YES 4.268 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
  ((max :: (Ord b, Ord a) => (b,a)  ->  (b,a)  ->  (b,a)) :: (Ord b, Ord a) => (b,a)  ->  (b,a)  ->  (b,a))

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
  ((max :: (Ord b, Ord a) => (a,b)  ->  (a,b)  ->  (a,b)) :: (Ord b, Ord a) => (a,b)  ->  (a,b)  ->  (a,b))

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
  ((max :: (Ord a, Ord b) => (a,b)  ->  (a,b)  ->  (a,b)) :: (Ord a, Ord b) => (a,b)  ->  (a,b)  ->  (a,b))

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
  ((max :: (Ord a, Ord b) => (a,b)  ->  (a,b)  ->  (a,b)) :: (Ord a, Ord b) => (a,b)  ->  (a,b)  ->  (a,b))

module Main where
  import qualified Prelude


Cond Reductions:
The following Function with conditions
max x y
 | x <= y
 = y
 | otherwise
 = x

is transformed to
max x y = max2 x y

max0 x y True = x

max1 x y True = y
max1 x y False = max0 x y otherwise

max2 x y = max1 x y (x <= y)

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

is transformed to
compare x y = compare3 x y

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

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

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

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
  ((max :: (Ord a, Ord b) => (a,b)  ->  (a,b)  ->  (a,b)) :: (Ord b, Ord a) => (a,b)  ->  (a,b)  ->  (a,b))

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

reduce2D vwv vww = gcd vwv vww

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

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

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



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

mainModule Main
  ((max :: (Ord a, Ord b) => (b,a)  ->  (b,a)  ->  (b,a)) :: (Ord a, Ord b) => (b,a)  ->  (b,a)  ->  (b,a))

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
  (max :: (Ord b, Ord a) => (b,a)  ->  (b,a)  ->  (b,a))

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(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
                                ↳ QDPSizeChangeProof
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_primPlusNat(Succ(vwx15800), Succ(vwx400000)) → new_primPlusNat(vwx15800, 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
                              ↳ QDP
                                ↳ QDPSizeChangeProof
                              ↳ 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
                              ↳ QDP
                                ↳ QDPSizeChangeProof
                              ↳ QDP
                              ↳ 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
                                ↳ QDPSizeChangeProof
                              ↳ QDP

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

new_esEs0(:(vwx300, vwx301), :(vwx400, vwx401), app(app(ty_@2, fd), ff)) → new_esEs3(vwx300, vwx400, fd, ff)
new_esEs1(Left(vwx300), Left(vwx400), app(app(ty_@2, hc), hd), gf) → new_esEs3(vwx300, vwx400, hc, hd)
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_esEs3(@2(vwx300, vwx301), @2(vwx400, vwx401), app(app(ty_Either, bce), bcf), bcc) → new_esEs1(vwx300, vwx400, bce, bcf)
new_esEs3(@2(vwx300, vwx301), @2(vwx400, vwx401), bdb, app(ty_Maybe, bea)) → new_esEs2(vwx301, vwx401, bea)
new_esEs1(Left(vwx300), Left(vwx400), app(ty_[], gg), gf) → new_esEs0(vwx300, vwx400, gg)
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_esEs3(@2(vwx300, vwx301), @2(vwx400, vwx401), app(app(app(ty_@3, bbh), bca), bcb), bcc) → new_esEs(vwx300, vwx400, bbh, bca, bcb)
new_esEs(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), cd, app(ty_Maybe, dd), be) → new_esEs2(vwx301, vwx401, dd)
new_esEs(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), cd, app(app(ty_Either, db), dc), be) → new_esEs1(vwx301, vwx401, db, dc)
new_esEs0(:(vwx300, vwx301), :(vwx400, vwx401), app(app(app(ty_@3, fg), fh), ga)) → new_esEs(vwx300, vwx400, fg, fh, ga)
new_esEs1(Right(vwx300), Right(vwx400), he, app(ty_[], baa)) → new_esEs0(vwx300, vwx400, baa)
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_esEs1(Left(vwx300), Left(vwx400), app(app(ty_Either, gh), ha), gf) → new_esEs1(vwx300, vwx400, gh, ha)
new_esEs2(Just(vwx300), Just(vwx400), app(ty_Maybe, bbe)) → new_esEs2(vwx300, vwx400, bbe)
new_esEs1(Right(vwx300), Right(vwx400), he, app(app(ty_Either, bab), bac)) → new_esEs1(vwx300, vwx400, bab, bac)
new_esEs(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), app(app(ty_Either, bg), bh), bd, be) → new_esEs1(vwx300, vwx400, bg, bh)
new_esEs1(Right(vwx300), Right(vwx400), he, app(app(app(ty_@3, hf), hg), hh)) → new_esEs(vwx300, vwx400, hf, hg, hh)
new_esEs(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), cd, bd, app(app(ty_@2, ef), eg)) → new_esEs3(vwx302, vwx402, ef, eg)
new_esEs3(@2(vwx300, vwx301), @2(vwx400, vwx401), bdb, app(app(app(ty_@3, bdc), bdd), bde)) → new_esEs(vwx301, vwx401, bdc, bdd, bde)
new_esEs3(@2(vwx300, vwx301), @2(vwx400, vwx401), bdb, app(app(ty_@2, beb), bec)) → new_esEs3(vwx301, vwx401, beb, bec)
new_esEs2(Just(vwx300), Just(vwx400), app(app(ty_Either, bbc), bbd)) → new_esEs1(vwx300, vwx400, bbc, bbd)
new_esEs3(@2(vwx300, vwx301), @2(vwx400, vwx401), app(ty_Maybe, bcg), bcc) → new_esEs2(vwx300, vwx400, bcg)
new_esEs(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), app(app(ty_@2, cb), cc), bd, be) → new_esEs3(vwx300, vwx400, cb, cc)
new_esEs3(@2(vwx300, vwx301), @2(vwx400, vwx401), bdb, app(app(ty_Either, bdg), bdh)) → new_esEs1(vwx301, vwx401, bdg, bdh)
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_esEs(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), cd, bd, app(app(ty_Either, ec), ed)) → new_esEs1(vwx302, vwx402, ec, ed)
new_esEs2(Just(vwx300), Just(vwx400), app(ty_[], bbb)) → new_esEs0(vwx300, vwx400, bbb)
new_esEs1(Left(vwx300), Left(vwx400), app(ty_Maybe, hb), gf) → new_esEs2(vwx300, vwx400, hb)
new_esEs3(@2(vwx300, vwx301), @2(vwx400, vwx401), app(app(ty_@2, bch), bda), bcc) → new_esEs3(vwx300, vwx400, bch, bda)
new_esEs1(Left(vwx300), Left(vwx400), app(app(app(ty_@3, gc), gd), ge), gf) → new_esEs(vwx300, vwx400, gc, gd, ge)
new_esEs3(@2(vwx300, vwx301), @2(vwx400, vwx401), bdb, app(ty_[], bdf)) → new_esEs0(vwx301, vwx401, bdf)
new_esEs0(:(vwx300, vwx301), :(vwx400, vwx401), app(ty_Maybe, fc)) → new_esEs2(vwx300, vwx400, fc)
new_esEs0(:(vwx300, vwx301), :(vwx400, vwx401), app(app(ty_Either, eh), fa)) → new_esEs1(vwx300, vwx400, eh, fa)
new_esEs(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), app(ty_[], bf), bd, be) → new_esEs0(vwx300, vwx400, bf)
new_esEs2(Just(vwx300), Just(vwx400), app(app(ty_@2, bbf), bbg)) → new_esEs3(vwx300, vwx400, bbf, bbg)
new_esEs0(:(vwx300, vwx301), :(vwx400, vwx401), app(ty_[], fb)) → new_esEs0(vwx300, vwx400, fb)
new_esEs1(Right(vwx300), Right(vwx400), he, app(app(ty_@2, bae), baf)) → new_esEs3(vwx300, vwx400, bae, baf)
new_esEs3(@2(vwx300, vwx301), @2(vwx400, vwx401), app(ty_[], bcd), bcc) → new_esEs0(vwx300, vwx400, bcd)
new_esEs1(Right(vwx300), Right(vwx400), he, app(ty_Maybe, bad)) → new_esEs2(vwx300, vwx400, bad)
new_esEs0(:(vwx300, vwx301), :(vwx400, vwx401), gb) → new_esEs0(vwx301, vwx401, gb)
new_esEs(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), cd, app(app(ty_@2, de), df), be) → new_esEs3(vwx301, vwx401, de, df)
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
                                ↳ DependencyGraphProof

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

new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), bec, bdb, app(app(ty_Either, bfe), bff)) → new_ltEs(vwx312, vwx412, bfe, bff)
new_ltEs2(@2(vwx310, vwx311), @2(vwx410, vwx411), app(app(ty_@2, bad), bae), baa) → new_lt2(vwx310, vwx410, bad, bae)
new_lt(vwx30, vwx40, ba, bb) → new_compare2(vwx30, vwx40, new_esEs4(vwx30, vwx40, ba, bb), ba, bb)
new_ltEs2(@2(vwx310, vwx311), @2(vwx410, vwx411), bba, app(app(ty_Either, bbb), bbc)) → new_ltEs(vwx311, vwx411, bbb, bbc)
new_primCompAux0(vwx148, vwx149, EQ, app(app(ty_@2, fh), ga)) → new_compare5(vwx148, vwx149, fh, ga)
new_compare2(vwx30, vwx40, False, ba, bb) → new_ltEs(vwx30, vwx40, ba, bb)
new_ltEs(Left(vwx310), Left(vwx410), app(app(ty_Either, bc), bd), be) → new_ltEs(vwx310, vwx410, bc, bd)
new_ltEs(Right(vwx310), Right(vwx410), ce, app(app(ty_Either, cf), cg)) → new_ltEs(vwx310, vwx410, cf, cg)
new_compare1(vwx300, vwx400, eb, ec) → new_compare3(vwx300, vwx400, eb, ec)
new_compare32(vwx30, vwx40, bce, bcf, bcg) → new_compare22(vwx30, vwx40, new_esEs7(vwx30, vwx40, bce, bcf, bcg), bce, bcf, bcg)
new_ltEs2(@2(vwx310, vwx311), @2(vwx410, vwx411), bba, app(app(app(ty_@3, bbh), bca), bcb)) → new_ltEs3(vwx311, vwx411, bbh, bca, bcb)
new_ltEs2(@2(vwx310, vwx311), @2(vwx410, vwx411), app(ty_[], bab), baa) → new_lt0(vwx310, vwx410, bab)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), bec, app(ty_[], bef), bdc) → new_lt0(vwx311, vwx411, bef)
new_compare(:(vwx310, vwx311), :(vwx410, vwx411), dh) → new_primCompAux(vwx310, vwx410, vwx311, vwx411, dh)
new_ltEs1(Just(vwx310), Just(vwx410), app(ty_Maybe, ha)) → new_ltEs1(vwx310, vwx410, ha)
new_compare31(vwx30, vwx40, bcc, bcd) → new_compare21(vwx30, vwx40, new_esEs6(vwx30, vwx40, bcc, bcd), bcc, bcd)
new_ltEs(Right(vwx310), Right(vwx410), ce, app(ty_[], da)) → new_ltEs0(vwx310, vwx410, da)
new_primCompAux(vwx300, vwx400, vwx301, vwx401, ea) → new_primCompAux0(vwx301, vwx401, new_compare0(vwx300, vwx400, ea), app(ty_[], ea))
new_ltEs(Right(vwx310), Right(vwx410), ce, app(app(app(ty_@3, de), df), dg)) → new_ltEs3(vwx310, vwx410, de, df, dg)
new_primCompAux(vwx300, vwx400, vwx301, vwx401, app(app(ty_Either, eb), ec)) → new_compare3(vwx300, vwx400, eb, ec)
new_compare22(vwx30, vwx40, False, bce, bcf, bcg) → new_ltEs3(vwx30, vwx40, bce, bcf, bcg)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), app(ty_[], bdd), bdb, bdc) → new_lt0(vwx310, vwx410, bdd)
new_compare20(vwx30, vwx40, False, ge) → new_ltEs1(vwx30, vwx40, ge)
new_ltEs1(Just(vwx310), Just(vwx410), app(app(app(ty_@3, hd), he), hf)) → new_ltEs3(vwx310, vwx410, hd, he, hf)
new_lt3(vwx30, vwx40, bce, bcf, bcg) → new_compare22(vwx30, vwx40, new_esEs7(vwx30, vwx40, bce, bcf, bcg), bce, bcf, bcg)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), bec, bdb, app(ty_Maybe, bfh)) → new_ltEs1(vwx312, vwx412, bfh)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), app(app(ty_@2, bdf), bdg), bdb, bdc) → new_lt2(vwx310, vwx410, bdf, bdg)
new_primCompAux0(vwx148, vwx149, EQ, app(ty_Maybe, fg)) → new_compare4(vwx148, vwx149, fg)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), app(app(ty_Either, bch), bda), bdb, bdc) → new_lt(vwx310, vwx410, bch, bda)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), bec, app(app(ty_Either, bed), bee), bdc) → new_lt(vwx311, vwx411, bed, bee)
new_primCompAux0(vwx148, vwx149, EQ, app(app(app(ty_@3, gb), gc), gd)) → new_compare6(vwx148, vwx149, gb, gc, gd)
new_compare6(vwx300, vwx400, eh, fa, fb) → new_compare32(vwx300, vwx400, eh, fa, fb)
new_primCompAux(vwx300, vwx400, vwx301, vwx401, app(app(app(ty_@3, eh), fa), fb)) → new_compare32(vwx300, vwx400, eh, fa, fb)
new_compare5(vwx300, vwx400, ef, eg) → new_compare31(vwx300, vwx400, ef, eg)
new_lt1(vwx30, vwx40, ge) → new_compare20(vwx30, vwx40, new_esEs5(vwx30, vwx40, ge), ge)
new_ltEs2(@2(vwx310, vwx311), @2(vwx410, vwx411), app(app(ty_Either, hg), hh), baa) → new_lt(vwx310, vwx410, hg, hh)
new_ltEs2(@2(vwx310, vwx311), @2(vwx410, vwx411), bba, app(ty_[], bbd)) → new_ltEs0(vwx311, vwx411, bbd)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), bec, app(app(ty_@2, beh), bfa), bdc) → new_lt2(vwx311, vwx411, beh, bfa)
new_primCompAux0(vwx148, vwx149, EQ, app(app(ty_Either, fc), fd)) → new_compare1(vwx148, vwx149, fc, fd)
new_compare3(vwx30, vwx40, ba, bb) → new_compare2(vwx30, vwx40, new_esEs4(vwx30, vwx40, ba, bb), ba, bb)
new_compare30(vwx30, vwx40, ge) → new_compare20(vwx30, vwx40, new_esEs5(vwx30, vwx40, ge), ge)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), bec, bdb, app(app(ty_@2, bga), bgb)) → new_ltEs2(vwx312, vwx412, bga, bgb)
new_compare21(vwx30, vwx40, False, bcc, bcd) → new_ltEs2(vwx30, vwx40, bcc, bcd)
new_ltEs(Left(vwx310), Left(vwx410), app(ty_[], bf), be) → new_ltEs0(vwx310, vwx410, bf)
new_ltEs1(Just(vwx310), Just(vwx410), app(app(ty_Either, gf), gg)) → new_ltEs(vwx310, vwx410, gf, gg)
new_primCompAux(vwx300, vwx400, vwx301, vwx401, app(ty_[], ed)) → new_compare(vwx300, vwx400, ed)
new_primCompAux0(vwx148, vwx149, EQ, app(ty_[], ff)) → new_compare(vwx148, vwx149, ff)
new_ltEs2(@2(vwx310, vwx311), @2(vwx410, vwx411), app(app(app(ty_@3, baf), bag), bah), baa) → new_lt3(vwx310, vwx410, baf, bag, bah)
new_ltEs2(@2(vwx310, vwx311), @2(vwx410, vwx411), app(ty_Maybe, bac), baa) → new_lt1(vwx310, vwx410, bac)
new_ltEs1(Just(vwx310), Just(vwx410), app(app(ty_@2, hb), hc)) → new_ltEs2(vwx310, vwx410, hb, hc)
new_ltEs2(@2(vwx310, vwx311), @2(vwx410, vwx411), bba, app(ty_Maybe, bbe)) → new_ltEs1(vwx311, vwx411, bbe)
new_lt0(:(vwx300, vwx301), :(vwx400, vwx401), app(app(ty_@2, ef), eg)) → new_compare31(vwx300, vwx400, ef, eg)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), bec, bdb, app(ty_[], bfg)) → new_ltEs0(vwx312, vwx412, bfg)
new_ltEs1(Just(vwx310), Just(vwx410), app(ty_[], gh)) → new_ltEs0(vwx310, vwx410, gh)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), bec, app(ty_Maybe, beg), bdc) → new_lt1(vwx311, vwx411, beg)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), bec, bdb, app(app(app(ty_@3, bgc), bgd), bge)) → new_ltEs3(vwx312, vwx412, bgc, bgd, bge)
new_lt2(vwx30, vwx40, bcc, bcd) → new_compare21(vwx30, vwx40, new_esEs6(vwx30, vwx40, bcc, bcd), bcc, bcd)
new_ltEs2(@2(vwx310, vwx311), @2(vwx410, vwx411), bba, app(app(ty_@2, bbf), bbg)) → new_ltEs2(vwx311, vwx411, bbf, bbg)
new_lt0(:(vwx300, vwx301), :(vwx400, vwx401), ea) → new_primCompAux0(vwx301, vwx401, new_compare0(vwx300, vwx400, ea), app(ty_[], ea))
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), app(app(app(ty_@3, bdh), bea), beb), bdb, bdc) → new_lt3(vwx310, vwx410, bdh, bea, beb)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), app(ty_Maybe, bde), bdb, bdc) → new_lt1(vwx310, vwx410, bde)
new_ltEs(Left(vwx310), Left(vwx410), app(ty_Maybe, bg), be) → new_ltEs1(vwx310, vwx410, bg)
new_ltEs0(:(vwx310, vwx311), :(vwx410, vwx411), dh) → new_primCompAux(vwx310, vwx410, vwx311, vwx411, dh)
new_ltEs(Left(vwx310), Left(vwx410), app(app(app(ty_@3, cb), cc), cd), be) → new_ltEs3(vwx310, vwx410, cb, cc, cd)
new_ltEs(Right(vwx310), Right(vwx410), ce, app(app(ty_@2, dc), dd)) → new_ltEs2(vwx310, vwx410, dc, dd)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), bec, app(app(app(ty_@3, bfb), bfc), bfd), bdc) → new_lt3(vwx311, vwx411, bfb, bfc, bfd)
new_compare4(vwx300, vwx400, ee) → new_compare30(vwx300, vwx400, ee)
new_lt0(:(vwx300, vwx301), :(vwx400, vwx401), app(ty_[], ed)) → new_compare(vwx300, vwx400, ed)
new_primCompAux(vwx300, vwx400, vwx301, vwx401, app(ty_Maybe, ee)) → new_compare30(vwx300, vwx400, ee)
new_lt0(:(vwx300, vwx301), :(vwx400, vwx401), app(app(app(ty_@3, eh), fa), fb)) → new_compare32(vwx300, vwx400, eh, fa, fb)
new_primCompAux(vwx300, vwx400, vwx301, vwx401, app(app(ty_@2, ef), eg)) → new_compare31(vwx300, vwx400, ef, eg)
new_ltEs(Left(vwx310), Left(vwx410), app(app(ty_@2, bh), ca), be) → new_ltEs2(vwx310, vwx410, bh, ca)
new_lt0(:(vwx300, vwx301), :(vwx400, vwx401), app(ty_Maybe, ee)) → new_compare30(vwx300, vwx400, ee)
new_ltEs(Right(vwx310), Right(vwx410), ce, app(ty_Maybe, db)) → new_ltEs1(vwx310, vwx410, db)
new_lt0(:(vwx300, vwx301), :(vwx400, vwx401), app(app(ty_Either, eb), ec)) → new_compare3(vwx300, vwx400, eb, ec)

The TRS R consists of the following rules:

new_esEs7(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), bce, bcf, bcg) → new_asAs(new_esEs24(vwx300, vwx400, bce), new_asAs(new_esEs25(vwx301, vwx401, bcf), new_esEs26(vwx302, vwx402, bcg)))
new_esEs28(vwx311, vwx411, ty_Int) → new_esEs8(vwx311, vwx411)
new_esEs25(vwx301, vwx401, ty_Ordering) → new_esEs17(vwx301, vwx401)
new_compare7(:(vwx310, vwx311), [], dh) → GT
new_esEs21(vwx310, vwx410, app(app(ty_@2, bad), bae)) → new_esEs6(vwx310, vwx410, bad, bae)
new_esEs19(vwx300, vwx400, ty_Int) → new_esEs8(vwx300, vwx400)
new_esEs18(vwx300, vwx400, app(app(ty_@2, ef), eg)) → new_esEs6(vwx300, vwx400, ef, eg)
new_lt9(vwx310, vwx410, ty_Double) → new_lt16(vwx310, vwx410)
new_lt19(vwx310, vwx410, ty_Char) → new_lt4(vwx310, vwx410)
new_esEs18(vwx300, vwx400, ty_Integer) → new_esEs16(vwx300, vwx400)
new_compare7([], :(vwx410, vwx411), dh) → LT
new_esEs4(Left(vwx300), Left(vwx400), ty_Bool, bb) → new_esEs14(vwx300, vwx400)
new_esEs24(vwx300, vwx400, ty_Char) → new_esEs9(vwx300, vwx400)
new_ltEs13(Left(vwx310), Left(vwx410), app(ty_[], bf), be) → new_ltEs4(vwx310, vwx410, bf)
new_ltEs13(Right(vwx310), Right(vwx410), ce, app(app(app(ty_@3, de), df), dg)) → new_ltEs15(vwx310, vwx410, de, df, dg)
new_esEs23(vwx301, vwx401, ty_Bool) → new_esEs14(vwx301, vwx401)
new_esEs21(vwx310, vwx410, ty_Ordering) → new_esEs17(vwx310, vwx410)
new_primCompAux00(vwx148, vwx149, EQ, ty_Char) → new_compare12(vwx148, vwx149)
new_esEs4(Right(vwx300), Right(vwx400), ba, app(ty_Maybe, ccd)) → new_esEs5(vwx300, vwx400, ccd)
new_ltEs13(Left(vwx310), Left(vwx410), ty_Char, be) → new_ltEs5(vwx310, vwx410)
new_esEs18(vwx300, vwx400, app(ty_Ratio, bhh)) → new_esEs12(vwx300, vwx400, bhh)
new_lt11(:%(vwx300, vwx301), :%(vwx400, vwx401), cch) → new_esEs17(new_compare39(vwx300, vwx401, vwx400, vwx301, cch), LT)
new_ltEs6(True, False) → False
new_ltEs12(Nothing, Nothing, cab) → True
new_primMulNat0(Zero, Zero) → Zero
new_esEs26(vwx302, vwx402, ty_Float) → new_esEs15(vwx302, vwx402)
new_esEs4(Left(vwx300), Left(vwx400), ty_Ordering, bb) → new_esEs17(vwx300, vwx400)
new_lt20(vwx311, vwx411, app(ty_[], bef)) → new_lt8(vwx311, vwx411, bef)
new_compare19(vwx30, vwx40, True, ge) → LT
new_compare29(vwx30, vwx40, True) → EQ
new_ltEs12(Just(vwx310), Just(vwx410), ty_Float) → new_ltEs17(vwx310, vwx410)
new_esEs4(Right(vwx300), Right(vwx400), ba, app(ty_[], cca)) → new_esEs11(vwx300, vwx400, cca)
new_ltEs18(vwx311, vwx411, ty_Bool) → new_ltEs6(vwx311, vwx411)
new_esEs18(vwx300, vwx400, ty_Double) → new_esEs13(vwx300, vwx400)
new_esEs22(vwx300, vwx400, ty_Char) → new_esEs9(vwx300, vwx400)
new_esEs18(vwx300, vwx400, ty_Char) → new_esEs9(vwx300, vwx400)
new_ltEs11(vwx31, vwx41) → new_not(new_esEs17(new_compare10(vwx31, vwx41), GT))
new_esEs13(Double(vwx300, vwx301), Double(vwx400, vwx401)) → new_esEs8(new_sr(vwx300, vwx400), new_sr(vwx301, vwx401))
new_compare40(vwx31, vwx41) → new_primCmpFloat(vwx31, vwx41)
new_primCompAux00(vwx148, vwx149, EQ, ty_Bool) → new_compare13(vwx148, vwx149)
new_lt9(vwx310, vwx410, ty_@0) → new_lt10(vwx310, vwx410)
new_primCompAux00(vwx148, vwx149, EQ, app(ty_Maybe, fg)) → new_compare41(vwx148, vwx149, fg)
new_compare19(vwx30, vwx40, False, ge) → GT
new_ltEs13(Right(vwx310), Right(vwx410), ce, ty_Int) → new_ltEs11(vwx310, vwx410)
new_esEs4(Right(vwx300), Right(vwx400), ba, app(app(app(ty_@3, cbf), cbg), cbh)) → new_esEs7(vwx300, vwx400, cbf, cbg, cbh)
new_compare18(@0, @0) → EQ
new_ltEs18(vwx311, vwx411, app(ty_Ratio, cdb)) → new_ltEs9(vwx311, vwx411, cdb)
new_esEs5(Just(vwx300), Just(vwx400), ty_Ordering) → new_esEs17(vwx300, vwx400)
new_esEs4(Left(vwx300), Left(vwx400), app(app(ty_@2, cbd), cbe), bb) → new_esEs6(vwx300, vwx400, cbd, cbe)
new_lt9(vwx310, vwx410, ty_Int) → new_lt15(vwx310, vwx410)
new_ltEs12(Just(vwx310), Just(vwx410), ty_Int) → new_ltEs11(vwx310, vwx410)
new_ltEs19(vwx312, vwx412, ty_Ordering) → new_ltEs10(vwx312, vwx412)
new_esEs11([], [], ea) → True
new_ltEs12(Just(vwx310), Just(vwx410), ty_Ordering) → new_ltEs10(vwx310, vwx410)
new_esEs21(vwx310, vwx410, app(app(app(ty_@3, baf), bag), bah)) → new_esEs7(vwx310, vwx410, baf, bag, bah)
new_compare0(vwx300, vwx400, ty_Bool) → new_compare13(vwx300, vwx400)
new_esEs5(Just(vwx300), Just(vwx400), app(ty_Maybe, bhd)) → new_esEs5(vwx300, vwx400, bhd)
new_compare210(vwx30, vwx40, False, bce, bcf, bcg) → new_compare110(vwx30, vwx40, new_ltEs15(vwx30, vwx40, bce, bcf, bcg), bce, bcf, bcg)
new_esEs23(vwx301, vwx401, ty_Double) → new_esEs13(vwx301, vwx401)
new_esEs4(Right(vwx300), Right(vwx400), ba, ty_Float) → new_esEs15(vwx300, vwx400)
new_ltEs10(EQ, GT) → True
new_compare16(vwx300, vwx400, eb, ec) → new_compare36(vwx300, vwx400, eb, ec)
new_ltEs13(Left(vwx310), Left(vwx410), ty_Integer, be) → new_ltEs7(vwx310, vwx410)
new_esEs5(Just(vwx300), Just(vwx400), ty_Char) → new_esEs9(vwx300, vwx400)
new_ltEs19(vwx312, vwx412, app(ty_Maybe, bfh)) → new_ltEs12(vwx312, vwx412, bfh)
new_lt6(vwx30, vwx40, bcc, bcd) → new_esEs17(new_compare37(vwx30, vwx40, bcc, bcd), LT)
new_compare9(:%(vwx310, vwx311), :%(vwx410, vwx411), ty_Int) → new_compare10(new_sr(vwx310, vwx411), new_sr(vwx410, vwx311))
new_esEs4(Left(vwx300), Left(vwx400), app(ty_[], cag), bb) → new_esEs11(vwx300, vwx400, cag)
new_compare15(vwx30, vwx40, False) → GT
new_lt8([], :(vwx400, vwx401), ea) → new_esEs17(LT, LT)
new_primCompAux00(vwx148, vwx149, EQ, ty_Double) → new_compare8(vwx148, vwx149)
new_lt20(vwx311, vwx411, ty_Char) → new_lt4(vwx311, vwx411)
new_primCompAux00(vwx148, vwx149, EQ, app(app(ty_@2, fh), ga)) → new_compare42(vwx148, vwx149, fh, ga)
new_pePe(False, vwx117) → vwx117
new_ltEs9(vwx31, vwx41, caa) → new_not(new_esEs17(new_compare9(vwx31, vwx41, caa), GT))
new_esEs25(vwx301, vwx401, app(app(ty_Either, chg), chh)) → new_esEs4(vwx301, vwx401, chg, chh)
new_esEs22(vwx300, vwx400, app(app(ty_Either, cea), ceb)) → new_esEs4(vwx300, vwx400, cea, ceb)
new_esEs25(vwx301, vwx401, ty_Bool) → new_esEs14(vwx301, vwx401)
new_lt19(vwx310, vwx410, app(ty_[], bdd)) → new_lt8(vwx310, vwx410, bdd)
new_compare0(vwx300, vwx400, ty_Char) → new_compare12(vwx300, vwx400)
new_lt9(vwx310, vwx410, ty_Float) → new_lt18(vwx310, vwx410)
new_ltEs13(Left(vwx310), Left(vwx410), app(app(app(ty_@3, cb), cc), cd), be) → new_ltEs15(vwx310, vwx410, cb, cc, cd)
new_compare15(vwx30, vwx40, True) → LT
new_lt19(vwx310, vwx410, app(ty_Maybe, bde)) → new_lt14(vwx310, vwx410, bde)
new_ltEs12(Just(vwx310), Just(vwx410), app(app(ty_@2, hb), hc)) → new_ltEs14(vwx310, vwx410, hb, hc)
new_compare0(vwx300, vwx400, ty_@0) → new_compare18(vwx300, vwx400)
new_ltEs8(vwx31, vwx41) → new_not(new_esEs17(new_compare18(vwx31, vwx41), GT))
new_compare12(vwx31, vwx41) → new_primCmpChar(vwx31, vwx41)
new_lt9(vwx310, vwx410, ty_Integer) → new_lt17(vwx310, vwx410)
new_ltEs13(Right(vwx310), Right(vwx410), ce, app(app(ty_@2, dc), dd)) → new_ltEs14(vwx310, vwx410, dc, dd)
new_compare111(vwx30, vwx40, False) → GT
new_compare111(vwx30, vwx40, True) → LT
new_esEs24(vwx300, vwx400, app(ty_[], cgd)) → new_esEs11(vwx300, vwx400, cgd)
new_lt20(vwx311, vwx411, app(app(ty_Either, bed), bee)) → new_lt7(vwx311, vwx411, bed, bee)
new_lt12(vwx30, vwx40) → new_esEs17(new_compare34(vwx30, vwx40), LT)
new_esEs23(vwx301, vwx401, app(app(app(ty_@3, ceg), ceh), cfa)) → new_esEs7(vwx301, vwx401, ceg, ceh, cfa)
new_esEs21(vwx310, vwx410, ty_Bool) → new_esEs14(vwx310, vwx410)
new_primCmpNat0(Zero, Succ(vwx4000)) → LT
new_esEs22(vwx300, vwx400, ty_Float) → new_esEs15(vwx300, vwx400)
new_esEs27(vwx310, vwx410, app(app(app(ty_@3, bdh), bea), beb)) → new_esEs7(vwx310, vwx410, bdh, bea, beb)
new_esEs21(vwx310, vwx410, ty_Char) → new_esEs9(vwx310, vwx410)
new_esEs4(Left(vwx300), Left(vwx400), ty_Char, bb) → new_esEs9(vwx300, vwx400)
new_esEs17(LT, LT) → True
new_ltEs19(vwx312, vwx412, ty_Bool) → new_ltEs6(vwx312, vwx412)
new_esEs25(vwx301, vwx401, app(app(ty_@2, dac), dad)) → new_esEs6(vwx301, vwx401, dac, dad)
new_esEs4(Left(vwx300), Left(vwx400), app(ty_Ratio, cbc), bb) → new_esEs12(vwx300, vwx400, cbc)
new_esEs27(vwx310, vwx410, ty_@0) → new_esEs10(vwx310, vwx410)
new_ltEs12(Just(vwx310), Just(vwx410), app(ty_Ratio, cac)) → new_ltEs9(vwx310, vwx410, cac)
new_compare26(vwx300, vwx400) → new_compare38(vwx300, vwx400)
new_esEs28(vwx311, vwx411, app(ty_[], bef)) → new_esEs11(vwx311, vwx411, bef)
new_lt14(vwx30, vwx40, ge) → new_esEs17(new_compare33(vwx30, vwx40, ge), LT)
new_compare0(vwx300, vwx400, app(app(app(ty_@3, eh), fa), fb)) → new_compare43(vwx300, vwx400, eh, fa, fb)
new_esEs28(vwx311, vwx411, ty_Integer) → new_esEs16(vwx311, vwx411)
new_compare7([], [], dh) → EQ
new_esEs24(vwx300, vwx400, app(app(ty_@2, cha), chb)) → new_esEs6(vwx300, vwx400, cha, chb)
new_pePe(True, vwx117) → True
new_compare28(vwx30, vwx40, False, ba, bb) → new_compare17(vwx30, vwx40, new_ltEs13(vwx30, vwx40, ba, bb), ba, bb)
new_compare14(vwx30, vwx40, False, bcc, bcd) → GT
new_primEqNat0(Zero, Zero) → True
new_primMulNat0(Succ(vwx30000), Succ(vwx40000)) → new_primPlusNat1(new_primMulNat0(vwx30000, Succ(vwx40000)), vwx40000)
new_lt20(vwx311, vwx411, ty_Int) → new_lt15(vwx311, vwx411)
new_ltEs19(vwx312, vwx412, app(ty_[], bfg)) → new_ltEs4(vwx312, vwx412, bfg)
new_esEs4(Left(vwx300), Left(vwx400), ty_Integer, bb) → new_esEs16(vwx300, vwx400)
new_lt9(vwx310, vwx410, app(app(app(ty_@3, baf), bag), bah)) → new_lt5(vwx310, vwx410, baf, bag, bah)
new_esEs18(vwx300, vwx400, ty_Float) → new_esEs15(vwx300, vwx400)
new_lt8(:(vwx300, vwx301), [], ea) → new_esEs17(GT, LT)
new_ltEs13(Left(vwx310), Left(vwx410), ty_Ordering, be) → new_ltEs10(vwx310, vwx410)
new_primCompAux00(vwx148, vwx149, EQ, app(ty_[], ff)) → new_compare7(vwx148, vwx149, ff)
new_sr(vwx300, vwx400) → new_primMulInt(vwx300, vwx400)
new_esEs4(Left(vwx300), Left(vwx400), ty_Int, bb) → new_esEs8(vwx300, vwx400)
new_esEs22(vwx300, vwx400, app(ty_Ratio, ced)) → new_esEs12(vwx300, vwx400, ced)
new_esEs25(vwx301, vwx401, ty_@0) → new_esEs10(vwx301, vwx401)
new_esEs22(vwx300, vwx400, ty_Int) → new_esEs8(vwx300, vwx400)
new_lt19(vwx310, vwx410, app(ty_Ratio, dbg)) → new_lt11(vwx310, vwx410, dbg)
new_compare33(vwx30, vwx40, ge) → new_compare23(vwx30, vwx40, new_esEs5(vwx30, vwx40, ge), ge)
new_primCmpFloat(Float(vwx300, vwx301), Float(vwx400, vwx401)) → new_compare25(vwx300, vwx400, vwx301, vwx401)
new_ltEs19(vwx312, vwx412, app(app(app(ty_@3, bgc), bgd), bge)) → new_ltEs15(vwx312, vwx412, bgc, bgd, bge)
new_compare17(vwx30, vwx40, True, ba, bb) → LT
new_ltEs12(Just(vwx310), Just(vwx410), ty_Bool) → new_ltEs6(vwx310, vwx410)
new_esEs4(Right(vwx300), Right(vwx400), ba, app(app(ty_Either, ccb), ccc)) → new_esEs4(vwx300, vwx400, ccb, ccc)
new_primEqInt(Neg(Succ(vwx3000)), Neg(Succ(vwx4000))) → new_primEqNat0(vwx3000, vwx4000)
new_ltEs13(Right(vwx310), Right(vwx410), ce, ty_Ordering) → new_ltEs10(vwx310, vwx410)
new_lt20(vwx311, vwx411, app(ty_Ratio, dbh)) → new_lt11(vwx311, vwx411, dbh)
new_esEs4(Left(vwx300), Left(vwx400), app(app(ty_Either, cah), cba), bb) → new_esEs4(vwx300, vwx400, cah, cba)
new_esEs24(vwx300, vwx400, ty_Bool) → new_esEs14(vwx300, vwx400)
new_esEs26(vwx302, vwx402, app(app(app(ty_@3, dae), daf), dag)) → new_esEs7(vwx302, vwx402, dae, daf, dag)
new_esEs4(Left(vwx300), Left(vwx400), ty_Double, bb) → new_esEs13(vwx300, vwx400)
new_ltEs19(vwx312, vwx412, app(ty_Ratio, dca)) → new_ltEs9(vwx312, vwx412, dca)
new_lt17(Integer(vwx300), Integer(vwx400)) → new_esEs17(new_primCmpInt(vwx300, vwx400), LT)
new_esEs22(vwx300, vwx400, ty_Ordering) → new_esEs17(vwx300, vwx400)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs17(EQ, EQ) → True
new_esEs28(vwx311, vwx411, ty_Double) → new_esEs13(vwx311, vwx411)
new_esEs28(vwx311, vwx411, ty_Ordering) → new_esEs17(vwx311, vwx411)
new_compare39(Integer(vwx3000), Integer(vwx4010), vwx400, vwx301, ty_Integer) → new_compare11(Integer(new_primMulInt(vwx3000, vwx4010)), new_sr0(vwx400, vwx301))
new_lt19(vwx310, vwx410, ty_Double) → new_lt16(vwx310, vwx410)
new_primEqInt(Neg(Succ(vwx3000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(vwx4000))) → False
new_primPlusNat1(Zero, vwx40000) → Succ(vwx40000)
new_esEs11(:(vwx300, vwx301), :(vwx400, vwx401), ea) → new_asAs(new_esEs18(vwx300, vwx400, ea), new_esEs11(vwx301, vwx401, ea))
new_esEs23(vwx301, vwx401, ty_Integer) → new_esEs16(vwx301, vwx401)
new_lt20(vwx311, vwx411, ty_@0) → new_lt10(vwx311, vwx411)
new_lt20(vwx311, vwx411, ty_Ordering) → new_lt13(vwx311, vwx411)
new_ltEs13(Right(vwx310), Right(vwx410), ce, ty_Integer) → new_ltEs7(vwx310, vwx410)
new_primCompAux00(vwx148, vwx149, EQ, ty_@0) → new_compare18(vwx148, vwx149)
new_esEs20(vwx301, vwx401, ty_Integer) → new_esEs16(vwx301, vwx401)
new_esEs21(vwx310, vwx410, app(app(ty_Either, hg), hh)) → new_esEs4(vwx310, vwx410, hg, hh)
new_ltEs13(Left(vwx310), Left(vwx410), ty_Double, be) → new_ltEs16(vwx310, vwx410)
new_ltEs18(vwx311, vwx411, ty_Double) → new_ltEs16(vwx311, vwx411)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_esEs5(Just(vwx300), Just(vwx400), ty_@0) → new_esEs10(vwx300, vwx400)
new_esEs27(vwx310, vwx410, ty_Float) → new_esEs15(vwx310, vwx410)
new_ltEs12(Just(vwx310), Just(vwx410), app(app(app(ty_@3, hd), he), hf)) → new_ltEs15(vwx310, vwx410, hd, he, hf)
new_ltEs18(vwx311, vwx411, ty_@0) → new_ltEs8(vwx311, vwx411)
new_primCompAux00(vwx148, vwx149, EQ, app(app(ty_Either, fc), fd)) → new_compare16(vwx148, vwx149, fc, fd)
new_primCmpNat0(Succ(vwx3000), Succ(vwx4000)) → new_primCmpNat0(vwx3000, vwx4000)
new_esEs26(vwx302, vwx402, ty_Integer) → new_esEs16(vwx302, vwx402)
new_compare0(vwx300, vwx400, ty_Float) → new_compare40(vwx300, vwx400)
new_ltEs18(vwx311, vwx411, app(app(ty_Either, bbb), bbc)) → new_ltEs13(vwx311, vwx411, bbb, bbc)
new_primEqInt(Pos(Succ(vwx3000)), Pos(Succ(vwx4000))) → new_primEqNat0(vwx3000, vwx4000)
new_ltEs17(vwx31, vwx41) → new_not(new_esEs17(new_compare40(vwx31, vwx41), GT))
new_ltEs12(Just(vwx310), Just(vwx410), app(app(ty_Either, gf), gg)) → new_ltEs13(vwx310, vwx410, gf, gg)
new_compare27(vwx30, vwx40, True, bcc, bcd) → EQ
new_esEs25(vwx301, vwx401, app(ty_Maybe, daa)) → new_esEs5(vwx301, vwx401, daa)
new_ltEs18(vwx311, vwx411, app(app(app(ty_@3, bbh), bca), bcb)) → new_ltEs15(vwx311, vwx411, bbh, bca, bcb)
new_esEs14(True, False) → False
new_esEs14(False, True) → False
new_ltEs6(False, True) → True
new_esEs17(LT, GT) → False
new_esEs17(GT, LT) → False
new_ltEs10(GT, EQ) → False
new_primEqNat0(Succ(vwx3000), Succ(vwx4000)) → new_primEqNat0(vwx3000, vwx4000)
new_esEs17(EQ, GT) → False
new_esEs17(GT, EQ) → False
new_ltEs6(True, True) → True
new_esEs21(vwx310, vwx410, app(ty_Ratio, cda)) → new_esEs12(vwx310, vwx410, cda)
new_ltEs19(vwx312, vwx412, app(app(ty_Either, bfe), bff)) → new_ltEs13(vwx312, vwx412, bfe, bff)
new_lt9(vwx310, vwx410, ty_Bool) → new_lt12(vwx310, vwx410)
new_lt19(vwx310, vwx410, app(app(ty_@2, bdf), bdg)) → new_lt6(vwx310, vwx410, bdf, bdg)
new_esEs4(Left(vwx300), Left(vwx400), app(app(app(ty_@3, cad), cae), caf), bb) → new_esEs7(vwx300, vwx400, cad, cae, caf)
new_lt20(vwx311, vwx411, ty_Integer) → new_lt17(vwx311, vwx411)
new_esEs26(vwx302, vwx402, app(ty_[], dah)) → new_esEs11(vwx302, vwx402, dah)
new_esEs24(vwx300, vwx400, app(ty_Ratio, cgh)) → new_esEs12(vwx300, vwx400, cgh)
new_primCmpInt(Neg(Succ(vwx3000)), Neg(vwx400)) → new_primCmpNat0(vwx400, Succ(vwx3000))
new_esEs22(vwx300, vwx400, ty_Bool) → new_esEs14(vwx300, vwx400)
new_ltEs13(Right(vwx310), Right(vwx410), ce, app(ty_[], da)) → new_ltEs4(vwx310, vwx410, da)
new_lt19(vwx310, vwx410, app(app(ty_Either, bch), bda)) → new_lt7(vwx310, vwx410, bch, bda)
new_ltEs13(Right(vwx310), Right(vwx410), ce, app(ty_Maybe, db)) → new_ltEs12(vwx310, vwx410, db)
new_esEs21(vwx310, vwx410, ty_Int) → new_esEs8(vwx310, vwx410)
new_esEs25(vwx301, vwx401, ty_Char) → new_esEs9(vwx301, vwx401)
new_primEqInt(Pos(Succ(vwx3000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(vwx4000))) → False
new_primPlusNat0(Zero, Succ(vwx400000)) → Succ(vwx400000)
new_primPlusNat0(Succ(vwx15800), Zero) → Succ(vwx15800)
new_esEs24(vwx300, vwx400, ty_Float) → new_esEs15(vwx300, vwx400)
new_compare0(vwx300, vwx400, ty_Int) → new_compare10(vwx300, vwx400)
new_esEs24(vwx300, vwx400, ty_@0) → new_esEs10(vwx300, vwx400)
new_ltEs19(vwx312, vwx412, ty_Float) → new_ltEs17(vwx312, vwx412)
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(vwx3000), Zero) → GT
new_esEs4(Right(vwx300), Right(vwx400), ba, ty_@0) → new_esEs10(vwx300, vwx400)
new_ltEs10(LT, EQ) → True
new_primCmpInt(Neg(Zero), Pos(Succ(vwx4000))) → LT
new_esEs25(vwx301, vwx401, ty_Int) → new_esEs8(vwx301, vwx401)
new_compare27(vwx30, vwx40, False, bcc, bcd) → new_compare14(vwx30, vwx40, new_ltEs14(vwx30, vwx40, bcc, bcd), bcc, bcd)
new_esEs21(vwx310, vwx410, ty_Float) → new_esEs15(vwx310, vwx410)
new_compare210(vwx30, vwx40, True, bce, bcf, bcg) → EQ
new_ltEs13(Right(vwx310), Right(vwx410), ce, ty_Float) → new_ltEs17(vwx310, vwx410)
new_compare39(vwx300, vwx401, vwx400, vwx301, ty_Int) → new_compare25(vwx300, vwx401, vwx400, vwx301)
new_esEs18(vwx300, vwx400, app(app(app(ty_@3, eh), fa), fb)) → new_esEs7(vwx300, vwx400, eh, fa, fb)
new_lt15(vwx30, vwx40) → new_esEs17(new_primCmpInt(vwx30, vwx40), LT)
new_esEs21(vwx310, vwx410, ty_Double) → new_esEs13(vwx310, vwx410)
new_esEs4(Left(vwx300), Left(vwx400), ty_Float, bb) → new_esEs15(vwx300, vwx400)
new_sr0(Integer(vwx4000), Integer(vwx3010)) → Integer(new_primMulInt(vwx4000, vwx3010))
new_compare28(vwx30, vwx40, True, ba, bb) → EQ
new_primCompAux00(vwx148, vwx149, EQ, app(app(app(ty_@3, gb), gc), gd)) → new_compare43(vwx148, vwx149, gb, gc, gd)
new_primEqInt(Pos(Succ(vwx3000)), Neg(vwx400)) → False
new_primEqInt(Neg(Succ(vwx3000)), Pos(vwx400)) → False
new_ltEs19(vwx312, vwx412, ty_Double) → new_ltEs16(vwx312, vwx412)
new_esEs26(vwx302, vwx402, ty_Double) → new_esEs13(vwx302, vwx402)
new_ltEs12(Just(vwx310), Just(vwx410), app(ty_Maybe, ha)) → new_ltEs12(vwx310, vwx410, ha)
new_compare35(vwx30, vwx40, bce, bcf, bcg) → new_compare210(vwx30, vwx40, new_esEs7(vwx30, vwx40, bce, bcf, bcg), bce, bcf, bcg)
new_ltEs18(vwx311, vwx411, app(app(ty_@2, bbf), bbg)) → new_ltEs14(vwx311, vwx411, bbf, bbg)
new_lt9(vwx310, vwx410, app(ty_[], bab)) → new_lt8(vwx310, vwx410, bab)
new_esEs27(vwx310, vwx410, app(ty_Maybe, bde)) → new_esEs5(vwx310, vwx410, bde)
new_compare37(vwx30, vwx40, bcc, bcd) → new_compare27(vwx30, vwx40, new_esEs6(vwx30, vwx40, bcc, bcd), bcc, bcd)
new_ltEs10(GT, GT) → True
new_lt19(vwx310, vwx410, app(app(app(ty_@3, bdh), bea), beb)) → new_lt5(vwx310, vwx410, bdh, bea, beb)
new_primCompAux00(vwx148, vwx149, EQ, ty_Ordering) → new_compare26(vwx148, vwx149)
new_ltEs12(Just(vwx310), Just(vwx410), app(ty_[], gh)) → new_ltEs4(vwx310, vwx410, gh)
new_esEs11([], :(vwx400, vwx401), ea) → False
new_esEs11(:(vwx300, vwx301), [], ea) → False
new_esEs23(vwx301, vwx401, app(ty_Ratio, cff)) → new_esEs12(vwx301, vwx401, cff)
new_esEs22(vwx300, vwx400, app(app(ty_@2, cee), cef)) → new_esEs6(vwx300, vwx400, cee, cef)
new_esEs4(Right(vwx300), Right(vwx400), ba, ty_Bool) → new_esEs14(vwx300, vwx400)
new_primCompAux00(vwx148, vwx149, EQ, ty_Integer) → new_compare11(vwx148, vwx149)
new_primEqInt(Pos(Zero), Neg(Succ(vwx4000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(vwx4000))) → False
new_compare38(vwx30, vwx40) → new_compare29(vwx30, vwx40, new_esEs17(vwx30, vwx40))
new_esEs22(vwx300, vwx400, app(ty_[], cdh)) → new_esEs11(vwx300, vwx400, cdh)
new_primCmpInt(Pos(Zero), Pos(Succ(vwx4000))) → new_primCmpNat0(Zero, Succ(vwx4000))
new_compare24(vwx30, vwx40, True) → EQ
new_primCompAux00(vwx148, vwx149, EQ, ty_Int) → new_compare10(vwx148, vwx149)
new_esEs25(vwx301, vwx401, ty_Float) → new_esEs15(vwx301, vwx401)
new_compare17(vwx30, vwx40, False, ba, bb) → GT
new_ltEs18(vwx311, vwx411, ty_Float) → new_ltEs17(vwx311, vwx411)
new_ltEs13(Right(vwx310), Right(vwx410), ce, ty_@0) → new_ltEs8(vwx310, vwx410)
new_esEs4(Right(vwx300), Right(vwx400), ba, ty_Char) → new_esEs9(vwx300, vwx400)
new_ltEs12(Just(vwx310), Just(vwx410), ty_@0) → new_ltEs8(vwx310, vwx410)
new_ltEs13(Left(vwx310), Left(vwx410), ty_@0, be) → new_ltEs8(vwx310, vwx410)
new_not(False) → True
new_ltEs13(Right(vwx310), Right(vwx410), ce, app(ty_Ratio, dcc)) → new_ltEs9(vwx310, vwx410, dcc)
new_esEs5(Just(vwx300), Just(vwx400), ty_Int) → new_esEs8(vwx300, vwx400)
new_primCmpInt(Pos(Succ(vwx3000)), Pos(vwx400)) → new_primCmpNat0(Succ(vwx3000), vwx400)
new_lt19(vwx310, vwx410, ty_Int) → new_lt15(vwx310, vwx410)
new_lt7(vwx30, vwx40, ba, bb) → new_esEs17(new_compare36(vwx30, vwx40, ba, bb), LT)
new_esEs23(vwx301, vwx401, app(app(ty_@2, cfg), cfh)) → new_esEs6(vwx301, vwx401, cfg, cfh)
new_esEs25(vwx301, vwx401, ty_Double) → new_esEs13(vwx301, vwx401)
new_lt19(vwx310, vwx410, ty_Integer) → new_lt17(vwx310, vwx410)
new_esEs26(vwx302, vwx402, ty_Bool) → new_esEs14(vwx302, vwx402)
new_esEs28(vwx311, vwx411, ty_Char) → new_esEs9(vwx311, vwx411)
new_esEs18(vwx300, vwx400, ty_Int) → new_esEs8(vwx300, vwx400)
new_ltEs13(Left(vwx310), Left(vwx410), ty_Bool, be) → new_ltEs6(vwx310, vwx410)
new_compare0(vwx300, vwx400, app(app(ty_@2, ef), eg)) → new_compare42(vwx300, vwx400, ef, eg)
new_esEs24(vwx300, vwx400, app(ty_Maybe, cgg)) → new_esEs5(vwx300, vwx400, cgg)
new_esEs4(Right(vwx300), Right(vwx400), ba, app(app(ty_@2, ccf), ccg)) → new_esEs6(vwx300, vwx400, ccf, ccg)
new_esEs23(vwx301, vwx401, ty_@0) → new_esEs10(vwx301, vwx401)
new_esEs18(vwx300, vwx400, app(app(ty_Either, eb), ec)) → new_esEs4(vwx300, vwx400, eb, ec)
new_esEs5(Just(vwx300), Just(vwx400), ty_Double) → new_esEs13(vwx300, vwx400)
new_compare43(vwx300, vwx400, eh, fa, fb) → new_compare35(vwx300, vwx400, eh, fa, fb)
new_esEs22(vwx300, vwx400, app(app(app(ty_@3, cde), cdf), cdg)) → new_esEs7(vwx300, vwx400, cde, cdf, cdg)
new_lt9(vwx310, vwx410, app(app(ty_Either, hg), hh)) → new_lt7(vwx310, vwx410, hg, hh)
new_primCmpInt(Pos(Succ(vwx3000)), Neg(vwx400)) → GT
new_esEs21(vwx310, vwx410, ty_Integer) → new_esEs16(vwx310, vwx410)
new_lt9(vwx310, vwx410, app(app(ty_@2, bad), bae)) → new_lt6(vwx310, vwx410, bad, bae)
new_compare41(vwx300, vwx400, ee) → new_compare33(vwx300, vwx400, ee)
new_esEs26(vwx302, vwx402, ty_@0) → new_esEs10(vwx302, vwx402)
new_primMulInt(Pos(vwx3000), Pos(vwx4000)) → Pos(new_primMulNat0(vwx3000, vwx4000))
new_lt19(vwx310, vwx410, ty_Bool) → new_lt12(vwx310, vwx410)
new_esEs24(vwx300, vwx400, ty_Int) → new_esEs8(vwx300, vwx400)
new_ltEs7(vwx31, vwx41) → new_not(new_esEs17(new_compare11(vwx31, vwx41), GT))
new_esEs24(vwx300, vwx400, ty_Integer) → new_esEs16(vwx300, vwx400)
new_esEs28(vwx311, vwx411, app(app(app(ty_@3, bfb), bfc), bfd)) → new_esEs7(vwx311, vwx411, bfb, bfc, bfd)
new_lt8(:(vwx300, vwx301), :(vwx400, vwx401), ea) → new_esEs17(new_primCompAux1(vwx300, vwx400, vwx301, vwx401, ea), LT)
new_esEs23(vwx301, vwx401, app(app(ty_Either, cfc), cfd)) → new_esEs4(vwx301, vwx401, cfc, cfd)
new_esEs22(vwx300, vwx400, ty_Double) → new_esEs13(vwx300, vwx400)
new_esEs27(vwx310, vwx410, app(app(ty_@2, bdf), bdg)) → new_esEs6(vwx310, vwx410, bdf, bdg)
new_primMulInt(Neg(vwx3000), Neg(vwx4000)) → Pos(new_primMulNat0(vwx3000, vwx4000))
new_compare29(vwx30, vwx40, False) → new_compare111(vwx30, vwx40, new_ltEs10(vwx30, vwx40))
new_compare0(vwx300, vwx400, app(app(ty_Either, eb), ec)) → new_compare16(vwx300, vwx400, eb, ec)
new_esEs5(Just(vwx300), Just(vwx400), ty_Bool) → new_esEs14(vwx300, vwx400)
new_primEqNat0(Succ(vwx3000), Zero) → False
new_primEqNat0(Zero, Succ(vwx4000)) → False
new_esEs21(vwx310, vwx410, ty_@0) → new_esEs10(vwx310, vwx410)
new_primPlusNat0(Zero, Zero) → Zero
new_esEs12(:%(vwx300, vwx301), :%(vwx400, vwx401), cch) → new_asAs(new_esEs19(vwx300, vwx400, cch), new_esEs20(vwx301, vwx401, cch))
new_ltEs14(@2(vwx310, vwx311), @2(vwx410, vwx411), bba, baa) → new_pePe(new_lt9(vwx310, vwx410, bba), new_asAs(new_esEs21(vwx310, vwx410, bba), new_ltEs18(vwx311, vwx411, baa)))
new_esEs15(Float(vwx300, vwx301), Float(vwx400, vwx401)) → new_esEs8(new_sr(vwx300, vwx400), new_sr(vwx301, vwx401))
new_lt9(vwx310, vwx410, app(ty_Ratio, cda)) → new_lt11(vwx310, vwx410, cda)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs24(vwx300, vwx400, app(app(ty_Either, cge), cgf)) → new_esEs4(vwx300, vwx400, cge, cgf)
new_esEs25(vwx301, vwx401, app(ty_[], chf)) → new_esEs11(vwx301, vwx401, chf)
new_ltEs13(Left(vwx310), Left(vwx410), app(app(ty_@2, bh), ca), be) → new_ltEs14(vwx310, vwx410, bh, ca)
new_esEs26(vwx302, vwx402, ty_Int) → new_esEs8(vwx302, vwx402)
new_esEs27(vwx310, vwx410, app(app(ty_Either, bch), bda)) → new_esEs4(vwx310, vwx410, bch, bda)
new_ltEs18(vwx311, vwx411, ty_Integer) → new_ltEs7(vwx311, vwx411)
new_compare34(vwx30, vwx40) → new_compare24(vwx30, vwx40, new_esEs14(vwx30, vwx40))
new_esEs4(Right(vwx300), Right(vwx400), ba, ty_Integer) → new_esEs16(vwx300, vwx400)
new_lt10(@0, @0) → new_esEs17(EQ, LT)
new_ltEs13(Right(vwx310), Right(vwx410), ce, ty_Char) → new_ltEs5(vwx310, vwx410)
new_compare42(vwx300, vwx400, ef, eg) → new_compare37(vwx300, vwx400, ef, eg)
new_ltEs12(Just(vwx310), Just(vwx410), ty_Double) → new_ltEs16(vwx310, vwx410)
new_esEs27(vwx310, vwx410, ty_Integer) → new_esEs16(vwx310, vwx410)
new_lt20(vwx311, vwx411, ty_Float) → new_lt18(vwx311, vwx411)
new_esEs6(@2(vwx300, vwx301), @2(vwx400, vwx401), bcc, bcd) → new_asAs(new_esEs22(vwx300, vwx400, bcc), new_esEs23(vwx301, vwx401, bcd))
new_lt13(vwx30, vwx40) → new_esEs17(new_compare38(vwx30, vwx40), LT)
new_esEs26(vwx302, vwx402, app(ty_Maybe, dbc)) → new_esEs5(vwx302, vwx402, dbc)
new_primPlusNat1(Succ(vwx1580), vwx40000) → Succ(Succ(new_primPlusNat0(vwx1580, vwx40000)))
new_lt9(vwx310, vwx410, ty_Char) → new_lt4(vwx310, vwx410)
new_esEs22(vwx300, vwx400, ty_@0) → new_esEs10(vwx300, vwx400)
new_primCompAux00(vwx148, vwx149, EQ, ty_Float) → new_compare40(vwx148, vwx149)
new_esEs25(vwx301, vwx401, ty_Integer) → new_esEs16(vwx301, vwx401)
new_primCmpInt(Neg(Zero), Neg(Succ(vwx4000))) → new_primCmpNat0(Succ(vwx4000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(vwx4000))) → GT
new_primCmpDouble(Double(vwx300, vwx301), Double(vwx400, vwx401)) → new_compare25(vwx300, vwx400, vwx301, vwx401)
new_lt9(vwx310, vwx410, app(ty_Maybe, bac)) → new_lt14(vwx310, vwx410, bac)
new_esEs4(Right(vwx300), Right(vwx400), ba, app(ty_Ratio, cce)) → new_esEs12(vwx300, vwx400, cce)
new_esEs28(vwx311, vwx411, app(ty_Ratio, dbh)) → new_esEs12(vwx311, vwx411, dbh)
new_compare23(vwx30, vwx40, True, ge) → EQ
new_esEs23(vwx301, vwx401, app(ty_[], cfb)) → new_esEs11(vwx301, vwx401, cfb)
new_lt20(vwx311, vwx411, app(app(ty_@2, beh), bfa)) → new_lt6(vwx311, vwx411, beh, bfa)
new_ltEs19(vwx312, vwx412, ty_Int) → new_ltEs11(vwx312, vwx412)
new_ltEs13(Left(vwx310), Left(vwx410), ty_Float, be) → new_ltEs17(vwx310, vwx410)
new_compare0(vwx300, vwx400, ty_Double) → new_compare8(vwx300, vwx400)
new_esEs28(vwx311, vwx411, app(app(ty_@2, beh), bfa)) → new_esEs6(vwx311, vwx411, beh, bfa)
new_ltEs15(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), bec, bdb, bdc) → new_pePe(new_lt19(vwx310, vwx410, bec), new_asAs(new_esEs27(vwx310, vwx410, bec), new_pePe(new_lt20(vwx311, vwx411, bdb), new_asAs(new_esEs28(vwx311, vwx411, bdb), new_ltEs19(vwx312, vwx412, bdc)))))
new_esEs27(vwx310, vwx410, app(ty_Ratio, dbg)) → new_esEs12(vwx310, vwx410, dbg)
new_compare8(vwx31, vwx41) → new_primCmpDouble(vwx31, vwx41)
new_ltEs13(Left(vwx310), Left(vwx410), app(app(ty_Either, bc), bd), be) → new_ltEs13(vwx310, vwx410, bc, bd)
new_lt20(vwx311, vwx411, ty_Double) → new_lt16(vwx311, vwx411)
new_esEs16(Integer(vwx300), Integer(vwx400)) → new_primEqInt(vwx300, vwx400)
new_ltEs13(Right(vwx310), Right(vwx410), ce, app(app(ty_Either, cf), cg)) → new_ltEs13(vwx310, vwx410, cf, cg)
new_esEs23(vwx301, vwx401, ty_Ordering) → new_esEs17(vwx301, vwx401)
new_ltEs18(vwx311, vwx411, ty_Int) → new_ltEs11(vwx311, vwx411)
new_esEs18(vwx300, vwx400, app(ty_[], ed)) → new_esEs11(vwx300, vwx400, ed)
new_esEs18(vwx300, vwx400, ty_Ordering) → new_esEs17(vwx300, vwx400)
new_esEs10(@0, @0) → True
new_esEs24(vwx300, vwx400, app(app(app(ty_@3, cga), cgb), cgc)) → new_esEs7(vwx300, vwx400, cga, cgb, cgc)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_ltEs16(vwx31, vwx41) → new_not(new_esEs17(new_compare8(vwx31, vwx41), GT))
new_esEs5(Just(vwx300), Just(vwx400), ty_Float) → new_esEs15(vwx300, vwx400)
new_esEs28(vwx311, vwx411, ty_@0) → new_esEs10(vwx311, vwx411)
new_lt19(vwx310, vwx410, ty_Ordering) → new_lt13(vwx310, vwx410)
new_ltEs13(Left(vwx310), Left(vwx410), app(ty_Maybe, bg), be) → new_ltEs12(vwx310, vwx410, bg)
new_esEs4(Right(vwx300), Right(vwx400), ba, ty_Double) → new_esEs13(vwx300, vwx400)
new_lt9(vwx310, vwx410, ty_Ordering) → new_lt13(vwx310, vwx410)
new_asAs(False, vwx143) → False
new_compare0(vwx300, vwx400, app(ty_Maybe, ee)) → new_compare41(vwx300, vwx400, ee)
new_ltEs12(Just(vwx310), Just(vwx410), ty_Char) → new_ltEs5(vwx310, vwx410)
new_esEs4(Left(vwx300), Left(vwx400), ty_@0, bb) → new_esEs10(vwx300, vwx400)
new_primMulInt(Pos(vwx3000), Neg(vwx4000)) → Neg(new_primMulNat0(vwx3000, vwx4000))
new_primMulInt(Neg(vwx3000), Pos(vwx4000)) → Neg(new_primMulNat0(vwx3000, vwx4000))
new_ltEs10(LT, GT) → True
new_ltEs13(Right(vwx310), Right(vwx410), ce, ty_Bool) → new_ltEs6(vwx310, vwx410)
new_primMulNat0(Zero, Succ(vwx40000)) → Zero
new_primMulNat0(Succ(vwx30000), Zero) → Zero
new_esEs27(vwx310, vwx410, ty_Double) → new_esEs13(vwx310, vwx410)
new_ltEs13(Left(vwx310), Right(vwx410), ce, be) → True
new_esEs24(vwx300, vwx400, ty_Double) → new_esEs13(vwx300, vwx400)
new_compare0(vwx300, vwx400, app(ty_[], ed)) → new_compare7(vwx300, vwx400, ed)
new_esEs27(vwx310, vwx410, ty_Int) → new_esEs8(vwx310, vwx410)
new_ltEs4(vwx31, vwx41, dh) → new_not(new_esEs17(new_compare7(vwx31, vwx41, dh), GT))
new_ltEs18(vwx311, vwx411, app(ty_[], bbd)) → new_ltEs4(vwx311, vwx411, bbd)
new_esEs5(Just(vwx300), Just(vwx400), app(ty_[], bha)) → new_esEs11(vwx300, vwx400, bha)
new_compare11(Integer(vwx310), Integer(vwx410)) → new_primCmpInt(vwx310, vwx410)
new_esEs28(vwx311, vwx411, ty_Bool) → new_esEs14(vwx311, vwx411)
new_esEs5(Just(vwx300), Just(vwx400), app(app(ty_@2, bhf), bhg)) → new_esEs6(vwx300, vwx400, bhf, bhg)
new_compare0(vwx300, vwx400, ty_Ordering) → new_compare26(vwx300, vwx400)
new_esEs18(vwx300, vwx400, app(ty_Maybe, ee)) → new_esEs5(vwx300, vwx400, ee)
new_ltEs18(vwx311, vwx411, app(ty_Maybe, bbe)) → new_ltEs12(vwx311, vwx411, bbe)
new_compare110(vwx30, vwx40, True, bce, bcf, bcg) → LT
new_esEs23(vwx301, vwx401, ty_Float) → new_esEs15(vwx301, vwx401)
new_esEs4(Left(vwx300), Left(vwx400), app(ty_Maybe, cbb), bb) → new_esEs5(vwx300, vwx400, cbb)
new_primCompAux00(vwx148, vwx149, LT, cdc) → LT
new_esEs28(vwx311, vwx411, app(app(ty_Either, bed), bee)) → new_esEs4(vwx311, vwx411, bed, bee)
new_primCompAux00(vwx148, vwx149, GT, cdc) → GT
new_esEs23(vwx301, vwx401, app(ty_Maybe, cfe)) → new_esEs5(vwx301, vwx401, cfe)
new_esEs4(Right(vwx300), Right(vwx400), ba, ty_Ordering) → new_esEs17(vwx300, vwx400)
new_primCompAux00(vwx148, vwx149, EQ, app(ty_Ratio, cdd)) → new_compare9(vwx148, vwx149, cdd)
new_lt20(vwx311, vwx411, app(ty_Maybe, beg)) → new_lt14(vwx311, vwx411, beg)
new_ltEs18(vwx311, vwx411, ty_Char) → new_ltEs5(vwx311, vwx411)
new_esEs23(vwx301, vwx401, ty_Char) → new_esEs9(vwx301, vwx401)
new_ltEs10(EQ, EQ) → True
new_lt8([], [], ea) → new_esEs17(EQ, LT)
new_ltEs12(Nothing, Just(vwx410), cab) → True
new_ltEs10(LT, LT) → True
new_esEs17(LT, EQ) → False
new_esEs17(EQ, LT) → False
new_esEs14(True, True) → True
new_esEs27(vwx310, vwx410, ty_Bool) → new_esEs14(vwx310, vwx410)
new_ltEs13(Right(vwx310), Left(vwx410), ce, be) → False
new_ltEs19(vwx312, vwx412, ty_@0) → new_ltEs8(vwx312, vwx412)
new_esEs5(Nothing, Just(vwx400), ge) → False
new_esEs5(Just(vwx300), Nothing, ge) → False
new_esEs26(vwx302, vwx402, app(ty_Ratio, dbd)) → new_esEs12(vwx302, vwx402, dbd)
new_esEs19(vwx300, vwx400, ty_Integer) → new_esEs16(vwx300, vwx400)
new_compare0(vwx300, vwx400, app(ty_Ratio, bhh)) → new_compare9(vwx300, vwx400, bhh)
new_esEs25(vwx301, vwx401, app(app(app(ty_@3, chc), chd), che)) → new_esEs7(vwx301, vwx401, chc, chd, che)
new_esEs18(vwx300, vwx400, ty_@0) → new_esEs10(vwx300, vwx400)
new_esEs24(vwx300, vwx400, ty_Ordering) → new_esEs17(vwx300, vwx400)
new_lt18(vwx30, vwx40) → new_esEs17(new_primCmpFloat(vwx30, vwx40), LT)
new_compare10(vwx31, vwx41) → new_primCmpInt(vwx31, vwx41)
new_esEs27(vwx310, vwx410, app(ty_[], bdd)) → new_esEs11(vwx310, vwx410, bdd)
new_primCompAux1(vwx300, vwx400, vwx301, vwx401, ea) → new_primCompAux00(vwx301, vwx401, new_compare0(vwx300, vwx400, ea), app(ty_[], ea))
new_ltEs13(Left(vwx310), Left(vwx410), app(ty_Ratio, dcb), be) → new_ltEs9(vwx310, vwx410, dcb)
new_esEs26(vwx302, vwx402, ty_Ordering) → new_esEs17(vwx302, vwx402)
new_lt16(vwx30, vwx40) → new_esEs17(new_primCmpDouble(vwx30, vwx40), LT)
new_ltEs5(vwx31, vwx41) → new_not(new_esEs17(new_compare12(vwx31, vwx41), GT))
new_esEs27(vwx310, vwx410, ty_Ordering) → new_esEs17(vwx310, vwx410)
new_esEs5(Nothing, Nothing, ge) → True
new_esEs28(vwx311, vwx411, app(ty_Maybe, beg)) → new_esEs5(vwx311, vwx411, beg)
new_lt20(vwx311, vwx411, ty_Bool) → new_lt12(vwx311, vwx411)
new_esEs5(Just(vwx300), Just(vwx400), app(app(app(ty_@3, bgf), bgg), bgh)) → new_esEs7(vwx300, vwx400, bgf, bgg, bgh)
new_esEs5(Just(vwx300), Just(vwx400), ty_Integer) → new_esEs16(vwx300, vwx400)
new_compare14(vwx30, vwx40, True, bcc, bcd) → LT
new_esEs21(vwx310, vwx410, app(ty_[], bab)) → new_esEs11(vwx310, vwx410, bab)
new_ltEs10(EQ, LT) → False
new_esEs14(False, False) → True
new_esEs22(vwx300, vwx400, ty_Integer) → new_esEs16(vwx300, vwx400)
new_lt19(vwx310, vwx410, ty_Float) → new_lt18(vwx310, vwx410)
new_esEs26(vwx302, vwx402, ty_Char) → new_esEs9(vwx302, vwx402)
new_compare36(vwx30, vwx40, ba, bb) → new_compare28(vwx30, vwx40, new_esEs4(vwx30, vwx40, ba, bb), ba, bb)
new_ltEs19(vwx312, vwx412, ty_Integer) → new_ltEs7(vwx312, vwx412)
new_compare13(vwx300, vwx400) → new_compare34(vwx300, vwx400)
new_lt19(vwx310, vwx410, ty_@0) → new_lt10(vwx310, vwx410)
new_ltEs10(GT, LT) → False
new_esEs18(vwx300, vwx400, ty_Bool) → new_esEs14(vwx300, vwx400)
new_esEs9(Char(vwx300), Char(vwx400)) → new_primEqNat0(vwx300, vwx400)
new_lt5(vwx30, vwx40, bce, bcf, bcg) → new_esEs17(new_compare35(vwx30, vwx40, bce, bcf, bcg), LT)
new_lt20(vwx311, vwx411, app(app(app(ty_@3, bfb), bfc), bfd)) → new_lt5(vwx311, vwx411, bfb, bfc, bfd)
new_esEs22(vwx300, vwx400, app(ty_Maybe, cec)) → new_esEs5(vwx300, vwx400, cec)
new_primPlusNat0(Succ(vwx15800), Succ(vwx400000)) → Succ(Succ(new_primPlusNat0(vwx15800, vwx400000)))
new_esEs21(vwx310, vwx410, app(ty_Maybe, bac)) → new_esEs5(vwx310, vwx410, bac)
new_esEs28(vwx311, vwx411, ty_Float) → new_esEs15(vwx311, vwx411)
new_ltEs13(Left(vwx310), Left(vwx410), ty_Int, be) → new_ltEs11(vwx310, vwx410)
new_esEs26(vwx302, vwx402, app(app(ty_Either, dba), dbb)) → new_esEs4(vwx302, vwx402, dba, dbb)
new_esEs20(vwx301, vwx401, ty_Int) → new_esEs8(vwx301, vwx401)
new_primCmpChar(Char(vwx300), Char(vwx400)) → new_primCmpNat0(vwx300, vwx400)
new_asAs(True, vwx143) → vwx143
new_compare0(vwx300, vwx400, ty_Integer) → new_compare11(vwx300, vwx400)
new_compare7(:(vwx310, vwx311), :(vwx410, vwx411), dh) → new_primCompAux1(vwx310, vwx410, vwx311, vwx411, dh)
new_esEs4(Left(vwx300), Right(vwx400), ba, bb) → False
new_esEs4(Right(vwx300), Left(vwx400), ba, bb) → False
new_esEs17(GT, GT) → True
new_compare9(:%(vwx310, vwx311), :%(vwx410, vwx411), ty_Integer) → new_compare11(new_sr0(vwx310, vwx411), new_sr0(vwx410, vwx311))
new_esEs5(Just(vwx300), Just(vwx400), app(ty_Ratio, bhe)) → new_esEs12(vwx300, vwx400, bhe)
new_ltEs12(Just(vwx310), Nothing, cab) → False
new_compare23(vwx30, vwx40, False, ge) → new_compare19(vwx30, vwx40, new_ltEs12(vwx30, vwx40, ge), ge)
new_ltEs19(vwx312, vwx412, ty_Char) → new_ltEs5(vwx312, vwx412)
new_compare25(vwx300, vwx401, vwx400, vwx301) → new_primCmpInt(new_sr(vwx300, vwx401), new_sr(vwx400, vwx301))
new_lt4(vwx30, vwx40) → new_esEs17(new_primCmpChar(vwx30, vwx40), LT)
new_esEs4(Right(vwx300), Right(vwx400), ba, ty_Int) → new_esEs8(vwx300, vwx400)
new_esEs26(vwx302, vwx402, app(app(ty_@2, dbe), dbf)) → new_esEs6(vwx302, vwx402, dbe, dbf)
new_ltEs6(False, False) → True
new_ltEs19(vwx312, vwx412, app(app(ty_@2, bga), bgb)) → new_ltEs14(vwx312, vwx412, bga, bgb)
new_compare110(vwx30, vwx40, False, bce, bcf, bcg) → GT
new_esEs5(Just(vwx300), Just(vwx400), app(app(ty_Either, bhb), bhc)) → new_esEs4(vwx300, vwx400, bhb, bhc)
new_compare24(vwx30, vwx40, False) → new_compare15(vwx30, vwx40, new_ltEs6(vwx30, vwx40))
new_ltEs13(Right(vwx310), Right(vwx410), ce, ty_Double) → new_ltEs16(vwx310, vwx410)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_ltEs12(Just(vwx310), Just(vwx410), ty_Integer) → new_ltEs7(vwx310, vwx410)
new_esEs23(vwx301, vwx401, ty_Int) → new_esEs8(vwx301, vwx401)
new_ltEs18(vwx311, vwx411, ty_Ordering) → new_ltEs10(vwx311, vwx411)
new_esEs25(vwx301, vwx401, app(ty_Ratio, dab)) → new_esEs12(vwx301, vwx401, dab)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_esEs27(vwx310, vwx410, ty_Char) → new_esEs9(vwx310, vwx410)
new_esEs8(vwx30, vwx40) → new_primEqInt(vwx30, vwx40)
new_primCmpInt(Neg(Succ(vwx3000)), Pos(vwx400)) → LT
new_not(True) → False

The set Q consists of the following terms:

new_ltEs18(x0, x1, ty_Ordering)
new_esEs25(x0, x1, ty_Double)
new_compare36(x0, x1, x2, x3)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_lt9(x0, x1, app(ty_Ratio, x2))
new_esEs17(LT, GT)
new_esEs17(GT, LT)
new_esEs24(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Float)
new_lt20(x0, x1, ty_Float)
new_lt19(x0, x1, ty_Double)
new_lt8(:(x0, x1), :(x2, x3), x4)
new_lt7(x0, x1, x2, x3)
new_esEs19(x0, x1, ty_Int)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_compare40(x0, x1)
new_esEs23(x0, x1, ty_@0)
new_esEs21(x0, x1, ty_Ordering)
new_esEs21(x0, x1, ty_Double)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs4(Left(x0), Left(x1), ty_@0, x2)
new_compare23(x0, x1, False, x2)
new_lt9(x0, x1, ty_@0)
new_esEs26(x0, x1, ty_Ordering)
new_esEs17(LT, LT)
new_compare0(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs11(x0, x1)
new_esEs18(x0, x1, ty_Int)
new_lt13(x0, x1)
new_compare27(x0, x1, True, x2, x3)
new_esEs28(x0, x1, ty_@0)
new_esEs4(Left(x0), Right(x1), x2, x3)
new_esEs4(Right(x0), Left(x1), x2, x3)
new_ltEs13(Left(x0), Left(x1), ty_Bool, x2)
new_esEs4(Left(x0), Left(x1), ty_Bool, x2)
new_compare210(x0, x1, False, x2, x3, x4)
new_esEs18(x0, x1, app(app(ty_Either, x2), x3))
new_esEs18(x0, x1, ty_Ordering)
new_ltEs10(LT, LT)
new_lt19(x0, x1, ty_Bool)
new_primMulInt(Neg(x0), Neg(x1))
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_compare0(x0, x1, ty_Ordering)
new_esEs18(x0, x1, app(ty_Maybe, x2))
new_ltEs13(Left(x0), Left(x1), ty_Char, x2)
new_ltEs18(x0, x1, ty_Int)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs17(GT, EQ)
new_esEs17(EQ, GT)
new_esEs24(x0, x1, ty_Ordering)
new_esEs18(x0, x1, app(ty_[], x2))
new_ltEs12(Just(x0), Just(x1), ty_@0)
new_compare43(x0, x1, x2, x3, x4)
new_asAs(True, x0)
new_compare19(x0, x1, False, x2)
new_esEs22(x0, x1, ty_Bool)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_ltEs18(x0, x1, app(ty_[], x2))
new_esEs4(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs12(Just(x0), Just(x1), ty_Float)
new_ltEs13(Right(x0), Right(x1), x2, ty_Int)
new_esEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_primPlusNat0(Succ(x0), Zero)
new_compare0(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Char)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs11([], [], x0)
new_primCompAux00(x0, x1, EQ, app(app(app(ty_@3, x2), x3), x4))
new_pePe(True, x0)
new_ltEs12(Just(x0), Nothing, x1)
new_ltEs12(Just(x0), Just(x1), app(ty_[], x2))
new_esEs4(Right(x0), Right(x1), x2, ty_Double)
new_esEs28(x0, x1, ty_Ordering)
new_ltEs6(True, True)
new_esEs24(x0, x1, ty_Float)
new_primCompAux00(x0, x1, LT, x2)
new_compare27(x0, x1, False, x2, x3)
new_primCompAux00(x0, x1, EQ, app(ty_Ratio, x2))
new_compare29(x0, x1, True)
new_esEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_lt19(x0, x1, ty_Int)
new_esEs5(Just(x0), Just(x1), ty_Float)
new_esEs22(x0, x1, app(ty_[], x2))
new_primCompAux00(x0, x1, EQ, ty_Int)
new_esEs17(GT, GT)
new_compare29(x0, x1, False)
new_ltEs12(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, ty_Float)
new_esEs23(x0, x1, ty_Integer)
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt16(x0, x1)
new_ltEs8(x0, x1)
new_sr(x0, x1)
new_compare18(@0, @0)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs5(Just(x0), Nothing, x1)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs14(True, True)
new_ltEs13(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_compare0(x0, x1, ty_Double)
new_ltEs12(Nothing, Just(x0), x1)
new_ltEs13(Right(x0), Right(x1), x2, ty_Integer)
new_primEqNat0(Zero, Zero)
new_lt20(x0, x1, ty_@0)
new_compare7([], :(x0, x1), x2)
new_compare9(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs18(x0, x1, ty_@0)
new_esEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs25(x0, x1, ty_Float)
new_esEs23(x0, x1, ty_Char)
new_esEs16(Integer(x0), Integer(x1))
new_primMulInt(Pos(x0), Pos(x1))
new_ltEs12(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_primCompAux00(x0, x1, EQ, ty_Bool)
new_esEs22(x0, x1, ty_Char)
new_ltEs7(x0, x1)
new_esEs25(x0, x1, ty_Integer)
new_lt15(x0, x1)
new_ltEs13(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_primMulNat0(Zero, Zero)
new_esEs4(Right(x0), Right(x1), x2, ty_Char)
new_ltEs13(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_lt17(Integer(x0), Integer(x1))
new_esEs22(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_Ordering)
new_ltEs10(EQ, LT)
new_ltEs13(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs10(LT, EQ)
new_esEs21(x0, x1, ty_Integer)
new_compare23(x0, x1, True, x2)
new_compare0(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Just(x0), Just(x1), ty_Double)
new_primCompAux00(x0, x1, EQ, ty_Char)
new_compare10(x0, x1)
new_esEs4(Right(x0), Right(x1), x2, ty_@0)
new_lt9(x0, x1, ty_Float)
new_ltEs18(x0, x1, ty_Double)
new_esEs22(x0, x1, ty_@0)
new_lt8([], :(x0, x1), x2)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs18(x0, x1, ty_Float)
new_ltEs13(Left(x0), Left(x1), app(ty_[], x2), x3)
new_compare19(x0, x1, True, x2)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs18(x0, x1, app(ty_Ratio, x2))
new_ltEs15(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_lt19(x0, x1, ty_@0)
new_ltEs12(Nothing, Nothing, x0)
new_esEs18(x0, x1, ty_Bool)
new_compare38(x0, x1)
new_esEs8(x0, x1)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, ty_Int)
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs5(Nothing, Nothing, x0)
new_primMulNat0(Zero, Succ(x0))
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs4(Left(x0), Left(x1), ty_Double, x2)
new_compare41(x0, x1, x2)
new_ltEs12(Just(x0), Just(x1), ty_Char)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Integer)
new_esEs11(:(x0, x1), [], x2)
new_compare14(x0, x1, True, x2, x3)
new_ltEs13(Right(x0), Right(x1), x2, ty_@0)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Bool)
new_compare111(x0, x1, True)
new_esEs4(Right(x0), Right(x1), x2, ty_Float)
new_lt9(x0, x1, app(ty_Maybe, x2))
new_ltEs13(Right(x0), Right(x1), x2, ty_Char)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_compare0(x0, x1, app(ty_[], x2))
new_esEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs5(Just(x0), Just(x1), ty_Char)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs20(x0, x1, ty_Int)
new_esEs22(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_Int)
new_esEs4(Left(x0), Left(x1), ty_Int, x2)
new_primCompAux00(x0, x1, EQ, ty_Ordering)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs13(Left(x0), Left(x1), ty_@0, x2)
new_compare39(x0, x1, x2, x3, ty_Int)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, app(ty_[], x2))
new_primEqNat0(Succ(x0), Zero)
new_esEs13(Double(x0, x1), Double(x2, x3))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs27(x0, x1, ty_Bool)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_Float)
new_primPlusNat0(Zero, Zero)
new_ltEs13(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_primCompAux1(x0, x1, x2, x3, x4)
new_ltEs12(Just(x0), Just(x1), ty_Bool)
new_lt20(x0, x1, ty_Double)
new_esEs21(x0, x1, ty_Float)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_ltEs13(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs27(x0, x1, ty_Integer)
new_esEs23(x0, x1, ty_Bool)
new_ltEs13(Right(x0), Right(x1), x2, ty_Double)
new_esEs5(Just(x0), Just(x1), ty_Bool)
new_esEs25(x0, x1, ty_Bool)
new_esEs23(x0, x1, ty_Double)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, ty_@0)
new_esEs5(Just(x0), Just(x1), app(ty_[], x2))
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_ltEs6(False, True)
new_ltEs6(True, False)
new_lt9(x0, x1, ty_Ordering)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, ty_Int)
new_esEs23(x0, x1, app(ty_[], x2))
new_compare33(x0, x1, x2)
new_lt9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs10(GT, LT)
new_esEs23(x0, x1, ty_Ordering)
new_ltEs10(LT, GT)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs19(x0, x1, ty_Integer)
new_lt9(x0, x1, ty_Int)
new_compare34(x0, x1)
new_compare8(x0, x1)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs10(@0, @0)
new_compare7(:(x0, x1), [], x2)
new_ltEs9(x0, x1, x2)
new_esEs26(x0, x1, ty_@0)
new_lt18(x0, x1)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Float)
new_lt8(:(x0, x1), [], x2)
new_lt9(x0, x1, app(app(ty_Either, x2), x3))
new_lt9(x0, x1, ty_Double)
new_compare15(x0, x1, False)
new_esEs5(Just(x0), Just(x1), ty_Ordering)
new_esEs20(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_Char)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_compare42(x0, x1, x2, x3)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Double)
new_esEs4(Left(x0), Left(x1), ty_Integer, x2)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_lt10(@0, @0)
new_lt11(:%(x0, x1), :%(x2, x3), x4)
new_ltEs13(Right(x0), Right(x1), x2, ty_Float)
new_esEs18(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs13(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs13(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare26(x0, x1)
new_ltEs19(x0, x1, app(ty_[], x2))
new_primCompAux00(x0, x1, EQ, app(app(ty_@2, x2), x3))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_ltEs6(False, False)
new_esEs11(:(x0, x1), :(x2, x3), x4)
new_primCompAux00(x0, x1, EQ, app(app(ty_Either, x2), x3))
new_ltEs13(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs13(Right(x0), Left(x1), x2, x3)
new_ltEs13(Left(x0), Right(x1), x2, x3)
new_esEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs22(x0, x1, ty_Double)
new_compare110(x0, x1, True, x2, x3, x4)
new_ltEs18(x0, x1, ty_@0)
new_esEs5(Just(x0), Just(x1), ty_Int)
new_esEs14(True, False)
new_esEs14(False, True)
new_esEs11([], :(x0, x1), x2)
new_compare24(x0, x1, False)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs28(x0, x1, app(ty_[], x2))
new_lt9(x0, x1, app(app(ty_@2, x2), x3))
new_lt19(x0, x1, ty_Float)
new_esEs21(x0, x1, ty_Char)
new_primCompAux00(x0, x1, EQ, app(ty_Maybe, x2))
new_lt19(x0, x1, ty_Integer)
new_compare0(x0, x1, ty_Integer)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_compare0(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_Float)
new_ltEs13(Left(x0), Left(x1), ty_Float, x2)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_asAs(False, x0)
new_primCmpNat0(Zero, Succ(x0))
new_esEs25(x0, x1, ty_Char)
new_esEs28(x0, x1, ty_Integer)
new_lt9(x0, x1, app(ty_[], x2))
new_ltEs12(Just(x0), Just(x1), ty_Double)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Nothing, Just(x0), x1)
new_compare0(x0, x1, ty_@0)
new_primCompAux00(x0, x1, GT, x2)
new_compare0(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, ty_Bool)
new_ltEs13(Right(x0), Right(x1), x2, ty_Bool)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_primPlusNat1(Succ(x0), x1)
new_esEs26(x0, x1, ty_Double)
new_esEs28(x0, x1, ty_Char)
new_compare25(x0, x1, x2, x3)
new_ltEs14(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_compare35(x0, x1, x2, x3, x4)
new_esEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare17(x0, x1, False, x2, x3)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_ltEs13(Left(x0), Left(x1), ty_Double, x2)
new_primPlusNat1(Zero, x0)
new_lt20(x0, x1, ty_Char)
new_esEs25(x0, x1, ty_Ordering)
new_ltEs12(Just(x0), Just(x1), ty_Ordering)
new_lt12(x0, x1)
new_primCmpNat0(Zero, Zero)
new_ltEs19(x0, x1, ty_Int)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt5(x0, x1, x2, x3, x4)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_ltEs12(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_lt9(x0, x1, ty_Bool)
new_lt19(x0, x1, ty_Char)
new_compare15(x0, x1, True)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, ty_Ordering)
new_esEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_primCompAux00(x0, x1, EQ, ty_@0)
new_compare17(x0, x1, True, x2, x3)
new_ltEs13(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_compare11(Integer(x0), Integer(x1))
new_esEs5(Just(x0), Just(x1), ty_Integer)
new_ltEs19(x0, x1, ty_@0)
new_esEs24(x0, x1, ty_Double)
new_compare9(:%(x0, x1), :%(x2, x3), ty_Int)
new_lt19(x0, x1, ty_Ordering)
new_esEs18(x0, x1, ty_Double)
new_primEqNat0(Zero, Succ(x0))
new_primCmpDouble(Double(x0, x1), Double(x2, x3))
new_compare13(x0, x1)
new_lt4(x0, x1)
new_ltEs13(Left(x0), Left(x1), ty_Int, x2)
new_lt14(x0, x1, x2)
new_pePe(False, x0)
new_primMulNat0(Succ(x0), Zero)
new_ltEs10(GT, GT)
new_ltEs12(Just(x0), Just(x1), app(ty_Ratio, x2))
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs21(x0, x1, ty_Bool)
new_esEs12(:%(x0, x1), :%(x2, x3), x4)
new_esEs26(x0, x1, ty_Char)
new_primCmpNat0(Succ(x0), Succ(x1))
new_ltEs12(Just(x0), Just(x1), ty_Integer)
new_compare0(x0, x1, ty_Bool)
new_esEs5(Just(x0), Just(x1), ty_@0)
new_compare12(x0, x1)
new_esEs25(x0, x1, ty_@0)
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, app(ty_[], x2))
new_not(True)
new_compare28(x0, x1, False, x2, x3)
new_ltEs13(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs21(x0, x1, ty_Int)
new_compare24(x0, x1, True)
new_lt20(x0, x1, ty_Ordering)
new_esEs4(Left(x0), Left(x1), ty_Float, x2)
new_lt9(x0, x1, ty_Char)
new_compare7([], [], x0)
new_ltEs19(x0, x1, ty_Integer)
new_compare37(x0, x1, x2, x3)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_ltEs18(x0, x1, ty_Char)
new_ltEs13(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_not(False)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs17(x0, x1)
new_lt20(x0, x1, ty_Bool)
new_ltEs5(x0, x1)
new_ltEs10(GT, EQ)
new_ltEs10(EQ, GT)
new_esEs26(x0, x1, ty_Integer)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs19(x0, x1, ty_Float)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs21(x0, x1, app(ty_[], x2))
new_ltEs13(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs21(x0, x1, ty_@0)
new_primEqNat0(Succ(x0), Succ(x1))
new_compare0(x0, x1, ty_Char)
new_sr0(Integer(x0), Integer(x1))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs28(x0, x1, ty_Bool)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare0(x0, x1, ty_Int)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, app(ty_[], x2))
new_compare28(x0, x1, True, x2, x3)
new_compare111(x0, x1, False)
new_ltEs12(Just(x0), Just(x1), app(ty_Maybe, x2))
new_primCompAux00(x0, x1, EQ, ty_Double)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_compare110(x0, x1, False, x2, x3, x4)
new_ltEs13(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs4(Right(x0), Right(x1), x2, ty_Integer)
new_compare14(x0, x1, False, x2, x3)
new_primCmpFloat(Float(x0, x1), Float(x2, x3))
new_compare16(x0, x1, x2, x3)
new_ltEs4(x0, x1, x2)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs15(Float(x0, x1), Float(x2, x3))
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs18(x0, x1, ty_Integer)
new_esEs27(x0, x1, ty_Double)
new_esEs4(Right(x0), Right(x1), x2, ty_Int)
new_compare39(Integer(x0), Integer(x1), x2, x3, ty_Integer)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_primCompAux00(x0, x1, EQ, app(ty_[], x2))
new_ltEs18(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_Bool)
new_esEs9(Char(x0), Char(x1))
new_compare210(x0, x1, True, x2, x3, x4)
new_esEs14(False, False)
new_ltEs12(Just(x0), Just(x1), ty_Int)
new_primEqInt(Pos(Zero), Pos(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_esEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs24(x0, x1, ty_Char)
new_primCompAux00(x0, x1, EQ, ty_Float)
new_lt9(x0, x1, ty_Integer)
new_primPlusNat0(Succ(x0), Succ(x1))
new_lt20(x0, x1, app(ty_[], x2))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Int)
new_compare7(:(x0, x1), :(x2, x3), x4)
new_primCompAux00(x0, x1, EQ, ty_Integer)
new_esEs17(EQ, EQ)
new_primCmpChar(Char(x0), Char(x1))
new_esEs4(Left(x0), Left(x1), ty_Char, x2)
new_ltEs18(x0, x1, ty_Integer)
new_esEs17(LT, EQ)
new_esEs17(EQ, LT)
new_lt8([], [], x0)
new_esEs24(x0, x1, ty_@0)
new_primCmpNat0(Succ(x0), Zero)
new_ltEs16(x0, x1)
new_esEs25(x0, x1, ty_Int)
new_esEs28(x0, x1, ty_Float)
new_compare0(x0, x1, ty_Float)
new_lt6(x0, x1, x2, x3)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs18(x0, x1, ty_Char)
new_esEs27(x0, x1, ty_Ordering)
new_ltEs10(EQ, EQ)

We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 8 less nodes.

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

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

new_ltEs2(@2(vwx310, vwx311), @2(vwx410, vwx411), app(app(ty_@2, bad), bae), baa) → new_lt2(vwx310, vwx410, bad, bae)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), bec, bdb, app(app(ty_Either, bfe), bff)) → new_ltEs(vwx312, vwx412, bfe, bff)
new_ltEs2(@2(vwx310, vwx311), @2(vwx410, vwx411), bba, app(app(ty_Either, bbb), bbc)) → new_ltEs(vwx311, vwx411, bbb, bbc)
new_lt(vwx30, vwx40, ba, bb) → new_compare2(vwx30, vwx40, new_esEs4(vwx30, vwx40, ba, bb), ba, bb)
new_compare2(vwx30, vwx40, False, ba, bb) → new_ltEs(vwx30, vwx40, ba, bb)
new_ltEs(Left(vwx310), Left(vwx410), app(app(ty_Either, bc), bd), be) → new_ltEs(vwx310, vwx410, bc, bd)
new_ltEs(Right(vwx310), Right(vwx410), ce, app(app(ty_Either, cf), cg)) → new_ltEs(vwx310, vwx410, cf, cg)
new_compare32(vwx30, vwx40, bce, bcf, bcg) → new_compare22(vwx30, vwx40, new_esEs7(vwx30, vwx40, bce, bcf, bcg), bce, bcf, bcg)
new_ltEs2(@2(vwx310, vwx311), @2(vwx410, vwx411), bba, app(app(app(ty_@3, bbh), bca), bcb)) → new_ltEs3(vwx311, vwx411, bbh, bca, bcb)
new_ltEs2(@2(vwx310, vwx311), @2(vwx410, vwx411), app(ty_[], bab), baa) → new_lt0(vwx310, vwx410, bab)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), bec, app(ty_[], bef), bdc) → new_lt0(vwx311, vwx411, bef)
new_compare(:(vwx310, vwx311), :(vwx410, vwx411), dh) → new_primCompAux(vwx310, vwx410, vwx311, vwx411, dh)
new_compare31(vwx30, vwx40, bcc, bcd) → new_compare21(vwx30, vwx40, new_esEs6(vwx30, vwx40, bcc, bcd), bcc, bcd)
new_ltEs1(Just(vwx310), Just(vwx410), app(ty_Maybe, ha)) → new_ltEs1(vwx310, vwx410, ha)
new_ltEs(Right(vwx310), Right(vwx410), ce, app(ty_[], da)) → new_ltEs0(vwx310, vwx410, da)
new_primCompAux(vwx300, vwx400, vwx301, vwx401, ea) → new_primCompAux0(vwx301, vwx401, new_compare0(vwx300, vwx400, ea), app(ty_[], ea))
new_ltEs(Right(vwx310), Right(vwx410), ce, app(app(app(ty_@3, de), df), dg)) → new_ltEs3(vwx310, vwx410, de, df, dg)
new_primCompAux(vwx300, vwx400, vwx301, vwx401, app(app(ty_Either, eb), ec)) → new_compare3(vwx300, vwx400, eb, ec)
new_compare22(vwx30, vwx40, False, bce, bcf, bcg) → new_ltEs3(vwx30, vwx40, bce, bcf, bcg)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), app(ty_[], bdd), bdb, bdc) → new_lt0(vwx310, vwx410, bdd)
new_compare20(vwx30, vwx40, False, ge) → new_ltEs1(vwx30, vwx40, ge)
new_ltEs1(Just(vwx310), Just(vwx410), app(app(app(ty_@3, hd), he), hf)) → new_ltEs3(vwx310, vwx410, hd, he, hf)
new_lt3(vwx30, vwx40, bce, bcf, bcg) → new_compare22(vwx30, vwx40, new_esEs7(vwx30, vwx40, bce, bcf, bcg), bce, bcf, bcg)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), bec, bdb, app(ty_Maybe, bfh)) → new_ltEs1(vwx312, vwx412, bfh)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), app(app(ty_@2, bdf), bdg), bdb, bdc) → new_lt2(vwx310, vwx410, bdf, bdg)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), app(app(ty_Either, bch), bda), bdb, bdc) → new_lt(vwx310, vwx410, bch, bda)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), bec, app(app(ty_Either, bed), bee), bdc) → new_lt(vwx311, vwx411, bed, bee)
new_primCompAux(vwx300, vwx400, vwx301, vwx401, app(app(app(ty_@3, eh), fa), fb)) → new_compare32(vwx300, vwx400, eh, fa, fb)
new_lt1(vwx30, vwx40, ge) → new_compare20(vwx30, vwx40, new_esEs5(vwx30, vwx40, ge), ge)
new_ltEs2(@2(vwx310, vwx311), @2(vwx410, vwx411), app(app(ty_Either, hg), hh), baa) → new_lt(vwx310, vwx410, hg, hh)
new_ltEs2(@2(vwx310, vwx311), @2(vwx410, vwx411), bba, app(ty_[], bbd)) → new_ltEs0(vwx311, vwx411, bbd)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), bec, app(app(ty_@2, beh), bfa), bdc) → new_lt2(vwx311, vwx411, beh, bfa)
new_compare3(vwx30, vwx40, ba, bb) → new_compare2(vwx30, vwx40, new_esEs4(vwx30, vwx40, ba, bb), ba, bb)
new_compare30(vwx30, vwx40, ge) → new_compare20(vwx30, vwx40, new_esEs5(vwx30, vwx40, ge), ge)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), bec, bdb, app(app(ty_@2, bga), bgb)) → new_ltEs2(vwx312, vwx412, bga, bgb)
new_compare21(vwx30, vwx40, False, bcc, bcd) → new_ltEs2(vwx30, vwx40, bcc, bcd)
new_ltEs(Left(vwx310), Left(vwx410), app(ty_[], bf), be) → new_ltEs0(vwx310, vwx410, bf)
new_ltEs1(Just(vwx310), Just(vwx410), app(app(ty_Either, gf), gg)) → new_ltEs(vwx310, vwx410, gf, gg)
new_primCompAux(vwx300, vwx400, vwx301, vwx401, app(ty_[], ed)) → new_compare(vwx300, vwx400, ed)
new_primCompAux0(vwx148, vwx149, EQ, app(ty_[], ff)) → new_compare(vwx148, vwx149, ff)
new_ltEs2(@2(vwx310, vwx311), @2(vwx410, vwx411), app(app(app(ty_@3, baf), bag), bah), baa) → new_lt3(vwx310, vwx410, baf, bag, bah)
new_ltEs2(@2(vwx310, vwx311), @2(vwx410, vwx411), app(ty_Maybe, bac), baa) → new_lt1(vwx310, vwx410, bac)
new_ltEs1(Just(vwx310), Just(vwx410), app(app(ty_@2, hb), hc)) → new_ltEs2(vwx310, vwx410, hb, hc)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), bec, bdb, app(ty_[], bfg)) → new_ltEs0(vwx312, vwx412, bfg)
new_ltEs2(@2(vwx310, vwx311), @2(vwx410, vwx411), bba, app(ty_Maybe, bbe)) → new_ltEs1(vwx311, vwx411, bbe)
new_lt0(:(vwx300, vwx301), :(vwx400, vwx401), app(app(ty_@2, ef), eg)) → new_compare31(vwx300, vwx400, ef, eg)
new_ltEs1(Just(vwx310), Just(vwx410), app(ty_[], gh)) → new_ltEs0(vwx310, vwx410, gh)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), bec, app(ty_Maybe, beg), bdc) → new_lt1(vwx311, vwx411, beg)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), bec, bdb, app(app(app(ty_@3, bgc), bgd), bge)) → new_ltEs3(vwx312, vwx412, bgc, bgd, bge)
new_lt2(vwx30, vwx40, bcc, bcd) → new_compare21(vwx30, vwx40, new_esEs6(vwx30, vwx40, bcc, bcd), bcc, bcd)
new_ltEs2(@2(vwx310, vwx311), @2(vwx410, vwx411), bba, app(app(ty_@2, bbf), bbg)) → new_ltEs2(vwx311, vwx411, bbf, bbg)
new_lt0(:(vwx300, vwx301), :(vwx400, vwx401), ea) → new_primCompAux0(vwx301, vwx401, new_compare0(vwx300, vwx400, ea), app(ty_[], ea))
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), app(app(app(ty_@3, bdh), bea), beb), bdb, bdc) → new_lt3(vwx310, vwx410, bdh, bea, beb)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), app(ty_Maybe, bde), bdb, bdc) → new_lt1(vwx310, vwx410, bde)
new_ltEs(Left(vwx310), Left(vwx410), app(ty_Maybe, bg), be) → new_ltEs1(vwx310, vwx410, bg)
new_ltEs0(:(vwx310, vwx311), :(vwx410, vwx411), dh) → new_primCompAux(vwx310, vwx410, vwx311, vwx411, dh)
new_ltEs(Left(vwx310), Left(vwx410), app(app(app(ty_@3, cb), cc), cd), be) → new_ltEs3(vwx310, vwx410, cb, cc, cd)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), bec, app(app(app(ty_@3, bfb), bfc), bfd), bdc) → new_lt3(vwx311, vwx411, bfb, bfc, bfd)
new_ltEs(Right(vwx310), Right(vwx410), ce, app(app(ty_@2, dc), dd)) → new_ltEs2(vwx310, vwx410, dc, dd)
new_lt0(:(vwx300, vwx301), :(vwx400, vwx401), app(ty_[], ed)) → new_compare(vwx300, vwx400, ed)
new_primCompAux(vwx300, vwx400, vwx301, vwx401, app(ty_Maybe, ee)) → new_compare30(vwx300, vwx400, ee)
new_lt0(:(vwx300, vwx301), :(vwx400, vwx401), app(app(app(ty_@3, eh), fa), fb)) → new_compare32(vwx300, vwx400, eh, fa, fb)
new_primCompAux(vwx300, vwx400, vwx301, vwx401, app(app(ty_@2, ef), eg)) → new_compare31(vwx300, vwx400, ef, eg)
new_ltEs(Left(vwx310), Left(vwx410), app(app(ty_@2, bh), ca), be) → new_ltEs2(vwx310, vwx410, bh, ca)
new_lt0(:(vwx300, vwx301), :(vwx400, vwx401), app(ty_Maybe, ee)) → new_compare30(vwx300, vwx400, ee)
new_ltEs(Right(vwx310), Right(vwx410), ce, app(ty_Maybe, db)) → new_ltEs1(vwx310, vwx410, db)
new_lt0(:(vwx300, vwx301), :(vwx400, vwx401), app(app(ty_Either, eb), ec)) → new_compare3(vwx300, vwx400, eb, ec)

The TRS R consists of the following rules:

new_esEs7(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), bce, bcf, bcg) → new_asAs(new_esEs24(vwx300, vwx400, bce), new_asAs(new_esEs25(vwx301, vwx401, bcf), new_esEs26(vwx302, vwx402, bcg)))
new_esEs28(vwx311, vwx411, ty_Int) → new_esEs8(vwx311, vwx411)
new_esEs25(vwx301, vwx401, ty_Ordering) → new_esEs17(vwx301, vwx401)
new_compare7(:(vwx310, vwx311), [], dh) → GT
new_esEs21(vwx310, vwx410, app(app(ty_@2, bad), bae)) → new_esEs6(vwx310, vwx410, bad, bae)
new_esEs19(vwx300, vwx400, ty_Int) → new_esEs8(vwx300, vwx400)
new_esEs18(vwx300, vwx400, app(app(ty_@2, ef), eg)) → new_esEs6(vwx300, vwx400, ef, eg)
new_lt9(vwx310, vwx410, ty_Double) → new_lt16(vwx310, vwx410)
new_lt19(vwx310, vwx410, ty_Char) → new_lt4(vwx310, vwx410)
new_esEs18(vwx300, vwx400, ty_Integer) → new_esEs16(vwx300, vwx400)
new_compare7([], :(vwx410, vwx411), dh) → LT
new_esEs4(Left(vwx300), Left(vwx400), ty_Bool, bb) → new_esEs14(vwx300, vwx400)
new_esEs24(vwx300, vwx400, ty_Char) → new_esEs9(vwx300, vwx400)
new_ltEs13(Left(vwx310), Left(vwx410), app(ty_[], bf), be) → new_ltEs4(vwx310, vwx410, bf)
new_ltEs13(Right(vwx310), Right(vwx410), ce, app(app(app(ty_@3, de), df), dg)) → new_ltEs15(vwx310, vwx410, de, df, dg)
new_esEs23(vwx301, vwx401, ty_Bool) → new_esEs14(vwx301, vwx401)
new_esEs21(vwx310, vwx410, ty_Ordering) → new_esEs17(vwx310, vwx410)
new_primCompAux00(vwx148, vwx149, EQ, ty_Char) → new_compare12(vwx148, vwx149)
new_esEs4(Right(vwx300), Right(vwx400), ba, app(ty_Maybe, ccd)) → new_esEs5(vwx300, vwx400, ccd)
new_ltEs13(Left(vwx310), Left(vwx410), ty_Char, be) → new_ltEs5(vwx310, vwx410)
new_esEs18(vwx300, vwx400, app(ty_Ratio, bhh)) → new_esEs12(vwx300, vwx400, bhh)
new_lt11(:%(vwx300, vwx301), :%(vwx400, vwx401), cch) → new_esEs17(new_compare39(vwx300, vwx401, vwx400, vwx301, cch), LT)
new_ltEs6(True, False) → False
new_ltEs12(Nothing, Nothing, cab) → True
new_primMulNat0(Zero, Zero) → Zero
new_esEs26(vwx302, vwx402, ty_Float) → new_esEs15(vwx302, vwx402)
new_esEs4(Left(vwx300), Left(vwx400), ty_Ordering, bb) → new_esEs17(vwx300, vwx400)
new_lt20(vwx311, vwx411, app(ty_[], bef)) → new_lt8(vwx311, vwx411, bef)
new_compare19(vwx30, vwx40, True, ge) → LT
new_compare29(vwx30, vwx40, True) → EQ
new_ltEs12(Just(vwx310), Just(vwx410), ty_Float) → new_ltEs17(vwx310, vwx410)
new_esEs4(Right(vwx300), Right(vwx400), ba, app(ty_[], cca)) → new_esEs11(vwx300, vwx400, cca)
new_ltEs18(vwx311, vwx411, ty_Bool) → new_ltEs6(vwx311, vwx411)
new_esEs18(vwx300, vwx400, ty_Double) → new_esEs13(vwx300, vwx400)
new_esEs22(vwx300, vwx400, ty_Char) → new_esEs9(vwx300, vwx400)
new_esEs18(vwx300, vwx400, ty_Char) → new_esEs9(vwx300, vwx400)
new_ltEs11(vwx31, vwx41) → new_not(new_esEs17(new_compare10(vwx31, vwx41), GT))
new_esEs13(Double(vwx300, vwx301), Double(vwx400, vwx401)) → new_esEs8(new_sr(vwx300, vwx400), new_sr(vwx301, vwx401))
new_compare40(vwx31, vwx41) → new_primCmpFloat(vwx31, vwx41)
new_primCompAux00(vwx148, vwx149, EQ, ty_Bool) → new_compare13(vwx148, vwx149)
new_lt9(vwx310, vwx410, ty_@0) → new_lt10(vwx310, vwx410)
new_primCompAux00(vwx148, vwx149, EQ, app(ty_Maybe, fg)) → new_compare41(vwx148, vwx149, fg)
new_compare19(vwx30, vwx40, False, ge) → GT
new_ltEs13(Right(vwx310), Right(vwx410), ce, ty_Int) → new_ltEs11(vwx310, vwx410)
new_esEs4(Right(vwx300), Right(vwx400), ba, app(app(app(ty_@3, cbf), cbg), cbh)) → new_esEs7(vwx300, vwx400, cbf, cbg, cbh)
new_compare18(@0, @0) → EQ
new_ltEs18(vwx311, vwx411, app(ty_Ratio, cdb)) → new_ltEs9(vwx311, vwx411, cdb)
new_esEs5(Just(vwx300), Just(vwx400), ty_Ordering) → new_esEs17(vwx300, vwx400)
new_esEs4(Left(vwx300), Left(vwx400), app(app(ty_@2, cbd), cbe), bb) → new_esEs6(vwx300, vwx400, cbd, cbe)
new_lt9(vwx310, vwx410, ty_Int) → new_lt15(vwx310, vwx410)
new_ltEs12(Just(vwx310), Just(vwx410), ty_Int) → new_ltEs11(vwx310, vwx410)
new_ltEs19(vwx312, vwx412, ty_Ordering) → new_ltEs10(vwx312, vwx412)
new_esEs11([], [], ea) → True
new_ltEs12(Just(vwx310), Just(vwx410), ty_Ordering) → new_ltEs10(vwx310, vwx410)
new_esEs21(vwx310, vwx410, app(app(app(ty_@3, baf), bag), bah)) → new_esEs7(vwx310, vwx410, baf, bag, bah)
new_compare0(vwx300, vwx400, ty_Bool) → new_compare13(vwx300, vwx400)
new_esEs5(Just(vwx300), Just(vwx400), app(ty_Maybe, bhd)) → new_esEs5(vwx300, vwx400, bhd)
new_compare210(vwx30, vwx40, False, bce, bcf, bcg) → new_compare110(vwx30, vwx40, new_ltEs15(vwx30, vwx40, bce, bcf, bcg), bce, bcf, bcg)
new_esEs23(vwx301, vwx401, ty_Double) → new_esEs13(vwx301, vwx401)
new_esEs4(Right(vwx300), Right(vwx400), ba, ty_Float) → new_esEs15(vwx300, vwx400)
new_ltEs10(EQ, GT) → True
new_compare16(vwx300, vwx400, eb, ec) → new_compare36(vwx300, vwx400, eb, ec)
new_ltEs13(Left(vwx310), Left(vwx410), ty_Integer, be) → new_ltEs7(vwx310, vwx410)
new_esEs5(Just(vwx300), Just(vwx400), ty_Char) → new_esEs9(vwx300, vwx400)
new_ltEs19(vwx312, vwx412, app(ty_Maybe, bfh)) → new_ltEs12(vwx312, vwx412, bfh)
new_lt6(vwx30, vwx40, bcc, bcd) → new_esEs17(new_compare37(vwx30, vwx40, bcc, bcd), LT)
new_compare9(:%(vwx310, vwx311), :%(vwx410, vwx411), ty_Int) → new_compare10(new_sr(vwx310, vwx411), new_sr(vwx410, vwx311))
new_esEs4(Left(vwx300), Left(vwx400), app(ty_[], cag), bb) → new_esEs11(vwx300, vwx400, cag)
new_compare15(vwx30, vwx40, False) → GT
new_lt8([], :(vwx400, vwx401), ea) → new_esEs17(LT, LT)
new_primCompAux00(vwx148, vwx149, EQ, ty_Double) → new_compare8(vwx148, vwx149)
new_lt20(vwx311, vwx411, ty_Char) → new_lt4(vwx311, vwx411)
new_primCompAux00(vwx148, vwx149, EQ, app(app(ty_@2, fh), ga)) → new_compare42(vwx148, vwx149, fh, ga)
new_pePe(False, vwx117) → vwx117
new_ltEs9(vwx31, vwx41, caa) → new_not(new_esEs17(new_compare9(vwx31, vwx41, caa), GT))
new_esEs25(vwx301, vwx401, app(app(ty_Either, chg), chh)) → new_esEs4(vwx301, vwx401, chg, chh)
new_esEs22(vwx300, vwx400, app(app(ty_Either, cea), ceb)) → new_esEs4(vwx300, vwx400, cea, ceb)
new_esEs25(vwx301, vwx401, ty_Bool) → new_esEs14(vwx301, vwx401)
new_lt19(vwx310, vwx410, app(ty_[], bdd)) → new_lt8(vwx310, vwx410, bdd)
new_compare0(vwx300, vwx400, ty_Char) → new_compare12(vwx300, vwx400)
new_lt9(vwx310, vwx410, ty_Float) → new_lt18(vwx310, vwx410)
new_ltEs13(Left(vwx310), Left(vwx410), app(app(app(ty_@3, cb), cc), cd), be) → new_ltEs15(vwx310, vwx410, cb, cc, cd)
new_compare15(vwx30, vwx40, True) → LT
new_lt19(vwx310, vwx410, app(ty_Maybe, bde)) → new_lt14(vwx310, vwx410, bde)
new_ltEs12(Just(vwx310), Just(vwx410), app(app(ty_@2, hb), hc)) → new_ltEs14(vwx310, vwx410, hb, hc)
new_compare0(vwx300, vwx400, ty_@0) → new_compare18(vwx300, vwx400)
new_ltEs8(vwx31, vwx41) → new_not(new_esEs17(new_compare18(vwx31, vwx41), GT))
new_compare12(vwx31, vwx41) → new_primCmpChar(vwx31, vwx41)
new_lt9(vwx310, vwx410, ty_Integer) → new_lt17(vwx310, vwx410)
new_ltEs13(Right(vwx310), Right(vwx410), ce, app(app(ty_@2, dc), dd)) → new_ltEs14(vwx310, vwx410, dc, dd)
new_compare111(vwx30, vwx40, False) → GT
new_compare111(vwx30, vwx40, True) → LT
new_esEs24(vwx300, vwx400, app(ty_[], cgd)) → new_esEs11(vwx300, vwx400, cgd)
new_lt20(vwx311, vwx411, app(app(ty_Either, bed), bee)) → new_lt7(vwx311, vwx411, bed, bee)
new_lt12(vwx30, vwx40) → new_esEs17(new_compare34(vwx30, vwx40), LT)
new_esEs23(vwx301, vwx401, app(app(app(ty_@3, ceg), ceh), cfa)) → new_esEs7(vwx301, vwx401, ceg, ceh, cfa)
new_esEs21(vwx310, vwx410, ty_Bool) → new_esEs14(vwx310, vwx410)
new_primCmpNat0(Zero, Succ(vwx4000)) → LT
new_esEs22(vwx300, vwx400, ty_Float) → new_esEs15(vwx300, vwx400)
new_esEs27(vwx310, vwx410, app(app(app(ty_@3, bdh), bea), beb)) → new_esEs7(vwx310, vwx410, bdh, bea, beb)
new_esEs21(vwx310, vwx410, ty_Char) → new_esEs9(vwx310, vwx410)
new_esEs4(Left(vwx300), Left(vwx400), ty_Char, bb) → new_esEs9(vwx300, vwx400)
new_esEs17(LT, LT) → True
new_ltEs19(vwx312, vwx412, ty_Bool) → new_ltEs6(vwx312, vwx412)
new_esEs25(vwx301, vwx401, app(app(ty_@2, dac), dad)) → new_esEs6(vwx301, vwx401, dac, dad)
new_esEs4(Left(vwx300), Left(vwx400), app(ty_Ratio, cbc), bb) → new_esEs12(vwx300, vwx400, cbc)
new_esEs27(vwx310, vwx410, ty_@0) → new_esEs10(vwx310, vwx410)
new_ltEs12(Just(vwx310), Just(vwx410), app(ty_Ratio, cac)) → new_ltEs9(vwx310, vwx410, cac)
new_compare26(vwx300, vwx400) → new_compare38(vwx300, vwx400)
new_esEs28(vwx311, vwx411, app(ty_[], bef)) → new_esEs11(vwx311, vwx411, bef)
new_lt14(vwx30, vwx40, ge) → new_esEs17(new_compare33(vwx30, vwx40, ge), LT)
new_compare0(vwx300, vwx400, app(app(app(ty_@3, eh), fa), fb)) → new_compare43(vwx300, vwx400, eh, fa, fb)
new_esEs28(vwx311, vwx411, ty_Integer) → new_esEs16(vwx311, vwx411)
new_compare7([], [], dh) → EQ
new_esEs24(vwx300, vwx400, app(app(ty_@2, cha), chb)) → new_esEs6(vwx300, vwx400, cha, chb)
new_pePe(True, vwx117) → True
new_compare28(vwx30, vwx40, False, ba, bb) → new_compare17(vwx30, vwx40, new_ltEs13(vwx30, vwx40, ba, bb), ba, bb)
new_compare14(vwx30, vwx40, False, bcc, bcd) → GT
new_primEqNat0(Zero, Zero) → True
new_primMulNat0(Succ(vwx30000), Succ(vwx40000)) → new_primPlusNat1(new_primMulNat0(vwx30000, Succ(vwx40000)), vwx40000)
new_lt20(vwx311, vwx411, ty_Int) → new_lt15(vwx311, vwx411)
new_ltEs19(vwx312, vwx412, app(ty_[], bfg)) → new_ltEs4(vwx312, vwx412, bfg)
new_esEs4(Left(vwx300), Left(vwx400), ty_Integer, bb) → new_esEs16(vwx300, vwx400)
new_lt9(vwx310, vwx410, app(app(app(ty_@3, baf), bag), bah)) → new_lt5(vwx310, vwx410, baf, bag, bah)
new_esEs18(vwx300, vwx400, ty_Float) → new_esEs15(vwx300, vwx400)
new_lt8(:(vwx300, vwx301), [], ea) → new_esEs17(GT, LT)
new_ltEs13(Left(vwx310), Left(vwx410), ty_Ordering, be) → new_ltEs10(vwx310, vwx410)
new_primCompAux00(vwx148, vwx149, EQ, app(ty_[], ff)) → new_compare7(vwx148, vwx149, ff)
new_sr(vwx300, vwx400) → new_primMulInt(vwx300, vwx400)
new_esEs4(Left(vwx300), Left(vwx400), ty_Int, bb) → new_esEs8(vwx300, vwx400)
new_esEs22(vwx300, vwx400, app(ty_Ratio, ced)) → new_esEs12(vwx300, vwx400, ced)
new_esEs25(vwx301, vwx401, ty_@0) → new_esEs10(vwx301, vwx401)
new_esEs22(vwx300, vwx400, ty_Int) → new_esEs8(vwx300, vwx400)
new_lt19(vwx310, vwx410, app(ty_Ratio, dbg)) → new_lt11(vwx310, vwx410, dbg)
new_compare33(vwx30, vwx40, ge) → new_compare23(vwx30, vwx40, new_esEs5(vwx30, vwx40, ge), ge)
new_primCmpFloat(Float(vwx300, vwx301), Float(vwx400, vwx401)) → new_compare25(vwx300, vwx400, vwx301, vwx401)
new_ltEs19(vwx312, vwx412, app(app(app(ty_@3, bgc), bgd), bge)) → new_ltEs15(vwx312, vwx412, bgc, bgd, bge)
new_compare17(vwx30, vwx40, True, ba, bb) → LT
new_ltEs12(Just(vwx310), Just(vwx410), ty_Bool) → new_ltEs6(vwx310, vwx410)
new_esEs4(Right(vwx300), Right(vwx400), ba, app(app(ty_Either, ccb), ccc)) → new_esEs4(vwx300, vwx400, ccb, ccc)
new_primEqInt(Neg(Succ(vwx3000)), Neg(Succ(vwx4000))) → new_primEqNat0(vwx3000, vwx4000)
new_ltEs13(Right(vwx310), Right(vwx410), ce, ty_Ordering) → new_ltEs10(vwx310, vwx410)
new_lt20(vwx311, vwx411, app(ty_Ratio, dbh)) → new_lt11(vwx311, vwx411, dbh)
new_esEs4(Left(vwx300), Left(vwx400), app(app(ty_Either, cah), cba), bb) → new_esEs4(vwx300, vwx400, cah, cba)
new_esEs24(vwx300, vwx400, ty_Bool) → new_esEs14(vwx300, vwx400)
new_esEs26(vwx302, vwx402, app(app(app(ty_@3, dae), daf), dag)) → new_esEs7(vwx302, vwx402, dae, daf, dag)
new_esEs4(Left(vwx300), Left(vwx400), ty_Double, bb) → new_esEs13(vwx300, vwx400)
new_ltEs19(vwx312, vwx412, app(ty_Ratio, dca)) → new_ltEs9(vwx312, vwx412, dca)
new_lt17(Integer(vwx300), Integer(vwx400)) → new_esEs17(new_primCmpInt(vwx300, vwx400), LT)
new_esEs22(vwx300, vwx400, ty_Ordering) → new_esEs17(vwx300, vwx400)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_esEs17(EQ, EQ) → True
new_esEs28(vwx311, vwx411, ty_Double) → new_esEs13(vwx311, vwx411)
new_esEs28(vwx311, vwx411, ty_Ordering) → new_esEs17(vwx311, vwx411)
new_compare39(Integer(vwx3000), Integer(vwx4010), vwx400, vwx301, ty_Integer) → new_compare11(Integer(new_primMulInt(vwx3000, vwx4010)), new_sr0(vwx400, vwx301))
new_lt19(vwx310, vwx410, ty_Double) → new_lt16(vwx310, vwx410)
new_primEqInt(Neg(Succ(vwx3000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(vwx4000))) → False
new_primPlusNat1(Zero, vwx40000) → Succ(vwx40000)
new_esEs11(:(vwx300, vwx301), :(vwx400, vwx401), ea) → new_asAs(new_esEs18(vwx300, vwx400, ea), new_esEs11(vwx301, vwx401, ea))
new_esEs23(vwx301, vwx401, ty_Integer) → new_esEs16(vwx301, vwx401)
new_lt20(vwx311, vwx411, ty_@0) → new_lt10(vwx311, vwx411)
new_lt20(vwx311, vwx411, ty_Ordering) → new_lt13(vwx311, vwx411)
new_ltEs13(Right(vwx310), Right(vwx410), ce, ty_Integer) → new_ltEs7(vwx310, vwx410)
new_primCompAux00(vwx148, vwx149, EQ, ty_@0) → new_compare18(vwx148, vwx149)
new_esEs20(vwx301, vwx401, ty_Integer) → new_esEs16(vwx301, vwx401)
new_esEs21(vwx310, vwx410, app(app(ty_Either, hg), hh)) → new_esEs4(vwx310, vwx410, hg, hh)
new_ltEs13(Left(vwx310), Left(vwx410), ty_Double, be) → new_ltEs16(vwx310, vwx410)
new_ltEs18(vwx311, vwx411, ty_Double) → new_ltEs16(vwx311, vwx411)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_esEs5(Just(vwx300), Just(vwx400), ty_@0) → new_esEs10(vwx300, vwx400)
new_esEs27(vwx310, vwx410, ty_Float) → new_esEs15(vwx310, vwx410)
new_ltEs12(Just(vwx310), Just(vwx410), app(app(app(ty_@3, hd), he), hf)) → new_ltEs15(vwx310, vwx410, hd, he, hf)
new_ltEs18(vwx311, vwx411, ty_@0) → new_ltEs8(vwx311, vwx411)
new_primCompAux00(vwx148, vwx149, EQ, app(app(ty_Either, fc), fd)) → new_compare16(vwx148, vwx149, fc, fd)
new_primCmpNat0(Succ(vwx3000), Succ(vwx4000)) → new_primCmpNat0(vwx3000, vwx4000)
new_esEs26(vwx302, vwx402, ty_Integer) → new_esEs16(vwx302, vwx402)
new_compare0(vwx300, vwx400, ty_Float) → new_compare40(vwx300, vwx400)
new_ltEs18(vwx311, vwx411, app(app(ty_Either, bbb), bbc)) → new_ltEs13(vwx311, vwx411, bbb, bbc)
new_primEqInt(Pos(Succ(vwx3000)), Pos(Succ(vwx4000))) → new_primEqNat0(vwx3000, vwx4000)
new_ltEs17(vwx31, vwx41) → new_not(new_esEs17(new_compare40(vwx31, vwx41), GT))
new_ltEs12(Just(vwx310), Just(vwx410), app(app(ty_Either, gf), gg)) → new_ltEs13(vwx310, vwx410, gf, gg)
new_compare27(vwx30, vwx40, True, bcc, bcd) → EQ
new_esEs25(vwx301, vwx401, app(ty_Maybe, daa)) → new_esEs5(vwx301, vwx401, daa)
new_ltEs18(vwx311, vwx411, app(app(app(ty_@3, bbh), bca), bcb)) → new_ltEs15(vwx311, vwx411, bbh, bca, bcb)
new_esEs14(True, False) → False
new_esEs14(False, True) → False
new_ltEs6(False, True) → True
new_esEs17(LT, GT) → False
new_esEs17(GT, LT) → False
new_ltEs10(GT, EQ) → False
new_primEqNat0(Succ(vwx3000), Succ(vwx4000)) → new_primEqNat0(vwx3000, vwx4000)
new_esEs17(EQ, GT) → False
new_esEs17(GT, EQ) → False
new_ltEs6(True, True) → True
new_esEs21(vwx310, vwx410, app(ty_Ratio, cda)) → new_esEs12(vwx310, vwx410, cda)
new_ltEs19(vwx312, vwx412, app(app(ty_Either, bfe), bff)) → new_ltEs13(vwx312, vwx412, bfe, bff)
new_lt9(vwx310, vwx410, ty_Bool) → new_lt12(vwx310, vwx410)
new_lt19(vwx310, vwx410, app(app(ty_@2, bdf), bdg)) → new_lt6(vwx310, vwx410, bdf, bdg)
new_esEs4(Left(vwx300), Left(vwx400), app(app(app(ty_@3, cad), cae), caf), bb) → new_esEs7(vwx300, vwx400, cad, cae, caf)
new_lt20(vwx311, vwx411, ty_Integer) → new_lt17(vwx311, vwx411)
new_esEs26(vwx302, vwx402, app(ty_[], dah)) → new_esEs11(vwx302, vwx402, dah)
new_esEs24(vwx300, vwx400, app(ty_Ratio, cgh)) → new_esEs12(vwx300, vwx400, cgh)
new_primCmpInt(Neg(Succ(vwx3000)), Neg(vwx400)) → new_primCmpNat0(vwx400, Succ(vwx3000))
new_esEs22(vwx300, vwx400, ty_Bool) → new_esEs14(vwx300, vwx400)
new_ltEs13(Right(vwx310), Right(vwx410), ce, app(ty_[], da)) → new_ltEs4(vwx310, vwx410, da)
new_lt19(vwx310, vwx410, app(app(ty_Either, bch), bda)) → new_lt7(vwx310, vwx410, bch, bda)
new_ltEs13(Right(vwx310), Right(vwx410), ce, app(ty_Maybe, db)) → new_ltEs12(vwx310, vwx410, db)
new_esEs21(vwx310, vwx410, ty_Int) → new_esEs8(vwx310, vwx410)
new_esEs25(vwx301, vwx401, ty_Char) → new_esEs9(vwx301, vwx401)
new_primEqInt(Pos(Succ(vwx3000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(vwx4000))) → False
new_primPlusNat0(Zero, Succ(vwx400000)) → Succ(vwx400000)
new_primPlusNat0(Succ(vwx15800), Zero) → Succ(vwx15800)
new_esEs24(vwx300, vwx400, ty_Float) → new_esEs15(vwx300, vwx400)
new_compare0(vwx300, vwx400, ty_Int) → new_compare10(vwx300, vwx400)
new_esEs24(vwx300, vwx400, ty_@0) → new_esEs10(vwx300, vwx400)
new_ltEs19(vwx312, vwx412, ty_Float) → new_ltEs17(vwx312, vwx412)
new_primCmpNat0(Zero, Zero) → EQ
new_primCmpNat0(Succ(vwx3000), Zero) → GT
new_esEs4(Right(vwx300), Right(vwx400), ba, ty_@0) → new_esEs10(vwx300, vwx400)
new_ltEs10(LT, EQ) → True
new_primCmpInt(Neg(Zero), Pos(Succ(vwx4000))) → LT
new_esEs25(vwx301, vwx401, ty_Int) → new_esEs8(vwx301, vwx401)
new_compare27(vwx30, vwx40, False, bcc, bcd) → new_compare14(vwx30, vwx40, new_ltEs14(vwx30, vwx40, bcc, bcd), bcc, bcd)
new_esEs21(vwx310, vwx410, ty_Float) → new_esEs15(vwx310, vwx410)
new_compare210(vwx30, vwx40, True, bce, bcf, bcg) → EQ
new_ltEs13(Right(vwx310), Right(vwx410), ce, ty_Float) → new_ltEs17(vwx310, vwx410)
new_compare39(vwx300, vwx401, vwx400, vwx301, ty_Int) → new_compare25(vwx300, vwx401, vwx400, vwx301)
new_esEs18(vwx300, vwx400, app(app(app(ty_@3, eh), fa), fb)) → new_esEs7(vwx300, vwx400, eh, fa, fb)
new_lt15(vwx30, vwx40) → new_esEs17(new_primCmpInt(vwx30, vwx40), LT)
new_esEs21(vwx310, vwx410, ty_Double) → new_esEs13(vwx310, vwx410)
new_esEs4(Left(vwx300), Left(vwx400), ty_Float, bb) → new_esEs15(vwx300, vwx400)
new_sr0(Integer(vwx4000), Integer(vwx3010)) → Integer(new_primMulInt(vwx4000, vwx3010))
new_compare28(vwx30, vwx40, True, ba, bb) → EQ
new_primCompAux00(vwx148, vwx149, EQ, app(app(app(ty_@3, gb), gc), gd)) → new_compare43(vwx148, vwx149, gb, gc, gd)
new_primEqInt(Pos(Succ(vwx3000)), Neg(vwx400)) → False
new_primEqInt(Neg(Succ(vwx3000)), Pos(vwx400)) → False
new_ltEs19(vwx312, vwx412, ty_Double) → new_ltEs16(vwx312, vwx412)
new_esEs26(vwx302, vwx402, ty_Double) → new_esEs13(vwx302, vwx402)
new_ltEs12(Just(vwx310), Just(vwx410), app(ty_Maybe, ha)) → new_ltEs12(vwx310, vwx410, ha)
new_compare35(vwx30, vwx40, bce, bcf, bcg) → new_compare210(vwx30, vwx40, new_esEs7(vwx30, vwx40, bce, bcf, bcg), bce, bcf, bcg)
new_ltEs18(vwx311, vwx411, app(app(ty_@2, bbf), bbg)) → new_ltEs14(vwx311, vwx411, bbf, bbg)
new_lt9(vwx310, vwx410, app(ty_[], bab)) → new_lt8(vwx310, vwx410, bab)
new_esEs27(vwx310, vwx410, app(ty_Maybe, bde)) → new_esEs5(vwx310, vwx410, bde)
new_compare37(vwx30, vwx40, bcc, bcd) → new_compare27(vwx30, vwx40, new_esEs6(vwx30, vwx40, bcc, bcd), bcc, bcd)
new_ltEs10(GT, GT) → True
new_lt19(vwx310, vwx410, app(app(app(ty_@3, bdh), bea), beb)) → new_lt5(vwx310, vwx410, bdh, bea, beb)
new_primCompAux00(vwx148, vwx149, EQ, ty_Ordering) → new_compare26(vwx148, vwx149)
new_ltEs12(Just(vwx310), Just(vwx410), app(ty_[], gh)) → new_ltEs4(vwx310, vwx410, gh)
new_esEs11([], :(vwx400, vwx401), ea) → False
new_esEs11(:(vwx300, vwx301), [], ea) → False
new_esEs23(vwx301, vwx401, app(ty_Ratio, cff)) → new_esEs12(vwx301, vwx401, cff)
new_esEs22(vwx300, vwx400, app(app(ty_@2, cee), cef)) → new_esEs6(vwx300, vwx400, cee, cef)
new_esEs4(Right(vwx300), Right(vwx400), ba, ty_Bool) → new_esEs14(vwx300, vwx400)
new_primCompAux00(vwx148, vwx149, EQ, ty_Integer) → new_compare11(vwx148, vwx149)
new_primEqInt(Pos(Zero), Neg(Succ(vwx4000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(vwx4000))) → False
new_compare38(vwx30, vwx40) → new_compare29(vwx30, vwx40, new_esEs17(vwx30, vwx40))
new_esEs22(vwx300, vwx400, app(ty_[], cdh)) → new_esEs11(vwx300, vwx400, cdh)
new_primCmpInt(Pos(Zero), Pos(Succ(vwx4000))) → new_primCmpNat0(Zero, Succ(vwx4000))
new_compare24(vwx30, vwx40, True) → EQ
new_primCompAux00(vwx148, vwx149, EQ, ty_Int) → new_compare10(vwx148, vwx149)
new_esEs25(vwx301, vwx401, ty_Float) → new_esEs15(vwx301, vwx401)
new_compare17(vwx30, vwx40, False, ba, bb) → GT
new_ltEs18(vwx311, vwx411, ty_Float) → new_ltEs17(vwx311, vwx411)
new_ltEs13(Right(vwx310), Right(vwx410), ce, ty_@0) → new_ltEs8(vwx310, vwx410)
new_esEs4(Right(vwx300), Right(vwx400), ba, ty_Char) → new_esEs9(vwx300, vwx400)
new_ltEs12(Just(vwx310), Just(vwx410), ty_@0) → new_ltEs8(vwx310, vwx410)
new_ltEs13(Left(vwx310), Left(vwx410), ty_@0, be) → new_ltEs8(vwx310, vwx410)
new_not(False) → True
new_ltEs13(Right(vwx310), Right(vwx410), ce, app(ty_Ratio, dcc)) → new_ltEs9(vwx310, vwx410, dcc)
new_esEs5(Just(vwx300), Just(vwx400), ty_Int) → new_esEs8(vwx300, vwx400)
new_primCmpInt(Pos(Succ(vwx3000)), Pos(vwx400)) → new_primCmpNat0(Succ(vwx3000), vwx400)
new_lt19(vwx310, vwx410, ty_Int) → new_lt15(vwx310, vwx410)
new_lt7(vwx30, vwx40, ba, bb) → new_esEs17(new_compare36(vwx30, vwx40, ba, bb), LT)
new_esEs23(vwx301, vwx401, app(app(ty_@2, cfg), cfh)) → new_esEs6(vwx301, vwx401, cfg, cfh)
new_esEs25(vwx301, vwx401, ty_Double) → new_esEs13(vwx301, vwx401)
new_lt19(vwx310, vwx410, ty_Integer) → new_lt17(vwx310, vwx410)
new_esEs26(vwx302, vwx402, ty_Bool) → new_esEs14(vwx302, vwx402)
new_esEs28(vwx311, vwx411, ty_Char) → new_esEs9(vwx311, vwx411)
new_esEs18(vwx300, vwx400, ty_Int) → new_esEs8(vwx300, vwx400)
new_ltEs13(Left(vwx310), Left(vwx410), ty_Bool, be) → new_ltEs6(vwx310, vwx410)
new_compare0(vwx300, vwx400, app(app(ty_@2, ef), eg)) → new_compare42(vwx300, vwx400, ef, eg)
new_esEs24(vwx300, vwx400, app(ty_Maybe, cgg)) → new_esEs5(vwx300, vwx400, cgg)
new_esEs4(Right(vwx300), Right(vwx400), ba, app(app(ty_@2, ccf), ccg)) → new_esEs6(vwx300, vwx400, ccf, ccg)
new_esEs23(vwx301, vwx401, ty_@0) → new_esEs10(vwx301, vwx401)
new_esEs18(vwx300, vwx400, app(app(ty_Either, eb), ec)) → new_esEs4(vwx300, vwx400, eb, ec)
new_esEs5(Just(vwx300), Just(vwx400), ty_Double) → new_esEs13(vwx300, vwx400)
new_compare43(vwx300, vwx400, eh, fa, fb) → new_compare35(vwx300, vwx400, eh, fa, fb)
new_esEs22(vwx300, vwx400, app(app(app(ty_@3, cde), cdf), cdg)) → new_esEs7(vwx300, vwx400, cde, cdf, cdg)
new_lt9(vwx310, vwx410, app(app(ty_Either, hg), hh)) → new_lt7(vwx310, vwx410, hg, hh)
new_primCmpInt(Pos(Succ(vwx3000)), Neg(vwx400)) → GT
new_esEs21(vwx310, vwx410, ty_Integer) → new_esEs16(vwx310, vwx410)
new_lt9(vwx310, vwx410, app(app(ty_@2, bad), bae)) → new_lt6(vwx310, vwx410, bad, bae)
new_compare41(vwx300, vwx400, ee) → new_compare33(vwx300, vwx400, ee)
new_esEs26(vwx302, vwx402, ty_@0) → new_esEs10(vwx302, vwx402)
new_primMulInt(Pos(vwx3000), Pos(vwx4000)) → Pos(new_primMulNat0(vwx3000, vwx4000))
new_lt19(vwx310, vwx410, ty_Bool) → new_lt12(vwx310, vwx410)
new_esEs24(vwx300, vwx400, ty_Int) → new_esEs8(vwx300, vwx400)
new_ltEs7(vwx31, vwx41) → new_not(new_esEs17(new_compare11(vwx31, vwx41), GT))
new_esEs24(vwx300, vwx400, ty_Integer) → new_esEs16(vwx300, vwx400)
new_esEs28(vwx311, vwx411, app(app(app(ty_@3, bfb), bfc), bfd)) → new_esEs7(vwx311, vwx411, bfb, bfc, bfd)
new_lt8(:(vwx300, vwx301), :(vwx400, vwx401), ea) → new_esEs17(new_primCompAux1(vwx300, vwx400, vwx301, vwx401, ea), LT)
new_esEs23(vwx301, vwx401, app(app(ty_Either, cfc), cfd)) → new_esEs4(vwx301, vwx401, cfc, cfd)
new_esEs22(vwx300, vwx400, ty_Double) → new_esEs13(vwx300, vwx400)
new_esEs27(vwx310, vwx410, app(app(ty_@2, bdf), bdg)) → new_esEs6(vwx310, vwx410, bdf, bdg)
new_primMulInt(Neg(vwx3000), Neg(vwx4000)) → Pos(new_primMulNat0(vwx3000, vwx4000))
new_compare29(vwx30, vwx40, False) → new_compare111(vwx30, vwx40, new_ltEs10(vwx30, vwx40))
new_compare0(vwx300, vwx400, app(app(ty_Either, eb), ec)) → new_compare16(vwx300, vwx400, eb, ec)
new_esEs5(Just(vwx300), Just(vwx400), ty_Bool) → new_esEs14(vwx300, vwx400)
new_primEqNat0(Succ(vwx3000), Zero) → False
new_primEqNat0(Zero, Succ(vwx4000)) → False
new_esEs21(vwx310, vwx410, ty_@0) → new_esEs10(vwx310, vwx410)
new_primPlusNat0(Zero, Zero) → Zero
new_esEs12(:%(vwx300, vwx301), :%(vwx400, vwx401), cch) → new_asAs(new_esEs19(vwx300, vwx400, cch), new_esEs20(vwx301, vwx401, cch))
new_ltEs14(@2(vwx310, vwx311), @2(vwx410, vwx411), bba, baa) → new_pePe(new_lt9(vwx310, vwx410, bba), new_asAs(new_esEs21(vwx310, vwx410, bba), new_ltEs18(vwx311, vwx411, baa)))
new_esEs15(Float(vwx300, vwx301), Float(vwx400, vwx401)) → new_esEs8(new_sr(vwx300, vwx400), new_sr(vwx301, vwx401))
new_lt9(vwx310, vwx410, app(ty_Ratio, cda)) → new_lt11(vwx310, vwx410, cda)
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_esEs24(vwx300, vwx400, app(app(ty_Either, cge), cgf)) → new_esEs4(vwx300, vwx400, cge, cgf)
new_esEs25(vwx301, vwx401, app(ty_[], chf)) → new_esEs11(vwx301, vwx401, chf)
new_ltEs13(Left(vwx310), Left(vwx410), app(app(ty_@2, bh), ca), be) → new_ltEs14(vwx310, vwx410, bh, ca)
new_esEs26(vwx302, vwx402, ty_Int) → new_esEs8(vwx302, vwx402)
new_esEs27(vwx310, vwx410, app(app(ty_Either, bch), bda)) → new_esEs4(vwx310, vwx410, bch, bda)
new_ltEs18(vwx311, vwx411, ty_Integer) → new_ltEs7(vwx311, vwx411)
new_compare34(vwx30, vwx40) → new_compare24(vwx30, vwx40, new_esEs14(vwx30, vwx40))
new_esEs4(Right(vwx300), Right(vwx400), ba, ty_Integer) → new_esEs16(vwx300, vwx400)
new_lt10(@0, @0) → new_esEs17(EQ, LT)
new_ltEs13(Right(vwx310), Right(vwx410), ce, ty_Char) → new_ltEs5(vwx310, vwx410)
new_compare42(vwx300, vwx400, ef, eg) → new_compare37(vwx300, vwx400, ef, eg)
new_ltEs12(Just(vwx310), Just(vwx410), ty_Double) → new_ltEs16(vwx310, vwx410)
new_esEs27(vwx310, vwx410, ty_Integer) → new_esEs16(vwx310, vwx410)
new_lt20(vwx311, vwx411, ty_Float) → new_lt18(vwx311, vwx411)
new_esEs6(@2(vwx300, vwx301), @2(vwx400, vwx401), bcc, bcd) → new_asAs(new_esEs22(vwx300, vwx400, bcc), new_esEs23(vwx301, vwx401, bcd))
new_lt13(vwx30, vwx40) → new_esEs17(new_compare38(vwx30, vwx40), LT)
new_esEs26(vwx302, vwx402, app(ty_Maybe, dbc)) → new_esEs5(vwx302, vwx402, dbc)
new_primPlusNat1(Succ(vwx1580), vwx40000) → Succ(Succ(new_primPlusNat0(vwx1580, vwx40000)))
new_lt9(vwx310, vwx410, ty_Char) → new_lt4(vwx310, vwx410)
new_esEs22(vwx300, vwx400, ty_@0) → new_esEs10(vwx300, vwx400)
new_primCompAux00(vwx148, vwx149, EQ, ty_Float) → new_compare40(vwx148, vwx149)
new_esEs25(vwx301, vwx401, ty_Integer) → new_esEs16(vwx301, vwx401)
new_primCmpInt(Neg(Zero), Neg(Succ(vwx4000))) → new_primCmpNat0(Succ(vwx4000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(vwx4000))) → GT
new_primCmpDouble(Double(vwx300, vwx301), Double(vwx400, vwx401)) → new_compare25(vwx300, vwx400, vwx301, vwx401)
new_lt9(vwx310, vwx410, app(ty_Maybe, bac)) → new_lt14(vwx310, vwx410, bac)
new_esEs4(Right(vwx300), Right(vwx400), ba, app(ty_Ratio, cce)) → new_esEs12(vwx300, vwx400, cce)
new_esEs28(vwx311, vwx411, app(ty_Ratio, dbh)) → new_esEs12(vwx311, vwx411, dbh)
new_compare23(vwx30, vwx40, True, ge) → EQ
new_esEs23(vwx301, vwx401, app(ty_[], cfb)) → new_esEs11(vwx301, vwx401, cfb)
new_lt20(vwx311, vwx411, app(app(ty_@2, beh), bfa)) → new_lt6(vwx311, vwx411, beh, bfa)
new_ltEs19(vwx312, vwx412, ty_Int) → new_ltEs11(vwx312, vwx412)
new_ltEs13(Left(vwx310), Left(vwx410), ty_Float, be) → new_ltEs17(vwx310, vwx410)
new_compare0(vwx300, vwx400, ty_Double) → new_compare8(vwx300, vwx400)
new_esEs28(vwx311, vwx411, app(app(ty_@2, beh), bfa)) → new_esEs6(vwx311, vwx411, beh, bfa)
new_ltEs15(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), bec, bdb, bdc) → new_pePe(new_lt19(vwx310, vwx410, bec), new_asAs(new_esEs27(vwx310, vwx410, bec), new_pePe(new_lt20(vwx311, vwx411, bdb), new_asAs(new_esEs28(vwx311, vwx411, bdb), new_ltEs19(vwx312, vwx412, bdc)))))
new_esEs27(vwx310, vwx410, app(ty_Ratio, dbg)) → new_esEs12(vwx310, vwx410, dbg)
new_compare8(vwx31, vwx41) → new_primCmpDouble(vwx31, vwx41)
new_ltEs13(Left(vwx310), Left(vwx410), app(app(ty_Either, bc), bd), be) → new_ltEs13(vwx310, vwx410, bc, bd)
new_lt20(vwx311, vwx411, ty_Double) → new_lt16(vwx311, vwx411)
new_esEs16(Integer(vwx300), Integer(vwx400)) → new_primEqInt(vwx300, vwx400)
new_ltEs13(Right(vwx310), Right(vwx410), ce, app(app(ty_Either, cf), cg)) → new_ltEs13(vwx310, vwx410, cf, cg)
new_esEs23(vwx301, vwx401, ty_Ordering) → new_esEs17(vwx301, vwx401)
new_ltEs18(vwx311, vwx411, ty_Int) → new_ltEs11(vwx311, vwx411)
new_esEs18(vwx300, vwx400, app(ty_[], ed)) → new_esEs11(vwx300, vwx400, ed)
new_esEs18(vwx300, vwx400, ty_Ordering) → new_esEs17(vwx300, vwx400)
new_esEs10(@0, @0) → True
new_esEs24(vwx300, vwx400, app(app(app(ty_@3, cga), cgb), cgc)) → new_esEs7(vwx300, vwx400, cga, cgb, cgc)
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_ltEs16(vwx31, vwx41) → new_not(new_esEs17(new_compare8(vwx31, vwx41), GT))
new_esEs5(Just(vwx300), Just(vwx400), ty_Float) → new_esEs15(vwx300, vwx400)
new_esEs28(vwx311, vwx411, ty_@0) → new_esEs10(vwx311, vwx411)
new_lt19(vwx310, vwx410, ty_Ordering) → new_lt13(vwx310, vwx410)
new_ltEs13(Left(vwx310), Left(vwx410), app(ty_Maybe, bg), be) → new_ltEs12(vwx310, vwx410, bg)
new_esEs4(Right(vwx300), Right(vwx400), ba, ty_Double) → new_esEs13(vwx300, vwx400)
new_lt9(vwx310, vwx410, ty_Ordering) → new_lt13(vwx310, vwx410)
new_asAs(False, vwx143) → False
new_compare0(vwx300, vwx400, app(ty_Maybe, ee)) → new_compare41(vwx300, vwx400, ee)
new_ltEs12(Just(vwx310), Just(vwx410), ty_Char) → new_ltEs5(vwx310, vwx410)
new_esEs4(Left(vwx300), Left(vwx400), ty_@0, bb) → new_esEs10(vwx300, vwx400)
new_primMulInt(Pos(vwx3000), Neg(vwx4000)) → Neg(new_primMulNat0(vwx3000, vwx4000))
new_primMulInt(Neg(vwx3000), Pos(vwx4000)) → Neg(new_primMulNat0(vwx3000, vwx4000))
new_ltEs10(LT, GT) → True
new_ltEs13(Right(vwx310), Right(vwx410), ce, ty_Bool) → new_ltEs6(vwx310, vwx410)
new_primMulNat0(Zero, Succ(vwx40000)) → Zero
new_primMulNat0(Succ(vwx30000), Zero) → Zero
new_esEs27(vwx310, vwx410, ty_Double) → new_esEs13(vwx310, vwx410)
new_ltEs13(Left(vwx310), Right(vwx410), ce, be) → True
new_esEs24(vwx300, vwx400, ty_Double) → new_esEs13(vwx300, vwx400)
new_compare0(vwx300, vwx400, app(ty_[], ed)) → new_compare7(vwx300, vwx400, ed)
new_esEs27(vwx310, vwx410, ty_Int) → new_esEs8(vwx310, vwx410)
new_ltEs4(vwx31, vwx41, dh) → new_not(new_esEs17(new_compare7(vwx31, vwx41, dh), GT))
new_ltEs18(vwx311, vwx411, app(ty_[], bbd)) → new_ltEs4(vwx311, vwx411, bbd)
new_esEs5(Just(vwx300), Just(vwx400), app(ty_[], bha)) → new_esEs11(vwx300, vwx400, bha)
new_compare11(Integer(vwx310), Integer(vwx410)) → new_primCmpInt(vwx310, vwx410)
new_esEs28(vwx311, vwx411, ty_Bool) → new_esEs14(vwx311, vwx411)
new_esEs5(Just(vwx300), Just(vwx400), app(app(ty_@2, bhf), bhg)) → new_esEs6(vwx300, vwx400, bhf, bhg)
new_compare0(vwx300, vwx400, ty_Ordering) → new_compare26(vwx300, vwx400)
new_esEs18(vwx300, vwx400, app(ty_Maybe, ee)) → new_esEs5(vwx300, vwx400, ee)
new_ltEs18(vwx311, vwx411, app(ty_Maybe, bbe)) → new_ltEs12(vwx311, vwx411, bbe)
new_compare110(vwx30, vwx40, True, bce, bcf, bcg) → LT
new_esEs23(vwx301, vwx401, ty_Float) → new_esEs15(vwx301, vwx401)
new_esEs4(Left(vwx300), Left(vwx400), app(ty_Maybe, cbb), bb) → new_esEs5(vwx300, vwx400, cbb)
new_primCompAux00(vwx148, vwx149, LT, cdc) → LT
new_esEs28(vwx311, vwx411, app(app(ty_Either, bed), bee)) → new_esEs4(vwx311, vwx411, bed, bee)
new_primCompAux00(vwx148, vwx149, GT, cdc) → GT
new_esEs23(vwx301, vwx401, app(ty_Maybe, cfe)) → new_esEs5(vwx301, vwx401, cfe)
new_esEs4(Right(vwx300), Right(vwx400), ba, ty_Ordering) → new_esEs17(vwx300, vwx400)
new_primCompAux00(vwx148, vwx149, EQ, app(ty_Ratio, cdd)) → new_compare9(vwx148, vwx149, cdd)
new_lt20(vwx311, vwx411, app(ty_Maybe, beg)) → new_lt14(vwx311, vwx411, beg)
new_ltEs18(vwx311, vwx411, ty_Char) → new_ltEs5(vwx311, vwx411)
new_esEs23(vwx301, vwx401, ty_Char) → new_esEs9(vwx301, vwx401)
new_ltEs10(EQ, EQ) → True
new_lt8([], [], ea) → new_esEs17(EQ, LT)
new_ltEs12(Nothing, Just(vwx410), cab) → True
new_ltEs10(LT, LT) → True
new_esEs17(LT, EQ) → False
new_esEs17(EQ, LT) → False
new_esEs14(True, True) → True
new_esEs27(vwx310, vwx410, ty_Bool) → new_esEs14(vwx310, vwx410)
new_ltEs13(Right(vwx310), Left(vwx410), ce, be) → False
new_ltEs19(vwx312, vwx412, ty_@0) → new_ltEs8(vwx312, vwx412)
new_esEs5(Nothing, Just(vwx400), ge) → False
new_esEs5(Just(vwx300), Nothing, ge) → False
new_esEs26(vwx302, vwx402, app(ty_Ratio, dbd)) → new_esEs12(vwx302, vwx402, dbd)
new_esEs19(vwx300, vwx400, ty_Integer) → new_esEs16(vwx300, vwx400)
new_compare0(vwx300, vwx400, app(ty_Ratio, bhh)) → new_compare9(vwx300, vwx400, bhh)
new_esEs25(vwx301, vwx401, app(app(app(ty_@3, chc), chd), che)) → new_esEs7(vwx301, vwx401, chc, chd, che)
new_esEs18(vwx300, vwx400, ty_@0) → new_esEs10(vwx300, vwx400)
new_esEs24(vwx300, vwx400, ty_Ordering) → new_esEs17(vwx300, vwx400)
new_lt18(vwx30, vwx40) → new_esEs17(new_primCmpFloat(vwx30, vwx40), LT)
new_compare10(vwx31, vwx41) → new_primCmpInt(vwx31, vwx41)
new_esEs27(vwx310, vwx410, app(ty_[], bdd)) → new_esEs11(vwx310, vwx410, bdd)
new_primCompAux1(vwx300, vwx400, vwx301, vwx401, ea) → new_primCompAux00(vwx301, vwx401, new_compare0(vwx300, vwx400, ea), app(ty_[], ea))
new_ltEs13(Left(vwx310), Left(vwx410), app(ty_Ratio, dcb), be) → new_ltEs9(vwx310, vwx410, dcb)
new_esEs26(vwx302, vwx402, ty_Ordering) → new_esEs17(vwx302, vwx402)
new_lt16(vwx30, vwx40) → new_esEs17(new_primCmpDouble(vwx30, vwx40), LT)
new_ltEs5(vwx31, vwx41) → new_not(new_esEs17(new_compare12(vwx31, vwx41), GT))
new_esEs27(vwx310, vwx410, ty_Ordering) → new_esEs17(vwx310, vwx410)
new_esEs5(Nothing, Nothing, ge) → True
new_esEs28(vwx311, vwx411, app(ty_Maybe, beg)) → new_esEs5(vwx311, vwx411, beg)
new_lt20(vwx311, vwx411, ty_Bool) → new_lt12(vwx311, vwx411)
new_esEs5(Just(vwx300), Just(vwx400), app(app(app(ty_@3, bgf), bgg), bgh)) → new_esEs7(vwx300, vwx400, bgf, bgg, bgh)
new_esEs5(Just(vwx300), Just(vwx400), ty_Integer) → new_esEs16(vwx300, vwx400)
new_compare14(vwx30, vwx40, True, bcc, bcd) → LT
new_esEs21(vwx310, vwx410, app(ty_[], bab)) → new_esEs11(vwx310, vwx410, bab)
new_ltEs10(EQ, LT) → False
new_esEs14(False, False) → True
new_esEs22(vwx300, vwx400, ty_Integer) → new_esEs16(vwx300, vwx400)
new_lt19(vwx310, vwx410, ty_Float) → new_lt18(vwx310, vwx410)
new_esEs26(vwx302, vwx402, ty_Char) → new_esEs9(vwx302, vwx402)
new_compare36(vwx30, vwx40, ba, bb) → new_compare28(vwx30, vwx40, new_esEs4(vwx30, vwx40, ba, bb), ba, bb)
new_ltEs19(vwx312, vwx412, ty_Integer) → new_ltEs7(vwx312, vwx412)
new_compare13(vwx300, vwx400) → new_compare34(vwx300, vwx400)
new_lt19(vwx310, vwx410, ty_@0) → new_lt10(vwx310, vwx410)
new_ltEs10(GT, LT) → False
new_esEs18(vwx300, vwx400, ty_Bool) → new_esEs14(vwx300, vwx400)
new_esEs9(Char(vwx300), Char(vwx400)) → new_primEqNat0(vwx300, vwx400)
new_lt5(vwx30, vwx40, bce, bcf, bcg) → new_esEs17(new_compare35(vwx30, vwx40, bce, bcf, bcg), LT)
new_lt20(vwx311, vwx411, app(app(app(ty_@3, bfb), bfc), bfd)) → new_lt5(vwx311, vwx411, bfb, bfc, bfd)
new_esEs22(vwx300, vwx400, app(ty_Maybe, cec)) → new_esEs5(vwx300, vwx400, cec)
new_primPlusNat0(Succ(vwx15800), Succ(vwx400000)) → Succ(Succ(new_primPlusNat0(vwx15800, vwx400000)))
new_esEs21(vwx310, vwx410, app(ty_Maybe, bac)) → new_esEs5(vwx310, vwx410, bac)
new_esEs28(vwx311, vwx411, ty_Float) → new_esEs15(vwx311, vwx411)
new_ltEs13(Left(vwx310), Left(vwx410), ty_Int, be) → new_ltEs11(vwx310, vwx410)
new_esEs26(vwx302, vwx402, app(app(ty_Either, dba), dbb)) → new_esEs4(vwx302, vwx402, dba, dbb)
new_esEs20(vwx301, vwx401, ty_Int) → new_esEs8(vwx301, vwx401)
new_primCmpChar(Char(vwx300), Char(vwx400)) → new_primCmpNat0(vwx300, vwx400)
new_asAs(True, vwx143) → vwx143
new_compare0(vwx300, vwx400, ty_Integer) → new_compare11(vwx300, vwx400)
new_compare7(:(vwx310, vwx311), :(vwx410, vwx411), dh) → new_primCompAux1(vwx310, vwx410, vwx311, vwx411, dh)
new_esEs4(Left(vwx300), Right(vwx400), ba, bb) → False
new_esEs4(Right(vwx300), Left(vwx400), ba, bb) → False
new_esEs17(GT, GT) → True
new_compare9(:%(vwx310, vwx311), :%(vwx410, vwx411), ty_Integer) → new_compare11(new_sr0(vwx310, vwx411), new_sr0(vwx410, vwx311))
new_esEs5(Just(vwx300), Just(vwx400), app(ty_Ratio, bhe)) → new_esEs12(vwx300, vwx400, bhe)
new_ltEs12(Just(vwx310), Nothing, cab) → False
new_compare23(vwx30, vwx40, False, ge) → new_compare19(vwx30, vwx40, new_ltEs12(vwx30, vwx40, ge), ge)
new_ltEs19(vwx312, vwx412, ty_Char) → new_ltEs5(vwx312, vwx412)
new_compare25(vwx300, vwx401, vwx400, vwx301) → new_primCmpInt(new_sr(vwx300, vwx401), new_sr(vwx400, vwx301))
new_lt4(vwx30, vwx40) → new_esEs17(new_primCmpChar(vwx30, vwx40), LT)
new_esEs4(Right(vwx300), Right(vwx400), ba, ty_Int) → new_esEs8(vwx300, vwx400)
new_esEs26(vwx302, vwx402, app(app(ty_@2, dbe), dbf)) → new_esEs6(vwx302, vwx402, dbe, dbf)
new_ltEs6(False, False) → True
new_ltEs19(vwx312, vwx412, app(app(ty_@2, bga), bgb)) → new_ltEs14(vwx312, vwx412, bga, bgb)
new_compare110(vwx30, vwx40, False, bce, bcf, bcg) → GT
new_esEs5(Just(vwx300), Just(vwx400), app(app(ty_Either, bhb), bhc)) → new_esEs4(vwx300, vwx400, bhb, bhc)
new_compare24(vwx30, vwx40, False) → new_compare15(vwx30, vwx40, new_ltEs6(vwx30, vwx40))
new_ltEs13(Right(vwx310), Right(vwx410), ce, ty_Double) → new_ltEs16(vwx310, vwx410)
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_ltEs12(Just(vwx310), Just(vwx410), ty_Integer) → new_ltEs7(vwx310, vwx410)
new_esEs23(vwx301, vwx401, ty_Int) → new_esEs8(vwx301, vwx401)
new_ltEs18(vwx311, vwx411, ty_Ordering) → new_ltEs10(vwx311, vwx411)
new_esEs25(vwx301, vwx401, app(ty_Ratio, dab)) → new_esEs12(vwx301, vwx401, dab)
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_esEs27(vwx310, vwx410, ty_Char) → new_esEs9(vwx310, vwx410)
new_esEs8(vwx30, vwx40) → new_primEqInt(vwx30, vwx40)
new_primCmpInt(Neg(Succ(vwx3000)), Pos(vwx400)) → LT
new_not(True) → False

The set Q consists of the following terms:

new_ltEs18(x0, x1, ty_Ordering)
new_esEs25(x0, x1, ty_Double)
new_compare36(x0, x1, x2, x3)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_lt9(x0, x1, app(ty_Ratio, x2))
new_esEs17(LT, GT)
new_esEs17(GT, LT)
new_esEs24(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Float)
new_lt20(x0, x1, ty_Float)
new_lt19(x0, x1, ty_Double)
new_lt8(:(x0, x1), :(x2, x3), x4)
new_lt7(x0, x1, x2, x3)
new_esEs19(x0, x1, ty_Int)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_compare40(x0, x1)
new_esEs23(x0, x1, ty_@0)
new_esEs21(x0, x1, ty_Ordering)
new_esEs21(x0, x1, ty_Double)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs4(Left(x0), Left(x1), ty_@0, x2)
new_compare23(x0, x1, False, x2)
new_lt9(x0, x1, ty_@0)
new_esEs26(x0, x1, ty_Ordering)
new_esEs17(LT, LT)
new_compare0(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs11(x0, x1)
new_esEs18(x0, x1, ty_Int)
new_lt13(x0, x1)
new_compare27(x0, x1, True, x2, x3)
new_esEs28(x0, x1, ty_@0)
new_esEs4(Left(x0), Right(x1), x2, x3)
new_esEs4(Right(x0), Left(x1), x2, x3)
new_ltEs13(Left(x0), Left(x1), ty_Bool, x2)
new_esEs4(Left(x0), Left(x1), ty_Bool, x2)
new_compare210(x0, x1, False, x2, x3, x4)
new_esEs18(x0, x1, app(app(ty_Either, x2), x3))
new_esEs18(x0, x1, ty_Ordering)
new_ltEs10(LT, LT)
new_lt19(x0, x1, ty_Bool)
new_primMulInt(Neg(x0), Neg(x1))
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_compare0(x0, x1, ty_Ordering)
new_esEs18(x0, x1, app(ty_Maybe, x2))
new_ltEs13(Left(x0), Left(x1), ty_Char, x2)
new_ltEs18(x0, x1, ty_Int)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs17(GT, EQ)
new_esEs17(EQ, GT)
new_esEs24(x0, x1, ty_Ordering)
new_esEs18(x0, x1, app(ty_[], x2))
new_ltEs12(Just(x0), Just(x1), ty_@0)
new_compare43(x0, x1, x2, x3, x4)
new_asAs(True, x0)
new_compare19(x0, x1, False, x2)
new_esEs22(x0, x1, ty_Bool)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_ltEs18(x0, x1, app(ty_[], x2))
new_esEs4(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs12(Just(x0), Just(x1), ty_Float)
new_ltEs13(Right(x0), Right(x1), x2, ty_Int)
new_esEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_primPlusNat0(Succ(x0), Zero)
new_compare0(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Char)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs11([], [], x0)
new_primCompAux00(x0, x1, EQ, app(app(app(ty_@3, x2), x3), x4))
new_pePe(True, x0)
new_ltEs12(Just(x0), Nothing, x1)
new_ltEs12(Just(x0), Just(x1), app(ty_[], x2))
new_esEs4(Right(x0), Right(x1), x2, ty_Double)
new_esEs28(x0, x1, ty_Ordering)
new_ltEs6(True, True)
new_esEs24(x0, x1, ty_Float)
new_primCompAux00(x0, x1, LT, x2)
new_compare27(x0, x1, False, x2, x3)
new_primCompAux00(x0, x1, EQ, app(ty_Ratio, x2))
new_compare29(x0, x1, True)
new_esEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_lt19(x0, x1, ty_Int)
new_esEs5(Just(x0), Just(x1), ty_Float)
new_esEs22(x0, x1, app(ty_[], x2))
new_primCompAux00(x0, x1, EQ, ty_Int)
new_esEs17(GT, GT)
new_compare29(x0, x1, False)
new_ltEs12(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, ty_Float)
new_esEs23(x0, x1, ty_Integer)
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt16(x0, x1)
new_ltEs8(x0, x1)
new_sr(x0, x1)
new_compare18(@0, @0)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs5(Just(x0), Nothing, x1)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs14(True, True)
new_ltEs13(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_compare0(x0, x1, ty_Double)
new_ltEs12(Nothing, Just(x0), x1)
new_ltEs13(Right(x0), Right(x1), x2, ty_Integer)
new_primEqNat0(Zero, Zero)
new_lt20(x0, x1, ty_@0)
new_compare7([], :(x0, x1), x2)
new_compare9(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs18(x0, x1, ty_@0)
new_esEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs25(x0, x1, ty_Float)
new_esEs23(x0, x1, ty_Char)
new_esEs16(Integer(x0), Integer(x1))
new_primMulInt(Pos(x0), Pos(x1))
new_ltEs12(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_primCompAux00(x0, x1, EQ, ty_Bool)
new_esEs22(x0, x1, ty_Char)
new_ltEs7(x0, x1)
new_esEs25(x0, x1, ty_Integer)
new_lt15(x0, x1)
new_ltEs13(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_primMulNat0(Zero, Zero)
new_esEs4(Right(x0), Right(x1), x2, ty_Char)
new_ltEs13(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_lt17(Integer(x0), Integer(x1))
new_esEs22(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_Ordering)
new_ltEs10(EQ, LT)
new_ltEs13(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs10(LT, EQ)
new_esEs21(x0, x1, ty_Integer)
new_compare23(x0, x1, True, x2)
new_compare0(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Just(x0), Just(x1), ty_Double)
new_primCompAux00(x0, x1, EQ, ty_Char)
new_compare10(x0, x1)
new_esEs4(Right(x0), Right(x1), x2, ty_@0)
new_lt9(x0, x1, ty_Float)
new_ltEs18(x0, x1, ty_Double)
new_esEs22(x0, x1, ty_@0)
new_lt8([], :(x0, x1), x2)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs18(x0, x1, ty_Float)
new_ltEs13(Left(x0), Left(x1), app(ty_[], x2), x3)
new_compare19(x0, x1, True, x2)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs18(x0, x1, app(ty_Ratio, x2))
new_ltEs15(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_lt19(x0, x1, ty_@0)
new_ltEs12(Nothing, Nothing, x0)
new_esEs18(x0, x1, ty_Bool)
new_compare38(x0, x1)
new_esEs8(x0, x1)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, ty_Int)
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs5(Nothing, Nothing, x0)
new_primMulNat0(Zero, Succ(x0))
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs4(Left(x0), Left(x1), ty_Double, x2)
new_compare41(x0, x1, x2)
new_ltEs12(Just(x0), Just(x1), ty_Char)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Integer)
new_esEs11(:(x0, x1), [], x2)
new_compare14(x0, x1, True, x2, x3)
new_ltEs13(Right(x0), Right(x1), x2, ty_@0)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Bool)
new_compare111(x0, x1, True)
new_esEs4(Right(x0), Right(x1), x2, ty_Float)
new_lt9(x0, x1, app(ty_Maybe, x2))
new_ltEs13(Right(x0), Right(x1), x2, ty_Char)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_compare0(x0, x1, app(ty_[], x2))
new_esEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs5(Just(x0), Just(x1), ty_Char)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs20(x0, x1, ty_Int)
new_esEs22(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_Int)
new_esEs4(Left(x0), Left(x1), ty_Int, x2)
new_primCompAux00(x0, x1, EQ, ty_Ordering)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs13(Left(x0), Left(x1), ty_@0, x2)
new_compare39(x0, x1, x2, x3, ty_Int)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, app(ty_[], x2))
new_primEqNat0(Succ(x0), Zero)
new_esEs13(Double(x0, x1), Double(x2, x3))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs27(x0, x1, ty_Bool)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_Float)
new_primPlusNat0(Zero, Zero)
new_ltEs13(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_primCompAux1(x0, x1, x2, x3, x4)
new_ltEs12(Just(x0), Just(x1), ty_Bool)
new_lt20(x0, x1, ty_Double)
new_esEs21(x0, x1, ty_Float)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_ltEs13(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs27(x0, x1, ty_Integer)
new_esEs23(x0, x1, ty_Bool)
new_ltEs13(Right(x0), Right(x1), x2, ty_Double)
new_esEs5(Just(x0), Just(x1), ty_Bool)
new_esEs25(x0, x1, ty_Bool)
new_esEs23(x0, x1, ty_Double)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, ty_@0)
new_esEs5(Just(x0), Just(x1), app(ty_[], x2))
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_ltEs6(False, True)
new_ltEs6(True, False)
new_lt9(x0, x1, ty_Ordering)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, ty_Int)
new_esEs23(x0, x1, app(ty_[], x2))
new_compare33(x0, x1, x2)
new_lt9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs10(GT, LT)
new_esEs23(x0, x1, ty_Ordering)
new_ltEs10(LT, GT)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs19(x0, x1, ty_Integer)
new_lt9(x0, x1, ty_Int)
new_compare34(x0, x1)
new_compare8(x0, x1)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs10(@0, @0)
new_compare7(:(x0, x1), [], x2)
new_ltEs9(x0, x1, x2)
new_esEs26(x0, x1, ty_@0)
new_lt18(x0, x1)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Float)
new_lt8(:(x0, x1), [], x2)
new_lt9(x0, x1, app(app(ty_Either, x2), x3))
new_lt9(x0, x1, ty_Double)
new_compare15(x0, x1, False)
new_esEs5(Just(x0), Just(x1), ty_Ordering)
new_esEs20(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_Char)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_compare42(x0, x1, x2, x3)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Double)
new_esEs4(Left(x0), Left(x1), ty_Integer, x2)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_lt10(@0, @0)
new_lt11(:%(x0, x1), :%(x2, x3), x4)
new_ltEs13(Right(x0), Right(x1), x2, ty_Float)
new_esEs18(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs13(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs13(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare26(x0, x1)
new_ltEs19(x0, x1, app(ty_[], x2))
new_primCompAux00(x0, x1, EQ, app(app(ty_@2, x2), x3))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_ltEs6(False, False)
new_esEs11(:(x0, x1), :(x2, x3), x4)
new_primCompAux00(x0, x1, EQ, app(app(ty_Either, x2), x3))
new_ltEs13(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs13(Right(x0), Left(x1), x2, x3)
new_ltEs13(Left(x0), Right(x1), x2, x3)
new_esEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs22(x0, x1, ty_Double)
new_compare110(x0, x1, True, x2, x3, x4)
new_ltEs18(x0, x1, ty_@0)
new_esEs5(Just(x0), Just(x1), ty_Int)
new_esEs14(True, False)
new_esEs14(False, True)
new_esEs11([], :(x0, x1), x2)
new_compare24(x0, x1, False)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs28(x0, x1, app(ty_[], x2))
new_lt9(x0, x1, app(app(ty_@2, x2), x3))
new_lt19(x0, x1, ty_Float)
new_esEs21(x0, x1, ty_Char)
new_primCompAux00(x0, x1, EQ, app(ty_Maybe, x2))
new_lt19(x0, x1, ty_Integer)
new_compare0(x0, x1, ty_Integer)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_compare0(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_Float)
new_ltEs13(Left(x0), Left(x1), ty_Float, x2)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_asAs(False, x0)
new_primCmpNat0(Zero, Succ(x0))
new_esEs25(x0, x1, ty_Char)
new_esEs28(x0, x1, ty_Integer)
new_lt9(x0, x1, app(ty_[], x2))
new_ltEs12(Just(x0), Just(x1), ty_Double)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Nothing, Just(x0), x1)
new_compare0(x0, x1, ty_@0)
new_primCompAux00(x0, x1, GT, x2)
new_compare0(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, ty_Bool)
new_ltEs13(Right(x0), Right(x1), x2, ty_Bool)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_primPlusNat1(Succ(x0), x1)
new_esEs26(x0, x1, ty_Double)
new_esEs28(x0, x1, ty_Char)
new_compare25(x0, x1, x2, x3)
new_ltEs14(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_compare35(x0, x1, x2, x3, x4)
new_esEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare17(x0, x1, False, x2, x3)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_ltEs13(Left(x0), Left(x1), ty_Double, x2)
new_primPlusNat1(Zero, x0)
new_lt20(x0, x1, ty_Char)
new_esEs25(x0, x1, ty_Ordering)
new_ltEs12(Just(x0), Just(x1), ty_Ordering)
new_lt12(x0, x1)
new_primCmpNat0(Zero, Zero)
new_ltEs19(x0, x1, ty_Int)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt5(x0, x1, x2, x3, x4)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_ltEs12(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_lt9(x0, x1, ty_Bool)
new_lt19(x0, x1, ty_Char)
new_compare15(x0, x1, True)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, ty_Ordering)
new_esEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_primCompAux00(x0, x1, EQ, ty_@0)
new_compare17(x0, x1, True, x2, x3)
new_ltEs13(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_compare11(Integer(x0), Integer(x1))
new_esEs5(Just(x0), Just(x1), ty_Integer)
new_ltEs19(x0, x1, ty_@0)
new_esEs24(x0, x1, ty_Double)
new_compare9(:%(x0, x1), :%(x2, x3), ty_Int)
new_lt19(x0, x1, ty_Ordering)
new_esEs18(x0, x1, ty_Double)
new_primEqNat0(Zero, Succ(x0))
new_primCmpDouble(Double(x0, x1), Double(x2, x3))
new_compare13(x0, x1)
new_lt4(x0, x1)
new_ltEs13(Left(x0), Left(x1), ty_Int, x2)
new_lt14(x0, x1, x2)
new_pePe(False, x0)
new_primMulNat0(Succ(x0), Zero)
new_ltEs10(GT, GT)
new_ltEs12(Just(x0), Just(x1), app(ty_Ratio, x2))
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs21(x0, x1, ty_Bool)
new_esEs12(:%(x0, x1), :%(x2, x3), x4)
new_esEs26(x0, x1, ty_Char)
new_primCmpNat0(Succ(x0), Succ(x1))
new_ltEs12(Just(x0), Just(x1), ty_Integer)
new_compare0(x0, x1, ty_Bool)
new_esEs5(Just(x0), Just(x1), ty_@0)
new_compare12(x0, x1)
new_esEs25(x0, x1, ty_@0)
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, app(ty_[], x2))
new_not(True)
new_compare28(x0, x1, False, x2, x3)
new_ltEs13(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs21(x0, x1, ty_Int)
new_compare24(x0, x1, True)
new_lt20(x0, x1, ty_Ordering)
new_esEs4(Left(x0), Left(x1), ty_Float, x2)
new_lt9(x0, x1, ty_Char)
new_compare7([], [], x0)
new_ltEs19(x0, x1, ty_Integer)
new_compare37(x0, x1, x2, x3)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_ltEs18(x0, x1, ty_Char)
new_ltEs13(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_not(False)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs17(x0, x1)
new_lt20(x0, x1, ty_Bool)
new_ltEs5(x0, x1)
new_ltEs10(GT, EQ)
new_ltEs10(EQ, GT)
new_esEs26(x0, x1, ty_Integer)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs19(x0, x1, ty_Float)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs21(x0, x1, app(ty_[], x2))
new_ltEs13(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs21(x0, x1, ty_@0)
new_primEqNat0(Succ(x0), Succ(x1))
new_compare0(x0, x1, ty_Char)
new_sr0(Integer(x0), Integer(x1))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs28(x0, x1, ty_Bool)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare0(x0, x1, ty_Int)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, app(ty_[], x2))
new_compare28(x0, x1, True, x2, x3)
new_compare111(x0, x1, False)
new_ltEs12(Just(x0), Just(x1), app(ty_Maybe, x2))
new_primCompAux00(x0, x1, EQ, ty_Double)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_compare110(x0, x1, False, x2, x3, x4)
new_ltEs13(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs4(Right(x0), Right(x1), x2, ty_Integer)
new_compare14(x0, x1, False, x2, x3)
new_primCmpFloat(Float(x0, x1), Float(x2, x3))
new_compare16(x0, x1, x2, x3)
new_ltEs4(x0, x1, x2)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs15(Float(x0, x1), Float(x2, x3))
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs18(x0, x1, ty_Integer)
new_esEs27(x0, x1, ty_Double)
new_esEs4(Right(x0), Right(x1), x2, ty_Int)
new_compare39(Integer(x0), Integer(x1), x2, x3, ty_Integer)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_primCompAux00(x0, x1, EQ, app(ty_[], x2))
new_ltEs18(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_Bool)
new_esEs9(Char(x0), Char(x1))
new_compare210(x0, x1, True, x2, x3, x4)
new_esEs14(False, False)
new_ltEs12(Just(x0), Just(x1), ty_Int)
new_primEqInt(Pos(Zero), Pos(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_esEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs24(x0, x1, ty_Char)
new_primCompAux00(x0, x1, EQ, ty_Float)
new_lt9(x0, x1, ty_Integer)
new_primPlusNat0(Succ(x0), Succ(x1))
new_lt20(x0, x1, app(ty_[], x2))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Int)
new_compare7(:(x0, x1), :(x2, x3), x4)
new_primCompAux00(x0, x1, EQ, ty_Integer)
new_esEs17(EQ, EQ)
new_primCmpChar(Char(x0), Char(x1))
new_esEs4(Left(x0), Left(x1), ty_Char, x2)
new_ltEs18(x0, x1, ty_Integer)
new_esEs17(LT, EQ)
new_esEs17(EQ, LT)
new_lt8([], [], x0)
new_esEs24(x0, x1, ty_@0)
new_primCmpNat0(Succ(x0), Zero)
new_ltEs16(x0, x1)
new_esEs25(x0, x1, ty_Int)
new_esEs28(x0, x1, ty_Float)
new_compare0(x0, x1, ty_Float)
new_lt6(x0, x1, x2, x3)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs18(x0, x1, ty_Char)
new_esEs27(x0, x1, ty_Ordering)
new_ltEs10(EQ, EQ)

We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.

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

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

new_ltEs2(@2(vwx310, vwx311), @2(vwx410, vwx411), app(app(ty_@2, bad), bae), baa) → new_lt2(vwx310, vwx410, bad, bae)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), bec, bdb, app(app(ty_Either, bfe), bff)) → new_ltEs(vwx312, vwx412, bfe, bff)
new_ltEs2(@2(vwx310, vwx311), @2(vwx410, vwx411), bba, app(app(ty_Either, bbb), bbc)) → new_ltEs(vwx311, vwx411, bbb, bbc)
new_lt(vwx30, vwx40, ba, bb) → new_compare2(vwx30, vwx40, new_esEs4(vwx30, vwx40, ba, bb), ba, bb)
new_compare2(vwx30, vwx40, False, ba, bb) → new_ltEs(vwx30, vwx40, ba, bb)
new_ltEs(Left(vwx310), Left(vwx410), app(app(ty_Either, bc), bd), be) → new_ltEs(vwx310, vwx410, bc, bd)
new_ltEs(Right(vwx310), Right(vwx410), ce, app(app(ty_Either, cf), cg)) → new_ltEs(vwx310, vwx410, cf, cg)
new_compare32(vwx30, vwx40, bce, bcf, bcg) → new_compare22(vwx30, vwx40, new_esEs7(vwx30, vwx40, bce, bcf, bcg), bce, bcf, bcg)
new_ltEs2(@2(vwx310, vwx311), @2(vwx410, vwx411), bba, app(app(app(ty_@3, bbh), bca), bcb)) → new_ltEs3(vwx311, vwx411, bbh, bca, bcb)
new_ltEs2(@2(vwx310, vwx311), @2(vwx410, vwx411), app(ty_[], bab), baa) → new_lt0(vwx310, vwx410, bab)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), bec, app(ty_[], bef), bdc) → new_lt0(vwx311, vwx411, bef)
new_compare(:(vwx310, vwx311), :(vwx410, vwx411), dh) → new_primCompAux(vwx310, vwx410, vwx311, vwx411, dh)
new_compare31(vwx30, vwx40, bcc, bcd) → new_compare21(vwx30, vwx40, new_esEs6(vwx30, vwx40, bcc, bcd), bcc, bcd)
new_ltEs1(Just(vwx310), Just(vwx410), app(ty_Maybe, ha)) → new_ltEs1(vwx310, vwx410, ha)
new_ltEs(Right(vwx310), Right(vwx410), ce, app(ty_[], da)) → new_ltEs0(vwx310, vwx410, da)
new_primCompAux(vwx300, vwx400, vwx301, vwx401, ea) → new_primCompAux0(vwx301, vwx401, new_compare0(vwx300, vwx400, ea), app(ty_[], ea))
new_ltEs(Right(vwx310), Right(vwx410), ce, app(app(app(ty_@3, de), df), dg)) → new_ltEs3(vwx310, vwx410, de, df, dg)
new_primCompAux(vwx300, vwx400, vwx301, vwx401, app(app(ty_Either, eb), ec)) → new_compare3(vwx300, vwx400, eb, ec)
new_compare22(vwx30, vwx40, False, bce, bcf, bcg) → new_ltEs3(vwx30, vwx40, bce, bcf, bcg)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), app(ty_[], bdd), bdb, bdc) → new_lt0(vwx310, vwx410, bdd)
new_compare20(vwx30, vwx40, False, ge) → new_ltEs1(vwx30, vwx40, ge)
new_ltEs1(Just(vwx310), Just(vwx410), app(app(app(ty_@3, hd), he), hf)) → new_ltEs3(vwx310, vwx410, hd, he, hf)
new_lt3(vwx30, vwx40, bce, bcf, bcg) → new_compare22(vwx30, vwx40, new_esEs7(vwx30, vwx40, bce, bcf, bcg), bce, bcf, bcg)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), bec, bdb, app(ty_Maybe, bfh)) → new_ltEs1(vwx312, vwx412, bfh)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), app(app(ty_@2, bdf), bdg), bdb, bdc) → new_lt2(vwx310, vwx410, bdf, bdg)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), app(app(ty_Either, bch), bda), bdb, bdc) → new_lt(vwx310, vwx410, bch, bda)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), bec, app(app(ty_Either, bed), bee), bdc) → new_lt(vwx311, vwx411, bed, bee)
new_primCompAux(vwx300, vwx400, vwx301, vwx401, app(app(app(ty_@3, eh), fa), fb)) → new_compare32(vwx300, vwx400, eh, fa, fb)
new_lt1(vwx30, vwx40, ge) → new_compare20(vwx30, vwx40, new_esEs5(vwx30, vwx40, ge), ge)
new_ltEs2(@2(vwx310, vwx311), @2(vwx410, vwx411), app(app(ty_Either, hg), hh), baa) → new_lt(vwx310, vwx410, hg, hh)
new_ltEs2(@2(vwx310, vwx311), @2(vwx410, vwx411), bba, app(ty_[], bbd)) → new_ltEs0(vwx311, vwx411, bbd)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), bec, app(app(ty_@2, beh), bfa), bdc) → new_lt2(vwx311, vwx411, beh, bfa)
new_compare3(vwx30, vwx40, ba, bb) → new_compare2(vwx30, vwx40, new_esEs4(vwx30, vwx40, ba, bb), ba, bb)
new_compare30(vwx30, vwx40, ge) → new_compare20(vwx30, vwx40, new_esEs5(vwx30, vwx40, ge), ge)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), bec, bdb, app(app(ty_@2, bga), bgb)) → new_ltEs2(vwx312, vwx412, bga, bgb)
new_compare21(vwx30, vwx40, False, bcc, bcd) → new_ltEs2(vwx30, vwx40, bcc, bcd)
new_ltEs(Left(vwx310), Left(vwx410), app(ty_[], bf), be) → new_ltEs0(vwx310, vwx410, bf)
new_ltEs1(Just(vwx310), Just(vwx410), app(app(ty_Either, gf), gg)) → new_ltEs(vwx310, vwx410, gf, gg)
new_primCompAux(vwx300, vwx400, vwx301, vwx401, app(ty_[], ed)) → new_compare(vwx300, vwx400, ed)
new_primCompAux0(vwx148, vwx149, EQ, app(ty_[], ff)) → new_compare(vwx148, vwx149, ff)
new_ltEs2(@2(vwx310, vwx311), @2(vwx410, vwx411), app(app(app(ty_@3, baf), bag), bah), baa) → new_lt3(vwx310, vwx410, baf, bag, bah)
new_ltEs2(@2(vwx310, vwx311), @2(vwx410, vwx411), app(ty_Maybe, bac), baa) → new_lt1(vwx310, vwx410, bac)
new_ltEs1(Just(vwx310), Just(vwx410), app(app(ty_@2, hb), hc)) → new_ltEs2(vwx310, vwx410, hb, hc)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), bec, bdb, app(ty_[], bfg)) → new_ltEs0(vwx312, vwx412, bfg)
new_ltEs2(@2(vwx310, vwx311), @2(vwx410, vwx411), bba, app(ty_Maybe, bbe)) → new_ltEs1(vwx311, vwx411, bbe)
new_lt0(:(vwx300, vwx301), :(vwx400, vwx401), app(app(ty_@2, ef), eg)) → new_compare31(vwx300, vwx400, ef, eg)
new_ltEs1(Just(vwx310), Just(vwx410), app(ty_[], gh)) → new_ltEs0(vwx310, vwx410, gh)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), bec, app(ty_Maybe, beg), bdc) → new_lt1(vwx311, vwx411, beg)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), bec, bdb, app(app(app(ty_@3, bgc), bgd), bge)) → new_ltEs3(vwx312, vwx412, bgc, bgd, bge)
new_lt2(vwx30, vwx40, bcc, bcd) → new_compare21(vwx30, vwx40, new_esEs6(vwx30, vwx40, bcc, bcd), bcc, bcd)
new_ltEs2(@2(vwx310, vwx311), @2(vwx410, vwx411), bba, app(app(ty_@2, bbf), bbg)) → new_ltEs2(vwx311, vwx411, bbf, bbg)
new_lt0(:(vwx300, vwx301), :(vwx400, vwx401), ea) → new_primCompAux0(vwx301, vwx401, new_compare0(vwx300, vwx400, ea), app(ty_[], ea))
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), app(app(app(ty_@3, bdh), bea), beb), bdb, bdc) → new_lt3(vwx310, vwx410, bdh, bea, beb)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), app(ty_Maybe, bde), bdb, bdc) → new_lt1(vwx310, vwx410, bde)
new_ltEs(Left(vwx310), Left(vwx410), app(ty_Maybe, bg), be) → new_ltEs1(vwx310, vwx410, bg)
new_ltEs0(:(vwx310, vwx311), :(vwx410, vwx411), dh) → new_primCompAux(vwx310, vwx410, vwx311, vwx411, dh)
new_ltEs(Left(vwx310), Left(vwx410), app(app(app(ty_@3, cb), cc), cd), be) → new_ltEs3(vwx310, vwx410, cb, cc, cd)
new_ltEs3(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), bec, app(app(app(ty_@3, bfb), bfc), bfd), bdc) → new_lt3(vwx311, vwx411, bfb, bfc, bfd)
new_ltEs(Right(vwx310), Right(vwx410), ce, app(app(ty_@2, dc), dd)) → new_ltEs2(vwx310, vwx410, dc, dd)
new_lt0(:(vwx300, vwx301), :(vwx400, vwx401), app(ty_[], ed)) → new_compare(vwx300, vwx400, ed)
new_primCompAux(vwx300, vwx400, vwx301, vwx401, app(ty_Maybe, ee)) → new_compare30(vwx300, vwx400, ee)
new_lt0(:(vwx300, vwx301), :(vwx400, vwx401), app(app(app(ty_@3, eh), fa), fb)) → new_compare32(vwx300, vwx400, eh, fa, fb)
new_primCompAux(vwx300, vwx400, vwx301, vwx401, app(app(ty_@2, ef), eg)) → new_compare31(vwx300, vwx400, ef, eg)
new_ltEs(Left(vwx310), Left(vwx410), app(app(ty_@2, bh), ca), be) → new_ltEs2(vwx310, vwx410, bh, ca)
new_lt0(:(vwx300, vwx301), :(vwx400, vwx401), app(ty_Maybe, ee)) → new_compare30(vwx300, vwx400, ee)
new_ltEs(Right(vwx310), Right(vwx410), ce, app(ty_Maybe, db)) → new_ltEs1(vwx310, vwx410, db)
new_lt0(:(vwx300, vwx301), :(vwx400, vwx401), app(app(ty_Either, eb), ec)) → new_compare3(vwx300, vwx400, eb, ec)

The TRS R consists of the following rules:

new_compare0(vwx300, vwx400, ty_Bool) → new_compare13(vwx300, vwx400)
new_compare0(vwx300, vwx400, ty_Char) → new_compare12(vwx300, vwx400)
new_compare0(vwx300, vwx400, ty_@0) → new_compare18(vwx300, vwx400)
new_compare0(vwx300, vwx400, app(app(app(ty_@3, eh), fa), fb)) → new_compare43(vwx300, vwx400, eh, fa, fb)
new_compare0(vwx300, vwx400, ty_Float) → new_compare40(vwx300, vwx400)
new_compare0(vwx300, vwx400, ty_Int) → new_compare10(vwx300, vwx400)
new_compare0(vwx300, vwx400, app(app(ty_@2, ef), eg)) → new_compare42(vwx300, vwx400, ef, eg)
new_compare0(vwx300, vwx400, app(app(ty_Either, eb), ec)) → new_compare16(vwx300, vwx400, eb, ec)
new_compare0(vwx300, vwx400, ty_Double) → new_compare8(vwx300, vwx400)
new_compare0(vwx300, vwx400, app(ty_Maybe, ee)) → new_compare41(vwx300, vwx400, ee)
new_compare0(vwx300, vwx400, app(ty_[], ed)) → new_compare7(vwx300, vwx400, ed)
new_compare0(vwx300, vwx400, ty_Ordering) → new_compare26(vwx300, vwx400)
new_compare0(vwx300, vwx400, app(ty_Ratio, bhh)) → new_compare9(vwx300, vwx400, bhh)
new_compare0(vwx300, vwx400, ty_Integer) → new_compare11(vwx300, vwx400)
new_compare11(Integer(vwx310), Integer(vwx410)) → new_primCmpInt(vwx310, vwx410)
new_primCmpInt(Neg(Zero), Pos(Zero)) → EQ
new_primCmpInt(Pos(Zero), Neg(Zero)) → EQ
new_primCmpInt(Neg(Succ(vwx3000)), Neg(vwx400)) → new_primCmpNat0(vwx400, Succ(vwx3000))
new_primCmpInt(Neg(Zero), Pos(Succ(vwx4000))) → LT
new_primCmpInt(Pos(Zero), Pos(Succ(vwx4000))) → new_primCmpNat0(Zero, Succ(vwx4000))
new_primCmpInt(Pos(Succ(vwx3000)), Pos(vwx400)) → new_primCmpNat0(Succ(vwx3000), vwx400)
new_primCmpInt(Pos(Succ(vwx3000)), Neg(vwx400)) → GT
new_primCmpInt(Neg(Zero), Neg(Succ(vwx4000))) → new_primCmpNat0(Succ(vwx4000), Zero)
new_primCmpInt(Pos(Zero), Neg(Succ(vwx4000))) → GT
new_primCmpInt(Neg(Zero), Neg(Zero)) → EQ
new_primCmpInt(Pos(Zero), Pos(Zero)) → EQ
new_primCmpInt(Neg(Succ(vwx3000)), Pos(vwx400)) → LT
new_primCmpNat0(Succ(vwx3000), Zero) → GT
new_primCmpNat0(Succ(vwx3000), Succ(vwx4000)) → new_primCmpNat0(vwx3000, vwx4000)
new_primCmpNat0(Zero, Succ(vwx4000)) → LT
new_primCmpNat0(Zero, Zero) → EQ
new_compare9(:%(vwx310, vwx311), :%(vwx410, vwx411), ty_Int) → new_compare10(new_sr(vwx310, vwx411), new_sr(vwx410, vwx311))
new_compare9(:%(vwx310, vwx311), :%(vwx410, vwx411), ty_Integer) → new_compare11(new_sr0(vwx310, vwx411), new_sr0(vwx410, vwx311))
new_sr0(Integer(vwx4000), Integer(vwx3010)) → Integer(new_primMulInt(vwx4000, vwx3010))
new_primMulInt(Pos(vwx3000), Pos(vwx4000)) → Pos(new_primMulNat0(vwx3000, vwx4000))
new_primMulInt(Neg(vwx3000), Neg(vwx4000)) → Pos(new_primMulNat0(vwx3000, vwx4000))
new_primMulInt(Pos(vwx3000), Neg(vwx4000)) → Neg(new_primMulNat0(vwx3000, vwx4000))
new_primMulInt(Neg(vwx3000), Pos(vwx4000)) → Neg(new_primMulNat0(vwx3000, vwx4000))
new_primMulNat0(Zero, Zero) → Zero
new_primMulNat0(Succ(vwx30000), Succ(vwx40000)) → new_primPlusNat1(new_primMulNat0(vwx30000, Succ(vwx40000)), vwx40000)
new_primMulNat0(Zero, Succ(vwx40000)) → Zero
new_primMulNat0(Succ(vwx30000), Zero) → Zero
new_primPlusNat1(Zero, vwx40000) → Succ(vwx40000)
new_primPlusNat1(Succ(vwx1580), vwx40000) → Succ(Succ(new_primPlusNat0(vwx1580, vwx40000)))
new_primPlusNat0(Zero, Succ(vwx400000)) → Succ(vwx400000)
new_primPlusNat0(Succ(vwx15800), Zero) → Succ(vwx15800)
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(vwx15800), Succ(vwx400000)) → Succ(Succ(new_primPlusNat0(vwx15800, vwx400000)))
new_sr(vwx300, vwx400) → new_primMulInt(vwx300, vwx400)
new_compare10(vwx31, vwx41) → new_primCmpInt(vwx31, vwx41)
new_compare26(vwx300, vwx400) → new_compare38(vwx300, vwx400)
new_compare38(vwx30, vwx40) → new_compare29(vwx30, vwx40, new_esEs17(vwx30, vwx40))
new_esEs17(LT, LT) → True
new_esEs17(EQ, EQ) → True
new_esEs17(LT, GT) → False
new_esEs17(GT, LT) → False
new_esEs17(EQ, GT) → False
new_esEs17(GT, EQ) → False
new_esEs17(LT, EQ) → False
new_esEs17(EQ, LT) → False
new_esEs17(GT, GT) → True
new_compare29(vwx30, vwx40, True) → EQ
new_compare29(vwx30, vwx40, False) → new_compare111(vwx30, vwx40, new_ltEs10(vwx30, vwx40))
new_ltEs10(EQ, GT) → True
new_ltEs10(GT, EQ) → False
new_ltEs10(LT, EQ) → True
new_ltEs10(GT, GT) → True
new_ltEs10(LT, GT) → True
new_ltEs10(EQ, EQ) → True
new_ltEs10(LT, LT) → True
new_ltEs10(EQ, LT) → False
new_ltEs10(GT, LT) → False
new_compare111(vwx30, vwx40, False) → GT
new_compare111(vwx30, vwx40, True) → LT
new_compare7(:(vwx310, vwx311), [], dh) → GT
new_compare7([], :(vwx410, vwx411), dh) → LT
new_compare7([], [], dh) → EQ
new_primCompAux00(vwx148, vwx149, EQ, app(ty_[], ff)) → new_compare7(vwx148, vwx149, ff)
new_compare7(:(vwx310, vwx311), :(vwx410, vwx411), dh) → new_primCompAux1(vwx310, vwx410, vwx311, vwx411, dh)
new_primCompAux1(vwx300, vwx400, vwx301, vwx401, ea) → new_primCompAux00(vwx301, vwx401, new_compare0(vwx300, vwx400, ea), app(ty_[], ea))
new_primCompAux00(vwx148, vwx149, LT, cdc) → LT
new_primCompAux00(vwx148, vwx149, GT, cdc) → GT
new_compare41(vwx300, vwx400, ee) → new_compare33(vwx300, vwx400, ee)
new_compare33(vwx30, vwx40, ge) → new_compare23(vwx30, vwx40, new_esEs5(vwx30, vwx40, ge), ge)
new_esEs5(Just(vwx300), Just(vwx400), ty_Ordering) → new_esEs17(vwx300, vwx400)
new_esEs5(Just(vwx300), Just(vwx400), ty_Char) → new_esEs9(vwx300, vwx400)
new_esEs5(Just(vwx300), Just(vwx400), ty_@0) → new_esEs10(vwx300, vwx400)
new_esEs5(Just(vwx300), Just(vwx400), ty_Int) → new_esEs8(vwx300, vwx400)
new_esEs5(Just(vwx300), Just(vwx400), ty_Double) → new_esEs13(vwx300, vwx400)
new_esEs5(Just(vwx300), Just(vwx400), ty_Bool) → new_esEs14(vwx300, vwx400)
new_esEs5(Just(vwx300), Just(vwx400), ty_Float) → new_esEs15(vwx300, vwx400)
new_esEs5(Just(vwx300), Just(vwx400), app(ty_[], bha)) → new_esEs11(vwx300, vwx400, bha)
new_esEs5(Just(vwx300), Just(vwx400), app(app(ty_@2, bhf), bhg)) → new_esEs6(vwx300, vwx400, bhf, bhg)
new_esEs5(Nothing, Just(vwx400), ge) → False
new_esEs5(Just(vwx300), Nothing, ge) → False
new_esEs5(Nothing, Nothing, ge) → True
new_esEs5(Just(vwx300), Just(vwx400), app(app(app(ty_@3, bgf), bgg), bgh)) → new_esEs7(vwx300, vwx400, bgf, bgg, bgh)
new_esEs5(Just(vwx300), Just(vwx400), ty_Integer) → new_esEs16(vwx300, vwx400)
new_esEs5(Just(vwx300), Just(vwx400), app(ty_Ratio, bhe)) → new_esEs12(vwx300, vwx400, bhe)
new_compare23(vwx30, vwx40, True, ge) → EQ
new_compare23(vwx30, vwx40, False, ge) → new_compare19(vwx30, vwx40, new_ltEs12(vwx30, vwx40, ge), ge)
new_esEs4(Right(vwx300), Right(vwx400), ba, app(app(ty_Either, ccb), ccc)) → new_esEs4(vwx300, vwx400, ccb, ccc)
new_esEs4(Left(vwx300), Left(vwx400), app(ty_Maybe, cbb), bb) → new_esEs5(vwx300, vwx400, cbb)
new_esEs5(Just(vwx300), Just(vwx400), app(ty_Maybe, bhd)) → new_esEs5(vwx300, vwx400, bhd)
new_esEs4(Left(vwx300), Left(vwx400), app(app(ty_Either, cah), cba), bb) → new_esEs4(vwx300, vwx400, cah, cba)
new_esEs4(Right(vwx300), Right(vwx400), ba, app(ty_Maybe, ccd)) → new_esEs5(vwx300, vwx400, ccd)
new_esEs5(Just(vwx300), Just(vwx400), app(app(ty_Either, bhb), bhc)) → new_esEs4(vwx300, vwx400, bhb, bhc)
new_esEs4(Left(vwx300), Left(vwx400), ty_Bool, bb) → new_esEs14(vwx300, vwx400)
new_esEs4(Left(vwx300), Left(vwx400), ty_Ordering, bb) → new_esEs17(vwx300, vwx400)
new_esEs4(Right(vwx300), Right(vwx400), ba, app(ty_[], cca)) → new_esEs11(vwx300, vwx400, cca)
new_esEs4(Right(vwx300), Right(vwx400), ba, app(app(app(ty_@3, cbf), cbg), cbh)) → new_esEs7(vwx300, vwx400, cbf, cbg, cbh)
new_esEs4(Left(vwx300), Left(vwx400), app(app(ty_@2, cbd), cbe), bb) → new_esEs6(vwx300, vwx400, cbd, cbe)
new_esEs4(Right(vwx300), Right(vwx400), ba, ty_Float) → new_esEs15(vwx300, vwx400)
new_esEs4(Left(vwx300), Left(vwx400), app(ty_[], cag), bb) → new_esEs11(vwx300, vwx400, cag)
new_esEs4(Left(vwx300), Left(vwx400), ty_Char, bb) → new_esEs9(vwx300, vwx400)
new_esEs4(Left(vwx300), Left(vwx400), app(ty_Ratio, cbc), bb) → new_esEs12(vwx300, vwx400, cbc)
new_esEs4(Left(vwx300), Left(vwx400), ty_Integer, bb) → new_esEs16(vwx300, vwx400)
new_esEs4(Left(vwx300), Left(vwx400), ty_Int, bb) → new_esEs8(vwx300, vwx400)
new_esEs4(Left(vwx300), Left(vwx400), ty_Double, bb) → new_esEs13(vwx300, vwx400)
new_esEs4(Left(vwx300), Left(vwx400), app(app(app(ty_@3, cad), cae), caf), bb) → new_esEs7(vwx300, vwx400, cad, cae, caf)
new_esEs4(Right(vwx300), Right(vwx400), ba, ty_@0) → new_esEs10(vwx300, vwx400)
new_esEs4(Left(vwx300), Left(vwx400), ty_Float, bb) → new_esEs15(vwx300, vwx400)
new_esEs4(Right(vwx300), Right(vwx400), ba, ty_Bool) → new_esEs14(vwx300, vwx400)
new_esEs4(Right(vwx300), Right(vwx400), ba, ty_Char) → new_esEs9(vwx300, vwx400)
new_esEs4(Right(vwx300), Right(vwx400), ba, app(app(ty_@2, ccf), ccg)) → new_esEs6(vwx300, vwx400, ccf, ccg)
new_esEs4(Right(vwx300), Right(vwx400), ba, ty_Integer) → new_esEs16(vwx300, vwx400)
new_esEs4(Right(vwx300), Right(vwx400), ba, app(ty_Ratio, cce)) → new_esEs12(vwx300, vwx400, cce)
new_esEs4(Right(vwx300), Right(vwx400), ba, ty_Double) → new_esEs13(vwx300, vwx400)
new_esEs4(Left(vwx300), Left(vwx400), ty_@0, bb) → new_esEs10(vwx300, vwx400)
new_esEs4(Right(vwx300), Right(vwx400), ba, ty_Ordering) → new_esEs17(vwx300, vwx400)
new_esEs4(Left(vwx300), Right(vwx400), ba, bb) → False
new_esEs4(Right(vwx300), Left(vwx400), ba, bb) → False
new_esEs4(Right(vwx300), Right(vwx400), ba, ty_Int) → new_esEs8(vwx300, vwx400)
new_esEs8(vwx30, vwx40) → new_primEqInt(vwx30, vwx40)
new_primEqInt(Neg(Succ(vwx3000)), Neg(Succ(vwx4000))) → new_primEqNat0(vwx3000, vwx4000)
new_primEqInt(Neg(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Succ(vwx3000)), Neg(Zero)) → False
new_primEqInt(Neg(Zero), Neg(Succ(vwx4000))) → False
new_primEqInt(Pos(Succ(vwx3000)), Pos(Succ(vwx4000))) → new_primEqNat0(vwx3000, vwx4000)
new_primEqInt(Pos(Succ(vwx3000)), Pos(Zero)) → False
new_primEqInt(Pos(Zero), Pos(Succ(vwx4000))) → False
new_primEqInt(Pos(Succ(vwx3000)), Neg(vwx400)) → False
new_primEqInt(Neg(Succ(vwx3000)), Pos(vwx400)) → False
new_primEqInt(Pos(Zero), Neg(Succ(vwx4000))) → False
new_primEqInt(Neg(Zero), Pos(Succ(vwx4000))) → False
new_primEqInt(Pos(Zero), Pos(Zero)) → True
new_primEqInt(Pos(Zero), Neg(Zero)) → True
new_primEqInt(Neg(Zero), Pos(Zero)) → True
new_primEqNat0(Zero, Zero) → True
new_primEqNat0(Succ(vwx3000), Succ(vwx4000)) → new_primEqNat0(vwx3000, vwx4000)
new_primEqNat0(Succ(vwx3000), Zero) → False
new_primEqNat0(Zero, Succ(vwx4000)) → False
new_esEs10(@0, @0) → True
new_esEs13(Double(vwx300, vwx301), Double(vwx400, vwx401)) → new_esEs8(new_sr(vwx300, vwx400), new_sr(vwx301, vwx401))
new_esEs12(:%(vwx300, vwx301), :%(vwx400, vwx401), cch) → new_asAs(new_esEs19(vwx300, vwx400, cch), new_esEs20(vwx301, vwx401, cch))
new_esEs19(vwx300, vwx400, ty_Int) → new_esEs8(vwx300, vwx400)
new_esEs19(vwx300, vwx400, ty_Integer) → new_esEs16(vwx300, vwx400)
new_esEs20(vwx301, vwx401, ty_Integer) → new_esEs16(vwx301, vwx401)
new_esEs20(vwx301, vwx401, ty_Int) → new_esEs8(vwx301, vwx401)
new_asAs(False, vwx143) → False
new_asAs(True, vwx143) → vwx143
new_esEs16(Integer(vwx300), Integer(vwx400)) → new_primEqInt(vwx300, vwx400)
new_esEs6(@2(vwx300, vwx301), @2(vwx400, vwx401), bcc, bcd) → new_asAs(new_esEs22(vwx300, vwx400, bcc), new_esEs23(vwx301, vwx401, bcd))
new_esEs22(vwx300, vwx400, ty_Char) → new_esEs9(vwx300, vwx400)
new_esEs22(vwx300, vwx400, app(app(ty_Either, cea), ceb)) → new_esEs4(vwx300, vwx400, cea, ceb)
new_esEs22(vwx300, vwx400, ty_Float) → new_esEs15(vwx300, vwx400)
new_esEs22(vwx300, vwx400, app(ty_Ratio, ced)) → new_esEs12(vwx300, vwx400, ced)
new_esEs22(vwx300, vwx400, ty_Int) → new_esEs8(vwx300, vwx400)
new_esEs22(vwx300, vwx400, ty_Ordering) → new_esEs17(vwx300, vwx400)
new_esEs22(vwx300, vwx400, ty_Bool) → new_esEs14(vwx300, vwx400)
new_esEs22(vwx300, vwx400, app(app(ty_@2, cee), cef)) → new_esEs6(vwx300, vwx400, cee, cef)
new_esEs22(vwx300, vwx400, app(ty_[], cdh)) → new_esEs11(vwx300, vwx400, cdh)
new_esEs22(vwx300, vwx400, app(app(app(ty_@3, cde), cdf), cdg)) → new_esEs7(vwx300, vwx400, cde, cdf, cdg)
new_esEs22(vwx300, vwx400, ty_Double) → new_esEs13(vwx300, vwx400)
new_esEs22(vwx300, vwx400, ty_@0) → new_esEs10(vwx300, vwx400)
new_esEs22(vwx300, vwx400, ty_Integer) → new_esEs16(vwx300, vwx400)
new_esEs22(vwx300, vwx400, app(ty_Maybe, cec)) → new_esEs5(vwx300, vwx400, cec)
new_esEs23(vwx301, vwx401, ty_Bool) → new_esEs14(vwx301, vwx401)
new_esEs23(vwx301, vwx401, ty_Double) → new_esEs13(vwx301, vwx401)
new_esEs23(vwx301, vwx401, app(app(app(ty_@3, ceg), ceh), cfa)) → new_esEs7(vwx301, vwx401, ceg, ceh, cfa)
new_esEs23(vwx301, vwx401, ty_Integer) → new_esEs16(vwx301, vwx401)
new_esEs23(vwx301, vwx401, app(ty_Ratio, cff)) → new_esEs12(vwx301, vwx401, cff)
new_esEs23(vwx301, vwx401, app(app(ty_@2, cfg), cfh)) → new_esEs6(vwx301, vwx401, cfg, cfh)
new_esEs23(vwx301, vwx401, ty_@0) → new_esEs10(vwx301, vwx401)
new_esEs23(vwx301, vwx401, app(app(ty_Either, cfc), cfd)) → new_esEs4(vwx301, vwx401, cfc, cfd)
new_esEs23(vwx301, vwx401, app(ty_[], cfb)) → new_esEs11(vwx301, vwx401, cfb)
new_esEs23(vwx301, vwx401, ty_Ordering) → new_esEs17(vwx301, vwx401)
new_esEs23(vwx301, vwx401, ty_Float) → new_esEs15(vwx301, vwx401)
new_esEs23(vwx301, vwx401, app(ty_Maybe, cfe)) → new_esEs5(vwx301, vwx401, cfe)
new_esEs23(vwx301, vwx401, ty_Char) → new_esEs9(vwx301, vwx401)
new_esEs23(vwx301, vwx401, ty_Int) → new_esEs8(vwx301, vwx401)
new_esEs9(Char(vwx300), Char(vwx400)) → new_primEqNat0(vwx300, vwx400)
new_esEs15(Float(vwx300, vwx301), Float(vwx400, vwx401)) → new_esEs8(new_sr(vwx300, vwx400), new_sr(vwx301, vwx401))
new_esEs11([], [], ea) → True
new_esEs11(:(vwx300, vwx301), :(vwx400, vwx401), ea) → new_asAs(new_esEs18(vwx300, vwx400, ea), new_esEs11(vwx301, vwx401, ea))
new_esEs11([], :(vwx400, vwx401), ea) → False
new_esEs11(:(vwx300, vwx301), [], ea) → False
new_esEs18(vwx300, vwx400, app(app(ty_@2, ef), eg)) → new_esEs6(vwx300, vwx400, ef, eg)
new_esEs18(vwx300, vwx400, ty_Integer) → new_esEs16(vwx300, vwx400)
new_esEs18(vwx300, vwx400, app(ty_Ratio, bhh)) → new_esEs12(vwx300, vwx400, bhh)
new_esEs18(vwx300, vwx400, ty_Double) → new_esEs13(vwx300, vwx400)
new_esEs18(vwx300, vwx400, ty_Char) → new_esEs9(vwx300, vwx400)
new_esEs18(vwx300, vwx400, ty_Float) → new_esEs15(vwx300, vwx400)
new_esEs18(vwx300, vwx400, app(app(app(ty_@3, eh), fa), fb)) → new_esEs7(vwx300, vwx400, eh, fa, fb)
new_esEs18(vwx300, vwx400, ty_Int) → new_esEs8(vwx300, vwx400)
new_esEs18(vwx300, vwx400, app(app(ty_Either, eb), ec)) → new_esEs4(vwx300, vwx400, eb, ec)
new_esEs18(vwx300, vwx400, app(ty_[], ed)) → new_esEs11(vwx300, vwx400, ed)
new_esEs18(vwx300, vwx400, ty_Ordering) → new_esEs17(vwx300, vwx400)
new_esEs18(vwx300, vwx400, app(ty_Maybe, ee)) → new_esEs5(vwx300, vwx400, ee)
new_esEs18(vwx300, vwx400, ty_@0) → new_esEs10(vwx300, vwx400)
new_esEs18(vwx300, vwx400, ty_Bool) → new_esEs14(vwx300, vwx400)
new_esEs14(True, False) → False
new_esEs14(False, True) → False
new_esEs14(True, True) → True
new_esEs14(False, False) → True
new_esEs7(@3(vwx300, vwx301, vwx302), @3(vwx400, vwx401, vwx402), bce, bcf, bcg) → new_asAs(new_esEs24(vwx300, vwx400, bce), new_asAs(new_esEs25(vwx301, vwx401, bcf), new_esEs26(vwx302, vwx402, bcg)))
new_esEs24(vwx300, vwx400, ty_Char) → new_esEs9(vwx300, vwx400)
new_esEs24(vwx300, vwx400, app(ty_[], cgd)) → new_esEs11(vwx300, vwx400, cgd)
new_esEs24(vwx300, vwx400, app(app(ty_@2, cha), chb)) → new_esEs6(vwx300, vwx400, cha, chb)
new_esEs24(vwx300, vwx400, ty_Bool) → new_esEs14(vwx300, vwx400)
new_esEs24(vwx300, vwx400, app(ty_Ratio, cgh)) → new_esEs12(vwx300, vwx400, cgh)
new_esEs24(vwx300, vwx400, ty_Float) → new_esEs15(vwx300, vwx400)
new_esEs24(vwx300, vwx400, ty_@0) → new_esEs10(vwx300, vwx400)
new_esEs24(vwx300, vwx400, app(ty_Maybe, cgg)) → new_esEs5(vwx300, vwx400, cgg)
new_esEs24(vwx300, vwx400, ty_Int) → new_esEs8(vwx300, vwx400)
new_esEs24(vwx300, vwx400, ty_Integer) → new_esEs16(vwx300, vwx400)
new_esEs24(vwx300, vwx400, app(app(ty_Either, cge), cgf)) → new_esEs4(vwx300, vwx400, cge, cgf)
new_esEs24(vwx300, vwx400, app(app(app(ty_@3, cga), cgb), cgc)) → new_esEs7(vwx300, vwx400, cga, cgb, cgc)
new_esEs24(vwx300, vwx400, ty_Double) → new_esEs13(vwx300, vwx400)
new_esEs24(vwx300, vwx400, ty_Ordering) → new_esEs17(vwx300, vwx400)
new_esEs25(vwx301, vwx401, ty_Ordering) → new_esEs17(vwx301, vwx401)
new_esEs25(vwx301, vwx401, app(app(ty_Either, chg), chh)) → new_esEs4(vwx301, vwx401, chg, chh)
new_esEs25(vwx301, vwx401, ty_Bool) → new_esEs14(vwx301, vwx401)
new_esEs25(vwx301, vwx401, app(app(ty_@2, dac), dad)) → new_esEs6(vwx301, vwx401, dac, dad)
new_esEs25(vwx301, vwx401, ty_@0) → new_esEs10(vwx301, vwx401)
new_esEs25(vwx301, vwx401, app(ty_Maybe, daa)) → new_esEs5(vwx301, vwx401, daa)
new_esEs25(vwx301, vwx401, ty_Char) → new_esEs9(vwx301, vwx401)
new_esEs25(vwx301, vwx401, ty_Int) → new_esEs8(vwx301, vwx401)
new_esEs25(vwx301, vwx401, ty_Float) → new_esEs15(vwx301, vwx401)
new_esEs25(vwx301, vwx401, ty_Double) → new_esEs13(vwx301, vwx401)
new_esEs25(vwx301, vwx401, app(ty_[], chf)) → new_esEs11(vwx301, vwx401, chf)
new_esEs25(vwx301, vwx401, ty_Integer) → new_esEs16(vwx301, vwx401)
new_esEs25(vwx301, vwx401, app(app(app(ty_@3, chc), chd), che)) → new_esEs7(vwx301, vwx401, chc, chd, che)
new_esEs25(vwx301, vwx401, app(ty_Ratio, dab)) → new_esEs12(vwx301, vwx401, dab)
new_esEs26(vwx302, vwx402, ty_Float) → new_esEs15(vwx302, vwx402)
new_esEs26(vwx302, vwx402, app(app(app(ty_@3, dae), daf), dag)) → new_esEs7(vwx302, vwx402, dae, daf, dag)
new_esEs26(vwx302, vwx402, ty_Integer) → new_esEs16(vwx302, vwx402)
new_esEs26(vwx302, vwx402, app(ty_[], dah)) → new_esEs11(vwx302, vwx402, dah)
new_esEs26(vwx302, vwx402, ty_Double) → new_esEs13(vwx302, vwx402)
new_esEs26(vwx302, vwx402, ty_Bool) → new_esEs14(vwx302, vwx402)
new_esEs26(vwx302, vwx402, ty_@0) → new_esEs10(vwx302, vwx402)
new_esEs26(vwx302, vwx402, ty_Int) → new_esEs8(vwx302, vwx402)
new_esEs26(vwx302, vwx402, app(ty_Maybe, dbc)) → new_esEs5(vwx302, vwx402, dbc)
new_esEs26(vwx302, vwx402, app(ty_Ratio, dbd)) → new_esEs12(vwx302, vwx402, dbd)
new_esEs26(vwx302, vwx402, ty_Ordering) → new_esEs17(vwx302, vwx402)
new_esEs26(vwx302, vwx402, ty_Char) → new_esEs9(vwx302, vwx402)
new_esEs26(vwx302, vwx402, app(app(ty_Either, dba), dbb)) → new_esEs4(vwx302, vwx402, dba, dbb)
new_esEs26(vwx302, vwx402, app(app(ty_@2, dbe), dbf)) → new_esEs6(vwx302, vwx402, dbe, dbf)
new_ltEs12(Nothing, Nothing, cab) → True
new_ltEs12(Just(vwx310), Just(vwx410), ty_Float) → new_ltEs17(vwx310, vwx410)
new_ltEs12(Just(vwx310), Just(vwx410), ty_Int) → new_ltEs11(vwx310, vwx410)
new_ltEs12(Just(vwx310), Just(vwx410), ty_Ordering) → new_ltEs10(vwx310, vwx410)
new_ltEs12(Just(vwx310), Just(vwx410), app(app(ty_@2, hb), hc)) → new_ltEs14(vwx310, vwx410, hb, hc)
new_ltEs12(Just(vwx310), Just(vwx410), app(ty_Ratio, cac)) → new_ltEs9(vwx310, vwx410, cac)
new_ltEs12(Just(vwx310), Just(vwx410), ty_Bool) → new_ltEs6(vwx310, vwx410)
new_ltEs12(Just(vwx310), Just(vwx410), app(app(app(ty_@3, hd), he), hf)) → new_ltEs15(vwx310, vwx410, hd, he, hf)
new_ltEs12(Just(vwx310), Just(vwx410), app(ty_[], gh)) → new_ltEs4(vwx310, vwx410, gh)
new_ltEs12(Just(vwx310), Just(vwx410), ty_@0) → new_ltEs8(vwx310, vwx410)
new_ltEs12(Just(vwx310), Just(vwx410), ty_Double) → new_ltEs16(vwx310, vwx410)
new_ltEs12(Just(vwx310), Just(vwx410), ty_Char) → new_ltEs5(vwx310, vwx410)
new_ltEs12(Nothing, Just(vwx410), cab) → True
new_ltEs12(Just(vwx310), Nothing, cab) → False
new_ltEs12(Just(vwx310), Just(vwx410), ty_Integer) → new_ltEs7(vwx310, vwx410)
new_compare19(vwx30, vwx40, True, ge) → LT
new_compare19(vwx30, vwx40, False, ge) → GT
new_ltEs12(Just(vwx310), Just(vwx410), app(app(ty_Either, gf), gg)) → new_ltEs13(vwx310, vwx410, gf, gg)
new_ltEs12(Just(vwx310), Just(vwx410), app(ty_Maybe, ha)) → new_ltEs12(vwx310, vwx410, ha)
new_ltEs13(Left(vwx310), Left(vwx410), app(ty_Maybe, bg), be) → new_ltEs12(vwx310, vwx410, bg)
new_ltEs13(Right(vwx310), Right(vwx410), ce, app(ty_Maybe, db)) → new_ltEs12(vwx310, vwx410, db)
new_ltEs13(Right(vwx310), Right(vwx410), ce, app(app(ty_Either, cf), cg)) → new_ltEs13(vwx310, vwx410, cf, cg)
new_ltEs13(Left(vwx310), Left(vwx410), app(app(ty_Either, bc), bd), be) → new_ltEs13(vwx310, vwx410, bc, bd)
new_ltEs13(Left(vwx310), Left(vwx410), app(ty_[], bf), be) → new_ltEs4(vwx310, vwx410, bf)
new_ltEs13(Right(vwx310), Right(vwx410), ce, app(app(app(ty_@3, de), df), dg)) → new_ltEs15(vwx310, vwx410, de, df, dg)
new_ltEs13(Left(vwx310), Left(vwx410), ty_Char, be) → new_ltEs5(vwx310, vwx410)
new_ltEs13(Right(vwx310), Right(vwx410), ce, ty_Int) → new_ltEs11(vwx310, vwx410)
new_ltEs13(Left(vwx310), Left(vwx410), ty_Integer, be) → new_ltEs7(vwx310, vwx410)
new_ltEs13(Left(vwx310), Left(vwx410), app(app(app(ty_@3, cb), cc), cd), be) → new_ltEs15(vwx310, vwx410, cb, cc, cd)
new_ltEs13(Right(vwx310), Right(vwx410), ce, app(app(ty_@2, dc), dd)) → new_ltEs14(vwx310, vwx410, dc, dd)
new_ltEs13(Left(vwx310), Left(vwx410), ty_Ordering, be) → new_ltEs10(vwx310, vwx410)
new_ltEs13(Right(vwx310), Right(vwx410), ce, ty_Ordering) → new_ltEs10(vwx310, vwx410)
new_ltEs13(Right(vwx310), Right(vwx410), ce, ty_Integer) → new_ltEs7(vwx310, vwx410)
new_ltEs13(Left(vwx310), Left(vwx410), ty_Double, be) → new_ltEs16(vwx310, vwx410)
new_ltEs13(Right(vwx310), Right(vwx410), ce, app(ty_[], da)) → new_ltEs4(vwx310, vwx410, da)
new_ltEs13(Right(vwx310), Right(vwx410), ce, ty_Float) → new_ltEs17(vwx310, vwx410)
new_ltEs13(Right(vwx310), Right(vwx410), ce, ty_@0) → new_ltEs8(vwx310, vwx410)
new_ltEs13(Left(vwx310), Left(vwx410), ty_@0, be) → new_ltEs8(vwx310, vwx410)
new_ltEs13(Right(vwx310), Right(vwx410), ce, app(ty_Ratio, dcc)) → new_ltEs9(vwx310, vwx410, dcc)
new_ltEs13(Left(vwx310), Left(vwx410), ty_Bool, be) → new_ltEs6(vwx310, vwx410)
new_ltEs13(Left(vwx310), Left(vwx410), app(app(ty_@2, bh), ca), be) → new_ltEs14(vwx310, vwx410, bh, ca)
new_ltEs13(Right(vwx310), Right(vwx410), ce, ty_Char) → new_ltEs5(vwx310, vwx410)
new_ltEs13(Left(vwx310), Left(vwx410), ty_Float, be) → new_ltEs17(vwx310, vwx410)
new_ltEs13(Right(vwx310), Right(vwx410), ce, ty_Bool) → new_ltEs6(vwx310, vwx410)
new_ltEs13(Left(vwx310), Right(vwx410), ce, be) → True
new_ltEs13(Right(vwx310), Left(vwx410), ce, be) → False
new_ltEs13(Left(vwx310), Left(vwx410), app(ty_Ratio, dcb), be) → new_ltEs9(vwx310, vwx410, dcb)
new_ltEs13(Left(vwx310), Left(vwx410), ty_Int, be) → new_ltEs11(vwx310, vwx410)
new_ltEs13(Right(vwx310), Right(vwx410), ce, ty_Double) → new_ltEs16(vwx310, vwx410)
new_ltEs16(vwx31, vwx41) → new_not(new_esEs17(new_compare8(vwx31, vwx41), GT))
new_compare8(vwx31, vwx41) → new_primCmpDouble(vwx31, vwx41)
new_not(False) → True
new_not(True) → False
new_primCmpDouble(Double(vwx300, vwx301), Double(vwx400, vwx401)) → new_compare25(vwx300, vwx400, vwx301, vwx401)
new_compare25(vwx300, vwx401, vwx400, vwx301) → new_primCmpInt(new_sr(vwx300, vwx401), new_sr(vwx400, vwx301))
new_ltEs11(vwx31, vwx41) → new_not(new_esEs17(new_compare10(vwx31, vwx41), GT))
new_ltEs9(vwx31, vwx41, caa) → new_not(new_esEs17(new_compare9(vwx31, vwx41, caa), GT))
new_ltEs6(True, False) → False
new_ltEs6(False, True) → True
new_ltEs6(True, True) → True
new_ltEs6(False, False) → True
new_ltEs17(vwx31, vwx41) → new_not(new_esEs17(new_compare40(vwx31, vwx41), GT))
new_compare40(vwx31, vwx41) → new_primCmpFloat(vwx31, vwx41)
new_primCmpFloat(Float(vwx300, vwx301), Float(vwx400, vwx401)) → new_compare25(vwx300, vwx400, vwx301, vwx401)
new_ltEs5(vwx31, vwx41) → new_not(new_esEs17(new_compare12(vwx31, vwx41), GT))
new_compare12(vwx31, vwx41) → new_primCmpChar(vwx31, vwx41)
new_primCmpChar(Char(vwx300), Char(vwx400)) → new_primCmpNat0(vwx300, vwx400)
new_ltEs14(@2(vwx310, vwx311), @2(vwx410, vwx411), bba, baa) → new_pePe(new_lt9(vwx310, vwx410, bba), new_asAs(new_esEs21(vwx310, vwx410, bba), new_ltEs18(vwx311, vwx411, baa)))
new_lt9(vwx310, vwx410, ty_Double) → new_lt16(vwx310, vwx410)
new_lt9(vwx310, vwx410, ty_@0) → new_lt10(vwx310, vwx410)
new_lt9(vwx310, vwx410, ty_Int) → new_lt15(vwx310, vwx410)
new_lt9(vwx310, vwx410, ty_Float) → new_lt18(vwx310, vwx410)
new_lt9(vwx310, vwx410, ty_Integer) → new_lt17(vwx310, vwx410)
new_lt9(vwx310, vwx410, app(app(app(ty_@3, baf), bag), bah)) → new_lt5(vwx310, vwx410, baf, bag, bah)
new_lt9(vwx310, vwx410, ty_Bool) → new_lt12(vwx310, vwx410)
new_lt9(vwx310, vwx410, app(ty_[], bab)) → new_lt8(vwx310, vwx410, bab)
new_lt9(vwx310, vwx410, app(app(ty_Either, hg), hh)) → new_lt7(vwx310, vwx410, hg, hh)
new_lt9(vwx310, vwx410, app(app(ty_@2, bad), bae)) → new_lt6(vwx310, vwx410, bad, bae)
new_lt9(vwx310, vwx410, app(ty_Ratio, cda)) → new_lt11(vwx310, vwx410, cda)
new_lt9(vwx310, vwx410, ty_Char) → new_lt4(vwx310, vwx410)
new_lt9(vwx310, vwx410, app(ty_Maybe, bac)) → new_lt14(vwx310, vwx410, bac)
new_lt9(vwx310, vwx410, ty_Ordering) → new_lt13(vwx310, vwx410)
new_esEs21(vwx310, vwx410, app(app(ty_@2, bad), bae)) → new_esEs6(vwx310, vwx410, bad, bae)
new_esEs21(vwx310, vwx410, ty_Ordering) → new_esEs17(vwx310, vwx410)
new_esEs21(vwx310, vwx410, app(app(app(ty_@3, baf), bag), bah)) → new_esEs7(vwx310, vwx410, baf, bag, bah)
new_esEs21(vwx310, vwx410, ty_Bool) → new_esEs14(vwx310, vwx410)
new_esEs21(vwx310, vwx410, ty_Char) → new_esEs9(vwx310, vwx410)
new_esEs21(vwx310, vwx410, app(app(ty_Either, hg), hh)) → new_esEs4(vwx310, vwx410, hg, hh)
new_esEs21(vwx310, vwx410, app(ty_Ratio, cda)) → new_esEs12(vwx310, vwx410, cda)
new_esEs21(vwx310, vwx410, ty_Int) → new_esEs8(vwx310, vwx410)
new_esEs21(vwx310, vwx410, ty_Float) → new_esEs15(vwx310, vwx410)
new_esEs21(vwx310, vwx410, ty_Double) → new_esEs13(vwx310, vwx410)
new_esEs21(vwx310, vwx410, ty_Integer) → new_esEs16(vwx310, vwx410)
new_esEs21(vwx310, vwx410, ty_@0) → new_esEs10(vwx310, vwx410)
new_esEs21(vwx310, vwx410, app(ty_[], bab)) → new_esEs11(vwx310, vwx410, bab)
new_esEs21(vwx310, vwx410, app(ty_Maybe, bac)) → new_esEs5(vwx310, vwx410, bac)
new_ltEs18(vwx311, vwx411, ty_Bool) → new_ltEs6(vwx311, vwx411)
new_ltEs18(vwx311, vwx411, app(ty_Ratio, cdb)) → new_ltEs9(vwx311, vwx411, cdb)
new_ltEs18(vwx311, vwx411, ty_Double) → new_ltEs16(vwx311, vwx411)
new_ltEs18(vwx311, vwx411, ty_@0) → new_ltEs8(vwx311, vwx411)
new_ltEs18(vwx311, vwx411, app(app(ty_Either, bbb), bbc)) → new_ltEs13(vwx311, vwx411, bbb, bbc)
new_ltEs18(vwx311, vwx411, app(app(app(ty_@3, bbh), bca), bcb)) → new_ltEs15(vwx311, vwx411, bbh, bca, bcb)
new_ltEs18(vwx311, vwx411, app(app(ty_@2, bbf), bbg)) → new_ltEs14(vwx311, vwx411, bbf, bbg)
new_ltEs18(vwx311, vwx411, ty_Float) → new_ltEs17(vwx311, vwx411)
new_ltEs18(vwx311, vwx411, ty_Integer) → new_ltEs7(vwx311, vwx411)
new_ltEs18(vwx311, vwx411, ty_Int) → new_ltEs11(vwx311, vwx411)
new_ltEs18(vwx311, vwx411, app(ty_[], bbd)) → new_ltEs4(vwx311, vwx411, bbd)
new_ltEs18(vwx311, vwx411, app(ty_Maybe, bbe)) → new_ltEs12(vwx311, vwx411, bbe)
new_ltEs18(vwx311, vwx411, ty_Char) → new_ltEs5(vwx311, vwx411)
new_ltEs18(vwx311, vwx411, ty_Ordering) → new_ltEs10(vwx311, vwx411)
new_pePe(False, vwx117) → vwx117
new_pePe(True, vwx117) → True
new_ltEs4(vwx31, vwx41, dh) → new_not(new_esEs17(new_compare7(vwx31, vwx41, dh), GT))
new_ltEs7(vwx31, vwx41) → new_not(new_esEs17(new_compare11(vwx31, vwx41), GT))
new_ltEs15(@3(vwx310, vwx311, vwx312), @3(vwx410, vwx411, vwx412), bec, bdb, bdc) → new_pePe(new_lt19(vwx310, vwx410, bec), new_asAs(new_esEs27(vwx310, vwx410, bec), new_pePe(new_lt20(vwx311, vwx411, bdb), new_asAs(new_esEs28(vwx311, vwx411, bdb), new_ltEs19(vwx312, vwx412, bdc)))))
new_lt19(vwx310, vwx410, ty_Char) → new_lt4(vwx310, vwx410)
new_lt19(vwx310, vwx410, app(ty_[], bdd)) → new_lt8(vwx310, vwx410, bdd)
new_lt19(vwx310, vwx410, app(ty_Maybe, bde)) → new_lt14(vwx310, vwx410, bde)
new_lt19(vwx310, vwx410, app(ty_Ratio, dbg)) → new_lt11(vwx310, vwx410, dbg)
new_lt19(vwx310, vwx410, ty_Double) → new_lt16(vwx310, vwx410)
new_lt19(vwx310, vwx410, app(app(ty_@2, bdf), bdg)) → new_lt6(vwx310, vwx410, bdf, bdg)
new_lt19(vwx310, vwx410, app(app(ty_Either, bch), bda)) → new_lt7(vwx310, vwx410, bch, bda)
new_lt19(vwx310, vwx410, app(app(app(ty_@3, bdh), bea), beb)) → new_lt5(vwx310, vwx410, bdh, bea, beb)
new_lt19(vwx310, vwx410, ty_Int) → new_lt15(vwx310, vwx410)
new_lt19(vwx310, vwx410, ty_Integer) → new_lt17(vwx310, vwx410)
new_lt19(vwx310, vwx410, ty_Bool) → new_lt12(vwx310, vwx410)
new_lt19(vwx310, vwx410, ty_Ordering) → new_lt13(vwx310, vwx410)
new_lt19(vwx310, vwx410, ty_Float) → new_lt18(vwx310, vwx410)
new_lt19(vwx310, vwx410, ty_@0) → new_lt10(vwx310, vwx410)
new_esEs27(vwx310, vwx410, app(app(app(ty_@3, bdh), bea), beb)) → new_esEs7(vwx310, vwx410, bdh, bea, beb)
new_esEs27(vwx310, vwx410, ty_@0) → new_esEs10(vwx310, vwx410)
new_esEs27(vwx310, vwx410, ty_Float) → new_esEs15(vwx310, vwx410)
new_esEs27(vwx310, vwx410, app(ty_Maybe, bde)) → new_esEs5(vwx310, vwx410, bde)
new_esEs27(vwx310, vwx410, app(app(ty_@2, bdf), bdg)) → new_esEs6(vwx310, vwx410, bdf, bdg)
new_esEs27(vwx310, vwx410, app(app(ty_Either, bch), bda)) → new_esEs4(vwx310, vwx410, bch, bda)
new_esEs27(vwx310, vwx410, ty_Integer) → new_esEs16(vwx310, vwx410)
new_esEs27(vwx310, vwx410, app(ty_Ratio, dbg)) → new_esEs12(vwx310, vwx410, dbg)
new_esEs27(vwx310, vwx410, ty_Double) → new_esEs13(vwx310, vwx410)
new_esEs27(vwx310, vwx410, ty_Int) → new_esEs8(vwx310, vwx410)
new_esEs27(vwx310, vwx410, ty_Bool) → new_esEs14(vwx310, vwx410)
new_esEs27(vwx310, vwx410, app(ty_[], bdd)) → new_esEs11(vwx310, vwx410, bdd)
new_esEs27(vwx310, vwx410, ty_Ordering) → new_esEs17(vwx310, vwx410)
new_esEs27(vwx310, vwx410, ty_Char) → new_esEs9(vwx310, vwx410)
new_lt20(vwx311, vwx411, app(ty_[], bef)) → new_lt8(vwx311, vwx411, bef)
new_lt20(vwx311, vwx411, ty_Char) → new_lt4(vwx311, vwx411)
new_lt20(vwx311, vwx411, app(app(ty_Either, bed), bee)) → new_lt7(vwx311, vwx411, bed, bee)
new_lt20(vwx311, vwx411, ty_Int) → new_lt15(vwx311, vwx411)
new_lt20(vwx311, vwx411, app(ty_Ratio, dbh)) → new_lt11(vwx311, vwx411, dbh)
new_lt20(vwx311, vwx411, ty_@0) → new_lt10(vwx311, vwx411)
new_lt20(vwx311, vwx411, ty_Ordering) → new_lt13(vwx311, vwx411)
new_lt20(vwx311, vwx411, ty_Integer) → new_lt17(vwx311, vwx411)
new_lt20(vwx311, vwx411, ty_Float) → new_lt18(vwx311, vwx411)
new_lt20(vwx311, vwx411, app(app(ty_@2, beh), bfa)) → new_lt6(vwx311, vwx411, beh, bfa)
new_lt20(vwx311, vwx411, ty_Double) → new_lt16(vwx311, vwx411)
new_lt20(vwx311, vwx411, app(ty_Maybe, beg)) → new_lt14(vwx311, vwx411, beg)
new_lt20(vwx311, vwx411, ty_Bool) → new_lt12(vwx311, vwx411)
new_lt20(vwx311, vwx411, app(app(app(ty_@3, bfb), bfc), bfd)) → new_lt5(vwx311, vwx411, bfb, bfc, bfd)
new_esEs28(vwx311, vwx411, ty_Int) → new_esEs8(vwx311, vwx411)
new_esEs28(vwx311, vwx411, app(ty_[], bef)) → new_esEs11(vwx311, vwx411, bef)
new_esEs28(vwx311, vwx411, ty_Integer) → new_esEs16(vwx311, vwx411)
new_esEs28(vwx311, vwx411, ty_Double) → new_esEs13(vwx311, vwx411)
new_esEs28(vwx311, vwx411, ty_Ordering) → new_esEs17(vwx311, vwx411)
new_esEs28(vwx311, vwx411, ty_Char) → new_esEs9(vwx311, vwx411)
new_esEs28(vwx311, vwx411, app(app(app(ty_@3, bfb), bfc), bfd)) → new_esEs7(vwx311, vwx411, bfb, bfc, bfd)
new_esEs28(vwx311, vwx411, app(ty_Ratio, dbh)) → new_esEs12(vwx311, vwx411, dbh)
new_esEs28(vwx311, vwx411, app(app(ty_@2, beh), bfa)) → new_esEs6(vwx311, vwx411, beh, bfa)
new_esEs28(vwx311, vwx411, ty_@0) → new_esEs10(vwx311, vwx411)
new_esEs28(vwx311, vwx411, ty_Bool) → new_esEs14(vwx311, vwx411)
new_esEs28(vwx311, vwx411, app(app(ty_Either, bed), bee)) → new_esEs4(vwx311, vwx411, bed, bee)
new_esEs28(vwx311, vwx411, app(ty_Maybe, beg)) → new_esEs5(vwx311, vwx411, beg)
new_esEs28(vwx311, vwx411, ty_Float) → new_esEs15(vwx311, vwx411)
new_ltEs19(vwx312, vwx412, ty_Ordering) → new_ltEs10(vwx312, vwx412)
new_ltEs19(vwx312, vwx412, app(ty_Maybe, bfh)) → new_ltEs12(vwx312, vwx412, bfh)
new_ltEs19(vwx312, vwx412, ty_Bool) → new_ltEs6(vwx312, vwx412)
new_ltEs19(vwx312, vwx412, app(ty_[], bfg)) → new_ltEs4(vwx312, vwx412, bfg)
new_ltEs19(vwx312, vwx412, app(app(app(ty_@3, bgc), bgd), bge)) → new_ltEs15(vwx312, vwx412, bgc, bgd, bge)
new_ltEs19(vwx312, vwx412, app(ty_Ratio, dca)) → new_ltEs9(vwx312, vwx412, dca)
new_ltEs19(vwx312, vwx412, app(app(ty_Either, bfe), bff)) → new_ltEs13(vwx312, vwx412, bfe, bff)
new_ltEs19(vwx312, vwx412, ty_Float) → new_ltEs17(vwx312, vwx412)
new_ltEs19(vwx312, vwx412, ty_Double) → new_ltEs16(vwx312, vwx412)
new_ltEs19(vwx312, vwx412, ty_Int) → new_ltEs11(vwx312, vwx412)
new_ltEs19(vwx312, vwx412, ty_@0) → new_ltEs8(vwx312, vwx412)
new_ltEs19(vwx312, vwx412, ty_Integer) → new_ltEs7(vwx312, vwx412)
new_ltEs19(vwx312, vwx412, ty_Char) → new_ltEs5(vwx312, vwx412)
new_ltEs19(vwx312, vwx412, app(app(ty_@2, bga), bgb)) → new_ltEs14(vwx312, vwx412, bga, bgb)
new_ltEs8(vwx31, vwx41) → new_not(new_esEs17(new_compare18(vwx31, vwx41), GT))
new_compare18(@0, @0) → EQ
new_lt5(vwx30, vwx40, bce, bcf, bcg) → new_esEs17(new_compare35(vwx30, vwx40, bce, bcf, bcg), LT)
new_compare35(vwx30, vwx40, bce, bcf, bcg) → new_compare210(vwx30, vwx40, new_esEs7(vwx30, vwx40, bce, bcf, bcg), bce, bcf, bcg)
new_compare210(vwx30, vwx40, False, bce, bcf, bcg) → new_compare110(vwx30, vwx40, new_ltEs15(vwx30, vwx40, bce, bcf, bcg), bce, bcf, bcg)
new_compare210(vwx30, vwx40, True, bce, bcf, bcg) → EQ
new_compare110(vwx30, vwx40, True, bce, bcf, bcg) → LT
new_compare110(vwx30, vwx40, False, bce, bcf, bcg) → GT
new_lt12(vwx30, vwx40) → new_esEs17(new_compare34(vwx30, vwx40), LT)
new_compare34(vwx30, vwx40) → new_compare24(vwx30, vwx40, new_esEs14(vwx30, vwx40))
new_compare24(vwx30, vwx40, True) → EQ
new_compare24(vwx30, vwx40, False) → new_compare15(vwx30, vwx40, new_ltEs6(vwx30, vwx40))
new_compare15(vwx30, vwx40, False) → GT
new_compare15(vwx30, vwx40, True) → LT
new_lt14(vwx30, vwx40, ge) → new_esEs17(new_compare33(vwx30, vwx40, ge), LT)
new_lt16(vwx30, vwx40) → new_esEs17(new_primCmpDouble(vwx30, vwx40), LT)
new_lt6(vwx30, vwx40, bcc, bcd) → new_esEs17(new_compare37(vwx30, vwx40, bcc, bcd), LT)
new_compare37(vwx30, vwx40, bcc, bcd) → new_compare27(vwx30, vwx40, new_esEs6(vwx30, vwx40, bcc, bcd), bcc, bcd)
new_compare27(vwx30, vwx40, True, bcc, bcd) → EQ
new_compare27(vwx30, vwx40, False, bcc, bcd) → new_compare14(vwx30, vwx40, new_ltEs14(vwx30, vwx40, bcc, bcd), bcc, bcd)
new_compare14(vwx30, vwx40, False, bcc, bcd) → GT
new_compare14(vwx30, vwx40, True, bcc, bcd) → LT
new_lt18(vwx30, vwx40) → new_esEs17(new_primCmpFloat(vwx30, vwx40), LT)
new_lt17(Integer(vwx300), Integer(vwx400)) → new_esEs17(new_primCmpInt(vwx300, vwx400), LT)
new_lt13(vwx30, vwx40) → new_esEs17(new_compare38(vwx30, vwx40), LT)
new_lt10(@0, @0) → new_esEs17(EQ, LT)
new_lt11(:%(vwx300, vwx301), :%(vwx400, vwx401), cch) → new_esEs17(new_compare39(vwx300, vwx401, vwx400, vwx301, cch), LT)
new_compare39(Integer(vwx3000), Integer(vwx4010), vwx400, vwx301, ty_Integer) → new_compare11(Integer(new_primMulInt(vwx3000, vwx4010)), new_sr0(vwx400, vwx301))
new_compare39(vwx300, vwx401, vwx400, vwx301, ty_Int) → new_compare25(vwx300, vwx401, vwx400, vwx301)
new_lt15(vwx30, vwx40) → new_esEs17(new_primCmpInt(vwx30, vwx40), LT)
new_lt7(vwx30, vwx40, ba, bb) → new_esEs17(new_compare36(vwx30, vwx40, ba, bb), LT)
new_compare36(vwx30, vwx40, ba, bb) → new_compare28(vwx30, vwx40, new_esEs4(vwx30, vwx40, ba, bb), ba, bb)
new_compare28(vwx30, vwx40, False, ba, bb) → new_compare17(vwx30, vwx40, new_ltEs13(vwx30, vwx40, ba, bb), ba, bb)
new_compare28(vwx30, vwx40, True, ba, bb) → EQ
new_compare17(vwx30, vwx40, True, ba, bb) → LT
new_compare17(vwx30, vwx40, False, ba, bb) → GT
new_lt4(vwx30, vwx40) → new_esEs17(new_primCmpChar(vwx30, vwx40), LT)
new_lt8([], :(vwx400, vwx401), ea) → new_esEs17(LT, LT)
new_lt8(:(vwx300, vwx301), [], ea) → new_esEs17(GT, LT)
new_lt8(:(vwx300, vwx301), :(vwx400, vwx401), ea) → new_esEs17(new_primCompAux1(vwx300, vwx400, vwx301, vwx401, ea), LT)
new_lt8([], [], ea) → new_esEs17(EQ, LT)
new_compare16(vwx300, vwx400, eb, ec) → new_compare36(vwx300, vwx400, eb, ec)
new_compare42(vwx300, vwx400, ef, eg) → new_compare37(vwx300, vwx400, ef, eg)
new_compare43(vwx300, vwx400, eh, fa, fb) → new_compare35(vwx300, vwx400, eh, fa, fb)
new_compare13(vwx300, vwx400) → new_compare34(vwx300, vwx400)

The set Q consists of the following terms:

new_ltEs18(x0, x1, ty_Ordering)
new_esEs25(x0, x1, ty_Double)
new_compare36(x0, x1, x2, x3)
new_esEs23(x0, x1, app(app(ty_@2, x2), x3))
new_lt9(x0, x1, app(ty_Ratio, x2))
new_esEs17(LT, GT)
new_esEs17(GT, LT)
new_esEs24(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Float)
new_lt20(x0, x1, ty_Float)
new_lt19(x0, x1, ty_Double)
new_lt8(:(x0, x1), :(x2, x3), x4)
new_lt7(x0, x1, x2, x3)
new_esEs19(x0, x1, ty_Int)
new_esEs23(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, app(app(ty_@2, x2), x3))
new_compare40(x0, x1)
new_esEs23(x0, x1, ty_@0)
new_esEs21(x0, x1, ty_Ordering)
new_esEs21(x0, x1, ty_Double)
new_primCmpInt(Neg(Succ(x0)), Pos(x1))
new_esEs5(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_primCmpInt(Pos(Succ(x0)), Neg(x1))
new_esEs23(x0, x1, app(ty_Maybe, x2))
new_esEs4(Left(x0), Left(x1), ty_@0, x2)
new_compare23(x0, x1, False, x2)
new_lt9(x0, x1, ty_@0)
new_esEs26(x0, x1, ty_Ordering)
new_esEs17(LT, LT)
new_compare0(x0, x1, app(ty_Maybe, x2))
new_esEs28(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_ltEs11(x0, x1)
new_esEs18(x0, x1, ty_Int)
new_lt13(x0, x1)
new_compare27(x0, x1, True, x2, x3)
new_esEs28(x0, x1, ty_@0)
new_esEs4(Left(x0), Right(x1), x2, x3)
new_esEs4(Right(x0), Left(x1), x2, x3)
new_ltEs13(Left(x0), Left(x1), ty_Bool, x2)
new_esEs4(Left(x0), Left(x1), ty_Bool, x2)
new_compare210(x0, x1, False, x2, x3, x4)
new_esEs18(x0, x1, app(app(ty_Either, x2), x3))
new_esEs18(x0, x1, ty_Ordering)
new_ltEs10(LT, LT)
new_lt19(x0, x1, ty_Bool)
new_primMulInt(Neg(x0), Neg(x1))
new_ltEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Right(x0), Right(x1), x2, ty_Ordering)
new_compare0(x0, x1, ty_Ordering)
new_esEs18(x0, x1, app(ty_Maybe, x2))
new_ltEs13(Left(x0), Left(x1), ty_Char, x2)
new_ltEs18(x0, x1, ty_Int)
new_esEs25(x0, x1, app(ty_Maybe, x2))
new_esEs17(GT, EQ)
new_esEs17(EQ, GT)
new_esEs24(x0, x1, ty_Ordering)
new_esEs18(x0, x1, app(ty_[], x2))
new_ltEs12(Just(x0), Just(x1), ty_@0)
new_compare43(x0, x1, x2, x3, x4)
new_asAs(True, x0)
new_compare19(x0, x1, False, x2)
new_esEs22(x0, x1, ty_Bool)
new_primEqInt(Neg(Zero), Pos(Succ(x0)))
new_primEqInt(Pos(Zero), Neg(Succ(x0)))
new_ltEs18(x0, x1, app(ty_[], x2))
new_esEs4(Right(x0), Right(x1), x2, ty_Bool)
new_ltEs12(Just(x0), Just(x1), ty_Float)
new_ltEs13(Right(x0), Right(x1), x2, ty_Int)
new_esEs5(Just(x0), Just(x1), app(ty_Maybe, x2))
new_primPlusNat0(Succ(x0), Zero)
new_compare0(x0, x1, app(ty_Ratio, x2))
new_esEs28(x0, x1, ty_Double)
new_esEs27(x0, x1, ty_Char)
new_ltEs19(x0, x1, app(app(ty_@2, x2), x3))
new_esEs11([], [], x0)
new_primCompAux00(x0, x1, EQ, app(app(app(ty_@3, x2), x3), x4))
new_pePe(True, x0)
new_ltEs12(Just(x0), Nothing, x1)
new_ltEs12(Just(x0), Just(x1), app(ty_[], x2))
new_esEs4(Right(x0), Right(x1), x2, ty_Double)
new_esEs28(x0, x1, ty_Ordering)
new_ltEs6(True, True)
new_esEs24(x0, x1, ty_Float)
new_primCompAux00(x0, x1, LT, x2)
new_compare27(x0, x1, False, x2, x3)
new_primCompAux00(x0, x1, EQ, app(ty_Ratio, x2))
new_compare29(x0, x1, True)
new_esEs7(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_lt19(x0, x1, ty_Int)
new_esEs5(Just(x0), Just(x1), ty_Float)
new_esEs22(x0, x1, app(ty_[], x2))
new_primCompAux00(x0, x1, EQ, ty_Int)
new_esEs17(GT, GT)
new_compare29(x0, x1, False)
new_ltEs12(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, ty_Float)
new_esEs23(x0, x1, ty_Integer)
new_esEs6(@2(x0, x1), @2(x2, x3), x4, x5)
new_lt16(x0, x1)
new_ltEs8(x0, x1)
new_sr(x0, x1)
new_compare18(@0, @0)
new_lt20(x0, x1, app(ty_Ratio, x2))
new_esEs5(Just(x0), Nothing, x1)
new_esEs22(x0, x1, app(app(ty_Either, x2), x3))
new_esEs14(True, True)
new_ltEs13(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs21(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs18(x0, x1, app(ty_Maybe, x2))
new_compare0(x0, x1, ty_Double)
new_ltEs12(Nothing, Just(x0), x1)
new_ltEs13(Right(x0), Right(x1), x2, ty_Integer)
new_primEqNat0(Zero, Zero)
new_lt20(x0, x1, ty_@0)
new_compare7([], :(x0, x1), x2)
new_compare9(:%(x0, x1), :%(x2, x3), ty_Integer)
new_esEs18(x0, x1, ty_@0)
new_esEs4(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_esEs25(x0, x1, ty_Float)
new_esEs23(x0, x1, ty_Char)
new_esEs16(Integer(x0), Integer(x1))
new_primMulInt(Pos(x0), Pos(x1))
new_ltEs12(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_primCompAux00(x0, x1, EQ, ty_Bool)
new_esEs22(x0, x1, ty_Char)
new_ltEs7(x0, x1)
new_esEs25(x0, x1, ty_Integer)
new_lt15(x0, x1)
new_ltEs13(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_primMulNat0(Zero, Zero)
new_esEs4(Right(x0), Right(x1), x2, ty_Char)
new_ltEs13(Right(x0), Right(x1), x2, ty_Ordering)
new_esEs22(x0, x1, app(ty_Ratio, x2))
new_lt17(Integer(x0), Integer(x1))
new_esEs22(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_Ordering)
new_ltEs10(EQ, LT)
new_ltEs13(Left(x0), Left(x1), ty_Integer, x2)
new_ltEs10(LT, EQ)
new_esEs21(x0, x1, ty_Integer)
new_compare23(x0, x1, True, x2)
new_compare0(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Just(x0), Just(x1), ty_Double)
new_primCompAux00(x0, x1, EQ, ty_Char)
new_compare10(x0, x1)
new_esEs4(Right(x0), Right(x1), x2, ty_@0)
new_lt9(x0, x1, ty_Float)
new_ltEs18(x0, x1, ty_Double)
new_esEs22(x0, x1, ty_@0)
new_lt8([], :(x0, x1), x2)
new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
new_esEs18(x0, x1, ty_Float)
new_ltEs13(Left(x0), Left(x1), app(ty_[], x2), x3)
new_compare19(x0, x1, True, x2)
new_esEs25(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs27(x0, x1, app(ty_Maybe, x2))
new_esEs26(x0, x1, app(app(ty_Either, x2), x3))
new_esEs25(x0, x1, app(app(ty_@2, x2), x3))
new_esEs18(x0, x1, app(ty_Ratio, x2))
new_ltEs15(@3(x0, x1, x2), @3(x3, x4, x5), x6, x7, x8)
new_lt19(x0, x1, ty_@0)
new_ltEs12(Nothing, Nothing, x0)
new_esEs18(x0, x1, ty_Bool)
new_compare38(x0, x1)
new_esEs8(x0, x1)
new_primCmpInt(Pos(Zero), Pos(Succ(x0)))
new_esEs25(x0, x1, app(app(ty_Either, x2), x3))
new_esEs28(x0, x1, ty_Int)
new_esEs26(x0, x1, app(ty_[], x2))
new_esEs5(Nothing, Nothing, x0)
new_primMulNat0(Zero, Succ(x0))
new_esEs24(x0, x1, app(ty_Ratio, x2))
new_esEs22(x0, x1, app(ty_Maybe, x2))
new_esEs4(Left(x0), Left(x1), ty_Double, x2)
new_compare41(x0, x1, x2)
new_ltEs12(Just(x0), Just(x1), ty_Char)
new_esEs25(x0, x1, app(ty_Ratio, x2))
new_esEs23(x0, x1, ty_Int)
new_lt20(x0, x1, ty_Integer)
new_esEs11(:(x0, x1), [], x2)
new_compare14(x0, x1, True, x2, x3)
new_ltEs13(Right(x0), Right(x1), x2, ty_@0)
new_esEs24(x0, x1, app(ty_Maybe, x2))
new_ltEs19(x0, x1, ty_Bool)
new_compare111(x0, x1, True)
new_esEs4(Right(x0), Right(x1), x2, ty_Float)
new_lt9(x0, x1, app(ty_Maybe, x2))
new_ltEs13(Right(x0), Right(x1), x2, ty_Char)
new_primEqInt(Neg(Succ(x0)), Neg(Zero))
new_esEs5(Just(x0), Just(x1), app(app(ty_Either, x2), x3))
new_compare0(x0, x1, app(ty_[], x2))
new_esEs4(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs5(Just(x0), Just(x1), ty_Char)
new_primCmpInt(Neg(Zero), Pos(Succ(x0)))
new_primCmpInt(Pos(Zero), Neg(Succ(x0)))
new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
new_esEs20(x0, x1, ty_Int)
new_esEs22(x0, x1, ty_Integer)
new_esEs24(x0, x1, ty_Int)
new_esEs4(Left(x0), Left(x1), ty_Int, x2)
new_primCompAux00(x0, x1, EQ, ty_Ordering)
new_lt19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs18(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs13(Left(x0), Left(x1), ty_@0, x2)
new_compare39(x0, x1, x2, x3, ty_Int)
new_esEs22(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs25(x0, x1, app(ty_[], x2))
new_primEqNat0(Succ(x0), Zero)
new_esEs13(Double(x0, x1), Double(x2, x3))
new_primCmpInt(Neg(Succ(x0)), Neg(x1))
new_esEs4(Left(x0), Left(x1), app(ty_[], x2), x3)
new_esEs27(x0, x1, ty_Bool)
new_lt19(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, ty_Float)
new_primPlusNat0(Zero, Zero)
new_ltEs13(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_primCompAux1(x0, x1, x2, x3, x4)
new_ltEs12(Just(x0), Just(x1), ty_Bool)
new_lt20(x0, x1, ty_Double)
new_esEs21(x0, x1, ty_Float)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Maybe, x3))
new_ltEs19(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs21(x0, x1, app(ty_Ratio, x2))
new_ltEs13(Left(x0), Left(x1), ty_Ordering, x2)
new_esEs27(x0, x1, ty_Integer)
new_esEs23(x0, x1, ty_Bool)
new_ltEs13(Right(x0), Right(x1), x2, ty_Double)
new_esEs5(Just(x0), Just(x1), ty_Bool)
new_esEs25(x0, x1, ty_Bool)
new_esEs23(x0, x1, ty_Double)
new_primCmpInt(Neg(Zero), Neg(Zero))
new_esEs26(x0, x1, app(ty_Maybe, x2))
new_esEs27(x0, x1, ty_@0)
new_esEs5(Just(x0), Just(x1), app(ty_[], x2))
new_esEs28(x0, x1, app(ty_Maybe, x2))
new_ltEs6(False, True)
new_ltEs6(True, False)
new_lt9(x0, x1, ty_Ordering)
new_esEs26(x0, x1, app(app(ty_@2, x2), x3))
new_esEs27(x0, x1, ty_Int)
new_esEs23(x0, x1, app(ty_[], x2))
new_compare33(x0, x1, x2)
new_lt9(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs10(GT, LT)
new_esEs23(x0, x1, ty_Ordering)
new_ltEs10(LT, GT)
new_esEs22(x0, x1, app(app(ty_@2, x2), x3))
new_esEs19(x0, x1, ty_Integer)
new_lt9(x0, x1, ty_Int)
new_compare34(x0, x1)
new_compare8(x0, x1)
new_esEs21(x0, x1, app(ty_Maybe, x2))
new_primEqInt(Pos(Succ(x0)), Pos(Zero))
new_esEs10(@0, @0)
new_compare7(:(x0, x1), [], x2)
new_ltEs9(x0, x1, x2)
new_esEs26(x0, x1, ty_@0)
new_lt18(x0, x1)
new_esEs23(x0, x1, app(app(ty_Either, x2), x3))
new_esEs22(x0, x1, ty_Float)
new_lt8(:(x0, x1), [], x2)
new_lt9(x0, x1, app(app(ty_Either, x2), x3))
new_lt9(x0, x1, ty_Double)
new_compare15(x0, x1, False)
new_esEs5(Just(x0), Just(x1), ty_Ordering)
new_esEs20(x0, x1, ty_Integer)
new_esEs26(x0, x1, ty_Int)
new_ltEs19(x0, x1, ty_Char)
new_primEqInt(Pos(Zero), Neg(Zero))
new_primEqInt(Neg(Zero), Pos(Zero))
new_compare42(x0, x1, x2, x3)
new_esEs24(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_ltEs19(x0, x1, ty_Double)
new_esEs4(Left(x0), Left(x1), ty_Integer, x2)
new_lt20(x0, x1, app(app(ty_Either, x2), x3))
new_lt10(@0, @0)
new_lt11(:%(x0, x1), :%(x2, x3), x4)
new_ltEs13(Right(x0), Right(x1), x2, ty_Float)
new_esEs18(x0, x1, app(app(ty_@2, x2), x3))
new_ltEs13(Left(x0), Left(x1), app(app(ty_@2, x2), x3), x4)
new_ltEs13(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_esEs5(Just(x0), Just(x1), app(ty_Ratio, x2))
new_compare26(x0, x1)
new_ltEs19(x0, x1, app(ty_[], x2))
new_primCompAux00(x0, x1, EQ, app(app(ty_@2, x2), x3))
new_primCmpInt(Pos(Zero), Pos(Zero))
new_ltEs6(False, False)
new_esEs11(:(x0, x1), :(x2, x3), x4)
new_primCompAux00(x0, x1, EQ, app(app(ty_Either, x2), x3))
new_ltEs13(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs13(Right(x0), Left(x1), x2, x3)
new_ltEs13(Left(x0), Right(x1), x2, x3)
new_esEs4(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_primEqInt(Neg(Zero), Neg(Zero))
new_esEs22(x0, x1, ty_Double)
new_compare110(x0, x1, True, x2, x3, x4)
new_ltEs18(x0, x1, ty_@0)
new_esEs5(Just(x0), Just(x1), ty_Int)
new_esEs14(True, False)
new_esEs14(False, True)
new_esEs11([], :(x0, x1), x2)
new_compare24(x0, x1, False)
new_esEs28(x0, x1, app(app(ty_Either, x2), x3))
new_primMulInt(Neg(x0), Pos(x1))
new_primMulInt(Pos(x0), Neg(x1))
new_esEs28(x0, x1, app(ty_[], x2))
new_lt9(x0, x1, app(app(ty_@2, x2), x3))
new_lt19(x0, x1, ty_Float)
new_esEs21(x0, x1, ty_Char)
new_primCompAux00(x0, x1, EQ, app(ty_Maybe, x2))
new_lt19(x0, x1, ty_Integer)
new_compare0(x0, x1, ty_Integer)
new_lt19(x0, x1, app(ty_Maybe, x2))
new_esEs24(x0, x1, app(app(ty_@2, x2), x3))
new_compare0(x0, x1, app(app(ty_@2, x2), x3))
new_esEs23(x0, x1, ty_Float)
new_ltEs13(Left(x0), Left(x1), ty_Float, x2)
new_ltEs19(x0, x1, app(ty_Maybe, x2))
new_asAs(False, x0)
new_primCmpNat0(Zero, Succ(x0))
new_esEs25(x0, x1, ty_Char)
new_esEs28(x0, x1, ty_Integer)
new_lt9(x0, x1, app(ty_[], x2))
new_ltEs12(Just(x0), Just(x1), ty_Double)
new_esEs21(x0, x1, app(app(ty_Either, x2), x3))
new_esEs5(Nothing, Just(x0), x1)
new_compare0(x0, x1, ty_@0)
new_primCompAux00(x0, x1, GT, x2)
new_compare0(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs24(x0, x1, ty_Bool)
new_ltEs13(Right(x0), Right(x1), x2, ty_Bool)
new_lt19(x0, x1, app(app(ty_@2, x2), x3))
new_primPlusNat1(Succ(x0), x1)
new_esEs26(x0, x1, ty_Double)
new_esEs28(x0, x1, ty_Char)
new_compare25(x0, x1, x2, x3)
new_ltEs14(@2(x0, x1), @2(x2, x3), x4, x5)
new_ltEs19(x0, x1, app(ty_Ratio, x2))
new_compare35(x0, x1, x2, x3, x4)
new_esEs5(Just(x0), Just(x1), app(app(app(ty_@3, x2), x3), x4))
new_compare17(x0, x1, False, x2, x3)
new_esEs27(x0, x1, app(ty_Ratio, x2))
new_ltEs13(Left(x0), Left(x1), ty_Double, x2)
new_primPlusNat1(Zero, x0)
new_lt20(x0, x1, ty_Char)
new_esEs25(x0, x1, ty_Ordering)
new_ltEs12(Just(x0), Just(x1), ty_Ordering)
new_lt12(x0, x1)
new_primCmpNat0(Zero, Zero)
new_ltEs19(x0, x1, ty_Int)
new_esEs4(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_lt5(x0, x1, x2, x3, x4)
new_esEs24(x0, x1, app(app(ty_Either, x2), x3))
new_ltEs18(x0, x1, app(ty_Ratio, x2))
new_ltEs12(Just(x0), Just(x1), app(app(ty_@2, x2), x3))
new_lt9(x0, x1, ty_Bool)
new_lt19(x0, x1, ty_Char)
new_compare15(x0, x1, True)
new_esEs26(x0, x1, app(ty_Ratio, x2))
new_esEs27(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs22(x0, x1, ty_Ordering)
new_esEs4(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_primCompAux00(x0, x1, EQ, ty_@0)
new_compare17(x0, x1, True, x2, x3)
new_ltEs13(Right(x0), Right(x1), x2, app(app(app(ty_@3, x3), x4), x5))
new_compare11(Integer(x0), Integer(x1))
new_esEs5(Just(x0), Just(x1), ty_Integer)
new_ltEs19(x0, x1, ty_@0)
new_esEs24(x0, x1, ty_Double)
new_compare9(:%(x0, x1), :%(x2, x3), ty_Int)
new_lt19(x0, x1, ty_Ordering)
new_esEs18(x0, x1, ty_Double)
new_primEqNat0(Zero, Succ(x0))
new_primCmpDouble(Double(x0, x1), Double(x2, x3))
new_compare13(x0, x1)
new_lt4(x0, x1)
new_ltEs13(Left(x0), Left(x1), ty_Int, x2)
new_lt14(x0, x1, x2)
new_pePe(False, x0)
new_primMulNat0(Succ(x0), Zero)
new_ltEs10(GT, GT)
new_ltEs12(Just(x0), Just(x1), app(ty_Ratio, x2))
new_primMulNat0(Succ(x0), Succ(x1))
new_esEs21(x0, x1, ty_Bool)
new_esEs12(:%(x0, x1), :%(x2, x3), x4)
new_esEs26(x0, x1, ty_Char)
new_primCmpNat0(Succ(x0), Succ(x1))
new_ltEs12(Just(x0), Just(x1), ty_Integer)
new_compare0(x0, x1, ty_Bool)
new_esEs5(Just(x0), Just(x1), ty_@0)
new_compare12(x0, x1)
new_esEs25(x0, x1, ty_@0)
new_esEs24(x0, x1, app(ty_[], x2))
new_esEs27(x0, x1, app(ty_[], x2))
new_not(True)
new_compare28(x0, x1, False, x2, x3)
new_ltEs13(Left(x0), Left(x1), app(ty_Maybe, x2), x3)
new_esEs21(x0, x1, ty_Int)
new_compare24(x0, x1, True)
new_lt20(x0, x1, ty_Ordering)
new_esEs4(Left(x0), Left(x1), ty_Float, x2)
new_lt9(x0, x1, ty_Char)
new_compare7([], [], x0)
new_ltEs19(x0, x1, ty_Integer)
new_compare37(x0, x1, x2, x3)
new_esEs28(x0, x1, app(ty_Ratio, x2))
new_ltEs18(x0, x1, ty_Char)
new_ltEs13(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_primCmpInt(Neg(Zero), Pos(Zero))
new_primCmpInt(Pos(Zero), Neg(Zero))
new_not(False)
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_@2, x3), x4))
new_ltEs17(x0, x1)
new_lt20(x0, x1, ty_Bool)
new_ltEs5(x0, x1)
new_ltEs10(GT, EQ)
new_ltEs10(EQ, GT)
new_esEs26(x0, x1, ty_Integer)
new_lt20(x0, x1, app(app(ty_@2, x2), x3))
new_esEs4(Left(x0), Left(x1), app(app(app(ty_@3, x2), x3), x4), x5)
new_ltEs19(x0, x1, ty_Float)
new_primEqInt(Pos(Zero), Pos(Succ(x0)))
new_esEs21(x0, x1, app(ty_[], x2))
new_ltEs13(Right(x0), Right(x1), x2, app(ty_Ratio, x3))
new_esEs28(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_esEs4(Right(x0), Right(x1), x2, app(ty_[], x3))
new_esEs21(x0, x1, ty_@0)
new_primEqNat0(Succ(x0), Succ(x1))
new_compare0(x0, x1, ty_Char)
new_sr0(Integer(x0), Integer(x1))
new_esEs23(x0, x1, app(ty_Ratio, x2))
new_esEs18(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_primCmpInt(Neg(Zero), Neg(Succ(x0)))
new_esEs28(x0, x1, ty_Bool)
new_lt20(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_compare0(x0, x1, ty_Int)
new_esEs27(x0, x1, app(app(ty_@2, x2), x3))
new_lt19(x0, x1, app(app(ty_Either, x2), x3))
new_lt19(x0, x1, app(ty_[], x2))
new_compare28(x0, x1, True, x2, x3)
new_compare111(x0, x1, False)
new_ltEs12(Just(x0), Just(x1), app(ty_Maybe, x2))
new_primCompAux00(x0, x1, EQ, ty_Double)
new_primEqInt(Neg(Zero), Neg(Succ(x0)))
new_compare110(x0, x1, False, x2, x3, x4)
new_ltEs13(Left(x0), Left(x1), app(ty_Ratio, x2), x3)
new_esEs4(Right(x0), Right(x1), x2, ty_Integer)
new_compare14(x0, x1, False, x2, x3)
new_primCmpFloat(Float(x0, x1), Float(x2, x3))
new_compare16(x0, x1, x2, x3)
new_ltEs4(x0, x1, x2)
new_ltEs19(x0, x1, app(app(ty_Either, x2), x3))
new_esEs15(Float(x0, x1), Float(x2, x3))
new_esEs4(Right(x0), Right(x1), x2, app(app(ty_Either, x3), x4))
new_lt20(x0, x1, app(ty_Maybe, x2))
new_esEs18(x0, x1, ty_Integer)
new_esEs27(x0, x1, ty_Double)
new_esEs4(Right(x0), Right(x1), x2, ty_Int)
new_compare39(Integer(x0), Integer(x1), x2, x3, ty_Integer)
new_esEs27(x0, x1, app(app(ty_Either, x2), x3))
new_primCompAux00(x0, x1, EQ, app(ty_[], x2))
new_ltEs18(x0, x1, ty_Bool)
new_esEs26(x0, x1, ty_Bool)
new_esEs9(Char(x0), Char(x1))
new_compare210(x0, x1, True, x2, x3, x4)
new_esEs14(False, False)
new_ltEs12(Just(x0), Just(x1), ty_Int)
new_primEqInt(Pos(Zero), Pos(Zero))
new_primPlusNat0(Zero, Succ(x0))
new_esEs4(Left(x0), Left(x1), app(app(ty_Either, x2), x3), x4)
new_esEs24(x0, x1, ty_Char)
new_primCompAux00(x0, x1, EQ, ty_Float)
new_lt9(x0, x1, ty_Integer)
new_primPlusNat0(Succ(x0), Succ(x1))
new_lt20(x0, x1, app(ty_[], x2))
new_primEqInt(Neg(Succ(x0)), Pos(x1))
new_primEqInt(Pos(Succ(x0)), Neg(x1))
new_esEs26(x0, x1, app(app(app(ty_@3, x2), x3), x4))
new_lt20(x0, x1, ty_Int)
new_compare7(:(x0, x1), :(x2, x3), x4)
new_primCompAux00(x0, x1, EQ, ty_Integer)
new_esEs17(EQ, EQ)
new_primCmpChar(Char(x0), Char(x1))
new_esEs4(Left(x0), Left(x1), ty_Char, x2)
new_ltEs18(x0, x1, ty_Integer)
new_esEs17(LT, EQ)
new_esEs17(EQ, LT)
new_lt8([], [], x0)
new_esEs24(x0, x1, ty_@0)
new_primCmpNat0(Succ(x0), Zero)
new_ltEs16(x0, x1)
new_esEs25(x0, x1, ty_Int)
new_esEs28(x0, x1, ty_Float)
new_compare0(x0, x1, ty_Float)
new_lt6(x0, x1, x2, x3)
new_primCmpInt(Pos(Succ(x0)), Pos(x1))
new_esEs18(x0, x1, ty_Char)
new_esEs27(x0, x1, ty_Ordering)
new_ltEs10(EQ, EQ)

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: