YES 3.281 H-Termination proof of /home/matraf/haskell/eval_FullyBlown_Fast/List.hs
H-Termination of the given Haskell-Program with start terms could successfully be proven:



↳ HASKELL
  ↳ LR

mainModule List
  ((elemIndex :: (Eq a, Eq b) => Either a b  ->  [Either a b]  ->  Maybe Int) :: (Eq b, Eq a) => Either a b  ->  [Either a b]  ->  Maybe Int)

module List where
  import qualified Maybe
import qualified Prelude
  elemIndex :: Eq a => a  ->  [a]  ->  Maybe Int
elemIndex x = findIndex (== x)

  findIndex :: (a  ->  Bool)  ->  [a]  ->  Maybe Int
findIndex p = Maybe.listToMaybe . findIndices p

  findIndices :: (a  ->  Bool)  ->  [a]  ->  [Int]
findIndices p xs = concatMap (\vv1 ->
case vv1 of
  (x,i)->  if p x then i : [] else []
  _-> []
) (zip xs (enumFrom 0))


module Maybe where
  import qualified List
import qualified Prelude
  listToMaybe :: [a]  ->  Maybe a
listToMaybe [] = Nothing
listToMaybe (a : _) = Just a



Lambda Reductions:
The following Lambda expression
\vv1→
case vv1 of
 (x,i) → if p x then i : [] else []
 _ → []

is transformed to
findIndices0 p vv1 = 
case vv1 of
 (x,i) → if p x then i : [] else []
 _ → []

The following Lambda expression
\ab→(a,b)

is transformed to
zip0 a b = (a,b)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR

mainModule List
  ((elemIndex :: (Eq b, Eq a) => Either a b  ->  [Either a b]  ->  Maybe Int) :: (Eq b, Eq a) => Either a b  ->  [Either a b]  ->  Maybe Int)

module List where
  import qualified Maybe
import qualified Prelude
  elemIndex :: Eq a => a  ->  [a]  ->  Maybe Int
elemIndex x = findIndex (== x)

  findIndex :: (a  ->  Bool)  ->  [a]  ->  Maybe Int
findIndex p = Maybe.listToMaybe . findIndices p

  findIndices :: (a  ->  Bool)  ->  [a]  ->  [Int]
findIndices p xs = concatMap (findIndices0 p) (zip xs (enumFrom 0))

  
findIndices0 p vv1 = 
case vv1 of
  (x,i)->  if p x then i : [] else []
  _-> []


module Maybe where
  import qualified List
import qualified Prelude
  listToMaybe :: [a]  ->  Maybe a
listToMaybe [] = Nothing
listToMaybe (a : _) = Just a



Case Reductions:
The following Case expression
case vv1 of
 (x,i) → if p x then i : [] else []
 _ → []

is transformed to
findIndices00 p (x,i) = if p x then i : [] else []
findIndices00 p _ = []



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

mainModule List
  ((elemIndex :: (Eq b, Eq a) => Either b a  ->  [Either b a]  ->  Maybe Int) :: (Eq a, Eq b) => Either b a  ->  [Either b a]  ->  Maybe Int)

module List where
  import qualified Maybe
import qualified Prelude
  elemIndex :: Eq a => a  ->  [a]  ->  Maybe Int
elemIndex x = findIndex (== x)

  findIndex :: (a  ->  Bool)  ->  [a]  ->  Maybe Int
findIndex p = Maybe.listToMaybe . findIndices p

  findIndices :: (a  ->  Bool)  ->  [a]  ->  [Int]
findIndices p xs = concatMap (findIndices0 p) (zip xs (enumFrom 0))

  
findIndices0 p vv1 = findIndices00 p vv1

  
findIndices00 p (x,i) =  if p x then i : [] else []
findIndices00 p _ = []


module Maybe where
  import qualified List
import qualified Prelude
  listToMaybe :: [a]  ->  Maybe a
listToMaybe [] = Nothing
listToMaybe (a : _) = Just a



If Reductions:
The following If expression
if p x then i : [] else []

is transformed to
findIndices000 i True = i : []
findIndices000 i False = []



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

mainModule List
  ((elemIndex :: (Eq a, Eq b) => Either b a  ->  [Either b a]  ->  Maybe Int) :: (Eq a, Eq b) => Either b a  ->  [Either b a]  ->  Maybe Int)

module List where
  import qualified Maybe
import qualified Prelude
  elemIndex :: Eq a => a  ->  [a]  ->  Maybe Int
elemIndex x = findIndex (== x)

  findIndex :: (a  ->  Bool)  ->  [a]  ->  Maybe Int
findIndex p = Maybe.listToMaybe . findIndices p

  findIndices :: (a  ->  Bool)  ->  [a]  ->  [Int]
findIndices p xs = concatMap (findIndices0 p) (zip xs (enumFrom 0))

  
findIndices0 p vv1 = findIndices00 p vv1

  
findIndices00 p (x,i) = findIndices000 i (p x)
findIndices00 p _ = []

  
findIndices000 i True = i : []
findIndices000 i False = []


module Maybe where
  import qualified List
import qualified Prelude
  listToMaybe :: [a]  ->  Maybe a
listToMaybe [] = Nothing
listToMaybe (a : _) = Just a



Replaced joker patterns by fresh variables and removed binding patterns.

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

mainModule List
  ((elemIndex :: (Eq b, Eq a) => Either a b  ->  [Either a b]  ->  Maybe Int) :: (Eq b, Eq a) => Either a b  ->  [Either a b]  ->  Maybe Int)

module List where
  import qualified Maybe
import qualified Prelude
  elemIndex :: Eq a => a  ->  [a]  ->  Maybe Int
elemIndex x = findIndex (== x)

  findIndex :: (a  ->  Bool)  ->  [a]  ->  Maybe Int
findIndex p = Maybe.listToMaybe . findIndices p

  findIndices :: (a  ->  Bool)  ->  [a]  ->  [Int]
findIndices p xs = concatMap (findIndices0 p) (zip xs (enumFrom 0))

  
findIndices0 p vv1 = findIndices00 p vv1

  
findIndices00 p (x,i) = findIndices000 i (p x)
findIndices00 p vw = []

  
findIndices000 i True = i : []
findIndices000 i False = []


module Maybe where
  import qualified List
import qualified Prelude
  listToMaybe :: [a]  ->  Maybe a
listToMaybe [] = Nothing
listToMaybe (a : vx) = Just a



Cond Reductions:
The following Function with conditions
undefined 
 | False
 = undefined

is transformed to
undefined  = undefined1

undefined0 True = undefined

undefined1  = undefined0 False



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

mainModule List
  ((elemIndex :: (Eq a, Eq b) => Either b a  ->  [Either b a]  ->  Maybe Int) :: (Eq a, Eq b) => Either b a  ->  [Either b a]  ->  Maybe Int)

module List where
  import qualified Maybe
import qualified Prelude
  elemIndex :: Eq a => a  ->  [a]  ->  Maybe Int
elemIndex x = findIndex (== x)

  findIndex :: (a  ->  Bool)  ->  [a]  ->  Maybe Int
findIndex p = Maybe.listToMaybe . findIndices p

  findIndices :: (a  ->  Bool)  ->  [a]  ->  [Int]
findIndices p xs = concatMap (findIndices0 p) (zip xs (enumFrom 0))

  
findIndices0 p vv1 = findIndices00 p vv1

  
findIndices00 p (x,i) = findIndices000 i (p x)
findIndices00 p vw = []

  
findIndices000 i True = i : []
findIndices000 i False = []


module Maybe where
  import qualified List
import qualified Prelude
  listToMaybe :: [a]  ->  Maybe a
listToMaybe [] = Nothing
listToMaybe (a : vx) = Just a



Num Reduction: All numbers are transformed to thier corresponding representation with Pos, Neg, Succ and Zero.

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

mainModule List
  (elemIndex :: (Eq a, Eq b) => Either a b  ->  [Either a b]  ->  Maybe Int)

module List where
  import qualified Maybe
import qualified Prelude
  elemIndex :: Eq a => a  ->  [a]  ->  Maybe Int
elemIndex x = findIndex (== x)

  findIndex :: (a  ->  Bool)  ->  [a]  ->  Maybe Int
findIndex p = Maybe.listToMaybe . findIndices p

  findIndices :: (a  ->  Bool)  ->  [a]  ->  [Int]
findIndices p xs = concatMap (findIndices0 p) (zip xs (enumFrom (Pos Zero)))

  
findIndices0 p vv1 = findIndices00 p vv1

  
findIndices00 p (x,i) = findIndices000 i (p x)
findIndices00 p vw = []

  
findIndices000 i True = i : []
findIndices000 i False = []


module Maybe where
  import qualified List
import qualified Prelude
  listToMaybe :: [a]  ->  Maybe a
listToMaybe [] = Nothing
listToMaybe (a : vx) = Just a



Haskell To QDPs


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

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

new_primPlusNat(Succ(yv3800), Succ(yv4000000)) → new_primPlusNat(yv3800, yv4000000)

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

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



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

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

new_primMulNat(Succ(yv30000), Succ(yv400000)) → new_primMulNat(yv30000, Succ(yv400000))

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

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



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

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

new_primEqNat(Succ(yv3000), Succ(yv40000)) → new_primEqNat(yv3000, yv40000)

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

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



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

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

new_esEs0(@2(yv300, yv301), @2(yv4000, yv4001), app(app(app(ty_@3, ec), ed), ee), dg) → new_esEs2(yv300, yv4000, ec, ed, ee)
new_esEs2(@3(yv300, yv301, yv302), @3(yv4000, yv4001, yv4002), gb, app(ty_Maybe, baa), hf) → new_esEs1(yv301, yv4001, baa)
new_esEs2(@3(yv300, yv301, yv302), @3(yv4000, yv4001, yv4002), app(ty_Maybe, bbb), gc, hf) → new_esEs1(yv300, yv4000, bbb)
new_esEs2(@3(yv300, yv301, yv302), @3(yv4000, yv4001, yv4002), app(app(app(ty_@3, bbc), bbd), bbe), gc, hf) → new_esEs2(yv300, yv4000, bbc, bbd, bbe)
new_esEs3(Right(yv300), Right(yv4000), bdb, app(ty_[], bdc)) → new_esEs(yv300, yv4000, bdc)
new_esEs2(@3(yv300, yv301, yv302), @3(yv4000, yv4001, yv4002), gb, gc, app(ty_[], gd)) → new_esEs(yv302, yv4002, gd)
new_esEs(:(yv300, yv301), :(yv4000, yv4001), app(app(ty_@2, bc), bd)) → new_esEs0(yv300, yv4000, bc, bd)
new_esEs2(@3(yv300, yv301, yv302), @3(yv4000, yv4001, yv4002), gb, app(app(ty_@2, hg), hh), hf) → new_esEs0(yv301, yv4001, hg, hh)
new_esEs0(@2(yv300, yv301), @2(yv4000, yv4001), app(app(ty_Either, ef), eg), dg) → new_esEs3(yv300, yv4000, ef, eg)
new_esEs0(@2(yv300, yv301), @2(yv4000, yv4001), cc, app(app(app(ty_@3, da), db), dc)) → new_esEs2(yv301, yv4001, da, db, dc)
new_esEs2(@3(yv300, yv301, yv302), @3(yv4000, yv4001, yv4002), gb, app(app(ty_Either, bae), baf), hf) → new_esEs3(yv301, yv4001, bae, baf)
new_esEs2(@3(yv300, yv301, yv302), @3(yv4000, yv4001, yv4002), gb, gc, app(app(ty_@2, ge), gf)) → new_esEs0(yv302, yv4002, ge, gf)
new_esEs(:(yv300, yv301), :(yv4000, yv4001), app(app(app(ty_@3, bf), bg), bh)) → new_esEs2(yv300, yv4000, bf, bg, bh)
new_esEs3(Left(yv300), Left(yv4000), app(ty_Maybe, bcd), bca) → new_esEs1(yv300, yv4000, bcd)
new_esEs3(Right(yv300), Right(yv4000), bdb, app(app(ty_Either, beb), bec)) → new_esEs3(yv300, yv4000, beb, bec)
new_esEs2(@3(yv300, yv301, yv302), @3(yv4000, yv4001, yv4002), app(ty_[], bag), gc, hf) → new_esEs(yv300, yv4000, bag)
new_esEs2(@3(yv300, yv301, yv302), @3(yv4000, yv4001, yv4002), app(app(ty_@2, bah), bba), gc, hf) → new_esEs0(yv300, yv4000, bah, bba)
new_esEs3(Left(yv300), Left(yv4000), app(ty_[], bbh), bca) → new_esEs(yv300, yv4000, bbh)
new_esEs0(@2(yv300, yv301), @2(yv4000, yv4001), cc, app(app(ty_Either, dd), de)) → new_esEs3(yv301, yv4001, dd, de)
new_esEs3(Left(yv300), Left(yv4000), app(app(ty_Either, bch), bda), bca) → new_esEs3(yv300, yv4000, bch, bda)
new_esEs0(@2(yv300, yv301), @2(yv4000, yv4001), cc, app(ty_[], cd)) → new_esEs(yv301, yv4001, cd)
new_esEs1(Just(yv300), Just(yv4000), app(app(ty_@2, fa), fb)) → new_esEs0(yv300, yv4000, fa, fb)
new_esEs1(Just(yv300), Just(yv4000), app(app(ty_Either, fh), ga)) → new_esEs3(yv300, yv4000, fh, ga)
new_esEs1(Just(yv300), Just(yv4000), app(ty_[], eh)) → new_esEs(yv300, yv4000, eh)
new_esEs(:(yv300, yv301), :(yv4000, yv4001), ba) → new_esEs(yv301, yv4001, ba)
new_esEs(:(yv300, yv301), :(yv4000, yv4001), app(app(ty_Either, ca), cb)) → new_esEs3(yv300, yv4000, ca, cb)
new_esEs3(Left(yv300), Left(yv4000), app(app(ty_@2, bcb), bcc), bca) → new_esEs0(yv300, yv4000, bcb, bcc)
new_esEs2(@3(yv300, yv301, yv302), @3(yv4000, yv4001, yv4002), app(app(ty_Either, bbf), bbg), gc, hf) → new_esEs3(yv300, yv4000, bbf, bbg)
new_esEs3(Right(yv300), Right(yv4000), bdb, app(app(ty_@2, bdd), bde)) → new_esEs0(yv300, yv4000, bdd, bde)
new_esEs3(Right(yv300), Right(yv4000), bdb, app(ty_Maybe, bdf)) → new_esEs1(yv300, yv4000, bdf)
new_esEs2(@3(yv300, yv301, yv302), @3(yv4000, yv4001, yv4002), gb, app(app(app(ty_@3, bab), bac), bad), hf) → new_esEs2(yv301, yv4001, bab, bac, bad)
new_esEs2(@3(yv300, yv301, yv302), @3(yv4000, yv4001, yv4002), gb, app(ty_[], he), hf) → new_esEs(yv301, yv4001, he)
new_esEs1(Just(yv300), Just(yv4000), app(ty_Maybe, fc)) → new_esEs1(yv300, yv4000, fc)
new_esEs3(Right(yv300), Right(yv4000), bdb, app(app(app(ty_@3, bdg), bdh), bea)) → new_esEs2(yv300, yv4000, bdg, bdh, bea)
new_esEs2(@3(yv300, yv301, yv302), @3(yv4000, yv4001, yv4002), gb, gc, app(ty_Maybe, gg)) → new_esEs1(yv302, yv4002, gg)
new_esEs0(@2(yv300, yv301), @2(yv4000, yv4001), app(app(ty_@2, dh), ea), dg) → new_esEs0(yv300, yv4000, dh, ea)
new_esEs1(Just(yv300), Just(yv4000), app(app(app(ty_@3, fd), ff), fg)) → new_esEs2(yv300, yv4000, fd, ff, fg)
new_esEs0(@2(yv300, yv301), @2(yv4000, yv4001), app(ty_[], df), dg) → new_esEs(yv300, yv4000, df)
new_esEs0(@2(yv300, yv301), @2(yv4000, yv4001), cc, app(ty_Maybe, cg)) → new_esEs1(yv301, yv4001, cg)
new_esEs0(@2(yv300, yv301), @2(yv4000, yv4001), app(ty_Maybe, eb), dg) → new_esEs1(yv300, yv4000, eb)
new_esEs3(Left(yv300), Left(yv4000), app(app(app(ty_@3, bce), bcf), bcg), bca) → new_esEs2(yv300, yv4000, bce, bcf, bcg)
new_esEs2(@3(yv300, yv301, yv302), @3(yv4000, yv4001, yv4002), gb, gc, app(app(ty_Either, hc), hd)) → new_esEs3(yv302, yv4002, hc, hd)
new_esEs0(@2(yv300, yv301), @2(yv4000, yv4001), cc, app(app(ty_@2, ce), cf)) → new_esEs0(yv301, yv4001, ce, cf)
new_esEs(:(yv300, yv301), :(yv4000, yv4001), app(ty_[], bb)) → new_esEs(yv300, yv4000, bb)
new_esEs2(@3(yv300, yv301, yv302), @3(yv4000, yv4001, yv4002), gb, gc, app(app(app(ty_@3, gh), ha), hb)) → new_esEs2(yv302, yv4002, gh, ha, hb)
new_esEs(:(yv300, yv301), :(yv4000, yv4001), app(ty_Maybe, be)) → new_esEs1(yv300, yv4000, be)

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

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



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

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

new_listToMaybe0(yv17, yv1810, yv41, yv1811, yv42, ba, bb) → new_listToMaybe(yv41, new_esEs4(Right(yv17), yv1810, ba, bb), yv17, yv1811, yv42, ba, bb)
new_listToMaybe(yv28, False, yv17, :(yv1810, yv1811), yv29, ba, bb) → new_listToMaybe0(yv17, yv1810, new_primPlusNat0(yv29, Zero), yv1811, new_primPlusNat0(yv29, Zero), ba, bb)

The TRS R consists of the following rules:

new_esEs21(yv300, yv4000, ty_Double) → new_esEs6(yv300, yv4000)
new_esEs21(yv300, yv4000, ty_Float) → new_esEs15(yv300, yv4000)
new_esEs16(Just(yv300), Just(yv4000), app(app(ty_Either, bac), bad)) → new_esEs4(yv300, yv4000, bac, bad)
new_esEs4(Left(yv300), Left(yv4000), ty_Float, bd) → new_esEs15(yv300, yv4000)
new_primPlusNat1(Succ(yv3800), Succ(yv4000000)) → Succ(Succ(new_primPlusNat1(yv3800, yv4000000)))
new_primEqInt(Neg(Succ(yv3000)), Pos(yv4000)) → False
new_primEqInt(Pos(Succ(yv3000)), Neg(yv4000)) → False
new_esEs21(yv300, yv4000, app(ty_Maybe, gc)) → new_esEs16(yv300, yv4000, gc)
new_esEs13(False, True) → False
new_esEs13(True, False) → False
new_esEs4(Left(yv300), Left(yv4000), app(ty_Ratio, ca), bd) → new_esEs8(yv300, yv4000, ca)
new_esEs4(Left(yv300), Left(yv4000), ty_@0, bd) → new_esEs17(yv300, yv4000)
new_esEs4(Right(yv300), Right(yv4000), cg, ty_Char) → new_esEs11(yv300, yv4000)
new_primEqInt(Neg(Zero), Pos(Succ(yv40000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(yv40000))) → False
new_esEs21(yv300, yv4000, ty_Int) → new_esEs7(yv300, yv4000)
new_esEs20(yv301, yv4001, app(ty_[], ee)) → new_esEs12(yv301, yv4001, ee)
new_esEs21(yv300, yv4000, ty_Char) → new_esEs11(yv300, yv4000)
new_esEs9(yv301, yv4001, ty_Integer) → new_esEs5(yv301, yv4001)
new_esEs25(yv300, yv4000, ty_Float) → new_esEs15(yv300, yv4000)
new_esEs25(yv300, yv4000, app(app(ty_@2, beh), bfa)) → new_esEs14(yv300, yv4000, beh, bfa)
new_esEs24(yv301, yv4001, app(app(app(ty_@3, beb), bec), bed)) → new_esEs18(yv301, yv4001, beb, bec, bed)
new_esEs21(yv300, yv4000, ty_@0) → new_esEs17(yv300, yv4000)
new_esEs16(Just(yv300), Just(yv4000), ty_Float) → new_esEs15(yv300, yv4000)
new_primMulNat0(Zero, Zero) → Zero
new_esEs18(@3(yv300, yv301, yv302), @3(yv4000, yv4001, yv4002), bbh, bca, bcb) → new_asAs(new_esEs25(yv300, yv4000, bbh), new_asAs(new_esEs24(yv301, yv4001, bca), new_esEs23(yv302, yv4002, bcb)))
new_esEs22(yv300, yv4000, app(ty_Ratio, bbb)) → new_esEs8(yv300, yv4000, bbb)
new_esEs16(Nothing, Nothing, hb) → True
new_esEs16(Just(yv300), Just(yv4000), ty_Ordering) → new_esEs19(yv300, yv4000)
new_esEs4(Left(yv300), Left(yv4000), ty_Ordering, bd) → new_esEs19(yv300, yv4000)
new_esEs21(yv300, yv4000, ty_Integer) → new_esEs5(yv300, yv4000)
new_esEs20(yv301, yv4001, app(app(ty_@2, ef), eg)) → new_esEs14(yv301, yv4001, ef, eg)
new_primPlusNat0(Zero, yv400000) → Succ(yv400000)
new_esEs4(Right(yv300), Right(yv4000), cg, app(ty_[], da)) → new_esEs12(yv300, yv4000, da)
new_esEs22(yv300, yv4000, ty_@0) → new_esEs17(yv300, yv4000)
new_esEs15(Float(yv300, yv301), Float(yv4000, yv4001)) → new_esEs7(new_sr(yv300, yv4000), new_sr(yv301, yv4001))
new_esEs20(yv301, yv4001, app(ty_Maybe, eh)) → new_esEs16(yv301, yv4001, eh)
new_esEs25(yv300, yv4000, ty_Int) → new_esEs7(yv300, yv4000)
new_esEs23(yv302, yv4002, ty_Int) → new_esEs7(yv302, yv4002)
new_esEs24(yv301, yv4001, ty_Ordering) → new_esEs19(yv301, yv4001)
new_sr(Neg(yv3000), Pos(yv40000)) → Neg(new_primMulNat0(yv3000, yv40000))
new_sr(Pos(yv3000), Neg(yv40000)) → Neg(new_primMulNat0(yv3000, yv40000))
new_esEs24(yv301, yv4001, ty_Bool) → new_esEs13(yv301, yv4001)
new_esEs16(Just(yv300), Just(yv4000), ty_Bool) → new_esEs13(yv300, yv4000)
new_esEs20(yv301, yv4001, app(app(ty_Either, ff), fg)) → new_esEs4(yv301, yv4001, ff, fg)
new_esEs4(Left(yv300), Left(yv4000), ty_Int, bd) → new_esEs7(yv300, yv4000)
new_esEs12([], [], bae) → True
new_esEs19(GT, LT) → False
new_esEs19(LT, GT) → False
new_esEs16(Just(yv300), Just(yv4000), app(ty_Maybe, hf)) → new_esEs16(yv300, yv4000, hf)
new_esEs23(yv302, yv4002, ty_Double) → new_esEs6(yv302, yv4002)
new_esEs5(Integer(yv300), Integer(yv4000)) → new_primEqInt(yv300, yv4000)
new_esEs22(yv300, yv4000, ty_Char) → new_esEs11(yv300, yv4000)
new_esEs24(yv301, yv4001, app(ty_Ratio, bea)) → new_esEs8(yv301, yv4001, bea)
new_esEs4(Right(yv300), Right(yv4000), cg, ty_Float) → new_esEs15(yv300, yv4000)
new_esEs16(Just(yv300), Just(yv4000), app(app(app(ty_@3, hh), baa), bab)) → new_esEs18(yv300, yv4000, hh, baa, bab)
new_esEs23(yv302, yv4002, app(ty_Ratio, bcg)) → new_esEs8(yv302, yv4002, bcg)
new_esEs24(yv301, yv4001, ty_@0) → new_esEs17(yv301, yv4001)
new_esEs23(yv302, yv4002, app(app(ty_Either, bdc), bdd)) → new_esEs4(yv302, yv4002, bdc, bdd)
new_esEs20(yv301, yv4001, ty_Char) → new_esEs11(yv301, yv4001)
new_esEs4(Left(yv300), Left(yv4000), ty_Integer, bd) → new_esEs5(yv300, yv4000)
new_esEs23(yv302, yv4002, ty_Bool) → new_esEs13(yv302, yv4002)
new_esEs16(Just(yv300), Just(yv4000), ty_Char) → new_esEs11(yv300, yv4000)
new_esEs4(Right(yv300), Right(yv4000), cg, ty_Int) → new_esEs7(yv300, yv4000)
new_esEs25(yv300, yv4000, ty_Bool) → new_esEs13(yv300, yv4000)
new_primEqNat0(Zero, Succ(yv40000)) → False
new_primEqNat0(Succ(yv3000), Zero) → False
new_esEs24(yv301, yv4001, app(ty_[], bde)) → new_esEs12(yv301, yv4001, bde)
new_esEs21(yv300, yv4000, app(ty_[], fh)) → new_esEs12(yv300, yv4000, fh)
new_esEs17(@0, @0) → True
new_esEs23(yv302, yv4002, app(app(app(ty_@3, bch), bda), bdb)) → new_esEs18(yv302, yv4002, bch, bda, bdb)
new_esEs22(yv300, yv4000, app(app(ty_@2, bag), bah)) → new_esEs14(yv300, yv4000, bag, bah)
new_esEs4(Left(yv300), Left(yv4000), app(app(ty_@2, bf), bg), bd) → new_esEs14(yv300, yv4000, bf, bg)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs24(yv301, yv4001, app(app(ty_Either, bee), bef)) → new_esEs4(yv301, yv4001, bee, bef)
new_esEs19(GT, GT) → True
new_esEs21(yv300, yv4000, app(app(ty_@2, ga), gb)) → new_esEs14(yv300, yv4000, ga, gb)
new_esEs10(yv300, yv4000, ty_Integer) → new_esEs5(yv300, yv4000)
new_esEs25(yv300, yv4000, app(app(ty_Either, bfg), bfh)) → new_esEs4(yv300, yv4000, bfg, bfh)
new_esEs25(yv300, yv4000, ty_Char) → new_esEs11(yv300, yv4000)
new_esEs12([], :(yv4000, yv4001), bae) → False
new_esEs12(:(yv300, yv301), [], bae) → False
new_esEs4(Right(yv300), Right(yv4000), cg, ty_Double) → new_esEs6(yv300, yv4000)
new_esEs8(:%(yv300, yv301), :%(yv4000, yv4001), bc) → new_asAs(new_esEs10(yv300, yv4000, bc), new_esEs9(yv301, yv4001, bc))
new_esEs20(yv301, yv4001, ty_Int) → new_esEs7(yv301, yv4001)
new_esEs20(yv301, yv4001, ty_Integer) → new_esEs5(yv301, yv4001)
new_esEs22(yv300, yv4000, app(app(ty_Either, bbf), bbg)) → new_esEs4(yv300, yv4000, bbf, bbg)
new_esEs10(yv300, yv4000, ty_Int) → new_esEs7(yv300, yv4000)
new_esEs14(@2(yv300, yv301), @2(yv4000, yv4001), ec, ed) → new_asAs(new_esEs21(yv300, yv4000, ec), new_esEs20(yv301, yv4001, ed))
new_esEs12(:(yv300, yv301), :(yv4000, yv4001), bae) → new_asAs(new_esEs22(yv300, yv4000, bae), new_esEs12(yv301, yv4001, bae))
new_esEs24(yv301, yv4001, app(app(ty_@2, bdf), bdg)) → new_esEs14(yv301, yv4001, bdf, bdg)
new_esEs22(yv300, yv4000, ty_Int) → new_esEs7(yv300, yv4000)
new_esEs24(yv301, yv4001, ty_Int) → new_esEs7(yv301, yv4001)
new_esEs25(yv300, yv4000, ty_Ordering) → new_esEs19(yv300, yv4000)
new_esEs19(LT, LT) → True
new_esEs11(Char(yv300), Char(yv4000)) → new_primEqNat0(yv300, yv4000)
new_esEs22(yv300, yv4000, ty_Float) → new_esEs15(yv300, yv4000)
new_esEs19(GT, EQ) → False
new_esEs19(EQ, GT) → False
new_esEs21(yv300, yv4000, app(app(app(ty_@3, ge), gf), gg)) → new_esEs18(yv300, yv4000, ge, gf, gg)
new_sr(Neg(yv3000), Neg(yv40000)) → Pos(new_primMulNat0(yv3000, yv40000))
new_esEs24(yv301, yv4001, ty_Char) → new_esEs11(yv301, yv4001)
new_sr(Pos(yv3000), Pos(yv40000)) → Pos(new_primMulNat0(yv3000, yv40000))
new_asAs(False, yv37) → False
new_primEqNat0(Zero, Zero) → True
new_primMulNat0(Zero, Succ(yv400000)) → Zero
new_primMulNat0(Succ(yv30000), Zero) → Zero
new_esEs21(yv300, yv4000, ty_Bool) → new_esEs13(yv300, yv4000)
new_esEs25(yv300, yv4000, app(ty_Ratio, bfc)) → new_esEs8(yv300, yv4000, bfc)
new_esEs4(Left(yv300), Left(yv4000), app(app(app(ty_@3, cb), cc), cd), bd) → new_esEs18(yv300, yv4000, cb, cc, cd)
new_esEs16(Just(yv300), Just(yv4000), ty_@0) → new_esEs17(yv300, yv4000)
new_esEs16(Just(yv300), Just(yv4000), app(ty_[], hc)) → new_esEs12(yv300, yv4000, hc)
new_esEs7(yv30, yv400) → new_primEqInt(yv30, yv400)
new_esEs24(yv301, yv4001, ty_Integer) → new_esEs5(yv301, yv4001)
new_esEs20(yv301, yv4001, ty_Bool) → new_esEs13(yv301, yv4001)
new_esEs22(yv300, yv4000, ty_Integer) → new_esEs5(yv300, yv4000)
new_esEs24(yv301, yv4001, app(ty_Maybe, bdh)) → new_esEs16(yv301, yv4001, bdh)
new_esEs23(yv302, yv4002, ty_Integer) → new_esEs5(yv302, yv4002)
new_esEs4(Right(yv300), Right(yv4000), cg, app(app(ty_@2, db), dc)) → new_esEs14(yv300, yv4000, db, dc)
new_esEs23(yv302, yv4002, ty_Float) → new_esEs15(yv302, yv4002)
new_esEs20(yv301, yv4001, app(ty_Ratio, fa)) → new_esEs8(yv301, yv4001, fa)
new_esEs13(False, False) → True
new_esEs4(Left(yv300), Left(yv4000), app(ty_Maybe, bh), bd) → new_esEs16(yv300, yv4000, bh)
new_primPlusNat0(Succ(yv380), yv400000) → Succ(Succ(new_primPlusNat1(yv380, yv400000)))
new_esEs20(yv301, yv4001, ty_Double) → new_esEs6(yv301, yv4001)
new_esEs21(yv300, yv4000, ty_Ordering) → new_esEs19(yv300, yv4000)
new_esEs25(yv300, yv4000, app(app(app(ty_@3, bfd), bfe), bff)) → new_esEs18(yv300, yv4000, bfd, bfe, bff)
new_esEs22(yv300, yv4000, app(ty_[], baf)) → new_esEs12(yv300, yv4000, baf)
new_esEs25(yv300, yv4000, app(ty_[], beg)) → new_esEs12(yv300, yv4000, beg)
new_esEs4(Right(yv300), Right(yv4000), cg, app(app(ty_Either, ea), eb)) → new_esEs4(yv300, yv4000, ea, eb)
new_primEqInt(Neg(Succ(yv3000)), Neg(Succ(yv40000))) → new_primEqNat0(yv3000, yv40000)
new_esEs24(yv301, yv4001, ty_Double) → new_esEs6(yv301, yv4001)
new_esEs21(yv300, yv4000, app(ty_Ratio, gd)) → new_esEs8(yv300, yv4000, gd)
new_esEs16(Just(yv300), Just(yv4000), ty_Int) → new_esEs7(yv300, yv4000)
new_esEs4(Right(yv300), Right(yv4000), cg, ty_Ordering) → new_esEs19(yv300, yv4000)
new_esEs4(Left(yv300), Left(yv4000), app(app(ty_Either, ce), cf), bd) → new_esEs4(yv300, yv4000, ce, cf)
new_esEs19(EQ, EQ) → True
new_esEs22(yv300, yv4000, ty_Ordering) → new_esEs19(yv300, yv4000)
new_primPlusNat1(Zero, Succ(yv4000000)) → Succ(yv4000000)
new_primPlusNat1(Succ(yv3800), Zero) → Succ(yv3800)
new_esEs23(yv302, yv4002, app(ty_Maybe, bcf)) → new_esEs16(yv302, yv4002, bcf)
new_esEs9(yv301, yv4001, ty_Int) → new_esEs7(yv301, yv4001)
new_esEs4(Right(yv300), Right(yv4000), cg, app(ty_Maybe, dd)) → new_esEs16(yv300, yv4000, dd)
new_esEs16(Just(yv300), Just(yv4000), app(app(ty_@2, hd), he)) → new_esEs14(yv300, yv4000, hd, he)
new_esEs6(Double(yv300, yv301), Double(yv4000, yv4001)) → new_esEs7(new_sr(yv300, yv4000), new_sr(yv301, yv4001))
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs23(yv302, yv4002, ty_Char) → new_esEs11(yv302, yv4002)
new_esEs16(Nothing, Just(yv4000), hb) → False
new_esEs16(Just(yv300), Nothing, hb) → False
new_primEqInt(Neg(Zero), Neg(Succ(yv40000))) → False
new_primEqInt(Neg(Succ(yv3000)), Neg(Zero)) → False
new_esEs25(yv300, yv4000, app(ty_Maybe, bfb)) → new_esEs16(yv300, yv4000, bfb)
new_esEs4(Right(yv300), Right(yv4000), cg, ty_@0) → new_esEs17(yv300, yv4000)
new_esEs21(yv300, yv4000, app(app(ty_Either, gh), ha)) → new_esEs4(yv300, yv4000, gh, ha)
new_esEs23(yv302, yv4002, ty_Ordering) → new_esEs19(yv302, yv4002)
new_esEs16(Just(yv300), Just(yv4000), app(ty_Ratio, hg)) → new_esEs8(yv300, yv4000, hg)
new_esEs20(yv301, yv4001, ty_@0) → new_esEs17(yv301, yv4001)
new_primPlusNat1(Zero, Zero) → Zero
new_esEs4(Left(yv300), Left(yv4000), ty_Char, bd) → new_esEs11(yv300, yv4000)
new_esEs25(yv300, yv4000, ty_Double) → new_esEs6(yv300, yv4000)
new_esEs4(Right(yv300), Right(yv4000), cg, ty_Integer) → new_esEs5(yv300, yv4000)
new_esEs4(Left(yv300), Left(yv4000), app(ty_[], be), bd) → new_esEs12(yv300, yv4000, be)
new_esEs4(Right(yv300), Right(yv4000), cg, app(app(app(ty_@3, df), dg), dh)) → new_esEs18(yv300, yv4000, df, dg, dh)
new_asAs(True, yv37) → yv37
new_esEs22(yv300, yv4000, ty_Double) → new_esEs6(yv300, yv4000)
new_esEs22(yv300, yv4000, app(ty_Maybe, bba)) → new_esEs16(yv300, yv4000, bba)
new_primMulNat0(Succ(yv30000), Succ(yv400000)) → new_primPlusNat0(new_primMulNat0(yv30000, Succ(yv400000)), yv400000)
new_esEs25(yv300, yv4000, ty_@0) → new_esEs17(yv300, yv4000)
new_esEs13(True, True) → True
new_esEs4(Right(yv300), Left(yv4000), cg, bd) → False
new_esEs4(Left(yv300), Right(yv4000), cg, bd) → False
new_esEs19(EQ, LT) → False
new_esEs16(Just(yv300), Just(yv4000), ty_Integer) → new_esEs5(yv300, yv4000)
new_esEs19(LT, EQ) → False
new_esEs4(Left(yv300), Left(yv4000), ty_Bool, bd) → new_esEs13(yv300, yv4000)
new_esEs4(Right(yv300), Right(yv4000), cg, ty_Bool) → new_esEs13(yv300, yv4000)
new_primEqInt(Pos(Succ(yv3000)), Pos(Succ(yv40000))) → new_primEqNat0(yv3000, yv40000)
new_esEs22(yv300, yv4000, ty_Bool) → new_esEs13(yv300, yv4000)
new_esEs25(yv300, yv4000, ty_Integer) → new_esEs5(yv300, yv4000)
new_esEs4(Right(yv300), Right(yv4000), cg, app(ty_Ratio, de)) → new_esEs8(yv300, yv4000, de)
new_esEs23(yv302, yv4002, app(ty_[], bcc)) → new_esEs12(yv302, yv4002, bcc)
new_esEs20(yv301, yv4001, ty_Ordering) → new_esEs19(yv301, yv4001)
new_primEqNat0(Succ(yv3000), Succ(yv40000)) → new_primEqNat0(yv3000, yv40000)
new_esEs4(Left(yv300), Left(yv4000), ty_Double, bd) → new_esEs6(yv300, yv4000)
new_esEs16(Just(yv300), Just(yv4000), ty_Double) → new_esEs6(yv300, yv4000)
new_esEs23(yv302, yv4002, app(app(ty_@2, bcd), bce)) → new_esEs14(yv302, yv4002, bcd, bce)
new_esEs20(yv301, yv4001, ty_Float) → new_esEs15(yv301, yv4001)
new_primEqInt(Pos(Zero), Pos(Succ(yv40000))) → False
new_primEqInt(Pos(Succ(yv3000)), Pos(Zero)) → False
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_esEs24(yv301, yv4001, ty_Float) → new_esEs15(yv301, yv4001)
new_esEs23(yv302, yv4002, ty_@0) → new_esEs17(yv302, yv4002)
new_esEs22(yv300, yv4000, app(app(app(ty_@3, bbc), bbd), bbe)) → new_esEs18(yv300, yv4000, bbc, bbd, bbe)
new_esEs20(yv301, yv4001, app(app(app(ty_@3, fb), fc), fd)) → new_esEs18(yv301, yv4001, fb, fc, fd)

The set Q consists of the following terms:

new_esEs4(Right(x0), Right(x1), x2, ty_Float)
new_esEs16(Just(x0), Just(x1), ty_Float)
new_esEs10(x0, x1, ty_Integer)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs9(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_@0)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_esEs24(x0, x1, ty_@0)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs4(Left(x0), Left(x1), ty_Char, x2)
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, ty_Double)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_Float)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs16(Just(x0), Just(x1), ty_Double)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_Ordering)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs16(Just(x0), Just(x1), ty_Integer)
new_esEs9(x0, x1, ty_Int)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs15(Float(x0, x1), Float(x2, x3))
new_esEs22(x0, x1, ty_Integer)
new_primPlusNat1(Succ(x0), Zero)
new_esEs16(Nothing, Nothing, x0)
new_asAs(True, x0)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_esEs20(x0, x1, ty_Double)
new_esEs21(x0, x1, ty_Integer)
new_esEs7(x0, x1)
new_esEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs6(Double(x0, x1), Double(x2, x3))
new_esEs20(x0, x1, ty_@0)
new_esEs4(Right(x0), Right(x1), x2, ty_Bool)
new_esEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs16(Just(x0), Just(x1), ty_Char)
new_esEs21(x0, x1, ty_Int)
new_esEs4(Right(x0), Right(x1), x2, ty_Double)
new_esEs16(Just(x0), Nothing, x1)
new_esEs25(x0, x1, ty_Int)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Char)
new_esEs25(x0, x1, ty_Ordering)
new_esEs25(x0, x1, ty_Integer)
new_esEs4(Left(x0), Left(x1), ty_Float, x2)
new_esEs25(x0, x1, ty_Bool)
new_esEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs21(x0, x1, ty_Bool)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs16(Just(x0), Just(x1), ty_@0)
new_esEs4(Right(x0), Right(x1), x2, ty_Integer)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs24(x0, x1, ty_Int)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs10(x0, x1, ty_Int)
new_sr(Pos(x0), Pos(x1))
new_esEs4(Left(x0), Right(x1), x2, x3)
new_esEs4(Right(x0), Left(x1), x2, x3)
new_esEs16(Just(x0), Just(x1), app(ty_[], x2))
new_esEs22(x0, x1, app(ty_[], x2))
new_primPlusNat0(Zero, x0)
new_esEs24(x0, x1, ty_Double)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_sr(Neg(x0), Neg(x1))
new_sr(Pos(x0), Neg(x1))
new_sr(Neg(x0), Pos(x1))
new_primEqNat0(Zero, Zero)
new_esEs21(x0, x1, ty_Float)
new_esEs11(Char(x0), Char(x1))
new_esEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs21(x0, x1, ty_Double)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs12([], [], x0)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs19(GT, GT)
new_esEs22(x0, x1, ty_Char)
new_esEs24(x0, x1, ty_Ordering)
new_primEqNat0(Zero, Succ(x0))
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_Integer)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_primMulNat0(Zero, Zero)
new_esEs13(False, False)
new_esEs23(x0, x1, ty_Char)
new_esEs22(x0, x1, ty_Float)
new_esEs19(EQ, EQ)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs14(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs16(Nothing, Just(x0), x1)
new_esEs13(True, False)
new_esEs13(False, True)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs20(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_Char)
new_esEs12(:(x0, x1), [], x2)
new_esEs16(Just(x0), Just(x1), ty_Ordering)
new_esEs24(x0, x1, ty_Bool)
new_esEs19(LT, EQ)
new_esEs19(EQ, LT)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_esEs4(Left(x0), Left(x1), ty_Integer, x2)
new_esEs16(Just(x0), Just(x1), app(ty_Ratio, x2))
new_primMulNat0(Zero, Succ(x0))
new_esEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs19(LT, GT)
new_esEs19(GT, LT)
new_esEs23(x0, x1, ty_Bool)
new_esEs13(True, True)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs19(LT, LT)
new_esEs4(Left(x0), Left(x1), ty_Bool, x2)
new_esEs22(x0, x1, ty_Bool)
new_esEs4(Right(x0), Right(x1), x2, ty_Char)
new_esEs19(EQ, GT)
new_esEs19(GT, EQ)
new_esEs16(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs12([], :(x0, x1), x2)
new_esEs12(:(x0, x1), :(x2, x3), x4)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs8(:%(x0, x1), :%(x2, x3), x4)
new_esEs16(Just(x0), Just(x1), ty_Bool)
new_esEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_primPlusNat1(Zero, Succ(x0))
new_esEs23(x0, x1, ty_Double)
new_esEs4(Left(x0), Left(x1), ty_@0, x2)
new_esEs4(Left(x0), Left(x1), ty_Double, x2)
new_primEqNat0(Succ(x0), Zero)
new_esEs20(x0, x1, ty_Char)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs24(x0, x1, app(ty_[], x2))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs20(x0, x1, ty_Integer)
new_esEs20(x0, x1, app(ty_[], x2))
new_esEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs20(x0, x1, ty_Float)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs25(x0, x1, ty_Double)
new_esEs23(x0, x1, ty_Ordering)
new_esEs16(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs22(x0, x1, ty_Ordering)
new_esEs25(x0, x1, ty_Float)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs22(x0, x1, ty_@0)
new_esEs24(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_Ordering)
new_esEs25(x0, x1, ty_Char)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs5(Integer(x0), Integer(x1))
new_primPlusNat1(Zero, Zero)
new_esEs24(x0, x1, ty_Float)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Left(x0), Left(x1), ty_Int, x2)
new_esEs4(Right(x0), Right(x1), x2, ty_@0)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs25(x0, x1, ty_@0)
new_primMulNat0(Succ(x0), Zero)
new_esEs18(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs4(Right(x0), Right(x1), x2, ty_Int)
new_asAs(False, x0)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primPlusNat0(Succ(x0), x1)
new_esEs16(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs17(@0, @0)
new_esEs21(x0, x1, ty_@0)
new_esEs22(x0, x1, ty_Int)
new_esEs16(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs16(Just(x0), Just(x1), ty_Int)

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

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



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

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

new_listToMaybe2(yv26, False, yv10, :(yv1110, yv1111), yv27, ba, bb) → new_listToMaybe1(yv10, yv1110, new_primPlusNat0(yv27, Zero), yv1111, new_primPlusNat0(yv27, Zero), ba, bb)
new_listToMaybe1(yv10, yv1110, yv39, yv1111, yv40, ba, bb) → new_listToMaybe2(yv39, new_esEs4(Left(yv10), yv1110, ba, bb), yv10, yv1111, yv40, ba, bb)

The TRS R consists of the following rules:

new_esEs21(yv300, yv4000, ty_Double) → new_esEs6(yv300, yv4000)
new_esEs21(yv300, yv4000, ty_Float) → new_esEs15(yv300, yv4000)
new_esEs16(Just(yv300), Just(yv4000), app(app(ty_Either, bac), bad)) → new_esEs4(yv300, yv4000, bac, bad)
new_esEs4(Left(yv300), Left(yv4000), ty_Float, bd) → new_esEs15(yv300, yv4000)
new_primPlusNat1(Succ(yv3800), Succ(yv4000000)) → Succ(Succ(new_primPlusNat1(yv3800, yv4000000)))
new_primEqInt(Neg(Succ(yv3000)), Pos(yv4000)) → False
new_primEqInt(Pos(Succ(yv3000)), Neg(yv4000)) → False
new_esEs21(yv300, yv4000, app(ty_Maybe, gc)) → new_esEs16(yv300, yv4000, gc)
new_esEs13(False, True) → False
new_esEs13(True, False) → False
new_esEs4(Left(yv300), Left(yv4000), app(ty_Ratio, ca), bd) → new_esEs8(yv300, yv4000, ca)
new_esEs4(Left(yv300), Left(yv4000), ty_@0, bd) → new_esEs17(yv300, yv4000)
new_esEs4(Right(yv300), Right(yv4000), cg, ty_Char) → new_esEs11(yv300, yv4000)
new_primEqInt(Neg(Zero), Pos(Succ(yv40000))) → False
new_primEqInt(Pos(Zero), Neg(Succ(yv40000))) → False
new_esEs21(yv300, yv4000, ty_Int) → new_esEs7(yv300, yv4000)
new_esEs20(yv301, yv4001, app(ty_[], ee)) → new_esEs12(yv301, yv4001, ee)
new_esEs21(yv300, yv4000, ty_Char) → new_esEs11(yv300, yv4000)
new_esEs9(yv301, yv4001, ty_Integer) → new_esEs5(yv301, yv4001)
new_esEs25(yv300, yv4000, ty_Float) → new_esEs15(yv300, yv4000)
new_esEs25(yv300, yv4000, app(app(ty_@2, beh), bfa)) → new_esEs14(yv300, yv4000, beh, bfa)
new_esEs24(yv301, yv4001, app(app(app(ty_@3, beb), bec), bed)) → new_esEs18(yv301, yv4001, beb, bec, bed)
new_esEs21(yv300, yv4000, ty_@0) → new_esEs17(yv300, yv4000)
new_esEs16(Just(yv300), Just(yv4000), ty_Float) → new_esEs15(yv300, yv4000)
new_primMulNat0(Zero, Zero) → Zero
new_esEs18(@3(yv300, yv301, yv302), @3(yv4000, yv4001, yv4002), bbh, bca, bcb) → new_asAs(new_esEs25(yv300, yv4000, bbh), new_asAs(new_esEs24(yv301, yv4001, bca), new_esEs23(yv302, yv4002, bcb)))
new_esEs22(yv300, yv4000, app(ty_Ratio, bbb)) → new_esEs8(yv300, yv4000, bbb)
new_esEs16(Nothing, Nothing, hb) → True
new_esEs16(Just(yv300), Just(yv4000), ty_Ordering) → new_esEs19(yv300, yv4000)
new_esEs4(Left(yv300), Left(yv4000), ty_Ordering, bd) → new_esEs19(yv300, yv4000)
new_esEs21(yv300, yv4000, ty_Integer) → new_esEs5(yv300, yv4000)
new_esEs20(yv301, yv4001, app(app(ty_@2, ef), eg)) → new_esEs14(yv301, yv4001, ef, eg)
new_primPlusNat0(Zero, yv400000) → Succ(yv400000)
new_esEs4(Right(yv300), Right(yv4000), cg, app(ty_[], da)) → new_esEs12(yv300, yv4000, da)
new_esEs22(yv300, yv4000, ty_@0) → new_esEs17(yv300, yv4000)
new_esEs15(Float(yv300, yv301), Float(yv4000, yv4001)) → new_esEs7(new_sr(yv300, yv4000), new_sr(yv301, yv4001))
new_esEs20(yv301, yv4001, app(ty_Maybe, eh)) → new_esEs16(yv301, yv4001, eh)
new_esEs25(yv300, yv4000, ty_Int) → new_esEs7(yv300, yv4000)
new_esEs23(yv302, yv4002, ty_Int) → new_esEs7(yv302, yv4002)
new_esEs24(yv301, yv4001, ty_Ordering) → new_esEs19(yv301, yv4001)
new_sr(Neg(yv3000), Pos(yv40000)) → Neg(new_primMulNat0(yv3000, yv40000))
new_sr(Pos(yv3000), Neg(yv40000)) → Neg(new_primMulNat0(yv3000, yv40000))
new_esEs24(yv301, yv4001, ty_Bool) → new_esEs13(yv301, yv4001)
new_esEs16(Just(yv300), Just(yv4000), ty_Bool) → new_esEs13(yv300, yv4000)
new_esEs20(yv301, yv4001, app(app(ty_Either, ff), fg)) → new_esEs4(yv301, yv4001, ff, fg)
new_esEs4(Left(yv300), Left(yv4000), ty_Int, bd) → new_esEs7(yv300, yv4000)
new_esEs12([], [], bae) → True
new_esEs19(GT, LT) → False
new_esEs19(LT, GT) → False
new_esEs16(Just(yv300), Just(yv4000), app(ty_Maybe, hf)) → new_esEs16(yv300, yv4000, hf)
new_esEs23(yv302, yv4002, ty_Double) → new_esEs6(yv302, yv4002)
new_esEs5(Integer(yv300), Integer(yv4000)) → new_primEqInt(yv300, yv4000)
new_esEs22(yv300, yv4000, ty_Char) → new_esEs11(yv300, yv4000)
new_esEs24(yv301, yv4001, app(ty_Ratio, bea)) → new_esEs8(yv301, yv4001, bea)
new_esEs4(Right(yv300), Right(yv4000), cg, ty_Float) → new_esEs15(yv300, yv4000)
new_esEs16(Just(yv300), Just(yv4000), app(app(app(ty_@3, hh), baa), bab)) → new_esEs18(yv300, yv4000, hh, baa, bab)
new_esEs23(yv302, yv4002, app(ty_Ratio, bcg)) → new_esEs8(yv302, yv4002, bcg)
new_esEs24(yv301, yv4001, ty_@0) → new_esEs17(yv301, yv4001)
new_esEs23(yv302, yv4002, app(app(ty_Either, bdc), bdd)) → new_esEs4(yv302, yv4002, bdc, bdd)
new_esEs20(yv301, yv4001, ty_Char) → new_esEs11(yv301, yv4001)
new_esEs4(Left(yv300), Left(yv4000), ty_Integer, bd) → new_esEs5(yv300, yv4000)
new_esEs23(yv302, yv4002, ty_Bool) → new_esEs13(yv302, yv4002)
new_esEs16(Just(yv300), Just(yv4000), ty_Char) → new_esEs11(yv300, yv4000)
new_esEs4(Right(yv300), Right(yv4000), cg, ty_Int) → new_esEs7(yv300, yv4000)
new_esEs25(yv300, yv4000, ty_Bool) → new_esEs13(yv300, yv4000)
new_primEqNat0(Zero, Succ(yv40000)) → False
new_primEqNat0(Succ(yv3000), Zero) → False
new_esEs24(yv301, yv4001, app(ty_[], bde)) → new_esEs12(yv301, yv4001, bde)
new_esEs21(yv300, yv4000, app(ty_[], fh)) → new_esEs12(yv300, yv4000, fh)
new_esEs17(@0, @0) → True
new_esEs23(yv302, yv4002, app(app(app(ty_@3, bch), bda), bdb)) → new_esEs18(yv302, yv4002, bch, bda, bdb)
new_esEs22(yv300, yv4000, app(app(ty_@2, bag), bah)) → new_esEs14(yv300, yv4000, bag, bah)
new_esEs4(Left(yv300), Left(yv4000), app(app(ty_@2, bf), bg), bd) → new_esEs14(yv300, yv4000, bf, bg)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs24(yv301, yv4001, app(app(ty_Either, bee), bef)) → new_esEs4(yv301, yv4001, bee, bef)
new_esEs19(GT, GT) → True
new_esEs21(yv300, yv4000, app(app(ty_@2, ga), gb)) → new_esEs14(yv300, yv4000, ga, gb)
new_esEs10(yv300, yv4000, ty_Integer) → new_esEs5(yv300, yv4000)
new_esEs25(yv300, yv4000, app(app(ty_Either, bfg), bfh)) → new_esEs4(yv300, yv4000, bfg, bfh)
new_esEs25(yv300, yv4000, ty_Char) → new_esEs11(yv300, yv4000)
new_esEs12([], :(yv4000, yv4001), bae) → False
new_esEs12(:(yv300, yv301), [], bae) → False
new_esEs4(Right(yv300), Right(yv4000), cg, ty_Double) → new_esEs6(yv300, yv4000)
new_esEs8(:%(yv300, yv301), :%(yv4000, yv4001), bc) → new_asAs(new_esEs10(yv300, yv4000, bc), new_esEs9(yv301, yv4001, bc))
new_esEs20(yv301, yv4001, ty_Int) → new_esEs7(yv301, yv4001)
new_esEs20(yv301, yv4001, ty_Integer) → new_esEs5(yv301, yv4001)
new_esEs22(yv300, yv4000, app(app(ty_Either, bbf), bbg)) → new_esEs4(yv300, yv4000, bbf, bbg)
new_esEs10(yv300, yv4000, ty_Int) → new_esEs7(yv300, yv4000)
new_esEs14(@2(yv300, yv301), @2(yv4000, yv4001), ec, ed) → new_asAs(new_esEs21(yv300, yv4000, ec), new_esEs20(yv301, yv4001, ed))
new_esEs12(:(yv300, yv301), :(yv4000, yv4001), bae) → new_asAs(new_esEs22(yv300, yv4000, bae), new_esEs12(yv301, yv4001, bae))
new_esEs24(yv301, yv4001, app(app(ty_@2, bdf), bdg)) → new_esEs14(yv301, yv4001, bdf, bdg)
new_esEs22(yv300, yv4000, ty_Int) → new_esEs7(yv300, yv4000)
new_esEs24(yv301, yv4001, ty_Int) → new_esEs7(yv301, yv4001)
new_esEs25(yv300, yv4000, ty_Ordering) → new_esEs19(yv300, yv4000)
new_esEs19(LT, LT) → True
new_esEs11(Char(yv300), Char(yv4000)) → new_primEqNat0(yv300, yv4000)
new_esEs22(yv300, yv4000, ty_Float) → new_esEs15(yv300, yv4000)
new_esEs19(GT, EQ) → False
new_esEs19(EQ, GT) → False
new_esEs21(yv300, yv4000, app(app(app(ty_@3, ge), gf), gg)) → new_esEs18(yv300, yv4000, ge, gf, gg)
new_sr(Neg(yv3000), Neg(yv40000)) → Pos(new_primMulNat0(yv3000, yv40000))
new_esEs24(yv301, yv4001, ty_Char) → new_esEs11(yv301, yv4001)
new_sr(Pos(yv3000), Pos(yv40000)) → Pos(new_primMulNat0(yv3000, yv40000))
new_asAs(False, yv37) → False
new_primEqNat0(Zero, Zero) → True
new_primMulNat0(Zero, Succ(yv400000)) → Zero
new_primMulNat0(Succ(yv30000), Zero) → Zero
new_esEs21(yv300, yv4000, ty_Bool) → new_esEs13(yv300, yv4000)
new_esEs25(yv300, yv4000, app(ty_Ratio, bfc)) → new_esEs8(yv300, yv4000, bfc)
new_esEs4(Left(yv300), Left(yv4000), app(app(app(ty_@3, cb), cc), cd), bd) → new_esEs18(yv300, yv4000, cb, cc, cd)
new_esEs16(Just(yv300), Just(yv4000), ty_@0) → new_esEs17(yv300, yv4000)
new_esEs16(Just(yv300), Just(yv4000), app(ty_[], hc)) → new_esEs12(yv300, yv4000, hc)
new_esEs7(yv30, yv400) → new_primEqInt(yv30, yv400)
new_esEs24(yv301, yv4001, ty_Integer) → new_esEs5(yv301, yv4001)
new_esEs20(yv301, yv4001, ty_Bool) → new_esEs13(yv301, yv4001)
new_esEs22(yv300, yv4000, ty_Integer) → new_esEs5(yv300, yv4000)
new_esEs24(yv301, yv4001, app(ty_Maybe, bdh)) → new_esEs16(yv301, yv4001, bdh)
new_esEs23(yv302, yv4002, ty_Integer) → new_esEs5(yv302, yv4002)
new_esEs4(Right(yv300), Right(yv4000), cg, app(app(ty_@2, db), dc)) → new_esEs14(yv300, yv4000, db, dc)
new_esEs23(yv302, yv4002, ty_Float) → new_esEs15(yv302, yv4002)
new_esEs20(yv301, yv4001, app(ty_Ratio, fa)) → new_esEs8(yv301, yv4001, fa)
new_esEs13(False, False) → True
new_esEs4(Left(yv300), Left(yv4000), app(ty_Maybe, bh), bd) → new_esEs16(yv300, yv4000, bh)
new_primPlusNat0(Succ(yv380), yv400000) → Succ(Succ(new_primPlusNat1(yv380, yv400000)))
new_esEs20(yv301, yv4001, ty_Double) → new_esEs6(yv301, yv4001)
new_esEs21(yv300, yv4000, ty_Ordering) → new_esEs19(yv300, yv4000)
new_esEs25(yv300, yv4000, app(app(app(ty_@3, bfd), bfe), bff)) → new_esEs18(yv300, yv4000, bfd, bfe, bff)
new_esEs22(yv300, yv4000, app(ty_[], baf)) → new_esEs12(yv300, yv4000, baf)
new_esEs25(yv300, yv4000, app(ty_[], beg)) → new_esEs12(yv300, yv4000, beg)
new_esEs4(Right(yv300), Right(yv4000), cg, app(app(ty_Either, ea), eb)) → new_esEs4(yv300, yv4000, ea, eb)
new_primEqInt(Neg(Succ(yv3000)), Neg(Succ(yv40000))) → new_primEqNat0(yv3000, yv40000)
new_esEs24(yv301, yv4001, ty_Double) → new_esEs6(yv301, yv4001)
new_esEs21(yv300, yv4000, app(ty_Ratio, gd)) → new_esEs8(yv300, yv4000, gd)
new_esEs16(Just(yv300), Just(yv4000), ty_Int) → new_esEs7(yv300, yv4000)
new_esEs4(Right(yv300), Right(yv4000), cg, ty_Ordering) → new_esEs19(yv300, yv4000)
new_esEs4(Left(yv300), Left(yv4000), app(app(ty_Either, ce), cf), bd) → new_esEs4(yv300, yv4000, ce, cf)
new_esEs19(EQ, EQ) → True
new_esEs22(yv300, yv4000, ty_Ordering) → new_esEs19(yv300, yv4000)
new_primPlusNat1(Zero, Succ(yv4000000)) → Succ(yv4000000)
new_primPlusNat1(Succ(yv3800), Zero) → Succ(yv3800)
new_esEs23(yv302, yv4002, app(ty_Maybe, bcf)) → new_esEs16(yv302, yv4002, bcf)
new_esEs9(yv301, yv4001, ty_Int) → new_esEs7(yv301, yv4001)
new_esEs4(Right(yv300), Right(yv4000), cg, app(ty_Maybe, dd)) → new_esEs16(yv300, yv4000, dd)
new_esEs16(Just(yv300), Just(yv4000), app(app(ty_@2, hd), he)) → new_esEs14(yv300, yv4000, hd, he)
new_esEs6(Double(yv300, yv301), Double(yv4000, yv4001)) → new_esEs7(new_sr(yv300, yv4000), new_sr(yv301, yv4001))
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs23(yv302, yv4002, ty_Char) → new_esEs11(yv302, yv4002)
new_esEs16(Nothing, Just(yv4000), hb) → False
new_esEs16(Just(yv300), Nothing, hb) → False
new_primEqInt(Neg(Zero), Neg(Succ(yv40000))) → False
new_primEqInt(Neg(Succ(yv3000)), Neg(Zero)) → False
new_esEs25(yv300, yv4000, app(ty_Maybe, bfb)) → new_esEs16(yv300, yv4000, bfb)
new_esEs4(Right(yv300), Right(yv4000), cg, ty_@0) → new_esEs17(yv300, yv4000)
new_esEs21(yv300, yv4000, app(app(ty_Either, gh), ha)) → new_esEs4(yv300, yv4000, gh, ha)
new_esEs23(yv302, yv4002, ty_Ordering) → new_esEs19(yv302, yv4002)
new_esEs16(Just(yv300), Just(yv4000), app(ty_Ratio, hg)) → new_esEs8(yv300, yv4000, hg)
new_esEs20(yv301, yv4001, ty_@0) → new_esEs17(yv301, yv4001)
new_primPlusNat1(Zero, Zero) → Zero
new_esEs4(Left(yv300), Left(yv4000), ty_Char, bd) → new_esEs11(yv300, yv4000)
new_esEs25(yv300, yv4000, ty_Double) → new_esEs6(yv300, yv4000)
new_esEs4(Right(yv300), Right(yv4000), cg, ty_Integer) → new_esEs5(yv300, yv4000)
new_esEs4(Left(yv300), Left(yv4000), app(ty_[], be), bd) → new_esEs12(yv300, yv4000, be)
new_esEs4(Right(yv300), Right(yv4000), cg, app(app(app(ty_@3, df), dg), dh)) → new_esEs18(yv300, yv4000, df, dg, dh)
new_asAs(True, yv37) → yv37
new_esEs22(yv300, yv4000, ty_Double) → new_esEs6(yv300, yv4000)
new_esEs22(yv300, yv4000, app(ty_Maybe, bba)) → new_esEs16(yv300, yv4000, bba)
new_primMulNat0(Succ(yv30000), Succ(yv400000)) → new_primPlusNat0(new_primMulNat0(yv30000, Succ(yv400000)), yv400000)
new_esEs25(yv300, yv4000, ty_@0) → new_esEs17(yv300, yv4000)
new_esEs13(True, True) → True
new_esEs4(Right(yv300), Left(yv4000), cg, bd) → False
new_esEs4(Left(yv300), Right(yv4000), cg, bd) → False
new_esEs19(EQ, LT) → False
new_esEs16(Just(yv300), Just(yv4000), ty_Integer) → new_esEs5(yv300, yv4000)
new_esEs19(LT, EQ) → False
new_esEs4(Left(yv300), Left(yv4000), ty_Bool, bd) → new_esEs13(yv300, yv4000)
new_esEs4(Right(yv300), Right(yv4000), cg, ty_Bool) → new_esEs13(yv300, yv4000)
new_primEqInt(Pos(Succ(yv3000)), Pos(Succ(yv40000))) → new_primEqNat0(yv3000, yv40000)
new_esEs22(yv300, yv4000, ty_Bool) → new_esEs13(yv300, yv4000)
new_esEs25(yv300, yv4000, ty_Integer) → new_esEs5(yv300, yv4000)
new_esEs4(Right(yv300), Right(yv4000), cg, app(ty_Ratio, de)) → new_esEs8(yv300, yv4000, de)
new_esEs23(yv302, yv4002, app(ty_[], bcc)) → new_esEs12(yv302, yv4002, bcc)
new_esEs20(yv301, yv4001, ty_Ordering) → new_esEs19(yv301, yv4001)
new_primEqNat0(Succ(yv3000), Succ(yv40000)) → new_primEqNat0(yv3000, yv40000)
new_esEs4(Left(yv300), Left(yv4000), ty_Double, bd) → new_esEs6(yv300, yv4000)
new_esEs16(Just(yv300), Just(yv4000), ty_Double) → new_esEs6(yv300, yv4000)
new_esEs23(yv302, yv4002, app(app(ty_@2, bcd), bce)) → new_esEs14(yv302, yv4002, bcd, bce)
new_esEs20(yv301, yv4001, ty_Float) → new_esEs15(yv301, yv4001)
new_primEqInt(Pos(Zero), Pos(Succ(yv40000))) → False
new_primEqInt(Pos(Succ(yv3000)), Pos(Zero)) → False
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_esEs24(yv301, yv4001, ty_Float) → new_esEs15(yv301, yv4001)
new_esEs23(yv302, yv4002, ty_@0) → new_esEs17(yv302, yv4002)
new_esEs22(yv300, yv4000, app(app(app(ty_@3, bbc), bbd), bbe)) → new_esEs18(yv300, yv4000, bbc, bbd, bbe)
new_esEs20(yv301, yv4001, app(app(app(ty_@3, fb), fc), fd)) → new_esEs18(yv301, yv4001, fb, fc, fd)

The set Q consists of the following terms:

new_esEs4(Right(x0), Right(x1), x2, ty_Float)
new_esEs16(Just(x0), Just(x1), ty_Float)
new_esEs10(x0, x1, ty_Integer)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs9(x0, x1, ty_Integer)
new_esEs20(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_@0)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_esEs24(x0, x1, ty_@0)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs4(Left(x0), Left(x1), ty_Char, x2)
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs22(x0, x1, ty_Double)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_Float)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs16(Just(x0), Just(x1), ty_Double)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_Ordering)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs16(Just(x0), Just(x1), ty_Integer)
new_esEs9(x0, x1, ty_Int)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs15(Float(x0, x1), Float(x2, x3))
new_esEs22(x0, x1, ty_Integer)
new_primPlusNat1(Succ(x0), Zero)
new_esEs16(Nothing, Nothing, x0)
new_asAs(True, x0)
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_esEs20(x0, x1, ty_Double)
new_esEs21(x0, x1, ty_Integer)
new_esEs7(x0, x1)
new_esEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs6(Double(x0, x1), Double(x2, x3))
new_esEs20(x0, x1, ty_@0)
new_esEs4(Right(x0), Right(x1), x2, ty_Bool)
new_esEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs16(Just(x0), Just(x1), ty_Char)
new_esEs21(x0, x1, ty_Int)
new_esEs4(Right(x0), Right(x1), x2, ty_Double)
new_esEs16(Just(x0), Nothing, x1)
new_esEs25(x0, x1, ty_Int)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, ty_Char)
new_esEs25(x0, x1, ty_Ordering)
new_esEs25(x0, x1, ty_Integer)
new_esEs4(Left(x0), Left(x1), ty_Float, x2)
new_esEs25(x0, x1, ty_Bool)
new_esEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs21(x0, x1, ty_Bool)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs16(Just(x0), Just(x1), ty_@0)
new_esEs4(Right(x0), Right(x1), x2, ty_Integer)
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs24(x0, x1, ty_Int)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs10(x0, x1, ty_Int)
new_sr(Pos(x0), Pos(x1))
new_esEs4(Left(x0), Right(x1), x2, x3)
new_esEs4(Right(x0), Left(x1), x2, x3)
new_esEs16(Just(x0), Just(x1), app(ty_[], x2))
new_esEs22(x0, x1, app(ty_[], x2))
new_primPlusNat0(Zero, x0)
new_esEs24(x0, x1, ty_Double)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_sr(Neg(x0), Neg(x1))
new_sr(Pos(x0), Neg(x1))
new_sr(Neg(x0), Pos(x1))
new_primEqNat0(Zero, Zero)
new_esEs21(x0, x1, ty_Float)
new_esEs11(Char(x0), Char(x1))
new_esEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs21(x0, x1, ty_Double)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs12([], [], x0)
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs19(GT, GT)
new_esEs22(x0, x1, ty_Char)
new_esEs24(x0, x1, ty_Ordering)
new_primEqNat0(Zero, Succ(x0))
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_Integer)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_primMulNat0(Zero, Zero)
new_esEs13(False, False)
new_esEs23(x0, x1, ty_Char)
new_esEs22(x0, x1, ty_Float)
new_esEs19(EQ, EQ)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs14(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs16(Nothing, Just(x0), x1)
new_esEs13(True, False)
new_esEs13(False, True)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs20(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_Char)
new_esEs12(:(x0, x1), [], x2)
new_esEs16(Just(x0), Just(x1), ty_Ordering)
new_esEs24(x0, x1, ty_Bool)
new_esEs19(LT, EQ)
new_esEs19(EQ, LT)
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_esEs4(Left(x0), Left(x1), ty_Integer, x2)
new_esEs16(Just(x0), Just(x1), app(ty_Ratio, x2))
new_primMulNat0(Zero, Succ(x0))
new_esEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs19(LT, GT)
new_esEs19(GT, LT)
new_esEs23(x0, x1, ty_Bool)
new_esEs13(True, True)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs19(LT, LT)
new_esEs4(Left(x0), Left(x1), ty_Bool, x2)
new_esEs22(x0, x1, ty_Bool)
new_esEs4(Right(x0), Right(x1), x2, ty_Char)
new_esEs19(EQ, GT)
new_esEs19(GT, EQ)
new_esEs16(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs12([], :(x0, x1), x2)
new_esEs12(:(x0, x1), :(x2, x3), x4)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs8(:%(x0, x1), :%(x2, x3), x4)
new_esEs16(Just(x0), Just(x1), ty_Bool)
new_esEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_primPlusNat1(Zero, Succ(x0))
new_esEs23(x0, x1, ty_Double)
new_esEs4(Left(x0), Left(x1), ty_@0, x2)
new_esEs4(Left(x0), Left(x1), ty_Double, x2)
new_primEqNat0(Succ(x0), Zero)
new_esEs20(x0, x1, ty_Char)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs24(x0, x1, app(ty_[], x2))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs20(x0, x1, ty_Integer)
new_esEs20(x0, x1, app(ty_[], x2))
new_esEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs20(x0, x1, ty_Float)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs25(x0, x1, ty_Double)
new_esEs23(x0, x1, ty_Ordering)
new_esEs16(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs22(x0, x1, ty_Ordering)
new_esEs25(x0, x1, ty_Float)
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs22(x0, x1, ty_@0)
new_esEs24(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_Ordering)
new_esEs25(x0, x1, ty_Char)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs5(Integer(x0), Integer(x1))
new_primPlusNat1(Zero, Zero)
new_esEs24(x0, x1, ty_Float)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Left(x0), Left(x1), ty_Int, x2)
new_esEs4(Right(x0), Right(x1), x2, ty_@0)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs25(x0, x1, ty_@0)
new_primMulNat0(Succ(x0), Zero)
new_esEs18(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs4(Right(x0), Right(x1), x2, ty_Int)
new_asAs(False, x0)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primPlusNat0(Succ(x0), x1)
new_esEs16(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs17(@0, @0)
new_esEs21(x0, x1, ty_@0)
new_esEs22(x0, x1, ty_Int)
new_esEs16(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs16(Just(x0), Just(x1), ty_Int)

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

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