YES 3.294 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
  ↳ BR

mainModule List
  ((nub :: (Eq b, Eq a) => [(b,a)]  ->  [(b,a)]) :: (Eq b, Eq a) => [(b,a)]  ->  [(b,a)])

module List where
  import qualified Maybe
import qualified Prelude
  nub :: Eq a => [a]  ->  [a]
nub l = 
nub' l [] where 
nub' [] _ = []
nub' (x : xs) ls 
 | x `elem` ls = 
nub' xs ls
 | otherwise = 
x : nub' xs (x : ls)


module Maybe where
  import qualified List
import qualified Prelude


Replaced joker patterns by fresh variables and removed binding patterns.

↳ HASKELL
  ↳ BR
    ↳ HASKELL
      ↳ COR

mainModule List
  ((nub :: (Eq a, Eq b) => [(a,b)]  ->  [(a,b)]) :: (Eq a, Eq b) => [(a,b)]  ->  [(a,b)])

module List where
  import qualified Maybe
import qualified Prelude
  nub :: Eq a => [a]  ->  [a]
nub l = 
nub' l [] where 
nub' [] vw = []
nub' (x : xs) ls 
 | x `elem` ls = 
nub' xs ls
 | otherwise = 
x : nub' xs (x : ls)


module Maybe where
  import qualified List
import qualified Prelude


Cond Reductions:
The following Function with conditions
nub' [] vw = []
nub' (x : xs) ls
 | x `elem` ls
 = nub' xs ls
 | otherwise
 = x : nub' xs (x : ls)

is transformed to
nub' [] vw = nub'3 [] vw
nub' (x : xs) ls = nub'2 (x : xs) ls

nub'0 x xs ls True = x : nub' xs (x : ls)

nub'1 x xs ls True = nub' xs ls
nub'1 x xs ls False = nub'0 x xs ls otherwise

nub'2 (x : xs) ls = nub'1 x xs ls (x `elem` ls)

nub'3 [] vw = []
nub'3 xz yu = nub'2 xz yu

The following Function with conditions
undefined 
 | False
 = undefined

is transformed to
undefined  = undefined1

undefined0 True = undefined

undefined1  = undefined0 False



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

mainModule List
  ((nub :: (Eq a, Eq b) => [(b,a)]  ->  [(b,a)]) :: (Eq a, Eq b) => [(b,a)]  ->  [(b,a)])

module List where
  import qualified Maybe
import qualified Prelude
  nub :: Eq a => [a]  ->  [a]
nub l = 
nub' l [] where 
nub' [] vw = nub'3 [] vw
nub' (x : xs) ls = nub'2 (x : xs) ls
nub'0 x xs ls True = x : nub' xs (x : ls)
nub'1 x xs ls True = nub' xs ls
nub'1 x xs ls False = nub'0 x xs ls otherwise
nub'2 (x : xs) ls = nub'1 x xs ls (x `elem` ls)
nub'3 [] vw = []
nub'3 xz yu = nub'2 xz yu


module Maybe where
  import qualified List
import qualified Prelude


Let/Where Reductions:
The bindings of the following Let/Where expression
nub' l []
where 
nub' [] vw = nub'3 [] vw
nub' (x : xs) ls = nub'2 (x : xs) ls
nub'0 x xs ls True = x : nub' xs (x : ls)
nub'1 x xs ls True = nub' xs ls
nub'1 x xs ls False = nub'0 x xs ls otherwise
nub'2 (x : xs) ls = nub'1 x xs ls (x `elem` ls)
nub'3 [] vw = []
nub'3 xz yu = nub'2 xz yu

are unpacked to the following functions on top level
nubNub'1 x xs ls True = nubNub' xs ls
nubNub'1 x xs ls False = nubNub'0 x xs ls otherwise

nubNub'3 [] vw = []
nubNub'3 xz yu = nubNub'2 xz yu

nubNub' [] vw = nubNub'3 [] vw
nubNub' (x : xs) ls = nubNub'2 (x : xs) ls

nubNub'2 (x : xs) ls = nubNub'1 x xs ls (x `elem` ls)

nubNub'0 x xs ls True = x : nubNub' xs (x : ls)



↳ HASKELL
  ↳ BR
    ↳ HASKELL
      ↳ COR
        ↳ HASKELL
          ↳ LetRed
            ↳ HASKELL
              ↳ Narrow

mainModule List
  (nub :: (Eq a, Eq b) => [(a,b)]  ->  [(a,b)])

module List where
  import qualified Maybe
import qualified Prelude
  nub :: Eq a => [a]  ->  [a]
nub l = nubNub' l []

  
nubNub' [] vw = nubNub'3 [] vw
nubNub' (x : xs) ls = nubNub'2 (x : xs) ls

  
nubNub'0 x xs ls True = x : nubNub' xs (x : ls)

  
nubNub'1 x xs ls True = nubNub' xs ls
nubNub'1 x xs ls False = nubNub'0 x xs ls otherwise

  
nubNub'2 (x : xs) ls = nubNub'1 x xs ls (x `elem` ls)

  
nubNub'3 [] vw = []
nubNub'3 xz yu = nubNub'2 xz yu


module Maybe where
  import qualified List
import qualified Prelude


Haskell To QDPs


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

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

new_primPlusNat(Succ(yv18500), Succ(yv1571000)) → new_primPlusNat(yv18500, yv1571000)

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

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

new_primMulNat(Succ(yv153100), Succ(yv157100)) → new_primMulNat(yv153100, Succ(yv157100))

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

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

new_primEqNat(Succ(yv15300), Succ(yv15700)) → new_primEqNat(yv15300, yv15700)

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

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

new_esEs(@2(yv1530, yv1531), @2(yv1570, yv1571), app(app(ty_@2, cc), cd), ce) → new_esEs(yv1530, yv1570, cc, cd)
new_esEs(@2(yv1530, yv1531), @2(yv1570, yv1571), app(ty_[], cf), ce) → new_esEs0(yv1530, yv1570, cf)
new_esEs0(:(yv1530, yv1531), :(yv1570, yv1571), app(ty_Maybe, eg)) → new_esEs3(yv1530, yv1570, eg)
new_esEs1(@3(yv1530, yv1531, yv1532), @3(yv1570, yv1571, yv1572), eh, app(app(app(ty_@3, gh), ha), hb), gf) → new_esEs1(yv1531, yv1571, gh, ha, hb)
new_esEs1(@3(yv1530, yv1531, yv1532), @3(yv1570, yv1571, yv1572), eh, fa, app(app(ty_Either, ga), gb)) → new_esEs2(yv1532, yv1572, ga, gb)
new_esEs1(@3(yv1530, yv1531, yv1532), @3(yv1570, yv1571, yv1572), eh, app(app(ty_@2, gd), ge), gf) → new_esEs(yv1531, yv1571, gd, ge)
new_esEs(@2(yv1530, yv1531), @2(yv1570, yv1571), app(ty_Maybe, de), ce) → new_esEs3(yv1530, yv1570, de)
new_esEs1(@3(yv1530, yv1531, yv1532), @3(yv1570, yv1571, yv1572), app(app(ty_Either, bad), bae), fa, gf) → new_esEs2(yv1530, yv1570, bad, bae)
new_esEs1(@3(yv1530, yv1531, yv1532), @3(yv1570, yv1571, yv1572), app(ty_[], hh), fa, gf) → new_esEs0(yv1530, yv1570, hh)
new_esEs1(@3(yv1530, yv1531, yv1532), @3(yv1570, yv1571, yv1572), eh, app(ty_Maybe, he), gf) → new_esEs3(yv1531, yv1571, he)
new_esEs1(@3(yv1530, yv1531, yv1532), @3(yv1570, yv1571, yv1572), eh, fa, app(app(app(ty_@3, ff), fg), fh)) → new_esEs1(yv1532, yv1572, ff, fg, fh)
new_esEs2(Left(yv1530), Left(yv1570), app(app(ty_Either, bbf), bbg), bba) → new_esEs2(yv1530, yv1570, bbf, bbg)
new_esEs3(Just(yv1530), Just(yv1570), app(app(ty_Either, bea), beb)) → new_esEs2(yv1530, yv1570, bea, beb)
new_esEs3(Just(yv1530), Just(yv1570), app(ty_[], bde)) → new_esEs0(yv1530, yv1570, bde)
new_esEs1(@3(yv1530, yv1531, yv1532), @3(yv1570, yv1571, yv1572), eh, app(app(ty_Either, hc), hd), gf) → new_esEs2(yv1531, yv1571, hc, hd)
new_esEs(@2(yv1530, yv1531), @2(yv1570, yv1571), ba, app(ty_Maybe, cb)) → new_esEs3(yv1531, yv1571, cb)
new_esEs1(@3(yv1530, yv1531, yv1532), @3(yv1570, yv1571, yv1572), eh, fa, app(app(ty_@2, fb), fc)) → new_esEs(yv1532, yv1572, fb, fc)
new_esEs2(Right(yv1530), Right(yv1570), bca, app(app(app(ty_@3, bce), bcf), bcg)) → new_esEs1(yv1530, yv1570, bce, bcf, bcg)
new_esEs3(Just(yv1530), Just(yv1570), app(app(app(ty_@3, bdf), bdg), bdh)) → new_esEs1(yv1530, yv1570, bdf, bdg, bdh)
new_esEs(@2(yv1530, yv1531), @2(yv1570, yv1571), ba, app(app(app(ty_@3, be), bf), bg)) → new_esEs1(yv1531, yv1571, be, bf, bg)
new_esEs1(@3(yv1530, yv1531, yv1532), @3(yv1570, yv1571, yv1572), eh, fa, app(ty_[], fd)) → new_esEs0(yv1532, yv1572, fd)
new_esEs1(@3(yv1530, yv1531, yv1532), @3(yv1570, yv1571, yv1572), app(app(app(ty_@3, baa), bab), bac), fa, gf) → new_esEs1(yv1530, yv1570, baa, bab, bac)
new_esEs2(Left(yv1530), Left(yv1570), app(app(app(ty_@3, bbc), bbd), bbe), bba) → new_esEs1(yv1530, yv1570, bbc, bbd, bbe)
new_esEs1(@3(yv1530, yv1531, yv1532), @3(yv1570, yv1571, yv1572), eh, fa, app(ty_Maybe, gc)) → new_esEs3(yv1532, yv1572, gc)
new_esEs0(:(yv1530, yv1531), :(yv1570, yv1571), app(app(ty_Either, ee), ef)) → new_esEs2(yv1530, yv1570, ee, ef)
new_esEs0(:(yv1530, yv1531), :(yv1570, yv1571), app(app(app(ty_@3, eb), ec), ed)) → new_esEs1(yv1530, yv1570, eb, ec, ed)
new_esEs1(@3(yv1530, yv1531, yv1532), @3(yv1570, yv1571, yv1572), eh, app(ty_[], gg), gf) → new_esEs0(yv1531, yv1571, gg)
new_esEs(@2(yv1530, yv1531), @2(yv1570, yv1571), ba, app(app(ty_Either, bh), ca)) → new_esEs2(yv1531, yv1571, bh, ca)
new_esEs1(@3(yv1530, yv1531, yv1532), @3(yv1570, yv1571, yv1572), app(ty_Maybe, baf), fa, gf) → new_esEs3(yv1530, yv1570, baf)
new_esEs2(Right(yv1530), Right(yv1570), bca, app(app(ty_@2, bcb), bcc)) → new_esEs(yv1530, yv1570, bcb, bcc)
new_esEs2(Right(yv1530), Right(yv1570), bca, app(ty_[], bcd)) → new_esEs0(yv1530, yv1570, bcd)
new_esEs2(Right(yv1530), Right(yv1570), bca, app(app(ty_Either, bch), bda)) → new_esEs2(yv1530, yv1570, bch, bda)
new_esEs3(Just(yv1530), Just(yv1570), app(ty_Maybe, bec)) → new_esEs3(yv1530, yv1570, bec)
new_esEs(@2(yv1530, yv1531), @2(yv1570, yv1571), ba, app(ty_[], bd)) → new_esEs0(yv1531, yv1571, bd)
new_esEs3(Just(yv1530), Just(yv1570), app(app(ty_@2, bdc), bdd)) → new_esEs(yv1530, yv1570, bdc, bdd)
new_esEs2(Right(yv1530), Right(yv1570), bca, app(ty_Maybe, bdb)) → new_esEs3(yv1530, yv1570, bdb)
new_esEs(@2(yv1530, yv1531), @2(yv1570, yv1571), ba, app(app(ty_@2, bb), bc)) → new_esEs(yv1531, yv1571, bb, bc)
new_esEs2(Left(yv1530), Left(yv1570), app(app(ty_@2, bag), bah), bba) → new_esEs(yv1530, yv1570, bag, bah)
new_esEs(@2(yv1530, yv1531), @2(yv1570, yv1571), app(app(ty_Either, dc), dd), ce) → new_esEs2(yv1530, yv1570, dc, dd)
new_esEs0(:(yv1530, yv1531), :(yv1570, yv1571), app(app(ty_@2, dg), dh)) → new_esEs(yv1530, yv1570, dg, dh)
new_esEs(@2(yv1530, yv1531), @2(yv1570, yv1571), app(app(app(ty_@3, cg), da), db), ce) → new_esEs1(yv1530, yv1570, cg, da, db)
new_esEs2(Left(yv1530), Left(yv1570), app(ty_Maybe, bbh), bba) → new_esEs3(yv1530, yv1570, bbh)
new_esEs0(:(yv1530, yv1531), :(yv1570, yv1571), app(ty_[], ea)) → new_esEs0(yv1530, yv1570, ea)
new_esEs1(@3(yv1530, yv1531, yv1532), @3(yv1570, yv1571, yv1572), app(app(ty_@2, hf), hg), fa, gf) → new_esEs(yv1530, yv1570, hf, hg)
new_esEs2(Left(yv1530), Left(yv1570), app(ty_[], bbb), bba) → new_esEs0(yv1530, yv1570, bbb)
new_esEs0(:(yv1530, yv1531), :(yv1570, yv1571), df) → new_esEs0(yv1531, yv1571, df)

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

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

new_nubNub'1(yv153, yv154, yv155, yv156, yv157, yv158, ba) → new_nubNub'10(yv153, yv154, yv155, yv156, new_esEs4(yv153, yv157, ba), yv158, ba)
new_nubNub'10(yv166, yv167, yv168, yv169, False, :(yv1710, yv1711), bb) → new_nubNub'1(yv166, yv167, yv168, yv169, yv1710, yv1711, bb)
new_nubNub'10(yv166, yv167, yv168, yv169, False, [], bb) → new_nubNub'(yv167, yv166, :(yv168, yv169), bb)
new_nubNub'10(yv166, :(yv1670, yv1671), yv168, yv169, True, yv171, bb) → new_nubNub'11(yv1670, yv1671, yv168, yv169, bb)
new_nubNub'(:(yv1670, yv1671), yv168, yv169, bb) → new_nubNub'11(yv1670, yv1671, yv168, yv169, bb)
new_nubNub'11(yv59, yv60, yv61, yv62, bc) → new_nubNub'1(yv59, yv60, yv61, yv62, yv61, yv62, bc)

The TRS R consists of the following rules:

new_esEs14(Just(yv1530), Just(yv1570), ty_@0) → new_esEs18(yv1530, yv1570)
new_esEs24(yv1532, yv1572, app(app(ty_Either, bdb), bdc)) → new_esEs5(yv1532, yv1572, bdb, bdc)
new_esEs20(yv1531, yv1571, app(app(ty_Either, hd), he)) → new_esEs5(yv1531, yv1571, hd, he)
new_esEs25(yv1531, yv1571, app(ty_Maybe, bef)) → new_esEs14(yv1531, yv1571, bef)
new_primPlusNat1(Succ(yv18500), Succ(yv1571000)) → Succ(Succ(new_primPlusNat1(yv18500, yv1571000)))
new_esEs26(yv1530, yv1570, app(app(app(ty_@3, bfc), bfd), bfe)) → new_esEs12(yv1530, yv1570, bfc, bfd, bfe)
new_esEs14(Just(yv1530), Just(yv1570), ty_Bool) → new_esEs7(yv1530, yv1570)
new_primEqInt(Pos(Succ(yv15300)), Neg(yv1570)) → False
new_primEqInt(Neg(Succ(yv15300)), Pos(yv1570)) → False
new_esEs20(yv1531, yv1571, ty_@0) → new_esEs18(yv1531, yv1571)
new_esEs25(yv1531, yv1571, ty_Char) → new_esEs8(yv1531, yv1571)
new_esEs4(yv153, yv157, ty_Ordering) → new_esEs15(yv153, yv157)
new_esEs5(Left(yv1530), Left(yv1570), ty_Float, bd) → new_esEs6(yv1530, yv1570)
new_esEs11([], :(yv1570, yv1571), ec) → False
new_esEs11(:(yv1530, yv1531), [], ec) → False
new_primEqInt(Pos(Zero), Neg(Succ(yv15700))) → False
new_primEqInt(Neg(Zero), Pos(Succ(yv15700))) → False
new_esEs15(EQ, EQ) → True
new_esEs14(Just(yv1530), Just(yv1570), app(ty_[], bbd)) → new_esEs11(yv1530, yv1570, bbd)
new_esEs4(yv153, yv157, app(app(ty_@2, fg), fh)) → new_esEs10(yv153, yv157, fg, fh)
new_esEs20(yv1531, yv1571, app(ty_Maybe, hf)) → new_esEs14(yv1531, yv1571, hf)
new_esEs5(Left(yv1530), Left(yv1570), ty_Char, bd) → new_esEs8(yv1530, yv1570)
new_esEs5(Right(yv1530), Right(yv1570), cg, ty_Integer) → new_esEs16(yv1530, yv1570)
new_primMulNat0(Zero, Zero) → Zero
new_esEs21(yv1530, yv1570, ty_@0) → new_esEs18(yv1530, yv1570)
new_esEs17(:%(yv1530, yv1531), :%(yv1570, yv1571), ge) → new_asAs(new_esEs23(yv1530, yv1570, ge), new_esEs22(yv1531, yv1571, ge))
new_esEs24(yv1532, yv1572, ty_Double) → new_esEs9(yv1532, yv1572)
new_esEs24(yv1532, yv1572, ty_Int) → new_esEs13(yv1532, yv1572)
new_esEs12(@3(yv1530, yv1531, yv1532), @3(yv1570, yv1571, yv1572), ga, gb, gc) → new_asAs(new_esEs26(yv1530, yv1570, ga), new_asAs(new_esEs25(yv1531, yv1571, gb), new_esEs24(yv1532, yv1572, gc)))
new_primPlusNat0(Zero, yv157100) → Succ(yv157100)
new_esEs14(Just(yv1530), Just(yv1570), ty_Integer) → new_esEs16(yv1530, yv1570)
new_esEs20(yv1531, yv1571, app(app(app(ty_@3, ha), hb), hc)) → new_esEs12(yv1531, yv1571, ha, hb, hc)
new_esEs5(Left(yv1530), Left(yv1570), ty_@0, bd) → new_esEs18(yv1530, yv1570)
new_esEs19(yv1530, yv1570, ty_Bool) → new_esEs7(yv1530, yv1570)
new_esEs20(yv1531, yv1571, app(ty_[], gh)) → new_esEs11(yv1531, yv1571, gh)
new_esEs26(yv1530, yv1570, ty_Float) → new_esEs6(yv1530, yv1570)
new_sr(Neg(yv15310), Pos(yv15710)) → Neg(new_primMulNat0(yv15310, yv15710))
new_sr(Pos(yv15310), Neg(yv15710)) → Neg(new_primMulNat0(yv15310, yv15710))
new_esEs5(Right(yv1530), Right(yv1570), cg, ty_@0) → new_esEs18(yv1530, yv1570)
new_esEs9(Double(yv1530, yv1531), Double(yv1570, yv1571)) → new_esEs13(new_sr(yv1530, yv1570), new_sr(yv1531, yv1571))
new_esEs5(Left(yv1530), Left(yv1570), app(ty_Ratio, cf), bd) → new_esEs17(yv1530, yv1570, cf)
new_esEs26(yv1530, yv1570, app(app(ty_Either, bff), bfg)) → new_esEs5(yv1530, yv1570, bff, bfg)
new_esEs19(yv1530, yv1570, app(ty_Maybe, fd)) → new_esEs14(yv1530, yv1570, fd)
new_esEs4(yv153, yv157, ty_Float) → new_esEs6(yv153, yv157)
new_esEs5(Right(yv1530), Right(yv1570), cg, ty_Ordering) → new_esEs15(yv1530, yv1570)
new_esEs11([], [], ec) → True
new_esEs19(yv1530, yv1570, app(app(app(ty_@3, eg), eh), fa)) → new_esEs12(yv1530, yv1570, eg, eh, fa)
new_esEs21(yv1530, yv1570, ty_Integer) → new_esEs16(yv1530, yv1570)
new_esEs5(Left(yv1530), Left(yv1570), ty_Ordering, bd) → new_esEs15(yv1530, yv1570)
new_esEs21(yv1530, yv1570, ty_Float) → new_esEs6(yv1530, yv1570)
new_esEs19(yv1530, yv1570, ty_Int) → new_esEs13(yv1530, yv1570)
new_esEs24(yv1532, yv1572, ty_Integer) → new_esEs16(yv1532, yv1572)
new_esEs20(yv1531, yv1571, app(app(ty_@2, gf), gg)) → new_esEs10(yv1531, yv1571, gf, gg)
new_esEs10(@2(yv1530, yv1531), @2(yv1570, yv1571), fg, fh) → new_asAs(new_esEs21(yv1530, yv1570, fg), new_esEs20(yv1531, yv1571, fh))
new_esEs5(Left(yv1530), Right(yv1570), cg, bd) → False
new_esEs5(Right(yv1530), Left(yv1570), cg, bd) → False
new_esEs5(Right(yv1530), Right(yv1570), cg, ty_Bool) → new_esEs7(yv1530, yv1570)
new_primEqNat0(Zero, Succ(yv15700)) → False
new_primEqNat0(Succ(yv15300), Zero) → False
new_esEs24(yv1532, yv1572, app(ty_Maybe, bdd)) → new_esEs14(yv1532, yv1572, bdd)
new_esEs19(yv1530, yv1570, app(app(ty_Either, fb), fc)) → new_esEs5(yv1530, yv1570, fb, fc)
new_esEs25(yv1531, yv1571, app(ty_Ratio, beg)) → new_esEs17(yv1531, yv1571, beg)
new_esEs25(yv1531, yv1571, ty_Double) → new_esEs9(yv1531, yv1571)
new_esEs15(GT, LT) → False
new_esEs15(LT, GT) → False
new_esEs24(yv1532, yv1572, app(app(app(ty_@3, bcg), bch), bda)) → new_esEs12(yv1532, yv1572, bcg, bch, bda)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs25(yv1531, yv1571, app(ty_[], bdh)) → new_esEs11(yv1531, yv1571, bdh)
new_esEs4(yv153, yv157, app(app(ty_Either, cg), bd)) → new_esEs5(yv153, yv157, cg, bd)
new_esEs24(yv1532, yv1572, ty_Bool) → new_esEs7(yv1532, yv1572)
new_esEs5(Right(yv1530), Right(yv1570), cg, ty_Double) → new_esEs9(yv1530, yv1570)
new_esEs15(LT, LT) → True
new_esEs14(Just(yv1530), Just(yv1570), app(app(ty_@2, bbb), bbc)) → new_esEs10(yv1530, yv1570, bbb, bbc)
new_esEs7(False, False) → True
new_esEs21(yv1530, yv1570, app(app(app(ty_@3, bac), bad), bae)) → new_esEs12(yv1530, yv1570, bac, bad, bae)
new_esEs4(yv153, yv157, app(ty_[], ec)) → new_esEs11(yv153, yv157, ec)
new_esEs26(yv1530, yv1570, app(ty_Ratio, bga)) → new_esEs17(yv1530, yv1570, bga)
new_esEs4(yv153, yv157, ty_Int) → new_esEs13(yv153, yv157)
new_esEs26(yv1530, yv1570, ty_Ordering) → new_esEs15(yv1530, yv1570)
new_esEs25(yv1531, yv1571, ty_Integer) → new_esEs16(yv1531, yv1571)
new_esEs6(Float(yv1530, yv1531), Float(yv1570, yv1571)) → new_esEs13(new_sr(yv1530, yv1570), new_sr(yv1531, yv1571))
new_esEs14(Just(yv1530), Just(yv1570), app(ty_Ratio, bcc)) → new_esEs17(yv1530, yv1570, bcc)
new_esEs25(yv1531, yv1571, ty_Bool) → new_esEs7(yv1531, yv1571)
new_esEs15(EQ, LT) → False
new_esEs15(LT, EQ) → False
new_esEs20(yv1531, yv1571, app(ty_Ratio, hg)) → new_esEs17(yv1531, yv1571, hg)
new_esEs26(yv1530, yv1570, ty_Char) → new_esEs8(yv1530, yv1570)
new_esEs24(yv1532, yv1572, app(ty_[], bcf)) → new_esEs11(yv1532, yv1572, bcf)
new_esEs4(yv153, yv157, app(ty_Ratio, ge)) → new_esEs17(yv153, yv157, ge)
new_esEs23(yv1530, yv1570, ty_Int) → new_esEs13(yv1530, yv1570)
new_esEs16(Integer(yv1530), Integer(yv1570)) → new_primEqInt(yv1530, yv1570)
new_esEs24(yv1532, yv1572, ty_Char) → new_esEs8(yv1532, yv1572)
new_esEs19(yv1530, yv1570, ty_Ordering) → new_esEs15(yv1530, yv1570)
new_esEs15(GT, EQ) → False
new_esEs15(EQ, GT) → False
new_esEs25(yv1531, yv1571, app(app(ty_Either, bed), bee)) → new_esEs5(yv1531, yv1571, bed, bee)
new_esEs4(yv153, yv157, ty_Integer) → new_esEs16(yv153, yv157)
new_esEs26(yv1530, yv1570, ty_Bool) → new_esEs7(yv1530, yv1570)
new_esEs21(yv1530, yv1570, ty_Double) → new_esEs9(yv1530, yv1570)
new_esEs25(yv1531, yv1571, ty_Float) → new_esEs6(yv1531, yv1571)
new_sr(Neg(yv15310), Neg(yv15710)) → Pos(new_primMulNat0(yv15310, yv15710))
new_esEs4(yv153, yv157, ty_@0) → new_esEs18(yv153, yv157)
new_esEs14(Nothing, Nothing, gd) → True
new_esEs5(Left(yv1530), Left(yv1570), ty_Int, bd) → new_esEs13(yv1530, yv1570)
new_sr(Pos(yv15310), Pos(yv15710)) → Pos(new_primMulNat0(yv15310, yv15710))
new_asAs(False, yv184) → False
new_primEqNat0(Zero, Zero) → True
new_esEs26(yv1530, yv1570, ty_Double) → new_esEs9(yv1530, yv1570)
new_primMulNat0(Zero, Succ(yv157100)) → Zero
new_primMulNat0(Succ(yv153100), Zero) → Zero
new_esEs21(yv1530, yv1570, app(app(ty_Either, baf), bag)) → new_esEs5(yv1530, yv1570, baf, bag)
new_esEs14(Just(yv1530), Just(yv1570), ty_Ordering) → new_esEs15(yv1530, yv1570)
new_esEs4(yv153, yv157, ty_Bool) → new_esEs7(yv153, yv157)
new_esEs19(yv1530, yv1570, app(ty_[], ef)) → new_esEs11(yv1530, yv1570, ef)
new_esEs5(Right(yv1530), Right(yv1570), cg, app(ty_Ratio, eb)) → new_esEs17(yv1530, yv1570, eb)
new_esEs24(yv1532, yv1572, app(ty_Ratio, bde)) → new_esEs17(yv1532, yv1572, bde)
new_esEs24(yv1532, yv1572, ty_Ordering) → new_esEs15(yv1532, yv1572)
new_esEs14(Just(yv1530), Just(yv1570), ty_Char) → new_esEs8(yv1530, yv1570)
new_esEs4(yv153, yv157, app(app(app(ty_@3, ga), gb), gc)) → new_esEs12(yv153, yv157, ga, gb, gc)
new_esEs19(yv1530, yv1570, ty_Double) → new_esEs9(yv1530, yv1570)
new_esEs5(Right(yv1530), Right(yv1570), cg, ty_Char) → new_esEs8(yv1530, yv1570)
new_esEs4(yv153, yv157, ty_Double) → new_esEs9(yv153, yv157)
new_esEs25(yv1531, yv1571, ty_Int) → new_esEs13(yv1531, yv1571)
new_esEs26(yv1530, yv1570, ty_@0) → new_esEs18(yv1530, yv1570)
new_esEs5(Left(yv1530), Left(yv1570), ty_Bool, bd) → new_esEs7(yv1530, yv1570)
new_esEs26(yv1530, yv1570, app(app(ty_@2, beh), bfa)) → new_esEs10(yv1530, yv1570, beh, bfa)
new_esEs14(Just(yv1530), Just(yv1570), app(ty_Maybe, bcb)) → new_esEs14(yv1530, yv1570, bcb)
new_esEs14(Just(yv1530), Just(yv1570), ty_Float) → new_esEs6(yv1530, yv1570)
new_esEs14(Just(yv1530), Just(yv1570), app(app(ty_Either, bbh), bca)) → new_esEs5(yv1530, yv1570, bbh, bca)
new_esEs21(yv1530, yv1570, ty_Int) → new_esEs13(yv1530, yv1570)
new_esEs5(Right(yv1530), Right(yv1570), cg, ty_Int) → new_esEs13(yv1530, yv1570)
new_esEs25(yv1531, yv1571, ty_@0) → new_esEs18(yv1531, yv1571)
new_esEs13(yv153, yv157) → new_primEqInt(yv153, yv157)
new_primPlusNat0(Succ(yv1850), yv157100) → Succ(Succ(new_primPlusNat1(yv1850, yv157100)))
new_esEs5(Right(yv1530), Right(yv1570), cg, app(ty_Maybe, ea)) → new_esEs14(yv1530, yv1570, ea)
new_esEs19(yv1530, yv1570, app(ty_Ratio, ff)) → new_esEs17(yv1530, yv1570, ff)
new_esEs5(Right(yv1530), Right(yv1570), cg, app(ty_[], dc)) → new_esEs11(yv1530, yv1570, dc)
new_esEs19(yv1530, yv1570, ty_Integer) → new_esEs16(yv1530, yv1570)
new_esEs14(Just(yv1530), Nothing, gd) → False
new_esEs14(Nothing, Just(yv1570), gd) → False
new_primEqInt(Neg(Succ(yv15300)), Neg(Succ(yv15700))) → new_primEqNat0(yv15300, yv15700)
new_esEs5(Left(yv1530), Left(yv1570), ty_Integer, bd) → new_esEs16(yv1530, yv1570)
new_esEs14(Just(yv1530), Just(yv1570), ty_Double) → new_esEs9(yv1530, yv1570)
new_primPlusNat1(Succ(yv18500), Zero) → Succ(yv18500)
new_primPlusNat1(Zero, Succ(yv1571000)) → Succ(yv1571000)
new_esEs24(yv1532, yv1572, ty_Float) → new_esEs6(yv1532, yv1572)
new_esEs7(True, True) → True
new_esEs5(Right(yv1530), Right(yv1570), cg, app(app(app(ty_@3, dd), de), df)) → new_esEs12(yv1530, yv1570, dd, de, df)
new_esEs4(yv153, yv157, ty_Char) → new_esEs8(yv153, yv157)
new_esEs21(yv1530, yv1570, ty_Char) → new_esEs8(yv1530, yv1570)
new_esEs20(yv1531, yv1571, ty_Bool) → new_esEs7(yv1531, yv1571)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs5(Left(yv1530), Left(yv1570), app(app(ty_Either, cc), cd), bd) → new_esEs5(yv1530, yv1570, cc, cd)
new_esEs5(Left(yv1530), Left(yv1570), app(app(app(ty_@3, bh), ca), cb), bd) → new_esEs12(yv1530, yv1570, bh, ca, cb)
new_esEs26(yv1530, yv1570, app(ty_Maybe, bfh)) → new_esEs14(yv1530, yv1570, bfh)
new_esEs21(yv1530, yv1570, app(ty_[], bab)) → new_esEs11(yv1530, yv1570, bab)
new_esEs5(Left(yv1530), Left(yv1570), ty_Double, bd) → new_esEs9(yv1530, yv1570)
new_esEs22(yv1531, yv1571, ty_Integer) → new_esEs16(yv1531, yv1571)
new_primEqInt(Neg(Succ(yv15300)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(yv15700))) → False
new_esEs20(yv1531, yv1571, ty_Float) → new_esEs6(yv1531, yv1571)
new_esEs24(yv1532, yv1572, ty_@0) → new_esEs18(yv1532, yv1572)
new_esEs21(yv1530, yv1570, ty_Ordering) → new_esEs15(yv1530, yv1570)
new_esEs7(False, True) → False
new_esEs7(True, False) → False
new_esEs23(yv1530, yv1570, ty_Integer) → new_esEs16(yv1530, yv1570)
new_esEs21(yv1530, yv1570, ty_Bool) → new_esEs7(yv1530, yv1570)
new_esEs20(yv1531, yv1571, ty_Integer) → new_esEs16(yv1531, yv1571)
new_primPlusNat1(Zero, Zero) → Zero
new_esEs5(Left(yv1530), Left(yv1570), app(ty_Maybe, ce), bd) → new_esEs14(yv1530, yv1570, ce)
new_esEs25(yv1531, yv1571, app(app(ty_@2, bdf), bdg)) → new_esEs10(yv1531, yv1571, bdf, bdg)
new_esEs21(yv1530, yv1570, app(ty_Ratio, bba)) → new_esEs17(yv1530, yv1570, bba)
new_asAs(True, yv184) → yv184
new_esEs20(yv1531, yv1571, ty_Double) → new_esEs9(yv1531, yv1571)
new_primMulNat0(Succ(yv153100), Succ(yv157100)) → new_primPlusNat0(new_primMulNat0(yv153100, Succ(yv157100)), yv157100)
new_esEs5(Left(yv1530), Left(yv1570), app(ty_[], bg), bd) → new_esEs11(yv1530, yv1570, bg)
new_esEs19(yv1530, yv1570, ty_@0) → new_esEs18(yv1530, yv1570)
new_esEs24(yv1532, yv1572, app(app(ty_@2, bcd), bce)) → new_esEs10(yv1532, yv1572, bcd, bce)
new_esEs25(yv1531, yv1571, app(app(app(ty_@3, bea), beb), bec)) → new_esEs12(yv1531, yv1571, bea, beb, bec)
new_esEs26(yv1530, yv1570, ty_Integer) → new_esEs16(yv1530, yv1570)
new_esEs11(:(yv1530, yv1531), :(yv1570, yv1571), ec) → new_asAs(new_esEs19(yv1530, yv1570, ec), new_esEs11(yv1531, yv1571, ec))
new_esEs5(Right(yv1530), Right(yv1570), cg, app(app(ty_@2, da), db)) → new_esEs10(yv1530, yv1570, da, db)
new_esEs19(yv1530, yv1570, app(app(ty_@2, ed), ee)) → new_esEs10(yv1530, yv1570, ed, ee)
new_primEqInt(Pos(Succ(yv15300)), Pos(Succ(yv15700))) → new_primEqNat0(yv15300, yv15700)
new_esEs5(Left(yv1530), Left(yv1570), app(app(ty_@2, be), bf), bd) → new_esEs10(yv1530, yv1570, be, bf)
new_esEs18(@0, @0) → True
new_esEs5(Right(yv1530), Right(yv1570), cg, app(app(ty_Either, dg), dh)) → new_esEs5(yv1530, yv1570, dg, dh)
new_esEs26(yv1530, yv1570, ty_Int) → new_esEs13(yv1530, yv1570)
new_esEs8(Char(yv1530), Char(yv1570)) → new_primEqNat0(yv1530, yv1570)
new_primEqNat0(Succ(yv15300), Succ(yv15700)) → new_primEqNat0(yv15300, yv15700)
new_esEs21(yv1530, yv1570, app(ty_Maybe, bah)) → new_esEs14(yv1530, yv1570, bah)
new_esEs15(GT, GT) → True
new_esEs20(yv1531, yv1571, ty_Ordering) → new_esEs15(yv1531, yv1571)
new_esEs4(yv153, yv157, app(ty_Maybe, gd)) → new_esEs14(yv153, yv157, gd)
new_esEs5(Right(yv1530), Right(yv1570), cg, ty_Float) → new_esEs6(yv1530, yv1570)
new_esEs22(yv1531, yv1571, ty_Int) → new_esEs13(yv1531, yv1571)
new_esEs20(yv1531, yv1571, ty_Char) → new_esEs8(yv1531, yv1571)
new_esEs26(yv1530, yv1570, app(ty_[], bfb)) → new_esEs11(yv1530, yv1570, bfb)
new_esEs25(yv1531, yv1571, ty_Ordering) → new_esEs15(yv1531, yv1571)
new_esEs19(yv1530, yv1570, ty_Float) → new_esEs6(yv1530, yv1570)
new_esEs20(yv1531, yv1571, ty_Int) → new_esEs13(yv1531, yv1571)
new_esEs14(Just(yv1530), Just(yv1570), app(app(app(ty_@3, bbe), bbf), bbg)) → new_esEs12(yv1530, yv1570, bbe, bbf, bbg)
new_esEs21(yv1530, yv1570, app(app(ty_@2, hh), baa)) → new_esEs10(yv1530, yv1570, hh, baa)
new_primEqInt(Pos(Succ(yv15300)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(yv15700))) → False
new_esEs19(yv1530, yv1570, ty_Char) → new_esEs8(yv1530, yv1570)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_esEs14(Just(yv1530), Just(yv1570), ty_Int) → new_esEs13(yv1530, yv1570)

The set Q consists of the following terms:

new_esEs20(x0, x1, app(ty_[], x2))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs14(Nothing, Nothing, x0)
new_asAs(True, x0)
new_esEs14(Nothing, Just(x0), x1)
new_esEs14(Just(x0), Just(x1), ty_Double)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs20(x0, x1, ty_Integer)
new_esEs19(x0, x1, ty_Double)
new_esEs5(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs18(@0, @0)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs5(Left(x0), Left(x1), ty_Bool, x2)
new_esEs14(Just(x0), Just(x1), ty_Bool)
new_esEs5(Left(x0), Left(x1), ty_Double, x2)
new_esEs4(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Float)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_primPlusNat0(Zero, x0)
new_esEs5(Left(x0), Left(x1), ty_Ordering, x2)
new_sr(Pos(x0), Pos(x1))
new_esEs5(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_sr(Neg(x0), Neg(x1))
new_esEs19(x0, x1, ty_Int)
new_esEs25(x0, x1, app(ty_[], x2))
new_esEs25(x0, x1, ty_Char)
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, ty_Double)
new_esEs24(x0, x1, ty_Int)
new_esEs4(x0, x1, ty_Ordering)
new_esEs5(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_primPlusNat1(Succ(x0), Zero)
new_esEs24(x0, x1, ty_Integer)
new_esEs7(False, False)
new_esEs24(x0, x1, ty_Double)
new_esEs20(x0, x1, ty_@0)
new_esEs14(Just(x0), Just(x1), ty_Char)
new_esEs4(x0, x1, app(ty_Ratio, x2))
new_esEs10(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs19(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs24(x0, x1, ty_Float)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Ordering)
new_esEs4(x0, x1, app(ty_[], x2))
new_esEs4(x0, x1, ty_Float)
new_esEs12(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs24(x0, x1, ty_@0)
new_esEs5(Right(x0), Right(x1), x2, ty_Double)
new_esEs4(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Right(x0), Right(x1), x2, ty_Char)
new_esEs20(x0, x1, ty_Bool)
new_esEs9(Double(x0, x1), Double(x2, x3))
new_esEs5(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_sr(Pos(x0), Neg(x1))
new_sr(Neg(x0), Pos(x1))
new_primMulNat0(Zero, Succ(x0))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs14(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, ty_Bool)
new_esEs4(x0, x1, ty_Integer)
new_esEs7(True, False)
new_esEs7(False, True)
new_esEs25(x0, x1, ty_Integer)
new_esEs4(x0, x1, ty_Int)
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_esEs21(x0, x1, ty_Ordering)
new_esEs5(Right(x0), Right(x1), x2, ty_Int)
new_esEs14(Just(x0), Nothing, x1)
new_esEs26(x0, x1, ty_Int)
new_esEs14(Just(x0), Just(x1), ty_@0)
new_esEs24(x0, x1, ty_Char)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_@0)
new_esEs14(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_@0)
new_esEs4(x0, x1, ty_Double)
new_esEs4(x0, x1, ty_Char)
new_esEs11(:(x0, x1), :(x2, x3), x4)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Double)
new_esEs5(Left(x0), Right(x1), x2, x3)
new_esEs5(Right(x0), Left(x1), x2, x3)
new_esEs8(Char(x0), Char(x1))
new_esEs11([], :(x0, x1), x2)
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Right(x0), Right(x1), x2, ty_@0)
new_primEqNat0(Succ(x0), Succ(x1))
new_esEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs19(x0, x1, ty_Bool)
new_esEs22(x0, x1, ty_Integer)
new_esEs21(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Ordering)
new_esEs16(Integer(x0), Integer(x1))
new_esEs5(Left(x0), Left(x1), ty_Int, x2)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs20(x0, x1, ty_Ordering)
new_esEs14(Just(x0), Just(x1), ty_Int)
new_esEs4(x0, x1, ty_Bool)
new_primEqNat0(Succ(x0), Zero)
new_primEqNat0(Zero, Zero)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, ty_Int)
new_esEs4(x0, x1, ty_@0)
new_esEs14(Just(x0), Just(x1), ty_Integer)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs15(GT, GT)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs14(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_primPlusNat1(Succ(x0), Succ(x1))
new_esEs23(x0, x1, ty_Int)
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs15(GT, LT)
new_esEs15(LT, GT)
new_esEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primMulNat0(Zero, Zero)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs4(x0, x1, app(app(ty_@2, x2), x3))
new_esEs24(x0, x1, ty_Bool)
new_esEs5(Left(x0), Left(x1), ty_Char, x2)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs11([], [], x0)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, ty_Char)
new_primPlusNat1(Zero, Succ(x0))
new_esEs5(Right(x0), Right(x1), x2, ty_Bool)
new_esEs5(Left(x0), Left(x1), ty_@0, x2)
new_esEs20(x0, x1, ty_Float)
new_esEs26(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs21(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Int)
new_esEs19(x0, x1, ty_Char)
new_esEs5(Left(x0), Left(x1), ty_Integer, x2)
new_esEs7(True, True)
new_esEs26(x0, x1, ty_Char)
new_esEs14(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs15(EQ, EQ)
new_esEs5(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs23(x0, x1, ty_Integer)
new_esEs5(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs5(Right(x0), Right(x1), x2, ty_Float)
new_primMulNat0(Succ(x0), Zero)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs19(x0, x1, ty_Float)
new_esEs24(x0, x1, ty_Ordering)
new_esEs21(x0, x1, ty_Double)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs14(Just(x0), Just(x1), ty_Ordering)
new_esEs13(x0, x1)
new_esEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs14(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs19(x0, x1, ty_@0)
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs4(x0, x1, app(app(ty_Either, x2), x3))
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs19(x0, x1, app(ty_[], x2))
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs19(x0, x1, ty_Integer)
new_esEs5(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs21(x0, x1, ty_Char)
new_esEs21(x0, x1, ty_@0)
new_primEqNat0(Zero, Succ(x0))
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primPlusNat1(Zero, Zero)
new_esEs21(x0, x1, ty_Integer)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_esEs14(Just(x0), Just(x1), ty_Float)
new_esEs25(x0, x1, ty_Double)
new_esEs26(x0, x1, ty_Float)
new_esEs19(x0, x1, ty_Ordering)
new_esEs21(x0, x1, ty_Float)
new_esEs15(EQ, LT)
new_esEs15(LT, EQ)
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs11(:(x0, x1), [], x2)
new_esEs17(:%(x0, x1), :%(x2, x3), x4)
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs5(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs14(Just(x0), Just(x1), app(ty_[], x2))
new_esEs6(Float(x0, x1), Float(x2, x3))
new_esEs5(Left(x0), Left(x1), ty_Float, x2)
new_esEs20(x0, x1, ty_Int)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Right(x0), Right(x1), x2, ty_Integer)
new_primPlusNat0(Succ(x0), x1)
new_esEs26(x0, x1, ty_Bool)
new_esEs15(LT, LT)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_esEs19(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_asAs(False, x0)
new_esEs15(GT, EQ)
new_esEs15(EQ, GT)

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

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