YES 3.615 H-Termination proof of /home/matraf/haskell/eval_FullyBlown_Fast/empty.hs
H-Termination of the given Haskell-Program with start terms could successfully be proven:



↳ HASKELL
  ↳ CR

mainModule Main
  (((<) :: Ord a => Maybe a  ->  Maybe a  ->  Bool) :: Ord a => Maybe a  ->  Maybe a  ->  Bool)

module Main where
  import qualified Prelude


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

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



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ IFR

mainModule Main
  (((<) :: Ord a => Maybe a  ->  Maybe a  ->  Bool) :: Ord a => Maybe a  ->  Maybe a  ->  Bool)

module Main where
  import qualified Prelude


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

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

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

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



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

mainModule Main
  (((<) :: Ord a => Maybe a  ->  Maybe a  ->  Bool) :: Ord a => Maybe a  ->  Maybe a  ->  Bool)

module Main where
  import qualified Prelude


Replaced joker patterns by fresh variables and removed binding patterns.

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

mainModule Main
  (((<) :: Ord a => Maybe a  ->  Maybe a  ->  Bool) :: Ord a => Maybe a  ->  Maybe a  ->  Bool)

module Main where
  import qualified Prelude


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

is transformed to
compare x y = compare3 x y

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

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

compare0 x y True = GT

compare3 x y = compare2 x y (x == y)

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

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

gcd'0 x y = gcd' y (x `rem` y)

gcd'1 True x zx = x
gcd'1 zy zz vuu = gcd'0 zz vuu

gcd'2 x zx = gcd'1 (zx == 0) x zx
gcd'2 vuv vuw = gcd'0 vuv vuw

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

is transformed to
gcd vux vuy = gcd3 vux vuy
gcd x y = gcd0 x y

gcd0 x y = 
gcd' (abs x) (abs y)
where 
gcd' x zx = gcd'2 x zx
gcd' x y = gcd'0 x y
gcd'0 x y = gcd' y (x `rem` y)
gcd'1 True x zx = x
gcd'1 zy zz vuu = gcd'0 zz vuu
gcd'2 x zx = gcd'1 (zx == 0) x zx
gcd'2 vuv vuw = gcd'0 vuv vuw

gcd1 True vux vuy = error []
gcd1 vuz vvu vvv = gcd0 vvu vvv

gcd2 True vux vuy = gcd1 (vuy == 0) vux vuy
gcd2 vvw vvx vvy = gcd0 vvx vvy

gcd3 vux vuy = gcd2 (vux == 0) vux vuy
gcd3 vvz vwu = gcd0 vvz vwu

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

is transformed to
absReal x = absReal2 x

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

absReal0 x True = `negate` x

absReal2 x = absReal1 x (x >= 0)

The following Function with conditions
undefined 
 | False
 = undefined

is transformed to
undefined  = undefined1

undefined0 True = undefined

undefined1  = undefined0 False

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

is transformed to
reduce x y = reduce2 x y

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



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

mainModule Main
  (((<) :: Ord a => Maybe a  ->  Maybe a  ->  Bool) :: Ord a => Maybe a  ->  Maybe a  ->  Bool)

module Main where
  import qualified Prelude


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

are unpacked to the following functions on top level
reduce2D vwv vww = gcd vwv vww

reduce2Reduce0 vwv vww x y True = x `quot` reduce2D vwv vww :% (y `quot` reduce2D vwv vww)

reduce2Reduce1 vwv vww x y True = error []
reduce2Reduce1 vwv vww x y False = reduce2Reduce0 vwv vww x y otherwise

The bindings of the following Let/Where expression
gcd' (abs x) (abs y)
where 
gcd' x zx = gcd'2 x zx
gcd' x y = gcd'0 x y
gcd'0 x y = gcd' y (x `rem` y)
gcd'1 True x zx = x
gcd'1 zy zz vuu = gcd'0 zz vuu
gcd'2 x zx = gcd'1 (zx == 0) x zx
gcd'2 vuv vuw = gcd'0 vuv vuw

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

gcd0Gcd'1 True x zx = x
gcd0Gcd'1 zy zz vuu = gcd0Gcd'0 zz vuu

gcd0Gcd'2 x zx = gcd0Gcd'1 (zx == 0) x zx
gcd0Gcd'2 vuv vuw = gcd0Gcd'0 vuv vuw

gcd0Gcd' x zx = gcd0Gcd'2 x zx
gcd0Gcd' x y = gcd0Gcd'0 x y



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

mainModule Main
  (((<) :: Ord a => Maybe a  ->  Maybe a  ->  Bool) :: Ord a => Maybe a  ->  Maybe a  ->  Bool)

module Main where
  import qualified Prelude


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

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

mainModule Main
  ((<) :: Ord a => Maybe a  ->  Maybe a  ->  Bool)

module Main where
  import qualified Prelude


Haskell To QDPs


↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ IFR
        ↳ HASKELL
          ↳ BR
            ↳ HASKELL
              ↳ COR
                ↳ HASKELL
                  ↳ LetRed
                    ↳ 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(vwx4500), Succ(vwx400000)) → new_primPlusNat(vwx4500, vwx400000)

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

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



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ IFR
        ↳ HASKELL
          ↳ BR
            ↳ HASKELL
              ↳ COR
                ↳ HASKELL
                  ↳ LetRed
                    ↳ 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(vwx30000), Succ(vwx40000)) → new_primMulNat(vwx30000, Succ(vwx40000))

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

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



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ IFR
        ↳ HASKELL
          ↳ BR
            ↳ HASKELL
              ↳ COR
                ↳ HASKELL
                  ↳ LetRed
                    ↳ 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(vwx3000), Succ(vwx4000)) → new_primEqNat(vwx3000, vwx4000)

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

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



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

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

new_primCmpNat(Succ(vwx900), Succ(vwx1000)) → new_primCmpNat(vwx900, vwx1000)

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

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



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

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

new_esEs(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), cd, app(ty_[], da), be) → new_esEs0(vwx301, vwx401, da)
new_esEs2(Just(vwx300), Just(vwx400), app(app(app(ty_@3, bag), bah), bba)) → new_esEs(vwx300, vwx400, bag, bah, bba)
new_esEs(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), cd, app(app(ty_@2, db), dc), be) → new_esEs1(vwx301, vwx401, db, dc)
new_esEs(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), app(app(ty_Either, cb), cc), bd, be) → new_esEs3(vwx300, vwx400, cb, cc)
new_esEs(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), app(ty_Maybe, ca), bd, be) → new_esEs2(vwx300, vwx400, ca)
new_esEs(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), cd, bd, app(ty_Maybe, ee)) → new_esEs2(vwx302, vwx402, ee)
new_esEs(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), cd, bd, app(ty_[], eb)) → new_esEs0(vwx302, vwx402, eb)
new_esEs1(@2(vwx300, vwx301), @2(vwx400, vwx401), app(ty_[], gg), gf) → new_esEs0(vwx300, vwx400, gg)
new_esEs3(Right(vwx300), Right(vwx400), bdb, app(app(ty_Either, beb), bec)) → new_esEs3(vwx300, vwx400, beb, bec)
new_esEs(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), cd, app(ty_Maybe, dd), be) → new_esEs2(vwx301, vwx401, dd)
new_esEs0(:(vwx300, vwx301), :(vwx400, vwx401), app(app(app(ty_@3, eh), fa), fb)) → new_esEs(vwx300, vwx400, eh, fa, fb)
new_esEs(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), app(app(app(ty_@3, ba), bb), bc), bd, be) → new_esEs(vwx300, vwx400, ba, bb, bc)
new_esEs2(Just(vwx300), Just(vwx400), app(ty_Maybe, bbe)) → new_esEs2(vwx300, vwx400, bbe)
new_esEs1(@2(vwx300, vwx301), @2(vwx400, vwx401), he, app(ty_[], baa)) → new_esEs0(vwx301, vwx401, baa)
new_esEs3(Left(vwx300), Left(vwx400), app(app(ty_Either, bch), bda), bcc) → new_esEs3(vwx300, vwx400, bch, bda)
new_esEs(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), cd, bd, app(app(ty_@2, ec), ed)) → new_esEs1(vwx302, vwx402, ec, ed)
new_esEs2(Just(vwx300), Just(vwx400), app(app(ty_@2, bbc), bbd)) → new_esEs1(vwx300, vwx400, bbc, bbd)
new_esEs0(:(vwx300, vwx301), :(vwx400, vwx401), app(app(ty_Either, fh), ga)) → new_esEs3(vwx300, vwx400, fh, ga)
new_esEs1(@2(vwx300, vwx301), @2(vwx400, vwx401), app(ty_Maybe, hb), gf) → new_esEs2(vwx300, vwx400, hb)
new_esEs1(@2(vwx300, vwx301), @2(vwx400, vwx401), he, app(app(ty_Either, bae), baf)) → new_esEs3(vwx301, vwx401, bae, baf)
new_esEs1(@2(vwx300, vwx301), @2(vwx400, vwx401), he, app(app(ty_@2, bab), bac)) → new_esEs1(vwx301, vwx401, bab, bac)
new_esEs3(Right(vwx300), Right(vwx400), bdb, app(app(app(ty_@3, bdc), bdd), bde)) → new_esEs(vwx300, vwx400, bdc, bdd, bde)
new_esEs3(Left(vwx300), Left(vwx400), app(ty_Maybe, bcg), bcc) → new_esEs2(vwx300, vwx400, bcg)
new_esEs3(Left(vwx300), Left(vwx400), app(ty_[], bcd), bcc) → new_esEs0(vwx300, vwx400, bcd)
new_esEs0(:(vwx300, vwx301), :(vwx400, vwx401), app(app(ty_@2, fd), ff)) → new_esEs1(vwx300, vwx400, fd, ff)
new_esEs3(Left(vwx300), Left(vwx400), app(app(ty_@2, bce), bcf), bcc) → new_esEs1(vwx300, vwx400, bce, bcf)
new_esEs3(Right(vwx300), Right(vwx400), bdb, app(ty_[], bdf)) → new_esEs0(vwx300, vwx400, bdf)
new_esEs(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), cd, app(app(app(ty_@3, ce), cf), cg), be) → new_esEs(vwx301, vwx401, ce, cf, cg)
new_esEs2(Just(vwx300), Just(vwx400), app(ty_[], bbb)) → new_esEs0(vwx300, vwx400, bbb)
new_esEs1(@2(vwx300, vwx301), @2(vwx400, vwx401), app(app(ty_@2, gh), ha), gf) → new_esEs1(vwx300, vwx400, gh, ha)
new_esEs0(:(vwx300, vwx301), :(vwx400, vwx401), app(ty_Maybe, fg)) → new_esEs2(vwx300, vwx400, fg)
new_esEs(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), app(ty_[], bf), bd, be) → new_esEs0(vwx300, vwx400, bf)
new_esEs1(@2(vwx300, vwx301), @2(vwx400, vwx401), app(app(ty_Either, hc), hd), gf) → new_esEs3(vwx300, vwx400, hc, hd)
new_esEs3(Right(vwx300), Right(vwx400), bdb, app(ty_Maybe, bea)) → new_esEs2(vwx300, vwx400, bea)
new_esEs0(:(vwx300, vwx301), :(vwx400, vwx401), app(ty_[], fc)) → new_esEs0(vwx300, vwx400, fc)
new_esEs1(@2(vwx300, vwx301), @2(vwx400, vwx401), he, app(app(app(ty_@3, hf), hg), hh)) → new_esEs(vwx301, vwx401, hf, hg, hh)
new_esEs1(@2(vwx300, vwx301), @2(vwx400, vwx401), he, app(ty_Maybe, bad)) → new_esEs2(vwx301, vwx401, bad)
new_esEs(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), app(app(ty_@2, bg), bh), bd, be) → new_esEs1(vwx300, vwx400, bg, bh)
new_esEs(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), cd, app(app(ty_Either, de), df), be) → new_esEs3(vwx301, vwx401, de, df)
new_esEs3(Right(vwx300), Right(vwx400), bdb, app(app(ty_@2, bdg), bdh)) → new_esEs1(vwx300, vwx400, bdg, bdh)
new_esEs2(Just(vwx300), Just(vwx400), app(app(ty_Either, bbf), bbg)) → new_esEs3(vwx300, vwx400, bbf, bbg)
new_esEs1(@2(vwx300, vwx301), @2(vwx400, vwx401), app(app(app(ty_@3, gc), gd), ge), gf) → new_esEs(vwx300, vwx400, gc, gd, ge)
new_esEs3(Left(vwx300), Left(vwx400), app(app(app(ty_@3, bbh), bca), bcb), bcc) → new_esEs(vwx300, vwx400, bbh, bca, bcb)
new_esEs0(:(vwx300, vwx301), :(vwx400, vwx401), gb) → new_esEs0(vwx301, vwx401, gb)
new_esEs(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), cd, bd, app(app(ty_Either, ef), eg)) → new_esEs3(vwx302, vwx402, ef, eg)
new_esEs(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), cd, bd, app(app(app(ty_@3, dg), dh), ea)) → new_esEs(vwx302, vwx402, dg, dh, ea)

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

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



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

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

new_esEs4(Right(vwx90), Right(vwx100), False, app(app(ty_Either, cc), app(ty_[], cf))) → new_ltEs0(vwx90, vwx100, cf)
new_ltEs(Right(vwx90), Right(vwx100), cc, app(ty_Maybe, dc)) → new_ltEs2(vwx90, vwx100, dc)
new_ltEs1(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), fb, app(app(app(ty_@3, fg), fh), ga), eb) → new_lt2(vwx91, vwx101, fg, fh, ga)
new_ltEs(Right(vwx90), Right(vwx100), cc, app(app(ty_Either, cd), ce)) → new_ltEs(vwx90, vwx100, cd, ce)
new_compare0(:(vwx90, vwx91), :(vwx100, vwx101), df) → new_compare0(vwx91, vwx101, df)
new_ltEs3(@2(vwx90, vwx91), @2(vwx100, vwx101), bca, app(app(app(ty_@3, bce), bcf), bcg)) → new_ltEs1(vwx91, vwx101, bce, bcf, bcg)
new_esEs4(:(vwx90, vwx91), :(vwx100, vwx101), False, app(ty_[], df)) → new_primCompAux(vwx90, vwx100, new_compare(vwx91, vwx101, df), df)
new_compare21(vwx90, vwx100, False, eh, fa) → new_ltEs3(vwx90, vwx100, eh, fa)
new_lt0(vwx90, vwx100, dg, dh) → new_compare2(vwx90, vwx100, new_esEs5(vwx90, vwx100, dg, dh), dg, dh)
new_esEs4(Left(vwx90), Left(vwx100), False, app(app(ty_Either, app(app(ty_Either, ba), bb)), bc)) → new_ltEs(vwx90, vwx100, ba, bb)
new_esEs4(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), False, app(app(app(ty_@3, fb), ea), app(ty_[], gg))) → new_ltEs0(vwx92, vwx102, gg)
new_esEs4(Right(vwx90), Right(vwx100), False, app(app(ty_Either, cc), app(app(ty_@2, dd), de))) → new_ltEs3(vwx90, vwx100, dd, de)
new_ltEs(Left(vwx90), Left(vwx100), app(app(ty_@2, ca), cb), bc) → new_ltEs3(vwx90, vwx100, ca, cb)
new_esEs4(Just(vwx90), Just(vwx100), False, app(ty_Maybe, app(app(ty_@2, bae), baf))) → new_ltEs3(vwx90, vwx100, bae, baf)
new_ltEs(Right(vwx90), Right(vwx100), cc, app(app(app(ty_@3, cg), da), db)) → new_ltEs1(vwx90, vwx100, cg, da, db)
new_esEs4(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), False, app(app(app(ty_@3, app(app(ty_Either, dg), dh)), ea), eb)) → new_compare2(vwx90, vwx100, new_esEs5(vwx90, vwx100, dg, dh), dg, dh)
new_esEs4(@2(vwx90, vwx91), @2(vwx100, vwx101), False, app(app(ty_@2, bca), app(app(app(ty_@3, bce), bcf), bcg))) → new_ltEs1(vwx91, vwx101, bce, bcf, bcg)
new_ltEs3(@2(vwx90, vwx91), @2(vwx100, vwx101), bca, app(app(ty_@2, bda), bdb)) → new_ltEs3(vwx91, vwx101, bda, bdb)
new_esEs4(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), False, app(app(app(ty_@3, fb), ea), app(app(ty_Either, ge), gf))) → new_ltEs(vwx92, vwx102, ge, gf)
new_esEs4(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), False, app(app(app(ty_@3, app(ty_[], ec)), ea), eb)) → new_compare0(vwx90, vwx100, ec)
new_esEs4(Just(vwx90), Just(vwx100), False, app(ty_Maybe, app(app(app(ty_@3, baa), bab), bac))) → new_ltEs1(vwx90, vwx100, baa, bab, bac)
new_ltEs(Right(vwx90), Right(vwx100), cc, app(app(ty_@2, dd), de)) → new_ltEs3(vwx90, vwx100, dd, de)
new_esEs4(Right(vwx90), Right(vwx100), False, app(app(ty_Either, cc), app(app(app(ty_@3, cg), da), db))) → new_ltEs1(vwx90, vwx100, cg, da, db)
new_ltEs3(@2(vwx90, vwx91), @2(vwx100, vwx101), bca, app(app(ty_Either, bcb), bcc)) → new_ltEs(vwx91, vwx101, bcb, bcc)
new_ltEs3(@2(vwx90, vwx91), @2(vwx100, vwx101), app(app(ty_@2, bbg), bbh), bba) → new_lt3(vwx90, vwx100, bbg, bbh)
new_ltEs1(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), fb, app(ty_Maybe, gb), eb) → new_lt(vwx91, vwx101, gb)
new_ltEs2(Just(vwx90), Just(vwx100), app(app(ty_@2, bae), baf)) → new_ltEs3(vwx90, vwx100, bae, baf)
new_esEs4(@2(vwx90, vwx91), @2(vwx100, vwx101), False, app(app(ty_@2, bca), app(ty_[], bcd))) → new_ltEs0(vwx91, vwx101, bcd)
new_esEs4(Just(vwx90), Just(vwx100), False, app(ty_Maybe, app(ty_Maybe, bad))) → new_ltEs2(vwx90, vwx100, bad)
new_lt(Just(vwx30), Just(vwx40), bed) → new_esEs4(vwx30, vwx40, new_esEs9(vwx30, vwx40, bed), bed)
new_esEs4(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), False, app(app(app(ty_@3, app(app(app(ty_@3, ed), ee), ef)), ea), eb)) → new_compare20(vwx90, vwx100, new_esEs6(vwx90, vwx100, ed, ee, ef), ed, ee, ef)
new_primCompAux(vwx90, vwx100, vwx71, app(app(app(ty_@3, bdf), bdg), bdh)) → new_compare3(vwx90, vwx100, bdf, bdg, bdh)
new_ltEs1(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), app(ty_[], ec), ea, eb) → new_compare0(vwx90, vwx100, ec)
new_ltEs1(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), fb, ea, app(app(app(ty_@3, gh), ha), hb)) → new_ltEs1(vwx92, vwx102, gh, ha, hb)
new_ltEs(Left(vwx90), Left(vwx100), app(app(app(ty_@3, be), bf), bg), bc) → new_ltEs1(vwx90, vwx100, be, bf, bg)
new_esEs4(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), False, app(app(app(ty_@3, fb), app(ty_Maybe, gb)), eb)) → new_lt(vwx91, vwx101, gb)
new_esEs4(@2(vwx90, vwx91), @2(vwx100, vwx101), False, app(app(ty_@2, app(app(ty_Either, bag), bah)), bba)) → new_lt0(vwx90, vwx100, bag, bah)
new_ltEs2(Just(vwx90), Just(vwx100), app(ty_[], hh)) → new_ltEs0(vwx90, vwx100, hh)
new_lt2(vwx90, vwx100, ed, ee, ef) → new_compare20(vwx90, vwx100, new_esEs6(vwx90, vwx100, ed, ee, ef), ed, ee, ef)
new_esEs4(@2(vwx90, vwx91), @2(vwx100, vwx101), False, app(app(ty_@2, app(app(ty_@2, bbg), bbh)), bba)) → new_lt3(vwx90, vwx100, bbg, bbh)
new_ltEs1(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), fb, ea, app(app(ty_Either, ge), gf)) → new_ltEs(vwx92, vwx102, ge, gf)
new_esEs4(Right(vwx90), Right(vwx100), False, app(app(ty_Either, cc), app(app(ty_Either, cd), ce))) → new_ltEs(vwx90, vwx100, cd, ce)
new_esEs4(@2(vwx90, vwx91), @2(vwx100, vwx101), False, app(app(ty_@2, bca), app(ty_Maybe, bch))) → new_ltEs2(vwx91, vwx101, bch)
new_ltEs3(@2(vwx90, vwx91), @2(vwx100, vwx101), app(ty_[], bbb), bba) → new_lt1(vwx90, vwx100, bbb)
new_ltEs1(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), app(app(ty_Either, dg), dh), ea, eb) → new_compare2(vwx90, vwx100, new_esEs5(vwx90, vwx100, dg, dh), dg, dh)
new_ltEs(Left(vwx90), Left(vwx100), app(ty_Maybe, bh), bc) → new_ltEs2(vwx90, vwx100, bh)
new_ltEs1(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), fb, app(app(ty_Either, fc), fd), eb) → new_lt0(vwx91, vwx101, fc, fd)
new_esEs4(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), False, app(app(app(ty_@3, fb), ea), app(app(app(ty_@3, gh), ha), hb))) → new_ltEs1(vwx92, vwx102, gh, ha, hb)
new_esEs4(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), False, app(app(app(ty_@3, fb), app(ty_[], ff)), eb)) → new_lt1(vwx91, vwx101, ff)
new_compare0(:(vwx90, vwx91), :(vwx100, vwx101), df) → new_primCompAux(vwx90, vwx100, new_compare(vwx91, vwx101, df), df)
new_compare2(vwx90, vwx100, False, dg, dh) → new_ltEs(vwx90, vwx100, dg, dh)
new_esEs4(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), False, app(app(app(ty_@3, app(ty_Maybe, eg)), ea), eb)) → new_lt(vwx90, vwx100, eg)
new_ltEs1(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), fb, ea, app(app(ty_@2, hd), he)) → new_ltEs3(vwx92, vwx102, hd, he)
new_ltEs0(:(vwx90, vwx91), :(vwx100, vwx101), df) → new_primCompAux(vwx90, vwx100, new_compare(vwx91, vwx101, df), df)
new_ltEs1(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), app(app(app(ty_@3, ed), ee), ef), ea, eb) → new_compare20(vwx90, vwx100, new_esEs6(vwx90, vwx100, ed, ee, ef), ed, ee, ef)
new_ltEs(Left(vwx90), Left(vwx100), app(app(ty_Either, ba), bb), bc) → new_ltEs(vwx90, vwx100, ba, bb)
new_esEs4(Left(vwx90), Left(vwx100), False, app(app(ty_Either, app(ty_[], bd)), bc)) → new_ltEs0(vwx90, vwx100, bd)
new_ltEs1(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), fb, ea, app(ty_Maybe, hc)) → new_ltEs2(vwx92, vwx102, hc)
new_compare3(vwx90, vwx100, ed, ee, ef) → new_compare20(vwx90, vwx100, new_esEs6(vwx90, vwx100, ed, ee, ef), ed, ee, ef)
new_esEs4(Right(vwx90), Right(vwx100), False, app(app(ty_Either, cc), app(ty_Maybe, dc))) → new_ltEs2(vwx90, vwx100, dc)
new_ltEs1(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), app(ty_Maybe, eg), ea, eb) → new_lt(vwx90, vwx100, eg)
new_ltEs1(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), fb, app(app(ty_@2, gc), gd), eb) → new_lt3(vwx91, vwx101, gc, gd)
new_ltEs(Right(vwx90), Right(vwx100), cc, app(ty_[], cf)) → new_ltEs0(vwx90, vwx100, cf)
new_compare1(vwx90, vwx100, dg, dh) → new_compare2(vwx90, vwx100, new_esEs5(vwx90, vwx100, dg, dh), dg, dh)
new_esEs4(@2(vwx90, vwx91), @2(vwx100, vwx101), False, app(app(ty_@2, app(ty_[], bbb)), bba)) → new_lt1(vwx90, vwx100, bbb)
new_ltEs3(@2(vwx90, vwx91), @2(vwx100, vwx101), app(app(ty_Either, bag), bah), bba) → new_lt0(vwx90, vwx100, bag, bah)
new_ltEs2(Just(vwx90), Just(vwx100), app(app(ty_Either, hf), hg)) → new_ltEs(vwx90, vwx100, hf, hg)
new_esEs4(Just(vwx90), Just(vwx100), False, app(ty_Maybe, app(app(ty_Either, hf), hg))) → new_ltEs(vwx90, vwx100, hf, hg)
new_primCompAux(vwx90, vwx100, vwx71, app(ty_[], bde)) → new_compare0(vwx90, vwx100, bde)
new_ltEs2(Just(vwx90), Just(vwx100), app(app(app(ty_@3, baa), bab), bac)) → new_ltEs1(vwx90, vwx100, baa, bab, bac)
new_esEs4(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), False, app(app(app(ty_@3, fb), ea), app(ty_Maybe, hc))) → new_ltEs2(vwx92, vwx102, hc)
new_primCompAux(vwx90, vwx100, vwx71, app(ty_Maybe, bea)) → new_compare22(vwx90, vwx100, new_esEs8(vwx90, vwx100, bea), bea)
new_primCompAux(vwx90, vwx100, vwx71, app(app(ty_Either, bdc), bdd)) → new_compare1(vwx90, vwx100, bdc, bdd)
new_esEs4(Left(vwx90), Left(vwx100), False, app(app(ty_Either, app(app(ty_@2, ca), cb)), bc)) → new_ltEs3(vwx90, vwx100, ca, cb)
new_esEs4(Just(vwx90), Just(vwx100), False, app(ty_Maybe, app(ty_[], hh))) → new_ltEs0(vwx90, vwx100, hh)
new_ltEs(Left(vwx90), Left(vwx100), app(ty_[], bd), bc) → new_ltEs0(vwx90, vwx100, bd)
new_lt1(vwx90, vwx100, ec) → new_compare0(vwx90, vwx100, ec)
new_compare4(vwx90, vwx100, eh, fa) → new_compare21(vwx90, vwx100, new_esEs7(vwx90, vwx100, eh, fa), eh, fa)
new_compare22(vwx90, vwx100, False, bea) → new_ltEs2(vwx90, vwx100, bea)
new_esEs4(Left(vwx90), Left(vwx100), False, app(app(ty_Either, app(app(app(ty_@3, be), bf), bg)), bc)) → new_ltEs1(vwx90, vwx100, be, bf, bg)
new_esEs4(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), False, app(app(app(ty_@3, fb), ea), app(app(ty_@2, hd), he))) → new_ltEs3(vwx92, vwx102, hd, he)
new_esEs4(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), False, app(app(app(ty_@3, fb), app(app(ty_Either, fc), fd)), eb)) → new_lt0(vwx91, vwx101, fc, fd)
new_ltEs3(@2(vwx90, vwx91), @2(vwx100, vwx101), app(app(app(ty_@3, bbc), bbd), bbe), bba) → new_lt2(vwx90, vwx100, bbc, bbd, bbe)
new_ltEs2(Just(vwx90), Just(vwx100), app(ty_Maybe, bad)) → new_ltEs2(vwx90, vwx100, bad)
new_esEs4(:(vwx90, vwx91), :(vwx100, vwx101), False, app(ty_[], df)) → new_compare0(vwx91, vwx101, df)
new_esEs4(@2(vwx90, vwx91), @2(vwx100, vwx101), False, app(app(ty_@2, app(app(app(ty_@3, bbc), bbd), bbe)), bba)) → new_lt2(vwx90, vwx100, bbc, bbd, bbe)
new_esEs4(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), False, app(app(app(ty_@3, fb), app(app(app(ty_@3, fg), fh), ga)), eb)) → new_lt2(vwx91, vwx101, fg, fh, ga)
new_ltEs1(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), app(app(ty_@2, eh), fa), ea, eb) → new_compare21(vwx90, vwx100, new_esEs7(vwx90, vwx100, eh, fa), eh, fa)
new_primCompAux(vwx90, vwx100, vwx71, app(app(ty_@2, beb), bec)) → new_compare4(vwx90, vwx100, beb, bec)
new_esEs4(Left(vwx90), Left(vwx100), False, app(app(ty_Either, app(ty_Maybe, bh)), bc)) → new_ltEs2(vwx90, vwx100, bh)
new_ltEs1(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), fb, ea, app(ty_[], gg)) → new_ltEs0(vwx92, vwx102, gg)
new_esEs4(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), False, app(app(app(ty_@3, fb), app(app(ty_@2, gc), gd)), eb)) → new_lt3(vwx91, vwx101, gc, gd)
new_ltEs3(@2(vwx90, vwx91), @2(vwx100, vwx101), app(ty_Maybe, bbf), bba) → new_lt(vwx90, vwx100, bbf)
new_esEs4(@2(vwx90, vwx91), @2(vwx100, vwx101), False, app(app(ty_@2, bca), app(app(ty_@2, bda), bdb))) → new_ltEs3(vwx91, vwx101, bda, bdb)
new_esEs4(@2(vwx90, vwx91), @2(vwx100, vwx101), False, app(app(ty_@2, bca), app(app(ty_Either, bcb), bcc))) → new_ltEs(vwx91, vwx101, bcb, bcc)
new_lt3(vwx90, vwx100, eh, fa) → new_compare21(vwx90, vwx100, new_esEs7(vwx90, vwx100, eh, fa), eh, fa)
new_ltEs1(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), fb, app(ty_[], ff), eb) → new_lt1(vwx91, vwx101, ff)
new_esEs4(@2(vwx90, vwx91), @2(vwx100, vwx101), False, app(app(ty_@2, app(ty_Maybe, bbf)), bba)) → new_lt(vwx90, vwx100, bbf)
new_ltEs0(:(vwx90, vwx91), :(vwx100, vwx101), df) → new_compare0(vwx91, vwx101, df)
new_esEs4(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), False, app(app(app(ty_@3, app(app(ty_@2, eh), fa)), ea), eb)) → new_compare21(vwx90, vwx100, new_esEs7(vwx90, vwx100, eh, fa), eh, fa)
new_ltEs3(@2(vwx90, vwx91), @2(vwx100, vwx101), bca, app(ty_[], bcd)) → new_ltEs0(vwx91, vwx101, bcd)
new_ltEs3(@2(vwx90, vwx91), @2(vwx100, vwx101), bca, app(ty_Maybe, bch)) → new_ltEs2(vwx91, vwx101, bch)
new_compare20(vwx90, vwx100, False, ed, ee, ef) → new_ltEs1(vwx90, vwx100, ed, ee, ef)

The TRS R consists of the following rules:

new_esEs28(vwx301, vwx401, ty_Integer) → new_esEs17(vwx301, vwx401)
new_esEs29(vwx90, vwx100, ty_Integer) → new_esEs17(vwx90, vwx100)
new_esEs26(vwx300, vwx400, ty_@0) → new_esEs15(vwx300, vwx400)
new_esEs25(vwx301, vwx401, ty_Int) → new_esEs19(vwx301, vwx401)
new_esEs24(vwx300, vwx400, app(app(ty_Either, cfd), cfe)) → new_esEs5(vwx300, vwx400, cfd, cfe)
new_ltEs20(vwx92, vwx102, ty_Int) → new_ltEs9(vwx92, vwx102)
new_ltEs16(vwx9, vwx10) → new_not(new_esEs10(new_compare8(vwx9, vwx10), GT))
new_esEs13(True, False) → False
new_esEs13(False, True) → False
new_ltEs20(vwx92, vwx102, app(ty_[], gg)) → new_ltEs10(vwx92, vwx102, gg)
new_esEs23(vwx302, vwx402, app(app(ty_Either, cdh), cea)) → new_esEs5(vwx302, vwx402, cdh, cea)
new_esEs31(vwx91, vwx101, app(ty_[], ff)) → new_esEs12(vwx91, vwx101, ff)
new_ltEs7(LT, EQ) → True
new_compare([], :(vwx100, vwx101), df) → LT
new_ltEs19(vwx91, vwx101, ty_Float) → new_ltEs4(vwx91, vwx101)
new_lt19(vwx90, vwx100, ty_Double) → new_lt15(vwx90, vwx100)
new_ltEs15(vwx9, vwx10, bhf) → new_not(new_esEs10(new_compare5(vwx9, vwx10, bhf), GT))
new_ltEs20(vwx92, vwx102, app(ty_Ratio, dcd)) → new_ltEs15(vwx92, vwx102, dcd)
new_ltEs4(vwx9, vwx10) → new_not(new_esEs10(new_compare6(vwx9, vwx10), GT))
new_primMulNat0(Zero, Zero) → Zero
new_lt16(vwx90, vwx100, app(ty_Maybe, bbf)) → new_lt14(vwx90, vwx100, bbf)
new_compare(:(vwx90, vwx91), [], df) → GT
new_esEs5(Left(vwx300), Left(vwx400), app(ty_Ratio, bfc), bef) → new_esEs14(vwx300, vwx400, bfc)
new_lt12(vwx90, vwx100) → new_esEs10(new_compare6(vwx90, vwx100), LT)
new_lt20(vwx91, vwx101, ty_Int) → new_lt11(vwx91, vwx101)
new_esEs9(vwx30, vwx40, ty_@0) → new_esEs15(vwx30, vwx40)
new_compare6(Float(vwx90, vwx91), Float(vwx100, vwx101)) → new_compare9(new_sr(vwx90, vwx100), new_sr(vwx91, vwx101))
new_esEs5(Left(vwx300), Left(vwx400), ty_Char, bef) → new_esEs16(vwx300, vwx400)
new_ltEs5(vwx9, vwx10, ty_Integer) → new_ltEs11(vwx9, vwx10)
new_lt20(vwx91, vwx101, app(app(app(ty_@3, fg), fh), ga)) → new_lt18(vwx91, vwx101, fg, fh, ga)
new_esEs23(vwx302, vwx402, ty_Double) → new_esEs11(vwx302, vwx402)
new_compare30(vwx90, vwx100, app(app(app(ty_@3, bdf), bdg), bdh)) → new_compare17(vwx90, vwx100, bdf, bdg, bdh)
new_esEs30(vwx90, vwx100, ty_Bool) → new_esEs13(vwx90, vwx100)
new_esEs26(vwx300, vwx400, ty_Ordering) → new_esEs10(vwx300, vwx400)
new_esEs24(vwx300, vwx400, ty_Bool) → new_esEs13(vwx300, vwx400)
new_ltEs20(vwx92, vwx102, app(app(ty_@2, hd), he)) → new_ltEs18(vwx92, vwx102, hd, he)
new_lt16(vwx90, vwx100, app(app(ty_Either, bag), bah)) → new_lt6(vwx90, vwx100, bag, bah)
new_esEs12([], [], dac) → True
new_ltEs6(Left(vwx90), Left(vwx100), app(app(ty_Either, ba), bb), bc) → new_ltEs6(vwx90, vwx100, ba, bb)
new_compare26(vwx90, vwx100, False, dg, dh) → new_compare14(vwx90, vwx100, new_ltEs6(vwx90, vwx100, dg, dh), dg, dh)
new_compare12(Char(vwx90), Char(vwx100)) → new_primCmpNat0(vwx90, vwx100)
new_ltEs5(vwx9, vwx10, ty_@0) → new_ltEs17(vwx9, vwx10)
new_ltEs5(vwx9, vwx10, app(app(ty_Either, cc), bc)) → new_ltEs6(vwx9, vwx10, cc, bc)
new_ltEs6(Right(vwx90), Right(vwx100), cc, ty_Float) → new_ltEs4(vwx90, vwx100)
new_lt19(vwx90, vwx100, ty_Ordering) → new_lt8(vwx90, vwx100)
new_ltEs5(vwx9, vwx10, ty_Bool) → new_ltEs13(vwx9, vwx10)
new_esEs22(vwx301, vwx401, app(ty_Ratio, ccb)) → new_esEs14(vwx301, vwx401, ccb)
new_ltEs13(True, False) → False
new_esEs26(vwx300, vwx400, ty_Float) → new_esEs18(vwx300, vwx400)
new_esEs21(vwx300, vwx400, app(ty_Ratio, cah)) → new_esEs14(vwx300, vwx400, cah)
new_esEs23(vwx302, vwx402, ty_Ordering) → new_esEs10(vwx302, vwx402)
new_esEs25(vwx301, vwx401, ty_Integer) → new_esEs17(vwx301, vwx401)
new_lt20(vwx91, vwx101, ty_Float) → new_lt12(vwx91, vwx101)
new_compare24(vwx90, vwx100, False, bea) → new_compare10(vwx90, vwx100, new_ltEs14(vwx90, vwx100, bea), bea)
new_lt20(vwx91, vwx101, ty_@0) → new_lt5(vwx91, vwx101)
new_esEs29(vwx90, vwx100, ty_Float) → new_esEs18(vwx90, vwx100)
new_esEs23(vwx302, vwx402, ty_Bool) → new_esEs13(vwx302, vwx402)
new_ltEs6(Right(vwx90), Right(vwx100), cc, app(ty_Ratio, bhh)) → new_ltEs15(vwx90, vwx100, bhh)
new_esEs25(vwx301, vwx401, ty_Bool) → new_esEs13(vwx301, vwx401)
new_esEs31(vwx91, vwx101, ty_Double) → new_esEs11(vwx91, vwx101)
new_ltEs6(Left(vwx90), Left(vwx100), ty_Double, bc) → new_ltEs16(vwx90, vwx100)
new_esEs17(Integer(vwx300), Integer(vwx400)) → new_primEqInt(vwx300, vwx400)
new_esEs5(Right(vwx300), Right(vwx400), bga, app(app(app(ty_@3, bgb), bgc), bgd)) → new_esEs6(vwx300, vwx400, bgb, bgc, bgd)
new_esEs24(vwx300, vwx400, app(ty_[], ceg)) → new_esEs12(vwx300, vwx400, ceg)
new_ltEs14(Just(vwx90), Just(vwx100), ty_Integer) → new_ltEs11(vwx90, vwx100)
new_pePe(False, vwx70) → vwx70
new_esEs24(vwx300, vwx400, app(ty_Ratio, ceh)) → new_esEs14(vwx300, vwx400, ceh)
new_esEs25(vwx301, vwx401, app(app(ty_@2, cgc), cgd)) → new_esEs7(vwx301, vwx401, cgc, cgd)
new_esEs5(Right(vwx300), Right(vwx400), bga, ty_Bool) → new_esEs13(vwx300, vwx400)
new_compare30(vwx90, vwx100, ty_Int) → new_compare9(vwx90, vwx100)
new_esEs12([], :(vwx400, vwx401), dac) → False
new_esEs12(:(vwx300, vwx301), [], dac) → False
new_compare28(vwx90, vwx100, False) → new_compare19(vwx90, vwx100, new_ltEs13(vwx90, vwx100))
new_ltEs6(Right(vwx90), Right(vwx100), cc, app(ty_[], cf)) → new_ltEs10(vwx90, vwx100, cf)
new_ltEs6(Left(vwx90), Left(vwx100), app(ty_[], bd), bc) → new_ltEs10(vwx90, vwx100, bd)
new_esEs30(vwx90, vwx100, ty_Char) → new_esEs16(vwx90, vwx100)
new_compare23(vwx90, vwx100, True) → EQ
new_lt19(vwx90, vwx100, app(ty_[], ec)) → new_lt9(vwx90, vwx100, ec)
new_ltEs5(vwx9, vwx10, app(ty_Maybe, bhe)) → new_ltEs14(vwx9, vwx10, bhe)
new_esEs25(vwx301, vwx401, ty_Double) → new_esEs11(vwx301, vwx401)
new_esEs5(Right(vwx300), Right(vwx400), bga, ty_Double) → new_esEs11(vwx300, vwx400)
new_ltEs14(Just(vwx90), Just(vwx100), app(ty_Maybe, bad)) → new_ltEs14(vwx90, vwx100, bad)
new_esEs22(vwx301, vwx401, ty_@0) → new_esEs15(vwx301, vwx401)
new_lt19(vwx90, vwx100, app(ty_Maybe, eg)) → new_lt14(vwx90, vwx100, eg)
new_compare9(vwx9, vwx10) → new_primCmpInt(vwx9, vwx10)
new_esEs24(vwx300, vwx400, ty_Double) → new_esEs11(vwx300, vwx400)
new_ltEs14(Just(vwx90), Just(vwx100), app(ty_Ratio, dbg)) → new_ltEs15(vwx90, vwx100, dbg)
new_ltEs7(GT, GT) → True
new_esEs5(Right(vwx300), Right(vwx400), bga, ty_@0) → new_esEs15(vwx300, vwx400)
new_compare19(vwx90, vwx100, True) → LT
new_compare10(vwx90, vwx100, True, bea) → LT
new_esEs5(Left(vwx300), Left(vwx400), ty_Double, bef) → new_esEs11(vwx300, vwx400)
new_esEs29(vwx90, vwx100, app(ty_Maybe, bbf)) → new_esEs8(vwx90, vwx100, bbf)
new_lt20(vwx91, vwx101, app(app(ty_@2, gc), gd)) → new_lt7(vwx91, vwx101, gc, gd)
new_esEs27(vwx300, vwx400, ty_Int) → new_esEs19(vwx300, vwx400)
new_ltEs6(Left(vwx90), Left(vwx100), app(app(ty_@2, ca), cb), bc) → new_ltEs18(vwx90, vwx100, ca, cb)
new_primCmpNat0(Zero, Succ(vwx1000)) → LT
new_ltEs19(vwx91, vwx101, app(ty_Ratio, dcb)) → new_ltEs15(vwx91, vwx101, dcb)
new_esEs6(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), caa, cab, cac) → new_asAs(new_esEs21(vwx300, vwx400, caa), new_asAs(new_esEs22(vwx301, vwx401, cab), new_esEs23(vwx302, vwx402, cac)))
new_ltEs14(Just(vwx90), Nothing, bhe) → False
new_esEs25(vwx301, vwx401, app(app(ty_Either, cgf), cgg)) → new_esEs5(vwx301, vwx401, cgf, cgg)
new_lt16(vwx90, vwx100, app(app(ty_@2, bbg), bbh)) → new_lt7(vwx90, vwx100, bbg, bbh)
new_ltEs13(False, True) → True
new_esEs30(vwx90, vwx100, ty_Float) → new_esEs18(vwx90, vwx100)
new_ltEs5(vwx9, vwx10, ty_Ordering) → new_ltEs7(vwx9, vwx10)
new_ltEs6(Left(vwx90), Left(vwx100), app(app(app(ty_@3, be), bf), bg), bc) → new_ltEs12(vwx90, vwx100, be, bf, bg)
new_ltEs14(Just(vwx90), Just(vwx100), ty_Ordering) → new_ltEs7(vwx90, vwx100)
new_esEs9(vwx30, vwx40, app(ty_Ratio, dbh)) → new_esEs14(vwx30, vwx40, dbh)
new_esEs29(vwx90, vwx100, app(app(ty_@2, bbg), bbh)) → new_esEs7(vwx90, vwx100, bbg, bbh)
new_esEs29(vwx90, vwx100, ty_Bool) → new_esEs13(vwx90, vwx100)
new_esEs10(LT, LT) → True
new_esEs10(GT, EQ) → False
new_esEs10(EQ, GT) → False
new_compare10(vwx90, vwx100, False, bea) → GT
new_lt16(vwx90, vwx100, ty_Double) → new_lt15(vwx90, vwx100)
new_pePe(True, vwx70) → True
new_primEqNat0(Zero, Zero) → True
new_compare14(vwx90, vwx100, False, dg, dh) → GT
new_ltEs9(vwx9, vwx10) → new_not(new_esEs10(new_compare9(vwx9, vwx10), GT))
new_ltEs19(vwx91, vwx101, app(ty_Maybe, bch)) → new_ltEs14(vwx91, vwx101, bch)
new_esEs22(vwx301, vwx401, app(ty_Maybe, cce)) → new_esEs8(vwx301, vwx401, cce)
new_ltEs20(vwx92, vwx102, app(app(app(ty_@3, gh), ha), hb)) → new_ltEs12(vwx92, vwx102, gh, ha, hb)
new_compare111(vwx90, vwx100, False, eh, fa) → GT
new_compare7(vwx90, vwx100) → new_compare23(vwx90, vwx100, new_esEs10(vwx90, vwx100))
new_esEs9(vwx30, vwx40, app(ty_Maybe, cgh)) → new_esEs8(vwx30, vwx40, cgh)
new_esEs8(Just(vwx300), Just(vwx400), ty_Int) → new_esEs19(vwx300, vwx400)
new_esEs8(Just(vwx300), Just(vwx400), ty_Float) → new_esEs18(vwx300, vwx400)
new_esEs5(Right(vwx300), Right(vwx400), bga, ty_Float) → new_esEs18(vwx300, vwx400)
new_lt20(vwx91, vwx101, app(ty_[], ff)) → new_lt9(vwx91, vwx101, ff)
new_esEs22(vwx301, vwx401, app(app(ty_@2, ccc), ccd)) → new_esEs7(vwx301, vwx401, ccc, ccd)
new_esEs9(vwx30, vwx40, ty_Ordering) → new_esEs10(vwx30, vwx40)
new_esEs21(vwx300, vwx400, app(ty_Maybe, cbc)) → new_esEs8(vwx300, vwx400, cbc)
new_esEs9(vwx30, vwx40, ty_Double) → new_esEs11(vwx30, vwx40)
new_sr(vwx300, vwx400) → new_primMulInt(vwx300, vwx400)
new_compare30(vwx90, vwx100, ty_Bool) → new_compare29(vwx90, vwx100)
new_ltEs10(vwx9, vwx10, df) → new_not(new_esEs10(new_compare(vwx9, vwx10, df), GT))
new_ltEs19(vwx91, vwx101, app(app(app(ty_@3, bce), bcf), bcg)) → new_ltEs12(vwx91, vwx101, bce, bcf, bcg)
new_esEs24(vwx300, vwx400, app(app(ty_@2, cfa), cfb)) → new_esEs7(vwx300, vwx400, cfa, cfb)
new_primPlusNat0(Succ(vwx450), vwx40000) → Succ(Succ(new_primPlusNat1(vwx450, vwx40000)))
new_esEs29(vwx90, vwx100, ty_Double) → new_esEs11(vwx90, vwx100)
new_ltEs20(vwx92, vwx102, app(app(ty_Either, ge), gf)) → new_ltEs6(vwx92, vwx102, ge, gf)
new_esEs26(vwx300, vwx400, app(app(app(ty_@3, dad), dae), daf)) → new_esEs6(vwx300, vwx400, dad, dae, daf)
new_esEs5(Right(vwx300), Right(vwx400), bga, app(ty_[], bge)) → new_esEs12(vwx300, vwx400, bge)
new_esEs22(vwx301, vwx401, ty_Char) → new_esEs16(vwx301, vwx401)
new_esEs30(vwx90, vwx100, ty_Int) → new_esEs19(vwx90, vwx100)
new_compare25(vwx90, vwx100, False, eh, fa) → new_compare111(vwx90, vwx100, new_ltEs18(vwx90, vwx100, eh, fa), eh, fa)
new_esEs31(vwx91, vwx101, ty_Float) → new_esEs18(vwx91, vwx101)
new_esEs8(Just(vwx300), Just(vwx400), app(app(ty_Either, daa), dab)) → new_esEs5(vwx300, vwx400, daa, dab)
new_esEs16(Char(vwx300), Char(vwx400)) → new_primEqNat0(vwx300, vwx400)
new_esEs8(Just(vwx300), Nothing, cgh) → False
new_esEs8(Nothing, Just(vwx400), cgh) → False
new_esEs25(vwx301, vwx401, app(ty_[], cga)) → new_esEs12(vwx301, vwx401, cga)
new_esEs10(EQ, EQ) → True
new_ltEs6(Right(vwx90), Right(vwx100), cc, app(app(app(ty_@3, cg), da), db)) → new_ltEs12(vwx90, vwx100, cg, da, db)
new_primEqInt(Neg(Succ(vwx3000)), Neg(Succ(vwx4000))) → new_primEqNat0(vwx3000, vwx4000)
new_ltEs20(vwx92, vwx102, ty_Integer) → new_ltEs11(vwx92, vwx102)
new_esEs26(vwx300, vwx400, app(ty_Maybe, dbc)) → new_esEs8(vwx300, vwx400, dbc)
new_ltEs8(vwx9, vwx10) → new_not(new_esEs10(new_compare12(vwx9, vwx10), GT))
new_esEs22(vwx301, vwx401, app(app(app(ty_@3, cbf), cbg), cbh)) → new_esEs6(vwx301, vwx401, cbf, cbg, cbh)
new_ltEs6(Left(vwx90), Left(vwx100), ty_Char, bc) → new_ltEs8(vwx90, vwx100)
new_primPlusNat1(Zero, Succ(vwx400000)) → Succ(vwx400000)
new_primPlusNat1(Succ(vwx4500), Zero) → Succ(vwx4500)
new_esEs21(vwx300, vwx400, ty_Ordering) → new_esEs10(vwx300, vwx400)
new_lt5(vwx90, vwx100) → new_esEs10(new_compare13(vwx90, vwx100), LT)
new_compare30(vwx90, vwx100, ty_Float) → new_compare6(vwx90, vwx100)
new_esEs29(vwx90, vwx100, app(app(ty_Either, bag), bah)) → new_esEs5(vwx90, vwx100, bag, bah)
new_esEs21(vwx300, vwx400, ty_@0) → new_esEs15(vwx300, vwx400)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs31(vwx91, vwx101, app(app(app(ty_@3, fg), fh), ga)) → new_esEs6(vwx91, vwx101, fg, fh, ga)
new_ltEs5(vwx9, vwx10, ty_Double) → new_ltEs16(vwx9, vwx10)
new_esEs24(vwx300, vwx400, app(app(app(ty_@3, ced), cee), cef)) → new_esEs6(vwx300, vwx400, ced, cee, cef)
new_ltEs5(vwx9, vwx10, ty_Float) → new_ltEs4(vwx9, vwx10)
new_esEs21(vwx300, vwx400, app(app(ty_@2, cba), cbb)) → new_esEs7(vwx300, vwx400, cba, cbb)
new_ltEs7(EQ, EQ) → True
new_compare16(vwx90, vwx100, dg, dh) → new_compare26(vwx90, vwx100, new_esEs5(vwx90, vwx100, dg, dh), dg, dh)
new_esEs18(Float(vwx300, vwx301), Float(vwx400, vwx401)) → new_esEs19(new_sr(vwx300, vwx400), new_sr(vwx301, vwx401))
new_primEqInt(Neg(Succ(vwx3000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(vwx4000))) → False
new_compare30(vwx90, vwx100, ty_Integer) → new_compare18(vwx90, vwx100)
new_lt16(vwx90, vwx100, app(ty_Ratio, dca)) → new_lt4(vwx90, vwx100, dca)
new_compare26(vwx90, vwx100, True, dg, dh) → EQ
new_lt20(vwx91, vwx101, ty_Ordering) → new_lt8(vwx91, vwx101)
new_esEs23(vwx302, vwx402, ty_Integer) → new_esEs17(vwx302, vwx402)
new_esEs31(vwx91, vwx101, app(app(ty_Either, fc), fd)) → new_esEs5(vwx91, vwx101, fc, fd)
new_esEs5(Right(vwx300), Right(vwx400), bga, app(ty_Ratio, bgf)) → new_esEs14(vwx300, vwx400, bgf)
new_ltEs6(Right(vwx90), Right(vwx100), cc, ty_Char) → new_ltEs8(vwx90, vwx100)
new_esEs25(vwx301, vwx401, ty_Char) → new_esEs16(vwx301, vwx401)
new_compare([], [], df) → EQ
new_esEs24(vwx300, vwx400, ty_Ordering) → new_esEs10(vwx300, vwx400)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_compare30(vwx90, vwx100, ty_Double) → new_compare8(vwx90, vwx100)
new_ltEs19(vwx91, vwx101, ty_Bool) → new_ltEs13(vwx91, vwx101)
new_esEs9(vwx30, vwx40, ty_Float) → new_esEs18(vwx30, vwx40)
new_esEs20(vwx9, vwx10, False, bhd) → new_esEs10(new_compare10(Just(vwx9), Just(vwx10), new_ltEs5(vwx9, vwx10, bhd), bhd), LT)
new_esEs28(vwx301, vwx401, ty_Int) → new_esEs19(vwx301, vwx401)
new_ltEs7(GT, LT) → False
new_esEs23(vwx302, vwx402, ty_Char) → new_esEs16(vwx302, vwx402)
new_primCmpNat0(Succ(vwx900), Succ(vwx1000)) → new_primCmpNat0(vwx900, vwx1000)
new_esEs26(vwx300, vwx400, ty_Double) → new_esEs11(vwx300, vwx400)
new_esEs11(Double(vwx300, vwx301), Double(vwx400, vwx401)) → new_esEs19(new_sr(vwx300, vwx400), new_sr(vwx301, vwx401))
new_esEs30(vwx90, vwx100, ty_@0) → new_esEs15(vwx90, vwx100)
new_ltEs6(Right(vwx90), Right(vwx100), cc, ty_Ordering) → new_ltEs7(vwx90, vwx100)
new_ltEs7(GT, EQ) → False
new_esEs26(vwx300, vwx400, ty_Integer) → new_esEs17(vwx300, vwx400)
new_primEqInt(Pos(Succ(vwx3000)), Pos(Succ(vwx4000))) → new_primEqNat0(vwx3000, vwx4000)
new_esEs21(vwx300, vwx400, ty_Double) → new_esEs11(vwx300, vwx400)
new_esEs22(vwx301, vwx401, ty_Bool) → new_esEs13(vwx301, vwx401)
new_esEs8(Just(vwx300), Just(vwx400), app(app(app(ty_@3, cha), chb), chc)) → new_esEs6(vwx300, vwx400, cha, chb, chc)
new_esEs9(vwx30, vwx40, app(app(ty_@2, ceb), cec)) → new_esEs7(vwx30, vwx40, ceb, cec)
new_esEs8(Just(vwx300), Just(vwx400), ty_Integer) → new_esEs17(vwx300, vwx400)
new_esEs21(vwx300, vwx400, ty_Int) → new_esEs19(vwx300, vwx400)
new_lt6(vwx90, vwx100, dg, dh) → new_esEs10(new_compare16(vwx90, vwx100, dg, dh), LT)
new_esEs23(vwx302, vwx402, app(ty_[], cdc)) → new_esEs12(vwx302, vwx402, cdc)
new_ltEs11(vwx9, vwx10) → new_not(new_esEs10(new_compare18(vwx9, vwx10), GT))
new_ltEs5(vwx9, vwx10, app(app(ty_@2, bca), bba)) → new_ltEs18(vwx9, vwx10, bca, bba)
new_esEs5(Right(vwx300), Right(vwx400), bga, app(app(ty_Either, bhb), bhc)) → new_esEs5(vwx300, vwx400, bhb, bhc)
new_primEqNat0(Succ(vwx3000), Succ(vwx4000)) → new_primEqNat0(vwx3000, vwx4000)
new_esEs5(Left(vwx300), Left(vwx400), app(ty_[], bfb), bef) → new_esEs12(vwx300, vwx400, bfb)
new_ltEs14(Just(vwx90), Just(vwx100), ty_Int) → new_ltEs9(vwx90, vwx100)
new_esEs27(vwx300, vwx400, ty_Integer) → new_esEs17(vwx300, vwx400)
new_esEs23(vwx302, vwx402, app(ty_Ratio, cdd)) → new_esEs14(vwx302, vwx402, cdd)
new_lt20(vwx91, vwx101, ty_Integer) → new_lt17(vwx91, vwx101)
new_primCompAux00(vwx75, LT) → LT
new_primCmpInt(Neg(Succ(vwx900)), Neg(vwx100)) → new_primCmpNat0(vwx100, Succ(vwx900))
new_lt16(vwx90, vwx100, ty_Float) → new_lt12(vwx90, vwx100)
new_esEs5(Left(vwx300), Left(vwx400), ty_Int, bef) → new_esEs19(vwx300, vwx400)
new_esEs9(vwx30, vwx40, app(ty_[], dac)) → new_esEs12(vwx30, vwx40, dac)
new_ltEs6(Left(vwx90), Right(vwx100), cc, bc) → True
new_esEs30(vwx90, vwx100, app(ty_Ratio, bee)) → new_esEs14(vwx90, vwx100, bee)
new_compare5(:%(vwx90, vwx91), :%(vwx100, vwx101), ty_Integer) → new_compare18(new_sr0(vwx90, vwx101), new_sr0(vwx100, vwx91))
new_ltEs6(Right(vwx90), Left(vwx100), cc, bc) → False
new_ltEs6(Left(vwx90), Left(vwx100), ty_@0, bc) → new_ltEs17(vwx90, vwx100)
new_primEqInt(Pos(Succ(vwx3000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(vwx4000))) → False
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(vwx900), Zero) → GT
new_compare30(vwx90, vwx100, app(ty_Maybe, bea)) → new_compare24(vwx90, vwx100, new_esEs8(vwx90, vwx100, bea), bea)
new_esEs24(vwx300, vwx400, ty_@0) → new_esEs15(vwx300, vwx400)
new_primCmpInt(Neg(Zero), Pos(Succ(vwx1000))) → LT
new_compare19(vwx90, vwx100, False) → GT
new_esEs21(vwx300, vwx400, ty_Char) → new_esEs16(vwx300, vwx400)
new_esEs8(Just(vwx300), Just(vwx400), ty_Char) → new_esEs16(vwx300, vwx400)
new_esEs12(:(vwx300, vwx301), :(vwx400, vwx401), dac) → new_asAs(new_esEs26(vwx300, vwx400, dac), new_esEs12(vwx301, vwx401, dac))
new_esEs22(vwx301, vwx401, ty_Double) → new_esEs11(vwx301, vwx401)
new_ltEs6(Right(vwx90), Right(vwx100), cc, ty_@0) → new_ltEs17(vwx90, vwx100)
new_sr0(Integer(vwx900), Integer(vwx1010)) → Integer(new_primMulInt(vwx900, vwx1010))
new_primPlusNat1(Succ(vwx4500), Succ(vwx400000)) → Succ(Succ(new_primPlusNat1(vwx4500, vwx400000)))
new_compare30(vwx90, vwx100, app(ty_[], bde)) → new_compare(vwx90, vwx100, bde)
new_ltEs6(Left(vwx90), Left(vwx100), ty_Ordering, bc) → new_ltEs7(vwx90, vwx100)
new_lt4(vwx90, vwx100, bee) → new_esEs10(new_compare5(vwx90, vwx100, bee), LT)
new_primEqInt(Pos(Succ(vwx3000)), Neg(vwx400)) → False
new_primEqInt(Neg(Succ(vwx3000)), Pos(vwx400)) → False
new_ltEs19(vwx91, vwx101, ty_Double) → new_ltEs16(vwx91, vwx101)
new_esEs29(vwx90, vwx100, app(ty_[], bbb)) → new_esEs12(vwx90, vwx100, bbb)
new_compare(:(vwx90, vwx91), :(vwx100, vwx101), df) → new_primCompAux0(vwx90, vwx100, new_compare(vwx91, vwx101, df), df)
new_lt8(vwx90, vwx100) → new_esEs10(new_compare7(vwx90, vwx100), LT)
new_lt16(vwx90, vwx100, ty_@0) → new_lt5(vwx90, vwx100)
new_compare18(Integer(vwx90), Integer(vwx100)) → new_primCmpInt(vwx90, vwx100)
new_esEs8(Just(vwx300), Just(vwx400), ty_Double) → new_esEs11(vwx300, vwx400)
new_esEs9(vwx30, vwx40, app(app(ty_Either, bga), bef)) → new_esEs5(vwx30, vwx40, bga, bef)
new_ltEs7(EQ, GT) → True
new_primEqInt(Pos(Zero), Neg(Succ(vwx4000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(vwx4000))) → False
new_esEs31(vwx91, vwx101, ty_Integer) → new_esEs17(vwx91, vwx101)
new_esEs8(Just(vwx300), Just(vwx400), app(app(ty_@2, chf), chg)) → new_esEs7(vwx300, vwx400, chf, chg)
new_primCompAux00(vwx75, EQ) → vwx75
new_primCmpInt(Pos(Zero), Pos(Succ(vwx1000))) → new_primCmpNat0(Zero, Succ(vwx1000))
new_lt14(Just(vwx30), Just(vwx40), bed) → new_esEs20(vwx30, vwx40, new_esEs9(vwx30, vwx40, bed), bed)
new_ltEs6(Left(vwx90), Left(vwx100), ty_Float, bc) → new_ltEs4(vwx90, vwx100)
new_esEs7(@2(vwx300, vwx301), @2(vwx400, vwx401), ceb, cec) → new_asAs(new_esEs24(vwx300, vwx400, ceb), new_esEs25(vwx301, vwx401, cec))
new_ltEs6(Left(vwx90), Left(vwx100), ty_Int, bc) → new_ltEs9(vwx90, vwx100)
new_lt20(vwx91, vwx101, ty_Bool) → new_lt13(vwx91, vwx101)
new_lt20(vwx91, vwx101, app(ty_Ratio, dcc)) → new_lt4(vwx91, vwx101, dcc)
new_ltEs6(Right(vwx90), Right(vwx100), cc, ty_Bool) → new_ltEs13(vwx90, vwx100)
new_esEs9(vwx30, vwx40, ty_Integer) → new_esEs17(vwx30, vwx40)
new_ltEs14(Nothing, Just(vwx100), bhe) → True
new_esEs22(vwx301, vwx401, ty_Float) → new_esEs18(vwx301, vwx401)
new_ltEs19(vwx91, vwx101, ty_Char) → new_ltEs8(vwx91, vwx101)
new_esEs23(vwx302, vwx402, ty_Int) → new_esEs19(vwx302, vwx402)
new_not(False) → True
new_esEs5(Right(vwx300), Right(vwx400), bga, app(ty_Maybe, bha)) → new_esEs8(vwx300, vwx400, bha)
new_lt19(vwx90, vwx100, ty_Char) → new_lt10(vwx90, vwx100)
new_compare24(vwx90, vwx100, True, bea) → EQ
new_esEs5(Right(vwx300), Right(vwx400), bga, ty_Ordering) → new_esEs10(vwx300, vwx400)
new_esEs9(vwx30, vwx40, ty_Bool) → new_esEs13(vwx30, vwx40)
new_primCmpInt(Pos(Succ(vwx900)), Pos(vwx100)) → new_primCmpNat0(Succ(vwx900), vwx100)
new_primPlusNat0(Zero, vwx40000) → Succ(vwx40000)
new_esEs23(vwx302, vwx402, ty_@0) → new_esEs15(vwx302, vwx402)
new_esEs26(vwx300, vwx400, app(ty_Ratio, dah)) → new_esEs14(vwx300, vwx400, dah)
new_ltEs19(vwx91, vwx101, app(ty_[], bcd)) → new_ltEs10(vwx91, vwx101, bcd)
new_lt19(vwx90, vwx100, ty_Int) → new_lt11(vwx90, vwx100)
new_esEs30(vwx90, vwx100, app(app(ty_@2, eh), fa)) → new_esEs7(vwx90, vwx100, eh, fa)
new_ltEs14(Just(vwx90), Just(vwx100), ty_@0) → new_ltEs17(vwx90, vwx100)
new_esEs8(Just(vwx300), Just(vwx400), app(ty_[], chd)) → new_esEs12(vwx300, vwx400, chd)
new_lt19(vwx90, vwx100, ty_Integer) → new_lt17(vwx90, vwx100)
new_esEs23(vwx302, vwx402, ty_Float) → new_esEs18(vwx302, vwx402)
new_ltEs14(Just(vwx90), Just(vwx100), app(app(ty_Either, hf), hg)) → new_ltEs6(vwx90, vwx100, hf, hg)
new_esEs31(vwx91, vwx101, app(ty_Ratio, dcc)) → new_esEs14(vwx91, vwx101, dcc)
new_esEs31(vwx91, vwx101, ty_@0) → new_esEs15(vwx91, vwx101)
new_compare17(vwx90, vwx100, ed, ee, ef) → new_compare27(vwx90, vwx100, new_esEs6(vwx90, vwx100, ed, ee, ef), ed, ee, ef)
new_esEs8(Just(vwx300), Just(vwx400), app(ty_Ratio, che)) → new_esEs14(vwx300, vwx400, che)
new_esEs25(vwx301, vwx401, ty_@0) → new_esEs15(vwx301, vwx401)
new_lt20(vwx91, vwx101, app(app(ty_Either, fc), fd)) → new_lt6(vwx91, vwx101, fc, fd)
new_esEs25(vwx301, vwx401, ty_Float) → new_esEs18(vwx301, vwx401)
new_lt14(Nothing, Nothing, bed) → False
new_esEs8(Just(vwx300), Just(vwx400), ty_Ordering) → new_esEs10(vwx300, vwx400)
new_compare30(vwx90, vwx100, ty_@0) → new_compare13(vwx90, vwx100)
new_esEs9(vwx30, vwx40, ty_Char) → new_esEs16(vwx30, vwx40)
new_esEs23(vwx302, vwx402, app(ty_Maybe, cdg)) → new_esEs8(vwx302, vwx402, cdg)
new_lt16(vwx90, vwx100, ty_Bool) → new_lt13(vwx90, vwx100)
new_ltEs6(Left(vwx90), Left(vwx100), ty_Bool, bc) → new_ltEs13(vwx90, vwx100)
new_esEs20(vwx9, vwx10, True, bhd) → new_esEs10(EQ, LT)
new_lt16(vwx90, vwx100, ty_Int) → new_lt11(vwx90, vwx100)
new_lt18(vwx90, vwx100, ed, ee, ef) → new_esEs10(new_compare17(vwx90, vwx100, ed, ee, ef), LT)
new_compare28(vwx90, vwx100, True) → EQ
new_esEs26(vwx300, vwx400, app(app(ty_Either, dbd), dbe)) → new_esEs5(vwx300, vwx400, dbd, dbe)
new_lt16(vwx90, vwx100, ty_Integer) → new_lt17(vwx90, vwx100)
new_ltEs20(vwx92, vwx102, ty_@0) → new_ltEs17(vwx92, vwx102)
new_lt15(vwx90, vwx100) → new_esEs10(new_compare8(vwx90, vwx100), LT)
new_primCmpInt(Pos(Succ(vwx900)), Neg(vwx100)) → GT
new_ltEs19(vwx91, vwx101, ty_Int) → new_ltEs9(vwx91, vwx101)
new_esEs24(vwx300, vwx400, ty_Float) → new_esEs18(vwx300, vwx400)
new_esEs30(vwx90, vwx100, app(ty_[], ec)) → new_esEs12(vwx90, vwx100, ec)
new_esEs9(vwx30, vwx40, ty_Int) → new_esEs19(vwx30, vwx40)
new_compare5(:%(vwx90, vwx91), :%(vwx100, vwx101), ty_Int) → new_compare9(new_sr(vwx90, vwx101), new_sr(vwx100, vwx91))
new_esEs5(Left(vwx300), Left(vwx400), ty_Ordering, bef) → new_esEs10(vwx300, vwx400)
new_lt20(vwx91, vwx101, ty_Double) → new_lt15(vwx91, vwx101)
new_primMulInt(Pos(vwx3000), Pos(vwx4000)) → Pos(new_primMulNat0(vwx3000, vwx4000))
new_ltEs14(Just(vwx90), Just(vwx100), app(app(ty_@2, bae), baf)) → new_ltEs18(vwx90, vwx100, bae, baf)
new_compare30(vwx90, vwx100, app(app(ty_Either, bdc), bdd)) → new_compare16(vwx90, vwx100, bdc, bdd)
new_ltEs6(Right(vwx90), Right(vwx100), cc, app(app(ty_@2, dd), de)) → new_ltEs18(vwx90, vwx100, dd, de)
new_esEs30(vwx90, vwx100, app(ty_Maybe, eg)) → new_esEs8(vwx90, vwx100, eg)
new_lt16(vwx90, vwx100, ty_Char) → new_lt10(vwx90, vwx100)
new_esEs5(Right(vwx300), Left(vwx400), bga, bef) → False
new_esEs5(Left(vwx300), Right(vwx400), bga, bef) → False
new_primMulInt(Neg(vwx3000), Neg(vwx4000)) → Pos(new_primMulNat0(vwx3000, vwx4000))
new_primEqNat0(Zero, Succ(vwx4000)) → False
new_primEqNat0(Succ(vwx3000), Zero) → False
new_esEs24(vwx300, vwx400, ty_Char) → new_esEs16(vwx300, vwx400)
new_esEs26(vwx300, vwx400, app(app(ty_@2, dba), dbb)) → new_esEs7(vwx300, vwx400, dba, dbb)
new_esEs21(vwx300, vwx400, app(ty_[], cag)) → new_esEs12(vwx300, vwx400, cag)
new_esEs5(Right(vwx300), Right(vwx400), bga, ty_Integer) → new_esEs17(vwx300, vwx400)
new_compare25(vwx90, vwx100, True, eh, fa) → EQ
new_lt13(vwx90, vwx100) → new_esEs10(new_compare29(vwx90, vwx100), LT)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_lt14(Just(vwx30), Nothing, bed) → new_esEs10(GT, LT)
new_ltEs17(vwx9, vwx10) → new_not(new_esEs10(new_compare13(vwx9, vwx10), GT))
new_esEs5(Right(vwx300), Right(vwx400), bga, ty_Char) → new_esEs16(vwx300, vwx400)
new_ltEs5(vwx9, vwx10, ty_Int) → new_ltEs9(vwx9, vwx10)
new_ltEs19(vwx91, vwx101, ty_@0) → new_ltEs17(vwx91, vwx101)
new_ltEs20(vwx92, vwx102, ty_Float) → new_ltEs4(vwx92, vwx102)
new_ltEs6(Left(vwx90), Left(vwx100), app(ty_Maybe, bh), bc) → new_ltEs14(vwx90, vwx100, bh)
new_compare30(vwx90, vwx100, app(app(ty_@2, beb), bec)) → new_compare15(vwx90, vwx100, beb, bec)
new_esEs8(Just(vwx300), Just(vwx400), ty_@0) → new_esEs15(vwx300, vwx400)
new_primCmpInt(Neg(Zero), Neg(Succ(vwx1000))) → new_primCmpNat0(Succ(vwx1000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(vwx1000))) → GT
new_ltEs20(vwx92, vwx102, ty_Char) → new_ltEs8(vwx92, vwx102)
new_esEs25(vwx301, vwx401, app(ty_Ratio, cgb)) → new_esEs14(vwx301, vwx401, cgb)
new_esEs29(vwx90, vwx100, ty_@0) → new_esEs15(vwx90, vwx100)
new_lt16(vwx90, vwx100, app(ty_[], bbb)) → new_lt9(vwx90, vwx100, bbb)
new_ltEs20(vwx92, vwx102, app(ty_Maybe, hc)) → new_ltEs14(vwx92, vwx102, hc)
new_ltEs6(Left(vwx90), Left(vwx100), app(ty_Ratio, bhg), bc) → new_ltEs15(vwx90, vwx100, bhg)
new_esEs29(vwx90, vwx100, ty_Int) → new_esEs19(vwx90, vwx100)
new_ltEs6(Right(vwx90), Right(vwx100), cc, ty_Double) → new_ltEs16(vwx90, vwx100)
new_esEs21(vwx300, vwx400, ty_Float) → new_esEs18(vwx300, vwx400)
new_ltEs19(vwx91, vwx101, ty_Integer) → new_ltEs11(vwx91, vwx101)
new_compare15(vwx90, vwx100, eh, fa) → new_compare25(vwx90, vwx100, new_esEs7(vwx90, vwx100, eh, fa), eh, fa)
new_ltEs6(Right(vwx90), Right(vwx100), cc, app(app(ty_Either, cd), ce)) → new_ltEs6(vwx90, vwx100, cd, ce)
new_esEs19(vwx30, vwx40) → new_primEqInt(vwx30, vwx40)
new_esEs5(Left(vwx300), Left(vwx400), app(app(ty_@2, bfd), bfe), bef) → new_esEs7(vwx300, vwx400, bfd, bfe)
new_lt20(vwx91, vwx101, ty_Char) → new_lt10(vwx91, vwx101)
new_esEs21(vwx300, vwx400, ty_Integer) → new_esEs17(vwx300, vwx400)
new_primCompAux0(vwx90, vwx100, vwx71, df) → new_primCompAux00(vwx71, new_compare30(vwx90, vwx100, df))
new_esEs8(Nothing, Nothing, cgh) → True
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_ltEs19(vwx91, vwx101, app(app(ty_@2, bda), bdb)) → new_ltEs18(vwx91, vwx101, bda, bdb)
new_lt16(vwx90, vwx100, app(app(app(ty_@3, bbc), bbd), bbe)) → new_lt18(vwx90, vwx100, bbc, bbd, bbe)
new_ltEs14(Just(vwx90), Just(vwx100), ty_Float) → new_ltEs4(vwx90, vwx100)
new_lt16(vwx90, vwx100, ty_Ordering) → new_lt8(vwx90, vwx100)
new_lt19(vwx90, vwx100, ty_Bool) → new_lt13(vwx90, vwx100)
new_lt9(vwx90, vwx100, ec) → new_esEs10(new_compare(vwx90, vwx100, ec), LT)
new_esEs15(@0, @0) → True
new_ltEs6(Right(vwx90), Right(vwx100), cc, ty_Integer) → new_ltEs11(vwx90, vwx100)
new_asAs(False, vwx35) → False
new_ltEs20(vwx92, vwx102, ty_Double) → new_ltEs16(vwx92, vwx102)
new_lt10(vwx90, vwx100) → new_esEs10(new_compare12(vwx90, vwx100), LT)
new_primMulInt(Pos(vwx3000), Neg(vwx4000)) → Neg(new_primMulNat0(vwx3000, vwx4000))
new_primMulInt(Neg(vwx3000), Pos(vwx4000)) → Neg(new_primMulNat0(vwx3000, vwx4000))
new_esEs8(Just(vwx300), Just(vwx400), ty_Bool) → new_esEs13(vwx300, vwx400)
new_primMulNat0(Succ(vwx30000), Zero) → Zero
new_primMulNat0(Zero, Succ(vwx40000)) → Zero
new_lt19(vwx90, vwx100, ty_Float) → new_lt12(vwx90, vwx100)
new_esEs21(vwx300, vwx400, app(app(ty_Either, cbd), cbe)) → new_esEs5(vwx300, vwx400, cbd, cbe)
new_esEs31(vwx91, vwx101, ty_Ordering) → new_esEs10(vwx91, vwx101)
new_esEs23(vwx302, vwx402, app(app(app(ty_@3, cch), cda), cdb)) → new_esEs6(vwx302, vwx402, cch, cda, cdb)
new_esEs26(vwx300, vwx400, app(ty_[], dag)) → new_esEs12(vwx300, vwx400, dag)
new_esEs21(vwx300, vwx400, ty_Bool) → new_esEs13(vwx300, vwx400)
new_lt7(vwx90, vwx100, eh, fa) → new_esEs10(new_compare15(vwx90, vwx100, eh, fa), LT)
new_esEs5(Left(vwx300), Left(vwx400), app(app(app(ty_@3, beg), beh), bfa), bef) → new_esEs6(vwx300, vwx400, beg, beh, bfa)
new_esEs31(vwx91, vwx101, app(ty_Maybe, gb)) → new_esEs8(vwx91, vwx101, gb)
new_esEs10(GT, GT) → True
new_esEs25(vwx301, vwx401, ty_Ordering) → new_esEs10(vwx301, vwx401)
new_esEs23(vwx302, vwx402, app(app(ty_@2, cde), cdf)) → new_esEs7(vwx302, vwx402, cde, cdf)
new_lt19(vwx90, vwx100, app(app(app(ty_@3, ed), ee), ef)) → new_lt18(vwx90, vwx100, ed, ee, ef)
new_compare110(vwx90, vwx100, True, ed, ee, ef) → LT
new_esEs24(vwx300, vwx400, ty_Integer) → new_esEs17(vwx300, vwx400)
new_ltEs20(vwx92, vwx102, ty_Bool) → new_ltEs13(vwx92, vwx102)
new_compare30(vwx90, vwx100, ty_Char) → new_compare12(vwx90, vwx100)
new_compare13(@0, @0) → EQ
new_esEs13(False, False) → True
new_esEs5(Right(vwx300), Right(vwx400), bga, ty_Int) → new_esEs19(vwx300, vwx400)
new_esEs31(vwx91, vwx101, ty_Int) → new_esEs19(vwx91, vwx101)
new_lt19(vwx90, vwx100, app(ty_Ratio, bee)) → new_lt4(vwx90, vwx100, bee)
new_lt20(vwx91, vwx101, app(ty_Maybe, gb)) → new_lt14(vwx91, vwx101, gb)
new_esEs25(vwx301, vwx401, app(app(app(ty_@3, cff), cfg), cfh)) → new_esEs6(vwx301, vwx401, cff, cfg, cfh)
new_esEs5(Left(vwx300), Left(vwx400), ty_Bool, bef) → new_esEs13(vwx300, vwx400)
new_ltEs6(Right(vwx90), Right(vwx100), cc, app(ty_Maybe, dc)) → new_ltEs14(vwx90, vwx100, dc)
new_ltEs14(Just(vwx90), Just(vwx100), ty_Bool) → new_ltEs13(vwx90, vwx100)
new_esEs30(vwx90, vwx100, app(app(ty_Either, dg), dh)) → new_esEs5(vwx90, vwx100, dg, dh)
new_esEs29(vwx90, vwx100, ty_Ordering) → new_esEs10(vwx90, vwx100)
new_esEs5(Left(vwx300), Left(vwx400), ty_@0, bef) → new_esEs15(vwx300, vwx400)
new_esEs31(vwx91, vwx101, ty_Char) → new_esEs16(vwx91, vwx101)
new_ltEs18(@2(vwx90, vwx91), @2(vwx100, vwx101), bca, bba) → new_pePe(new_lt16(vwx90, vwx100, bca), new_asAs(new_esEs29(vwx90, vwx100, bca), new_ltEs19(vwx91, vwx101, bba)))
new_esEs22(vwx301, vwx401, app(ty_[], cca)) → new_esEs12(vwx301, vwx401, cca)
new_esEs30(vwx90, vwx100, ty_Double) → new_esEs11(vwx90, vwx100)
new_ltEs5(vwx9, vwx10, app(ty_[], df)) → new_ltEs10(vwx9, vwx10, df)
new_esEs5(Left(vwx300), Left(vwx400), app(ty_Maybe, bff), bef) → new_esEs8(vwx300, vwx400, bff)
new_ltEs13(True, True) → True
new_compare29(vwx90, vwx100) → new_compare28(vwx90, vwx100, new_esEs13(vwx90, vwx100))
new_ltEs13(False, False) → True
new_esEs22(vwx301, vwx401, ty_Int) → new_esEs19(vwx301, vwx401)
new_compare11(vwx90, vwx100, False) → GT
new_compare8(Double(vwx90, vwx91), Double(vwx100, vwx101)) → new_compare9(new_sr(vwx90, vwx100), new_sr(vwx91, vwx101))
new_esEs24(vwx300, vwx400, app(ty_Maybe, cfc)) → new_esEs8(vwx300, vwx400, cfc)
new_ltEs5(vwx9, vwx10, app(ty_Ratio, bhf)) → new_ltEs15(vwx9, vwx10, bhf)
new_esEs30(vwx90, vwx100, ty_Ordering) → new_esEs10(vwx90, vwx100)
new_compare11(vwx90, vwx100, True) → LT
new_esEs26(vwx300, vwx400, ty_Int) → new_esEs19(vwx300, vwx400)
new_esEs5(Left(vwx300), Left(vwx400), app(app(ty_Either, bfg), bfh), bef) → new_esEs5(vwx300, vwx400, bfg, bfh)
new_ltEs14(Just(vwx90), Just(vwx100), app(ty_[], hh)) → new_ltEs10(vwx90, vwx100, hh)
new_esEs29(vwx90, vwx100, app(app(app(ty_@3, bbc), bbd), bbe)) → new_esEs6(vwx90, vwx100, bbc, bbd, bbe)
new_compare14(vwx90, vwx100, True, dg, dh) → LT
new_ltEs14(Just(vwx90), Just(vwx100), ty_Char) → new_ltEs8(vwx90, vwx100)
new_esEs22(vwx301, vwx401, ty_Integer) → new_esEs17(vwx301, vwx401)
new_esEs10(GT, LT) → False
new_esEs10(LT, GT) → False
new_esEs29(vwx90, vwx100, ty_Char) → new_esEs16(vwx90, vwx100)
new_ltEs7(EQ, LT) → False
new_lt19(vwx90, vwx100, app(app(ty_@2, eh), fa)) → new_lt7(vwx90, vwx100, eh, fa)
new_compare23(vwx90, vwx100, False) → new_compare11(vwx90, vwx100, new_ltEs7(vwx90, vwx100))
new_esEs10(EQ, LT) → False
new_esEs10(LT, EQ) → False
new_ltEs7(LT, LT) → True
new_esEs5(Right(vwx300), Right(vwx400), bga, app(app(ty_@2, bgg), bgh)) → new_esEs7(vwx300, vwx400, bgg, bgh)
new_esEs9(vwx30, vwx40, app(app(app(ty_@3, caa), cab), cac)) → new_esEs6(vwx30, vwx40, caa, cab, cac)
new_primPlusNat1(Zero, Zero) → Zero
new_compare111(vwx90, vwx100, True, eh, fa) → LT
new_ltEs14(Nothing, Nothing, bhe) → True
new_esEs21(vwx300, vwx400, app(app(app(ty_@3, cad), cae), caf)) → new_esEs6(vwx300, vwx400, cad, cae, caf)
new_esEs31(vwx91, vwx101, ty_Bool) → new_esEs13(vwx91, vwx101)
new_asAs(True, vwx35) → vwx35
new_lt11(vwx90, vwx100) → new_esEs10(new_compare9(vwx90, vwx100), LT)
new_ltEs7(LT, GT) → True
new_primMulNat0(Succ(vwx30000), Succ(vwx40000)) → new_primPlusNat0(new_primMulNat0(vwx30000, Succ(vwx40000)), vwx40000)
new_esEs30(vwx90, vwx100, ty_Integer) → new_esEs17(vwx90, vwx100)
new_esEs13(True, True) → True
new_lt17(vwx90, vwx100) → new_esEs10(new_compare18(vwx90, vwx100), LT)
new_esEs8(Just(vwx300), Just(vwx400), app(ty_Maybe, chh)) → new_esEs8(vwx300, vwx400, chh)
new_ltEs14(Just(vwx90), Just(vwx100), ty_Double) → new_ltEs16(vwx90, vwx100)
new_esEs24(vwx300, vwx400, ty_Int) → new_esEs19(vwx300, vwx400)
new_lt14(Nothing, Just(vwx40), bed) → new_esEs10(LT, LT)
new_compare27(vwx90, vwx100, True, ed, ee, ef) → EQ
new_esEs22(vwx301, vwx401, ty_Ordering) → new_esEs10(vwx301, vwx401)
new_ltEs5(vwx9, vwx10, ty_Char) → new_ltEs8(vwx9, vwx10)
new_ltEs19(vwx91, vwx101, ty_Ordering) → new_ltEs7(vwx91, vwx101)
new_esEs26(vwx300, vwx400, ty_Char) → new_esEs16(vwx300, vwx400)
new_ltEs6(Right(vwx90), Right(vwx100), cc, ty_Int) → new_ltEs9(vwx90, vwx100)
new_compare30(vwx90, vwx100, ty_Ordering) → new_compare7(vwx90, vwx100)
new_esEs29(vwx90, vwx100, app(ty_Ratio, dca)) → new_esEs14(vwx90, vwx100, dca)
new_ltEs5(vwx9, vwx10, app(app(app(ty_@3, fb), ea), eb)) → new_ltEs12(vwx9, vwx10, fb, ea, eb)
new_esEs14(:%(vwx300, vwx301), :%(vwx400, vwx401), dbh) → new_asAs(new_esEs27(vwx300, vwx400, dbh), new_esEs28(vwx301, vwx401, dbh))
new_compare30(vwx90, vwx100, app(ty_Ratio, dbf)) → new_compare5(vwx90, vwx100, dbf)
new_lt19(vwx90, vwx100, app(app(ty_Either, dg), dh)) → new_lt6(vwx90, vwx100, dg, dh)
new_compare110(vwx90, vwx100, False, ed, ee, ef) → GT
new_ltEs12(@3(vwx90, vwx91, vwx92), @3(vwx100, vwx101, vwx102), fb, ea, eb) → new_pePe(new_lt19(vwx90, vwx100, fb), new_asAs(new_esEs30(vwx90, vwx100, fb), new_pePe(new_lt20(vwx91, vwx101, ea), new_asAs(new_esEs31(vwx91, vwx101, ea), new_ltEs20(vwx92, vwx102, eb)))))
new_esEs5(Left(vwx300), Left(vwx400), ty_Integer, bef) → new_esEs17(vwx300, vwx400)
new_esEs22(vwx301, vwx401, app(app(ty_Either, ccf), ccg)) → new_esEs5(vwx301, vwx401, ccf, ccg)
new_primCompAux00(vwx75, GT) → GT
new_ltEs20(vwx92, vwx102, ty_Ordering) → new_ltEs7(vwx92, vwx102)
new_ltEs14(Just(vwx90), Just(vwx100), app(app(app(ty_@3, baa), bab), bac)) → new_ltEs12(vwx90, vwx100, baa, bab, bac)
new_esEs30(vwx90, vwx100, app(app(app(ty_@3, ed), ee), ef)) → new_esEs6(vwx90, vwx100, ed, ee, ef)
new_compare27(vwx90, vwx100, False, ed, ee, ef) → new_compare110(vwx90, vwx100, new_ltEs12(vwx90, vwx100, ed, ee, ef), ed, ee, ef)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_esEs26(vwx300, vwx400, ty_Bool) → new_esEs13(vwx300, vwx400)
new_esEs25(vwx301, vwx401, app(ty_Maybe, cge)) → new_esEs8(vwx301, vwx401, cge)
new_ltEs19(vwx91, vwx101, app(app(ty_Either, bcb), bcc)) → new_ltEs6(vwx91, vwx101, bcb, bcc)
new_esEs5(Left(vwx300), Left(vwx400), ty_Float, bef) → new_esEs18(vwx300, vwx400)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_lt19(vwx90, vwx100, ty_@0) → new_lt5(vwx90, vwx100)
new_esEs31(vwx91, vwx101, app(app(ty_@2, gc), gd)) → new_esEs7(vwx91, vwx101, gc, gd)
new_primCmpInt(Neg(Succ(vwx900)), Pos(vwx100)) → LT
new_not(True) → False
new_ltEs6(Left(vwx90), Left(vwx100), ty_Integer, bc) → new_ltEs11(vwx90, vwx100)

The set Q consists of the following terms:

new_lt19(x0, x1, ty_Char)
new_esEs25(x0, x1, ty_Double)
new_esEs24(x0, x1, ty_Integer)
new_compare24(x0, x1, True, x2)
new_esEs8(Just(x0), Just(x1), app(ty_Maybe, x2))
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_compare30(x0, x1, ty_Bool)
new_esEs31(x0, x1, app(ty_Ratio, x2))
new_lt19(x0, x1, app(ty_[], x2))
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs6(Left(x0), Left(x1), ty_@0, x2)
new_esEs21(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, ty_Double)
new_esEs5(Left(x0), Left(x1), ty_@0, x2)
new_esEs8(Just(x0), Just(x1), ty_Bool)
new_esEs31(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs31(x0, x1, ty_Float)
new_esEs8(Nothing, Just(x0), x1)
new_compare25(x0, x1, False, x2, x3)
new_esEs6(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_compare30(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(Just(x0), Just(x1), app(ty_Maybe, x2))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs31(x0, x1, ty_Ordering)
new_ltEs6(Left(x0), Left(x1), ty_Int, x2)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs5(Left(x0), Left(x1), ty_Float, x2)
new_esEs19(x0, x1)
new_compare7(x0, x1)
new_ltEs14(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare30(x0, x1, ty_Double)
new_ltEs5(x0, x1, ty_Char)
new_esEs5(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs29(x0, x1, ty_Double)
new_ltEs19(x0, x1, ty_Integer)
new_esEs29(x0, x1, app(ty_[], x2))
new_ltEs4(x0, x1)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_esEs5(Left(x0), Left(x1), ty_Ordering, x2)
new_lt15(x0, x1)
new_esEs5(Right(x0), Right(x1), x2, ty_Float)
new_primMulInt(Neg(x0), Neg(x1))
new_esEs12([], [], x0)
new_esEs26(x0, x1, app(ty_[], x2))
new_lt20(x0, x1, ty_Float)
new_compare11(x0, x1, False)
new_ltEs7(EQ, EQ)
new_compare14(x0, x1, True, x2, x3)
new_esEs29(x0, x1, ty_Char)
new_esEs10(GT, EQ)
new_esEs10(EQ, GT)
new_lt19(x0, x1, ty_Ordering)
new_ltEs20(x0, x1, ty_Bool)
new_esEs5(Right(x0), Right(x1), x2, ty_Int)
new_esEs10(EQ, LT)
new_esEs10(LT, EQ)
new_ltEs20(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs9(x0, x1, ty_Ordering)
new_lt19(x0, x1, ty_Double)
new_esEs31(x0, x1, ty_Char)
new_esEs24(x0, x1, ty_Ordering)
new_ltEs6(Right(x0), Right(x1), x2, ty_@0)
new_ltEs7(EQ, LT)
new_ltEs7(LT, EQ)
new_ltEs20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs29(x0, x1, ty_@0)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_esEs8(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_ltEs20(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, ty_Double)
new_esEs21(x0, x1, ty_Int)
new_lt16(x0, x1, app(ty_Ratio, x2))
new_compare19(x0, x1, False)
new_esEs9(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt19(x0, x1, ty_Integer)
new_compare23(x0, x1, True)
new_esEs30(x0, x1, app(ty_[], x2))
new_lt9(x0, x1, x2)
new_ltEs6(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs9(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs29(x0, x1, ty_Bool)
new_esEs24(x0, x1, ty_Float)
new_esEs8(Just(x0), Just(x1), ty_Int)
new_ltEs7(LT, LT)
new_esEs30(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs6(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs14(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare27(x0, x1, False, x2, x3, x4)
new_compare(:(x0, x1), :(x2, x3), x4)
new_esEs31(x0, x1, app(ty_Maybe, x2))
new_compare30(x0, x1, ty_Integer)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs14(Just(x0), Just(x1), ty_Integer)
new_ltEs6(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_sr(x0, x1)
new_esEs5(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs7(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs6(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_compare30(x0, x1, app(ty_Ratio, x2))
new_esEs30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs29(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs6(Left(x0), Right(x1), x2, x3)
new_ltEs6(Right(x0), Left(x1), x2, x3)
new_esEs21(x0, x1, ty_Char)
new_primCompAux00(x0, GT)
new_esEs30(x0, x1, ty_Ordering)
new_primEqNat0(Zero, Zero)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(Just(x0), Just(x1), ty_Bool)
new_esEs5(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs8(Just(x0), Just(x1), ty_Double)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, ty_Float)
new_esEs5(Left(x0), Left(x1), ty_Char, x2)
new_primMulInt(Pos(x0), Pos(x1))
new_compare30(x0, x1, app(ty_[], x2))
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare30(x0, x1, ty_Ordering)
new_esEs29(x0, x1, ty_Ordering)
new_esEs25(x0, x1, ty_Integer)
new_ltEs19(x0, x1, ty_Ordering)
new_ltEs6(Right(x0), Right(x1), x2, ty_Integer)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs26(x0, x1, ty_Integer)
new_esEs5(Left(x0), Left(x1), ty_Int, x2)
new_sr0(Integer(x0), Integer(x1))
new_lt20(x0, x1, ty_Int)
new_lt10(x0, x1)
new_compare111(x0, x1, False, x2, x3)
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs13(False, False)
new_primMulNat0(Zero, Zero)
new_ltEs6(Left(x0), Left(x1), ty_Bool, x2)
new_asAs(False, x0)
new_esEs8(Nothing, Nothing, x0)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs30(x0, x1, ty_@0)
new_esEs9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt16(x0, x1, app(ty_[], x2))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_compare26(x0, x1, False, x2, x3)
new_ltEs5(x0, x1, ty_@0)
new_esEs31(x0, x1, ty_Integer)
new_compare25(x0, x1, True, x2, x3)
new_compare110(x0, x1, True, x2, x3, x4)
new_compare26(x0, x1, True, x2, x3)
new_esEs23(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, ty_Char)
new_compare([], :(x0, x1), x2)
new_lt5(x0, x1)
new_ltEs14(Just(x0), Just(x1), ty_Float)
new_esEs23(x0, x1, ty_Ordering)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_lt7(x0, x1, x2, x3)
new_esEs20(x0, x1, True, x2)
new_ltEs14(Nothing, Nothing, x0)
new_esEs9(x0, x1, ty_Char)
new_ltEs11(x0, x1)
new_esEs10(GT, LT)
new_esEs10(LT, GT)
new_esEs5(Left(x0), Right(x1), x2, x3)
new_esEs5(Right(x0), Left(x1), x2, x3)
new_compare29(x0, x1)
new_esEs25(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, ty_@0)
new_esEs22(x0, x1, ty_Double)
new_esEs12([], :(x0, x1), x2)
new_esEs22(x0, x1, ty_Integer)
new_primMulNat0(Zero, Succ(x0))
new_compare24(x0, x1, False, x2)
new_lt20(x0, x1, ty_Bool)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs31(x0, x1, ty_@0)
new_lt20(x0, x1, ty_Char)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs8(Just(x0), Just(x1), app(ty_[], x2))
new_ltEs5(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Right(x0), Right(x1), x2, app(ty_[], x3))
new_lt16(x0, x1, app(app(ty_@2, x2), x3))
new_esEs30(x0, x1, app(ty_Maybe, x2))
new_compare14(x0, x1, False, x2, x3)
new_lt14(Just(x0), Nothing, x1)
new_esEs23(x0, x1, ty_Integer)
new_pePe(False, x0)
new_esEs31(x0, x1, ty_Int)
new_lt19(x0, x1, ty_Bool)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs21(x0, x1, ty_Float)
new_esEs31(x0, x1, ty_Bool)
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs24(x0, x1, ty_Int)
new_lt14(Just(x0), Just(x1), x2)
new_esEs31(x0, x1, app(ty_[], x2))
new_compare23(x0, x1, False)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs6(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs21(x0, x1, ty_@0)
new_lt12(x0, x1)
new_primPlusNat0(Zero, x0)
new_esEs30(x0, x1, ty_Float)
new_lt20(x0, x1, ty_Ordering)
new_primEqNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, Zero)
new_ltEs13(True, True)
new_esEs28(x0, x1, ty_Integer)
new_ltEs9(x0, x1)
new_esEs9(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_Char)
new_ltEs6(Right(x0), Right(x1), x2, ty_Double)
new_ltEs5(x0, x1, app(ty_Maybe, x2))
new_esEs21(x0, x1, ty_Integer)
new_lt13(x0, x1)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs10(EQ, EQ)
new_ltEs14(Just(x0), Nothing, x1)
new_primCmpNat0(Succ(x0), Zero)
new_ltEs6(Left(x0), Left(x1), ty_Float, x2)
new_esEs25(x0, x1, ty_Bool)
new_esEs31(x0, x1, ty_Double)
new_ltEs5(x0, x1, ty_Bool)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Neg(Zero), Neg(Zero))
new_compare8(Double(x0, x1), Double(x2, x3))
new_ltEs13(False, False)
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs16(Char(x0), Char(x1))
new_compare11(x0, x1, True)
new_esEs8(Just(x0), Just(x1), ty_Ordering)
new_ltEs5(x0, x1, ty_Int)
new_lt19(x0, x1, ty_@0)
new_ltEs20(x0, x1, ty_@0)
new_ltEs10(x0, x1, x2)
new_ltEs13(False, True)
new_ltEs13(True, False)
new_lt19(x0, x1, ty_Float)
new_compare28(x0, x1, True)
new_primCompAux00(x0, LT)
new_ltEs17(x0, x1)
new_esEs30(x0, x1, ty_Int)
new_ltEs20(x0, x1, ty_Float)
new_ltEs5(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs6(Left(x0), Left(x1), ty_Char, x2)
new_primCompAux00(x0, EQ)
new_lt16(x0, x1, ty_Char)
new_esEs22(x0, x1, ty_@0)
new_esEs21(x0, x1, ty_Bool)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_lt16(x0, x1, ty_Int)
new_ltEs8(x0, x1)
new_esEs9(x0, x1, app(app(ty_Either, x2), x3))
new_lt16(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Ordering)
new_esEs22(x0, x1, app(ty_[], x2))
new_esEs9(x0, x1, ty_Float)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpNat0(Succ(x0), Succ(x1))
new_primPlusNat1(Succ(x0), Succ(x1))
new_lt4(x0, x1, x2)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_ltEs12(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs30(x0, x1, app(app(ty_Either, x2), x3))
new_esEs26(x0, x1, ty_@0)
new_lt16(x0, x1, ty_@0)
new_esEs27(x0, x1, ty_Int)
new_compare18(Integer(x0), Integer(x1))
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_primCompAux0(x0, x1, x2, x3)
new_lt16(x0, x1, ty_Ordering)
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs8(Just(x0), Just(x1), ty_Float)
new_compare12(Char(x0), Char(x1))
new_esEs21(x0, x1, ty_Ordering)
new_compare13(@0, @0)
new_ltEs18(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs15(x0, x1, x2)
new_ltEs14(Just(x0), Just(x1), app(ty_[], x2))
new_esEs28(x0, x1, ty_Int)
new_pePe(True, x0)
new_esEs20(x0, x1, False, x2)
new_esEs14(:%(x0, x1), :%(x2, x3), x4)
new_compare30(x0, x1, app(ty_Maybe, x2))
new_ltEs6(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_ltEs16(x0, x1)
new_esEs23(x0, x1, ty_Bool)
new_ltEs6(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs5(Right(x0), Right(x1), x2, ty_Bool)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs29(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Just(x0), Just(x1), ty_Ordering)
new_compare30(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs12(:(x0, x1), :(x2, x3), x4)
new_compare19(x0, x1, True)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_compare([], [], x0)
new_compare30(x0, x1, ty_Float)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_compare5(:%(x0, x1), :%(x2, x3), ty_Integer)
new_ltEs19(x0, x1, ty_Double)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_compare111(x0, x1, True, x2, x3)
new_esEs5(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs8(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, app(ty_[], x2))
new_esEs25(x0, x1, ty_Char)
new_esEs31(x0, x1, app(app(ty_@2, x2), x3))
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs24(x0, x1, ty_Bool)
new_ltEs14(Just(x0), Just(x1), ty_Int)
new_esEs10(LT, LT)
new_esEs29(x0, x1, app(app(ty_Either, x2), x3))
new_primPlusNat0(Succ(x0), x1)
new_esEs22(x0, x1, ty_Int)
new_compare16(x0, x1, x2, x3)
new_esEs23(x0, x1, ty_Float)
new_compare27(x0, x1, True, x2, x3, x4)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_ltEs20(x0, x1, ty_Int)
new_ltEs5(x0, x1, app(ty_Ratio, x2))
new_esEs9(x0, x1, app(ty_[], x2))
new_ltEs20(x0, x1, ty_Ordering)
new_compare28(x0, x1, False)
new_esEs5(Right(x0), Right(x1), x2, ty_Char)
new_ltEs20(x0, x1, app(ty_[], x2))
new_esEs25(x0, x1, ty_Ordering)
new_ltEs6(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt16(x0, x1, ty_Bool)
new_ltEs5(x0, x1, ty_Ordering)
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs29(x0, x1, ty_Int)
new_primCmpNat0(Zero, Zero)
new_compare5(:%(x0, x1), :%(x2, x3), ty_Int)
new_esEs5(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_lt11(x0, x1)
new_ltEs14(Nothing, Just(x0), x1)
new_esEs23(x0, x1, ty_Char)
new_esEs30(x0, x1, ty_Bool)
new_ltEs6(Right(x0), Right(x1), x2, ty_Bool)
new_lt19(x0, x1, ty_Int)
new_compare30(x0, x1, ty_Char)
new_esEs26(x0, x1, ty_Char)
new_compare(:(x0, x1), [], x2)
new_esEs8(Just(x0), Just(x1), ty_Char)
new_ltEs14(Just(x0), Just(x1), ty_Char)
new_ltEs20(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs6(Right(x0), Right(x1), x2, ty_Int)
new_ltEs19(x0, x1, ty_Bool)
new_esEs5(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs15(@0, @0)
new_compare30(x0, x1, app(app(ty_@2, x2), x3))
new_lt17(x0, x1)
new_esEs5(Right(x0), Right(x1), x2, ty_@0)
new_esEs30(x0, x1, ty_Integer)
new_esEs22(x0, x1, ty_Float)
new_esEs24(x0, x1, ty_Double)
new_esEs5(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs9(x0, x1, app(ty_Maybe, x2))
new_compare15(x0, x1, x2, x3)
new_esEs5(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs26(x0, x1, ty_Float)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10(GT, GT)
new_primEqNat0(Zero, Succ(x0))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(x0, x1, ty_Float)
new_esEs17(Integer(x0), Integer(x1))
new_primMulNat0(Succ(x0), Zero)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_esEs5(Left(x0), Left(x1), app(ty_[], x2), x3)
new_lt14(Nothing, Just(x0), x1)
new_esEs11(Double(x0, x1), Double(x2, x3))
new_primMulNat0(Succ(x0), Succ(x1))
new_ltEs7(LT, GT)
new_esEs13(True, False)
new_esEs13(False, True)
new_ltEs7(GT, LT)
new_esEs5(Left(x0), Left(x1), ty_Double, x2)
new_esEs29(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Ordering)
new_ltEs5(x0, x1, ty_Double)
new_lt20(x0, x1, ty_Integer)
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_Integer)
new_esEs30(x0, x1, app(ty_Ratio, x2))
new_esEs30(x0, x1, ty_Char)
new_esEs25(x0, x1, ty_@0)
new_ltEs6(Left(x0), Left(x1), ty_Integer, x2)
new_esEs5(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_lt20(x0, x1, ty_@0)
new_esEs12(:(x0, x1), [], x2)
new_not(True)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_ltEs14(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs6(Right(x0), Right(x1), x2, ty_Char)
new_compare17(x0, x1, x2, x3, x4)
new_esEs22(x0, x1, ty_Char)
new_esEs13(True, True)
new_esEs5(Left(x0), Left(x1), ty_Bool, x2)
new_compare30(x0, x1, ty_Int)
new_esEs8(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_lt16(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs14(Just(x0), Just(x1), ty_@0)
new_esEs26(x0, x1, ty_Bool)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_esEs9(x0, x1, ty_@0)
new_not(False)
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs26(x0, x1, ty_Int)
new_esEs9(x0, x1, ty_Integer)
new_primCmpNat0(Zero, Succ(x0))
new_compare6(Float(x0, x1), Float(x2, x3))
new_ltEs20(x0, x1, ty_Integer)
new_lt16(x0, x1, app(ty_Maybe, x2))
new_esEs5(Right(x0), Right(x1), x2, ty_Double)
new_esEs22(x0, x1, ty_Bool)
new_esEs8(Just(x0), Just(x1), app(ty_Ratio, x2))
new_esEs5(Right(x0), Right(x1), x2, ty_Integer)
new_esEs30(x0, x1, ty_Double)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs6(Left(x0), Left(x1), ty_Double, x2)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs9(x0, x1, ty_Bool)
new_primEqNat0(Succ(x0), Succ(x1))
new_lt14(Nothing, Nothing, x0)
new_ltEs6(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_compare110(x0, x1, False, x2, x3, x4)
new_ltEs6(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs6(Right(x0), Right(x1), x2, ty_Float)
new_esEs8(Just(x0), Nothing, x1)
new_compare10(x0, x1, True, x2)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_ltEs6(Right(x0), Right(x1), x2, ty_Ordering)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_lt18(x0, x1, x2, x3, x4)
new_ltEs14(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs9(x0, x1, ty_Double)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_ltEs14(Just(x0), Just(x1), ty_Double)
new_ltEs6(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs19(x0, x1, ty_Int)
new_ltEs6(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs18(Float(x0, x1), Float(x2, x3))
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_lt16(x0, x1, ty_Integer)
new_primEqInt(Pos(Zero), Pos(Zero))
new_asAs(True, x0)
new_lt8(x0, x1)
new_compare30(x0, x1, ty_@0)
new_esEs24(x0, x1, ty_Char)
new_lt16(x0, x1, ty_Double)
new_esEs8(Just(x0), Just(x1), ty_@0)
new_lt16(x0, x1, ty_Float)
new_primPlusNat1(Succ(x0), Zero)
new_compare10(x0, x1, False, x2)
new_esEs29(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_ltEs5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs5(x0, x1, app(ty_[], x2))
new_ltEs19(x0, x1, ty_Float)
new_esEs31(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Left(x0), Left(x1), ty_Integer, x2)
new_esEs5(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs29(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Double)
new_ltEs6(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs29(x0, x1, ty_Float)
new_compare9(x0, x1)
new_lt20(x0, x1, ty_Double)
new_primPlusNat1(Zero, Succ(x0))
new_lt20(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, ty_@0)
new_ltEs7(GT, EQ)
new_ltEs7(EQ, GT)
new_esEs25(x0, x1, ty_Int)
new_esEs23(x0, x1, ty_Int)
new_ltEs7(GT, GT)
new_esEs23(x0, x1, ty_Double)
new_esEs8(Just(x0), Just(x1), ty_Integer)
new_esEs23(x0, x1, ty_@0)
new_lt6(x0, x1, x2, x3)
new_ltEs5(x0, x1, ty_Integer)

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: