YES 3.404 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

compare0 x y True = GT

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

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

absReal0 x True = `negate` x

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

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

reduce2D vwv vww = gcd 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'2 x zx = gcd0Gcd'1 (zx == 0) x zx
gcd0Gcd'2 vuv vuw = gcd0Gcd'0 vuv vuw

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

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_primEqNat(Succ(vwx2300), Succ(vwx2400)) → new_primEqNat(vwx2300, vwx2400)

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_primPlusNat(Succ(vwx5300), Succ(vwx401000)) → new_primPlusNat(vwx5300, vwx401000)

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_primMulNat(Succ(vwx30000), Succ(vwx40100)) → new_primMulNat(vwx30000, Succ(vwx40100))

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_esEs1(@2(vwx230, vwx231), @2(vwx240, vwx241), eh, app(ty_Maybe, gb)) → new_esEs3(vwx231, vwx241, gb)
new_esEs0(Left(vwx230), Left(vwx240), app(ty_[], cf), ce) → new_esEs(vwx230, vwx240, cf)
new_esEs2(@3(vwx230, vwx231, vwx232), @3(vwx240, vwx241, vwx242), app(app(app(ty_@3, bcg), bch), bda), hf, bbb) → new_esEs2(vwx230, vwx240, bcg, bch, bda)
new_esEs2(@3(vwx230, vwx231, vwx232), @3(vwx240, vwx241, vwx242), he, hf, app(ty_[], baa)) → new_esEs(vwx232, vwx242, baa)
new_esEs3(Just(vwx230), Just(vwx240), app(app(ty_@2, bdf), bdg)) → new_esEs1(vwx230, vwx240, bdf, bdg)
new_esEs2(@3(vwx230, vwx231, vwx232), @3(vwx240, vwx241, vwx242), he, app(ty_Maybe, bca), bbb) → new_esEs3(vwx231, vwx241, bca)
new_esEs2(@3(vwx230, vwx231, vwx232), @3(vwx240, vwx241, vwx242), he, hf, app(app(ty_@2, bab), bac)) → new_esEs1(vwx232, vwx242, bab, bac)
new_esEs1(@2(vwx230, vwx231), @2(vwx240, vwx241), app(app(ty_Either, gc), gd), ge) → new_esEs0(vwx230, vwx240, gc, gd)
new_esEs(:(vwx230, vwx231), :(vwx240, vwx241), app(app(app(ty_@3, bg), bh), ca)) → new_esEs2(vwx230, vwx240, bg, bh, ca)
new_esEs1(@2(vwx230, vwx231), @2(vwx240, vwx241), eh, app(app(app(ty_@3, fg), fh), ga)) → new_esEs2(vwx231, vwx241, fg, fh, ga)
new_esEs1(@2(vwx230, vwx231), @2(vwx240, vwx241), eh, app(app(ty_Either, fa), fb)) → new_esEs0(vwx231, vwx241, fa, fb)
new_esEs3(Just(vwx230), Just(vwx240), app(app(ty_Either, bdc), bdd)) → new_esEs0(vwx230, vwx240, bdc, bdd)
new_esEs2(@3(vwx230, vwx231, vwx232), @3(vwx240, vwx241, vwx242), he, hf, app(ty_Maybe, bag)) → new_esEs3(vwx232, vwx242, bag)
new_esEs2(@3(vwx230, vwx231, vwx232), @3(vwx240, vwx241, vwx242), app(ty_[], bcd), hf, bbb) → new_esEs(vwx230, vwx240, bcd)
new_esEs2(@3(vwx230, vwx231, vwx232), @3(vwx240, vwx241, vwx242), app(app(ty_Either, bcb), bcc), hf, bbb) → new_esEs0(vwx230, vwx240, bcb, bcc)
new_esEs0(Right(vwx230), Right(vwx240), df, app(app(ty_@2, eb), ec)) → new_esEs1(vwx230, vwx240, eb, ec)
new_esEs1(@2(vwx230, vwx231), @2(vwx240, vwx241), app(ty_Maybe, hd), ge) → new_esEs3(vwx230, vwx240, hd)
new_esEs0(Left(vwx230), Left(vwx240), app(ty_Maybe, de), ce) → new_esEs3(vwx230, vwx240, de)
new_esEs0(Left(vwx230), Left(vwx240), app(app(app(ty_@3, db), dc), dd), ce) → new_esEs2(vwx230, vwx240, db, dc, dd)
new_esEs0(Left(vwx230), Left(vwx240), app(app(ty_Either, cc), cd), ce) → new_esEs0(vwx230, vwx240, cc, cd)
new_esEs1(@2(vwx230, vwx231), @2(vwx240, vwx241), eh, app(ty_[], fc)) → new_esEs(vwx231, vwx241, fc)
new_esEs1(@2(vwx230, vwx231), @2(vwx240, vwx241), app(ty_[], gf), ge) → new_esEs(vwx230, vwx240, gf)
new_esEs0(Right(vwx230), Right(vwx240), df, app(app(ty_Either, dg), dh)) → new_esEs0(vwx230, vwx240, dg, dh)
new_esEs2(@3(vwx230, vwx231, vwx232), @3(vwx240, vwx241, vwx242), app(app(ty_@2, bce), bcf), hf, bbb) → new_esEs1(vwx230, vwx240, bce, bcf)
new_esEs3(Just(vwx230), Just(vwx240), app(ty_[], bde)) → new_esEs(vwx230, vwx240, bde)
new_esEs1(@2(vwx230, vwx231), @2(vwx240, vwx241), eh, app(app(ty_@2, fd), ff)) → new_esEs1(vwx231, vwx241, fd, ff)
new_esEs(:(vwx230, vwx231), :(vwx240, vwx241), app(app(ty_@2, be), bf)) → new_esEs1(vwx230, vwx240, be, bf)
new_esEs(:(vwx230, vwx231), :(vwx240, vwx241), app(app(ty_Either, bb), bc)) → new_esEs0(vwx230, vwx240, bb, bc)
new_esEs(:(vwx230, vwx231), :(vwx240, vwx241), ba) → new_esEs(vwx231, vwx241, ba)
new_esEs2(@3(vwx230, vwx231, vwx232), @3(vwx240, vwx241, vwx242), he, app(app(ty_@2, bbd), bbe), bbb) → new_esEs1(vwx231, vwx241, bbd, bbe)
new_esEs2(@3(vwx230, vwx231, vwx232), @3(vwx240, vwx241, vwx242), he, app(app(app(ty_@3, bbf), bbg), bbh), bbb) → new_esEs2(vwx231, vwx241, bbf, bbg, bbh)
new_esEs1(@2(vwx230, vwx231), @2(vwx240, vwx241), app(app(ty_@2, gg), gh), ge) → new_esEs1(vwx230, vwx240, gg, gh)
new_esEs0(Right(vwx230), Right(vwx240), df, app(app(app(ty_@3, ed), ee), ef)) → new_esEs2(vwx230, vwx240, ed, ee, ef)
new_esEs3(Just(vwx230), Just(vwx240), app(app(app(ty_@3, bdh), bea), beb)) → new_esEs2(vwx230, vwx240, bdh, bea, beb)
new_esEs3(Just(vwx230), Just(vwx240), app(ty_Maybe, bec)) → new_esEs3(vwx230, vwx240, bec)
new_esEs2(@3(vwx230, vwx231, vwx232), @3(vwx240, vwx241, vwx242), he, app(ty_[], bbc), bbb) → new_esEs(vwx231, vwx241, bbc)
new_esEs2(@3(vwx230, vwx231, vwx232), @3(vwx240, vwx241, vwx242), app(ty_Maybe, bdb), hf, bbb) → new_esEs3(vwx230, vwx240, bdb)
new_esEs(:(vwx230, vwx231), :(vwx240, vwx241), app(ty_Maybe, cb)) → new_esEs3(vwx230, vwx240, cb)
new_esEs0(Right(vwx230), Right(vwx240), df, app(ty_[], ea)) → new_esEs(vwx230, vwx240, ea)
new_esEs0(Right(vwx230), Right(vwx240), df, app(ty_Maybe, eg)) → new_esEs3(vwx230, vwx240, eg)
new_esEs2(@3(vwx230, vwx231, vwx232), @3(vwx240, vwx241, vwx242), he, app(app(ty_Either, bah), bba), bbb) → new_esEs0(vwx231, vwx241, bah, bba)
new_esEs2(@3(vwx230, vwx231, vwx232), @3(vwx240, vwx241, vwx242), he, hf, app(app(ty_Either, hg), hh)) → new_esEs0(vwx232, vwx242, hg, hh)
new_esEs(:(vwx230, vwx231), :(vwx240, vwx241), app(ty_[], bd)) → new_esEs(vwx230, vwx240, bd)
new_esEs2(@3(vwx230, vwx231, vwx232), @3(vwx240, vwx241, vwx242), he, hf, app(app(app(ty_@3, bad), bae), baf)) → new_esEs2(vwx232, vwx242, bad, bae, baf)
new_esEs1(@2(vwx230, vwx231), @2(vwx240, vwx241), app(app(app(ty_@3, ha), hb), hc), ge) → new_esEs2(vwx230, vwx240, ha, hb, hc)
new_esEs0(Left(vwx230), Left(vwx240), app(app(ty_@2, cg), da), ce) → new_esEs1(vwx230, vwx240, cg, da)

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_primCmpNat(Succ(vwx3000), Succ(vwx4000)) → new_primCmpNat(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
                              ↳ QDP
QDP
                                ↳ QDPSizeChangeProof

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

new_ltEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), bba, hh, app(app(ty_Either, bcc), bcd)) → new_ltEs(vwx302, vwx402, bcc, bcd)
new_ltEs1(Just(@2(vwx300, vwx301)), Just(@2(vwx400, vwx401)), app(app(ty_@2, gd), app(app(ty_@2, ha), hb))) → new_ltEs2(vwx301, vwx401, ha, hb)
new_ltEs2(@2(vwx300, vwx301), @2(vwx400, vwx401), gd, app(app(ty_Either, ge), gf)) → new_ltEs(vwx301, vwx401, ge, gf)
new_ltEs1(Just(Left(vwx300)), Just(Left(vwx400)), app(app(ty_Either, app(app(ty_@2, bf), bg)), bc)) → new_ltEs2(vwx300, vwx400, bf, bg)
new_lt(vwx300, vwx400, eh, fa) → new_compare20(vwx300, vwx400, new_esEs4(vwx300, vwx400, eh, fa), eh, fa)
new_ltEs2(@2(vwx300, vwx301), @2(vwx400, vwx401), app(ty_Maybe, fb), fd) → new_compare21(vwx300, vwx400, new_esEs5(vwx300, vwx400, fb), fb)
new_compare0(:(vwx300, vwx301), :(vwx400, vwx401), df) → new_primCompAux(vwx300, vwx400, new_compare(vwx301, vwx401, df), df)
new_ltEs1(Just(@3(vwx300, vwx301, vwx302)), Just(@3(vwx400, vwx401, vwx402)), app(app(app(ty_@3, app(app(app(ty_@3, baf), bag), bah)), hh), baa)) → new_lt3(vwx300, vwx400, baf, bag, bah)
new_ltEs0(:(vwx300, vwx301), :(vwx400, vwx401), df) → new_primCompAux(vwx300, vwx400, new_compare(vwx301, vwx401, df), df)
new_ltEs1(Just(:(vwx300, vwx301)), Just(:(vwx400, vwx401)), app(ty_[], df)) → new_compare0(vwx301, vwx401, df)
new_ltEs1(Just(Right(vwx300)), Just(Right(vwx400)), app(app(ty_Either, cc), app(app(ty_Either, cd), ce))) → new_ltEs(vwx300, vwx400, cd, ce)
new_lt3(vwx300, vwx400, ga, gb, gc) → new_compare23(vwx300, vwx400, new_esEs7(vwx300, vwx400, ga, gb, gc), ga, gb, gc)
new_ltEs(Right(vwx300), Right(vwx400), cc, app(app(ty_Either, cd), ce)) → new_ltEs(vwx300, vwx400, cd, ce)
new_ltEs(Left(vwx300), Left(vwx400), app(app(ty_Either, ba), bb), bc) → new_ltEs(vwx300, vwx400, ba, bb)
new_ltEs2(@2(vwx300, vwx301), @2(vwx400, vwx401), gd, app(app(app(ty_@3, hc), hd), he)) → new_ltEs3(vwx301, vwx401, hc, hd, he)
new_compare0(:(vwx300, vwx301), :(vwx400, vwx401), df) → new_compare0(vwx301, vwx401, df)
new_primCompAux(vwx300, vwx400, vwx35, app(app(ty_@2, ec), ed)) → new_compare3(vwx300, vwx400, ec, ed)
new_ltEs1(Just(@2(vwx300, vwx301)), Just(@2(vwx400, vwx401)), app(app(ty_@2, app(ty_Maybe, fb)), fd)) → new_compare21(vwx300, vwx400, new_esEs5(vwx300, vwx400, fb), fb)
new_ltEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), bba, app(ty_[], bbd), baa) → new_lt0(vwx301, vwx401, bbd)
new_ltEs1(Just(@3(vwx300, vwx301, vwx302)), Just(@3(vwx400, vwx401, vwx402)), app(app(app(ty_@3, app(ty_[], bab)), hh), baa)) → new_lt0(vwx300, vwx400, bab)
new_ltEs1(Just(vwx30), Just(vwx40), app(ty_Maybe, fc)) → new_ltEs1(vwx30, vwx40, fc)
new_ltEs(Right(vwx300), Right(vwx400), cc, app(ty_[], cf)) → new_ltEs0(vwx300, vwx400, cf)
new_ltEs(Right(vwx300), Right(vwx400), cc, app(app(app(ty_@3, dc), dd), de)) → new_ltEs3(vwx300, vwx400, dc, dd, de)
new_ltEs1(Just(@2(vwx300, vwx301)), Just(@2(vwx400, vwx401)), app(app(ty_@2, gd), app(app(app(ty_@3, hc), hd), he))) → new_ltEs3(vwx301, vwx401, hc, hd, he)
new_compare3(vwx300, vwx400, fg, fh) → new_compare22(vwx300, vwx400, new_esEs6(vwx300, vwx400, fg, fh), fg, fh)
new_ltEs1(Just(Right(vwx300)), Just(Right(vwx400)), app(app(ty_Either, cc), app(ty_Maybe, cg))) → new_ltEs1(vwx300, vwx400, cg)
new_ltEs1(Just(@3(vwx300, vwx301, vwx302)), Just(@3(vwx400, vwx401, vwx402)), app(app(app(ty_@3, app(ty_Maybe, bac)), hh), baa)) → new_lt1(vwx300, vwx400, bac)
new_ltEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), app(ty_[], bab), hh, baa) → new_lt0(vwx300, vwx400, bab)
new_ltEs1(Just(@3(vwx300, vwx301, vwx302)), Just(@3(vwx400, vwx401, vwx402)), app(app(app(ty_@3, app(app(ty_@2, bad), bae)), hh), baa)) → new_lt2(vwx300, vwx400, bad, bae)
new_ltEs1(Just(@3(vwx300, vwx301, vwx302)), Just(@3(vwx400, vwx401, vwx402)), app(app(app(ty_@3, bba), hh), app(ty_[], bce))) → new_ltEs0(vwx302, vwx402, bce)
new_lt1(vwx300, vwx400, fb) → new_compare21(vwx300, vwx400, new_esEs5(vwx300, vwx400, fb), fb)
new_ltEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), bba, hh, app(ty_Maybe, bcf)) → new_ltEs1(vwx302, vwx402, bcf)
new_ltEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), app(app(ty_@2, bad), bae), hh, baa) → new_lt2(vwx300, vwx400, bad, bae)
new_ltEs1(Just(Left(vwx300)), Just(Left(vwx400)), app(app(ty_Either, app(app(app(ty_@3, bh), ca), cb)), bc)) → new_ltEs3(vwx300, vwx400, bh, ca, cb)
new_primCompAux(vwx300, vwx400, vwx35, app(ty_[], ea)) → new_compare0(vwx300, vwx400, ea)
new_ltEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), app(app(ty_Either, hf), hg), hh, baa) → new_lt(vwx300, vwx400, hf, hg)
new_ltEs1(Just(Left(vwx300)), Just(Left(vwx400)), app(app(ty_Either, app(ty_Maybe, be)), bc)) → new_ltEs1(vwx300, vwx400, be)
new_ltEs1(Just(@3(vwx300, vwx301, vwx302)), Just(@3(vwx400, vwx401, vwx402)), app(app(app(ty_@3, bba), hh), app(ty_Maybe, bcf))) → new_ltEs1(vwx302, vwx402, bcf)
new_ltEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), bba, app(app(ty_Either, bbb), bbc), baa) → new_lt(vwx301, vwx401, bbb, bbc)
new_ltEs1(Just(@3(vwx300, vwx301, vwx302)), Just(@3(vwx400, vwx401, vwx402)), app(app(app(ty_@3, bba), hh), app(app(ty_Either, bcc), bcd))) → new_ltEs(vwx302, vwx402, bcc, bcd)
new_primCompAux(vwx300, vwx400, vwx35, app(ty_Maybe, eb)) → new_compare2(vwx300, vwx400, eb)
new_ltEs2(@2(vwx300, vwx301), @2(vwx400, vwx401), gd, app(ty_[], gg)) → new_ltEs0(vwx301, vwx401, gg)
new_ltEs2(@2(vwx300, vwx301), @2(vwx400, vwx401), app(ty_[], ff), fd) → new_compare0(vwx300, vwx400, ff)
new_ltEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), bba, app(app(ty_@2, bbf), bbg), baa) → new_lt2(vwx301, vwx401, bbf, bbg)
new_primCompAux(vwx300, vwx400, vwx35, app(app(ty_Either, dg), dh)) → new_compare1(vwx300, vwx400, dg, dh)
new_ltEs1(Just(@3(vwx300, vwx301, vwx302)), Just(@3(vwx400, vwx401, vwx402)), app(app(app(ty_@3, bba), app(ty_[], bbd)), baa)) → new_lt0(vwx301, vwx401, bbd)
new_ltEs1(Just(@3(vwx300, vwx301, vwx302)), Just(@3(vwx400, vwx401, vwx402)), app(app(app(ty_@3, bba), app(app(ty_@2, bbf), bbg)), baa)) → new_lt2(vwx301, vwx401, bbf, bbg)
new_ltEs1(Just(@3(vwx300, vwx301, vwx302)), Just(@3(vwx400, vwx401, vwx402)), app(app(app(ty_@3, bba), app(app(ty_Either, bbb), bbc)), baa)) → new_lt(vwx301, vwx401, bbb, bbc)
new_ltEs1(Just(:(vwx300, vwx301)), Just(:(vwx400, vwx401)), app(ty_[], df)) → new_primCompAux(vwx300, vwx400, new_compare(vwx301, vwx401, df), df)
new_ltEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), bba, hh, app(app(ty_@2, bcg), bch)) → new_ltEs2(vwx302, vwx402, bcg, bch)
new_ltEs1(Just(Right(vwx300)), Just(Right(vwx400)), app(app(ty_Either, cc), app(app(app(ty_@3, dc), dd), de))) → new_ltEs3(vwx300, vwx400, dc, dd, de)
new_ltEs(Left(vwx300), Left(vwx400), app(ty_[], bd), bc) → new_ltEs0(vwx300, vwx400, bd)
new_ltEs1(Just(@2(vwx300, vwx301)), Just(@2(vwx400, vwx401)), app(app(ty_@2, gd), app(ty_[], gg))) → new_ltEs0(vwx301, vwx401, gg)
new_compare20(vwx300, vwx400, False, eh, fa) → new_ltEs(vwx300, vwx400, eh, fa)
new_ltEs1(Just(@2(vwx300, vwx301)), Just(@2(vwx400, vwx401)), app(app(ty_@2, app(ty_[], ff)), fd)) → new_compare0(vwx300, vwx400, ff)
new_ltEs2(@2(vwx300, vwx301), @2(vwx400, vwx401), app(app(app(ty_@3, ga), gb), gc), fd) → new_compare23(vwx300, vwx400, new_esEs7(vwx300, vwx400, ga, gb, gc), ga, gb, gc)
new_ltEs2(@2(vwx300, vwx301), @2(vwx400, vwx401), gd, app(ty_Maybe, gh)) → new_ltEs1(vwx301, vwx401, gh)
new_ltEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), bba, hh, app(ty_[], bce)) → new_ltEs0(vwx302, vwx402, bce)
new_ltEs1(Just(@3(vwx300, vwx301, vwx302)), Just(@3(vwx400, vwx401, vwx402)), app(app(app(ty_@3, bba), hh), app(app(ty_@2, bcg), bch))) → new_ltEs2(vwx302, vwx402, bcg, bch)
new_ltEs1(Just(@3(vwx300, vwx301, vwx302)), Just(@3(vwx400, vwx401, vwx402)), app(app(app(ty_@3, app(app(ty_Either, hf), hg)), hh), baa)) → new_lt(vwx300, vwx400, hf, hg)
new_lt0(vwx300, vwx400, ff) → new_compare0(vwx300, vwx400, ff)
new_ltEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), bba, app(ty_Maybe, bbe), baa) → new_lt1(vwx301, vwx401, bbe)
new_ltEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), bba, hh, app(app(app(ty_@3, bda), bdb), bdc)) → new_ltEs3(vwx302, vwx402, bda, bdb, bdc)
new_ltEs1(Just(Right(vwx300)), Just(Right(vwx400)), app(app(ty_Either, cc), app(app(ty_@2, da), db))) → new_ltEs2(vwx300, vwx400, da, db)
new_ltEs2(@2(vwx300, vwx301), @2(vwx400, vwx401), gd, app(app(ty_@2, ha), hb)) → new_ltEs2(vwx301, vwx401, ha, hb)
new_ltEs1(Just(@2(vwx300, vwx301)), Just(@2(vwx400, vwx401)), app(app(ty_@2, gd), app(ty_Maybe, gh))) → new_ltEs1(vwx301, vwx401, gh)
new_ltEs1(Just(Left(vwx300)), Just(Left(vwx400)), app(app(ty_Either, app(ty_[], bd)), bc)) → new_ltEs0(vwx300, vwx400, bd)
new_ltEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), app(app(app(ty_@3, baf), bag), bah), hh, baa) → new_lt3(vwx300, vwx400, baf, bag, bah)
new_ltEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), app(ty_Maybe, bac), hh, baa) → new_lt1(vwx300, vwx400, bac)
new_ltEs(Left(vwx300), Left(vwx400), app(ty_Maybe, be), bc) → new_ltEs1(vwx300, vwx400, be)
new_ltEs1(Just(@2(vwx300, vwx301)), Just(@2(vwx400, vwx401)), app(app(ty_@2, gd), app(app(ty_Either, ge), gf))) → new_ltEs(vwx301, vwx401, ge, gf)
new_ltEs(Left(vwx300), Left(vwx400), app(app(app(ty_@3, bh), ca), cb), bc) → new_ltEs3(vwx300, vwx400, bh, ca, cb)
new_ltEs2(@2(vwx300, vwx301), @2(vwx400, vwx401), app(app(ty_@2, fg), fh), fd) → new_compare22(vwx300, vwx400, new_esEs6(vwx300, vwx400, fg, fh), fg, fh)
new_ltEs(Right(vwx300), Right(vwx400), cc, app(app(ty_@2, da), db)) → new_ltEs2(vwx300, vwx400, da, db)
new_ltEs3(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), bba, app(app(app(ty_@3, bbh), bca), bcb), baa) → new_lt3(vwx301, vwx401, bbh, bca, bcb)
new_ltEs1(Just(@2(vwx300, vwx301)), Just(@2(vwx400, vwx401)), app(app(ty_@2, app(app(ty_@2, fg), fh)), fd)) → new_compare22(vwx300, vwx400, new_esEs6(vwx300, vwx400, fg, fh), fg, fh)
new_ltEs1(Just(@3(vwx300, vwx301, vwx302)), Just(@3(vwx400, vwx401, vwx402)), app(app(app(ty_@3, bba), hh), app(app(app(ty_@3, bda), bdb), bdc))) → new_ltEs3(vwx302, vwx402, bda, bdb, bdc)
new_compare2(vwx300, vwx400, fb) → new_compare21(vwx300, vwx400, new_esEs5(vwx300, vwx400, fb), fb)
new_lt2(vwx300, vwx400, fg, fh) → new_compare22(vwx300, vwx400, new_esEs6(vwx300, vwx400, fg, fh), fg, fh)
new_compare22(vwx300, vwx400, False, fg, fh) → new_ltEs2(vwx300, vwx400, fg, fh)
new_ltEs1(Just(@2(vwx300, vwx301)), Just(@2(vwx400, vwx401)), app(app(ty_@2, app(app(app(ty_@3, ga), gb), gc)), fd)) → new_compare23(vwx300, vwx400, new_esEs7(vwx300, vwx400, ga, gb, gc), ga, gb, gc)
new_ltEs0(:(vwx300, vwx301), :(vwx400, vwx401), df) → new_compare0(vwx301, vwx401, df)
new_compare4(vwx300, vwx400, ga, gb, gc) → new_compare23(vwx300, vwx400, new_esEs7(vwx300, vwx400, ga, gb, gc), ga, gb, gc)
new_ltEs(Left(vwx300), Left(vwx400), app(app(ty_@2, bf), bg), bc) → new_ltEs2(vwx300, vwx400, bf, bg)
new_compare1(vwx300, vwx400, eh, fa) → new_compare20(vwx300, vwx400, new_esEs4(vwx300, vwx400, eh, fa), eh, fa)
new_ltEs1(Just(@3(vwx300, vwx301, vwx302)), Just(@3(vwx400, vwx401, vwx402)), app(app(app(ty_@3, bba), app(ty_Maybe, bbe)), baa)) → new_lt1(vwx301, vwx401, bbe)
new_ltEs1(Just(@2(vwx300, vwx301)), Just(@2(vwx400, vwx401)), app(app(ty_@2, app(app(ty_Either, eh), fa)), fd)) → new_compare20(vwx300, vwx400, new_esEs4(vwx300, vwx400, eh, fa), eh, fa)
new_ltEs(Right(vwx300), Right(vwx400), cc, app(ty_Maybe, cg)) → new_ltEs1(vwx300, vwx400, cg)
new_compare21(vwx300, vwx400, False, fb) → new_ltEs1(vwx300, vwx400, fb)
new_ltEs2(@2(vwx300, vwx301), @2(vwx400, vwx401), app(app(ty_Either, eh), fa), fd) → new_compare20(vwx300, vwx400, new_esEs4(vwx300, vwx400, eh, fa), eh, fa)
new_primCompAux(vwx300, vwx400, vwx35, app(app(app(ty_@3, ee), ef), eg)) → new_compare4(vwx300, vwx400, ee, ef, eg)
new_compare23(vwx300, vwx400, False, ga, gb, gc) → new_ltEs3(vwx300, vwx400, ga, gb, gc)
new_ltEs1(Just(Left(vwx300)), Just(Left(vwx400)), app(app(ty_Either, app(app(ty_Either, ba), bb)), bc)) → new_ltEs(vwx300, vwx400, ba, bb)
new_ltEs1(Just(@3(vwx300, vwx301, vwx302)), Just(@3(vwx400, vwx401, vwx402)), app(app(app(ty_@3, bba), app(app(app(ty_@3, bbh), bca), bcb)), baa)) → new_lt3(vwx301, vwx401, bbh, bca, bcb)
new_ltEs1(Just(Right(vwx300)), Just(Right(vwx400)), app(app(ty_Either, cc), app(ty_[], cf))) → new_ltEs0(vwx300, vwx400, cf)

The TRS R consists of the following rules:

new_esEs25(vwx230, vwx240, ty_Char) → new_esEs19(vwx230, vwx240)
new_esEs21(vwx231, vwx241, app(app(ty_@2, ccc), ccd)) → new_esEs6(vwx231, vwx241, ccc, ccd)
new_ltEs11(LT, GT) → True
new_compare10(vwx300, vwx400, True, ga, gb, gc) → LT
new_esEs25(vwx230, vwx240, ty_Bool) → new_esEs15(vwx230, vwx240)
new_esEs4(Right(vwx230), Right(vwx240), bgg, ty_Integer) → new_esEs14(vwx230, vwx240)
new_lt6(vwx301, vwx401, ty_@0) → new_lt8(vwx301, vwx401)
new_ltEs10(False, True) → True
new_ltEs19(vwx301, vwx401, ty_Char) → new_ltEs15(vwx301, vwx401)
new_compare110(vwx300, vwx400, True, fg, fh) → LT
new_compare([], :(vwx400, vwx401), df) → LT
new_ltEs9(Right(vwx300), Right(vwx400), cc, app(app(app(ty_@3, dc), dd), de)) → new_ltEs4(vwx300, vwx400, dc, dd, de)
new_compare27(vwx300, vwx400, False) → new_compare11(vwx300, vwx400, new_ltEs10(vwx300, vwx400))
new_ltEs9(Right(vwx300), Right(vwx400), cc, ty_Char) → new_ltEs15(vwx300, vwx400)
new_ltEs6(Nothing, Just(vwx40), bdd) → True
new_compare28(Float(vwx300, vwx301), Float(vwx400, vwx401)) → new_compare5(new_sr0(vwx300, vwx400), new_sr0(vwx301, vwx401))
new_esEs20(vwx232, vwx242, ty_Int) → new_esEs9(vwx232, vwx242)
new_esEs7(@3(vwx230, vwx231, vwx232), @3(vwx240, vwx241, vwx242), cab, cac, cad) → new_asAs(new_esEs22(vwx230, vwx240, cab), new_asAs(new_esEs21(vwx231, vwx241, cac), new_esEs20(vwx232, vwx242, cad)))
new_ltEs7(vwx30, vwx40, bde) → new_not(new_compare16(vwx30, vwx40, bde))
new_esEs4(Right(vwx230), Right(vwx240), bgg, app(ty_Maybe, caa)) → new_esEs5(vwx230, vwx240, caa)
new_esEs23(vwx23, vwx24, ty_Float) → new_esEs16(vwx23, vwx24)
new_primMulNat0(Zero, Zero) → Zero
new_ltEs9(Right(vwx300), Right(vwx400), cc, ty_Int) → new_ltEs5(vwx300, vwx400)
new_compare(:(vwx300, vwx301), [], df) → GT
new_esEs24(vwx231, vwx241, ty_@0) → new_esEs13(vwx231, vwx241)
new_lt7(vwx300, vwx400, cec) → new_esEs8(new_compare16(vwx300, vwx400, cec))
new_esEs5(Just(vwx230), Just(vwx240), ty_Int) → new_esEs9(vwx230, vwx240)
new_esEs11(vwx230, vwx240, app(ty_Ratio, bee)) → new_esEs17(vwx230, vwx240, bee)
new_sr(Integer(vwx3000), Integer(vwx4010)) → Integer(new_primMulInt(vwx3000, vwx4010))
new_esEs11(vwx230, vwx240, ty_Float) → new_esEs16(vwx230, vwx240)
new_ltEs9(Right(vwx300), Right(vwx400), cc, ty_Double) → new_ltEs12(vwx300, vwx400)
new_ltEs18(vwx302, vwx402, app(ty_[], bce)) → new_ltEs13(vwx302, vwx402, bce)
new_lt6(vwx301, vwx401, ty_Integer) → new_lt19(vwx301, vwx401)
new_esEs4(Right(vwx230), Right(vwx240), bgg, ty_Int) → new_esEs9(vwx230, vwx240)
new_lt20(vwx300, vwx400, ty_@0) → new_lt8(vwx300, vwx400)
new_esEs21(vwx231, vwx241, app(ty_[], cca)) → new_esEs10(vwx231, vwx241, cca)
new_esEs4(Left(vwx230), Left(vwx240), app(ty_Ratio, bfh), bff) → new_esEs17(vwx230, vwx240, bfh)
new_lt20(vwx300, vwx400, app(app(app(ty_@3, ga), gb), gc)) → new_lt18(vwx300, vwx400, ga, gb, gc)
new_not(GT) → False
new_esEs5(Just(vwx230), Just(vwx240), ty_Bool) → new_esEs15(vwx230, vwx240)
new_lt5(vwx300, vwx400, app(ty_[], bab)) → new_lt13(vwx300, vwx400, bab)
new_ltEs16(vwx30, vwx40) → new_not(new_compare28(vwx30, vwx40))
new_esEs20(vwx232, vwx242, app(app(ty_Either, cae), caf)) → new_esEs4(vwx232, vwx242, cae, caf)
new_esEs12(LT, GT) → False
new_esEs12(GT, LT) → False
new_esEs4(Right(vwx230), Right(vwx240), bgg, app(app(app(ty_@3, bhf), bhg), bhh)) → new_esEs7(vwx230, vwx240, bhf, bhg, bhh)
new_esEs23(vwx23, vwx24, ty_@0) → new_esEs13(vwx23, vwx24)
new_esEs4(Right(vwx230), Right(vwx240), bgg, ty_Ordering) → new_esEs12(vwx230, vwx240)
new_esEs4(Left(vwx230), Left(vwx240), app(app(ty_@2, bga), bgb), bff) → new_esEs6(vwx230, vwx240, bga, bgb)
new_ltEs15(vwx30, vwx40) → new_not(new_compare7(vwx30, vwx40))
new_ltEs18(vwx302, vwx402, app(app(app(ty_@3, bda), bdb), bdc)) → new_ltEs4(vwx302, vwx402, bda, bdb, bdc)
new_esEs21(vwx231, vwx241, ty_Double) → new_esEs18(vwx231, vwx241)
new_esEs18(Double(vwx230, vwx231), Double(vwx240, vwx241)) → new_esEs9(new_sr0(vwx230, vwx240), new_sr0(vwx231, vwx241))
new_ltEs9(Right(vwx300), Right(vwx400), cc, ty_Ordering) → new_ltEs11(vwx300, vwx400)
new_compare17(vwx300, vwx400, app(app(app(ty_@3, ee), ef), eg)) → new_compare13(vwx300, vwx400, ee, ef, eg)
new_esEs21(vwx231, vwx241, app(app(app(ty_@3, cce), ccf), ccg)) → new_esEs7(vwx231, vwx241, cce, ccf, ccg)
new_esEs5(Just(vwx230), Just(vwx240), app(ty_Maybe, cga)) → new_esEs5(vwx230, vwx240, cga)
new_ltEs18(vwx302, vwx402, app(ty_Ratio, bdh)) → new_ltEs7(vwx302, vwx402, bdh)
new_ltEs18(vwx302, vwx402, ty_Bool) → new_ltEs10(vwx302, vwx402)
new_esEs11(vwx230, vwx240, app(app(app(ty_@3, beh), bfa), bfb)) → new_esEs7(vwx230, vwx240, beh, bfa, bfb)
new_ltEs10(False, False) → True
new_lt20(vwx300, vwx400, app(ty_[], ff)) → new_lt13(vwx300, vwx400, ff)
new_esEs26(vwx231, vwx241, ty_Integer) → new_esEs14(vwx231, vwx241)
new_pePe(False, vwx23, vwx24, vwx25, cgb) → new_asAs(new_esEs23(vwx23, vwx24, cgb), vwx25)
new_esEs20(vwx232, vwx242, app(app(ty_@2, cba), cbb)) → new_esEs6(vwx232, vwx242, cba, cbb)
new_lt20(vwx300, vwx400, ty_Float) → new_lt17(vwx300, vwx400)
new_ltEs6(Just(vwx30), Just(vwx40), ty_Bool) → new_ltEs10(vwx30, vwx40)
new_esEs17(:%(vwx230, vwx231), :%(vwx240, vwx241), cgc) → new_asAs(new_esEs27(vwx230, vwx240, cgc), new_esEs26(vwx231, vwx241, cgc))
new_esEs22(vwx230, vwx240, ty_Ordering) → new_esEs12(vwx230, vwx240)
new_ltEs19(vwx301, vwx401, ty_Float) → new_ltEs16(vwx301, vwx401)
new_esEs25(vwx230, vwx240, app(ty_[], dab)) → new_esEs10(vwx230, vwx240, dab)
new_esEs25(vwx230, vwx240, app(app(ty_Either, chh), daa)) → new_esEs4(vwx230, vwx240, chh, daa)
new_esEs4(Left(vwx230), Left(vwx240), ty_Float, bff) → new_esEs16(vwx230, vwx240)
new_esEs15(False, True) → False
new_esEs15(True, False) → False
new_lt5(vwx300, vwx400, app(ty_Ratio, bdf)) → new_lt7(vwx300, vwx400, bdf)
new_ltEs9(Left(vwx300), Left(vwx400), ty_Ordering, bc) → new_ltEs11(vwx300, vwx400)
new_ltEs5(vwx30, vwx40) → new_not(new_compare5(vwx30, vwx40))
new_esEs22(vwx230, vwx240, app(app(ty_Either, cda), cdb)) → new_esEs4(vwx230, vwx240, cda, cdb)
new_esEs4(Left(vwx230), Left(vwx240), ty_@0, bff) → new_esEs13(vwx230, vwx240)
new_compare13(vwx300, vwx400, ga, gb, gc) → new_compare24(vwx300, vwx400, new_esEs7(vwx300, vwx400, ga, gb, gc), ga, gb, gc)
new_lt20(vwx300, vwx400, ty_Double) → new_lt12(vwx300, vwx400)
new_compare14(@0, @0) → EQ
new_ltEs9(Right(vwx300), Right(vwx400), cc, ty_@0) → new_ltEs8(vwx300, vwx400)
new_ltEs17(vwx30, vwx40) → new_not(new_compare29(vwx30, vwx40))
new_ltEs6(Just(vwx30), Just(vwx40), app(ty_[], df)) → new_ltEs13(vwx30, vwx40, df)
new_compare25(vwx300, vwx400, False, fg, fh) → new_compare110(vwx300, vwx400, new_ltEs14(vwx300, vwx400, fg, fh), fg, fh)
new_lt5(vwx300, vwx400, ty_Bool) → new_lt10(vwx300, vwx400)
new_lt4(vwx300, vwx400) → new_esEs8(new_compare5(vwx300, vwx400))
new_esEs20(vwx232, vwx242, app(ty_Ratio, cah)) → new_esEs17(vwx232, vwx242, cah)
new_esEs14(Integer(vwx230), Integer(vwx240)) → new_primEqInt(vwx230, vwx240)
new_lt9(vwx300, vwx400, eh, fa) → new_esEs8(new_compare15(vwx300, vwx400, eh, fa))
new_esEs23(vwx23, vwx24, app(app(app(ty_@3, cab), cac), cad)) → new_esEs7(vwx23, vwx24, cab, cac, cad)
new_primCmpNat0(Zero, Succ(vwx4000)) → LT
new_lt6(vwx301, vwx401, app(ty_[], bbd)) → new_lt13(vwx301, vwx401, bbd)
new_ltEs9(Left(vwx300), Left(vwx400), ty_Integer, bc) → new_ltEs17(vwx300, vwx400)
new_ltEs9(Left(vwx300), Left(vwx400), ty_@0, bc) → new_ltEs8(vwx300, vwx400)
new_compare17(vwx300, vwx400, ty_Int) → new_compare5(vwx300, vwx400)
new_esEs25(vwx230, vwx240, app(app(ty_@2, dad), dae)) → new_esEs6(vwx230, vwx240, dad, dae)
new_ltEs9(Left(vwx300), Left(vwx400), app(ty_Maybe, be), bc) → new_ltEs6(vwx300, vwx400, be)
new_ltEs19(vwx301, vwx401, app(app(app(ty_@3, hc), hd), he)) → new_ltEs4(vwx301, vwx401, hc, hd, he)
new_esEs12(LT, LT) → True
new_ltEs13(vwx30, vwx40, df) → new_not(new_compare(vwx30, vwx40, df))
new_esEs24(vwx231, vwx241, app(app(ty_@2, chb), chc)) → new_esEs6(vwx231, vwx241, chb, chc)
new_primEqNat0(Zero, Zero) → True
new_esEs4(Right(vwx230), Right(vwx240), bgg, app(ty_[], bhb)) → new_esEs10(vwx230, vwx240, bhb)
new_primMulNat0(Succ(vwx30000), Succ(vwx40100)) → new_primPlusNat1(new_primMulNat0(vwx30000, Succ(vwx40100)), vwx40100)
new_esEs16(Float(vwx230, vwx231), Float(vwx240, vwx241)) → new_esEs9(new_sr0(vwx230, vwx240), new_sr0(vwx231, vwx241))
new_compare111(vwx300, vwx400, False, eh, fa) → GT
new_lt15(vwx300, vwx400, fg, fh) → new_esEs8(new_compare6(vwx300, vwx400, fg, fh))
new_esEs4(Left(vwx230), Left(vwx240), app(ty_[], bfg), bff) → new_esEs10(vwx230, vwx240, bfg)
new_ltEs6(Just(vwx30), Just(vwx40), ty_@0) → new_ltEs8(vwx30, vwx40)
new_esEs24(vwx231, vwx241, app(ty_Ratio, cha)) → new_esEs17(vwx231, vwx241, cha)
new_compare110(vwx300, vwx400, False, fg, fh) → GT
new_compare12(vwx300, vwx400, False, fb) → GT
new_lt13(vwx300, vwx400, ff) → new_esEs8(new_compare(vwx300, vwx400, ff))
new_ltEs18(vwx302, vwx402, ty_Int) → new_ltEs5(vwx302, vwx402)
new_esEs5(Just(vwx230), Just(vwx240), ty_Integer) → new_esEs14(vwx230, vwx240)
new_esEs4(Right(vwx230), Right(vwx240), bgg, ty_@0) → new_esEs13(vwx230, vwx240)
new_esEs4(Left(vwx230), Left(vwx240), ty_Int, bff) → new_esEs9(vwx230, vwx240)
new_esEs24(vwx231, vwx241, ty_Char) → new_esEs19(vwx231, vwx241)
new_esEs11(vwx230, vwx240, ty_Ordering) → new_esEs12(vwx230, vwx240)
new_esEs25(vwx230, vwx240, ty_Float) → new_esEs16(vwx230, vwx240)
new_ltEs9(Right(vwx300), Left(vwx400), cc, bc) → False
new_compare26(vwx300, vwx400, False, fb) → new_compare12(vwx300, vwx400, new_ltEs6(vwx300, vwx400, fb), fb)
new_esEs20(vwx232, vwx242, app(app(app(ty_@3, cbc), cbd), cbe)) → new_esEs7(vwx232, vwx242, cbc, cbd, cbe)
new_lt6(vwx301, vwx401, ty_Double) → new_lt12(vwx301, vwx401)
new_ltEs9(Right(vwx300), Right(vwx400), cc, ty_Float) → new_ltEs16(vwx300, vwx400)
new_esEs11(vwx230, vwx240, ty_@0) → new_esEs13(vwx230, vwx240)
new_ltEs18(vwx302, vwx402, ty_Double) → new_ltEs12(vwx302, vwx402)
new_lt5(vwx300, vwx400, ty_Double) → new_lt12(vwx300, vwx400)
new_lt19(vwx300, vwx400) → new_esEs8(new_compare29(vwx300, vwx400))
new_esEs25(vwx230, vwx240, ty_Ordering) → new_esEs12(vwx230, vwx240)
new_esEs4(Right(vwx230), Right(vwx240), bgg, app(app(ty_Either, bgh), bha)) → new_esEs4(vwx230, vwx240, bgh, bha)
new_compare24(vwx300, vwx400, True, ga, gb, gc) → EQ
new_primEqInt(Neg(Succ(vwx2300)), Neg(Succ(vwx2400))) → new_primEqNat0(vwx2300, vwx2400)
new_esEs15(True, True) → True
new_esEs4(Left(vwx230), Left(vwx240), app(app(ty_Either, bfd), bfe), bff) → new_esEs4(vwx230, vwx240, bfd, bfe)
new_compare10(vwx300, vwx400, False, ga, gb, gc) → GT
new_compare17(vwx300, vwx400, app(app(ty_Either, dg), dh)) → new_compare15(vwx300, vwx400, dg, dh)
new_esEs4(Right(vwx230), Right(vwx240), bgg, ty_Float) → new_esEs16(vwx230, vwx240)
new_lt20(vwx300, vwx400, ty_Int) → new_lt4(vwx300, vwx400)
new_esEs12(EQ, LT) → False
new_esEs12(LT, EQ) → False
new_esEs11(vwx230, vwx240, ty_Int) → new_esEs9(vwx230, vwx240)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_ltEs9(Right(vwx300), Right(vwx400), cc, app(ty_Maybe, cg)) → new_ltEs6(vwx300, vwx400, cg)
new_lt5(vwx300, vwx400, ty_Int) → new_lt4(vwx300, vwx400)
new_compare29(Integer(vwx300), Integer(vwx400)) → new_primCmpInt(vwx300, vwx400)
new_primEqInt(Neg(Succ(vwx2300)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(vwx2400))) → False
new_esEs20(vwx232, vwx242, ty_Bool) → new_esEs15(vwx232, vwx242)
new_esEs5(Just(vwx230), Just(vwx240), ty_Float) → new_esEs16(vwx230, vwx240)
new_primPlusNat1(Zero, vwx40100) → Succ(vwx40100)
new_esEs4(Right(vwx230), Right(vwx240), bgg, ty_Double) → new_esEs18(vwx230, vwx240)
new_lt20(vwx300, vwx400, ty_Char) → new_lt16(vwx300, vwx400)
new_compare7(Char(vwx300), Char(vwx400)) → new_primCmpNat0(vwx300, vwx400)
new_esEs21(vwx231, vwx241, app(app(ty_Either, cbg), cbh)) → new_esEs4(vwx231, vwx241, cbg, cbh)
new_esEs4(Right(vwx230), Right(vwx240), bgg, ty_Bool) → new_esEs15(vwx230, vwx240)
new_compare([], [], df) → EQ
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_esEs21(vwx231, vwx241, app(ty_Ratio, ccb)) → new_esEs17(vwx231, vwx241, ccb)
new_esEs23(vwx23, vwx24, ty_Integer) → new_esEs14(vwx23, vwx24)
new_esEs10([], :(vwx240, vwx241), bea) → False
new_esEs10(:(vwx230, vwx231), [], bea) → False
new_ltEs18(vwx302, vwx402, ty_@0) → new_ltEs8(vwx302, vwx402)
new_primCmpNat0(Succ(vwx3000), Succ(vwx4000)) → new_primCmpNat0(vwx3000, vwx4000)
new_lt6(vwx301, vwx401, app(ty_Maybe, bbe)) → new_lt14(vwx301, vwx401, bbe)
new_compare112(vwx300, vwx400, True) → LT
new_compare16(:%(vwx300, vwx301), :%(vwx400, vwx401), ty_Int) → new_compare5(new_sr0(vwx300, vwx401), new_sr0(vwx400, vwx301))
new_lt5(vwx300, vwx400, app(ty_Maybe, bac)) → new_lt14(vwx300, vwx400, bac)
new_primEqInt(Pos(Succ(vwx2300)), Pos(Succ(vwx2400))) → new_primEqNat0(vwx2300, vwx2400)
new_esEs6(@2(vwx230, vwx231), @2(vwx240, vwx241), cgd, cge) → new_asAs(new_esEs25(vwx230, vwx240, cgd), new_esEs24(vwx231, vwx241, cge))
new_ltEs19(vwx301, vwx401, ty_Integer) → new_ltEs17(vwx301, vwx401)
new_esEs25(vwx230, vwx240, app(ty_Maybe, dba)) → new_esEs5(vwx230, vwx240, dba)
new_esEs25(vwx230, vwx240, ty_Int) → new_esEs9(vwx230, vwx240)
new_compare17(vwx300, vwx400, app(app(ty_@2, ec), ed)) → new_compare6(vwx300, vwx400, ec, ed)
new_esEs10([], [], bea) → True
new_compare18(vwx300, vwx400) → new_compare27(vwx300, vwx400, new_esEs15(vwx300, vwx400))
new_primEqNat0(Succ(vwx2300), Succ(vwx2400)) → new_primEqNat0(vwx2300, vwx2400)
new_esEs4(Left(vwx230), Left(vwx240), app(app(app(ty_@3, bgc), bgd), bge), bff) → new_esEs7(vwx230, vwx240, bgc, bgd, bge)
new_primCompAux00(vwx39, LT) → LT
new_ltEs18(vwx302, vwx402, ty_Char) → new_ltEs15(vwx302, vwx402)
new_ltEs8(vwx30, vwx40) → new_not(new_compare14(vwx30, vwx40))
new_primCmpInt(Neg(Succ(vwx3000)), Neg(vwx400)) → new_primCmpNat0(vwx400, Succ(vwx3000))
new_lt5(vwx300, vwx400, ty_Ordering) → new_lt11(vwx300, vwx400)
new_esEs23(vwx23, vwx24, ty_Bool) → new_esEs15(vwx23, vwx24)
new_lt5(vwx300, vwx400, ty_Char) → new_lt16(vwx300, vwx400)
new_esEs12(EQ, EQ) → True
new_primEqInt(Pos(Succ(vwx2300)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(vwx2400))) → False
new_compare210(vwx300, vwx400, False, eh, fa) → new_compare111(vwx300, vwx400, new_ltEs9(vwx300, vwx400, eh, fa), eh, fa)
new_esEs21(vwx231, vwx241, ty_Bool) → new_esEs15(vwx231, vwx241)
new_compare8(vwx300, vwx400, fb) → new_compare26(vwx300, vwx400, new_esEs5(vwx300, vwx400, fb), fb)
new_ltEs19(vwx301, vwx401, app(ty_Maybe, gh)) → new_ltEs6(vwx301, vwx401, gh)
new_lt5(vwx300, vwx400, ty_Integer) → new_lt19(vwx300, vwx400)
new_primPlusNat0(Succ(vwx5300), Zero) → Succ(vwx5300)
new_primPlusNat0(Zero, Succ(vwx401000)) → Succ(vwx401000)
new_ltEs6(Just(vwx30), Nothing, bdd) → False
new_ltEs6(Just(vwx30), Just(vwx40), ty_Float) → new_ltEs16(vwx30, vwx40)
new_primCmpNat0(Zero, Zero) → EQ
new_ltEs11(GT, EQ) → False
new_ltEs9(Left(vwx300), Right(vwx400), cc, bc) → True
new_primCmpNat0(Succ(vwx3000), Zero) → GT
new_esEs21(vwx231, vwx241, ty_@0) → new_esEs13(vwx231, vwx241)
new_esEs22(vwx230, vwx240, ty_Integer) → new_esEs14(vwx230, vwx240)
new_primCmpInt(Neg(Zero), Pos(Succ(vwx4000))) → LT
new_esEs8(LT) → True
new_esEs24(vwx231, vwx241, ty_Double) → new_esEs18(vwx231, vwx241)
new_compare17(vwx300, vwx400, ty_Integer) → new_compare29(vwx300, vwx400)
new_ltEs9(Left(vwx300), Left(vwx400), ty_Int, bc) → new_ltEs5(vwx300, vwx400)
new_compare17(vwx300, vwx400, app(ty_[], ea)) → new_compare(vwx300, vwx400, ea)
new_lt6(vwx301, vwx401, ty_Float) → new_lt17(vwx301, vwx401)
new_compare12(vwx300, vwx400, True, fb) → LT
new_ltEs9(Right(vwx300), Right(vwx400), cc, app(ty_[], cf)) → new_ltEs13(vwx300, vwx400, cf)
new_lt6(vwx301, vwx401, app(app(app(ty_@3, bbh), bca), bcb)) → new_lt18(vwx301, vwx401, bbh, bca, bcb)
new_primEqInt(Pos(Succ(vwx2300)), Neg(vwx240)) → False
new_primEqInt(Neg(Succ(vwx2300)), Pos(vwx240)) → False
new_compare17(vwx300, vwx400, app(ty_Maybe, eb)) → new_compare8(vwx300, vwx400, eb)
new_esEs25(vwx230, vwx240, ty_@0) → new_esEs13(vwx230, vwx240)
new_ltEs18(vwx302, vwx402, app(app(ty_@2, bcg), bch)) → new_ltEs14(vwx302, vwx402, bcg, bch)
new_compare(:(vwx300, vwx301), :(vwx400, vwx401), df) → new_primCompAux0(vwx300, vwx400, new_compare(vwx301, vwx401, df), df)
new_esEs8(GT) → False
new_esEs5(Just(vwx230), Just(vwx240), ty_Char) → new_esEs19(vwx230, vwx240)
new_ltEs6(Just(vwx30), Just(vwx40), app(ty_Maybe, fc)) → new_ltEs6(vwx30, vwx40, fc)
new_esEs21(vwx231, vwx241, ty_Ordering) → new_esEs12(vwx231, vwx241)
new_esEs11(vwx230, vwx240, ty_Double) → new_esEs18(vwx230, vwx240)
new_esEs22(vwx230, vwx240, app(app(ty_@2, cde), cdf)) → new_esEs6(vwx230, vwx240, cde, cdf)
new_esEs26(vwx231, vwx241, ty_Int) → new_esEs9(vwx231, vwx241)
new_esEs5(Just(vwx230), Just(vwx240), ty_@0) → new_esEs13(vwx230, vwx240)
new_ltEs11(GT, LT) → False
new_primEqInt(Pos(Zero), Neg(Succ(vwx2400))) → False
new_primEqInt(Neg(Zero), Pos(Succ(vwx2400))) → False
new_esEs13(@0, @0) → True
new_lt5(vwx300, vwx400, app(app(ty_@2, bad), bae)) → new_lt15(vwx300, vwx400, bad, bae)
new_esEs24(vwx231, vwx241, ty_Ordering) → new_esEs12(vwx231, vwx241)
new_primCmpInt(Pos(Zero), Pos(Succ(vwx4000))) → new_primCmpNat0(Zero, Succ(vwx4000))
new_primCompAux00(vwx39, EQ) → vwx39
new_compare17(vwx300, vwx400, ty_Char) → new_compare7(vwx300, vwx400)
new_esEs4(Left(vwx230), Left(vwx240), ty_Integer, bff) → new_esEs14(vwx230, vwx240)
new_lt16(vwx300, vwx400) → new_esEs8(new_compare7(vwx300, vwx400))
new_esEs20(vwx232, vwx242, ty_Char) → new_esEs19(vwx232, vwx242)
new_ltEs11(LT, EQ) → True
new_compare17(vwx300, vwx400, ty_@0) → new_compare14(vwx300, vwx400)
new_compare26(vwx300, vwx400, True, fb) → EQ
new_ltEs11(LT, LT) → True
new_esEs10(:(vwx230, vwx231), :(vwx240, vwx241), bea) → new_asAs(new_esEs11(vwx230, vwx240, bea), new_esEs10(vwx231, vwx241, bea))
new_compare17(vwx300, vwx400, ty_Bool) → new_compare18(vwx300, vwx400)
new_esEs21(vwx231, vwx241, ty_Integer) → new_esEs14(vwx231, vwx241)
new_primCmpInt(Pos(Succ(vwx3000)), Pos(vwx400)) → new_primCmpNat0(Succ(vwx3000), vwx400)
new_compare210(vwx300, vwx400, True, eh, fa) → EQ
new_esEs12(EQ, GT) → False
new_esEs4(Right(vwx230), Right(vwx240), bgg, app(ty_Ratio, bhc)) → new_esEs17(vwx230, vwx240, bhc)
new_esEs12(GT, EQ) → False
new_esEs23(vwx23, vwx24, app(app(ty_@2, cgd), cge)) → new_esEs6(vwx23, vwx24, cgd, cge)
new_lt18(vwx300, vwx400, ga, gb, gc) → new_esEs8(new_compare13(vwx300, vwx400, ga, gb, gc))
new_ltEs9(Right(vwx300), Right(vwx400), cc, ty_Integer) → new_ltEs17(vwx300, vwx400)
new_lt5(vwx300, vwx400, app(app(app(ty_@3, baf), bag), bah)) → new_lt18(vwx300, vwx400, baf, bag, bah)
new_not0True
new_esEs23(vwx23, vwx24, app(ty_[], bea)) → new_esEs10(vwx23, vwx24, bea)
new_compare15(vwx300, vwx400, eh, fa) → new_compare210(vwx300, vwx400, new_esEs4(vwx300, vwx400, eh, fa), eh, fa)
new_ltEs11(GT, GT) → True
new_esEs24(vwx231, vwx241, app(ty_Maybe, chg)) → new_esEs5(vwx231, vwx241, chg)
new_esEs4(Right(vwx230), Right(vwx240), bgg, app(app(ty_@2, bhd), bhe)) → new_esEs6(vwx230, vwx240, bhd, bhe)
new_primCompAux0(vwx300, vwx400, vwx35, df) → new_primCompAux00(vwx35, new_compare17(vwx300, vwx400, df))
new_lt6(vwx301, vwx401, ty_Bool) → new_lt10(vwx301, vwx401)
new_ltEs9(Left(vwx300), Left(vwx400), app(ty_[], bd), bc) → new_ltEs13(vwx300, vwx400, bd)
new_primCmpInt(Pos(Succ(vwx3000)), Neg(vwx400)) → GT
new_ltEs9(Right(vwx300), Right(vwx400), cc, ty_Bool) → new_ltEs10(vwx300, vwx400)
new_esEs22(vwx230, vwx240, app(app(app(ty_@3, cdg), cdh), cea)) → new_esEs7(vwx230, vwx240, cdg, cdh, cea)
new_ltEs18(vwx302, vwx402, ty_Ordering) → new_ltEs11(vwx302, vwx402)
new_ltEs9(Right(vwx300), Right(vwx400), cc, app(app(ty_@2, da), db)) → new_ltEs14(vwx300, vwx400, da, db)
new_esEs11(vwx230, vwx240, app(ty_Maybe, bfc)) → new_esEs5(vwx230, vwx240, bfc)
new_primMulInt(Pos(vwx3000), Pos(vwx4010)) → Pos(new_primMulNat0(vwx3000, vwx4010))
new_esEs22(vwx230, vwx240, ty_Double) → new_esEs18(vwx230, vwx240)
new_esEs4(Left(vwx230), Left(vwx240), ty_Bool, bff) → new_esEs15(vwx230, vwx240)
new_lt10(vwx300, vwx400) → new_esEs8(new_compare18(vwx300, vwx400))
new_esEs23(vwx23, vwx24, app(app(ty_Either, bgg), bff)) → new_esEs4(vwx23, vwx24, bgg, bff)
new_ltEs9(Right(vwx300), Right(vwx400), cc, app(app(ty_Either, cd), ce)) → new_ltEs9(vwx300, vwx400, cd, ce)
new_compare24(vwx300, vwx400, False, ga, gb, gc) → new_compare10(vwx300, vwx400, new_ltEs4(vwx300, vwx400, ga, gb, gc), ga, gb, gc)
new_ltEs18(vwx302, vwx402, ty_Integer) → new_ltEs17(vwx302, vwx402)
new_esEs5(Just(vwx230), Just(vwx240), ty_Double) → new_esEs18(vwx230, vwx240)
new_primMulInt(Neg(vwx3000), Neg(vwx4010)) → Pos(new_primMulNat0(vwx3000, vwx4010))
new_esEs24(vwx231, vwx241, ty_Bool) → new_esEs15(vwx231, vwx241)
new_ltEs19(vwx301, vwx401, ty_Int) → new_ltEs5(vwx301, vwx401)
new_primEqNat0(Zero, Succ(vwx2400)) → False
new_primEqNat0(Succ(vwx2300), Zero) → False
new_ltEs6(Just(vwx30), Just(vwx40), ty_Double) → new_ltEs12(vwx30, vwx40)
new_esEs21(vwx231, vwx241, ty_Int) → new_esEs9(vwx231, vwx241)
new_lt11(vwx300, vwx400) → new_esEs8(new_compare19(vwx300, vwx400))
new_compare17(vwx300, vwx400, app(ty_Ratio, ced)) → new_compare16(vwx300, vwx400, ced)
new_primPlusNat0(Zero, Zero) → Zero
new_esEs25(vwx230, vwx240, app(ty_Ratio, dac)) → new_esEs17(vwx230, vwx240, dac)
new_lt5(vwx300, vwx400, app(app(ty_Either, hf), hg)) → new_lt9(vwx300, vwx400, hf, hg)
new_compare16(:%(vwx300, vwx301), :%(vwx400, vwx401), ty_Integer) → new_compare29(new_sr(vwx300, vwx401), new_sr(vwx400, vwx301))
new_compare25(vwx300, vwx400, True, fg, fh) → EQ
new_esEs20(vwx232, vwx242, app(ty_[], cag)) → new_esEs10(vwx232, vwx242, cag)
new_esEs11(vwx230, vwx240, ty_Char) → new_esEs19(vwx230, vwx240)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs24(vwx231, vwx241, app(app(ty_Either, cgf), cgg)) → new_esEs4(vwx231, vwx241, cgf, cgg)
new_esEs5(Just(vwx230), Just(vwx240), app(ty_[], cfb)) → new_esEs10(vwx230, vwx240, cfb)
new_lt6(vwx301, vwx401, app(app(ty_Either, bbb), bbc)) → new_lt9(vwx301, vwx401, bbb, bbc)
new_esEs22(vwx230, vwx240, ty_Int) → new_esEs9(vwx230, vwx240)
new_ltEs19(vwx301, vwx401, ty_Ordering) → new_ltEs11(vwx301, vwx401)
new_lt6(vwx301, vwx401, ty_Int) → new_lt4(vwx301, vwx401)
new_lt8(vwx300, vwx400) → new_esEs8(new_compare14(vwx300, vwx400))
new_ltEs19(vwx301, vwx401, ty_Bool) → new_ltEs10(vwx301, vwx401)
new_ltEs6(Just(vwx30), Just(vwx40), app(app(ty_@2, gd), fd)) → new_ltEs14(vwx30, vwx40, gd, fd)
new_pePe(True, vwx23, vwx24, vwx25, cgb) → True
new_primPlusNat1(Succ(vwx530), vwx40100) → Succ(Succ(new_primPlusNat0(vwx530, vwx40100)))
new_esEs23(vwx23, vwx24, ty_Double) → new_esEs18(vwx23, vwx24)
new_compare6(vwx300, vwx400, fg, fh) → new_compare25(vwx300, vwx400, new_esEs6(vwx300, vwx400, fg, fh), fg, fh)
new_esEs24(vwx231, vwx241, ty_Int) → new_esEs9(vwx231, vwx241)
new_esEs23(vwx23, vwx24, app(ty_Ratio, cgc)) → new_esEs17(vwx23, vwx24, cgc)
new_primCmpInt(Neg(Zero), Neg(Succ(vwx4000))) → new_primCmpNat0(Succ(vwx4000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(vwx4000))) → GT
new_lt20(vwx300, vwx400, app(app(ty_@2, fg), fh)) → new_lt15(vwx300, vwx400, fg, fh)
new_ltEs12(vwx30, vwx40) → new_not(new_compare9(vwx30, vwx40))
new_compare5(vwx30, vwx40) → new_primCmpInt(vwx30, vwx40)
new_esEs25(vwx230, vwx240, ty_Integer) → new_esEs14(vwx230, vwx240)
new_ltEs9(Left(vwx300), Left(vwx400), ty_Float, bc) → new_ltEs16(vwx300, vwx400)
new_lt6(vwx301, vwx401, app(ty_Ratio, bdg)) → new_lt7(vwx301, vwx401, bdg)
new_sr0(vwx300, vwx401) → new_primMulInt(vwx300, vwx401)
new_esEs27(vwx230, vwx240, ty_Int) → new_esEs9(vwx230, vwx240)
new_ltEs4(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), bba, hh, baa) → new_pePe(new_lt5(vwx300, vwx400, bba), vwx300, vwx400, new_pePe(new_lt6(vwx301, vwx401, hh), vwx301, vwx401, new_ltEs18(vwx302, vwx402, baa), hh), bba)
new_esEs24(vwx231, vwx241, app(ty_[], cgh)) → new_esEs10(vwx231, vwx241, cgh)
new_esEs19(Char(vwx230), Char(vwx240)) → new_primEqNat0(vwx230, vwx240)
new_esEs22(vwx230, vwx240, ty_Char) → new_esEs19(vwx230, vwx240)
new_ltEs11(EQ, EQ) → True
new_esEs11(vwx230, vwx240, app(app(ty_@2, bef), beg)) → new_esEs6(vwx230, vwx240, bef, beg)
new_esEs24(vwx231, vwx241, app(app(app(ty_@3, chd), che), chf)) → new_esEs7(vwx231, vwx241, chd, che, chf)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_ltEs6(Just(vwx30), Just(vwx40), app(app(app(ty_@3, bba), hh), baa)) → new_ltEs4(vwx30, vwx40, bba, hh, baa)
new_esEs20(vwx232, vwx242, app(ty_Maybe, cbf)) → new_esEs5(vwx232, vwx242, cbf)
new_esEs11(vwx230, vwx240, ty_Bool) → new_esEs15(vwx230, vwx240)
new_ltEs10(True, False) → False
new_asAs(False, vwx34) → False
new_primMulInt(Neg(vwx3000), Pos(vwx4010)) → Neg(new_primMulNat0(vwx3000, vwx4010))
new_primMulInt(Pos(vwx3000), Neg(vwx4010)) → Neg(new_primMulNat0(vwx3000, vwx4010))
new_primMulNat0(Zero, Succ(vwx40100)) → Zero
new_primMulNat0(Succ(vwx30000), Zero) → Zero
new_ltEs9(Left(vwx300), Left(vwx400), ty_Double, bc) → new_ltEs12(vwx300, vwx400)
new_esEs11(vwx230, vwx240, app(app(ty_Either, beb), bec)) → new_esEs4(vwx230, vwx240, beb, bec)
new_ltEs11(EQ, LT) → False
new_compare17(vwx300, vwx400, ty_Double) → new_compare9(vwx300, vwx400)
new_compare17(vwx300, vwx400, ty_Ordering) → new_compare19(vwx300, vwx400)
new_lt6(vwx301, vwx401, app(app(ty_@2, bbf), bbg)) → new_lt15(vwx301, vwx401, bbf, bbg)
new_esEs23(vwx23, vwx24, ty_Ordering) → new_esEs12(vwx23, vwx24)
new_ltEs6(Just(vwx30), Just(vwx40), ty_Ordering) → new_ltEs11(vwx30, vwx40)
new_esEs22(vwx230, vwx240, app(ty_[], cdc)) → new_esEs10(vwx230, vwx240, cdc)
new_esEs23(vwx23, vwx24, ty_Int) → new_esEs9(vwx23, vwx24)
new_ltEs19(vwx301, vwx401, app(app(ty_Either, ge), gf)) → new_ltEs9(vwx301, vwx401, ge, gf)
new_ltEs6(Just(vwx30), Just(vwx40), ty_Char) → new_ltEs15(vwx30, vwx40)
new_esEs20(vwx232, vwx242, ty_Float) → new_esEs16(vwx232, vwx242)
new_esEs5(Just(vwx230), Just(vwx240), app(app(ty_@2, cfd), cfe)) → new_esEs6(vwx230, vwx240, cfd, cfe)
new_ltEs19(vwx301, vwx401, ty_Double) → new_ltEs12(vwx301, vwx401)
new_not(EQ) → new_not0
new_esEs4(Left(vwx230), Left(vwx240), app(ty_Maybe, bgf), bff) → new_esEs5(vwx230, vwx240, bgf)
new_esEs23(vwx23, vwx24, app(ty_Maybe, ceg)) → new_esEs5(vwx23, vwx24, ceg)
new_lt20(vwx300, vwx400, app(ty_Maybe, fb)) → new_lt14(vwx300, vwx400, fb)
new_lt6(vwx301, vwx401, ty_Ordering) → new_lt11(vwx301, vwx401)
new_ltEs6(Just(vwx30), Just(vwx40), app(ty_Ratio, bde)) → new_ltEs7(vwx30, vwx40, bde)
new_compare27(vwx300, vwx400, True) → EQ
new_esEs20(vwx232, vwx242, ty_Integer) → new_esEs14(vwx232, vwx242)
new_ltEs19(vwx301, vwx401, ty_@0) → new_ltEs8(vwx301, vwx401)
new_esEs5(Just(vwx230), Nothing, ceg) → False
new_esEs5(Nothing, Just(vwx240), ceg) → False
new_esEs24(vwx231, vwx241, ty_Integer) → new_esEs14(vwx231, vwx241)
new_esEs22(vwx230, vwx240, ty_Bool) → new_esEs15(vwx230, vwx240)
new_ltEs6(Nothing, Nothing, bdd) → True
new_esEs4(Left(vwx230), Left(vwx240), ty_Ordering, bff) → new_esEs12(vwx230, vwx240)
new_esEs4(Right(vwx230), Right(vwx240), bgg, ty_Char) → new_esEs19(vwx230, vwx240)
new_esEs22(vwx230, vwx240, ty_Float) → new_esEs16(vwx230, vwx240)
new_lt20(vwx300, vwx400, ty_Integer) → new_lt19(vwx300, vwx400)
new_esEs25(vwx230, vwx240, app(app(app(ty_@3, daf), dag), dah)) → new_esEs7(vwx230, vwx240, daf, dag, dah)
new_ltEs18(vwx302, vwx402, app(app(ty_Either, bcc), bcd)) → new_ltEs9(vwx302, vwx402, bcc, bcd)
new_lt6(vwx301, vwx401, ty_Char) → new_lt16(vwx301, vwx401)
new_lt12(vwx300, vwx400) → new_esEs8(new_compare9(vwx300, vwx400))
new_ltEs9(Left(vwx300), Left(vwx400), app(ty_Ratio, cee), bc) → new_ltEs7(vwx300, vwx400, cee)
new_lt20(vwx300, vwx400, ty_Ordering) → new_lt11(vwx300, vwx400)
new_compare211(vwx300, vwx400, False) → new_compare112(vwx300, vwx400, new_ltEs11(vwx300, vwx400))
new_compare11(vwx300, vwx400, False) → GT
new_compare19(vwx300, vwx400) → new_compare211(vwx300, vwx400, new_esEs12(vwx300, vwx400))
new_esEs20(vwx232, vwx242, ty_Ordering) → new_esEs12(vwx232, vwx242)
new_not(LT) → new_not0
new_ltEs18(vwx302, vwx402, ty_Float) → new_ltEs16(vwx302, vwx402)
new_esEs5(Just(vwx230), Just(vwx240), ty_Ordering) → new_esEs12(vwx230, vwx240)
new_compare11(vwx300, vwx400, True) → LT
new_esEs25(vwx230, vwx240, ty_Double) → new_esEs18(vwx230, vwx240)
new_ltEs9(Left(vwx300), Left(vwx400), app(app(ty_Either, ba), bb), bc) → new_ltEs9(vwx300, vwx400, ba, bb)
new_ltEs9(Right(vwx300), Right(vwx400), cc, app(ty_Ratio, cef)) → new_ltEs7(vwx300, vwx400, cef)
new_esEs23(vwx23, vwx24, ty_Char) → new_esEs19(vwx23, vwx24)
new_esEs5(Nothing, Nothing, ceg) → True
new_ltEs9(Left(vwx300), Left(vwx400), ty_Bool, bc) → new_ltEs10(vwx300, vwx400)
new_ltEs18(vwx302, vwx402, app(ty_Maybe, bcf)) → new_ltEs6(vwx302, vwx402, bcf)
new_lt17(vwx300, vwx400) → new_esEs8(new_compare28(vwx300, vwx400))
new_esEs5(Just(vwx230), Just(vwx240), app(app(app(ty_@3, cff), cfg), cfh)) → new_esEs7(vwx230, vwx240, cff, cfg, cfh)
new_compare112(vwx300, vwx400, False) → GT
new_esEs5(Just(vwx230), Just(vwx240), app(ty_Ratio, cfc)) → new_esEs17(vwx230, vwx240, cfc)
new_esEs12(GT, GT) → True
new_esEs22(vwx230, vwx240, app(ty_Ratio, cdd)) → new_esEs17(vwx230, vwx240, cdd)
new_lt5(vwx300, vwx400, ty_Float) → new_lt17(vwx300, vwx400)
new_esEs8(EQ) → False
new_primPlusNat0(Succ(vwx5300), Succ(vwx401000)) → Succ(Succ(new_primPlusNat0(vwx5300, vwx401000)))
new_esEs22(vwx230, vwx240, app(ty_Maybe, ceb)) → new_esEs5(vwx230, vwx240, ceb)
new_esEs21(vwx231, vwx241, app(ty_Maybe, cch)) → new_esEs5(vwx231, vwx241, cch)
new_esEs22(vwx230, vwx240, ty_@0) → new_esEs13(vwx230, vwx240)
new_compare111(vwx300, vwx400, True, eh, fa) → LT
new_ltEs10(True, True) → True
new_compare17(vwx300, vwx400, ty_Float) → new_compare28(vwx300, vwx400)
new_esEs27(vwx230, vwx240, ty_Integer) → new_esEs14(vwx230, vwx240)
new_esEs24(vwx231, vwx241, ty_Float) → new_esEs16(vwx231, vwx241)
new_asAs(True, vwx34) → vwx34
new_ltEs19(vwx301, vwx401, app(ty_Ratio, dbb)) → new_ltEs7(vwx301, vwx401, dbb)
new_esEs11(vwx230, vwx240, app(ty_[], bed)) → new_esEs10(vwx230, vwx240, bed)
new_esEs4(Left(vwx230), Right(vwx240), bgg, bff) → False
new_esEs4(Right(vwx230), Left(vwx240), bgg, bff) → False
new_esEs4(Left(vwx230), Left(vwx240), ty_Char, bff) → new_esEs19(vwx230, vwx240)
new_compare211(vwx300, vwx400, True) → EQ
new_ltEs9(Left(vwx300), Left(vwx400), app(app(app(ty_@3, bh), ca), cb), bc) → new_ltEs4(vwx300, vwx400, bh, ca, cb)
new_ltEs6(Just(vwx30), Just(vwx40), ty_Int) → new_ltEs5(vwx30, vwx40)
new_lt5(vwx300, vwx400, ty_@0) → new_lt8(vwx300, vwx400)
new_lt14(vwx300, vwx400, fb) → new_esEs8(new_compare8(vwx300, vwx400, fb))
new_esEs11(vwx230, vwx240, ty_Integer) → new_esEs14(vwx230, vwx240)
new_ltEs19(vwx301, vwx401, app(app(ty_@2, ha), hb)) → new_ltEs14(vwx301, vwx401, ha, hb)
new_esEs9(vwx23, vwx24) → new_primEqInt(vwx23, vwx24)
new_ltEs14(@2(vwx300, vwx301), @2(vwx400, vwx401), gd, fd) → new_pePe(new_lt20(vwx300, vwx400, gd), vwx300, vwx400, new_ltEs19(vwx301, vwx401, fd), gd)
new_lt20(vwx300, vwx400, app(ty_Ratio, cec)) → new_lt7(vwx300, vwx400, cec)
new_esEs4(Left(vwx230), Left(vwx240), ty_Double, bff) → new_esEs18(vwx230, vwx240)
new_ltEs6(Just(vwx30), Just(vwx40), app(app(ty_Either, cc), bc)) → new_ltEs9(vwx30, vwx40, cc, bc)
new_primCompAux00(vwx39, GT) → GT
new_esEs5(Just(vwx230), Just(vwx240), app(app(ty_Either, ceh), cfa)) → new_esEs4(vwx230, vwx240, ceh, cfa)
new_esEs21(vwx231, vwx241, ty_Float) → new_esEs16(vwx231, vwx241)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_ltEs6(Just(vwx30), Just(vwx40), ty_Integer) → new_ltEs17(vwx30, vwx40)
new_esEs20(vwx232, vwx242, ty_@0) → new_esEs13(vwx232, vwx242)
new_ltEs11(EQ, GT) → True
new_esEs21(vwx231, vwx241, ty_Char) → new_esEs19(vwx231, vwx241)
new_ltEs19(vwx301, vwx401, app(ty_[], gg)) → new_ltEs13(vwx301, vwx401, gg)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_lt20(vwx300, vwx400, ty_Bool) → new_lt10(vwx300, vwx400)
new_lt20(vwx300, vwx400, app(app(ty_Either, eh), fa)) → new_lt9(vwx300, vwx400, eh, fa)
new_primCmpInt(Neg(Succ(vwx3000)), Pos(vwx400)) → LT
new_esEs20(vwx232, vwx242, ty_Double) → new_esEs18(vwx232, vwx242)
new_ltEs9(Left(vwx300), Left(vwx400), ty_Char, bc) → new_ltEs15(vwx300, vwx400)
new_ltEs9(Left(vwx300), Left(vwx400), app(app(ty_@2, bf), bg), bc) → new_ltEs14(vwx300, vwx400, bf, bg)
new_compare9(Double(vwx300, vwx301), Double(vwx400, vwx401)) → new_compare5(new_sr0(vwx300, vwx400), new_sr0(vwx301, vwx401))
new_esEs15(False, False) → True

The set Q consists of the following terms:

new_lt14(x0, x1, x2)
new_esEs13(@0, @0)
new_ltEs9(Left(x0), Left(x1), ty_@0, x2)
new_compare6(x0, x1, x2, x3)
new_ltEs11(EQ, GT)
new_ltEs11(GT, EQ)
new_esEs25(x0, x1, ty_Int)
new_primPlusNat1(Zero, x0)
new_lt5(x0, x1, ty_@0)
new_esEs23(x0, x1, ty_Float)
new_esEs4(Right(x0), Right(x1), x2, ty_Float)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs16(Float(x0, x1), Float(x2, x3))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_ltEs9(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_primCompAux0(x0, x1, x2, x3)
new_ltEs9(Right(x0), Left(x1), x2, x3)
new_ltEs9(Left(x0), Right(x1), x2, x3)
new_esEs22(x0, x1, ty_Ordering)
new_lt7(x0, x1, x2)
new_compare17(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, ty_Integer)
new_ltEs11(EQ, EQ)
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_compare17(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_lt20(x0, x1, ty_Double)
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs24(x0, x1, ty_Float)
new_compare18(x0, x1)
new_compare16(:%(x0, x1), :%(x2, x3), ty_Integer)
new_ltEs12(x0, x1)
new_lt20(x0, x1, ty_Integer)
new_esEs15(True, True)
new_lt5(x0, x1, ty_Bool)
new_esEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs24(x0, x1, ty_Ordering)
new_esEs20(x0, x1, ty_Ordering)
new_lt6(x0, x1, ty_Integer)
new_ltEs6(Just(x0), Just(x1), ty_Bool)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_compare26(x0, x1, False, x2)
new_esEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_esEs5(Just(x0), Just(x1), ty_Float)
new_lt5(x0, x1, ty_Double)
new_esEs20(x0, x1, ty_Double)
new_esEs11(x0, x1, ty_Int)
new_ltEs18(x0, x1, ty_Char)
new_esEs9(x0, x1)
new_esEs8(LT)
new_lt5(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_asAs(False, x0)
new_esEs15(False, False)
new_primCompAux00(x0, LT)
new_esEs12(GT, EQ)
new_esEs12(EQ, GT)
new_esEs11(x0, x1, app(ty_Maybe, x2))
new_esEs11(x0, x1, ty_Float)
new_lt6(x0, x1, ty_Bool)
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Left(x0), Right(x1), x2, x3)
new_esEs4(Right(x0), Left(x1), x2, x3)
new_compare12(x0, x1, True, x2)
new_primPlusNat0(Succ(x0), Zero)
new_esEs12(GT, GT)
new_ltEs18(x0, x1, ty_Bool)
new_compare25(x0, x1, True, x2, x3)
new_esEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_esEs23(x0, x1, ty_Double)
new_ltEs6(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_lt20(x0, x1, ty_Float)
new_ltEs9(Right(x0), Right(x1), x2, ty_Bool)
new_esEs5(Just(x0), Just(x1), ty_Double)
new_compare5(x0, x1)
new_ltEs19(x0, x1, ty_@0)
new_ltEs9(Right(x0), Right(x1), x2, ty_Integer)
new_esEs23(x0, x1, ty_@0)
new_compare210(x0, x1, True, x2, x3)
new_esEs24(x0, x1, ty_Integer)
new_ltEs9(Right(x0), Right(x1), x2, app(ty_[], x3))
new_ltEs6(Nothing, Nothing, x0)
new_esEs25(x0, x1, ty_Ordering)
new_ltEs11(LT, GT)
new_ltEs11(GT, LT)
new_esEs5(Just(x0), Just(x1), app(ty_[], x2))
new_compare9(Double(x0, x1), Double(x2, x3))
new_compare11(x0, x1, False)
new_esEs21(x0, x1, ty_Int)
new_ltEs6(Just(x0), Just(x1), ty_Ordering)
new_compare17(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Right(x0), Right(x1), x2, ty_Int)
new_compare110(x0, x1, True, x2, x3)
new_primEqNat0(Zero, Zero)
new_esEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_esEs24(x0, x1, ty_Int)
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_esEs22(x0, x1, app(ty_[], x2))
new_lt18(x0, x1, x2, x3, x4)
new_esEs8(EQ)
new_lt5(x0, x1, ty_Char)
new_esEs5(Just(x0), Just(x1), ty_Char)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_primMulNat0(Zero, Zero)
new_compare24(x0, x1, True, x2, x3, x4)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_compare17(x0, x1, ty_Ordering)
new_esEs11(x0, x1, app(app(ty_Either, x2), x3))
new_esEs11(x0, x1, ty_Integer)
new_ltEs14(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt5(x0, x1, ty_Ordering)
new_ltEs8(x0, x1)
new_ltEs9(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_esEs22(x0, x1, ty_@0)
new_lt6(x0, x1, app(ty_Maybe, x2))
new_compare17(x0, x1, ty_Bool)
new_lt13(x0, x1, x2)
new_esEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_esEs14(Integer(x0), Integer(x1))
new_esEs22(x0, x1, ty_Bool)
new_lt9(x0, x1, x2, x3)
new_compare17(x0, x1, ty_Double)
new_compare17(x0, x1, app(ty_Ratio, x2))
new_esEs20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, ty_@0)
new_compare17(x0, x1, app(app(ty_@2, x2), x3))
new_primMulInt(Pos(x0), Pos(x1))
new_ltEs6(Just(x0), Just(x1), ty_Char)
new_lt20(x0, x1, ty_Char)
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare17(x0, x1, ty_Char)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs10([], :(x0, x1), x2)
new_compare26(x0, x1, True, x2)
new_compare111(x0, x1, False, x2, x3)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_ltEs9(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs13(x0, x1, x2)
new_esEs18(Double(x0, x1), Double(x2, x3))
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs10([], [], x0)
new_lt6(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs22(x0, x1, ty_Char)
new_lt20(x0, x1, ty_@0)
new_esEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, ty_Int)
new_lt5(x0, x1, app(ty_[], x2))
new_pePe(False, x0, x1, x2, x3)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_compare12(x0, x1, False, x2)
new_compare17(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_esEs11(x0, x1, ty_Bool)
new_esEs25(x0, x1, ty_Double)
new_esEs21(x0, x1, app(ty_[], x2))
new_esEs20(x0, x1, ty_Integer)
new_esEs5(Nothing, Nothing, x0)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_esEs11(x0, x1, ty_@0)
new_lt6(x0, x1, ty_Ordering)
new_lt20(x0, x1, app(ty_[], x2))
new_primEqNat0(Zero, Succ(x0))
new_ltEs6(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_ltEs9(Left(x0), Left(x1), ty_Float, x2)
new_compare211(x0, x1, False)
new_compare211(x0, x1, True)
new_ltEs19(x0, x1, ty_Integer)
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_compare25(x0, x1, False, x2, x3)
new_lt10(x0, x1)
new_compare8(x0, x1, x2)
new_compare27(x0, x1, False)
new_lt5(x0, x1, app(ty_Ratio, x2))
new_esEs12(EQ, LT)
new_esEs12(LT, EQ)
new_esEs20(x0, x1, app(ty_[], x2))
new_lt12(x0, x1)
new_pePe(True, x0, x1, x2, x3)
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_not0
new_lt6(x0, x1, app(app(ty_@2, x2), x3))
new_esEs12(EQ, EQ)
new_primPlusNat0(Zero, Zero)
new_primEqNat0(Succ(x0), Succ(x1))
new_ltEs10(False, False)
new_ltEs19(x0, x1, ty_Char)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_ltEs6(Just(x0), Just(x1), ty_Integer)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_ltEs19(x0, x1, app(ty_[], x2))
new_compare17(x0, x1, app(ty_[], x2))
new_ltEs6(Nothing, Just(x0), x1)
new_esEs17(:%(x0, x1), :%(x2, x3), x4)
new_sr0(x0, x1)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Left(x0), Left(x1), ty_Bool, x2)
new_primMulNat0(Zero, Succ(x0))
new_esEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_esEs5(Just(x0), Just(x1), ty_@0)
new_esEs20(x0, x1, ty_Float)
new_compare(:(x0, x1), :(x2, x3), x4)
new_esEs12(LT, GT)
new_esEs12(GT, LT)
new_primPlusNat0(Zero, Succ(x0))
new_ltEs6(Just(x0), Just(x1), ty_Double)
new_ltEs18(x0, x1, ty_Double)
new_esEs5(Just(x0), Just(x1), ty_Integer)
new_esEs5(Just(x0), Just(x1), ty_Ordering)
new_esEs4(Right(x0), Right(x1), x2, ty_Integer)
new_ltEs9(Right(x0), Right(x1), x2, ty_Int)
new_ltEs15(x0, x1)
new_ltEs9(Left(x0), Left(x1), ty_Double, x2)
new_esEs21(x0, x1, ty_Bool)
new_not(GT)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs9(Left(x0), Left(x1), ty_Int, x2)
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs8(GT)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs4(Right(x0), Right(x1), x2, ty_@0)
new_esEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_ltEs9(Right(x0), Right(x1), x2, ty_Ordering)
new_compare15(x0, x1, x2, x3)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_lt11(x0, x1)
new_compare112(x0, x1, False)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_lt17(x0, x1)
new_compare27(x0, x1, True)
new_primEqNat0(Succ(x0), Zero)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_ltEs18(x0, x1, ty_Integer)
new_esEs23(x0, x1, ty_Ordering)
new_esEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs25(x0, x1, ty_Char)
new_lt5(x0, x1, app(ty_Maybe, x2))
new_lt19(x0, x1)
new_ltEs19(x0, x1, ty_Float)
new_esEs22(x0, x1, ty_Integer)
new_primCompAux00(x0, GT)
new_primCmpInt(Pos(Zero), Pos(Zero))
new_esEs15(True, False)
new_esEs15(False, True)
new_esEs25(x0, x1, ty_Bool)
new_ltEs9(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs4(Left(x0), Left(x1), ty_Float, x2)
new_esEs20(x0, x1, app(ty_Ratio, x2))
new_esEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, ty_Float)
new_lt16(x0, x1)
new_esEs24(x0, x1, ty_Double)
new_compare([], :(x0, x1), x2)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_compare14(@0, @0)
new_esEs4(Left(x0), Left(x1), ty_Char, x2)
new_esEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs20(x0, x1, ty_Bool)
new_esEs21(x0, x1, ty_Double)
new_ltEs6(Just(x0), Nothing, x1)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_compare([], [], x0)
new_compare111(x0, x1, True, x2, x3)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs11(x0, x1, app(ty_[], x2))
new_esEs25(x0, x1, app(ty_[], x2))
new_ltEs18(x0, x1, ty_Ordering)
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, ty_Float)
new_esEs5(Just(x0), Nothing, x1)
new_primCmpNat0(Zero, Succ(x0))
new_ltEs19(x0, x1, ty_Bool)
new_ltEs6(Just(x0), Just(x1), app(ty_Maybe, x2))
new_lt5(x0, x1, ty_Float)
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_compare210(x0, x1, False, x2, x3)
new_esEs22(x0, x1, ty_Float)
new_ltEs18(x0, x1, ty_@0)
new_compare29(Integer(x0), Integer(x1))
new_ltEs11(LT, LT)
new_lt20(x0, x1, ty_Ordering)
new_compare11(x0, x1, True)
new_primPlusNat1(Succ(x0), x1)
new_esEs23(x0, x1, ty_Integer)
new_ltEs11(LT, EQ)
new_ltEs11(EQ, LT)
new_ltEs9(Left(x0), Left(x1), ty_Integer, x2)
new_esEs5(Just(x0), Just(x1), ty_Bool)
new_esEs21(x0, x1, ty_Integer)
new_esEs11(x0, x1, app(ty_Ratio, x2))
new_lt6(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs9(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_ltEs9(Left(x0), Left(x1), ty_Bool, x2)
new_esEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs25(x0, x1, ty_Float)
new_esEs27(x0, x1, ty_Int)
new_compare19(x0, x1)
new_ltEs4(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_esEs4(Left(x0), Left(x1), ty_Integer, x2)
new_primCmpNat0(Zero, Zero)
new_esEs10(:(x0, x1), [], x2)
new_lt5(x0, x1, app(app(ty_@2, x2), x3))
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_compare112(x0, x1, True)
new_compare13(x0, x1, x2, x3, x4)
new_esEs4(Right(x0), Right(x1), x2, ty_Bool)
new_esEs20(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs6(Just(x0), Just(x1), ty_@0)
new_compare16(:%(x0, x1), :%(x2, x3), ty_Int)
new_lt6(x0, x1, ty_@0)
new_ltEs10(True, True)
new_lt6(x0, x1, ty_Double)
new_ltEs19(x0, x1, ty_Ordering)
new_ltEs6(Just(x0), Just(x1), ty_Float)
new_compare7(Char(x0), Char(x1))
new_esEs20(x0, x1, ty_Int)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs5(Nothing, Just(x0), x1)
new_ltEs9(Right(x0), Right(x1), x2, ty_Double)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_ltEs9(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs24(x0, x1, ty_@0)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs5(Just(x0), Just(x1), ty_Int)
new_esEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_primMulNat0(Succ(x0), Zero)
new_esEs4(Left(x0), Left(x1), ty_Double, x2)
new_compare17(x0, x1, ty_Int)
new_esEs26(x0, x1, ty_Int)
new_esEs24(x0, x1, ty_Bool)
new_compare28(Float(x0, x1), Float(x2, x3))
new_lt6(x0, x1, ty_Char)
new_lt5(x0, x1, app(app(ty_Either, x2), x3))
new_primCmpNat0(Succ(x0), Succ(x1))
new_esEs22(x0, x1, ty_Int)
new_lt5(x0, x1, ty_Int)
new_ltEs9(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_lt5(x0, x1, ty_Integer)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_esEs20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs11(x0, x1, ty_Double)
new_compare10(x0, x1, False, x2, x3, x4)
new_esEs24(x0, x1, ty_Char)
new_not(EQ)
new_ltEs16(x0, x1)
new_ltEs6(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs5(x0, x1)
new_esEs21(x0, x1, ty_Char)
new_compare110(x0, x1, False, x2, x3)
new_lt15(x0, x1, x2, x3)
new_esEs27(x0, x1, ty_Integer)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_lt8(x0, x1)
new_primMulInt(Pos(x0), Neg(x1))
new_primMulInt(Neg(x0), Pos(x1))
new_esEs10(:(x0, x1), :(x2, x3), x4)
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_lt6(x0, x1, ty_Float)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs23(x0, x1, app(ty_[], x2))
new_esEs4(Left(x0), Left(x1), ty_@0, x2)
new_ltEs6(Just(x0), Just(x1), app(ty_Ratio, x2))
new_ltEs9(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_asAs(True, x0)
new_ltEs9(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs4(Left(x0), Left(x1), ty_Int, x2)
new_sr(Integer(x0), Integer(x1))
new_esEs20(x0, x1, ty_Char)
new_ltEs6(Just(x0), Just(x1), ty_Int)
new_ltEs9(Right(x0), Right(x1), x2, ty_Float)
new_ltEs9(Right(x0), Right(x1), x2, ty_@0)
new_lt4(x0, x1)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs11(x0, x1, ty_Ordering)
new_lt6(x0, x1, ty_Int)
new_lt6(x0, x1, app(ty_[], x2))
new_ltEs18(x0, x1, ty_Int)
new_esEs19(Char(x0), Char(x1))
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs11(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_Bool)
new_lt6(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_compare24(x0, x1, False, x2, x3, x4)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_esEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_compare(:(x0, x1), [], x2)
new_ltEs10(False, True)
new_ltEs10(True, False)
new_primPlusNat0(Succ(x0), Succ(x1))
new_esEs21(x0, x1, ty_Ordering)
new_ltEs9(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs6(Just(x0), Just(x1), app(ty_[], x2))
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Right(x0), Right(x1), x2, ty_Char)
new_ltEs18(x0, x1, app(ty_[], x2))
new_esEs4(Right(x0), Right(x1), x2, ty_Double)
new_esEs22(x0, x1, ty_Double)
new_primMulInt(Neg(x0), Neg(x1))
new_ltEs19(x0, x1, ty_Int)
new_primCompAux00(x0, EQ)
new_esEs23(x0, x1, ty_Char)
new_esEs11(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primEqInt(Pos(Zero), Pos(Zero))
new_esEs20(x0, x1, app(ty_Maybe, x2))
new_esEs25(x0, x1, ty_Integer)
new_compare17(x0, x1, ty_@0)
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs11(x0, x1, ty_Char)
new_ltEs19(x0, x1, ty_Double)
new_esEs20(x0, x1, ty_@0)
new_lt20(x0, x1, ty_Bool)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs9(Right(x0), Right(x1), x2, ty_Char)
new_esEs12(LT, LT)
new_ltEs9(Left(x0), Left(x1), ty_Ordering, x2)
new_primCmpNat0(Succ(x0), Zero)
new_compare17(x0, x1, ty_Float)
new_not(LT)
new_ltEs9(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_lt20(x0, x1, ty_Int)
new_ltEs17(x0, x1)
new_ltEs7(x0, x1, x2)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_ltEs9(Left(x0), Left(x1), ty_Char, x2)
new_compare10(x0, x1, True, x2, x3, x4)
new_esEs21(x0, x1, ty_@0)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_ltEs11(GT, 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: