YES 9.091 H-Termination proof of /home/matraf/haskell/eval_FullyBlown_Fast/FiniteMap.hs
H-Termination of the given Haskell-Program with start terms could successfully be proven:



HASKELL
  ↳ LR

mainModule FiniteMap
  ((addToFM_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 b a = EmptyFM  | Branch b a Int (FiniteMap b a) (FiniteMap b a


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

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

  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 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
  ((addToFM_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

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

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

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

  sIZE_RATIO :: Int
sIZE_RATIO 5

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude



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

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

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

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

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

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

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

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

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

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



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
HASKELL
          ↳ IFR

mainModule FiniteMap
  ((addToFM_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 b a = EmptyFM  | Branch b a Int (FiniteMap b a) (FiniteMap b a


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

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

  emptyFM :: FiniteMap b a
emptyFM EmptyFM

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

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

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

  
fmToList0 key elt rest (key,elt: rest

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

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

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

  sIZE_RATIO :: Int
sIZE_RATIO 5

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude



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

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

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

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



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

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

module FiniteMap where
  import qualified Maybe
import qualified Prelude

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


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

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

  emptyFM :: FiniteMap a b
emptyFM EmptyFM

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

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

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

  
fmToList0 key elt rest (key,elt: rest

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

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

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

  sIZE_RATIO :: Int
sIZE_RATIO 5

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude



Replaced joker patterns by fresh variables and removed binding patterns.

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

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

  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 xx xy EmptyFM(key,elt)
findMax (Branch key elt xz yu 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 :: (b  ->  a  ->  c  ->  c ->  c  ->  FiniteMap b a  ->  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 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 zz (Branch key_rl elt_rl vuu 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 zu fm_ll (Branch key_lr elt_lr zv 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 vuv vuw vux 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 zw zx zy 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 vuy 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 yz fm_ll fm_lrfm_r mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r)
size_l sizeFM fm_L
size_r sizeFM fm_R

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

  sIZE_RATIO :: Int
sIZE_RATIO 5

  sizeFM :: FiniteMap b a  ->  Int
sizeFM EmptyFM 0
sizeFM (Branch yv yw size yx yysize

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

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

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

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

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

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

addToFM_C4 combiner EmptyFM key elt = unitFM key elt
addToFM_C4 vzy vzz wuu wuv = addToFM_C3 vzy vzz wuu wuv

The following Function with conditions
mkBalBranch1 fm_L fm_R (Branch zw zx zy 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 zw zx zy fm_ll fm_lr) = mkBalBranch12 fm_L fm_R (Branch zw zx zy fm_ll fm_lr)

mkBalBranch11 fm_L fm_R zw zx zy fm_ll fm_lr True = single_R fm_L fm_R
mkBalBranch11 fm_L fm_R zw zx zy fm_ll fm_lr False = mkBalBranch10 fm_L fm_R zw zx zy fm_ll fm_lr otherwise

mkBalBranch10 fm_L fm_R zw zx zy fm_ll fm_lr True = double_R fm_L fm_R

mkBalBranch12 fm_L fm_R (Branch zw zx zy fm_ll fm_lr) = mkBalBranch11 fm_L fm_R zw zx zy fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll)

The following Function with conditions
mkBalBranch0 fm_L fm_R (Branch vuv vuw vux 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 vuv vuw vux fm_rl fm_rr) = mkBalBranch02 fm_L fm_R (Branch vuv vuw vux fm_rl fm_rr)

mkBalBranch01 fm_L fm_R vuv vuw vux fm_rl fm_rr True = single_L fm_L fm_R
mkBalBranch01 fm_L fm_R vuv vuw vux fm_rl fm_rr False = mkBalBranch00 fm_L fm_R vuv vuw vux fm_rl fm_rr otherwise

mkBalBranch00 fm_L fm_R vuv vuw vux fm_rl fm_rr True = double_L fm_L fm_R

mkBalBranch02 fm_L fm_R (Branch vuv vuw vux fm_rl fm_rr) = mkBalBranch01 fm_L fm_R vuv vuw vux 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 zz (Branch key_rl elt_rl vuu 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 zu fm_ll (Branch key_lr elt_lr zv 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 vuv vuw vux 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 zw zx zy 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 vuy 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 yz 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 zz (Branch key_rl elt_rl vuu 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 zu fm_ll (Branch key_lr elt_lr zv 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 vuv vuw vux fm_rl fm_rr) = mkBalBranch02 fm_L fm_R (Branch vuv vuw vux fm_rl fm_rr)
mkBalBranch00 fm_L fm_R vuv vuw vux fm_rl fm_rr True = double_L fm_L fm_R
mkBalBranch01 fm_L fm_R vuv vuw vux fm_rl fm_rr True = single_L fm_L fm_R
mkBalBranch01 fm_L fm_R vuv vuw vux fm_rl fm_rr False = mkBalBranch00 fm_L fm_R vuv vuw vux fm_rl fm_rr otherwise
mkBalBranch02 fm_L fm_R (Branch vuv vuw vux fm_rl fm_rr) = mkBalBranch01 fm_L fm_R vuv vuw vux fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr)
mkBalBranch1 fm_L fm_R (Branch zw zx zy fm_ll fm_lr) = mkBalBranch12 fm_L fm_R (Branch zw zx zy fm_ll fm_lr)
mkBalBranch10 fm_L fm_R zw zx zy fm_ll fm_lr True = double_R fm_L fm_R
mkBalBranch11 fm_L fm_R zw zx zy fm_ll fm_lr True = single_R fm_L fm_R
mkBalBranch11 fm_L fm_R zw zx zy fm_ll fm_lr False = mkBalBranch10 fm_L fm_R zw zx zy fm_ll fm_lr otherwise
mkBalBranch12 fm_L fm_R (Branch zw zx zy fm_ll fm_lr) = mkBalBranch11 fm_L fm_R zw zx zy 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 vuy 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 yz 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
compare x y
 | x == y
 = EQ
 | x <= y
 = LT
 | otherwise
 = GT

is transformed to
compare x y = compare3 x y

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

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

compare0 x y True = GT

compare3 x y = compare2 x y (x == y)

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

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

gcd'0 x y = gcd' y (x `rem` y)

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

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

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

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

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

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

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

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

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

is transformed to
absReal x = absReal2 x

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

absReal0 x True = `negate` x

absReal2 x = absReal1 x (x >= 0)

The following Function with conditions
undefined 
 | False
 = undefined

is transformed to
undefined  = undefined1

undefined0 True = undefined

undefined1  = undefined0 False

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

is transformed to
reduce x y = reduce2 x y

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



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

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

module FiniteMap where
  import qualified Maybe
import qualified Prelude

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


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

  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 vzy vzz wuu wuv addToFM_C3 vzy vzz wuu wuv

  emptyFM :: FiniteMap a b
emptyFM EmptyFM

  findMax :: FiniteMap a b  ->  (a,b)
findMax (Branch key elt xx xy EmptyFM(key,elt)
findMax (Branch key elt xz yu fm_rfindMax fm_r

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

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

  
fmToList0 key elt rest (key,elt: rest

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

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

  
mkBalBranch6 key elt fm_L fm_R 
mkBalBranch5 key elt fm_L fm_R (size_l + size_r < 2) where 
double_L fm_l (Branch key_r elt_r zz (Branch key_rl elt_rl vuu 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 zu fm_ll (Branch key_lr elt_lr zv 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 vuv vuw vux fm_rl fm_rrmkBalBranch02 fm_L fm_R (Branch vuv vuw vux fm_rl fm_rr)
mkBalBranch00 fm_L fm_R vuv vuw vux fm_rl fm_rr True double_L fm_L fm_R
mkBalBranch01 fm_L fm_R vuv vuw vux fm_rl fm_rr True single_L fm_L fm_R
mkBalBranch01 fm_L fm_R vuv vuw vux fm_rl fm_rr False mkBalBranch00 fm_L fm_R vuv vuw vux fm_rl fm_rr otherwise
mkBalBranch02 fm_L fm_R (Branch vuv vuw vux fm_rl fm_rrmkBalBranch01 fm_L fm_R vuv vuw vux fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr)
mkBalBranch1 fm_L fm_R (Branch zw zx zy fm_ll fm_lrmkBalBranch12 fm_L fm_R (Branch zw zx zy fm_ll fm_lr)
mkBalBranch10 fm_L fm_R zw zx zy fm_ll fm_lr True double_R fm_L fm_R
mkBalBranch11 fm_L fm_R zw zx zy fm_ll fm_lr True single_R fm_L fm_R
mkBalBranch11 fm_L fm_R zw zx zy fm_ll fm_lr False mkBalBranch10 fm_L fm_R zw zx zy fm_ll fm_lr otherwise
mkBalBranch12 fm_L fm_R (Branch zw zx zy fm_ll fm_lrmkBalBranch11 fm_L fm_R zw zx zy 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 vuy 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 yz fm_ll fm_lrfm_r mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r)
size_l sizeFM fm_L
size_r sizeFM fm_R

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

  sIZE_RATIO :: Int
sIZE_RATIO 5

  sizeFM :: FiniteMap a b  ->  Int
sizeFM EmptyFM 0
sizeFM (Branch yv yw size yx yysize

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude



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

are unpacked to the following functions on top level
mkBranchLeft_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_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

mkBranchLeft_size wxw wxx wxy = sizeFM wxw

mkBranchBalance_ok wxw wxx wxy = True

mkBranchUnbox wxw wxx wxy x = x

mkBranchRight_size wxw wxx wxy = sizeFM wxx

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

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

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 wyw wxz (1 + mkBranchLeft_size wyv wyw wxz + mkBranchRight_size wyv wyw wxz)) 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 zz (Branch key_rl elt_rl vuu 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 zu fm_ll (Branch key_lr elt_lr zv 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 vuv vuw vux fm_rl fm_rr) = mkBalBranch02 fm_L fm_R (Branch vuv vuw vux fm_rl fm_rr)
mkBalBranch00 fm_L fm_R vuv vuw vux fm_rl fm_rr True = double_L fm_L fm_R
mkBalBranch01 fm_L fm_R vuv vuw vux fm_rl fm_rr True = single_L fm_L fm_R
mkBalBranch01 fm_L fm_R vuv vuw vux fm_rl fm_rr False = mkBalBranch00 fm_L fm_R vuv vuw vux fm_rl fm_rr otherwise
mkBalBranch02 fm_L fm_R (Branch vuv vuw vux fm_rl fm_rr) = mkBalBranch01 fm_L fm_R vuv vuw vux fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr)
mkBalBranch1 fm_L fm_R (Branch zw zx zy fm_ll fm_lr) = mkBalBranch12 fm_L fm_R (Branch zw zx zy fm_ll fm_lr)
mkBalBranch10 fm_L fm_R zw zx zy fm_ll fm_lr True = double_R fm_L fm_R
mkBalBranch11 fm_L fm_R zw zx zy fm_ll fm_lr True = single_R fm_L fm_R
mkBalBranch11 fm_L fm_R zw zx zy fm_ll fm_lr False = mkBalBranch10 fm_L fm_R zw zx zy fm_ll fm_lr otherwise
mkBalBranch12 fm_L fm_R (Branch zw zx zy fm_ll fm_lr) = mkBalBranch11 fm_L fm_R zw zx zy 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 vuy 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 yz 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
mkBalBranch6MkBalBranch01 wyx wyy wyz wzu fm_L fm_R vuv vuw vux fm_rl fm_rr True = mkBalBranch6Single_L wyx wyy wyz wzu fm_L fm_R
mkBalBranch6MkBalBranch01 wyx wyy wyz wzu fm_L fm_R vuv vuw vux fm_rl fm_rr False = mkBalBranch6MkBalBranch00 wyx wyy wyz wzu fm_L fm_R vuv vuw vux fm_rl fm_rr otherwise

mkBalBranch6MkBalBranch1 wyx wyy wyz wzu fm_L fm_R (Branch zw zx zy fm_ll fm_lr) = mkBalBranch6MkBalBranch12 wyx wyy wyz wzu fm_L fm_R (Branch zw zx zy fm_ll fm_lr)

mkBalBranch6MkBalBranch02 wyx wyy wyz wzu fm_L fm_R (Branch vuv vuw vux fm_rl fm_rr) = mkBalBranch6MkBalBranch01 wyx wyy wyz wzu fm_L fm_R vuv vuw vux fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr)

mkBalBranch6MkBalBranch0 wyx wyy wyz wzu fm_L fm_R (Branch vuv vuw vux fm_rl fm_rr) = mkBalBranch6MkBalBranch02 wyx wyy wyz wzu fm_L fm_R (Branch vuv vuw vux fm_rl fm_rr)

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

mkBalBranch6MkBalBranch11 wyx wyy wyz wzu fm_L fm_R zw zx zy fm_ll fm_lr True = mkBalBranch6Single_R wyx wyy wyz wzu fm_L fm_R
mkBalBranch6MkBalBranch11 wyx wyy wyz wzu fm_L fm_R zw zx zy fm_ll fm_lr False = mkBalBranch6MkBalBranch10 wyx wyy wyz wzu fm_L fm_R zw zx zy fm_ll fm_lr otherwise

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 vuy fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 wyx wyy fm_l fm_rlfm_rr

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_l wyx wyy wyz wzu = sizeFM wyz

mkBalBranch6Double_R wyx wyy wyz wzu (Branch key_l elt_l zu fm_ll (Branch key_lr elt_lr zv 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)

mkBalBranch6Size_r wyx wyy wyz wzu = sizeFM wzu

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

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

mkBalBranch6MkBalBranch00 wyx wyy wyz wzu fm_L fm_R vuv vuw vux fm_rl fm_rr True = mkBalBranch6Double_L wyx wyy wyz wzu fm_L fm_R

mkBalBranch6MkBalBranch10 wyx wyy wyz wzu fm_L fm_R zw zx zy fm_ll fm_lr True = mkBalBranch6Double_R wyx wyy wyz wzu fm_L fm_R

mkBalBranch6Double_L wyx wyy wyz wzu fm_l (Branch key_r elt_r zz (Branch key_rl elt_rl vuu 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)

mkBalBranch6MkBalBranch12 wyx wyy wyz wzu fm_L fm_R (Branch zw zx zy fm_ll fm_lr) = mkBalBranch6MkBalBranch11 wyx wyy wyz wzu fm_L fm_R zw zx zy fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll)

The bindings of the following Let/Where expression
let 
biggest_left_key  = fst (findMax fm_l)
in biggest_left_key < key

are unpacked to the following functions on top level
mkBranchLeft_ok0Biggest_left_key wzv = fst (findMax wzv)

The bindings of the following Let/Where expression
let 
smallest_right_key  = fst (findMin fm_r)
in key < smallest_right_key

are unpacked to the following functions on top level
mkBranchRight_ok0Smallest_right_key wzw = fst (findMin wzw)

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

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

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

reduce2D wzx wzy = gcd wzx wzy

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

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

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

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

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



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

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

  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 vzy vzz wuu wuv addToFM_C3 vzy vzz wuu wuv

  emptyFM :: FiniteMap b a
emptyFM EmptyFM

  findMax :: FiniteMap a b  ->  (a,b)
findMax (Branch key elt xx xy EmptyFM(key,elt)
findMax (Branch key elt xz yu 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 :: (b  ->  a  ->  c  ->  c ->  c  ->  FiniteMap b a  ->  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 mkBalBranch6 key elt fm_L fm_R

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

  
mkBalBranch6Double_L wyx wyy wyz wzu fm_l (Branch key_r elt_r zz (Branch key_rl elt_rl vuu 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 zu fm_ll (Branch key_lr elt_lr zv 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 vuv vuw vux fm_rl fm_rrmkBalBranch6MkBalBranch02 wyx wyy wyz wzu fm_L fm_R (Branch vuv vuw vux fm_rl fm_rr)

  
mkBalBranch6MkBalBranch00 wyx wyy wyz wzu fm_L fm_R vuv vuw vux fm_rl fm_rr True mkBalBranch6Double_L wyx wyy wyz wzu fm_L fm_R

  
mkBalBranch6MkBalBranch01 wyx wyy wyz wzu fm_L fm_R vuv vuw vux fm_rl fm_rr True mkBalBranch6Single_L wyx wyy wyz wzu fm_L fm_R
mkBalBranch6MkBalBranch01 wyx wyy wyz wzu fm_L fm_R vuv vuw vux fm_rl fm_rr False mkBalBranch6MkBalBranch00 wyx wyy wyz wzu fm_L fm_R vuv vuw vux fm_rl fm_rr otherwise

  
mkBalBranch6MkBalBranch02 wyx wyy wyz wzu fm_L fm_R (Branch vuv vuw vux fm_rl fm_rrmkBalBranch6MkBalBranch01 wyx wyy wyz wzu fm_L fm_R vuv vuw vux fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr)

  
mkBalBranch6MkBalBranch1 wyx wyy wyz wzu fm_L fm_R (Branch zw zx zy fm_ll fm_lrmkBalBranch6MkBalBranch12 wyx wyy wyz wzu fm_L fm_R (Branch zw zx zy fm_ll fm_lr)

  
mkBalBranch6MkBalBranch10 wyx wyy wyz wzu fm_L fm_R zw zx zy fm_ll fm_lr True mkBalBranch6Double_R wyx wyy wyz wzu fm_L fm_R

  
mkBalBranch6MkBalBranch11 wyx wyy wyz wzu fm_L fm_R zw zx zy fm_ll fm_lr True mkBalBranch6Single_R wyx wyy wyz wzu fm_L fm_R
mkBalBranch6MkBalBranch11 wyx wyy wyz wzu fm_L fm_R zw zx zy fm_ll fm_lr False mkBalBranch6MkBalBranch10 wyx wyy wyz wzu fm_L fm_R zw zx zy fm_ll fm_lr otherwise

  
mkBalBranch6MkBalBranch12 wyx wyy wyz wzu fm_L fm_R (Branch zw zx zy fm_ll fm_lrmkBalBranch6MkBalBranch11 wyx wyy wyz wzu fm_L fm_R zw zx zy 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 vuy 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 yz fm_ll fm_lrfm_r mkBranch 8 key_l elt_l fm_ll (mkBranch 9 wyx wyy fm_lr fm_r)

  
mkBalBranch6Size_l wyx wyy wyz wzu sizeFM wyz

  
mkBalBranch6Size_r wyx wyy wyz wzu sizeFM wzu

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

  
mkBranchBalance_ok wxw wxx wxy True

  
mkBranchLeft_ok wxw wxx wxy mkBranchLeft_ok0 wxw wxx wxy wxw wxy wxw

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

  
mkBranchLeft_ok0Biggest_left_key wzv fst (findMax wzv)

  
mkBranchLeft_size wxw wxx wxy sizeFM wxw

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

  
mkBranchRight_ok wxw wxx wxy mkBranchRight_ok0 wxw wxx wxy wxx wxy wxx

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

  
mkBranchRight_ok0Smallest_right_key wzw fst (findMin wzw)

  
mkBranchRight_size wxw wxx wxy sizeFM wxx

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

  sIZE_RATIO :: Int
sIZE_RATIO 5

  sizeFM :: FiniteMap b a  ->  Int
sizeFM EmptyFM 0
sizeFM (Branch yv yw size yx yysize

  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
  (addToFM_C :: (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

  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 vzy vzz wuu wuv addToFM_C3 vzy vzz wuu wuv

  emptyFM :: FiniteMap b a
emptyFM EmptyFM

  findMax :: FiniteMap b a  ->  (b,a)
findMax (Branch key elt xx xy EmptyFM(key,elt)
findMax (Branch key elt xz yu fm_rfindMax fm_r

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

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

  
fmToList0 key elt rest (key,elt: rest

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

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

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

  
mkBalBranch6Double_L wyx wyy wyz wzu fm_l (Branch key_r elt_r zz (Branch key_rl elt_rl vuu 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 zu fm_ll (Branch key_lr elt_lr zv 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 vuv vuw vux fm_rl fm_rrmkBalBranch6MkBalBranch02 wyx wyy wyz wzu fm_L fm_R (Branch vuv vuw vux fm_rl fm_rr)

  
mkBalBranch6MkBalBranch00 wyx wyy wyz wzu fm_L fm_R vuv vuw vux fm_rl fm_rr True mkBalBranch6Double_L wyx wyy wyz wzu fm_L fm_R

  
mkBalBranch6MkBalBranch01 wyx wyy wyz wzu fm_L fm_R vuv vuw vux fm_rl fm_rr True mkBalBranch6Single_L wyx wyy wyz wzu fm_L fm_R
mkBalBranch6MkBalBranch01 wyx wyy wyz wzu fm_L fm_R vuv vuw vux fm_rl fm_rr False mkBalBranch6MkBalBranch00 wyx wyy wyz wzu fm_L fm_R vuv vuw vux fm_rl fm_rr otherwise

  
mkBalBranch6MkBalBranch02 wyx wyy wyz wzu fm_L fm_R (Branch vuv vuw vux fm_rl fm_rrmkBalBranch6MkBalBranch01 wyx wyy wyz wzu fm_L fm_R vuv vuw vux fm_rl fm_rr (sizeFM fm_rl < Pos (Succ (Succ Zero)) * sizeFM fm_rr)

  
mkBalBranch6MkBalBranch1 wyx wyy wyz wzu fm_L fm_R (Branch zw zx zy fm_ll fm_lrmkBalBranch6MkBalBranch12 wyx wyy wyz wzu fm_L fm_R (Branch zw zx zy fm_ll fm_lr)

  
mkBalBranch6MkBalBranch10 wyx wyy wyz wzu fm_L fm_R zw zx zy fm_ll fm_lr True mkBalBranch6Double_R wyx wyy wyz wzu fm_L fm_R

  
mkBalBranch6MkBalBranch11 wyx wyy wyz wzu fm_L fm_R zw zx zy fm_ll fm_lr True mkBalBranch6Single_R wyx wyy wyz wzu fm_L fm_R
mkBalBranch6MkBalBranch11 wyx wyy wyz wzu fm_L fm_R zw zx zy fm_ll fm_lr False mkBalBranch6MkBalBranch10 wyx wyy wyz wzu fm_L fm_R zw zx zy fm_ll fm_lr otherwise

  
mkBalBranch6MkBalBranch12 wyx wyy wyz wzu fm_L fm_R (Branch zw zx zy fm_ll fm_lrmkBalBranch6MkBalBranch11 wyx wyy wyz wzu fm_L fm_R zw zx zy 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 vuy 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 yz fm_ll fm_lrfm_r mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))) key_l elt_l fm_ll (mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))) wyx wyy fm_lr fm_r)

  
mkBalBranch6Size_l wyx wyy wyz wzu sizeFM wyz

  
mkBalBranch6Size_r wyx wyy wyz wzu sizeFM wzu

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

  
mkBranchBalance_ok wxw wxx wxy True

  
mkBranchLeft_ok wxw wxx wxy mkBranchLeft_ok0 wxw wxx wxy wxw wxy wxw

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

  
mkBranchLeft_ok0Biggest_left_key wzv fst (findMax wzv)

  
mkBranchLeft_size wxw wxx wxy sizeFM wxw

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

  
mkBranchRight_ok wxw wxx wxy mkBranchRight_ok0 wxw wxx wxy wxx wxy wxx

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

  
mkBranchRight_ok0Smallest_right_key wzw fst (findMin wzw)

  
mkBranchRight_size wxw wxx wxy sizeFM wxx

  mkBranchUnbox :: Ord a =>  ->  (FiniteMap a b) ( ->  (FiniteMap a b) ( ->  a (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 yv yw size yx yysize

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude



Haskell To QDPs


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

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

new_primEqNat(Succ(wzz5000), Succ(wzz40000)) → new_primEqNat(wzz5000, wzz40000)

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

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



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

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

new_primCmpNat(Succ(wzz50000), Succ(wzz52000)) → new_primCmpNat(wzz50000, wzz52000)

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

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



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

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

new_primMinusNat(Succ(wzz42200), Succ(wzz9600)) → new_primMinusNat(wzz42200, wzz9600)

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

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



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

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

new_primPlusNat(Succ(wzz42200), Succ(wzz9600)) → new_primPlusNat(wzz42200, wzz9600)

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

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



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

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

new_primMulNat(Succ(wzz50000), Succ(wzz400000)) → new_primMulNat(wzz50000, Succ(wzz400000))

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

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



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

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

new_esEs1(Left(wzz500), Left(wzz4000), app(app(ty_@2, hb), hc), gc) → new_esEs3(wzz500, wzz4000, hb, hc)
new_esEs0(@3(wzz500, wzz501, wzz502), @3(wzz4000, wzz4001, wzz4002), df, cc, app(app(ty_@2, fh), ga)) → new_esEs3(wzz502, wzz4002, fh, ga)
new_esEs0(@3(wzz500, wzz501, wzz502), @3(wzz4000, wzz4001, wzz4002), df, cc, app(app(ty_Either, fd), ff)) → new_esEs1(wzz502, wzz4002, fd, ff)
new_esEs2(Just(wzz500), Just(wzz4000), app(ty_[], baf)) → new_esEs(wzz500, wzz4000, baf)
new_esEs3(@2(wzz500, wzz501), @2(wzz4000, wzz4001), app(app(ty_Either, bcd), bce), bbh) → new_esEs1(wzz500, wzz4000, bcd, bce)
new_esEs3(@2(wzz500, wzz501), @2(wzz4000, wzz4001), bda, app(ty_Maybe, bdh)) → new_esEs2(wzz501, wzz4001, bdh)
new_esEs1(Left(wzz500), Left(wzz4000), app(app(app(ty_@3, gd), ge), gf), gc) → new_esEs0(wzz500, wzz4000, gd, ge, gf)
new_esEs0(@3(wzz500, wzz501, wzz502), @3(wzz4000, wzz4001, wzz4002), df, cc, app(ty_Maybe, fg)) → new_esEs2(wzz502, wzz4002, fg)
new_esEs0(@3(wzz500, wzz501, wzz502), @3(wzz4000, wzz4001, wzz4002), app(app(ty_Either, da), db), cc, cd) → new_esEs1(wzz500, wzz4000, da, db)
new_esEs0(@3(wzz500, wzz501, wzz502), @3(wzz4000, wzz4001, wzz4002), app(ty_Maybe, dc), cc, cd) → new_esEs2(wzz500, wzz4000, dc)
new_esEs1(Right(wzz500), Right(wzz4000), hd, app(app(app(ty_@3, hf), hg), hh)) → new_esEs0(wzz500, wzz4000, hf, hg, hh)
new_esEs3(@2(wzz500, wzz501), @2(wzz4000, wzz4001), app(ty_[], bbg), bbh) → new_esEs(wzz500, wzz4000, bbg)
new_esEs3(@2(wzz500, wzz501), @2(wzz4000, wzz4001), app(app(app(ty_@3, bca), bcb), bcc), bbh) → new_esEs0(wzz500, wzz4000, bca, bcb, bcc)
new_esEs1(Left(wzz500), Left(wzz4000), app(app(ty_Either, gg), gh), gc) → new_esEs1(wzz500, wzz4000, gg, gh)
new_esEs2(Just(wzz500), Just(wzz4000), app(ty_Maybe, bbd)) → new_esEs2(wzz500, wzz4000, bbd)
new_esEs1(Right(wzz500), Right(wzz4000), hd, app(app(ty_Either, baa), bab)) → new_esEs1(wzz500, wzz4000, baa, bab)
new_esEs0(@3(wzz500, wzz501, wzz502), @3(wzz4000, wzz4001, wzz4002), df, app(app(app(ty_@3, dh), ea), eb), cd) → new_esEs0(wzz501, wzz4001, dh, ea, eb)
new_esEs0(@3(wzz500, wzz501, wzz502), @3(wzz4000, wzz4001, wzz4002), df, cc, app(ty_[], eh)) → new_esEs(wzz502, wzz4002, eh)
new_esEs0(@3(wzz500, wzz501, wzz502), @3(wzz4000, wzz4001, wzz4002), df, app(app(ty_Either, ec), ed), cd) → new_esEs1(wzz501, wzz4001, ec, ed)
new_esEs(:(wzz500, wzz501), :(wzz4000, wzz4001), app(ty_Maybe, bf)) → new_esEs2(wzz500, wzz4000, bf)
new_esEs0(@3(wzz500, wzz501, wzz502), @3(wzz4000, wzz4001, wzz4002), df, app(app(ty_@2, ef), eg), cd) → new_esEs3(wzz501, wzz4001, ef, eg)
new_esEs3(@2(wzz500, wzz501), @2(wzz4000, wzz4001), bda, app(ty_[], bdb)) → new_esEs(wzz501, wzz4001, bdb)
new_esEs3(@2(wzz500, wzz501), @2(wzz4000, wzz4001), bda, app(app(ty_@2, bea), beb)) → new_esEs3(wzz501, wzz4001, bea, beb)
new_esEs2(Just(wzz500), Just(wzz4000), app(app(app(ty_@3, bag), bah), bba)) → new_esEs0(wzz500, wzz4000, bag, bah, bba)
new_esEs0(@3(wzz500, wzz501, wzz502), @3(wzz4000, wzz4001, wzz4002), app(app(ty_@2, dd), de), cc, cd) → new_esEs3(wzz500, wzz4000, dd, de)
new_esEs2(Just(wzz500), Just(wzz4000), app(app(ty_Either, bbb), bbc)) → new_esEs1(wzz500, wzz4000, bbb, bbc)
new_esEs0(@3(wzz500, wzz501, wzz502), @3(wzz4000, wzz4001, wzz4002), app(ty_[], cb), cc, cd) → new_esEs(wzz500, wzz4000, cb)
new_esEs(:(wzz500, wzz501), :(wzz4000, wzz4001), ca) → new_esEs(wzz501, wzz4001, ca)
new_esEs3(@2(wzz500, wzz501), @2(wzz4000, wzz4001), app(ty_Maybe, bcf), bbh) → new_esEs2(wzz500, wzz4000, bcf)
new_esEs3(@2(wzz500, wzz501), @2(wzz4000, wzz4001), bda, app(app(ty_Either, bdf), bdg)) → new_esEs1(wzz501, wzz4001, bdf, bdg)
new_esEs0(@3(wzz500, wzz501, wzz502), @3(wzz4000, wzz4001, wzz4002), df, cc, app(app(app(ty_@3, fa), fb), fc)) → new_esEs0(wzz502, wzz4002, fa, fb, fc)
new_esEs0(@3(wzz500, wzz501, wzz502), @3(wzz4000, wzz4001, wzz4002), df, app(ty_[], dg), cd) → new_esEs(wzz501, wzz4001, dg)
new_esEs1(Left(wzz500), Left(wzz4000), app(ty_Maybe, ha), gc) → new_esEs2(wzz500, wzz4000, ha)
new_esEs3(@2(wzz500, wzz501), @2(wzz4000, wzz4001), app(app(ty_@2, bcg), bch), bbh) → new_esEs3(wzz500, wzz4000, bcg, bch)
new_esEs(:(wzz500, wzz501), :(wzz4000, wzz4001), app(app(app(ty_@3, ba), bb), bc)) → new_esEs0(wzz500, wzz4000, ba, bb, bc)
new_esEs(:(wzz500, wzz501), :(wzz4000, wzz4001), app(app(ty_@2, bg), bh)) → new_esEs3(wzz500, wzz4000, bg, bh)
new_esEs2(Just(wzz500), Just(wzz4000), app(app(ty_@2, bbe), bbf)) → new_esEs3(wzz500, wzz4000, bbe, bbf)
new_esEs3(@2(wzz500, wzz501), @2(wzz4000, wzz4001), bda, app(app(app(ty_@3, bdc), bdd), bde)) → new_esEs0(wzz501, wzz4001, bdc, bdd, bde)
new_esEs(:(wzz500, wzz501), :(wzz4000, wzz4001), app(app(ty_Either, bd), be)) → new_esEs1(wzz500, wzz4000, bd, be)
new_esEs1(Right(wzz500), Right(wzz4000), hd, app(ty_[], he)) → new_esEs(wzz500, wzz4000, he)
new_esEs1(Left(wzz500), Left(wzz4000), app(ty_[], gb), gc) → new_esEs(wzz500, wzz4000, gb)
new_esEs1(Right(wzz500), Right(wzz4000), hd, app(app(ty_@2, bad), bae)) → new_esEs3(wzz500, wzz4000, bad, bae)
new_esEs0(@3(wzz500, wzz501, wzz502), @3(wzz4000, wzz4001, wzz4002), df, app(ty_Maybe, ee), cd) → new_esEs2(wzz501, wzz4001, ee)
new_esEs1(Right(wzz500), Right(wzz4000), hd, app(ty_Maybe, bac)) → new_esEs2(wzz500, wzz4000, bac)
new_esEs(:(wzz500, wzz501), :(wzz4000, wzz4001), app(ty_[], h)) → new_esEs(wzz500, wzz4000, h)
new_esEs0(@3(wzz500, wzz501, wzz502), @3(wzz4000, wzz4001, wzz4002), app(app(app(ty_@3, ce), cf), cg), cc, cd) → new_esEs0(wzz500, wzz4000, ce, cf, cg)

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

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



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

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

new_ltEs1(@2(wzz5010, wzz5011), @2(wzz5210, wzz5211), hd, app(app(ty_@2, bab), bac)) → new_ltEs1(wzz5011, wzz5211, bab, bac)
new_compare20(wzz500, wzz520, False, bed, bee, bef) → new_ltEs(wzz500, wzz520, bed, bee, bef)
new_ltEs1(@2(wzz5010, wzz5011), @2(wzz5210, wzz5211), app(app(ty_Either, bbb), bbc), bba) → new_lt0(wzz5010, wzz5210, bbb, bbc)
new_compare22(@2(wzz500, @3(wzz5010, wzz5011, wzz5012)), @2(wzz520, @3(wzz5210, wzz5211, wzz5212)), False, bfe, app(app(app(ty_@3, h), ba), app(app(app(ty_@3, bb), bc), bd))) → new_ltEs(wzz5012, wzz5212, bb, bc, bd)
new_ltEs(@3(wzz5010, wzz5011, wzz5012), @3(wzz5210, wzz5211, wzz5212), h, ba, app(ty_Maybe, ca)) → new_ltEs2(wzz5012, wzz5212, ca)
new_compare22(@2(wzz500, Left(wzz5010)), @2(wzz520, Left(wzz5210)), False, bfe, app(app(ty_Either, app(app(ty_Either, fc), fd)), fb)) → new_ltEs0(wzz5010, wzz5210, fc, fd)
new_compare22(@2(wzz500, @3(wzz5010, wzz5011, wzz5012)), @2(wzz520, @3(wzz5210, wzz5211, wzz5212)), False, bfe, app(app(app(ty_@3, h), app(ty_[], de)), cf)) → new_lt3(wzz5011, wzz5211, de)
new_compare22(@2(wzz500, Left(wzz5010)), @2(wzz520, Left(wzz5210)), False, bfe, app(app(ty_Either, app(app(ty_@2, ff), fg)), fb)) → new_ltEs1(wzz5010, wzz5210, ff, fg)
new_compare22(@2(wzz500, @3(wzz5010, wzz5011, wzz5012)), @2(wzz520, @3(wzz5210, wzz5211, wzz5212)), False, bfe, app(app(app(ty_@3, app(app(ty_Either, ea), eb)), ba), cf)) → new_lt0(wzz5010, wzz5210, ea, eb)
new_compare22(@2(wzz500, @3(wzz5010, wzz5011, wzz5012)), @2(wzz520, @3(wzz5210, wzz5211, wzz5212)), False, bfe, app(app(app(ty_@3, app(app(app(ty_@3, df), dg), dh)), ba), cf)) → new_lt(wzz5010, wzz5210, df, dg, dh)
new_ltEs1(@2(wzz5010, wzz5011), @2(wzz5210, wzz5211), hd, app(ty_Maybe, bad)) → new_ltEs2(wzz5011, wzz5211, bad)
new_ltEs2(Just(wzz5010), Just(wzz5210), app(ty_[], bch)) → new_ltEs3(wzz5010, wzz5210, bch)
new_ltEs1(@2(wzz5010, wzz5011), @2(wzz5210, wzz5211), app(ty_[], bbg), bba) → new_lt3(wzz5010, wzz5210, bbg)
new_ltEs(@3(wzz5010, wzz5011, wzz5012), @3(wzz5210, wzz5211, wzz5212), h, ba, app(app(ty_@2, bg), bh)) → new_ltEs1(wzz5012, wzz5212, bg, bh)
new_ltEs1(@2(wzz5010, wzz5011), @2(wzz5210, wzz5211), hd, app(ty_[], bae)) → new_ltEs3(wzz5011, wzz5211, bae)
new_compare3(wzz500, wzz520, bfa, bfb) → new_compare22(wzz500, wzz520, new_esEs6(wzz500, wzz520, bfa, bfb), bfa, bfb)
new_primCompAux(wzz5000, wzz5200, wzz130, app(ty_[], bec)) → new_compare(wzz5000, wzz5200, bec)
new_compare22(@2(:(wzz5000, wzz5001), wzz501), @2(:(wzz5200, wzz5201), wzz521), False, app(ty_[], bdb), bfc) → new_compare(wzz5001, wzz5201, bdb)
new_compare22(@2(wzz500, @3(wzz5010, wzz5011, wzz5012)), @2(wzz520, @3(wzz5210, wzz5211, wzz5212)), False, bfe, app(app(app(ty_@3, app(app(ty_@2, ec), ed)), ba), cf)) → new_lt1(wzz5010, wzz5210, ec, ed)
new_compare22(@2(wzz500, Right(wzz5010)), @2(wzz520, Right(wzz5210)), False, bfe, app(app(ty_Either, gb), app(ty_Maybe, hb))) → new_ltEs2(wzz5010, wzz5210, hb)
new_ltEs0(Left(wzz5010), Left(wzz5210), app(app(app(ty_@3, eg), eh), fa), fb) → new_ltEs(wzz5010, wzz5210, eg, eh, fa)
new_compare1(wzz500, wzz520, bed, bee, bef) → new_compare20(wzz500, wzz520, new_esEs4(wzz500, wzz520, bed, bee, bef), bed, bee, bef)
new_compare22(@2(wzz500, @2(wzz5010, wzz5011)), @2(wzz520, @2(wzz5210, wzz5211)), False, bfe, app(app(ty_@2, app(app(ty_@2, bbd), bbe)), bba)) → new_lt1(wzz5010, wzz5210, bbd, bbe)
new_compare22(@2(wzz500, wzz501), @2(wzz520, wzz521), False, app(ty_Maybe, bfd), bfc) → new_compare23(wzz500, wzz520, new_esEs7(wzz500, wzz520, bfd), bfd)
new_compare22(@2(wzz500, Right(wzz5010)), @2(wzz520, Right(wzz5210)), False, bfe, app(app(ty_Either, gb), app(app(ty_@2, gh), ha))) → new_ltEs1(wzz5010, wzz5210, gh, ha)
new_ltEs1(@2(wzz5010, wzz5011), @2(wzz5210, wzz5211), hd, app(app(app(ty_@3, he), hf), hg)) → new_ltEs(wzz5011, wzz5211, he, hf, hg)
new_compare22(@2(wzz500, @2(wzz5010, wzz5011)), @2(wzz520, @2(wzz5210, wzz5211)), False, bfe, app(app(ty_@2, app(app(app(ty_@3, baf), bag), bah)), bba)) → new_lt(wzz5010, wzz5210, baf, bag, bah)
new_ltEs0(Right(wzz5010), Right(wzz5210), gb, app(app(ty_Either, gf), gg)) → new_ltEs0(wzz5010, wzz5210, gf, gg)
new_ltEs(@3(wzz5010, wzz5011, wzz5012), @3(wzz5210, wzz5211, wzz5212), h, app(app(ty_@2, db), dc), cf) → new_lt1(wzz5011, wzz5211, db, dc)
new_ltEs0(Right(wzz5010), Right(wzz5210), gb, app(ty_Maybe, hb)) → new_ltEs2(wzz5010, wzz5210, hb)
new_ltEs0(Right(wzz5010), Right(wzz5210), gb, app(ty_[], hc)) → new_ltEs3(wzz5010, wzz5210, hc)
new_ltEs(@3(wzz5010, wzz5011, wzz5012), @3(wzz5210, wzz5211, wzz5212), h, app(app(app(ty_@3, cc), cd), ce), cf) → new_lt(wzz5011, wzz5211, cc, cd, ce)
new_ltEs(@3(wzz5010, wzz5011, wzz5012), @3(wzz5210, wzz5211, wzz5212), app(app(ty_@2, ec), ed), ba, cf) → new_lt1(wzz5010, wzz5210, ec, ed)
new_compare22(@2(:(wzz5000, wzz5001), wzz501), @2(:(wzz5200, wzz5201), wzz521), False, app(ty_[], bdb), bfc) → new_primCompAux(wzz5000, wzz5200, new_compare0(wzz5001, wzz5201, bdb), bdb)
new_ltEs(@3(wzz5010, wzz5011, wzz5012), @3(wzz5210, wzz5211, wzz5212), h, ba, app(ty_[], cb)) → new_ltEs3(wzz5012, wzz5212, cb)
new_ltEs(@3(wzz5010, wzz5011, wzz5012), @3(wzz5210, wzz5211, wzz5212), h, app(ty_[], de), cf) → new_lt3(wzz5011, wzz5211, de)
new_compare22(@2(wzz500, Left(wzz5010)), @2(wzz520, Left(wzz5210)), False, bfe, app(app(ty_Either, app(app(app(ty_@3, eg), eh), fa)), fb)) → new_ltEs(wzz5010, wzz5210, eg, eh, fa)
new_ltEs0(Left(wzz5010), Left(wzz5210), app(ty_Maybe, fh), fb) → new_ltEs2(wzz5010, wzz5210, fh)
new_compare22(@2(wzz500, @3(wzz5010, wzz5011, wzz5012)), @2(wzz520, @3(wzz5210, wzz5211, wzz5212)), False, bfe, app(app(app(ty_@3, h), app(ty_Maybe, dd)), cf)) → new_lt2(wzz5011, wzz5211, dd)
new_compare22(@2(wzz500, @3(wzz5010, wzz5011, wzz5012)), @2(wzz520, @3(wzz5210, wzz5211, wzz5212)), False, bfe, app(app(app(ty_@3, h), ba), app(ty_Maybe, ca))) → new_ltEs2(wzz5012, wzz5212, ca)
new_ltEs1(@2(wzz5010, wzz5011), @2(wzz5210, wzz5211), hd, app(app(ty_Either, hh), baa)) → new_ltEs0(wzz5011, wzz5211, hh, baa)
new_compare22(@2(wzz500, Just(wzz5010)), @2(wzz520, Just(wzz5210)), False, bfe, app(ty_Maybe, app(ty_Maybe, bcg))) → new_ltEs2(wzz5010, wzz5210, bcg)
new_compare22(@2(wzz500, @3(wzz5010, wzz5011, wzz5012)), @2(wzz520, @3(wzz5210, wzz5211, wzz5212)), False, bfe, app(app(app(ty_@3, h), ba), app(ty_[], cb))) → new_ltEs3(wzz5012, wzz5212, cb)
new_ltEs(@3(wzz5010, wzz5011, wzz5012), @3(wzz5210, wzz5211, wzz5212), app(ty_[], ef), ba, cf) → new_lt3(wzz5010, wzz5210, ef)
new_compare22(@2(wzz500, @3(wzz5010, wzz5011, wzz5012)), @2(wzz520, @3(wzz5210, wzz5211, wzz5212)), False, bfe, app(app(app(ty_@3, h), ba), app(app(ty_@2, bg), bh))) → new_ltEs1(wzz5012, wzz5212, bg, bh)
new_compare22(@2(wzz500, @3(wzz5010, wzz5011, wzz5012)), @2(wzz520, @3(wzz5210, wzz5211, wzz5212)), False, bfe, app(app(app(ty_@3, h), app(app(ty_@2, db), dc)), cf)) → new_lt1(wzz5011, wzz5211, db, dc)
new_compare22(@2(wzz500, Just(wzz5010)), @2(wzz520, Just(wzz5210)), False, bfe, app(ty_Maybe, app(app(ty_Either, bcc), bcd))) → new_ltEs0(wzz5010, wzz5210, bcc, bcd)
new_ltEs(@3(wzz5010, wzz5011, wzz5012), @3(wzz5210, wzz5211, wzz5212), h, ba, app(app(app(ty_@3, bb), bc), bd)) → new_ltEs(wzz5012, wzz5212, bb, bc, bd)
new_lt0(wzz500, wzz520, beg, beh) → new_compare21(wzz500, wzz520, new_esEs5(wzz500, wzz520, beg, beh), beg, beh)
new_compare22(@2(wzz500, wzz501), @2(wzz520, wzz521), False, app(app(app(ty_@3, bed), bee), bef), bfc) → new_compare20(wzz500, wzz520, new_esEs4(wzz500, wzz520, bed, bee, bef), bed, bee, bef)
new_ltEs(@3(wzz5010, wzz5011, wzz5012), @3(wzz5210, wzz5211, wzz5212), h, app(ty_Maybe, dd), cf) → new_lt2(wzz5011, wzz5211, dd)
new_compare22(@2(wzz500, Right(wzz5010)), @2(wzz520, Right(wzz5210)), False, bfe, app(app(ty_Either, gb), app(ty_[], hc))) → new_ltEs3(wzz5010, wzz5210, hc)
new_lt2(wzz500, wzz520, bfd) → new_compare23(wzz500, wzz520, new_esEs7(wzz500, wzz520, bfd), bfd)
new_ltEs(@3(wzz5010, wzz5011, wzz5012), @3(wzz5210, wzz5211, wzz5212), h, app(app(ty_Either, cg), da), cf) → new_lt0(wzz5011, wzz5211, cg, da)
new_ltEs2(Just(wzz5010), Just(wzz5210), app(app(ty_@2, bce), bcf)) → new_ltEs1(wzz5010, wzz5210, bce, bcf)
new_compare22(@2(wzz500, @2(wzz5010, wzz5011)), @2(wzz520, @2(wzz5210, wzz5211)), False, bfe, app(app(ty_@2, hd), app(app(ty_@2, bab), bac))) → new_ltEs1(wzz5011, wzz5211, bab, bac)
new_ltEs0(Left(wzz5010), Left(wzz5210), app(ty_[], ga), fb) → new_ltEs3(wzz5010, wzz5210, ga)
new_compare22(@2(wzz500, @3(wzz5010, wzz5011, wzz5012)), @2(wzz520, @3(wzz5210, wzz5211, wzz5212)), False, bfe, app(app(app(ty_@3, h), app(app(ty_Either, cg), da)), cf)) → new_lt0(wzz5011, wzz5211, cg, da)
new_ltEs3(wzz501, wzz521, bda) → new_compare(wzz501, wzz521, bda)
new_ltEs0(Left(wzz5010), Left(wzz5210), app(app(ty_@2, ff), fg), fb) → new_ltEs1(wzz5010, wzz5210, ff, fg)
new_primCompAux(wzz5000, wzz5200, wzz130, app(app(app(ty_@3, bdc), bdd), bde)) → new_compare1(wzz5000, wzz5200, bdc, bdd, bde)
new_compare22(@2(wzz500, @3(wzz5010, wzz5011, wzz5012)), @2(wzz520, @3(wzz5210, wzz5211, wzz5212)), False, bfe, app(app(app(ty_@3, app(ty_Maybe, ee)), ba), cf)) → new_lt2(wzz5010, wzz5210, ee)
new_compare22(@2(wzz500, @2(wzz5010, wzz5011)), @2(wzz520, @2(wzz5210, wzz5211)), False, bfe, app(app(ty_@2, app(ty_Maybe, bbf)), bba)) → new_lt2(wzz5010, wzz5210, bbf)
new_primCompAux(wzz5000, wzz5200, wzz130, app(app(ty_@2, bdh), bea)) → new_compare3(wzz5000, wzz5200, bdh, bea)
new_ltEs2(Just(wzz5010), Just(wzz5210), app(app(ty_Either, bcc), bcd)) → new_ltEs0(wzz5010, wzz5210, bcc, bcd)
new_compare22(@2(wzz500, Left(wzz5010)), @2(wzz520, Left(wzz5210)), False, bfe, app(app(ty_Either, app(ty_Maybe, fh)), fb)) → new_ltEs2(wzz5010, wzz5210, fh)
new_ltEs0(Right(wzz5010), Right(wzz5210), gb, app(app(app(ty_@3, gc), gd), ge)) → new_ltEs(wzz5010, wzz5210, gc, gd, ge)
new_compare22(@2(wzz500, Just(wzz5010)), @2(wzz520, Just(wzz5210)), False, bfe, app(ty_Maybe, app(ty_[], bch))) → new_ltEs3(wzz5010, wzz5210, bch)
new_compare2(wzz500, wzz520, beg, beh) → new_compare21(wzz500, wzz520, new_esEs5(wzz500, wzz520, beg, beh), beg, beh)
new_compare22(@2(wzz500, @2(wzz5010, wzz5011)), @2(wzz520, @2(wzz5210, wzz5211)), False, bfe, app(app(ty_@2, hd), app(app(ty_Either, hh), baa))) → new_ltEs0(wzz5011, wzz5211, hh, baa)
new_ltEs0(Right(wzz5010), Right(wzz5210), gb, app(app(ty_@2, gh), ha)) → new_ltEs1(wzz5010, wzz5210, gh, ha)
new_compare21(wzz500, wzz520, False, beg, beh) → new_ltEs0(wzz500, wzz520, beg, beh)
new_compare22(@2(wzz500, wzz501), @2(wzz520, wzz521), False, app(app(ty_Either, beg), beh), bfc) → new_compare21(wzz500, wzz520, new_esEs5(wzz500, wzz520, beg, beh), beg, beh)
new_ltEs0(Left(wzz5010), Left(wzz5210), app(app(ty_Either, fc), fd), fb) → new_ltEs0(wzz5010, wzz5210, fc, fd)
new_compare22(@2(wzz500, @2(wzz5010, wzz5011)), @2(wzz520, @2(wzz5210, wzz5211)), False, bfe, app(app(ty_@2, hd), app(ty_[], bae))) → new_ltEs3(wzz5011, wzz5211, bae)
new_compare22(@2(wzz500, wzz501), @2(wzz520, wzz521), False, bfe, app(ty_[], bda)) → new_compare(wzz501, wzz521, bda)
new_compare22(@2(wzz500, @2(wzz5010, wzz5011)), @2(wzz520, @2(wzz5210, wzz5211)), False, bfe, app(app(ty_@2, hd), app(ty_Maybe, bad))) → new_ltEs2(wzz5011, wzz5211, bad)
new_compare22(@2(wzz500, @2(wzz5010, wzz5011)), @2(wzz520, @2(wzz5210, wzz5211)), False, bfe, app(app(ty_@2, app(ty_[], bbg)), bba)) → new_lt3(wzz5010, wzz5210, bbg)
new_compare22(@2(wzz500, @3(wzz5010, wzz5011, wzz5012)), @2(wzz520, @3(wzz5210, wzz5211, wzz5212)), False, bfe, app(app(app(ty_@3, h), ba), app(app(ty_Either, be), bf))) → new_ltEs0(wzz5012, wzz5212, be, bf)
new_compare22(@2(wzz500, @2(wzz5010, wzz5011)), @2(wzz520, @2(wzz5210, wzz5211)), False, bfe, app(app(ty_@2, hd), app(app(app(ty_@3, he), hf), hg))) → new_ltEs(wzz5011, wzz5211, he, hf, hg)
new_compare23(wzz500, wzz520, False, bfd) → new_ltEs2(wzz500, wzz520, bfd)
new_primCompAux(wzz5000, wzz5200, wzz130, app(app(ty_Either, bdf), bdg)) → new_compare2(wzz5000, wzz5200, bdf, bdg)
new_compare22(@2(wzz500, @2(wzz5010, wzz5011)), @2(wzz520, @2(wzz5210, wzz5211)), False, bfe, app(app(ty_@2, app(app(ty_Either, bbb), bbc)), bba)) → new_lt0(wzz5010, wzz5210, bbb, bbc)
new_compare22(@2(wzz500, Just(wzz5010)), @2(wzz520, Just(wzz5210)), False, bfe, app(ty_Maybe, app(app(ty_@2, bce), bcf))) → new_ltEs1(wzz5010, wzz5210, bce, bcf)
new_compare22(@2(wzz500, Just(wzz5010)), @2(wzz520, Just(wzz5210)), False, bfe, app(ty_Maybe, app(app(app(ty_@3, bbh), bca), bcb))) → new_ltEs(wzz5010, wzz5210, bbh, bca, bcb)
new_compare22(@2(wzz500, Right(wzz5010)), @2(wzz520, Right(wzz5210)), False, bfe, app(app(ty_Either, gb), app(app(app(ty_@3, gc), gd), ge))) → new_ltEs(wzz5010, wzz5210, gc, gd, ge)
new_ltEs1(@2(wzz5010, wzz5011), @2(wzz5210, wzz5211), app(app(ty_@2, bbd), bbe), bba) → new_lt1(wzz5010, wzz5210, bbd, bbe)
new_compare22(@2(wzz500, Left(wzz5010)), @2(wzz520, Left(wzz5210)), False, bfe, app(app(ty_Either, app(ty_[], ga)), fb)) → new_ltEs3(wzz5010, wzz5210, ga)
new_ltEs(@3(wzz5010, wzz5011, wzz5012), @3(wzz5210, wzz5211, wzz5212), app(app(app(ty_@3, df), dg), dh), ba, cf) → new_lt(wzz5010, wzz5210, df, dg, dh)
new_ltEs(@3(wzz5010, wzz5011, wzz5012), @3(wzz5210, wzz5211, wzz5212), h, ba, app(app(ty_Either, be), bf)) → new_ltEs0(wzz5012, wzz5212, be, bf)
new_ltEs2(Just(wzz5010), Just(wzz5210), app(ty_Maybe, bcg)) → new_ltEs2(wzz5010, wzz5210, bcg)
new_compare(:(wzz5000, wzz5001), :(wzz5200, wzz5201), bdb) → new_compare(wzz5001, wzz5201, bdb)
new_ltEs2(Just(wzz5010), Just(wzz5210), app(app(app(ty_@3, bbh), bca), bcb)) → new_ltEs(wzz5010, wzz5210, bbh, bca, bcb)
new_lt1(wzz500, wzz520, bfa, bfb) → new_compare22(wzz500, wzz520, new_esEs6(wzz500, wzz520, bfa, bfb), bfa, bfb)
new_compare(:(wzz5000, wzz5001), :(wzz5200, wzz5201), bdb) → new_primCompAux(wzz5000, wzz5200, new_compare0(wzz5001, wzz5201, bdb), bdb)
new_compare22(@2(wzz500, @3(wzz5010, wzz5011, wzz5012)), @2(wzz520, @3(wzz5210, wzz5211, wzz5212)), False, bfe, app(app(app(ty_@3, h), app(app(app(ty_@3, cc), cd), ce)), cf)) → new_lt(wzz5011, wzz5211, cc, cd, ce)
new_ltEs(@3(wzz5010, wzz5011, wzz5012), @3(wzz5210, wzz5211, wzz5212), app(app(ty_Either, ea), eb), ba, cf) → new_lt0(wzz5010, wzz5210, ea, eb)
new_ltEs1(@2(wzz5010, wzz5011), @2(wzz5210, wzz5211), app(app(app(ty_@3, baf), bag), bah), bba) → new_lt(wzz5010, wzz5210, baf, bag, bah)
new_compare22(@2(wzz500, Right(wzz5010)), @2(wzz520, Right(wzz5210)), False, bfe, app(app(ty_Either, gb), app(app(ty_Either, gf), gg))) → new_ltEs0(wzz5010, wzz5210, gf, gg)
new_compare4(wzz500, wzz520, bfd) → new_compare23(wzz500, wzz520, new_esEs7(wzz500, wzz520, bfd), bfd)
new_lt3(:(wzz5000, wzz5001), :(wzz5200, wzz5201), bdb) → new_compare(wzz5001, wzz5201, bdb)
new_primCompAux(wzz5000, wzz5200, wzz130, app(ty_Maybe, beb)) → new_compare4(wzz5000, wzz5200, beb)
new_compare22(@2(wzz500, @3(wzz5010, wzz5011, wzz5012)), @2(wzz520, @3(wzz5210, wzz5211, wzz5212)), False, bfe, app(app(app(ty_@3, app(ty_[], ef)), ba), cf)) → new_lt3(wzz5010, wzz5210, ef)
new_lt(wzz500, wzz520, bed, bee, bef) → new_compare20(wzz500, wzz520, new_esEs4(wzz500, wzz520, bed, bee, bef), bed, bee, bef)
new_ltEs1(@2(wzz5010, wzz5011), @2(wzz5210, wzz5211), app(ty_Maybe, bbf), bba) → new_lt2(wzz5010, wzz5210, bbf)
new_ltEs(@3(wzz5010, wzz5011, wzz5012), @3(wzz5210, wzz5211, wzz5212), app(ty_Maybe, ee), ba, cf) → new_lt2(wzz5010, wzz5210, ee)
new_lt3(:(wzz5000, wzz5001), :(wzz5200, wzz5201), bdb) → new_primCompAux(wzz5000, wzz5200, new_compare0(wzz5001, wzz5201, bdb), bdb)
new_compare22(@2(wzz500, wzz501), @2(wzz520, wzz521), False, app(app(ty_@2, bfa), bfb), bfc) → new_compare22(wzz500, wzz520, new_esEs6(wzz500, wzz520, bfa, bfb), bfa, bfb)

The TRS R consists of the following rules:

new_esEs7(Just(wzz500), Just(wzz4000), app(ty_Maybe, ccb)) → new_esEs7(wzz500, wzz4000, ccb)
new_primCmpNat0(wzz5000, Succ(wzz5200)) → new_primCmpNat2(wzz5000, wzz5200)
new_esEs20(wzz500, wzz4000, app(ty_Maybe, cdf)) → new_esEs7(wzz500, wzz4000, cdf)
new_esEs24(wzz5010, wzz5210, app(app(ty_Either, ea), eb)) → new_esEs5(wzz5010, wzz5210, ea, eb)
new_lt4(wzz500, wzz520) → new_esEs8(new_compare5(wzz500, wzz520), LT)
new_esEs21(wzz501, wzz4001, app(app(ty_@2, cfb), cfc)) → new_esEs6(wzz501, wzz4001, cfb, cfc)
new_compare31(wzz5000, wzz5200, ty_@0) → new_compare7(wzz5000, wzz5200)
new_lt15(wzz500, wzz520) → new_esEs8(new_compare16(wzz500, wzz520), LT)
new_ltEs13(Just(wzz5010), Just(wzz5210), app(app(app(ty_@3, bbh), bca), bcb)) → new_ltEs6(wzz5010, wzz5210, bbh, bca, bcb)
new_ltEs13(Just(wzz5010), Just(wzz5210), app(ty_[], bch)) → new_ltEs15(wzz5010, wzz5210, bch)
new_compare8(Integer(wzz5000), Integer(wzz5200)) → new_primCmpInt(wzz5000, wzz5200)
new_compare31(wzz5000, wzz5200, app(ty_Ratio, chd)) → new_compare12(wzz5000, wzz5200, chd)
new_lt19(wzz5011, wzz5211, app(app(app(ty_@3, cc), cd), ce)) → new_lt8(wzz5011, wzz5211, cc, cd, ce)
new_lt20(wzz5010, wzz5210, app(ty_[], ef)) → new_lt18(wzz5010, wzz5210, ef)
new_esEs17(Char(wzz500), Char(wzz4000)) → new_primEqNat0(wzz500, wzz4000)
new_esEs20(wzz500, wzz4000, ty_Bool) → new_esEs12(wzz500, wzz4000)
new_esEs24(wzz5010, wzz5210, ty_Char) → new_esEs17(wzz5010, wzz5210)
new_ltEs18(wzz5011, wzz5211, app(ty_[], bae)) → new_ltEs15(wzz5011, wzz5211, bae)
new_esEs23(wzz500, wzz4000, app(app(ty_Either, cgc), cgd)) → new_esEs5(wzz500, wzz4000, cgc, cgd)
new_compare10(wzz500, wzz520, True, beg, beh) → LT
new_esEs26(wzz500, wzz4000, ty_Float) → new_esEs10(wzz500, wzz4000)
new_ltEs13(Just(wzz5010), Just(wzz5210), ty_Char) → new_ltEs12(wzz5010, wzz5210)
new_esEs21(wzz501, wzz4001, ty_@0) → new_esEs19(wzz501, wzz4001)
new_lt20(wzz5010, wzz5210, app(app(app(ty_@3, df), dg), dh)) → new_lt8(wzz5010, wzz5210, df, dg, dh)
new_esEs27(wzz501, wzz4001, app(ty_Maybe, dbh)) → new_esEs7(wzz501, wzz4001, dbh)
new_ltEs5(Right(wzz5010), Right(wzz5210), gb, ty_Bool) → new_ltEs14(wzz5010, wzz5210)
new_ltEs19(wzz5012, wzz5212, ty_Double) → new_ltEs11(wzz5012, wzz5212)
new_esEs25(wzz5011, wzz5211, ty_Char) → new_esEs17(wzz5011, wzz5211)
new_compare31(wzz5000, wzz5200, ty_Ordering) → new_compare16(wzz5000, wzz5200)
new_lt19(wzz5011, wzz5211, ty_Int) → new_lt4(wzz5011, wzz5211)
new_primMulNat0(Zero, Zero) → Zero
new_esEs5(Left(wzz500), Left(wzz4000), app(ty_Ratio, bhd), bgd) → new_esEs14(wzz500, wzz4000, bhd)
new_lt12(wzz5010, wzz5210, app(ty_[], bbg)) → new_lt18(wzz5010, wzz5210, bbg)
new_esEs27(wzz501, wzz4001, app(app(app(ty_@3, dbc), dbd), dbe)) → new_esEs4(wzz501, wzz4001, dbc, dbd, dbe)
new_lt14(wzz500, wzz520, bfa, bfb) → new_esEs8(new_compare28(wzz500, wzz520, bfa, bfb), LT)
new_esEs12(True, True) → True
new_ltEs9(GT, LT) → False
new_lt20(wzz5010, wzz5210, app(app(ty_Either, ea), eb)) → new_lt13(wzz5010, wzz5210, ea, eb)
new_compare18(wzz500, wzz520, True, bed, bee, bef) → LT
new_ltEs13(Nothing, Just(wzz5210), ddf) → True
new_esEs26(wzz500, wzz4000, ty_@0) → new_esEs19(wzz500, wzz4000)
new_ltEs13(Just(wzz5010), Just(wzz5210), ty_Ordering) → new_ltEs9(wzz5010, wzz5210)
new_esEs22(wzz5010, wzz5210, ty_Char) → new_esEs17(wzz5010, wzz5210)
new_esEs23(wzz500, wzz4000, ty_Bool) → new_esEs12(wzz500, wzz4000)
new_ltEs20(wzz501, wzz521, app(ty_Maybe, ddf)) → new_ltEs13(wzz501, wzz521, ddf)
new_ltEs14(False, True) → True
new_esEs18(:(wzz500, wzz501), :(wzz4000, wzz4001), cff) → new_asAs(new_esEs23(wzz500, wzz4000, cff), new_esEs18(wzz501, wzz4001, cff))
new_ltEs5(Right(wzz5010), Right(wzz5210), gb, ty_Ordering) → new_ltEs9(wzz5010, wzz5210)
new_esEs29(wzz500, wzz520, app(ty_Maybe, bfd)) → new_esEs7(wzz500, wzz520, bfd)
new_esEs20(wzz500, wzz4000, app(ty_Ratio, cdg)) → new_esEs14(wzz500, wzz4000, cdg)
new_esEs5(Left(wzz500), Left(wzz4000), ty_Bool, bgd) → new_esEs12(wzz500, wzz4000)
new_ltEs13(Just(wzz5010), Just(wzz5210), ty_Int) → new_ltEs17(wzz5010, wzz5210)
new_lt21(wzz500, wzz520, app(ty_Maybe, bfd)) → new_lt11(wzz500, wzz520, bfd)
new_lt20(wzz5010, wzz5210, ty_Integer) → new_lt9(wzz5010, wzz5210)
new_lt19(wzz5011, wzz5211, ty_Bool) → new_lt17(wzz5011, wzz5211)
new_esEs5(Right(wzz500), Right(wzz4000), bhg, ty_Integer) → new_esEs9(wzz500, wzz4000)
new_ltEs13(Just(wzz5010), Just(wzz5210), ty_Double) → new_ltEs11(wzz5010, wzz5210)
new_ltEs5(Left(wzz5010), Right(wzz5210), gb, fb) → True
new_esEs7(Just(wzz500), Just(wzz4000), app(app(ty_@2, ccd), cce)) → new_esEs6(wzz500, wzz4000, ccd, cce)
new_ltEs18(wzz5011, wzz5211, app(ty_Ratio, cfe)) → new_ltEs7(wzz5011, wzz5211, cfe)
new_lt8(wzz500, wzz520, bed, bee, bef) → new_esEs8(new_compare6(wzz500, wzz520, bed, bee, bef), LT)
new_esEs22(wzz5010, wzz5210, app(ty_Ratio, cfd)) → new_esEs14(wzz5010, wzz5210, cfd)
new_esEs21(wzz501, wzz4001, app(ty_Ratio, cfa)) → new_esEs14(wzz501, wzz4001, cfa)
new_esEs23(wzz500, wzz4000, ty_Double) → new_esEs13(wzz500, wzz4000)
new_esEs5(Left(wzz500), Left(wzz4000), app(app(app(ty_@3, bgf), bgg), bgh), bgd) → new_esEs4(wzz500, wzz4000, bgf, bgg, bgh)
new_esEs22(wzz5010, wzz5210, ty_Integer) → new_esEs9(wzz5010, wzz5210)
new_ltEs5(Right(wzz5010), Right(wzz5210), gb, app(app(ty_Either, gf), gg)) → new_ltEs5(wzz5010, wzz5210, gf, gg)
new_lt12(wzz5010, wzz5210, ty_Bool) → new_lt17(wzz5010, wzz5210)
new_lt21(wzz500, wzz520, app(ty_[], bdb)) → new_lt18(wzz500, wzz520, bdb)
new_ltEs9(EQ, GT) → True
new_lt20(wzz5010, wzz5210, ty_@0) → new_lt5(wzz5010, wzz5210)
new_esEs7(Just(wzz500), Just(wzz4000), app(ty_Ratio, ccc)) → new_esEs14(wzz500, wzz4000, ccc)
new_esEs20(wzz500, wzz4000, app(app(ty_@2, cdh), cea)) → new_esEs6(wzz500, wzz4000, cdh, cea)
new_esEs6(@2(wzz500, wzz501), @2(wzz4000, wzz4001), ccf, ccg) → new_asAs(new_esEs20(wzz500, wzz4000, ccf), new_esEs21(wzz501, wzz4001, ccg))
new_lt20(wzz5010, wzz5210, ty_Ordering) → new_lt15(wzz5010, wzz5210)
new_lt12(wzz5010, wzz5210, ty_Integer) → new_lt9(wzz5010, wzz5210)
new_compare15(wzz500, wzz520, False, bfd) → GT
new_lt6(wzz500, wzz520) → new_esEs8(new_compare11(wzz500, wzz520), LT)
new_ltEs5(Right(wzz5010), Left(wzz5210), gb, fb) → False
new_ltEs17(wzz501, wzz521) → new_fsEs(new_compare5(wzz501, wzz521))
new_ltEs9(LT, EQ) → True
new_esEs5(Left(wzz500), Left(wzz4000), ty_@0, bgd) → new_esEs19(wzz500, wzz4000)
new_ltEs19(wzz5012, wzz5212, app(app(ty_@2, bg), bh)) → new_ltEs8(wzz5012, wzz5212, bg, bh)
new_ltEs20(wzz501, wzz521, app(ty_Ratio, cbb)) → new_ltEs7(wzz501, wzz521, cbb)
new_ltEs19(wzz5012, wzz5212, ty_Float) → new_ltEs16(wzz5012, wzz5212)
new_pePe(False, wzz135) → wzz135
new_esEs24(wzz5010, wzz5210, app(ty_Ratio, cha)) → new_esEs14(wzz5010, wzz5210, cha)
new_compare31(wzz5000, wzz5200, ty_Int) → new_compare5(wzz5000, wzz5200)
new_esEs23(wzz500, wzz4000, ty_@0) → new_esEs19(wzz500, wzz4000)
new_esEs18([], :(wzz4000, wzz4001), cff) → False
new_esEs18(:(wzz500, wzz501), [], cff) → False
new_lt19(wzz5011, wzz5211, app(ty_Ratio, chb)) → new_lt7(wzz5011, wzz5211, chb)
new_ltEs20(wzz501, wzz521, app(app(ty_@2, hd), bba)) → new_ltEs8(wzz501, wzz521, hd, bba)
new_lt20(wzz5010, wzz5210, ty_Float) → new_lt10(wzz5010, wzz5210)
new_ltEs20(wzz501, wzz521, ty_@0) → new_ltEs10(wzz501, wzz521)
new_esEs26(wzz500, wzz4000, ty_Int) → new_esEs11(wzz500, wzz4000)
new_esEs24(wzz5010, wzz5210, app(ty_Maybe, ee)) → new_esEs7(wzz5010, wzz5210, ee)
new_esEs22(wzz5010, wzz5210, ty_Int) → new_esEs11(wzz5010, wzz5210)
new_esEs26(wzz500, wzz4000, ty_Bool) → new_esEs12(wzz500, wzz4000)
new_esEs28(wzz502, wzz4002, app(app(app(ty_@3, dce), dcf), dcg)) → new_esEs4(wzz502, wzz4002, dce, dcf, dcg)
new_esEs23(wzz500, wzz4000, app(ty_Maybe, cge)) → new_esEs7(wzz500, wzz4000, cge)
new_lt20(wzz5010, wzz5210, app(app(ty_@2, ec), ed)) → new_lt14(wzz5010, wzz5210, ec, ed)
new_lt12(wzz5010, wzz5210, app(app(app(ty_@3, baf), bag), bah)) → new_lt8(wzz5010, wzz5210, baf, bag, bah)
new_ltEs9(EQ, EQ) → True
new_compare19(Float(wzz5000, wzz5001), Float(wzz5200, wzz5201)) → new_compare5(new_sr(wzz5000, wzz5200), new_sr(wzz5001, wzz5201))
new_esEs22(wzz5010, wzz5210, ty_Ordering) → new_esEs8(wzz5010, wzz5210)
new_lt12(wzz5010, wzz5210, app(app(ty_@2, bbd), bbe)) → new_lt14(wzz5010, wzz5210, bbd, bbe)
new_esEs20(wzz500, wzz4000, app(ty_[], cch)) → new_esEs18(wzz500, wzz4000, cch)
new_esEs5(Left(wzz500), Left(wzz4000), app(app(ty_@2, bhe), bhf), bgd) → new_esEs6(wzz500, wzz4000, bhe, bhf)
new_compare111(wzz500, wzz520, False) → GT
new_compare111(wzz500, wzz520, True) → LT
new_esEs5(Left(wzz500), Left(wzz4000), ty_Int, bgd) → new_esEs11(wzz500, wzz4000)
new_ltEs5(Left(wzz5010), Left(wzz5210), ty_Float, fb) → new_ltEs16(wzz5010, wzz5210)
new_compare17(wzz109, wzz110, wzz111, wzz112, True, bgb, bgc) → LT
new_esEs5(Left(wzz500), Left(wzz4000), ty_Ordering, bgd) → new_esEs8(wzz500, wzz4000)
new_ltEs5(Left(wzz5010), Left(wzz5210), ty_Int, fb) → new_ltEs17(wzz5010, wzz5210)
new_esEs5(Right(wzz500), Right(wzz4000), bhg, ty_Char) → new_esEs17(wzz500, wzz4000)
new_primCmpInt(Neg(Succ(wzz5000)), Neg(wzz520)) → new_primCmpNat1(wzz520, wzz5000)
new_ltEs13(Nothing, Nothing, ddf) → True
new_ltEs4(wzz501, wzz521) → new_fsEs(new_compare8(wzz501, wzz521))
new_ltEs20(wzz501, wzz521, ty_Bool) → new_ltEs14(wzz501, wzz521)
new_esEs25(wzz5011, wzz5211, app(app(ty_Either, cg), da)) → new_esEs5(wzz5011, wzz5211, cg, da)
new_esEs25(wzz5011, wzz5211, app(app(ty_@2, db), dc)) → new_esEs6(wzz5011, wzz5211, db, dc)
new_esEs8(LT, LT) → True
new_ltEs13(Just(wzz5010), Just(wzz5210), ty_@0) → new_ltEs10(wzz5010, wzz5210)
new_ltEs18(wzz5011, wzz5211, ty_Integer) → new_ltEs4(wzz5011, wzz5211)
new_esEs25(wzz5011, wzz5211, ty_Ordering) → new_esEs8(wzz5011, wzz5211)
new_compare25(wzz500, wzz520, False, beg, beh) → new_compare10(wzz500, wzz520, new_ltEs5(wzz500, wzz520, beg, beh), beg, beh)
new_esEs28(wzz502, wzz4002, ty_Float) → new_esEs10(wzz502, wzz4002)
new_compare12(:%(wzz5000, wzz5001), :%(wzz5200, wzz5201), ty_Integer) → new_compare8(new_sr0(wzz5000, wzz5201), new_sr0(wzz5200, wzz5001))
new_esEs24(wzz5010, wzz5210, app(app(ty_@2, ec), ed)) → new_esEs6(wzz5010, wzz5210, ec, ed)
new_pePe(True, wzz135) → True
new_compare0([], [], bdb) → EQ
new_lt12(wzz5010, wzz5210, app(ty_Maybe, bbf)) → new_lt11(wzz5010, wzz5210, bbf)
new_primEqNat0(Zero, Zero) → True
new_lt12(wzz5010, wzz5210, ty_@0) → new_lt5(wzz5010, wzz5210)
new_compare26(wzz500, wzz520, True) → EQ
new_esEs20(wzz500, wzz4000, ty_Int) → new_esEs11(wzz500, wzz4000)
new_esEs5(Right(wzz500), Right(wzz4000), bhg, app(app(ty_@2, cah), cba)) → new_esEs6(wzz500, wzz4000, cah, cba)
new_esEs26(wzz500, wzz4000, ty_Char) → new_esEs17(wzz500, wzz4000)
new_esEs25(wzz5011, wzz5211, app(ty_[], de)) → new_esEs18(wzz5011, wzz5211, de)
new_compare29(wzz50, wzz52, True, bfe, bfc) → EQ
new_primMulNat0(Succ(wzz50000), Succ(wzz400000)) → new_primPlusNat1(new_primMulNat0(wzz50000, Succ(wzz400000)), wzz400000)
new_esEs5(Right(wzz500), Right(wzz4000), bhg, ty_Double) → new_esEs13(wzz500, wzz4000)
new_compare26(wzz500, wzz520, False) → new_compare111(wzz500, wzz520, new_ltEs9(wzz500, wzz520))
new_esEs23(wzz500, wzz4000, ty_Integer) → new_esEs9(wzz500, wzz4000)
new_ltEs5(Right(wzz5010), Right(wzz5210), gb, app(app(app(ty_@3, gc), gd), ge)) → new_ltEs6(wzz5010, wzz5210, gc, gd, ge)
new_compare211(wzz500, wzz520, False) → new_compare13(wzz500, wzz520, new_ltEs14(wzz500, wzz520))
new_lt21(wzz500, wzz520, app(app(ty_Either, beg), beh)) → new_lt13(wzz500, wzz520, beg, beh)
new_esEs24(wzz5010, wzz5210, app(ty_[], ef)) → new_esEs18(wzz5010, wzz5210, ef)
new_esEs29(wzz500, wzz520, ty_@0) → new_esEs19(wzz500, wzz520)
new_compare31(wzz5000, wzz5200, ty_Bool) → new_compare30(wzz5000, wzz5200)
new_ltEs9(EQ, LT) → False
new_compare6(wzz500, wzz520, bed, bee, bef) → new_compare24(wzz500, wzz520, new_esEs4(wzz500, wzz520, bed, bee, bef), bed, bee, bef)
new_sr(wzz500, wzz4000) → new_primMulInt(wzz500, wzz4000)
new_compare14(wzz500, wzz520, beg, beh) → new_compare25(wzz500, wzz520, new_esEs5(wzz500, wzz520, beg, beh), beg, beh)
new_ltEs5(Left(wzz5010), Left(wzz5210), ty_Ordering, fb) → new_ltEs9(wzz5010, wzz5210)
new_primCmpInt(Neg(Zero), Neg(Succ(wzz5200))) → new_primCmpNat0(wzz5200, Zero)
new_compare31(wzz5000, wzz5200, ty_Double) → new_compare9(wzz5000, wzz5200)
new_esEs26(wzz500, wzz4000, ty_Ordering) → new_esEs8(wzz500, wzz4000)
new_esEs8(GT, GT) → True
new_lt20(wzz5010, wzz5210, app(ty_Maybe, ee)) → new_lt11(wzz5010, wzz5210, ee)
new_esEs20(wzz500, wzz4000, ty_Integer) → new_esEs9(wzz500, wzz4000)
new_esEs16(wzz501, wzz4001, ty_Int) → new_esEs11(wzz501, wzz4001)
new_primCmpInt(Pos(Zero), Pos(Succ(wzz5200))) → new_primCmpNat1(Zero, wzz5200)
new_esEs12(False, False) → True
new_esEs5(Right(wzz500), Right(wzz4000), bhg, app(ty_[], bhh)) → new_esEs18(wzz500, wzz4000, bhh)
new_esEs26(wzz500, wzz4000, app(app(app(ty_@3, daa), dab), dac)) → new_esEs4(wzz500, wzz4000, daa, dab, dac)
new_esEs8(GT, LT) → False
new_esEs8(LT, GT) → False
new_ltEs18(wzz5011, wzz5211, app(app(ty_Either, hh), baa)) → new_ltEs5(wzz5011, wzz5211, hh, baa)
new_esEs22(wzz5010, wzz5210, app(ty_[], bbg)) → new_esEs18(wzz5010, wzz5210, bbg)
new_lt12(wzz5010, wzz5210, ty_Float) → new_lt10(wzz5010, wzz5210)
new_ltEs20(wzz501, wzz521, ty_Float) → new_ltEs16(wzz501, wzz521)
new_lt11(wzz500, wzz520, bfd) → new_esEs8(new_compare27(wzz500, wzz520, bfd), LT)
new_compare16(wzz500, wzz520) → new_compare26(wzz500, wzz520, new_esEs8(wzz500, wzz520))
new_compare24(wzz500, wzz520, True, bed, bee, bef) → EQ
new_primEqInt(Neg(Succ(wzz5000)), Neg(Succ(wzz40000))) → new_primEqNat0(wzz5000, wzz40000)
new_esEs5(Left(wzz500), Left(wzz4000), ty_Float, bgd) → new_esEs10(wzz500, wzz4000)
new_esEs20(wzz500, wzz4000, ty_Ordering) → new_esEs8(wzz500, wzz4000)
new_lt21(wzz500, wzz520, ty_Integer) → new_lt9(wzz500, wzz520)
new_esEs23(wzz500, wzz4000, ty_Ordering) → new_esEs8(wzz500, wzz4000)
new_lt20(wzz5010, wzz5210, ty_Char) → new_lt6(wzz5010, wzz5210)
new_compare13(wzz500, wzz520, False) → GT
new_ltEs5(Right(wzz5010), Right(wzz5210), gb, app(app(ty_@2, gh), ha)) → new_ltEs8(wzz5010, wzz5210, gh, ha)
new_lt12(wzz5010, wzz5210, app(ty_Ratio, cfd)) → new_lt7(wzz5010, wzz5210, cfd)
new_esEs29(wzz500, wzz520, app(app(ty_Either, beg), beh)) → new_esEs5(wzz500, wzz520, beg, beh)
new_ltEs5(Right(wzz5010), Right(wzz5210), gb, app(ty_Ratio, bfg)) → new_ltEs7(wzz5010, wzz5210, bfg)
new_lt20(wzz5010, wzz5210, ty_Int) → new_lt4(wzz5010, wzz5210)
new_ltEs16(wzz501, wzz521) → new_fsEs(new_compare19(wzz501, wzz521))
new_primCmpNat1(Zero, wzz5000) → LT
new_esEs21(wzz501, wzz4001, app(ty_[], ceb)) → new_esEs18(wzz501, wzz4001, ceb)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_compare110(wzz109, wzz110, wzz111, wzz112, True, wzz114, bgb, bgc) → new_compare17(wzz109, wzz110, wzz111, wzz112, True, bgb, bgc)
new_ltEs5(Right(wzz5010), Right(wzz5210), gb, ty_Double) → new_ltEs11(wzz5010, wzz5210)
new_ltEs5(Left(wzz5010), Left(wzz5210), ty_Integer, fb) → new_ltEs4(wzz5010, wzz5210)
new_esEs7(Just(wzz500), Just(wzz4000), ty_Ordering) → new_esEs8(wzz500, wzz4000)
new_esEs5(Left(wzz500), Left(wzz4000), app(ty_Maybe, bhc), bgd) → new_esEs7(wzz500, wzz4000, bhc)
new_ltEs11(wzz501, wzz521) → new_fsEs(new_compare9(wzz501, wzz521))
new_esEs28(wzz502, wzz4002, ty_Double) → new_esEs13(wzz502, wzz4002)
new_esEs27(wzz501, wzz4001, app(app(ty_Either, dbf), dbg)) → new_esEs5(wzz501, wzz4001, dbf, dbg)
new_ltEs20(wzz501, wzz521, ty_Char) → new_ltEs12(wzz501, wzz521)
new_lt19(wzz5011, wzz5211, ty_Double) → new_lt16(wzz5011, wzz5211)
new_ltEs19(wzz5012, wzz5212, ty_Integer) → new_ltEs4(wzz5012, wzz5212)
new_primEqInt(Neg(Zero), Neg(Succ(wzz40000))) → False
new_primEqInt(Neg(Succ(wzz5000)), Neg(Zero)) → False
new_ltEs19(wzz5012, wzz5212, ty_Char) → new_ltEs12(wzz5012, wzz5212)
new_compare210(wzz500, wzz520, False, bfd) → new_compare15(wzz500, wzz520, new_ltEs13(wzz500, wzz520, bfd), bfd)
new_primCompAux0(wzz144, GT) → GT
new_esEs8(EQ, EQ) → True
new_primPlusNat1(Zero, wzz400000) → Succ(wzz400000)
new_esEs24(wzz5010, wzz5210, ty_Integer) → new_esEs9(wzz5010, wzz5210)
new_esEs23(wzz500, wzz4000, app(app(app(ty_@3, cfh), cga), cgb)) → new_esEs4(wzz500, wzz4000, cfh, cga, cgb)
new_ltEs9(LT, LT) → True
new_esEs5(Right(wzz500), Right(wzz4000), bhg, app(ty_Ratio, cag)) → new_esEs14(wzz500, wzz4000, cag)
new_esEs26(wzz500, wzz4000, app(ty_[], chh)) → new_esEs18(wzz500, wzz4000, chh)
new_esEs20(wzz500, wzz4000, ty_@0) → new_esEs19(wzz500, wzz4000)
new_esEs19(@0, @0) → True
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_esEs21(wzz501, wzz4001, ty_Float) → new_esEs10(wzz501, wzz4001)
new_ltEs5(Left(wzz5010), Left(wzz5210), app(app(ty_@2, ff), fg), fb) → new_ltEs8(wzz5010, wzz5210, ff, fg)
new_esEs23(wzz500, wzz4000, ty_Float) → new_esEs10(wzz500, wzz4000)
new_esEs22(wzz5010, wzz5210, ty_@0) → new_esEs19(wzz5010, wzz5210)
new_esEs9(Integer(wzz500), Integer(wzz4000)) → new_primEqInt(wzz500, wzz4000)
new_compare31(wzz5000, wzz5200, app(app(app(ty_@3, bdc), bdd), bde)) → new_compare6(wzz5000, wzz5200, bdc, bdd, bde)
new_compare12(:%(wzz5000, wzz5001), :%(wzz5200, wzz5201), ty_Int) → new_compare5(new_sr(wzz5000, wzz5201), new_sr(wzz5200, wzz5001))
new_lt21(wzz500, wzz520, app(app(app(ty_@3, bed), bee), bef)) → new_lt8(wzz500, wzz520, bed, bee, bef)
new_compare31(wzz5000, wzz5200, app(ty_Maybe, beb)) → new_compare27(wzz5000, wzz5200, beb)
new_lt12(wzz5010, wzz5210, ty_Ordering) → new_lt15(wzz5010, wzz5210)
new_primEqInt(Pos(Succ(wzz5000)), Pos(Succ(wzz40000))) → new_primEqNat0(wzz5000, wzz40000)
new_compare10(wzz500, wzz520, False, beg, beh) → GT
new_ltEs5(Left(wzz5010), Left(wzz5210), app(app(ty_Either, fc), fd), fb) → new_ltEs5(wzz5010, wzz5210, fc, fd)
new_ltEs19(wzz5012, wzz5212, ty_Bool) → new_ltEs14(wzz5012, wzz5212)
new_ltEs18(wzz5011, wzz5211, ty_@0) → new_ltEs10(wzz5011, wzz5211)
new_esEs28(wzz502, wzz4002, ty_Char) → new_esEs17(wzz502, wzz4002)
new_esEs23(wzz500, wzz4000, ty_Char) → new_esEs17(wzz500, wzz4000)
new_esEs5(Right(wzz500), Right(wzz4000), bhg, app(app(ty_Either, cad), cae)) → new_esEs5(wzz500, wzz4000, cad, cae)
new_ltEs5(Left(wzz5010), Left(wzz5210), app(app(app(ty_@3, eg), eh), fa), fb) → new_ltEs6(wzz5010, wzz5210, eg, eh, fa)
new_primEqNat0(Succ(wzz5000), Succ(wzz40000)) → new_primEqNat0(wzz5000, wzz40000)
new_esEs27(wzz501, wzz4001, ty_Ordering) → new_esEs8(wzz501, wzz4001)
new_ltEs14(False, False) → True
new_esEs23(wzz500, wzz4000, app(ty_Ratio, cgf)) → new_esEs14(wzz500, wzz4000, cgf)
new_lt5(wzz500, wzz520) → new_esEs8(new_compare7(wzz500, wzz520), LT)
new_compare7(@0, @0) → EQ
new_compare31(wzz5000, wzz5200, app(app(ty_@2, bdh), bea)) → new_compare28(wzz5000, wzz5200, bdh, bea)
new_lt21(wzz500, wzz520, ty_Char) → new_lt6(wzz500, wzz520)
new_esEs22(wzz5010, wzz5210, ty_Bool) → new_esEs12(wzz5010, wzz5210)
new_esEs20(wzz500, wzz4000, ty_Float) → new_esEs10(wzz500, wzz4000)
new_esEs25(wzz5011, wzz5211, ty_@0) → new_esEs19(wzz5011, wzz5211)
new_esEs28(wzz502, wzz4002, ty_Int) → new_esEs11(wzz502, wzz4002)
new_esEs24(wzz5010, wzz5210, ty_Ordering) → new_esEs8(wzz5010, wzz5210)
new_ltEs13(Just(wzz5010), Just(wzz5210), app(ty_Ratio, ddg)) → new_ltEs7(wzz5010, wzz5210, ddg)
new_ltEs13(Just(wzz5010), Just(wzz5210), ty_Integer) → new_ltEs4(wzz5010, wzz5210)
new_ltEs19(wzz5012, wzz5212, ty_Int) → new_ltEs17(wzz5012, wzz5212)
new_esEs10(Float(wzz500, wzz501), Float(wzz4000, wzz4001)) → new_esEs11(new_sr(wzz500, wzz4000), new_sr(wzz501, wzz4001))
new_esEs21(wzz501, wzz4001, ty_Int) → new_esEs11(wzz501, wzz4001)
new_ltEs18(wzz5011, wzz5211, ty_Double) → new_ltEs11(wzz5011, wzz5211)
new_compare31(wzz5000, wzz5200, ty_Char) → new_compare11(wzz5000, wzz5200)
new_esEs7(Nothing, Nothing, cbc) → True
new_esEs28(wzz502, wzz4002, ty_Ordering) → new_esEs8(wzz502, wzz4002)
new_esEs8(EQ, LT) → False
new_esEs8(LT, EQ) → False
new_primEqInt(Pos(Zero), Pos(Succ(wzz40000))) → False
new_primEqInt(Pos(Succ(wzz5000)), Pos(Zero)) → False
new_esEs4(@3(wzz500, wzz501, wzz502), @3(wzz4000, wzz4001, wzz4002), che, chf, chg) → new_asAs(new_esEs26(wzz500, wzz4000, che), new_asAs(new_esEs27(wzz501, wzz4001, chf), new_esEs28(wzz502, wzz4002, chg)))
new_esEs27(wzz501, wzz4001, ty_@0) → new_esEs19(wzz501, wzz4001)
new_primPlusNat0(Succ(wzz42200), Zero) → Succ(wzz42200)
new_primPlusNat0(Zero, Succ(wzz9600)) → Succ(wzz9600)
new_ltEs5(Right(wzz5010), Right(wzz5210), gb, ty_Integer) → new_ltEs4(wzz5010, wzz5210)
new_esEs5(Right(wzz500), Right(wzz4000), bhg, ty_Float) → new_esEs10(wzz500, wzz4000)
new_ltEs19(wzz5012, wzz5212, ty_Ordering) → new_ltEs9(wzz5012, wzz5212)
new_esEs20(wzz500, wzz4000, app(app(app(ty_@3, cda), cdb), cdc)) → new_esEs4(wzz500, wzz4000, cda, cdb, cdc)
new_primCmpInt(Neg(Zero), Pos(Succ(wzz5200))) → LT
new_esEs7(Just(wzz500), Just(wzz4000), app(app(ty_Either, cbh), cca)) → new_esEs5(wzz500, wzz4000, cbh, cca)
new_esEs29(wzz500, wzz520, app(app(app(ty_@3, bed), bee), bef)) → new_esEs4(wzz500, wzz520, bed, bee, bef)
new_lt19(wzz5011, wzz5211, ty_Ordering) → new_lt15(wzz5011, wzz5211)
new_esEs20(wzz500, wzz4000, app(app(ty_Either, cdd), cde)) → new_esEs5(wzz500, wzz4000, cdd, cde)
new_compare110(wzz109, wzz110, wzz111, wzz112, False, wzz114, bgb, bgc) → new_compare17(wzz109, wzz110, wzz111, wzz112, wzz114, bgb, bgc)
new_esEs21(wzz501, wzz4001, ty_Double) → new_esEs13(wzz501, wzz4001)
new_esEs27(wzz501, wzz4001, ty_Integer) → new_esEs9(wzz501, wzz4001)
new_compare13(wzz500, wzz520, True) → LT
new_sr0(Integer(wzz52000), Integer(wzz50010)) → Integer(new_primMulInt(wzz52000, wzz50010))
new_esEs7(Just(wzz500), Just(wzz4000), app(app(app(ty_@3, cbe), cbf), cbg)) → new_esEs4(wzz500, wzz4000, cbe, cbf, cbg)
new_compare27(wzz500, wzz520, bfd) → new_compare210(wzz500, wzz520, new_esEs7(wzz500, wzz520, bfd), bfd)
new_primEqInt(Neg(Succ(wzz5000)), Pos(wzz4000)) → False
new_primEqInt(Pos(Succ(wzz5000)), Neg(wzz4000)) → False
new_esEs5(Right(wzz500), Right(wzz4000), bhg, ty_@0) → new_esEs19(wzz500, wzz4000)
new_esEs28(wzz502, wzz4002, app(app(ty_Either, dch), dda)) → new_esEs5(wzz502, wzz4002, dch, dda)
new_esEs7(Just(wzz500), Just(wzz4000), ty_Integer) → new_esEs9(wzz500, wzz4000)
new_esEs26(wzz500, wzz4000, ty_Double) → new_esEs13(wzz500, wzz4000)
new_esEs7(Nothing, Just(wzz4000), cbc) → False
new_esEs7(Just(wzz500), Nothing, cbc) → False
new_ltEs20(wzz501, wzz521, ty_Integer) → new_ltEs4(wzz501, wzz521)
new_compare210(wzz500, wzz520, True, bfd) → EQ
new_esEs13(Double(wzz500, wzz501), Double(wzz4000, wzz4001)) → new_esEs11(new_sr(wzz500, wzz4000), new_sr(wzz501, wzz4001))
new_primCmpNat2(Zero, Succ(wzz52000)) → LT
new_esEs22(wzz5010, wzz5210, app(app(ty_@2, bbd), bbe)) → new_esEs6(wzz5010, wzz5210, bbd, bbe)
new_primEqInt(Neg(Zero), Pos(Succ(wzz40000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(wzz40000))) → False
new_compare30(wzz500, wzz520) → new_compare211(wzz500, wzz520, new_esEs12(wzz500, wzz520))
new_compare9(Double(wzz5000, wzz5001), Double(wzz5200, wzz5201)) → new_compare5(new_sr(wzz5000, wzz5200), new_sr(wzz5001, wzz5201))
new_esEs27(wzz501, wzz4001, ty_Float) → new_esEs10(wzz501, wzz4001)
new_esEs8(GT, EQ) → False
new_esEs8(EQ, GT) → False
new_esEs7(Just(wzz500), Just(wzz4000), ty_Double) → new_esEs13(wzz500, wzz4000)
new_lt12(wzz5010, wzz5210, ty_Char) → new_lt6(wzz5010, wzz5210)
new_esEs28(wzz502, wzz4002, app(ty_Ratio, ddc)) → new_esEs14(wzz502, wzz4002, ddc)
new_lt21(wzz500, wzz520, ty_Bool) → new_lt17(wzz500, wzz520)
new_primCompAux0(wzz144, LT) → LT
new_ltEs5(Left(wzz5010), Left(wzz5210), ty_Bool, fb) → new_ltEs14(wzz5010, wzz5210)
new_ltEs15(wzz501, wzz521, bda) → new_fsEs(new_compare0(wzz501, wzz521, bda))
new_esEs20(wzz500, wzz4000, ty_Double) → new_esEs13(wzz500, wzz4000)
new_ltEs20(wzz501, wzz521, app(app(app(ty_@3, h), ba), cf)) → new_ltEs6(wzz501, wzz521, h, ba, cf)
new_esEs11(wzz50, wzz400) → new_primEqInt(wzz50, wzz400)
new_not(False) → True
new_lt16(wzz500, wzz520) → new_esEs8(new_compare9(wzz500, wzz520), LT)
new_lt19(wzz5011, wzz5211, app(app(ty_Either, cg), da)) → new_lt13(wzz5011, wzz5211, cg, da)
new_esEs26(wzz500, wzz4000, app(ty_Ratio, dag)) → new_esEs14(wzz500, wzz4000, dag)
new_esEs23(wzz500, wzz4000, app(app(ty_@2, cgg), cgh)) → new_esEs6(wzz500, wzz4000, cgg, cgh)
new_ltEs5(Left(wzz5010), Left(wzz5210), app(ty_Ratio, bff), fb) → new_ltEs7(wzz5010, wzz5210, bff)
new_lt10(wzz500, wzz520) → new_esEs8(new_compare19(wzz500, wzz520), LT)
new_esEs25(wzz5011, wzz5211, ty_Double) → new_esEs13(wzz5011, wzz5211)
new_ltEs18(wzz5011, wzz5211, app(app(app(ty_@3, he), hf), hg)) → new_ltEs6(wzz5011, wzz5211, he, hf, hg)
new_compare17(wzz109, wzz110, wzz111, wzz112, False, bgb, bgc) → GT
new_ltEs9(LT, GT) → True
new_esEs24(wzz5010, wzz5210, ty_@0) → new_esEs19(wzz5010, wzz5210)
new_esEs25(wzz5011, wzz5211, ty_Float) → new_esEs10(wzz5011, wzz5211)
new_ltEs8(@2(wzz5010, wzz5011), @2(wzz5210, wzz5211), hd, bba) → new_pePe(new_lt12(wzz5010, wzz5210, hd), new_asAs(new_esEs22(wzz5010, wzz5210, hd), new_ltEs18(wzz5011, wzz5211, bba)))
new_lt21(wzz500, wzz520, ty_Ordering) → new_lt15(wzz500, wzz520)
new_esEs25(wzz5011, wzz5211, app(app(app(ty_@3, cc), cd), ce)) → new_esEs4(wzz5011, wzz5211, cc, cd, ce)
new_compare0(:(wzz5000, wzz5001), [], bdb) → GT
new_ltEs19(wzz5012, wzz5212, app(app(app(ty_@3, bb), bc), bd)) → new_ltEs6(wzz5012, wzz5212, bb, bc, bd)
new_esEs5(Left(wzz500), Left(wzz4000), ty_Double, bgd) → new_esEs13(wzz500, wzz4000)
new_ltEs7(wzz501, wzz521, cbb) → new_fsEs(new_compare12(wzz501, wzz521, cbb))
new_esEs22(wzz5010, wzz5210, app(app(app(ty_@3, baf), bag), bah)) → new_esEs4(wzz5010, wzz5210, baf, bag, bah)
new_esEs27(wzz501, wzz4001, app(ty_[], dbb)) → new_esEs18(wzz501, wzz4001, dbb)
new_lt21(wzz500, wzz520, ty_@0) → new_lt5(wzz500, wzz520)
new_esEs26(wzz500, wzz4000, app(app(ty_Either, dad), dae)) → new_esEs5(wzz500, wzz4000, dad, dae)
new_esEs7(Just(wzz500), Just(wzz4000), ty_Bool) → new_esEs12(wzz500, wzz4000)
new_esEs27(wzz501, wzz4001, ty_Int) → new_esEs11(wzz501, wzz4001)
new_ltEs19(wzz5012, wzz5212, app(ty_[], cb)) → new_ltEs15(wzz5012, wzz5212, cb)
new_lt13(wzz500, wzz520, beg, beh) → new_esEs8(new_compare14(wzz500, wzz520, beg, beh), LT)
new_lt19(wzz5011, wzz5211, ty_Char) → new_lt6(wzz5011, wzz5211)
new_primCmpInt(Pos(Succ(wzz5000)), Neg(wzz520)) → GT
new_ltEs5(Left(wzz5010), Left(wzz5210), ty_Char, fb) → new_ltEs12(wzz5010, wzz5210)
new_esEs28(wzz502, wzz4002, app(ty_Maybe, ddb)) → new_esEs7(wzz502, wzz4002, ddb)
new_lt21(wzz500, wzz520, app(app(ty_@2, bfa), bfb)) → new_lt14(wzz500, wzz520, bfa, bfb)
new_esEs29(wzz500, wzz520, ty_Integer) → new_esEs9(wzz500, wzz520)
new_esEs21(wzz501, wzz4001, app(ty_Maybe, ceh)) → new_esEs7(wzz501, wzz4001, ceh)
new_esEs16(wzz501, wzz4001, ty_Integer) → new_esEs9(wzz501, wzz4001)
new_primMulInt(Pos(wzz5000), Pos(wzz40000)) → Pos(new_primMulNat0(wzz5000, wzz40000))
new_lt19(wzz5011, wzz5211, app(app(ty_@2, db), dc)) → new_lt14(wzz5011, wzz5211, db, dc)
new_lt21(wzz500, wzz520, ty_Float) → new_lt10(wzz500, wzz520)
new_esEs27(wzz501, wzz4001, ty_Char) → new_esEs17(wzz501, wzz4001)
new_esEs22(wzz5010, wzz5210, ty_Double) → new_esEs13(wzz5010, wzz5210)
new_esEs5(Right(wzz500), Right(wzz4000), bhg, app(app(app(ty_@3, caa), cab), cac)) → new_esEs4(wzz500, wzz4000, caa, cab, cac)
new_lt19(wzz5011, wzz5211, app(ty_Maybe, dd)) → new_lt11(wzz5011, wzz5211, dd)
new_esEs5(Left(wzz500), Right(wzz4000), bhg, bgd) → False
new_esEs5(Right(wzz500), Left(wzz4000), bhg, bgd) → False
new_primMulInt(Neg(wzz5000), Neg(wzz40000)) → Pos(new_primMulNat0(wzz5000, wzz40000))
new_esEs27(wzz501, wzz4001, app(app(ty_@2, dcb), dcc)) → new_esEs6(wzz501, wzz4001, dcb, dcc)
new_primCmpNat2(Zero, Zero) → EQ
new_esEs5(Right(wzz500), Right(wzz4000), bhg, ty_Ordering) → new_esEs8(wzz500, wzz4000)
new_ltEs5(Right(wzz5010), Right(wzz5210), gb, app(ty_[], hc)) → new_ltEs15(wzz5010, wzz5210, hc)
new_lt9(wzz500, wzz520) → new_esEs8(new_compare8(wzz500, wzz520), LT)
new_esEs29(wzz500, wzz520, app(app(ty_@2, bfa), bfb)) → new_esEs6(wzz500, wzz520, bfa, bfb)
new_ltEs19(wzz5012, wzz5212, app(app(ty_Either, be), bf)) → new_ltEs5(wzz5012, wzz5212, be, bf)
new_primEqNat0(Zero, Succ(wzz40000)) → False
new_primEqNat0(Succ(wzz5000), Zero) → False
new_primPlusNat0(Zero, Zero) → Zero
new_esEs7(Just(wzz500), Just(wzz4000), ty_Int) → new_esEs11(wzz500, wzz4000)
new_compare31(wzz5000, wzz5200, ty_Integer) → new_compare8(wzz5000, wzz5200)
new_lt12(wzz5010, wzz5210, ty_Double) → new_lt16(wzz5010, wzz5210)
new_compare25(wzz500, wzz520, True, beg, beh) → EQ
new_ltEs14(True, True) → True
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_lt7(wzz500, wzz520, bfh) → new_esEs8(new_compare12(wzz500, wzz520, bfh), LT)
new_primCmpNat2(Succ(wzz50000), Succ(wzz52000)) → new_primCmpNat2(wzz50000, wzz52000)
new_primCmpInt(Pos(Succ(wzz5000)), Pos(wzz520)) → new_primCmpNat0(wzz5000, wzz520)
new_esEs5(Right(wzz500), Right(wzz4000), bhg, ty_Bool) → new_esEs12(wzz500, wzz4000)
new_esEs5(Left(wzz500), Left(wzz4000), app(ty_[], bge), bgd) → new_esEs18(wzz500, wzz4000, bge)
new_primCmpNat0(wzz5000, Zero) → GT
new_ltEs9(GT, GT) → True
new_esEs23(wzz500, wzz4000, ty_Int) → new_esEs11(wzz500, wzz4000)
new_ltEs20(wzz501, wzz521, ty_Int) → new_ltEs17(wzz501, wzz521)
new_primPlusNat1(Succ(wzz1000), wzz400000) → Succ(Succ(new_primPlusNat0(wzz1000, wzz400000)))
new_esEs21(wzz501, wzz4001, ty_Char) → new_esEs17(wzz501, wzz4001)
new_primCmpInt(Pos(Zero), Neg(Succ(wzz5200))) → GT
new_esEs5(Right(wzz500), Right(wzz4000), bhg, ty_Int) → new_esEs11(wzz500, wzz4000)
new_compare5(wzz50, wzz52) → new_primCmpInt(wzz50, wzz52)
new_esEs25(wzz5011, wzz5211, app(ty_Ratio, chb)) → new_esEs14(wzz5011, wzz5211, chb)
new_compare0(:(wzz5000, wzz5001), :(wzz5200, wzz5201), bdb) → new_primCompAux1(wzz5000, wzz5200, new_compare0(wzz5001, wzz5201, bdb), bdb)
new_ltEs5(Right(wzz5010), Right(wzz5210), gb, ty_Char) → new_ltEs12(wzz5010, wzz5210)
new_lt19(wzz5011, wzz5211, app(ty_[], de)) → new_lt18(wzz5011, wzz5211, de)
new_ltEs5(Left(wzz5010), Left(wzz5210), ty_@0, fb) → new_ltEs10(wzz5010, wzz5210)
new_ltEs5(Right(wzz5010), Right(wzz5210), gb, ty_@0) → new_ltEs10(wzz5010, wzz5210)
new_esEs21(wzz501, wzz4001, app(app(app(ty_@3, cec), ced), cee)) → new_esEs4(wzz501, wzz4001, cec, ced, cee)
new_esEs24(wzz5010, wzz5210, ty_Int) → new_esEs11(wzz5010, wzz5210)
new_esEs28(wzz502, wzz4002, app(app(ty_@2, ddd), dde)) → new_esEs6(wzz502, wzz4002, ddd, dde)
new_lt20(wzz5010, wzz5210, ty_Double) → new_lt16(wzz5010, wzz5210)
new_esEs25(wzz5011, wzz5211, app(ty_Maybe, dd)) → new_esEs7(wzz5011, wzz5211, dd)
new_ltEs13(Just(wzz5010), Just(wzz5210), app(ty_Maybe, bcg)) → new_ltEs13(wzz5010, wzz5210, bcg)
new_esEs15(wzz500, wzz4000, ty_Int) → new_esEs11(wzz500, wzz4000)
new_esEs28(wzz502, wzz4002, app(ty_[], dcd)) → new_esEs18(wzz502, wzz4002, dcd)
new_esEs28(wzz502, wzz4002, ty_Integer) → new_esEs9(wzz502, wzz4002)
new_ltEs13(Just(wzz5010), Nothing, ddf) → False
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs27(wzz501, wzz4001, app(ty_Ratio, dca)) → new_esEs14(wzz501, wzz4001, dca)
new_esEs25(wzz5011, wzz5211, ty_Bool) → new_esEs12(wzz5011, wzz5211)
new_compare11(Char(wzz5000), Char(wzz5200)) → new_primCmpNat2(wzz5000, wzz5200)
new_primCompAux1(wzz5000, wzz5200, wzz130, bdb) → new_primCompAux0(wzz130, new_compare31(wzz5000, wzz5200, bdb))
new_esEs7(Just(wzz500), Just(wzz4000), app(ty_[], cbd)) → new_esEs18(wzz500, wzz4000, cbd)
new_asAs(False, wzz60) → False
new_esEs29(wzz500, wzz520, ty_Bool) → new_esEs12(wzz500, wzz520)
new_primMulInt(Pos(wzz5000), Neg(wzz40000)) → Neg(new_primMulNat0(wzz5000, wzz40000))
new_primMulInt(Neg(wzz5000), Pos(wzz40000)) → Neg(new_primMulNat0(wzz5000, wzz40000))
new_esEs27(wzz501, wzz4001, ty_Double) → new_esEs13(wzz501, wzz4001)
new_primMulNat0(Succ(wzz50000), Zero) → Zero
new_primMulNat0(Zero, Succ(wzz400000)) → Zero
new_esEs24(wzz5010, wzz5210, ty_Double) → new_esEs13(wzz5010, wzz5210)
new_esEs18([], [], cff) → True
new_esEs21(wzz501, wzz4001, app(app(ty_Either, cef), ceg)) → new_esEs5(wzz501, wzz4001, cef, ceg)
new_esEs21(wzz501, wzz4001, ty_Ordering) → new_esEs8(wzz501, wzz4001)
new_ltEs20(wzz501, wzz521, ty_Double) → new_ltEs11(wzz501, wzz521)
new_esEs24(wzz5010, wzz5210, ty_Float) → new_esEs10(wzz5010, wzz5210)
new_ltEs5(Left(wzz5010), Left(wzz5210), app(ty_[], ga), fb) → new_ltEs15(wzz5010, wzz5210, ga)
new_esEs29(wzz500, wzz520, ty_Int) → new_esEs11(wzz500, wzz520)
new_compare29(@2(wzz500, wzz501), @2(wzz520, wzz521), False, bfe, bfc) → new_compare110(wzz500, wzz501, wzz520, wzz521, new_lt21(wzz500, wzz520, bfe), new_asAs(new_esEs29(wzz500, wzz520, bfe), new_ltEs20(wzz501, wzz521, bfc)), bfe, bfc)
new_esEs26(wzz500, wzz4000, app(ty_Maybe, daf)) → new_esEs7(wzz500, wzz4000, daf)
new_esEs29(wzz500, wzz520, ty_Char) → new_esEs17(wzz500, wzz520)
new_ltEs19(wzz5012, wzz5212, ty_@0) → new_ltEs10(wzz5012, wzz5212)
new_esEs29(wzz500, wzz520, ty_Double) → new_esEs13(wzz500, wzz520)
new_compare31(wzz5000, wzz5200, ty_Float) → new_compare19(wzz5000, wzz5200)
new_ltEs20(wzz501, wzz521, ty_Ordering) → new_ltEs9(wzz501, wzz521)
new_primCmpNat1(Succ(wzz5200), wzz5000) → new_primCmpNat2(wzz5200, wzz5000)
new_primCmpNat2(Succ(wzz50000), Zero) → GT
new_ltEs18(wzz5011, wzz5211, ty_Bool) → new_ltEs14(wzz5011, wzz5211)
new_ltEs5(Left(wzz5010), Left(wzz5210), app(ty_Maybe, fh), fb) → new_ltEs13(wzz5010, wzz5210, fh)
new_esEs29(wzz500, wzz520, ty_Float) → new_esEs10(wzz500, wzz520)
new_compare31(wzz5000, wzz5200, app(ty_[], bec)) → new_compare0(wzz5000, wzz5200, bec)
new_esEs21(wzz501, wzz4001, ty_Integer) → new_esEs9(wzz501, wzz4001)
new_esEs28(wzz502, wzz4002, ty_@0) → new_esEs19(wzz502, wzz4002)
new_ltEs18(wzz5011, wzz5211, ty_Char) → new_ltEs12(wzz5011, wzz5211)
new_compare18(wzz500, wzz520, False, bed, bee, bef) → GT
new_ltEs18(wzz5011, wzz5211, ty_Int) → new_ltEs17(wzz5011, wzz5211)
new_ltEs18(wzz5011, wzz5211, app(app(ty_@2, bab), bac)) → new_ltEs8(wzz5011, wzz5211, bab, bac)
new_esEs26(wzz500, wzz4000, ty_Integer) → new_esEs9(wzz500, wzz4000)
new_esEs24(wzz5010, wzz5210, ty_Bool) → new_esEs12(wzz5010, wzz5210)
new_ltEs18(wzz5011, wzz5211, app(ty_Maybe, bad)) → new_ltEs13(wzz5011, wzz5211, bad)
new_lt21(wzz500, wzz520, ty_Double) → new_lt16(wzz500, wzz520)
new_ltEs9(GT, EQ) → False
new_esEs12(True, False) → False
new_esEs12(False, True) → False
new_compare31(wzz5000, wzz5200, app(app(ty_Either, bdf), bdg)) → new_compare14(wzz5000, wzz5200, bdf, bdg)
new_ltEs12(wzz501, wzz521) → new_fsEs(new_compare11(wzz501, wzz521))
new_lt18(wzz500, wzz520, bdb) → new_esEs8(new_compare0(wzz500, wzz520, bdb), LT)
new_esEs15(wzz500, wzz4000, ty_Integer) → new_esEs9(wzz500, wzz4000)
new_esEs14(:%(wzz500, wzz501), :%(wzz4000, wzz4001), bga) → new_asAs(new_esEs15(wzz500, wzz4000, bga), new_esEs16(wzz501, wzz4001, bga))
new_esEs27(wzz501, wzz4001, ty_Bool) → new_esEs12(wzz501, wzz4001)
new_ltEs13(Just(wzz5010), Just(wzz5210), app(app(ty_@2, bce), bcf)) → new_ltEs8(wzz5010, wzz5210, bce, bcf)
new_ltEs5(Right(wzz5010), Right(wzz5210), gb, ty_Int) → new_ltEs17(wzz5010, wzz5210)
new_esEs7(Just(wzz500), Just(wzz4000), ty_Char) → new_esEs17(wzz500, wzz4000)
new_lt12(wzz5010, wzz5210, ty_Int) → new_lt4(wzz5010, wzz5210)
new_ltEs6(@3(wzz5010, wzz5011, wzz5012), @3(wzz5210, wzz5211, wzz5212), h, ba, cf) → new_pePe(new_lt20(wzz5010, wzz5210, h), new_asAs(new_esEs24(wzz5010, wzz5210, h), new_pePe(new_lt19(wzz5011, wzz5211, ba), new_asAs(new_esEs25(wzz5011, wzz5211, ba), new_ltEs19(wzz5012, wzz5212, cf)))))
new_esEs7(Just(wzz500), Just(wzz4000), ty_@0) → new_esEs19(wzz500, wzz4000)
new_ltEs20(wzz501, wzz521, app(ty_[], bda)) → new_ltEs15(wzz501, wzz521, bda)
new_ltEs19(wzz5012, wzz5212, app(ty_Maybe, ca)) → new_ltEs13(wzz5012, wzz5212, ca)
new_esEs7(Just(wzz500), Just(wzz4000), ty_Float) → new_esEs10(wzz500, wzz4000)
new_ltEs13(Just(wzz5010), Just(wzz5210), app(app(ty_Either, bcc), bcd)) → new_ltEs5(wzz5010, wzz5210, bcc, bcd)
new_ltEs14(True, False) → False
new_ltEs18(wzz5011, wzz5211, ty_Float) → new_ltEs16(wzz5011, wzz5211)
new_ltEs18(wzz5011, wzz5211, ty_Ordering) → new_ltEs9(wzz5011, wzz5211)
new_lt12(wzz5010, wzz5210, app(app(ty_Either, bbb), bbc)) → new_lt13(wzz5010, wzz5210, bbb, bbc)
new_esEs5(Left(wzz500), Left(wzz4000), app(app(ty_Either, bha), bhb), bgd) → new_esEs5(wzz500, wzz4000, bha, bhb)
new_lt21(wzz500, wzz520, ty_Int) → new_lt4(wzz500, wzz520)
new_lt21(wzz500, wzz520, app(ty_Ratio, bfh)) → new_lt7(wzz500, wzz520, bfh)
new_lt19(wzz5011, wzz5211, ty_Integer) → new_lt9(wzz5011, wzz5211)
new_ltEs10(wzz501, wzz521) → new_fsEs(new_compare7(wzz501, wzz521))
new_esEs22(wzz5010, wzz5210, ty_Float) → new_esEs10(wzz5010, wzz5210)
new_esEs20(wzz500, wzz4000, ty_Char) → new_esEs17(wzz500, wzz4000)
new_primPlusNat0(Succ(wzz42200), Succ(wzz9600)) → Succ(Succ(new_primPlusNat0(wzz42200, wzz9600)))
new_esEs29(wzz500, wzz520, app(ty_[], bdb)) → new_esEs18(wzz500, wzz520, bdb)
new_compare0([], :(wzz5200, wzz5201), bdb) → LT
new_compare15(wzz500, wzz520, True, bfd) → LT
new_asAs(True, wzz60) → wzz60
new_esEs25(wzz5011, wzz5211, ty_Int) → new_esEs11(wzz5011, wzz5211)
new_ltEs19(wzz5012, wzz5212, app(ty_Ratio, chc)) → new_ltEs7(wzz5012, wzz5212, chc)
new_lt20(wzz5010, wzz5210, ty_Bool) → new_lt17(wzz5010, wzz5210)
new_ltEs5(Right(wzz5010), Right(wzz5210), gb, ty_Float) → new_ltEs16(wzz5010, wzz5210)
new_lt19(wzz5011, wzz5211, ty_Float) → new_lt10(wzz5011, wzz5211)
new_ltEs13(Just(wzz5010), Just(wzz5210), ty_Float) → new_ltEs16(wzz5010, wzz5210)
new_compare211(wzz500, wzz520, True) → EQ
new_fsEs(wzz121) → new_not(new_esEs8(wzz121, GT))
new_compare28(wzz500, wzz520, bfa, bfb) → new_compare29(wzz500, wzz520, new_esEs6(wzz500, wzz520, bfa, bfb), bfa, bfb)
new_esEs26(wzz500, wzz4000, app(app(ty_@2, dah), dba)) → new_esEs6(wzz500, wzz4000, dah, dba)
new_ltEs5(Right(wzz5010), Right(wzz5210), gb, app(ty_Maybe, hb)) → new_ltEs13(wzz5010, wzz5210, hb)
new_esEs29(wzz500, wzz520, app(ty_Ratio, bfh)) → new_esEs14(wzz500, wzz520, bfh)
new_lt20(wzz5010, wzz5210, app(ty_Ratio, cha)) → new_lt7(wzz5010, wzz5210, cha)
new_lt17(wzz500, wzz520) → new_esEs8(new_compare30(wzz500, wzz520), LT)
new_esEs24(wzz5010, wzz5210, app(app(app(ty_@3, df), dg), dh)) → new_esEs4(wzz5010, wzz5210, df, dg, dh)
new_esEs23(wzz500, wzz4000, app(ty_[], cfg)) → new_esEs18(wzz500, wzz4000, cfg)
new_esEs21(wzz501, wzz4001, ty_Bool) → new_esEs12(wzz501, wzz4001)
new_esEs5(Left(wzz500), Left(wzz4000), ty_Integer, bgd) → new_esEs9(wzz500, wzz4000)
new_compare24(wzz500, wzz520, False, bed, bee, bef) → new_compare18(wzz500, wzz520, new_ltEs6(wzz500, wzz520, bed, bee, bef), bed, bee, bef)
new_esEs22(wzz5010, wzz5210, app(app(ty_Either, bbb), bbc)) → new_esEs5(wzz5010, wzz5210, bbb, bbc)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCompAux0(wzz144, EQ) → wzz144
new_ltEs13(Just(wzz5010), Just(wzz5210), ty_Bool) → new_ltEs14(wzz5010, wzz5210)
new_esEs29(wzz500, wzz520, ty_Ordering) → new_esEs8(wzz500, wzz520)
new_ltEs20(wzz501, wzz521, app(app(ty_Either, gb), fb)) → new_ltEs5(wzz501, wzz521, gb, fb)
new_esEs28(wzz502, wzz4002, ty_Bool) → new_esEs12(wzz502, wzz4002)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_lt19(wzz5011, wzz5211, ty_@0) → new_lt5(wzz5011, wzz5211)
new_esEs22(wzz5010, wzz5210, app(ty_Maybe, bbf)) → new_esEs7(wzz5010, wzz5210, bbf)
new_ltEs5(Left(wzz5010), Left(wzz5210), ty_Double, fb) → new_ltEs11(wzz5010, wzz5210)
new_esEs5(Right(wzz500), Right(wzz4000), bhg, app(ty_Maybe, caf)) → new_esEs7(wzz500, wzz4000, caf)
new_primCmpInt(Neg(Succ(wzz5000)), Pos(wzz520)) → LT
new_not(True) → False
new_esEs25(wzz5011, wzz5211, ty_Integer) → new_esEs9(wzz5011, wzz5211)
new_esEs5(Left(wzz500), Left(wzz4000), ty_Char, bgd) → new_esEs17(wzz500, wzz4000)

The set Q consists of the following terms:

new_compare10(x0, x1, False, x2, x3)
new_primPlusNat0(Zero, Succ(x0))
new_sr(x0, x1)
new_esEs5(Right(x0), Right(x1), x2, ty_Double)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_primEqNat0(Succ(x0), Zero)
new_esEs5(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs22(x0, x1, ty_Double)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs26(x0, x1, ty_Char)
new_ltEs20(x0, x1, app(ty_[], x2))
new_ltEs5(Right(x0), Right(x1), x2, ty_Char)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs5(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_lt19(x0, x1, ty_@0)
new_ltEs5(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs21(x0, x1, ty_Double)
new_esEs9(Integer(x0), Integer(x1))
new_esEs21(x0, x1, ty_Ordering)
new_esEs5(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs20(x0, x1, ty_Float)
new_esEs26(x0, x1, ty_Int)
new_asAs(True, x0)
new_compare111(x0, x1, True)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqNat0(Zero, Succ(x0))
new_ltEs20(x0, x1, ty_Int)
new_esEs5(Left(x0), Left(x1), ty_Integer, x2)
new_esEs5(Right(x0), Right(x1), x2, ty_Integer)
new_lt21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs22(x0, x1, ty_Bool)
new_esEs12(False, False)
new_ltEs5(Right(x0), Right(x1), x2, ty_Integer)
new_compare15(x0, x1, False, x2)
new_compare31(x0, x1, app(ty_[], x2))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_esEs7(Nothing, Just(x0), x1)
new_primCmpNat2(Zero, Succ(x0))
new_compare19(Float(x0, x1), Float(x2, x3))
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_primCmpNat0(x0, Zero)
new_compare11(Char(x0), Char(x1))
new_ltEs19(x0, x1, ty_Double)
new_ltEs20(x0, x1, ty_@0)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_compare10(x0, x1, True, x2, x3)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs20(x0, x1, ty_Integer)
new_lt20(x0, x1, ty_Double)
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_primCompAux0(x0, LT)
new_compare31(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_Integer)
new_compare24(x0, x1, False, x2, x3, x4)
new_compare31(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Bool)
new_lt20(x0, x1, ty_Bool)
new_compare16(x0, x1)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs20(x0, x1, ty_Int)
new_esEs17(Char(x0), Char(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_ltEs14(True, False)
new_ltEs14(False, True)
new_ltEs13(Just(x0), Just(x1), app(ty_Ratio, x2))
new_lt21(x0, x1, ty_@0)
new_esEs8(GT, GT)
new_compare13(x0, x1, True)
new_ltEs5(Right(x0), Right(x1), x2, ty_Bool)
new_compare30(x0, x1)
new_ltEs15(x0, x1, x2)
new_esEs23(x0, x1, ty_Double)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(ty_[], x2))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_compare31(x0, x1, app(ty_Maybe, x2))
new_ltEs13(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs5(Right(x0), Right(x1), x2, ty_Int)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs8(LT, LT)
new_esEs29(x0, x1, ty_Integer)
new_lt8(x0, x1, x2, x3, x4)
new_esEs23(x0, x1, ty_Ordering)
new_ltEs13(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primCmpNat1(Succ(x0), x1)
new_esEs14(:%(x0, x1), :%(x2, x3), x4)
new_esEs18([], [], x0)
new_compare9(Double(x0, x1), Double(x2, x3))
new_lt21(x0, x1, ty_Bool)
new_esEs5(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Left(x0), Left(x1), ty_Char, x2)
new_compare26(x0, x1, False)
new_lt7(x0, x1, x2)
new_compare29(x0, x1, True, x2, x3)
new_lt12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs5(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt4(x0, x1)
new_compare12(:%(x0, x1), :%(x2, x3), ty_Int)
new_compare31(x0, x1, ty_Integer)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs28(x0, x1, ty_@0)
new_compare15(x0, x1, True, x2)
new_esEs22(x0, x1, ty_Integer)
new_esEs15(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Float)
new_ltEs5(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs8(GT, LT)
new_esEs8(LT, GT)
new_ltEs5(Left(x0), Left(x1), ty_Int, x2)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_ltEs20(x0, x1, ty_Bool)
new_compare28(x0, x1, x2, x3)
new_lt20(x0, x1, ty_Int)
new_primEqNat0(Succ(x0), Succ(x1))
new_ltEs13(Just(x0), Just(x1), ty_Integer)
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs9(EQ, EQ)
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_compare26(x0, x1, True)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare13(x0, x1, False)
new_esEs20(x0, x1, ty_@0)
new_esEs22(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Int)
new_primEqNat0(Zero, Zero)
new_ltEs18(x0, x1, ty_Int)
new_esEs20(x0, x1, ty_Double)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, ty_Float)
new_esEs5(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs13(Just(x0), Just(x1), ty_Float)
new_sr0(Integer(x0), Integer(x1))
new_ltEs12(x0, x1)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, ty_Bool)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, ty_Ordering)
new_esEs27(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Integer)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, ty_@0)
new_compare14(x0, x1, x2, x3)
new_esEs5(Right(x0), Right(x1), x2, ty_Char)
new_lt21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs18(:(x0, x1), [], x2)
new_esEs5(Left(x0), Left(x1), ty_Bool, x2)
new_esEs23(x0, x1, ty_Integer)
new_primMulNat0(Zero, Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_lt20(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, ty_Integer)
new_compare31(x0, x1, app(ty_Ratio, x2))
new_lt15(x0, x1)
new_esEs7(Just(x0), Nothing, x1)
new_ltEs19(x0, x1, ty_@0)
new_esEs29(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_@0)
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs18(x0, x1, ty_Ordering)
new_compare24(x0, x1, True, x2, x3, x4)
new_ltEs5(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_compare27(x0, x1, x2)
new_compare0([], [], x0)
new_esEs27(x0, x1, ty_Float)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_ltEs13(Nothing, Just(x0), x1)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_lt21(x0, x1, ty_Int)
new_esEs7(Just(x0), Just(x1), ty_Char)
new_ltEs5(Right(x0), Right(x1), x2, ty_@0)
new_esEs28(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Float)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, ty_@0)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs27(x0, x1, ty_@0)
new_esEs21(x0, x1, ty_Integer)
new_ltEs5(Right(x0), Right(x1), x2, ty_Double)
new_ltEs13(Just(x0), Just(x1), ty_Char)
new_lt17(x0, x1)
new_esEs16(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Int)
new_compare0([], :(x0, x1), x2)
new_lt12(x0, x1, ty_Integer)
new_compare17(x0, x1, x2, x3, False, x4, x5)
new_esEs25(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, ty_Bool)
new_ltEs5(Left(x0), Left(x1), ty_Bool, x2)
new_esEs5(Left(x0), Left(x1), ty_Double, x2)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_primCmpNat0(x0, Succ(x1))
new_ltEs5(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_compare25(x0, x1, True, x2, x3)
new_esEs4(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs7(Just(x0), Just(x1), ty_@0)
new_ltEs9(GT, EQ)
new_ltEs9(EQ, GT)
new_esEs27(x0, x1, ty_Double)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_compare25(x0, x1, False, x2, x3)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, ty_Float)
new_ltEs13(Just(x0), Just(x1), ty_@0)
new_ltEs18(x0, x1, ty_Char)
new_lt19(x0, x1, app(ty_[], x2))
new_ltEs5(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_lt12(x0, x1, ty_Double)
new_esEs24(x0, x1, ty_@0)
new_ltEs13(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs5(Left(x0), Left(x1), ty_Char, x2)
new_esEs5(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_lt12(x0, x1, ty_Char)
new_lt21(x0, x1, ty_Ordering)
new_compare31(x0, x1, ty_Bool)
new_primCmpNat2(Zero, Zero)
new_primPlusNat1(Zero, x0)
new_esEs26(x0, x1, ty_Double)
new_primPlusNat0(Zero, Zero)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_compare111(x0, x1, False)
new_esEs20(x0, x1, app(ty_[], x2))
new_compare6(x0, x1, x2, x3, x4)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_esEs26(x0, x1, ty_Bool)
new_ltEs18(x0, x1, ty_Integer)
new_lt21(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_lt12(x0, x1, app(ty_[], x2))
new_esEs21(x0, x1, ty_Float)
new_esEs23(x0, x1, ty_Int)
new_lt19(x0, x1, ty_Ordering)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_ltEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs18(x0, x1, app(ty_[], x2))
new_pePe(False, x0)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, ty_Integer)
new_primCmpNat2(Succ(x0), Zero)
new_lt5(x0, x1)
new_esEs18(:(x0, x1), :(x2, x3), x4)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt21(x0, x1, ty_Integer)
new_lt19(x0, x1, ty_Integer)
new_esEs5(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs24(x0, x1, ty_Double)
new_ltEs18(x0, x1, ty_Double)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs5(Right(x0), Right(x1), x2, ty_Int)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt21(x0, x1, app(ty_[], x2))
new_ltEs9(EQ, LT)
new_ltEs9(LT, EQ)
new_esEs11(x0, x1)
new_esEs12(True, True)
new_lt21(x0, x1, app(app(ty_Either, x2), x3))
new_compare31(x0, x1, ty_@0)
new_esEs10(Float(x0, x1), Float(x2, x3))
new_ltEs19(x0, x1, ty_Char)
new_ltEs5(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_compare211(x0, x1, False)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_lt19(x0, x1, ty_Int)
new_primCompAux0(x0, EQ)
new_primCompAux1(x0, x1, x2, x3)
new_lt12(x0, x1, app(app(ty_Either, x2), x3))
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_lt13(x0, x1, x2, x3)
new_lt12(x0, x1, app(app(ty_@2, x2), x3))
new_lt18(x0, x1, x2)
new_esEs24(x0, x1, ty_Integer)
new_ltEs18(x0, x1, ty_Float)
new_ltEs5(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_lt20(x0, x1, ty_Integer)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_lt12(x0, x1, ty_Int)
new_esEs20(x0, x1, ty_Ordering)
new_esEs5(Left(x0), Left(x1), ty_Int, x2)
new_ltEs5(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt10(x0, x1)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs8(EQ, EQ)
new_esEs18([], :(x0, x1), x2)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs13(Just(x0), Just(x1), ty_Bool)
new_compare110(x0, x1, x2, x3, True, x4, x5, x6)
new_compare31(x0, x1, ty_Double)
new_primPlusNat0(Succ(x0), Zero)
new_esEs22(x0, x1, ty_Ordering)
new_ltEs16(x0, x1)
new_primEqInt(Neg(Zero), Neg(Zero))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_ltEs20(x0, x1, ty_Char)
new_lt12(x0, x1, ty_Ordering)
new_esEs28(x0, x1, ty_Ordering)
new_esEs22(x0, x1, ty_Int)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_lt21(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs29(x0, x1, ty_Double)
new_esEs25(x0, x1, ty_Ordering)
new_lt21(x0, x1, ty_Float)
new_esEs29(x0, x1, ty_Char)
new_compare0(:(x0, x1), :(x2, x3), x4)
new_primCompAux0(x0, GT)
new_esEs5(Left(x0), Left(x1), ty_Float, x2)
new_compare31(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, ty_Ordering)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_compare211(x0, x1, True)
new_compare7(@0, @0)
new_esEs20(x0, x1, ty_Char)
new_ltEs18(x0, x1, ty_@0)
new_lt11(x0, x1, x2)
new_primPlusNat0(Succ(x0), Succ(x1))
new_lt12(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_fsEs(x0)
new_compare29(@2(x0, x1), @2(x2, x3), False, x4, x5)
new_lt12(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Bool)
new_ltEs19(x0, x1, ty_Float)
new_ltEs9(LT, LT)
new_ltEs5(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs17(x0, x1)
new_esEs23(x0, x1, ty_@0)
new_ltEs20(x0, x1, ty_Float)
new_ltEs5(Left(x0), Right(x1), x2, x3)
new_ltEs5(Right(x0), Left(x1), x2, x3)
new_esEs5(Left(x0), Left(x1), ty_@0, x2)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, ty_Char)
new_esEs22(x0, x1, ty_Char)
new_esEs8(EQ, GT)
new_esEs8(GT, EQ)
new_ltEs13(Nothing, Nothing, x0)
new_compare5(x0, x1)
new_esEs22(x0, x1, ty_Float)
new_ltEs13(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_compare31(x0, x1, ty_Float)
new_esEs5(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs13(Double(x0, x1), Double(x2, x3))
new_esEs29(x0, x1, app(ty_[], x2))
new_ltEs13(Just(x0), Just(x1), ty_Int)
new_lt19(x0, x1, ty_Double)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs13(Just(x0), Just(x1), ty_Double)
new_esEs21(x0, x1, ty_Bool)
new_lt6(x0, x1)
new_ltEs5(Right(x0), Right(x1), x2, ty_Float)
new_lt14(x0, x1, x2, x3)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_lt21(x0, x1, ty_Double)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_pePe(True, x0)
new_esEs23(x0, x1, ty_Bool)
new_compare31(x0, x1, ty_Ordering)
new_compare18(x0, x1, True, x2, x3, x4)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primPlusNat1(Succ(x0), x1)
new_esEs5(Right(x0), Right(x1), x2, ty_@0)
new_esEs5(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs5(Left(x0), Left(x1), ty_Float, x2)
new_esEs25(x0, x1, ty_@0)
new_esEs24(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Ordering)
new_esEs5(Right(x0), Left(x1), x2, x3)
new_esEs5(Left(x0), Right(x1), x2, x3)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, ty_Float)
new_esEs16(x0, x1, ty_Int)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs5(Left(x0), Left(x1), ty_@0, x2)
new_ltEs5(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs12(True, False)
new_esEs12(False, True)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs13(Just(x0), Just(x1), app(ty_[], x2))
new_esEs5(Right(x0), Right(x1), x2, ty_Ordering)
new_compare17(x0, x1, x2, x3, True, x4, x5)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, ty_Ordering)
new_primMulNat0(Succ(x0), Zero)
new_esEs5(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs14(True, True)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_lt16(x0, x1)
new_ltEs14(False, False)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs9(GT, LT)
new_esEs7(Nothing, Nothing, x0)
new_ltEs9(LT, GT)
new_ltEs13(Just(x0), Just(x1), ty_Ordering)
new_esEs27(x0, x1, ty_Bool)
new_lt12(x0, x1, ty_Float)
new_compare210(x0, x1, True, x2)
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_asAs(False, x0)
new_ltEs5(Left(x0), Left(x1), ty_Ordering, x2)
new_primCmpNat1(Zero, x0)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_not(True)
new_compare31(x0, x1, ty_Char)
new_esEs25(x0, x1, ty_Int)
new_primMulNat0(Zero, Succ(x0))
new_ltEs13(Just(x0), Nothing, x1)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Bool)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Right(x0), Right(x1), x2, ty_Float)
new_esEs25(x0, x1, ty_Char)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs7(Just(x0), Just(x1), ty_Float)
new_compare8(Integer(x0), Integer(x1))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_not(False)
new_esEs29(x0, x1, ty_Bool)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_lt19(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs4(x0, x1)
new_esEs7(Just(x0), Just(x1), ty_Double)
new_esEs24(x0, x1, ty_Ordering)
new_ltEs7(x0, x1, x2)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, ty_Char)
new_ltEs5(Left(x0), Left(x1), ty_Integer, x2)
new_compare210(x0, x1, False, x2)
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare110(x0, x1, x2, x3, False, x4, x5, x6)
new_ltEs18(x0, x1, ty_Bool)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, app(ty_[], x2))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_ltEs10(x0, x1)
new_esEs28(x0, x1, app(ty_[], x2))
new_esEs28(x0, x1, ty_Double)
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_esEs28(x0, x1, ty_Float)
new_esEs23(x0, x1, ty_Float)
new_esEs8(LT, EQ)
new_esEs8(EQ, LT)
new_ltEs8(@2(x0, x1), @2(x2, x3), x4, x5)
new_compare18(x0, x1, False, x2, x3, x4)
new_esEs24(x0, x1, ty_Float)
new_lt9(x0, x1)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, ty_Int)
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpNat2(Succ(x0), Succ(x1))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_ltEs9(GT, GT)
new_esEs25(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Char)
new_esEs27(x0, x1, ty_Char)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, app(ty_[], x2))
new_lt19(x0, x1, ty_Char)
new_lt12(x0, x1, app(ty_Ratio, x2))
new_ltEs20(x0, x1, ty_Double)
new_esEs20(x0, x1, ty_Bool)
new_esEs7(Just(x0), Just(x1), ty_Int)
new_esEs5(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, ty_Ordering)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs25(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_Int)
new_ltEs5(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_ltEs5(Left(x0), Left(x1), ty_Double, x2)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs29(x0, x1, ty_Ordering)
new_esEs19(@0, @0)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_compare12(:%(x0, x1), :%(x2, x3), ty_Integer)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_lt21(x0, x1, ty_Char)
new_compare0(:(x0, x1), [], x2)
new_primMulInt(Pos(x0), Pos(x1))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_lt12(x0, x1, ty_Bool)
new_ltEs5(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs11(x0, x1)
new_esEs23(x0, x1, ty_Char)
new_esEs15(x0, x1, ty_Integer)
new_lt20(x0, x1, ty_@0)

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

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



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

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

new_addToFM_C2(wzz19, wzz20, wzz21, wzz22, wzz23, wzz24, wzz25, wzz26, wzz27, wzz28, False, h, ba, bb) → new_addToFM_C1(wzz19, wzz20, wzz21, wzz22, wzz23, wzz24, wzz25, wzz26, wzz27, wzz28, new_esEs8(new_compare29(@2(wzz26, wzz27), @2(wzz20, wzz21), new_esEs6(@2(wzz26, wzz27), @2(wzz20, wzz21), h, ba), h, ba), GT), h, ba, bb)
new_addToFM_C2(wzz19, wzz20, wzz21, wzz22, wzz23, wzz24, wzz25, wzz26, wzz27, wzz28, True, h, ba, bb) → new_addToFM_C(wzz19, wzz24, @2(wzz26, wzz27), wzz28, h, ba, bb)
new_addToFM_C1(wzz19, wzz20, wzz21, wzz22, wzz23, wzz24, wzz25, wzz26, wzz27, wzz28, True, h, ba, bb) → new_addToFM_C(wzz19, wzz25, @2(wzz26, wzz27), wzz28, h, ba, bb)
new_addToFM_C(wzz3, Branch(@2(wzz400, wzz401), wzz41, wzz42, wzz43, wzz44), @2(wzz50, wzz51), wzz6, bc, bd, be) → new_addToFM_C2(wzz3, wzz400, wzz401, wzz41, wzz42, wzz43, wzz44, wzz50, wzz51, wzz6, new_esEs30(wzz50, wzz51, wzz400, wzz401, new_esEs31(wzz50, wzz400, bc), bc, bd), bc, bd, be)

The TRS R consists of the following rules:

new_esEs7(Just(wzz500), Just(wzz4000), app(ty_Maybe, bec)) → new_esEs7(wzz500, wzz4000, bec)
new_primCmpNat0(wzz5000, Succ(wzz5200)) → new_primCmpNat2(wzz5000, wzz5200)
new_esEs20(wzz500, wzz4000, app(ty_Maybe, bfe)) → new_esEs7(wzz500, wzz4000, bfe)
new_esEs24(wzz5010, wzz5210, app(app(ty_Either, ceb), cec)) → new_esEs5(wzz5010, wzz5210, ceb, cec)
new_lt4(wzz500, wzz520) → new_esEs8(new_compare5(wzz500, wzz520), LT)
new_esEs21(wzz501, wzz4001, app(app(ty_@2, bha), bhb)) → new_esEs6(wzz501, wzz4001, bha, bhb)
new_compare31(wzz5000, wzz5200, ty_@0) → new_compare7(wzz5000, wzz5200)
new_lt15(wzz500, wzz520) → new_esEs8(new_compare16(wzz500, wzz520), LT)
new_ltEs13(Just(wzz5010), Just(wzz5210), app(app(app(ty_@3, deh), dfa), dfb)) → new_ltEs6(wzz5010, wzz5210, deh, dfa, dfb)
new_ltEs13(Just(wzz5010), Just(wzz5210), app(ty_[], dga)) → new_ltEs15(wzz5010, wzz5210, dga)
new_compare8(Integer(wzz5000), Integer(wzz5200)) → new_primCmpInt(wzz5000, wzz5200)
new_compare31(wzz5000, wzz5200, app(ty_Ratio, chh)) → new_compare12(wzz5000, wzz5200, chh)
new_lt19(wzz5011, wzz5211, app(app(app(ty_@3, ceh), cfa), cfb)) → new_lt8(wzz5011, wzz5211, ceh, cfa, cfb)
new_lt20(wzz5010, wzz5210, app(ty_[], ceg)) → new_lt18(wzz5010, wzz5210, ceg)
new_esEs17(Char(wzz500), Char(wzz4000)) → new_primEqNat0(wzz500, wzz4000)
new_esEs20(wzz500, wzz4000, ty_Bool) → new_esEs12(wzz500, wzz4000)
new_esEs24(wzz5010, wzz5210, ty_Char) → new_esEs17(wzz5010, wzz5210)
new_ltEs18(wzz5011, wzz5211, app(ty_[], cbh)) → new_ltEs15(wzz5011, wzz5211, cbh)
new_esEs31(wzz50, wzz400, ty_Ordering) → new_esEs8(wzz50, wzz400)
new_esEs23(wzz500, wzz4000, app(app(ty_Either, cce), ccf)) → new_esEs5(wzz500, wzz4000, cce, ccf)
new_compare10(wzz500, wzz520, True, gc, gd) → LT
new_esEs26(wzz500, wzz4000, ty_Float) → new_esEs10(wzz500, wzz4000)
new_ltEs13(Just(wzz5010), Just(wzz5210), ty_Char) → new_ltEs12(wzz5010, wzz5210)
new_esEs21(wzz501, wzz4001, ty_@0) → new_esEs19(wzz501, wzz4001)
new_lt20(wzz5010, wzz5210, app(app(app(ty_@3, cdf), cdg), cdh)) → new_lt8(wzz5010, wzz5210, cdf, cdg, cdh)
new_esEs27(wzz501, wzz4001, app(ty_Maybe, dcg)) → new_esEs7(wzz501, wzz4001, dcg)
new_ltEs5(Right(wzz5010), Right(wzz5210), eg, ty_Bool) → new_ltEs14(wzz5010, wzz5210)
new_ltEs19(wzz5012, wzz5212, ty_Double) → new_ltEs11(wzz5012, wzz5212)
new_esEs25(wzz5011, wzz5211, ty_Char) → new_esEs17(wzz5011, wzz5211)
new_compare31(wzz5000, wzz5200, ty_Ordering) → new_compare16(wzz5000, wzz5200)
new_lt19(wzz5011, wzz5211, ty_Int) → new_lt4(wzz5011, wzz5211)
new_primMulNat0(Zero, Zero) → Zero
new_esEs5(Left(wzz500), Left(wzz4000), app(ty_Ratio, bbd), cc) → new_esEs14(wzz500, wzz4000, bbd)
new_lt12(wzz5010, wzz5210, app(ty_[], caf)) → new_lt18(wzz5010, wzz5210, caf)
new_esEs27(wzz501, wzz4001, app(app(app(ty_@3, dcb), dcc), dcd)) → new_esEs4(wzz501, wzz4001, dcb, dcc, dcd)
new_lt14(wzz500, wzz520, bdc, bdd) → new_esEs8(new_compare28(wzz500, wzz520, bdc, bdd), LT)
new_esEs12(True, True) → True
new_ltEs9(GT, LT) → False
new_lt20(wzz5010, wzz5210, app(app(ty_Either, ceb), cec)) → new_lt13(wzz5010, wzz5210, ceb, cec)
new_compare18(wzz500, wzz520, True, da, db, dc) → LT
new_ltEs13(Nothing, Just(wzz5210), deg) → True
new_esEs26(wzz500, wzz4000, ty_@0) → new_esEs19(wzz500, wzz4000)
new_ltEs13(Just(wzz5010), Just(wzz5210), ty_Ordering) → new_ltEs9(wzz5010, wzz5210)
new_esEs22(wzz5010, wzz5210, ty_Char) → new_esEs17(wzz5010, wzz5210)
new_esEs23(wzz500, wzz4000, ty_Bool) → new_esEs12(wzz500, wzz4000)
new_ltEs20(wzz501, wzz521, app(ty_Maybe, deg)) → new_ltEs13(wzz501, wzz521, deg)
new_ltEs14(False, True) → True
new_esEs18(:(wzz500, wzz501), :(wzz4000, wzz4001), bf) → new_asAs(new_esEs23(wzz500, wzz4000, bf), new_esEs18(wzz501, wzz4001, bf))
new_ltEs5(Right(wzz5010), Right(wzz5210), eg, ty_Ordering) → new_ltEs9(wzz5010, wzz5210)
new_esEs29(wzz500, wzz520, app(ty_Maybe, gf)) → new_esEs7(wzz500, wzz520, gf)
new_esEs20(wzz500, wzz4000, app(ty_Ratio, bff)) → new_esEs14(wzz500, wzz4000, bff)
new_esEs30(wzz37, wzz38, wzz39, wzz40, False, gg, gh) → new_esEs8(new_compare29(@2(wzz37, wzz38), @2(wzz39, wzz40), False, gg, gh), LT)
new_esEs5(Left(wzz500), Left(wzz4000), ty_Bool, cc) → new_esEs12(wzz500, wzz4000)
new_ltEs13(Just(wzz5010), Just(wzz5210), ty_Int) → new_ltEs17(wzz5010, wzz5210)
new_lt21(wzz500, wzz520, app(ty_Maybe, gf)) → new_lt11(wzz500, wzz520, gf)
new_lt19(wzz5011, wzz5211, ty_Bool) → new_lt17(wzz5011, wzz5211)
new_lt20(wzz5010, wzz5210, ty_Integer) → new_lt9(wzz5010, wzz5210)
new_esEs5(Right(wzz500), Right(wzz4000), cb, ty_Integer) → new_esEs9(wzz500, wzz4000)
new_ltEs13(Just(wzz5010), Just(wzz5210), ty_Double) → new_ltEs11(wzz5010, wzz5210)
new_esEs31(wzz50, wzz400, ty_Char) → new_esEs17(wzz50, wzz400)
new_ltEs5(Left(wzz5010), Right(wzz5210), eg, dg) → True
new_esEs32(wzz38, wzz40, app(ty_[], ha)) → new_esEs18(wzz38, wzz40, ha)
new_esEs7(Just(wzz500), Just(wzz4000), app(app(ty_@2, bee), bef)) → new_esEs6(wzz500, wzz4000, bee, bef)
new_ltEs18(wzz5011, wzz5211, app(ty_Ratio, cbb)) → new_ltEs7(wzz5011, wzz5211, cbb)
new_lt8(wzz500, wzz520, da, db, dc) → new_esEs8(new_compare6(wzz500, wzz520, da, db, dc), LT)
new_esEs22(wzz5010, wzz5210, app(ty_Ratio, bhh)) → new_esEs14(wzz5010, wzz5210, bhh)
new_esEs21(wzz501, wzz4001, app(ty_Ratio, bgh)) → new_esEs14(wzz501, wzz4001, bgh)
new_esEs23(wzz500, wzz4000, ty_Double) → new_esEs13(wzz500, wzz4000)
new_esEs5(Left(wzz500), Left(wzz4000), app(app(app(ty_@3, baf), bag), bah), cc) → new_esEs4(wzz500, wzz4000, baf, bag, bah)
new_esEs22(wzz5010, wzz5210, ty_Integer) → new_esEs9(wzz5010, wzz5210)
new_ltEs5(Right(wzz5010), Right(wzz5210), eg, app(app(ty_Either, fd), ff)) → new_ltEs5(wzz5010, wzz5210, fd, ff)
new_lt12(wzz5010, wzz5210, ty_Bool) → new_lt17(wzz5010, wzz5210)
new_lt21(wzz500, wzz520, app(ty_[], chd)) → new_lt18(wzz500, wzz520, chd)
new_ltEs9(EQ, GT) → True
new_esEs7(Just(wzz500), Just(wzz4000), app(ty_Ratio, bed)) → new_esEs14(wzz500, wzz4000, bed)
new_lt20(wzz5010, wzz5210, ty_@0) → new_lt5(wzz5010, wzz5210)
new_esEs20(wzz500, wzz4000, app(app(ty_@2, bfg), bfh)) → new_esEs6(wzz500, wzz4000, bfg, bfh)
new_esEs6(@2(wzz500, wzz501), @2(wzz4000, wzz4001), cf, cg) → new_asAs(new_esEs20(wzz500, wzz4000, cf), new_esEs21(wzz501, wzz4001, cg))
new_lt12(wzz5010, wzz5210, ty_Integer) → new_lt9(wzz5010, wzz5210)
new_compare15(wzz500, wzz520, False, gf) → GT
new_lt20(wzz5010, wzz5210, ty_Ordering) → new_lt15(wzz5010, wzz5210)
new_lt6(wzz500, wzz520) → new_esEs8(new_compare11(wzz500, wzz520), LT)
new_ltEs5(Right(wzz5010), Left(wzz5210), eg, dg) → False
new_ltEs17(wzz501, wzz521) → new_fsEs(new_compare5(wzz501, wzz521))
new_ltEs9(LT, EQ) → True
new_esEs5(Left(wzz500), Left(wzz4000), ty_@0, cc) → new_esEs19(wzz500, wzz4000)
new_ltEs19(wzz5012, wzz5212, app(app(ty_@2, cgh), cha)) → new_ltEs8(wzz5012, wzz5212, cgh, cha)
new_ltEs20(wzz501, wzz521, app(ty_Ratio, bdb)) → new_ltEs7(wzz501, wzz521, bdb)
new_ltEs19(wzz5012, wzz5212, ty_Float) → new_ltEs16(wzz5012, wzz5212)
new_esEs32(wzz38, wzz40, app(app(ty_@2, baa), bab)) → new_esEs6(wzz38, wzz40, baa, bab)
new_pePe(False, wzz135) → wzz135
new_esEs24(wzz5010, wzz5210, app(ty_Ratio, cea)) → new_esEs14(wzz5010, wzz5210, cea)
new_compare31(wzz5000, wzz5200, ty_Int) → new_compare5(wzz5000, wzz5200)
new_esEs23(wzz500, wzz4000, ty_@0) → new_esEs19(wzz500, wzz4000)
new_esEs18([], :(wzz4000, wzz4001), bf) → False
new_esEs18(:(wzz500, wzz501), [], bf) → False
new_esEs31(wzz50, wzz400, app(app(app(ty_@3, bg), bh), ca)) → new_esEs4(wzz50, wzz400, bg, bh, ca)
new_lt19(wzz5011, wzz5211, app(ty_Ratio, cfc)) → new_lt7(wzz5011, wzz5211, cfc)
new_ltEs20(wzz501, wzz521, app(app(ty_@2, bhc), bhd)) → new_ltEs8(wzz501, wzz521, bhc, bhd)
new_lt20(wzz5010, wzz5210, ty_Float) → new_lt10(wzz5010, wzz5210)
new_ltEs20(wzz501, wzz521, ty_@0) → new_ltEs10(wzz501, wzz521)
new_esEs26(wzz500, wzz4000, ty_Int) → new_esEs11(wzz500, wzz4000)
new_esEs32(wzz38, wzz40, app(ty_Maybe, hg)) → new_esEs7(wzz38, wzz40, hg)
new_esEs24(wzz5010, wzz5210, app(ty_Maybe, cef)) → new_esEs7(wzz5010, wzz5210, cef)
new_esEs22(wzz5010, wzz5210, ty_Int) → new_esEs11(wzz5010, wzz5210)
new_esEs26(wzz500, wzz4000, ty_Bool) → new_esEs12(wzz500, wzz4000)
new_esEs28(wzz502, wzz4002, app(app(app(ty_@3, ddd), dde), ddf)) → new_esEs4(wzz502, wzz4002, ddd, dde, ddf)
new_esEs23(wzz500, wzz4000, app(ty_Maybe, ccg)) → new_esEs7(wzz500, wzz4000, ccg)
new_lt20(wzz5010, wzz5210, app(app(ty_@2, ced), cee)) → new_lt14(wzz5010, wzz5210, ced, cee)
new_lt12(wzz5010, wzz5210, app(app(app(ty_@3, bhe), bhf), bhg)) → new_lt8(wzz5010, wzz5210, bhe, bhf, bhg)
new_ltEs9(EQ, EQ) → True
new_compare19(Float(wzz5000, wzz5001), Float(wzz5200, wzz5201)) → new_compare5(new_sr(wzz5000, wzz5200), new_sr(wzz5001, wzz5201))
new_esEs22(wzz5010, wzz5210, ty_Ordering) → new_esEs8(wzz5010, wzz5210)
new_esEs31(wzz50, wzz400, ty_Double) → new_esEs13(wzz50, wzz400)
new_lt12(wzz5010, wzz5210, app(app(ty_@2, cac), cad)) → new_lt14(wzz5010, wzz5210, cac, cad)
new_esEs20(wzz500, wzz4000, app(ty_[], beg)) → new_esEs18(wzz500, wzz4000, beg)
new_esEs5(Left(wzz500), Left(wzz4000), app(app(ty_@2, bbe), bbf), cc) → new_esEs6(wzz500, wzz4000, bbe, bbf)
new_compare111(wzz500, wzz520, False) → GT
new_compare111(wzz500, wzz520, True) → LT
new_esEs5(Left(wzz500), Left(wzz4000), ty_Int, cc) → new_esEs11(wzz500, wzz4000)
new_ltEs5(Left(wzz5010), Left(wzz5210), ty_Float, dg) → new_ltEs16(wzz5010, wzz5210)
new_compare17(wzz109, wzz110, wzz111, wzz112, True, bac, bad) → LT
new_esEs5(Left(wzz500), Left(wzz4000), ty_Ordering, cc) → new_esEs8(wzz500, wzz4000)
new_ltEs5(Left(wzz5010), Left(wzz5210), ty_Int, dg) → new_ltEs17(wzz5010, wzz5210)
new_esEs5(Right(wzz500), Right(wzz4000), cb, ty_Char) → new_esEs17(wzz500, wzz4000)
new_primCmpInt(Neg(Succ(wzz5000)), Neg(wzz520)) → new_primCmpNat1(wzz520, wzz5000)
new_ltEs13(Nothing, Nothing, deg) → True
new_ltEs4(wzz501, wzz521) → new_fsEs(new_compare8(wzz501, wzz521))
new_ltEs20(wzz501, wzz521, ty_Bool) → new_ltEs14(wzz501, wzz521)
new_esEs25(wzz5011, wzz5211, app(app(ty_Either, cfd), cfe)) → new_esEs5(wzz5011, wzz5211, cfd, cfe)
new_esEs25(wzz5011, wzz5211, app(app(ty_@2, cff), cfg)) → new_esEs6(wzz5011, wzz5211, cff, cfg)
new_esEs8(LT, LT) → True
new_ltEs13(Just(wzz5010), Just(wzz5210), ty_@0) → new_ltEs10(wzz5010, wzz5210)
new_ltEs18(wzz5011, wzz5211, ty_Integer) → new_ltEs4(wzz5011, wzz5211)
new_esEs25(wzz5011, wzz5211, ty_Ordering) → new_esEs8(wzz5011, wzz5211)
new_compare25(wzz500, wzz520, False, gc, gd) → new_compare10(wzz500, wzz520, new_ltEs5(wzz500, wzz520, gc, gd), gc, gd)
new_esEs28(wzz502, wzz4002, ty_Float) → new_esEs10(wzz502, wzz4002)
new_compare12(:%(wzz5000, wzz5001), :%(wzz5200, wzz5201), ty_Integer) → new_compare8(new_sr0(wzz5000, wzz5201), new_sr0(wzz5200, wzz5001))
new_esEs24(wzz5010, wzz5210, app(app(ty_@2, ced), cee)) → new_esEs6(wzz5010, wzz5210, ced, cee)
new_pePe(True, wzz135) → True
new_compare0([], [], chd) → EQ
new_lt12(wzz5010, wzz5210, app(ty_Maybe, cae)) → new_lt11(wzz5010, wzz5210, cae)
new_primEqNat0(Zero, Zero) → True
new_lt12(wzz5010, wzz5210, ty_@0) → new_lt5(wzz5010, wzz5210)
new_esEs20(wzz500, wzz4000, ty_Int) → new_esEs11(wzz500, wzz4000)
new_compare26(wzz500, wzz520, True) → EQ
new_esEs5(Right(wzz500), Right(wzz4000), cb, app(app(ty_@2, bcg), bch)) → new_esEs6(wzz500, wzz4000, bcg, bch)
new_esEs26(wzz500, wzz4000, ty_Char) → new_esEs17(wzz500, wzz4000)
new_esEs25(wzz5011, wzz5211, app(ty_[], cga)) → new_esEs18(wzz5011, wzz5211, cga)
new_compare29(wzz50, wzz52, True, dee, def) → EQ
new_primMulNat0(Succ(wzz50000), Succ(wzz400000)) → new_primPlusNat1(new_primMulNat0(wzz50000, Succ(wzz400000)), wzz400000)
new_esEs5(Right(wzz500), Right(wzz4000), cb, ty_Double) → new_esEs13(wzz500, wzz4000)
new_compare26(wzz500, wzz520, False) → new_compare111(wzz500, wzz520, new_ltEs9(wzz500, wzz520))
new_esEs23(wzz500, wzz4000, ty_Integer) → new_esEs9(wzz500, wzz4000)
new_ltEs5(Right(wzz5010), Right(wzz5210), eg, app(app(app(ty_@3, eh), fa), fb)) → new_ltEs6(wzz5010, wzz5210, eh, fa, fb)
new_compare211(wzz500, wzz520, False) → new_compare13(wzz500, wzz520, new_ltEs14(wzz500, wzz520))
new_lt21(wzz500, wzz520, app(app(ty_Either, gc), gd)) → new_lt13(wzz500, wzz520, gc, gd)
new_esEs24(wzz5010, wzz5210, app(ty_[], ceg)) → new_esEs18(wzz5010, wzz5210, ceg)
new_esEs29(wzz500, wzz520, ty_@0) → new_esEs19(wzz500, wzz520)
new_compare31(wzz5000, wzz5200, ty_Bool) → new_compare30(wzz5000, wzz5200)
new_esEs32(wzz38, wzz40, ty_Bool) → new_esEs12(wzz38, wzz40)
new_ltEs9(EQ, LT) → False
new_compare6(wzz500, wzz520, da, db, dc) → new_compare24(wzz500, wzz520, new_esEs4(wzz500, wzz520, da, db, dc), da, db, dc)
new_sr(wzz500, wzz4000) → new_primMulInt(wzz500, wzz4000)
new_compare14(wzz500, wzz520, gc, gd) → new_compare25(wzz500, wzz520, new_esEs5(wzz500, wzz520, gc, gd), gc, gd)
new_ltEs5(Left(wzz5010), Left(wzz5210), ty_Ordering, dg) → new_ltEs9(wzz5010, wzz5210)
new_primCmpInt(Neg(Zero), Neg(Succ(wzz5200))) → new_primCmpNat0(wzz5200, Zero)
new_compare31(wzz5000, wzz5200, ty_Double) → new_compare9(wzz5000, wzz5200)
new_esEs26(wzz500, wzz4000, ty_Ordering) → new_esEs8(wzz500, wzz4000)
new_esEs8(GT, GT) → True
new_esEs20(wzz500, wzz4000, ty_Integer) → new_esEs9(wzz500, wzz4000)
new_lt20(wzz5010, wzz5210, app(ty_Maybe, cef)) → new_lt11(wzz5010, wzz5210, cef)
new_esEs16(wzz501, wzz4001, ty_Int) → new_esEs11(wzz501, wzz4001)
new_primCmpInt(Pos(Zero), Pos(Succ(wzz5200))) → new_primCmpNat1(Zero, wzz5200)
new_esEs12(False, False) → True
new_esEs5(Right(wzz500), Right(wzz4000), cb, app(ty_[], bbg)) → new_esEs18(wzz500, wzz4000, bbg)
new_esEs26(wzz500, wzz4000, app(app(app(ty_@3, dah), dba), dbb)) → new_esEs4(wzz500, wzz4000, dah, dba, dbb)
new_ltEs18(wzz5011, wzz5211, app(app(ty_Either, cbc), cbd)) → new_ltEs5(wzz5011, wzz5211, cbc, cbd)
new_esEs22(wzz5010, wzz5210, app(ty_[], caf)) → new_esEs18(wzz5010, wzz5210, caf)
new_esEs8(LT, GT) → False
new_esEs8(GT, LT) → False
new_lt12(wzz5010, wzz5210, ty_Float) → new_lt10(wzz5010, wzz5210)
new_ltEs20(wzz501, wzz521, ty_Float) → new_ltEs16(wzz501, wzz521)
new_lt11(wzz500, wzz520, gf) → new_esEs8(new_compare27(wzz500, wzz520, gf), LT)
new_compare16(wzz500, wzz520) → new_compare26(wzz500, wzz520, new_esEs8(wzz500, wzz520))
new_compare24(wzz500, wzz520, True, da, db, dc) → EQ
new_primEqInt(Neg(Succ(wzz5000)), Neg(Succ(wzz40000))) → new_primEqNat0(wzz5000, wzz40000)
new_esEs5(Left(wzz500), Left(wzz4000), ty_Float, cc) → new_esEs10(wzz500, wzz4000)
new_esEs20(wzz500, wzz4000, ty_Ordering) → new_esEs8(wzz500, wzz4000)
new_lt21(wzz500, wzz520, ty_Integer) → new_lt9(wzz500, wzz520)
new_esEs23(wzz500, wzz4000, ty_Ordering) → new_esEs8(wzz500, wzz4000)
new_lt20(wzz5010, wzz5210, ty_Char) → new_lt6(wzz5010, wzz5210)
new_compare13(wzz500, wzz520, False) → GT
new_ltEs5(Right(wzz5010), Right(wzz5210), eg, app(app(ty_@2, fg), fh)) → new_ltEs8(wzz5010, wzz5210, fg, fh)
new_lt12(wzz5010, wzz5210, app(ty_Ratio, bhh)) → new_lt7(wzz5010, wzz5210, bhh)
new_esEs29(wzz500, wzz520, app(app(ty_Either, gc), gd)) → new_esEs5(wzz500, wzz520, gc, gd)
new_ltEs5(Right(wzz5010), Right(wzz5210), eg, app(ty_Ratio, fc)) → new_ltEs7(wzz5010, wzz5210, fc)
new_lt20(wzz5010, wzz5210, ty_Int) → new_lt4(wzz5010, wzz5210)
new_ltEs16(wzz501, wzz521) → new_fsEs(new_compare19(wzz501, wzz521))
new_primCmpNat1(Zero, wzz5000) → LT
new_esEs21(wzz501, wzz4001, app(ty_[], bga)) → new_esEs18(wzz501, wzz4001, bga)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_compare110(wzz109, wzz110, wzz111, wzz112, True, wzz114, bac, bad) → new_compare17(wzz109, wzz110, wzz111, wzz112, True, bac, bad)
new_ltEs5(Right(wzz5010), Right(wzz5210), eg, ty_Double) → new_ltEs11(wzz5010, wzz5210)
new_ltEs5(Left(wzz5010), Left(wzz5210), ty_Integer, dg) → new_ltEs4(wzz5010, wzz5210)
new_esEs7(Just(wzz500), Just(wzz4000), ty_Ordering) → new_esEs8(wzz500, wzz4000)
new_esEs5(Left(wzz500), Left(wzz4000), app(ty_Maybe, bbc), cc) → new_esEs7(wzz500, wzz4000, bbc)
new_ltEs11(wzz501, wzz521) → new_fsEs(new_compare9(wzz501, wzz521))
new_esEs28(wzz502, wzz4002, ty_Double) → new_esEs13(wzz502, wzz4002)
new_esEs27(wzz501, wzz4001, app(app(ty_Either, dce), dcf)) → new_esEs5(wzz501, wzz4001, dce, dcf)
new_ltEs20(wzz501, wzz521, ty_Char) → new_ltEs12(wzz501, wzz521)
new_lt19(wzz5011, wzz5211, ty_Double) → new_lt16(wzz5011, wzz5211)
new_ltEs19(wzz5012, wzz5212, ty_Integer) → new_ltEs4(wzz5012, wzz5212)
new_primEqInt(Neg(Zero), Neg(Succ(wzz40000))) → False
new_primEqInt(Neg(Succ(wzz5000)), Neg(Zero)) → False
new_ltEs19(wzz5012, wzz5212, ty_Char) → new_ltEs12(wzz5012, wzz5212)
new_compare210(wzz500, wzz520, False, gf) → new_compare15(wzz500, wzz520, new_ltEs13(wzz500, wzz520, gf), gf)
new_primCompAux0(wzz144, GT) → GT
new_esEs8(EQ, EQ) → True
new_primPlusNat1(Zero, wzz400000) → Succ(wzz400000)
new_esEs24(wzz5010, wzz5210, ty_Integer) → new_esEs9(wzz5010, wzz5210)
new_esEs23(wzz500, wzz4000, app(app(app(ty_@3, ccb), ccc), ccd)) → new_esEs4(wzz500, wzz4000, ccb, ccc, ccd)
new_esEs31(wzz50, wzz400, app(app(ty_Either, cb), cc)) → new_esEs5(wzz50, wzz400, cb, cc)
new_ltEs9(LT, LT) → True
new_esEs32(wzz38, wzz40, ty_Char) → new_esEs17(wzz38, wzz40)
new_esEs5(Right(wzz500), Right(wzz4000), cb, app(ty_Ratio, bcf)) → new_esEs14(wzz500, wzz4000, bcf)
new_esEs26(wzz500, wzz4000, app(ty_[], dag)) → new_esEs18(wzz500, wzz4000, dag)
new_esEs20(wzz500, wzz4000, ty_@0) → new_esEs19(wzz500, wzz4000)
new_esEs19(@0, @0) → True
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_esEs21(wzz501, wzz4001, ty_Float) → new_esEs10(wzz501, wzz4001)
new_ltEs5(Left(wzz5010), Left(wzz5210), app(app(ty_@2, ec), ed), dg) → new_ltEs8(wzz5010, wzz5210, ec, ed)
new_esEs23(wzz500, wzz4000, ty_Float) → new_esEs10(wzz500, wzz4000)
new_esEs22(wzz5010, wzz5210, ty_@0) → new_esEs19(wzz5010, wzz5210)
new_esEs9(Integer(wzz500), Integer(wzz4000)) → new_primEqInt(wzz500, wzz4000)
new_compare31(wzz5000, wzz5200, app(app(app(ty_@3, che), chf), chg)) → new_compare6(wzz5000, wzz5200, che, chf, chg)
new_compare12(:%(wzz5000, wzz5001), :%(wzz5200, wzz5201), ty_Int) → new_compare5(new_sr(wzz5000, wzz5201), new_sr(wzz5200, wzz5001))
new_lt21(wzz500, wzz520, app(app(app(ty_@3, da), db), dc)) → new_lt8(wzz500, wzz520, da, db, dc)
new_compare31(wzz5000, wzz5200, app(ty_Maybe, dae)) → new_compare27(wzz5000, wzz5200, dae)
new_lt12(wzz5010, wzz5210, ty_Ordering) → new_lt15(wzz5010, wzz5210)
new_primEqInt(Pos(Succ(wzz5000)), Pos(Succ(wzz40000))) → new_primEqNat0(wzz5000, wzz40000)
new_compare10(wzz500, wzz520, False, gc, gd) → GT
new_ltEs5(Left(wzz5010), Left(wzz5210), app(app(ty_Either, ea), eb), dg) → new_ltEs5(wzz5010, wzz5210, ea, eb)
new_ltEs19(wzz5012, wzz5212, ty_Bool) → new_ltEs14(wzz5012, wzz5212)
new_ltEs18(wzz5011, wzz5211, ty_@0) → new_ltEs10(wzz5011, wzz5211)
new_esEs28(wzz502, wzz4002, ty_Char) → new_esEs17(wzz502, wzz4002)
new_esEs23(wzz500, wzz4000, ty_Char) → new_esEs17(wzz500, wzz4000)
new_esEs5(Right(wzz500), Right(wzz4000), cb, app(app(ty_Either, bcc), bcd)) → new_esEs5(wzz500, wzz4000, bcc, bcd)
new_ltEs5(Left(wzz5010), Left(wzz5210), app(app(app(ty_@3, dd), de), df), dg) → new_ltEs6(wzz5010, wzz5210, dd, de, df)
new_primEqNat0(Succ(wzz5000), Succ(wzz40000)) → new_primEqNat0(wzz5000, wzz40000)
new_esEs27(wzz501, wzz4001, ty_Ordering) → new_esEs8(wzz501, wzz4001)
new_ltEs14(False, False) → True
new_esEs23(wzz500, wzz4000, app(ty_Ratio, cch)) → new_esEs14(wzz500, wzz4000, cch)
new_compare7(@0, @0) → EQ
new_lt5(wzz500, wzz520) → new_esEs8(new_compare7(wzz500, wzz520), LT)
new_compare31(wzz5000, wzz5200, app(app(ty_@2, dac), dad)) → new_compare28(wzz5000, wzz5200, dac, dad)
new_lt21(wzz500, wzz520, ty_Char) → new_lt6(wzz500, wzz520)
new_esEs22(wzz5010, wzz5210, ty_Bool) → new_esEs12(wzz5010, wzz5210)
new_esEs20(wzz500, wzz4000, ty_Float) → new_esEs10(wzz500, wzz4000)
new_esEs32(wzz38, wzz40, ty_@0) → new_esEs19(wzz38, wzz40)
new_esEs25(wzz5011, wzz5211, ty_@0) → new_esEs19(wzz5011, wzz5211)
new_esEs28(wzz502, wzz4002, ty_Int) → new_esEs11(wzz502, wzz4002)
new_esEs24(wzz5010, wzz5210, ty_Ordering) → new_esEs8(wzz5010, wzz5210)
new_ltEs13(Just(wzz5010), Just(wzz5210), app(ty_Ratio, dfc)) → new_ltEs7(wzz5010, wzz5210, dfc)
new_ltEs13(Just(wzz5010), Just(wzz5210), ty_Integer) → new_ltEs4(wzz5010, wzz5210)
new_ltEs19(wzz5012, wzz5212, ty_Int) → new_ltEs17(wzz5012, wzz5212)
new_esEs10(Float(wzz500, wzz501), Float(wzz4000, wzz4001)) → new_esEs11(new_sr(wzz500, wzz4000), new_sr(wzz501, wzz4001))
new_esEs21(wzz501, wzz4001, ty_Int) → new_esEs11(wzz501, wzz4001)
new_ltEs18(wzz5011, wzz5211, ty_Double) → new_ltEs11(wzz5011, wzz5211)
new_compare31(wzz5000, wzz5200, ty_Char) → new_compare11(wzz5000, wzz5200)
new_esEs7(Nothing, Nothing, cd) → True
new_esEs28(wzz502, wzz4002, ty_Ordering) → new_esEs8(wzz502, wzz4002)
new_esEs8(LT, EQ) → False
new_esEs8(EQ, LT) → False
new_primEqInt(Pos(Zero), Pos(Succ(wzz40000))) → False
new_primEqInt(Pos(Succ(wzz5000)), Pos(Zero)) → False
new_esEs4(@3(wzz500, wzz501, wzz502), @3(wzz4000, wzz4001, wzz4002), bg, bh, ca) → new_asAs(new_esEs26(wzz500, wzz4000, bg), new_asAs(new_esEs27(wzz501, wzz4001, bh), new_esEs28(wzz502, wzz4002, ca)))
new_esEs27(wzz501, wzz4001, ty_@0) → new_esEs19(wzz501, wzz4001)
new_primPlusNat0(Zero, Succ(wzz9600)) → Succ(wzz9600)
new_primPlusNat0(Succ(wzz42200), Zero) → Succ(wzz42200)
new_ltEs5(Right(wzz5010), Right(wzz5210), eg, ty_Integer) → new_ltEs4(wzz5010, wzz5210)
new_esEs5(Right(wzz500), Right(wzz4000), cb, ty_Float) → new_esEs10(wzz500, wzz4000)
new_ltEs19(wzz5012, wzz5212, ty_Ordering) → new_ltEs9(wzz5012, wzz5212)
new_esEs20(wzz500, wzz4000, app(app(app(ty_@3, beh), bfa), bfb)) → new_esEs4(wzz500, wzz4000, beh, bfa, bfb)
new_esEs7(Just(wzz500), Just(wzz4000), app(app(ty_Either, bea), beb)) → new_esEs5(wzz500, wzz4000, bea, beb)
new_primCmpInt(Neg(Zero), Pos(Succ(wzz5200))) → LT
new_esEs29(wzz500, wzz520, app(app(app(ty_@3, da), db), dc)) → new_esEs4(wzz500, wzz520, da, db, dc)
new_lt19(wzz5011, wzz5211, ty_Ordering) → new_lt15(wzz5011, wzz5211)
new_esEs20(wzz500, wzz4000, app(app(ty_Either, bfc), bfd)) → new_esEs5(wzz500, wzz4000, bfc, bfd)
new_compare110(wzz109, wzz110, wzz111, wzz112, False, wzz114, bac, bad) → new_compare17(wzz109, wzz110, wzz111, wzz112, wzz114, bac, bad)
new_esEs21(wzz501, wzz4001, ty_Double) → new_esEs13(wzz501, wzz4001)
new_esEs27(wzz501, wzz4001, ty_Integer) → new_esEs9(wzz501, wzz4001)
new_esEs7(Just(wzz500), Just(wzz4000), app(app(app(ty_@3, bdf), bdg), bdh)) → new_esEs4(wzz500, wzz4000, bdf, bdg, bdh)
new_compare13(wzz500, wzz520, True) → LT
new_sr0(Integer(wzz52000), Integer(wzz50010)) → Integer(new_primMulInt(wzz52000, wzz50010))
new_compare27(wzz500, wzz520, gf) → new_compare210(wzz500, wzz520, new_esEs7(wzz500, wzz520, gf), gf)
new_primEqInt(Neg(Succ(wzz5000)), Pos(wzz4000)) → False
new_primEqInt(Pos(Succ(wzz5000)), Neg(wzz4000)) → False
new_esEs5(Right(wzz500), Right(wzz4000), cb, ty_@0) → new_esEs19(wzz500, wzz4000)
new_esEs28(wzz502, wzz4002, app(app(ty_Either, ddg), ddh)) → new_esEs5(wzz502, wzz4002, ddg, ddh)
new_esEs7(Just(wzz500), Just(wzz4000), ty_Integer) → new_esEs9(wzz500, wzz4000)
new_esEs26(wzz500, wzz4000, ty_Double) → new_esEs13(wzz500, wzz4000)
new_esEs7(Nothing, Just(wzz4000), cd) → False
new_esEs7(Just(wzz500), Nothing, cd) → False
new_ltEs20(wzz501, wzz521, ty_Integer) → new_ltEs4(wzz501, wzz521)
new_compare210(wzz500, wzz520, True, gf) → EQ
new_esEs32(wzz38, wzz40, app(app(ty_Either, he), hf)) → new_esEs5(wzz38, wzz40, he, hf)
new_esEs32(wzz38, wzz40, app(ty_Ratio, hh)) → new_esEs14(wzz38, wzz40, hh)
new_esEs13(Double(wzz500, wzz501), Double(wzz4000, wzz4001)) → new_esEs11(new_sr(wzz500, wzz4000), new_sr(wzz501, wzz4001))
new_primCmpNat2(Zero, Succ(wzz52000)) → LT
new_esEs22(wzz5010, wzz5210, app(app(ty_@2, cac), cad)) → new_esEs6(wzz5010, wzz5210, cac, cad)
new_primEqInt(Neg(Zero), Pos(Succ(wzz40000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(wzz40000))) → False
new_compare30(wzz500, wzz520) → new_compare211(wzz500, wzz520, new_esEs12(wzz500, wzz520))
new_compare9(Double(wzz5000, wzz5001), Double(wzz5200, wzz5201)) → new_compare5(new_sr(wzz5000, wzz5200), new_sr(wzz5001, wzz5201))
new_esEs27(wzz501, wzz4001, ty_Float) → new_esEs10(wzz501, wzz4001)
new_esEs7(Just(wzz500), Just(wzz4000), ty_Double) → new_esEs13(wzz500, wzz4000)
new_esEs8(EQ, GT) → False
new_esEs8(GT, EQ) → False
new_lt12(wzz5010, wzz5210, ty_Char) → new_lt6(wzz5010, wzz5210)
new_esEs28(wzz502, wzz4002, app(ty_Ratio, deb)) → new_esEs14(wzz502, wzz4002, deb)
new_lt21(wzz500, wzz520, ty_Bool) → new_lt17(wzz500, wzz520)
new_primCompAux0(wzz144, LT) → LT
new_ltEs5(Left(wzz5010), Left(wzz5210), ty_Bool, dg) → new_ltEs14(wzz5010, wzz5210)
new_esEs20(wzz500, wzz4000, ty_Double) → new_esEs13(wzz500, wzz4000)
new_ltEs15(wzz501, wzz521, bda) → new_fsEs(new_compare0(wzz501, wzz521, bda))
new_ltEs20(wzz501, wzz521, app(app(app(ty_@3, cdc), cdd), cde)) → new_ltEs6(wzz501, wzz521, cdc, cdd, cde)
new_esEs11(wzz50, wzz400) → new_primEqInt(wzz50, wzz400)
new_not(False) → True
new_lt19(wzz5011, wzz5211, app(app(ty_Either, cfd), cfe)) → new_lt13(wzz5011, wzz5211, cfd, cfe)
new_lt16(wzz500, wzz520) → new_esEs8(new_compare9(wzz500, wzz520), LT)
new_esEs26(wzz500, wzz4000, app(ty_Ratio, dbf)) → new_esEs14(wzz500, wzz4000, dbf)
new_esEs23(wzz500, wzz4000, app(app(ty_@2, cda), cdb)) → new_esEs6(wzz500, wzz4000, cda, cdb)
new_ltEs5(Left(wzz5010), Left(wzz5210), app(ty_Ratio, dh), dg) → new_ltEs7(wzz5010, wzz5210, dh)
new_lt10(wzz500, wzz520) → new_esEs8(new_compare19(wzz500, wzz520), LT)
new_esEs25(wzz5011, wzz5211, ty_Double) → new_esEs13(wzz5011, wzz5211)
new_ltEs18(wzz5011, wzz5211, app(app(app(ty_@3, cag), cah), cba)) → new_ltEs6(wzz5011, wzz5211, cag, cah, cba)
new_compare17(wzz109, wzz110, wzz111, wzz112, False, bac, bad) → GT
new_ltEs9(LT, GT) → True
new_esEs24(wzz5010, wzz5210, ty_@0) → new_esEs19(wzz5010, wzz5210)
new_esEs32(wzz38, wzz40, ty_Ordering) → new_esEs8(wzz38, wzz40)
new_esEs31(wzz50, wzz400, app(ty_Ratio, ce)) → new_esEs14(wzz50, wzz400, ce)
new_esEs25(wzz5011, wzz5211, ty_Float) → new_esEs10(wzz5011, wzz5211)
new_ltEs8(@2(wzz5010, wzz5011), @2(wzz5210, wzz5211), bhc, bhd) → new_pePe(new_lt12(wzz5010, wzz5210, bhc), new_asAs(new_esEs22(wzz5010, wzz5210, bhc), new_ltEs18(wzz5011, wzz5211, bhd)))
new_lt21(wzz500, wzz520, ty_Ordering) → new_lt15(wzz500, wzz520)
new_esEs25(wzz5011, wzz5211, app(app(app(ty_@3, ceh), cfa), cfb)) → new_esEs4(wzz5011, wzz5211, ceh, cfa, cfb)
new_esEs31(wzz50, wzz400, ty_Integer) → new_esEs9(wzz50, wzz400)
new_compare0(:(wzz5000, wzz5001), [], chd) → GT
new_ltEs19(wzz5012, wzz5212, app(app(app(ty_@3, cgb), cgc), cgd)) → new_ltEs6(wzz5012, wzz5212, cgb, cgc, cgd)
new_esEs5(Left(wzz500), Left(wzz4000), ty_Double, cc) → new_esEs13(wzz500, wzz4000)
new_ltEs7(wzz501, wzz521, bdb) → new_fsEs(new_compare12(wzz501, wzz521, bdb))
new_esEs32(wzz38, wzz40, app(app(app(ty_@3, hb), hc), hd)) → new_esEs4(wzz38, wzz40, hb, hc, hd)
new_esEs22(wzz5010, wzz5210, app(app(app(ty_@3, bhe), bhf), bhg)) → new_esEs4(wzz5010, wzz5210, bhe, bhf, bhg)
new_esEs27(wzz501, wzz4001, app(ty_[], dca)) → new_esEs18(wzz501, wzz4001, dca)
new_lt21(wzz500, wzz520, ty_@0) → new_lt5(wzz500, wzz520)
new_esEs26(wzz500, wzz4000, app(app(ty_Either, dbc), dbd)) → new_esEs5(wzz500, wzz4000, dbc, dbd)
new_esEs7(Just(wzz500), Just(wzz4000), ty_Bool) → new_esEs12(wzz500, wzz4000)
new_esEs27(wzz501, wzz4001, ty_Int) → new_esEs11(wzz501, wzz4001)
new_ltEs19(wzz5012, wzz5212, app(ty_[], chc)) → new_ltEs15(wzz5012, wzz5212, chc)
new_lt13(wzz500, wzz520, gc, gd) → new_esEs8(new_compare14(wzz500, wzz520, gc, gd), LT)
new_lt19(wzz5011, wzz5211, ty_Char) → new_lt6(wzz5011, wzz5211)
new_primCmpInt(Pos(Succ(wzz5000)), Neg(wzz520)) → GT
new_ltEs5(Left(wzz5010), Left(wzz5210), ty_Char, dg) → new_ltEs12(wzz5010, wzz5210)
new_esEs28(wzz502, wzz4002, app(ty_Maybe, dea)) → new_esEs7(wzz502, wzz4002, dea)
new_lt21(wzz500, wzz520, app(app(ty_@2, bdc), bdd)) → new_lt14(wzz500, wzz520, bdc, bdd)
new_esEs29(wzz500, wzz520, ty_Integer) → new_esEs9(wzz500, wzz520)
new_esEs21(wzz501, wzz4001, app(ty_Maybe, bgg)) → new_esEs7(wzz501, wzz4001, bgg)
new_esEs31(wzz50, wzz400, app(ty_[], bf)) → new_esEs18(wzz50, wzz400, bf)
new_esEs16(wzz501, wzz4001, ty_Integer) → new_esEs9(wzz501, wzz4001)
new_primMulInt(Pos(wzz5000), Pos(wzz40000)) → Pos(new_primMulNat0(wzz5000, wzz40000))
new_lt19(wzz5011, wzz5211, app(app(ty_@2, cff), cfg)) → new_lt14(wzz5011, wzz5211, cff, cfg)
new_lt21(wzz500, wzz520, ty_Float) → new_lt10(wzz500, wzz520)
new_esEs27(wzz501, wzz4001, ty_Char) → new_esEs17(wzz501, wzz4001)
new_esEs22(wzz5010, wzz5210, ty_Double) → new_esEs13(wzz5010, wzz5210)
new_esEs5(Right(wzz500), Right(wzz4000), cb, app(app(app(ty_@3, bbh), bca), bcb)) → new_esEs4(wzz500, wzz4000, bbh, bca, bcb)
new_lt19(wzz5011, wzz5211, app(ty_Maybe, cfh)) → new_lt11(wzz5011, wzz5211, cfh)
new_esEs5(Left(wzz500), Right(wzz4000), cb, cc) → False
new_esEs5(Right(wzz500), Left(wzz4000), cb, cc) → False
new_primMulInt(Neg(wzz5000), Neg(wzz40000)) → Pos(new_primMulNat0(wzz5000, wzz40000))
new_esEs27(wzz501, wzz4001, app(app(ty_@2, dda), ddb)) → new_esEs6(wzz501, wzz4001, dda, ddb)
new_primCmpNat2(Zero, Zero) → EQ
new_esEs5(Right(wzz500), Right(wzz4000), cb, ty_Ordering) → new_esEs8(wzz500, wzz4000)
new_ltEs5(Right(wzz5010), Right(wzz5210), eg, app(ty_[], gb)) → new_ltEs15(wzz5010, wzz5210, gb)
new_lt9(wzz500, wzz520) → new_esEs8(new_compare8(wzz500, wzz520), LT)
new_esEs29(wzz500, wzz520, app(app(ty_@2, bdc), bdd)) → new_esEs6(wzz500, wzz520, bdc, bdd)
new_ltEs19(wzz5012, wzz5212, app(app(ty_Either, cgf), cgg)) → new_ltEs5(wzz5012, wzz5212, cgf, cgg)
new_primEqNat0(Succ(wzz5000), Zero) → False
new_primEqNat0(Zero, Succ(wzz40000)) → False
new_primPlusNat0(Zero, Zero) → Zero
new_esEs7(Just(wzz500), Just(wzz4000), ty_Int) → new_esEs11(wzz500, wzz4000)
new_compare31(wzz5000, wzz5200, ty_Integer) → new_compare8(wzz5000, wzz5200)
new_lt12(wzz5010, wzz5210, ty_Double) → new_lt16(wzz5010, wzz5210)
new_compare25(wzz500, wzz520, True, gc, gd) → EQ
new_ltEs14(True, True) → True
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_lt7(wzz500, wzz520, ge) → new_esEs8(new_compare12(wzz500, wzz520, ge), LT)
new_primCmpNat2(Succ(wzz50000), Succ(wzz52000)) → new_primCmpNat2(wzz50000, wzz52000)
new_primCmpInt(Pos(Succ(wzz5000)), Pos(wzz520)) → new_primCmpNat0(wzz5000, wzz520)
new_esEs5(Right(wzz500), Right(wzz4000), cb, ty_Bool) → new_esEs12(wzz500, wzz4000)
new_esEs5(Left(wzz500), Left(wzz4000), app(ty_[], bae), cc) → new_esEs18(wzz500, wzz4000, bae)
new_esEs32(wzz38, wzz40, ty_Integer) → new_esEs9(wzz38, wzz40)
new_esEs30(wzz37, wzz38, wzz39, wzz40, True, gg, gh) → new_esEs8(new_compare29(@2(wzz37, wzz38), @2(wzz39, wzz40), new_esEs32(wzz38, wzz40, gh), gg, gh), LT)
new_primCmpNat0(wzz5000, Zero) → GT
new_ltEs9(GT, GT) → True
new_esEs23(wzz500, wzz4000, ty_Int) → new_esEs11(wzz500, wzz4000)
new_ltEs20(wzz501, wzz521, ty_Int) → new_ltEs17(wzz501, wzz521)
new_primPlusNat1(Succ(wzz1000), wzz400000) → Succ(Succ(new_primPlusNat0(wzz1000, wzz400000)))
new_esEs21(wzz501, wzz4001, ty_Char) → new_esEs17(wzz501, wzz4001)
new_primCmpInt(Pos(Zero), Neg(Succ(wzz5200))) → GT
new_esEs5(Right(wzz500), Right(wzz4000), cb, ty_Int) → new_esEs11(wzz500, wzz4000)
new_compare5(wzz50, wzz52) → new_primCmpInt(wzz50, wzz52)
new_esEs25(wzz5011, wzz5211, app(ty_Ratio, cfc)) → new_esEs14(wzz5011, wzz5211, cfc)
new_compare0(:(wzz5000, wzz5001), :(wzz5200, wzz5201), chd) → new_primCompAux1(wzz5000, wzz5200, new_compare0(wzz5001, wzz5201, chd), chd)
new_ltEs5(Right(wzz5010), Right(wzz5210), eg, ty_Char) → new_ltEs12(wzz5010, wzz5210)
new_esEs32(wzz38, wzz40, ty_Int) → new_esEs11(wzz38, wzz40)
new_lt19(wzz5011, wzz5211, app(ty_[], cga)) → new_lt18(wzz5011, wzz5211, cga)
new_esEs21(wzz501, wzz4001, app(app(app(ty_@3, bgb), bgc), bgd)) → new_esEs4(wzz501, wzz4001, bgb, bgc, bgd)
new_ltEs5(Right(wzz5010), Right(wzz5210), eg, ty_@0) → new_ltEs10(wzz5010, wzz5210)
new_ltEs5(Left(wzz5010), Left(wzz5210), ty_@0, dg) → new_ltEs10(wzz5010, wzz5210)
new_esEs24(wzz5010, wzz5210, ty_Int) → new_esEs11(wzz5010, wzz5210)
new_esEs28(wzz502, wzz4002, app(app(ty_@2, dec), ded)) → new_esEs6(wzz502, wzz4002, dec, ded)
new_lt20(wzz5010, wzz5210, ty_Double) → new_lt16(wzz5010, wzz5210)
new_esEs25(wzz5011, wzz5211, app(ty_Maybe, cfh)) → new_esEs7(wzz5011, wzz5211, cfh)
new_ltEs13(Just(wzz5010), Just(wzz5210), app(ty_Maybe, dfh)) → new_ltEs13(wzz5010, wzz5210, dfh)
new_esEs15(wzz500, wzz4000, ty_Int) → new_esEs11(wzz500, wzz4000)
new_esEs28(wzz502, wzz4002, app(ty_[], ddc)) → new_esEs18(wzz502, wzz4002, ddc)
new_esEs28(wzz502, wzz4002, ty_Integer) → new_esEs9(wzz502, wzz4002)
new_ltEs13(Just(wzz5010), Nothing, deg) → False
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_esEs27(wzz501, wzz4001, app(ty_Ratio, dch)) → new_esEs14(wzz501, wzz4001, dch)
new_esEs25(wzz5011, wzz5211, ty_Bool) → new_esEs12(wzz5011, wzz5211)
new_compare11(Char(wzz5000), Char(wzz5200)) → new_primCmpNat2(wzz5000, wzz5200)
new_primCompAux1(wzz5000, wzz5200, wzz130, chd) → new_primCompAux0(wzz130, new_compare31(wzz5000, wzz5200, chd))
new_esEs32(wzz38, wzz40, ty_Double) → new_esEs13(wzz38, wzz40)
new_esEs7(Just(wzz500), Just(wzz4000), app(ty_[], bde)) → new_esEs18(wzz500, wzz4000, bde)
new_asAs(False, wzz60) → False
new_esEs29(wzz500, wzz520, ty_Bool) → new_esEs12(wzz500, wzz520)
new_primMulInt(Neg(wzz5000), Pos(wzz40000)) → Neg(new_primMulNat0(wzz5000, wzz40000))
new_primMulInt(Pos(wzz5000), Neg(wzz40000)) → Neg(new_primMulNat0(wzz5000, wzz40000))
new_esEs27(wzz501, wzz4001, ty_Double) → new_esEs13(wzz501, wzz4001)
new_primMulNat0(Succ(wzz50000), Zero) → Zero
new_primMulNat0(Zero, Succ(wzz400000)) → Zero
new_esEs24(wzz5010, wzz5210, ty_Double) → new_esEs13(wzz5010, wzz5210)
new_esEs18([], [], bf) → True
new_esEs21(wzz501, wzz4001, app(app(ty_Either, bge), bgf)) → new_esEs5(wzz501, wzz4001, bge, bgf)
new_esEs21(wzz501, wzz4001, ty_Ordering) → new_esEs8(wzz501, wzz4001)
new_ltEs20(wzz501, wzz521, ty_Double) → new_ltEs11(wzz501, wzz521)
new_esEs24(wzz5010, wzz5210, ty_Float) → new_esEs10(wzz5010, wzz5210)
new_ltEs5(Left(wzz5010), Left(wzz5210), app(ty_[], ef), dg) → new_ltEs15(wzz5010, wzz5210, ef)
new_esEs29(wzz500, wzz520, ty_Int) → new_esEs11(wzz500, wzz520)
new_compare29(@2(wzz500, wzz501), @2(wzz520, wzz521), False, dee, def) → new_compare110(wzz500, wzz501, wzz520, wzz521, new_lt21(wzz500, wzz520, dee), new_asAs(new_esEs29(wzz500, wzz520, dee), new_ltEs20(wzz501, wzz521, def)), dee, def)
new_esEs26(wzz500, wzz4000, app(ty_Maybe, dbe)) → new_esEs7(wzz500, wzz4000, dbe)
new_esEs29(wzz500, wzz520, ty_Char) → new_esEs17(wzz500, wzz520)
new_ltEs19(wzz5012, wzz5212, ty_@0) → new_ltEs10(wzz5012, wzz5212)
new_esEs29(wzz500, wzz520, ty_Double) → new_esEs13(wzz500, wzz520)
new_compare31(wzz5000, wzz5200, ty_Float) → new_compare19(wzz5000, wzz5200)
new_ltEs20(wzz501, wzz521, ty_Ordering) → new_ltEs9(wzz501, wzz521)
new_primCmpNat1(Succ(wzz5200), wzz5000) → new_primCmpNat2(wzz5200, wzz5000)
new_primCmpNat2(Succ(wzz50000), Zero) → GT
new_ltEs18(wzz5011, wzz5211, ty_Bool) → new_ltEs14(wzz5011, wzz5211)
new_ltEs5(Left(wzz5010), Left(wzz5210), app(ty_Maybe, ee), dg) → new_ltEs13(wzz5010, wzz5210, ee)
new_esEs29(wzz500, wzz520, ty_Float) → new_esEs10(wzz500, wzz520)
new_compare31(wzz5000, wzz5200, app(ty_[], daf)) → new_compare0(wzz5000, wzz5200, daf)
new_esEs21(wzz501, wzz4001, ty_Integer) → new_esEs9(wzz501, wzz4001)
new_esEs28(wzz502, wzz4002, ty_@0) → new_esEs19(wzz502, wzz4002)
new_ltEs18(wzz5011, wzz5211, ty_Char) → new_ltEs12(wzz5011, wzz5211)
new_compare18(wzz500, wzz520, False, da, db, dc) → GT
new_ltEs18(wzz5011, wzz5211, ty_Int) → new_ltEs17(wzz5011, wzz5211)
new_ltEs18(wzz5011, wzz5211, app(app(ty_@2, cbe), cbf)) → new_ltEs8(wzz5011, wzz5211, cbe, cbf)
new_esEs31(wzz50, wzz400, ty_@0) → new_esEs19(wzz50, wzz400)
new_esEs26(wzz500, wzz4000, ty_Integer) → new_esEs9(wzz500, wzz4000)
new_esEs24(wzz5010, wzz5210, ty_Bool) → new_esEs12(wzz5010, wzz5210)
new_ltEs18(wzz5011, wzz5211, app(ty_Maybe, cbg)) → new_ltEs13(wzz5011, wzz5211, cbg)
new_lt21(wzz500, wzz520, ty_Double) → new_lt16(wzz500, wzz520)
new_ltEs9(GT, EQ) → False
new_esEs12(True, False) → False
new_esEs12(False, True) → False
new_compare31(wzz5000, wzz5200, app(app(ty_Either, daa), dab)) → new_compare14(wzz5000, wzz5200, daa, dab)
new_ltEs12(wzz501, wzz521) → new_fsEs(new_compare11(wzz501, wzz521))
new_lt18(wzz500, wzz520, chd) → new_esEs8(new_compare0(wzz500, wzz520, chd), LT)
new_esEs15(wzz500, wzz4000, ty_Integer) → new_esEs9(wzz500, wzz4000)
new_esEs14(:%(wzz500, wzz501), :%(wzz4000, wzz4001), ce) → new_asAs(new_esEs15(wzz500, wzz4000, ce), new_esEs16(wzz501, wzz4001, ce))
new_esEs27(wzz501, wzz4001, ty_Bool) → new_esEs12(wzz501, wzz4001)
new_ltEs13(Just(wzz5010), Just(wzz5210), app(app(ty_@2, dff), dfg)) → new_ltEs8(wzz5010, wzz5210, dff, dfg)
new_ltEs5(Right(wzz5010), Right(wzz5210), eg, ty_Int) → new_ltEs17(wzz5010, wzz5210)
new_esEs7(Just(wzz500), Just(wzz4000), ty_Char) → new_esEs17(wzz500, wzz4000)
new_lt12(wzz5010, wzz5210, ty_Int) → new_lt4(wzz5010, wzz5210)
new_ltEs6(@3(wzz5010, wzz5011, wzz5012), @3(wzz5210, wzz5211, wzz5212), cdc, cdd, cde) → new_pePe(new_lt20(wzz5010, wzz5210, cdc), new_asAs(new_esEs24(wzz5010, wzz5210, cdc), new_pePe(new_lt19(wzz5011, wzz5211, cdd), new_asAs(new_esEs25(wzz5011, wzz5211, cdd), new_ltEs19(wzz5012, wzz5212, cde)))))
new_esEs7(Just(wzz500), Just(wzz4000), ty_@0) → new_esEs19(wzz500, wzz4000)
new_ltEs20(wzz501, wzz521, app(ty_[], bda)) → new_ltEs15(wzz501, wzz521, bda)
new_ltEs19(wzz5012, wzz5212, app(ty_Maybe, chb)) → new_ltEs13(wzz5012, wzz5212, chb)
new_esEs7(Just(wzz500), Just(wzz4000), ty_Float) → new_esEs10(wzz500, wzz4000)
new_ltEs13(Just(wzz5010), Just(wzz5210), app(app(ty_Either, dfd), dfe)) → new_ltEs5(wzz5010, wzz5210, dfd, dfe)
new_ltEs14(True, False) → False
new_ltEs18(wzz5011, wzz5211, ty_Float) → new_ltEs16(wzz5011, wzz5211)
new_ltEs18(wzz5011, wzz5211, ty_Ordering) → new_ltEs9(wzz5011, wzz5211)
new_lt12(wzz5010, wzz5210, app(app(ty_Either, caa), cab)) → new_lt13(wzz5010, wzz5210, caa, cab)
new_esEs5(Left(wzz500), Left(wzz4000), app(app(ty_Either, bba), bbb), cc) → new_esEs5(wzz500, wzz4000, bba, bbb)
new_lt21(wzz500, wzz520, ty_Int) → new_lt4(wzz500, wzz520)
new_lt21(wzz500, wzz520, app(ty_Ratio, ge)) → new_lt7(wzz500, wzz520, ge)
new_lt19(wzz5011, wzz5211, ty_Integer) → new_lt9(wzz5011, wzz5211)
new_ltEs10(wzz501, wzz521) → new_fsEs(new_compare7(wzz501, wzz521))
new_esEs22(wzz5010, wzz5210, ty_Float) → new_esEs10(wzz5010, wzz5210)
new_esEs20(wzz500, wzz4000, ty_Char) → new_esEs17(wzz500, wzz4000)
new_primPlusNat0(Succ(wzz42200), Succ(wzz9600)) → Succ(Succ(new_primPlusNat0(wzz42200, wzz9600)))
new_esEs29(wzz500, wzz520, app(ty_[], chd)) → new_esEs18(wzz500, wzz520, chd)
new_compare0([], :(wzz5200, wzz5201), chd) → LT
new_compare15(wzz500, wzz520, True, gf) → LT
new_asAs(True, wzz60) → wzz60
new_esEs25(wzz5011, wzz5211, ty_Int) → new_esEs11(wzz5011, wzz5211)
new_ltEs19(wzz5012, wzz5212, app(ty_Ratio, cge)) → new_ltEs7(wzz5012, wzz5212, cge)
new_esEs31(wzz50, wzz400, app(ty_Maybe, cd)) → new_esEs7(wzz50, wzz400, cd)
new_esEs31(wzz50, wzz400, ty_Bool) → new_esEs12(wzz50, wzz400)
new_lt20(wzz5010, wzz5210, ty_Bool) → new_lt17(wzz5010, wzz5210)
new_ltEs5(Right(wzz5010), Right(wzz5210), eg, ty_Float) → new_ltEs16(wzz5010, wzz5210)
new_lt19(wzz5011, wzz5211, ty_Float) → new_lt10(wzz5011, wzz5211)
new_ltEs13(Just(wzz5010), Just(wzz5210), ty_Float) → new_ltEs16(wzz5010, wzz5210)
new_fsEs(wzz121) → new_not(new_esEs8(wzz121, GT))
new_compare211(wzz500, wzz520, True) → EQ
new_compare28(wzz500, wzz520, bdc, bdd) → new_compare29(wzz500, wzz520, new_esEs6(wzz500, wzz520, bdc, bdd), bdc, bdd)
new_esEs26(wzz500, wzz4000, app(app(ty_@2, dbg), dbh)) → new_esEs6(wzz500, wzz4000, dbg, dbh)
new_esEs31(wzz50, wzz400, ty_Int) → new_esEs11(wzz50, wzz400)
new_ltEs5(Right(wzz5010), Right(wzz5210), eg, app(ty_Maybe, ga)) → new_ltEs13(wzz5010, wzz5210, ga)
new_esEs32(wzz38, wzz40, ty_Float) → new_esEs10(wzz38, wzz40)
new_esEs31(wzz50, wzz400, ty_Float) → new_esEs10(wzz50, wzz400)
new_esEs29(wzz500, wzz520, app(ty_Ratio, ge)) → new_esEs14(wzz500, wzz520, ge)
new_lt20(wzz5010, wzz5210, app(ty_Ratio, cea)) → new_lt7(wzz5010, wzz5210, cea)
new_lt17(wzz500, wzz520) → new_esEs8(new_compare30(wzz500, wzz520), LT)
new_esEs24(wzz5010, wzz5210, app(app(app(ty_@3, cdf), cdg), cdh)) → new_esEs4(wzz5010, wzz5210, cdf, cdg, cdh)
new_esEs23(wzz500, wzz4000, app(ty_[], cca)) → new_esEs18(wzz500, wzz4000, cca)
new_esEs21(wzz501, wzz4001, ty_Bool) → new_esEs12(wzz501, wzz4001)
new_esEs5(Left(wzz500), Left(wzz4000), ty_Integer, cc) → new_esEs9(wzz500, wzz4000)
new_compare24(wzz500, wzz520, False, da, db, dc) → new_compare18(wzz500, wzz520, new_ltEs6(wzz500, wzz520, da, db, dc), da, db, dc)
new_esEs22(wzz5010, wzz5210, app(app(ty_Either, caa), cab)) → new_esEs5(wzz5010, wzz5210, caa, cab)
new_esEs31(wzz50, wzz400, app(app(ty_@2, cf), cg)) → new_esEs6(wzz50, wzz400, cf, cg)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCompAux0(wzz144, EQ) → wzz144
new_ltEs13(Just(wzz5010), Just(wzz5210), ty_Bool) → new_ltEs14(wzz5010, wzz5210)
new_esEs29(wzz500, wzz520, ty_Ordering) → new_esEs8(wzz500, wzz520)
new_ltEs20(wzz501, wzz521, app(app(ty_Either, eg), dg)) → new_ltEs5(wzz501, wzz521, eg, dg)
new_esEs28(wzz502, wzz4002, ty_Bool) → new_esEs12(wzz502, wzz4002)
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_lt19(wzz5011, wzz5211, ty_@0) → new_lt5(wzz5011, wzz5211)
new_esEs22(wzz5010, wzz5210, app(ty_Maybe, cae)) → new_esEs7(wzz5010, wzz5210, cae)
new_ltEs5(Left(wzz5010), Left(wzz5210), ty_Double, dg) → new_ltEs11(wzz5010, wzz5210)
new_esEs5(Right(wzz500), Right(wzz4000), cb, app(ty_Maybe, bce)) → new_esEs7(wzz500, wzz4000, bce)
new_primCmpInt(Neg(Succ(wzz5000)), Pos(wzz520)) → LT
new_not(True) → False
new_esEs25(wzz5011, wzz5211, ty_Integer) → new_esEs9(wzz5011, wzz5211)
new_esEs5(Left(wzz500), Left(wzz4000), ty_Char, cc) → new_esEs17(wzz500, wzz4000)

The set Q consists of the following terms:

new_esEs25(x0, x1, app(ty_[], x2))
new_compare210(x0, x1, False, x2)
new_ltEs5(Left(x0), Left(x1), ty_@0, x2)
new_primPlusNat0(Zero, Succ(x0))
new_sr(x0, x1)
new_esEs5(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs32(x0, x1, ty_Bool)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_primEqNat0(Succ(x0), Zero)
new_ltEs5(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs22(x0, x1, ty_Double)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs26(x0, x1, ty_Char)
new_ltEs20(x0, x1, app(ty_[], x2))
new_lt19(x0, x1, ty_@0)
new_compare17(x0, x1, x2, x3, False, x4, x5)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_esEs21(x0, x1, ty_Double)
new_esEs30(x0, x1, x2, x3, True, x4, x5)
new_esEs9(Integer(x0), Integer(x1))
new_lt20(x0, x1, app(ty_[], x2))
new_esEs21(x0, x1, ty_Ordering)
new_esEs20(x0, x1, ty_Float)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare0(:(x0, x1), :(x2, x3), x4)
new_esEs26(x0, x1, ty_Int)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_esEs31(x0, x1, app(ty_Maybe, x2))
new_compare31(x0, x1, app(app(ty_Either, x2), x3))
new_asAs(True, x0)
new_compare111(x0, x1, True)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_primEqNat0(Zero, Succ(x0))
new_ltEs20(x0, x1, ty_Int)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_esEs32(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Bool)
new_ltEs5(Right(x0), Right(x1), x2, ty_@0)
new_esEs12(False, False)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs5(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_lt8(x0, x1, x2, x3, x4)
new_primCmpNat2(Zero, Succ(x0))
new_primCmpNat0(x0, Zero)
new_ltEs5(Right(x0), Right(x1), x2, app(ty_[], x3))
new_compare19(Float(x0, x1), Float(x2, x3))
new_compare11(Char(x0), Char(x1))
new_ltEs19(x0, x1, ty_Double)
new_ltEs20(x0, x1, ty_@0)
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_ltEs5(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs5(Left(x0), Left(x1), ty_Char, x2)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs20(x0, x1, ty_Integer)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs14(:%(x0, x1), :%(x2, x3), x4)
new_lt20(x0, x1, ty_Double)
new_esEs31(x0, x1, app(ty_[], x2))
new_esEs7(Just(x0), Just(x1), ty_Integer)
new_primCompAux0(x0, LT)
new_compare31(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_Bool)
new_lt20(x0, x1, ty_Bool)
new_compare16(x0, x1)
new_esEs20(x0, x1, ty_Int)
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs17(Char(x0), Char(x1))
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_ltEs14(True, False)
new_esEs32(x0, x1, ty_Int)
new_ltEs14(False, True)
new_ltEs13(Nothing, Just(x0), x1)
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_lt21(x0, x1, ty_@0)
new_esEs8(GT, GT)
new_compare13(x0, x1, True)
new_compare30(x0, x1)
new_ltEs15(x0, x1, x2)
new_esEs23(x0, x1, ty_Double)
new_esEs18([], :(x0, x1), x2)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Right(x0), Right(x1), x2, ty_Integer)
new_compare15(x0, x1, True, x2)
new_ltEs13(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs8(LT, LT)
new_esEs29(x0, x1, ty_Integer)
new_esEs23(x0, x1, ty_Ordering)
new_esEs7(Just(x0), Just(x1), app(ty_[], x2))
new_primCmpNat1(Succ(x0), x1)
new_compare9(Double(x0, x1), Double(x2, x3))
new_lt21(x0, x1, ty_Bool)
new_lt11(x0, x1, x2)
new_compare26(x0, x1, False)
new_esEs31(x0, x1, ty_Float)
new_lt4(x0, x1)
new_esEs31(x0, x1, app(ty_Ratio, x2))
new_ltEs5(Right(x0), Right(x1), x2, ty_Ordering)
new_compare31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs31(x0, x1, ty_Double)
new_compare12(:%(x0, x1), :%(x2, x3), ty_Int)
new_compare31(x0, x1, ty_Integer)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs28(x0, x1, ty_@0)
new_esEs18(:(x0, x1), :(x2, x3), x4)
new_esEs22(x0, x1, ty_Integer)
new_esEs15(x0, x1, ty_Int)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_Float)
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs8(LT, GT)
new_esEs8(GT, LT)
new_ltEs13(Nothing, Nothing, x0)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs5(Right(x0), Right(x1), x2, ty_Int)
new_ltEs20(x0, x1, ty_Bool)
new_lt20(x0, x1, ty_Int)
new_primEqNat0(Succ(x0), Succ(x1))
new_ltEs13(Just(x0), Just(x1), ty_Integer)
new_ltEs9(EQ, EQ)
new_esEs7(Just(x0), Just(x1), ty_Ordering)
new_compare26(x0, x1, True)
new_compare13(x0, x1, False)
new_esEs20(x0, x1, ty_@0)
new_esEs5(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs22(x0, x1, ty_@0)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs27(x0, x1, ty_Int)
new_compare110(x0, x1, x2, x3, False, x4, x5, x6)
new_primEqNat0(Zero, Zero)
new_ltEs18(x0, x1, ty_Int)
new_esEs20(x0, x1, ty_Double)
new_esEs29(x0, x1, ty_Float)
new_esEs7(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs13(Just(x0), Just(x1), ty_Float)
new_esEs5(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_sr0(Integer(x0), Integer(x1))
new_ltEs12(x0, x1)
new_esEs31(x0, x1, ty_Bool)
new_lt12(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, ty_Bool)
new_esEs5(Right(x0), Left(x1), x2, x3)
new_esEs5(Left(x0), Right(x1), x2, x3)
new_esEs31(x0, x1, ty_Integer)
new_esEs27(x0, x1, ty_Ordering)
new_esEs32(x0, x1, ty_Float)
new_esEs27(x0, x1, ty_Integer)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs26(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_@0)
new_ltEs5(Left(x0), Left(x1), ty_Bool, x2)
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_Integer)
new_primMulNat0(Zero, Zero)
new_ltEs5(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, ty_Integer)
new_lt15(x0, x1)
new_ltEs19(x0, x1, ty_@0)
new_ltEs5(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_esEs29(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_@0)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_ltEs18(x0, x1, ty_Ordering)
new_esEs27(x0, x1, ty_Float)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs5(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs7(Nothing, Nothing, x0)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_lt21(x0, x1, ty_Int)
new_esEs7(Just(x0), Just(x1), ty_Char)
new_esEs31(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Float)
new_esEs29(x0, x1, ty_@0)
new_primMulInt(Neg(x0), Neg(x1))
new_ltEs5(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_compare25(x0, x1, True, x2, x3)
new_esEs27(x0, x1, ty_@0)
new_esEs21(x0, x1, ty_Integer)
new_lt21(x0, x1, app(ty_Maybe, x2))
new_ltEs13(Just(x0), Just(x1), ty_Char)
new_lt17(x0, x1)
new_esEs16(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_Int)
new_lt12(x0, x1, ty_Integer)
new_ltEs13(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs5(Left(x0), Left(x1), ty_Int, x2)
new_ltEs19(x0, x1, ty_Bool)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_primCmpNat0(x0, Succ(x1))
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Left(x0), Left(x1), ty_Float, x2)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs13(Just(x0), Nothing, x1)
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_lt21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs32(x0, x1, ty_Ordering)
new_esEs5(Left(x0), Left(x1), ty_Double, x2)
new_esEs7(Just(x0), Just(x1), ty_@0)
new_esEs7(Just(x0), Nothing, x1)
new_esEs7(Nothing, Just(x0), x1)
new_ltEs9(GT, EQ)
new_ltEs9(EQ, GT)
new_esEs27(x0, x1, ty_Double)
new_compare18(x0, x1, False, x2, x3, x4)
new_compare18(x0, x1, True, x2, x3, x4)
new_esEs25(x0, x1, ty_Float)
new_esEs32(x0, x1, ty_Integer)
new_ltEs13(Just(x0), Just(x1), ty_@0)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_lt12(x0, x1, app(ty_Maybe, x2))
new_ltEs18(x0, x1, ty_Char)
new_lt12(x0, x1, ty_Double)
new_ltEs5(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs24(x0, x1, ty_@0)
new_compare31(x0, x1, app(ty_Maybe, x2))
new_esEs7(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_compare31(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs5(Right(x0), Right(x1), x2, ty_Char)
new_lt12(x0, x1, ty_Char)
new_lt21(x0, x1, ty_Ordering)
new_compare31(x0, x1, ty_Bool)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpNat2(Zero, Zero)
new_esEs31(x0, x1, ty_Int)
new_compare29(x0, x1, True, x2, x3)
new_primPlusNat1(Zero, x0)
new_primPlusNat0(Zero, Zero)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_ltEs5(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs26(x0, x1, ty_Double)
new_compare111(x0, x1, False)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_esEs32(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, ty_Bool)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_Float)
new_esEs32(x0, x1, ty_@0)
new_esEs23(x0, x1, ty_Int)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_compare0([], [], x0)
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt12(x0, x1, app(app(ty_@2, x2), x3))
new_lt19(x0, x1, ty_Ordering)
new_compare0(:(x0, x1), [], x2)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_lt7(x0, x1, x2)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_lt14(x0, x1, x2, x3)
new_pePe(False, x0)
new_lt21(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, ty_Integer)
new_primCmpNat2(Succ(x0), Zero)
new_lt5(x0, x1)
new_compare210(x0, x1, True, x2)
new_ltEs5(Left(x0), Left(x1), ty_Double, x2)
new_ltEs5(Left(x0), Left(x1), ty_Float, x2)
new_lt21(x0, x1, ty_Integer)
new_lt19(x0, x1, ty_Integer)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, ty_Double)
new_lt21(x0, x1, app(ty_Ratio, x2))
new_ltEs18(x0, x1, ty_Double)
new_lt12(x0, x1, app(ty_[], x2))
new_esEs5(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_ltEs9(EQ, LT)
new_ltEs9(LT, EQ)
new_esEs11(x0, x1)
new_esEs12(True, True)
new_esEs32(x0, x1, ty_Char)
new_ltEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_compare31(x0, x1, ty_@0)
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs10(Float(x0, x1), Float(x2, x3))
new_ltEs8(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs19(x0, x1, ty_Char)
new_compare24(x0, x1, False, x2, x3, x4)
new_compare28(x0, x1, x2, x3)
new_compare211(x0, x1, False)
new_esEs32(x0, x1, app(ty_[], x2))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_lt18(x0, x1, x2)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_primEqInt(Neg(Zero), Pos(Zero))
new_primEqInt(Pos(Zero), Neg(Zero))
new_lt19(x0, x1, ty_Int)
new_primCompAux0(x0, EQ)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, ty_Integer)
new_ltEs18(x0, x1, ty_Float)
new_lt20(x0, x1, ty_Integer)
new_lt12(x0, x1, ty_Int)
new_esEs20(x0, x1, ty_Ordering)
new_compare10(x0, x1, False, x2, x3)
new_lt21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt10(x0, x1)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs8(EQ, EQ)
new_compare24(x0, x1, True, x2, x3, x4)
new_esEs5(Left(x0), Left(x1), ty_Integer, x2)
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_ltEs13(Just(x0), Just(x1), ty_Bool)
new_compare31(x0, x1, ty_Double)
new_primPlusNat0(Succ(x0), Zero)
new_esEs22(x0, x1, ty_Ordering)
new_ltEs16(x0, x1)
new_lt13(x0, x1, x2, x3)
new_primEqInt(Neg(Zero), Neg(Zero))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_ltEs20(x0, x1, ty_Char)
new_lt12(x0, x1, ty_Ordering)
new_esEs28(x0, x1, ty_Ordering)
new_esEs7(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs22(x0, x1, ty_Int)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, ty_Double)
new_esEs25(x0, x1, ty_Ordering)
new_lt21(x0, x1, ty_Float)
new_esEs29(x0, x1, ty_Char)
new_primCompAux0(x0, GT)
new_esEs5(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs26(x0, x1, ty_Ordering)
new_esEs5(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs5(Left(x0), Left(x1), ty_Char, x2)
new_compare211(x0, x1, True)
new_ltEs5(Right(x0), Right(x1), x2, ty_Float)
new_compare7(@0, @0)
new_esEs20(x0, x1, ty_Char)
new_ltEs18(x0, x1, ty_@0)
new_ltEs19(x0, x1, app(ty_[], x2))
new_primPlusNat0(Succ(x0), Succ(x1))
new_esEs5(Right(x0), Right(x1), x2, ty_Char)
new_fsEs(x0)
new_lt12(x0, x1, ty_@0)
new_esEs28(x0, x1, ty_Bool)
new_esEs32(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Float)
new_ltEs9(LT, LT)
new_compare27(x0, x1, x2)
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs17(x0, x1)
new_esEs23(x0, x1, ty_@0)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, ty_Float)
new_esEs5(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs21(x0, x1, ty_Char)
new_esEs22(x0, x1, ty_Char)
new_esEs8(GT, EQ)
new_esEs8(EQ, GT)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_ltEs5(Right(x0), Right(x1), x2, ty_Double)
new_esEs31(x0, x1, app(app(ty_@2, x2), x3))
new_compare5(x0, x1)
new_esEs22(x0, x1, ty_Float)
new_compare31(x0, x1, ty_Float)
new_esEs13(Double(x0, x1), Double(x2, x3))
new_ltEs13(Just(x0), Just(x1), ty_Int)
new_lt19(x0, x1, ty_Double)
new_ltEs13(Just(x0), Just(x1), ty_Double)
new_esEs21(x0, x1, ty_Bool)
new_lt6(x0, x1)
new_ltEs13(Just(x0), Just(x1), app(ty_[], x2))
new_lt21(x0, x1, ty_Double)
new_compare0([], :(x0, x1), x2)
new_ltEs5(Left(x0), Left(x1), app(ty_[], x2), x3)
new_pePe(True, x0)
new_esEs23(x0, x1, ty_Bool)
new_compare31(x0, x1, ty_Ordering)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Right(x0), Right(x1), x2, ty_Float)
new_primPlusNat1(Succ(x0), x1)
new_compare110(x0, x1, x2, x3, True, x4, x5, x6)
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_esEs5(Right(x0), Right(x1), x2, ty_Bool)
new_esEs5(Left(x0), Left(x1), ty_@0, x2)
new_ltEs5(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs32(x0, x1, ty_Double)
new_esEs5(Right(x0), Right(x1), x2, ty_@0)
new_compare10(x0, x1, True, x2, x3)
new_esEs25(x0, x1, ty_@0)
new_lt20(x0, x1, ty_Ordering)
new_esEs4(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_ltEs5(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_compare6(x0, x1, x2, x3, x4)
new_ltEs13(Just(x0), Just(x1), app(ty_Maybe, x2))
new_lt19(x0, x1, ty_Float)
new_esEs5(Left(x0), Left(x1), ty_Bool, x2)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_lt21(x0, x1, app(ty_[], x2))
new_esEs32(x0, x1, app(ty_Ratio, x2))
new_esEs16(x0, x1, ty_Int)
new_esEs31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs12(True, False)
new_esEs12(False, True)
new_ltEs18(x0, x1, app(ty_[], x2))
new_esEs31(x0, x1, ty_Ordering)
new_ltEs19(x0, x1, ty_Ordering)
new_esEs31(x0, x1, ty_@0)
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_primMulNat0(Succ(x0), Zero)
new_ltEs14(True, True)
new_ltEs5(Right(x0), Right(x1), x2, ty_Integer)
new_esEs20(x0, x1, app(ty_[], x2))
new_lt16(x0, x1)
new_ltEs14(False, False)
new_esEs5(Left(x0), Left(x1), app(ty_[], x2), x3)
new_ltEs9(GT, LT)
new_ltEs9(LT, GT)
new_ltEs13(Just(x0), Just(x1), ty_Ordering)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_Bool)
new_lt12(x0, x1, ty_Float)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs7(Just(x0), Just(x1), ty_Bool)
new_asAs(False, x0)
new_esEs5(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_primCmpNat1(Zero, x0)
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_not(True)
new_compare31(x0, x1, ty_Char)
new_esEs25(x0, x1, ty_Int)
new_primMulNat0(Zero, Succ(x0))
new_esEs27(x0, x1, app(ty_[], x2))
new_esEs25(x0, x1, ty_Bool)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, ty_Char)
new_esEs7(Just(x0), Just(x1), ty_Float)
new_esEs18([], [], x0)
new_compare8(Integer(x0), Integer(x1))
new_esEs7(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_not(False)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs29(x0, x1, ty_Bool)
new_ltEs5(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs5(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs4(x0, x1)
new_esEs7(Just(x0), Just(x1), ty_Double)
new_esEs24(x0, x1, ty_Ordering)
new_primCompAux1(x0, x1, x2, x3)
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs28(x0, x1, ty_Char)
new_ltEs18(x0, x1, ty_Bool)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_ltEs10(x0, x1)
new_compare31(x0, x1, app(ty_Ratio, x2))
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs28(x0, x1, ty_Double)
new_esEs28(x0, x1, ty_Float)
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs5(Left(x0), Left(x1), ty_Int, x2)
new_esEs23(x0, x1, ty_Float)
new_esEs8(EQ, LT)
new_esEs8(LT, EQ)
new_lt12(x0, x1, app(ty_Ratio, x2))
new_compare17(x0, x1, x2, x3, True, x4, x5)
new_esEs24(x0, x1, ty_Float)
new_lt12(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt9(x0, x1)
new_compare31(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, ty_Int)
new_primCmpNat2(Succ(x0), Succ(x1))
new_ltEs9(GT, GT)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Double)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Char)
new_esEs27(x0, x1, ty_Char)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs18(:(x0, x1), [], x2)
new_compare15(x0, x1, False, x2)
new_lt19(x0, x1, ty_Char)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Right(x0), Right(x1), x2, ty_Double)
new_esEs31(x0, x1, ty_Char)
new_esEs5(Right(x0), Right(x1), x2, ty_Int)
new_esEs28(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, ty_Double)
new_esEs20(x0, x1, ty_Bool)
new_ltEs7(x0, x1, x2)
new_esEs7(Just(x0), Just(x1), ty_Int)
new_esEs29(x0, x1, app(ty_[], x2))
new_esEs30(x0, x1, x2, x3, False, x4, x5)
new_ltEs20(x0, x1, ty_Ordering)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs5(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs5(Left(x0), Right(x1), x2, x3)
new_esEs5(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs5(Right(x0), Left(x1), x2, x3)
new_esEs25(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_Int)
new_compare14(x0, x1, x2, x3)
new_esEs32(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs29(x0, x1, ty_Ordering)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_esEs19(@0, @0)
new_compare12(:%(x0, x1), :%(x2, x3), ty_Integer)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_lt21(x0, x1, ty_Char)
new_primMulInt(Pos(x0), Pos(x1))
new_lt19(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_ltEs13(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, app(ty_[], x2))
new_compare25(x0, x1, False, x2, x3)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_compare29(@2(x0, x1), @2(x2, x3), False, x4, x5)
new_lt12(x0, x1, ty_Bool)
new_ltEs11(x0, x1)
new_esEs23(x0, x1, ty_Char)
new_esEs15(x0, x1, ty_Integer)
new_lt20(x0, x1, ty_@0)
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs13(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))

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

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