
new_compare111(x0, x1, x2, x3, True, x4, x5)
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs12(x0, x1, ty_@0)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt17(x0, x1)
new_esEs7(Left(x0), Left(x1), ty_Float, x2)
new_primCompAux00(x0, EQ)
new_lt19(x0, x1, ty_Double)
new_esEs28(x0, x1, ty_Char)
new_esEs20(x0, x1, ty_@0)
new_ltEs10(Just(x0), Just(x1), app(ty_Ratio, x2))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs6(Just(x0), Nothing, x1)
new_primMulNat0(Succ(x0), Zero)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_ltEs14(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs14(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs31(x0, x1, app(ty_Ratio, x2))
new_ltEs13(True, True)
new_esEs21(x0, x1, ty_Double)
new_esEs22(x0, x1, ty_Int)
new_ltEs10(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs19(x0, x1, ty_@0)
new_primPlusNat0(Zero, Zero)
new_compare25(x0, x1, False, x2, x3)
new_esEs6(Just(x0), Just(x1), ty_Bool)
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_lt19(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_ltEs13(False, False)
new_asAs(False, x0)
new_compare30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs12(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Bool)
new_esEs27(x0, x1, ty_Ordering)
new_primEqNat0(Succ(x0), Zero)
new_ltEs19(x0, x1, ty_@0)
new_esEs22(x0, x1, ty_Integer)
new_esEs6(Just(x0), Just(x1), ty_Integer)
new_compare13(x0, x1, x2)
new_esEs29(x0, x1, ty_Float)
new_esEs6(Just(x0), Just(x1), ty_Int)
new_esEs32(x0, x1, ty_Bool)
new_lt20(x0, x1, ty_Int)
new_esEs17(@0, @0)
new_esEs25(x0, x1, app(ty_[], x2))
new_ltEs13(False, True)
new_ltEs13(True, False)
new_esEs25(x0, x1, ty_Double)
new_ltEs14(Right(x0), Right(x1), x2, ty_Integer)
new_esEs32(x0, x1, ty_Char)
new_lt9(x0, x1, ty_Float)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, ty_@0)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare30(x0, x1, ty_Bool)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_compare30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs15(x0, x1)
new_ltEs19(x0, x1, ty_Float)
new_esEs27(x0, x1, ty_@0)
new_ltEs6(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs6(x0, x1, app(ty_Maybe, x2))
new_esEs20(x0, x1, ty_Integer)
new_esEs7(Left(x0), Left(x1), ty_@0, x2)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, ty_Bool)
new_compare(:(x0, x1), :(x2, x3), x4)
new_esEs7(Right(x0), Right(x1), x2, app(ty_[], x3))
new_compare30(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_Int)
new_lt7(x0, x1)
new_esEs7(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_compare14(x0, x1, x2, x3, True, x4, x5, x6)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Float)
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_compare29(x0, x1, True, x2)
new_compare15(x0, x1, True)
new_ltEs10(Just(x0), Just(x1), ty_Int)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, app(ty_[], x2))
new_lt16(x0, x1, x2, x3)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_compare23(x0, x1, True, x2, x3)
new_esEs31(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_@0)
new_esEs26(x0, x1, ty_@0)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, ty_Float)
new_esEs6(Just(x0), Just(x1), app(ty_[], x2))
new_esEs24(x0, x1, ty_Integer)
new_esEs7(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs20(x0, x1, ty_Char)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_sr0(x0, x1)
new_esEs29(x0, x1, ty_Integer)
new_primMulInt(Neg(x0), Neg(x1))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_compare17(x0, x1, True)
new_compare([], [], x0)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_lt9(x0, x1, app(app(ty_@2, x2), x3))
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs25(x0, x1, ty_Ordering)
new_primPlusNat0(Succ(x0), Succ(x1))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_lt9(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare6(:%(x0, x1), :%(x2, x3), ty_Int)
new_compare30(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, app(ty_[], x2))
new_ltEs18(x0, x1)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs14(Left(x0), Left(x1), ty_Float, x2)
new_lt20(x0, x1, ty_Bool)
new_esEs12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs7(Left(x0), Left(x1), ty_Double, x2)
new_esEs22(x0, x1, ty_Char)
new_esEs29(x0, x1, ty_Char)
new_esEs7(Left(x0), Right(x1), x2, x3)
new_esEs7(Right(x0), Left(x1), x2, x3)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_primCmpNat0(x0, Succ(x1))
new_esEs7(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs32(x0, x1, ty_Float)
new_ltEs14(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_primCmpNat1(Succ(x0), Succ(x1))
new_esEs28(x0, x1, ty_Bool)
new_esEs7(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs10(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs6(x0, x1, app(ty_[], x2))
new_compare10(Char(x0), Char(x1))
new_compare30(x0, x1, ty_@0)
new_lt19(x0, x1, ty_Float)
new_esEs13(Float(x0, x1), Float(x2, x3))
new_lt21(x0, x1, ty_Ordering)
new_compare112(x0, x1, False, x2)
new_lt21(x0, x1, app(app(ty_Either, x2), x3))
new_lt9(x0, x1, ty_Double)
new_ltEs12(x0, x1)
new_esEs26(x0, x1, ty_Double)
new_lt9(x0, x1, ty_Char)
new_esEs32(x0, x1, app(ty_Ratio, x2))
new_primPlusNat0(Zero, Succ(x0))
new_ltEs11(LT, LT)
new_compare(:(x0, x1), [], x2)
new_ltEs14(Left(x0), Left(x1), ty_Double, x2)
new_ltEs10(Just(x0), Just(x1), ty_Ordering)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_esEs25(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Int)
new_esEs7(Left(x0), Left(x1), ty_Int, x2)
new_ltEs11(EQ, LT)
new_ltEs11(LT, EQ)
new_esEs20(x0, x1, ty_Ordering)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs6(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs5(x0, x1, x2)
new_esEs19(x0, x1, ty_Char)
new_compare113(x0, x1, True, x2, x3, x4)
new_ltEs6(x0, x1, ty_Double)
new_compare29(x0, x1, False, x2)
new_ltEs14(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs19(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, ty_Integer)
new_ltEs16(x0, x1)
new_compare210(x0, x1, False, x2, x3, x4)
new_esEs12(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primPlusNat0(Succ(x0), Zero)
new_esEs30(x0, x1, x2, x3, False, x4, x5)
new_compare15(x0, x1, False)
new_esEs7(Left(x0), Left(x1), ty_Bool, x2)
new_primCmpNat2(Zero, x0)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs32(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, ty_Integer)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, ty_Integer)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_ltEs14(Left(x0), Left(x1), ty_Int, x2)
new_ltEs6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Bool)
new_lt9(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1, ty_Ordering)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_pePe(False, x0)
new_lt20(x0, x1, ty_Char)
new_esEs29(x0, x1, ty_@0)
new_esEs31(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Bool)
new_esEs32(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs20(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Ordering)
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_esEs25(x0, x1, ty_Integer)
new_esEs16(False, False)
new_compare30(x0, x1, app(app(ty_@2, x2), x3))
new_esEs31(x0, x1, ty_@0)
new_ltEs20(x0, x1, ty_Int)
new_esEs20(x0, x1, app(ty_[], x2))
new_lt21(x0, x1, ty_@0)
new_esEs15(Integer(x0), Integer(x1))
new_esEs24(x0, x1, ty_Int)
new_esEs9(Double(x0, x1), Double(x2, x3))
new_ltEs14(Right(x0), Right(x1), x2, ty_Float)
new_primEqNat0(Zero, Succ(x0))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs14(:(x0, x1), :(x2, x3), x4)
new_lt21(x0, x1, ty_Integer)
new_lt9(x0, x1, ty_@0)
new_sr(Integer(x0), Integer(x1))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_lt21(x0, x1, app(ty_[], x2))
new_esEs12(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs32(x0, x1, ty_Double)
new_esEs32(x0, x1, app(ty_Maybe, x2))
new_esEs31(x0, x1, ty_Char)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_lt13(x0, x1, x2)
new_esEs22(x0, x1, ty_Ordering)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs12(x0, x1, app(ty_Ratio, x2))
new_esEs10(x0, x1)
new_not(True)
new_ltEs9(x0, x1)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_compare24(x0, x1, False)
new_esEs7(Right(x0), Right(x1), x2, ty_Float)
new_esEs12(x0, x1, ty_Float)
new_lt14(x0, x1)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs25(x0, x1, ty_@0)
new_esEs32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_not(False)
new_esEs7(Right(x0), Right(x1), x2, ty_@0)
new_esEs6(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare23(@2(x0, x1), @2(x2, x3), False, x4, x5)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt9(x0, x1, app(ty_Maybe, x2))
new_esEs32(x0, x1, ty_@0)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_compare7(Integer(x0), Integer(x1))
new_primCmpNat2(Succ(x0), x1)
new_primPlusNat1(Succ(x0), x1)
new_compare110(x0, x1, False, x2, x3)
new_esEs6(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_@0)
new_primPlusNat1(Zero, x0)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, ty_Float)
new_compare24(x0, x1, True)
new_compare30(x0, x1, ty_Int)
new_pePe(True, x0)
new_compare210(x0, x1, True, x2, x3, x4)
new_lt11(x0, x1, x2, x3, x4)
new_esEs25(x0, x1, ty_Float)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_lt18(x0, x1)
new_esEs7(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs19(x0, x1, ty_Bool)
new_ltEs10(Nothing, Nothing, x0)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_compare19(@0, @0)
new_ltEs20(x0, x1, ty_Ordering)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs11(Char(x0), Char(x1))
new_ltEs6(x0, x1, ty_Ordering)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_esEs7(Right(x0), Right(x1), x2, ty_Char)
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_lt19(x0, x1, ty_Bool)
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_esEs32(x0, x1, ty_Int)
new_lt9(x0, x1, ty_Ordering)
new_compare28(x0, x1, x2, x3, x4)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare30(x0, x1, ty_Ordering)
new_esEs20(x0, x1, ty_Int)
new_esEs32(x0, x1, ty_Ordering)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_primMulNat0(Zero, Succ(x0))
new_lt21(x0, x1, ty_Bool)
new_ltEs6(x0, x1, ty_Char)
new_ltEs20(x0, x1, ty_Integer)
new_ltEs6(x0, x1, ty_Bool)
new_lt12(x0, x1)
new_compare30(x0, x1, app(ty_[], x2))
new_esEs7(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs6(Nothing, Just(x0), x1)
new_esEs27(x0, x1, ty_Double)
new_esEs26(x0, x1, ty_Char)
new_lt9(x0, x1, ty_Integer)
new_esEs31(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs31(x0, x1, ty_Integer)
new_esEs19(x0, x1, ty_Float)
new_asAs(True, x0)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_ltEs19(x0, x1, ty_Integer)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_compare12(x0, x1, x2, x3)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs12(x0, x1, ty_Int)
new_esEs19(x0, x1, ty_Integer)
new_ltEs14(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_primCompAux00(x0, GT)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs31(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs10(Just(x0), Just(x1), ty_Double)
new_esEs28(x0, x1, ty_@0)
new_esEs6(Just(x0), Just(x1), ty_@0)
new_esEs12(x0, x1, app(app(ty_@2, x2), x3))
new_esEs12(x0, x1, ty_Double)
new_lt21(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, ty_Int)
new_ltEs14(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_ltEs6(x0, x1, ty_Integer)
new_lt21(x0, x1, ty_Double)
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs19(x0, x1, ty_Bool)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs29(x0, x1, ty_Bool)
new_compare30(x0, x1, ty_Integer)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs6(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs14(Right(x0), Right(x1), x2, ty_Double)
new_ltEs10(Just(x0), Just(x1), ty_Bool)
new_ltEs10(Just(x0), Nothing, x1)
new_lt15(x0, x1)
new_compare25(x0, x1, True, x2, x3)
new_compare6(:%(x0, x1), :%(x2, x3), ty_Integer)
new_ltEs14(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs31(x0, x1, ty_Double)
new_esEs21(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_Double)
new_ltEs11(GT, GT)

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

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



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

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

new_foldl(xuu3, :(xuu50, xuu51), h, ba, bb) → new_foldl(xuu3, xuu51, h, ba, bb)

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: