YES 290.862 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
  ↳ CR

mainModule FiniteMap
  ((addToFM_C :: (a  ->  a  ->  a ->  FiniteMap Bool a  ->  Bool  ->  a  ->  FiniteMap Bool a) :: (a  ->  a  ->  a ->  FiniteMap Bool a  ->  Bool  ->  a  ->  FiniteMap Bool 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 

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

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

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

  sIZE_RATIO :: Int
sIZE_RATIO 5

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude



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

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

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

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

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

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

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

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



↳ HASKELL
  ↳ CR
HASKELL
      ↳ BR

mainModule FiniteMap
  ((addToFM_C :: (a  ->  a  ->  a ->  FiniteMap Bool a  ->  Bool  ->  a  ->  FiniteMap Bool a) :: (a  ->  a  ->  a ->  FiniteMap Bool a  ->  Bool  ->  a  ->  FiniteMap Bool 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 

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

  emptyFM :: FiniteMap a b
emptyFM EmptyFM

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

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

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

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

  sIZE_RATIO :: Int
sIZE_RATIO 5

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude



Replaced joker patterns by fresh variables and removed binding patterns.

↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
HASKELL
          ↳ COR

mainModule FiniteMap
  ((addToFM_C :: (a  ->  a  ->  a ->  FiniteMap Bool a  ->  Bool  ->  a  ->  FiniteMap Bool a) :: (a  ->  a  ->  a ->  FiniteMap Bool a  ->  Bool  ->  a  ->  FiniteMap Bool a)

module FiniteMap where
  import qualified Maybe
import qualified Prelude

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


  instance (Eq a, Eq b) => Eq (FiniteMap b a) where 

  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 xw xx EmptyFM(key,elt)
findMax (Branch key elt xy xz fm_rfindMax fm_r

  findMin :: FiniteMap a b  ->  (a,b)
findMin (Branch key elt wy EmptyFM wz(key,elt)
findMin (Branch key elt xu fm_l xvfindMin 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 zy (Branch key_rl elt_rl zz 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 zw fm_ll (Branch key_lr elt_lr zx 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 vuu vuv vuw 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 yz zu zv 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 vux 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 yy 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 wu wv ww wx
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 vw vx vy vz
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 yu yv size yw yxsize

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude



Cond Reductions:
The following Function with conditions
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_C2 combiner key elt size fm_l fm_r new_key new_elt True = mkBalBranch key elt (addToFM_C combiner fm_l new_key new_eltfm_r
addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt False = addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt (new_key > key)

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

addToFM_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_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 vvx vvy vvz vwu = addToFM_C3 vvx vvy vvz vwu

The following Function with conditions
mkBalBranch1 fm_L fm_R (Branch yz zu zv 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 yz zu zv fm_ll fm_lr) = mkBalBranch12 fm_L fm_R (Branch yz zu zv fm_ll fm_lr)

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

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

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

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

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

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

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

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

compare0 x y True = GT

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

compare3 x y = compare2 x y (x == y)

The following Function with conditions
undefined 
 | False
 = undefined

is transformed to
undefined  = undefined1

undefined0 True = undefined

undefined1  = undefined0 False



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
HASKELL
              ↳ LetRed

mainModule FiniteMap
  ((addToFM_C :: (a  ->  a  ->  a ->  FiniteMap Bool a  ->  Bool  ->  a  ->  FiniteMap Bool a) :: (a  ->  a  ->  a ->  FiniteMap Bool a  ->  Bool  ->  a  ->  FiniteMap Bool a)

module FiniteMap where
  import qualified Maybe
import qualified Prelude

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


  instance (Eq a, Eq b) => Eq (FiniteMap b a) where 

  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 vvx vvy vvz vwu addToFM_C3 vvx vvy vvz vwu

  emptyFM :: FiniteMap a b
emptyFM EmptyFM

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

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

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

  
mkBalBranch6 key elt fm_L fm_R 
mkBalBranch5 key elt fm_L fm_R (size_l + size_r < 2) where 
double_L fm_l (Branch key_r elt_r zy (Branch key_rl elt_rl zz 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 zw fm_ll (Branch key_lr elt_lr zx 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 vuu vuv vuw fm_rl fm_rrmkBalBranch02 fm_L fm_R (Branch vuu vuv vuw fm_rl fm_rr)
mkBalBranch00 fm_L fm_R vuu vuv vuw fm_rl fm_rr True double_L fm_L fm_R
mkBalBranch01 fm_L fm_R vuu vuv vuw fm_rl fm_rr True single_L fm_L fm_R
mkBalBranch01 fm_L fm_R vuu vuv vuw fm_rl fm_rr False mkBalBranch00 fm_L fm_R vuu vuv vuw fm_rl fm_rr otherwise
mkBalBranch02 fm_L fm_R (Branch vuu vuv vuw fm_rl fm_rrmkBalBranch01 fm_L fm_R vuu vuv vuw fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr)
mkBalBranch1 fm_L fm_R (Branch yz zu zv fm_ll fm_lrmkBalBranch12 fm_L fm_R (Branch yz zu zv fm_ll fm_lr)
mkBalBranch10 fm_L fm_R yz zu zv fm_ll fm_lr True double_R fm_L fm_R
mkBalBranch11 fm_L fm_R yz zu zv fm_ll fm_lr True single_R fm_L fm_R
mkBalBranch11 fm_L fm_R yz zu zv fm_ll fm_lr False mkBalBranch10 fm_L fm_R yz zu zv fm_ll fm_lr otherwise
mkBalBranch12 fm_L fm_R (Branch yz zu zv fm_ll fm_lrmkBalBranch11 fm_L fm_R yz zu zv 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 vux 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 yy 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 wu wv ww wx
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 vw vx vy vz
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 yu yv size yw yxsize

  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 wu wv ww wx) = 
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 vw vx vy vz) = 
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_size vwx vwy vwz = sizeFM vwx

mkBranchUnbox vwx vwy vwz x = x

mkBranchRight_ok0 vwx vwy vwz fm_r key EmptyFM = True
mkBranchRight_ok0 vwx vwy vwz fm_r key (Branch right_key vw vx vy vz) = key < mkBranchRight_ok0Smallest_right_key fm_r

mkBranchRight_size vwx vwy vwz = sizeFM vwy

mkBranchRight_ok vwx vwy vwz = mkBranchRight_ok0 vwx vwy vwz vwy vwz vwy

mkBranchLeft_ok vwx vwy vwz = mkBranchLeft_ok0 vwx vwy vwz vwx vwz vwx

mkBranchBalance_ok vwx vwy vwz = True

mkBranchLeft_ok0 vwx vwy vwz fm_l key EmptyFM = True
mkBranchLeft_ok0 vwx vwy vwz fm_l key (Branch left_key wu wv ww wx) = mkBranchLeft_ok0Biggest_left_key fm_l < key

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 vxu vxv vxw vxx = Branch vxu vxv (mkBranchUnbox vxw vxx vxu (1 + mkBranchLeft_size vxw vxx vxu + mkBranchRight_size vxw vxx vxu)) vxw vxx

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 zy (Branch key_rl elt_rl zz 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 zw fm_ll (Branch key_lr elt_lr zx 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 vuu vuv vuw fm_rl fm_rr) = mkBalBranch02 fm_L fm_R (Branch vuu vuv vuw fm_rl fm_rr)
mkBalBranch00 fm_L fm_R vuu vuv vuw fm_rl fm_rr True = double_L fm_L fm_R
mkBalBranch01 fm_L fm_R vuu vuv vuw fm_rl fm_rr True = single_L fm_L fm_R
mkBalBranch01 fm_L fm_R vuu vuv vuw fm_rl fm_rr False = mkBalBranch00 fm_L fm_R vuu vuv vuw fm_rl fm_rr otherwise
mkBalBranch02 fm_L fm_R (Branch vuu vuv vuw fm_rl fm_rr) = mkBalBranch01 fm_L fm_R vuu vuv vuw fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr)
mkBalBranch1 fm_L fm_R (Branch yz zu zv fm_ll fm_lr) = mkBalBranch12 fm_L fm_R (Branch yz zu zv fm_ll fm_lr)
mkBalBranch10 fm_L fm_R yz zu zv fm_ll fm_lr True = double_R fm_L fm_R
mkBalBranch11 fm_L fm_R yz zu zv fm_ll fm_lr True = single_R fm_L fm_R
mkBalBranch11 fm_L fm_R yz zu zv fm_ll fm_lr False = mkBalBranch10 fm_L fm_R yz zu zv fm_ll fm_lr otherwise
mkBalBranch12 fm_L fm_R (Branch yz zu zv fm_ll fm_lr) = mkBalBranch11 fm_L fm_R yz zu zv 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 vux 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 yy 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
mkBalBranch6MkBalBranch10 vxy vxz vyu vyv fm_L fm_R yz zu zv fm_ll fm_lr True = mkBalBranch6Double_R vxy vxz vyu vyv fm_L fm_R

mkBalBranch6Double_L vxy vxz vyu vyv fm_l (Branch key_r elt_r zy (Branch key_rl elt_rl zz fm_rll fm_rlrfm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 vxy vxz fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr)

mkBalBranch6MkBalBranch00 vxy vxz vyu vyv fm_L fm_R vuu vuv vuw fm_rl fm_rr True = mkBalBranch6Double_L vxy vxz vyu vyv fm_L fm_R

mkBalBranch6Single_R vxy vxz vyu vyv (Branch key_l elt_l yy fm_ll fm_lrfm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 vxy vxz fm_lr fm_r)

mkBalBranch6MkBalBranch5 vxy vxz vyu vyv key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R
mkBalBranch6MkBalBranch5 vxy vxz vyu vyv key elt fm_L fm_R False = mkBalBranch6MkBalBranch4 vxy vxz vyu vyv key elt fm_L fm_R (mkBalBranch6Size_r vxy vxz vyu vyv > sIZE_RATIO * mkBalBranch6Size_l vxy vxz vyu vyv)

mkBalBranch6Single_L vxy vxz vyu vyv fm_l (Branch key_r elt_r vux fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 vxy vxz fm_l fm_rlfm_rr

mkBalBranch6MkBalBranch2 vxy vxz vyu vyv key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R

mkBalBranch6Size_r vxy vxz vyu vyv = sizeFM vyu

mkBalBranch6MkBalBranch01 vxy vxz vyu vyv fm_L fm_R vuu vuv vuw fm_rl fm_rr True = mkBalBranch6Single_L vxy vxz vyu vyv fm_L fm_R
mkBalBranch6MkBalBranch01 vxy vxz vyu vyv fm_L fm_R vuu vuv vuw fm_rl fm_rr False = mkBalBranch6MkBalBranch00 vxy vxz vyu vyv fm_L fm_R vuu vuv vuw fm_rl fm_rr otherwise

mkBalBranch6Double_R vxy vxz vyu vyv (Branch key_l elt_l zw fm_ll (Branch key_lr elt_lr zx fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 vxy vxz fm_lrr fm_r)

mkBalBranch6MkBalBranch3 vxy vxz vyu vyv key elt fm_L fm_R True = mkBalBranch6MkBalBranch1 vxy vxz vyu vyv fm_L fm_R fm_L
mkBalBranch6MkBalBranch3 vxy vxz vyu vyv key elt fm_L fm_R False = mkBalBranch6MkBalBranch2 vxy vxz vyu vyv key elt fm_L fm_R otherwise

mkBalBranch6Size_l vxy vxz vyu vyv = sizeFM vyv

mkBalBranch6MkBalBranch1 vxy vxz vyu vyv fm_L fm_R (Branch yz zu zv fm_ll fm_lr) = mkBalBranch6MkBalBranch12 vxy vxz vyu vyv fm_L fm_R (Branch yz zu zv fm_ll fm_lr)

mkBalBranch6MkBalBranch12 vxy vxz vyu vyv fm_L fm_R (Branch yz zu zv fm_ll fm_lr) = mkBalBranch6MkBalBranch11 vxy vxz vyu vyv fm_L fm_R yz zu zv fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll)

mkBalBranch6MkBalBranch02 vxy vxz vyu vyv fm_L fm_R (Branch vuu vuv vuw fm_rl fm_rr) = mkBalBranch6MkBalBranch01 vxy vxz vyu vyv fm_L fm_R vuu vuv vuw fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr)

mkBalBranch6MkBalBranch0 vxy vxz vyu vyv fm_L fm_R (Branch vuu vuv vuw fm_rl fm_rr) = mkBalBranch6MkBalBranch02 vxy vxz vyu vyv fm_L fm_R (Branch vuu vuv vuw fm_rl fm_rr)

mkBalBranch6MkBalBranch11 vxy vxz vyu vyv fm_L fm_R yz zu zv fm_ll fm_lr True = mkBalBranch6Single_R vxy vxz vyu vyv fm_L fm_R
mkBalBranch6MkBalBranch11 vxy vxz vyu vyv fm_L fm_R yz zu zv fm_ll fm_lr False = mkBalBranch6MkBalBranch10 vxy vxz vyu vyv fm_L fm_R yz zu zv fm_ll fm_lr otherwise

mkBalBranch6MkBalBranch4 vxy vxz vyu vyv key elt fm_L fm_R True = mkBalBranch6MkBalBranch0 vxy vxz vyu vyv fm_L fm_R fm_R
mkBalBranch6MkBalBranch4 vxy vxz vyu vyv key elt fm_L fm_R False = mkBalBranch6MkBalBranch3 vxy vxz vyu vyv key elt fm_L fm_R (mkBalBranch6Size_l vxy vxz vyu vyv > sIZE_RATIO * mkBalBranch6Size_r vxy vxz vyu vyv)

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 vyw = fst (findMin vyw)

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 vyx = fst (findMax vyx)



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ LetRed
HASKELL
                  ↳ NumRed

mainModule FiniteMap
  ((addToFM_C :: (a  ->  a  ->  a ->  FiniteMap Bool a  ->  Bool  ->  a  ->  FiniteMap Bool a) :: (a  ->  a  ->  a ->  FiniteMap Bool a  ->  Bool  ->  a  ->  FiniteMap Bool 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 

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

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

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

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

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

  
addToFM_C4 combiner EmptyFM key elt unitFM key elt
addToFM_C4 vvx vvy vvz vwu addToFM_C3 vvx vvy vvz vwu

  emptyFM :: FiniteMap b a
emptyFM EmptyFM

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

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

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

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

  
mkBalBranch6Double_L vxy vxz vyu vyv fm_l (Branch key_r elt_r zy (Branch key_rl elt_rl zz fm_rll fm_rlr) fm_rrmkBranch 5 key_rl elt_rl (mkBranch 6 vxy vxz fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr)

  
mkBalBranch6Double_R vxy vxz vyu vyv (Branch key_l elt_l zw fm_ll (Branch key_lr elt_lr zx fm_lrl fm_lrr)) fm_r mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 vxy vxz fm_lrr fm_r)

  
mkBalBranch6MkBalBranch0 vxy vxz vyu vyv fm_L fm_R (Branch vuu vuv vuw fm_rl fm_rrmkBalBranch6MkBalBranch02 vxy vxz vyu vyv fm_L fm_R (Branch vuu vuv vuw fm_rl fm_rr)

  
mkBalBranch6MkBalBranch00 vxy vxz vyu vyv fm_L fm_R vuu vuv vuw fm_rl fm_rr True mkBalBranch6Double_L vxy vxz vyu vyv fm_L fm_R

  
mkBalBranch6MkBalBranch01 vxy vxz vyu vyv fm_L fm_R vuu vuv vuw fm_rl fm_rr True mkBalBranch6Single_L vxy vxz vyu vyv fm_L fm_R
mkBalBranch6MkBalBranch01 vxy vxz vyu vyv fm_L fm_R vuu vuv vuw fm_rl fm_rr False mkBalBranch6MkBalBranch00 vxy vxz vyu vyv fm_L fm_R vuu vuv vuw fm_rl fm_rr otherwise

  
mkBalBranch6MkBalBranch02 vxy vxz vyu vyv fm_L fm_R (Branch vuu vuv vuw fm_rl fm_rrmkBalBranch6MkBalBranch01 vxy vxz vyu vyv fm_L fm_R vuu vuv vuw fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr)

  
mkBalBranch6MkBalBranch1 vxy vxz vyu vyv fm_L fm_R (Branch yz zu zv fm_ll fm_lrmkBalBranch6MkBalBranch12 vxy vxz vyu vyv fm_L fm_R (Branch yz zu zv fm_ll fm_lr)

  
mkBalBranch6MkBalBranch10 vxy vxz vyu vyv fm_L fm_R yz zu zv fm_ll fm_lr True mkBalBranch6Double_R vxy vxz vyu vyv fm_L fm_R

  
mkBalBranch6MkBalBranch11 vxy vxz vyu vyv fm_L fm_R yz zu zv fm_ll fm_lr True mkBalBranch6Single_R vxy vxz vyu vyv fm_L fm_R
mkBalBranch6MkBalBranch11 vxy vxz vyu vyv fm_L fm_R yz zu zv fm_ll fm_lr False mkBalBranch6MkBalBranch10 vxy vxz vyu vyv fm_L fm_R yz zu zv fm_ll fm_lr otherwise

  
mkBalBranch6MkBalBranch12 vxy vxz vyu vyv fm_L fm_R (Branch yz zu zv fm_ll fm_lrmkBalBranch6MkBalBranch11 vxy vxz vyu vyv fm_L fm_R yz zu zv fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll)

  
mkBalBranch6MkBalBranch2 vxy vxz vyu vyv key elt fm_L fm_R True mkBranch 2 key elt fm_L fm_R

  
mkBalBranch6MkBalBranch3 vxy vxz vyu vyv key elt fm_L fm_R True mkBalBranch6MkBalBranch1 vxy vxz vyu vyv fm_L fm_R fm_L
mkBalBranch6MkBalBranch3 vxy vxz vyu vyv key elt fm_L fm_R False mkBalBranch6MkBalBranch2 vxy vxz vyu vyv key elt fm_L fm_R otherwise

  
mkBalBranch6MkBalBranch4 vxy vxz vyu vyv key elt fm_L fm_R True mkBalBranch6MkBalBranch0 vxy vxz vyu vyv fm_L fm_R fm_R
mkBalBranch6MkBalBranch4 vxy vxz vyu vyv key elt fm_L fm_R False mkBalBranch6MkBalBranch3 vxy vxz vyu vyv key elt fm_L fm_R (mkBalBranch6Size_l vxy vxz vyu vyv > sIZE_RATIO * mkBalBranch6Size_r vxy vxz vyu vyv)

  
mkBalBranch6MkBalBranch5 vxy vxz vyu vyv key elt fm_L fm_R True mkBranch 1 key elt fm_L fm_R
mkBalBranch6MkBalBranch5 vxy vxz vyu vyv key elt fm_L fm_R False mkBalBranch6MkBalBranch4 vxy vxz vyu vyv key elt fm_L fm_R (mkBalBranch6Size_r vxy vxz vyu vyv > sIZE_RATIO * mkBalBranch6Size_l vxy vxz vyu vyv)

  
mkBalBranch6Single_L vxy vxz vyu vyv fm_l (Branch key_r elt_r vux fm_rl fm_rrmkBranch 3 key_r elt_r (mkBranch 4 vxy vxz fm_l fm_rl) fm_rr

  
mkBalBranch6Single_R vxy vxz vyu vyv (Branch key_l elt_l yy fm_ll fm_lrfm_r mkBranch 8 key_l elt_l fm_ll (mkBranch 9 vxy vxz fm_lr fm_r)

  
mkBalBranch6Size_l vxy vxz vyu vyv sizeFM vyv

  
mkBalBranch6Size_r vxy vxz vyu vyv sizeFM vyu

  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 vwx vwy vwz True

  
mkBranchLeft_ok vwx vwy vwz mkBranchLeft_ok0 vwx vwy vwz vwx vwz vwx

  
mkBranchLeft_ok0 vwx vwy vwz fm_l key EmptyFM True
mkBranchLeft_ok0 vwx vwy vwz fm_l key (Branch left_key wu wv ww wxmkBranchLeft_ok0Biggest_left_key fm_l < key

  
mkBranchLeft_ok0Biggest_left_key vyx fst (findMax vyx)

  
mkBranchLeft_size vwx vwy vwz sizeFM vwx

  
mkBranchResult vxu vxv vxw vxx Branch vxu vxv (mkBranchUnbox vxw vxx vxu (1 + mkBranchLeft_size vxw vxx vxu + mkBranchRight_size vxw vxx vxu)) vxw vxx

  
mkBranchRight_ok vwx vwy vwz mkBranchRight_ok0 vwx vwy vwz vwy vwz vwy

  
mkBranchRight_ok0 vwx vwy vwz fm_r key EmptyFM True
mkBranchRight_ok0 vwx vwy vwz fm_r key (Branch right_key vw vx vy vzkey < mkBranchRight_ok0Smallest_right_key fm_r

  
mkBranchRight_ok0Smallest_right_key vyw fst (findMin vyw)

  
mkBranchRight_size vwx vwy vwz sizeFM vwy

  mkBranchUnbox :: Ord a =>  ->  (FiniteMap a b) ( ->  (FiniteMap a b) ( ->  a (Int  ->  Int)))
mkBranchUnbox vwx vwy vwz x x

  sIZE_RATIO :: Int
sIZE_RATIO 5

  sizeFM :: FiniteMap b a  ->  Int
sizeFM EmptyFM 0
sizeFM (Branch yu yv size yw yxsize

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

mainModule FiniteMap
  (addToFM_C :: (a  ->  a  ->  a ->  FiniteMap Bool a  ->  Bool  ->  a  ->  FiniteMap Bool 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 

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

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

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

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

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

  
addToFM_C4 combiner EmptyFM key elt unitFM key elt
addToFM_C4 vvx vvy vvz vwu addToFM_C3 vvx vvy vvz vwu

  emptyFM :: FiniteMap a b
emptyFM EmptyFM

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

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

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

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

  
mkBalBranch6Double_L vxy vxz vyu vyv fm_l (Branch key_r elt_r zy (Branch key_rl elt_rl zz 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))))))) vxy vxz fm_l fm_rll) (mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) key_r elt_r fm_rlr fm_rr)

  
mkBalBranch6Double_R vxy vxz vyu vyv (Branch key_l elt_l zw fm_ll (Branch key_lr elt_lr zx 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))))))))))))) vxy vxz fm_lrr fm_r)

  
mkBalBranch6MkBalBranch0 vxy vxz vyu vyv fm_L fm_R (Branch vuu vuv vuw fm_rl fm_rrmkBalBranch6MkBalBranch02 vxy vxz vyu vyv fm_L fm_R (Branch vuu vuv vuw fm_rl fm_rr)

  
mkBalBranch6MkBalBranch00 vxy vxz vyu vyv fm_L fm_R vuu vuv vuw fm_rl fm_rr True mkBalBranch6Double_L vxy vxz vyu vyv fm_L fm_R

  
mkBalBranch6MkBalBranch01 vxy vxz vyu vyv fm_L fm_R vuu vuv vuw fm_rl fm_rr True mkBalBranch6Single_L vxy vxz vyu vyv fm_L fm_R
mkBalBranch6MkBalBranch01 vxy vxz vyu vyv fm_L fm_R vuu vuv vuw fm_rl fm_rr False mkBalBranch6MkBalBranch00 vxy vxz vyu vyv fm_L fm_R vuu vuv vuw fm_rl fm_rr otherwise

  
mkBalBranch6MkBalBranch02 vxy vxz vyu vyv fm_L fm_R (Branch vuu vuv vuw fm_rl fm_rrmkBalBranch6MkBalBranch01 vxy vxz vyu vyv fm_L fm_R vuu vuv vuw fm_rl fm_rr (sizeFM fm_rl < Pos (Succ (Succ Zero)) * sizeFM fm_rr)

  
mkBalBranch6MkBalBranch1 vxy vxz vyu vyv fm_L fm_R (Branch yz zu zv fm_ll fm_lrmkBalBranch6MkBalBranch12 vxy vxz vyu vyv fm_L fm_R (Branch yz zu zv fm_ll fm_lr)

  
mkBalBranch6MkBalBranch10 vxy vxz vyu vyv fm_L fm_R yz zu zv fm_ll fm_lr True mkBalBranch6Double_R vxy vxz vyu vyv fm_L fm_R

  
mkBalBranch6MkBalBranch11 vxy vxz vyu vyv fm_L fm_R yz zu zv fm_ll fm_lr True mkBalBranch6Single_R vxy vxz vyu vyv fm_L fm_R
mkBalBranch6MkBalBranch11 vxy vxz vyu vyv fm_L fm_R yz zu zv fm_ll fm_lr False mkBalBranch6MkBalBranch10 vxy vxz vyu vyv fm_L fm_R yz zu zv fm_ll fm_lr otherwise

  
mkBalBranch6MkBalBranch12 vxy vxz vyu vyv fm_L fm_R (Branch yz zu zv fm_ll fm_lrmkBalBranch6MkBalBranch11 vxy vxz vyu vyv fm_L fm_R yz zu zv fm_ll fm_lr (sizeFM fm_lr < Pos (Succ (Succ Zero)) * sizeFM fm_ll)

  
mkBalBranch6MkBalBranch2 vxy vxz vyu vyv key elt fm_L fm_R True mkBranch (Pos (Succ (Succ Zero))) key elt fm_L fm_R

  
mkBalBranch6MkBalBranch3 vxy vxz vyu vyv key elt fm_L fm_R True mkBalBranch6MkBalBranch1 vxy vxz vyu vyv fm_L fm_R fm_L
mkBalBranch6MkBalBranch3 vxy vxz vyu vyv key elt fm_L fm_R False mkBalBranch6MkBalBranch2 vxy vxz vyu vyv key elt fm_L fm_R otherwise

  
mkBalBranch6MkBalBranch4 vxy vxz vyu vyv key elt fm_L fm_R True mkBalBranch6MkBalBranch0 vxy vxz vyu vyv fm_L fm_R fm_R
mkBalBranch6MkBalBranch4 vxy vxz vyu vyv key elt fm_L fm_R False mkBalBranch6MkBalBranch3 vxy vxz vyu vyv key elt fm_L fm_R (mkBalBranch6Size_l vxy vxz vyu vyv > sIZE_RATIO * mkBalBranch6Size_r vxy vxz vyu vyv)

  
mkBalBranch6MkBalBranch5 vxy vxz vyu vyv key elt fm_L fm_R True mkBranch (Pos (Succ Zero)) key elt fm_L fm_R
mkBalBranch6MkBalBranch5 vxy vxz vyu vyv key elt fm_L fm_R False mkBalBranch6MkBalBranch4 vxy vxz vyu vyv key elt fm_L fm_R (mkBalBranch6Size_r vxy vxz vyu vyv > sIZE_RATIO * mkBalBranch6Size_l vxy vxz vyu vyv)

  
mkBalBranch6Single_L vxy vxz vyu vyv fm_l (Branch key_r elt_r vux fm_rl fm_rrmkBranch (Pos (Succ (Succ (Succ Zero)))) key_r elt_r (mkBranch (Pos (Succ (Succ (Succ (Succ Zero))))) vxy vxz fm_l fm_rl) fm_rr

  
mkBalBranch6Single_R vxy vxz vyu vyv (Branch key_l elt_l yy 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)))))))))) vxy vxz fm_lr fm_r)

  
mkBalBranch6Size_l vxy vxz vyu vyv sizeFM vyv

  
mkBalBranch6Size_r vxy vxz vyu vyv sizeFM vyu

  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 vwx vwy vwz True

  
mkBranchLeft_ok vwx vwy vwz mkBranchLeft_ok0 vwx vwy vwz vwx vwz vwx

  
mkBranchLeft_ok0 vwx vwy vwz fm_l key EmptyFM True
mkBranchLeft_ok0 vwx vwy vwz fm_l key (Branch left_key wu wv ww wxmkBranchLeft_ok0Biggest_left_key fm_l < key

  
mkBranchLeft_ok0Biggest_left_key vyx fst (findMax vyx)

  
mkBranchLeft_size vwx vwy vwz sizeFM vwx

  
mkBranchResult vxu vxv vxw vxx Branch vxu vxv (mkBranchUnbox vxw vxx vxu (Pos (Succ Zero+ mkBranchLeft_size vxw vxx vxu + mkBranchRight_size vxw vxx vxu)) vxw vxx

  
mkBranchRight_ok vwx vwy vwz mkBranchRight_ok0 vwx vwy vwz vwy vwz vwy

  
mkBranchRight_ok0 vwx vwy vwz fm_r key EmptyFM True
mkBranchRight_ok0 vwx vwy vwz fm_r key (Branch right_key vw vx vy vzkey < mkBranchRight_ok0Smallest_right_key fm_r

  
mkBranchRight_ok0Smallest_right_key vyw fst (findMin vyw)

  
mkBranchRight_size vwx vwy vwz sizeFM vwy

  mkBranchUnbox :: Ord a =>  ->  (FiniteMap a b) ( ->  (FiniteMap a b) ( ->  a (Int  ->  Int)))
mkBranchUnbox vwx vwy vwz 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 yu yv size yw yxsize

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude



Haskell To QDPs


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

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

new_primMinusNat(Succ(vyy2460), Succ(vyy308000)) → new_primMinusNat(vyy2460, vyy308000)

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

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

new_primPlusNat(Succ(vyy720000), Succ(vyy442000)) → new_primPlusNat(vyy720000, vyy442000)

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

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

new_mkBalBranch6MkBalBranch01(vyy3365, vyy3366, vyy3367, vyy3368, vyy3369, vyy3370, vyy3371, vyy3372, vyy3373, vyy3374, vyy3375, vyy3376, vyy3377, Succ(vyy33780), Succ(vyy33790), h) → new_mkBalBranch6MkBalBranch01(vyy3365, vyy3366, vyy3367, vyy3368, vyy3369, vyy3370, vyy3371, vyy3372, vyy3373, vyy3374, vyy3375, vyy3376, vyy3377, vyy33780, vyy33790, h)

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

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

new_mkBalBranch6MkBalBranch010(vyy3349, vyy3350, vyy3351, vyy3352, vyy3353, vyy3354, vyy3355, vyy3356, vyy3357, vyy3358, vyy3359, vyy3360, vyy3361, Succ(vyy33620), Succ(vyy33630), h) → new_mkBalBranch6MkBalBranch010(vyy3349, vyy3350, vyy3351, vyy3352, vyy3353, vyy3354, vyy3355, vyy3356, vyy3357, vyy3358, vyy3359, vyy3360, vyy3361, vyy33620, vyy33630, h)

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

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

new_mkBalBranch6MkBalBranch011(vyy3332, vyy3333, vyy3334, vyy3335, vyy3336, vyy3337, vyy3338, vyy3339, vyy3340, vyy3341, vyy3342, vyy3343, vyy3344, vyy3345, Succ(vyy33460), Succ(vyy33470), h) → new_mkBalBranch6MkBalBranch011(vyy3332, vyy3333, vyy3334, vyy3335, vyy3336, vyy3337, vyy3338, vyy3339, vyy3340, vyy3341, vyy3342, vyy3343, vyy3344, vyy3345, vyy33460, vyy33470, h)

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

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

new_mkBalBranch6MkBalBranch012(vyy3315, vyy3316, vyy3317, vyy3318, vyy3319, vyy3320, vyy3321, vyy3322, vyy3323, vyy3324, vyy3325, vyy3326, vyy3327, vyy3328, Succ(vyy33290), Succ(vyy33300), h) → new_mkBalBranch6MkBalBranch012(vyy3315, vyy3316, vyy3317, vyy3318, vyy3319, vyy3320, vyy3321, vyy3322, vyy3323, vyy3324, vyy3325, vyy3326, vyy3327, vyy3328, vyy33290, vyy33300, h)

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

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

new_mkBalBranch6MkBalBranch013(vyy41, vyy80, vyy81, vyy83, vyy84, vyy430, vyy431, vyy433, vyy434, Succ(vyy786000), Succ(vyy122500), h) → new_mkBalBranch6MkBalBranch013(vyy41, vyy80, vyy81, vyy83, vyy84, vyy430, vyy431, vyy433, vyy434, vyy786000, vyy122500, h)

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

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

new_mkBalBranch6MkBalBranch014(vyy41, vyy80, vyy81, vyy8200000, vyy83, vyy84, vyy430, vyy431, vyy433, vyy434, Succ(vyy784000), Succ(vyy121700), h) → new_mkBalBranch6MkBalBranch014(vyy41, vyy80, vyy81, vyy8200000, vyy83, vyy84, vyy430, vyy431, vyy433, vyy434, vyy784000, vyy121700, h)

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

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

new_mkBalBranch6MkBalBranch015(vyy41, vyy80, vyy81, vyy83, vyy84, vyy430, vyy431, vyy433, vyy434, Succ(vyy866000), Succ(vyy135200), h) → new_mkBalBranch6MkBalBranch015(vyy41, vyy80, vyy81, vyy83, vyy84, vyy430, vyy431, vyy433, vyy434, vyy866000, vyy135200, h)

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

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

new_mkBalBranch6MkBalBranch016(vyy41, vyy80, vyy81, vyy82000000, vyy83, vyy84, vyy430, vyy431, vyy433, vyy434, Succ(vyy864000), Succ(vyy134400), h) → new_mkBalBranch6MkBalBranch016(vyy41, vyy80, vyy81, vyy82000000, vyy83, vyy84, vyy430, vyy431, vyy433, vyy434, vyy864000, vyy134400, h)

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

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

new_mkBalBranch6MkBalBranch017(vyy496, vyy497, vyy498, vyy499, vyy500, vyy501, vyy502, vyy503, vyy504, vyy505, Succ(vyy1124000), Succ(vyy152500), h) → new_mkBalBranch6MkBalBranch017(vyy496, vyy497, vyy498, vyy499, vyy500, vyy501, vyy502, vyy503, vyy504, vyy505, vyy1124000, vyy152500, h)

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

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

new_mkBalBranch6MkBalBranch11(vyy2836, vyy2837, vyy2838, vyy2839, vyy2840, vyy2841, vyy2842, vyy2843, vyy2844, vyy2845, vyy2846, Succ(vyy3113000), Succ(vyy329000), h) → new_mkBalBranch6MkBalBranch11(vyy2836, vyy2837, vyy2838, vyy2839, vyy2840, vyy2841, vyy2842, vyy2843, vyy2844, vyy2845, vyy2846, vyy3113000, vyy329000, h)

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

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

new_mkBalBranch6MkBalBranch3(vyy2836, vyy2837, vyy2838, vyy2839, vyy2840, vyy2841, vyy2842, vyy2843, vyy2844, vyy2845, vyy2846, Succ(vyy2935000), Succ(vyy305800), h) → new_mkBalBranch6MkBalBranch3(vyy2836, vyy2837, vyy2838, vyy2839, vyy2840, vyy2841, vyy2842, vyy2843, vyy2844, vyy2845, vyy2846, vyy2935000, vyy305800, h)

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

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

new_mkBalBranch6MkBalBranch018(vyy2836, vyy2837, vyy2838, vyy2839, vyy2840, vyy2841, vyy2842, vyy2843, vyy2844, vyy2845, vyy2846, Succ(vyy2921000), Succ(vyy302100), h) → new_mkBalBranch6MkBalBranch018(vyy2836, vyy2837, vyy2838, vyy2839, vyy2840, vyy2841, vyy2842, vyy2843, vyy2844, vyy2845, vyy2846, vyy2921000, vyy302100, h)

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

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

new_mkBalBranch6MkBalBranch4(vyy2836, vyy2837, vyy2838, vyy2839, vyy2840, vyy2841, vyy2842, vyy2843, vyy2844, vyy2845, vyy2846, Succ(vyy28470), Succ(vyy28480), h) → new_mkBalBranch6MkBalBranch4(vyy2836, vyy2837, vyy2838, vyy2839, vyy2840, vyy2841, vyy2842, vyy2843, vyy2844, vyy2845, vyy2846, vyy28470, vyy28480, h)

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

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

new_mkBalBranch6MkBalBranch110(vyy3220, vyy3221, vyy3222, vyy3223, vyy3224, vyy3225, vyy3226, vyy3227, vyy3228, vyy3229, Succ(vyy3288000), Succ(vyy330400), h) → new_mkBalBranch6MkBalBranch110(vyy3220, vyy3221, vyy3222, vyy3223, vyy3224, vyy3225, vyy3226, vyy3227, vyy3228, vyy3229, vyy3288000, vyy330400, h)

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

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

new_mkBalBranch6MkBalBranch30(vyy3220, vyy3221, vyy3222, vyy3223, vyy3224, vyy3225, vyy3226, vyy3227, vyy3228, vyy3229, Succ(vyy32300), Succ(vyy32310), h) → new_mkBalBranch6MkBalBranch30(vyy3220, vyy3221, vyy3222, vyy3223, vyy3224, vyy3225, vyy3226, vyy3227, vyy3228, vyy3229, vyy32300, vyy32310, h)

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

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

new_mkBalBranch6MkBalBranch111(vyy41, vyy80, vyy81, vyy83, vyy84, vyy430, vyy431, vyy433, vyy434, Succ(vyy1381000), Succ(vyy210400), h) → new_mkBalBranch6MkBalBranch111(vyy41, vyy80, vyy81, vyy83, vyy84, vyy430, vyy431, vyy433, vyy434, vyy1381000, vyy210400, h)

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

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

new_mkBalBranch6MkBalBranch31(vyy41, vyy80, vyy81, vyy83, vyy84, vyy430, vyy431, vyy433, vyy434, Succ(vyy781000), Succ(vyy120700), h) → new_mkBalBranch6MkBalBranch31(vyy41, vyy80, vyy81, vyy83, vyy84, vyy430, vyy431, vyy433, vyy434, vyy781000, vyy120700, h)

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

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

new_mkBalBranch6MkBalBranch112(vyy347, vyy348, vyy349, vyy350, vyy351, vyy352, vyy353, vyy354, vyy355, vyy356, Succ(vyy2053000), Succ(vyy311100), h) → new_mkBalBranch6MkBalBranch112(vyy347, vyy348, vyy349, vyy350, vyy351, vyy352, vyy353, vyy354, vyy355, vyy356, vyy2053000, vyy311100, h)

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

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

new_mkBalBranch6MkBalBranch32(vyy347, vyy348, vyy349, vyy350, vyy351, vyy352, vyy353, vyy354, vyy355, vyy356, Succ(vyy1198000), Succ(vyy151700), h) → new_mkBalBranch6MkBalBranch32(vyy347, vyy348, vyy349, vyy350, vyy351, vyy352, vyy353, vyy354, vyy355, vyy356, vyy1198000, vyy151700, h)

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

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

new_mkBalBranch6MkBalBranch019(vyy2822, vyy2823, vyy2824, vyy2825, vyy2826, vyy2827, vyy2828, vyy2829, vyy2830, vyy2831, vyy2832, Succ(vyy2919000), Succ(vyy305000), h) → new_mkBalBranch6MkBalBranch019(vyy2822, vyy2823, vyy2824, vyy2825, vyy2826, vyy2827, vyy2828, vyy2829, vyy2830, vyy2831, vyy2832, vyy2919000, vyy305000, h)

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

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

new_mkBalBranch6MkBalBranch113(vyy2822, vyy2823, vyy2824, vyy2825, vyy2826, vyy2827, vyy2828, vyy2829, vyy2830, vyy2831, vyy2832, Succ(vyy3025000), Succ(vyy308000), h) → new_mkBalBranch6MkBalBranch113(vyy2822, vyy2823, vyy2824, vyy2825, vyy2826, vyy2827, vyy2828, vyy2829, vyy2830, vyy2831, vyy2832, vyy3025000, vyy308000, h)

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

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

new_mkBalBranch6MkBalBranch33(vyy2822, vyy2823, vyy2824, vyy2825, vyy2826, vyy2827, vyy2828, vyy2829, vyy2830, vyy2831, vyy2832, Succ(vyy2923000), Succ(vyy299800), h) → new_mkBalBranch6MkBalBranch33(vyy2822, vyy2823, vyy2824, vyy2825, vyy2826, vyy2827, vyy2828, vyy2829, vyy2830, vyy2831, vyy2832, vyy2923000, vyy299800, h)

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

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

new_mkBalBranch6MkBalBranch40(vyy2822, vyy2823, vyy2824, vyy2825, vyy2826, vyy2827, vyy2828, vyy2829, vyy2830, vyy2831, vyy2832, Succ(vyy28330), Succ(vyy28340), h) → new_mkBalBranch6MkBalBranch40(vyy2822, vyy2823, vyy2824, vyy2825, vyy2826, vyy2827, vyy2828, vyy2829, vyy2830, vyy2831, vyy2832, vyy28330, vyy28340, h)

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

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

new_mkBalBranch6MkBalBranch0110(vyy3566, vyy3567, vyy3568, vyy3569, vyy3570, vyy3571, vyy3572, vyy3573, vyy3574, vyy3575, vyy3576, vyy3577, vyy3578, Succ(vyy35790), Succ(vyy35800), h) → new_mkBalBranch6MkBalBranch0110(vyy3566, vyy3567, vyy3568, vyy3569, vyy3570, vyy3571, vyy3572, vyy3573, vyy3574, vyy3575, vyy3576, vyy3577, vyy3578, vyy35790, vyy35800, h)

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

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

new_mkBalBranch6MkBalBranch0111(vyy3550, vyy3551, vyy3552, vyy3553, vyy3554, vyy3555, vyy3556, vyy3557, vyy3558, vyy3559, vyy3560, vyy3561, vyy3562, Succ(vyy35630), Succ(vyy35640), h) → new_mkBalBranch6MkBalBranch0111(vyy3550, vyy3551, vyy3552, vyy3553, vyy3554, vyy3555, vyy3556, vyy3557, vyy3558, vyy3559, vyy3560, vyy3561, vyy3562, vyy35630, vyy35640, h)

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

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

new_mkBalBranch6MkBalBranch0112(vyy3533, vyy3534, vyy3535, vyy3536, vyy3537, vyy3538, vyy3539, vyy3540, vyy3541, vyy3542, vyy3543, vyy3544, vyy3545, vyy3546, Succ(vyy35470), Succ(vyy35480), h) → new_mkBalBranch6MkBalBranch0112(vyy3533, vyy3534, vyy3535, vyy3536, vyy3537, vyy3538, vyy3539, vyy3540, vyy3541, vyy3542, vyy3543, vyy3544, vyy3545, vyy3546, vyy35470, vyy35480, h)

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

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

new_mkBalBranch6MkBalBranch0113(vyy3516, vyy3517, vyy3518, vyy3519, vyy3520, vyy3521, vyy3522, vyy3523, vyy3524, vyy3525, vyy3526, vyy3527, vyy3528, vyy3529, Succ(vyy35300), Succ(vyy35310), h) → new_mkBalBranch6MkBalBranch0113(vyy3516, vyy3517, vyy3518, vyy3519, vyy3520, vyy3521, vyy3522, vyy3523, vyy3524, vyy3525, vyy3526, vyy3527, vyy3528, vyy3529, vyy35300, vyy35310, h)

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

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

new_mkBalBranch6MkBalBranch114(vyy3207, vyy3208, vyy3209, vyy3210, vyy3211, vyy3212, vyy3213, vyy3214, vyy3215, vyy3216, Succ(vyy3286000), Succ(vyy329600), h) → new_mkBalBranch6MkBalBranch114(vyy3207, vyy3208, vyy3209, vyy3210, vyy3211, vyy3212, vyy3213, vyy3214, vyy3215, vyy3216, vyy3286000, vyy329600, h)

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

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

new_mkBalBranch6MkBalBranch34(vyy3207, vyy3208, vyy3209, vyy3210, vyy3211, vyy3212, vyy3213, vyy3214, vyy3215, vyy3216, Succ(vyy32170), Succ(vyy32180), h) → new_mkBalBranch6MkBalBranch34(vyy3207, vyy3208, vyy3209, vyy3210, vyy3211, vyy3212, vyy3213, vyy3214, vyy3215, vyy3216, vyy32170, vyy32180, h)

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

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

new_mkBalBranch6MkBalBranch115(vyy1834, vyy1835, vyy1836, vyy1837, vyy1838, vyy1839, vyy1840, vyy1841, vyy1842, vyy1843, Succ(vyy2098000), Succ(vyy233800), h) → new_mkBalBranch6MkBalBranch115(vyy1834, vyy1835, vyy1836, vyy1837, vyy1838, vyy1839, vyy1840, vyy1841, vyy1842, vyy1843, vyy2098000, vyy233800, h)

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

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

new_mkBalBranch6MkBalBranch35(vyy1834, vyy1835, vyy1836, vyy1837, vyy1838, vyy1839, vyy1840, vyy1841, vyy1842, vyy1843, Succ(vyy1984000), Succ(vyy206300), h) → new_mkBalBranch6MkBalBranch35(vyy1834, vyy1835, vyy1836, vyy1837, vyy1838, vyy1839, vyy1840, vyy1841, vyy1842, vyy1843, vyy1984000, vyy206300, h)

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

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

new_mkBalBranch6MkBalBranch0114(vyy1834, vyy1835, vyy1836, vyy1837, vyy1838, vyy1839, vyy1840, vyy1841, vyy1842, vyy1843, Succ(vyy1964000), Succ(vyy205500), h) → new_mkBalBranch6MkBalBranch0114(vyy1834, vyy1835, vyy1836, vyy1837, vyy1838, vyy1839, vyy1840, vyy1841, vyy1842, vyy1843, vyy1964000, vyy205500, h)

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

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

new_mkBalBranch6MkBalBranch41(vyy1834, vyy1835, vyy1836, vyy1837, vyy1838, vyy1839, vyy1840, vyy1841, vyy1842, vyy1843, Succ(vyy18440), Succ(vyy18450), h) → new_mkBalBranch6MkBalBranch41(vyy1834, vyy1835, vyy1836, vyy1837, vyy1838, vyy1839, vyy1840, vyy1841, vyy1842, vyy1843, vyy18440, vyy18450, h)

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

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

new_mkBalBranch6MkBalBranch116(vyy1252, vyy1253, vyy1254, vyy1255, vyy1256, vyy1257, vyy1258, vyy1259, vyy1260, vyy1261, vyy1262, Succ(vyy1549000), Succ(vyy233000), h) → new_mkBalBranch6MkBalBranch116(vyy1252, vyy1253, vyy1254, vyy1255, vyy1256, vyy1257, vyy1258, vyy1259, vyy1260, vyy1261, vyy1262, vyy1549000, vyy233000, h)

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

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

new_mkBalBranch6MkBalBranch36(vyy1252, vyy1253, vyy1254, vyy1255, vyy1256, vyy1257, vyy1258, vyy1259, vyy1260, vyy1261, vyy1262, Succ(vyy1289000), Succ(vyy131000), h) → new_mkBalBranch6MkBalBranch36(vyy1252, vyy1253, vyy1254, vyy1255, vyy1256, vyy1257, vyy1258, vyy1259, vyy1260, vyy1261, vyy1262, vyy1289000, vyy131000, h)

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

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

new_mkBalBranch6MkBalBranch0115(vyy1252, vyy1253, vyy1254, vyy1255, vyy1256, vyy1257, vyy1258, vyy1259, vyy1260, vyy1261, vyy1262, Succ(vyy1286000), Succ(vyy130200), h) → new_mkBalBranch6MkBalBranch0115(vyy1252, vyy1253, vyy1254, vyy1255, vyy1256, vyy1257, vyy1258, vyy1259, vyy1260, vyy1261, vyy1262, vyy1286000, vyy130200, h)

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

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

new_mkBalBranch6MkBalBranch42(vyy1252, vyy1253, vyy1254, vyy1255, vyy1256, vyy1257, vyy1258, vyy1259, vyy1260, vyy1261, vyy1262, Succ(vyy12630), Succ(vyy12640), h) → new_mkBalBranch6MkBalBranch42(vyy1252, vyy1253, vyy1254, vyy1255, vyy1256, vyy1257, vyy1258, vyy1259, vyy1260, vyy1261, vyy1262, vyy12630, vyy12640, h)

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

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

new_mkBalBranch6MkBalBranch117(vyy3103, vyy3104, vyy3105, vyy3106, vyy3107, vyy3108, Succ(vyy3119000), Succ(vyy319800), h) → new_mkBalBranch6MkBalBranch117(vyy3103, vyy3104, vyy3105, vyy3106, vyy3107, vyy3108, vyy3119000, vyy319800, h)

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

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

new_mkBalBranch6MkBalBranch37(vyy3103, vyy3104, vyy3105, vyy3106, vyy3107, vyy3108, Succ(vyy31090), Succ(vyy31100), h) → new_mkBalBranch6MkBalBranch37(vyy3103, vyy3104, vyy3105, vyy3106, vyy3107, vyy3108, vyy31090, vyy31100, h)

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

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

new_mkBalBranch6MkBalBranch0116(vyy3275, vyy3276, vyy3277, vyy3278, vyy3279, vyy3280, vyy3281, vyy3282, vyy3283, Succ(vyy32840), Succ(vyy32850), h) → new_mkBalBranch6MkBalBranch0116(vyy3275, vyy3276, vyy3277, vyy3278, vyy3279, vyy3280, vyy3281, vyy3282, vyy3283, vyy32840, vyy32850, h)

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

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

new_mkBalBranch6MkBalBranch0117(vyy3263, vyy3264, vyy3265, vyy3266, vyy3267, vyy3268, vyy3269, vyy3270, vyy3271, Succ(vyy32720), Succ(vyy32730), h) → new_mkBalBranch6MkBalBranch0117(vyy3263, vyy3264, vyy3265, vyy3266, vyy3267, vyy3268, vyy3269, vyy3270, vyy3271, vyy32720, vyy32730, h)

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

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

new_mkBalBranch6MkBalBranch0118(vyy3250, vyy3251, vyy3252, vyy3253, vyy3254, vyy3255, vyy3256, vyy3257, vyy3258, vyy3259, Succ(vyy32600), Succ(vyy32610), h) → new_mkBalBranch6MkBalBranch0118(vyy3250, vyy3251, vyy3252, vyy3253, vyy3254, vyy3255, vyy3256, vyy3257, vyy3258, vyy3259, vyy32600, vyy32610, h)

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

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

new_mkBalBranch6MkBalBranch0119(vyy2347, vyy2348, vyy2349, vyy2350, vyy2351, vyy2352, vyy2353, vyy2354, vyy2355, vyy2356, Succ(vyy23570), Succ(vyy23580), h) → new_mkBalBranch6MkBalBranch0119(vyy2347, vyy2348, vyy2349, vyy2350, vyy2351, vyy2352, vyy2353, vyy2354, vyy2355, vyy2356, vyy23570, vyy23580, h)

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

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

new_mkBalBranch6MkBalBranch0120(vyy2311, vyy2312, vyy2313, vyy2314, vyy2315, vyy2316, vyy2317, vyy2318, vyy2319, vyy2320, vyy2321, vyy2322, vyy2323, vyy2324, vyy2325, vyy2326, vyy2327, Succ(vyy23280), Succ(vyy23290), h) → new_mkBalBranch6MkBalBranch0120(vyy2311, vyy2312, vyy2313, vyy2314, vyy2315, vyy2316, vyy2317, vyy2318, vyy2319, vyy2320, vyy2321, vyy2322, vyy2323, vyy2324, vyy2325, vyy2326, vyy2327, vyy23280, vyy23290, h)

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

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

new_mkBalBranch6MkBalBranch0121(vyy2291, vyy2292, vyy2293, vyy2294, vyy2295, vyy2296, vyy2297, vyy2298, vyy2299, vyy2300, vyy2301, vyy2302, vyy2303, vyy2304, vyy2305, vyy2306, vyy2307, Succ(vyy23080), Succ(vyy23090), h) → new_mkBalBranch6MkBalBranch0121(vyy2291, vyy2292, vyy2293, vyy2294, vyy2295, vyy2296, vyy2297, vyy2298, vyy2299, vyy2300, vyy2301, vyy2302, vyy2303, vyy2304, vyy2305, vyy2306, vyy2307, vyy23080, vyy23090, h)

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

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

new_mkBalBranch6MkBalBranch0122(vyy2270, vyy2271, vyy2272, vyy2273, vyy2274, vyy2275, vyy2276, vyy2277, vyy2278, vyy2279, vyy2280, vyy2281, vyy2282, vyy2283, vyy2284, vyy2285, vyy2286, vyy2287, Succ(vyy22880), Succ(vyy22890), h) → new_mkBalBranch6MkBalBranch0122(vyy2270, vyy2271, vyy2272, vyy2273, vyy2274, vyy2275, vyy2276, vyy2277, vyy2278, vyy2279, vyy2280, vyy2281, vyy2282, vyy2283, vyy2284, vyy2285, vyy2286, vyy2287, vyy22880, vyy22890, h)

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

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

new_mkBalBranch6MkBalBranch0123(vyy1442, vyy1443, vyy1444, vyy1445, vyy1446, vyy1447, vyy1448, vyy1449, vyy1450, vyy1451, vyy1452, vyy1453, vyy1454, vyy1455, vyy1456, vyy1457, vyy1458, vyy1459, Succ(vyy14600), Succ(vyy14610), h) → new_mkBalBranch6MkBalBranch0123(vyy1442, vyy1443, vyy1444, vyy1445, vyy1446, vyy1447, vyy1448, vyy1449, vyy1450, vyy1451, vyy1452, vyy1453, vyy1454, vyy1455, vyy1456, vyy1457, vyy1458, vyy1459, vyy14600, vyy14610, h)

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

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

new_mkBalBranch6MkBalBranch0124(vyy2707, vyy2708, vyy2709, vyy2710, vyy2711, vyy2712, vyy2713, vyy2714, vyy2715, vyy2716, vyy2717, vyy2718, vyy2719, vyy2720, vyy2721, vyy2722, vyy2723, vyy2724, vyy2725, Succ(vyy27260), Succ(vyy27270), h) → new_mkBalBranch6MkBalBranch0124(vyy2707, vyy2708, vyy2709, vyy2710, vyy2711, vyy2712, vyy2713, vyy2714, vyy2715, vyy2716, vyy2717, vyy2718, vyy2719, vyy2720, vyy2721, vyy2722, vyy2723, vyy2724, vyy2725, vyy27260, vyy27270, h)

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

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

new_mkBalBranch6MkBalBranch0125(vyy2685, vyy2686, vyy2687, vyy2688, vyy2689, vyy2690, vyy2691, vyy2692, vyy2693, vyy2694, vyy2695, vyy2696, vyy2697, vyy2698, vyy2699, vyy2700, vyy2701, vyy2702, vyy2703, Succ(vyy27040), Succ(vyy27050), h) → new_mkBalBranch6MkBalBranch0125(vyy2685, vyy2686, vyy2687, vyy2688, vyy2689, vyy2690, vyy2691, vyy2692, vyy2693, vyy2694, vyy2695, vyy2696, vyy2697, vyy2698, vyy2699, vyy2700, vyy2701, vyy2702, vyy2703, vyy27040, vyy27050, h)

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

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

new_mkBalBranch6MkBalBranch118(vyy3464, vyy3465, vyy3466, vyy3467, vyy3468, vyy3469, vyy3470, vyy3471, vyy3472, vyy3473, vyy3474, vyy3475, vyy3476, Succ(vyy34770), Succ(vyy34780), h) → new_mkBalBranch6MkBalBranch118(vyy3464, vyy3465, vyy3466, vyy3467, vyy3468, vyy3469, vyy3470, vyy3471, vyy3472, vyy3473, vyy3474, vyy3475, vyy3476, vyy34770, vyy34780, h)

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

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

new_mkBalBranch6MkBalBranch119(vyy3448, vyy3449, vyy3450, vyy3451, vyy3452, vyy3453, vyy3454, vyy3455, vyy3456, vyy3457, vyy3458, vyy3459, vyy3460, Succ(vyy34610), Succ(vyy34620), h) → new_mkBalBranch6MkBalBranch119(vyy3448, vyy3449, vyy3450, vyy3451, vyy3452, vyy3453, vyy3454, vyy3455, vyy3456, vyy3457, vyy3458, vyy3459, vyy3460, vyy34610, vyy34620, h)

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

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

new_mkBalBranch6MkBalBranch1110(vyy3431, vyy3432, vyy3433, vyy3434, vyy3435, vyy3436, vyy3437, vyy3438, vyy3439, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, Succ(vyy34450), Succ(vyy34460), h) → new_mkBalBranch6MkBalBranch1110(vyy3431, vyy3432, vyy3433, vyy3434, vyy3435, vyy3436, vyy3437, vyy3438, vyy3439, vyy3440, vyy3441, vyy3442, vyy3443, vyy3444, vyy34450, vyy34460, h)

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

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

new_mkBalBranch6MkBalBranch1111(vyy3233, vyy3234, vyy3235, vyy3236, vyy3237, vyy3238, vyy3239, vyy3240, vyy3241, vyy3242, vyy3243, vyy3244, vyy3245, vyy3246, Succ(vyy32470), Succ(vyy32480), h) → new_mkBalBranch6MkBalBranch1111(vyy3233, vyy3234, vyy3235, vyy3236, vyy3237, vyy3238, vyy3239, vyy3240, vyy3241, vyy3242, vyy3243, vyy3244, vyy3245, vyy3246, vyy32470, vyy32480, h)

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

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

new_mkBalBranch6MkBalBranch1112(vyy3498, vyy3499, vyy3500, vyy3501, vyy3502, vyy3503, vyy3504, vyy3505, vyy3506, vyy3507, vyy3508, vyy3509, vyy3510, vyy3511, vyy3512, Succ(vyy35130), Succ(vyy35140), h) → new_mkBalBranch6MkBalBranch1112(vyy3498, vyy3499, vyy3500, vyy3501, vyy3502, vyy3503, vyy3504, vyy3505, vyy3506, vyy3507, vyy3508, vyy3509, vyy3510, vyy3511, vyy3512, vyy35130, vyy35140, h)

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

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

new_mkBalBranch6MkBalBranch1113(vyy3480, vyy3481, vyy3482, vyy3483, vyy3484, vyy3485, vyy3486, vyy3487, vyy3488, vyy3489, vyy3490, vyy3491, vyy3492, vyy3493, vyy3494, Succ(vyy34950), Succ(vyy34960), h) → new_mkBalBranch6MkBalBranch1113(vyy3480, vyy3481, vyy3482, vyy3483, vyy3484, vyy3485, vyy3486, vyy3487, vyy3488, vyy3489, vyy3490, vyy3491, vyy3492, vyy3493, vyy3494, vyy34950, vyy34960, h)

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

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

new_mkBalBranch6MkBalBranch0126(vyy2575, vyy2576, vyy2577, vyy2578, vyy2579, vyy2580, vyy2581, vyy2582, vyy2583, vyy2584, vyy2585, vyy2586, vyy2587, vyy2588, vyy2589, vyy2590, vyy2591, Succ(vyy25920), Succ(vyy25930), h) → new_mkBalBranch6MkBalBranch0126(vyy2575, vyy2576, vyy2577, vyy2578, vyy2579, vyy2580, vyy2581, vyy2582, vyy2583, vyy2584, vyy2585, vyy2586, vyy2587, vyy2588, vyy2589, vyy2590, vyy2591, vyy25920, vyy25930, h)

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

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

new_mkBalBranch6MkBalBranch0127(vyy2555, vyy2556, vyy2557, vyy2558, vyy2559, vyy2560, vyy2561, vyy2562, vyy2563, vyy2564, vyy2565, vyy2566, vyy2567, vyy2568, vyy2569, vyy2570, vyy2571, Succ(vyy25720), Succ(vyy25730), h) → new_mkBalBranch6MkBalBranch0127(vyy2555, vyy2556, vyy2557, vyy2558, vyy2559, vyy2560, vyy2561, vyy2562, vyy2563, vyy2564, vyy2565, vyy2566, vyy2567, vyy2568, vyy2569, vyy2570, vyy2571, vyy25720, vyy25730, h)

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

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

new_mkBalBranch6MkBalBranch0128(vyy2534, vyy2535, vyy2536, vyy2537, vyy2538, vyy2539, vyy2540, vyy2541, vyy2542, vyy2543, vyy2544, vyy2545, vyy2546, vyy2547, vyy2548, vyy2549, vyy2550, vyy2551, Succ(vyy25520), Succ(vyy25530), h) → new_mkBalBranch6MkBalBranch0128(vyy2534, vyy2535, vyy2536, vyy2537, vyy2538, vyy2539, vyy2540, vyy2541, vyy2542, vyy2543, vyy2544, vyy2545, vyy2546, vyy2547, vyy2548, vyy2549, vyy2550, vyy2551, vyy25520, vyy25530, h)

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

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

new_mkBalBranch6MkBalBranch0129(vyy2513, vyy2514, vyy2515, vyy2516, vyy2517, vyy2518, vyy2519, vyy2520, vyy2521, vyy2522, vyy2523, vyy2524, vyy2525, vyy2526, vyy2527, vyy2528, vyy2529, vyy2530, Succ(vyy25310), Succ(vyy25320), h) → new_mkBalBranch6MkBalBranch0129(vyy2513, vyy2514, vyy2515, vyy2516, vyy2517, vyy2518, vyy2519, vyy2520, vyy2521, vyy2522, vyy2523, vyy2524, vyy2525, vyy2526, vyy2527, vyy2528, vyy2529, vyy2530, vyy25310, vyy25320, h)

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

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

new_mkBalBranch6MkBalBranch1114(vyy41, vyy440, vyy441, vyy443, vyy444, vyy70, vyy71, vyy73, vyy74, Succ(vyy760000), Succ(vyy108900), h) → new_mkBalBranch6MkBalBranch1114(vyy41, vyy440, vyy441, vyy443, vyy444, vyy70, vyy71, vyy73, vyy74, vyy760000, vyy108900, h)

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

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

new_mkBalBranch6MkBalBranch1115(vyy41, vyy440, vyy441, vyy443, vyy444, vyy70, vyy71, vyy720000, vyy73, vyy74, Succ(vyy758000), Succ(vyy108100), h) → new_mkBalBranch6MkBalBranch1115(vyy41, vyy440, vyy441, vyy443, vyy444, vyy70, vyy71, vyy720000, vyy73, vyy74, vyy758000, vyy108100, h)

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

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

new_mkBalBranch6MkBalBranch1116(vyy605, vyy606, vyy607, vyy608, vyy609, vyy610, vyy611, vyy612, vyy613, vyy614, Succ(vyy832000), Succ(vyy128400), h) → new_mkBalBranch6MkBalBranch1116(vyy605, vyy606, vyy607, vyy608, vyy609, vyy610, vyy611, vyy612, vyy613, vyy614, vyy832000, vyy128400, h)

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

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

new_mkBalBranch6MkBalBranch0130(vyy2978, vyy2979, vyy2980, vyy2981, vyy2982, vyy2983, vyy2984, vyy2985, vyy2986, vyy2987, vyy2988, vyy2989, vyy2990, vyy2991, vyy2992, vyy2993, vyy2994, vyy2995, Succ(vyy29960), Succ(vyy29970), h) → new_mkBalBranch6MkBalBranch0130(vyy2978, vyy2979, vyy2980, vyy2981, vyy2982, vyy2983, vyy2984, vyy2985, vyy2986, vyy2987, vyy2988, vyy2989, vyy2990, vyy2991, vyy2992, vyy2993, vyy2994, vyy2995, vyy29960, vyy29970, h)

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

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

new_mkBalBranch6MkBalBranch0131(vyy2957, vyy2958, vyy2959, vyy2960, vyy2961, vyy2962, vyy2963, vyy2964, vyy2965, vyy2966, vyy2967, vyy2968, vyy2969, vyy2970, vyy2971, vyy2972, vyy2973, vyy2974, Succ(vyy29750), Succ(vyy29760), h) → new_mkBalBranch6MkBalBranch0131(vyy2957, vyy2958, vyy2959, vyy2960, vyy2961, vyy2962, vyy2963, vyy2964, vyy2965, vyy2966, vyy2967, vyy2968, vyy2969, vyy2970, vyy2971, vyy2972, vyy2973, vyy2974, vyy29750, vyy29760, h)

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

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

new_mkBalBranch6MkBalBranch43(vyy605, vyy606, vyy607, vyy608, vyy609, vyy610, vyy611, vyy612, vyy613, vyy614, Succ(vyy6150), Succ(vyy6160), h) → new_mkBalBranch6MkBalBranch43(vyy605, vyy606, vyy607, vyy608, vyy609, vyy610, vyy611, vyy612, vyy613, vyy614, vyy6150, vyy6160, h)

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

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

new_mkBalBranch6MkBalBranch1117(vyy933, vyy934, vyy935, vyy936, vyy937, vyy938, vyy939, vyy940, vyy941, vyy942, vyy943, Succ(vyy995000), Succ(vyy123300), h) → new_mkBalBranch6MkBalBranch1117(vyy933, vyy934, vyy935, vyy936, vyy937, vyy938, vyy939, vyy940, vyy941, vyy942, vyy943, vyy995000, vyy123300, h)

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

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

new_mkBalBranch6MkBalBranch38(vyy933, vyy934, vyy935, vyy936, vyy937, vyy938, vyy939, vyy940, vyy941, vyy942, vyy943, Succ(vyy959000), Succ(vyy99000), h) → new_mkBalBranch6MkBalBranch38(vyy933, vyy934, vyy935, vyy936, vyy937, vyy938, vyy939, vyy940, vyy941, vyy942, vyy943, vyy959000, vyy99000, h)

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

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

new_mkBalBranch6MkBalBranch0132(vyy933, vyy934, vyy935, vyy936, vyy937, vyy938, vyy939, vyy940, vyy941, vyy942, vyy943, Succ(vyy956000), Succ(vyy97200), h) → new_mkBalBranch6MkBalBranch0132(vyy933, vyy934, vyy935, vyy936, vyy937, vyy938, vyy939, vyy940, vyy941, vyy942, vyy943, vyy956000, vyy97200, h)

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

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

new_mkBalBranch6MkBalBranch44(vyy933, vyy934, vyy935, vyy936, vyy937, vyy938, vyy939, vyy940, vyy941, vyy942, vyy943, Succ(vyy9440), Succ(vyy9450), h) → new_mkBalBranch6MkBalBranch44(vyy933, vyy934, vyy935, vyy936, vyy937, vyy938, vyy939, vyy940, vyy941, vyy942, vyy943, vyy9440, vyy9450, h)

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

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

new_mkBalBranch6MkBalBranch1118(vyy3419, vyy3420, vyy3421, vyy3422, vyy3423, vyy3424, vyy3425, vyy3426, vyy3427, Succ(vyy34280), Succ(vyy34290), h) → new_mkBalBranch6MkBalBranch1118(vyy3419, vyy3420, vyy3421, vyy3422, vyy3423, vyy3424, vyy3425, vyy3426, vyy3427, vyy34280, vyy34290, h)

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

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

new_mkBalBranch6MkBalBranch1119(vyy3407, vyy3408, vyy3409, vyy3410, vyy3411, vyy3412, vyy3413, vyy3414, vyy3415, Succ(vyy34160), Succ(vyy34170), h) → new_mkBalBranch6MkBalBranch1119(vyy3407, vyy3408, vyy3409, vyy3410, vyy3411, vyy3412, vyy3413, vyy3414, vyy3415, vyy34160, vyy34170, h)

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

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

new_mkBalBranch6MkBalBranch1120(vyy3394, vyy3395, vyy3396, vyy3397, vyy3398, vyy3399, vyy3400, vyy3401, vyy3402, vyy3403, Succ(vyy34040), Succ(vyy34050), h) → new_mkBalBranch6MkBalBranch1120(vyy3394, vyy3395, vyy3396, vyy3397, vyy3398, vyy3399, vyy3400, vyy3401, vyy3402, vyy3403, vyy34040, vyy34050, h)

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

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

new_mkBalBranch6MkBalBranch1121(vyy3381, vyy3382, vyy3383, vyy3384, vyy3385, vyy3386, vyy3387, vyy3388, vyy3389, vyy3390, Succ(vyy33910), Succ(vyy33920), h) → new_mkBalBranch6MkBalBranch1121(vyy3381, vyy3382, vyy3383, vyy3384, vyy3385, vyy3386, vyy3387, vyy3388, vyy3389, vyy3390, vyy33910, vyy33920, h)

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

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

new_mkBalBranch6MkBalBranch0133(vyy2246, vyy2247, vyy2248, vyy2249, vyy2250, vyy2251, vyy2252, vyy2253, vyy2254, vyy2255, vyy2256, vyy2257, vyy2258, Succ(vyy22590), Succ(vyy22600), h) → new_mkBalBranch6MkBalBranch0133(vyy2246, vyy2247, vyy2248, vyy2249, vyy2250, vyy2251, vyy2252, vyy2253, vyy2254, vyy2255, vyy2256, vyy2257, vyy2258, vyy22590, vyy22600, h)

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

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

new_mkBalBranch6MkBalBranch0134(vyy2230, vyy2231, vyy2232, vyy2233, vyy2234, vyy2235, vyy2236, vyy2237, vyy2238, vyy2239, vyy2240, vyy2241, vyy2242, Succ(vyy22430), Succ(vyy22440), h) → new_mkBalBranch6MkBalBranch0134(vyy2230, vyy2231, vyy2232, vyy2233, vyy2234, vyy2235, vyy2236, vyy2237, vyy2238, vyy2239, vyy2240, vyy2241, vyy2242, vyy22430, vyy22440, h)

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

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

new_mkBalBranch6MkBalBranch0135(vyy2213, vyy2214, vyy2215, vyy2216, vyy2217, vyy2218, vyy2219, vyy2220, vyy2221, vyy2222, vyy2223, vyy2224, vyy2225, vyy2226, Succ(vyy22270), Succ(vyy22280), h) → new_mkBalBranch6MkBalBranch0135(vyy2213, vyy2214, vyy2215, vyy2216, vyy2217, vyy2218, vyy2219, vyy2220, vyy2221, vyy2222, vyy2223, vyy2224, vyy2225, vyy2226, vyy22270, vyy22280, h)

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

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

new_mkBalBranch6MkBalBranch0136(vyy2196, vyy2197, vyy2198, vyy2199, vyy2200, vyy2201, vyy2202, vyy2203, vyy2204, vyy2205, vyy2206, vyy2207, vyy2208, vyy2209, Succ(vyy22100), Succ(vyy22110), h) → new_mkBalBranch6MkBalBranch0136(vyy2196, vyy2197, vyy2198, vyy2199, vyy2200, vyy2201, vyy2202, vyy2203, vyy2204, vyy2205, vyy2206, vyy2207, vyy2208, vyy2209, vyy22100, vyy22110, h)

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

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

new_addToFM_C(vyy3, Branch(True, vyy41, vyy42, vyy43, vyy44), False, vyy6, h) → new_addToFM_C(vyy3, vyy43, False, vyy6, h)
new_addToFM_C(vyy3, Branch(False, vyy41, vyy42, vyy43, vyy44), True, vyy6, h) → new_addToFM_C(vyy3, vyy44, True, vyy6, h)

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

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

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

new_addToFM_C(vyy3, Branch(False, vyy41, vyy42, vyy43, vyy44), True, vyy6, h) → new_addToFM_C(vyy3, vyy44, True, vyy6, h)

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

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

new_addToFM_C(vyy3, Branch(True, vyy41, vyy42, vyy43, vyy44), False, vyy6, h) → new_addToFM_C(vyy3, vyy43, False, vyy6, h)

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: